GENERAL DISCUSSIONDr. A. Vrij (van’t HofSLab., Utrecht) said : Prof. Scheludko, Sofia, kindly providedme with some experimental results of Exerowa and Kolarovl who measured thecritical thickness of microscopic circular films drawn from an aqueous solution ccn-taining 5 x 10-2M isovaleric acid and 0.1 M KC1 as a function of film diameter.They suggest that h, should be proportional to rt (because of the cylindrical symmetryof the system), but they find experimentally a linear relation betwecn (the mostprobable) values of hc and r*, with an extrapolated value h, = 155 A at r = 0.Our theory also predicts that h, should be proportional to r+ when h, is so sniallthat PO can be neglected with respect to n,. It can be verified, however, that in therange of h, as determined experimentally, a much better approximation is obtainedwhen lIw is neglected with respect to PO in eqn.(7.3), when eqn. (7.6) becomesh,=0.268(A2r2/P, fy)‘I7.To test this equation thelogarithm of the experimental h, of Exerowa and Kolarov is plotted against log Y (seefig.). The plot is linear and its slope is 0.27 which is close to 5 = 0.286. From thisThis predicts that h, should be proportional to r2”.-5‘J rline one obtains AN^-5 x 10-13 (PO = 482 dynes cm-2 : f = 6 ; y = 55.5 dynes/cm).From the drainage speed of the film Exerowa and Kolarov obtained A ~ 3 . 8 x 10-12which is about 25 times larger. For lower concentrations of isovaleric acid (3 x 10-3and 5 x 10-3 M) the authors found an A value close to that determined earlier forwater (4 to 7 x lO-13).2Dr.H. Sonntag (Inst.-Plzys. Cllem., Berlin) said: Recently we tried to obtaininformation 3 about the factors which determine the rupture of microscopic liquid1 Exerowa and Kolarov, Ann. I’Uniu. Sofin, Facultt de Chim., 1964-65, 59, to be published.2 Scheludko and Exerowa, Kolloid-Z., 1960, 168, 24.3 Sonntag and Netzel, Tenside, 1966, 3, 296.6GENERAL DISCUSSION 61films (4 0.1 mm) between emulsion droplets by experimental means and comparedour results with the calculations of Dr. Vrij. In aqueous films between oil dropletswe measured and calculated with Vrij’s equation the critical thickness of rupture. Asin foam films we obtained a deviation of about the factor 2. Water films, stabilizedwith NP 20, between octane droplets ( A = 7 x 10-14 erg) had a critical thickness of185 A, calculated 406 A.In confirmation of Vrij’s theory the critical thickness doesnot show any dependence on the viscosity of the liquid film.A noticeable influence of the interfacial tension follows from his equation. Emul-sion droplets offer the possibility of studying the influence of interfacial tension with-out the necessity of raising the surfactant concentration in the film itself. By dissolv-ing small quantities of a surfactant in the dispersed phase it is possible to attain anadditional structure in the adsorption layer of the emulsifying agent and consequentlyto vary the interfacial tension in the desired way. We obtained the result in contrastto his theory, that the rupture thickness in the range studied (16-4 dyn/cm) does notdepend markedly on the interfacial tension. A variation of the rupture thickness isto be expected if there is a change in the nature of the oil medium and the structureof the surfactant.The investigated materials will of course only differ slightly in themacroscopic van der Waals-Hamaker-constant, so that the rupture thicknesses donot differ in order of magnitude but change markedly for instance between octanedroplets 185 A and between decaline droplets 215 A.Prof. B. TeZak (Zagreb, Yugoslavia) said: With respect to thin films, I wouldemphasize the similarities and differences between the structures encountered incoagulating or flocculating systems on the one hand, and those of the thin films on theother.The similarities are seen by regarding the physics and chemistry of thin films as thephysics and chemistry of small spaces, which may be compared to the methorical layerof coagulating and flocculating systems.However, the differences are more marked owing to the presence of neighbouringphases.Usually, the films are methorical layers between two gaseous (or exception-ally liquid) phases forming the wall of more or less empty bubbles. In coagulating orflocculating systems, there is usually the solid (generally, the crystal phase), themethorical layer as a borderline region of such a distorted crystal phase, incorporatingsome distinctive groups of lattice or foreign constituents (complexoids or specificallyadsorbed species) all in a specific pattern (texture), and the specific concentration ofmicrocomponents (ions and molecules) conditioned by the concentration and