' f 1 f f 1 1" f .' A .. • " .. Chemistry Chung-Sin SU Ph.D. Polymer Solution Thenriodynamics and Gas-Liquid Chromatography copy 1 Pleàsa notice that mw short title (less than strokes and spaces) 15: Polymer Thermodynamics 'and Gas Chromatography i " .. .' . ' . l .. ) ,. . . f 1/ • l', ., . 1
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
~, '
f 1 f f
1 1 " f
.'
A
..
•
-~/ " ..
Chemistry Chung-Sin SU Ph.D.
Polymer Solution Thenriodynamics and Gas-Liquid Chromatography
copy 1
Pleàsa notice that mw short title (less than ~6 strokes and spaces) 15:
Polymer S~lution Thermodynamics ~
'and Gas Chromatography
i
"
..
.' . '
. l
.. )
,. . . f
1/
• l',
., .
1
• ' 1
. .
(
,
"
i 1 Polymer /iSolution Thermodynam'ics
, ~ .. _-'
and <
Ga~-Liquid Chromatography
,!
Chung/Sin SU
. A Thuis Submitted to thl
Flculty of Grlduati Studil' & RI.larch
in P art il' Fu If~ment 0 f the RI quire m 1 n~1 for the tl.
DIgr.. 0 f
D,octor of Philosop'hy
Chemistry Dlpartment ,
McGill University Novlmbtr 1976
•
\ 0 Chu~9-s;n SU 1978
" ,
\
, .,Montrlll
Canad,
, >
•
\ \
.. 1:' I,~ . r
(
1 •
• ",
, (
'~.
1 ,
1
- J . Il
, Chemistry Chung-Sin SU • Ph.P •
Polymer Soluti'on Thermodyn,amics' and Gas-Liquid Chromatography
l '
ABSTRACT
Gas-liquid chromatography (glc) has been applied to the
meàsurem~t of thermodynamic parameters ()() for the interaction of / •
• vapour' phase molecules with poly(dimethyl siloxane) (PDMS). An
inter~à.boratory comparison of results has" shown that th~.accuracy and
reproducibility of the method is satlsfactory: It i8 then used to
obtain X values for the interactions' between two components in mixed
. ;
l J
, , '
stationary phases. Four pairs wexle chosen, involving PDMS, n-tetrat:osane, , '0: 1
di-n-octyl phthalate and squalane. Results are compared with geometric
• mean rule predictions. The effectiveness of di-n-octyl phthalate as a
plasticizer of poly(vinyl chloride) is studied by glc over the entirê
, concentration range. An èmpirical correlation has been found between )(
-
parameters and the processing ,,(melt v~scosity) ~nd usel- (Tg) characteristics
of the mixtures. A determination is also made of the interaction b'etween J>'
a pair of compatible polymers, polystyrene and poly(vinyl methyl ether) ••
Finally, the enthalpic part of the parameter between a vapour phase
probe and a nematic liquid is~ound to depend on the sh~pe of the probe , r
molecule and also on the àupport matetial.
/
.. o
c
~,
J
, l'
1
1 \
Chimie Chung-'Sin SU Ph.D. , r ,
Thermodynamique des Solutions de Polym~res et Chromatographie en'Phase Gazeuse
(1 RESUME':'
, .
La chromatographie eu phase ga~~use fut appliquée à la
mesure de paramétres the~d\namiques/ CX,) établissant l'interaction • Il> t
entre les molécules de la phase vap~ur et le polydiméthyl siloxane
" (PDMS). Une comparaison des résultats entre laboraoires démontra que l ' .)
la précision et la reproductibilité de la méthode est satisfaisanté. , -C7s mêmes résultats sont par laVsuite utilisés pour déterminer les ?(
, ,. interactions entre' deux composés sur une phase stationnaire mixte •
./
, i ~ -Quatre paires furen~ choisies impliquant le PDMS, n-tétracosane,'
l' ' - . di-n-octyl phthalate et le squalane. Les résultats sont comparés avec
les prédictions de la règle, ~e la moyenne géométrique. L'efficacité du
di-n-octyl phtaalate comme plastifiant du chlorure de polyvinyle fut
étudiée par c.p.g. sur toute la gamme de concentration. Une corrélation , , empirique fut établ~è entre le tra1temen~., (viscosité ~ l'état fondu) et
"
l'usage (T ) du mélange et les paramétres caractéristiques de celui-ci. g ,
L'interaction entre une paire de polymères compatibles, polystyrène et
'"
polyvinylméthyl éther fut aussi déte~inée. Finalement, il a été établi r
que la partie enthalpique du paramètre entre la sonde de la pha~e vapeur 1 •
et un liquiéIe nématique dépend ,de la forme de celle-ci et de, la nature
du support.
" ! ,
1 .,. .
, '. ,0#
~
!
, 1
.'
'tfl,~ 11: ".".-~ .. _ tit.\~ 1
" . . ' " '!'i' IIlW-4! ., . " :1 1 __
".J''' .a !"'a'{;4;' ..
5
\
, t
. .t. .....
.. \ ACKNOWLEOOEMENT
, " ~'
The author cordially thanks his supervisor, Dr DJ Patte~son,
for his guidance., Dr H.P. Schreiber for his c011aboration and advice in (Il
.,. r parts of this work; Dr D. Deshphande for his introduction to the glc
technique; tQe National ~esearch Courtcil'of Canada for a scholarship and ,
McGUl University for providing the facilitfes as weIl ~s. a teaching
ass ist,antship.
,'He'would also like ta express his gratitude to his friends,
Mr Elias M.C. Lam, Mr and Mr~ Bing and Juliet,Luh, Mr Robert T. Whillans, "
Dr Millard Schumaker, Dr Richard S.C. Yeo, Dr Jaffy C.F. Lau! Dr K.C. Cole,
Mr Michel Barbe and Mr J.M. Yang for their encouragement and companionship
throughout these yelirs.-
fi " J
c,
"
"
-, ,
L .ls .... sl_
.... ' , ,
';. ~I ' 1
•
)., / ,
l '
o
)
1 J
)
/ .,
To ''my • parents
Tsan-En Su M.D.
and J
Chiu Fong-Ing Su Reg'd Nurse
to whom 1 dedïcated' these years • 6!
r "
\ ..
\
"
----'-------------- -- -,--- -
,
"
CONTENTS
CHAPTER 1 GENERAJ:. n~:i'RODUCTION ••.•••.••••.•••••••••••.•••••••••.•• 1 , ~ .
CHAPTER 2 THEORETICAL BACKGROUND ..... : •• .' .•••.•• '.' ••... ',' •••.•.••• 4 o .
Sectio~2.l The Specific Re~enti?n Volume (Vg ••.••••••.•••••••••• 4 Section 2.2 Thé Partition Coefficient (Ky ana the
Activity Coefficient Cy) ......................... ~.5 Section 2.3 Free Energies, Enthalpies and Entropies of Mixing •••• 9 ~ection 2.4 Interaction Parameter (X} .. : •••. , •••.••••• : .•.. , •..•.... lO Section 2.5 Mixed Stationary Phase Sy!?tem!;l ••..•.••••.....•..•..•. 14 Section 2.6 Modified Interaction Parameter (X) •••••••••••••••••• 16 Section 2.7' Calorimetrie Measurements •.•.•• ',' ..................... -.19 Section 2.8 Column Preparation and Analysis •..... ~ ••....••..•••• 2l Section 2.9 Standard Retention Volume CVg) Measurements ••••••••• 22 Section 2.10 Sources .of Experimental Errorp ••••••..••..•.••.••• ~. 25
'. CHAPTER 3 'SYSTEMS WITij. REPULSIVE INTERACTIONS: TETRACOSANE; , SQUALANE, POLY (DlMETHYL SILOXANE) & DI-N-OCTYL. PHTHAtATE ....... 27, Section 3.1 Introduction ••••••••••.••••••••.•..•..••..•.••••.•.• 27 Section 3.2 Inteilab'oratory Da-ta CQmparisons ••.•.••••.•..••••••• 28 Section 3.3 Experimental Techniques .•••••• ' •••.••.••••.•••••••.•• 30 Section 3'.4 Results .' .•• ' ••••••.•••••..•••••••...•.. ~ ....•...••...• 32
l • Section. 3.5 The Simple Stationary Phases ••• ,: .. " •..• -; ....•••••••• 36 Section 3.6 The Mixed S tationary Phases ." ..•••••••••••.•.•••••••• 39 Section 3.7 The Geometric Mean Rule •••••••••••.•. ~ .....•..••.•.. 43 Section 3.8 The Entropic Parameters ............................. 45
"~ • 4 S.ectioIÎ 3.9 Conclusions •..•..•••••..•••.••••.••••••••..•••••••.. 6
CHAPTER 4 A POLYME~-PLASTICIZER SYSTEM: POLY~VINYL CHLORIDE) AND DI-N-OCTYL PHTHALATE .•••••. ~ ••••••••• 48
Section 4.1 Introduction •••.••••..•..••.••••.•.•••••.•••••..•..• 48 Section 4.2 Experimental •.•••••••••••••••••..•..••••.•. : ..•.•.•• 49 Section 4.3 Results ••••••••...••.. ' •.•. '" •••.•..•••...•••••••.•• 50 Section 4.4 P~re Stationàry Phase Systems •••••••••••.•••••.••.•• 53 Section 4.5 PVC-DOP InÇeraction •••••••••••••.•..•••• \ •..•.•.••.. 54
"" Section 4.5 Composition Dependence of PVC-Plastlcizer Interaction •• 56 Section' 4.7 Plasticizer Effecti veness •.•.•••••••••••.••••••••••• 58 Section 4.8 Conclusion ............................ ~ •••.•••••••••.• 61 . ,
CHAPTER 5 A COMPATIBLE POLYMER PAIR: ~ .
"
POLYSTYRENE AND POI:;Y (VINYL METHYL EHTER) '\, •.••••••..•..••...... 62,. Section 5.1 Introduction ••••••••••••••.•.•.••.••••••.•..••••.•.• 62 Section 5.2 Experimental ••.•.••.•.•••.•.••••.••.••••.•••••••••• '.64 Section 5.3 Results •••••...••..•••••••••••••••••••••••.••••.••.. 64 Séction 5.4 The Interaction Parameters .••.•••...••••....••••.••• 66 Section 5.5 Relationships with Critica1 Solution Temperatures ••• 68 Section 5.6 Conclusions •.•.••.••.••••••.••••••••.•••••••••••.••. 71
CHAPTER 6 NEMATIC LIQUIDS: METHOXY AND ETHOXY BENZYLIDENE BUTYLANILINE ••••••••.•••••••••• 73
Sect'ion 6.1 Introduction .••.•••••••••••••••.•••••••.•.•••••••••• 73 Se.ction 6.2 Experimental •• , •••••..•.••••.••... : .••••.•••.•••••••• 75 Section 6.3 Results •••••.••.••••.••••••.•••....••••• ! ............ 76 Section 6.4 General Discussions ••••••••••••••••••••••.•••...•• ' •• 81
--,·-',Section 6.5 Ef.fects of the Solid" Support •••••••••••.•.••• ~ •• '., ••• 82 \. Section 6.6 Conclusions •..•.••••.•.•••••.••..••••••••••••••• ' •• '; • 84
Suggestions for Furtp.er Work ••••••• , •••••••••..••••••••..••••• \ .•• 85 Claims ta Original Contribut;ion ••••••••.•..••.••..•••.•••••••••••• 81} Bibliography .............. ~ .... lolo ........... • c.(' •• If •• lolo .' .••••••••••••• 1(>' ••• /11 87
_rmt'!
~
l i J ,
','fI l
··1 < .1
cf t , , t ,
i ' } • J 7.
...........
r
...
~
. /
, J
"
Chapter
3:2.1-3.'4.1 3.4.2 3.4.3 3.4.4 3.4.5
3.,7.1
3.8.1
Chapter
4.2:1 -4.3.1 4.3.2 4.3.3 4.3.4
ChaEter
5.3.1
5-. 3.2 5.3.3
Chapter
6.3.1 6./3.2 Q'. 3.3 6.3.4 6.3.5
, 6.3.6
t LIST Of TABLES
3 (' ,Topic Page
Interlaboratory Cotltparison of v; Data 'for PDMS CH) ••••• '~ ' ••••••• 29 Abbreviations Used .. ~ ........................................ . 32 Çolumn. Da ta ........•.... Il ••••••••••••••••• • ~ •••••••••• ~ ........ • 32 l!arameters Used for Calcu1ations ••••••••••.•••••••••.•••• -••••• 33 Data for Pure Stationary Phases •• , ••••••••••••••• :' ••••••••••••• 34
• Data for Mixed Stationary Phases •.•••••••••••••••••••••••••••• 35
4
VI (_·X V2
23)! and (X2,31 s~); for Mi~e~_'Stat1Qnary Phases at 65 0C •• 44 "
(V* /V*) Values at 65°C 1 2 XS',23 ................................ ".45 . ,
ColUJDJl Gomposition~ •••....•. ,l, .................. ; •••••••• ~ ••••••• 50 V~ Cînl/gm) for PVC-DOP Co1upms •••••••••• ' ••..•••••••.••••••••••• 50 Interaction Parameters for Pure PVC (X12) •••••••••••• ~ •••• ~.:.51 Interaction Parameters for Pùre -DOP (X13) •••••••••••••••• , ••••• 51
I(V l/V 2) X23 Betwe'en pve and DOP ............................... 52 . ,
5
V~ (m1/gm) for the Pure Sta~ionary Phases ••••••••••••••••••••• 64
V~ (m1/gm) for' the Mixed Stationary Pha~es ................. ' ... 65 Flory Fre~ Energy and Entha1py Parameters at 40°C ••••••••••••• 66
"
6 -Col\JlDD Data .•..• 0 •• ~ ••••••• ......................... ",' •••••••••••• 76
,Abbreviations for Probes •••••••••• \ ............................ 76 ,Average V~ (m1/gm) for MBBA on Chr;omosorb ••••••••••• " •••••••••• 77
,/ X, XH and Xs for .l-fBBA .••••••.••••••••••••••.•••••....•.....•• 7 a v~ (m1/gm) for EBBA on Glass Beads (Co1umn E) •••• ~ •.•••••••••• 79 X, X
H and Xs for iBBA on Glass Beads (Co1umn~) ••••••••••• ' •••• 79
•
1\
'1 _ • .,. .........
'J#> \
\ \
/
.-
qJ
'. .
, .
Jo
1 (.
J
1 , 1
1
r-'
•
1 f
,
·t ,-, ,
.
....
, .
.'
..)
" '. / .
~
...
- -/ -----
1 ft
) "
f , "?
LIST OF 'FIGURES!
Chapt'er 2 Tapie •
2.9.1 Schematic Outlin~ of gic Set Up , .
" Chapter 4
4.6.1 Comp~sition Dependenc~ of X2i ~f
'l ..
..... ................................ 24
tile PVC-DOP System •••. : •••••• 57
" 4.7.1 Viscosity and- T Reduction Numbers vs: . ,,--g
X23 ;for PVC-DOP ........ 59
Chapter 5 Il
X23
against the~ST for the PS-P~ Sy stem •• ;;1' ........... ~. ;-.69 5.5.1
Cha!ter 6 , 6.3,.1 X agains t 100~ /T.ox" for EBB~ on Glassfe~dl Co~umn ' •••• ,' •.••••••• 80"
\,
"
010
. ,
/'
\--' / -J,
" t "
- '.
~
"
-.(
'-,
. ,
• .... , "
"'"
1/ ,
,fi!
" 1("
\ •
Î'
.,'
'.
1.
,
1 1
1
~-
, -r
j'
1 l j
.' i o'
j
...
!
A ..
1
"
f '.' ': ·1 "
i. " ''p' l,
l-I> i, ~ ~~r
?~ ~ .. " ~
r \ , " 'ft
~ "'"' l,
" t ..
'.'
J
, " , ,
1
/
1
t
0
"
..
... J.
.<, .
, ,
• v
GENERAL Im'RODUCTION
'. The app lieation of gas~l1quid chrOmatograp~y (glc) to
therxoody:nam:f.c studies of polymer solutions bas' been a comparat1vely
l
. 1-6 recent development." . Gle has long been used, however, as an ailà1'Ytical
tool for analysw mixed vapour phases. By uaing a su1tably ehosen " , \
liquid stat10nary phase, the varioùs'" components oe a vapour phase .,
mixture can be separated, due to their d1fferent lI~teraetio~s" or' , ,. -
parti~1on coefficients with the stationary phas~ material.
~re recently, stationary phases., ,part:l:cularly' if they are 1 7. .
po-l~r1c , have beén studied in the fqrm of !t'inverse chromatography".
Whereas in c~nventional gle, some properties of an Jt<t,llÙCnown" sample in . . ") ...... the lOOving phase are determined by the, use of a ''known'' statt10nary phase,
in inverse ebromatography 8 , the properdes of an "un1cnown" stati.onary . phase are detendned with"C. a ''know'' ~ving phase. The ~'lecules 'of this
phase are called "probes" "and ente~ the stationary phase at infini.te
dilution. • Basieally,' th, gle method measures the standard retent10n
. . !O lumes . (\Pg) of the probes. Atr will be shown in chapter 2, this 19
re1ated to the a~t1vtty c:oeffi~ient of th~ probe in the stationary
phase, ~hich in... turn depends on the .thermodynamic interaction betweaD ~. 1
-'-
the tw:o. Patterson et a). 9 extend~d this treatment to ~over polymerie
o ,
/
(
,"
t ~ ••
) , ~ .
v
•
. '
\ '
o ;" .\::----~ ...... '" .,. '~ "1,: '.'",
"".J'-' j' . , . , . , , J-
------------~-------------------.------------~---
" 1 ~ .... ___ ~_ • ,
.1.,
,\ \" 2 . \
~. '-./
"':terlals. "t'th un!mown moleeular weights, bY\ making use, of the Plory-
Huggins theory for polymer solutions and re,fi~ the activi-ty
coefficient.
Glc is ~ctual~y.the only conven~en\ meth~d ~or thermod;Uamic r;-:' ,,,,,"'
studies of the tnteraction between polymers and d~luents at élose to . unit mole fraction of the polyme'r, due to the minute qUantity of the
\ '
probe requi~ed. Other methode are either impracticahle due to the 1 0
polymer's high viscosity or und~ly slow, e.g. the sorption method,
because of the polymer' s low diffusion constant. This type of wrk has ~k ~
',- ~ i' ,
been carried out by a number o.f authors on vu:ious systems and the
resutts they oa,tained have beau generally in agreement with those by ,
other means. Its speed, versatility and capability makes it a highly ... .. J v
deslrable method for studying a wide range of both po,lymeric' and, simple.
systems. 1 ..A.'
In 1969,.S~idrod and Guillet fixst suggested 7a the use of glc for
such stud ies. 'Then Guillet reV:l.ewed8 the range of capabilities of the '. 1 8 .
method, inçluding the effects of diffusion constantdt ' glass trans1tioû - ' . '. "
temperatul'8s 10 and crys tal1J.zation rate;1: f f po lymer. SBmp las. About , l ' ~of ~ 13
the saœ t~7' Newman,' and, 7ausniotzL~ Hammer~ an~ .figny an~ thi~ laboratory , have applied it to polyme;.k systems like poly(dimethyl
........--. \.. /1 (I l' 1
,~J " siloxane) anÇloligo1De,1"s' like n-tetracos~. The present work was . ./ consequently c01JlDenced at that stage. In the past few years, a number
of other authors bave a1so entared th!s field. They inc1ude MBrtire 3a,3b, 15a, L5b, 15c 0 ilS 19
et al ' who studied nematic 1iquid stationary phases - , r'
Î
< 20 N' h· d TT, 'i21 d d 'L 'i 't Th cp" 1 it f ,: 01ahisi, ~s ~ an -I.'..we who. stu ie po ymer c sys ems. e po u ar y ~ .
this type of research is fast increasing.
"
A ............ aB.} i ... Ii L'.' ._.:x:: UAA .. Si_J,JiZW S_ ... <SZ .c
~
1 1
o "
o
, -"""'"
"
l
1 ,
l , , , l
t > , , ..
1
, 1.
o
, .
..
..
1 - ~-- - ----
.. 3
, ., By studying two pure stat~onary phase materials individuaUy,
. '1:l . " as well as in thf!ir mixtures of 1cnown composition, the itl,teraction between '. . .22 these two components can be obta1nea. It can caver the entire range of
composition of ~he two materials, even if they are high polymers 23 v 24,
proViCled that they do not phase separat" under the given conditipns. It . - ..
should ,bé notl!d tbat these interaction values are obtained via the , 0 #a.. f(
1 (;< ~ • e l ""'\
"observations" of the "molecular probes". l'his may not be as direct as
one would desire, but hitherto no method has beau devised to study
directly the thermodynamic interaction between two polymers without. the " .
introduction ara third component, namely.a eOlDlMn solvent.
In this work, both "repulsive" and natt~t1vè" systems have ~
been ~~ed.' The former.inel~des normal and branc~ed alkaneS,~IY(dimethyl siloxane) and di-n-oetyl phthalate •. The latter inclu~s olymer-. p1ast~eizer pairs, e.g. poly(~yl chlorid:) with di-n-octyl phthalaté5 ,
and highly eompa~ible polymer-polymer systems, e.g. polystyrene with , "
poly(vin1"l methyl éther)~6. Other t~ these, soma uemat;1e liquid~, e.g. . . n .. (p-Kethoxybenztlidene)-p~utylan!l1ne, bave beau of 1nte~st. By
working over a range of teJI!'Bratures t enthalpie, .besides free energetie 1 _ ,~
~'" _ -;, ; -j" •• f 1
~~ ,', ./" interaetioQ,s cao be obtalned. ...
J' -'~, . , .
\
.:/ The accuraq- and rel1abllity of the ~j.,l , \,,'"
gle mathoèi has been examined
27 . ' by interlaboratory comparlson o-f results, obtained by this as wall as ,
o~ ~, auch ~,/tbe static method and e&loria!aay. ro date, limita
"
-:1-J
,Qf accuracy of.glc therDX>~e data have not been establ1shed unequivocally.
It ls clear, however, that gle la a most rapid and eonvenient method for
" sueh studies.
1., ~ ___ ~~~ ________ ---,,--. (
, ,
: , ." .
1),
,," 1
o
••
l'
• \J 1 • J
\
4
CHAPTER 2
THEORETICAL & EXPERIMENTAL BACKGROUND
/ Section 2.1 The Specifie Retention Volume (Vg)
For thermoçynamic stuaies of the (bulk) stationary phase in
glc, th~ basic requlrement ls ,that equilibrium conditiou.s must be
attAiued. This is assumed to be true throughout this work.
