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