343 research outputs found
Glass transition of an epoxy resin induced by temperature, pressure and chemical conversion: a configurational entropy rationale
A comparative study is reported on the dynamics of a glass-forming epoxy
resin when the glass transition is approached through different paths: cooling,
compression, and polymerization. In particular, the influence of temperature,
pressure and chemical conversion on the dynamics has been investigated by
dielectric spectroscopy. Deep similarities are found in dynamic properties. A
unified reading of our experimental results for the structural relaxation time
is given in the framework of the Adam-Gibbs theory. The quantitative agreement
with the experimental data is remarkable, joined with physical values of the
fitting parameters. In particular, the fitting function of the isothermal
tau(P) data gives a well reasonable prediction for the molar thermal expansion
of the neat system, and the fitting function of the isobaric-isothermal tau(C)
data under step- polymerization conforms to the prediction of diverging tau at
complete conversion of the system.Comment: 16 pages, 8 figures, from the talk given at the 4th International
Discussion Meeting on Relaxations in Complex Systems (IDMRCS), Hersonissos,
Helaklion, Crete (Greece), 17-23 June 200
Unicyclic Components in Random Graphs
The distribution of unicyclic components in a random graph is obtained
analytically. The number of unicyclic components of a given size approaches a
self-similar form in the vicinity of the gelation transition. At the gelation
point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a
result, the total number of unicyclic components grows logarithmically with the
system size.Comment: 4 pages, 2 figure
Universality and its Origins at the Amorphous Solidification Transition
Systems undergoing an equilibrium phase transition from a liquid state to an
amorphous solid state exhibit certain universal characteristics. Chief among
these are the fraction of particles that are randomly localized and the scaling
functions that describe the order parameter and (equivalently) the statistical
distribution of localization lengths for these localized particles. The purpose
of this Paper is to discuss the origins and consequences of this universality,
and in doing so, three themes are explored. First, a replica-Landau-type
approach is formulated for the universality class of systems that are composed
of extended objects connected by permanent random constraints and undergo
amorphous solidification at a critical density of constraints. This formulation
generalizes the cases of randomly cross-linked and end-linked macromolecular
systems, discussed previously. The universal replica free energy is
constructed, in terms of the replica order parameter appropriate to amorphous
solidification, the value of the order parameter is obtained in the liquid and
amorphous solid states, and the chief universal characteristics are determined.
Second, the theory is reformulated in terms of the distribution of local static
density fluctuations rather than the replica order parameter. It is shown that
a suitable free energy can be constructed, depending on the distribution of
static density fluctuations, and that this formulation yields precisely the
same conclusions as the replica approach. Third, the universal predictions of
the theory are compared with the results of extensive numerical simulations of
randomly cross-linked macromolecular systems, due to Barsky and Plischke, and
excellent agreement is found.Comment: 10 pages, including 3 figures (REVTEX
Critical Dynamics of Gelation
Shear relaxation and dynamic density fluctuations are studied within a Rouse
model, generalized to include the effects of permanent random crosslinks. We
derive an exact correspondence between the static shear viscosity and the
resistance of a random resistor network. This relation allows us to compute the
static shear viscosity exactly for uncorrelated crosslinks. For more general
percolation models, which are amenable to a scaling description, it yields the
scaling relation for the critical exponent of the shear
viscosity. Here is the thermal exponent for the gel fraction and
is the crossover exponent of the resistor network. The results on the shear
viscosity are also used in deriving upper and lower bounds on the incoherent
scattering function in the long-time limit, thereby corroborating previous
results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor
changes
Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
We study crossover phenomena in a model of self-avoiding walks with
medium-range jumps, that corresponds to the limit of an -vector
spin system with medium-range interactions. In particular, we consider the
critical crossover limit that interpolates between the Gaussian and the
Wilson-Fisher fixed point. The corresponding crossover functions are computed
using field-theoretical methods and an appropriate mean-field expansion. The
critical crossover limit is accurately studied by numerical Monte Carlo
simulations, which are much more efficient for walk models than for spin
systems. Monte Carlo data are compared with the field-theoretical predictions
concerning the critical crossover functions, finding a good agreement. We also
verify the predictions for the scaling behavior of the leading nonuniversal
corrections. We determine phenomenological parametrizations that are exact in
the critical crossover limit, have the correct scaling behavior for the leading
correction, and describe the nonuniversal lscrossover behavior of our data for
any finite range.Comment: 43 pages, revte
Elasticity near the vulcanization transition
Signatures of the vulcanization transition--amorphous solidification induced
by the random crosslinking of macromolecules--include the random localization
of a fraction of the particles and the emergence of a nonzero static shear
modulus. A semi-microscopic statistical-mechanical theory is presented of the
latter signature that accounts for both thermal fluctuations and quenched
disorder. It is found (i) that the shear modulus grows continuously from zero
at the transition, and does so with the classical exponent, i.e., with the
third power of the excess cross-link density and, quite surprisingly, (ii) that
near the transition the external stresses do not spoil the spherical symmetry
of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
Interfacial Profile and Propagation of Frontal Photopolymerization Waves
We investigate the frontal photopolymerization
of a thiol–ene
system with a combination of experiments and modeling, focusing on
the interfacial conversion profile and its planar wave propagation.
We spatially resolve the solid-to-liquid front by FT-IR and AFM mechanical
measurements, supplemented by differential scanning calorimetry. A
simple coarse-grained model is found to describe remarkably well the
frontal kinetics and the sigmoidal interface, capturing the effects
of UV light exposure time (or dose) and temperature, as well as the
front position and resulting patterned dimensions after development.
Analytical solutions for the conversion profile enable the description
of all conditions with a single master curve in the moving frame of
the front position. Building on this understanding, we demonstrate
the design and fabrication of gradient polymer materials, with tunable
properties <i>along</i> the direction of illumination, which
can be coupled with lateral patterning by modulated illumination or
grayscale lithography
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