Langmuir 1989,5, 293-295 number of investigations but ignore the work of Cohan and Meyerlg and that of Woodland and MacklBon concave menisci, as well as that of Cross and Picknett.20 Similarly, the review by Fisher and I~raelachvili’~ ignores the work of Woodland and Mack, while that of Cohan and Meyer is said not to “bear close examination”. Only the work of Cross and Picknett is said to be “not open to serious criticism”. Unfortunately, Fisher and Israelachvili do not state their reason for objecting to the work of Cohan and Meyer. The second point to be considered is the possible role of contaminants. In this connection Fisher and Israelachvili13suggest that the main problem, in the tests of the Kelvin equation prior to their own,13133was that of “unavoidable accumulation of contaminants”. They thus cast doubt on the use of the Kelvin equation in “practical cases”. They further suggest that Skinner and Sambles12 had reached the same conclusion. It would appear, however, that Skinner and Sambles offered no interpretation of the Shereshevsky results. It should be noted that in their own experiments Fisher and I ~ r a e l a c h v i l i show l ~ ~ ~convincingly ~ that the Kelvin equation is applicable to menisci with radii of curvature in the range from 0.004 to 0.02 pm. Whatever difficulties due to contaminants may have been encountered in these experiments, it is difficult to conceive that such difficulties could account for the results obtained by Shereshevsky. In capillary tubes having radii in the range from 1 to 10 pm any change in the effective tube radius due to the presence of contaminants in the form of an adsorbed film would certainly be negligible. I t is also clear that, in the case of water at least, any conceivable changes in contact angle or vapor/liquid surface tension due to organic contaminants would produce a decrease in the apparent surface tension, rather than a 10-fold or greater increase. If, on the other hand, a water-soluble contaminant were to be responsible for an enhanced lowering of the vapor pressure, the extent of the contamination would have to vary systematically, as pointed out previously, with the electrolyte concentration of the reservoir solution. As has been suggested, this seems highly unlikely. I t is concluded, therefore, that Shereshevsky’s experiments cannot be explained by the formation of an “anomalous component” of a siliceous nature, such as seems to have been involved in studies of the polywater phen~menon.~~ An exception to this conclusion is the case of the initial experiments with soft glass’ mentioned above. In fact, Shereshevsky’s concern over this type of contamination may have contributed to the evident lack of attention to the problem of equilibration. Thus, as has been suggested in the present discussion, the most likely flaw in the Shereshevsky work is the failure to ensure that equilibrium conditions were actually achieved. A further point to be considered relates both to the question of the relevance of capillary rise experiments with water and to that of possible massive contamination by soluble material leached from the solid surfaces in contact with the capillary held liquid. This type of contamination would, of course, have a relatively minor effect in the case of capillary rise, since neither the density nor the surface tension would be markedly affected. Hence, the results of the water capillary rise experiments which have been cited18J9could conceivably lack the relevance which has been indicated. However, if this type of contamination (33) Fisher, L. R.; Israelachvili, J. N. Nature (London) 1979,277,548. (34)Everett, D.H.; Haynes, J. M.; McElroy, P. J. Sci. B o g . (Oxford)
1971,59, 279.
0743-7463189 124Q5-0293$01.50/0
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were actually to occur in these, qs well as in Shereshevsky’s experiments, it would also be expected to occur in those of Cross and PicknetLm These latter experiments clearly show that massive contamination by soluble material leached from solid surfaces did not occur in this case. The recently reported results for high surface area reservoir rock samples5p6also provide evidence that contamination of this type does not vitiate the applicability of the Kelvin equation. Finally, reference should be made to the adhesion force experiments reported by Fisher and Israela~hvili.~~ This work, an extension of the Kelvin equation s t ~ d i e s l ~ ~ ~ ~ previously referred to, showed that for water the macroscopic value of the surface tension was applicable to the relative pressure range above about 0.95. This range encompasses the relative pressure range involved in the Shereshevsky experiments. Fisher and I~raelachvili~~ also conclude that for relative pressures below 0.99 the wetting film thicknesses were always less than about 1 nm. No evidence for massive contamination by a water-soluble component was found in this work.
