Langmuir 1988,4, 1305-1307
1305
Anomalous Adsorption at a Three-phase Contact Line Karol J . Mysels Departments of Chemistry and Medicine, B-017, University of California, Sun Diego, La Jolla, California 92093 Received March 31, 1988
Published line tension data for Newton black film of solutions of sodium dodecyl sulfate in varying concentrations of NaCl are used to obtain the adsorption of the film/solution contact line. The calculated adsorption seems clearly excessive, but no easy explanation for this anomaly can be proposed. Introduction
J. W. Gibbs observed in two footnotes' that just as there are excess surface quantities and a surface tension where two phases meet so there must be excess linear quantities and a line tension where three surfaces are in contact. He did not elaborate further beyond remarking that the line tension could be negative as well as positive, nor did he present any mathematical formulation. After a long hiatus, considerable progress has been made of late in this area, and Toshev, Platikanov, and Scheludko2 have recently reviewed the present theoretical and experimental status. They summarize the evidence, which shows that a line tension, 7,exists in a variety of systems and that, though small (much below a millidyne), it can be measured by several independent methods. Solutions of sodium dodecyl sulfate (SDS) containing NaC1, and the Newton black f b s formed from them, have been especially studied. The contact line where the film and the two surfaces of the solution (on both sides of the film) form a definite film contact angle exhibits a 7 which varies from positive to negative as the concentration of NaCl increases. Two independent methods gave basically concordant results as shown in Figure 1. One was based on measured variations of the contact angle as the diameter of the film became very small. The other determined the critical minimum size of a bubble that formed a Newton black film when rising by buoyancy to the ~ u r f a c e . ~In the former case positive r produced a two-dimensional Laplace pressure that increased the contact angle; in the latter case it inhibited the nucleation of the film. Three different experimental appro ache^^^ were used with the first method. I t seemed to me that one should be able to obtain additional information about the structure of the contact line from the variation of r with concentration by calculating an adsorption T per unit length. It turned out however that the values of T found are so large that they are not likely to correspond to reality. Several potential explanations will be considered, but none can be recommended. Adsorption Equation Gibb's equation relating r, the adsorption per unit area, to the change in u, the surface tension, and to a , the activity of the solute, expresses the fact that in an isothermal, (1) Gibbs, J. W. The Collected Works;Longmans, Green: New York, 1931; pp 288, 296. (2) Toshev, B. V.;Platikanov,D.; Sheludko, A. Langmuir 1988,4,489. (3) Platikanov, D.;Nedyalkov, M. In Microscopic Aspects of Adhesion and Lubrication; Georges, J. M., Ed.; Elsevier: Amsterdam, 1982; p 97. (4) Zorin, Z. M.; Platikanov, D.; Rangelova, N.; Scheludko, A. In Surface Forces and Interfacial Liquid Layers; Derjaguin, B. V., Ed.; Nauka: Moscow, 1983; p 200. Note: Tables I and I1 are transposed. (5) Platikanov, D.; Nedyalkov, M.; Nasteva, V. J . Colloid Interface Sci. 1983, 75, 620. (6) Nedyalkov, M.; Platikanov, D., Abh. Akad. Wiss. DDR.,Abt. Mat., Naturwiss., Tech. 1986, No. l N , 123.
