Scenarios of heterogeneous nucleation and growth studied by cell dynamics simulation

The dynamics of phase transformation due to homogeneous nucleation has long been analyzed using the classic Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. However, the dynamics of phase transformation due to heterogeneous nucleation has not been studied systematically even though it is vitally important technologically. In this report, we study the dynamics of heterogeneous nucleation theoretically and systematically using the phenomenological time-dependent Ginzburg-Landau (TDGL)-type model combined with the cell dynamics method. In this study we focus on the dynamics of phase transformation when the material is sandwiched by two supporting substrates. This model is supposed to simulates phase change storage media. Since both homogeneous and heterogeneous nucleation can occur simultaneously, we predict a few scenarios of phase transformation including: homogeneous-nucleation regime, heterogeneous-nucleation regime, and the homogeneous-heterogeneous coexistence regime. These predictions are directly confirmed by numerical simulation using the TDGL model. The outcome of the study was that the KJMA formula has limited use when heterogeneous nucleation exist, but it could still give some information about the microscopic mechanism of phase transformation at various stages during phase transformation.Comment: 10 pages, 11 figures, J. Chem. Phys. accepted for publicatio

A note on the nucleation with multiple steps: Parallel and series nucleation

Parallel and series nucleation are the basic elements of the complex nucleation process when two saddle points exist on the free-energy landscape. It is pointed out that the nucleation rates follow formulas similar to those of parallel and series connection of resistors or conductors in an electric circuit. Necessary formulas to calculate individual nucleation rates at the saddle points and the total nucleation rate are summarized and the extension to the more complex nucleation process is suggested.Comment: 5 pages, 4 figures, to be published in Journal of Chemical Physic

Line-tension-induced scenario of heterogeneous nucleation on a spherical substrate and in a spherical cavity

Line-tension-induced {scenario of heterogeneous nucleation} is studied for a lens-shaped nucleus with a finite contact angle nucleated on a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the free energy of a critical nucleus can be separated from the usual volume term. By comparing the free energy of a lens-shaped critical nucleus of a finite contact angle with that of a spherical nucleus, we find that a spherical nucleus may have a lower free energy than a lens-shaped nucleus when the line tension is positive and large, which is similar to the drying transition predicted by Widom [B. Widom, J. Phys. Chem. {\bf 99} 2803 (1995)]. Then, the homogeneous nucleation rather than the heterogeneous nucleation will be favorable. Similarly, the free energy of a lens-shaped nucleus becomes negative when the line tension is negative and large. Then, the barrier-less nucleation with no thermal activation called athermal nucleation will be realized.Comment: 13 pages, 13 figures, Journal of Chemical Physics to be publishe

Nucleation pathway of core-shell composite nucleus in size and composition space and in component space

The kinetics of nucleation of a core-shell composite nucleus that consists of a core of stable final phase surrounded by a wetting layer of intermediate metastable phase is studied using the kinetic theory of binary nucleation not only in the size and composition space but also in the component space. The steady-state solution of the Fokker-Planck equation is considered. Various formulas for the critical nucleus at the saddle point as well as for the post-critical nucleus are derived. The kinetics of nucleation at the saddle point is more appropriately characterized in the size and composition space, while the kinetics of the post-critical nucleus is more appropriately described in the component space. Although both the free-energy landscape and the reaction rates play decisive role to determine the kinetics of nucleation at the saddle point, the details of the free energy landscape are irrelevant to the kinetics of the post critical nucleus.Comment: 9 pages, 2 figures, Physical Review E to be publishe

Cell dynamics modeling of phase transformation and metastable phase formation

The phase transition kinetics in three phase systems was investigated using the numerically efficient cell dynamics method. A phasefield model with a simple analytical free energy and single order parameter was used to study the kinetics and the thermodynamics of a three-phase system. This free energy is able to achieve three phases coexistence, which for simplicity we call \alpha, \beta and \gamma phases. Our study focused on the kinetics of phase transition rather than the nucleation of a seed of a new phase that was introduced into the matrix of the old phase when the relative stability of the three phases were changed. We found dynamical as well as kinetically arrested static scenarios in the appearance of the macroscopic metastable phase. A few other interesting scenarios of the kinetics of phase transition in this three-phase system will be demonstrated and discussed.Comment: 4 pages 8 figures, conference (ISMANAM2009) paper, to be published in Jouranl of Alloys and Compound

Dynamics of condensation of wetting layer in time-dependent Ginzburg-Landau model

The dynamics of liquid condensation on a substrate or within a capillary is studied when the wetting film grows via interface-limited growth. We use a phenomenological time-dependent Ginzburg-Landau (TDGL)-type model with long-range substrate potential. Using an order parameter, which does not directly represent the density, we can derive an analytic formula for the interfacial growth velocity that is directly related to the substrate potential. Using this analytic expression the growth of wetting film is shown to conform to a power-law-type growth, which is due to the presence of a long-range dispersion force.Comment: 12 pages, 3 figures, J.Colloid Interface Sci. accepted for publicatio

Topography- and topology-driven spreading of non-Newtonian power-law liquids on a flat and a spherical substrate

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle $\theta$ of a droplet obeys a power law decay $\theta \sim t^{-\alpha}$ except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent $\alpha$ of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.Comment: 12 pages, 6 figures, Physical Review E to be publishe

The validity of Cassie's law: A simple exercise using a simplified model

The contact angle of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model which can lead to the augmented Young-Laplace equation. Droplets under the condition of constant volume as well as constant vapor pressure are considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy of the interface displacement model, we derive an equation which is similar but different from the well known Cassie's law. Our modified Cassie's law is essentially the same as the formula obtained previously by Marmur [J.Colloid Interface Sci. {\bf 168}, 40 (1994)]. A few consequences from this modified Cassie's law will be briefly described in the following sections of this paper. Several sets of recent experimental results seem to support the validity of our modified Cassie's law.Comment: 13 pages, 3 figure

Heterogeneous nucleation on a completely wettable substrate

It is widely believed that heterogeneous nucleation occurs without an activation process when the surface is completely wettable. In this report, we review our previous work [J.Chem.Phys {\bf 134}, 234709 (2011)] to show that the critical nucleus (droplet) can exist and the activation process may be observable. In fact, a critical nucleus and a free energy barrier always exist if the surface potential or the disjoining pressure allows for the first-order pre-wetting transition on a completely wettable substrate where the contact angle is zero. Furthermore, the critical nucleus changes character from the critical nucleus of surface phase transition below bulk coexistence (undersaturation) to the critical nucleus of bulk heterogeneous nucleation above the coexistence (oversaturation) when it crosses the coexistence. In this paper the morphology and work of formation of a critical nucleus on a completely-wettable substrate are re-examined to point out the possibility of observing a critical droplet on a completely wettable substrate.Comment: 28 pages 12 figures, Chapter 3 of "Advances in Contact Angle, Wettability and Adhesion", ed. by K.L. Mittal, Scrivener Publishing LLC, ISBN:9781118472927 to be publise

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

A generalized Young's equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid-vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman's formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of $\mu$N so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretical calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible.Comment: 15 pages, 3 figures, Journal of Adhesion Science and Technology (Taylor & Francis) accepted for publicatio