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# Polymer Chemistry. The Basic Concepts - Himenz P.C.

Himenz P.C. Polymer Chemistry. The Basic Concepts - Copyright, 1984. - 736 p.
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size to the ring polymer equilibrium.
Example 5.6
For the reaction
Cyclic alkane (CH2)j (liq) polymer (cryst)
330 Condensation or Step-Growth
Polymerization
the following values of ÄÍ° and AS° have been estimated at 25°C:
1 ÄÍ° (kJ mol"1) AS° (J Ê"1 òîÃ1)
4 -105.0 -55.2
6 +2.9 + 10.5
8 -34.7 +37.2
Evaluate AG° and Keq at 25°C for each of the polymerization reactions
and comment on the results.
Solution
We use the relationships AG° = ÄÍ° - T AS° and AG° = -RT In Keq, being
careful about units: T = 298 Ê and R = 8.314 J K-1 mol-1. Using the above
values of ÄÍ° and AS°, the following are readily calculated:
1 AG° (kJ mol"1) In Keq Keq
4 -88.5 35.7 3.3 X 1015
6 -0.19 0.08 1.08
8 -45.8 18.5 1.1 X 108
Several observations come to mind:
1. For both 1 = 4 and 1 = 8, the polymer is favored over the ring to a
far greater degree than for 1 = 6. In the latter case the difference
between ÄÍ° and T AS° is so small that there is probably no justification
for retaining as many figures as shown in the calculated results.
2. For 1 = 4, ÄÍ° makes a favorable contribution to AG°, while the
contribution of AS° is unfavorable. The effect of the former outweighs
the latter.
3. For 1 = 6 the contribution of ÄÍ° is unfavorable and that of AS° is
favorable. The specific values make T = 298 Ê very close to the
equilibrium temperature. This implies that the reaction is shifted to
favor polymer at higher temperatures and to favor the cyclic monomer at
lower temperatures. Since the difference between ÄÍ° and T AS° is so
small, the temperature dependence of ÄÍ° and AS° could alter this
conclusion.
4. For 1 = 8 both ÄÍ° and AS° contribute favorably to AG°.

Thus both combustion and polymerization data indicate a
stabilization of
rings in the neighborhood of 1 = 6.
Generally speaking, the replacement of carbon atoms in the rings by
-O- or
-NH- causes relatively minor alterations in the picture of ring
stability. For
Rings 'n Things
331
Table 5.8 Values for ÄÍ and AS for the Ring-Opening Polymerization,
Reaction (5.FF), for Monomers with the Indicated Values of 1
1 AH (kJ mol-1) AS (J K"1 mol"1)
5 -5.4 -30.5
6 -4.6 -25.1
7 -12.6 -4.6
8 -23.8 -16.7
9 -40.2 -
13 -6.3 -
Source : G. Odian, Principles of Polymerization, 1st ed., McGraw-Hill,
New York, 1970. Used with the permission of the McGraw-Hill Book Company.
evidence of this, we turn to the data in Table 5.8, which applies to the
ring-opening polymerization reaction (5.FF). Table 5.8 lists values of ÄÍ
and AS for the reaction of monomers with several different 1 values. The
values of AH follow the same trend as discussed above for the combustion
data. AS passes through a maximum as ring size increases. If we assume
that AH and AS values in Table 5.8 apply at 400 K, AG = -12.3 kJ mol-1
for 1 = 7, e-caprolactam, while this quantity is +3.7 kJ mol-1 for 1 = 5
(2-pyrrolidone) and +2.9 kJ mol-1 for 1 = 6 (2-piperidone). The negative
value of AG for the polymerization of e-caprolactam results in the
formation of the important product nylon-6. The positive values of AG for
rings with 1 = 5 and 1 = 6 reflects the special stability of rings of
this size.
Thermodynamics provides only one of the criteria for
polymerizability. A favorable value for AG says nothing about the rate of
a reaction. It is not particularly difficult to see that a reaction like
the reverse of (5.EE) becomes kinetically improbable for large values of
m, that is, for the cyclization of a large linear molecule. For the
terminal A and Â groups of a single chain to react with each other for
ring closure, they must first diffuse together. We have seen in Chap. 1
that for long chains the end-to-end distance varies with the square root
of the degree of polymerization, or with m1/2 in the present context. The
volume associated with a length of this magnitude varies with length3 ,
or m3/2 . Hence as m increases, the concentration of chain ends varies
with m-3/2. By contrast, the probability that an A group reacts with a Â
group from another molecule depends on the number of molecules present,
and the number of chains in a reaction mixture varies with m-1. Hence as
m increases, reaction between different molecules becomes increasingly
favored over ring closure simply by a dilution effect. Use of random walk
statistics clearly limits the above
332
Condensation or Step-Growth Polymerization
argument to chains which are considerably longer than others we have
discussed in this section.
At the smaller end of the size range, kinetic studies show that the
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