reversible process the change in the work of extending the surface by unit area, da, must cancel the change in the work of removing r, the amount adsorbed on that area, from the solution, i.e., rRT d In a. Thus for a system of several components du = -RTCI';d In ai
(1)
The change in the work of extending a contact line by unit length is dr, and the amount adsorbed on that length is T,so the work of removing the latter from the soution is TRT d In a. Hence the corresponding equation for a system of several components is d r = -RTCTid In ai
(2)
More formal derivations of this relationship have been given, e.g., by Toshev and E r i ~ k s o nRowlinson ,~ and Widom,8 and Rowli~on.~Analogous expressions have been obtained by Lane'O for the slightly different tension at the boundary of two surface phases and by Guard and Fine'' for line dislocations within a single crystalline phase. NaCl/SDS System
The results of Figure 1 were all obtained on solutions containing 0.05% SDS, i.e., about 1.74 mM. The micellization of SDS in salt solutions has been studied by Matijevic and Pethica12 and by Mysels and My~e1s.I~The straight line relationship given by the latter corresponds to In cmc = 3.523 - 0.685 In CNe+
(3)
where all concentrations are measured in millimolarity. Accordingly, micelles are present when CNa+exceeds 76 mM, i.e., in all the solutions of interest which vary between about 300 and 400 mM. If we assume that the monomer concentration does not differ significantly from the cmc, then as the salt concentration increases that of monomeric DS- decreases according to eq 3. In 300 mM NaCl the SDS is about 60% micellized, in 400 mM about 68%. Thus we have two potentially line-active substances: NaCl and monomeric SDS, whose concentrations vary in opposite sense but not independently. We also have an ionic strength sufficiently high for activity coefficients to depart significantly from unity. On the other hand, the ~
(7) Toshev, B.V.;Erikson, J. C. Ann. Uniu. Sofia Fac. Chem. 1975/ 1976, 70(1),75. (8)Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Clarendon: Oxford, 1982; section 8.3. (9) Rowlinson, J. S. J . Chem. Soc., Faraday Trans 1 1973, 79, 77. (10) Lane, J. E. Trans. Faraday SOC.1968, 64, 221. (11) Guard, R.; Fine, M. E. Trans. Metall. SOC.AZME 1965,233,1383. (12) Matijevic, E.; Pethica, B. A. Trans. Faraday SOC.1958,54,587. (13) Mysels, E. K.;Mysels, K. J. J.Colloid Interface Sci. 1965,20,315.
0743-7463/88/2404-1305$01.50/0 0 1988 American Chemical Society
1306 Langmuir, Vol. 4, No. 6,1988
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times larger in absolute terms than that of NaC1. This result does not seem unreasonable, but a problem arises in the next step. At a somewhat higher concentration the slope of the line tension becomes quite significant and, as indicated by the straight line in the figure, has a value of about -125 X lo4. This corresponds to a value of 5 X mol/cm for the bracket of eq 8. Thus if the two adsorptions were equal, each would be 5 X 10-14/2.46 or about 2.03 X mol/cm. Minimum total adsorption would occur if the adsorption of SDS were nil; that of NaCl would then be 2.4 X mol/cm. In the converse case of zero NaCl adsorption the adsorption of SDS would be almost 13 X If either were negative the other would correspondingly increase.
400
The same result is obtained if eq 2 is used with individual ion constituents provided electroneutrality is taken into account. Thus the slope of the 7 vs In c curve cannot give us information about the individual adsorptions of NaCl or SDS or their ions but only about their weighted sum, with the NaCl weighted by a relative factor of about 5.35. Though incomplete, such information about linear adsorption may nevertheless be of interest. Figure 1 indicates that around 0.33 M NaCl the line tension passes through a maximum so that according to eq 8 the value of the bracket must be zero and the two adsorptions must be of opposite sign with that of SDS 5.35
Discussion Adsorption at the contact line is by definition due to the changes, in the immediate vicinity of that line, of surface concentrations on the intersecting surfaces which form the line. As a densely packed (20 A2/ion) monolayer has 8.3 X mol/cm2, mol/cm adsorbed on the line corresponds to the addition of a strip about 300 A wide of such a packed monolayer on each of the four surfaces involved in our case (two for the black film and two for the bulk liquid). Three hundred angstroms seems to be excessive for any explanation based on intermolecular forces, yet it is clear that the calculated adsorption would have to extend much further, for thousands of angstroms, away from the geometrical line. This