Crossover model for the work of critical cluster formation in nucleation theory

We propose a relation for the work of critical cluster formation in nucleation theory W for the systems with long-range interparticle interactions. The method of bridge functions is used to combine the system behavior at sufficiently small quenches, adequately predicted by the classical nucleation theory, with nonclassical effects at deep quenches in the vicinity of the thermodynamic spinodal, described within the framework of the field theoretical approach with an appropriate Ginzburg-Landau functional. The crossover between the two types of nucleation behavior takes place in the vicinity of the kinetic spinodal where the lifetime of a metastable state is of the order of the relaxation time to local equilibrium. We argue that the kinetic spinodal corresponds to the minimum of the excess number of molecules in the critical cluster. This conjecture leads to the form of W containing no adjustable parameters. The barrier scaling function Gamma = W/W(cl), where W(cl) is the classical nucleation barrier, depends parametrically on temperature through the dimensionless combination of material properties. The results for argon nucleation are presented.     

Critical cavities and the kinetic spinodal for superheated liquids

We present density-functional theory (DFT) calculations for critical cavities inside model superheated liquids with varying intermolecular potentials. Our calculations show that the radius of the critical cavity and the ratio of the work of formation of the critical cavity to the work of formation of the critical bubble as predicted by the classical nucleation theory exhibit universal scaling across similar intermolecular potentials. We then utilize this observed scaling behavior by proposing two new criteria for the kinetic spinodal of superheated liquids. These criteria are based on various properties of the critical cavity as obtained from our DFT studies of the superheated Lenanrd-Jones liquid. Our predictions of the kinetic spinodal compare favorably with experimental data of the limits of superheating for various organic liquids.     

Neutron scattering and monte carlo determination of the variation of the critical nucleus size with quench depth

We have used a combination of neutron scattering experiments and Monte Carlo simulations to study the initial stages of first-order phase transitions. We focus on quenches wherein the nascent phase is formed by homogeneous nucleation, and we approach the spinodal, i.e., the quench depth at which the original phase becomes unstable. In this regime, we show how critical nuclei sizes are determined from neutron scattering structure factors. Prevailing thought is that the size of the critical nucleus should increase with increasing quench depth and diverge at the spinodal. To the contrary, our experiments and simulations indicate that the critical nucleus size decreases monotonically as quench depth is increased and is finite at the spinodal.     

Does conventional nucleation occur during phase separation in polymer blends?

The kinetics of liquid–liquid phase separation in off-critical polymer blends was studied with time-resolved small-angle neutron scattering. Our objective was to study the nature of the nuclei that formed during the initial stages of the phase transition. The blends were composed of model polyolefins—deuterium-labeled poly(methyl butylene) (PMB) and poly(ethyl butylene) (PEB)—with molecular weights of about 200 kg/mol. A direct examination of the initial clustering of molecules before macroscopic phase separation was possible because of the large size of the polymer chains and concomitant entanglement effects. We discovered that the scattering profiles obtained during nucleation merged at a well-defined critical scattering vector. We propose that this is the signature of the critical nucleus and that the size of the critical nucleus is inversely proportional to the magnitude of the critical scattering vector. The kinetic studies were preceded by a thorough characterization of the equilibrium thermodynamic properties of our PMB/PEB blends. The locations of the binodal and spinodal curves of our system are consistent with predictions based on the Flory–Huggins theory. This combination of thermodynamic and kinetic experiments enabled the quantification of the dependence of the size and structure of the critical nuclei on the quench depth. Our results do not agree with any of the previous theories on nucleation. Some aspects of our results are addressed in recent theoretical work by Wang in which the effects of fluctuations on the classical binodal and spinodal curves in polymer blends are incorporated. Both theory and experiment support the notion that the traditional stability limit (spinodal) should be replaced by a metastability limit. Although Wang's theory provides an explanation for some of our observations, many fundamental issues regarding nucleation in polymer blends remain unresolved. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1793–1809, 2004     

Determining the nucleation rate from the dimer growth probability

A new method is proposed for the determination of the stationary one-component nucleation rate J with the help of data for the growth probability P2 of a dimer which is the smallest cluster of the nucleating phase. The method is based on an exact formula relating J and P2, and is readily applicable to computer simulations of nucleation. Using the method, the dependence of J on the supersaturation s is determined by kinetic Monte Carlo simulations of two-dimensional (2D) nucleation of monolayers on the (100) face of Kossel crystal. The change of J over nearly 11 orders of magnitude is followed and it is found that the classical nucleation theory overestimates the simulation J values by an s-dependent factor. The 2D nucleus size evaluated via the nucleation theorem is described satisfactorily by the classical Gibbs-Thomson equation and its corrected version accounting for the spinodal limit of 2D nucleation.     

