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Anisimov MA, Kostko AF, Sengers JV, Yudin IK. Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions. J Chem Phys 2005; 123:164901. [PMID: 16268722 DOI: 10.1063/1.2056543] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.
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Affiliation(s)
- M A Anisimov
- Department of Chemical and Biomolecular Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
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Hager JS, Anisimov MA, Sengers JV, Gorodetskiı̆ EE. Scaling of demixing curves and crossover from critical to tricritical behavior in polymer solutions. J Chem Phys 2002. [DOI: 10.1063/1.1502249] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Lubensky TC, Dasgupta C, Chaves CM. Statistics of trees and branched polymers from a generalised Hilhorst model. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/11/11/010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Hernandez R, Somer FL. Stochastic Dynamics in Irreversible Nonequilibrium Environments. 2. A Model for Thermosetting Polymerization. J Phys Chem B 1999. [DOI: 10.1021/jp9836269] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Rigoberto Hernandez
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400
| | - Frank L. Somer
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400
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