50 research outputs found

### 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

### 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

### 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

### Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat
substrate is studied using the interface displacement model. First, the
apparent contact angle of a droplet on a heterogeneous surface under the
condition of constant volume is considered. By assuming a cylindrical
liquid-vapor surface (meniscus) and minimizing the total free energy, we derive
an equation for the apparent contact angle, which is similar but different from
the well-known Cassie's law. Next, using this modified Cassie's law as a guide
to predict the behavior of a droplet on a heterogeneous striped surface, we
examine several scenarios of contact angle hysteresis using a periodically
striped surface model. By changing the volume of the droplet, we predict a
sudden jump of the droplet edge, and a continuous change of the apparent
contact angle at the edge of two stripes. Our results suggest that as drop
volume is increased (advancing contact lines), the predominant drop
configuration observed is the one whose contact angle is large; whereas,
decreasing drop volume from a large value (receding contact lines) yields drop
configuration that predominantly exhibit the smaller contact angle.Comment: 14 pages, 7 figures, to be published in Journal of Colloid and
Interface Scienc

### 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