4,137 research outputs found

### Dynamics of Diblock Copolymers in Dilute Solutions

We consider the dynamics of freely translating and rotating diblock (A-B),
Gaussian copolymers, in dilute solutions. Using the multiple scattering
technique, we have computed the diffusion and the friction coefficients D_AB
and Zeta_AB, and the change Eta_AB in the viscosity of the solution as
functions of x = N_A/N and t = l_B/l_A, where N_A, N are the number of segments
of the A block and of the whole copolymer, respectively, and l_A, l_B are the
Kuhn lengths of the A and B blocks. Specific regimes that maximize the
efficiency of separation of copolymers with distinct "t" values, have been
identified.Comment: 20 pages Revtex, 7 eps figures, needs epsf.tex and amssymb.sty,
submitted to Macromolecule

### Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

The critical behavior of long straight rigid rods of length $k$ ($k$-mers) on
square and triangular lattices at intermediate density has been studied. A
nematic phase, characterized by a big domain of parallel $k$-mers, was found.
This ordered phase is separated from the isotropic state by a continuous
transition occurring at a intermediate density $\theta_c$. Two analytical
techniques were combined with Monte Carlo simulations to predict the dependence
of $\theta_c$ on $k$, being $\theta_c(k) \propto k^{-1}$. The first involves
simple geometrical arguments, while the second is based on entropy
considerations. Our analysis allowed us also to determine the minimum value of
$k$ ($k_{min}=7$), which allows the formation of a nematic phase on a
triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic

### Apex Exponents for Polymer--Probe Interactions

We consider self-avoiding polymers attached to the tip of an impenetrable
probe. The scaling exponents $\gamma_1$ and $\gamma_2$, characterizing the
number of configurations for the attachment of the polymer by one end, or at
its midpoint, vary continuously with the tip's angle. These apex exponents are
calculated analytically by $\epsilon$-expansion, and numerically by simulations
in three dimensions. We find that when the polymer can move through the
attachment point, it typically slides to one end; the apex exponents quantify
the entropic barrier to threading the eye of the probe

### Self-consistent variational theory for globules

A self-consistent variational theory for globules based on the uniform
expansion method is presented. This method, first introduced by Edwards and
Singh to estimate the size of a self-avoiding chain, is restricted to a good
solvent regime, where two-body repulsion leads to chain swelling. We extend the
variational method to a poor solvent regime where the balance between the
two-body attractive and the three-body repulsive interactions leads to
contraction of the chain to form a globule. By employing the Ginzburg
criterion, we recover the correct scaling for the $\theta$-temperature. The
introduction of the three-body interaction term in the variational scheme
recovers the correct scaling for the two important length scales in the globule
- its overall size $R$, and the thermal blob size $\xi_{T}$. Since these two
length scales follow very different statistics - Gaussian on length scales
$\xi_{T}$, and space filling on length scale $R$ - our approach extends the
validity of the uniform expansion method to non-uniform contraction rendering
it applicable to polymeric systems with attractive interactions. We present one
such application by studying the Rayleigh instability of polyelectrolyte
globules in poor solvents. At a critical fraction of charged monomers, $f_c$,
along the chain backbone, we observe a clear indication of a first-order
transition from a globular state at small $f$, to a stretched state at large
$f$; in the intermediate regime the bistable equilibrium between these two
states shows the existence of a pearl-necklace structure.Comment: 7 pages, 1 figur

### One size fits all: equilibrating chemically different polymer liquids through universal long-wavelength description

Mesoscale behavior of polymers is frequently described by universal laws.
This physical property motivates us to propose a new modeling concept, grouping
polymers into classes with a common long-wavelength representation. In the same
class samples of different materials can be generated from this representation,
encoded in a single library system. We focus on homopolymer melts, grouped
according to the invariant degree of polymerization. They are described with a
bead-spring model, varying chain stiffness and density to mimic chemical
diversity. In a renormalization group-like fashion library samples provide a
universal blob-based description, hierarchically backmapped to create
configurations of other class-members. Thus large systems with
experimentally-relevant invariant degree of polymerizations (so far accessible
only on very coarse-grained level) can be microscopically described.
Equilibration is verified comparing conformations and melt structure with
smaller scale conventional simulations

### T-duality and Differential K-Theory

We give a precise formulation of T-duality for Ramond-Ramond fields. This
gives a canonical isomorphism between the "geometrically invariant" subgroups
of the twisted differential K-theory of certain principal torus bundles. Our
result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy

### Corrections to scaling in multicomponent polymer solutions

We calculate the correction-to-scaling exponent $\omega_T$ that characterizes
the approach to the scaling limit in multicomponent polymer solutions. A direct
Monte Carlo determination of $\omega_T$ in a system of interacting
self-avoiding walks gives $\omega_T = 0.415(20)$. A field-theory analysis based
on five- and six-loop perturbative series leads to $\omega_T = 0.41(4)$. We
also verify the renormalization-group predictions for the scaling behavior
close to the ideal-mixing point.Comment: 21 page

### Some Relations between Twisted K-theory and E8 Gauge Theory

Recently, Diaconescu, Moore and Witten provided a nontrivial link between
K-theory and M-theory, by deriving the partition function of the Ramond-Ramond
fields of Type IIA string theory from an E8 gauge theory in eleven dimensions.
We give some relations between twisted K-theory and M-theory by adapting the
method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we
construct the twisted K-theory torus which defines the partition function, and
also discuss the problem from the E8 loop group picture, in which the
Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this,
we encounter some mathematics that is new to the physics literature. In
particular, the eta differential form, which is the generalization of the eta
invariant, arises naturally in this context. We conclude with several open
problems in mathematics and string theory.Comment: 23 pages, latex2e, corrected minor errors and typos in published
versio

### Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration
omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when
the distance between the position of the i-th and j-th step are less than or
equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in
which polymers of length N have weights corresponding to simple and
self-avoiding random walks, SRW and SAW, with "a" the minimal permissible
distance. We prove that to leading order in N, the number of matrices equals
the number of walks for SRW, but not for SAW. The coarse grained Shannon
entropies for SRW agree with the fine grained ones for n <= 2, but differs for
n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is
rewritten in a less formal way with the main results explained in simple
term

### A Formalism for Scattering of Complex Composite Structures. 1 Applications to Branched Structures of Asymmetric Sub-Units

We present a formalism for the scattering of an arbitrary linear or acyclic
branched structure build by joining mutually non-interacting arbitrary
functional sub-units. The formalism consists of three equations expressing the
structural scattering in terms of three equations expressing the sub-unit
scattering. The structural scattering expressions allows a composite structures
to be used as sub-units within the formalism itself. This allows the scattering
expressions for complex hierarchical structures to be derived with great ease.
The formalism is furthermore generic in the sense that the scattering due to
structural connectivity is completely decoupled from internal structure of the
sub-units. This allows sub-units to be replaced by more complex structures. We
illustrate the physical interpretation of the formalism diagrammatically. By
applying a self-consistency requirement we derive the pair distributions of an
ideal flexible polymer sub-unit. We illustrate the formalism by deriving
generic scattering expressions for branched structures such as stars, pom-poms,
bottle-brushes, and dendrimers build out of asymmetric two-functional
sub-units.Comment: Complete rewrite generalizing the formalism to arbitrary functional
sub-units and including a new Feynmann like diagrammatic interpretatio

- …