24 research outputs found
Density Functional approach to Nonlinear Rheology
We present a density functional based closure of the pair Smoluchowski
equation for Brownian particles under shear flow. Given an equilibrium free
energy functional as input the theory provides first-principles predictions for
the flow-distorted pair correlation function and associated rheological
quantities over a wide range of volume fractions and flow rates. Taking
two-dimensional hard-disks under shear flow as an illustrative model we
calculate the pair correlation function, viscosity and normal stress difference
under both steady and start-up shear
Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
We analyze the slow, glassy structural relaxation as measured through
collective and tagged-particle density correlation functions obtained from
Brownian dynamics simulations for a polydisperse system of quasi-hard spheres
in the framework of the mode-coupling theory of the glass transition (MCT).
Asymptotic analyses show good agreement for the collective dynamics when
polydispersity effects are taken into account in a multi-component calculation,
but qualitative disagreement at small when the system is treated as
effectively monodisperse. The origin of the different small- behaviour is
attributed to the interplay between interdiffusion processes and structural
relaxation. Numerical solutions of the MCT equations are obtained taking
properly binned partial static structure factors from the simulations as input.
Accounting for a shift in the critical density, the collective density
correlation functions are well described by the theory at all densities
investigated in the simulations, with quantitative agreement best around the
maxima of the static structure factor, and worst around its minima. A
parameter-free comparison of the tagged-particle dynamics however reveals large
quantiative errors for small wave numbers that are connected to the well-known
decoupling of self-diffusion from structural relaxation and to dynamical
heterogeneities. While deviations from MCT behaviour are clearly seen in the
tagged-particle quantities for densities close to and on the liquid side of the
MCT glass transition, no such deviations are seen in the collective dynamics.Comment: 23 pages, 26 figure
Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time
The shear modulus G of two glass-forming colloidal model systems in d=3 and
d=2 dimensions is investigated by means of, respectively, molecular dynamics
and Monte Carlo simulations. Comparing ensembles where either the shear strain
gamma or the conjugated (mean) shear stress tau are imposed, we compute G from
the respective stress and strain fluctuations as a function of temperature T
while keeping a constant normal pressure P. The choice of the ensemble is seen
to be highly relevant for the shear stress fluctuations mu_F(T) which at
constant tau decay monotonously with T following the affine shear elasticity
mu_A(T), i.e. a simple two-point correlation function. At variance,
non-monotonous behavior with a maximum at the glass transition temperature T_g
is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is
reasonably fitted for both models by a continuous cusp singularity, G(T) is
proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent
replica calculations. It is argued, however, that longer sampling times may
lead to a sharper transition. The additive jump discontinuity predicted by
mode-coupling theory and other replica calculations thus cannot ultimately be
ruled out
Communication: Pressure fluctuations in isotropic solids and fluids
International audienceComparing isotropic solids and fluids at either imposed volume or pressure, we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K, it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K-row of the compression modulus for NPT-ensembles. It is shown theoretically and numerically that K-row vertical bar P = P-id(2 - P-id/K) with P-id being the ideal pressure contribution
Simulated glass-forming polymer melts: Dynamic scattering functions, chain length effects, and mode-coupling theory analysis
We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T
c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T
c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T
c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T
c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T
c
∞
. This increase can be described by T
c
∞
− T
c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ
c = ρ
c
T
c
−1/4, where ρ
c is the monomer density at T
c. In addition, we also estimate T
c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T
c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data