The basic quantity obtalued from gle experiments is the
standard specifie retention volume (V~) • This quantity is related to
1 •
the' partition coefficient (K'), which in turo is related to the activity , , .
coefficient;, ( y) of the ~.robe in the stationary phase and then to t!he
interaction paramf!!ter (X) •
When a sample prob~ and au insoluble, non-adsorbable aud ~
inert gas are injected into a column, the time in which the sample , ,
probe passes through and out of the column is called the r~tention time ~
,(ta)' The inert ~as will also take a certain leugth of time,~ to pass
out of the column. This iueludes contributions due to the interstitial o ... ~
volume of the column and the effective vôlumes of the sample injector
a~d the detector. ~e net ret~ntiou time (~)' for the sample, due to its
retention by the stationary phase is therefore given by tN
- tR
- ,tM
•
If the flow rate of-the carrier gas through the column (volume per unit
t!me) 18 fc', then th~ net retention volume VN '· t N fc • For simplicity,
,-,- .
l"~ ~ ~ -:. .,
. .' " '-')
.',.1
.. :,.'" ~"-'"
, .. 1 ~ 'J ..
).
; J
0,
5
correction factors for pressure gradien~, gas non-ideality etc. will not
be'discussed here. Experimentally, with known chart speed, the distance
between the air peak and the sample peak gives ~ '. The flow rate can be
measured by the soap-bubble in burette method, with the necessary correctrons,
of course. ( see section 2.9 )
Ideally, and neglecting adsorption contributions etc., the net
retention volume is directly proportional to the mass of the stationary
o phase, wL ' causing the retention. Standardizing to 0 C, we have the
\
,standard retention volume (vi), (per unit mass of stationary phase).
V~ • 273.15 VN • 273.15
wL Tr Wr. Tr (2.1.1)
where VR
• tR
fe ; VM
• tH fc and Tr is the absolute temperature at which
the flow rate 18 measured (usually room temperature). 'l
Section 2.2 The Partition Coefficient (IC.) and the
Activity Coefficient (y)
The ,vi can be,.related to a d1mensionless phys1co-chemical
property of the solute-solvent system at equilibrium, thè pa~t1tion 1
coefficient (IC.), which 15 defined as /
/( •
-(weight of solute/volume) of stationary phase
(weight of solu~e/volume) of gas phase
wt. of solute in stat. phase wt. of solute in gas phase
, vol. of gas phase x vol. of stat. phase
1 \'
(2.2.1)
If the density of the stationary phase is PL ' its volume 1s
wL 1 PL • The volume of the gas phase 1s equal to the retention volume of
1
1 ~-
.'
r
)
1
o
"
--- -~-----~--
, /' ( \
_ "" ~_t
" . an inert gas V
M,. Therefore,
1 were 1( •
x VM PL
wL
wt: of so14te in stat. phase wt. of sdïute in gas phase
, . 6
(2.2.2)
at equilibrium..
Consider the sample probe passing through the column. Only the ~
gas phase mov~s, the stationary phase does n~t. If e9uilibrium exists,
the ratio of the quantities of the probe between the two phases', '1(' ,
should be,maintained throughout the column. When the probe is first '.
injected, the beginning cf the column has a comparatively high concentration
of the probe in both phases. As the p'robe in the gas phase tOOves Qn, its
concentration at the beginning of the column drops, causing a propor't'ional
drop in the stationary phase. The later portions of the column become . more concentrated, as the beginning has been previously. This continues
throughout the column, always keeping the equilibrium proportions.,Since o
the wole sample passes through the combinat ion of both phases of the ~
column, the ratio of the number of molecules in the stationary phase to
tbat in the gas phase should be the same as th. e ratio of the averagJ time , ' 1
li a molecule spends in the stationary phase compared to that in the gas 1
phase. Th~~efore, for a given solute probe,
time probe retained in stationary phase (tN) time probe retained in gas phase (ÏM)
So, from equation 2.1.3
le • •
With equation 2.1.1
1
, ~ ..
, r
!
o
1
, \
7
(2.2.3)
, (2.,.2.4)
where x and Xl are the probe' s lDOle fractions in the stationary and gas
phases, p Is the total'pressure of the gas'phase, Pl and Pl are
" respectively the probe's gas phase part~l pressure ~d pure state
vàpour pressure at the temperature of the column and Y has been defined
before.
Bere,
For the gas phase, assuming the ideal gas law, wi
n'RT - - RT l ~
, Where n stands t~r the number of moles and the prime denotes the gas
• phase. From equations 2e.2.4 and 2.2.6 ,
w' • l
(2.2.7)
From equations 2.2.1, 2.2.5 and 2.2.7,
1( .• W1 x II wi P
wL " . -• P-L
wL ~x
Mt. RT - x
(2.2.8)-
From equatlous 2.2.3 and 2.2.8
•
, ,
1
, ,
,1
f
1 t
1 1 1
,
, -',
/
o
8
, ~ • "
0 273.1S PL RT 273.15 R (2.2.9) Vg - x ~ .. ~ y pî PL Ir' ~ y pî
" This can be rewritten as ..
y - 273.15 R (2.2.10) Kr. P~ V~ , J
Adding the correction factors for the"non-idea1ity of the
solute probe
ln y • ln 273.15 R
where Bll i8 the
phase and \r 1 is
~ P~ Vi second vidal
po 1 - iT <,B11 - V1 ) ~, (2.2.11)
coefficient of the solute proDe ~n the gas "
the molar volume of the pure solute probe in the liquid ..
state. The reasoning for such corrections can be found in various texts \
28~3l and papers • The Bll accounts for the existence of intermolecular,
attractions io the vapour phase probe and VI corrects for the finite
volume of the probe molecules.
For polymerie stationary phases, ML io equatioo 2.2.11 may oot
be known. This has been overeome br Patterson et a16" as follows: 1
. ' Instegd of ?sing the activity coefficient ,'use
a x - • y-Cù Cù (2.2.12)
where a andCùsre the probe's activity and wight fraction respective1y.
From equation 2.2.5, it gives
/~ ~ 'a wl ~
1 wl - - Y-Cù wL Mr w1+wL
• y~ for wL »w{ \ (2,-2.13)
~ .
~) , , ,..,
Substitutiog this ioto equation '2.2.,11, ,#'
0, \
" ..
~'j' . ::::1{t ". ,
.'
t 273.15 R - n Ml P~ Vg
1/
J
Section 2.3 Free Energies, Enthalpies and
Entropies of Mixing
9
(2.2.14)
,4 ~
The free energy of mixing ( A'~) i5 gi ven as fo llows: (usual
notations)
P - RI ln ...1 o
Pl
- RT ln Yx
(2.3.1)
(2.3.3),
(2.3.4)
t'
~J This'shows how the vi from glcS is related to the free energy-
quantities through Y. Enthalpie valués can be obtained by stu~ying the
temperature dependence of the free energy quantiti~s.
(2.3.5)
. \ (2;3.6)
..
, ,
( -, .
,
/
o
- --- -- -----------r--;-,~, -----~-~--
\ 10
The enthalpic values so obtained from glc can',.-;'compared ----' ,
with those from other methods, like calo~~~try. KnoWing both theofree
ènergy and the enthalpy, the correspond ing' entropy is given by
G - H - TS (2.3.7)
" . r
Section 2.4 Interaction Parame ter ()()
The ma'éroscopic the:;modynamic qua..ntities observed can be , . .
explained at the molecular level by one of the solution theories, namely,
the regular solu~ion theory for simple solution and the Flory th~or: for,
~ polymer solutionst The regular solution model assumes the following:
(i) molecules are arranged in a lattice form with one molecu1e per site, 1
~he ~ites being of equal size,
(.H) molecular internal energies do not change in mixing,
(1ii) nea.rest neighbour ("contact") interactions on1y,
(iv) no change in volume due to mix1ng,
(v) random mixing.
Consider the contact "interaction .... energies" between two molecu1es
of species 1, ~wo mole cules of species 2 and a molecule each o~ species
1 and 2 to be En ' (22 and (12 respectively. The "1?teraction energy"
per "contact" betWeen species l and 2 is given by
(2.4.1)
If each molecule ~n a 1attice mode1 has z nearest neighbour
contacts of ~n1ike specie~, then its interchange energy is z ~w12 • The zàw
'quan ti ty _-..;;;l~2 kT
is defined as the "interaction parameter" (X) be~en
species 1 and 2, with k being Bo1t~n's constant and T the absolute 1
temperature. lt corresponds to the non-combinatorial free energy of mix1ng. :..J o
. .. l
f~" r~
"
'. 1 J \~ , i l~' "'-
t ~ If
F" i ~l ç .; ~ \ )
.. ~ t l,
~ 1 . ~ ~
1 ! !
1 " .: 1
o
.',
" ,
For NI molecules of species 1 mixing with N2 molecules of
species 2, the combinatorial entropy of mixing is
.. - R (nlin xl +rt'Zln x 2) .}
'(2.4.2)
\ where R is the gas constant and n represents number of moles. The non-
combinatoria1 free energy is given by
'(2.4.3)
~ Notice, that
~ z xlN2 • zNlxa 'and this is the number of unlike
species contact in random m~ing. From the above, the total free energy "'t
of mixin~ (tl GM) is gi ven by
A~. zAwiz RT • nlln xl + n2 ?n ~Z + (N1+N2)xl ~Z RT
... n1/n xl + 'CJ.2/n )(2 + (n1+n 2)xl)(25<12
Taking the derivative
l\ III _ «8A~1 RT1~ • P,T,n2
, Co aring equations
1 . 2 .. n xl + x 2 )( 12
\
2.4.5, 2.3.2 and 2.3.4
(?4.4)
(2.4.5)
(2.4.6)
Notice that for ideal solutions, Y .. l and )(12-0. The non-ideality' in
regular solutions arise from )(12 • Fdr glc experiments, th~ probe is
at infin~te dilution and x2~1, so, from equation 2.4.6 and equation Z.2.11,
)( _ ln 273.15 R 12 l1, Pl Vi
. (2.4.7)
/
--- ....... ,--1
l' • .'
" ~ 1.
. "
/.
, . '~ -... ~.
, ~" 1
:"~'-~~1' • . ~.
; .. J' i
\
' .~: . , . '.' ' .. 4 ~
..... ~ '-
1 .. .
1
,0
----- - -----
12
AS"mentioned befo~e, Xl2 1s a non-eombinator1al free energy
parameter. lt ean be qivided into an enthalpie and a (non-eombinatortal)
entropie part. J'..
_ z ~wH,l2 kT
t - X 1 + X H,12 S,12
z ~wS ,12
k
Notiee that Xs and ~ Ws have opposite signs •.
From equations 2.3.5, 2.4.6 and 2.4.\
- RT XH,12
2 R 1-2
for '2 ~1 ,fi ~
z 4wH,12 (1-"k .11
• ,U T ~)
The total change. in partial molar ent~opy is
--
RT XH.12 - il ln xl - RT X12
T
/
• j,
(2.4.8)
(2.4.9)
(2.4.10)
, Il
with the first and second terms respect1vely gi~ng the combinator1al and
non-combinatorial contributions. Strictly speaking, for a regular solution,
XS,12 should be zero. In most practical cases, h6wever, 'it is note
The regular solution theory has to b~ modified·when appl~ed to
polymerie materia+s. The ,usual ~thod 1s by applyirig the F.lory model. o •
Basically, the Flory model considers a polymerie molécule as ~ string of
segments, eaeh of which is like a molecule occupying one lattice site, in
the'regular solution theory, except that these are tied to each other to
form. a chain. The number of segments and "sites" occupied by. a p61ymeric
molecule is considered as the ratio of the volume of the polymerie molecule
1
!
• c
. ! f.-
~ ... ~I 1
" .).
" l: • ~. 0
(
Il
o
~-----
13
to that of the solvent mol,eeule. By, reeognizing ,the v t differenee in
size between polymer and simple mo1ecules, the per quanti basts of the
X' parameter has to be carefullY defined. By convention, X efers to __ ' . ij
per ~lê~-ré of species i,. so Xij';' Xji '. In gle, ,the simpl,e p obe is f'
refeqed< t;~/ as species l.
According to Flory's theory > •
ds .... .;. k (NI in M,comb
Oc
(2.4.11)
where r ts the number of segments of the polymer and ~ refera to the
segment fraction ( and therefQre volume fraction, as explained before ) •
It is interesting to compare th~s with equation 2.4.2.
 ' ' _ z NI (rN2) Â~ ~,non.comb N + rN 12
1 ~
• , • ~(Nl +rN~)'\~2 ÂW12 • / .~,~ , jj
Therefore, the total Â~ is given by "
Z(Nl+rN2)6l~2 ÂW12 - nI '~ '1 + n2 ln ~ 2 + , -------------
RT
- nI ln 11 + n~ ln ~2 +a z(nl+rn2)'1~2 Xl2
Taking the derivative,
API 1 2 - ln ~1 + ( i-r ) fJ2 + ~2 X12 ,
RT
- ln ~1 + ( l~ ) '2 + Xl2
for '1 ~o and ~ 2 ~l as in glc.
From equations 2.4.14, 2.3.2, 2.3.4 and 2.2.12,
• J
(2.4.12)
-1
(2.4.13)
(2.4.14)
,/
r .
___ 1
1
/
\1 f
J.
, '",-, '-. \",
1 0
ln S't + ( l-f ) + X 12 - 'n "X - ln 'f. ~ ) W
14
. ,
This, "together with equation 2.2.14' gives '
")( -,J' 273.15 R (nI ~) - ~ (B _;") _ ln n1!i.vl - 1 for M_ »K-
. ~ 12 I~ 'pî ~ 112~ RT 11 1 n2~v2 -L-""1
. ~
- ln 273.15 RV2 pî o Vi - iT (BU-VI) - 1
~ Pl vI (2.4.15) , ,
where v indicates the specifie volume of the species.
Sect'ion 2.5 Mixed Stationa!! Phase Systems
Mixed stationary phases of known compositions can a1so beJ~tudied i _
" 32 33 ' the glc method ' • Some modifications tn calculatio~s h~ve to .be mad~, . ~' , ..
however. For a t.ernary system with a probe (1) and a two component (2 and 3)
"'-" stationary phase, '~, ,,0 _)
"\ , \
", '.
'ds • -. M,comb
""- --'-, and (2.5.2)
" 2 . 2 wh~r~"'2 ' '3 an~ 2'2'3. respective1y represent the fraction of 2-2, 3-3 and
" 2-3 contacts ori~inally present in the stationary phase. \
. The 'totai L1 G 18 therefore , M
~' ,'" ,
• RT • {nI ,~ '1 ~~U2+n3) ln ("2+'13) }
~ 2 2 + (nli:r,2n2+r3n3) ~1 ('2 X'12-H'3 )(,13+2'/3 )(23) (2.5.3)
T~king the #er1vative, .~
., L1 "1 -RT • ln (2.5.4)
The ~a/t three ~erms can be taken together as
.. .. '
J . ,
·.". " , ""!
,~,t
J }
~
, Xl (23) • ln
~ l '273.15 R
• n(. ~ ~ p~ ~
where
-15
(2.5.5)
Ja;fon 2.4.15
, 0
Kn6wing X 1 (23), f.rom the ~ed column, and X 12 and, X.l~"trom
,1 the respec;~ve single-component statf-çmary 'pha~, columns,' X23
can "be
calculated f~om '""'et(uation 2.5.5. Notice that the X23
in that .equation has
been ~Itiplied by l , the r~ciprocai of the nu.mber or "segments" per r '
moiecule of componen? 2, which 1s taken as equal to ~ vI , to "standardize" , ,'J:J.2v2
~t to the samè per quantity footing,(i.e.- per mol~cular Volum~~!, the probe) ;!J 3- """-1:.( "
J the other X terms (so, "preferablyo, one Gf t~e stationary phase, c~onents ,"''''
"should have a known molecular'weight)~ JuS! as in, the case of the other
" parame ters , X- has i ts own 'X and X componen t'li. Howev:er, s ince 23 'H, 23 S , 2~
'J >
~he X 23 values
ind1rectly frÇ)1l1
tiiemse~ves are usually less' accurate (being obtained' • r' ..
) ..' the differences ~ng other observables) in the case of
t ~ (J ..,.
,
:ic, ,the y values. if needed; are often obtained. fram other methods II~ J. ~Il,23 ' ,',
~ , zcaiorimetry.. \ , '{ i.
As ment10ned before '" the Flory X parameters are based fÎh the
1 tice 'mod~l. which'makes no allowance for change in ;olume due to mixing
.or equation of state effects. The definition of the segments is arbitrarily .J
, .~ ~ 1 ......
, "
" .
>.
, .'
~ , ". . -j
t
" . )
• 0
,0
1
/ 16
constrainèd to a volume basis. This treatment has been fo~nd to be , .
inadequate for many systems. &re recently, new theoriei4 have b~en 4
developed which take into account such effects, while considering the , , .
interactions between molecules as contingent upon the sUlfaces of the1r 1 7'
\'
s~le ''bard cores". Such c~siderations are partieularly ifortant for
tmol~eu1es ~xing with very dense polymerie subs,t,tes, because us~ally l' ,
~re i8 a 'significant negative volume of mixu{g resulting in the more
"rarefied" simple substance ttc~ndenSing" intt the denser polymerie
substance. ~decrease in the free volume of the mixture leads to an ..
exothermic contribution to the enthalpy of mixing. Such effects should be ~
accounted for by the use of'the neWer t eories to be discussed below.
7
Section 2.6 MOdified Interaction Parameter ( X ) " '
~ f . ~ U~ing the corresponding states formulation of the ,FIory-PrigOgine)
theory, the non-~ombinatorial Gibb's free energy per gram (g) of a mixture
can be réiated to a dtmen~ionless reduced func~ion G(T) by
* .. .. g • u G(T)
;
(2.6.1)
* .. Bere, u is a reduction parameter (per gr~) for quantities
having dimensions pf energy. ,It 1s re1aeed, for a b~nary syst_~, to the
corresponding u~ of the'pur~ components through
~ . * *, * u - w1u1 + Cu 2u2 - tùl~2vl Xl2
.....
'. ~
(2.6.2)
~ere 112 is a new F1o~-Prigogine iQteraetion parameter between the ,~
'fr * components, CI) represents weigJat action, v represents , ç • l'
- volume, 8.Il"d e - CUiv~s:fr Il:: CUiv~si '- .,,ï~-
l;I.~h '. b;ing\he ".ur~~,,:,· to ~o~ume!' ~atio. ~èi ~a~~e of
estimated or obtained fiom the literature (e •• fsee. table \
.. ... ( ;
, .. ..
, "core" specifie
(2.6.3)
s cau e ither be
3.4.3).
" -,
,
l, " f
, '
~. l ,
-~ ,
1
,
o /
/
17
* ' . The Ut may also be expressed in terms of the pressure reducti~n
parame~~r p ~ * * '* (2.6.4) ( ui • Pi vi
The reduced temperatare ~ of the mixt4re can be related to Ti of
the pure component by
(2.6.5)
Fol10wing the new nory-Prigogine model and going through a
35,36 0
le~thy dedvation , and keeping fn mind that for the glc case., "'1 ~.O,
/(tJ2~1, ,~~~ and e~l, t~e following will be obtai..ned \l
* *2 -* / l\ 1'1 ,non-comb If RTXl l 2 - ~TX12 (2.6.6)
- "IV;~2 {,7 GcT.2Y': T2(:~ ~ } + p~v: t G(T2) - G<T1) + - ... ~6a) } CT -T ) -r-'
1 2 6T .. / P
(2.6.7)
- M~ V~2 {- Û<T2>}
, + p~v~ {Û<T2)-Û(Tl )+Tl [ScTl >:-S(T2)] } '> (2.6.8'-\
" .... , .... where U is the reduced energy, S the reduced entrèpy, P the reduced pressure,
li" ' is the non-combinatorial change in chemical potential for l',non-comb
" the "probe due to mixing, the other symbols have been defined before.
, Note that for the calc~lation of X v~, the ){*:nd ,* terms ,
used ar~ based on "core molar volumes" which -refer ,to volUmes of the r'
molecular ''bard core" (which are presumed to be 1lldependent of temperature) • .
, In this aspect, they are different from those X and , terme which are not
used for X calculations-in this thesis.
In equation 2.6.8, the new Flory-Prigogine model assumes Û • _~-l,
,~ --------------------------~--
r -
< r
... ~
'.,
, ,
'.
" r
, , . .
", "
o
o
S - 3 ln (Vl !3 - 1) and T • (Vl !3 - 1) v-4/3 , with Vi- Vi!v~ • This gives J
(with equation 2.6~6)
(2.6.9)
For a ternary system 'with a mixed stationary phase 17, the
corresponding equations are
* u -* * *
(ù 1 u l " + (ù'2u2 ~' CI) 3 u3
- W192v~12 - Cl)193v~13 - (2.6.10)
~
• ~,~~ [X1292 + X1393 '- X23 :1 9 293] {-Û<To)}
, + P~lV~ {Û(T?)-Û<T1)+T1 LS(T1)-S<TO)] } (2.6.11)
,
+ *'M *{L-J. +3Tl/n'Titl~3_1} , ~1'1 vI ...... , ... 1 3
VI, Vo . Vo - 1 (2.6.12)
For ca1culations of the X parameters, a consistent procedure has \
, ! ,
b~en fol1owed throughout. Values of p* and v* are taken at a fixed
o temperature, say 25 C, fram standard 1iterature sources. These are kept ..
cons~ant, regard1ess of the exp,erimental temperature. Then the V value of
~ the same (25°C) temperature 18' calcu1ated from the equation'
"'1!3 aT V - 1 + -~;..:..-":"'
3 (1,+aT) (2.6.I3 )
~sing (2.S°C) coefficient of cubic expansion (a) values, a1so from standard ...
literature. Then T (for 250 C) 1s calculated by
"
; 11\ ' , . i !>
:!' i;' ';,
j, ' K "~y
,~ , /,-~ ~~
l' ~ 11-
," < \ ~,
f r. Il ~
1 l'
f 1
1 . , <
!
1
.
o
and
. T • 1 V-1/ 3
V
with T • 298.15'1<
19
(2.6.14)
(2.6.15)
/
This T* i8 taken as 'constant for all temperatures. Then'V values
for any other (experimenta1) temperature witt- have to be ''back calculated"
by ite~ation us!ng equation 2.6.14. ... ..
For temary systems, the Vo To and Xij values are calculated
with a c~uter programme usiht the iterated self-consistent approach. lt
can be outlined as fo11ows:
where
and
First Xn if! taken as zero. Then To is obtained by the equation
\ T _ tJl 2TZ + "'/i:3
a 1 - "'293X23!P;
~* p, "'2· * a * * f1 2 P2 -H'3 P3
- "'3· l -"'2
(2.6.16) ~,
Then, the,corresponding Vo ls obtaln~d b~ Iteration from equation
2.6.14. Then the resul~ing Xl2 ' X13
and X23
values are obtained rram
equatio~s 2.6.9 and 2.6.12. Then this new X23 ia used 'to get a new To fram
equation 2.6.16, thus giving a new Vo and a new X23 value. This cyclic
process is repeated u?til two consecutive, Xl) values differ by less than
0.01 cal/cm~. Notice that ~nlike the X parameter, which ls a d~sionlesa '
ratio, the X parameter 18 in energy pet unit surface. 1
Section 2.7 Calorimetrie Méasurement~ i
" :7. '\ In this work, calorimetrie measurements have'been made bot ~
compare with and complement the glc results. Generally speaking, th e cau ~ , ,
r. t
1
,1 '0
< 1
'-, . J 20
be divided into two types.