com-position factors of the solution in bulk.Thus, the dispersed phase and the dispersing medium are parts of the systemswhich, only by a very careful analysis, can be compared with the gaseous or liquidphases of films.I would urge caution in comparing the situations in films with thosein systems where the colloid stability is being considered.Dr. J. A. Kitchener (Iniperial College, London) said: Black films considerablythinner than those obtained with two back-to-back fatty compounds have beenobserved by Mussellwhite and myself with solutions of protein. With bovine serumalbumen it was possible to record the thinning of microscopic films over a period of10 to 15 min during which they levelled out at about 33 A before breaking. It maybe that these fragile films are of the transient rather than metastable type; probablythe protein molecules unravel themselves to a considerable degree in the interface aselastic threads which bestow high visco-elasticity on the liquid lamella.Withy-globulin no such very thin films could be obtained-only tough films about 15062 GENERAL DISCUSSIONthick. This protein apparently does not unravel, so extensively, so the films may wellbe back-to-back native protein molecules.Prof. E. Matijevi6 (Potsdam, New York) said: We have recently observed thinfilm formation during precipitation of calcium oleate and calcium elaidate in aqueoussolutions.Fig. 1 gives an electron micrograph of calcium oleate particles whichappear to consist of a thin film stretched on a heavier frame. The diameter of therim is approximately 40-5Omp while the thickness of the film is -10mp. Suchparticles are obtained when the ratio of the precipitating components (calciumnitrate and potassium oleate) is approximately equimolar. The solutions containingthese particles show strong flow birefringence. The possibility that these oddlyshaped particles with stretched films are formed during the sample preparation forelectron microscopy cannot as yet be eliminated. However, there exists some evidencethat these particles are actually present in the same form in aqueous dispersions.Dr. K. J. MyseIs (R.J. Reynolds, Winston-Salem) said: As Overbeek stated inhis introduction the stability of soap films and colloidal dispersions should involve thesame forces and lead to the same type of potential energy against distance curves.Most of this curve is now accessible to measurement and interpretation and theremainder will be difficult to study.OF1FIG. 1.-Schematic plot of free energy AF against distance 6 showing the resultant of the doublelayer repulsion @.L) and van der Waals attraction (v.d.W) curves. The two double-layer-repulsioncurves are for different ionic strengths (I).Fig. 1 shows schematically the combination of a van der Waals attraction inde-pendent of ionic strength and a double-layer repulsion, which is effective at largedistances when the ionic strength is low and at shorter distances when the ionicstrength is higher.The minimum in the resultant curve is responsible for the rneta-stable existence of the " equilibrium " soap films. The distance at which the minimumoccurs is given by a measurement of the film thickness with only minor uncertainties dueto the optical effects in the sandwich structure of the film. The depth of the minimumequals the difference of surface free energy between the film and bulk surface which iFIG. 1 .-An electron micrograph of calcium oleate particles obtained by precipitation of Ca(NO&( 5 x 10-4 M) with K-oleate ( 5 x 10-4 M) in aqueous solutions at 25". The sphere is a polystyrenelatex particle with a diameter of 814 mp.[To face page 62GENERAL DISCUSSION 63also the difference of their surface tensions.This difference can be directly deter-mined from measurement of the contact angle between the film and solution.1 Theslowly descending part of the curve should be determinable by the light scatteringtechnique of Vrij.2The sharply rising part of the curve is the one which was of concern in our work.At sufficiently short distances the van der Waals forces will again predominate andcause the film to drop to zero thickness as shown by the dotted line in fig. 1. Theeffect of compressing the film is indicated in fig. 2 and corresponds to a tilting of thebase line, with a corresponding shift of the minima, which follows closely the double-layer-repulsion line at low ionic strengths and involves also the van der Waals forces1 1 D.L .FIG.2.