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ment because of the uncertainties involved jn our selection of the density and dielectric constant values. The density of the "SF" iron particles is 7.81 g./ cc. If the dielectric constant is taken as infinity, 24 I equation 1 becomes A e = 0.3%' X Figure 4 s? shows this line, together with the ohserved points. X 16 Our measurements on iron are probably less accurate than those on the other aerosols because of the 4 refractometer background drift caused by settling of iron particles in the first cavity. It was assumed 8 that this drift was linear with time, but this may not be exactly true. The best line which can be 0 drawn through the experimental points will have 0 5 10 16 20 25 an intercept of +0.6 X IOw8 for Ae, which can pg./cc. reasonably be attributed to instrumental error, and Fig. 3.-Dielrctric constant increment for oil smoke aerosols a slope of 0.28. This, qualitatively, is the effect we as a function of mass concentration. have seen should be observed for an aerosol made up of conducting particles, but it is doubtful here whether it is beyond the limits of experimental error. Conclusions Equation 1, developed by different authors on the basis of various highly restrictive models, has been shown to have surprisingly wide applicability in predicting the dielectric constant of aerosols. It is to be expected that this relationship might break down at high aerosol concentrations, because of interaction between the charge distribution in closely adjacent particles. Although we have tried to produce very dense aerosols, and have measured con0 centrations 65 times as high as those studied by 0 10 20 30 40 50 Doraiii,lawe have seen no evidence of such a deviarg./cc. tion. While it is recognized that suspensions of Fig. 4.-Dielect,ric constant increment for iron powder materials with high electrical conductivity or peraerosols as a function of mass concentration. meability will have a magnetic as well as an electric equation 1 becomes A E = 1.54C X A € be- interaction with electromagnetic radiation, no such comes rather insensitive t,o variations in el if z1 is effect was observed with oil smoke and only a small large. Thus, a value of 50 for the dielectric con- effect, possibly not beyond experimental error, for stant of oil smoke would reduce the slope of the iron powder. Our measurements have been made on substances line by only about 6% from that calculated for an infinite dielectric constant. The predicted line and with densities ranging from 1.032 to 7.81 g./cc., with the observed points are compared in Fig. 3. It can dielectric constants from 2.21 t o infinity, with and be seen that the agreement is good in spite of the without high permeability, on aerosols in concenfact that no allowance has been made for magnetic trations from 2 to 50 micrograms per cc.,. having interaction caused by the conductivity of the parti- particles of widely different sizes and distributions cles. Minor effects might not appear in our experi- of sizes and of widely varying degrees of clustering. 32
20.
NOTES that in general the surface tension of liquids decreases with increasing gas pressures. Theoretical treatments of the effect are more numerous, with BY EMIL J. SLOWINSKI, JR.,ERNEST E. GATESA N D CHARLES Gibbs,2 Guggenheims and Rice' among those who E. WARINO have made important contributions. The effect Chsmislrs Department, (Iniveraitg of Connecticut, Storm, Connecticut is attributed to adsorption of the pressurizing gas
THE EFFECT OF PRESSURE ON THE SURFACE TENSIONS OF LIQUIDS
Received August 10, 1068
The only reported experimental measurements of the effect of pressurizing gases on the surface tensions of liquids are those of Kundt.' He found
( 1 ) A. Kundt, Ann. phveik. Chem., 12, 638 (1881). (2) J. W. Gibbs, "Collected Works," Vol. I, Yale Univeraity Preus, New Haven, Conn., 1948, pp. 219-269. (3) E. A. Guggenheim, J . Chem. Soc., 128 (1940). ( 4 ) 0. K.Rioe, J . Chem. Phyr., 16, 333 (1847).
