Calculation of Chloride Diffusion - C. Andrade

mechanisms, are

724

In therate 01asswnirof ste.paste"diffufcalcu1ccoeffic

This mEas follto unr'eobtaincontair

In thespec imecondi tiia soluprofilEis app.(6) :

This e,condit:

c,

. and th,

c,

Obtain11) •

CHLORIDE DlFFUSrON. AASHTOTEST. RESISTIVITY 725

enetration

dC dC(x)-J(X) = [1)

dt dxThis methodology presents some limitations which may be sumarizedas follows: a) cement paste and not concrete is used which can leadto unrealistic results, b) it is time-consuming and takes weeks toobtain one result, c) a constant concentration in the chambercontaining chlorides from the beginning should be maintained.

- ~~• ) In the case of non-stationary conditions I concrete blocks or

" specimens can be used which results in much more realistic. conditions. These concrete blocks are maintained in contact with

.,. a solution of constant chloride concentration and the chloride~~ profile along the time is measured. In this case second Fick's law(f. is applied to calculate the, an Apparent Diffusion Coefficient D•

. • ''/ (6):

-J(x) = D. (2)oC(x)

atThis equation is usually solved applying the following boundaryconditions:

c,= C'I x = 0, t > 0

and the initial condition: (3)

cs= 0, x > 0, t o

Obtaining the following solution which is the most widely used (7-11) •

C. x------ = 1 - erf --------

C, 2 (D.t) 112

, This type of test also results very time-consuming and maintainsseveral uncertainties on the rigorous application of Fick's law.Some authors (12) rather prefer to compare chloride profiles thancalculate D•.In addit' .hot lon, ln both steady and non-steady test conditions, it is

'ce- USually calculated the reaction or ads tion of chlorides y,.me~Phases. Thisci c ns ance considered 0 mlnor lnfluence,

[4 )

/'

•..,:.~...<:/,\, ...-

726 C. Andrade

although few researchers (13-14) do take into account. ThuBAtkinson (3) refers to it by defining: a) a D.: Apparent Diffusio~'Coefficient in a porous medium, which considers the averaconcentration gradients of the diffusing substance, therefore t~e.adsorption phenomena, and b) a D,: Intrinsic Diffusion coefficien~which tries to take into account the average flux per unit of area -and therefore, the volume fraction of porosity. '

along 6 hohigher amoiconcrete t(

There are also a variety of improvement proposals to thesebasic approaches (15-18) which make much more complexcalculation of the chloride ~. When the (

electricalmainly of f

shOWS. Thidifferent:

Electrical methods

Because of testing "natural" chloride penetration results time-consuming, attempts have been made to calculate the D. from'resistivity measurementes (3) (19) or to accelerate the rate ofpenetration of chloride ions by applying an-electrical field(1) (20-29).

In additiorions occur:

'. only chlor:spent incommentedsimul t.aneoion the re L.

Both kind of test types will be commented in present paper in orderto analyse their possibilities and limitations. First a criticalreview will be done on the test known as "AASHTO TEST" (30)explaining Why its mode of operation leads to erroneousconclusions. Secondly a brief summary will be made on the basicknowledge needed to understand migration phenomena in electrolytes. I

Finally, a proposal will be presented on how to calculate Diffusion ,.Coefficient from electrical (migration) measurements and which are .the theoretical limitations. Numerical examples will be given.Extensive experimental trials will be needed to verify whether theassumptions taken in the numerical examples are reliable or not.

Then the prfield is aj

Elect:

a.1)

CRITICAL REVIEW OF THE RAPID CHLORIDE PERMEABILITY TEST a.2)That chlorides move quicker troughout the concrete when anelectrical field is applied arose from earlier experiments,(31) (32) on that known at present as chloride removal (33~ (34).Actually, this fact on chloride migration was already experlenced.by many researchers using electrochemical techniques (as cathodic.protection (12) for instance). However, it was Whiting who, (20-21) (30) proposed a "Rapid Chloride Permeability Test" in order tQobtain in few hours an appraisal on concrete permeabili~y. Th!standard test has promoted a strong controversy (28) (29), wlth m~'~,heat than light in clarifying the meaning of the test an~ ..ability to predict concrete resistance to permeation of chlorldes.The real fact is that the test is increasingly being used althoU9jeverybody recognizes some still unknown uncertainties.

