The equation of state for hard spheres in a spherical cavity is calculated and compared with the results previously found when the containing boundary was a channel. It was found that the spherical surface provides a focusing effect on both the pressure and the compressibility factor. An examination of the results suggested that the density and compressibility factors could be expanded in a series of Maxwellian functions. It was found that a six-term series which was modified in the immediate vicinity of the wall was sufficient. This has an advantage over the usual Fourier series expansion in that less terms are required. In addition, an argument can be made that such a series has a foundation in the physics of the problem.

Solid‐state 13C‐NMR spectroscopy has been used to investigate the structure of cellulose nitrates prepared from cotton linters. The solid‐state technique has the advantage that the entire range of substitution can be studied, which is not possible at present by solution methods. The spectra change progressively with increasing degree of substitution (DOS = 3 for cellulose trinitrate), and can be used to quantify the extent of substitution at C6, C2, and C3. Progressive nitration leads to elimination of the original C6 resonances of native cellulose by DOS = 1.39. The first nitration of C6 occurs in the amorphous regions, and this is complete by DOS = 0.50. Substitution at C6 is accompanied by decrystallization, as indicated by the decrease in the resonance assigned to crystalline C4, which also disappears at DOS = 1.39. A new resonance assigned to C1 appears at DOS = 0.28 at 101 ppm; the original C1 resonance for cellulose declines steadily and disappears by DOS = 2.65. This change is assigned to nitration of C2, based on the published solution spectra. Finally, development of intensity at 82 ppm at DOS = 1.83 is assigned to the effect of nitration at C3. There is no indication of any rearrangement of the unsubstituted regions analogous to those that occur on Mercerization of native cellulose.

The properties of a collapsing spherical bubble have been studied in the past using the methods of continuum gas dynamics. In this report the problem is approached in an entirely new way by using the molecular dynamics of hard spheres to represent a dense gas during the final stages of cavity collapse. The advantage of this method is that it is only necessary to assume that the laws of classical mechanics are valid in order to ensure that all the transport properties and equation of state for the gas are properly taken into account. The disadvantage is that the trajectories of only a relatively small number of particles can be followed on even today's fastest computers, so that the calculations are limited to small systems. The methods used are essentially the same as those already employed to study hard spheres in a channel or a spherical cavity. Four cases are examined, with wall Mach numbers of 0.5, 1.0, 1.5 and 15.0. The temperature, pressure and density distributions are calculated inside the cavity for several average densities during the course of bubble collapse. Our simulation also indicates that a heavier gas will gain more energy from the wall than a light gas, possibly explaining the observation that heavy, dissolved gases yield more luminosity than light gases during cavity collapse.

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A molecular dynamics study of the thermodynamics properties, including equation of state, of hard spheres in a narrow channel is presented. Four densities are studied and it is found that the pressure profile is directly correlated to the density profile. Further, the fraction of the total pressure due to collisions in a direction normal to the wall is also correlated to the density profile. The equation of state is that of a hard sphere fluid at a density higher then the fluid and it varies across the channel. The motion of particles near the wall is constrained as found earlier in Monte Carlo studies.