Conclusions The experimental work of Shereshevsky relating to the applicability of the Kelvin equation has been directly and unequivocally refuted by the experiments of other investigators. Reviews and comments in the literature concerning Shereshevsky’s work have usually overlooked or downplayed the key experiments refuting this work. Neither the presence of contaminants nor the existence of adsorbed wetting films provides an explanation for the experimental observations reported by Shereshevsky. The most probable flaw in all of Shereshevsky’s work is the failure to ensure the attainment of equilibrium conditions. There exists no reason to doubt the applicability of the Kelvin equation to vapor/liquid systems in capillaries and pores in which the mean radius of curvature of the interface is comparable to those involved in the experiments of Shereshevsky. Acknowledgment. Critical comments on a preliminary draft of this communication by Dr. N. R. Morrow and by the Editor of Langmuir, Professor A. W. Adamson, are gratefully acknowledged. (35)Fisher, L. R.; Israelachvili, J. N. Colloids Surf. 1981,3, 303.
J. C. Melrose Petroleum Engineering Department, Stanford University, Stanford, California 94305 Received June 24, 1988
An Evaluation of Neumann’s “Surface Equation of State”
We have been very interested in the continuing controversy surrounding Neumann’s concept of the “surface equation of state”.l” We present here two unambiguous tests of the theory and then some comments about his thermodynamic analysis. (1) SDelt, J. K.: Neumann, A. W. J. Colloid Interface Sci. 1988,122, 294. (2) Spelt, J. K.; Neumann, A. W. Langrnuir 1987,3, 588. (3)Van Oss, C. J.; Good,R. J.; Chaudhury, M. K. J . Colloid Interface
Sci. 1986,Ill, 378. (4)Spelt, J. K.;Absolom, D. R.; Neumann, A. W. Langrnuir 1986,2, 620.
(5) Neumann, A. W. Adu. Colloid Interface Sci. 1974,4 , 1.
0 1989 American Chemical Society
294 Langmuir, Vol. 5, No. 1, 1989
”
3
23
‘
22
27
Comments
ii
i5
Lc
2‘
L“
SURFACE TENSION OF ALKANES ( m N / m )
SURFACE TENSION OF ALKANES ( m N / m )
Figure 1. Equilibrium wettability of water and pentafluoropropanol by n-alkanes.
Figure 2. Wettability of stearic acid, poly(tetrafluoroethylene), and water by n-alkanes.
Table I. Substrate Surface Tensions: Experimental and Calculated by the Method of Neumann surface tensions, mN/m liquid measured calculated difference PPA 17.4 12.8 4.6 water 72.1 19.7 52.4
liquid has the same contact angle on two different substrates, the Zisman plots for the two surfaces should superimpose. Figure 2 shows Zisman plots of poly(tetrafluoroethy1ene) (PTFE),7water,6 and stearic acid.* We note that these curves cross but do not superimpose. The differences in slopes are well outside experimental error. The equation of state is not valid for either solid or liquid substrates. Since the equation of state was derived from supposedly general thermodynamics, it behooves us to make a few comments about Neumann’s derivation. Neumann’s system consists of two components and three phases, solid, liquid, and vapor, in equilibrium. The surface GibbsDuhem equations for this system are
The first test depends upon recognizing that the thermodynamic analysis of Neumann does not require the substrate to be solid. Every statement applies as well to liquid substrates. Liquid-liquid systems are extremely useful for testing wetting theories because all the surface and interfacial tensions are directly measureable. An exact analogy exists between liquid and solid systems when an equivalent contact angle, e,,: is defined in terms of the relevant surface and interfacial tensions Ysl
- Ysv
cos e,, = -
(1)
Ylv
where the subscripts s, 1, and v refer to the liquid substrate, the wetting liquid, and the vapor, respectively. Figure 1 shows Zisman plots of the cosine of the equivalent contact angle vs the surface tensions of wetting alkanes for two low-energy liquid surfaces, pentafluropropanol (PPA) and water. The data are taken from ref 6. These plots are typical of those for low-energy solid surfaces with similar critical surface tensions. Measured surface tensions and surface tensions calculated by the method of Neumann5 are shown in Table I. The differences between the two values of substrate surface tension are very large, well outside any possible experimental error. The surface tensions were calculated numerically with equation 110 of ref 5, using hexadecane as the wetting liquid. The results were not significantly different for other alkanes. ( 0 . 0 1 5 -~ ~~ .~O O ) ( Y ~ ~ Y+~ ~ylV )”~ (110) Yiv(o.o~~(YsvY~v)”2 - 1) The second test of Neumann’s ideas depends on the corollary, deduced from the equation of state, that if one cos 0 =
(6) Johnson, R. E.; Dettre, R. H. J.Colloid Interface Sci. 1966,21,610.