Summing up, this test uses a thick (usually 5 cm) concrete ~i~~between two electrodes (usually copper meshes) in an arrangem&similar to that of the diffusion cell. Sodium chloride (3t Pt I

weight) is added to one of the chambers and NaOH of about 0.1 H ~the other. Then, an electrical field of 60V is recommended to I

applied between electrodes and the amount of coulombs record

dercal30) •

-oussiccs.

.t .

an.ts ,<1) •Iced',die'20-to

'his!IOre

itsles.lugh

128 C.Andnde

As well as oxygen reduction following thereaction,negative electrode: 202 + H20 + 4e- -> 40H-

All these reactions tends to maintain theelectroneutrality of the experiment which is onefundamentals of electrochemical reactions .

OH

.'!

0) DIFFUSION Mi

e 0

No·--- --C,-

__ OH- No+--

. I

TJ

,~b) MIGRATION

~I 0',-" e Concrete

No·-- --CI-

-OH No+-

c) DIFFUSION + MIGRATION

Figure 1. Mass transport processes in concrete.

e•.•••'.o

o· -.-- OH-o'•o

'0o'0• ••'.o•o'.••

No+-

2H20-01+2~·

CI-CI2'CU-CU·1

2H20-H2t.20H-

O2+ 2HtO - 40H

Figure 2. Processes occurring when an electrical field is appliedin a diffusion cell: Joule effect, anode dissolution,electrolysis of the electrolite (gas evolution atelectrodes and reduction reactions) and ionic migrationand diffusion.

b) Migration-The third process happening in a cell is the movement ofions in the electrolyte in order to carry the electricitypassing through the cell. Therefore, migration isdeveloped and diffusion may appear if this migrationleads to concentration differences.As it was mentioned, not only chlorides move but all ionstake part in migration in a proportion what is known astheir "transport or transference number".

Transference number -Let us -try to explain something here about thisparameter. The transference number of an ion moving underthe action of an external electrical field is defined bythe "proportion of the current carried by this ion inrelation to the current carried by the rest of the ions"(36). It is formulated as:

t;=ij ZjCj~ ~------ = ------------- =i 1: ZCh A

{5]

Hence, the transference number is a function of the ionicmobility or the equivalent conductivity. This means thatOH" ions will carry much more proportion of current thanCl' ones due to the ionic conductivity of 011 is 198,5 ohm"l·cm1·ecrl and that of Cl" is 76,34 ohm-I'cm1'ecrl(36). Thisfact is ve.ry important in the case of concrete because

C.Andnde VaL 23. No. 3

it means that the main proportion of the current wouldbe taken by OH' ions and not by the Cl- and therefore,hydroxydes might behave as a "supporting electrolyte".Therefore, only if chloride transference numbers arecalculated is possible to specifically deduce chloridetransport feasability, which is not taken into accountby the Rapid Chloride permeability test which onlyrecords the total amount of current (that correspondingto the movement of all ions). In addition when flowingthrough the concrete the chlorides may react with the ~Aand therefore a stationary flow cannot be achieved untilall reactive sites are saturated.

Movement of cations -An additional aspect to be stressed now is related to the"anomalous" Diffusion Coefficient that is measured in thecase of the cations of small ionic radius, as Na+ and K+(1). This behaviour is very well described by Bockris(36) and Glasstone (37) considering that these ionsmigrate solvated, that is, due to its small ionic radius,Na+ and K+ diffuse or migrate surrounded by watermolecules, as they normally are in solution. That makestheir movement more difficult and therefore, 0 valuessmaller than those of chloride ions are reported (1).This fact also explains why water may concentrate at thecathode, as was sometimes noticed in the case of cathodicprotection. Na+ and K+ migration means that 'a net flow ofwater (electroosmosis) is also simultaneously produced.This fact can be also applied to explain the basicprocess of electrochemical realkalization: there,hydroxydes are produced at the rebar acting as cathode,and solvated Na+ ions move from the external carbonatesolution in order to balance the electrical charges and,finally they support the reconstruction of a NaOHsolution around the rebars. Anyway, as water issimultaneously reduced at the cathode together withoxygen, the dilution effect may be balanced.In the case of the migration test, having two chamberswith solutions, the effect of increasing water around therebar is not noticeable, but in the case of concrete(cathodic protection, realkalization or chloride removal)the effect will be dependent of the potential applied orthe lasting of the treatment. A consequence of thiseffect in the case of cathodic protection, is that the ~resistivity will increase at the anolyte (and thereforedecreasing the efficiency of the anodes) .and a dilutionof the solution around the cathode, and therefore a"bUffering" of the increase in pH value on the catholyte,may happen.

