Index of content:
Volume 50, Issue 2, March 2006
Experimental and numerical analysis of irreversibilities among particles suspended in a Couette device50(2006); http://dx.doi.org/10.1122/1.2169806View Description Hide Description
An experimental and numerical study is performed of irreversibilities among particles in a wide-gap Couette device. Five spheres are placed in the Couette in a tightly packed arrangement. The inner cylinder is rotated five revolutions counterclockwise and subsequently five revolutions clockwise. Irreversibilities in the system are characterized by the radial spread of the particles measured by a radial moment. The experimental results are compared to a set of numerical simulations performed using a lubrication-corrected completed double layerboundary element method with a particle roughnessmodel. In both the experiments and simulations, there is a critical value of the initial radial moment above which there is little irreversibility in the systems and below which irreversibilities accumulate rapidly. Particle roughness in the simulations can be used as a parameter to achieve the best agreement with experiment. It is noteworthy that the roughness value producing the best agreement is different than the actual average roughness of the particles used in the experiments.
50(2006); http://dx.doi.org/10.1122/1.2167448View Description Hide Description
The nonlinear rheology of styrene-butadiene rubber filled with carbon-black or silica particles is investigated by complementary viscosimetric devices on a wide range of deformation and deformation rates. The effect of filler volume fraction on the rheological behavior is systematically studied. The importance of a critical volume fraction (percolation threshold) is outlined, giving rise to a network structure at rest. At finite deformation, this structure is destroyed and the compounds exhibit a nonlinear rheology quite similar to the unfilled rubber. The separability of time and strain effects on the relaxation modulus is observed not only for the pure elastomer, but also for the filled compounds. Several viscoelastic functions of the filled compounds(linear viscoelasticmoduli, damping function, and shear stress) can be rescaled using a concentration shift factor that is identical to the one used in Newtonian suspension rheology.
Concentration dependence of shear and extensional rheology of polymer solutions: Brownian dynamics simulations50(2006); http://dx.doi.org/10.1122/1.2167468View Description Hide Description
We consider the effects of concentration on the structural and rheological properties of dilute polymer solutions via the use of Brownian dynamics simulations. The model used here is that of Jendrejack et al. [J. Chem. Phys.116, 7752–7759 (2002)] for -phage DNA under good solvent conditions, which incorporates excluded volume and hydrodynamic interaction effects, and has been shown to quantitatively predict the nonequilibrium behavior of the molecule in the dilute limit. Our work covers the entire dilute regime, with selected investigations into the semidilute regime, as well as spanning multiple decades of both shear and extensional flow rates. In simple shear flow, as much as a 20% increase in chain extension and 30% increase in the reduced polymerviscosity is observed at the overlap concentration, as compared to the infinitely dilute case. Additionally, predicted shear viscosities are in very good agreement with experimental observations. In elongational flow, we observe much stronger concentration dependences than in shear, with a 110% increase in chain extension and 500% increase in reduced viscosity when results are compared at equivalent extension rates. Significant concentration effects are observed at concentrations as low as 10% of the overlap concentration and are largely the result of interchain hydrodynamic interactions.
50(2006); http://dx.doi.org/10.1122/1.2167449View Description Hide Description
Previous studies establish that adsorbed layers of telechelic polymers can exchange ends, increasing the entropy and allowing the loops to relax. The resulting entropic attraction amounts to approximately per bridging chain for ideal chains but decreases with increasing degree of stretching. From the interactions between planar brushes of highly stretched chains, we calculate the pair potential between spheres via the Derjaguin approximation. The softness of the repulsion and the depth of the attraction depend on the degree of stretching of the chains, the aggregation number or adsorption density, and the ratio of the overall size to the layer thickness. From the interaction potential, second virial coefficients in the osmotic pressure and the high-frequency modulus, characterizing dilute micellar solutions, follow directly. The second virial coefficient in the osmotic pressure is very negative with modest stretching but approaches the hard sphere limit as the chains become very strongly stretched. The coefficient of the leading term for the high-frequency modulus depends nonmonotonically on the stretching with the attractive well dominating for modest stretching and the repulsive core taking over for strong stretching. Combining these calculations with estimates of the relaxation time for end exchange should provide useful predictions of low shear viscosities for these Maxwellian fluids.
50(2006); http://dx.doi.org/10.1122/1.2167467View Description Hide Description
Employing theory derived in previous papers [Meng and Russel, Macromolecules36, 10112–10119 (2003); 38, 593–600 (2005)] to describe the micellar structure of aqueous solutions of telechelic polymers with a poly(ethylene oxide) (PEO) backbone and alkane end groups, we predict the high-frequency modulus and low shear viscosity for comparison with data from the literature and our own experiments. In these solutions the molecular structure determines the aggregation number and radius of the micelles. Interactions between micelles lead to exchange of end blocks and compression of loops, generating a pair potential with an attractive well and soft core. Computing the high-frequency modulus from the intermicellar potential and constructing a correlation for the relaxation time from experimental data allows us to predict the low shear viscosity. Comparison with measurements for our model associative polymers, as well as relatively monodisperse systems from the conventional synthesis, suggests an alternative to the structure-property relations constructed by Annable et al., J. Rheol.37, 695 (1993) by modifying reversible network theory. The distinctions lie in our incorporation of excluded volume repulsions and entropic attractions between micelles, which produce strong correlations that determine the concentration dependence.
50(2006); http://dx.doi.org/10.1122/1.2167487View Description Hide Description
We present a general algorithm for predicting the linear rheology of branched polymers. While the method draws heavily on existing theoretical understanding of the relaxation processes in entangled polymer melts, a number of new concepts are developed to handle diverse polymer architectures including branch-on-branch structures. We validate the algorithm with experimental examples from model polymer architectures to fix the parameters of the model. We use experimentally determined parameters to generate a numerical ensemble of branched metallocene-catalyzed polyethylene resins. Application of our algorithm shows the importance of branch-on-branch chains in the system and predicts the linear rheology with good quantitative agreement over a wide range of branching density and molecular weight.