819 research outputs found

### Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain,
through Monte Carlo lattice simulations. The affinity of monomer $i$ for water
is characterized by a (scalar) charge $\lambda_{i}$, and the monomer-water
interaction is short-ranged. Assuming incompressibility yields an effective
short ranged interaction between monomer pairs $(i,j)$, proportional to
$(\lambda_i+\lambda_j)$. In this article, we take $\lambda_i=+1$ (resp.
($\lambda_i=- 1$)) for hydrophilic (resp. hydrophobic) monomers and consider a
chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a
periodic distribution of the $\lambda_{i}$ along the chain, with periodicity
$2p$. The simulations are done for various chain lengths $N$, in $d=2$ (square
lattice) and $d=3$ (cubic lattice). There is a critical value $p_c(d,N)$ of the
periodicity, which distinguishes between different low temperature structures.
For $p >p_c$, the ground state corresponds to a macroscopic phase separation
between a dense hydrophobic core and hydrophilic loops. For $p <p_c$ (but not
too small), one gets a microscopic (finite scale) phase separation, and the
ground state corresponds to a chain or network of hydrophobic droplets, coated
by hydrophilic monomers. We restrict our study to two extreme cases, $p \sim
O(N)$ and $p\sim O(1)$ to illustrate the physics of the various phase
transitions. A tentative variational approach is also presented.Comment: 21 pages, 17 eps figures, accepted for publication in Eur. Phys. J.

### Comment on " A simple model for DNA denaturation"

The replacment of mutual avoidance of polymers by a long-range interaction of
the type proposed by Garel etal (Europhys. Lett. 55, 132 (2001),
cond-mat/0101058) is inconsistent with the prevalent renormalization group
arguments.Comment: 2 pages, Comment on Garel etal. Europhys. Lett 55, 132(2001)
cond-mat/0101058. Appeared in Europhys Let

### 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.

### Phase diagram of a semiflexible polymer chain in a $\theta$ solvent: application to protein folding

We consider a lattice model of a semiflexible homopolymer chain in a bad
solvent. Beside the temperature $T$, this model is described by (i) a curvature
energy $\varepsilon_h$, representing the stiffness of the chain (ii) a
nearest-neighbour attractive energy $\varepsilon_v$, representing the solvent
(iii) the monomer density $\rho={N \over \Omega}$, where $N$ and $\Omega$
denote respectively the number of monomers and the number of lattice sites.
This model is a simplified view of the protein folding problem, which
encompasses the geometrical competition between secondary structures (the
curvature term modelling helix formation) and the global compactness (modeled
here by the attractive energy), but contains no side chain information...Comment: 17 pages, plain tex, 2 figures available upon reques

### Random Hydrophilic-Hydrophobic Copolymers

We study a single statistical amphiphilic copolymer chain AB in a selective
solvent (e.g.water). Two situations are considered. In the annealed case,
hydrophilic (A) and hydrophobic (B) monomers are at local chemical equilibrium
and both the fraction of A monomers and their location along the chain can
vary, whereas in the quenched case (which is relevant to proteins), the
chemical sequence along the chain is fixed by synthesis. In both cases, the
physical behaviour depends on the average hydrophobicity of the polymer chain.
For a strongly hydrophobic chain (large fraction of B), we find an ordinary
continuous $\theta$ collapse, with a large conformational entropy in the
collapsed phase. For a weakly hydrophobic, or a hydrophilic chain, there is an
unusual first-order collapse transition. In particular, for the case of
Gaussian disorder, this discontinuous transition is driven by a change of sign
of the third virial coefficient. The entropy of this collapsed phase is
strongly reduced with respect to the $\theta$ collapsed phase. Email contact:
[email protected]: Saclay-T94/077 Email: [email protected]

### 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

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