For cases in which both'mixing components are of comparable~ amount8, the molar heat of mixing,
oC. A âlIobs " .u~. ____ ~_ Total nUmber of ,moles
(2. L 1)
where â Robs i8 the heat change determined calorimett'ically and is giyen (').
by the area of the peak observed times the calibration constant.
Such calor~etricâBM can be obtained for the t~ stationary
phase components of a gic ternary system, provided that they âre not tao
viscous. They can be converted to XH 23 as follows 38 , the &~ being enthalpy , per mole:
~~
. This g,ives âR 23 ,
""T X H, 23,s2~3 '" V 2 where Vi· Mi v i
• 6.l\i(x ZV2"i-X3V3)
RTxZx3V3
i (2.7.2)
(2.7.3)
This, together with the)(23 obtained from glc will give XS,23 ' just as
in equation,2.4.8. ,
The other type of calorimetrie measurements consist of dissolving
a amall quantity of one camponent, say a nemat'ic liquid or a po1ymet'ic
material in a large quantity of the ather camponent, usually an or~anic
solvent. Such a'case corresponds to dissolving a high molecular weight ,
component in a low mo1ecular weight solvent to'infinite dilution. This 1s
just the reverse in composition to the gic experiments with a probe and a
one component stationary phase. In such a case • âh • ____ &_~~b~s __________ __
2,soln no. - of f 2 gms. 0. camponent
\ (2.7.4)
where àh2 -s-o-ln-J.-upe enthalpy of solution per gram of component 2, -the t
stationary phase material, whose molecular weight may be unknown.
1 1
\
1
, -
o
\tJ
21
1
Section 2.8 Column Preparation and Analysis
Throughout this thesis, the gic columns used a~e packed by
this author :in this laboratory (e~cept those specif{cally mentioned in
section 3.2). The materials Qused and the specifie treatments given to , such materials, if any, are described in the individual chapters. Unless
otherwise stated, the general procedure of coating and packing tne
colunms are as fo'liows:
A known weight (usually about 1 gm.) of thé stationary phase . ~
material i8 dissolved in a volatile solvent. A suitable,known quantity /11
o~ t~e so1id support, e.g. 15 gms. of chromosorb, is then added, and "
the suspension is allowed to sit for at least a few:hlfurs' to make sure
that the solution completely wets the surface of the support material.
This is then dried under vacuum fGr severai hours at temperatures around
Booe, with a rotary evaporator. The resulting coated and dried chromosorb
is then cooled in a vacuum cr
desiccator at room temperature overnight. , . This material is J:hen packed in a piece of copper tubing of
/J (0,
a quarter inch outer diameter and about 5 .ft. long. It is first . /
" t!ansferred from a weighed beaker through a funnel into the tubing
with Us bottom end plugged wi1:h glass wool. The tubing is const~tly
tapped to ensure even packing of the coated support. The beaker is
weighe~ again af~er the packing process, thus ~iving the weight of the
coàted support in the column. The actual weight,of the stationary phase
material, wL' can then be caiculated if the weight percentage of the
stationary phase mat~rial on the coated support is known.
To obtain this information, tbe coated cbromosorb is analysed
by "a~hing" if the stationary phase does not contain sil~on atoms, or
1
.1
l f
~
l \ f ~ 1
r,. ~ l, '.
J
1" • o
"22
by "sohxletting" if it does. Ashing 18 done by heating the coated
chromosorb in a cruciblè with a Bunsen burner to over lOOOoC for seve
hours·Cto const~t weight). The coated chr~mosorb ls weighed
and after this process,. glving the weight of the stationary phase mat
in the known weight of the coated chramosorb. The principle behind-th
"sohxletting"'method ils the SaIlle, except 'that it is more cumbersome, d
is used only if the stationary phase ma~erial cannot be completely
"ignited" by the "ashing" process. A volatile liquid in which the
statlonary phase material ls soluble is used for "sohxlettingll• The
process is usually carried on for thrèe or more days. The solution so
obtained is th{m dried in a vacuum oven at elevated temperatures (without
decomposing the compound) \mtil constant weight ls obtained. This gives
the weight of the (non-volatile) stationary phase material recovered fram . '
a known weight of coated chromosorb. Results are found to ,
be satisfactory.22
The weight percentage of the stationary phase on, the coated
~ chromosorb as obtained fram "asbing" or " sohxlettingll will give the
"coating efficiency" of the particular system wher,. compared with that
of the 'stationary phase n'laterial present in the original solution used
to coat the chromosorb. This will be mentioned again later in sectton 3.3.
Section 2,9 Standard Retention Volume·~) Measurements
A dual colùmn glc apparatus baslcally the sarne as that used by .. Tewari et al. 39 has been employed. The flow rate of the purified helium ..
carrier gas la measured by the soap bubble in burette method. An electric Il
r
, ~ 1
\ 1 :
'1
1
~I 1 1
1. 1
,
o
tUner is used to measure t~e tUne required for the soap bubble to pass
through 50 mIs. of burette volume. This gives the flow rate (fc') in
ml'B./sec. The vapour pressure of water (Pw)' at the temperature this is
measured (room temperature), is corrected for~
'The colunms are immersed, i11 an oil.hath controlled by a Haake
regulator. Its eveness and-èonsistency has been checked with a quartz 1
S electronic thermometer. The effect of the gas phase pressure drop across
the length of the column has been corrected for. This is done by measuring
the inlet pressure (P i\" inmediately before the colUIllIl. with a mercury
manometer. The outlet pressur~ (Po) is assumed to be equal to that of 1
the atmosphere and this is measured by a barometer in the "laboratory. The
retention time (~) is obtained by measuring the distance between a <
reference air peak aà~,the sample peak as recorded by a constant speed
recorder.
The standard retention volume, ~ is gi~en by
V~(ml /gm) • ~(sec) x fc(ml /sec)
wL
(gm)
:P -P 273.15 0 W 3
x T x-px2'x r 0
(2.9.1)
Comparihg this equation with equation 2.1.1, it is quite apparent th t on
the left hand side, the second term "standardises" the volume to OOC, the ,
third term corrects for the partial pressure of water vapoùr in the soa
bubble enclbsed burette, while the last terms accotint for the column
pressure drop effectS. The theory behind this can be found in standard
, 28-30 .. 0' ) \ textpooks • From such vg values, interaction parameters can be
calculated 'as described in the eariier sections of this chapter. A
schematic diagram of the gic set up ia given in figure 2.9.1.
24
c 0, ,
a:t::p:unq a\qqnq-deOS p.,.np":n ( \
..
\ ~ ,
- , \ ,
1-0 0 1 1-0
01-1 <II C) - '"0 Q)
'--- 1-0 01-1 0 Q) C)
"0-- <II , , 1-0 ,
" - "T' - - - - - - - - ., , 1
1 , · t:l.
::l
, " 1 -
• . ~ , 1
~ , .... 1 (pal'Elaq) . 0 , C) , 1 1 . \
1 saldums ~ pod ~
aqo.ld uonoafll1 1 ..) 1 -,
1 " j - - - - - - - - - - "
t
1
01-1 <II
'"0 11.1 <II i 01-1 ~l ct!.c 01-101-1 ~ 1
CIl ct! 1-~.o ~
1-0 .... 1: <II .~ ~ .c 0 ~ 1-0
00 ct! , ~
'"0
C) ~ 01-1 tU
, a <II .c U4 tIl
.la:tamouem ~
CTI , \ · N
. · ~ --j
.. ~
~
1-0 0
01-1 ~
.lapUJ:l.Âo CII~ seg mnnaH ct! ::l bObO
<II 1-0 .
~ ;~~; -0 ~' ... '.:J
':"..,-i1
::i' , .... ~ •• ,!
, 1
, -. -, ' .
. ' ~
> •
• j'
(j
25
S~ction 2,10 Sources of Experimental Errors
The distance between the air peak and the probe peak, which
gives the retent"ion time, is measured by a ruler. This cao give an error
of a frac~ion of a millimet:re white the peak distance may vary from
around 1 cm. ta more than la cm. The measurement of the flow rate depends . . Il ::=
on the persQna1 error of timing, which may be a fraction of a second,
compared to &round 50 seconds required for the 50 ml. burette. (The ~ ,.
reading of the burette may have an error of + 0.1 ml.) 't"'"
rA The injection of the probe samp1e ,is done with a manua1
Hamilton micro-syringe, which may take a fraction of a second for -each
injection. This has to be, compared with the retention time which may
vary from a few seconds (;0 several minutes. Furthermore, the probe
sample (liquid at room temperature) takes Unite time ta vapourize . .
completely in the injection heater before actually entering the column.
o Errors from Buch sources cannot be accurately estimated.
'The manometel' l'eading for the inlet gas pressure may be off by
0.2 p.s.i" out of a total of 3 to 5 p,s.i. The hob wire detector has a
c~ volume of '''d,ead· space", which is not known, AlI these contr ibute
to errors in the obser'Q'ed retention volume, Repetition helps ta decrease
the error ma!gin by taking an average of the repeated values, but, in any
case, at 'least as it is done here, an accu!'ate theoretical estimation of
the experimental errors may not be achieved,
lt is therefore decided that for this work, instead of predicting ,
, the error limits theoretically, the accuracy and reliability of the glc
data will be considered via comparisons with data obtaipe~ from other
laboratories, e,g, section -3.2. Also, they may boe compared in.~hermodynamic
--'
, , .
J 1. l
1
o
/ / ....
26
terms (which is "the~ main interest of this work) with results obtained
from ether sources such as ~alor imetry or the sorption method. Discussions
in this regard will be given in the ind ividual sections •
•
or
.' 1 ~
).
,.
l' II· .'.~.
,
o
/
t
, , 27
CHAPTER 3
SYSTEMS WITH REPULS\IVE INTERACTIONS'.
TETRACOSANE, SQUALANE, POLY(DlMETHY4 SILOXANE} & DI-N-OCTYL PHTHALATE
Section 3.1 Introduction
/ For glc thèrmodynamic studies on materials in "bulk", the
required conditions include the absence of adso~tion effects and the 1
ready attainment of thermodynamic equ~librium. To minimize the adsorption
effects, the solid support used should have been properly treated to
o • 40 . give a non-reacting or adsorptive surface with a reasonable texture •
• Also, it should be non-polar to avoid~ny serious interac~ion with the
, s,tationary phase or the probes. 'The stationary phase coated on the
" solid support ought ta be thick enough to render aIl surface effects
AO '41 42 ,. insignificant ' , .. To ensure t~e ~ady attainment of thermodynamic
equilibrium, the ~ffusion coefficient of the probes in, the stationary
phase must be sufficiently high. .
In this chapter, stationary phases and probes with repulsive
interactions (i.e. positive interaction parameters) will be exwnined.
> --In these systems, it is believed that'''specific interaction" effêèts 'b
arising from hydrogen-bonc3ing, polar attractions or the formation' of " .
charge-.transfer complexes do not existe Some of the consequences of ,
pos sib 1 e (&i fic interaction" will be discussed in later chapters.
.'
o
t
AlI the four stationary phase components used are liquids at column ~ é
temperature with low viscosities and high diffusion constants for the
probes. N7't~tracosane a~ squalane are non-polar while poly(dimethyl., '1 siloxane), abbreviate"lf~{lS PDMS, and di-n-oct~l phthalate, abbreviated
as DOP lire only slightly polar. All the alkane and aromatic probes used fi' "
are virtually non-polar. These s)(stems serve as a test of _the validity
Qf the glc method as applied to mixed stationary phases. They can also ,
be cons idet'~ed the "control" experiments for other materials reported
in chap ters 4 and 5.
As discussed in chapter 2, the interaction parameter bet~.een
the t~ c?mponents of a mixed s,tationary phase (t. 23)' is obtained via
the difference between the probe-stationary phase interaction for the
pure (X12 'X13
) and mixed ct1.1(23» st~tionary phases (equation 2.5.5).
This means that percentage errors of X 23 will be inherently more serious
than those of '1. 12 or 1.. 13 • v In order to obtain reasonably reliable ':(23
results, high accuracies- in X. 12' "'13 an~ ')(1(23) are requ~red::~
Section 3.'2 _Interlaboratory Data Oomparisons
, ",With the above in mind, an interlaboratory comp_arison of tlœ ..
"
g1 7 data for high molecular weight poly(dimethyl siloxane) to be called
PDMS(H), was carried out betwe~n this laboratory and tha't of Prausnitz
27 ~ et al. Six sets of results were assembled:. Set A refers to results of
39 Suumers et al. ; Set B refers to results from a Oflumn pa~ked by this
author using a PDMS(H) sample belonging to this laboratory; Set C refers
" to ~results from- a column packed by this author, 'usiug PDMS(H) supplied
J ~
1 (
'Ii""
,
/
29
py,Prausnitz et al. of the Univers;i ty of California at Berkeley; Set ~D
érefers to, resu~ ts obtained, Dy this author using â ~olumn packed by
Prausnitz et al. using their own sample; Set E refel's to -results obtained
43 by Prausnitz et ~Ù. ,using their own columnj ~and Set F refus to results
-optaiilf~d by Prausnitz et al. us:tn:g a co1umn packed by this author 'using
1 • , ), r
PDMS(H) b~longing to this 1aboratory.., L-
• 7
Table 3. 2.1 Inter1ab~rat9ry c>ompariso,n of ~ Ps.tâ~for PD~ (H)
,Probe ~
25°C nP:, " - 74.76 nHx ," 211.1 bet)zene 340.4 40°C nP, 43.6,5
, "114,8" nRx nBp to1uene
290.8 463.7
benzene 181. 2 55°C • nP 27.43 nRx° 66.45 nBp 157.8 nOct 367.1
1 toluEme 251.4 benzene 105.4
B
76.8-78.8 ' . 214.8-220.6 348. 4-3S6~7
46.6-47.1 • 119.,2-,120.2 305;0-307.0 493.3-494.4 ~,~ 1. 1-191. ~
\
29.3-29.4 , 70.~70.2
164.3":'165.3 385. 8-:f86. 4 26~. 0- 26~\ 5 110.0-110.\1 ~
" \
. C
75.2-:77.1 210.5-217.4 342.0-353.6
45.8-46.5° H~,9-120.o. 303.7-308.3 492.4-504.9 190.1-192.5
29.4-30. r 70.2-70.8
165.3-166.6 385.9-388.5 264.0-266.0 110.7-111.0
D
77.8-79:5 219.2- 224.2
'353.3-372.0
47. 3':48~1 123,. 2-123.9 312.8-318.Z 508.5-52Ô.8 197.3-198.2 •
29.9 72.6
168.4 39,8.9 267.S 113.1
7'9. ~-8l.d 226.4- 230.4 366.8-J,80.0
47.1-48.6 123:,0-126.8
316.7 504. 8-525.1 196.2-203.3
29.7-29.8 70.5-72.1.
1'69.5 395.3
268.4"'269.2 111.6-112.5
nP means n-pentane. Other symi;l,ols are defined in table 3.4.1 .\ \..,
\ 0 \.....
,.-77 .l'
219.9 354.1
46.1 120.0 307.6
,494.1 192.9
29.2 70.6
165.6
264.6 110.1
\ \ 39 • The T.{' ·va1ues from Set\A, obtaineo by Summers et' al years ago
g \
., 1
, .,
î
l 1 J
'1
, ~n co-operation with this 1aborato~ give thermod:am{~ parameters \ in good,
a~rêement with values obtained" fram \he conven~io~,. eqtillibrium sorp~ion 1 method 4~ The Berkeley group found thek ~ (Set E) teo be higher than Set A
da ta by 6 to 12%: This" se.... to be 0~1d. t~e ran~. of' comb 1ned ~~xpe;'i1D~~tal errors c1aimed for these techn,iq~is arouses intere~t in making an
inter1aboratory cOmParison of VO data27 • . ~g \
-J 0
7 " f
•
, .
(' ", "" " ,f' ~"
"~';
~. , W.' , a. (
~', ~-,'
f i
1
'\ \-, \.
,
J '\
f:-• . t
, ,
, i ,
-/
i J
1 • 1
f,
... '"
i ;
f r f r - .. ~ ..... ~--~-- r
r r
; r
f f ; ; ;
i /~'
Apparently, n~ the" yir'iablesl in~~d, 'e,g. the polymei' .,' ~.
~ample, the exact apparatus-operator combination, or the age of packed " columns serlously affects the vg data, excep't, the coating and packing
procedure. This ls indicated by the 'agreement of the results in Set D with ; ,
those in Set E and the agreement of those o~ Sets B, C and F with one
another .Both groups obtain the SaIne results :(Co within ± 1. 5% about a mean) ~ • : +
using, the sarne cqromatographic column, ~hereas the'results with the Berkeley,
column are always somewhat higher (about 2%) than th~se with a column packed "
and '-coated in this laboratory. However ,> the study has not fully resolved
the discrepancy,with the results in Set A. Most of the glc data remain :3 1
/ ~
to 5% higher than those reported by Summers et al. which are Bupported by \., 0 44
the supposedly accuta,te vapour sorption ,x.values • It is tm.1ikely that \
th\: discrepanliy atises from the inaccuracy in determining the weight of
" the ~tationary phase, wL. If the chromosorb contains volatile impurities, . \ ,JI . '
e.g. water, to start with, it ~nly increa~' the apparent wL. th~s - - J(
decrease the observe'd VS • Achoiee of absolute v~ is t~arefore diffieult.
This exercise doesjhqwever, show the degree of accuracy to be expected.
~ Section 3.3 EXJ)erimental Technigues
J
J '/
:1 ---:--~-_ A dual collllIU'l glc !lpparatus, mentioned before in'
, been sed. The inlet gas pressure is set between 3 to 5 p. s o
1 2,. has
1. A hot wire
o
.t de'tec tor eoup led to a t imed recordei is used for 'exh ib 11: in results.
The solid support used in the.column is Chromoso b W, AW-DMC&
trea~d, 6~-80 mesh, as supplied by Chromatographie Specialties Ltd., /
~ 1. 1 1 1
Ont;:ario, Canada. The s,ationary phase materials include P9% pl.lre n-,tetracosane
and squalaÎ1e, both supplied by Chemical Samples Co., Do~ Chemical 200 PDMS
fluid with a viseosity of 50 centistokes and plasticizer, grade DOP cOtmllercially :~
• 1
o
.~ "
:n
available for industrial use. The PDMS is purified by heating to l200 C under
vacuum to remove low molecular weight impurities and then dried with solid, 1
insoluble.. drying agen~s. It,s molecular weigllt is determined by ~iscosity
measurements to be 3700. The D,OP is used as supp lied.
1 The composition of a co1umn containing a pair of stationary phase
components is determined as follows. 'the viscosities of a series"of mixtures
of known compositions o,f this pair of materials are first determined under
a given set of conditions. This gives an empJrical 'viscosity-composition
.J _-curve. By sohxletting out the m~ed stati~nary phase from the coated
-~-
chromoBorb and determining its viscosity under exactly the same conditions,
its composition can be obtained. If the cQating efficiency (discussed in o
section 2.8') of a stationary phase mixture i9 found to, be 99% or better,
the composition of the coated column is deemed to be the same as that
in the solution originally lused for the coating ,procedure. In a11 cases,
the probes used are 99% pure commercial stock èhemicals, as supplied. A
Hamilton microsyr inge ~s used ~or injec1.ions. The columns are made from
quarter-inch outside diameter copper~~~g, each about ~ to 5 f~et long.
They are flushed with hexane and ~ne, then dried before use. ~
The/flo~ rate is usually bereen 0.5 ml. to l ml. per se~ond,
accurate to ~ithfu -0.; or at worst 2%, for eac'h set of ruJs. The temperature
of the column is kept constant by an &i1 bath with a Haake regulator, . capabl~ of keeping temperatures within 0.2oC. f.
Q
Iwo calorimetelt"s ,have been used for the calorimetrie experiments.
For measurements at roof;;.. temperature (2S0 C), a Tian-Calvet microcalorimeter
f S ... L F . d Th 1 . d . d45a rom eta~am, yon, rance ~s use. e usua accuracy ~s etermLDe to
~ , 4Sb be about ± 1,%' The operat i;on, of these instruments has been descr ibed
!lsewnere. F~r measurements at hlgher temperatures (up to 65°C), a CRMT
),
)
t i l , . f
\ ~ v i
1
, 1 1
l '
/
"-
!'
()
,t ; ..... , .
'1
32
monoce11 microca1orimeter 45ca1so manufactured by S~taram of F~ce i8
used. This is a variant of the one mentioned above. Its temperature can
be kept constant to wi~hin O.loC. In aIl cases, the heat change 1s
recorded on a Sefram recorder and the areas of the peaks observed are • 0
measJred by an Amsler planimete_r.
Section 3.4 Results
Table 3.4,1 Abbreviâtions Used
Nrune of Substance
n-tetracosane Abbreviation Used
..
o
poly(dimethyl siloxane) ~W.K3700 di-n-octy1 phtha1ate
n-hexane 2,2 dimethyl butane 2,3 dimethY4J butane
n-heptane 2 methy1 hexane 3 methyl hexane
~-octane 2,5 dlmethyl hexane 2,2,4 trimethyl hexane
cyclopentane eyclohexane
Table 3.4.2 Column Data
Stationary Composition Wt.of Stat. Phase hI vo1.at 65°C Phase wr--
. teteos pure 0.6316 gm. squalane, pure 0.6143 gm.
PDMS pure 0.6322 gm. DOP pure 0.4781 gm.
teteos/ sC(,ua1ane 0.50/0.50 0.5137 gm. tetcos/PDMS 0.50/0.50 0.5572 gm. squa1 ane/PDMS 0.50/0.50 0.5878 gm. teteos/DOP 0.44/0'.56 1.0157 gm~
v )
teteos PDMS DOP nHx
2, 20MB 2,3DMB nBp 2MHx 3MHx nOct,
2,5DMHx 2,2,4TMHx
cP eUx
Coat~ng Thickness 'J!.Llwt.of Coated SUEEort
8.77% 9.08'70
12.50'7. 9.62'70 9.55'7.
10.20'7. 10.48'7. 15.03'7.
, , , " ,
, -i
t_ ' ,
'1 J
~
\
1 Î 1 1
1
o
~ ....... 0-,,"_ 't""' ...... )~ ~. _ .. ~..... ___ .
