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After measuring ultrasonic velocity and density, the molecular compressibility values from Wada's formula were calculated, for alkali metal halide solutions in methyl, ethyl, butyl, and glycol alcohol. The temperature and concentration dependence were studied, finding deviations due to the hydrogen bonds of the solvent.
An empirical expression is derived to account for the molecular multiple scattering contribution to the almucantar radiance field. Formulas for the correction factors which incorporate the effects of multiple scattering and nonzero ground albedo are also given. The use and accuracy of the multiple-scattering approximation in direct problems of radiative transfer associated with almucantar radiance are discussed and illustrated by examples. It is shown that in almost all instances, inclusion of the molecular multiple-scattering contribution reduces the errors obtained with the single-scattering approximation by a factor of at least 2.
A direct and convenient method is presented for deriving expressions which equate any thermodynamic state function to averages of specific dynamical functions and their fluctuations over the classical microcanonical distribution. Specific expressions are obtained for a variety of thermodynamic quantities. The effect of various entropy definitions on the results are assessed, and the latter are compared to previous work in the literature. The derived formulas are applied to the analysis of molecular-dynamics computer simulations.
Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.
Molecular chaos breakdown under shear flow, calculating thermodynamic fluctuation formula for unlimited Reynolds number increase
Computer program calculates ideal gas thermodynamic properties for any species for which molecular constant data is available. Partial functions and derivatives from formulas based on statistical mechanics are provided by the program which is written in FORTRAN 4 and MAP.
The molecular velocity of sound was calculated according to Rao's formula and the temperature and concentration dependences of this value were studied in aqueous solutions of alkali and alkaline-earth halides. Study of relative association brought to light characteristic effects of ions. The variation of the relative association can be explained by a breaking of hydrogen bonds by ions and thermal agitation.
The generalization spectral line contour concept and formulas for a two component mixture, as well as consequences of the general formula are discussed. The calculation procedure, initial information, calculation results and comparison of calculations with available experimental data, for radiation absorption in three CO2 bands are presented.
Microwave thermal emission from a layer of cloud or rain consisting of spherical particles has been investigated. Scattering effects are studied in great detail with both numerical and analytical approaches. In the absence of ground emission, it is found that scattering induces brightening for optically thin layers and vice versa for optically thick layers. As a function of observation angle, brightening occurs near nadir, while darkening occurs at large angles in the case of small optical thickness. For large optical thickness, darkening occurs at all angles because of backscattering effects. When the layer of cloud or rain is above an air layer and an ocean surface at a higher temperature, it is found that the darkening effect at large optical thickness is much more pronounced. The darkening effect is also larger for vertical polarizations because the ocean emits more vertically polarized components. The effect of thermal emission and molecular absorption by atmospheric gases is also taken into account. Results obtained from analytical formulas under single-scattering assumptions are compared and illustrated.
Spherically symmetrical classical scattering theory shows dependence on phase shift through appearance in quantal formulas for scattering amplitude and total cross section
Remote-sensing reflectance (r(rs)) is defined as the ratio of upwelling radiance to downwelling irradiance. Relationships between remote-sensing reflectance and inherent optical properties serve as the basis for ocean-color modeling, as well as for spectral deduction of oceanic constituents through analytical/semi-analytical models of ocean color. A decade ago, a simple and concise formula based on Monte Carlo simulations was developed by relating rrs to a property u, the ratio of backscattering (b(b)) to the sum of absorption (a) and backscattering (u = b(b)/(a+b(b))). This relationship generally ignored the shape differences in phase functions between molecular scattering and particle scattering. In this study, the relationship is updated with separate parameters for molecular and particle scattering, based on the Radiative Transfer Equation through use of Hydrolight numerical solutions. The new approach fits r(rs) better than an earlier traditional formula, for both clear and turbid waters.
