A Monte Carlo Study of the Intrinsic Viscosity of Semiflexible Regular Three-Arm Star Polymers

Abstract

ABSTRACT:A Monte Carlo (MC) study is made of the intrinsic viscosity ½ and also of the mean-square radius of gyration hS 2 i for regular three-arm star freely rotating chains of bond angles ¼ 109 , 165 , and 175 and with the Lennard-Jones 6-12 potentials between beads having the parameter values corresponding to the  temperature, in the range of the total number n of bonds in the chain from 60 to 300. Three kinds of approximate values of ½ are calculated by the use of the Kirkwood-Riseman (KR) approximation, the Zimm rigid-body ensemble approximation which gives an upper bound ½ (U) to ½ , and by the Fixman method which gives a lower bound ½ (L) , the KR value of ½ being designated ½ (KR) . On the basis of the three kinds of MC values of ½ so obtained, the behavior of the ratio g of ½ for the star chain to that for the linear one, both having the same n, is examined as a function of the reduced contour length L as defined as the total contour length L of the corresponding Kratky-Porod (KP) wormlike chain divided by its stiffness parameter À1 , the values of L having been determined from an analysis of the present and previous MC data for hS 2 i on the basis of the KP chain. It is found that the KR value g (KR) of g as defined by ½ (KR) (star)= ½ (KR) (linear) lies between the values of an upper bound g (U) and a lower one g (L) , which are defined by The mean-square radius of gyration hS 2 i and/or the intrinsic viscosity ½ as measures of the average chain dimension of polymers in dilute solution depend largely on their molecular structure, e.g., linear or branched. It has therefore been of great interest to investigate the difference in hS 2 i or ½ between linear and branched polymer chains, and many theoretical and experimental studies 1-9 have already been made. However, almost all of those studies were of flexible polymers except for the theoretical one by Mansfield and Stockmayer, 4 the Monte Carlo (MC) one by Zimm, 5 and the experimental one by Goodson and Novak. 9 Mansfield and Stockmayer calculated hS 2 i of the Kratky-Porod (KP) wormlike 10,11 star chain (without excluded volume) and examined the behavior of its ratio g S to hS 2 i of the corresponding linear one having the same total length of the chain contour (molecular weight). Zimm evaluated ½ of ''wormlike'' four-and six-arm stars by the use of his rigidbody ensemble approximation. 12 Unfortunately, however, his calculation is rather limited, as mentioned by himself that it was a preliminary survey. Goodson and Novak synthesized three-arm star poly(n-hexyl isocyanate) by living titanium-catalized coordination polymerization, 9 and then investigated the behavior of hS 2 i, ½ , and g S as functions of molecular weight.In this paper, we make an extensive MC study of ½ for semiflexible regular three-arm star polymers in the  state, which has not yet been made.The regular three-arm star chain model used in this study is essentially the same as that used in previous MC studies 13,14 of hS 2 i and the second virial coefficient of linear chains with in...

Branched Semiflexible Polymers: Theoretical and Simulation Aspects

“…These tendencies are also in qualitative agreement with the simulation results of refs. [113,114] , where freely rotating chains and stars were studied. Turning off the excluded volume interactions in the BFM we find that the agreement with the theory gets much better, a sign that these interactions are the main source of the discrepancies.…”

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

“…where the sum is taken over N s sample configurations f k g with k being equal to 3m À 3 for the star chain and n À 2 for the linear one, f k g generated in an MC run by an application of the pivot algorithm 14,15 and the Metropolis method of importance sampling 16 as done in the previous MC studies. 1,12 For each sample configuration, S 2 as a function of f k g may be calculated from…”

“…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.…”

“…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 .…”

Intrinsic Viscosity of Wormlike Regular Three-Arm Stars

“…In a previous paper, 1 effects of chain stiffness on the ratio g of the intrinsic viscosity ½ of a regular three-arm star polymer chain to that of the corresponding linear one, both having the same structure and total chain length, have been examined by Monte Carlo (MC) simulation on the basis of the freely rotating chain with the Lennard-Jones 6-12 intramolecular potential between beads. Since there is no theoretical method of obtaining ½ without any approximations, we have evaluated it in the three approximate ways: the Kirkwood-Riseman (KR) approximation, 2,3 the Zimm rigid-body ensemble approximation, 4 and the Fixman method.…”