323 research outputs found
On the Kinetics of Body versus End Evaporation and Addition of Supramolecular Polymers
Although pathway-specific kinetic theories are fundamentally important to
describe and understand reversible polymerisation kinetics, they come in
principle at a cost of having a large number of system-specific parameters.
Here, we construct a dynamical Landau theory to describe the kinetics of
activated linear supramolecular self-assembly, which drastically reduces the
number of parameters and still describes most of the interesting and generic
behavior of the system in hand. This phenomenological approach hinges on the
fact that if nucleated, the polymerisation transition resembles a phase
transition. We are able to describe hysteresis, overshooting, undershooting and
the existence of a lag time before polymerisation takes off, and pinpoint the
conditions required for observing these types of phenomenon in the assembly and
disassembly kinetics. We argue that the phenomenological kinetic parameter in
our theory is a pathway controller, i.e., it controls the relative weights of
the molecular pathways through which self-assembly takes place
Connectedness percolation of hard convex polygonal rods and platelets
The properties of polymer composites with nanofiller particles change
drastically above a critical filler density known as the percolation threshold.
Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not
idealized disks and rods but are often modeled as such. Here we investigate the
effect of the shape of the particle cross section on the geometric percolation
threshold. Using connectedness percolation theory and the second-virial
approximation, we analytically calculate the percolation threshold of hard
convex particles in terms of three single-particle measures. We apply this
method to polygonal rods and platelets and find that the universal scaling of
the percolation threshold is lowered by decreasing the number of sides of the
particle cross section. This is caused by the increase of the surface area to
volume ratio with decreasing number of sides.Comment: 7 pages, 3 figures; added references, corrected typo, results
unchange
Impact of Interaction Range and Curvature on Crystal Growth of Particles Confined to Spherical Surfaces
When colloidal particles form a crystal phase on a spherical template, their
packing is governed by the effective interaction between them and the elastic
strain of bending the growing crystal. For example, if growth commences under
appropriate conditions, and the circular crystal that forms reaches a critical
size, growth continues by incorporation of defects to alleviate elastic strain.
Recently it was found experimentally that, if defect formation is somehow not
possible, the crystal instead continues growing in ribbons that protrude from
the original crystal. Here we report on computer simulations in which we
observe both the formation of ribbons at short interaction ranges and packings
that incorporate defects if the interaction is longer-ranged. The ribbons only
form above some critical crystal size, below which the nucleus is roughly
spherically shaped. We find that the scaling of the critical crystal size
differs slightly from the one proposed by the Manoharan group, and reason this
is because the actual process is a two-step heterogeneous nucleation of ribbons
on top of roughly circular crystals.Comment: 24 pages, 11 figure
A macroscopic model for sessile droplet evaporation on a flat surface
The evaporation of sessile droplets on a flat surface involves a complex
interplay between phase change, diffusion, advection and surface forces. In an
attempt to significantly reduce the complexity of the problem and to make it
manageable, we propose a simple model hinged on a surface free energy-based
relaxation dynamics of the droplet shape, a diffusive evaporation model and a
contact line pinning mechanism governed by a yield stress. Our model reproduces
the known dynamics of droplet shape relaxation and of droplet evaporation, both
in the absence and in the presence of contact line pinning. We show that shape
relaxation during evaporation significantly affects the lifetime of a drop. We
find that the dependence of the evaporation time on the initial contact angle
is a function of the competition between the shape relaxation and evaporation,
and is strongly affected by any contact line pinning.Comment: 13 pages, 8 figure
Comment on "Large Difference in the Elastic Properties of fcc and hcp Hard-Sphere Crystals"
As is well known, hard-sphere crystals of the fcc and hcp type differ very
little in their thermodynamic properties. Nonetheless, recent computer
simulations by Pronk and Frenkel indicate that the elastic response to
mechanical deformation of the two types of crystal should be quite different.
