Internal pressure or cohesion.-The internal pressure of a liquid or a solid has been defined as the rate of transfer of momentum across a unit plane area inside the liquid or solid; and the average force of attraction across this unit area, which is numerically equal to the internal pressure, is the cohesional force, or the cohesion. While the work and total energy of adhesion and of surface cohesion, and the energy of cohesion, may all be obtained from experimental results by the use of simple and exact thermodynamic equations, this is not true of the internal pressure or cohesion. As a matter of fact, there is at present no known means of calculating the cohesion, but there are many methods, which do not agree among themselves, of calculating from inexact equations, values which for various liquids are supposed, when arranged in order of magnitude, to lie in the same order in general as the cohesions themselves. In fact, the cohesion is often defined as equal to a/v,2 the pressure correction term in van der Waals equation. However, since this equation is far from exact in its application to liquids, it is obvious that the cohesion calculated cannot represent at all accurately the internal pressure. Molecular attraction.-All of the phenomena thus far considered in this paper may be considered as due to the attraction between the molecules in a liquid or a solid. It is customary to consider the molecules as spheres or as points, with the attractive forces dependent upon the distance between the molecules alone, when they are all alike. It has been shown by Harkins, Brown, and Davis,3 by a measurement of the amounts of energy involved, and by Langmuir by a less direct method, that the forces around different parts of a molecule may be very different in magnitude. Thus in the case of organic compounds the forces are very much higher around any groups containing oxygen, nitrogen, triple, or double bonds, than they are around the hydrocarbon chains. The investigations of Harkins, Grafton and Ewing (these PROCEEDINGS, 5, 1919, 571) show that if organic substances are arranged according to the magnitude of their adhesional surface work toward mercury, they are not so arranged with respect to water. In this respect the adhesional forces seem to have something of the specific nature which indicates chemical action, and it is well known that the recent work on crystal structure demonstrates that such crystals as those of diamond and of graphite are held together by primary valence bonds. Langmuir considers all cohesional and adhesional forces as chemical, while van Laars has recently published the results of an extensive series of calculations which show that the square root of van der Waals' con 5 stant of attraction (a) is additive, and therefore comes to the conclusion that all such forces are physical. The calculations of Einstein, Kleemann, and of Harkins and Clark," have also given coefficients of atomic attraction which are moderately exact constants. Since all of these facts when considered together make it probable that cohesional forces are often less specific than those involved in ordinary chemical reactions, while in many cases they are the same valence forces, it seems to me preferable to use neither of the two words, physical or chemical, and to consider that cohesion is due to electrical and magnetic, or electromagnetic forces, which are probably largely electrical. In a paper "An Electromagnetic Hypothesis of the Kinetics of Heterogeneous Equilibrium, the Structure of Liquids, and Cohesion" I have already traced a connection between cohesion and the completeness of the outer or valence shell, of electrons in the atom or the molecule. The cohesion decreases as the completeness of the outer shell of electrons in the molecule increases. 9 3c on On the relation between cohesion and cohesional and adhesional work and energy. A number of attempts have been made to calculate the cohesion, which is the cohesional force per unit area of the cohesional pressure, from the cohesional surface work, and this attempt has been more or less justified by the fact that the values thus obtained, while not good in numerical agreement with those given by a/3, lie on the whole in the same relative order. Such calculations have been made by Mathews, and by Hildebrand, 10 but neither of them have shown to what extent the cohesion and the cohesional surface work are related. The term a/v2 may be said to represent, more or less imperfectly it is true, the total effect of the molecular attraction in decreasing the external pressure, which decrease is the cohesion. The cohesional surface work, on the other hand does not represent the total effect of the molecular attraction, even as it acts in a surface, since the molecules move into the surface not only by means of the energy which is contributed in the form of work, but also by means of the utilization of the kinetic energy of molecular motion, or the latent heat of the surface. Thus the formation of the surface of a pure liquid, with the exception of a few liquids in which liquid crystal formation is involved, is always accompanied by cooling. It is, therefore, the total cohesional surface energy and not the related work, which represents the total effect of the molecular attraction, or the cohesional effect. It may seem remarkable, from the point of view of the last paragraph, that the calculation of even the relative cohesion of liquids1o from a very simple equation, y/v1/3, where V is the molecular volume, should give results which lie in somewhat the correct order. This is undoubtedly because, as shown by Harkins, the contribution of the kinetic energy of a molecule to the total energy of the surface, is on the whole, independent of the nature of the molecule,—at least for such substances as have been used in the calculation of cohesion,-and is dependent on the temperature alone. Therefore, so long as the molecular volume is nearly the same, and the orientation of the molecules in the surface is not an important factor, at any definite temperature the latent heat of the surface is nearly independent of the nature of the substance, so that when substances are arranged in the order of their cohesional