Physical models are developed for establishing criteria to decide on the acceptable contamination level of optical devices in space-borne conditions. Optical systems can be degraded in terms of decreased throughput, i.e., transmissivity or reflectivity, or increases in the total integrated scatter (TIS). Performance losses can be caused by particulate accretion, molecular film accretion, and impact cratering. A quantitative relationship is defined for film thickness and loss of throughput. Formulas are also developed for cases where induced surface defects are larger than the desired viewing wavelengths, or smaller or of the same order of the observed wavelengths. The techniques are used to quantify the degradation of a VUV solar coronagraph, a VUV stellar telescope, and a solar cell due to TIS. Applications are projected for estimating the contamination sensitivity of specific instruments, assessing the contamination hazard from known particulates, or to define clean room standards.
Simple closed-form, approximate, analytic expressions for Franck-Condon factors are given. They provide reliable estimates for Franck-Condon factor arrays for molecular band systems for which only vibrational-frequency, equilibrium internuclear separation and reduced mass values are known, as is often the case for astrophysically interesting molecules such as CeO, CoH, CrH, CrO, CuH, GeH, LaO, NiH, SnH, and ZnH for band systems of which Franck-Condon arrays have been calculated.
The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.
A decomposition of the molecular energy is presented that is motivated by the atom superposition and electron delocalization physical model of chemical binding. The energy appears in physically transparent form consisting of a classical electrostatic interaction, a zero order two electron exchange interaction, a relaxation energy, and the atomic energies. Detailed formulae are derived in zero and first order of approximation. The formulation extends beyond first order to any chosen level of approximation leading, in principle, to the exact energy. The structure of this energy decomposition lends itself to the fullest utilization of the solutions to the atomic sub problems to simplify the calculation of the molecular energy. If nonlinear relaxation effects remain minor, the molecular energy calculation requires at most the calculation of two center, two electron integrals. This scheme thus affords the prospects of substantially reducing the computational effort required for the calculation of molecular energies.
High molecular weight perfluorocarbon polyether gums were obtained by photolysis of perfluorodienes and discyl fluorides containing a perfluorocarbon polyether backbond. The materials obtained are represented by chemical formulas. A method was developed whereby reactive acyl fluoride and trifluorovinyl end groups are converted into inert structures. In order to investigate the possible preparation of difunctional molecules which may be useful in polymer synthesis, the reactions of hexafluoropropene oxide (HFPO) with Grignard and organolithium reagents have been studied. Reactions of various nucleophilic reagents with HFPO were also investigated.
The purposes of this vanadyl spin probe study are threefold: (1) to establish when the breakdown of motionally narrowed formulas occurs; (2) to analyze the experimental vanadyl EPR line shapes by the stochastic Lioville method as developed by Polnaszek et al. (1973) for slow tumbling in an anisotropic liquid; and (3) to compare the vanadyl probe study results with those of Polnaszek and Freed (1975). Spectral EPR line shapes are simulated for experimental spectra of vanadyl acetylacetonate (VOAA) in nematic liquid crystal butyl p-(p-ethoxyphenoxycarbonyl) phenyl carbonate (BEPC) and Phase V of EM laboratories. It is shown that the use of typical vanadyl complexes as spin probes for nematic liquid crystals simplifies the theoretical analysis and the subsequent interpretation. Guidelines for the breakdown of motionally narrowed formulas are established. Both the slow tumbling aspects and the effects of non-Brownian rotation should be resolved in order to extract quantitative information about molecular ordering and rotational mobility.
Hydrodynamic escape of hydrogen from a planetary atmosphere can remove heavier gases as well as hydrogen, provided that the escape rate is sufficiently large. Analytic approximations for the degree of mass fractionation of a trace species during hydrodynamic escape are compared with accurate numerical solutions for the case of transonic outflow. The analytic approximations are most accurate when the ratio of molecular weights of the heavier and lighter constituents is large so that nonlinear terms in the momentum equation for the heavy constituent become small. The simplest analytic formula is readily generalized to the case where a heavy constituent is also a major species. Application of the generalized formula to hypothetical episodes of hydrodynamic escape from Venus and Mars suggests that both hydrogen and oxygen could have escaped; thus, substantial quantities of water may have been lost without the need to oxidize large amounts of the crust.