Interdependent bond rotational potentials

Interdependent bond rotational potentials The origins of the interdependence of the bond rotational potentials in poly(methylene) can be understood in terms of the conformations of n-pentane (hence the phenomenon is termed the pentane effect). 

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Flory (1969 1971 1974) has developed the rotational isomeric state theory for predicting the conformation of polymer molecules. This incorporates the interdependence of the bond rotational potentials. This theory is fully explained in Flory s comprehensive monograph (Flory, 1969) and only the barest details will be mentioned here. 

Although the potentials affecting the rotation about a skeletal bond in a chain molecule such as PE usually depend only on rotations of immediately adjoining bonds, the interdependence of rotational states may be transmitted over greater distances. In the case of PE or of POM the effective range of correlation is only four or five bonds. This is established by calculating a priori probabilities for rotational states of a bond as a function of its location relative to the chain termini and of the total chain length. 

Calculations of the characteristic ratio and its temperature dependence for PE and isotactic PP have been performed using a RIS model that takes account of non-staggered conformations and the interdependence of the rotational potentials in sequences of four chain bonds. The experimental values are shown to be reproducible satisfactorily by a set of energy parameters consistent with the similarity between steric interactions in the two polymers. 

CA may be considered to have the following structural factors controlling the rigidity of the molecule an interdependent rotational potential, which controls the unperturbed dimension in solution, by (1) the steric interactions between neighboring pyranose rings with and without substituent groups, (2) the intramolecular hydrogen bonds... 

In the first part of this article the review of various theoretical models for polymer chains is given. The models of freely jointed chains, freely rotating chains (including wormlike chains), and chains with fixed bond angles and independent rotational potentials and with interdependent potentials, including rotatimial isomeric state approximation, are presented. 

For present purposes only the form of Eq. (3.27) is required. Detailed formulation of Z can be found in Ref. (47) For chains with independent rotational potentials Z is equal to the bond rotational partition function. For high molecular weight, with int dependent rotational potential, Z is the largest eigenvalue of the statistical weight matrix describing this interdependence. 

The restrictions upon bond rotation arising from short-range steric interactions are more difficult to quantify theoretically. The usual procedure is to assume that the conformations of each sequence of three backbone bonds are restricted to discrete rotational isomeric states corresponding to potential energy minima such as those shown for n-butane in Fig. 3.6. The effects of interdependent steric interactions of the backbone atoms also can be taken into account in this way (e.g. by excluding and g g sequences). For the simplest case of... 

The results of an illustrative calculation are depicted in Fig. 3.4. The chain has 0 = 112°, i = 3, and < > = 180° and 60°. The statistical weight matrix for all internal bonds is given by Eq. (3.9) with t = if/ = 1. When cr and freely rotating chain with the same bond angle. Imposition of a symmetric torsional potential that penalizes the g states, with tr = 0.4, increases the C . Introduction of a pair-wise interdependence, via cr = 0.4 and w = 0.1, produces a further increase in C . Obviously, the interdependence of the bonds can have a strong effect on the unperturbed dimensions of the chain. 

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