Table 3,.4.3 Parameters Used for Calculations " "
Substance T*(oK) v*(cm3{gm) p *(J/cm3)
t.etcos 5843 i 1. 039 i 471 i squa1ane 5890 h 1.023 ~ 457 h PDMS J 5578 k 0.855 353 a DOP 6003, m 0.850 m 552 n nHx 4446 a 1.155 a 436 a 2,2DMB 4323 b 1.161 b 386 b 2,3DMB 4396 b 1.161 c 386 c nBp 4707 a 1.133 a 428 a 2MHx 4624 b 1.150 b 417 b 3MHx 4647 b 1.140 b 419 b nDet 4863 a 1.120 a '428 a 2,5D~ 4696 b 1.122 b 416 b 2,2,4TMP 4728' b 1.127 b 390 b cP '444~ b 1. 018 b 524 b cHx 4719 P 1.001 p 531 p benzene 4708 a 0.889 a 620 a
,a Taken from reference 46 b Ca1cu1ated from values given in reference 41 cl Assumed to be the same as for 2,2DMB d Ca1culated assuming cP to be a sphere e Taken from reference 45a f Assumed to be the same as for nBp g Estimated' to be between QOct and 2,2,4TMP h Taken from reference 48' ,
-" ,
s {~-ll ,~ . ,
0.87 j '- 0.86 h
0.48 1 0.99 0
1.04 j 0.88 e 0.88 c 1.00 j 1.00 f 1.00 f 0.98- j 0.87 g 0.81 e 0.99 d 0.93 q 1.00 q
i Ca1culated from equations and data in referenc.e 49 '
33
"
.j Mo1ecular surfaëe/volume ratios are computed assuming the n-alkanes to be right cylinders of mo1ar volume V* as' iF reference 50
le Taken from reference 51 ~ " 1 Consistent with data in reference 46 m Determined in th~s laboratory n Calcu1ated from thermal pressure coefficient in r~ference 52 d Average of values for nOct and benzene p Taken from reference 53 /' q Calculated assuming molecules as spheres of molar volume V*
>
< •
"
,/
, ,
l i
1 1 4 l
;'\-1
:.',",: ~,' "" , ,
.,
. '. "~.~!, ,;.:t.~? \, ;t'~, '~:..--'( ~>l"' . (~ .~._:3,~. _, ...... ~ ~
n '-'
~
~
55°C nUx 2,2DMB 2.3DMB nHp 2MHx lMHx nOct 2,5DMHx 2,2,4'l'MP cP-cHx ben:tene
650 C* nHx 2,2DMB 2,3DMB . nHp 2MHx 3MHx nDct 2,5DMHx 2,2,4TMP cP eHx benzene
o Vg
129.8 68.0 92.5
353.6 247 .• 1 270.5 940.2 453.2 314.6 91.0
23,5.2 193.8
94.2 51.7 69.2
239.9 174.1 190.6 607.7 309.2 217 .0 68.3
169.5 140.9
TET COS
Xii
0.29 0.34 0.29 0.23 0.28 0.26 0.18 0.26 0.25 0.26 0.22 0.56
0.29 0.32 0.28 0.24 0.27 0.24 0.19 0.25 0.26 0.25 0.21 0.53
~ \.
_,..._ ~~'_""r""""" .. 4)04 ; <u::. ..... ~:;!1 \I!Z _ ~.,_ .... .,..
10
Table 1.4.4. Data for Pure Stationary Phases
Xq/S i
6.3 8.5 7.2 4.9 5.7 5.1 -3.5 5.5 5.8 9.4 7.5
25 .. 3
.. 6.3 8.3 6.9 5.4 5.6 5.0 3.9 5.5 6.4 9.2 7.1
24.8
~
SQUALANE
--o
Vg
130.4 70.1 94.9
344.0 248.9 273.4 '903.3 454.1 313.9
93.7 242.7
. 188.9
94.1 52.5 70.2 236.j~ 174.2 . 191.5 595.5 309.3 219.4 70.3
173.5 136.8
Xij
0.22 0.23 0.19 0.17 0.19 0.17 0.14 0.17 0.16 .0...18 0.13 0 .• 53
0.21 0'0-23 0.19
''0.17 0.19 0146 0.12 0.17 0.16 0.17 0.12 0.50
Xil
/Si
3.6 4.3 3.1 3.2 ~
2.9 2.3 2.1 2.6 2.9 4.9 3.1
23.6
3.6 4.5 3.2 3.2 3.0 2.2 1.9 2. ,. 2.8 4.6 3.0
23.2
t,,;: 0
Vg
75.3 43.7 56.5
180.8 135.1 145.7 425.2 239.2 167.0
56.8 129.3 -, 116.0
55.3 33.3 42.2
125.2 %.4
103.2 281.6 163.1 118.1 41.8 91.7 84.4
PDMS
Xij
0.38 0.32 0.33 0.41 0~39 0.39 0.45 0.37 0.35 0.36 0.41 0.70
0.36 0.30 0.32 0.40 0.37 0.37 0.44 0.31 d'. 33 0.37
- 0.41 0,.67
Xq/Si
11.3 10.4 10.9 12.0. 10.7 10.7", 12;.2 10.8 11.0 16.3 17.6 0
34.7
11.1 10.1 10.9 12.2 10.4 10.6 12.3 11.0 10.9 17 .5 18.5 34!..5
° Vg
39.1
90.7
208.2
77 .5 120.2
".-.
" DOP
~ Xii/Si
~
~ -
0.67
0.67 0,
0.68
0.70 0.19
19-.2
18.8
17.6 '
21.3 6.3
° o. * 75 C for DOP data. Vg in m1/gm. Xij and Xij are interaction parameters between probes i and stationary
~. / -8 2 phases j.' ~ij i8 unit1ess, Xij 8 i ·is in 10 J/cm.
~
~
, m'II.' Ipltrt sttn W11ppFW'mnc,rt'ÎriliÎT .nrnrH r fz "'>'.' J-' 'S * <t'ma ,...."lpMtb"""wC'!i>'$.lti'nr j' ........ --_.-'~- •• --~~,~-~~- ~,---~-
w ~
l
~-----
-<",J}',. r ~, --- _ ....... 11111:""-~-------~-----... --_-_____________________ _
0'
TETCOS+SQUALANE Probe
X" ~ 23 55°C nHx 136.0 0.18 2,2DMB 72.7 '0.21 2,3DMB 98.4 0.20 nHp 363.5 0.17 2Mlbc 259.3 0.18 3MHx 285.5 0.19 nOct 962.2 0.18 2,5DMIbt 474.9 0.18 2,2,4TMP 328.3 0.17 cP 95 •. 6 0.14 cHx 245.6 0.11 benzene 205.1 0.28
650 C* nHx 98.1 0.16 2,2DMB 54.5 0.18 2, 3D.MB 72.7 0.17 nHp 248.4 0.17 2MHx 181.5 0.17 3MHx 198.9 0.16 nOct 620.2 0.12 2,SDMHx 323.3 0.18 2,2,4TMP 228.3 0.19 cl' 71.5 0.12 cHx 176.1 0.11 . benzene 147.8 0.25
* 75°C for tetcos+DOP data.
Table 3.4.5 Data for Mixed Stationary Phases
TETCOS+PDMS SQUALANE+PDMS
Xb/ s 2 ~ R.._ j." .23 __ X23/s2 ~ X" 23 x23/s 2 ~
'5.4 112.6 0.53 15.7. 108.5 0.38 8.8 7.3 61.8 0.52 20.0 60.1 0.35 10.6 7.0 81.8 0.51 18.4 79.6 0.35 9.8 4.8, 298.;l 0.68 17.2 277 .3 0.44 8.9 5.1 211.0 0.59 15.5' 203.6 0.44 . 9.2 ,:>.4 230.2 .' 0.61 15.9 221.3 0.43 8.8 4.5 759.4 0.75 16.3 709.2 ' 0.56 10.2 5.4 390.1 0.69 19.3 368.2 0.46 10.2 5.4 268.4 0.65 19.0 254.4 0.44 10.4 6.1 80.0 0.44 18.2 76.8 0.22 4.8 4.6 198,1 0.52 17 .8 190.3 0.30 5.7
12.6 171.4 0.55 22.6' 158.9 0.30 9.1
,5:.3 82.4 0.54 16.7 78.3 0.34 8.2 61.7 . , 46.7 0.49 6.8 19.2 44.8 0.29 9.2 ._\
6.3 '60.9 0.49 18.5 58.6' 0.31 8. 9 .~-'..." -4.9 201.3 a.61 16.2 189.9 0.41 8.4 147.7 4.8 149.4 , 0.58 16.1 142.5 0.40 8.7 4.8 162.6 0.61 16.5 154.8 0.41 8.4 3.3 488.6 0.68 15.3 465.4 0.53 9.7 352.'4 5.4 263.0 Q..65 18.4 249.5 0.44 9.8 6.2 185.8 c 0.61 19.0 178.4 0.43 10.6 5.6 59.8 0.47 19.3 57.5 0.25 6.2 4.4 143.3 0.57 LO.2 136.5 0.33 7.0 112.8
·11.8 121.7 0.45 18.5 114.7 0.28 8.6 126.1
~ in 'm1!~. X23!s2 in 10-8 J/cm2• ~23 ... (V1!V2) j...2j-~
"
,..
TETCOS+DOP
.x" 23 X2/ 5 2
- f
0.72 25.5
0.77 25.5
0.87 26~4
"
0.62 28.5 0.43 19.2
w ~,
U'IIITtliliTSV"R'i - 'SZ.*n'f'twllé'lrti:r1tt."ttfCrww' ~n.· "~ '>Hi ni "ln'ta:ltn?f!Z.It:r:nH!,ibl:tr'+~w,."-'" -,,-~-~ .• " ... ~, -
"
"
o
.. 1. .. ~
36
Section 3.5 The Simple Stationary Phases ,)
~he vg data, the Flory interaction parameters X and the new
Flory-Prigogine pB;r)ameter X have beèn shown in table 3.4.4. The X values _lit
will be used for comparison with other publications,. inc1uding previous
work in this laboratory. This is more convenient because X values are
more readily available in the Uterature and they do not change sign1.ficanÜy
with 8mall differences in temperature, espectally for probes and stationary 1
phases of similar nature. ri
Each of the VS (or the corresponding i) quoted in section 3.4
is an average of several consecutive determinations which are consistent ":1
to within ± 1%. This represents the consistency obtainable r for a given
column in a single experiment. Results obtained from different columns of ,
the smne compound can vary by as much as 2.5% in VO (+0.025 in X) in g - .
separate experiments for systems being studied in this chapter.
For éxample, for the n-tetracosane ~tationary phase, reference
54 gives X 12 v~lues of 0.24, 0.20, 0.17 and 0.48 respectively for n-hexane,
n-heptane, n-octane an~ benzene probes between 76 and S8oe. Except for
benzene, whose ,X12
is expected to be more temperature dependent, the
present values are 0.02 to 0.05 higher than those in reference 54.,For . the squalane stationary phase, reference 4a gives X 12 values of 0.25 at
600 C for n-hexane, 0.25 at 30°C for 2,2 dimethyl butane and 0.16 at 300 a
for cyclohexane. This ls in excellent agreementwith the present values a~.
55°C. For the PDMS (mo1ecular weight-3700) system, earlier work in this
laboratory (ieference 22)gives 0.43, 0.45, 0.4~, 0.42 amà 0.62 respectively,
for n-hexane, n-heptane, n-octane, cyclohexane and benzene probes·at 60oe.
J
J ,
(
,.
, '~
\
,', ;\-~ ~
J~f(.t:; -' ::;p-'
1
..
a
o
1
37
Just opposite to the n-tetracosane case, the present results are 0.01
to 0.06 lower than those in reference 22.Finally, as shown la'ter in
table 6.3.3, ~erence 55 gives results in similar agreement with the
present work. . ' .... rhe a~ove mentioned discrepancies may arise from various
causes, like the packing of the column, insufficient corrections for
various experimental factor sand' variables, the pperators' personal
errors and differences in the samples used etc. The exact reasons are
not known. lt should be recognised, however, that glc experiments, as '" '
describJd here, ca~ have this order of error limits. 1
In a simple view of the Flory-Huggins theory, the quotient
X12/Vl should be independent of the size of the probe molecule and be . \ '\.
characteristic of the chemical natures of the interacting molecules. The
Xl2
valu~s for n-tetracosane and squalane (table 3.4.4), with the alkane
probes, if converted tot12/VI ' will not fill this expectation. This
difficulty is largely due to the neglect in the Flory-Huggins theory of
the free volume difference betweeu the probe and the stationary phasê
liquide As treated in chapter 2, the use of the new Flory-Prigogine
theory should help to overcome this proble~The actual results are less
optimistic. The ratio of the Xl2/Vl
values for n-octane ta n-hexane i8
\ larger than 2: 1, while that of Xl2/s1 .(table 3.4.4) ts still larger than
3 ~2.
The alkane probe-tetracosane and alkane probe-squalane X12/s1
are small, but not zero, as predicted. This tao, may refle~t9 deficiencies
.\ in the free volume term in the Flory-Prigogine theory. lt may also be
due to an "ordering" or "correlation of orientations" of neighbouring
long n-alkane chains, making the X12/s1 in the n-tetracosane case
"
:) Il
i •
. ..
î
1 l .'.
o
- 1 ,.( - ,
38
substantially higher th~n those in the squalane case. Furthermore,
possibly partially because of this, the X12
/s1
for the' various aîiphatic .
alkane probes seem~to be more 'consistent for squalane than for n-tetracosane.
(The branched alkane probes may'destroy "order" in n-~etracosane, while
squ.alane is not "ordered" to start with.) "Ordering" in long n-alkanes
has been show 45b to "'have an iinportant effect on the enthalpy of interaction ~
as obtained fram calorimetry. Such an enthalpie effect1s apparently
. , eompensatèd by a simu1 taneous entropie contribution. It is still possible,
however, that X'12 and Xl2 may reflect, to' some extent, the destruction of
orientational ordering of neighbouring n-tetracosane b~ branehed alkane
, probe molecu1.es.
The X12/ sl of the different alipha tic alkane probes are
remarkably consistent fO,r, PDMS. Like squlilane, PDMS i8 not ordered, and
it gives similar consistencies. Tancrede et a1. 45a ,b obtainéd calorimetrie
X12/s1 values of 4.6 a~ 7.8 x 10-8
Jcm-2
respectively for the n-hexane-PDMS
and n-octane-PDMS syste~, both at 250 C. These are not in agreement with
/the present gle findings (table 3.4.4); ,However, the 'same work gives 12.5
and 14.4 fqr n-dodecane-PDMS and n-hexadecane-PDMS at 2SoC. This agrees
c with the present glc results for the n-tetracosane-PDMS system at 55 and
J • 6SoC (table 3.4.5), considering the temperature d~fference and the
." ordering e.;fects or the n-alkane. Theoretically, the Xl2/ sl val~es should
be i~dependent of the method used and the alkane chain length. Aetually, <
calorimetrie x12
/sl
show45a ,b definitive dependence on the order of the
n-a1kane, inereasing with chain length. The gle results (table 3.4.4),
on the other hand, may show negligib1e or even reverse dependence for
small changes in low n-alkane sizes. 'Nevertheless, they do increase n
significant1y when a comparatively highly ordered high n-alkane, such as 1
i ~ l,'
r j
< ' ,
, , f "
;.
,
o
39
n-tetracosane, is involved (table 3.4.5). The reason why the X12/s 1 from
the two' diff~rentr methods do not agree ln the cases of non-ordered low
alkanes 18 not known.
DOP ls a rather poor solvent for the various alk~nes, as refl~eted
by the high vàlues of X12
apd X12/s l ' which are drastically re~uced when
the probe ts aromatic. This sho~ the predominantly aromatie nat~re of DOP. 1
lt will be further discussed later in chapter 4.
Section 3.6 The Mixed~ Stationary Phases
As discussed in chapter ,2, the X between the mixed stationary 23 .'
phase components is expecteft té be 1ess aceurate than the Xl2
between a 1 ( ",
probe and a pure stat~ona~hase. Raving thi~ in mind, the consistency
of the XÏ3 values (X 23 "normalised" to per molar volume of the probe by
multip1ying with Vl /V2 ) in regard to the various probes (table 3.4.~) has
been generally quite satisfaetory.
The X Ï3 f.or n-:tetracosane-squalane is very simi\ar to the X 12 );
for other low alkanes with s,qualane. ~e correspo~ding ~23/s,2 and Xl2/s1
are some~at different, witr the X23 /s 2 for n-tetracosane being higher
than the X12/sl for the lower alkanes. This a~rees with the reasqning that r;
the effect of destroying order in n-tetraeos~e is more distinetly shown
in the energy based X paramet~r than the free energy based i parameter
- due to an entropie compensation effeet (see last section). On the other
hand, this gle X23/s 2 for n-,tetracosane-squalane ls admitted~y higher than
expected. Calorimetrie studies give a X;,23 value of 0.18 and an X23/s2
-8 '-2 ' value of only 1.62 x 10 Jcm • (The asterisk indicates Flory-Huggins \
Xn,23 based on presumably telI!P~rature independent molecul~ar rrcore" volumes,
whicb refer to volUJIles of the' molecular hard core and cao be obtained from the
literature, e.g. see table 3.4.3, rather than the ordinary macroseop ic..,.,"gross" ,~
(
•
i
Cf
....
larg
40 . The fonœr does not inclfde intermolecular spaces whUe the latter
1(
Though the diff~rence as obtained by the two methods is not
quantity, in ratio it is large, since both are so close to
zero. This is a good ~llustration of the deficiencies of the glc method
for systems with small X or X values, particularly if a high degree,of
percentage aecuracy is required. In this present case, the calorimetrie
X23 /s 2 value is more reasonable than the glc cnes.
As mentioned in the last section, calorimetrie and glc data
,for the n-tetraeosane-PDMS system are quite similar. Calorimetrie
measurements by this author give a X:,23 value of 1.01 and an X23/s 2
·value of l~.7 x 10-8 JcJ-2. This is in excellent agreement with the
earlie;2 glc results, and reasonably close to the presen,t set of g1c
da~a. From table 3.4.5, it seems that the normalised (per probe molar
volume) glc X Ï3 between PDMS and n-tetracosane increasés moderately
with the alkane probe' s mo:!.ecular ~':!.gh~. The con;esponding X23/s 2 ) G
scat ter s~ightly around a mean and show no spe~ific trend. This is as
'li h h h 1 144 ,- i h . h d expecteu. Furt ermere, C a a et a us ng t e sorpt~on met 0 got
XH 23 of 0.3 for n-decane-PDMS and 0.6 for n-hexadecane-bMS. This , appears to be èonsistent with the present data of 1.01 for n-tetracosane
'"J PDMS .....
Despite the fact that the squa1ane-PDMS system gives 10wer
glc X 23 and calorimetrie X23 values th~ the n-tetracosane-;nMS system,
it has been found that at 50% by"yolume of each compo~ent at 650 C, the \-
squalane-PDMS (molecular weight - 3700) solution in bulk, phase separates
if it ls cool'ed to bëlow 40oC, while no su ch change occurs foa: the 1
n-tetracosane-PDMS ~Jstem. Special care has therefore been taken to make
sure that the entire process of eoating, column paeking and installation
in the_~lc apparatus has been carried out at temperatures above 50oC. ("
'r
1 i
\ " , , ~1
, 4 4 j
1 ~
4 ",
.' 1 , j ! l
! . ,
l ,
\ êj
~1 f '~ ? , 1 1 • ~
l-"!l -l ," ",
, "
i(
~" ~ .,.
\'"
, ,
è
t l.
t , "
41
1 This ensures that no phase separation has taken p1ace'before the . completion 6f experiments a~ 65 and 55°C consecutively. Afte!' this,
the temperature i5 lowered to 3~ and 25°C, to study if there i5 a
drastic change wi th the supposed phase 'separation. " ~,/
An estimation has been made on the effect of phase separation
on ~ • It 15 predicted that for the present case, phase separation
o should be accomp~ied by a decrease in Vg of a few percent. From the
actual experimental data, however, no clear eut change in the ensuing
':\23 (ca1culated by the usual method described befora) occurs wh~n the
temperatu~e drops be10w 40°C. This may be due to the insufficient
aceuracy of the experiments, or other factors not understood. It seems
unlikely that the phase separation temperature wil~ change by lSoC or ,
more, due to the mixture being coated on chromosorb, to affect' the
studies above 55°C or below 25°C. This should be 50 pecause both sqc~lane
and PDMS are supposed to be "inert" to, the silicious chromosorb material.
From tab,le 3.4.5, theX~3 values for the squalane-PDMS system
are generally slightly lower than those for n-tetraeosane-PDMS. The
corresponding difference in X23/s 2 is more pronounced. As discussed
before, this is expected, considering that the X parameter should show
more disti~ctly the effects of order in n-tetracosane. The consisteneies ,
of both XÏ3 and x2/s 2 for aU the probes except the éycloalkanes are
good. The s1milarity between the squalane-PDMS Xn and the alkane probe-
PDMS X12 1s excellent.
Calo~imetric measurements give a X; 23 value of 1. 00 for , fi
squaiane-PDMS, just about th~ same as for n-tetracosane-,PDMS. The X23! s2 -8' -2 \
value 1s ~O.2 x 10 ~~Jcm at 65°C, someWhat lower than that f~ .
n-tetracosane-PDMS. The 4greement 1n X23!s2,between glc and calorimetrie
,1
1
l, , ,
"
j /
1 ~ f " , , 1
\
t i .,
/'
(
o
-----~-~~-
42 f 1
.. .:! /
= . data for this system is the best among the last three discussed. This may be
due to the lack of order in both the components concerned. However, if it is ,-
sa, the ca'lorimetric X2r3
/s2
' which mea'sures the enthalpy direct:1y rather
,than via free energy-observables and is therefore expected to be somewhat
more sensi~ive to the effect of order~ should give higher values than
their glc counterparts in the ~ther two systems. The reverse has'beén
" observèd. An explanation to this has not be~n found, though it should
, - ;cr~~ -8 be pointed out here that the di~~_nCy 1s usually no more than 5 x 10 -
Jcm- 2, in aIl the cases studied. The corresponding Xï3 discrepancies
are usually within 0.2 (fO.l). This i8 a consequence~of the 0.05 (+0.025)
range encountered in th~ X12 values used to calculate the Xl) values.
DOP is immis'cible with PDMS (M.W.";3700) and wilP nof be used
in the "cycle" for geometric mean rule studies (section 3.7). However,
) as will be seen in the next chapter, it is an interesting and important
plasticizer. Ju~t as in the'previous case~, the XÏ3 for n-tetracosané-DOP
i8 slightly higher than the X12 between the low alkane probes and DOP.
The corresponding difference in X/a i8 somewhat larger, this may be due \
\ 1 _0'''' "-
to the "order" present in n-tetracosane. Howéver, unlike the other mixed :...,r'
atatio~ary p~ase systems, for which the ben~~ne probe gives a XÏ3 value !
within about ±D.l of the mean value given by the -a1iphatic alkane, probes
in the respective systems, (see table 3.4.5), the present n-tetracosane-DOP , '
column has a benzene probed X23 about 0,1.3 lower than those obtaiped with
aliphatic alkane probes. Due to the correction for free volume and surface
to volume ratio fac~ors, the variation in ~23/s2 as obtained byDthe
different type of probes ~s less severe; actually it becomes ~o worse , than for the n-tetracosane-squalané system.
,/
.,;'
/
" . , , 1
1 l , 1
.\
! Il ! 1 1 1
1
\
(-• J
1 ~
l I~ .-'
1 ~\ l' n "
1
l' /':.
l' )
1 ~,-( t "' ~ k
"-[
~ , '
"
l "
\. \
\
..
o
t'-/
" . .r-
• Section 3.7 The Geometrie Mean Rule ,.V
.) 56 . .
