Excluded-Volume Effects in Dilute Polymer Solutions. X. Polystyrene in Cyclohexane below the Theta Temperature

Abstract

ABSTRACT:Mean-square radii of gyration and viscosities of polystyrene samples covering a broad range of molecular weight M in cyclohexane were measured at temperatures above and below the theta temperature () in order to see how the coil of a linear flexible polymer collapses to a globule as T is lowered. The data for either the radius expansion factor or the viscosity expansion factor as a function of T and M gave a composite curve when plotted against (Tie-I)M 1 1 2 or (l-eiT)M 1 1 2 In the range of the abscissa values studied, this curve did not reach the asymptote for globular behavior. Thus, the coil-to-globule transition of a linear flexible polymer should be a very gradual process.KEY WORDS Coil-Globule Transition I Polystyrene I Cyclohexane I Radius of Gyration I Intrinsic Viscosity I Much still remains te be investigated theoretically and experimentally in regard to the chain dimensions and flow properties of a linear flexible polymer in a poor so.lvent below the theta temperature e. Long ago Stockmayer 1 suggested that a random coil might eventually collapse to a globule as the temperature Tis lowered below e. This coilglobule transition should manifest itself as a change in molecular weight dependence of (S 2 ) from the type (S 2 )a;:Mto the type (S 2 )ocM 213 , where (S 2 ) is the mean-square radius of gyration at infinite dilution and M is the molecular weight of the polymer.By extending Flory's mean-field theory to include a term associated with the ternary cluster integral {J3 and assuming that the binary cluster integral {J 2 is proportional to r and {J3 is independent of T, de Gennes 2 showed that as a coil shrinks to a globule, the dependence of (S 2 ) on M and Tasymptotically approaches the form (1) where r is a reduced temperature defined by r=(T-e)je (2)

Intrinsic viscosity of flexible macromolecules : transition from theta to collapsed state

“…For the whole range of molecular weight and concentration and for the three capillaries, the theta specific viscosity is always proportional to the concentration : K,,(O) (see form 2)is not detectable and [ tl]o = '1sp( C, 0)/C. For 2.4 x 101 M, 6.77 x 106 we find in agreement with other measurements [7,23]. One must note that a fit to a power low leads to (see Fig.…”

“…Many experimental [1][2][3][4][5][6][7][8][9][10] works have been devoted to the collapse of a flexible polymer chain using a great number of different techniques, each experiment being performed on a limited molecular weight range. They lead to puzzling results [11].…”

Critical phenomena and polymer coil-to-globule transition

“…Experiments on the transition from a single polymer coil behavior in the O state to a globule in the collapsed state did not agree with one another (Slagowski, Tsai & Mclntyre, 1976;Nierlich, Cotton & Farnoux, 1978;Bauer & UUman, 1980;Pritchard & Caroline, 1980;Miyaki & Fujita, 1981;Oyama, Shiokawa & Baba, 1982;Post & Zimm, 1982;Stepanek, Konak & Sedlacek, 1982;Perzynski, Adam & Delsanti, 1982;Perzynski, Delsanti & Adam, 1984;Vidakovic & Rondelez, 1984;Selser, 1985;Chu, Park, Wang & Wu, 1987). If we consider the collapsed state based on the radius of gyration Rg from static lightscattering measurements, recent experiments on the PS/CY system below the Ou temperature and the PS/methyl acetate (MA) system both below the Ov temperature and above the lower theta temperature (OD showed that a plateau 3 1/2 region [with constant (es IzlMw )3 could be reached in a plot of scaled expansion factor 3 1/2 o~ IzlMw versus scaled reduced temperature I'rlM 1/2 where ~= Rg(T)/Rg(O) and z = IT-O[/O.…”

A Semi-Theoretical Equation for the Chain Dimension in Dilute Solutions and Its Experimental Verification, and the Coil-Globule Transition

“…Plots of vs. (I-ejT)M 1 1 2 for polystyrene in cyclohexane: (0), Present work; (e), Miyaki and Fujita 8. The solid curve is calculated using eq 9 with ii0 M=0.0102 and ii3 =0.18.Polymer J., VoL 17, No 5,.…”

“…In the polymer chain statistics, the theta temperature plays an important role. This temperature is defined as the temperature (8) at which the second virial coefficient of segments (v 2 ) vanishes. On the other hand, the theta temperature is experimentally determined as the temperature (if) at which the second virial coefficient of polymer molecules (A2 ) vanishes.…”