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COMMUNICATION TO THE EDITOR
COMMUNICATION TO THE EDITOR SURFACE ROUGHNESS AND CONTACT ANGLE Dependence of the wetting characteristics of a solid on the roughness of its surface is inherent in the fundamental theory of wetting action (R. N. Wenzel: Ind. Eng. Chem. 28, 988 (1936)). This is immediately apparent when analyses of wetting phenomena take into account the actual areas of the several interfaces involved as well as their respective specific energy values. The same method of analysis has led to quantitative evaluation of the effects of surface heterogeneity and surface porosity (A. B. D. Cassie and S. Baxter: Trans. Faraday SOC. 40, 546 (1944)). It is important to recognize, however, that the roughness that modifies wetting characteristics is a ratio of surface areas and cannot be determined by measurement of surface profiles. In the equation relating specific interfacial energies, surface roughness, and the equilibrium contact angle, r(S, - SSL)= SLcos 6
the roughness factor r is defined as the ratio of the area of the actual surface to that of a smooth surface having the same geometric shape and dimensions:
r=
actual surface geometric surface
That roughness so defined has no relation to the root mean square of deviations from mean elevation, derived from a profile of the surface, can be readily demonstrated. Thus a horizontal corrugated surface with rectilinear profile in one direction and, normal thereto, a sawtooth profile in which all slopes are a t 45" from the horizontal, would obviously have a roughness factor, as defined above, of 4 5 or 1.414. This would be true whatever the size of the corrugations. They might be reduced to microscopic or to submicroscopic; as long as their slopes remained a t 45", the area ratio would remain the same, i.e., the roughness factor would be precisely 1.414. The concentration of surface energy, and therefore the wetting characteristics of the surface, could also be expected to remain unchanged. Recently Dr. J. J. Bikerman presented the results of contact angle measurements made on stainless steel plates of six commercial standard finishes (J. J. Bikerman : Abstracts of Papers, 116th Meeting, American Chemical Society, Atlantic City, New Jersey, September, 1949, page 8G). He found that the contact angles could be almost identical for plates on which the average height of elevations (determined by a tracer instrument) differed by a factor of more than 100. This is not in contradiction of the accepted theory. His conclusion, however, that "contact angles depend on the type of surface roughness rather than on its degree" would seem to suggest that the relation is something indefinite and not the exact one given above. It emphasizes the need for a careful definition of terms in discussing surface roughness.
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If “degree” of surface roughness is to be accepted as referring to the average height of elevations, as revealed by a profile, then for Dr. Bikerman’s “type” of surface roughness, which is a vague term, one should use the surface roughness factor. This is a precisely defined quantity. A better name perhaps would be the “roughness area ratio.” No satisfactory general method of arriving a t a numerical value for the roughness area ratio of a rough surface from analysis of profiles, taken at right angles or in any other way, is readily apparent. Gas adsorption technics for measurement of total area would appear to be the only applicable tool. ROBERTN. WENZEL. Westinghouse Research Laboratories East Pittsburgh, Pennsylvania October 25, 1949
NEW BOOKS Surface Active Agents. By ANTHONY M . SCHWARTZ AND JAMES W. PERRY. 579 pp.; 5 tables. New York: Interscience Publishers, Inc., 1949. Price: $10.00. The authors of this book have attempted “to present a well-integrated picture of the present state of development of surface active agents”and in this they have been successful. Hundreds of different commercial surface-active agents are known today and are used in a diversity of applications. This is surprising when one considers that practically the entire development of these materials has occurred within the last three decades. The surfaceactive agents have been classified by the authors as follows: I. Anionic, 11. Cationic, 111. Non-ionic, IV. Ampholytic, V. Water-insoluble emulsifying agents, and VI. Substances that are surface active in non-aqueous solutions. The book is divided into three parts: Part I deals with “Processes for Synthesizing and Manufacturing Surface Active Agents.” Methods for laboratory synthesis and for commercial production are carefully disclosed. Part I1 deals with the “Physical Chemistry of Surface Active Agents in Theory and Practice.” Fundamental theories underlying the effects of these materials are given detailed treatment. Some of the physical properties of the solutions such as wetting and spreading, film formation, osmotic pressure, electrical properties, dispersion, deflocculation, and suspending action as well as foaming, emulsification, and detergency, have been given special consideration. P a r t I11 deals with “Practical Applications of Surface Active Agents.’’ This part is well done and makes interesting reading, inasmuch as i t clearly emphasizes the very wide scope of application of wetting agents. The principal topics treated under this heading are applications to: the textile industry; cosmetics and personal use; pharmaceutical, germicidal, fungicidal, and disinfectant uses; household, laundering, dry cleaning and general use; metal technology; paints, lacquers, inks, and pigments; leather technology; petroleum and lubrication; ore flotation; other industries utilizing a variety of surface-active agents; and miscellaneous uses. Of particular value are the 1553 literature references. There is no question that this book is the most complete one dealing with this new, important, and rapidly developing subject. It is well organized and the material is clearly presented. The book would constitute a valuable addition to any chemistry library. F. E. BARTELL.
