Table Of ContentLIST OF ARTICLES ON THERMODYNAMICS OF POLYMERIZATION
BY HIDEO SAWADA PUBLISHED IN POLYMER REVIEWS
Sawada, Hideo (1969) 'Thermodynamics of Polymerization. I', Polymer Reviews, 3, 313 — 338
DOI: 10.1080/15583726908545926
URL: http://dx.doi.org/10.1080/15583726908545926
Sawada, Hideo (1969) 'Chapter 2. Heat of Polymerization', Polymer Reviews, 3, 339 — 356
DOI: 10.1080/15583726908545927
URL: http://dx.doi.org/10.1080/15583726908545927
Sawada, Hideo (1969) 'Chapter 3. Thermodynamics of Radical Polymerization', Polymer Reviews,
3, 357 — 386
DOI: 10.1080/15583726908545928
URL: http://dx.doi.org/10.1080/15583726908545928
Sawada, Hideo ((1969) 'Chapter 4. Thermodynamics of Polycondensation', Polymer Reviews, 3,
387 — 395
DOI: 10.1080/15583726908545929
URL: http://dx.doi.org/10.1080/15583726908545929
Sawada, Hideo (1970) 'Thermodynamics of Polymerization. II. Thermodynamics of Ring-
Opening Polymerization', Polymer Reviews, 5, 151 — 173
DOI: 10.1080/15583727008085366
URL: http://dx.doi.org/10.1080/15583727008085366
Sawada, Hideo (1972) 'Thermodynamics of Polymerization. III', Polymer Reviews, 7, 161 — 187
DOI: 10.1080/15321797208068162
URL: http://dx.doi.org/10.1080/15321797208068162
Sawada, Hideo (1972) 'Thermodynamics of Polymerization. IV. Thermodynamics of Equilibrium
Polymerization', Polymer Reviews, 8, 235 — 288
DOI: 10.1080/15321797208068172
URL: http://dx.doi.org/10.1080/15321797208068172
Sawada, Hideo (1974) 'Thermodynamics of Polymerization. V. Thermodynamics of
Copolymerization. Part I', Polymer Reviews, 10, 293 — 353
DOI: 10.1080/15321797408076101
URL: http://dx.doi.org/10.1080/15321797408076101
Sawada, Hideo (1974) 'Thermodynamics of Polymerization. VI. Thermodynamics of
Copolymerization. Part 2', Polymer Reviews, 11, 257 — 297
DOI: 10.1080/15583727408546025
URL: http://dx.doi.org/10.1080/15583727408546025
Table of Contents
Thermodynamics of Polymerization. I 5
Chapter 1. Introductory Survey 5
I. THE CEILING TEMPERATURE CONCEPT 6
A. Thermodynamic Approach 6
B. Kinetic Approach 7
C. Determination of Ceiling Temperatures 11
II. ENTROPY AND FREE ENERGY CHANGES OF
POLYMERIZATION 14
A. Entropy of Polymerization 14
B. Determination of Entropy of Polymerization 16
C. Free Energy Changes of Polymerization 22
REFERENCES 29
Chapter 2. Heat of Polymerization 31
I. GENERAL ASPECTS 31
A. Breaking a Multiple Bond 32
B. Resonance 32
C. Steric Strain 33
II. VARIATIONS IN HEATS OF POLYMERIZATION 33
A. Steric Strain in the Polymer 35
B. Conjugation and Hyperconjugation 38
C. Hydrogen Bond and Solvation 39
III. EMPIRICAL ESTIMATION OF HEAT OF POLYMERIZATION 39
REFERENCES 41
APPENDIX 42
Chapter 3. Thermodynamics of Radical Polymerization 49
I. GENERAL ASPECTS 50
A. Energetics of Radical Polymerization 50
B. Degree of Polymerization 51
C. Activation Energies of Elementary Reactions 53
II. GENERATION OF FREE RADICALS 53
III. PROPAGATION REACTION 58
A. The Polanyi Relation 58
B. Reactivity and Heat of Polymerization 60
C. Ceiling Temperature 63
IV. INTERACTION OF RADICALS 63
A. Combination and Disproportionation Reactions 63
B. Interaction of Small Hydrocarbon Radicals 64
C. Interaction of Large Hydrocarbon Radicals 65
D. Interaction of Some Large Radicals 66
V. FREE ENERGIES OF FORMATION OF POLYETHYLENE
AND POLYTETRAFLUOROETHYLENE 68
A. Free Energies of Polyethylene Synthesis 68
