Phase separation in polymer solutions near the critical point

Cherayil, Binny J.

doi:10.1063/1.461012

Cited by 22 publications

(10 citation statements)

References 35 publications

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“…And for problems such as the critical point of polymer solutions, even the proper theoretical approach is controversial, and hence it is unclear whether the exponent x ≈ 0.37 (Fig. 9) is a universal property at all [34][35][36][37][38][39][40][41][42][43].…”

Section: Discussionmentioning

confidence: 99%

“…Another very interesting crossover which can also be studied is that which occurs near the critical point of unmixing for polymer solutions in a bad solvent [12,[34][35][36][37][38][39][40][41][42][43]. For chain length N → ∞ the critical temperature T c (N) moves towards the Θ-temperature, where a single coil undergoes a transition from a swollen coil to a collapsed globule.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo investigations of phase transitions: status and perspectives

Binder

Luijten

Müller

et al. 2000

Physica A: Statistical Mechanics and its Applications

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Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finitesize scaling in Ising models above the marginal dimension (d * = 4) is discussed.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monte Carlo investigations of phase transitions: status and perspectives

Binder

Luijten

Müller

et al. 2000

Physica A: Statistical Mechanics and its Applications

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“…the chains should be free. One might question this since actually T c (N) < T Θ for any finite N. Accordingly, it was suggested in [16] that chains are partly collapsed,…”

Section: Introductionmentioning

confidence: 99%

“…This discrepancy has given rise to a number of speculations and more or less well founded conjectures [10,11,13,14,15,16,17]. One conjecture is that the chains might be partly collapsed at the critical point.…”

Section: Introductionmentioning

confidence: 99%

Critical unmixing of polymer solutions

Frauenkron¹,

Grassberger²,

Juelich³

1997

The Journal of Chemical Physics

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We present Monte Carlo simulations of semidilute solutions of long selfattracting chain polymers near their Ising type critical point. The polymers are modeled as monodisperse self-avoiding walks on the simple cubic lattice with attraction between non-bonded nearest neighbors. Chain lengths are up to N = 2048, system sizes are up to 2 21 lattice sites and 2.8 × 10 5 monomers. These simulations used the recently introduced pruned-enriched Rosenbluth method which proved extremely efficient, together with a histogram method for estimating finite size corrections. Our most clear result is that chains at the critical point are Gaussian for large N , having end-to-end distances R ∼ √ N. Also the distance T Θ − T c (N ) (where T Θ = lim N →∞ T c (N )) scales with the mean field exponent, T Θ − T c (N ) ∼ 1/ √ N . The critical density seems to scale with a non-trivial exponent similar to that observed in experiments. But we argue that this is due to large logarithmic corrections. These corrections are similar to the very large corrections to scaling seen in recent analyses of Θ-polymers, and qualitatively predicted by the field theoretic renormalization group. The only serious deviation from this simple global picture concerns the N -dependence of the order parameter amplitudes which disagrees with a minimalistic ansatz of de Gennes. But this might be due to problems with finite size scaling. We find that the finite size dependence of the density of states P (E, n) (where E is the total energy and n is the number of chains) is slightly but significantly different from that proposed recently by several authors.

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“…Since T ϑ − T c ∼ N -1/2 in Flory theory, N being a chain length, de Gennes has identified τ with the composite variable tN 1/2 (or equivalently with the variable tM 1/2 , where M is a molecular weight). As discussed in ref , if the classical (mean field) behavior of a property P of the polymer solution is known, the variable τ can be used to predict the chain length exponents in the relation that occurs near T c . Although quite successful, the scheme is purely phenomenological and has so far not been rigorously justified.…”

Section: Introductionmentioning

confidence: 99%

A Semiempirical Crossover Analysis of Phase Separation in Polymer Solutions

Cherayil

1997

Macromolecules

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The thermodynamic temperature variable appropriate for the description of the scaling behavior of chain dimensions R and density correlations ξ in polymer solutions in the critical through mean field limits is identified by setting up and solving the renormalization group (RG) equation for the system. The solution to the RG equation is obtained by expressing the set of renormalization constants that relate the bare parameters of the Hamiltonian to their renormalized counterparts as approximate resummed expansions in the coupling constants of the system. These expansions, which include unknown coefficients, are so defined that certain calculated asymptotic limits of R and ξ are reproduced. In satisfying these matching conditions, the unknown coefficients are determined self-consistently; they in turn fix the form of the relevant crossover variable. The predicted measure of distance to the critical temperature is found in this way to coincide with de Gennes's original proposal. This semiempirical approach to the calculation of asymptotic and crossover behavior in polymer solutions provides a more rigorous alternative to simple scaling prescriptions but eschews the elaborate mathematical machinery of field-theoretic methods.

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Phase separation in polymer solutions near the critical point

Cited by 22 publications

References 35 publications

Monte Carlo investigations of phase transitions: status and perspectives

Monte Carlo investigations of phase transitions: status and perspectives

Critical unmixing of polymer solutions

A Semiempirical Crossover Analysis of Phase Separation in Polymer Solutions

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