Structure of Black Foam FilmsBY J. S. CLUNIE, J. M. CORKILL AND J. F. GOODMANProcter and Gamble Ltd., Basic Research Dept., Newcastle-upon-Tyne, 12Received 14th June, 1966Radiotracer measurements have shown that black foam films possess a sandwich structure,consisting of two monolayers of surface-active agent enclosing an aqueous core. The reflectioncoefficient and the angle at which reflected light becomes fully plane-polarized have been used togetherwith the infra-red transmission at an absorption maximum for liquid water to calculate the totalthickness of the film and the thickness of the surface monolayers. Total film thicknesses obtainedusing this three-layer optical model are in good agreement with those obtained by low-angle X-rayscattering. The aqueous core of a thin black film has a limiting thickness of -20 A.Radiotracermethods have shown that the surface monolayers adsorb inorganic ions, and conductance measure-ments have indicated that these ions are mobile. It is suggested that the relative stability of thesefilms is determined by the free energy required to dehydrate the hydrophilic head groups of the surface-active ions and the inorganic electrolyte in the film.The theory of lyophobic colloid stability of Derjaguin, Landau, Verwey andQverbeek (DLVO) has been employed with success to explain the dependence ofthe equilibrium thickness of thin films (102-103 A) upon the hydrostatic pressureson the films and the ionic strengths of the solutions from which the Alms were drawn.1-3However, the DLVO theory requires some modification in order to explain the stabilityof thin films (- 50 A), for which the double-layer repulsion is inadequate to preventfilm collapse under the influence of van der Waals compressional forces.4 Suchthin films have been obtained from solutions of ionic surface-active agents containinghigh concentrations of added electrolyte and also from salt-free non-ionic surface-active systems.5 They may also be produced by evaporation, 6 but can sometimesco-exist in equilibrium with much thicker films.7 Before the range of the forcesstabilizing these films can be deduced, it is necessary to establish the detailed struc-ture of these thin films, in particular, the separation between the planes of the headgroups and the physical state of the film core.Radiotracer studies upon the thin films (-50A) drawn from solutions of de-cyltrimethylammonium decyl sulphate (C toC l o ) have established the identity ofthe monolayer composition at the film surface and at a single air/water interface.*Employing the generally-accepted sandwich model for these films, the thicknessof the aqueous core has been estimated from infra-red absorption data.The totalfilm thicknesses were calculated from the normal reflection coefficients using anoptically homogeneous model but these were found to exceed the thickness derivedfrom the infra-red data and the extended lengths of the surface-active ions.8 Thisanomaly was subsequently removed by employing a three-layer optical model andusing optical polarization data to compute the thickness and refractive index of thesurface m0nolayers.9~ 10 Although the determination of film reflection coefficientsand polarizations is relatively simple, such measurements do not give the total filmthickness unambiguously.In the present work, film thicknesses have been determined from low-angle(20 c 5") X-ray scattering.The inorganic electrolytic content of the aqueous core3J . S . CLUNIE, J . M. CORKILL AND J . F. GOODMAN 35has been determined by radiotracer methods and the mobilities of these ions in-vestigated from the conductivities of the films.EXPERIMENTALMATERIALSDecyltrimethylammonium decyl sulphate was prepared and purified by the methodspreviously described.* The sodium bromide used was A.R.grade and the water was purifiedby a final distillation in a silica apparatus. Radio-active sulphate was obtained as Na~S3504from the Radiochemical Centre, Amershani. Tagged magnesium sulphate solutions wereobtained by dilution of the sodium sulphate with A.R. magnesium sulphate to an activity levelof -5 mC/mmole of sulphate ion.X-RAY SCATTERINGThe scattering from thin films at glancing angles was observed at room temperature usingan apparatus similar to that described by Dasher and Mabis.11 A horizontal scanningHilger and Watts Y125 diffractometer was used in its 28 : 8 tracking mode with a PhilipsPWlOlO generator. The slit system of the digractometer was carefully aligned to be exactlycollinear with the vertical rotation axis of the goniometer.Since precise instrumentalalignment is highly critical for measurements in the low-angle region (28t5') this waschecked using a 13 layer barium behenate multilayer specimen which had been deposited on aglass-microscope slide by the Langmuir-Blodgett technique.12\\ 3fiFIG. 