Surface area and volume

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

UNIQUAC is significant because it provides a means to estimate multicomponent interactions using no more than binary interaction experimental data, bond angles, and bond distances. There is an implicit assumption that the combinatorial portion of the model, ie, the size and shape effects, can be averaged over a molecule and that these can be directly related to molecular surface area and volume. This assumption can be found in many QSAR methods and probably makes a significant contribution to the generally low accuracy of many QSAR prediction techniques. 

Pearlman, R. S. Molecular surface areas and volumes and their use in structure-activity relationships. In Physical Chemical... 

The combinatorial term Pcomb(X,S) in Eq. (11) denotes a usually small correction for size and somewhat also for shape dilferences of the solutes and solvents, which is reasonably well understood from chemical engineering models. It is an empirical function, depending only on the surface areas and volumes of solute and solvent molecules, which are reasonably known from the COSMO cavities. The error arising from the approximations made in the combinatorial term can be expected to be much less than IkJ mol, or 0.17 log units, and hence can be safely neglected in the context of drug solubiUty estimation. 

Pb-212 and S0% Distributions. The aerodynamic size distributions of Pb-212 and S0 were quite different, reflecting the different dependencies of surface area and volume on aerosol diameter (Friedlander, 19/7). Pb-212, like the other... 

Pearlman, R. S. (1980) Molecular surface areas and volumes and their use in structure/activity relationships. In Physical Chemical Properties of Drugs. Yalkowsky, S.H., Sinkula, A.A., Valvani, S.C., Eds., Medicinal Research Series, Vol. 10, pp. 321-317, Marcel Dekker, New York. 

Pearlman, R. S. (1986) Molecular surface area and volume Their calculation and use in predicting solubilities and free energies of desolvation. In Partition coefficient, Determination and Estimation. Dunn, III, W. J., Block, J. H., Pearlman R. S., Eds., pp. 3-20, Pergamon Press, New York. 

This 10-year longitudinal study is focused on the potential associations between ambient air pollution and respiratory health in children. The objectives are to document the respiratory growth of study participants, to assess whether ambient pollutants play a role in respiratory health, and to identify which pollutants are responsible for any observed effects. Ambient air quality is being monitored in each of twelve communities by centrally located regional stations, CA, which also collect standard meteorological data. Gaseous pollutants are monitored continuously, while ambient particle concentration and size are determined by a number of approaches. Additional exposure assessment occurs because of the establishment of the Particle Center, including more extensive particle size number, surface area, and volume distribution measurements. 

Pearlman RS (1980) Molecular surface area and volumes and their use in structure/ activity relationships. Marcel Dekker, New York, p 412... 

The simplest case of compositional dependence is the zero-order reaction, in which the concentration gradient is not affected by concentration. Denoting the molar concentration of the ith element (or component) as c, (and neglecting surface area and volume of solution effects), we have... 

The three neutrons produced when uranium splits have the ability to split other U-235 nuclei and start a self-sustaining chain reaction. Whether a chain reaction takes place depends on the amount of fissionable material present. The more fissionable material that is present, the greater the probability that a neutron will interact with another U-235 nucleus. The reason for this involves the basic relationship between surface area and volume as mass increases. If a cube with a length of 1 unit is compared to a cube of 2 units, it is found that the surface area to volume ratio of the 1 unit cube is twice that of the 2 unit cube (Figure 17.6). This shows that volume increases at a greater rate than surface area as size increases. The probability that neutrons escape rather than react also depends on the surface area to volume ratio. The higher this ratio is the more likely neutrons escape. When a U-235 nucleus contained in a small mass of fissionable uranium is bombarded by a neutron, the... 

Because of this need to know how the mass, surface, and volume are distributed among the various particle sizes, distribution functions for these parameters (i.e., mass, surface, and volume) are also commonly used for atmospheric aerosols in a manner analogous to the number distribution. That is, Am A log D, AS A log D, or AV A log D is plotted against D on a logarithmic scale, where Am, AS, and AV are the mass, surface area, and volume, respectively, found in a given size interval again the area under these curves gives... 

Working with surface areas and volumes of solid figures Considering practical applications with prisms Doing what you can with a cylinder... 

Interrelationships Among Surface Area and Volume Upon Scale-Up... 

According to the results in Table 1, SCD creates larger surface area at the expense of substantial loss in the surface area and volume of micropores. Sample SCD has a quite low apparent density, compared with the sample dried in air. Evidently, SCD treatment results in a significant change in the framework of the sample. The pillared layered structure which is... 

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