Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres

Wood, W. W.; Jacobson, J. D.

doi:10.1063/1.1743956

Cited by 524 publications

(167 citation statements)

References 5 publications

Supporting

Mentioning

163

Contrasting

Order By: Relevance

“…Fig. 2 presents the convergence of the matrix elements toward the asymptotic values A ϭ 2.74553 [3] and B ϭ 5.49095 [6]. One clearly sees that for the hard-spheres model the observed correction for the diagonal terms R nn scales like 1/n 3 , such that the 1/n 2 term, if it exists, is very weak.…”

Section: Application To Hard Spheresmentioning

confidence: 94%

Estimation of critical exponents from cluster coefficients and the application of this estimation to hard spheres

Eisenberg

Baram

2007

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix Rmn, whose elements converge to two constants with 1/n 2 correction. We find exact expressions in terms of these correction terms for the two critical exponents describing the density near the two singular termination points of the fluid phase. We apply the method to the hard-spheres model and find that the metastable fluid phase terminates at t ‫؍‬ 0.751 [5]. The density near the transition is given by t-ϳ (zt ؊ z) , where the critical exponent is predicted to be ‫؍‬ 0.0877 [25]. Interestingly, the termination density is close to the observed glass transition; thus, the above critical behavior is expected to be associated with the onset of glassy behavior in hard spheres.glass transition ͉ Mayer cluster integrals H ard-core models have long played a central role as models for structural ordering transitions. These models are purely entropy-driven, thus capturing the essential molecular mechanism that drives freezing transitions. In particular, the equation of state of classical hard spheres and their freezing transition have been extensively studied for over a century, dating back to the pioneering works of the founding fathers of statistical mechanics (1, 2). Nevertheless, there are still a lot of fundamental unresolved problems regarding this system. Early MonteCarlo works have established that in 3D the system freezes through a first-order phase transition at a density f ϭ 0.665[2] (3-6). [All densities here are scaled by the closest packing density; for hard spheres the volume fraction density ˆis given by ˆϭ /3 ͌ 2; here and throughout this paper, the numbers in square brackets represent the uncertainty in the last digit(s).] Increasing the density of the hard-sphere fluid quickly enough, crystallization can be avoided, and the system stays in a metastable supercooled fluid phase. As the density of supercooled fluid increases, its dynamics becomes slower and slower. Experimental (7,8) and computational (9-11) studies have shown that the typical relaxation times increase very fast around g ϳ 0.76. Despite its long history, the question of whether this increase is due to a true thermodynamic glass transition or a purely dynamical phenomenon is still hotly debated (12-18).The most pronounced manifestation (and, experimentally, the definition) of glassiness is through the dynamical properties. Thus, characterization of the onset of glassiness by using statistical-mechanics approaches is challenging. Several approaches have been taken to meet this challenge, including the ModeCoupling theory (19), using the replica method (16) and analysis of the virial expansion (20). In this work we suggest to use the Mayer cluster expansion for describing the metastable supercooled fluid and, in particular, the critical behavior near its termination point.It was previously shown that the Mayer cluster expansion for the fluid density can be represented by a real symmetric tridiagonal matri...

show abstract

Section: Application To Hard Spheresmentioning

confidence: 94%

Estimation of critical exponents from cluster coefficients and the application of this estimation to hard spheres

Eisenberg

Baram

2007

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…3,5,17,29,44,48,53 The extension to arbitrary dimensionality of this hard spherical particle system has been the object of several studies too. 7,14,15,27,31,32,54 Although the apparent simplicity of these systems, only a few exact analytical results for the homogeneous system are known concerning mainly the dimensional dependence of the first four virial coefficients 14,30,32 existing numerical extensions to higher order.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

Urrutia

Szybisz

2010

Journal of Mathematical Physics

View full text Add to dashboard Cite

Structures of hard-sphere fluids from a modified fundamental-measure theory J. Chem. Phys. 117, 10156 (2002) This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres ͑HSs͒ confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one-and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D + 1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS ͑a cavity inside of a bulk HS system͒ is also discussed.

show abstract

“…Though those values were calculated in late 1960s, the coexistence demonstrated by simulations was in the last decade [18][19][20]. Since the existence of crystalline phase in the HS system was shown by molecular dynamics [16] and Monte Carlo (MC) simulations [17] in 1957, the HS system was studies from a fundamental point of view.…”

Section: Introductionmentioning

confidence: 99%

Crystal structure of hard spheres under gravity by Monte Carlo simulation

Mori

Yanagiya

Suzuki

et al. 2006

Science and Technology of Advanced Materials

View full text Add to dashboard Cite

Monte Carlo simulations were performed for hard spheres (HSs) under gravity. The gravity was increased stepwise. HSs were placed between the bottom and the top hard walls. For g*R0.9, we observed that a 'sediment' was comprised of two crystalline and one fluid regions. Here, g* is defined by g*Zmgs/k B T with m being the mass of a particle, s the HS diameter, g the acceleration due to gravity, and k B T the temperature multiplied by Boltzmann's constant. The bottom crystal was less defective or well-ordered and the crystal lay between the bottom one and the fluid phase was defective or less-ordered. In this paper, we investigate the structure of the crystals. Despite no apparent defects, the crystal has highly been distorted. That is, the fcc lattice has been contracted in the vertical direction more than in the horizontal direction. The crystal-fluid coexistence condition for the bulk HS system does, in principle, not hold for the present systems at the crystal-fluid interface. In addition, though the fine scale density profile exhibits a discontinuity apparently across the crystal-crystal interface, the interlayer separation increases linearly with the height. q

show abstract

Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres

Cited by 524 publications

References 5 publications

Estimation of critical exponents from cluster coefficients and the application of this estimation to hard spheres

Estimation of critical exponents from cluster coefficients and the application of this estimation to hard spheres

Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

Crystal structure of hard spheres under gravity by Monte Carlo simulation

Contact Info

Product

Resources

About