-Schematic plot of free energy AF against distance 6 illustrating the effect of a hydrostaticpressure (pgh) on the position of the minimum at two ionic strengths.at high ones. In contrast to the contact-angle measurements which give the freeenergy, our measurements give the pressure and therefore only the slope of this curve.The combination of the two measurements should, however, permit unambiguousintegration to obtain, the course of the free-energy curve in this region. As shown infig. 1 the curves show a precipitous drop near zero thickness since the film has toliberate some 70 ergs cm-2 as it disappears along with its surface tension. Since thefilm is extremely unstable along this part of the curve there is little hope of being ableto study this region in detail.The maximum which must separate the two steep slopes and which accounts forthe stability of equilibrium films may, however, be approachable with the develop-ment of the bursting theory reported by Vrij and the possibility of subjecting the filmto very large pressures, i.e., coming closer to the maximum by our experimentalmethod.The free energy-distance curves are considerably more complicated when twominima are present corresponding to the " first " and " second " black film and oftenwith a significant maximum between them (see ref.(9) and (12)). The same methodsare, however, applicable in the experimental study of these curves.1 Mysels, Huisman and Razouk, J.Physic. Chern., 1966, 70, 1339.2 Vrij, f. Colloid Sci., 1964, 19, 164 GENERAL DISCUSSIONProf. J. T. G. Overbeek (Vdn’t HoSLab., Utrecht) said: Would it alter the X-raydiffraction pattern significantly if the 20 A thickness of water were spread out homo-geneously through the film? Could the X-ray diffraction methods be used for a muchthicker film of, say, 200A? What would be the accuracy of the estimate of thethickness ?Dr. J. M. Corkiil (Procter and Gamble Ltd., Newcastle upon Type) said: We haveonly observed the first two diffraction maxima from our film system and calculationsusing various electron density distributions show that the line profiles in these loworders of diffraction are relatively insensitive to the detailed film structure.As thefilm thickness increases the diffraction maxima move to lower angles. This method ofdetermining film thickness is thus limited by the collimation requirements of the inci-dent X-ray beam and the accuracy decreases with decreasing diffraction angle. Wehave therefore confined our measurements to films < 100 A in thickness, althoughwith a more refined apparatus thicker films could be studied.Dr. K. J. Mysels (R. J. Reynolds, Wimton-SaZem) said: The remarkable stabilityof the very thin films having a core of some 20A of water is not confined to theanionic-cationic surfactant system described by Clunie, Corkill and Goodman, butis also found in sodium and potassium alkyl sulphates. It is not clear at presentwhether the forces involved in the two systems are the same or not.However, in thelatter cases a high energy barrier due to hydration energies, though certainly important,is not likely to suffice to account for the stability of the thin films because they alsohave a great stability with respect to thicker films, i.e., lie in a deep minimum the depthof which is very sensitive to the nature of the counterions present.1 This seems tocorrespond in effect to some additional specific attractive forces between the surfaceswhereas hydration energy can yield only a repulsive effect.Dr. J. F. Goodman (Procter and Gamble Ltd., Newcastle-upon-Tyne) said: In replyto Mysels, for our very thin films there is the van der Waals attractive potential andalso a short-range attractive potential caused by the discrete positive and negativecharges in the formally neutral heteropolar head group planes. This additionalmosaic force is of the type encountered in crystals (e.g. micaz), and becomes ofcomparable magnitude to the van der Waals force in our system at core thicknesses-1OA.We believe the dominant repulsive potential in these thin films to beassociated with the free energy required for dehydration. Both the mosaic and thedehydration potentials will be sensitive to the number and type of counterionspresent at the monolayer surfaces. The forces important in the system described byMysels will also depend on the extent of counterion binding. Thus, in addition to theeffect of these ions on the dehydration potential, they may introduce an attractivepotential in very thin films due to charge fluctuations.Dr.F. M. Fswkes (Sprugue Electric Co., North Adams, Mass.) said : The stabilityof black films (and other bilayer structures) is now known to depend to a large extenton the anisotropy of dispersion forces between oriented long hydrocarbon chains inthe two monolayers. The enhanced interaction due to parallel orientation of theanisotropic polarizability results in about a 40 