SUDU1(dbsidEdepi

:. a) ')at Jtoele4of '

Rap1)

2)

3)

Thftrc"pI

AI'ChmuneWh

No"pmecc01tcmfPlbl

CHLORIDe DIFFUSION. AASIITOTEST. RESrsnvnY

up what has been said up to now, when an electrical fieldeot current) is applied between two electrodes placed both

SS of a concrete block, several phenomena develop as figure 2iets:The anodic material, if:l,ossiblei dissolves and gases may evolve~bOth electrodes, b) aIr' ~ons :of the electrolyte move in order:oarry the current passing' through the cell and to maintain

'eotroneutrality c) in addition'heat is produced as a consequencethe current flow. ' ",

At the sight of these co~ents, it can be deduced that, thepid Chloride Permeability test contains the following errors:

It accounts the total current and not that corresponding tothe chloride flow.When integrating the total current from the beginning of theexperiment it does not distinguish between chloride flow plusreaction and simple flow.The high voltage drop used (60v) induces heat (23) (27) whichin turn changes the flow speed.

Therefore a migration test of this type cannot at all inform ontransport of chlorides (38) and much less on porosity or"permeability" of the concrete specimen.

~heJ icof

.d •

COEFFICIENTS FROM MIGRATION MEASUREMENTS

;lc'e,le I

IteId,,OHisth

-How an attempt is presented on how to calculate, not he"permeability", but the Diffusion Coefficient from an electricalmeasurement similar to that described in the AASHTO test. Diffusioncoefficient is the parameter which may characterize a concrete inorder to predict its long term performance, that is, its resistanceto the penetration of ions. The calculation of 0 from electricalmeasurements has to be based in the fundamental of transportprocesses in electrolytes, very well established in the traditionalbooks of Electrochemistry Science (36)(37) (39-43).

rshete1)orisher:-eona

There, it appears that the general equation for transport processesin solution is that named Nernst-Planck (36) equation which can bewritten as:

oCj (x)

= ~ ---------- +oXoE(x)

--------- + GV(x)o(x)

(6JRT

731

D)

C)

opriate

:e flowstate

-re the,kes it.asuzea

ths of

enough

, liCHLORIDB DIFPUSION. AASfrrO 00. REsIS11V1TY 733

stationary flow - in order to apply equation [6] in itspresent formulation, a steady-state flow has to be establishedas figure 3 depicts. If non-stationary flow is produced, thenthe variation with the distance of the chloride concentration,should be also taken into account aiming to an equation inpartial derivatives of second order similar to second Fick'slaw.Reaction - the first chloride ions traversing the concretedisc will react with A~ and therefore an erroneous D may becalculated as has been detected in the case of pure diffusioncells. In order to neglect this fact, the calculation of D hasto be made when a linear increase of chlorides is recorded inthe chamber not containing them at the beginning, that is torecord the chloride flow when the reactive ACl was saturatedwith the first migrating Cl- (figure 4).Ionic strength - In order to take into account the high ionicstrength of the concrete pore solution, two main aspects haveto be considered: a) that activities instead of concentrationmust be considered and therefore, either a selective ionelectrode for chloride is used or activities must becalculated, for instance as is suggessted in (44), and b) theinfluence of the ionic strength in the transport number, ~'and in the value itself of D~ should be considered.

