Range Intramolecular Interactions

The configuration of the polymer molecule must depend also on its environment. In a good solvent, where the energy of interaction between a polymer element and a solvent molecule adjacent to it exceeds the mean of the energies of interaction between the polymer-polymer and solvent-solvent pairs, the molecule will tend to expand further so as to reduce the frequency of contacts between pairs of polymer elements. In a poor solvent, on the other hand, where the energy of interaction is unfavorable (endothermic), smaller configurations in which polymer-polymer contacts occur more frequently will be favored. 

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Intermolecular Interactions and Long-Range Intramolecular Interactions... 

The intermolecular interactions and long-range intramolecular interactions are incorporated via a pair-wise interaction potential. All pairs of beads from... 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

Equation (5.15b) is the fundamental assumption underlying London s theory, which is essential both for numerical evaluation and for physical interpretation of the perturbative expressions. Whereas short-range intramolecular interactions in (5.16a) and (5.16b) must be described with properly antisymmetric eigenfunctions satisfying... 

The numerical self-consistent (SC) MC/RISM procedure [51,52] employed to solve the matrix polymer RISM equation (4) with the RMMSA closure relation (6)-(7) was used in Ref. [53] to study water-containing Nafion systems. The single-chain MC simulation was based on the realistic rotational-isomeric-state (RIS) model [54], in which the short-range intramolecular interactions depending on the details of chemical structure were taken into account via appropriate matrices of statistical weights [54]. 

This concept was introduced by Flory and Krikbaum (3) who postulated the presence of an excluded volume for the polymer chain, i.e. the volume occupied by the polymer chain which exhibits long-range intramolecular interaction. These interactions were introduced as an enthalpic term k and an entropic term jf. The two terms become equal when AG mix = 0. The temperature at which these conditions prevail in a given solvent is the -temperature, given as follows ... 

In an actual chain, two remotely connected segments cannot occupy the same space at the same time. As a result of this long-range intramolecular interaction, the actual chain will have a more extended configuration than implied by the random flight consideration. 

This equation describes the conformation partition function, Z, as a serial product of statistical weight matrices, U that incorporate the energies of all of the important short-range intramolecular interactions. 

The subscript 0 in<5 >(, refers to the fact that this is the mean square radius of gyration for an ideal coil, without any long-range intramolecular interactions. 

Landau and Lifschitz [4] provided the further vector analysis needed to relate to the more experimentally useful . For a polymer with no long-range intramolecular interactions. 

The short range intramolecular interaction of a zeolite lattice can be represented by several potentials. The expressions that model the system most accurately are considered below. 

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