Calculation of vaporization rates assuming various rate determining steps: Application to the resistojet

The various steps that could control the vaporization rate of a material are discussed. These steps include the actual vaporization, flow rate of matrix gas, chemical reaction, gas diffusion, and solid state diffusion. The applicable equations have been collected from diverse appropriate sources, and their use is explained. Rate equations are derived for conditions where more than one step is rate controlling. Calculations are made for two model materials: rhenium which vaporizes congruently, and tantalum carbide which vaporizes incongruently. The case of vaporization under thermal gradient conditions is also treated. The existence of a thermal gradient in the resistojet means that the vaporization rate of a material may be only one thousandth of that predicted under isothermal conditions. Calculations show that rhenium might have a 100,000 hr lifetime at temperature in a 2500 C resistojet. Tantalum carbide would have a life of only 660 sec under similar conditions

Electrocrystallization in microgravity

Electrocrystallization under microgravity conditions is proposed as a potential method of crystallization that would be almost completely free of fluid convection. Such crystallization may result in purer, more perfect, and larger crystals than is possible under normal gravity conditions. Observations made and data collected during the crystallization process under convection-free conditions should add to our knowledge of the crystallization process. The proposed method would allow easy comparison of crystals growth in space with those grown under normal gravity conditions. Nine types of electrocrystallization are presented: an example of each is discussed. Electrocrystallization is compared with the compartmental crystallization method used by 3M Corporation in recent shuttle experiments

Fugacity and concentration gradients in a gravity field

Equations are reviewed which show that at equilibrium fugacity and concentration gradients can exist in gravitational fields. At equilibrium, the logarithm of the ratio of the fugacities of a species at two different locations in a gravitational field is proportional to the difference in the heights of the two locations and the molecular weight of the species. An analogous relation holds for the concentration ratios in a multicomponent system. The ratio is calculated for a variety of examples. The kinetics for the general process are derived, and the time required to approach equilibrium is calculated for several systems. The following special topics are discussed: ionic solutions, polymers, multiphase systems, hydrostatic pressure, osmotic pressure, and solubility gradients in a gravity field

Kinetics of chromium ion absorption by cross-linked polyacrylate films

Three cross-linked ion exchange membranes were studied as to their ability to absorb chromium ion from aqueous chromium III nitrate solutions. Attention was given to the mechanism of absorption, composition of the absorbed product, and the chemical bonding. The membranes were: calcium polyacrylate, polyacrylic acid, and a copolymer of acrylic acid and vinyl alcohol. For the calcium polyacrylate and the copolymer, parabolic kinetics were observed, indicating the formation of a chromium polyacrylate phase as a coating on the membrane. The rate of absorption is controlled by the diffusion of the chromium ion through this coating. The product formed in the copolymer involves the formation of a coordination complex of a chromium ion with 6 carboxylic acid groups from the same molecule. The absorption of the chromium ion by the polyacrylic acid membranes appears to be more complicated, involving cross-linking. This is due to the coordination of the chromium ion with carboxylic acid groups from more than one polymer molecule. The absorption rate of the chromium ion by the calcium salt membrane was found to be more rapid than that by the free polyacrylic acid membrane

Mechanism and models for zinc metal morphology in alkaline media

Based on experimental observations, a mechanism is presented to explain existence of the different morphologies of electrodeposited zinc in alkaline solution. The high current density dendrites appear to be due to more rapid growth on the nonbasal crystallographic planes than on the basal plane. The low current density moss apparently results from dissolution from the nonbasal planes at low cathodic voltages. Electrochemical models were sought which would produce such a phenomenon. The fundamental plating mechanism alone accounts only for different rates on different planes, not for zinc dissolution from a plane in the cathodic region. Fourteen models were explored; two models were in accord with the proposed mechanism. One involves rapid disproportionation of the zinc +1 species on the nonbasal planes. The other involves a redox reaction (corrosion) between the zinc-zincate and hydrogen-water systems

Decay of the zincate concentration gradient at an alkaline zinc cathode after charging

The transport of the zincate ion to the alkaline zinc cathode was studied by observing the decay of the zincate concentration gradient at a horizontal zinc cathode after charging. This decay was found to approximate first order kinetics as expected from a proposed boundary layer model. The concentrations were calculated from polarization voltages. The decay half life was shown to be a linear function of the thickness of porous zinc deposit on the cathode indicating a very rapid transport of zincate through porous zinc metal. The rapid transport is attributed to an electrochemical mechanism. From the linear dependence of the half life on the thickness the boundary layer thickness was found to be about 0.010 cm when the cathode was at the bottom of the cell. No significant dependence of the boundary layer thickness on the viscosity of electrolyte was observed. The data also indicated a relatively sharp transition between the diffusion and convection transport regions. When the cathode was at the top of the cell, the boundary layer thickness was found to be roughly 0.080 cm. The diffusion of zincate ion through asbestos submerged in alkaline electrolyte was shown to be comparable with that predicted from the bulk diffusion coefficient of the zincate ion in alkali

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given

Kinetics of copper ion absorption by cross-linked calcium polyacrylate membranes

The absorption of copper ions from aqueous copper acetate solutions by cross-linked calcium acrylate membranes was found to obey parabolic kinetics similar to that found for oxidation of metals that form protective oxide layers. For pure calcium polyacrylate membranes the rate constant was essentially independent of copper acetate concentration and film thickness. For a cross-linked copolymer film of polyvinyl alcohol and calcium polyacrylate, the rate constant was much greater and dependent on the concentration of copper acetate. The proposed mechanism in each case involves the formation of a copper polyacrylate phase on the surface of the membrane. The diffusion of the copper ion through this phase appears to be the rate controlling step for the copolymer film. The diffusion of the calcium ion is apparently the rate controlling step for the calcium polyacrylate. At low pH, the copper polyacrylate phase consists of the normal copper salt; at higher pH, the phase appears to be the basic copper salt

Anomalous Thermoluminescent Kinetics of Irradiated Alkali Halides

Anomalous thermoluminescent kinetics of irradiated alkali halide