surface work or their free surface energy, they are also arranged in the general order of their total surface energy. A second method of calculating the cohesion from the cohesional work or free surface energy, is based on the well-known assumption of Stefan," that the average work involved in bringing a molecule to the surface of a liquid, has one-half of the energy value involved on the average in its complete vaporization. It is obvious from Stefan's paper, that his principle does not involve the work but the total surface energy, which is supposed to be one-half of the latent heat of vaporization. That this rule is far from true is indicated by the results of extensive calculations by Mr. L. E. Roberts and myself, which show that the fractional contribution of the surface energy toward the complete vaporization increases with the temperature, with a normal range of from one-third at lower temperatures to 0.8 or more as the critical temperature is approached, though the higher values are uncertain. Thus a molecule which at a high corresponding temperature passes from the body of the liquid into the surface, goes, in a fractional sense with reference to energy, much more nearly into the vapor state than when the corresponding temperature is low. Negative surface energy.—The phenomenon of negative surface energy was first discovered two years ago by Dr. E. C. H. Davies and me, but has not been announced previous to this time in print. Not only Donnan, but also Tolman and Wolfgang Ostwald, have assumed the existence of a negative surface tension or free surface energy. My own investigations have convinced me that the discovery of a negative free surface energy for a plane, uncharged surface is improbable, though it is quite likely that there is such a phenomenon in the case of highly curved phase boundaries. What we have to announce here is the discovery of a negative total surface energy for a plane, uncharged sur face. Thus, contrary to the rule found in the past, the surface or interface between octyl alcohol and water gives off energy when it is extended, but, nevertheless, the surface cannot be formed without the expenditure of work. The apparent contradiction is due to the fact that while the molecular motion aids in the formation of an ordinary surface, in the case of the interface under discussion the molecular motion hinders the extension of the surface. This is in accord with the theory presented in our earlier papers, and by Langmuir, that at such an interface there is an orientation of the molecules, since the molecular motion reduces the extent of the orientation. When the interface between octyl alcohol and water is pulled out adiabatically there is thus a heating of the surface, while an ordinary surface is cooled, so that the potential energy of the molecules is decreased by passing into the alcohol-water interface. The negative surface energy, is, it is true, very small, with a numerical value of two ergs. per sq. cm., while the free surface energy is 8.33, and the latent heat is 10.3 ergs. In contrast with this, it is found that the total surface energy of the hexane-water interface is not only positive but large, with a value of 66.5 ergs. These relations are of considerable interest, and their bearing on interfacial structure, which is of great importance in physiology, will be discussed in a later paper in the Journal of the American Chemical Society. 1 Dupré, Theorie Mécanique de la Chaleur, Paris, 1869, p. 69; Lord Rayleigh, London, Phil. Mag., (5) 30, 1890, (461). 2 Hardy, London, Proc. Roy. Soc., 86B, 1911, (634). (a). Harkins, Brown, and Davies, J. Amer. Chem. Soc., 39, 1917, (354–64). (b). Harkins, Davies, and Clark, ibid., 541-96. (c). Harkins and King, ibid., 41, 970–92, (1919), these PROCEEDINGS, 5, 1919, (152–9). 4 Langmuir, J. Amer. Chem. Soc., 39, 1917, (1848-1906), these PROCEEDINGS, 3, 1917, (251-7); abstract in Met. Chem. Eng., 15, 1916, (468). Fraenkel, Phil. Mag., 33, 1917, (297– 322). 5 Einstein, Leipsig, Ann. Physik., 4, 1901, (513). 9 Mathews, J. Physic. Chem., 17, (603–28). 10 Hildebrand, J. Amer. Chem. Soc., 41, 1919, (1067–80). 11 Leipsig, Ann. Physik, 29, 1886, (655). THE ADHESION BETWEEN MERCURY, WATER, AND BY WILLIAM D. HARKINS KENT CHEMICAL LABORATORY, UNIVERSITY OF CHICAGO Communicated by W. A. Noyes, October 14, 1919 The primary purpose of this investigation was to determine the effects of the molecular attraction at the surface of a metal, and to compare these effects with those of the surface of an oxygen compound such as water. Since the flotation process depends upon the preferential wetting and adhesion of gas films on metals, including the heavy sulphides, etc., on the one hand and silica and similar substances on the other, the general principles learned in connection with such a study, should be fundamental for the study of the process. I have been informed by Dr. E. C. Bingham that the adhesion between organic substances and metals is also fundamental with respect to the characteristics of lubricants. The equation of Dupré1 and that of Harkins, both of which are based on pure thermodynamics, give us the most accurate means for the study of the effects of molecular attraction at surfaces. The equation of Dupré gives the adhesional work done during the approach of 1 sq. cm. of one surface to meet the same area of the other. This is numerically equal to the work necessary to pull the two surfaces apart. The work of approach is also equal to the decrease of free surface energy (—Ay) during the process which is given by the equation where y1 and 2 give the free energy of the two unlike surfaces before their approach, and y1,2 is the free energy of the interface. The equation of Harkins gives the total energy of approach (EA) and this may be called the total adhesional energy, as follows: EA=-AEs=(Y1+ls)+(r2+l2)− (Y1, 2 + 1, 2) where I represents the latent heat of the surface or interface in ergs per square centimeter. The total adhesional energy is closely related to the molecular surface attraction, while the adhesional work is the tensile force necessary to pull the two surfaces apart, integrated through the distance which they move during separation, but given a negative sign. |