valid, since the helix now is a flexible chain, albeit shorter and of
larger diameter.- Excluded volume and solvent quality. Up till here, the volume taken
up by the polymer itself, i.e.,ntimes the volume of a monomer,
has been neglected. In other words, such an ideal random chain
has no volume, which would imply that two different segments can
occupy the same place in the solvent at the same time. This is, of
course, physically impossible, which is why the statistics of a real
chain are different from those of a random walk (diffusion).
Instead of this, a self-avoiding random walk should be considered,
and the average conformation then is different, rm being
proportional ton^0 to the power 0.6, rather than 0.5. This means
that the molecule is more expanded than an ideal chain.
Another complication is that segments of a polymer
molecule may show a net interaction, either attractive or repulsive,
when close to each other. The tendency to interact is often
expressed in Flory’ssolvent–segment interaction parameterw.In
Section 3.2 the interaction energyUbetween solvent and solute
molecules is discussed.wis a dimensionless number proportional
toUnet, when adapting Eq. (3.2) (i.e.,Unet¼ 2 U 12 U 11 U 22 )
to interactions between solute molecules (1) and polymer segments
(2). Ifw¼0, i.e., there is no net solvent–segment interaction, the
conformation of a polymer molecule follows the self-avoiding
random walk just mentioned. In this case, the quality of the
solvent for the polymer is considered good. For a higherw, the
solvent has poorer quality. Forw¼ 0 :5 the solvent is said to be an
ideal or theta solvent: the net attraction between segments and the
effect of finite segment volume just compensate each other. This
means that the polymer molecule behaves as if it had no volume,
so that its conformation will be like that of an ideal chain ofn’
segments. Examples of the segment distributions for a polymer in
a good and an ideal solvent are in Figure 6.5.
Note Actually, the solvent–segment interaction may also involve
an entropic contribution called contact entropy, especially when the
solvent is water; see Section 3.2.
The solvent–polymer interaction can also be described by
other parameters, and in the following the excluded volume
parameterbwill be used. It is the factor by which the segment
volume must be multiplied in order to describe the conformation
of the polymer. It follows thatb¼ 1 2 w. For an ideal solvent,
b¼0, and ifb¼1, the conformation of the molecule follows a