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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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inventory of interactions can now be made for the mixture:
1. Each polymer segment (subscript 2) is surrounded, on the average, by
z2 polymer segments and z0t solvent molecules.
2. The contribution to the energy of this polymer segment interacting
its neighbors is z2w22 + w12 .
3. Since the lattice consists of N sites of which 02N are occupied by
polymer segments, the contribution to the energy of all interactions of
the sort described in item (2) is {lA) z02N[(l - 0i)w22 + 0iW12]. The
factor lA has been introduced, since all pairs are counted twice in
calculating this total.
4. Each solvent molecule (subscript 1) is surrounded, on the average,
by z2 polymer segments and zl solvent molecules.
5. The contribution to the energy of this molecule interacting with its
neighbors is z2wl2 + z0!Wu .
6. In parallel with item (3), the contribution of all solvent
interactions to the total energy is (Vl) z0tN[02w12 + (1 - 02)wn],
7. When either pure component is considered, all w12 terms are zero, as
well as the terms containing the volume fraction of the other component.
Thus, for pure polymer, item (3) becomes (^)z02Nw22, and for the pure
solvent item (6) becomes (1/i)z01Nw11.
The value of AHm can be assembled from the foregoing by adding the
energy contributions of items (3) and (6) and subtracting the
contributions of the pure components given by item (7):
= (1/i)zN(20102W12 - ! 02 w!! - 2^22)
or, substituting Eq. (8.39),
AHm = (1/i)zN0102 Aw
Since V Aw is the change in interaction energy per 1,2 pair, it can be
expressed as some multiple \ of kT per pair or of RT per mole of pairs.
It is also conventional to consolidate the lattice coordination number
and x into a single parameter x, since z and x' are not measured
separately. With this change of notation Viz Aw is replaced by its
equivalent xRT, and Eq. (8.41) becomes
The Flory-Huggins Theory: The Enthalpy of Mixing
AHm = N^xRT = N102 X RT
The quantity x is called the Flory-Huggins interaction parameter: It is
zero for athermal mixtures, positive for endothermic mixing, and negative
for exothermic mixing. These differences in sign originate from Eq.
(8.39) and reaction (8.A).
Until now we have been purposely vague about the quantity Aw. Since
we shall use the notation of Eq. (8.42) from now on, it is convenient to
say a few more things about Aw before we lose sight of it entirely.
Reaction (8.A) is clear enough; what is unspecific are the conditions
under which this "reaction" takes place. Several possibilities come to
mind, and each imparts a slightly different meaning to the "energy" w:
1. Since the solvent molecules, the polymer segments, and the lattice
sites are all assumed to be equal in volume, reaction (8.A) implies
constant volume conditions. Under these conditions, AU is needed and what
we have called Aw might be better viewed as the contribution to the
internal energy of a pairwise interaction AUpair, where the subscript
reminds us that this is the contribution of a single pair formation by
reaction A.
2. Especially for large values of Aw, there could be an additional
entropy effect beyond that calculated in the last section which arises
from the interaction of nearest neighbors. That is, reaction (8.A) might
be characterized by both a AHpair and a ASpair. In this case Aw might be
viewed as the pairwise contribution to a free energy AGpair with
= AHpair-TASpair
3. In writing Eq. (8.41), we have clearly treated Aw as a contribution
to enthalpy. This means we neglect volume changes (AHpair versus AUpair)
and entropy changes beyond the configurational changes discussed in the
last section (AGpair versus AHpair). In a subsequent development it is
convenient to allow an additional entropy effect, and we shall return to
Eq. (8.43) at that point.
The equations we have written until now in this section impose no
restrictions on the species they describe or on the origin of the
interaction energy. Volume and entropy effects associated with reaction
(8.A) will be less if x is not too large. Aside from this consideration,
any of the intermolecular forces listed above could be responsible for
the specific value of x- The relationships for ASm in the last section
are based on a specific model and are subject to whatever limitations
that imposes. There is nothing in the formalism for AHm that we have
developed until now that is obviously inapplicable to certain specific
systems. In the next section we shall introduce another approximation
Thermodynamics of Polymer Solutions
which will impose such a limitation, so it is important to recognize the
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