Let us again try to analyze this aspect of the influence ofthe ionic strength on D with more detail. It has beenestablished that 0 is not a constant, but a function of theconcentration of the solution (36) and therefore, high ionicstrength influences D value. In a recent paper (44) a simpleway to calculate activity factors from conductivitymeasurements has been offered, and therefore a trial will bepresented in the numerical examples, on how Dcff variation withconcentration is calculated.

CI- in thecotholitt

f the

TIME

Figure 4. Flux (J) of chlorides leaving the cathodic chamber alongtime.

734 C.Andrade

Anyway, it is important to stress that being the concrete pore)solution a very concentrated one, the influence of ionicistrength cannot be neglected in the calculation. .

D) J~ule .effect - The po~ential difference applied to drivem~grat~o~ should be as h~gh to promote a quick enough movementof c~lor~des, and as small as;to avoid a waste in heating. Tento f~fteen volts could be a sensible compromise.

Solving Nernst - Plank equation

.~

Really a rigourous solution for equation (6) cannot be achieved insolutions as concentrated as concrete pore solution (36)(43). Inpolielectrolytes (more than binary solutions) a rigourousapplication of flux equation (6) fails, an even more if thesolution is concentrated, because 0 bas to take into accountinteraction of all ionic species. Therefore at least two main 'difficulties arise when facing our particular problem: 1) firstthat of the high ionic strength previously commented and 2) how toapply the equation to a particular ion and not to the solution asa whole (19).

A semirigourous calculation might be undertaken using two possibleaproaches:a) To consider phenomenological onsager's equations (36), orb) To use a Mean 0 for the whole electrolyte (43).Both approaches lead to unsatisfactory solutions for the sake ofpractical purposes. The first because needs many and sophisticatedmathematical equations and the second, because does not allow todifferentiate between the different ions.ThUS, with the aim of looking for a simple and practical solution,a simplified approach should be tried. This will be based in;;several assumptions able to overcome previous difficulties.}

Simplified calculation of D~The several assumptions which have to be taken into accountorder to solve equation [6J are (36) (39-43):

only what happens inside the concrete disc is influencing th: .measurements. This assumption may be accepted from the taotthat ionic mobilities in solution are 3 or 4 orders 0 :'magnitude higher than in the concrete and therefore, tor t~~:sake of the measurement, the slowest process is the on .considered relevant.

2. The term dealing with convection in equation (6)neglected. This seems not difficult to be accepted,what happens inside the concrete disc is considered.The diffusion component of equation (6) is consider.negligible in comparison to that due to migration. As well

3.

Vol. 23. No. 3

ellofdi:ef

4. Thstrecha4}cc

5. Ttm1iJTJ0:

c'

Once aexpres

'I

in whexperaloneflux'

Calc1equa'

Anotduri43)the

iI •I' I'electroneutr~lity in this experiment is maintained by'means'

of the electrodic processes (gas evolution or ~et~~dissolution) and therefore counter diffusion or membraneeffects are not considered.

I

", I1 I

loRIDe DIFPUSION. AASHTO TEST. RESIS1TVITY-

!ved in:3). In;'

rourou.if the;;'LCCOunt;t;o mahi'first '"

how to. Lon as

The concrete disc is thin enough to allow to reach a steady-state condition is few hours, which in turns means that allreactive A~ in the disc is saturated with the first diffusingchlorides and therefore, after the transient initial period,a linear flux of chlorides along time, is established (figure4), This allows to make the term a E/a 1 = aE/l, being 1 theconcrete disc thickness, and 6E the potential applied.The concentration of chlorides in one chamber of the cell ismuch higher than in the other. That is, chloride concentrationin the catholite should be high and that in the anolite, zero.This allows to accept that the concentration (activity better)of chlorides in one side of the cell remains comparativelyconstant.

these assumptions are considered the equation can bein the following way:

)ssible mol ZFTotal flux= -J(------) = - ----

sg'cm2 RT6E

[7) ,-

_,.t I

li•• J • ..J

!,

1

where 1= disc thickness and Caions.

is the activity of chloridesake ot:icatedllow to

The equation may be also writen:J R T 1

lution,sed in

Our ---------- [8)z F Ca aE

J in which all parameters are known and J can be calculated from anexperimental test in which the amount of chlorides is monitoredalong the time. Thus, from a plot similar to that of figure 4, theflux J can be calculated from the slope of the linear part.