is because the surfaces must normally contain considerable (I’)adsorbed SDS; a densely packed monolayer of DS- is not likely to form because of ionic repulsion; if formed, it is even less likely to terminate abruptly, and the calculated adsorption, even at its minimum exceeds 10-14. The change in an airlliquid interface when it meets another would be expected to be less radical than that in a bulk liquid when it meets air. Hence instead of a monolayer one would expect at most a packed “monostring”. In such a monostring molecules or ions should occupy at least 5 A each so that linear adsorption for four surfaces should be about mol/cm. Thus there is a 100-fold or more discrepancy between this expectation and the above calculation. The measurement of 7 was done by two independent methods and four experimental approaches. Three of these agree quite well on the value of the slope, which is the important parameter. The other indicates a lower slope, which would reduce the discrepancy by 1 order of magnitude but not eliminate it. Thus it is not likely that a simple error in the measurement of 7 is the culprit. As with all experiments involving SDS there is always the probability that, unless extreme precautions are taken, trace amounts of the very surface-active dodecyl alcohol are present.15 This would add another component whose activity would decrease with NaCl concentration by solubilization in the micelles whose concentration increases as the cmc decreases. However, most of the SDS is already micellized in the most dilute solutions considered, so the logarithmic change in micellar concentration is much less than that in monomer concentration. Thus most of any alcohol should be always solubilized (the solutions would all be beyond any minimum in surface tension), and any remaining concentration should change very slowly, thus having little effect on the calculation unless alcohol adsorption on the line is much larger than those calculated
(14) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Academic: New York, 1959.
(15) Mysels, K.J. Langmuir 1986,2, 423. Lunkenheimer, K.; Miller, R. Tenside Detergents 1979, 16, 312.
Figure 1. Published values of line tension of 0.05% sodium dodecyl sulfate in salt solutions measured by different methods: m, critical bubble size: 0, average diminishing buble: A,individual
diminishing bubble;6 0,topographic m e t h ~ d . ~
difference between molarity and molality is completely negligible. Over the pertinent range of concentrations, the mean ionic activity coefficient, y, of NaC1, tabulated in ref 14, varies little and obeys closely the relation In y = 0.057 - 0.0361 In CNaCl (4) We assume that the activity coefficients of the SDS monomers follow the same relation, which should be a close approximation at these concentration^.'^ The difference between the molarities of NaCl and of Na+ ions is negligible in the area of interest.
Adsorption Taking THlo= 0 and in the absence of any evidence of preferential adsorption of hydrogen or hydroxyl ions, we can write eq 2 for our system as d r = -RT(TN,cid 1n aNaC1 + TsDsd In %DS) (5) or in terms of concentrations and activity coefficients d7 = -RTITNacl(d In y&+ + d In yccl-) + TsDs(d In YCNa+ d In TcDS-)] (6) Taking eq 3 into account, collecting terms gives d7 = -RT[d In C(2TNac1+ 0.315TsDs) + d In y(2TNaC1 + 2TSDS)I (7) where C is the concentration of the Na+ and C1- ions assumed to be equal. Dividing both sides by d In C, noting that according to eq 4 d In y / d In C is constant at 0.0361, gives d7/d In C = -RT(2.072TNacl+ 0.387TsDs) (8)
Langmuir 1988, 4, 1307-1311 above. Thus dodecyl alcohol and similar solubilizable impurities are not likely to account for the discrepancy. The fact that, strictly speaking, the experiment does not deal with three phases so that four surfaces (two pairs of identical ones) are involved rather than three different ones is a conceptual simplification and has been explicitly considered by ref 2 and by De Feiter and Vrij16 in analyzing the line tension concept. If we consider the detail of the junction between film and bulk, as calculated for some cases in ref 16, the sharp angular contact is replaced by a smooth curve. This decreases the area and increases the separation of the two surfaces in the transition region. The decrease in area should lead to a negative I’of NaLS. The increased separation should produce a positive I’of water and a limited positive I’of salts as the Cl- co-ions would be repelled by the surface charges. As the adsorptions are all measured relative to that of water, negative adsorptions of NaCl and (16)De Feyter, J. A.; Vrij, A. Electroanal. Chem., Interfacial Electrochem. 1972, 37, 9.