1 .-Plan of apparatus for siinultaneous optical reflection and X-ray scattering measurements.I , beam stop for transmitted light ; 2, velvet jacket ; 3, film ; 4, Mylar windows ; 5, film holder ;6 , off-set glass window ; 7, light beam ; 8, X-ray beam.To record the X-ray scattering from black foam films the standard specimen mount wasreplaced by a specially designed Perspex cell within which a single foam film could be held ina saturated vapour atmosphere (fig.I). The Perspex cell was fitted with sealed Mylar windowsfor the incident and diffracted X-ray beams and with an off-set glass window positioned atright angles to the X-ray beam so that the film reflection coefficient could be simultaneouslydetermined. Vertical foam films were formed on a rectangular steel frame which was rigidlysuspended from the lid of the cell. The Perspex cell was fitted with vertical and horizontalscrew adjustments which, together with the angular 0 control on the diffractometer, allowe36 BLACK FOAM FILMSthe flat vertical film to be positioned exactly parallel to and bisecting the incident X-ray beamat 28 = 0 and 180".For the optical measurements a black Perspex beam trap for the transmitted light wassituated behind the film and the cell was made light-tight by means of a black velvet jacket.The whole assembly was draped with a black velvet cloth during optical measurements on thedraining film.When a thin black film had been obtained well-developed diffraction tracescould be recorded, the 0 setting being optimised for maximum intensity of the first-orderdiffraction peak. Continuous X-ray scans at a speed of 0.25" (28)lmin were taken in therange 1-5" (28) and in the reverse direction, after which the optical reflection intensity wasredetermined to verify that the film thickness remained unchanged. Reproducible opticaland X-ray diffraction results were obtained from films drawn from solutions of decyltri-methylammonium decyl sulphate (5 x 10-4 M) containing NaBr (0-1-0.5 M).REFLECTION COEFFICIENTSThe light from a tungsten-iodine lamp was passed through a collimator and interferencefilter (1 = 5,190&50r%) and after limitation by stops fell normally onto the film.Thereflected beam, again limited by stops, fell on to the cathode of a 9-stage photomultiplier(RCA IP 21), the output from which was measured on a voltage bridge. The design andcalibration of this apparatus is similar to that previously described.%RADIOTRACER DETERMINATIONSThe sulphate ion content of the thin films was determined by measuring the activity of adefined film area using a thin windowed G.-M. tube.8 The counter was mounted through theback of a brass box with the window shielded by an aluminium sheet containing a narrow,- 4SFIG.2.-Radiotracer apparatus for studying thin films. 1, Perspcx window ; 2, incident and reflectedlight beams ; 3, off-set glass window ; 4, glass frame for films ; 5, glass tank containing solution ;6, metal shield ; 7, Geiger counter ; 8, guide for glass frame.horizontal slit (fig. 2). After the apparatus had been sealed for several hours at 25°C thefilm was drawn froin the solution on a glass frame which was located so that the film lay 2 m iin front of the slit. The front of the film box contained a small aperture, sealed with a cover-slip, to allow the passage or a light beain fa- reflection measurements. The apparatus waJ . S . CLUNIE, J . M. CORKILL A N D J . F . GOODMAN 37calibrated by evaporating droplets delivered from a micrometer syringe on a glass platewhich was then mounted in the position normally occupied by the film.FILM CONDUCTANCEFilm conductivities were measured parallel to the film surfaces using a Wayne-Kerrscreened a.c.bridge and a sealed conductivity cell fitted with an offset window for the opticalmeasurements. The cell, shown schematically in fig. 3, was placed in an air thermostat at11 fFIG. 3.-Apparatus for simultaneous optical and conductivity measurements. 