20 research outputs found
Elasticity of entangled polymer loops: Olympic gels
In this note we present a scaling theory for the elasticity of olympic gels,
i.e., gels where the elasticity is a consequence of topology only. It is shown
that two deformation regimes exist. The first is the non affine deformation
regime where the free energy scales linear with the deformation. In the large
(affine) deformation regime the free energy is shown to scale as where is the deformation ratio. Thus a highly non
Hookian stress - strain relation is predicted.Comment: latex, no figures, accepted in PRE Rapid Communicatio
New Method for Phase transitions in diblock copolymers: The Lamellar case
A new mean-field type theory is proposed to study order-disorder transitions
(ODT) in block copolymers. The theory applies to both the weak segregation (WS)
and the strong segregation (SS) regimes. A new energy functional is proposed
without appealing to the random phase approximation (RPA). We find new terms
unaccounted for within RPA. We work out in detail transitions to the lamellar
state and compare the method to other existing theories of ODT and numerical
simulations. We find good agreements with recent experimental results and
predict that the intermediate segregation regime may have more than one scaling
behavior.Comment: 23 pages, 8 figure
Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
The distributions of singular thermodynamic quantities in an ensemble
of quenched random samples of linear size at the critical point are
studied by Monte Carlo in two models. Our results confirm predictions of
Aharony and Harris based on Renormalization group considerations. For an
Ashkin-Teller model with strong but irrelevant bond randomness we find that the
relative squared width, , of is weakly self averaging. , where is the specific heat exponent and is the
correlation length exponent of the pure model fixed point governing the
transition. For the site dilute Ising model on a cubic lattice, known to be
governed by a random fixed point, we find that tends to a universal
constant independent of the amount of dilution (no self averaging). However
this constant is different for canonical and grand canonical disorder. We study
the distribution of the pseudo-critical temperatures of the ensemble
defined as the temperatures of the maximum susceptibility of each sample. We
find that its variance scales as and NOT as
R_\chi\sim 70R_\chi (T_c)\chiT_c(i,l)m_i(T_c,l)T_c(i,l)(T-T_c(i,l))/T_c$. This function is found to be universal and to behave
similarly to pure systems.Comment: 31 pages, 17 figures, submitted to Phys. Rev.
Diblock copolymers at a homopolymer-homopolymer-interface: a Monte Carlo simulation
The properties of diluted symmetric A-B diblock copolymers at the interface
between A and B homopolymer phases are studied by means of Monte Carlo (MC)
simulations of the bond fluctuation model. We calculate segment density
profiles as well as orientational properties of segments, of A and B blocks,
and of the whole chain. Our data support the picture of oriented ``dumbbells'',
which consist of mildly perturbed A and B Gaussian coils. The results are
compared to a self consistent field theory (SCFT) for single copolymer chains
at a homopolymer interface. We also discuss the number of interaction contacts
between monomers, which provide a measure for the ``active surface'' of
copolymers or homopolymers close to the interface