Sharp Crossover of the Susceptibility in Polymer Solutions near the Critical Demixing Point

Melnichenko, Yuri B.; Анисимов, М. А.; Povodyrev, A. A.; Wignall, G. D.; Sengers, J. V.; Hook, W. Alexander Van

doi:10.1103/physrevlett.79.5266

Cited by 91 publications

(101 citation statements)

References 19 publications

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“…The symbols represent experimental data, the dashed lines represent Ising asymptotic behavior and mean-field behavior, while the solid curve represents the crossover theory. In the insert: molecular-weight dependence of the inverse correlation length at the crossover temperature (crosses); closed circles are the normalized radius of gyration, Rg/ √ 3 , scaled as squared root of the molecular weight of polymer [8]. For Mw ≥ 10 6 , the values of Rg have been extrapolated.…”

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confidence: 99%

Competition of mesoscales and crossover to tricriticality in polymer solutions

2002

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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...

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Competition of mesoscales and crossover to tricriticality in polymer solutions

2002

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“…For simple fluids near the vapor-liquid critical point u < 1 [3,4,13] and the crossover behavior of "(eff is monotonic [13,20]; however, in this case for simple fluids the crossover from asymptotic Ising to true asymptotic classical critical behavior is not completed within the critical region, since ~ is large, while the cutoff A corresponds to only a molecular size. On the other hand, in complex fluids the crossover parameter A is not necessarily associated with the actual microscopic molecular cutoff, but may be related to another characteristic spacing on a scale larger than a molecular size [24]. If A is small enough (i.e., the characteristic spacing ~D is large), the crossover to asymptotic mean-field critical behavior is quite possible within the critical domain, even for u ?…”

Section: Two-term Crossover Landau Modelmentioning

confidence: 97%

“…If A is small enough (i.e., the characteristic spacing ~D is large), the crossover to asymptotic mean-field critical behavior is quite possible within the critical domain, even for u ? : 1 [20,24], i.e. for shortrange intermolecular forces.…”

Section: Two-term Crossover Landau Modelmentioning

confidence: 99%

“…The two-term crossover Landau model has been successfully applied to the description of the near-critical thermodynamic properties of various systems, that are physically very different: the 3-dimensional lattice gas (Ising model) [25], one-component fluids near the vapor-liquid critical point [3,20], binary liquid mixtures near the consolute point [20,26], aqueous and nonaqueous ionic solutions [20,27,28], and polymer solutions [24].…”

Section: Applications Of the Two-term Crossover Landau Modelmentioning

confidence: 99%

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Critical and Crossover Phenomena in Fluids and Fluid Mixtures

Анисимов

Sengers

2000

Supercritical Fluids

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“…This approach is based on the fundamental results of the renormalization group (RG) theory [100,101] and during the last few years has been successfully applied to the describing of the thermodynamic properties of such different systems as one-component fluids and fluid mixtures [102][103][104][105][106][107], ionic solutions [108][109][110], polymer blends [111][112][113][114], and microemulsions [115] near the second-order phase transitions, as well as to the conformation properties of linear [116,117] and star [118] polymers.…”

Section: Introductionmentioning

confidence: 99%

Star Polymers in Good Solvents From Dilute to Concentrated Regimes: Crossover Approach

Lue

Kiselev²

2002

Condens. Matter Phys.

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An introduction is given to the crossover theory of the conformational and thermodynamic properties of star polymers in good solvents. The crossover theory is tested against Monte Carlo simulation data for the structure and thermodynamics of model star polymers. In good solvent conditions, star polymers approach a "universal" limit as N → ∞ ; however, there are two types of approach towards this limit. In the dilute regime, a critical degree of polymerization N * is found to play a similar role as the Ginzburg number in the crossover theory for critical phenomena in simple fluids. A rescaled penetration function is found to control the free energy of star polymer solutions in the dilute and semidilute regions. This equation of state captures the scaling behaviour of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer-monomer interactions become important.

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Sharp Crossover of the Susceptibility in Polymer Solutions near the Critical Demixing Point

Cited by 91 publications

References 19 publications

Competition of mesoscales and crossover to tricriticality in polymer solutions

Competition of mesoscales and crossover to tricriticality in polymer solutions

Critical and Crossover Phenomena in Fluids and Fluid Mixtures

Star Polymers in Good Solvents From Dilute to Concentrated Regimes: Crossover Approach

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