2,297 research outputs found
Equilibrium properties of charged microgels: a Poisson-Boltzmann-Flory approach
The equilibrium properties of ionic microgels are investigated using a
combination of the Poisson-Boltzmann and Flory theories. Swelling behavior,
density profiles, and effective charges are all calculated in a self-consistent
way. Special attention is given to the effects of salinity on these quantities.
It is found that the equilibrium microgel size is strongly influenced by the
amount of added salt. Increasing the salt concentration leads to a considerable
reduction of the microgel volume, which therefore releases its internal
material -- solvent molecules and dissociated ions -- into the solution.
Finally, the question of charge renormalization of ionic microgels in the
context of the cell model is briefly addressed
Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods
Polydispersity is believed to have important effects on the formation of
liquid crystal phases in suspensions of rod-like particles. To understand such
effects, we analyse the phase behaviour of thin hard rods with length
polydispersity. Our treatment is based on a simplified Onsager theory, obtained
by truncating the series expansion of the angular dependence of the excluded
volume. We describe the model and give the full phase equilibrium equations;
these are then solved numerically using the moment free energy method which
reduces the problem from one with an infinite number of conserved densities to
one with a finite number of effective densities that are moments of the full
density distribution. The method yields exactly the onset of nematic ordering.
Beyond this, results are approximate but we show that they can be made
essentially arbitrarily precise by adding adaptively chosen extra moments,
while still avoiding the numerical complications of a direct solution of the
full phase equilibrium conditions.
We investigate in detail the phase behaviour of systems with three different
length distributions: a (unimodal) Schulz distribution, a bidisperse
distribution and a bimodal mixture of two Schulz distributions which
interpolates between these two cases. A three-phase isotropic-nematic-nematic
coexistence region is shown to exist for the bimodal and bidisperse length
distributions if the ratio of long and short rod lengths is sufficiently large,
but not for the unimodal one. We systematically explore the topology of the
phase diagram as a function of the width of the length distribution and of the
rod length ratio in the bidisperse and bimodal cases.Comment: 18 pages, 16 figure
Topological Solitons and Folded Proteins
We propose that protein loops can be interpreted as topological domain-wall
solitons. They interpolate between ground states that are the secondary
structures like alpha-helices and beta-strands. Entire proteins can then be
folded simply by assembling the solitons together, one after another. We
present a simple theoretical model that realizes our proposal and apply it to a
number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data
Bank codes). In all the examples that we have considered we are able to
construct solitons that reproduce secondary structural motifs such as
alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall
root-mean-square-distance accuracy of around 0.7 Angstrom or less for the
central alpha-carbons, i.e. within the limits of current experimental accuracy.Comment: 4 pages, 4 figure
A graph theoretical analysis of the energy landscape of model polymers
In systems characterized by a rough potential energy landscape, local
energetic minima and saddles define a network of metastable states whose
topology strongly influences the dynamics. Changes in temperature, causing the
merging and splitting of metastable states, have non trivial effects on such
networks and must be taken into account. We do this by means of a recently
proposed renormalization procedure. This method is applied to analyze the
topology of the network of metastable states for different polypeptidic
sequences in a minimalistic polymer model. A smaller spectral dimension emerges
as a hallmark of stability of the global energy minimum and highlights a
non-obvious link between dynamic and thermodynamic properties.Comment: 15 pages, 15 figure
The Branched Polymer Growth Model Revisited
The Branched Polymer Growth Model (BPGM) has been employed to study the
kinetic growth of ramified polymers in the presence of impurities. In this
article, the BPGM is revisited on the square lattice and a subtle modification
in its dynamics is proposed in order to adapt it to a scenario closer to
reality and experimentation. This new version of the model is denominated the
Adapted Branched Polymer Growth Model (ABPGM). It is shown that the ABPGM
preserves the functionalities of the monomers and so recovers the branching
probability b as an input parameter which effectively controls the relative
incidence of bifurcations. The critical locus separating infinite from finite
growth regimes of the ABPGM is obtained in the (b,c) space (where c is the
impurity concentration). Unlike the original model, the phase diagram of the
ABPGM exhibits a peculiar reentrance.Comment: 8 pages, 10 figures. To be published in PHYSICA
Long Range Bond-Bond Correlations in Dense Polymer Solutions
The scaling of the bond-bond correlation function along linear polymer
chains is investigated with respect to the curvilinear distance, , along the
flexible chain and the monomer density, , via Monte Carlo and molecular
dynamics simulations. % Surprisingly, the correlations in dense three
dimensional solutions are found to decay with a power law with and the exponential behavior commonly assumed is
clearly ruled out for long chains. % In semidilute solutions, the density
dependent scaling of with
( being Flory's exponent) is set by the
number of monomers contained in an excluded volume blob of size
. % Our computational findings compare well with simple scaling arguments
and perturbation calculation. The power-law behavior is due to
self-interactions of chains on distances caused by the connectivity
of chains and the incompressibility of the melt. %Comment: 4 pages, 4 figure
Colloid-Induced Polymer Compression
We consider a model mixture of hard colloidal spheres and non-adsorbing
polymer chains in a theta solvent. The polymer component is modelled as a
polydisperse mixture of effective spheres, mutually noninteracting but excluded
from the colloids, with radii that are free to adjust to allow for
colloid-induced compression. We investigate the bulk fluid demixing behaviour
of this model system using a geometry-based density-functional theory that
includes the polymer size polydispersity and configurational free energy,
obtained from the exact radius-of-gyration distribution for an ideal
(random-walk) chain. Free energies are computed by minimizing the free energy
functional with respect to the polymer size distribution. With increasing
colloid concentration and polymer-to-colloid size ratio, colloidal confinement
is found to increasingly compress the polymers. Correspondingly, the demixing
fluid binodal shifts, compared to the incompressible-polymer binodal, to higher
polymer densities on the colloid-rich branch, stabilizing the mixed phase.Comment: 14 pages, 4 figure
Effective interactions between star polymers and colloidal particles
Using monomer-resolved Molecular Dynamics simulations and theoretical
arguments based on the radial dependence of the osmotic pressure in the
interior of a star, we systematically investigate the effective interactions
between hard, colloidal particles and star polymers in a good solvent. The
relevant parameters are the size ratio q between the stars and the colloids, as
well as the number of polymeric arms f (functionality) attached to the common
center of the star. By covering a wide range of q's ranging from zero (star
against a flat wall) up to about 0.75, we establish analytical forms for the
star-colloid interaction which are in excellent agreement with simulation
results. A modified expression for the star-star interaction for low
functionalities, f < 10 is also introduced.Comment: 37 pages, 14 figures, preprint-versio
Percolation and jamming in random sequential adsorption of linear segments on square lattice
We present the results of study of random sequential adsorption of linear
segments (needles) on sites of a square lattice. We show that the percolation
threshold is a nonmonotonic function of the length of the adsorbed needle,
showing a minimum for a certain length of the needles, while the jamming
threshold decreases to a constant with a power law. The ratio of the two
thresholds is also nonmonotonic and it remains constant only in a restricted
range of the needles length. We determine the values of the correlation length
exponent for percolation, jamming and their ratio
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