erg/cm2 lowering of free energy of thebilayer with respect to thicker films.Prof. J. kyklema (Agric. Univ., Wdgeningen) said: I would ask Mysels whether itis imaginable that (e.g., during the rapid compression of the films) no equilibrium1 Jones, Mysels and Scholten, Trans. Furuday Soc., 1966, 62, 1336.Huisman and Mysels,2 Bowden and Tabor, The Friction ond Litbvicntion of Solids, vol. 2, chap. 20 (Oxford Clarendonunpublished work.Press, 1964)GENERAL DISCUSSION 65between the aqueous core of the film and the bulk liquid is attained, so that as aconsequence Csalt in the film would be different from csalt in bulk? Has he observedslow changes of thickness with time due to diffusion or effusion of ions?Prof. J. Lyklema (Wageningen) and Dr. P. F. Mijnlieff (Amsterdam) said: Inconnection with the calculation of the contribution of micelles to the ionic strengthwe would ask if there will be micelles within the soap film if one is working withdetergent solutions above the c.m.c. Such micelles could serve as a reservoir ofdetergent if the film surface area increases (film elasticity).Do Mysels and Jonesagree that micelles within the film can only be expected at detergent concentrationsin the bulk (with which the film is in equilibrium) sufficiently high to make theaverage intermicellar distance in the bulk of the order of half the film thickness orless ?Prof. J. T. G. Overbeek (van’t HofLab., Utreclzt) said: In his calculations Myselsused a value of A = 6 x 10-13 ergs for the Hamaker constant. By how much couldthis value be changed, without seriously altering the agreement between theory andexperiments that he obtained in his measurements ?Dr. K. J. Mysels (R. J. Reynolds, Winston-Salem) (communicated): In reply toLyklema, as stated in our paper, we have observed a lack of equilibrium which relaxedover periods of several minutes and was encountered each time the pressure waschanged by an appreciable amount.On the other hand, the lack of hysteresis betweenascending and descending pressures indicates that no relaxation time of about an houris significant, and we do not think that a longer one would be likely unless it involvesthe liquid at the bottom of the cell.The relaxation which we observed was also monotonic, but our measurements werenot intended to provide kinetic information. If our hypothesis that the departurefrom equilibrium is due to the rapid stretching of the film at constant composition iscorrect, the mechanism of relaxation may be complicated since there may be convec-tion as well as surface diffusion of the surfactant ion, and bulk diffusion of the counterion and of salt co-ions if these are present.The contribution of bulk diffusion ofsurfactant should be negligible because of the rapid equilibration between bulk andsurface. Electroneutrality will introduce a coupling of these flows. As mentionedin the paper, stretching of the film should lead to a reduction in surface concentrationof the potential determining ions and to a thinning beyond the equilibrium value. Ibelieve that the effect of stretching upon the salt concentration will give a smaller butadditive contribution so that the monotonic relaxation which we found is to be expected.In reply to Lyklema, the probability of finding a micelle within a film iscertainly much less than that of finding it within the solution, and it is less offinding it near the surfaces of the film than in the middle.The basic considerationshould be that the electrochemical potential of micelles be equal throughout theequilibrium system. Hence, the electric potential at any point, and in particular thenon-zero potential of overlapping double layers in the middle, determines theirconcentration. Consequently, I do not think that an estimate should be based on anintercomparison of the intermicellar distance with the film thickness. Consider aseries of solutions all slightly above the c.m.c. such that the concentration of micellesis the same but the ionic strength varies widely. These can be obtained by properlyadjusting the concentrations of surfactant and salt.They will all have the sameintermicellar distance but will give films having very different equilibrium film thick-nesses. At the same time, the potential in the middle of the film can change greatlyand as long as the van der Waals forces are negligible it will be decreasing as the ionicstrength increases and film thicknesses decreases. In this case, the chances of66 GENERAL DISCUSSIONfinding a micelle in the film will be also increasing even though the film thickness isgetting smaller as compared to the intermicellar distance.Another way of looking at the problem might be to establish