600 research outputs found

### Flory theory revisited

The Flory theory for a single polymer chain is derived as the lowest order of
a cumulant expansion. In this approach, the full original Flory free energy
(including the logarithmic term), is recovered. %This term does not change the
wandering exponent $\nu$ but turns out to %be responsible for the crossover
from Brownian $(d>4)$ to swollen $%(d\leq4)$ %regime. The prefactors of the
elastic and repulsive energy are calculated from the microscopic parameters.
The method can be applied to other types of monomer-monomer interactions, and
the case of a single chain in a bad solvent is discussed . The method is easily
generalized to many chain systems (polymers in solutions), yielding the usual
crossovers with chain concentration. Finally, this method is suitable for a
systematic expansion around the Flory theory. The corrections to Flory theory
consist of extensive terms (proportional to the number $N$ of monomers) and
powers of $N^{2-\nu d}$ . These last terms diverge in the thermodynamic limit,
but less rapidly than the usual Fixman expansion in $N^{2- d/2}$.Comment: Email contact: [email protected]

### Real symmetric random matrices and replicas

Various ensembles of random matrices with independent entries are analyzed by
the replica formalism in the large-N limit. A result on the Laplacian random
matrix with Wigner-rescaling is generalized to arbitrary probability
distribution.Comment: 17 page

### Phase diagram of magnetic polymers

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in
a good solvent. These polymers are modeled as self-avoiding walks on a cubic
lattice, and the ferromagnetic interaction between the spins carried by the
monomers is short-ranged in space. At low temperature, these polymers undergo a
magnetic induced first order collapse transition, that we study at the mean
field level. Contrasting with an ordinary $\Theta$ point, there is a strong
jump in the polymer density, as well as in its magnetization. In the presence
of a magnetic field, the collapse temperature increases, while the
discontinuities decrease. Beyond a multicritical point, the transition becomes
second order and $\Theta$-like. Monte Carlo simulations for the Ising case are
in qualitative agreement with these results.Comment: 29 pages, 15 eps figures (one color figure). Submitted for
publication to Eur.Phys.J.

### Random Polyelectrolytes and Polyampholytes in Solution

The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions
is investigated theoretically. Various statistical charge distributions along
the polyelectrolyte chains are considered: smeared, annealed, permuted and
quenched. Annealed polyampholytes are also considered. Path integral
formulation was used to derive mean field free energies for the different
models. Self-consistent field equation is obtained for the polymer order
parameter and a Poisson-Boltzmann like equation for the electrostatic
potential. The random phase approximation is used to calculate the
monomer-monomer structure factor S(q) for the different statistical charge
distribution models. We show that in the annealed model, fluctuations of the
the monomer charges contribute to the electrostatic screening in addition to
the free ions in the solution. The strength of this screening depends on the
variance of the monomer charge distribution and is especially important for
polyampholytes in bad solvent conditions where the mesophase separation is
enhanced. The ratio between the variance and the net average charge determines
whether polyampholytes behave as polyelectrolytes or as neutral chains.Comment: 18 pages, 5 figures, submitted to Eur. Phys. J.

### Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an
attractive interaction. These compact chains are represented by Hamiltonian
paths (HP), and the coupling favors the existence of common bonds between the
chains. Using a ($n=0$ component) spin representation for these paths, we show
the existence of a phase transition for strong coupling (i.e. at low
temperature) towards a ``frozen'' phase where one chain is completely adsorbed
onto the other. By performing a Legendre transform, we obtain the probability
distribution of overlaps. The fraction of common bonds between two HP, i.e.
their overlap $q$, has both lower ($q_m$) and upper ($q_M$) bounds. This means
in particuliar that two HP with overlap greater than $q_M$ coincide. These
results may be of interest in (bio)polymers and in optimization problems.Comment: 13 pages, 2 figure

### Prediction of RNA pseudoknots by Monte Carlo simulations

In this paper we consider the problem of RNA folding with pseudoknots. We use
a graphical representation in which the secondary structures are described by
planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze
the non-planar topologies of RNA structures and propose a classification of RNA
pseudoknots according to the minimal genus of the surface on which the RNA
structure can be embedded. This classification provides a simple and natural
way to tackle the problem of RNA folding prediction in presence of pseudoknots.
Based on that approach, we describe a Monte Carlo algorithm for the prediction
of pseudoknots in an RNA molecule.Comment: 22 pages, 14 figure

### Scaling Laws of Polyelectrolyte Adsorption

Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution
to a charged surface is investigated theoretically. We obtain simple scaling
laws for (i) the amount of polymer adsorbed to the surface, Gamma, and (ii) the
width of the adsorbed layer D, as function of the fractional charge per monomer
p and the salt concentration c_b. For strongly charged polyelectrolytes (p<1)
in a low-salt solution, both Gamma and D scale as p^{-1/2}. In salt-rich
solutions D~c_b^{1/2}/p whereas the scaling behavior of Gamma depends on the
strength of the polymer charge. For weak polyelectrolytes (p<<1) we find that
Gamma~p/c_b^{1/2} while for strong polyelectrolytes Gamma~c_b^{1/2}/p. Our
results are in good agreement with adsorption experiments and with numerical
solutions of mean-field equations.Comment: 13 pages, RevTex + epsf, 9 postscript figures; minor correction

- â€¦