B. Free Energies of Polytetrafluoroethylene Synthesis 73
REFERENCES 77
Chapter 4. Thermodynamics of Polycondensation 79
I. GENERAL ASPECTS 79
II. DEGREE OF POLYMERIZATION 80
III. EQUILIBRIUM CONSTANT 81
IV. RING FORMATION IN POLYCONDENSATION 86
ACKNOWLEDGMENTS 87
References 87
Thermodynamics of Polymerization. II. Thermodynamics of
Ring-Opening Polymerization 88
I. GENERAL ASPECTS 88
II. HOMOCYCLIC COMPOUNDS 89
A. Angle Strain 89
B. Conformational and Transannular Strain 99
C. Steric Effect of Side Group 100
III. HETEROCYCLIC COMPOUNDS 102
A. Cyclic Ethers 103
B. Lactams 105
C. Lactones 107
D. Miscellaneous Heterocyclic Compounds 107
IV. SUMMARY 109
ACKNOWLEDGMENTS 109
References 109
Thermodynamics of Polymerization. III (Cationic Polymerization) 111
I. GENERAL ASPECTS 112
II. FORMATION OF CARBONIUM ION 114
A. Ionization Potential 114
B. Proton Affinity 115
C. Acidity 118
D. Free Energy Change of Formation of Carbonium Ion 119
E. Ions and Ion Pairs 121
F. Energetics of Salvation 122
III. INITIATION OF CATIONIC POLYMERIZATION 124
A. Energetic Consideration of Initiation Reaction by Halogen Acid 124
B. Catalytic Activity in Cationic Polymerization by Lewis Acids 126
IV. PROPAGATION OF CATIONIC POLYMERIZATION 127
A. Energetics 127
B. Heats of Reaction of Cations with Olefins 129
C. Activation Entropy Changes of Propagation 132
D. Thermodynamics of Formation of Zwitterions 134
V. CHAIN TRANSFER AND TERMINATION 136
Acknowledgments 136
References 136
Thermodynamics of Polymerization. IV. Thermodynamics of
Equilibrium Polymerization 138
I. POSSIBLE TYPES OF EQUILIBRIUM POLYMERIZATION 139
II. SOME CASE STUDIES OF EQUILIBRIUM POLYMERIZATION 146
A. Vinyl Polymerizations 147
B. Ring-Opening Polymerizations 150
C. Polymerization of Aldehydes 165
III. TRANSITION PHENOMENA IN EQUILIBRIUM
POLYMERIZATION 167
IV. MOLECULAR WEIGHT DISTRIBUTION 173
A. Equilibrium Polymerization 173
B. Living Polymerization 179
V, THERMODYNAMICS OF EQUILIBRIUM POLYMERIZATION 183
Acknowledgment 188
References 189
Thermodynamics of Polymerization. V. Thermodynamics of
Copolymerization. Part I 192
I. THE GENERAL THEORY OF BINARY COPOLYMERIZATION 193
A. Heat of Copolymerization 193
B. Entropy of Copolymerization 200
C. Equilibrium Sequence Distribution 203
D. Free Energy Change in Binary Copolymerization System 209
E. Equilibrium Monomer Concentration 217
F. Penultimate Unit Effect 222
II. DEGREE OF POLYMERIZATION AND COPOLYMER
COMPOSITION OF BINARY COPOLYMERIZATION SYSTEM 224
A. Degree of Polymerization 224
B. Copolymer Composition Equation 228
III. MULTICOMPONENT COPOLYMERIZATION 243
A. Heat of Terpolymerization 243
B. General Theory of Multicomponent Copolymerization 248
Acknowledgment 250
References 251
Thermodynamics of Polymerization. VI. Thermodynamics of
Copolymerization. Part 2 253
I. RADICAL COPOLYMERIZATION 254
A. Heat of Copolymerization 254
B. Ceiling Temperature 259
C. Q-e Scheme 263
D. Substituent Effect 265
E. Effect of Polymerization Temperature 268
F. Effect of Solvent 272
II. IONIC COPOLYMERIZATION 274
A. Energetic Characteristics 274
B. Reactivity 279
C. Effect of Polymerization Temperature 280
III. OTHER COPOLYMERIZATIONS 282
A. Ring-Opening Copolymerization 282
B. Miscellaneous Copolymerizations 284
Acknowledgment 290
References 290
Thermodynamics of Polymerization. I
HIDEO SAWADA
Central Research Laboratory
Daicel Ltd.
