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

Himenz P.C. Polymer Chemistry. The Basic Concepts - Copyright, 1984. - 736 p.
Download (direct link): polymerchemistry1984.djvu
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fusion process is called a first-order transition. Vaporization and other
familiar phase transitions are also first-order transitions. The behavior
of V at Tg in Fig. 4.1 shows that the glass transition is not a first-
order transition. One of the objectives of this chapter is to gain a
better understanding of what else it might be. We shall return to this in
Sec. 4.8.
At T~, AGf = 0, but ASf, AVf, and AHf have nonzero values. For any
constant-temperature process such as fusion,
AG = AH - T AS
(4.4)
therefore at equilibrium AHf
T" = --
(4.5)
m ASf
V '
This fundamental relationship points out that the temperature at
which crystal and liquid are in equilibrium is determined by the
balancing of entropy and enthalpy effects. Remember, it is the difference
between the crystal and
208
The Glassy and Crystalline States
the liquid that is pertinent; sometimes these differences are not what
we might first expect.
Table 4.1 lists values of Tm as well as AHf and ASf per mole of
repeat units for several polymers. A variety of experiments and methods
of analysis have been used to evaluate these data, and because of an
assortment of experimental and theoretical approximations, the values
should be regarded as approximate. We assume Tm s T". In general, both
AHf and ASf may be broken into contributions H0 and S0 which are
independent of molecular weight and increments AHf 1 and ASf 1 for each
repeat unit in the chain. Therefore AHf = H0 + n AHf j, where n is the
degree of polymerization. In the limit of n -> AHf = n AHf j and ASf = n
ASf j, so T" = AHf l/ASf j. The values of AHf j and ASf j in Table 4.1
are expressed per mole of repeat units on this basis. Since no simple
trends exist within these data, the entries in Table 4.1 appear in
numbered sets, and some observations concerning these sets are listed
here:
1. Polyethylene. The crystal structure of this polymer is essentially
the same as those of linear alkanes containing 20-40 carbon atoms, and
the values of Tm and AHf j are what would be expected on the basis of an
extrapolation from data on the alkanes. Since there are no chain
substituents or intermolecular forces other than London forces in
polyethylene, we shall compare other polymers to it as a reference
substance.
2. Poly(l ,4-cis-isoprene). Although AHf j is slightly higher than that
of polyethylene, it is still completely reasonable for a hydrocarbon. The
Table 4.1 Values of Tm, AHf j, and ASf j for Several Polymers3
Polymer Tm (c) Per mole repeat units
AHf j (J mol'1) ASf (J K'1 mol'1)
1. Polyethylene 137.5 4,020 9.8
2. Poly (1,4- cis- isoprene) 28 4,390 14.5
3. Poly(ethylene oxide) 66 8,280 22.4
4. Poly(decamethylene 80 50,200 142.3
sebacate)
Poly(decamethylene 69 41,840 121.3
azelate)
5. Poly(decamethylene 216 34,700 71.1
sebacamide)
Poly(decamethylene 214 36,800 75.3
azelamide)
aThis notation indicates the contribution to the value for the fusion
process (subscript f) per mole of repeat units (subscript 1). Entries are
discussed by number in the text.
Source: Data from Ref. 5.
The Thermodynamics of Crystallization
209
lower Tm is the result of a value of ASf j, which is 50% higher than
that of polyethylene. The low melting point of this polymer makes natural
rubber a useful elastomer at ordinary temperatures.
3. Poly(ethylene oxide). Although AHf j is more than double that of
polyethylene, the effect is offset by an even greater increase for ASf j.
The latter may be due to increased chain flexibility in the liquid caused
by the regular insertion of ether oxygens along the chain backbone.
4. Polyesters. The next two polyesters have AHf j values an order of
magnitude higher than polyethylene. Our first thought might be to
attribute this to a strong interaction between the polar ester groups.
The repeat units of these compounds are considerably larger than in the
reference compound, so the AHf j values should be compared on a per gram
basis. When this is done, AHf j is actually less than for polyethylene.
This suggests that the larger value for AHf j is the result of a greater
number of methylene groups contributing London attraction for the
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