BRIEFS Summary of papers published in this month's research quarterly, I H E C Fundamentals THERMODYNAMICS OF POLYMER SOLUBILITY IN POLAR AND NONPOLAR SYSTEMS
An approximate description of the thermodynamic properties of polymer solutions is given by the Flory-Huggins equation. This equation includes a parameter x which depends upon the intermolecular forces acting between the molecules in the solution. The theoretical critical value of x is approximately 0.5; for a given polymer-solvent pair x must be less than 0.5 if the polymer is to be appreciably soluble in the solvent. Semiempirical techniques are prescribed for calculating x from pure-component properties of the solvent and polymer; these techniques are based on an extension of the Hildebrand-Scatchard theory of solutions and on the theory of intermolecular forces. Polar and nonpolar solubility parameters are presented for a variety of solvents and for several polymers. The calculations are useful for nonpolar systems, polar polymers or polar solvents, or both, but are not reliable for systems where specific interactions (such as hydrogen bonding) are important. Brief consideration is given to the solubility of polymers in mixed solvents.
R. F. Blanks and J . M . Prausnitz, University of California, Berkeley. Calif. IND.ENG.CHEM. FUNDAMENTALS 3 , l - 8 (1964) DEW AND BUBBLE ISOTHERM CALCULATIONAL METHOD FOR BINARY SYSTEM PHASE AND VOLUMETRIC BEHAVIOR
A method for calculation of liquid and vapor compositions together with saturated volumetric properties of binary systems was developed and sucessfully used on the helium-nitrogen system. These calculations require only quantities measured in the determination of the dew and bubble points. The phase rule specifies that for an isothermally univariant system, if the pressure is fixed, the intensive properties-X, Y , p l , pg-are set, regardless of the amount of the phases present. Obviously a numerical solution for these variables requires four simultaneous equations. Since it is possible to write two equations from material balances on nitrogen and helium at each volume per cent liquid, two independent tuns are required-a dew isotherm and a bubble isotherm. The quantities which must be measured are the amount of known composition gas metered to the cell and the volume per cent liquid at cell conditions. In the limit these equations go to the dew and bubble points.
N . C. Rodewald, J . A . D a h , and F. Kurata, Center for Research in Engineering Science, Univetsity of Kansas, Lawrence, Kan. IND.ENG.CHEM.FUNDAMENTALS 3, 8-14 (1964) PARTICLE INTERACTIONS IN AQUEOUS KAOLINITE DISPERSIONS
The pseudoplastic characteristics of acidic aqueous kaolinite dispersions are attributed to the formation of "card-house" flocs by coulombic interaction between cationic edges and anionic basal surfaces. As p H is elevated with NaOH, edge charges are neutralized with consequent increase in floc density, and reduction in floc size, suspension yield value, and viscosity. Polyphosphates deflocculate kaolinite under acidic conditions by adsorption on the cationic edge surfaces. Dilute deflocculated slurries exhibit Newtonian viscosities which closely obey Einstein's equation corrected for particle anisometry and electroviscous effects. Acid decomposition of kaolinite appears to liberate colloidal alumina and silica which adsorb on the basal and edge surfaces, weaken particle interactions, reduce the p H at which deflocculation occurs, and increase the polyphosphate required for deflocculation. A . S. Michaels and J . C. Bolger, Massachusetts Institute of Technology, Cambridge 42, Mass. IND.ENG.CHEM.FUNDAMENTALS 3, 14-20 (1964) RATE OF ISOMERIZATION OF CYCLOPROPANE IN A FLOW REACTOR
Experimental studies planned to investigate combined diffusional and chemical effects in porous solids or packed beds might be simplified by the use of a simple-order homogeneous gas phase
reaction. The isomerization of cyclopropane to propylene appears to satisfy these requirements potentially, and to retain the simplicity of a binary system. However, the reaction behavior at fast reaction rates must be known, if the reaction is to be used in a diffusion-controlled experiment. In the present work, the existing kinetic data for this isomerization, obtained in batch reactors and at temperatures from 460' to 550' C., were extended to 620' C. by use of flow reactors constructed of borosilicate glass. The extent of secondary decomposition of propylene at these temperatures was investigated, as well as the effect of large surface-volume ratios. Kinetic behavior was measured at all conversion levels by both integral and differential methods. At constant pressure, and temperatures to 620' C., this isomerization behaves as an ideal homogeneous first-order reaction in contact with borosilicate glass equipment.
B . R . Davis and D . S. Scott, Uniuersity of British Columbia, Vancouver, B. C., Canada IND.ENG.CHEM.FUNDAMENTALS 3, 20-23 (1964) KINETIC AND EQUILIBRIUM STUDIES OF BENZENE HYDROGENATION IN A BATCH RECYCLE REACTOR
Rate and equilibrium data are reported for vapor-phase hydrogenation of benzene over a pulverized platinum-alumina catalyst. The measurements were made with a fixed-bed differential reactor in a batch recycle system, and illustrate the possibilities of this unusual experimental technique. The reaction conditions studied range from 500" to 600' F., 2- t o 14-atm. total pressure, 6 to 12 convermoles of He charged per mole of benzene, and 0 to 99.9 70 sion. The results do not indicate a definite reaction order, but the initial rate varies approximately as the cube of the total pressure. No side reactions were observed.
Paul F. Korbach and Warren E. Stewart, University of Wisconsin, Madison, Wis. IND.ENG.CHEM.FUNDAMENTALS 3 , 24-27 (1964) THE ALGEBRA OF SYSTEMS OF SECOND-ORDER REACTIONS
It is shown how the differential equations of second-order reactions are related to nonassociative algebras. These algebras, and hence the system of reactions, can be classified in equivalent classes for which canonical forms can be found. This is illustrated by particular examples and a general treatment based on the notions of stoichiometric and kinetic equivalence is given, allowing the proof of general theorems on the structure of chemical algebras. Some further connections with reaction mechanisms, diffusion, and large or infinite systems are indicated.
Rutherford Aris, University of Minnesota, Minneapolis 74, Minn. IND.ENC.CHEM.FUNDAMENTALS 3 , 28-37 (1964) OPTIMIZATION OF SOME MULTISTAGE CHEMICAL PROCESSES
Performance of a number of stagewise chemical processes can be represented in a general manner by the following set of finite difference equations: xln-1
= xtn
+ tP+(xln); n = 1 , 2 , . . . ,N x10
xP-1
=
x2n
= a
+ .P+(xin); n = 1 , 2 , . . . , N x20
=
0
The optimizing solutions for such processes can be obtained uniquely by the use of a single recursion relation derived from Katz's algorithm for the maximum principle.
C. S. Wang and Liang-tseng Fan, Kansas State University, Manhattan, Kan. IND. ENG.CHEM. FUNDAMENTALS 3 , 38-42 (1964) (Continued on page 69) VOL 56
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