The geometric mean rule basically considers 'the interaction
between two different components as the product of the abi1ity of each
to i~"teract with the other. The "contact energy" ( (section 2.4) fs
-' taken as the prod~ct o,f ~he "1::nteracting ability" p of each component".
This value of fJ is .assumed to be .. characteristic of the component ~
co~erned and independent of the comp,on~nts with whi~f-it is interacting.
with this, equation 2.4~1 cau be rewritten as
(ij .. ~ 4 w:(j J d- ( ~ (11 + ~ f jj .
- (ij )
"" • ..!.. kT
(3.7.1)
'\.---r For three substances caUed 2, 3 and 4 forming a '''cycle'' o~.
three pairs 2-3,1-4 and 2-4, e'quation 3.7.1 give&., \
(3.7.2),
57 As evident fram the theory given in.Rowl~nson's bOOK ,the
, ~J r)
8eometri~ mean .ru1e sho~ld be in terms of energy'(or entha1py, at constant
pressure) rataer than free energy. The F10ry X par~eters, a~ given in
chapter 2, are in terms of free energy,. Consequently, the geome tric me,BP
rule should apply to XH,terms rather than to X terms. According to \
section 2.6, the glc X values c~ be convérted into" X wlues, which are \ ~
in tenn~ of enefgy. Thes~ X values,\ so obtained frein glc fr~e' energy X .
pa~~eters, should theoretica1ly be \~qual to the X value§ obtained fram
calortmetric· heats :f mixing, if eve\thin.g 1s 1d.~âl,.bY usi~g eqUa~iOn
2.7.3 and
RTX:,23 '~;- v; X23 ~~ V~l (l-~T)+P; v~ vil.' _~~l of' (T:-T~)a2T '(3.7.3)
\ cl \
, ,
Vo 1'0
",""". ~
f..' ~1t , ~
')
,,," , "
, l
(
, \ î , i ~
1 ,"
" , / ..
,Y
1
~
- - ------------,----~---~------
{
" !
44
(The symbols are as def~ned in ehapter 2). As diseussed before, this
i5 net always true experimentally. In this work, both the glc and
calorimetrie X values have been obtained for compar~?ns with the
/0- geometrie mean ru1e (table 3.7.1)
Cpnsidering that the' geome t:r 1c mean rulè i8 based on ideal
assumptlons,these' findings should be qu!te acceptable. This is partieu1ar1y . ., • 1 ~
so, sinee the components stù9ie~ hers are aIl relative1y large moleeules ~ ,< ,
with tens of segments or more and different shapes. Strietly speaking, the
geometrie mean rule ia based on the regular solution model in Which ,
molecules are equal sized hard spheres. An~how, the present study sho~ . . tq~t for non-s~ecifi~ interaeting systems, the geometric mean rule can
" rI' • p~ovide a general guideline as to the relative magnitudes of the irtter~ction
~
"-
pa~ahleters. , (
~ X' 23)~ and' (X23!s2)~ 65().C Table 3.7.1 for Mixed Stationary Phases at ~ .
1 2 \ JI ~( (Vl'23)~ 8 -2 ~
.(X23!s2 x l~. Jcm ) V2
/ teteos teteos squ'alane teteos tetees aqualane sgualane PDMS PDMS sgualane PDMS PDMS
Calerimetry 1.3 3.6 3.2 .. sIe :erobe C >1 -,
nHx 0.40 0.73 0,.58 2.3 4.1 2.9 2, 20MB 0.4Z 0.69 0.54 2.6 4.4 3.0 2.JDMB 0.41 0.70 0.56 2.5 4.3 3.0
'nHp 0.41 Q.78 O. 64~ 2.2 4.0 2 •. 9 "2MHX 0.41 '- 0.76 0.62 2.2 4.0 2.9 3MHx 0.40 0.77 0.63 2.2 4.0 2.9 nOct 0.35 J. 0.82 0."72 1.8 3.9 3.1 2,SDMHx 0.42' . 0..80 "0.66 2.3 4.3 3.1 2~2,4TMP- 0.44 0.77 0.65 2.5 4.4 3.3 eP 0.35 0 .. 68 0.50 2.4 4.4 2.5 eHx 0.33 0.75 0.57 2.1 • 4.5 2.7 ben~ene 0.51> 0.67 0.53 3.4 (1.3. 2.9
If the geometri~-mean r~le we!e strictly obeyed, columns 4 and 6 of
this table sbould acid up- ~ _giva col:uull5 •
• . Î
j'~
.l·
- ,
"
" '. ' ~~ ~
<~ ,f, .' .. ~"-i,
v.", ..... ,', ri
'. ;:1'
"
, ' ü
.,'
.
..
.,
\
/ \..
l .... 0 /
.J .,
Section 3.8 The Entropie Parameters •
glc and!iH 23 (therefore Vl~R 23) from , V2 '
can be calculated by equation 2.4.8.
Table 3.8.1 * * * 0 CV.l!V 2) "tS ,23 Values at 65 C
~ tetcoslsgualene tetcoslPDMS sgualanelPOMS
nRx 0.11 0.25 0.11 2, 20MB 0.13 0.19 0.06 2,SDMB ~tl1 0.20 0.08 nBp 0.1 0.28 0.15 2KBx 0.11 0.25 0.12 ,
0.10 0.27 0.14 3MBX o ,
nOct 0.05 "- 0.30 0.22 2,SDMHx 0.11 0.27 0.13 2,2,4TMP 0.12 0.23 0.13 cP 0.08 0.25 0.08
( cHx 0.07 0.32 0.13 benzene 0.21 0.25 0.12
* shows values· to b~ based on \ /)'. "core" molar volumes.
Slnce the1-s 23 comes from the differenc,e petween~23 1 and ' ,
t H,23 ' it ",has the inherent errors from both, which may l!lean !l,IOre t~an
±O.,l. Ravin, this in min~,/it is sufficient to say that all1s,23 'values
Sho~,in/ table 3.8.l are low. lt 18 known thât tl\e volumes of" xing
for both the n-~tracosane-PDMS and the squalane-PDMS systems are negative.
'Ibis is" i~ agreement with the positlve]:s 23 o,btain~d for those t,
"syst~ Since squa1ane is supposed toàestroy order in the mix ng ~ ~
n-tetracosane, tbel's,23 (opposite in si~ toàsM,non-comb) fo that
r sys~em ls expected to be negative. This disagreement witb the present
results may be due to experimental errors. In 80y case, ~oe gnltude of
tbe tg, 23 vill be small.
. ,
\ 1 i f " 1 l
//~ ! 1
l':'" t. ..t.'
!
1
"
l'
o
-~. ,
Section 3.9 Conclusions
,', Throughout this part of the thesis, the limitations of the 1
glc method as well as the difficult~es in interpreting certa~n gic
findings have been pointed out. In the systems with a simple stationary
phase, treated in this chapter, it seems that consistencies are good to
approximately zt (t1~) for a given column in a given set of experiments.
For example, the '12 values for a given alkane probe with'an alkane
stationary phase at 55 and 65°C respectiveIy, differ by less than 0.02,
as expected. However, for different columns of the same chemicals studied
by different authors, discrepancies can ~~,as large as 51.(±2.5%) for \
comparatively low molecular weight stationary phises and, even worse for
high molecular weight samples.
In the work being presented here, the gle ~ethod has jç~n
1 extended to measure the interaction between two non-volatile and non-
associated liquids in a mixed st~tionary phase. The results are generally
satisfactory, bu~ they are unexpectedly dependent on the nature of the \ .
probe. This 1s particularly unreasonable for stationary phase components
like n-tetracosane and squalane which are "inert" to a11 the probes
mentioned in every sense. There should be no significant adsorption
amang the stationary phase, the probes and the solid support. There 0-
should be no doubt in the attainment of thermodynamic equilibrium sinee
different exper1mencal, flow rates give the same value. It sfmply has
ta be recognised as a resuit of the limitations of the method and the
inappropriateness or insufficiency of the theories being used to treat
the experimental data.
Th~ importanc~ of such insufficiencies depends on the cas~. If
" 1
! .
o
"
T - -, 1
"
, "\" '.
47
only a fair idea of interaction ~trength is required, the gle method ô
is 'more than adequate. To date t limits of accuracy of thermodynamic
data derived from gle results have rtot been established unequivocally • .
Furth~rmore, as:mentioned in this and later chapters, the theoretical
implications of glc findings may be unexpected or diffieult to explain.
It ~y ~ven seem contradictory to results fr~m other means. tt 18 clear,
however, that the gle method is no worse thatt most other tnermo-physical
approaches' like surface tension,- sorption etc. It has the \dded advantage
of being faster, more ,convenient, and it alone cau be appropriately ;
applied to systems with viscous, high molec~lar we1ght components at
mole fractions of virtual unity.
/,
'/ ".,
, '
•
...
" (
\
1
f ,
\
o
48
"
CHAPTER 4
A POLYMER-PLASTICIZER SYSTEM
POLY(VINYL Cm.ORIDE) AND DI-N-OCTYL PHTHALATE
J
. Section 4.1 Introduction
It 18 intuitively probable that the 'processlng behaviour and
-certain end-product properties of complex polymer systems depend upon ~
the thermodynamic, interaction amang the components of 8uch systems.
Correlation among thermodynamic interaction parameters and selected .
processing and use properties may therefore represent a valuabl~ <
fundamental basls for pradictin~ b~hA'~our characteristics in new
formul~tions of polyme~ systems. The value of such c~rrelation~ has long
beeu recognised, but it has been dif~icult to measure the thermodynamic
properties in relevant composition and temperature ranges. It is an ,
overall objective of this work to h~lp overcome this difficulty. \
The motivation for the present work originates in studies 6 .. 12, ~3, 39
which have demonstrated the usefulness of· ·.~lc"-B:s· a means of evaluating .~" .. 4"
interactions between different component.~·~of a 1Ilixed stationary phase.
This chapter reports on the PVC-DOP system. The recognised importance of
plastic!zed PVC comp~sitions ~as led té> v'at'ious earli~r attemptsS5 • 58 to
determine X parameters for similar Qompounds. The methods·used by those
authors, however, restricted observations tQ very high concentrations of
plasticizer and/or to a narrow range of teœperatures centred upon room i
temperature or the reduced melting t~erature of the polymer-plasticizer
(
'.
;, ~ l • ! (~ f 1- --r
t -'î
, 1 1 •
1 l , -
o
- > ... ~-- -)
49
.55 combination -. This study éxtends into ranges of composition and
1
temperature more consistent with use conditions, and it makes a
preli:minary examination of' the interdependence between X parameters
and the effectiveness of DOP as a modifier of polymer melt viscosity 1 •
(proëessing behavJour) and of the polymer's glass transition temperature
(use characteristie) •
'Section A. 2 Experimental
The PVC used is ,a commercial sample for indus trial use ,
with an in,trinde viscosity in tetrahydrofuran at 2SoC of 1.16 dl/gm.,
and a density of 1.392 gm/ml. In aIl cases, it is used ln combination -with l~ of a liquid organo-tin thermal stabilizer. Plasticizer 'grade
DOP is used as received, without furt~er purification.
The~al procedures and equipment used are the same as
those deseribed in chapter 2. Details of column composition are shown
in table 4.2.1. Two entries are made for the ~olymer fraction; '2 is
based on the assumption that the PVC is non-erystalline. Considering
the microcrystallinity attributed to PVC, ,~ assumes that the polymer
is 20~ crystalline under the specified experimental conditions. The
total weight percent of stationary pha.~e of ,the columns is between ~ ,,l;) ,
4 and 71.: This eliminates inte~fering'effects due to sorption at the
'probe-support.interface.
The method used for d~termining the composition' of a mixed
stationary phase column"has been described in section 3.3. The 2&7-)
crystallinity chosen for ~~ calculations for PVC is arbitrary. lt is
merely used to illustrate the extreme possib11ity. The actual crystallinity (- A '
is'expected to be less than that, eapecially for the plasticized mixtures.
,
1 1
(·i
·0 1
50
}. -.. Table 4.2.1 Co1umn Composition
Column wt. 7. PVC ~ . 2
?1 2
A 0 0.00 0.00 B 38 0.28 0.24 ," C 62 0.51 0.46 D -74 0.645 0.59 E 82 0.745 0.70 F· 'e, 88 0.82 0.79 G 94.5 0.92 0.90: R. 100 1.00 1.00
C.~mns are thermosta~ted in the range 90 tç 130°c and the
retention ttmes of six volatile probes are measured from 3 to 5 times.
#a11 cases, symme tric peaks are obtained, indlcating the exis t'enee , , 28
of equilibrium sorption cond~tion8 • The measurements of me1t viscosities
and glass t~ansition te~eratures are described in reference 25 • ~
Section 4.3 Results
Table 4.3.1 ~ (m1/gm) for PVC-DOP C91umns
Columns (Assume No PVC C~sta11izationl
~ A B C D E IF G H
HOoC nBp è 34.0 21.3 14.0 9.6 6.5 6.3 5.6 ,5.1 nDet e 68.6 42.9 ' 27.4 18.'4 12.0 11.7 10.5 9.3 oNon a 137.0 87.5 53.4 34.7 24.1 21.5 18.8 17.8 nDec b 27f+..~0 104.1 64.9 41.3 39.6 34.3 33.4 toI e 93:'4 69.6 58.7 44.3 37.0 38.9 ' 34.7 33.0 ~C1 d 194.1 144.7 111.6 89.2 14.6 78.1 68.9 62.1
_ 120°C nHp 26.2 17.0 11.3 7.4 5.5 5.1 4.7 4.2 nDct 52.7 33.5 21.5 13.8 10.0 9.2 \ 8.3 7.5 nNon 100.6 69 .. 1 40.8 25.3 18.8 16.2 14.6 13.5 nDec 194.0 79.8 45.8 36.4 28.2 25.7 24.6 to1~ 73.2 54.5 43.0 33.6 28.9 29.5 26.9 25.3 ~C1 146,2 100.4 85.0 65.9 57.1 57.7 52.4 50.1 l300e nHp 21.3 4.8· 4.3 3.9 3.5 nDet 40.6 - 8.4 7.4 6.7 6.3 uNon 75.5 :/ 16.3 12.8 11.4 . 10.9 nDec 138.3 30.4' 21.9 19.5 19.0 toI 5'6.5 22.8 23.0 20.7 19.9 t'Cl .·109.5 ", - àl - 44.6 44.2 40.0 38.7 ,
d ~Claeh1orobenzenet a nNon-n-nonan~l b nDec-n-decane, c tOlato1ue7' e as defined in chapter 3.
,
, 1
1
i f
1· 1
o
i '" t'-,4: " , ,', ~~ ,
\ . -C 4
i 1 >Il
1 ~
~ t
k ~ ( • ~
. \
r ,
1
t
o
Table 4.3.2 Interaction Parameters for Pure PVC ( ,(12' ,
.1 t l2 ~
Probe llOoe a 1200 e a 1300e a 1300 e b
nBp 1.68 1.62 1.55 1.32 nOct 1.74 1.65 1.55 1.33 n,Non 1.77 1.70 1.61 1.38 nDec 1.79 1.73 1.64 1.42 to1 0.47 0.46 0.44 . 0.21 !6C1 0.41 0.40 0.37' , 0.15
a ASsume no pve crysta11inity b Assume 20% crysta1linity i~ PVC ~
Table 4.3.3 Interaction Parameters for Pure DOP ( X13'
Probe 750C a
nHp 0.67 nOet 0.68 uNon -nDec toI 0.16 'C1
a From reference 55
! J'
90°C a
0.64 0.64 0.66 0.67 -0.13 0.02
i 13
10tOe a nooe 120°C 130°C
0.63 0.6Z 0.63 0.60 0.63 0.61 0.59 0.58 0.64 0.63 0.61 0.60 0.65 0.63 0.62 . 0.62 0.13 0.16 0.14 0.14 0.03 0.06 0.05 0.06
#
#
1 l,' , "r' Ji
r:· ,~ o' • l, '
l .. ( • \' , ~
"li'
"
, '
------'---------- .,..~.
~ - ~ ~ .'.~.,.- ~~ ~~---
:/)", ,) 52 />r //
Table 4.3.4 (Vl !V2) X23 Between PVC and DOP
1 Column 4
~ B C D E F G
nooe a ,,>
nHp 0.42 0.41 ;;0.05 -1.21 -0.80 -0.76
1-'t., nOet 0.64 0.51 -0.04 -1.17 -0.75 -0.61
,( nNon 0.82 0.52 -0.12 -1.24 -1.03 -1.32 ' ~~ >, nDec 0.52 -0.26 -1.63 -1.29 -1.86 ~,
lt
~ -toI 0.10 0.12 ~0.21 -0,.72 -0.41 t6Cl 0.14 0.05 -0.28 -0.78 -0.74
1200C a -nHp 0.49 0.45 -0.28 -1.p4 -0.82 -0.57 nOet 0.55 0.45 -0.31 -1.07 -0.97 -0.88 nNon ;0.57 -0.30 -0.89 -1.14 -1.10 nDee t 0.74 -0.41 -0.67 -1.51 -1.67 toI 0.12 0.12 -0.34 -0.66 -0.37 ~Cl 0.2~ 0.10 -0.39 ,,;0.68 -O.SS
1300C a '--_/ rlllp -0.81 '0.70 -0.41 nOct -0.94 -1.09 -1.16 ~.
nNon ,-Of3 -1.18 -1.46 nDec -1.37 -1.80
,/ toI .. -0.60 -0.56 9Cl -0.56 -0.61
1300C b •
• nHp -1.00 -0.87 -O.~ nDet f .. "-1.13 -1.22 -1.23 nNon ~.68 -1.32 -1.50 nDec - .~ -1.49 -1.79 toI -0.64 -0.56
~CI - -0.61 -0.60 ,
a Assume no PVC c1:ystallinity b Assume 20% PVC trystallinity
" 1 , ,
"
J
t ~ ~
1 t
l 1 1
! ~ 1
'" <;
~ 1
l
\.
,
"
0
(
.. \
53
Se!ftion 4.4 Pure stems
Tables 4.3.2 and 4.3.3 present values of the interaction
~ar,ameters X 12 (probe·PVC) and t 13 (probe·DO?). The probe-DOP , 22 .
interaction extends pr~viously available data (chapter 3) to a
temperature range more consistent with the processing of plasticized
PVC., The values of X'13 are essent1ally 1ndependent of temperature,
however, so that the available results may be considered as va~d calibrations for more e~tended temperature ranges of applicatibn. The
chain-Iength dependence of n-alkane-DOP-interactions 18 negligible, but
markedly lowe~ values of X13 are'obtained for the aromatic p~obe molecules.
The higher affinity of these for the plasticizer molecule -is consistent
with expectations.
The X'12 results display vadous points of interest. The first
1s that a significant reduction in XI2 occurs when it is assumed that
, . '" the polymer retains 20% residual crystallinity~This portion of the polymer
would of course not interact with the probe. The va value, per gram of -g
amorphous polymer, ls thereby increased, accounting for the decreas'ed X.
However, the relative sequence of interactions with the vadous proèes , remain un al tered.' Secondly, the series 0 f n-alkane probes 19 highly
inco'!llPitible with PVC, the inc~mp4tibility' becoming, more pronounced with
increasing chain length, though slightly modified aS'temperature increases.
Finally, the aromatic probes here prQduce a drastically Iow X12
' they
are, in a sense, plastic:f:z1ng moiecules in their own r1ght.
59 It should be'noted that ,as shown~y Braun and Guillet ,
thermodynamic interaction values for a pure polymer should be sought at
temperatures-' seme 50°C above Tg • In the case of PVC, this woul:d entail
\ ; l t /' )
(
f
Ê
1 , • l
" ,
-.
1
o
, 1
~I
54
the risk of ~hermal instability. Thus, for the present purp'ose, the
somewhat lower temperature range of 30 to 500 above Tg has been selec.ted.
The mild t1rature depende;ce obs,;rved for ~2 suggests that thi.
procedure does 'not significantly compromise the validity of the
l,.
thermodynamic values. J
Secti0n 4.5 PVC-DOP Interaction
.An explicit illustration of (VI /V2
)X,23 values, let us call
""" this "'23 ' is given in table 4.3.4. Normally, the interacti,on between
c.omponents is characterised by pos~tive '(unfavour~le) X values, inpreasing
positive values indicating increasing incompatj..b1.lities. Thus the . , ...... . -~ .... -- -, strikingly large negatiye vaLues o'f "~3 for certain compositions indicate
a high degree of compatibility between the components. A possible
explanation may be the existence of "specifie interaction" between the F ~ ."'.
aromati:c groups of the DOP and the chlorine atoms_ 0;( the PVC. (Pouchly /'-
60' - aL and Biros have similar sugtrstions for their chlorinated alkane- .
tetrahydrofuran systems. They found that the en'thalpies of mixing depend--
" on the number of chlorine atoms present and the hydrogen-bonding capabil:lt:y
of the other component used. Though the exact nature of the "specifie ,
interactionll in their system is different from ours, the notion that
particular functional groups in a molecule can spe'cifically interact with
those in a neighbouring ~olecule seems to be well founded.), In our present .. -
case, our observations are entirely consistent with practical exper ience,
which would ran~ DOP as a very effective plasticizer for PVC.,
In principle, . the polymer-plasticizer interact'ion should be
independent of tbe probe. Chapter 3 and reference 22 h\ve already noted
.~
, ) , ' ,r
, ,"
'(
~
1
f ,\
" . , , '.>
~ f 1" i
~
l t t ~
o
,~
•
o
, --- .. '/
that this expectation is apparently not met :in a11 cases, and here.
t table 4.3.4 shows a considerab le variation of ~~3 with the probe. Part
of the variation may be due to the change of Vl • the normalizing quantity
~" in ~23 . ,Bowever, these results and those on other col~s do, show a
difference between sromatic and aliphatic probes. and this would seem to (_;"\
correspond to the -tifference in compatibility of the aromatic and aliphatic
probes with the individual components.
A number of reasons for the probe dependence of t ~3 may b'e put
forward. First, it may be speculated that the 2-3 interaction inde~ 1
depends on the nature of the probe. This, however, is difficult to reconcHe
with solution thermodynamic theory which usually considers 'a contact
between a pair of molecules as being independent of the nature of a
neighbouring molecule. Secondly, as pointed out before, the Flery X parameter is on a rIper molecular voluma~' hasts (or, for a polymer
molecule, on a per segmental volume basis arbitrarily chosen te be
equal to, and therefore dependent on, the molecular volume of the probe).
A more modern appiÇoach, like the new Flory-Prigogine X parameter, ia \
, , based on molecular surface areas, but it is not believed that very
• different results will be obtained by making this-change in the presen.t
case. it i8 probably more 'tmp6~tant that the assumption of the two 1
stationary phase components being randomly mixed may not be valid, and .,-
the probe may nct sensè 2-2, 3-3 and 2-3 contacts in a random manner.