runt; inCalculation of Ddi' from the value of intensity. Nernst-Binsteinequation

ing the.1e factlers offor thele only

I, Another way to calculate D~ is from the recording of the intensityduring the experiment, because it is also well established (36) (39-43) that the flux of a migrating species is also proportional tothe total intensity:

can beif only J= [9)

sideredswell,

nFbeing the transference number (of the chloride in this particular

'tease)the proportionality factor. Therefore, on the contrary fromhe value of J obtained in an experimental test, it is possible to

736 C.AndrIde Vol. 23. No. 3

calcu~ate th~ transference number ~, and by substitution ofequat10n [9) 1n equation [7), the following is obtained:

ZF------ = [10)

nF 1RT

This expression results similar to Nernst-Einstein (32) equationbut applied for a single ionic species through the use of thetransference number:

RT 1 1RT[ 11)

A

being A = cross section area of the concrete disc. This equationopens the door to the possibility of calculation of DiffusionCoefficients from a simple measurement of resistivity orconductivity providing that tj of the particular ion could beaccurately calculated (see numerical example later on). Thisapproach would represent a very promising 'simple way for thefuture, if the theoretical difficulties of calculating accuratetransference numbers of chloride ions in concrete, could be solved.Even, as it will be presented at the numerical example, thisequation serves for an approximate calculation of the order ofmagnitude of D from water saturated concrete resistivity values,once proper account of the influence of the ionic strength of poresolution is considered (3)(44)(45)(46).Finally it has to be mentioned that, if the calculation is madefrom resistivity measurements the reaction with the ACJ is also'misled and therefore, the values obtained are those of D~ and not~of ~. .

0.1 M NoOH 0.5 M Noel

-O.~m

Figure 5. Simple representation of the cell for testingmigration.

•• rJlst-PJ

Figure 5.catholytffol1owin~cross-selD = 10-8•R = 1.98'F = 2306Z = 1

AppliedConcreteConsiderproduced

ClJ =

This isin thistestingIn figu:with theis giveJcan Lncra poterdiffusi,As an Eorder 0w/c •••0,by the Iresult

Calcul

ionionorbe

histheateed.

. ;' ... ..:.•.'I" t ,,'i",;' ,,'

.~rnst-PlaDk equationFigure 5 depicts an example in which NaCl 0.5 M is added to thecatholyte of'a igration cell and NaOHO. 1 M to tl\e;iiil.n-d~yte.Thetollowinq parameters are assumed:cross-section area: 30 cm'o ==. 0, cm2'Sg-1R":: 1.987.2cal mol-I.<1\1F c 2306 cal·volt·l·eq-1Z ::1 '#' ..•.•.''''.

, >J'''':J

12 V ~,1Applied potential between electrodes dE'nt

- ,n .concrete~thickness I = 0,5 cm.considering the activity equal to the concentration, the fluxproduced for a concrete having a Dctf of 10" cm2.s·1wo~ld be:

hisof

.es ,lore

(1)(23063)(l0")(0.5XIO·)(12) molJ = ---------------------------------= 0,47 x 10" -------(1.9872) (293)(0.5) s'cm2

iade1150not

This is the order of magnitude of the flux that will be recordedin this kind of experiments, and a period of several hours oftes~ing a~e needed in order to minimize errors in monitoring it.

,In fi~e 6 a qraphic representation of the variation of flux Jwith'those of D~, C and dE being the rest of parameters constant,is given. It is apparent that an increase of ~E from 2 to 20 volts,can increase one order of magnitude the flux. As was refered in (1)a potential of 2 volts almost does not influences the purediffusional flux.As an ~ample too, in (47) chloride fluxes are reported of theorder of ~bout 10 mmol/day for a concrete cured at 20°C and with aw/c ••0,5. Thus taken into account the experimental conditions usedby.the aut~ors and assuming an stationary flow, the Dctf values wouldreult the sensible value of:

-e .f'4,~;, J ;,,;,1 i lItfi.'!lt r:

