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In previous work, we have established that the intrinsic viscosity [eta] of an object is nearly proportional to the average electrical polarizability tensor alphae = tr(alphae)/3 of a conducting object having the same shape, or equivalently, to the intrinsic conductivity [sigma]=alphae/V , which characterizes the conductivity of a dilute mixture of randomly(More)
The problem of calculating the electric polarizability tensor alpha(e) of objects of arbitrary shape has been reformulated in terms of path integration and implemented computationally. The method simultaneously yields the electrostatic capacity C and the equilibrium charge density. These functionals of particle shape are important in many materials science(More)
We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are(More)
It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently(More)
A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying(More)
A technique is presented for the identification of the knot group of knots, links, and other embedded graphs as a tool in numerical studies of entanglements of polymers. With this technique, the knot group is simultaneously more discriminating and easier to calculate than the knot invariants that have been used in such studies in the past. It can be applied(More)
By identifying the maximally random jammed state of freely jointed chains of tangent hard spheres we are able to determine the distinct scaling regimes characterizing the dependence of chain dimensions and topology on volume fraction. Calculated distributions of (i) the contour length of the primitive paths and (ii) the number of entanglements per chain(More)
Although the scaling theory of polymer solutions has had many successes, this type of argument is deficient when applied to hydrodynamic solution properties. Since the foundation of polymer science, it has been appreciated that measurements of polymer size from diffusivity, sedimentation, and solution viscosity reflect a convolution of effects relating to(More)
The integrals V (n1, n2, n3) = integral dr x(n)1 y(n)2 z(n)3, where integral dr represents integration over the volume of a body, such as a molecule, where x, y, and z are Cartesian coordinates of a point in the interior of the body relative to an arbitrary reference frame, and where n1, n2, and n3 are integers greater than or equal to zero, constitute(More)