641 research outputs found
Phase Diagram of alpha-Helical and beta-Sheet Forming Peptides
The intrinsic property of proteins to form structural motifs such as
alpha-helices and beta-sheets leads to a complex phase behavior in which
proteins can assemble into various types of aggregates including crystals,
liquidlike phases of unfolded or natively folded proteins, and amyloid fibrils.
Here we use a coarse-grained protein model that enables us to perform Monte
Carlo simulations for determining the phase diagram of natively folded
alpha-helical and unfolded beta-sheet forming peptides. The simulations reveal
the existence of various metastable peptide phases. The liquidlike phases are
metastable with respect to the fibrillar phases, and there is a hierarchy of
metastability
Nucleation of colloids and macromolecules: does the nucleation pathway matter?
A recent description of diffusion-limited nucleation based on fluctuating
hydrodynamics that extends classical nucleation theory predicts a very
non-classical two-step scenario whereby nucleation is most likely to occur in
spatially-extended, low-amplitude density fluctuations. In this paper, it is
shown how the formalism can be used to determine the maximum probability of
observing \emph{any} proposed nucleation pathway, thus allowing one to address
the question as to their relative likelihood, including of the newly proposed
pathway compared to classical scenarios. Calculations are presented for the
nucleation of high-concentration bubbles in a low-concentration solution of
globular proteins and it is found that the relative probabilities (new theory
compared to classical result) for reaching a critical nucleus containing
molecules scales as thus indicating that for all but the smallest
nuclei, the classical scenario is extremely unlikely.Comment: 7 pages, 5 figure
Stochastic self-assembly of incommensurate clusters
We examine the classic problem of homogeneous nucleation and growth by
deriving and analyzing a fully discrete stochastic master equation. Upon
comparison with results obtained from the corresponding mean-field
Becker-D\"{o}ring equations we find striking differences between the two
corresponding equilibrium mean cluster concentrations. These discrepancies
depend primarily on the divisibility of the total available mass by the maximum
allowed cluster size, and the remainder. When such mass incommensurability
arises, a single remainder particle can "emulsify" or "disperse" the system by
significantly broadening the mean cluster size distribution. This finite-sized
broadening effect is periodic in the total mass of the system and can arise
even when the system size is asymptotically large, provided the ratio of the
total mass to the maximum cluster size is finite. For such finite ratios we
show that homogeneous nucleation in the limit of large, closed systems is not
accurately described by classical mean-field mass-action approaches.Comment: 5 pages, 4 figures, 1 tabl
Heterogeneous condensation of the Lennard-Jones vapor onto a nanoscale seed particle
The heterogeneous condensation of a Lennard-Jones vapor onto a nanoscale seed
particle is studied using molecular dynamics simulations. Measuring the
nucleation rate and the height of the free energy barrier using the mean first
passage time method shows that the presence of a weakly interacting seed has
little effect on the work of forming very small cluster embryos but accelerates
the rate by lowering the barrier for larger clusters. We suggest that this
results from a competition between the energetic and entropic features of
cluster formation in the bulk and at the heterogeneity. As the interaction is
increased, the free energy of formation is reduced for all cluster sizes. We
also develop a simple phenomenological model of film formation on a small seed
that captures the general features of the nucleation process for small
heterogeneities. A comparison of our simulation results with the model shows
that heterogeneous classical nucleation theory provides a good estimate of the
critical size of the film but significantly over-estimates the size of the
barrier.Comment: 9 pages, 10 figures, In Print J. Chem. Phy
Crystal nucleation and cluster-growth kinetics in a model glass under shear
Crystal nucleation and growth processes induced by an externally applied
shear strain in a model metallic glass are studied by means of nonequilibrium
molecular dynamics simulations, in a range of temperatures. We observe that the
nucleation-growth process takes place after a transient, induction regime. The
critical cluster size and the lag-time associated with this induction period
are determined from a mean first-passage time analysis. The laws that describe
the cluster growth process are studied as a function of temperature and strain
rate. A theoretical model for crystallization kinetics that includes the time
dependence for nucleation and cluster growth is developed within the framework
of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the