Tsunigaoka, Oi, Intmagwi
Saitama, Japan
Chapter 1. Introductory Survey
I. THE CEILING TEMPERATURE CONCEPT 314
A. Thermodynamic Approach ; 314
B. Kinetic Approach 315
C. Determination of Ceiling Temperatures 319
II. ENTROPY AND FREE ENERGY CHANGES OF POLYM-
ERIZATION 322
A. Entropy of Polymerization 322
B. Determination of Entropy of Polymerization 324
C. Free Energy Changes of Polymerization 330
REFERENCES 337
313
314 HIDEO SAWADA
I. THE CEILING TEMPERATURE CONCEPT
A. Thermodynamic Approach
The Gib'bs free energy of a system at temperature T is defined as
G = H - TS (1)
where H is the enthalpy and S the entropy of the system. The free
energy change for any polymerization will be, therefore,
AG = Gpoiymer ~ G
monomer
= "polymer ~ H — T^Spoiyj^ej.— S ) (2)
monomer monomer
= AH -T AS
p
When the polymer has a lower free energy than the initial mono-
mer, a polymerization can occur spontaneously, and the sign of AG
is negative. A positive sign for AG signifies, therefore, that the
polymerization is not spontaneous. When the system is in equilib-
rium at a certain critical temperature, there is no tendency for
polymerization, and, hence, AG = 0 [1-3]. This temperature is
known as the ceiling temperature. These three possible conditions
for free energy change of polymerization may be summarized as
follows:
monomer — polymer AG = - (spontaneous)
monomer — polymer AG = + (nonspontaneous)
monomer — polymer AG = 0 (equilibrium)
At the ceiling temperature, T , AG is zero, so that
c
T = AHp/AS (3)
c p
where AHp and ASp are the enthalpy and entropy changes per mono-
mer unit. When the polymer chains are long these quantities are
identical with the heat and entropy changes of polymerization. If the
standard state refers to unit concentration and the monomer behaves
ideally, AS = AS° + R In [M]; thus
T AS° + R In [M] (4)
THERMODYNAMICS OF POLYMERIZATION. I 315
where AS0 is the entropy change accompanying polymerization at the
standard state when the concentration of monomer is unity. There-
fore, T can be raised by increasing the concentration of monomer
c
when a solvent is present. Equation (4) emphasizes that T is char-
c
acteristic of monomer-polymer equilibrium only and is quite inde-
pendent of the monomer or the nature of the active centers in the
system; for a given value of [M], the ceiling temperature should,
therefore, be the same whether the active centers are radicals or
ions.
Many polymers are stable even above the ceiling temperature
only because of the difficulty of initiating degradative centers on the
polymer molecule. In practice, terminated polymer appears stable
at temperatures above the ceiling temperature, being in a state of
metastable equilibrium. Therefore, the polymer cannot depolymerize
spontaneously but can do so under appropriate conditions. Catalyst
residues that are not removed during the purification of a polymer
may also cause depolymerization reaction.