This is particularly so since it is ilnprobable that perfectly random
mixing occurs for components such as PVC and DOP which interact in a ,
specifie fàshion. Furthermore, the n-alkane probes will tend to selectively
avoid contacts involving PVC with which they are extremely ~incompatible
. ,
...
;
1 r
-/ Î
' ..
,..
a ;
o
_ _ __ ~ ~....... ~.. __ 0.
56
---(s~e table 4.3.2). On the Q,ther ?and, the aromatic probes llIay be exp~cted
;
to l'\ave a more random view of their stationary phase envi-ronment. The ~
probe dependence of ,'Je ~3 c~nnot be assocoiated with' any one f~ctor. It can
merely be noted for present purpo,es that the dependence is not surprismg.
Section -4.(; Composition Dependence of PVC-P1asticizer Interaction
Of 'fJarticular interest to the pr'es~nt study is the apparent
i i "f IV." i h .. f h l 1· " var at on 0 .1"23 w t 'cOmpoS1.tlon 0 t e po Y1Qer-p astic-izer system. In l '-_ -:... ___ ~ ~<" ~ j , 1
f'IJ" order to represent this concise~y, the J'23 results for the a~ compositions ,'./ ~
at each temperature are averaged for the four n-alka~ probes. and the ~
resulting function of iC.23 .vs. PVC colunm fraction is rlottecl' in figure , 1
4.6.1. The bars indicate maXimum probe-to-probe variation of ~23 at , '
.Ja.p of the column compositibns. It i8 a:;sumed here that no residual ,1
crystallinity exists fu the PVC. The implications of the results in this
r'
figure are interesting. The' compatibility of the PVC-DOP system i8
1 ..,.. , l l' l~ uniform y high, i.e. /'"'23 is negative, up to p asticizer vo wne oadings
of about 25%. From 25% to abou't 60% by voJ.ume of DOP. ~3 r ises and l
"becomes positive. lt is reasonable to suppose that at these large r;t
concentrations of DOP, much of the p lasticizer is "mobile" ,/ Le. the .. DOP molecu1es can be in contact -with oth~r DOP mo1eculE!'s rather than
"bound" in contact with PVC molecules. In other words, the two stationar)' . . {.'-
phase components may not remain mixed homogeneously to the segmental level. . -
Having in mind tlrt! interaction paî:ameters a1ready obtained, it is clear
" that when the probe entera the stationary phase, the DqP-OOP contacts 'J •
-are much more easi1y broken thaQ the PVC-DOP and PVC-PVC cOntacts, and
this is especially so for the a1kane probes. This Leads to pOSSible nop.-'0 \
/
..
)-
r •
'.
--."
<0 t,,,,, .' ,~
"
~t,...:-..i,,-:" .:::.~
~ J Of ~
(------.
~ • "
• s 1.00 •• J -
.. > 1
Xia * '0.6
r ' ~~ " <!t-..
0.00 i';.
~.
dl': ... 'J.~.~ .. ~. -.".. ' .-..,.j ~~ .... .../.O!-....-t:!~IN ...... ~~~Wf ............ "I!"M'~~~;~. , ',--
"
'J
110°C • 1200 C 0' 130°C e
r,
rJt h .. ~
- ~
1.,
"f ' CD . -n
al ><-
~ -..."'"
..
1
f ." =01 X, 1
'-
\ ~ .. j
....
-1.09
~
"#
<-, ...... •
J
J 'I,.~~
0.4 fi> PVC 0.6 . -2.00· ,
O.à ' 1 1 0.2 . 0.8 'ID Figure 4.6~1 .. " CompositLon pe~endence of~3 of the PVC-DOP System
I.n .....,
L ""I,pnert_ ''',s:~- .en. <:l,rça $ " 0 .. :) .",':""," ';;;"',. 1 * rurem' ... -. ,,-.----~.---------~~~~;~ --{ :"'=7;-.:-.:.. . ~ ,,~:j. ~ -I~ -- ~":. to· ~"' ~ ~~:~. ""~~~>#A-.:/ ,"o.,...~.... , -
1
r
f
i '\
1 ~ , ,
1
'i ,1
\ 1 /!' 1
(
j
...
. ..,
---~-------';Iii~-----~---------
) / 58
,.
random ."sensing" of the stationary phase sites by the probe, which of , r
course corresponds to the greater compatib~lity of the probes with DOP r
" d
than with PVC or the stt'ongly bound PVC-DOP contact sites. By selectively l ,
brea'king d~ DOP-DOP contacts, the value of the overall "1(23) ls' lowered
b~low what it would be ·for a comp~etely random attack by the probe. This
has the effect of giving a positive ,appar~nt vs:lue to ~23' (see eq~ation / f ~
• ".1 ...J
2.5.,;», and this will occur in the re.,gion of 'high DOP- concentration where
the non-random sensing of 'the stationary.phase by th.e probe is facilitated.
" '~
Section 4.7 P1asticizer Effectiveness
/
J
In this work, an attempt has been made to seek, in a 1arge1y
empirical manner, the existence of intler"re1~ between the • v
thermodynamic interaction parameters of the PVC-DOP systém and the
èffectiyeness of the plasticizer as a modifier of the solid state and
processiIlg characteristic~: An empir!cal n0rJll!Llization procedure has
been adopted both for melt viscosity and glass~transition temperature
data ~in order tô study the point.
'~,;t'he reduction in apparent zero shear melt viscosity <, 0) of
the po1ymer, due to an increase in the plasticizer volume fraction frOm "' .. ~~ j
~k to s~ grèate~ value",.sj , ia' n~l.ized by the expres~ion 1
('10) .1f if P
3,
/ ( /Jf _ /Ji ) 3 3
the quotient defining a d imensionless viscosity reduction.
In a sUnilar manner, a Tg reductton number ls calculated from
the expression
- (T ) f / ( .sf - .s)i ) g .s -'.1 '3 ~
\
'.1<....
..
,1
\ . ./' 1-
__ .~_ .. ,f " Ir 'f'J' 0 '-'1 \
~ <----
•
41. " . , .-,
/~ / . --- ,~ r
l,
-'
~ 6·°1 1170 ... t> .
-< ,
\ ~ J'lIO '-.
b
'" 4.01- ~ ......... 130
~ Vol. of -dilution - '1 ,; u 1 ~
....
t effect . ~.
l~ \---
j • 1 predominott.. a. -----....... 0 .
Thermo. 1 z 1 0 z , 1
-0 .. 1 interac. effect 1 1 , - ~-d . .,
1 ., 2.0 predominafes . 90 .. -..,ç
1 .. , .
Olt -! ' ::::. . . 1 1-u ., 1
> " " . . .,,.. .-1
'" 1 1 1
0.01 1 Il -:r -2.0 -1.0 .. 0.0
-----------1.0 Ut -X23 \0
\ ~.
Figure 4.7 .• 1 Viscosity ancl Tg Reduction Numbers v~. ~:h for PVC-DOP -- "
• C .ff ,
'/! - (! #~ ~.!l<"-i:'!': • -. ~ \... ",4aw i*;- ......... _~. __ _
.... ~ -... q21! gr lm 1. t : "zr aM ,...-.- *"* .......... .---*""'....-_ ~ __
."
>
~, , (
lo;
t ~ ~ i
l r ~ ~
,
t f ~
l , , .
o
60
The reduction numbers are calculated for pairs of compounds with increasing
plasticizer content and plotted in each_ case against the (V1/V2)X23
' Le.
?Ç3 value for the more highly plasticized system. The results of this
procedure are shown in figure 4.7.1. For convenience ot presentation, a
X" single plot has been used, ,placing 23 on the abscissa. This procedure
illustrates the type of inter-relationship which may exist between
thermodynamic and processing properties ~f t~e.sys~s. but i? not meant
"tl " " to imply that the abso1ute value of 1'23 is the best independent variable.
The curve's for\.both 1) 0 and ~g 'reduction ehectiveness of DOP
suggest that both thermodynamic interaction and volume-of-dilution effects
are operative in the reduct-ion of '10 and Tg. The importarlce of the 1 ,
thermodynamic interaction contribution may.be inferred if it is a1ssbmed
c ",II that for negative (exothermic) values of A23 ' it is this effect which
is primarily responsible for the observed reduction. ~ this range of
concentrations, the plasticizer helps to 100SEn the polymer molecules'
state of association or entanglement, thus lowering its melt viscosity
with increasing plasticizer content. On the other hand, for ranges of
compositions with positive (endothermic) X.~3 ' (at,s3 ~ 0.5), additional " ~
reducti~s in the chosen parameters are due largely to the dilution of t
the polymer. Iù othf7r ~ords, the melt viscosity of the mixture decreases ,
as the more viscous polymer content decrea.ses. A sïmilar line of reasoning
applies to the glas,s trransitfm temperature. With the above argtmlent, a
separation of the' two different contributions to both ')0 and Tg lowering
should be possible upon the examination of systems utilizing a variety
of plasticizers, and this ls the subject of continuing studles in these .. , labora tor ie s ..
()
••
-
o •
'" - ........ _fA ...... ·- ... -·-· .. .,. .................... ....- .. ---- ------_._---------
61
... Section 4.8 Conclusion
The glc method has proved useful in evaluating interaction
parameters for a PVC-plasticizer system over a composition and temperaturC
r~ge ôf practical significance. The pVé,:-,IJ-0P X13 parameter is negative,
'l-indicating a specifie interaction. At a ~OP volume ,fraction of about 0.5,
the value of X 23 shifts to positive,' indicating a preferentia1 sensing by , the probe of weak contacts between DOP molecules. This proposed exp1aqation
co~cides with t.he practical rrco~atibility l:lmit'I-, of ttF PVC for the DOP
1 at about 0.5 volume fraction. A p'reliminary study pf plasticizer effectivene,!s
. suggests that the degree of thermodynamic interaction has a strong influence
on the lowering of melt viscosity and glas8 transition temperature of tJ1e
plasticized compounds. These results encourage more detailed studies of ~
polymer-diluent· interaction thermodynamics as a route to the rationalization
of behav.tour ch/racter1.stics in po1ymer-containing systems.
Ackndwledgeme~t: The melt viscosity ~d glass transit~ data are supplied
by Dr. H.P •. Sc;..hreiber of the Ecole Polytechnique, University of
Montreal, Canada.
) 1
<)
,'.
r .. ~ ,>t~ .... ~
: ~.('
!~r;~~~
"
" .",J ... ~~ , l':,.
> , ~~.;.i ~".~
.,.
.. )''''
, 1 "
;
-,' ~ ,~
, ;-l ~ ~
) . ., { ..... &,..<
·;;~.:rj i4ï~~ , :lf
(P~ ... fi"" , . ",
' .. -' ..
"
r
,"
CBAP'.ŒR 5
A COMPATIBLE POL'YMER PAIR
POLYSTYRENE AND POLY(~ METHYL ETHER) (!
The gas-liquid chromatogrpphy technique has been usèd to evaluate
\ free Elnergy and e,:thalpy par~ters ( X and X H) aroun~ 400 C for the
interaction of low molecular weight polystyrene (PS) and of poly(vtnyl
methyl ether) (PVME) with a range of vapol,Jr phase molecul~s: normal and
branched alkanes, aromat~c hydrocarbons, chlorinated hydrocarbons etc. A
détermination is also made of the interaction.X2J, be~en the two polymers,
which i8 smaii or negative in' conformity with the compatibili~ of these
polymers at ordinary t~eratu~es. The incompatibility of PS and PVHE in
chI qrp form , dichloromethane and trichlbroethane is related to a large )
difference in strength between the PS and PVME interactions with these
sol vents. f"
\
Section 5~1 Introduction ;1
The glc molecular probe technique uses a vapour phase component
(1) to dete~~ the interaction ~e~en two non-volatile components (2 and 3)
in the stationary p~ase. This has be~ described in detail before in chapters
" 2, 3 and 4. In gene&l, the atationary phase components of the system may
interact unfavourably, i.e. X~ ~y be PO~itive ~s in chapter 3 and reference
22. In that case, the components œust,be of aufficiently low molecular weight "
or the ,inc~~,tibl1ity must be ama11 enough, sucb t~t the mixture DUst not {,
•
(
<.,
,\ J
'11: ' , '
1 1 •
f , t î f
()
0,
/ r
phase separate. In pther systems, X23 may be negative as in a high
polymer + plasticizer, e.g. PVC and DOP (chapter 4 and reference ?5),
20 or as in a pair of compatible high polymers ,e.g. polystyrene +
poly(caprolactone). The best known compatible pair ~s probably PS+PVME, /' ' '
which forms clear films at ordinary temPerature~ but which phase separates21 ,
, '23-on raising the temperatuie. Kwei et 81. studiéd the PS .. PVME
tnterac~ at 30 and 500 e ,uling essentlally the probe method but with a
Cahn electrobalance in,tead of a gas chromatograph to dete~ne the uptake
of-vapour by the polymer. Large negatlve values w're obtained for (VI /V2) X23
'
\also'called XÏ3 ' at about -0.4, consistent with the compatibility of the
twp polymers. However, while both their PVME and their PS-PVME mixture
were in the liquid state, their high molecular weight PS WBS a glass • . ' 61 There is evidence that a polymer 'in tbe glassy state shows a greater
affinity for a diluent than it would as a liquid, i.e... the X12 value will ~
be anomalously low. According to equation 2.5.5, this will result in a
( n~gat1ve displacement of the calèulated XÏ3 value, suggesting that the
value of reference 21 may be tii negativ~. 1
In the present glc study of the PS-PVME system, a PS sample of •
low molecular weight <'Mn = 600) for which the Tg i~- measured to be around
-30°C has been used. Guillet and Braun59 have ~1ven, asa rough guide, L '
the recommendft:L;;n' [email protected] glc thermodyn~ic measurements should be carried
out at temper~tures at least 50°C above Tg • In the present ~as'e, a
temperâture rlnge of 25 to 55°C has been used. A very small effect
associated wilh a low rate of probe diffusion into PS 1s observed near
25°C, but this di t hi h t t sappears a g er empera ure. 1 ~
<
, '. ,i 1
1
, ,-4 ,
j 1
t 1 ~)
t f
. 1
o
•
64 . !
t ~
. ~ 1
Section 5.2 E!Eerimental 1
~ 1 The PS' sample i8 obtained from the Pressure Chemical C,o.,
• Pittsburgh ,Pennsylvania. It has a number average mo1ecular weight of \
[) 600 and a narrow dispersion, with Mi~ < 1.1. - The PVME samp1e (Gantrez
·go93) is obtained from the GAP Corporation. An intrinsie viseosity
determ1nation in 2-butanone (g1ven by reference 62 and repeated by this
author) gives ~ii 10,000. The experimental procedür~s havè been desaribed
in chapters 2 and 3 before. Here; two PS-PVME eo1umns have been used
eorresponding )to 0.45 :0.55 and 0.625:0.375 proportion by' we~ght. The
experimenta1~ measured quantity 18 the specifie retention volume corrected
to OOC, va • This 1s converted to t~e F10ry X parameters, &s before. g
Section 5.3 Resu1ts ! Table 5.3.1 ~ (nù/gm) for the ~re Stationary Phases
~ 25°C nRx a 124.1 nHp a 387.5 nOct a 1194.0 2,2,4TMP a 261.0 eP a 109.9 eEX a 307.1 benzene 620.2 to1uene 1922.4 ~F b 671.3 p-d1ox c 1268.3 i-pa1e d 93.4 i-petr e ' 149.9 P-aeet f 1048.8 C-teCl g 438.9 Clform h 395.7 dCIM 1 164.7, teC1e1 j 2457.7 trC1e1 k 848.3 acetone 114.2 MEK 1 346.1 ~
PS
400 C 79.7
223.8 609.0 166.7 73.4
--194.7 338.0 959.9 359.2 641.2
60.0 92.2
529.9 260.4 218.1 99.6
1245.9 457.4
67.4 186.7
55°C 50.0
123.6 314.6
99.5 48.1
1.17 .4 192.2 505.5 202.7 344.0 37.7 57.0
271.2 151,,9 128.9 ,61.0 621.6 245.8 43.6
107.5
25°C.
79.2 245.8 713.4 161.2
65.7 181..5 594.5
1692.7 843.1
1384.0 _ 606.3
112.2 1175.3 486.6
1088.0 332.7
2231.6, 1241.,1 155.8 421.9
40°C 52.5
141.7 372.9 110.9 48.3
120 ... 7 322.5 835.4 439.4 685.6 300.1 73.1
562.2 275.1 539.4 184.0
1061.4 610.1 91.7
223.9
35.1 84.3
199.5 71.5 33.8 79.5
181.9 434.1 237.5 360~7 153.2
46.6 292.4 155.8 284.1 101.2 521.3 312.8 57.8
127.7
,
o
65
a defined before in chapters 3 and 4; b fluorobenzene; c para-dioxane; d isopropyl a1coho1; e isopropyl ether; f propy1 acetate; g carbon tetrach1oride; h ch1oroform;'i dieh1oromethane; j tetraeh1oroeth k trichloroet~y1ene; 1 methylethyl ketone •
. Table 5.3. 2 ~ (ml/gm) for the Mixed Stationary Phases
PS!PVME(O.625!O.375) PS/PVME(O.45!0~55)
Probe --1?~ -40°C 55°C 25°C 400C 55°C
nRx 99.7 6~.6 42.9 93.5 63.4 40.6 nHp 316.5 184.4 105.0 293.3 174.8 100.4 nOet 950.6 218.5 264.6 875.1 461.0 243.4 2,2,4TMP 201.7 138.8 , - 85.5 188.0 132.7 82.0 cP 86.4 62.5 41.1 81.4 59.5 39.8 cHx 245.2 159.0 , 98.9 223.7 150.2 '93.3 benzene 595.1 . 336.)8 190.5 606.1 339.5 196.2< toluène 1781.2 926.4 480.8 1759.4 914.9 473.6 (JF-
->- 716.4 393.(5 217.8 777.8 419.2 226.7 p-diox 1257.7 658.1 346.7 1351~8 683.3 357.6 i-pa1c , 282.8 154.9 82.8 414.2, 203.7 108.4 i-petr 122.5 83.0 52.0 124.7 , 81.7 50.9 P-acet 1070.7 537.0 275.5 1112.4 555.5 ~84.5 C-teCI 451.4 266.6 153.9 473.9 278.6 158.'4 Clform 637.1
346.5 \ ,188.2 810.2 421.2 226.5
dCIM 224.5 129.4 75.9 265.3 1S0.5 86.3 teClel 2389.9 1178.0 ' 594.7 2388.8 . 1169.4 590.7 trClel 993.2 517.1 276.2 1094.1 568.6 296.1 acetone 124.2 80.2 '47.0 138.1 85.5 52.0 MEl{ 350':2 201.3 113.1 389.5 215.5 120.6
1
,
The ~ va1ue.s for aIl three temp~atures are .given here, for /,
possible future comparisons with other works. AB for the X parameters, ~ . '~
only those at 40°C are shown in table 5.3.3. J values for other
temperatures are stmi1ar.
700
As~shown in. the next table, the 'X- l2 and X.~3 values for,lisopr.opyl .. a1coho1 are ~xtremely large compared to the other probes. The gle peaks .. obtained fo~ this probe may be slightly skewed, but the data are quite
consistent for different f10w rates and temperatures. The skewness of the
peak here has litt1e effect on the retention time (distance be~een referenee
and sample peaks) meAured.
.'
\ l
t '
\
r t [
1 Î
1
G
o
66
~ ,
Table 5.3.3 F10ry Ffee Energy and Entha1py Parameters at 400C
PS PVME PS-PM X 23
~ nHx nHp nOct 2,2,4TMP cP cUx benzene to1uene
"'1 p-diox, i-pa1c i-petr P-acet C-teCl Clform dC1M teClel trClel acetone MEK
~12 0.97 0.95 0.95 1 •. 11 0.64 0.64 0.26 0.19 0.37 0.43 2.64 0.78 0.52 0.29 0.13 0.34 0.36 0.19 1.08 0.84
Xti.l2
2.7 2.1 1.9 3.4 2.4
" 2.5 0.8 0.6 1.0 0.2 7.7 2.4 1.0 1.3
-0.2 0.8 0.7 0.1 2.1 0.8
1.16 1.15 1.16 1.53 1.14 1 .. 16
l, 0.15 0.14 0.00 0.20 0.90 0.76 0.25 0.06
-0.92 -0.39 0.34
-0.26 0.75 0.5p
,Section 5.4 The Interaction Parameters ,.
X~!13 3.7 2.8 2.6 5.0 4.1 4.1 0.6 0.3 0.2
-0.2 2.7 3.4 0.6 0.4
-2.6 -0.7 0.0
-1.3 1.8 0.6
Compos! tion 0.625/0.375 0.45/,0.55
-0.10 -0.09 , -0.'13 -0.02 -0.10 0.06 0.07 0.07 0.00 1.47
-0.08 -0.04 0.01 0.53 • 0.14 0.02 0.06 0.25 0.03
0.00 0.02
-0.03 -0.01 0.08 0.01 0.12 0.11 0.18 0.11 1.36 0.03 0.06 ' 0.15 0.65 . 0.30 0.10 0.24 0.28 0.18
Values of Xa are calcu1ated from equation 2.4.9, using X data
at. 25, 40 and 55°C. At such low temperatures, despite th'e supposedly
slower diffusion in PS, siroilsr results~~re obta~ed at different flow rates. ~
The corresponding Xa,12 ' however, aDe c1early too positive. Measurements
at higher temperatures, up to 100o~, are subsequently taken. This gives " 0
generally sma11er Xa 12 for the various probes in PS, as one would expect. , , Presumab1y, at low temperatures, the fraction of the PS sensed by the
probe increases with temperature, resulting in a decrease of the effective
value of X12 ~d an anoma1ously l~rge Xa,12 •
-r For a uBua1 dispersion force interaction between a probe and a
, .
, '
po1ymer, both X and XH, \lOuld bl expected to be positive t particularly wen
('
l' 1
1
o
67
the probe enters the polymer at effectively infinite dilution. lt is
noteworthy that the aromatic probes give unusually small~13 and :x'i,13 , values with PVME. For halogenated hydrocarbon probes (except tetrachloro-
1
ethylene),)G13 and~,l3 are still smaller, or even negative. These
values reflect the formation of weak charge-transfer complexes in the ! 63,64 ' 60 65:
ether-aromatic' and ether-halogenated hydrocarb,on' systems. They
or are apparently good examples of "specific interaction" between, the probes
and a pure stationary phase. Anotner obvious illustration will be that
between the chloroform probe and PS, which gives a particularly sma11
value of ~2
formation of
and a negative,cH 12 ' which c?rresponds to the knQWO , a weak hydrogen bond57 between the ch1oroform and the aromatie
rings in PS. This complements the ~egative ~ observed between the PVC , ,
and DOP over certain concentration ranges (chapter 4).
