Competition of mesoscales and crossover to tricriticality in polymer solutions

Abstract

We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200,000 up to 11.4 million clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length. PACS: 64.75.+g; 61.25.Hg; 05.70.Jk Close enough to the critical point, the correlation length ξ of the fluctuations of the order parameter has grown so large that the microscopic and even the mesoscopic structure of fluids become unimportant: complex fluids become "simple". This feature is known as criticalpoint universality [1]. Within a universality class, determined by the nature of the order parameter, properly chosen physical properties of different systems exhibit the same near-critical behavior. All critical phase-separation transitions in fluids belong to the 3-dimensional Isingmodel universality class, as the order parameter (associated with density or/and concentration) is a scalar. However, in practice, the pure asymptotic regime is often hardly accessible. Even in simple fluids, like xenon and helium, the physical properties in the critical region show a tendency to crossover from Ising asymptotic behavior to mean-field behavior [2,3]. This crossover depends on the microscopic structure of the system, namely, on the range of interaction and on a molecular-size "cutoff". In simple fluids, crossover to mean-field critical behavior is never completed within the critical domain (which can be defined roughly as within 10% of the critical temperature): the "cutoff" length and the range of interactions are too short. In complex fluids, regardless of the range of interaction, the role of the cutoff is played by a mesoscopic characteristic length scale ξ D that is associated with a particular mesoscopic structure [4]. If the cutoff length is mesoscopic, it can compete with the correlation length ξ within the critical domain. The temperature at which the correlation length becomes equal to the structural length can be naturally defined as a crossover temperature between two regimes, namely, an Ising asymptotic critical regime and a regime determined by the nature of the mesoscopic structure of the complex fluid. In some complex fluids, like polymer solutions, it is possible to tune the structural length-scale and make it very large. If both lengths, the correlation length of the critical fluctuations associated with the fluid-fluid separation and the structural correlation length, diverge at the same point, this point will be a multicritical point. A perfect example of such a multicritical phenomenon appears in a polymer solution near the theta point. The theta p...

Specific Heat Capacity of Nitrobenzene–Tetradecane Near the Liquid–Liquid Critical Point

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Dynamic crossover to tricriticality and anomalous slowdown of critical fluctuations by entanglements in polymer solutions

“…In the asymptotic vicinity of the critical point, the correlation length becomes much larger than the radius of gyration and the polymer solution exhibits Ising critical behavior. With increase of the polymer molecular weight and, hence, of the radius of gyration, the range of asymptotic Ising critical behavior shrinks, ultimately yielding to theta-point tricritical behavior [2]. This competition of two mesoscales arises from a coupling between two different order parameters belonging to two different static universality classes, namely, one associated with phase separation and another one with self-avoiding-walk singularities of long polymer chains [3].…”

“…However, we have found that this mode being trapped by the entanglements, may become an order slower as compared to uncoupled critical slowdown. Moreover, the diffusivity, like static properties [2], exhibits crossover from critical (Ising) to theta-point tricritical (mean-field) behavior, becoming almost "classical" at the highest molecular weight. In fact, the coupling of two modes and the crossover to tricriticality are just two sides of the same physical phenomenon, caused by an interaction of two order parameters resulting in the emergence of a tricritical point.…”

Bulk and interfacial properties of a cationic micellar system near the critical point

“…The micelles set a mesoscopic scale in the system that can compete with the correlation length of the critical fluctuations. This fact may originate a complex crossover behaviour from mean-field to Ising behaviour [41][42][43][44]. While the existing experimental data are still somewhat contradictory for the crossover of bulk properties [42,43,45,46], no specific experimental search for the crossover effect on the interfacial properties has been reported yet.…”