Rotational isometric state

RIS rotational isometric state RTC room temperature cure... 

The occurrence of interactions that depend on pairs of skeletal bonds is the rule in chain molecules. In some of them, notably in vinyl polymers, such interactions may affect most of the conformations. Hence, interdependence of rotations usually plays a major role in determining the spatial configuration of the chain. The rotational isometric state approximation, whereby the continuous variation of each ( ) is replaced by discrete states, provides the key to mathematical solution of the problem posed by rotational interdependence, 20,2i,2 , 25... 

A conformation of the chain is specified in the rotational isometric state approximation by stipulation of the states for all internal bonds 2 to n-1 inclusive e.g., by g ttg-g , etc. Owing to the three-fold symmetry of the terminal methyl groups of the alkane chain, rotations about the terminal bonds are inconsequential and hence are ignored. The statistical weight for the specified conformation of the chain is obtained by selecting the appropriate factor for each bond from the array (15) according to the state of this bond and of its predecessor, and taking the product of such factors for all bonds 2 to n-1. In the example above this product is u ug t u t u8 8 , etc. It will be... 

The foregoing method enjoys great versatility. The chain may be of any specified length and structure. If it comprises a variety of skeletal bonds and repeat units, the factors entering into the serial products have merely to be fashioned to introduce the characteristics of the bond represented by each of the successive factors. The mathematical methods are exact the procedure is free of approximations beyond that involved in adoption of the rotational isometric state scheme. With judicious choice of rotational states, the error here Involved is generally within the limits of accuracy of basic information on bond rotations, nonbonded interact ions, etc. 

Mattice WL, Suter UW (1994) Conformational theory of large molecules The Rotational Isometric State model in macromolecular systems, Wiley Interscience, New York 31,97... 

The foregoing discussion allows to state the theorem The full isometric group JP( ) is a proper or improper subgroup ofthe symmetry group ft of the rotation internal motion hamiltonian H = T + V... 

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