Nucleation on cylindrical plates: sharp transitions and double barriers

We apply methods of density-functional theory in statistical mechanics to study the properties of droplets and bubbles formed on a single cylindrical plate or between two such disks immersed in a metastable fluid. Our approach allows us to analyze the properties of different types of aggregates and investigate the effect of disk size, disk separation, and solid-fluid interactions on the dynamics of a liquid-vapor phase transition. The finite size of disks induces nucleation phenomena that are not observed in the cases of either a planar wall or a slit pore. Heterogeneous nucleation on a single disk is characterized by the existence of two distinct types of critical nuclei that control the phase-transition dynamics at different supersaturations. Asymmetric droplets or bubbles formed on one side of the disk are the preferred nucleation path at high supersaturations. However, these types of aggregates become unstable close to the binodal, where they abruptly collapse into nuclei that engulf the cylindrical plates. Droplet or bubble nucleation in between two disks may occur through a free-energy barrier with one or two maxima depending on the value of the system parameters and the supersaturation. Metastable droplets or bubbles corresponding to local minima of the free energy are observed forming between two plates only after density fluctuations in the system achieve a critical size. These types of aggregates only exist for cylindrical plates larger than a minimum size given a fixed distance between the disks. The stability of these droplets and bubbles decreases when the plates are separated.     

Nucleation of self-associating fluids: free versus activated association

We use the density functional theory of statistical mechanics in a square gradient approximation to analyze the structure, size, and work of formation of critical nuclei in self-associating fluids where association reduces the strength of the interactions between bonded particles. This effect is expected in systems of strongly dipolar particles that associate into chains. In this work we analyze the nucleation behavior of two types of self-associating fluids: a system comprised of particles that can freely associate, and a system in which the association process involves a thermally activated initiation step. For the first case, we explore the properties of critical nuclei in fluids that exhibit a metastable critical point between a vapor phase and a highly associated liquid phase. In fluids where the association dynamics involves an initiation step, we investigate the nucleation behavior in the vicinity of the polymerization transition. In both cases critical nuclei undergo a structural transition that shares many of the features of the coil-globule transition reported in Monte Carlo simulations of strongly dipolar Stockmayer fluids. Our results suggest that the sharp structural transition observed in these simulations is evidence of the existence of a second-order or nearly second-order association transition in these model fluids.     

Spinodal for the solution-to-crystal phase transformation

The formation of crystalline nuclei from solution has been shown for many systems to occur in two steps: the formation of quasidroplets of a disordered intermediate, followed by the nucleation of ordered crystalline embryos within these droplets. The rate of each step depends on a respective free-energy barrier and on the growth rate of its near-critical clusters. We address experimentally the relative significance of the free-energy barriers and the kinetic factors for the nucleation of crystals from solution using a model protein system. We show that crystal nucleation is 8-10 orders of magnitude slower than the nucleation of dense liquid droplets, i.e., the second step is rate determining. We show that at supersaturations of three or four k(B)T units, crystal nuclei of five, four, or three molecules transform into single-molecule nuclei, i.e., the significant nucleation barrier vanishes below the thermal energy of the molecules. We show that the main factor, which determines the rate of crystal nucleation, is the slow growth of the near-critical ordered clusters within the quasidroplets of the disordered intermediate. Analogous to the spinodal in supersaturated fluids, we define a solution-to-crystal spinodal from the transition to single-molecule crystalline nuclei. We show that heterogeneous nucleation centers accelerate nucleation not only because of the wettinglike effects that lower the nucleation barrier, as envisioned by classical theory, but by helping the kinetics of growth of the ordered crystalline embryos.     

