Percus–Yevick Type of Integral Equation for the Excluded Volume Problem

Curro, John G.; Blatz, P. J.; Pings, C. J.

doi:10.1063/1.1671351

Cited by 22 publications

(15 citation statements)

References 18 publications

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“…In principle these site-site distribution functions can be calculated via the integral equation techniques of liquid state theory. [23][24][25][26][27] In this approach the site-site potential between nonbonded monomers is assumed to represent an effective potential which implicitly includes the effects of a continuum solvent. Thus, high and low temperatures correspond to good and poor solvent conditions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Collapse of a ring polymer: Comparison of Monte Carlo and Born–Green–Yvon integral equation results

Taylor

Mar

Lipson

1997

The Journal of Chemical Physics

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Monte Carlo simulation of polymer chain collapse in an athermal solventThe equilibrium properties of an isolated ring polymer are studied using a Born-Green-Yvon ͑BGY͒ integral equation and Monte Carlo simulation. The model polymer is composed of n identical spherical interaction sites connected by universal joints of bond length . In particular, we study rings composed of up to nϭ400 square-well spheres with hard-core diameter and well diameter ͑1рр2͒. Intramolecular site-site distribution functions and the resulting configurational and energetic properties are computed over a wide range of temperatures for the case of ϭ1.5. In the high temperature ͑good solvent͒ limit this model is identical to a tangent-hard-sphere ring. With decreasing temperature ͑worsening solvent͒ both the radius of gyration and the internal energy of the ring polymer decrease, and a collapse transition is signaled by a peak in the single ring specific heat. In comparison with the Monte Carlo calculations, the BGY theory yields quantitative to semiquantitative results for TտT and is qualitatively accurate for TՇT , where T is the theta temperature. The thermal behavior of an isolated square-well ring is found to be quite similar to the behavior of an isolated square-well chain. The BGY theory indicates that rings and chains have comparable theta and collapse transition temperatures. In the low temperature limit ͑collapsed state͒ the microscopic structure of rings and chains becomes nearly identical.

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Section: Introductionmentioning

confidence: 99%

Collapse of a ring polymer: Comparison of Monte Carlo and Born–Green–Yvon integral equation results

Taylor

Mar

Lipson

1997

The Journal of Chemical Physics

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“…A large macromolecule can be viewed as a small system of simple fluid monomers with bonding constraints and the techniques of liquid state theory can be applied to study the structure and thermodynamics of a single chain molecule. [13][14][15][16] In this approach the site-site potential between monomers in the chain is generally assumed to be an effective potential which implicitly includes the effects of a continuum solvent. For such an interaction-site chain good and poor solvent conditions correspond to high and low tem-peratures, respectively.…”

Section: Introductionmentioning

confidence: 99%

Collapse of a polymer chain: A Born–Green–Yvon integral equation study

Taylor

Lipson

1996

The Journal of Chemical Physics

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The collapse transition of a single polymer chain in two and three dimensions: A Monte Carlo study A Born-Green-Yvon ͑BGY͒ type integral equation is developed for the intramolecular distribution functions of an isolated flexible polymer chain. The polymer is modeled as a linear array of n identical spherical interaction sites connected by universal joints of bond length . In particular we study chains composed of up to nϭ400 square-well spheres with hard-core diameters and well diameters ͑1рр2͒. Intramolecular distribution functions and the resulting average configurational and energetic properties are computed over a wide range of temperatures. In the high temperature ͑good solvent͒ limit this model is identical to the tangent hard-sphere chain. With decreasing temperature ͑worsening solvent͒ the square-well chain undergoes a collapse transition identified by a sudden reduction in chain dimensions and a peak in the single chain specific heat. Extensive comparison is made between the BGY results and Monte Carlo results for square-well chains with ϭ1.5. The BGY theory is extremely accurate for square-well 4-mers at all temperatures. For longer chains the theory yields reasonably accurate results for reduced temperatures greater than T*Ϸ1 ͑expanded and theta states͒ and qualitatively correct behavior for T*Ͻ1 ͑collapsed state͒. Very accurate values for the theta temperatures for square-well chains with 1.25рр2.0 are also obtained.

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“…The excluded volume problem can be studied employing an OrnsteinZernike integro-difference equation suggested by Curro, Blatz, and Pings. 65 Combining the intramolecular correlation function, derived from this theory, with the PRISM equation yields good results for the structural correlations and the EoS of athermal polymeric lattice fluids. 66 The density dependence must be addressed using a self-consistent scheme, [45][46][47] in which an intrinsic coupling of ω(l, m, n) and g(l, m, n) is established, although such a scheme will only produce an accurate EoS if both ω(l, m, n) and g(l, m, n) are precisely obtained (i.e., if ω(l, m, n) shows the correct excluded volume behavior and if both ω(l, m, n) and g(l, m, n) display the correct density dependence).…”

Section: Structural Correlations In Figures 1 and 2 The Intermoleculmentioning

confidence: 99%

Athermal Lattice Polymers: A Comparison of RISM Theory and Monte Carlo Simulations

1997

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Polymer-RISM theory is applied to study athermal polymeric lattice fluids. The intermolecular segmental distributions and the compressibility equation of state (EoS) have been obtained within the approach for three different intramolecular distribution functions, i.e., the random flight, the non reversal random walk, and an intramolecular distribution obtained from Monte Carlo simulations. Both the intermolecular segmental distributions and the EoS are also compared to Monte Carlo simulations. From the comparison to the simulations it is seen that the polymer-RISM theory is well able to reproduce the intermolecular segmental distributions, but it underestimates the density dependence of the EoS: the EoS is worse than the classical Huggins EoS for the same model, and only for the computer simulated intramolecular distribution we find reasonable agreement between calculated and simulated EoS. The absence of liquidlike ordering effects in a lattice fluid allow us to show to what extent the deviations are due to the incomplete incorporation of excluded volume in the intramolecular distribution functions.

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Percus–Yevick Type of Integral Equation for the Excluded Volume Problem

Cited by 22 publications

References 18 publications

Collapse of a ring polymer: Comparison of Monte Carlo and Born–Green–Yvon integral equation results

Collapse of a ring polymer: Comparison of Monte Carlo and Born–Green–Yvon integral equation results

Collapse of a polymer chain: A Born–Green–Yvon integral equation study

Athermal Lattice Polymers: A Comparison of RISM Theory and Monte Carlo Simulations

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