molecular dynamics data. Scalings for the cluster growth laws and for the
crystallization kinetics are also proposed and tested. The observed nucleation
rates are found to display a nonmonotonic strain rate dependency
Nucleation in scale-free networks
We have studied nucleation dynamics of the Ising model in scale-free networks
with degree distribution by using forward flux sampling
method, focusing on how the network topology would influence the nucleation
rate and pathway. For homogeneous nucleation, the new phase clusters grow from
those nodes with smaller degree, while the cluster sizes follow a power-law
distribution. Interestingly, we find that the nucleation rate decays
exponentially with the network size , and accordingly the critical nucleus
size increases linearly with , implying that homogeneous nucleation is not
relevant in the thermodynamic limit. These observations are robust to the
change of and also present in random networks. In addition, we have
also studied the dynamics of heterogeneous nucleation, wherein impurities
are initially added, either to randomly selected nodes or to targeted ones with
largest degrees. We find that targeted impurities can enhance the nucleation
rate much more sharply than random ones. Moreover, scales as and for targeted and
random impurities, respectively. A simple mean field analysis is also present
to qualitatively illustrate above simulation results.Comment: 7 pages, 5 figure
A dynamical theory of homogeneous nucleation for colloids and macromolecules
Homogeneous nucleation is formulated within the context of fluctuating
hydrodynamics. It is shown that for a colloidal or macromolecular system in the
strong damping limit the most likely path for nucleation can be determined by
gradient descent in density space governed by a nontrivial metric fixed by the
dynamics. The theory provides a justification and extension of more heuristic
equilibrium approaches based solely on the free energy. It is illustrated by
application to liquid-vapor nucleation where it is shown that, in contrast to
most free energy-based studies, the smallest clusters correspond to long
wavelength, small amplitude perturbations.Comment: final version; 4 pages, 2 figure
Systematic Improvement of Classical Nucleation Theory
We reconsider the applicability of classical nucleation theory (CNT) to the
calculation of the free energy of solid cluster formation in a liquid and its
use to the evaluation of interface free energies from nucleation barriers.
Using two different freezing transitions (hard spheres and NaCl) as test cases,
we first observe that the interface-free-energy estimates based on CNT are
generally in error. As successive refinements of nucleation-barrier theory, we
consider corrections due to a non-sharp solid-liquid interface and to a
non-spherical cluster shape. Extensive calculations for the Ising model show
that corrections due to a non-sharp and thermally fluctuating interface account
for the barrier shape with excellent accuracy. The experimental solid
nucleation rates that are measured in colloids are better accounted for by
these non-CNT terms, whose effect appears to be crucial in the interpretation
of data and in the extraction of the interface tension from them.Comment: 20 pages (text + supplementary material
Modeling of Nucleation Processes
Nucleation is the onset of a first-order phase transition by which a
metastable phase transforms into a more stable one. Such a phase transition
occurs when an initial system initially in equilibrium is destabilized by the
change of an external parameter like the temperature or the pressure. If the
perturbation is small enough, the system does not become unstable but rather
stays metastable. In diffusive transformations, the system then evolves through
the nucleation, the growth and the coarsening of a second phase. Such a phase
transformation is found in a lot of situations in materials science like
condensation of liquid droplets from a supersaturated vapor, solidification,
precipitation from a supersaturated solid solution, ... The initial stage of
all these different processes can be well described within the same framework.
Since its initial formulation in 1927 by Volmer, Weber and Farkas and its
modification in 1935 by Becker and D\"oring the classical nucleation theory has
been a suitable tool to model the nucleation stage in phase transformations. In
this article, we first describe this theory. A kinetic approach, the cluster
dynamics, can also be used to describe nucleation. This constitutes the second
part of this article. The links as well as the difference between both
descriptions are emphasized. Since its initial formulation, the classical
nucleation theory has been enriched, so as to take into account the fact that
clusters other than monomers can migrate and react. It has been also extended
to multi-component systems. These generalizations of the initial formalism are
also presented
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