Inhomogeneous structure of penetrable spheres with bounded interactions

Kim, Soon-Chul; Suh, Soong‐Hyuck

doi:10.1063/1.1518689

Cited by 33 publications

(33 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the limit n → ∞, the generalized exponential model reduces to the penetrable-sphere (PS) model ϕ(r) = ǫ, r < σ, 0, r > σ. (1.1) This model has been extensively investigated from different perspectives [11,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]. Density-functional theory [19,20] predicts a freezing transition to fcc solid phases with multiply occupied lattice sites.…”

Section: Introductionmentioning

confidence: 99%

Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

2007

View full text Add to dashboard Cite

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.

show abstract

Section: Introductionmentioning

confidence: 99%

Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

2007

View full text Add to dashboard Cite

show abstract

“…The simplest bounded potential is that of so-called penetrable spheres (PS), which is defined as φ(r) = ǫ, r < σ, 0, r > σ, (1.1) where ǫ > 0. This interaction potential was suggested by Marquest and Witten [9] as a simple theoretical approach to the explanation of the experimentally observed crystallization of copolymer mesophases and it has been since then the subject of a number of studies [7,10,11,12,13,14,15,16,17,18,19,20,21]. The classical integral equation theories, in particular the Percus-Yevick (PY) and the hypernetted-chain (HNC) approximations, do not describe satisfactorily well the structure of the PS fluid, especially inside the overlapping region for low temperatures.…”

Section: Introductionmentioning

confidence: 99%

Radial distribution function of penetrable sphere fluids to the second order in density

Santos

Malijevský

2007

Phys. Rev. E

View full text Add to dashboard Cite

The simplest bounded potential is that of penetrable spheres, which takes a positive finite value ǫ if the two spheres are overlapped, being 0 otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of T * ≡ kBT /ǫ (where kB is the Boltzmann constant and T is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for T * < ∼ 1 only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancelation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for T * < ∼ 0.73, reaches a minimum negative value at T * ≈ 1.1, and then goes to zero from below as 1/T * 4 for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for T * < ∼ 0.7, while the virial route is preferable if T * > ∼ 0.7.

show abstract

“…As can be expected, it is known that the DFT based on the bridge density functional strongly depends on the functional form to be employed, which has some defects for describing the higher density behaviors of penetrable spheres in the pore systems. 6 To remedy these defects, we follow the method suggested by Rickayzen et al 18 together with the grand potential of the bulk system for penetrable sphere mixtures. In this case, Eq.…”

Section: ͑3͒mentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11] In this case, the model penetrable fluid is described by the pair potential…”

Section: Introductionmentioning

confidence: 99%

Structure of penetrable sphere fluids and mixtures near a slit hard wall: A modified bridge density functional approximation

Kim

Seong

Suh

2009

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The modified density functional theory, which is based both on the bridge density functional and the contact value theorem, has been proposed for the structural properties of penetrable sphere fluids and their mixtures near a slit hard wall. The Verlet-modified bridge function proposed by Choudhury and Ghosh [J. Chem. Phys. 119, 4827 (2003)] for one-component system has been extended for fluid mixtures. The radial distribution functions obtained from the Verlet-modified bridge function are in excellent agreement with computer simulations over a wide range of density and temperature and better than those obtained from the standard integral theories including the Percus-Yevick and hypernetted-chain closures. The calculated particle density distributions confined in a slit pore are also found to be reasonably good compared to the simulation data. Even for high density systems the accuracy of the hypernetted-chain and the mean-field approximation functionals increase with increasing temperature. However, the agreement between theory and simulation slightly deteriorates in the systems of low temperature.

show abstract

Inhomogeneous structure of penetrable spheres with bounded interactions

Cited by 33 publications

References 31 publications

Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

Radial distribution function of penetrable sphere fluids to the second order in density

Structure of penetrable sphere fluids and mixtures near a slit hard wall: A modified bridge density functional approximation

Contact Info

Product

Resources

About