There are four important possibilities of polymerization as follows:
a. In addition polymerization, AH and AS are usually both nega-
tive, and so AG becomes positive above the ceiling temperature of
the system. Thus, the high polymer cannot be formed above the ceil-
ing temperature.
b. If the polymerization is endothermic (AH > 0) and AS is greater
than zero, no polymer can exist below a floor temperature, above
which AG becomes negative. The phenomenon of floor temperature
is exhibited by the polymerization of S rings.
8
c. When AH is positive and AS negative, AG is always positive;
therefore, polymer cannot exist at any temperature.
d. When AH is negative and AS positive, AG is always negative;
therefore, polymer can exist at any temperature.
B. Kinetic Approach
It is interesting to consider the ceiling temperature phenomenon
from a kinetic point of view [1,3]. At ordinary temperatures the
rate constant for depolymerization is small. However, the activation
energy of this rate constant is quite high (10-26 kcal/mole) compared
to that for propagation, and at high temperature the depolymerization
can become important compared with the polymerization.
Let us consider the propagation reaction
p
k^ AAAARn*i
316 HIDEO SAWADA
The rate constants for propagation and depropagation reactions can
be expressed as
k = A exp(-E /RT), k = A exp(-E /RT)
p p p d d d
where A and A are the collision frequency factors which approxi-
p d
mate to the entropy of activation, and E and E are the activation
p d
energies for polymerization and depolymerization, respectively. If
the degree of polymerization is large, E - E = AHp. For long
p d
chains, AHp is equal to the heat of the overall polymerization.
The rate of propagation is essentially the same as the overall
rate of disappearance of monomer, since the number of monomers
used in chain transfer and initiation must be small compared to that
used in propagation if the polymer chains are long.
Therefore,
^I (5)
where [M*] is the concentration of propagating species, and [M] is
the concentration of monomer.
Depolymerization may now be considered to be the reverse of
propagation, then
vd = kdtMnl (6
Thus the overall rate of polymerization is
The degree of polymerization is given by the rate of polymerization
divided by the rate of termination, i.e.,
_ (k -k [M])[M
d p n] (8)
f([M ])
n
where f([M*]) is a function of the number of active centers, M*,
present.
AHp is usually negative (the polymerization is exothermic), and
so E is usually much larger than E . Therefore, although k may
d p d
be negligible compared with kp[M] at ordinary temperature, it will
increase more rapidly with increasing temperature.
At the ceiling temperature T the rate of depropagation becomes
c
THERMODYNAMICS OF POLYMERIZATION.
equal to that of propagation, regardless of the variations of [MJ^] and
) with temperature,
k [M*][M] =
p
which can also be written in the form:
A exp(-E /RT )[M] = A exp(-E /RT ) (9)
p p c d d c
and, therefore,
Ep - E AH
d p
Tc - R In (A [M]/A ) ~ R In (A [M]/A ) U0)
p d p d
At this temperature, the extrapolated Rp vs T and DP vs T curves
will cut the temperature axis. This is illustrated in Fig. 1.1. At
temperatures that are not far below the ceiling temperature, only
polymers of low molecular weight form.
It seems to be impossible to predict the variations of Rp and DP
with temperature right up to T from Eqs. (7) and (8). When k ap-
c d
proaches kp[M ], DP becomes small and consumption of monomer
x
in the initiation process is no longer negligible. Then, k and k
p d
may show a dependence on DP. Nevertheless the limiting slope of
dRp/dT as T approaches T may be numerically so large that such
c
effects are of very minor importance and operate only over the last
fraction of a degree below T . The limiting slope for the rate vs
c
temperature curve can be obtained by differentiating Eq. (7) with
respect to temperature:
dR /dT = [M*](k [M]E /RT*-k E /RT2)
p p p d d
+ (k [M]-k )d[M*]/dT
p d
and substituting k [M] = k when T = T :
p d c
lim (dR /dT) = k [M][M*] (E - E )/RT
T c p p p d C (n)
= k [M][M*]AH /RT
p p c
Then k[M][Mj![] is the rate that would have been observed at T in
p c
the absence of depropagation.
From transition state theory the frequency factor is given by
A = (kT/h) exp(AS*/R). Therefore,
