Second and third virial coefficients of low-molecular-weight polystyrene with a benzyl end in toluene

Abstract

Light-scattering measurements were taken on six samples of polystyrene (PS) with a benzyl group at one end of the chain (benzyl-PS) in toluene at 15 1C. The second and third virial coefficients (A 2 and A 3 , respectively) were determined as functions of weight-average molecular weight, M w , which ranges from 6.0Â10 2 to 1.2Â10 4 . It was found that values of A 2 for benzyl-PS were systematically smaller than those for PS with a butyl group at one end of the chain (butyl-PS) and that the difference becomes larger with decreasing M w . From the A 2 data obtained, the excess binary-cluster integral between the butyl end and the middle segments was estimated to be about three times larger than the binary-cluster integral between the benzyl end and the middle segments, where 'excess' means the difference from the binary-cluster integral between middle segments. The A 3 values for benzyl-PS for M w o10 4 were also smaller than those for butyl-PS. If we assume a term independent of molecular weight in A 3 , the excess ternary-cluster integral among one butyl end and two middle segments was estimated to be about five times larger than that among one benzyl end and two middle segments. Polymer Journal (2010) 42, 386-390; doi:10.1038/pj.2010.11; published online 10 March 2010Keywords: chain-end effect; good solvent; light scattering; polystyrene; second virial coefficient; third virial coefficient INTRODUCTION Solution properties of long flexible polymers are discussed on the basis of the two-parameter theory. 1,2 However, this theory cannot describe properties in low-molecular-weight regions, in which effects from stiffness and/or local conformations of the chain, chain-end groups and three-segment interactions become essential. 3 The importance of the effects of chain stiffness on A 2 was discussed by Yamakawa. 4 Einaga et al. 5 later showed that the effects of chain ends, as well as chain stiffness, must be considered to obtain a quantitative agreement between the theoretical and observed values of A 2 for polystyrene (PS) in toluene (a good solvent) for M w o10 4 , where M w denotes the weight-average molecular weight. The PS samples used by Einaga et al. 5 had a butyl group at one end of the chain. If we perform a similar study on PS samples with different chain ends, different results may be obtained.It is known that data for A 2 in cyclohexane solutions of PS with a butyl group (butyl-PS) versus PS with a benzyl group (benzyl-PS) at one end of the chain show very different tendencies for M w o10 4 at the theta point (34.5 1C), where A 2 for sufficiently large M w vanishes. The positive A 2 of butyl-PS increasing with decreasing M w is attributed to effects from the chain ends. 4 On the other hand, values of A 2 for benzyl-PS became negative and decreased with decreasing M w . 6 It was considered that the negative values of A 2 occurred because of the effects of the three-segment interactions and that effects from chain ends were negligibly small. From these results on the theta solvent system, we may expect to re...