Coil-Globule Transition in Gas-Liquid Nucleation of Polar Fluids

Abstract

We report computer simulations of homogeneous gas-liquid nucleation in a model for strongly polar fluids. We find that, in the early stages of the nucleation process, chainlike clusters are formed. Beyond a certain size, these collapse to form compact spherical clusters. However, the interface of the collapsed nuclei differs markedly from the planar interface. Classical nucleation theory underestimates both the size of the critical nucleus and the height of the nucleation barrier. [S0031-9007(98) PACS numbers: 64.60. Qb, 75.50.Mm, 82.60.Nh, 82.65.Dp The spontaneous condensation of water droplets in the vapor phase is probably the best known example of homogeneous nucleation of a polar fluid. However, best known is not the same as best understood. In fact, recent experiments indicate that classical nucleation theory [1] seriously overestimates the rate of nucleation for strongly polar substances, such as acetonitrile [2], although, surprisingly, it works well for water [3].The most important factor determining the gas-liquid nucleation rate is the height of the free-energy barrier for the formation of a critical nucleus. Classical nucleation theory (CNT) assumes that the nuclei at the top of the nucleation barrier are compact spherical objects that behave like small droplets of bulk liquid. Recent computer simulations on a nonpolar (Lennard-Jones) fluid support this picture [4]. However, for polar fluids, the nature of the critical nucleus is still under debate. Wright et al. [2] suggest that, for polar liquids, the critical nucleus is a prolate spheroid-thus increasing the surface-to-volume ratio, and thereby the nucleation barrier. The orientational distribution of dipoles inside this cluster is assumed to have cylindrical symmetry. Abraham [5] proposed a model in which the dipoles are assumed to be oriented perpendicular to the interface. This would give rise to a size-dependent surface tension due to the effect of surface curvature on the dipole-dipole interaction. However, both pictures are at odds with the findings of a recent density-functional study of the critical nucleus of a dipolar model fluid (the Stockmayer fluid) [6]. This study indicated that the dipoles on the liquid side of the interface of critical nuclei are oriented parallel to the surface, rather than perpendicular. Unfortunately, the applicability of the density-functional theory is limited to relatively weak polar fluids.In the present Letter, we present direct numerical simulations of the structure and free energy of precritical and postcritical nuclei of a strongly polar Stockmayer fluid. The Stockmayer potential is given byHere e is the Lennard-Jones well depth, s is the LennardJones diameter, m i denotes the dipole moment of particle i, and r ij is the vector joining particles i and j. The equilibrium phase behavior of this system has been studied in detail by computer simulation [7,8] and by theory [9,10]. The simulations suggest that attractive dispersion forces are essential for the existence of liquidvapor phase coexistence [7...

Liquid–liquid separation in solutions of normal and sickle cell hemoglobin

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Formation free energy of clusters in vapor-liquid nucleation: A Monte Carlo simulation study

“…To sample large critical clusters one has to choose a larger i max in conjunction with a larger system size and longer Monte Carlo runs. In this sense, our approach complements the umbrellasampling approach by ten Wolde et al, 9,20 which was designed particularly to study vapors at relatively low supersaturations. For the Lennard-Jones system, the highest supersaturation they considered was 2.2 and the size of critical cluster studied was as large as 300.…”

“…This value of the r cl has been used in several recent studies. 9,10 In particular, Reiss and co-workers 10 obtained r cl dependence of n/v-Stillinger cluster lifetime for the Lennard-Jones system and found that the lifetime increases rapidly with r cl until r cl reaches about 1.5 and enters a plateau corresponding to a roughly constant lifetime. Reiss and co-workers argued that it is advisable to choose a value of r cl within this plateau where the lifetime is long.…”

“…where N 1 is the number of monomers, k B is Boltzmann constant, and ⌬G i is the difference in the Gibbs free energy between the i-mer and the monomer at the pressure of the supersaturated vapor at temperature T. This equation has been derived previously 3,[7][8][9][10] and used to infer the formation free energy from the equilibrium distribution of clusters.…”

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

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