748 research outputs found
Crosslinked polymer chains with excluded volume: A new class of branched polymers?
In this note microgels with and without excluded volume interactions are
considered. Based on earlier exact computations on Gaussian mircogels, which
are formed by self-crosslinking (with crosslinks) of polymer chains with
chain length Flory type approximations are used to get first insight to
their behavior in solution. It is shown that two different types of microgels
exist: A special type of branched polymer whose size scales as , instead of . The second type are -
microgels whose average mesh sizes are swollen and form self avoiding walks
with a scaling law of the form .Comment: 5 pages, 2 figures, accepted in Macromol. Theory Simu
Elasticity in strongly interacting soft solids: polyelectrolyte network
This paper discusses the elastic behavior of a very long crosslinked
polyelectrolyte chain (Debye-H\"uckel chain), which is weakly charged.
Therefore the response of the crosslinked chain (network) on an external
constant force acting on the ends of the chain is considered. A
selfconsistent variational computation of an effective field theory is
employed. It is shown, that the modulus of the polyelectrolyte network has two
parts: the first term represents the usual entropy elasticity of connected
flexible chains and the second term takes into account the electrostatic
interaction of the monomers. It is proportional to the squared crosslink
density and the Debye - screening parameter.Comment: submitted for publication to PR
Polyelectrolyte Networks: Elasticity, Swelling, and the Violation of the Flory - Rehner Hypothesis
This paper discusses the elastic behavior of polyelectrolyte networks. The
deformation behavior of single polyelectrolyte chains is discussed. It is shown
that a strong coupling between interactions and chain elasticity exists. The
theory of the complete crosslinked networks shows that the Flory - Rehner -
Hypothesis (FRH) does not hold. The modulus contains contributions from the
classical rubber elasticity and from the electrostatic interactions. The
equilibrium degree of swelling is estimated by the assumption of a
-network.Comment: submitted to Computational and Theoretical Polymer Scienc
Semiflexible polymers in a random environment
We present using simple scaling arguments and one step replica symmetry
breaking a theory for the localization of semiflexible polymers in a quenched
random environment. In contrast to completely flexible polymers, localization
of semiflexible polymers depends not only on the details of the disorder but
also on the ease with which polymers can bend. The interplay of these two
effects can lead to the delocalization of a localized polymer with an increase
in either the disorder density or the stiffness. Our theory provides a general
criterion for the delocalization of polymers with varying degrees of
flexibility and allows us to propose a phase diagram for the highly folded
(localized) states of semiflexible polymers as a function of the disorder
strength and chain rigidity.Comment: 10 pages, 3 figures, Revtex
Collective Dynamics of Random Polyampholytes
We consider the Langevin dynamics of a semi-dilute system of chains which are
random polyampholytes of average monomer charge and with a fluctuations in
this charge of the size and with freely floating counter-ions in the
surrounding. We cast the dynamics into the functional integral formalism and
average over the quenched charge distribution in order to compute the dynamic
structure factor and the effective collective potential matrix. The results are
given for small charge fluctuations. In the limit of finite we then find
that the scattering approaches the limit of polyelectrolyte solutions.Comment: 13 pages including 6 figures, submitted J. Chem. Phy
Polymer adsorption on heterogeneous surfaces
The adsorption of a single ideal polymer chain on energetically heterogeneous
and rough surfaces is investigated using a variational procedure introduced by
Garel and Orland (Phys. Rev. B 55 (1997), 226). The mean polymer size is
calculated perpendicular and parallel to the surface and is compared to the
Gaussian conformation and to the results for polymers at flat and energetically
homogeneous surfaces. The disorder-induced enhancement of adsorption is
confirmed and is shown to be much more significant for a heterogeneous
interaction strength than for spatial roughness. This difference also applies
to the localization transition, where the polymer size becomes independent of
the chain length. The localization criterion can be quantified, depending on an
effective interaction strength and the length of the polymer chain.Comment: accepted in EPJB (the Journal formerly known as Journal de Physique
How to break the replica symmetry in structural glasses
The variational principle (VP) has been used to capture the metastable states
of a glass-forming molecular system without quenched disorder. It has been
shown that VP naturally leads to a self-consistent random field Ginzburg-Landau
model (RFGLM). In the framework of one-step replica symmetry breaking (1-RSB)
the general solution of RFGLM is discussed in the vicinity of the spinodal
temperature T_{A} in terms of ``hidden'' formfactors , g_{0}(k)
and . The self-generated disorder spontaneously arises. It is argued
that at T < T_{A} the activated dynamics is dominant.Comment: 11 pages, no figures, accepted by Europhys. Let
Langevin Dynamics of a Polymer with Internal Distance Constraints
We present a novel and rigorous approach to the Langevin dynamics of ideal
polymer chains subject to internal distance constraints. The permanent
constraints are modelled by harmonic potentials in the limit when the strength
of the potential approaches infinity (hard crosslinks). The crosslinks are
assumed to exist between arbitrary pairs of monomers. Formally exact
expressions for the resolvent and spectral density matrix of the system are
derived. To illustrate the method we study the diffusional behavior of monomers
in the vicinity of a single crosslink within the framework of the Rouse model.
The same problem has been studied previously by Warner (J. Phys. C: Solid State
Phys. {\bf 14}, 4985, (1981)) on the basis of Lagrangian multipliers. Here we
derive the full, hence exact, solution to the problem.Comment: To appear in PRE, Figures on reques
Size and scaling in ideal polymer networks
The scattering function and radius of gyration of an ideal polymer network
are calculated depending on the strength of the bonds that form the crosslinks.
Our calculations are based on an {\it exact} theorem for the characteristic
function of a polydisperse phantom network that allows for treating the
crosslinks between pairs of randomly selected monomers as quenched variables
without resorting to replica methods. From this new approach it is found that
the scattering function of an ideal network obeys a master curve which depends
on one single parameter , where is the product of the
persistence length times the scattering wavevector, the total number of
monomers and the crosslinks in the system. By varying the crosslinking
potential from infinity (hard -constraints) to zero (free chain), we
have also studied the crossover of the radius of gyration from the collapsed
regime where R_{\mbox{\tiny g}}\simeq {\cal O}(1) to the extended regime
R_{\mbox{\tiny g}}\simeq {\cal O}(\sqrt{N}). In the crossover regime the
network size R_{\mbox{\tiny g}} is found to be proportional to .Comment: latex, figures available on request, to be published: J. Phys I
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