Configuration partition function

Both Flory and Huggins derived statistical mechanical expressions for aS . Their expressions are still among the best available. For this reason, Prigogine and his co-workers concentrated their efforts on revising the statistical mechanical configurational partition function which leads, among other things, toAH. ... 

Let us consider a polymer chain with N->oo identical skeletal atoms, either in solution or in the melt, representing our polymer system. Our reference temperature is T0, i.e., the temperature above which no bundles may effectively contribute to crystallization. At T = T0 the chain is assumed to be unperturbed and its configurational partition function is ZN(T0) = kN (N -> oo) [107] for simplicity we use a reduced form Zn = Z /kN (henceforth simply the partition function) so that Zn(T0) = 1. Only at T < To effective bundles may form, see Fig. 1, and we have ZN(T) = 1 + AZN(T - T0) note that the unit term corresponds to the bundle-free infinite-chain configuration. Each bundle with n chain atoms in -c N) will contribute to AZn... 

In the present model the co-ordination number for the first bond of the chain is 4 and for the remaining bonds it is 3. Thus the configurational partition function of an N-bond, isolated chain (ie. in the limit of zero concentration) is... 

A component pn(N) of P(N) represents the relative probability of an N-segment chain terminating at a plane n with first segment located in any of the M planes. Therefore, the sum of the components of P(N) may be identified with the configurational partition function of the chain confined between 1 and M... 

By properly coupling the system to a heat bath, the configurational partition function of the hybrid potential is canonical... 

The APM relies essentially on two bases. The first one is the theorem of corresponding states which says that the configurational partition function of a classical assembly of N molecules may be written in the form ... 

The internal rotations around the skeletal bonds of PE are hindered due to interaction between the neighboring hydrogens. Since second and higher orders of interactions are not negligible, the internal rotations are interdependent. The statistics of such interdependent rotations is developed and applied to obtain the configurational partition function and the mean-square end-to-end... 

Unperturbed dimensions and dipole moments of polydialkylsiloxanes are investigated using RIS theory. Polymers are treated as branched molecules in which each silicon atom constitutes a tetrafunctional branch point. All significant first- and second-order interactions are included in the configuration partition function. Higher order interactions not suppressed by second-order interactions are also evaluated and accounted for in the statistical weights used. 

Isolated butyl branches in low-density polyethylene are formed by an intrachain radical rearrangement that is followed by repeated addition of ethylene without further rearrangement. Here, stereochemical selectivity during the formation of CH2R—CH2-CHR—CH2-branches in the free radical initiated polymerization of monosubstituted vinyl monomers is Investigated. The configuration partition functions are denoted by Zm and Zn respectively. They can be written as 2 Um Up Iv1 v2 v3]T and Zr = U U2 Up Ur Up [v3 v2 v3lT. Numerical values... 

The inter- and Intramolecular contributions to the entropy and energy of fusion are calculated for several linear aliphatic polyesters and polyamides assuming the fusion process consists of two Independent contributions the volume expansion (intermolecular contribution) and the increase in the conformational freedom of each polymer chain on melting (intramolecular contribution). The intramolecular entropy and energy contributions are obtained from the configurational partition function and Its temperature coefficient calculated for an isolated, unperturbed polymer chain using the RIS approximation. 

When a trifunctional branch point is present, the configuration partition function is written as Z = U1 Statistical weight matrices used are ... 

When a tetrafunctional branch point is present, the configuration partition function is written as... 

N 069 " Rotational Isomeric State Treatment of the Cystine Residue. Configuration Partition Function and... 

N 097 "Similar matrix expressions describe configuration partition functions for intrachain formation of antiparailel p sheets and interacting a halices"... 

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