NOTES
June, 1057 on the liquid surface, but it seems no clear dependence of surface tension on actual concentration of adsorbed molecules can be derived theoretically. The difficulty is related to the necessity of quite arbitrarily defining the position of the liquid surface, usually as was done by Gibbs, before any relation between surface tension and concentration of adsorbed molecules can be stated. It thus appears that experimental measurements of dependence of surface tension on pressure would be useful, both to establish more quantitatively than could Kundt the nature of the effect and to furnish data which might aid in further developing the theoretical interpretation. In a series of experiments we have measured the surface tensions of water and normal hexane under pressures of helium, hydrogen, nitrogen, methane, ethane and carbon dioxide. The capillary-rise technique was used and the procedures suggested by Richards5 and Harkins6 were followed. Experiments were carried out in a steel bomb provided with methyl methacrylate windows and having an inner diameter of about 2.5 inches and a usable length of about 6 inches. The U-tube surface-tension cell due to Richards was modified to satisfy space restrictions. The cell was of Pyrex glass, with the large tube about 38 mm. in diameter and the capillary tube made re-entrant above the level of the large meniscus and concentric with the large tube. The inner capillary diameter was about 0.4 mm. and was calibrated in accordance with Harkins’ methods. Capillary rise was measured during both increasing and decreasing gas pressure portions of a run. Calculated values of surface tension for a given system were found in general to lie on the same curve; this would imply that equilibrium conditions existed within the cell and that temperature held substantially constant during the time required for a run, Capillary rise was measured to 0.03 mm. with a cathetometer, and pressures, m measured on a Heise gage, were taken to 100 atm. where possible. All measurements were made a t room temperature, about 25”. An important feature of the surface-tension cell, necessary if one is to be able to ascertain the establishment of equilibrium, is a small capillary, made by drawing out ordinary capillary tubing, ntt,ached to the cell capillary with rubber tubing. This introduces a delay in the time for pressure equilibrium to be attained in the cell and allows one to raise or lower the small meniscus momentarily by simply increasing or decreasing gas pressure in the bomb. Since the data do not warrant the u w of e uations of higher precision, calculations of sur ace tensions were made on the basis of the simple relation
809
the density of the gas, all in c.g.s. units, Liquid density was taken to be that of the pure liquid cor. rected by a compressibility factor of 50 X atm. for water and 100 X 10-8/atm. for hexane. Gas density was calculated from the van der Waals equation. Experimental results are given in graphical form in Figs. 1 and 2, where relative surface tension, y / y o , is plotted against gas pressure in atmos-
40 60 80 100 Pressure in atm. Fig, 1.-The effect of gasee on the surface tension of water: 0,increasing pressure; e, decreasing pressure.
0
20
9
Y
=
‘/2Vh(PI
-
P d
where y is the surface tension, r is the capillary diameter, g is the acceleration of gravity, h is the capillary rise, PI is density of the liquid, and pg is ( 5 ) T. W. Richards, J . Am. Chem. Sac.. 48, 827 (1921). (6) W. D.Harkineand .4. Weissburger, ”Physical Methods of Organic
Chemistry,”, Chaptor IX, Interscience Publiahers, Inc., New York,
N. Y., 1949.
20
40 60 80 100 Pressure in atm. Fig. 2.-The effect of gases on the surface tension of nhexane: o, increasing pressure; e, decreasing pressure.
0
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pheres. It is seen that except for helium, which except for one isolated case. Wey13 has suggested shows no effect, surface tensions of the two liquids that in liquid water the surface molecules all havo decrease approximately linearly with increasing their oxygens exposed and hydrogens all pointing gas pressure. At a given pressure the magnitude inwards. of the effect increases with increase in critical temWe wish to propose that the surface entropy of a perature or boiling point of the pressurizing gas. liquid may be taken as a criterion of surface orientaThe relative effect of gas pressure on surface ten- tion. Orientation in the surface will lead to a lower sion is larger for hexane than for water, but if one entropy than that in the condition where the surcalculates the actual change in surface tension it is face moleciiles are disordered. The question is, found that for most of the gases a given pressure first, how much lower is the surface entropy of decreases the surface tension about the same num- polar substances than that of non-polar