INDUSTRIAL AND ENGINEERING CHEMISTRY
1476
predicted at any concentration of the pigment if two constants and the viscosity of the binder are known. These constants can be obtained readily by determining from finite shear velocity measurements on the high shear viscometer a t two or more levels of concentration of that pigment in the given vehicle and following the procedures as outlined.
1.
log
2.
log??,
70
Vol. 47, No. 7
+ d sD kc u = log to+ -
= log q,
~
u-c
CONCLUSIONS
.I 8 .I 6 .I 4 .I 2 .I0
tFigure 8.
Structure nomograph titanium dioxide in raw linseed oil
Although these theoretical relationships hold only a t infinitely high shear velocities, the viscosity at brushing shear velocities usually do not differ very materially from this value for most conventional oil paints. As a result, the four factors, 70,c, U,or p and k or K , will influence the brushing characteristics of paints strongly. Changes in any of these factors would alter the brushing characteristics very nearly according to these relationships. STRUCTURE EQUATION
In order to make the prediction for brushability of oil paints exact, or t o predict the viscosity of pigment/binder systems a t any high shear velocity, it is necessary to know the relationship between the rheological structure of a paint system and the concentration of pigment present in the system. This has been found empirically to follow quite closely the relationship
where is the slope of the viscosity curve in the basic plots of Figures 6 and 7. This equation, too, can be solved with a Z nomograph by plotting q , S against c. A plot of this type is shown in Figure 8 for the data obtained from Figure 6. The point of intersection of the projection of the v W S versus c lines determine the constants 01 and 6. The factors required for solving this equation are obtainable from the basic viscosity/shear velocity measurements required for obtaining v m r U , and k . More work is required before the limits of the structure relationship can be ascertained. The exact theoretical significanceof the constants CY and 6 is not apparent a t this time. For practical purposes, however, it seems possible with the aid of four constants, U ,k , CY and 6, which can be obtained easily by empirical means, to predict the viscosity of most oil paint systems at any given concentration of pigment, viscosity of vehicle, and high shear velocity down t o about 300 sec.-l This is accomplished by the equation
For the brushing shear velocity, D”2is equal to 100. It is usually easier to solve this equation in several steps through the three basic equations that make it up.
The Vand and Brailey equations relating the viscosity of suspensions to the concentration of pigment present may be employed in practical viscosity measurements of paint systems. Because of the difficulty of determining the constants K , the pigment shape factor and q, the immobilization constant for these derived equations, a hyperbolic form giving results very similar to the theoretical equations is employed. The two constants k and U are obtained for this equation by graphical computation. k is very nearly proportional to K , while U , the densest rheological packing system for the particular dispersion is a function of p. This rhelogical packing system is not equivalent to the densest physical packing system obtained by determining the ultimate pigment volume concentration (UPVC) of that dispersion. The UPVC method may find application in the paint industry to characterize pigments as a substitute for present oil absorption tests. A prediction of the viscosity of any concentration of pigment in a given Newtonian vehicle may be made for any chosen high shear velocity by combining the equations with a second empirical hyperbolic equation, correlating the structure of pigmented systems with concentration of pigment. The two constants required for the structure equation, 01 and 6, can be obtained from the same data required t o determine k and U . These basic data are obtained from the high shear viscosity curves of the system a t two or more levels of pigmentation, LITERATURE CITED (1) Asbeck, W. K., and Van Loo, M.,-IND.ENG.CHEM.,41, 1470 f 1 949). --I. \--
(2) Ibid., 46, 1291 (1954). (3) Asbeck, W. K., Laiderman, D. D., and Van Loo, M., J . Cotloid Sei., 7, 306 (1952). (4) Asbeck, W. K., Laiderman, D. D., and Van Loo, M., Ofic. Dig. Federation Paint & Varnish Production Clubs, No. 326, 156 (1952). , (5) Brailey, R. H., Division of Paint, Varnish and PlaBtics Chemistry preprint, p. 49, 120th Meeting ACS, New York, September 3-7, 1951. (6) Hull, H. H., J . Colloid Sci., 7 , 316 (1952). (7) Krieger, I. M., and Maron, S. H., Ibid., 6, 528 (1951). (8) Maron, S. H., Madow, €3. P., and Krieger, I. M., Ibid., 6, 584 (1951). (9) Mooney, M., Ibid., 6, 162 (1951). (10) Vand, V., Nature, 155, 364 (1945) ; J . Phys. & Colloid Chem.’ 52, 277 (1948). (11) Wachholtz, F., and Asbeck, W. K., Kolloid-Z., 93, 280 (1940); 94, 66 (1941).
RECFJ~ED for review November 12, 1954.
ACCEPTEDDecember 15, 1954. Presented before the Division of Paint, Plastics and Printing Ink Chemistry at the 126th Meeting, ACS, New York, September 13, 1954.
Correction In the article, “Hydroforming Reactions, Effect of Certain Catalyst Properties and Poisons [W. P. Hettinger, Jr., C. D. Keith, J. L. Gring, and J. W. Teter, IND.ENG.CHEM.,47, 719 (1955)] “Hydroforming” should n o t have been capitalized. The authors used the name “hydroforming” uncapitalized as a generic term referring to all hydroreforming processes.
