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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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solutions; a variety of other thermodynamic phenomena are ignored. In
this regard the chapter title would better read "Some aspects of . . . ."
Throughout this volume only a small part of what might be said about any
topic is actually presented, so this modifying phrase is taken to be
understood and is omitted.
In another sense the title is too restrictive, implying that only
pure, phenomenological thermodynamics are discussed herein. Actually,
this is far from true. Both thermodynamics and statistical thermodynamics
comprise the contents of the chapter, with the second making the larger
contribution. But the term statistical is omitted from the title, as it
is too intimidating.
The phenomena we discuss, phase separation and osmotic pressure, are
developed with particular attention to their applications in polymer
characterization. Phase separation can be used to fractionate poly
disperse polymer specimens into samples in which the molecular weight
distribution is more narrow. Osmostic pressure experiments can be used to
provide absolute values for the number average molecular weight of a
polymer. Alternative methods for both fractionation and molecular weight
determination exist, but the methods discussed in this chapter occupy a
place of prominence among the alternatives, both historically and in
contemporary practice.
505
506
Thermodynamics of Polymer Solutions
Throughout this book we have emphasized fundamental concepts, and
looking at the statistical basis for the phenomena we consider is the way
this point of view is maintained in this chapter. All theories are based
on models which only approximate the physical reality. To the extent that
a model is successful, however, it represents at least some features of
the actual system in a manageable way. This makes the study of such
models valuable, even if the fully developed theory falls short of
perfect success in quantitatively describing nature.
We shall devote a considerable portion of this chapter to discussing
the thermodynamics of mixing according to the Flory-Huggins theory. Other
important concepts we discuss in less detail include the cohesive energy
density, the Flory-Krigbaum theory, and a brief look at charged polymers.
This is really the first time in this text that we have explicitly
considered charged polymers as such. Even in the case of polymers
prepared by ionic mechanisms, we tend to ignore the charge associated
with the chain end as an insignificant end effect. Polymers in which
ionizable functional groups occur throughout the molecule also exist, and
these may carry quite high charges. Many biopolymers fall into this
category. Even though we consider only a single aspect of charged
polymers in this chapter, a number of pertinent considerations are
clearly revealed.
8.2 Classical and Statistical Thermodynamics
In this chapter we shall consider some thermodynamic properties of
solutions in which a polymer is the solute and some low molecular weight
species is the solvent. Our special interest is in the application of
solution thermodynamics to problems of phase equilibrium.
An important fact to remember about the field of thermodynamics is
that it is blind to details concerning the structure of matter.
Thermodynamics are concerned with observable, measurable quantities and
the relationships between them, although there is a danger of losing
sight of this fact in the somewhat abstract mathematical formalism of the
subject. In discussing elasticity in Chap. 3, we took the position that
entropy is often more intelligible from a statistical, atomistic point of
view than from a purely phenomenological perspective. It is the latter
that is pure thermodynamics; the former is the approach of statistical
thermodynamics. In this chapter, too, we shall make extensive use of the
statistical point of view to understand the molecular origin of certain
phenomena.
The treatment of heat capacity in physical chemistry provides an
excellent and familiar example of the relationship between pure and
statistical thermodynamics. Heat capacity is defined experimentally and
is measured by determining the heat required to change the temperature of
a sample in, say,
Classical and Statistical Thermodynamics
507
a constant-pressure experiment. Numerous thermodynamic equations exist
which relate the heat capacity to other thermodynamic quantities such as
and AS. An alternative approach to heat capacity is to account for the
storage of energy in molecules in terms of the various translational,
rotational, and vibrational storage modes. Doing thermodynamics does not
require so much as a knowledge that molecules exist, and much less how
they store energy; understanding thermodynamics benefits considerably
from the molecular point of view.
The drawback of the statistical approach is that it depends on a
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