Electric field effects in sodium bis(2-ethylhexyl)sulfosuccinate water-in-oil microemulsions: field-induced percolation and dynamics of structural changes

We investigate the effect of high electric fields on the percolation behaviour of sodium bis(2-ethylhexyl)sulfosuccinate water-in-oil microemulsions in the L₂ phase and examine the existence of critical fields as a function of droplet radius and droplet concentration. It is shown that there is no direct correlation with critical fields as discussed for electrorheological fluids. Very low critical fields are found in certain ranges of droplet radii. Clustering of droplets with material exchange may be postulated under these conditions. Received: 29 July 1999/Accepted: 8 February 2000     

How does a transient amorphous precursor template crystallization

Crystallization through metastable phases, such as polymorphism, plays an important role in chemical manufacture, biomineralization, and protein crystallization. However, the kinetics creating the final stable crystalline phase from metastable phases has so far remained unclear. In this study, crystallization via an amorphous precursor, the so-called multistep crystallization (MSC), is studied quantitatively in a colloidal model system. In MSC, amorphous dense droplets are first nucleated from the mother phase. Subsequently, a few unstable subcrystalline nuclei can be created simultaneously by fluctuation from the tiny dense droplets, which is different from previous theoretical predictions. It is necessary for these crystalline nuclei to reach a critical size N*(crys) to become stable. However, in contrast to subcrystalline nuclei, a stable mature crystalline nucleus is not created by fluctuation but by coalescence of subcrystalline nuclei, which is unexpected. To accommodate a mature crystalline nucleus larger than the critical size N*(crys), the dense droplets have to first acquire a critical size N*. This implies that only a fraction of amorphous dense droplets can serve as a precursor of crystal nucleation. As an outcome, the overall nucleation rate of the crystalline phase is, to a large extent, determined by the nucleation rate of crystals in the dense droplets, which is much lower than the previous theoretical expectation. Furthermore, it is surprising to see that MSC will promote the production of defect-free crystals. The knowledge acquired in this study will also significantly advance our understandings in polymorphism related processes.     

Evidence for the existence of supercooled ethane droplets under conditions prevalent in Titan's atmosphere

Recent evidence for ethane clouds and condensation in Titan's atmosphere raise the question whether liquid ethane condensation nuclei and supercooled liquid ethane droplets exist under the prevalent conditions. We present laboratory studies on the phase behaviour of pure ethane aerosols and ethane aerosols formed in the presence of other ice nuclei under conditions relevant to Titan's atmosphere. Combining bath gas cooling with infrared spectroscopy, we find evidence for the existence of supercooled liquid ethane aerosol droplets. The observed homogeneous freezing rates imply that supercooled ethane could be a long-lived species in ethane-rich regions of Titan's atmosphere similar to supercooled water in the Earth's atmosphere.     

Studies on fluids and their mixtures using the Born-Green-Yvon integral equation technique

We have developed the Born-Green-Yvon (BGY) integral equation theory for investigating the equilibrium properties of fluids and their mixtures both on the lattice and in the continuum. Using the continuum theory we have studied hard sphere fluids over a range in density having chain lengths between one and fifty sites. We have also investigated the collapse transition of a square well chain and a square well ring, each having up to four hundred sites, and have predicted the theta temperature for these systems. Turning to the case of a dilute (hard-sphere) solution we have been able to show the effect of solvation on a hard sphere chain, and captured the dependence of this effect on the ratio of hard sphere diameters of the solvent and chain segments. In all the continuum studies we have found good to excellent agreement with simulation results. We have also derived a lattice BGY theory which, while less sophisticated than the continuum version, has the advantage of producing simple closed-form expressions for thermodynamic properties of interest. This theory is capable of exhibiting the full range of miscibility behaviour observed experimentally, including upper and lower critical solution temperatures and closed-loop phase diagrams. We find that the theory does an excellent job of fitting to different kinds of experimental data and, making use of the parameters derived from fits to pure component data alone, we have been able to predict properties ranging from pure fluid vapour pressures and critical temperatures to changes in the volume and enthalpy on mixing as well as coexistence curves for solutions.     

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: renormalized local functional theory

We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ(∞). Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T, the transition line ends at a capillary critical point T=T(c) (ca) slightly lower than the bulk critical temperature T(c) for the upper critical solution temperature. The Casimir amplitudes are larger than their critical point values by 10-100 times at off-critical compositions near the capillary condensation line.     

