Polymer Chemistry, An Introduction: summary
Chapter 3: Polymerizability
Four conditions for a substance to meet in order to be able to polymerize as a monomer:
• A monomer must be at least difunctional;
• A monomer must be sufficiently reactive;
• A monomer must be very pure;
• Thermodynamics must allow a monomer to polymerize.
3.1 Functionality of monomers
Functionality of a monomer molecule is the number of chemical bonds it can form with other
molecules under the prevailing reaction conditions. For polymerization, a minimum functionality of 2
of both monomers is required: dicarboxylic acids (and cyclic anhydrides), diols, hydroxy acids (and
their cyclic lactones), diamines, amino acids (and cyclic lactams), diisocyanates, etc.
Also compounds with a reactive double bond or reactive ring can behave difunctionally.
Trifunctional monomers are, for instance, glycerol with three OH-groups.
Generally, the functionality of a monomer may depend on the polymerization conditions.
3.2 Reactivity of monomers
High degrees of polymerization with a slow reacting monomer would require long reaction
times, with a greater risk of undesired side reactions. Often, catalysts are applied. Increasing the
temperature would often only accelerate side reactions, which would result in a lowering of the average
degree of polymerization, even though product is formed faster.
Steric hindrance around functional groups should be avoided.
3.3 Purity of monomers
Monofunctional impurities may cause premature stopping of chain growth. Sometimes it is
desired to avoid formation of too high a molar mass polymer from very pure monomers. For
condensation polymerizations: by adding a monofunctional compound or by starting with non-
stoichiometric amounts of functional groups, the desired average molar mass can be precisely controlled.
For addition polymerization, chain transfer agents can control the polymer molar mass, and inhibitors
may even prevent start of polymerization.
3.4 Thermodynamics of polymerization
Polymerization only possible as long as the Gibbs free energy G of system decreases:
∆G = Gpol – Gmon < 0
At constant absolute temperature T we know that: ∆G = ∆H – T∆S.
If ∆G > 0, depolymerization will occur, while ∆G = 0, denotes a situation of chemical
equilibrium, where the rates of polymerization and depolymerization are equal.
Polymerization equilibrium occurs at a critical absolute temperature: Te = ∆H/∆S.
Exothermic polymerization, ∆H < 0 Endothermic polymerization, ∆H > 0
∆S > 0 Polymerization would be possible at each T Polymerization is possible if T∆S > ∆H
Floor temperature, Tf = ∆H/∆S
∆S < 0 Polymerization is possible if T|∆S| < |∆H| Polymerization is impossible at each T
Ceiling temperature, Tc = ∆H/∆S
1
, As a rule, entropy decreases (∆S < 0) upon
polymerization, because n separate monomer
molecules can be arranged in a larger number of
distinguishable ways than n monomer residues
connected in a single chain. This means that most
polymerizations must be exothermic and should
be performed below the ceiling temperature.
End groups can be stabilized; however, they can
still show depolymerization by thermal
degradation above ceiling temperature, which can
create new reactive chain ends.
(Back-)formation of cyclic monomers, dimers
from polymers below floor temperature can be explained by the fact that ring opening requires energy
while entropy can increase.
Chapter 4: Reactivity of polymer molecules
4.1 Flory’s principle of equal reactivity
Principle of equal reactivity: “The reactivities of all like functional groups are equal to each
other, irrespective the size of the polymer molecules to which they belong.”.
Therefore, it is sufficient to consider only one rate constant k for all propagation steps, and also only
one value k’ for the depolymerization. So, the reactivity of a functional group does not change if a
neighbouring group has reacted, and that the reactivity even becomes independent of the presence of a
second group in same molecule if the groups are separated by at least three CH2-units.
4.2 Influence of viscosity on reactivity
The duration of an encounter, of functional groups attached to different macro-molecules, and
consequently the number of collisions during each encounter will increase in a lower mobility state (high
viscosity). The distribution over time of collisions, in which any functional group participates, is
changed by a possibly lower mobility.
4.3 The functional group approach
All functional groups behave similarly in polymerization reactions and can be regarded as
reactants, whereas the polymer chain segments between or beside these groups are considered as a kind
of solvent. In the condensation polymerization, for the kinetics, we have to use concentrations of
functional groups, [-OH], [-COOH] and [-COO-], instead of concentrations of molecules.
During a redistribution reaction, the non-reacting end groups exchange polymer chains to which
they are attached. The average chain length remains the same but the chain length distribution alters.
Chapter 5: Condensation polymerization
5.1 Extent of reaction and average degree of polymerization
Polyesterification:
k
C + A Z + W
k’
Where, C = (number of) carboxylic acid groups Z = (number of) ester linkages
A = (number of) alcohol groups W = (number of) water molecules
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, U0 = total number of base units or monomer residues in the system.
If we start with U0 molecules of pure hydroxy acid (or ½ U0 of diol and ½ U0 of diacid), we know that:
C0 = A0 = U0 and Z0 = W0 = 0
p = the extent of reaction, or the fraction of functional groups which has reacted
$% &$ '% &'
𝑝= = ,
$% '%
From those equations, it follows that: C = A = (1-p) U0 and Z = W = C0 – C = pU0
Nt = total number of chain molecules, including monomer molecules
Nt = ½ (C + A) = (1-p) U0 (each linear chain contains two endgroups)
𝑃)* = number average degree of polymerization
*+,-./ 01 +*234 8% :
𝑃)* = = = , (:&;)8%
Carothers equation
*+,-./ 01 5672*4 :&;
Holds only for linear condensation polymers. To obtain polymers with interesting properties, almost
complete conversions are required.
For monomers with functionalities f > 2, branched/crosslinked polymers are formed:
C0 = A0 = ½ U0 f with, f = number of functionalities
The number of chains that disappear is half the number of groups that reacted.
8 :
𝑃)* = % = ? ,
=>
with, Nt = total number of polymer molecules
:& 1;
@
In practice, the network formation starts locally by the formation of small insoluble gel particles.
:
During first time, the gel point is reached, extent of reaction at point: 𝑝A.B = 1&:
5.2 Kinetics of condensation polymerization
Polyesterification:
k
C + A Z + W
k’
If we start with U0 molecules of pure hydroxy acid (or ½ U0 of diol and ½ U0 of diacid). Leads
D[$]
to a rate expression: − = 𝑘[𝐶][𝐴], in the case that W = 0, all water removed so that the reverse
D3
reaction does not contribute.
[𝐶] = [𝐴] =
(:&;)8% 𝑊.B
J
, with V = reaction volume and, 𝑝 = N𝑈
M
: 8%
𝑑 =𝑘 𝑑𝑡, with substituting in the rate expression and reorganisation.
:&; J
; : : 8% 3 8%
Integration results in: ∫M 𝑑 :&; = :&;
−1= 𝑘 J
∫M 𝑑𝑡 = 𝑘 J
𝑡
8
𝑃)* = 1 + 𝑘 J% 𝑡, substitution of the Carothers equation
Esterification reactions are usually catalysed by strong acids, the rate constant k is therefore
proportional to the constant catalyst concentration.
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