Intrinsic Viscosity and the Electric Polarizability of Arbitrarily Shaped Objects.
Intrinsic Viscosity and the Electric Polarizability of
Arbitrarily Shaped Objects.
Mansfield, M. L.; Douglas, J. F.; Garboczi, E. J.
Physical Review E, Vol. 64, No. 6, 61401-61416,
viscosity; polarizability; virial coefficient; intrinsic
viscosity; capacity; nanoparticles; path-integration;
particle shape; random walks
The problem of calculating the electric polarizability
tensor of objects of arbitrary shape has been
reformulated in terms of path integration and
implemented computationally. The method simultaneously
yields the electrostatic capacity and the equilibrium
charge density. These functionals of particle shape are
important in many materials science applications,
including the conductivity and viscosity of filled
materials and suspensions. The method has been validated
through comparison with exact results (for the sphere,
the circular disk, touching spheres, and tori), it has
been found that 106 trajectories yield an accuracy of
about four and three significant figures for C and e,
respectively. The method is fast: For simple objects,
106 trajectories require about 1 min on a PC. It is also
versatile: Switching from one object to another is easy.
Predictions have also been made for regular polygons,
polyhedra, and right circular cylinders, since these
shapes are important in applications and since numerical
calculations of high stated accuracy are available.
Finally, the path-integration method has been applied to
estimate transport properties of both linear flexible
polymers (random walk chains of spheres) and lattice
model dendrimer molecules. This requires probing of an
ensemble of objects. For linear chains, the distribution
function of C and of the trace (e), are found to be
universal in a size coordinate reduced by the chain
radius of gyration. For dendrimers, these distribution
functions become increasingly sharp with generation
number. It has been found that C and e provide important
information about the distribution of molecular size and
shape and that they are important for estimating the
Stokes friction and intrinsic viscosity of