379 research outputs found

### Minimum free-energy path of homogenous nucleation from the phase-field equation

The minimum free-energy path (MFEP) is the most probable route of the
nucleation process on the multidimensional free-energy surface. In this study,
the phase-field equation is used as a mathematical tool to deduce the minimum
free-energy path (MFEP) of homogeneous nucleation. We use a simple
square-gradient free-energy functional with a quartic local free-energy
function as an example and study the time evolution of a single nucleus placed
within a metastable environment. The time integration of the phase-field
equation is performed using the numerically efficient cell-dynamics method. By
monitoring the evolution of the size of the nucleus and the free energy of the
system simultaneously, we can easily deduce the free-energy barrier as a
function of the size of the sub- and the super-critical nucleus along the MFEP.Comment: 8 pages, 5 figures, Journal of Chemical Physics accepted for
publicatio

### A Finite-Size Scaling Study of a Model of Globular Proteins

Grand canonical Monte Carlo simulations are used to explore the metastable
fluid-fluid coexistence curve of the modified Lennard-Jones model of globular
proteins of ten Wolde and Frenkel (Science, v277, 1975 (1997)). Using both
mixed-field finite-size scaling and histogram reweighting methods, the joint
distribution of density and energy fluctuations is analyzed at coexistence to
accurately determine the critical-point parameters. The subcritical coexistence
region is explored using the recently developed hyper-parallel tempering Monte
Carlo simulation method along with histogram reweighting to obtain the density
distributions. The phase diagram for the metastable fluid-fluid coexistence
curve is calculated in close proximity to the critical point, a region
previously unattained by simulation.Comment: 17 pages, 10 figures, 2 Table

### Anharmonic quantum contribution to vibrational dephasing

Based on a quantum Langevin equation and its corresponding Hamiltonian within
a c-number formalism we calculate the vibrational dephasing rate of a cubic
oscillator. It is shown that leading order quantum correction due to
anharmonicity of the potential makes a significant contribution to the rate and
the frequency shift. We compare our theoretical estimates with those obtained
from experiments for small diatomics $N_2$, $O_2$ and $CO$.Comment: 21 pages, 1 figure and 1 tabl

### Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational
energy relaxation (VER) and dephasing for an anharmonic system oscillator using
a time-dependent perturbation theory. The system-bath Hamiltonian contains more
than the third order coupling terms since we take a normal mode picture as a
zeroth order approximation. When we invoke the Markov approximation, our theory
reduces to the Maradudin-Fein formula which is used to describe VER properties
of glass and proteins. When the system anharmonicity and the renormalization
effect due to the environment vanishes, our formulas reduce to those derived by
Mikami and Okazaki invoking the path-integral influence functional method [J.
Chem. Phys. 121 (2004) 10052]. We apply our formulas to VER of the amide I mode
of a small amino-acide like molecule, N-methylacetamide, in heavy water.Comment: 16 pages, 5 figures, 5 tables, submitted to J. Chem. Phy

### Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

The square-gradient density-functional model with triple-parabolic free
energy is used to study homogeneous bubble nucleation in a stretched liquid to
check the scaling rule for the work of formation of the critical bubble as a
function of scaled undersaturation $\Delta\mu/\Delta\mu_{\rm spin}$, the
difference in chemical potential $\Delta\mu$ between the bulk undersaturated
and saturated liquid divided by $\Delta\mu_{\rm spin}$ between the liquid
spinodal and saturated liquid. In contrast to our study, a similar
density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J.
Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation
but other various quantities related to the critical bubble show the scaling
rule, however, we found virtually no scaling relationships in our model near
the coexistence. Although some quantities show almost perfect scaling relations
near the spinodal, the work of formation divided by the value deduced from the
classical nucleation theory shows no scaling in this model even though it
correctly vanishes at the spinodal. Furthermore, the critical bubble does not
show any anomaly near the spinodal as predicted many years ago. In particular,
our model does not show diverging interfacial width at the spinodal, which is
due to the fact that compressibility remains finite until the spinodal is
reached in our parabolic models.Comment: 10 pages, 10 figures, Journal of Chemical Physics accepted for
publicatio

### Simulation and theory of vibrational phase relaxation in the critical and supercritical nitrogen: Origin of observed anomalies

