Mean square length and mean square radius of gyration of 1,4′‐polysaccharides and of polybutadienes

Abstract

The mean square length and mean square radius of gyration of 1,4′‐polysaccharides and of cis‐ and trans‐polybutadiene were calculated by an extension of the method of Eyring and Benoit, the results being expressed in terms of the degree of polymerization and of certain parameters of physical significance connected with the rotations about the various single bonds in these molecules. The calculations were based on the simplifying assumptions that no correlation exists between rotations about bonds separated by at least one pyranose ring or double bond and that the polysaccharide molecules are made up of pyranose rings in the “chair” form. The excluded volume effect was neglected throughout. The results obtained show that, if the mean square length is plotted against the degree of polymerization, n, then the deviations for small n from the limiting straight line obtained for larger n will have the form of a damped vibration, n appearing instead of the time. In certain cases, however, the results for odd and even n fall on different curves.

Local Dynamics of Carbohydrates. 1. Dynamics of Simple Glycans with Different Chain Linkages

“…Before entering into a description of the methods used here, we present some general aspects of the conformational description of polysaccharides in their random coil solution state. The early free rotation approximations [15][16][17] have been improved with the introduction of the rotational isomeric state approach. 18,19 Interdependence of the backbone torsional angles of a given glycosidic linkage is taken routinely into account, but the assumption of mutual independence of the successive glycosidic linkages is often justified by the spatial separation provided by the nearly rigid intervening sugar residues.…”

A General Treatment of the Configurational Statistics of Polysaccharides

“…Eliezer and Hayman subsequently extended the treatment of Benoit to amylose and pectic acid. 4 Similar considerations of a variety of other polysaccharides at the same levels of approximation have been put forth more recently by Burchard,5 by Cleland,6 and by Yathindra and Rao.7 The inadequacy of the free rotation approximation was recognized in the earliest work, and steric hindrances to rotation about the bonds of the glycosidic bridge were acknowledged through the introduction of simple torsional hindrance potentials. [3][4][5] However, the uncomplicated functional forms employed in these treatments to render the development analytically tractable bore little relation to the true rotational hindrance potentials, the varied and irregular forms of which are highly dependent upon the details of the geometric and electronic structure of the polymer chain.…”

“…4 Similar considerations of a variety of other polysaccharides at the same levels of approximation have been put forth more recently by Burchard,5 by Cleland,6 and by Yathindra and Rao.7 The inadequacy of the free rotation approximation was recognized in the earliest work, and steric hindrances to rotation about the bonds of the glycosidic bridge were acknowledged through the introduction of simple torsional hindrance potentials. [3][4][5] However, the uncomplicated functional forms employed in these treatments to render the development analytically tractable bore little relation to the true rotational hindrance potentials, the varied and irregular forms of which are highly dependent upon the details of the geometric and electronic structure of the polymer chain. Moreover, these treatments failed to account for the interdependence of the torsional hindrance potentials for rotations about the two bonds of a given glycosidic linkage, which is evident from a cursory inspection of space-filling molecular models, much less for interdependences which may be operative at longer range in the chain sequence.…”

Studies on cellulose derivatives. Part IV. The configuration of the polyelectrolyte sodium carboxymethyl cellulose in aqueous sodium chloride solutions

“…Comparison of the calculated and observed A2-values ( OROFINO and FLORY concluded, however, t h a t a similar discrepancy for their data on poly-(acrylic acid) was mainly due t o neglect of the ionic activity coefficients. These authors express the deviation in terms of a parameter p defined by: (11) where may be calculated from Eq. ( l o a ) employing the measured values of A, and radii of gyration (S2)ll2; (Xl)theois obtained from (lob).…”

“…Eq. (11) is tantamount t o lumping all deviations from expression ( l o a ) into a n effective degree of ionization, i. As these workers stated, this implies t h a t the charged sites on the polyion restrict the mobility of counterions which then gives rise t o a lower effective degree of ionization of the polyelectrolyte groups than expected from, for instance, titration measurements.…”