Phase Behavior and Morphology of Poly(Methyl Methacrylate)/Poly(α‐Methyl Styrene‐co‐Acrylonitrile) Blends Under Quiescent and Shear Flow

The kinetics of spinodal decomposition (SD) for the binary blend poly(methyl methacrylate), PMMA, and Poly(α‐methylstyrene‐co‐acrylonitrile), PαMSAN, with 31 wt% AN content (LCST‐type phase diagram) has been thoroughly studied using a time‐resolved light scattering technique. The early stage SD was dominated by a diffusion process and can be well described within the framework of the linearized Cahn‐Hilliard theory. The spinodal temperature could be evaluated from the analysis of the early stage SD based on the Cahn theory. In addition, viscoelastic properties of this system have been systematically investigated at temperatures below and above the LCST phase diagram. The linear viscoelastic properties of the blends were found to be greatly changed by phase separation in the two‐phase regime. This change in the linear viscoelastic properties attributed to an additional contribution of concentration fluctuations to the material functions at the phase separation temperatures. The phase diagram of the blends was also estimated rheologically through the dynamic temperature ramps of G′, G″ and η*. Furthermore, the phase behavior and morphology of this system has been studied under different shear rates using simple shear apparatus and transmission electron microscopy (TEM), respectively.     

Superheating Limit of Boiling n-Hexane Spinodal Decomposition Versus Nucleation Process

Two predicative theories for superheating limits of a boiling liquid are considered in this work. In the nucleation picture, classical homogeneous nucleation theory is used to calculate superheating temperature at various pressures. In spinodal decomposition picture, stability limits are taken as the superheating temperature. A perturbed-hard chain equation of state was developed and used for the purpose of calculating mechanical stability limit. Calculations are done for the case of normal hexane at different pressures and compared with experimental results. Classical nucleation theory gives good prediction at negative and smaller pressures. While near critical pressure, spinodal picture seems to be more accurate.     

RUPTURING OF POLYMER FILMS WITH RUBBING-INDUCED SURFACE DEFECTS

It has been a long-standing question whether dewetting of polymer film from non-wettable substrate surfaceswherein the bicontinuous morphology never forms in the dewetting film is due to spinodal instability or heterogeneousnucleation. In this experiment, we use a simple method to make the distinction through introduction of topographical defectsof the films by rubbing the sample surface with a rayon cloth. Spinodal dewetting is identified for those films that dewet by acharateristic wavevector, q, independent of the density of rubbing-induced defects. Heterogeneous nucleation, on the otherhand, is identified for those with q increasing with increasing density of defects. Our result shows that PS films on oxidecoated silicon with thickness less than ≈ 13 nm are dominated by spinodal dewetting, but the thicker films are dominated bynucleation dewetting. We also confirm that spinodal dewetting does not necessarily lead to a bicontinuous morphology in thedewetting film, contrary to the classic theory of Cahn.     

Critical conditions for stable dipole-bound dianions

We present finite size scaling calculations of the critical parameters for binding two electrons to a finite linear dipole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. A complete ground state stability diagram for the dipole-bound dianion is obtained using accurate variational and finite size scaling calculations. We also study the near threshold behavior of the ground state energy by calculating its critical exponent.     

高分子共混相分离动力学

本文综述了相容高分子共混体系相分离动力学的研究进展.介绍了 Cahn 理论,标度律和分形(Fractal)概念,在研究相分离动力学中的应用。     

Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

Structure of liquid solutions near the critical point

Specific features of the structure of the critical state of binary liquid solutions leading to an anomalous behavior of the Rayleigh line due to a dramatic increase in concentration and density fluctuations are considered. It is shown that an experimental treatment must deal with two fluctuation regions near the critical point of solvent vaporization. In the first region, one can achieve a sufficient degree of accuracy by using theories like selfconsistent field theory. In the second region, which is closer to the critical point than the first region, scaling theory of secondorder phase transitions may be applied. It is found that the anomalous behavior of the Rayleigh line associated with kinetic coefficients is determined by the equilibrium thermodynamic properties and by the radius of fluctuation correlation (rinc). A general theory is developed for calculating thermodynamic potentials, especially the chemical potential and its concentration derivative in the fluctuation region. The results of these calculations are compared with the experimental data briefly described in the paper. Translated fromZhumal Strukturnoi Khimii, Vol. 39, No. 4, pp. 655–668, July–August, 1998.     

Ice nucleation in aqueous electrolytes by light scattering observation

Nucleation of ice is studied in supercooled aqueous electrolytes, after quenching, by light scattering experiments. According to salt concentration heterogeneous nucleation can occur on cracks, decorating and locking most of them. In contrast the homogeneous nucleation results are in agreement with Turnbull's theory if the equilibrium temperature for crystallization is identified with the homogeneous nucleation temperature. The mean field scaling law is obtained for the steady state frequency of the ice nucleation per unit volume which gives some estimate for the quantity β^1/3related to the melting of ice and its interface with the solution near 140–145 K. The scaling law is also obtained for the transient nucleation period.     

