1,414 research outputs found
A Note on Distance-Based Entropy of Dendrimers
This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs
A model of inversion of DNA charge by a positive polymer: fractionization of the polymer charge
Charge inversion of a DNA double helix by an oppositely charged flexible
polyelectrolyte (PE) is considered. We assume that, in the neutral state of the
DNA-PE complex, each of the DNA charges is locally compensated by a PE charge.
When an additional PE molecule is adsorbed by DNA, its charge gets fractionized
into monomer charges of defects (tails and arches) on the background of the
perfectly neutralized DNA. These charges spread all over the DNA eliminating
the self-energy of PE. This fractionization mechanism leads to a substantial
inversion of the DNA charge, a phenomenon which is widely used for gene
delivery.Comment: 4 pages, 2 figures. Improved figures and various corrections to tex
A density-functional theory investigation of cluster formation in an effective-potential model of dendrimers
We consider a system of particles interacting via a purely repulsive,
soft-core potential recently introduced to model effective pair interactions
between dendrimers, which is expected to lead to the formation of crystals with
multiple occupancy of the lattice sites. The phase diagram is investigated by
density-functional theory (DFT) without making any a priori assumption on the
functional form of the density profile or on the type of crystal lattice. As
the average density is increased, the system displays first a transition
from a fluid to a bcc phase, and subsequently to hcp and fcc phases. In the
inhomogeneous region, the behavior is that found in previous investigations of
this class of cluster-forming potentials. Specifically, the particles arrange
into clusters strongly localized at the lattice sites, and the lattice constant
depends very weakly on , leading to an occupancy number of the sites
which is a nearly linear function of . These results are compared to
those predicted by the more widespread approach, in which the DFT minimization
is carried out by representing the density profile by a given functional form
depending on few variational parameters. We find that for the model potential
studied here, the latter approach recovers most of the predictions of the
unconstrained minimization.Comment: 22 pages, 7 figures. To appear in a Festschrift Issue of Transactions
of The Royal Norwegian Society of Sciences and Letters (DKNVS) dedicated to
Johan Hoye on his 70th birthda
Self Assembly of Soft Matter Quasicrystals and Their Approximants
The surprising recent discoveries of quasicrystals and their approximants in
soft matter systems poses the intriguing possibility that these structures can
be realized in a broad range of nano- and micro-scale assemblies. It has been
theorized that soft matter quasicrystals and approximants are largely
entropically stabilized, but the thermodynamic mechanism underlying their
formation remains elusive. Here, we use computer simulation and free energy
calculations to demonstrate a simple design heuristic for assembling
quasicrystals and approximants in soft matter systems. Our study builds on
previous simulation studies of the self-assembly of dodecagonal quasicrystals
and approximants in minimal systems of spherical particles with complex,
highly-specific interaction potentials. We demonstrate an alternative
entropy-based approach for assembling dodecagonal quasicrystals and
approximants based solely on particle functionalization and shape, thereby
recasting the interaction-potential-based assembly strategy in terms of
simpler-to-achieve bonded and excluded-volume interactions. Here, spherical
building blocks are functionalized with mobile surface entities to encourage
the formation of structures with low surface contact area, including
non-close-packed and polytetrahedral structures. The building blocks also
possess shape polydispersity, where a subset of the building blocks deviate
from the ideal spherical shape, discouraging the formation of close-packed
crystals. We show that three different model systems with both of these
features -- mobile surface entities and shape polydispersity -- consistently
assemble quasicrystals and/or approximants. We argue that this design strategy
can be widely exploited to assemble quasicrystals and approximants on the nano-
and micro- scales. In addition, our results further elucidate the formation of
soft matter quasicrystals in experiment.Comment: 12 pages 6 figure
Cluster and reentrant anomalies of nearly Gaussian core particles
We study through integral equation theory and numerical simulations the
structure and dynamics of fluids composed of ultrasoft, nearly Gaussian
particles. Namely, we explore the fluid phase diagram of a model in which
particles interact via the generalized exponential potential u(r)=\epsilon
exp[-(r/\sigma)^n], with a softness exponent n slightly larger than 2. In
addition to the well-known anomaly associated to reentrant melting, the
structure and dynamics of the fluid display two additional anomalies, which are
visible in the isothermal variation of the structure factor and diffusivity.
These features are correlated to the appearance of dimers in the fluid phase
and to the subsequent modification of the cluster structure upon compression.
We corroborate these results through an analysis of the local minima of the
potential energy surface, in which clusters appear as much tighter
conglomerates of particles. We find that reentrant melting and clustering
coexist for softness exponents ranging from 2^+ up to values relevant for the
description of amphiphilic dendrimers, i.e., n=3.Comment: 10 pages, 8 figure
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