Step-growth polymerization
Step growth polymerizationinvolves a series of reactions in
which any two species (monomers, dimers, trimers, etc.) can react
at any time, leading to a larger moleculeHigh-molecular-weight
polymer is formed only near the end of the polymerization when most
of the monomer has been depletedthe stepwise reaction occurs
between pairs of chemically reactive or functional groups on the
reacting molecules accompanied by the elimination of a small
molecule such as water as a by-productFor step growth
polymerisation to take place monomer must have a functionality of
at least twoA molecule may be classified as mono, bi, or
polyfunctional depending on whether it has one, two, or greater
than two sites available for linking with other moleculesAll step
polymerizations fall into two groups depending on the type of
monomer(s) employed1. A-B type step-growth polymerization, where
only one type of monomer is involved the functional groups on the
monomer are different and capable of intramolecular reactionsE.g
formation of polyamide from amino acids
2. AA/BB type step-growth polymerization
more than one type of molecule is involved, the functional
groups on each type of monomer are the same, but capable of
intermolecular reaction with the other type of monomerE.g formation
of polyamide from the reaction of diamines with diacids
The two groups of reactions can be represented in a general
manner by the equations
The two groups of reactions can be represented in a general
manner by the equations
Kinetics of Step PolymerizationStep polymerization proceeds by a
relatively slow increase in molecular weight of the polymer. E.g
Synthesis of polyester from a diol and a diacidThe polymerization
proceeds in a stepwise manner with the molecular weight of the
polymer continuously increasing with timeThe rate of a step
polymerization is, therefore, the sum of the rates of reaction
between molecules of various sizes
The reaction between various sized molecules can be summarized
asTo simplify the kinetics of this process an assumption is made
that: the reactivities of both functional groups of a bifunctional
monomer are the same, the reactivity of one functional group of a
bifunctional reactant is the same irrespective of whether the other
functional group has reacted, and the reactivity of a functional
group is independent of the size of the molecule to which it is
attached (i.e., independent of the values of n and m)
These simplifying assumptions are referred to as the concept of
equal reactivity of functional groupsPolyesterification can be
taken as illustrative step polymerization for kinetic
analysisSimple esterification is a well-known acid catalyzed
reaction and polyesterification follows the same course
CASE 1: Self Catalyzed Step Polymerization: Polymerization
without Added Strong Acid
Consider esterification for the formation of polyester from a
glycol and a dibasic acid
The rate can be expressed interms of disappearance of the
carboxyl functional groups
In the absence of an added strong acid, a second molecule of the
acid being esterified acts as the catalystThe rate of
polyesterification process can be written as (1), but
[COOH]=[OH]rate constant k is independent of molecular size of
reacting species and is the same for all functional groupsSo eqn 1
can be written as (2a) (2b)
Where [M] is [OH] OR [COOH]. of Equation 2b yields (3)
Where [M] 0 is the initial (at t = 0) concentration of hydroxyl
or carboxyl groupsEqn 3 can be written in terms of the extent or
fraction of reaction, pP is defined as the fraction of the hydroxyl
or carboxyl functional groups that has reacted at time tThe
concentration [M] at time t of either hydroxyl or carboxyl groups
is then given by:
(4) , Combining eqn 3&4
(5)
N.B Plot of 1/ (1 p) 2 versus t should be linear
Determination of molecular weightFor stoichiometric amounts of
diol and diacid, the # of unreacted carboxyl groups N = the total #
of molecules present in the system at some time t.The
number-average degree of polymerization, Xn is defined as the
average number of structural units per polymer chain (6)
But [M] =
So (6) becomes (7) (Carothers eqn)
relates the degree of polymerization to the extent of
reactionThe number-average molecular weight Mn (8)
Mo is the mean of the molecular weights of the two structural
units,
Meg is the molecular weight of the end groups = 0
(8) becomes: (9)
Combining eqn 5&9 becomes (10)
CASE II: External Catalyzed Step Polymerization: Polymerization
with Added Acid
to the achieve high-molecular-weight products in reasonable
reaction times small amounts of externally strong acids are added
as catalystsWith the catalyst concentration kept constant
throughout the process, the rate expression becomes (11)
applies to reactions between stoichiometric concentrations of
the diol and diacid
intergrate (11) becomes (12) , in terms of extent of conversion
this becomes:
(13 a, b)
Xn increases with time (more feasible!)
Molecular Weight Control in Step PolymerizationIts important to
control of molecular weight in polymerizations as this tends to
affect the properties of the polymersDesired molecular weight can
be obtained by quenching the reaction (e.g., by cooling) at the
appropriate timepolymer obtained in this manner is unstable in that
subsequent heating leads to changes in molecular weight
This situation is avoided by adjusting the concentrations of the
two monomers (e.g., diol and diacid) so that they are slightly
nonstoichiometricOne of the reactants is present in slight excess.
The polymerization then proceeds to a point at which one reactant
is completely used up and all the chain ends possess the same
functional group; the group that is in excess
Another method of achieving the desired molecular weight is by
addition of a small amount of a monofunctional monomer, a monomer
with only one functional groupThe monofunctional monomer, often
referred to as a chain stopper, controls and limits the
polymerization of bifunctional monomersThe growing polymer yields
chain ends devoid of functional groups and therefore incapable of
further reaction.Different reactant systems are employed in step
polymerizations:TYPE 1: Polymerization of the bifunctional monomers
A-A and B-B : B-B is present in excessthe numbers of A and B
functional groups are given by NA and NB, respectively;NA and NB
are equal to twice the number of A-A and B-B molecules,r, is the
stoichiometric ratio or imbalance
The total number of monomer molecules is given by: (14)
Since each polymer chain has two chain ends, the total number of
polymer molecules is one half the total numbers of chain ends
(15)
p -fraction of the limiting groups (A groups) that have reacted
at a particular timeRp - fraction of B groups that have
reacted(1-p) &(1 rp) -fractions of unreacted A and B groupsNA
(1-p) and NB (1 rp) -total numbers of unreacted A and B groups
The number-average degree of polymerization Xn is the total
number of A-A and B-B molecules initially present divided by the
total number of polymer molecules (16) This shows the variation of
Xn with the stoichiometric imbalance r and the extent of reaction
p
When the two bifunctional monomers are present in stoichiometric
amounts (r = 1), (17)
On the other hand, for 100% conversion (p = 1), it becomes
(18)
Type 2polymerization of an equimolar mixture A-A and B-B by the
addition of small amounts of a monofunctional reactantThe same
equations that apply to a type 1 polymerization are also applicable
here, except that r must be redefined as:NB -# of B molecules
present NA = NB. The coefficient 2 in front of NB is required since
one B molecule has the same quantitative effect as one excess B-B
molecule in limiting the growth of a polymer chain
Type 3Read on type 3 :Polymerizations of A-B type monomersand
number fraction distribution and weight fraction distribution