On the existence of a third-order phase transition beyond the Andrews critical point: a molecular dynamics study

The possibility of the existence of a gas-liquid third order phase transition for fluids is becoming a subject of growing interest. Experimental work suggests its existence for specific systems while recent theoretical models claim its universality. In this work, we employ Molecular Dynamics and investigate the third-order phase transition beyond the Andrews critical point by treating a system of Lennard-Jones particles along three isotherms. Two partial derivatives of the Gibbs free energy are measured, namely the molar constant pressure heat capacity and isothermal compressibility. The convergence of these simulations with respect to the system size as well as the cut-off radius is carefully checked. The obtained results show that partial derivatives certainly do not present sharp cusp singularities at the maxima, and actually suggest that there are no singularities at all. On these basis we then conclude that a third-order phase transition in the considered temperature region: T? ≥ 1.36 may indeed not exist.     

Swelling and deswelling kinetics of poly(N-isopropylacrylamide) gels

Swelling and deswelling kinetics was investigated for three types of cylindrical poly(N-isopropylacrylamide) (PNIPA) gels differing in crosslink density. The temperature dependence curves of the volume of the gel specimens were different from one another. One of the gel specimens was considered as a critical gel showing the continuous volume phase transition. The volume change process of the specimens after a temperature jump was examined. In the deswelling processes with temperature jumps to temperatures higher than 35 degrees C, a phase separation was observed in the gel specimens and the volume change slowed down due to the homogenization after the phase separation. The value of the diffusion constant obtained without the phase separation decreased rapidly as temperature approaches the transition temperature. The rapid decrease for the critical gel indicates the emergence of the critical slowing-down. The value of the critical exponent for the correlation length suggests that the universality class for the volume phase transition of the critical PNIPA gel belongs to the class for the classical theory.     

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: for very long pores, the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place, fluctuations occur between vapor- and liquidlike states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality), the system at phase coexistence is in an axially inhomogeneous multidomain state, where long cylindrical liquid- and vaporlike domains alternate. Using Monte Carlo simulations for the Ising/lattice gas model and the Asakura-Oosawa model of colloid-polymer mixtures, the transition between these two different scenarios is characterized. It is shown that the density distribution changes gradually from a double-peak structure to a triple-peak shape, and the correlation length in the axial direction (measuring the equilibrium domain length) becomes much smaller than the cylinder length. The (rounded) transition to the disordered phase of the fluid occurs when the axial correlation length has decreased to a value comparable to the cylinder diameter. It is also suggested that adsorption hysteresis vanishes when the transition from the simple domain state to the multidomain state of the cylindrical pore occurs. We predict that the difference between the pore critical temperature and the hysteresis critical temperature should increase logarithmically with the length of the pore.     

Wetting transitions

When a liquid droplet is put onto a surface, two situations distinguishable by the contact angle may result. If the contact angle is zero, the droplet spreads across the surface, a situation referred to as complete wetting. If the contact angle is between zero and 180°, the droplet does not spread, a situation called partial wetting. A wetting transition is a surface phase transition from partial to complete wetting. The wetting transition is generally first-order (discontinuous), implying a discontinuity in the first derivative of the surface free energy. As a consequence, at the transition a discontinuous jump in film thickness occurs from a molecularly thin to a thick film. We show here that the first-order nature of the transition can lead to the observation of metastable surface states and an accompanying hysteresis. The second part of this review deals with the exceptions to the first-order nature of the wetting transition. Two different types of continuous or critical wetting transitions have been reported, for which a discontinuity in a higher derivative of the surface free energy occurs. This consequently leads to a continuous divergence of the film thickness. The first type is long-range critical wetting, due to the long-range van der Waals forces. We show that this transition is preceded by the usual first-order wetting transition, which, however, is not achieved completely. This leads to the existence of a new intermediate wetting state, in which droplets coexist with a mesoscopic film: frustrated complete wetting. The film thickness diverges continuously from this mesoscopic film to a thick film. The second type of continuous transition is short-range critical wetting, for which the layer thickness diverges continuously all the way from a microscopic to a macroscopically thick film. This transition is interesting, as renormalization-group studies predict non-universal behaviour for the critical exponents characterizing the wetting transition. The experimental results, however, show mean field behaviour, the reason for which remains unclear.     

Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite L×L×L boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density ρ in the simple fluid or the relative concentration x(A) of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slablike configuration of two parallel flat interfaces. Extending the analysis of Schrader et al., [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy γ(R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case and present evidence that for R→∞ the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture, the expected nonexistence of the Tolman length is confirmed. In all cases and for a range of radii R relevant for nucleation theory, γ(R) deviates strongly from γ(∞) which can be accounted for by a term of order γ(∞)/γ(R)-1∝R(-2). Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory, and we find qualitative agreement in the behavior of γ(R) as well as in the sign and magnitude of the Tolman length.     

Theory of fragmentation of metal clusters

The theory of shell correction developed for discussing fissing of heavy nuclei is applied to symmetric fragmentation of charged metal clusters. Assuming the effective potential of an anisotropic harmonic oscillator, we calculate the shell correction. We also calculate the energy of deformed charged droplets in the two-dimensional parameter space describing the deformation of droplets such as elongation and neck formation. The symmetric fragmentation of microclusters of alkali and noble metals is discussed.     

球腔中氢键流体的吸附-解吸附转变:表面调控研究

集中讨论了球形微腔表面对腔中氢键流体相态结构的调控机制. 为了揭示微腔表面对腔中氢键流体相平衡的影响, 首先根据吸附-解吸附原理并利用经典流体的密度泛函理论计算了微腔中氢键流体的平衡密度分布, 进而通过吸附-解吸附等温线及巨势等温线绘制出体系的相图. 在此基础上, 重点考察了球腔尺寸、 表面作用强度和作用力程对氢键流体毛细凝聚及层化转变的影响. 结果表明, 这些因素可以有效地调控体系毛细凝聚和层化转变的临界约化温度、 临界密度和相区大小等特征, 从而阐明了表面调控的主要机制. 研究结果为设计相关吸附材料提供了理论参考.     

Nucleation from supersaturated water vapors onn-dodecane substrate: A reverse Wilson chamber (RWC) method study

The reverse Wilson chamber method (RWC), developed for heterogencous nucleation investigation is applied to critical supersaturation measurements and determination of the surface concentration of nuclei (droplets) vs. supersaturation dependence in the case of nucleation from supersaturated water vapors onn-dodecane substrate. The experimental results obtained are interpreted in terms of the classical (Volmer) theory of heterogeneous nucleation as well as in the framework of the theory of barrierless nucleation. The several times lower critical supersaturations measured at four different temperatures, covering the range between 20° and 35° C, are explained by taking into account the effect of the negative line tension of three-phase contact. The temperature dependence of line tension for the three-phase systemn-dodecane/water/water vapor is extracted from the data to fir the theory. The results obtained are in complete disagreement with those ones obtained by Wu and Maa for the same system using jet-tensimeter technique, however, in another temperature interval. This discrepancy is discussed in detail in the text.     

Evidence for the existence of an effective interfacial tension between miscible fluids: isobutyric acid-water and 1-butanol-water in a spinning-drop tensiometer