two c.m.c. planeswithin a film between which micelles might be found. The position of such planescould be determined by the potential at which the co-ion concentration corresponds tothe c.m.c.for the counter-ion concentration existing at the same point, both of thembeing determined by the prevailing potential.In reply to Overbeek, in our experiments at low ionic strength where the calculatedinfluence of van der Waals forces was negligible the result would of course not bechanged if the Hamaker constant were given any smaller value. It would also haveto be higher by about one order of magnitude before the effect would be significant.In the experiments at the higher ionic strength where the curvature was marked, afactor of two in the Hamaker constant shifts the calculated line by approximately 7 A.In view of the combined uncertainty in the experimental measurements and in theirinterpretation it is difficult to say what an acceptable agreement would be, but Ithink that Hamaker constants more than two times lower or four times higher wouldgive us reason to worry. I am sure that these uncertainties can be greatly reducedby further development of our technique and by a simultaneous determination of thesurface concentration of the surfactant.It may be that the difficulty of taking intoaccount the sandwich structure of the film in the calculation of the van der Waalsforces may then become the limiting factor.Dr. H. Sonntag (Inst.-Phys. Chem., Berlin) said: We have also measured thethickness of thin hydrocarbon-surfactant-films between mercury and between waterdroplets.1 We confirm Haydon’s results that the thickness is approximately twice thechain length of the stabilizing molecules.The thickness of a given surfactant filmdepends on the nature of the organic solvent. For instance, Span 80 films in octanehave a thickness of 39 A and in xylene of 28 A. Investigations of the breakdownvoltage showed that these differences in the thickness of one surfactant in various oilsexist, because the breakdown voltage of about 8.2 x 105 V/cm is independent of thesolvent. From interfacial tension measurements we calculated the area per moleculein the saturated Span 80 film in octane to be 40W2/mol. and in xylene 120A2/mol. Inthe latter case the stability of the black films is much smaller than in the first. In ouropinion, molecules of the organic solvents penetrate into the surfactant film.Haydon concluded theoretically that the chain length of the surfactant is sinlilarlyunimportant.This is contrary to the experimental facts. For instance, the stabilityof mercury droplets in xylene increases rapidly with the chain length of the appliedfatty acids.2 The drainage of the organic medium is inhomogeneous even in filmswith very small diameters and sometimes there is a residue of the solvent like a lense(“dimple”) surrounded by the black film. This may be an explanation for hisobservation that some of the films were irreproducible in thickness and time dependent.Dr. D. Rosen (Chelsea COX of Sci. and Technology) said: The physical model usedby Haydon might prove to be too simple. A study is being made with Sutton ofthe effects of applied d.c.bias on the capacitance of bimolecular lecithin membranes.The effects vary in a complicated way with salt concentration as well as with appliedd.c. voltage and might imply that double-layer capacitances play a role in the totalmeasured capacitance.Dr. D. A. Haydon (Cambridge) and Prof. J. T. G. Overbeek (Utreclzt) said: Apotential difference of, e.g., 100 mV across a membrane of 50 A thickness corresponds1 Sonntag, Mber. Akad. Wiss., Berlin, 1962, 4, 330.2 Sonntag, 2. physik. Chem., 1962,221, 365GENERAL DISCUSSION 67to a field strength of 200,000 V/cm and implies a great pressure on the film, which maywell explain the decrease in thickness found by Rosen on the application of anelectric field.Dr. D. A. Haydon and Dr. J. Taylor (Cambridge University) said: As pointed outin this discussion by Haydon and Overbeek, some variation in film capacitance withapplied voltage is to be expected owing to the compressive effect of the field. Themagnitude of this effect would depend on the gradient of the repulsion energy againstfilm thickness curve.This, in turn, would depend on the extent of adsorption andchain length homogeneity of the stabilizing molecules. We have varied the appliedvoltage in systems consisting of various types of film in various electrolyte concentra-tions and have not detected capacitance variations of more than a few per cent.Rosen mentioned increases of up to 15 % which, although still a relatively smalleffect, we should probably have detected had they