drsv = -ssvdT - 2 ( l ) F S V dP2
(774
drsl = -s,1dT - 2($Sl
dP2
(77b)
dYlv = -91vdT - 2(l)FlVdF2
(77c)
The equation numbers are those in Neumann’s re vie^.^ The subscripts s, 1, and v refer to solid, liquid, and vapor, respectively. Neumann considers both T and p2 to be independent variables. s is the surface entropy per unit area, and p2 is the chemical potential of the liquid. These equations are not consistent with the Gibbs phase rule, which tells us there is only one degree of freedom for this system; that is, each p2 is a function of temperature. A little thought should convince us that the only way to change p2 is by changing the temperature. If it were desired, a surface or interfacial tension (but only one) could be the independent variable. In that case temperature would be a function of the tension. Assuming there are two independent variables, Neumann derives eq 78 from the three surface Gibbs-Duhem equations listed above.
drSv= QdY,i + Rd7iv
(78)
where Q and R are functions of “surface entropies and excess concentrations”. This is equivalent to transforming (7) Fox, W. W.; Zisman, W. A. J. Colloid Sci. 1950, 5, 514. (8) Data obtained in our laboratory for stearic acid monolayers.
Book Reviews the independent variables from T and p2 to ysl and ylv. Since there is only one independent variable, eq 78 is equivalent to Ysv = Y S V ( Y 1 V ) which in turn is equivalent to Ysv = rsv(T) ysvis determined when T is fixed. This is consistent with both the Gibbs phase rule and our intuition. Neumann, however, makes the unjustified leap that eq 78 applies to all systems and that Q and R are the same for all liquidsolid combinations. A consequence of this is that any two liquids having the same surface tension must have the same contact angle on the same surface. There is no thermodynamic justification for this interpretation. What Neumann has called an “equation of state” is really a complicated statement of the Gibbs phase rule. It is worth pointing out that Neumann’s arguments about an equation of state are really only used to help justify his critical assumption. This assumption is given on page 157 of ref 5, “From our knowledge of liquid/liquid interfaces we know that zero is the lower limit for the interfacial tension between the two liquid phases at
Langmuir, Vol. 5, No. I , 1989 295 equilibrium. I t would therefore be very difficult to understand if arbitrarily small solid/liquid interfacial free energies were not possible. We therefore expect that the minimum value of the solid/liquid interfacial tension by equation 92 is equal to zero.” Equation 92 states that the interfacial tension becomes a minimum as the contact angle goes to zero. His critical assumption is that this minimum is zero. A simple test of this assumption comes from the system hexane on water. The equivalent contact angle is zero, yet the interfacial tension is about 51 mN/m. All of Neumann’s analysis depends upon this incorrect assumption of zero interfacial tension. Central Research Department.
* Chemicals and Pigments Department. Rulon
E. Johnson,
Jr.,*vt and Robert H. Dettre’
Central Research Department and Chemicals and Pigments Department] E . I. du Pont de Nemours & Co., D u Pont Experimental Station, Wilmington, Delaware 19898 Received June 24, 1988
Book Reviews Colloidal Systems and Interfaces. Sydney Rosa and Ian Douglas Morrison. Wiley: New York, 1988. 422 pages. ISBN 0-471-82848-3. $49.95.
