893 research outputs found
Adsorption of a semiflexible polymer onto interfaces and surfaces
We consider the adsorption of a semiflexible polymer chain onto interfaces
and surfaces by using the differential equation of the distribution function
of the end-to-end distance , which is associated with the moment
expansion of the latter. We present the results of the approximative treatment
consisting of taking into account the 2nd and 4th moments in the differential
equation for . The essential features of adsorption of the semiflexible
polymer are: {\it i}) the existence of a new local length scale, which results
in two-exponential decay of the monomer density of adsorbed polymer; {\it ii})
the binding of the semiflexible polymer is weaker than that for flexible one
for both interface and wall. The approximative theory presented is restricted
to the regime of weak adsorption, where the effect of the rodlike behavior of
the polymer on small scales is weak.Comment: 9 pages, 2 figure
Two harmonically coupled Brownian particles in random media
We study the behaviour of two Brownian particles coupled by an elastic
harmonic force in a quenched disordered medium. We found that to first order in
disorder strength, the relative motion weakens (with respect to the reference
state of a Brownian particle with the double mass) the effect of the quenched
forces on the centre of mass motion of the Brownian particles, so that the
motion will become less subdiffusive (superdiffusive) for potential
(solenoidal) disorder. The mean-square relative distance between the particles
behaves in a different way depending of whether the particles are free to move
or one particle is anchored in the space. While the effect of nonpotential
disorder consists in increasing the mean-square distance in both cases, the
potential disorder decreases the mean-square distance, when the particles are
free to move, and increases it when one particle is anchored in the space.Comment: 8 pages, 3 figure
Adsorption of a random heteropolymer with self-interactions onto an interface
We consider the adsorption of a random heteropolymer onto an interface within
the model by Garel et al. [1] by taking into account self-interactions between
the monomers. Within the replica trick and by using a self-consistent
preaveraging procedure we map the adsorption problem onto the problem of
binding state of a quantum mechanical Hamiltonian. The analysis of the latter
is treated within the variational method based on the 2-nd Legendre transform.
We have found that self-interactions favor the localization. The effect is
intensified with decrease of the temperature. Within a model without taking
into account the repulsive ternary monomer-monomer interactions we predict a
reentrant localization transition for large values of the asymmetry of the
heteropolymer and at low enough temperatures.Comment: 11 pages, 3 figure
Localization and freezing of a Gaussian chain in a quenched random potential
The Gaussian chain in a quenched random potential (which is characterized by
the disorder strength ) is investigated in the - dimensional space
by the replicated variational method. The general expression for the free
energy within so called one - step - replica symmetry breaking (1 - RSB)
scenario has been systematically derived. We have shown that the replica
symmetrical (RS) limit of this expression can describe the chain center of mass
localization and collapse. The critical disorder when the chain becomes
localized scales as (where is the length
of the Kuhn segment length and is the chain length) whereas the chain
gyration radius . The freezing of
the internal degrees of freedom follows to the 1-RSB - scenario and is
characterized by the beads localization length . It was
demonstrated that the solution for appears as a metastable
state at and behaves similarly to the corresponding frozen
states in heteropolymers or in - spin random spherical model.Comment: 18 pages, 6 figures, submitted to J. Chem. Phy
Bimodal distribution function of a 3d wormlike chain with a fixed orientation of one end
We study the distribution function of the three dimensional wormlike chain
with a fixed orientation of one chain end using the exact representation of the
distribution function in terms of the Green's function of the quantum rigid
rotator in a homogeneous external field. The transverse 1d distribution
function of the free chain end displays a bimodal shape in the intermediate
range of the chain lengths (). We present also
analytical results for short and long chains, which are in complete agreement
with the results of previous studies obtained using different methods.Comment: 6 pages, 3 figure
Statistical mechanics of semiflexible polymers
We present the statistical-mechanical theory of semiflexible polymers based
on the connection between the Kratky-Porod model and the quantum rigid rotator
in an external homogeneous field, and treatment of the latter using the quantum
mechanical propagator method. The expressions and relations existing for
flexible polymers can be generalized to semiflexible ones, if one replaces the
Fourier-Laplace transform of the end-to-end polymer distance, ,
through the matrix , where and are
related to the spectrum of the quantum rigid rotator, and considers an
appropriate matrix element of the expression under consideration. The present
work provides also the framework to study polymers in external fields, and
problems including the tangents of semiflexible polymers. We study the
structure factor of the polymer, the transversal fluctuations of a free end of
the polymer with fixed tangent of another end, and the localization of a
semiflexible polymer onto an interface. We obtain the partition function of a
semiflexible polymer in half space with Dirichlet boundary condition in terms
of the end-to-end distribution function of the free semiflexible polymer, study
the behaviour of a semiflexible polymer in the vicinity of a surface, and
adsorption onto a surface.Comment: 30 pages, 7 figures, changed conten
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