By invoking a geometrical argument put forward by R. Martin some time ago, we
suggest that this is largely due to the different symmetries of the fcc and hcp
crystal structures. Indeed, we find that elastic constants obtained by means of
computer simulations for the fcc hard-sphere crystal can be mapped onto the
equivalent ones of the hcp crystal to very high accuracy. The same procedure
applied to density functional theoretical predictions for the elastic
properties of the fcc hard-sphere crystal also produces remarkably accurate
predictions for those of the hcp hard-sphere crystal.Comment: 7 pages, 5 figure
Electrostatic Theory of the Acidity of the Solution in the Lumina of Viruses and Virus-Like Particles
Recently, Maassen et al. measured an appreciable pH difference between the bulk solution and the solution in the lumen of virus-like particles, self-assembled in an aqueous buffer solution containing the coat proteins of a simple plant virus and polyanions (Maassen, S. J.; et al. Small 2018, 14, 1802081). They attribute this to the Donnan effect, caused by an imbalance between the number of negative charges on the encapsulated polyelectrolyte molecules and the number of positive charges on the RNA binding domains of the coat proteins that make up the virus shell or capsid. By applying Poisson-Boltzmann theory, we confirm this conclusion and show that simple Donnan theory is accurate even for the smallest of viruses and virus-like particles. This, in part, is due to the additional screening caused by the presence of a large number of immobile charges in the cavity of the shell. The presence of a net charge on the outer surface of the capsid we find in practice to not have a large effect on the pH shift. Hence, Donnan theory can indeed be applied to connect the local pH and the amount of encapsulated material. The large shifts up to a full pH unit that we predict must have consequences for applications of virus capsids as nanocontainers in bionanotechnology and artificial cell organelles.</p
The effect of RNA stiffness on the self-assembly of virus particles
Under many in vitro conditions, some small viruses spontaneously encapsidate
a single stranded (ss) RNA into a protein shell called the capsid. While viral
RNAs are found to be compact and highly branched because of long distance
base-pairing between nucleotides, recent experiments reveal that in a
head-to-head competition between a ssRNA with no secondary or higher order
structure and a viral RNA, the capsid proteins preferentially encapsulate the
linear polymer! In this paper, we study the impact of genome stiffness on the
encapsidation free energy of the complex of RNA and capsid proteins. We show
that an increase in effective chain stiffness because of base-pairing could be
the reason why under certain conditions linear chains have an advantage over
branched chains when it comes to encapsidation efficiency. While branching
makes the genome more compact, RNA base-pairing increases the effective Kuhn
length of the RNA molecule, which could result in an increase of the free
energy of RNA confinement, that is, the work required to encapsidate RNA, and
thus less efficient packaging
Role of Genome in the Formation of Conical Retroviral Shells
Human immunodeficiency virus (HIV) capsid proteins spontaneously assemble
around the genome into a protective protein shell called the capsid, which can
take on a variety of shapes broadly classified as conical, cylindrical and
irregular. The majority of capsids seen in in vivo studies are conical in
shape, while in vitro experiments have shown a preference for cylindrical
capsids. The factors involved in the selection of the unique shape of HIV
capsids are not well understood, and in particular the impact of RNA on the
formation of the capsid is not known. In this work, we study the role of the
genome and its interaction with the capsid protein by modeling the genomic RNA
through a mean-field theory. Our results show that the confinement free energy
for a homopolymeric model genome confined in a conical capsid is lower than
that in a cylindrical capsid, at least when the genome does not interact with
the capsid, which seems to be the case in in vivo experiments. Conversely, the
confinement free energy for the cylinder is lower than for a conical capsid if
the genome is attracted to the capsid proteins as the in vitro experiments.
Understanding the factors that contribute to the formation of conical capsids
may shed light on the infectivity of HIV particles.Comment: 22 pages, 7 figures in J. Phys. Chem. B, 201
Quasiuniversal connectedness percolation of polydisperse rod systems
The connectedness percolation threshold (eta_c) and critical coordination
number (Z_c) of systems of penetrable spherocylinders characterized by a length
polydispersity are studied by way of Monte Carlo simulations for several aspect
ratio distributions. We find that (i) \eta_c is a nearly universal function of
the weight-averaged aspect ratio, with an approximate inverse dependence that
extends to aspect ratios that are well below the slender rod limit and (ii)
that percolation of impenetrable spherocylinders displays a similar
quasiuniversal behavior. For systems with a sufficiently high degree of
polydispersity, we find that Z_c can become smaller than unity, in analogy with
observations reported for generalized and complex networks.Comment: 5 pages with 3 figures + 2 pages and 4 figures of supplemental
materia
Impact of a non-uniform charge distribution on virus assembly
Many spherical viruses encapsulate their genome in protein shells with
icosahedral symmetry. This process is spontaneous and driven by electrostatic
interactions between positive domains on the virus coat proteins and the
negative genome. We model the effect of the icosahedral charge distribution
from the protein shell instead of uniform using a mean-field theory. We find
that the non-uniform charge distribution strongly affects the optimal genome
length, and that it can explain the experimentally observed phenomenon of
overcharging of virus and virus-like particles
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