large distances along the polymer chain are referred to as long-range interactions.
In previous chapters, these short-range interactions were referred to as the chain
connectivity while the long-range interferences were referred to as the excluded volume
effects. Also shown in these chapters, it is convenient to separate the interactions
responsible for short-range and long-range interferences. This separation produces
polymer theories in which the statistical mechanics of single ideal chain models with
only short-range interferences play a central role.
In modified iSAFT, the underlying ideal chain model is the freely jointed chain
model. In this model, the bond vectors connecting successive segments are constrained
to have a fixed bond length but the orientations of the bond vectors are distributed
isotropically and independently. Probability distribution of the end-to-end vector of
a freely jointed chain obeys the Gaussian distribution for a very long ideal chain. In
addition, since any two non-overlapping subchains of an ideal freely jointed chain are
statistically independent, the end-to-end vectors of any subchain obeys the Gaussian
distribution as well. Hence, a coarse-graining approach can be employed by elimi-
nating the information concerning the microscopic details, to describe the physical
propertied on large scales. Several segments of the chain can be grouped to form a
coarse-grained segment of the coarse-grained chain. The successive segments of this
coarse-grained chain are tethered by “spring potentials”, as shown in fig. 8.la, where
the spring potential is given by the Gaussian distribution. Hence, this model is known
as discrete Gaussian chain model.
208
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