Intrinsic Viscosity of Wormlike Regular Three-Arm Stars

Abstract

The ratio g of the intrinsic viscosity of the Kratky-Porod (KP) wormlike regular three-arm star touched-bead model to that of the KP linear one, both having the same (reduced) total contour length L and (reduced) bead diameter d b , is numerically evaluated in the Kirkwood-Riseman (KR) approximation. Prior to the evaluation of g , an interpolation formula for the mean reciprocal of the end-to-end distance of the once-broken KP chain, which is necessary for the theoretical calculation in the KR approximation, is constructed on the basis of the asymptotic forms derived by the use of the Daniels method near the random-coil limit and the method near the rod limit and also on the basis of the Monte Carlo results. From an examination of the behavior of g as a function of L and d b , it is found that the ratio g =g 0 of g to the rod-limiting value g 0 of g monotonically increases from 1 to 2.03 with increasing L and is almost independent of d b for d b. 0:2, although the behavior of g itself as a function of L remarkably depends on d b. An empirical interpolation formula is then constructed for g =g 0 as a function of L, which is considered to be useful for practical purposes.

Intrinsic viscosity of wormlike regular four-arm stars

“…Following the previous paper, 10 we have adopted the values of /R ij À1 S and /S i ÁS j S of the (continuous) KP regular four-arm star chain of total contour length L¼(4m+1)d b [or (n+1)d b ], as those of the regular four-arm star touchedbead model. Here, L has consistently been set equal to the total number 4m+1 (or n+1) of beads multiplied by d b for both the star and the linear chains.…”

“…To quantitatively examine the effect of the chain stiffness on [Z] of branched polymers, we recently made a study of [Z] of semiflexible regular three-arm star polymers without excluded volume on the basis of the KP chain. 10 It was then shown that the ratio g Z between the values of [Z] of the regular three-arm star and linear chains, both with the same total contour length and hydrodynamic thickness, decreases remarkably with increasing chain stiffness and is useful for characterizing the primary structure of a given star polymer. As a continuation of the previous study, 10 the present paper is aimed at elucidating the dependence of g Z on the number of arms constituting semiflexible regular star polymers.…”

“…10 It was then shown that the ratio g Z between the values of [Z] of the regular three-arm star and linear chains, both with the same total contour length and hydrodynamic thickness, decreases remarkably with increasing chain stiffness and is useful for characterizing the primary structure of a given star polymer. As a continuation of the previous study, 10 the present paper is aimed at elucidating the dependence of g Z on the number of arms constituting semiflexible regular star polymers. We calculated [Z] of the KP regular four-arm star without excluded volume using the touched-bead hydrodynamic model 8,11 along with the Kirkwood-Riseman (KR) approximation.…”

A Monte Carlo Study of the Second Virial Coefficient of Semiflexible Regular Three-Arm Star Polymers

“…In previous papers, 1,2 we have examined effects of chain stiffness on the intrinsic viscosity ½ of unperturbed regular three-arm star polymer chains by Monte Carlo (MC) simulations 1 or on the basis of the Kirkwood-Riseman theory. [2][3][4] The ratio g of ½ of an unperturbed regular three-arm star chain to that of an unperturbed linear one, both having the same molecular weight and chain stiffness, has been shown to become remarkably smaller than the value ca. 0.9 in the random-coil limit 5,6 as the chains become stiffer, as in the case of the ratio g S of the mean-square radius of gyration hS 2 i of the former chain to that of the latter.…”

“…In this paper, we make an MC study of g A2 as a necessary continuation of the previous papers. 1,2 An available theoretical value of g A2 for the regular threearm star chain is 0.968 in the random-coil limit obtained by Douglas and Freed 9 on the basis of the polymer renormalization group (RG) theory, being nearly equal to unity. Then the main question we must answer in this paper is whether or not g A2 becomes remarkably smaller than unity as the chains become stiffer, as in the cases of g and g S .…”