Low Velocity Granular Drag in Reduced Gravity

We probe the dependence of the low velocity drag force in granular materials on the effective gravitational acceleration (geff) through studies of spherical granular materials saturated within fluids of varying density. We vary geff by a factor of 20, and we find that the granular drag is proportional to geff, i.e., that the granular drag follows the expected relation Fprobe = {\eta} {\rho}grain geff dprobe hprobe^2 for the drag force, Fprobe on a vertical cylinder with depth of insertion, hprobe, diameter dprobe, moving through grains of density {\rho}grain, and where {\eta} is a dimensionless constant. This dimensionless constant shows no systematic variation over four orders of magnitude in effective grain weight, demonstrating that the relation holds over that entire range to within the precision of our data

Three‐Atom Scattering in Gas‐Phase Electron Diffraction: A Tractable Limiting Case

The contribution of intramolecular multiple scattering in electron diffraction patterns of gas molecules is investigated by Glauber's method. An analytical expression for three‐atom scattering is derived for the limiting case in which the distance between atoms is large compared with atomic radii. This expression accounts well for the discrepancies between observed and conventionally calculated scattered intensities reported by Jacob and Bartell in the case of ReF6. The analogous four‐atom scattering is found to be very small.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71249/2/JCPSA6-56-5-2364-1.pd

A new procedure for analyzing the nucleation kinetics of freezing in computer simulation

A new method for deriving the size of the critical nucleus and the Zeldovich factor directly from kinetic data is presented. Moreover, in principle, the form of G(n)G(n), the free energy of formation of nuclei consisting of nn molecules, can be inferred. The method involves measuring times of first appearance of nuclei of size nn in the transient regime and applying the Becker-Döring theory. Times of first appearance exhibit the same characteristics as the conventional times associated with N(n,t)N(n,t), the number of nuclei of at least size nn per unit volume that have materialized at time tt. That is, they are well represented by three nucleation parameters, the reduced moment, the time lag, and the steady state nucleation rate. But unlike the conventional steady state rate which is independent of nn, the steady state times of first appearance vary with nn. In order to characterize the three nucleation parameters with precision, however, thousands of independent stochastic events with known nn are required. Such sets of data are readily generated in molecular dynamic simulations but, so far, not in laboratory experiments. Results are illustrated by an analysis of simulations of the spontaneous freezing of large clusters of SeF6SeF6.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87865/2/194503_1.pd

Molecular structure of phosphabenzene: Analysis combining electron diffraction and microwave data

The average (ra) structure of vapor phase C5H5P, the phosphorus congener of pyridine, was deduced. Vibrational corrections of diffraction data and rotational constants were made via a normal coordinate analysis based on an approximate quadratic force field. The heterocyclic molecule was found to be planar with principal structure parameters and uncertainties (2.5σ) of rg(C�P) = 1.733±0.003 Årg(C�P)=1.733±0.003Å, rg(C2�C3) = 1.413±0.010 Årg(C2�C3)=1.413±0.010Å, rg(C3�C4) = 1.384±0.012 Årg(C3�C4)=1.384±0.012Å, rg(C�H) = 1.122±0.015 Årg(C�H)=1.122±0.015Å, ∡CPC = 101.1°±0.3°∡CPC=101.1°±0.3°, ∡PCC = 124.4°±0.7°∡PCC=124.4°±0.7°, and ∡C2C3C4 = 123.7°±0.8°∡C2C3C4=123.7°±0.8°. Amplitudes of vibration were determined in the diffraction analysis as well as in the normal coordinate computation. A variety of different types of error matrices were computed to assess the effect of data correlations and the possible coupling, over and above scale factor shifts, between systematic errors in intensities and derived parameters. Conventional treatments of data correlations appear to lead to overoptimistic error estimates in the case of the longer internuclear distances. The structural characteristics of phosphabenzene are those expected for an aromatic molecule. Semiempirical molecular orbital calculations, adjusted to fit the experimental structure, suggest a small but significant involvement of phosphorus d orbitals in the π bonding.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69578/2/JCPSA6-61-7-2840-1.pd

Three‐atom scattering in gas‐phase electron diffraction. II. A general treatment

Intramolecular multiple scattering of electrons by polyatomic gas molecules is investigated with the aid of Glauber's theory of high energy elastic scattering. The key to a simpler and more rapidly convergent expression for dynamic scattering corrections is found in a propitious transformation of variables. An analytical representation of the corrections averaged over molecular rotations and vibrations is presented in a form suitable for routine electron diffraction analyses of molecular structure. Magnitudes and practical considerations in analyses are briefly discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70806/2/JCPSA6-58-12-5654-1.pd