Cluster kinetics and dynamics during spinodal decomposition

Spinodal decomposition (barrierless phase transition) is a spontaneous phase separation caused by conditions that force the system to become thermodynamically unstable. We consider spinodal decomposition to occur under conditions of large supersaturation S and/or small ratio of interfacial to thermal energies omega, such that the computed number of monomers in a critical nucleus xi*=(omega/ln S)3 is less than unity. The small critical nucleus size is consistent with a negligible energy barrier for initiating condensation. Thus, in contrast to conventional opinion, it is suggested that the spinodal decomposition is related to the homogeneous nucleation of metastable fluids. Population balance equations show how clusters aggregate and rapidly lead to phase separation. Different mass dependences of aggregation rate coefficients are proposed to investigate the fundamental features of spinodal decomposition. When the mass dependency is an integer, the equations are solved by the moment technique to obtain analytical solutions. When the mass dependency is a noninteger, the general cases are solved numerically. All solutions predict the two time regimes observed experimentally: the average length scale of condensed-phase domains increases as a power law with an exponent of 1/3 at early times, followed by a linear increase at longer times.     

Kinetics of thermally induced phase separation in ternary polymer solutions. I. Modeling of phase separation dynamics

Simulations based on Cahn–Hilliard spinodal decomposition theory for phase separation in thermally quenched polymer/solvent/nonsolvent systems are presented. Two common membrane‐forming systems are studied, cellulose acetate [CA]/acetone/water, and poly(ethersulfone) [PES]/dimethylsulfoxide [DMSO]/water. The effects of initial polymer and nonsolvent composition on the structure‐formation dynamics are elucidated, and growth rates at specific points within the ternary phase diagram are quantified. Predicted pore growth rate curves exhibit a relative maximum with nonsolvent composition. For shallow quenches (lower nonsolvent content) near a phase boundary, the pore growth rate increases with increasing quench depth, whereas for deep quenches, where the composition of the polymer‐rich phase approaches that of a glass, the pore growth rate decreases with increasing quench depth. With increasing initial polymer concentration, the overall rate of structure growth is lowered and the growth rate maximum shifts to higher nonsolvent compositions. This behavior appears to be a universal phenomenon in quenched polymer solutions which can undergo a glass transition, and is a result of an interplay between thermodynamic and kinetic driving forces. These results suggest a mechanism for the locking‐in of the two‐phase structure that occurs during nonsolvent‐induced phase inversion. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1449–1460, 1999     

Heterogeneous multicomponent nucleation theorems for the analysis of nanoclusters

In this paper we present a new form of the nucleation theorems applicable to heterogeneous nucleation. These heterogeneous nucleation theorems allow, for the first time, direct determination of properties of nanoclusters formed on pre-existing particles from measured heterogeneous nucleation probabilities. The theorems can be used to analyze the size (first theorem) and the energetics (second theorem) of heterogeneous clusters independent of any specific nucleation model. We apply the first theorem to the study of small water and n-propanol clusters formed at the surface of 8 nm silver particles. According to the experiments the size of the two-component critical clusters is found to be below 90 molecules, and only less than 20 molecules for pure water, less than 300 molecules for pure n-propanol. These values are drastically smaller than the ones predicted by the classical nucleation theory, which clearly indicates that the nucleating clusters are too small to be quantitatively described using a macroscopic theory.     

Non‐linear dynamics of spinodal decomposition

A new approach is proposed to describe the spinodal decomposition, in particular, in polymer binary blends. In the framework of this approach, the spinodal decomposition is described as a relaxation of one‐time structure factor S(q,t) treated as an independent dynamic object (a peculiar two‐point order parameter). The dynamic equation for S(q,t), including the explicit expression for the corresponding effective kinetic coefficient, is derived. In the first approximation this equation is identical to the Langer equation. We first solved it both in terms of higher transcendental functions and numerically. The asymptotic behaviour of S(q,t) at large (from the onset of spinodal decomposition) times is analytically described. The values obtained for the power‐law growth exponent for the large‐time peak value and position of S(q,t) are in good agreement with experimental data and results of numerical integration of the Cahn‐Hilliard equation.     

Test of classical nucleation theory via molecular-dynamics simulation

A direct test of classical nucleation theory (CNT) is made using molecular-dynamics simulations. The relation between critical nucleus size and undercooling temperature is extracted and the result yields the solid-liquid interfacial energy. It is shown that the CNT, within the assumptions made for spherical nucleus in supercooled liquid, is valid in the critical regime of nucleation for a large range of undercooling and nucleus size.     

Contact angles, pore condensation, and hysteresis: insights from a simple molecular model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.