We report definitive evidence for an effective interfacial tension between two types of miscible fluids using spinning-drop tensiometry (SDT). Isobutyric acid (IBA) and water have an upper critical solution temperature (UCST) of 26.3 degrees C. We created a drop of the IBA-rich phase in the water-rich phase below the UCST and then increased the temperature above it. Long after the fluids have reached thermal equilibrium, the drop persists. By plotting the inverse of the drop radius cubed (r(-)(3)) vs the rotation rate squared (omega(2)), we confirmed that an interfacial tension exists and estimated its value. The transition between the miscible fluids remained sharp instead of becoming more diffuse, and the drop volume decreased with time. We observed droplet breakup via the Rayleigh-Tomotika instability above the UCST when the rotation rate was decreased by 80%, again demonstrating the existence of an effective interfacial tension. When pure IBA was injected into water above the UCST, drops formed inside the main drop even as the main drop decreased in volume with time. We also studied 1-butanol in water below the solubility limit. Effective interfacial tension values measured over time were practically constant, while the interface between the two phases remains sharp as the volume of the drop declines. The effective interfacial tension was found to be insensitive to changes in temperature and always larger than the equilibrium interfacial tension. Although these results may not apply to all miscible fluids, they clearly show that an effective interfacial tension can exist and be measured by SDT for some systems.     

Numerical approaches to determine the interface tension of curved interfaces from free energy calculations

A recently proposed method to obtain the surface free energy σ(R) of spherical droplets and bubbles of fluids, using a thermodynamic analysis of two-phase coexistence in finite boxes at fixed total density, is reconsidered and extended. Building on a comprehensive review of the basic thermodynamic theory, it is shown that from this analysis one can extract both the equimolar radius R(e) as well as the radius R(s) of the surface of tension. Hence the free energy barrier that needs to be overcome in nucleation events where critical droplets and bubbles are formed can be reliably estimated for the range of radii that is of physical interest. It is found that the conventional theory of nucleation, where the interface tension of planar liquid-vapor interfaces is used to predict nucleation barriers, leads to a significant overestimation, and this failure is particularly large for bubbles. Furthermore, different routes to estimate the effective radius-dependent Tolman length δ(R(s)) from simulations in the canonical ensemble are discussed. Thus we obtain an instructive exemplification of the basic quantities and relations of the thermodynamic theory of metastable droplets/bubbles using simulations. However, the simulation results for δ(R(s)) employing a truncated Lennard-Jones system suffer to some extent from unexplained finite size effects, while no such finite size effects are found in corresponding density functional calculations. The numerical results are compatible with the expectation that δ(R(s) → ∞) is slightly negative and of the order of one tenth of a Lennard-Jones diameter, but much larger systems need to be simulated to allow more precise estimates of δ(R(s) → ∞).     

Heterogeneous ice nucleation in aqueous solutions: the role of water activity

Heterogeneous ice nucleation experiments have been performed with four different ice nuclei (IN), namely nonadecanol, silica, silver iodide and Arizona test dust. All IN are either immersed in the droplets or located at the droplets surface. The IN were exposed to various aqueous solutions, which consist of (NH4)2SO4, H2SO4, MgCl2, NaCl, LiCl, Ca(NO3)2, K2CO3, CH3COONa, ethylene glycol, glycerol, malonic acid, PEG300 or a NaCl/malonic acid mixture. Freezing was studied using a differential scanning calorimeter and a cold finger cell. The results show that the heterogeneous ice freezing temperatures decrease with increasing solute concentration; however, the magnitude of this effect is solute dependent. In contrast, when the results are analyzed in terms of the solution water activity a very consistent behavior emerges: heterogeneous ice nucleation temperatures for all four IN converge each onto a single line, irrespective of the nature of the solute. We find that a constant offset with respect to the ice melting point curve, Deltaaw,het, can describe the observed freezing temperatures for each IN. Such a behavior is well-known for homogeneous ice nucleation from supercooled liquid droplets and has led to the development of water-activity-based ice nucleation theory. The large variety of investigated solutes together with different general types of ice nuclei studied (monolayers, ionic crystals, covalently bound network-forming compounds, and a mixture of chemically different crystallites) underlines the general applicability of water-activity-based ice nucleation theory also for heterogeneous ice nucleation in the immersion mode. Finally, the ice nucleation efficiencies of the various IN, as well as the atmospheric implication of the developed parametrization are discussed.