Realistic rotational- isomeric-state

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]. 

The valence angle model, though more realistic than the freely jointed model, still underestimates the true dimensions of polymer molecules, because it ignores restrictions upon bond rotation arising from short-range steric interactions. Such restrictions are, however, more difficult to quantify theoretically. A simpler procedure is to assume that the conformations of each sequence of three backbone bonds are restricted to the rotational isomeric states that correspond to the potential energy minima such as those shown for n-butane in Fig. 2.3. For the simplest case of polyethylene and for vinylidene-type polymers, the application of the rotational isomeric state theory yields the following equation... 

Determination of the unperturbed dimensions of the polymeric pro-cyanidins presents special challenges. Well-characterized samples of high molecular weight are not readily available, and the solubility characteristics of the high polymers are incompatible with the application of the classical techniques for the measurement of the dimensions of a macromolecule. An alternative route to the unperturbed dimensions exploits structural determinations in the solid state (8, 9), spectroscopic studies of well-characterized oligomers in dilute solution (iO, ii), molecular mechanics (MM2 software) (i2) calculations (i3, 14), and rotational isomeric state analysis (15-17) to provide a realistic description of the dimensions of the high polymers. A vital piece of information comes from the time-resolved fluorescence of the monomers and oligomers of well-defined covalent structure. The fluorescence measurements also show promise for the characterization of the com-... 

The coarse grained models we have considered thus far are valuable for examining qualitative trends. However, in order to make comparisons directly with experimental data, more local structural details presumably need to be taken into account in the calculation of d>(k). A realistic way of incorporating monomer structure is through the rotational isomeric state approximation, successfully employed [16] by Flory and others to describe isolated polymer chains in a theta solvent. In this description the continuous rotational potentials are replaced by discrete rotational states corresponding to the lowest vibrational... 

For all the afore-mentioned computations of Kx values Semiyen et al. used Eq. (5.24). The unperturbed mean square end-to-end distance of the linear precursors were calculated via the matrix algebraic methods of Flory and Jemigan [84, 85] using rotational isomeric state models based on detailed structural information [86]. However, Semiyen et al. [62, 63] also improved and applied another mathematical approach to the calculation of Kx, the so-called Direct Computational Method . The JS theory is limited to polymers obeying Gaussian statistics and cycles, free of enthalpic interactions. The Direct Computational Method does not need such restrictions [87-90]. The distances between terminal atoms of chains are calculated for all discrete conformations defined by the rotational isomeric state model. Any correlation between the directions of terminal bonds involved in the cyclization process can be investigated and their effect on Kx assessed. It can take into account favorable and unfavorable correlations between the directions of terminal bonds, as well as any excluded volume effect. Semiyen demonstrated [62, 63, 72] that the Direct Computational Method yields more realistic Kx values for small cyclic oligomers. 

Sometimes the transition state has as many bonds as the initial state, e.g., in isomerizations or internal rotations. LSD gives realistic barrier heights... 

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