This text is an outgrowth of the 4-day short course on emulsions and dispersions that has been taught by Professors S. Ross (Rensselaer Polytechnic Institute) and F. M. Fowkes since 1967, joined by Dr. I. D. Morrison (Xerox Corp.) in 1985. In the format of “an index of related topica”, it purports to “display the armory of concepts and techniques that are available to this discipline”. In many ways, the authors succeed in this effort. Compared with other introductory texts in surface and colloid science, this book offers some features that are different. It is written in a way that is sensitive to the industrial practitioner who is not fresh out of school. I t gives emphasis to descriptions of equipment and experimental techniques (with good qualitative explanations of the underlying principles) together with many tidbits of homespun advice for their application. We are advised on p 31, for example, to “look at the sample [of any dispersion] through a microscope before any particle-sizing technique is tried”, and on p 112 we learn the proper way to remove a grease spot from clothing using a solvent spot remover, viz., surround the spot with a ring of solvent so that the Marangoni effect will pull the spot inward, reducing it in size. On p 123 we learn not to rub a wet tent fabric, which leads to water dripping through, or to put scratches in a Teflon frying pan, which may lead to loss of its nonstick quality. The book is also replete with historical anecdotes, such as Dr. Mathew Hay’s test for jaundice, in which flowers of sulfur are dusted over the urine of the patient. “On normal urine sulfur floats, while the presence of bile salts [in that of a patient with jaundice] causes the sulfur to sink.” Another is the story of how the letter from a German servant girl (Agnes Pockels) put Lord Rayleigh onto the proper method for sweeping liquid surfaces in preparation for monolayer studies. The book details many of the “rules of thumb” that have come down through the years, and in some cases, the old names have been resurrected. We learn (p 150) that the inverse relationship between surfactant solubility and surface activity is “Lundelius’ Rule” and the fact that in a series of aliphatic surfactants the optimum chain length that can
be found [for detergency, etc.], in which the effects of solubility and relative adsorption are balanced, is the “Ferguson Effect”. The scientifically sound rules of thumb, historical anecdotes, and examples from everyday experience found on many pages of this book make it a delightful read and a treasure chest for teachers who seek to convey the fundamentals of surface and colloid science to their students. Other distinguishing and laudatory features of this book are its Definitions and Glossary of Terms (which needs, however, to be expanded to at least twice its present length) and its extensive listings of Manufacturers of Instruments and Manufacturers of Processing Equipment. Its Bibliography is also very good (although there are some notable omissions, e.g., Molliet, Collie, and Black Surface Activity; Van Nostrand Princeton, 1961) as is the listing of Lifetimes of Contributorsto Colloid and Interface Science and Kendall Awardees. The difficulty with the book is in ita general organization and layout. It is divided into four parts, (I) Particulates, (11)Interfaces, (111)Stability of Dispersions, and (IV) Dispersed Phase Systems, each split into three to seven chapters, labeled with letters. The chapters vary in length from 1 to 97 pages. The extent of coverage of each topic reflects the authors’ interests, as it should, so that emulsions and foams get greater treatment than they do in most texts at this level. Electrokinetic phenomena, on the other hand, get rather short shrift. Most of the important topics are at least touched upon, however, even if they are not easily located in the unconventional organization of the book. Regrettably, the book is plagued with small errors, typographical and otherwise. Many concepta are used before they are defined or introduced, e.g., Airy functions, Gibbs adsorption equation, work of adhesion, Marangoni effects, HLB, and { potential. Notation is often unconventional and inconsistent, e.g., both and {are used for {potential. Often terms in equations are not defined, and in one place, terms were defined that were not in the equation. Figures are sometimes labeled inconsistently with the text, and in other places, axis labels are missing altogether. Potential energies and free energies are sometimes used interchangeably. Parts of the text are repetitive of earlier portions; for example, the origin of the term “DLVO theory” is spelled out
