The rheological properties of self-assembling fluids are studied within the framework of a simple timedependent Landau-Ginzburg model. In addition to the Langevin relaxation dynamics, the order parameter field is subject to a kinematic deformation process due to a shear velocity field. The Hamiltonian contains a Gaussian part which has proven to be important in the study of self-assembly, as well as 4 and 2 ٌ͑͒ 2 contributions. In the disordered phase and for low shear rate, the relevant rheological coefficients ͑excess viscosity, first and second normal stress coefficient͒ can be calculated perturbatively. The essential ingredient is the one-loop, self-consistent solution of the evolution equation for the quasistatic structure factor. In the case of steady shear, we find shear thinning behavior, a positive first, and a negative second normal stress difference for all values of the shear rate. For oscillatory shear, it turns out that the self-assembling structures give rise to viscoelastic behavior. Analytic results are derived for the limiting cases of low and high frequency. For low steady shear, all results can be expressed in scaling form using the correlation lengths d and originally defined for microemulsion under equilibrium conditions and scaling functions already known from the pure Gaussian treatment. This suggests a class of experiments where neutron scattering data can be compared to viscosity results. For low to high shear rates, the one-loop equations have also been solved numerically, and we display the nonequilibrium structure factors arising from this approach. ͓S1063-651X͑96͒08708-9͔
We investigate the rheological properties of a Landau–Ginzburg model that has competing interaction terms. These interactions have earlier been shown to produce mesoscopic ordering and such models have been helpful in explaining microemulsion behavior. Our present study is based on time-dependent Landau–Ginzburg equations for the order parameter and velocity field. The possible influence of hydrodynamic fluctuations, though discussed, is neglected in our treatment. General expressions for the excess viscosity and the first normal stress coefficient are derived in terms of the quasistatic structure factor. For steady shear flows and in the mean field approximation, explicit relations are given in two space dimensions for a nonconserved order parameter and in three space dimensions for a conserved order parameter. The former case is the easiest one to study numerically in computer simulations. Our numerical results show that mean field theory for the excess viscosity is satisfactory at some distance from the ‘‘transition’’ curve to the lamellar phase. The normal stress coefficient turns out to be very small. It only becomes appreciable close to the phase boundary. Here the nonlinear dependencies of excess viscosity and stress coefficient on the shear rate become important. To explain the general behavior we have considered terms up to fourth order in the shear rate. Computer simulations as well as mean field theory indicate that the quadratic corrections to both coefficients are negative in the microemulsion region. With increasing shear rate one therefore first enters a regime of shear-thinning. The quartic corrections are found to be positive, so further increase of the shear rate will lead to shear-thickening.
We study the surface tension for thin, amorphous polymer films by means of computer simulation. Using molecular dynamics, we present surface tension measurements via the fluctuation spectrum of capillary waves in the long-wavelength limit for sufficiently large systems. We find good agreement with a theory based on continuum mechanics. In addition, we observe the spreading of the surface thickness with increasing lateral system size, an effect which allows another estimate of the surface tension. Furthermore, we studied the correlation between two surfaces and measured the transverse length scale by varying the film thickness. We also present data of the temperature dependence of the bulk density of the polymer film and the thickness of the surface region in the regime above the glass transition temperature.
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