Frank L. McCrackin

Errors arising from surface roughness in ellipsometric measurement of the refractive index of a surface

Abstract The roughness of a surface is generally neglected when the refractive index of a material is calculated from ellipsometer measurements. Errors produced by neglecting the roughness of the surface are evaluated for three models of the topography of the surface (square ridges, triangular ridges, and pyramids). A range of roughness from 0 to 500 A and six substrate materials (glass, silicon, chrome, mercury, gold, and silver) are considered. Large errors in determination of indices, even for small values of roughness (50 A), were found.

One‐Dimensional Model of Polymer Adsorption

A detailed treatment of the conformations of a one‐dimensional polymer molecule adsorbed to a surface is given. The average number of contacts of the chain with the surface, the end‐to‐end length, and the distribution of segments ρ(z) with respect to distance z from the surface are computed as functions of the chain length (N) of the polymer and the attractive energy of the surface. Both theoretical and Monte Carlo calculations are used. A transition is found at an attractive energy of kT ln 2. For attractive energies less than this value, the average number of contacts of the chain with the surface approaches a finite value as N approaches infinity, while the end‐to‐end length vaires as N½. However, above the transition the number of contacts is proportional to N and the end‐to‐end length is independent of N. The distribution of segments ρ(z) also shows a marked change as we go through the transition. The one‐dimensional model is shown to correspond to the projection of a three‐dimensional model on the d...

Monte Carlo Studies of Configurational and Thermodynamic Properties of Self‐Interacting Linear Polymer Chains

Non‐self‐intersecting walks on the simple cubic and face‐centered cubic lattices are used as a model for the linear polymer chain with excluded volume and nearest‐neighbor interactions between the chain elements. The statistical properties of this model are investigated using the modified Monte Carlo technique for inversely restricted sampling. The following properties are investigated: the limiting distribution function of chain dimensions, the dependence of mean square length of the chain on the number of chain elements, and the thermodynamic properties of the chain. The results of these investigations are presented by a set of parametric representations. Each of these representations includes a parameter which is descriptive of long‐range interactions in the polymer chain. These parameters are investigated for their dependence on the nearest‐neighbor interaction parameter. A particular value for the nearest‐neighbor interaction parameter is found, in which long‐range interaction parameters reduce to th...

Configuration of Isolated Polymer Molecules Adsorbed on Solid Surfaces Studied by Monte‐Carlo Computer Simulation

The configurations of adsorbed polymer molecules with excluded volume were simulated on a four‐choice simple cubic lattice using a computer. The average values of the fraction of segments on the surface, loops off the surface, normal distance of the end of the molecule from the surface, root mean square of the normal distance, maximum normal distance from the surface, and root‐mean‐square end‐to‐end distance were calculated for various lengths of the molecules and various attractive energies between segments and the surface. When these averages over the configurations are compared with previous results which do not account for the excluded‐volume effect, important differences are found.

Analyses and Corrections of Instrumental Errors in Ellipsometry

Expressions for the errors produced in an ellipsometer due to an imperfect compensator, due to birefringence in windows of a cell containing the sample, and due to tilting of the sample are derived. Methods of analyzing the ellipsometer readings to eliminate these errors are given.

Stress-Strain Relationships. in Yarns Subjected to Rapid Impact Loading

If a textile yarn, marked at intervals along its length, is struck transversely by a rifle bullet, a flash photograph taken shortly after impact will reveal a shifting of the marks caused by passage of a strain wave. Analysis of these shifts provides data on the dis tribution of strain and strain velocity in the wave. Tests were performed on specimens of a high-tenacity nylon and a high-tenacity polyester yarn, to determine strain-velocity distributions at various times after impact and at various impact velocities. The observed distributions were then compared with the predictions of a theory which assumed that stress-strain behavior was independent of strain rate. From discrepancies between theo retical and observed results, it was concluded that at strain levels up to 9%, significant creep and stress relaxation occurred within 30 μ sec after impact, but in the time interval 30 μ sec to 300 μ sec, creep and stress relaxation were negligible. For strains of the order of 1%, the 30 μ sec creep and stress ...

Stress-Strain Relationships in Yarns Subjected to Rapid Impact Loading Part IV: Transverse Impact Tests

If a textile yarn segment, clamped at each end, is impacted transversely at the mid point, the stress-strain curve for this yarn can be obtained from measurements on a high speed photographic record of the yarns motion. This paper describes the apparatus and procedure used. Stress-strain curves for high rates of straining, of the order 5000%/sec., obtained by this method are given for high tenacity nylon, Fortisan, and Fiberglas. Comparison with stress-strain data obtained at conventional rates shows that these mate rials have higher initial moduli, and that their stress-strain curves remain linear up to higher stress values, when the testing rate is high. The breaking tenacities are slightly greater and breaking elongation slightly smaller at these high test rates.

Molecular weight and polydispersity measurements of polystyrene by quasielastic light scattering

Abstract The molecular weight and polydispersity of a polydisperse polystyrene sample was measured by quasielastic light scattering. The molecular weight distribution of the polymer was represented by the Schultz distribution. The weight average molecular weight and polydispersity of distribution was adjusted until the quasielastic light scattering spectra calculated for the distribution agreed with the measured spectra. The calculation was repeated using the logarithmic normal distribution for the polymer. The calculated value of the weight average molecular weight is accurate and insensitive to the assumed molecular distribution function. However, the calculated values of the polydispersity are only of fair accuracy. Thus quasielastic light scattering gives values of the weight average molecular weight at least as accurate as elastic light scattering and gives a crude estimate of the polydispersity of the polymer.

Monte Carlo calculations of the number of ways to pack nonoverlapping rods on a square lattice

The number of configurations of nonoverlapping rods on a square lattice is computed for various packing fractions and orientations of the rods. From the number of configurations, the entropies of the configurations are computed and compared with the results of approximate formulas of DiMarzio that are much used in statistical–mechanical theories of liquid crystals. For rods of three lattice sites, our calculations and Dimarzio’s formulas agree to within 0.5% for packing fractions less than 0.5. Some calculations for rods of ten lattice sites also showed good agreement.

Relationship of intrinsic viscosity of polymer solutions to molecular weight

Abstract An equation derived by Han relating intrinsic visocity to molecular weight of a polymer has been fitted to experimental data over a large range of molecular weight. Excellent fits were obtained although the Mark-Houwink equation did not fit the data over the complete molecular weight range. Hans equation may be fit to intrinsic viscosity data over a moderate range of molecular weight, and is shown to then accurately predict the intrinsic viscosities for molecular weights outside this range. A method is given to compute the two parameters of Hans equation from the Mark-Houwink parameters of a polymer in a solvent.