The values of (VI/Y2)~3 ' i.e. XZ3 ' in table 5.3.3, depend
slightlyon the PS-PVME composition of the'column, being about 0.1 less
positive for the lower PVME concentration. However, t~ey vary considerably
more with the probej. CA small dependence 18 expeeted sinee ':'23 iB •
normalized to the probe size.) A sunHar probe dependenee of ;(23 has
been found 2.5, -'
for the PVÇ-DOP system and for the PVC-poly(eaprolactone)
,pair·2~ In those cases, the variation can be attributed to non-random \ . ' , .
mixing of the probe with the mixed stationary phase, :Le. the" probe
interacted preferentially wi~h the polymer of lower" value. This will '"
25 result in an effective raising of the value of i Z3 • This effect ,appears
clearlyw'ere the differencebetwe~n~12 and~3 is very'large, e.g. for , .
i~opropyl alcohol and chloroform probes. F~rthermore, thê effect 1s more
pronounced for the 1arger concentration of the preferred polymer 25, PVME "-
in the present case. Giving mast weight to the data for the column with \. .
\
l',
i 1 . \ 1
o
68
the lower PVME concentration, and neglecting anomalously laFge positive e
values, ~23 lies in the range of -0.1' to 0.1, i.~'. considerably smaller
than the va1ue of ~.4 found in reference 23.
Section 5.5 Relatianships with'Critical Solution Temperatures
21 The lower critical solution temperatures ~ (LCST) of PS-PvME
syst!ms of different polymer molecular weights provide evidencé"of very
smaU or negativ~ X 23 values. These were calculated using the FlorY-Hughns
formula
d'
l'tl" A 23 ,critical (5.5.1)
and are plotted in figure 5.5.1 against the critical temperatures to form '
a 'xï3 (T) plot. (In using equation 5.5.1 witq hexane as probe, the molar
volumes were ta~en independent of the temperature, i.e. V2 and V3 reflect
only the different molecular weights. The introduction of a temperature 1
dependence would not change the results greatly and would probably be contrary
to the spirit .of'the Flory-Huggins theory.) Figure 5.5.'1 indicates that the
;(23 are aIl le~s than'0.015 i.e. extreme1y small, and they extrapo1ate ta be
21 slightly negative at 40oC. Nishi and Kwei present evidence for an upper
critical solution temperature occ~rring in the syst~ at low temperature. If
this i8 the case,,c23 would remain s1ightly positive.~The glc estimate is
~onsistent with a very small negativ~ ~r positive ){23 ~ However, the ~ethod
is not capable of accurately measuring such small values as are faund in .
this system.
The temperature dependence shown in figure 5.5.1 is also of
interest tn considering the mechaniBm of the LCST in the PS-PVME system.
\ 66 MCMaster has stressed that any difference in thermal expansion coeffici~ntsJ
'(
,.
"
j Il -1
"'~: " r
'0
15 . 1 1 ?
"-.-., 't.... ~~
L
11) N . ".
~" x ""' ~ ., -> ~ 5 " \ . (
ft)
0 , - -
o f' à:
~' fOO L.CST
< t .. l'f!_Ji _____ ~.~ .--~_~ ... ot<~~""""",w.._ .. _ ... ~.,.~ _ .. _
\;
...
~~
oc
., r
..
<
1 01:
.-J -
-1 J' 1_ 150 200
0\ 10
~î?l~re 5.5.1 )Gï3 against the LeST for the P~-PVME System '
.. ?-.z.,.". " . .i21)1!7rtr 5!_·,.".~ oomn ... at;;;;""zlÎ!!" ., .. ..;~~:.,L n DWNT,s"3iaetèttmH?trttr W mM' _._,~--
"1 !,
1 t i ! 1
"
(- 1 ,-
o
/
1 1 /
70
- i.e. free vo1Ùme, between the t'Wo polymers in a compatible mi~ture gives,
a positive contribution to,cÏ3 which increases with temperature, tending ,
towards,an LCST. On the other hand, the compatibi1ity of the po1;mer pair
requires a ne~ative or very small positive value ofJCZ3 • Since the usua1
-~-dispersion force between un1ike polymers, gives.a sizable.positive
éontribution to)(Ï3 ' coœpatibility requires a special attractive interaction
bet~en the polymers. This in turn wou1d almost certain'ty be accompanied\
by a negative enthalpy of in~era~tion, i.e.Xn<O and therefore," followin~
equation 2.4.9, )tÏ3wou1d increase w1~h temperature. Thus, an LeST in a
compatible system would be favoured both by the free volume differenee
between the polymers aneS by the specifie interaction between t,hem. In the
present case, the specifie interaction presumably occurs between the ether
and pheny1 groups of the polymer pair, and indeed;iH for the interaction , ~
of benzene and toluene with PVME is sma~l in table 5.3.,3. Solution
calorimetry shows it becomes negative for lo:rr PVME concentration. The
, 67 68 thermal expansion coefficients of PS and, ~ are respectively 5.72.
and 6.45 x 10.4 K-1 at 25°C. Using the Flory-Prigogine theory, the free
volume c6ntr~buti.on 'to~ d ;(ï3 / d T is found to be 1ess than 1 x 10-5 deg- l .,
This is small éompared with the experimenta1 value of approx1mat;,ely
10 x 10.5 deg-1 , found from figure 5.5.1. The teST in the PS-PVME system
. seems due to }he breaking-up with increasing temperature of the specifie
interaeeion.between the PS and PVME chains, rather ehan to the 'free
volume difference between PSvand PVME. r
A final point concerns the compatibility of PS and PVME in
i.
/
i
1
\
,
-
--~_.--------------~-------------------.~
71
, ' 69 solution.- Bank and collaborators found that the DÛ,xture of the two
polymers with each of three solvents, benzene, tolu~ne and tetrachlo~~-{ • /
ethylene gave a one~phase ternary solution, and a· clèar film is 1eft on ~' '.
evaporating the solvent. On the other hand, when any of the three
solvents, chloroform, dichloromethane or trich1oroethy1ene is used, the
. solution is phase separated. The turbidi~ remairi on solvent evaporation
. 1 - - 70 ' giving a c oudy film. Zeman. and~tterson have pred1cted that the
comp811:ibility of po1ymers, in sol~tion .should reflect not on1y the interact:lon' 9' ' /
between the polymers themselv~6J i.e.}(23 ' but a1so any difference betweeuf
" / the interaction of the polymers with 'the so\~ent. i.e.
âX ·1~;2 ~ ~l31 >. 0
In the present case, the interaction betwlen
(5.5-.2)
the po\ymer~ 1s negligib1e
or attractive, indicat1ng that tbe stable state of the film should beJ . clear. P'r~ table 5.3.3, â'Â for benztene, toluene and tetrllchloroeth:ylene
1s respectively 0.1, 0.1 and 0.0. Uowever, for chJ,oroform, 'dichloromethane
,and trichloroethy1ene, Il''/., i8 respeotive1y 1.'2, 0.7 and O.~, i.e. subs~antial.
These results suggest that the 1ncomp~tibilitr of PS ànd PVME in the
second set of solvents 1s due to the tlâ~ effect" which' overco'tnes the , . 1 14
, normal PS-~ compatibilit1es. Further work h~s confirmed this in the
chloroform/(P5+PVME) '\
case.
Section 5,6 Conclusions
" ~ ,
!. l
"
In thi. part of the thesis, effects of specifie interaction,
which occur so usua11y in industrially interesting systems, have been
-- studied. Such phenomenon has long been 1cnoWn and various treatments have - ,
.' 25 71 72 73 been proposed by different authors ' , , • Bowever, none of them
a~ quantitative tnd readily applicable. Quantitative methods have been
o
/
o
.. J
, -~ --J, ~·Ji"'~'If4~ ~'T1!~~~"...... ______ • _ __ ~. ___ ."... ~~ -~ ... -..- -_ ... ~- -
/
1 ;
l ,
. '
" proposed for non-glc data ~(for binary systems with f1nlte volume
0j fractions)~ but even these are very eomplicated and they are based on
, 0 1 ~
assumptions ~ifficult ta jt+st1fy. In the presen·t work, it has been shown ~
that even-for such ''non-iaeal'' ~t praetieal systems, tbe gle ~thod cm
giva intultivelY-agreeable thoUgh qualitative relUits for bot~,polymer-~
"'; diluent and polymer-polime~ interactions: lt 115 a fast and convenlent >'
\ method for sueb studles, 'wlch are related to the processi,ng as well as '.
o
use characterlstlcs of industrlal polymers • •
\ .'
'11
1 -
••
\ . -t
"
" 0
\ ~\
,
r
! /,~
1
{ r
.\
.' , ',.
'.'
/
. . ()
/
! "
1.
r 1
,1
\i
-.--...... -~-. --r-- -- '1 .. -_ •• ~ ............. ~-~-,.-_.- ... -".-- - -- ._-- -
, /
CHAl'TER 6
-HEMATIe LlQUIDS
/ ,
METHOXY AND ETHOXY BENznIDENE BUTYLANnœ ,
1 lI'
Section 6.1 Introduction
The effect o~ order in nematic liquids bas long been a topie . \
of ~nterest. A great variety of methods,' e.g. calorimetry, ~ight
scattering, nuclear magnetie resonanee and density measur8llleUts have .. . ~
be~'l!uaed. ~e to the development of glc, this fas-t md simple method ~ . ,
has been applied to quite a number of ordered liquids~ For instance, . , . U~c
Mar.t.ire et al have used gl~ to study cholesteryl ~ristate, PAA, D~ ,
and MBBA on chromtsorb support. ~ ~ntion8d before, glc studies ,the
interaction of a ktationary phase ~th a probe at infinite,dilution.
'ÛUder sucb a condition, the structure, the orientation and other
characteristics of the (bulk) nemati'c liquid stationary phase sl:rould . / . 1.
not have beau affected by the probe. This makes the glc method, at ~
least'ideally speaking, most advantageous in studying the c~aracter ""
~f the stationary ph~se in its pure state. . '
In glc studies, the stationary phase ia spread in the fo~
of very thtn fUms covering. the soUd support. Tb~ thic1cne •• of the! " 1 •
8taUonarY pha •• dependa', on the relative amount of the 8~bat;rate u8ed, - ,) " , '
\:be l1~è ~f tbe .vpport partlc~e. and the teXt~re of the partiel.
-.urface. 'tQr·~~le~ryth1n"eb. bein, eC(\Ull, tbe uae of rougb ," .1.
• t, . ,
'"
'1
l
.' , ,
=~ \
,-
"!
f ().
1 &
t i 1 ~
v
, Il
, .
0- ) '"
r 74 , ~ 1
porous surfaced chromosorB support Wi~l ,give sta~on.ry phase film
thickOes; ?rders of magnitude smallerl than if ~oth surfaced glass 1
beads are used. In any case, the thiekness of the film should be small
enough in relation to the di~fusion properties of·the probes i~ the
film that equ1librium conditions are attained. This ia a~ necessâry , . -
condition ~or aIl thermodyn~c studies. The effeet of th~ support
,.
partiele surface on liquids like n-tetracosane and squalane should be
negligible. but for nèmatic liquids, orientation order ~y be signifieantly
a~fected. For glass bead support, the thickneas of the film ls estimated
to be in the order- Qf 103, to 104 X, whil~ for chr9IOOsorb 1t is about 102 î. To study the possible effect of the support surface, both chromosorb and
1 .,
glass beads have been used for MBBA columns here. , . Thermodynamic studies, using the glc methqd', expressed ln>
interaction perameters h~ve been diseussed in chapter~2. »y studying , ,
over a range of temperatures, the enthalpi,c contribution)tH to the j,.
'parameter 18 given by the reciprocal gradient
'j. • l~ B T d-
T
A
the entropie eontribution~s ~
Knowing both 1- and ~ cao be,obtained ,
simply from ~ - ~ + ~S ' note that the sign of;:lS is opposite t~ that
of the uflual entropie terms.
Normally, the enthalpie ~B a~i.ses lIlItinly from the chemica(~ ,
nature of the components being mixed. Calorimetry has shawn, however, ,
that ,~9.~/ordered liquid(s), t~~ breaking up of order does contribute to
the heat of ~g and· "n . 45a, b In lde~ lie) see whether thl. 18 true /~
for the glc d.t., a number of normal cul branched _.lkanea have bt!en uaed 1: ' ln thi. won. Alao, th. n_tlc '-l1quld. hava bem atuc!led .t t .... r.tur ••
\ ,.. .. • , .
.'
~ ,
1
o
- ~,. .- -- - , .---
75
~ entropic term, X S " should be of particular interest under such varied
conditions.
Section 6.2 Experimental
The glç apparatua uaed has been previoualy described in chapte~
'2. For MBBA, several columns hav~ been used. One of these employs glass
beads 60/80 mesh, aupplied by Chromatographie Specialties, Ltd." as the / '
solid support. In thia particular case, the column .i.a coated "in situ" ..
(The MBBA is a nematic liquid at room temp,ature, sa glass beads coated
~ '::.. 1 w:l:tp it will stick together and cannot be packed into the column.) Therefore,
~
instead of coating before packing, the column is fir6t packed with uncoated , -
glass beads. Then a solution of MBBA in n-hexane i.s' run through it. This
column is' then dr ied ') 600 C' with a stream of dry helimn ~Vernight before
use. This procesa coats the' collI1IlI\ wallé ~s well as the glass 'beads.
Apparently, for this column. it is impractical to dete~iIj.é the weight' of
the stationary phase, wL " accurately. This means that the absolute values
of ~ and X. have not' been obtained. However, since wL ia independent of
temperature, /<.H values, which depends on changes in X (ratio changes in ~~
, with reciprocal temperature can be computed., This is our main interest. The L ~ 1
other MBBA columns contain ordinary èhràmosorb W, AW-DMCS treated; 60/80 , ,t*
meah, as the support material. These are coated and analysed by as~~g as 1
in chapter 2. For these columns.~ accurate wL ' ~ and X h~ve been ob""bained.
)' Both ordinary grade (phase transi,i~ temperature 42°C) and high ~urity
(45°C) MBBA s~ flupplied by Varilight Corp. hâve been used.
As for EBBA~ the material was preparl!d in a laboratory of this ..
depart:ment by Dr. K.C. Cole. The phase transition temperature is 79°C •.
Oo.~ one colUllll has been studied. EBBA ta •• olüf at room teq»erature, /
, " 11 Gad sta .. bead. coatad vith it CCl be CODven1eDtly packed a. u.ual into . ~
, , : ~
",1 ,-
, . , i
7
•
.0' , i 1
r'
•
.< "
76 ..
~opper tube eol~s. The wL value'of this colump has been obtained by
sohxletting, as de~cribed in chapter 2 for silicon containing colunms. , -" With w
L accurately determined, ~ and ,. cau be obta1ned.
Section 6.3 Results
Tâb1e 6.3.1 Column Data
Column Stationary
Phase Sup,port
A MBBA glass beads B MBBA ',. chromosorb
. C MBBA chromosorb D MBBA(high purity) , chromosorb E EBBA glass beads
Coating Thickness ~'
~LLwt.of coated support
unknown 6.45t
12.101 7.071 0.351.
T4bIe 6.3.2 Apbreviations for Probes
~ Abbreviation , 2,2 dimethyl pe~tane 2,20MP 3,3 dimethyl pentane. 3,3DMP 2,4 d~thyl hexane 2,4DMHx 3,4 d~thyl hexane , 3,4DMHx
2,3,4 trtmethyl pentane 2,3,4TMP "
n-nonane n-Non 2,6 d1methyl heptane 2,6DMHp ,3,3 d~thyl heptane ,3,3DMHp
2,2,3,4 tetramethyl pentane 2,2,3,4TeMP 2,2,4,4 tetramethyl pentane 2,2,4,4TeMP 2,3,3,4 tetramethyl pentane 2,,3,3,4TeMP
Âbbreviations for other probes are as given in'table 3.4.1 ~ , .
)
\
,. '1.
'-
~ . :'
unknown 0.4004 0.8230 0.3627 0.1360
J,
il ~ ~ Il •
~~~\\} " '~i
'.:, i
';'::1~ ,
.. ,
',.
. \';~'\~'\
/ ,~
~
- -~ ~-. "'"'--.:".,..,., .......... ,.".. ...... '~_N __ w _ ~ ~ ,- - -'7
: ,'" 77 . -; !
1 t Table 6.3.3 Average VS (ml/gm) for MBBA on.Chromosorb
1 () CollProbe 25°C 300 e 35°C 40°C 45°C 50°C 55°C 60°c i t , t
Co1umn B ~
nHx '83.9 72.1 61.8 54.4 51.7 45.1 39.5 34.1 r 1 2,2DMB 33.3 29',1 26.2 23.4 23.8 21.2 .. 19.1 17.1 1 .J 2,3DMB . 49.8 30.6
f nHp '254.0 205.~ 118.4 2MHx 156.9 1j2.6 112.7 98.2 94.1 80.7 68.7 59.5
t 3MHx 173.8 146.9 124.6 108.5 103.9 89.3 76.8 66.4 ,~
1 nOet 740.4 306.4 l' \ 2,5mmx 280.2 .w 135.9 1
t38.8 i -2,2,4TMP . 167.2 ,. 90.5 --1 -cP '\ 68."5 40.2 1
cHx 176.1 94.9 ' 1 .. , benzene 424.8 .. 205.9 Co1umn C
: . riHx 71.2 45.0 2,2DMB 28.4 20.9 -..,. ,,-nHp 204.1 - ( 117.9 2MHx 131.2 79.7 3MHx 144.6 1
88.8 , -2,2,4TMP 137.2 1 89.6 Co1umn D
1 nHx 85.9 -.. 45.7 " 2,2DMB 33.2 21.6 ~
2,3DMB 50.4 31.3 \ ,; ,'f) .~
nHp 260.0 ,- 120.5 '2MHx ... "163.1 83.1 3MHx 180.3 91.0 "-
cP 70.9 41.0 cHx 183.8 97.2 benzene 47 208.4 -,
... \
) r
,
, '
J, 1
1
- -- --- ---- ~ - - ~-~~-----~---------------------------------------...,---.:J
"Vl~"- .-:' J , ;
j Z #.biUIII.UJ5.1 IdUAUAM »'A ._ .... ~ ...... )j;I'"Q ;;~k§J.!I .. (.MI,I,~JJ;!~!~4è .. li4\!ijiif.4Ifl."""~~ ... ~~~"'<'t'?~~~!'"~'$·;."lf';~~;;:;~~'~
~
/ <?
.. ,.,..
o (c
Table 6.3.4 -j.. ,)tH and t s for MBBA , 'j.. ~H "'8 .-
liiLmatic . (Column B) Isotr~ic Nematic Isotro2ic
Probe 2SoC SOOC Co1.A Col.B Ref. Col.A Co1.B Ref. Co1.B Reft Co1.B Ref.
nHx 1.88 1.52 5.0 3.5 3.5 2.5 2.3 3.0 -1.7 -2.0 -0.8 -1.8 2,2DMB 2.06 1.66 6.8 3.8 4.6 3.5 2.7 3.0 -1 ... 8 -3.0~ -1.1 -1.6 2,3DMB 1~91 1.5~ 5.7 4.4 2.7 2.7 .- -2.9 -1.5 nHp 1.84 1.48 5.3 3.6' 2.4.
, 2.8 -2.1 - -1.6
2HHx 2.03 1.'62 5.5 4.0 3.8 2.2 2.4 3.4 -2.0 ' -2.2 -0.8 -2.0 3MHx 2.00 1:.60 5.4 4.0 4.2 2.3
v 2.8 3.2 -2.1 -2.6 -1.2 -2.0
~2DKP .. 6.7 4.2 2.8 3.6 -2.5 -2.2
,3DHP 6.4 4.4 2.2 ).2 -2.8 -1.9 nOct 1.91 - 1.52 5.4 3.5 2.2 2.4 -2:0- -1.1 2,4DHRx 6.S - e 2.5 2,5D!mx 2.11 1.·6~ 6.1 2.5 3,4DMHX 7.6 2.2 2,2,4TMP 2.14 1.68 6.8 !'" 4.7 2.4 }.S -2.9 -2.0, 2,3,~'l.'HP ,:.
6.4 2.5 cP ~ 1.47 1.12 4.5 1.7 eUx 1.61 1.21 4.5 2.2 ::;-
benzene 0.87 0.55 3.5 .. - 2.8 0.8 - ( 1.5 -2.5 - -~-1.5
Hematie range studied from 25 to 40oe. Isotropie range studied from 45 to 60oe. f
,cH ,,cS values from referenee: ealeulated using ri - (hl-hl? - "'H RT and Se .. - R "s . .,
1>
~
of rr
~<'
/ ,
...
~~
;;-
...... 00
_ ~ , .> 4.. 0'" ....' '" .l'!''''' - t'ii sne ce p ,.,7 'S , !~,., ;.~Vl?'. 1. .) ",,>-Q!, .~ m. ']iilFTrnl.. > " 'ha. > 5*. S'tsn .,; .:::,. ,:- '. 1 ."' . _. " . " ' j.'. '. "<cr .. • Ii_V".1 "--; d ............... _ ..... - ---
• , , ... ,12. '- ....... ~...,. -~;:,,;,. ..... ' /':, -- ~ ir"'
~ 1
! , \
1 , J 1 1 ,
..,
/ .... 1
o
79 '')
-- "-
Table 6.3~5 ~ (ml/gm) for EBBA on Glass Reads (Co1umn E)
~ (ml/gm)
Probe
. nOet 2,2,4TMP nNon .
500 e 242.3 . 64.5
616.0 253.5 272.1 226.3 136.3 343.1 ·142.3
600 e " 168.8
99.8 410.7 180.7 195.9 165.9 101.7 247.3 106.4
70°C
123.4 ·40.0
287.1 132.2 145.6 129.4
85°C
95.0 34.7
208.6 105~3 119.0 106.4
95°C
" 71.2 28.1
150.3 79.1 89.9 82.3 53.7
105°C
54.8 22.3
110.4 60.0 68 .. 5
/62.,8
..
2,6DMBp 3,3DMBp (' 2,2,3,4TeMP 2,2,4,4TeMP 2,3,3,4TeMP benzene
4>
80.9 187.1.
-/nt~
68.7. 1·52.6
68.3 117 .4 53.3
~1.8 , 88.5 41.8
-/
Table 6.3.6 X,'xH and ~ for EBBA on Glass Beads (ColuJDn E)
Probe
nDet 2,2,4TMP nNon" 2,6D~ 3,3DMBp 2,2,3,4TeMP 2,2,4,4TeMP 2.3.3.4TeMP benzene
)(. ~ ~ -_ ....... _---.-600 e 1.64 i.