1307
SDS, rather than positive ones, would be expected from this point of view. It is easy to imagine a change in interfacial area without a change in bulk volume and a measurement of the corresponding force (e.g., by pulling a film from the liquid). It is not obvious how to go about increasing the length of a contact line without changing the area of the surfaces which form it. Thus line tension has a less direct operational meaning than surface tension, but it has one nevertheless as the relation between the two can be varied. This should not influence the mathematical formulations. Thus, in the absence of obvious flaws in either theory or experiment, the discrepancy between the simple structural expectation and the equally simple interpretation of the experiments remain puzzling.
Acknowledgment. I am grateful to Prof. A. Sheludko for making ref 2 available to me prior to publication and to Profs. A. Scheludko, J. Th. G. Overbeek, and G. Kuczynski for their comments. Registry No. SDS, 151-21-3;NaC1, 7647-14-5.
Highly Ordered Monolayer Films of [22.3.3]Propellanesf John G. Skabardonis and Chaim N. Sukenik*J Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106 Received March 15, 1988. I n Final Form: July 1,1988 Despite the unusual geometry of [22.3.3]propellaneswith their two perpendicular molecular planes, we have succeeded in forming well-ordered, compressed monolayer films of these molecules at an air-water interface. We present a model for the packing of these films. This model is based on crystallographic data from related [m.3.3]propellane dione and diol molecules (m= 4,10,12) and on pressure-area isotherm studies of the [22.3.3]propellane dione, ketols, and diols. Propellane dione ([22.3.3] and [12.3.3]) monolayers over an aqueous subphase saturated with NaCl corroborate the suggested orientation of the propellanes within this packing arrangement. Two general features of the propellane structure have been the focus of much attention.2 Firstly, the bond lengths and angles of the two bridgehead carbons, the geometry of the fusion of three rings around a single central bond, and the four sp3 C-C bonds that are on one side of a plane are all of interest in terms of strain and molecular distortion considerations. Secondly, the propeller-like arrangement of these three rings presents the chemist with a molecular scaffolding with either a Y- or T-like configuration, depending on the sizes and conformations of the individual rings. We have used [m.3.3]propellanes as probes for ordered binding in solution aggregatess3s4 We have also studied the stereochemistry and conformation of these molecules. We have reported the single-crystal structures of both dione la5and s,s-diol4a,3 as well as structural information from both NMR and C4H9-CIMSstudies for an array of [m.3.3]propellane diones, ketols, and diols (m = n + 2; n = 1, 2, 8, 10, 20).5 ‘This paper is dedicated t o the memory of Professor David Ginsburg of the Chemistry Department, Technion-Israel Institute of Technology, Haifa, Israel.
Dione 1 11-20 l a n-10
Syn Ketol 2 11-20
Syn,Syn D i o l 4 n-20 4a n- 8
Syn,Anti Diol 5 11-20
Anci Ketol 3 11-20
Anti,Anti Diol 6 11-20
The oriented binding of these molecules to aqueous micelles and vesicles required that the polymethylene ring (1)NIH Research Career Development Awardee (1983-1988). (2) Ginsburg, D. Propellanes: Structure and Reactions; Verlag Chemie: Weinheim, Germany, 1975 (and ita 1981 and 1985 sequels, published by the Technion Chemistry Department). (3) Natrajan, A.; Ferrara, J. D.; Youngs, W. J.; Sukenik, C. N. J. Am. Chem. SOC.1987, 109, 7477. (4) Natrajan, A.;Sukenik, C. N. J. Org.Chem. 1988,53, 3559-3563. (5)Natrajan, A.; Ferrara, J. D.; Hays, J. D.; Colonell, J.; Youngs, W. J.; Sukenik, C. N., manuscript submitted for publication.
0743-7463/88/2404-1307$01.50/00 1988 American Chemical Society
