Fluid Phase Equilibria 158–160 Ž1999. 537–547
Crossover critical phenomena in complex fluids Mikhail A. Anisimov, Andrei A. Povodyrev, Jan V. Sengers
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Institute for Physical Science and Technology and Department of Chemical Engineering, UniÕersity of Maryland, College Park, MD 20742, USA Received 19 April 1998; accepted 25 January 1999
Abstract It is assumed that near-critical complex fluids, such as polymer and ionic solutions, belong to the same universality class of criticality as simple fluids. However, the range of universal critical behavior in complex fluids is usually so small that it may not be experimentally accessible. In practice, physical properties of complex fluids in the critical region often exhibit some kind of crossover behavior rather than universal asymptotic critical behavior. The character of the crossover reflects an interplay between universality caused by long-range fluctuations and a specific supramolecular structure characterized by an additional nanoscopic or mesoscopic length scale. When the correlation length of the critical fluctuations becomes comparable to this supramolecular length scale, a specific sharp and even nonmonotonic crossover from classical Žvan der Waals-like. behavior to universal asymptotic behavior is exhibited. In the region far away from the critical point, where the correlation length is still smaller than the characteristic length scale, one can observe classical behavior. Ultimately, in the immediate vicinity of the critical point, the correlation length becomes dominant and one should expect universal asymptotic behavior. Such a crossover has been indeed observed in polymer and ionic solutions. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Critical phenomena; Crossover; Polymer solutions; Ionic solutions
1. Introduction It has been established that complex fluids, such as polymer and micellar solutions, microemulsions and solutions of electrolytes asymptotically close to the appropriate critical points exhibit the same universal behavior as simple fluids w1–12x. In other words, all fluids, simple and complex, belong to
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0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 4 0 - 5
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M.A. AnisimoÕ et al.r Fluid Phase Equilibria 158–160 (1999) 537–547
the same universality class, namely that of the 3-dimensional Ising-model criticality w13x. However, the range of Ising-like universal behavior in complex fluids can be so narrow that experimentally it is difficult to achieve. Instead, physical properties of complex fluids in the critical region usually exhibit some kind of intermediate Žcrossover. non-universal behavior rather than universal asymptotic behavior. The approach to universal critical behavior in such systems is affected by a competition between the correlation length of the critical fluctuations and an additional length associated with the supramolecular structure orrand with long-range interparticle interactions. Hence, even within the asymptotic Ising-like universality class, complex fluids may exhibit different crossover behavior upon approaching the critical point. It is known that simple fluids near the vapor–liquid critical point can also exhibit a crossover from asymptotic Ising-like behavior to van der Waals classical behavior upon increase of the distance from the critical point. This crossover is smooth and monotonic; it is basically controlled by a single crossover parameter, the Ginzburg number, and is never completed in the critical domain w14x. In contrast, in complex fluids the crossover is unusual: it is sharp, more pronounced, and sometimes even non-monotonic. Anisimov et al. w15,16x have shown that the character of the crossover behavior in ionic solutions can be quantitatively described by a crossover model that contains two independent crossover parameters associated with two different characteristic spatial scales. In low-dielectric-constant ionic systems, for example, these scales may reflect two different ranges of interparticle interactions: short-range solvophobic and long-range Coulombic w6x. A qualitatively sharp crossover to mean-field behavior and mesoscopic-range structure has been reported earlier for metal–ammonia solutions w17,18x. Crossover between Ising-like asymptotic behavior and mean-field classical behavior has also been reported for polymer blends w7–11x and for a microemulsion system w12x. Attempts w7,8,11,12x have been made to describe these data in terms of a version of the crossover theory that contains a single crossover scale w14,19x. On the other hand, solutions of polymers in low-molecular-weight solvents exhibit sharp nonmonotonic crossover behavior when the correlation length of the critical fluctuations and the polymer molecular size, as specified by the radius of gyration, are of the same order w20x. A description of this crossover phenomenon requires two independent parameters associated, respectively, with intramolecular and intermolecular correlations. Most recently, a sharp and non-monotonic crossover between Ising behavior and classical behavior has been observed through light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide w21x. The shape of this crossover shows a striking similarity with the crossover behavior previously observed for non-aqueous ionic solutions and for polymer solutions.
2. Theory In fluids with short-range intermolecular interactions the critical fluctuations affect the behavior of physical properties in a wide region around the critical point; in fact, wherever the correlation length exceeds the molecular size w22x. A property of one-component fluids, such as the isothermal compressibility, exhibits a tendency to cross over from universal asymptotic Ising-like behavior towards mean-field Ž classical van der Waals-like. behavior when the distance from the critical point increases and the correlation length decreases w14,22x. This crossover behavior is characterized by a single crossover scale, the Ginzburg number NG , that is to be compared with the distance to the
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critical point t s < T y Tc
