Phase equilibria of lattice polymer and solvent: tests of theories against simulations

Madden, William G.; Pesci, Adriana I.; Freed, Karl F.

doi:10.1021/ma00206a042

Cited by 123 publications

(116 citation statements)

References 8 publications

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“…Several applications of the LCT, e.g., to mixtures of chemically different polymers 17 and mixtures of linear and branched chain molecules, 18 have indicated the relevance of these theoretical refinements. In the case of athermal linear chains the LCT provides slightly better predictions of the compressibility factor than the Guggenheim approximation 7,8 ͑for athermal chains the Guggenheim theory reduces to the Huggins combinatorial entropy expression͒. For the chain lengths actually investigated the difference between the Guggenheim and LCT theory was only minor but was anticipated to increase in favor of the latter for longer chain lengths.…”

Section: Introductionmentioning

confidence: 93%

“…From these comparative studies it is now clear that the different refinements of the primitive FH theory indeed lead to improved predictions of the thermodynamic properties of the lattice model. [7][8][9][10][11][12] One of the first systematic studies of the lattice model by Monte Carlo ͑MC͒ computer simulations was pursued by Sariban and Binder who investigated symmetric binary polymer mixtures on a cubic lattice with a constant fraction of vacancies. [9][10][11][12] A variety of properties was investigated in these simulations.…”

Section: Introductionmentioning

confidence: 99%

“…For the chain lengths actually investigated the difference between the Guggenheim and LCT theory was only minor but was anticipated to increase in favor of the latter for longer chain lengths. 8 Despite the importance of the LCT theory also some drawbacks should be mentioned. For instance, as a function of chain length, peculiar critical behavior was found in the isomorphic conditions of liquid-liquid coexistence of an incompressible polymer solution and the vapor-liquid coexistence of a compressible pure component.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, as a function of chain length, peculiar critical behavior was found in the isomorphic conditions of liquid-liquid coexistence of an incompressible polymer solution and the vapor-liquid coexistence of a compressible pure component. 8,19,20 Further, as the LCT theory relies on a truncated expansion in the inverse lattice coordination number and inverse temperature it is unable to fully account for the long-range consequences of the excluded volume effects typical of chainlike fluids.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A theory for compressible binary lattice polymers: Influence of chain conformational properties

Wang

Nies

Cifra

1998

The Journal of Chemical Physics

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The influence of long-range chain connectivity on the thermodynamic properties of athermal compressible single component and binary polymer mixtures is studied for the lattice model both theoretically and by Monte Carlo simulations. Theoretical expressions for the thermodynamic properties are derived based on the chain insertion probabilities. The chain conformations enter the theoretical insertion probabilities by the number of intramolecular contacts. The distribution of the number of intramolecular contacts of a single athermal chain is taken as input, of which the dependence on density is predicted by the theory. The theory successfully predicts the Monte Carlo simulation data for the equation of state of pure components and mixtures. Also microscopic details on the different types of self-contacts and cross contacts in the mixtures are accurately predicted.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A theory for compressible binary lattice polymers: Influence of chain conformational properties

Wang

Nies

Cifra

1998

The Journal of Chemical Physics

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“…Recent simulation results [4][5][6] for reasonably long chains also give x 2 ϭ0.38Ϯ0.01; earlier simulation data gave much lower values for x 2 , but the chain lengths involved in those simulations were not long enough to be in the scaling regime. [7][8][9][10][11] Equation ͑3͒ describes the scaling behavior of the critical temperature as a function of chain length. All reported results from experiments and computer simulations agree that the exponent is x 3 ϭ0.5.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of lattice polymers studied by Monte Carlo simulations

Yan

Pablo

2000

The Journal of Chemical Physics

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A newly developed expanded grand-canonical formalism is applied to locate the critical point of systems of long polymeric molecules. Two polymer systems are investigated in this work; the first consists of chains in a simple cubic lattice, the second consists of bond-fluctuating molecules. For the former we simulate molecules of up to 16 000 sites, and for the latter we study molecules of up to 500 sites. These chain lengths are well above those investigated by all prior simulation studies of critical phenomena in polymer solutions. Critical parameters are determined as a function of chain length by means of field-mixing finite-size scaling techniques. Our results for the scaling behavior of the critical temperature are consistent with literature values. Our results for the scaling of the critical density, however, indicate that the corresponding critical exponent is higher than that reported by previous authors. The leading logarithmic term of the finite-chain-length correction to the critical density is confirmed by our results.

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Molecular thermodynamics of binary polymer solutions using modified double lattice model: Chain length dependence of primary lattice

Chang

Bae

1999

J. Appl. Polym. Sci.

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ABSTRACT:In a previous study we modified a double lattice model by introducing a new interaction parameter, which improved the mathematical approximation defect, and gave a new expression for the Helmholtz energy of mixing. In the model the universal constants C ␤ and C ␥ in the primary lattice were determined by comparing them with literature Monte Carlo simulation data, which is the only case for r 1 ϭ 1 and r 2 ϭ 100 (case I). In this study we introduce new universal constants, C ␤ and C ␥ , as a function of the chain length of a polymer in a solvent (case II) by comparing them with other literature simulation data for various polymer chain lengths. The proposed model is compared with polymer-solvent systems. In an upper critical solution temperature phase behavior the theoretical results of case II were improved over those of case I. However, in a lower critical solution temperature phase behavior those of case I were not very sensitive to C ␤ and C ␥ .

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Phase equilibria of lattice polymer and solvent: tests of theories against simulations

Cited by 123 publications

References 8 publications

A theory for compressible binary lattice polymers: Influence of chain conformational properties

A theory for compressible binary lattice polymers: Influence of chain conformational properties

Critical behavior of lattice polymers studied by Monte Carlo simulations

Molecular thermodynamics of binary polymer solutions using modified double lattice model: Chain length dependence of primary lattice

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