We present results of extensive computer simulations and theoretical analysis
of vibrational phase relaxation of a nitrogen molecule along the critical
isochore and also along the gas-liquid coexistence. The simulation includes all
the different contributions [atom-atom (AA), vibration-rotation (VR) and
resonant transfer] and their cross-correlations. Following Everitt and Skinner,
we have included the vibrational coordinate ($q$) dependence of the interatomic
potential. It is found that the latter makes an important contribution. The
principal important results are: (a) a crossover from a Lorentzian-type to a
Gaussian line shape is observed as the critical point is approached along the
isochore (from above), (b) the root mean square frequency fluctuation shows
nonmonotonic dependence on the temperature along critical isochore, (c) along
the coexistence line and the critical isochore the temperature dependent
linewidth shows a divergence-like $\lambda$-shape behavior, and (d) the value
of the critical exponents along the coexistence and along the isochore are
obtained by fitting. The origin of the anomalous temperature dependence of
linewidth can be traced to simultaneous occurrence of several factors, (i) the
enhancement of negative cross-correlations between AA and VR contributions and
(ii) the large density fluctuations as the critical point (CP) is approached.
The former makes the decay faster so that local density fluctuations are probed
on a femtosecond time scale. A mode coupling theory (MCT) analysis shows the
slow decay of the enhanced density fluctuations near critical point. The MCT
analysis demonstrates that the large enhancement of VR coupling near CP arises
from the non-Gaussian behavior of density fluctuation and this enters through a
nonzero value of the triplet direct correlation function.Comment: 35 pages, 15 figures, revtex4 (preprint form

### Stability of critical bubble in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

The square-gradient density-functional model with triple-parabolic free
energy, that was used previously to study the homogeneous bubble nucleation [J.
Chem. Phys. 129, 104508 (2008)], is used to study the stability of the critical
bubble nucleated within the bulk under-saturated stretched fluid. The stability
of the bubble is studied by solving the Schr\"odinger equation for the
fluctuation. The negative eigenvalue corresponds to the unstable growing mode
of the fluctuation. Our results show that there is only one negative eigenvalue
whose eigenfunction represents the fluctuation that corresponds to the
isotropically growing or shrinking nucleus. In particular, this negative
eigenvalue survives up to the spinodal point. Therefore the critical bubble is
not fractal or ramified near the spinodal.Comment: 9 pages, 8 figures, Journal of Chemical Physics accepted for
publicatio

### Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids

Notwithstanding the long and distinguished history of studies of vibrational
energy relaxation, exactly how it is that high frequency vibrations manage to
relax in a liquid remains somewhat of a mystery. Both experimental and
theoretical approaches seem to say that there is a natural frequency range
associated with intermolecular motions in liquids, typically spanning no more
than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent
can absorb any vibrational energy within this "band", but how is it that
molecules can rid themselves of superfluous vibrational energies significantly
in excess of these values? We develop a theory for such processes based on the
idea that the crucial liquid motions are those that most rapidly modulate the
force on the vibrating coordinate -- and that by far the most important of
these motions are those involving what we have called the mutual nearest
neighbors of the vibrating solute. Specifically, we suggest that whenever there
is a single solvent molecule sufficiently close to the solute that the solvent
and solute are each other's nearest neighbors, then the instantaneous
scattering dynamics of the solute-solvent pair alone suffices to explain the
high frequency relaxation. The many-body features of the liquid only appear in
the guise of a purely equilibrium problem, that of finding the likelihood of
particularly effective solvent arrangements around the solute. These results
are tested numerically on model diatomic solutes dissolved in atomic fluids
(including the experimentally and theoretically interesting case of I_2 in Xe).
The instantaneous pair theory leads to results in quantitative agreement with
those obtained from far more laborious exact molecular dynamics simulations.Comment: 55 pages, 6 figures Scheduled to appear in J. Chem. Phys., Jan, 199

### A diffusion-induced transition in the phase separation of binary fluid mixtures subjected to a temperature ramp

Demixing of binary fluids subjected to slow temperature ramps shows repeated
waves of nucleation which arise as a consequence of the competition between
generation of supersaturation by the temperature ramp and relaxation of
supersaturation by diffusive transport and flow. Here, we use an
advection-reaction-diffusion model to study the oscillations in the weak- and
strong-diffusion regime. There is a sharp transition between the two regimes,
which can only be understood based on the probability distribution function of
the composition rather than in terms of the average composition. We argue that
this transition might be responsible for some yet unclear features of
experiments, like the appearance of secondary oscillations and bimodal droplet
size distributions.Comment: 6 pages, 3 color figure

### Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Homogeneous nucleation and growth in a simplest two-dimensional phase field
model is numerically studied using the cell dynamics method. Whole process from
nucleation to growth is simulated and is shown to follow closely the
Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation.
Specifically the time evolution of the volume fraction of new stable phase is
found to follow closely the KJMA formula. By fitting the KJMA formula directly
to the simulation data, not only the Avrami exponent but the magnitude of
nucleation rate and, in particular, of incubation time are quantitatively
studied. The modified Avrami plot is also used to verify the derived KJMA
parameters. It is found that the Avrami exponent is close to the ideal
theoretical value m=3. The temperature dependence of nucleation rate follows
the activation-type behavior expected from the classical nucleation theory. On
the other hand, the temperature dependence of incubation time does not follow
the exponential activation-type behavior. Rather the incubation time is
inversely proportional to the temperature predicted from the theory of
Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to
restrict thermal noise in simulation to deduce correct Avrami exponent is also
discussed.Comment: 9 pages, 8 figures, Journal of Chemical Physics to be publishe

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