1.86 1.68 1.85 1.82 1.78 1.88 1.69 0.84
950 e 1.18 1.32 1.21 1.33 1.25 1.20 1.30 1.11 0.45
Nematie
3.2 4.2 3.4 3.8 4.2 4:7 4.6 4.3 2.6
Isotropie Nematie
2.1 \ -1 .. 5 2.2 -2.3 2.0 -1.7 2.2 -2.0 2.3 -2.4 2.3 -2.9 2.2 -2.7 2.3 -2.6
~', 1.0 -1.8
Isotropie
-0.9 -0.9 -0.7 -0.9 -1.'0 -1.1 -0.9 -1.2 -0.6
Nematic range studied from 50 to 70°C. Isotropie range studied from 85 to 10SoC •
.Just as an examp1e, the.~ vs. ~u graph for EBBA on slass beads
,for a number of probes is shown in figure 6.3.1. \
)
1
• •
~) •
)
'-
-'1
77, 4 ...... _ as ,_"P" J _ ____________ 'v_. __ _.._.. , .. , ____ , ____ _
2.0
1.5
~
1.D
Or e>
/ /
-,
.. z
~
-
ft·oct
o
•
~
r -" \ '--
------ '
t l
'l,?.A 1 '" t' , .... - ...... - ... .:. ...... ..-..- .......
......... ..-....... ..- .... -
~ ..- .... --..".. , ............. -
1
i ~ .,
.."
1
-1 ~/
1 ~ ta."I ... • ' - ~---------~--------__ ---------.r -
'\ .,,"
1 1alnz• nt
-----~-~---~----.---~---2.7 2.8 1000/ T 3.0
'. Figure 6.3.1 )(. against 1000/~K for EBBA on Glass B~ads Column
,.-... '" 'M -''''''Tt! -g IPZ?- PI r . ~-. nrWPEwr= to!:fe"_W'N_~.= ~_,_," ~ ~~., :. :~,,~.. ~, ' ... ~
co o
-
-1 \ r 1
! 1 r 1
81
Section 6tt General Discussions
" From table 6.3.3 (for MBBA), it is quite 'apparent that the
thickness of the coatings on ch~mosorq (6.45% by weight for column B,
and l~.l% for column C) has little effect on the specifie ~etention
volume ~ • It can be taken that under such conditions, thermodynamde
equilibrium has béen reached. AS œor the MBBA on glass bead column ,
(eolumn A), substantial work has beeu done on the ~ependenee of V; on /
flow rate. At flow rates twice or more times faster than the one whose
values are reported here, ~ values do begin to be.affeeted by flow ,
rate, especial}y for" the more spherical probe molecules. This author
has actually studied' the diffusion constants of the various probes for
8 " column A by,the Van Deempter equation approaeh • It is' found that at
the flow rates whose VS values are quoted here, the effeet of flow rate
is Il:egligible. ,
Tbe)Ca values are stmilar for aIl probes at isotropi~ temperatures 1
in ,table 6.3.4. This is true regardless of the solid support material
used. (The values obtained by Mart,ire 74 are generally tigher than ours,
though.) At nematic temperatures, the magn;'tudes o'f both'Xa and'f..s are'
l~rger than those at isotropie temperatures in aIl cases. The amount by ~
which the former 1s larger than the latter depends on both the probe
molecule and the solid support used. In general, for alkane molecules
of (1. g1ven number"of carbon atoms, the branehed mo1ecules give more
positive "a and more negativeXS than the straight chain molecules at ,
nematie temperatures. Al~o, unlike the isotropie case, thej(u valJes ,
are consistently M\te positive (and~s values more negative) ~en glass
be.ads are us~d instead of chromosorb.
"
... -~
.. ~
! i: ! () !
1 1, ,
.)
()
(
82,
The EBBA resu1ts (table"6.3.6) are generally similar to those
for MBBA. There are )a few poinés of interest, though. Both the ~ and
~ values at isotropie temperatu~es for EBBA are very close to those li
* '1/ J
for MBBA. The corresponding values at nematic temperatures are slightly'
different, however. The EBBA co1~ uses glass beads as the solid support.
lts ~ are'generatly 1ess po~itiv~ than those for MBBA also on glass beads, ,
but more positive than MBBA on -chromosorb. This ~y be due to severa1 , '
reasons; EBBA may be 1ess affected by the support than MBBX, or EBBA may
have less orientationa1 order than MBBA to start with. Whichever is the
case, one thing is still clear.·'The breaking up of order in a liquid in
the nematic phase does 1ead to an incre~se in' magnitude of both the
enthalpie and entropie interaction parameters, and, everything else being
equa1; the more branched a probe is, the more efficient it is in breaking
up arder of the ~tatio~a~ phase mo1ecules ~~ound it.
Section 6.5 Effects of the Solid Support
As mentioned before, the use of glass beads and chramosorb as
the soHd support matef.ials gives somewhat different 'tesu1ts for MBBA
at nematic temperatures (table 6.3.4). The glass bead Xa values are
consLstently higher than the chromosorb values obtained bath by this 74
author and. Martire • On the other hand, at isotropie temperatures, aIl
these results are similar and generally lower than those at nematic.
\
temperatures, regardless of the suppor~ used. This tends to suggest that
either the glass bead surfaces are enhancing arder in the nematic liquid, , ./,
or that th, chramosorb surfaces ar~ destroytng it. Considering that the
thickness ~f the MBBA layer on the glas.s be~.~ 18 est~ted ~o be, of ,.-the
order of loooi and the the thickne88 on the'porous chromolorb 18 even lell,
\ , '-
, • j
"
. ( ,
l,
i
/ 1
Il
/ o
/
83
such a possibility may well existe /'
To clarify the situation, a number of calo~imetric expertments
have been performed. (lt should be pointed out that the glc experiments ~"
are for an infinite dilution of the probes in MBBA whi1e calortmetric
experiments are at the opposite end of the concentration scale.)
Table 6.5.1 Beats of Solution of MBBA in Toluene*
Pure MBBA MBBA added ento glass beads MBBA added onto chromas orb MBBA recovered frcrm pre-coated chromosorb, th~n used
by itse1f
* In a1l cases, MBBA 1s about 64 by weight in to1uene.
8.85 J/gm 8.5 J/gm 6.4 J/gm 6.5 J/gm
From this table, it looks as if that the glass'beads have 1ittle effect ~
on the MBBA whi1e chromosorb leads to significant decreases in the heat
of solution. Efforts are then made to determine whether the MBBA is
somehow absorbed into the chromosorb particles, thereby making~t tnaccessiple
to the to1uene. The results are clearly negative. The fact that the MBBA
recovered from pre-coated chromosorb gives r'esul ts similar to MBBA added " ,
onto chromosorb has a particular significance. lt shows that it is not
just the presence of the chromosorb surface with the MB'BA that leads ta
" a lowering of the heat of solution. The' fact that once the MBBA ha been
in contact with the chromosorb, it gives lower heats of solption leads f
to 'speculations about impurities presen't in the chromosorb. As ;fuentioned
before, the chromosorb surface has bee~ acid-washed, silanized with DMCS
/ ,
\.
1
i
and treated by various methods of fluxfug. lt 1s possible that the J 4
1 V chromosorb 1B not absolutely dry. AlI these,may contribute to the destruction , of order, in the MBBA, thus lowe~g the'heat~ of solution. Martire75 ~ctual1y
measured the phase transition temperature of the MBBA coated on chromosorb
Î
.\
C),
84 ~':J ; __
. and found it to be Iower than the pure MBBA, but this Iowering is not
sufficiently large to "match the present observed Iowèring in the heat •
of solution. ri
Croucher48 in this Iaboratory has done a number of "doping"
calorimetric experiments with very smal~ amounts .af simple organic
solvents in S.' large quantity of MBBA. This is actually closer to the
.......... ,,\"
present gle concentration conditions. Someh~w these results agree better .
wi th the chromosorb glc data obtained by 'this author than the glass bead è
1 gic resul ts. Kronberg, also fram this labo~atory followed this up by
\ ~
studying the calorimetrie heats of mixing as a function of, the doping
<'-"' concentration. The results are inconclus::lve. So far, no satisfaetory
, !
explanation has been found for this'disclJ:'e~ancy. '" t Ij)~
\... '; , ,'/-,
Section 6. 6 C~n~îCsions 1 ( -
..
Thougn unexplained puzzles still exist in this study; with t1:}e • - q
correct ehoice of, experimental conditions, the gic method do es seem to give
. fai~l~ aecurate and reproduc1bIe results at a desirable' rate. I;.t gives the ..sr,.\!
free energetic,- enthalpie and therefore entropie interaction parameters at ~
,the same' time. Wh1chever the soUd support used, ~air1y unifo~ ,resul ts ~ . . C
(lo~er "H and less negative~S) have b~en obtained at the isotropic , , ,
t-emperatures, regardless of probe shape. At'nematic teuiperatures, the more ,.'
branched the probe, tff'è higher thel'H and 1re l~weJ" th,e~s • This general . )
behaviour i8 in good agreement With expeeta~ions. ,Controversy aside, the
gle method ,is still convenient and Rracticai (for .stu4ying the effects of
. , order in llematic liquids. , .
f f •
i \ ..
, .. • ••
1
1 , !
1 f {
l \
1
i
, '
'ù
, ,
o
. 0
'0
Suggestions for Further 1Work .,' / /
Il
. '
85
1. The appli~ation of gle ta PVC-DOP interaction studies provea..,to be
• interesting. The ume procedure may be a~plied to other "polymer-
plasticizer .systems as well, ;.g. PVC 1ith some s~lid plastic1zers, 0"
.,..
recently be1ng developed for industrial u~ag'i: Such' solid plastichers
are less volati:~. and ther~forE; less polluting. preli~nary i~k on
one system has, been earried out by( this au'thor.
" ~ It may be worthwhile to .tùdy the ~:cts of solvent. o~' compatible '-
, .--'
#
/'
polymer pairs by coating columns of such ~ixtures froJ diff~ren~ solvents. If more than one metastable state of ,a given polymer pair
__ ,~ i •
can exist over extended periods of time, di;fferent X23 parameters may-' , .
~ be ootained by using d~rferent' coating 801v~nts .. This may be of", '-"
interest to the paint industry.
() 1 .{
u 3. The ef.féet of the solid support; on the order of nematic 1 iquid~ has \
=0;;,
4
not qeen eompietely resolved. Some impuritie~ may be present in ther -, 1 , ~
po BQ support, particularly the chtomosorb, whieh Iooses weight { .
slightly on ashing. Thiso~ay be due to water Japour absorbed .frQm
atmospheric humidity, which may rea'ct wi~h the nematic liquid,
re~u~t[ng' ~n sensitive changes :. its ,order.', If such\mpuriti~S can '/1' . i 0 • "
be ana~ys~d bO~h~u,litatiVelY. and q~antitativè1y, the d1.screpaney
obsetved in 'thi~r~sent work may be explained. Y,
.. l'
• , ,
;.. .h - , ..
l' 1'"
\ D,
.. .... 'è
~ , . '
",. • . \
...
.. ~,
_ ;". r
/ /
'1 . ..
.... ~
\ ,
0\4/ ~
,; , +
" '.
-. , »
ft( -:':1 " ,,'
........ ~ :~,~
1
r
\ ,
,.
'" ) ,Claims to Original Contributions
86
1. The accuracy and reproducibility of the ''moleeular probe" or '''inverse''
gic method has been teste~y interlabor~tory comparisons of ~g results 27 '
with PDMS • For a given column, this is found to be within ± 11., while' /'
for different columns of the same material studied separ~tely, it is
wi thin ±1iS7.. i,
2. The glc m~thod has been applied for the first time to inv~stigat~2 .'
thermodynamic interactions (%23) between eomponents of mixed statibnary
phases. Tetracosane, squalane and PDMS have been used to form a "cycle"
of mixed stationary phase pairs, and this ls used to compare with the
geometric mean rule predl'ctions. As expected, the results are i11 qualitative
though not strictly quantitat~ve agreement. .,
3. Values of the )(23 parameter have been o~tained for a mixture of poly-~ 25
(vinyl chloride) and a well-known plasticizer, di-n-octyl phthalate (DOP).
,They ar~ negative at low plasticizef concentration, Indicating a strong ',"
favourable interaction ~etween the c'omponents, but change to positive as
the' fraction of nop iticreases. An explanatton' 18 given in terms of "specifie 1 •
interactions". An empirical correl~tion between the thermddynamic, interactions
of a polymer-plasticlzer system and its processing (melt viscosity) and use
'(Tg) charaeteris tics ",OVer the entire concent,r!ltion range has beeh developed. ;:7
4. The glc method has been used tO,study the interac~ion between two compatible
pol~rs, polYètyren~ and po~r(vinYl methyl ether). The value of "23 is
close to zero, but apparently depends on the probe used and an explanation
ia offered for thiS" e~~ect: TheidynamiC' parameters, ~2 and X13' are
obtained for the interaction of ,!the probes with the two pure polymers.
Probes with large differences betweenXl2 ,andJ(13 lead to an incompatibility 26
of the polymers in th~se probes.
o 76 5. The thermodynamic effect of, order in nemat,ic liquids MBBA and EBBA has
been"studied udng chromasorb and glass bead supports. ~ere appears te> J "1>. ~
be an effect of the support ~ the nematic order, but no satisfactory
e~lanation can be offered at this stage.
1/'
, '
.)
. .
.. '
r
1 e
,. /
1
\
,
87
/
BIBLIO~RAPHY
1. C.L. Young, ChrOmatogr. Rev., lQ, 129 (1968)
·2 •• D.H. Everett and C.T. Stoddard. Trans. Faraday Soc •• R, 746 (1961)
3. (a) D.E. Martire "Gas Chromatography", L. Fowler, Ed., Academie • Press, New York~ 1963, p.33
(b) D.E. MatUre and L.Z. pollara, "Advances in Chromatography". Vol. I. J.C. Giddi~and R.A. Kel1ard, Ed" Marcel Dekker, N.Y., 1966, p.335
4. (a) A.J.B. Cruickshank, M.L. Windsor and C.L. Young, Proc. Roy. Soc., Sel'. A, 295, 259, 271 (1966)
(b) A.J.B. Cruiekshank, B.W. Gainey and C.L. Young, Trans. Faraday Soc., .§i, 337 (1968)
5. J.R. Condel' in "Progress in Gas Chromatography", J,.H, Pumell, Ed., Wiley, New York. 1968. p.209
6. p. Patterson, Y.B. Tewari, H.P. Schreiber and J.E. Guillet. Macromo1eeules,~~. 356 (1971)
7. (a) O. Smidrod'and J.E. Guillet, Macromolecules. 2. 272 (1969) (b) A. Lavoie and J.E. Guillet, ibid •• 2, 443 (1969) (c) J.E. Guillet 'and A.N. Stein, ibid. ,-l, 102 (1970)
8. J.E. Guillet. New Deve10pments in Gas Chromatography, J.H. Purnell, Ed., p.lS7, 'Wiley (Interscience), New York, 1973
9.
10.
11.
,
D. Patterson, Y.B. Tewari and RI.P. Schreiber. J. Chem. Soc., Faraday Trans. II; 68, 885 (1972)
D.G. Gra~ and J.E. Guillet, Mac~omoleeules, 1. 244 (197~)
D.G. Gray and J.E. Guillet, Macr9Œolecules, Notes, ~, 129 (1971)
12. R.D. Newman and J.M. Prausnitz. J. Phys. Chem., 76, 1492 (1972) , -
13,-. W .. E. Hammers and C.L .• DeLigny, Ree. Trav. Cbim., 90. 912 (1971)
14. A. Robard and D. Patterson, to be publisheâ
15. (a) D.E. Martire. P;A. Blasco; P.F. Carone. L'.C. Chow and H. Vicini, J. Phys. Chem., 72, ~489 (1968) [
(D) L.C~ Chowand D.E. Martire, ibid., 73, 1~27 (1969) (c) L.C. Chow and D.E. Martire. ibid., li. 2005 (1971) ,
t 16. H. Kelker and E. VonSehivizhoffen. Adv. Chromatogr., !. 247 (1968)
17. L.C. Chow and D.E. Martire, Mo1ecu1ar Crysta~s and Liquid Crysta1s, ""- li. 291 (1971)
1
\
l
\ 1 1
, '
c}
, ~ ~
1 1 .
.,
\
()
~
. ,
18. A.B. Richmond, J. Chromatogr. Sei., .2.,.571 (1971)
,20.
19. D.N. Kir.~ and P.M. Shaw, J. Chem. So~., Ser. C, .3979 (1971)
O. Olabis!, Macromolecules, â, 316 (1975) r _
2I. . ,Ii
T. Nishi and T.K. Kwei, Po1ymer, 16, 285~(l975)
88
'-"'22. 0.0. Deshpande, D. Patterson, K.P. Schreiber and C.S. Su, Macromolecules, 2., 530 (1974)
23 •
24.
25·.
T.K. Kwei, T. Nishi and R.F. Roberts, Macromolecules, 1, 667 (1974)
. G. Àl1en, G. Gee and J .P. Nicholson, Po>lymer, l, 56 (1960) Il .
C.S. Su, D,~atterson and H.P. Schreiber, J.~pp1. Polymer Sei. 20, 1025 (l~6) ,
.%
26. C.S. Su and D. Patterson, Macromolecules (in press)
27. R.N. Lichtenthaler, J.M. Prausnitz, C.S. Su, H.P. Schreiber and D. Patterson y Macromo1ècu1es, 2., 136 f1974)
28. A.B. Littlewood, "Gas Chromatography", Academie Press., New York. 1962
29. H. Purnell, "Gas Chromatography", John Wiley & Sons, New York, 1962 .< .
30. S. DalNogare and R.S. Juvet Jr., "Gas-Liquid Chromatography", Intersci(nce " Publishers, New York, 1962
" . 31. A.B. Littlewood, C.S.G·. Phillips and D.T. Priee, J. Chem. ~e •• (1955),.
1480
\
.32. R.L. Scott, J. Chem. Phys., l?, 279 (1949)
33.
34.
H. TOII).pa, "Polymer Solutions", ButterwoÏ\ths, London, 1956, p. t8l. 1 tI ""'1
(a~ 1. Prigogine, "The !o(olecu1ar Theory of 501utiôns", (with the collaboration of V. Mathot and A. Belleman), North-Holland, Amsterdam, 1957, chapter 16
(b) P.J. Flory', Disc. Faraday Soc., 49, 7 (1970)
'35. D.' Patterson' and G. BeImas, Dise. Faraday Soc., !i2lJ 98 (1970)
36. D. Patterson, Pure t Appl. Chem., 31, 133 (1972)
37. J. Pouchly and D. Patterson, Macromolecules (in press)
38. D." Gaeck1e, Ph.D. thesis, Dept. of Chemistry, McGi11 Univ. (1972) \
39. W.R. Summers,'Y.B. Tewari' and H.P. Schreiber, Macromolecules, 1, 12 (1972)
• 40. D.M. Ottenstein; - J. Chromatogr. Sei., Il, 136 (1973) $)"\....
,{
, r
..
...
..
1 ..... ;:_~ ......... .,. ".~~-'f""'~ ...... ~ '1"''''''''' "...,. .. _ ..... -_ ........... ~ _~
- .
41. J. Serpinet, J. Chromatogr. 68, 9 (1972)
89
o •
42. J.R. Conder, D.C. Locke and J.H. Purnell, J. Phys. Chem., 21,700 (1969)'
43. R.N. Lichtentha1er, R.D l Newman and J.M. Prausnitz, Macromolecules, .§., 650 (1973)
44. R.S. Chaha1, W.P. Kao and D. Patte~son, J. Cry~. Soc., Faraday Trans. I, 69, 1834 (1973)
45. (a)
(b)
P. Tancrede, D, Pattersort and V.T. Lam, J. Chem. Soc., Faraday Trans. II, 71, 985 (1975) V.T. Lam, P-.-Pi~ker, D. Patterson and P. Tancrede, J. Chem •. Soc., Faraday Trans. II, 70, 1465 (1974) " M.D. Croucher and D:-Patterson, J. Chem. Soc., Faraday Trans. II, {c) 70, 1479 (1974) ~)~
46. S. Morimoto, Makromo1. Chim., 133, 197 (1970)
47. J.M.,Bardin, Ph.D. thesis, ~ept. of Chemistry, McGill Univ. (1972)
48. M.D. Croucher, Ph.D. thesis, Dept. of Chemistry, McGi11 Univ. (in preparation) \\
<:
49. R.A. Orwo11 and P.J. F1ory, J. Amer. Chem. Soc., 89, 6814 (1967)
50. P.J. F1ory, J.L. E11enson and B.E. Eichinger, Macromolecules, l, 279, .. (1968)
51. T. Kataoka and S. U~eda, J. Polym. Sei., Part B, ~, 317 (1964)
52. E.B. Bag1ey and H.H. Wood, Po1ym. Eng. ~ci., 141 (1966)
53. A~ Abe and P.J. F1ory, J. Amer. Chem. Soc~, ~, 1838 (1965)
54. Y.B .. Tewari, J.P. Sheridan and D.E. Mar tire , J. Phys. Chem., 74 , 3263 (1970) • ' ,
55. 1
C.E. Anagnastopou1os, A.Y.1 Coran and 'H.R. Gamrath, J. Appl. Po1ymer Sei., i, 181 (1960)
56. D.C. Berthelot, hebè. Seanc. Acad. Sei., Paris, 126, 1703, 1857 (1898)
57. J.S. Row1inson, "Liquida and Liquid Mixtures", Butterworth, London, 1969, chapter 7 • /
58.~ P. Dot y and H.S. Zab1e, J. Polymer Sci., l, 90 (1946)'
,59. J.E •. Gui11~t and J.M. Braun, Macromo1e~es, ~, 557 (1975) •
60. J. Pouehly and J. Biros, J. Po1ymer Sei. "Polymer Letters, B7, 467 (~69)
61. R.P. Kambour, E.E, Romagosa and C.L. Gruner, Macromolecules, 1, 335 \(1972)
f
1 •
,,'
• 1
1 1
1 l
t . , 1 •
()
-', "
1
()
- '1
90
6~. J.A. Manson and G.J •. Arquette, Macromol. Chem., E, 187 '(1960)
63. D.D. Deshpande and S;L. Oswa1, J. Chem. Soc., Faraday Trans. l, 68, 1059 (1972)
64. C. Booth and C.J. Devoy, Polymer. 11. 309, 320 (1968)
..
65. J.P. Shertdan, D.E~ Martire and Y.B. Tewari, J. Amer. Chem. Soc., ~, 3294 (1972)
66. L.P. McMaster, Macromolecules, !' 760 (1973)
67. H.Hocker, G.J. Blake and P:J. Flory, Tra?s. Faraday SOC" 21.. 2251"'S (1971)
68. ·R.A. Haldon, W.J. Shell and R. Simha, J. Macromo!. Sei., (Phys.) BI, 759 (1967)
, 6,9. M. Bank, J. Leff ingwell and C. Thies, Macromolecules, ,i, 43 (1971)
, . 70. L. Zeeman and D. Patterson, Macromolecules, 1. 513 (1972) ,
71.
72.
73.
74,
75.
76.
-".
A. Hartkopf 'i J. Chromatogr. S'CL, 12, 113 (1974)
A. Hartkopf, S. Grunfeld and R. Delumyea., J. Chromatogr. Sei., 1.2, 119 (1974) •
G. Castello and 1 ! G. D Amato, J. Chromatogr. , ~, 293 (1973)
D.E. Martlre, in preparation
D.E. Martire, Georgetown-University, Washington, D.C., private cODUDunication
C.S. Su and D. Pattersob, in preparation
8, •
.t
Related Documents
