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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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point to which the generality extends.
In this section and the last, we have examined the lattice model of
the Flory-Huggins theory for general expressions relating AHm and ASm to
the composition of the mixture. The separate components can therefore be
put together to give an expression for AGm as a function of temperature
and composition:
AGm = - T ASm = RT[N0!02x- (xt ln + x2 In 02)]
The contribution of ASm to this expression is given by Eq. (8.37) and is
always positive; hence it contributes to a negative value of AGm. The AHm
contribution, on the other hand, can be either positive or negative. If
,as given by Eq. (8.41), is negative, this also contributes to a
negative value for AGm. If is positive, however, ASm and AHm make
opposing contributions to AGm, and the net effect depends on the
magnitudes of the quantities involved. We shall return to an examination
of this possibility in Sec. 8.6.
There are several reasons for devoting so much attention to the
foregoing derivation of AGm. For one thing, a theory like this gives the
reader a "feel" for the origin of the various effects, which is valuable
even if the theory is somewhat oversimplified. This feature is of
considerable value in a textbook such as this. In addition, theories help
us both in the interpretation and the prediction of experimental
observations. We shall apply the ideas of the Flory-Huggins theory to the
interpretation of experiments in later sections. For the present let us
consider the predictive aspect. Suppose, for example, that a researcher
is seeking a solvent for a particular polymer such that the two would
show athermal mixing. The foregoing theory suggests that the search
should focus on solvents for which the interaction with polymer molecules
and among its own molecules are similar to polymer-polymer interactions.
In this sense, Eq. (8.40) quantifies the rule of thumb "like dissolves
like"; with no opposition from enthalpy, entropy considerations guarantee
mixing. In the next section we shall develop this idea still further,
although for a more limited range of systems.
8.5 Cohesive Energy Density
It is not particularly difficult to find macroscopic measures of
interactions between small molecules of the same type, that is,
quantities which are proportional to Wu and w22 in Eq. (8.40). Among the
possibilities, we consider the change in internal energy AUV for the
vaporization process for component i. This can be related to w;i in terms
of the lattice model by the expression
AUVji = fczNwji where N equals Avogadro's number when AUV is written
per mole.
Cohesive Energy Density
A more troublesome quantity is the interaction w12 between different
species. It seems reasonable to expect this quantity to be some sort of
hybrid of the w's for the separate components, at least provided that the
mixing does not open the possibility for some specific interactions that
is nonexistent among molecules of the pure components. We therefore
postulate that no such possibility exists and consider for the remainder
of this section only nonspecific interactions. In terms of the types of
intermolecular forces enumerated in the last section, London and dipole-
dipole attractions are certainly less specific than either acid-base or
hydrogen bond interactions. The first two types are essentially physical
interactions, depending on the distribution of charge in the interacting
species. London forces are proportional to the polarizability of the
molecules; dipole-dipole forces are proportional to their permanent
dipole moments. These molecular parameters are also discussed in Sec.
10.3. While different molecules differ in the specific values of their
polarizability and dipole moment, the notion that some sort of average
value of these properties applies to the mixed interaction seems quite
plausible. By contrast, the acidity or basicity of a molecule is the
consequence of either empty or filled orbitals, and describing their
interaction in terms of an "average orbital occupancy" is meaningless.
The application of these ideas to the mixing of low molecular weight
liquids has been the object of extensive research. As a result of these
investigations, the appropriate kind of "hybridization" of individual
molecular properties in w12 is found to be the geometrical mean:
w 12 = V wnw22
As argued above, this result is found to work best for substances in
which both
the 1,1 and 2,2 forces are either London or dipole-dipole. Even the case
of one molecule with a permanent dipole moment interacting with a
molecule which has only polarizability and no permanent dipole moment-
such species interact by permanent dipole-induced dipole attraction-is
not satisfactorily approximated by Eq. (8.46). In this context the "like
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