~t· E -,~ ;:,

calculation;f~om intensity valuest~~theoretical A~lculation of chloride transfer~nce ~umber in as,oluFionO.2M NaOH to. 5M NaCI from equation [5]~will q1.v~ a valueof: . . ."', ;

- ~- t: .,.G 1; ;/t. 1L 1",:~ ': '",

, (0.5) (76.34)

--(~~~)(~~~~)~~~~~)(;~~;~)~(~~;)(~;;r~(b~i)(~~~~)=0.338

Fiqt

SUlI1lIIohlorecoAlteof' c

" - statis a

2DCI~cmi'sg ) t:> o=O.lmol/cm3

o 0 =0-35 "x 0 =0.5 "

NERNST - EINSTE IN EQUAT ION

Figure 7. Graphic representation of Nernst-Einstein equation (10)in function of chloride activity values.

summing up, Nernst-Plank equation has to be used when values ofchloride flux along time in a Migration Cell, are accuratelyrecorded, providing steady-state conditions are established.Alternatively, Nernst-Einstein equation may be used when insteadof chloride flux, intensity values are accurately recorded, steady-state conditions are operating and the chloride transference numberis also accurately calculated.

CONCLUSIONS

More than conclusions, the following paragraphs are a summary ofcomments which can be drawn up from a thorough study of basic bookson electrochemistry and a careful meditation on their applicationto the particular case of concrete.

The Rapid Chloride Permeability Test (AASHTO) in its presentformulation cannot inform on concrete permeability tochlorides. The recording of the total current passing acrossthe cell is a function of the amount and type of ions, but notof the chloride flux or chloride mobility.The calculation of ionic migration can be only rigorouslyressolved in homogeneous, binary and dilute solutions.Concrete and concrete pore solution is a polielectrolyte withhigh ionic strength and therefore, a rigourous calculationcannot be performed or results very difficult.

Vol. 23;'No.

(5) ~l

(6) .:I

(7) }

~: (

'1(8) I

1

~ (9) I]

(10) ]]

(11) ]

(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)

(22)(23)(24)(25)(26)

(27)

(28)(29)(30)

(31)

(32)

740 C.Andnde Vol. 23. No. 3

However, as approximate v~lues may be enough for practicalpurposes, simplified way~" of calculation of DiffusionCoefficient of chlorides' may be tried. This supposes theacceptance of some assumptions and uncertainties.Thus, assuming some simplifications, Nernst-Plank and Nernst-Einstein equations can be used in a disposition similar to adiffusion cell (migration cell): the main being to accept thatconvection does not operate inside the concrete and thatdiffusion is negligible compar-edto migration when electricalfields higher than 10v are operating.From equations, (8) and (11), Effective Diffusion Coefficient,DefT'can be calculated in an experiment of few days. Nernst-Plank equation can be used.when only chloride flux along timeis recorded and Nernst-Einstein equation when intensity valuesand chloride transference numbers are accurately applied andmeasured respectively.An extensive experimental program, which at present isbeing carried out by the author, is needed to check whetherthe assumptions considered are correct or not.

Finally it has to be mentioned that the same equations can beapplied to calculate ionic movements in the case of cathodicprotection, chloride removal or realkalization, although in thesecases a non-stationary process is established which makes moresophisticated the solution of equation (6) and (11). speciallyseems very attractive the ressolution in the case of chlorideremoval, because it may give the theoretical time needed todecrease the amount of chlorides below a certain threshold.

ACKNOWLEDGEMENTS

The author is grateful to several researchers for their commentsand experimental trials. First she is grateful to Dr. J. Galveleof Argentina for the discussion on the preliminary states of thepaper and the comments introduced in the final version. Thanks arealso given for the discussions to her colleagues at the Institute:Dr. S. GoBi and Dr. C. Alonso~ and finally to Mr. M.A. sanju~n forhis experimental trials.

Jfl)(2)

(3)

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It' JJ ,t

oHLORJDE DIFFUSION. AASHTO TEST. RESISTIVITY i i"'1'.,. ',. ;;"v~:

:tic~l'usions the

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of Concrete. Report No. FHWA/RD-81/119, August 1981, NTIS DBNo. 82140724.

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Jan-Feb, pp 19-24 (1991).

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