We study a synthetic clay suspension of laponite at different particle and NaCl concentrations by measuring stationary shear viscosity and transient electrically induced birefringence (TEB). On one hand the viscosity data are consistent with the particles being spheres and the particles being associated with large amount bound water. On the other hand the viscosity data are also consistent with the particles being asymmetric, consistent with single laponite platelets associated with a very few monolayers of water. We analyze the TEB data by employing two different models of aggregate size (effective hydrodynamic radius) distribution: (1) bidisperse model and (2) log-normal distributed model. Both models fit, in the same manner, fairly well to the experimental TEB data and they indicate that the suspension consists of polydisperse particles. The models also appear to confirm that the aggregates increase in size vs increasing ionic strength. The smallest particles at low salt concentrations seem to be monomers and oligomers.
Semiflexible polymers are often modelled as consisting of rigid segments connected by rigid rods, ball–socket joints or springs. In this paper we focus on polymers consisting of two identical segments connected by a frictionless ball–socket joint. This introduces rigid constraints, resulting in the number of degrees of freedom being reduced. Using kinetic theory we derive the effective hydrodynamic mobility tensor of each segment in the chain, expressed in terms of the hydrodynamic mobility of an identical free segment. The result is used to obtain analytical and numerical expressions for the slowest decay mode in a typical transient electrically induced birefringence experiment. We show that under typical experimental conditions only this single mode will be present. The results we obtain are significantly different from results for a similar once-broken rod published by Wegener and co-workers and Garcia de la Torre and co-workers. In the last part of the paper Brownian dynamics simulations of the two-segment model is used to verify our analytically obtained expressions for the mobility tensor and decay modes and to obtain results for situations where analytical results are unavailable. The model assumes no hydrodynamic interaction between the segments.
It is well known that orientational correlations appear in polymer chain models when the subunits are linked by ball-socket joints implemented as rigid constraint conditions. These correlations do not appear when the subunits are connected by springlike potential forces, even in the limit of infinitely stiff springs. In a widely used class of algorithms for Brownian dynamics simulations, inertia effects are ignored. However, in the recently introduced needle chain and nugget chain algorithms, the rigid constraint correlations depend on the mass and moment of inertia. This inconsistency does not appear in the bead-rod (Kramers) polymer chain model, which also has orientational correlations introduced by rigid constraint conditions. Explicit expressions for the correlation functions are given for thermodynamic equilibrium states. Analytical expressions for the associated forces ("metric forces") and simulation results showing how the rigid constraint correlations influence dynamical properties, are also presented. Further we discuss the physical relevance of these correlations and show via simulations that their influence on stationary and dynamical properties depend significantly on chain length. We further show that if the metric forces are removed, algorithms designed with rigid constraint conditions describe a chain of segments connected by infinitely stiff springs. Finally we show that the results presented here for needle chains are relevant also for the bead-rod (Kramers) chain model, making it possible to simulate a bead-spring chain with infinitely stiff springs.
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