been present.We query, therefore,whether there might be, in Rosen’s systems, a smaller adsorption or lesser homo-geneity in the chain length of the stabilizing molecule.The variation of the effect with salt concentration, which Rosen mentions, is out-side our experience and seems difficult to understand. We think it unlikely thatdouble layer capacitances are involved, chiefly because our analysis of the system asa three layer dielectric 1 shows that series capacitances and conductances of the orderof those possessed by double layers should be experimentally undetectable, as indeed,is suggested, at least to a first approximation, by our own results. It is difficult tosay anything further without having the details of Rosen’s experiments.Dr. D. H. Napper (I.C.I.Ltd., Slough) said: The theory proposed by Taylor andHaydon to account for the stability of thin hydrocarbon films rests upon equilibriumconsiderations. This presupposes that the rate of film thinning is slow comparedwith the rate of surfactant desorption. But the converse might also occur. A non-equilibrium situation would then prevail, similar to that for Brownian encounters ofparticles sterically stabilized by strongly adsorbed macromolecules. The simplestnon-equilibrium case to consider is the extreme one in which no desorption of thesurfactant molecules occurs. Once the film thickness has decreased to twice the exten-sion of the oleophilic chains, further thinning can only occur by interleaving-or,possibly, compressing-these chains.Overlap of the oleophilic chains, however, alters the chemical potential of thehydrocarbon solvent molecules in the overlap volume.The work required to changethe chemical potential of the solvent molecules provides a potential energy barrier tothinning. An estimate of the order of magnitude of this barrier can be obtained fromthe van’t Hoff osmotic pressure equation. Assuming an area per adsorbed moleculeA* of 60 A2 and a film thickness of 40 A, the concentration of surfactant in the film,for incipient overlap, is ca. 1 M.For a 4 A overlap, the free energy change (perhaps an underestimate in a goodsolvent for the oleophilic chains) in ca. 1 erg/cm2. This is comparable to the value of0.73 erg/cm2 in the equilibrium case. Thus stable hydrocarbon films should beobserved irrespective of whether the rate of thinning is faster or slower than the rateof desorption.I therefore ask Haydon whether it is known which particular thinningregime is operative.Dr. D. A. Haydon and Dr. J. Taylor (Cambridge University) said: The experimentalevidence for assuming equilibrium between the thin film and the bulk solution at itsedges is as follows. First, the black film is usually formed from the thick hydrocarbon1 J. Theor. Biol., 1965, 9, 27868 GENERAL DISCUSSIONsolution in periods of 1-2min. Thereafter the thickness (or capacitance per unitarea) remains constant for periods of up to one week. Secondly, if the black film isextended to several times its former area, over a period of a few minutes, the tension inthe film remains constant, showing that stabilizer molecules migrate rapidly into thefilm from the adjacent bulk interfaces. We would suggest that the non-equilibriumsituation envisaged by Napper is far more likely to be encountered for the interactionof solid surfaces, than for the present mobile liquid surfaces.Prof. J. T. G. Overbeek (van’t HoflLab., Utrecht) said: According to fig. 5 ofHaydon’s paper, the thickness of the hydrocarbon layer of the thin films is close totwice the chain length of the stabilizer. On the other hand the remark near the end ofthe paper that A* 5 60 seems to imply that the stabilizer molecules are not closelypacked. How does he visualize the structure of the film a more-or-less crystallinearrangement, with the stabilizer chains always perpendicular to the film, the remainingspace being filled by solvent molecules, or rather as a liquid mixture of stabilizerchains only occasionally completely stretched and perpendicular to the film ?Dr. D. A. Haydon and Dr. J. Taylor (Cambridge University) said: Adsorptiondata generally for normal alkyl chain polar molecules at aliphatic hydrocarbonlwaterinterfaces strongly suggests that the adsorbed molecules are oriented approximatelyperpendicularly to the interface. The adsorption data so far obtained for the filmstabilizing molecules used in our work again suggests a perpendicular orientation. Ifthis is so, then it seems probable from packing requirements that the normal chainsolvent molecules must also be oriented predominantly perpendicularly to the surface.Notwithstanding this highly ordered structure, the films are mechanically liquid