1, glass tube to varypressure ; 2, conductivity leads ; 3, electrode guide ; 4, Perspex electrode holder ; 5, Teflon spacer ;6, incident and reflected light beams ; 7, liquid seal ; 8, platinum electrodes.25 fO.1"C. The contents of the cell were allowed to reach equilibrium conditions of tempera-ture and relative humidity before raising out of solution a pair of bright platinum electrodesin a " box kite " configuration with sharply rounded corners.A vertically draining openprismatic film was thus formed between the electrodes which were mamted in PerspexbIocks separated by Teflon spacers. A slight light excess pressure was applied to the interior ofthe film to keep the main film surfaces normal to the optical system and the reflection coeffi-cient measurements were made from one side of the film.RESULTSX-RAY MEASUREMENTSSince the diffractometer represents a one-dimensional detector, the diffractiontraces may be interpreted on the basis of the theory of coherent X-ray scatteringfrom a one-dimensional structure. The limiting black film has a sandwich structurein which the surface layers have a different electron density from the solvent core.Thus the cross-section of the film at rest may, in the absence of detailed atomic co-ordinates, be represented by a simple step function (fig.4). In this model thethickness of the surface layers is considered constant whereas that of the film coreis variable. The electron density p(z) with 0 <I z [ <l for a small element of volum38 BLACK FOAM FILMSdv, is related to the diffracted amplitude G(S) by the Fourier transformation :G(S) = 1 p(z) exp (-2niS . z)dv,. (1)The vector S = (s-so)/A, where SO and s are unit vectors defining the directionsof the incident and scattered waves. The vector S and the diffraction angle 20are related byThe scattered intensity from a black am is obtained from the amplitude functionby multiplication with its complex conjugate,Before comparison of observed and calculated scattering curves can be made the1 S I = 2 sin O/A.(2)I(S) = G(S)G*(S) = 1 G(S) 12. (3)02.0 2-5 3.0 3.5 4.0 4.520 (deg.)FIG. 4.-Typical X-ray diffractometer trace from black film. Full line gives experimental curve forfilm with optical thickness = 61 A. Calculated values (0) for illustrated film model were obtainedfrom eqn. (4). Inset-ordinates refer to p(z) (relative).appropriate geometrical correction factors which are responsible for the measurablescattering intensity from black films at low angles must be applied :where the first trigonometric factor is the Lorentz and polarization term, and thesecond factor gives the effective volume of film irradiated above the limiting 8value where the specimen completely subtends the incident beam.At the lowscattering angles studied here the geometrical factors cause a small shift to smallerscattering angles.A typical film trace showing two well-defined maxima is shown in fig. 4. Nomeasurable changes in peak positions were observed on the insertion of Soller slitsto limit axial beam divergence. The flat specimen aberration correction is thusthe only one to be considered and this is negligibly small for these measurements.13Corrected 28 values for the first and second diffraction maxima were calculateJ . S. CLUNIE, J . M. CORKILL A N D J . F. GOODMAN 39from (4) for a series of film thicknesses ranging from 40-70A.The X-ray filmthicknesses for 33 films are given in table 1 together with the thicknesses calculatedfrom simultaneous reflection measurements using the three-layer optical model,9* 10and the difference between the X-ray and optical thicknesses (A).no. ofobservations1156314131322TABLE 1X-ray opticalthickness (A) thickness (A)50 5152 5453 51-5754 50-5856 52-5957 5558 55-5959 6160 56-5961 6562 59-6563 59-6565 6 1 -67averagedifference (A)+ 1+2+ l00-2- 1+ 2-2+4+2- 1- 1RADIOTRACER MEASUREMENTSThe sulphate ion contents of the final films expressed as moles/cm2 of film sur-face are shown in fig. 5 as a function of the bulk solution concentration. Thesemeasurements are restricted to dilute solutions.In all cases the final film thick-nesses were in the range 50-55A.bulk concentration (moles 1-1) x 10FIG. 5.-Adsorption of MgS04 in C;nCio films from conductivity measurements (0) and radiotracermeasurements (9).FILM CONDUCTIVITYThe C,+,Cio films examined in the conductivity apparatus also drained to alimiting thickness of 50A. The conductivity per unit area of the Elms was com-puted from the observed conductances and length and perimeter of the film. Filmswith no additional electrolyte in the solutions from which they were drawn showeda small conductance, which was attributed to the surface monolayers. The con-ductivities from films containing electrolyte were corrected for this effect. Wit40 BLACK FOAM FILMSthe assumption that the ionic mobilities are the same as in bulk solution the electrs-lyte contents of the film per unit area as a function of concentration were calculated(fig.5).DISCUSSIONX-RAY THICKNESSESThe electron density difference between the hydrocarbon film surfaces and theaqueous core relative to air leads to scattering in the low-angle region that isessentially