substances? ber of dynes/cm. for hexane as for water. That is, And second, can we set up a simple model which d.r/dP seems to depend mainly on the nature of the will account for the lower entropy of polar liquids, pressurizing gas and only in a minor way on the as resulting from surface orientation? liquid. Ramsay and Shields4reached the conclusion emA simple theoretical expression for the depend- pirically that there was a “normal” value (2.1) ence of surface tension on pressure7is for the Eotvos constant, which is directly related to the molar surface entropyP-’ From various theoretical st~dies,~-9particularly that of Born and Courant, it might be expected that there should be where P is the pressure of the gas (assumed to be a “normal” value for nearly spherical non-polar ideal) and is taken to be the concentration of molecules. (The extension of this concept to nonadsorbed gas in moles per unit of surface area. spherical molecules cannot be made very simply, beSince d-y/dP is found experimentally to be essen- cause the number of molecules “in the surface” per tially constant a t low pressures, this means that unit area depends on the degree of orientation as r,(l) = KP , and hence concentration of adsorbed well as the ratio of length to thi~kness.~)The hygas as defined follows what might be considered to pothesis of Ramsay and Shields, that the degree of be either a sort of Henry’s law for the surface association could be calculated from the ratio of the phase or the limiting form of the Langmuir adsorp- observed Eotvos constant t o the “normal” value, tion equation (usually applied to solid surfaces). 2.1, has of course long since been discredited;’ If under these conditions we integrate (1) we ob- but it persists in textbooks and the literature, probtain as a relation consistent with our experimental ably because of the lack of a plausible alternative. results We will show that surface orientation furnishes a y - yo = -KPRT - rPRT (2) much more reasonable explanation. The molar surface entropy has been calculated Equation 2 essentially states that a concentration of one molecule per sq. cm. for any adsorbed for 214 organic liquids and 26 inorganic liquids of molecules will lower the surface tension of any molecular structure such that they could be conliquid by an amount equal to kT dynes/cm., where sidered approximately spherical. The formulae k is the Boltzmann constant. Since K in (2) appears in our work to have nearly the same value for a given gas over water and was used, where u is specific surface entropy, A is over hexane, it would seem that more precise molar surface area, V is molar volume, N the Avomeasurements on the effect of an inert gas such as gadro number, y the surface tension and T the abargon on the surface tensions of a group of liquids solute temperature, and f a factorg which depends would be of interest. If K in such experiments on the “packing” or “structure” of the liquid. were constant for all liquids an extension of this For hexagonal close-packed liquids, f = 1.09; sort of measurement might possibly be made to in- for body-centered cubic packing, f = 1.12. We clude the determination of the areas of solid sur- will employ a compromise between these two values faces. for convenieqce (though recognizing that this introduces an element of uncertainty of about 2 to (7) For a clear derivation of this relation and a discussion of the meaning of rdl)nee N. K. Adam, “The Physics and Chemistry of Sur3%), f = 1.10. d r / d T was calculated from data faces,” Oxford Press, 1941, pp. 107-117. given in the recent compilation of Quayle.’O Other data were taken from Harkins7 and from the International Critical Tables. Density data were taken SURFACE ENTROPY AND SURFACE from the authors who measured the surface tenORIENTATION OF POLAR LIQUIDS1 sions, from the International Critical Tables, from BY ROBERT J. GOOD’ (3) W. A. Weyl, J . Call. Sci., 6, 389 (1951). Contribulion from the Applied Science Research Laboratory, Uniuersiti/ o f Cincinnalz, Ctncznnalz. Ohio Received September 14, 1966
No generalizations have been made as to the surface orientat,ion of low molecular weight liquids, (1) Based on portion of WADC Technical Report 66-188, May’ 1956. (2) Convair Scientific Research Lahorntory. San Dirgn, California.
.-._...
I
-
.
_i
(4) (a) W. Rarnsay and J. Shields, P h i l . Trans., A M I , 647 (1893); (h) J . Chem. Soc.. 1089 (1893). (5) M. Born and R . Courant, P h y s . Z., 14, 7.11 (1913). ( 0 ) J. Frenkel, “Kinetic Theory of Liquids,” Oxford University Press, London, 1946. (7) W. D . Harkins, “Physical Chemistry of Surface Films,” Reinhold Puhl. Corp., New York. N. Y., 1952. ( 8 ) N. K. Adam, “Phynics and Chemistry of Surfltres,” Oxford University Press, London, 3rd Edition, 1941. (9) A. 8. Skapski, J . Chem. Phys., le, 386 (1948). (10) 0. R. Quayle, Chem. Rev., SS, 439 (1953).