independent of the film structure at constant total thickness. Thepositions of the higher-order diffraction maxima become progressively more sensi-tive to the structure but the scattering is too weak for these to be observed. Thus,although the postulated film structure cannot be confirmed from our experimentaldata the total film thickness can be determined independently of structural assump-tions.The differences between the X-ray and three-layer model optical thicknessesA have an average value of +0-1 A and a standard deviation of 3 A for 33 deter-minations. The total film thicknesses determined by the two methods are in goodagreenent for these thin films thus confirming the optical model. As the valuefor the surface layer thickness deduced from the optical studies is close to the ex-tended molecular length, the uncertainty in the core thickness (-20 A) is probablyless than 5 A.FILM COREThe radiotracer results from dilute solutions show that there is an excess ofinorganic electrolyte in the film core. From these results the excess free energyof the electrolyte in the film, compared to the bulk solution is calculated to be -3.0RT/mole.This free energy difference is in the range of the specific adsorption poten-tials for ion binding by ionized monolayers. The origin of the binding in theformally neutral head group plane of the C&Cio systems is probably due to thepolarization of the anionic species in the intense electrical field gradients that existclose to the head-group plane due to the mosaic charge structure.The ion concentrations calculated from the conductivity data show good agree-ment with the direct radiotracer results, and hence the ionic mobilities in the filmcore are of the same order as those in bulk solution. A more detailed treatment,allowing for the electro-endosmotic flow associated with the surface potentialin these systems 14 (5 = 100 mV) leads to similar results for the electrolyte contentof the core.Although the application of any conductance theory to a system inwhich one dimension is only an order of magnitude greater than the ionic radiican only give results of qualitative significance, we may conclude that the inorganicions adsorbed on the surface layer of the film are mobile.FILM STABILITYThe potential energy as the function of the thickness of a thin film can becalculated from the DLVO theory. The introduction of a short-range repulsionpotential leads to two minima in the dependence of potential energy on film thick-ness,' the one at greater thickness (secondary minimum) being governed by thevan der Waals attraction and the double-layer repulsion.The independence ofour film thicknesses upon bulk solution concentrations or ionic content of the coresuggests they are stabilized by short-range repulsive forces (primary minimum).Under strictly controlled conditions of temperature apd relative humidity filmJ . S. CLUNIE, J . M. CORKILL AND J . F. GOODMAN 41from C,',Cio solution containing NaBr at concentration >@05 M have been ob-tained with thicknesses corresponding to those calculated for the secondaryminimum. The film thicknesses decrease with increasing electrolyte content ofthe bulk solution and can be reduced to -20 A core thickness by employing -2 MNaEr. Under these conditions the distinction between primary and secondaryminima is arbitrary.The short-range repulsion potential thus appears to determine the equilibriumcore thickness when the latter is in the region of 20A.The hydrophilic heads ofthe detergent ions and the inorganic electrolyte in the film core will bind waterof hydration and it is possible that the repulsion potential arises from the fact thatfurther thinning would involve dehydration of these components. Thus, for filmswith a 20A core thickness there are only 3-4 layers of water molecules associatedwith each surface nionolayer. The water contents of these very thin films are thusof the right order to permit the identification of the short range repulsion potentialwith the free energy required for dehydration.1 Derjaguin, Titiyevskaya, Abricossova and Malkina, Disc. Faraday Soc., 1954, 18, 24.2 Scheludko, Kon. Ned. Akud. Weten. B, 1962, 65, 76.3 Lyklema and Mysels, J. Amer. Chem. SOC., 1965, 87, 2539.4 Kitchener, Endeauour, 1963,22, 118.5 Corkill, Goodman, Haisman and Harrold, Trans. Faraday Soc., 1961, 57, 821.6 Mysels, Shinoda and Frankel, Soup Films, Studies oftheir Thinning and u Bibliography (Pergamon7 Duyvis and Overbeek, Kon. Ned. Akad. Weten. B, 1962, 65,26.8 Corkill, Goodman, Ogden and Tate, Proc. Roy. Soc. A, 1963,273, 84.9 Corkill, Goodman and Ogden, Trans. Furuday Soc., 1965, 61, 583.10 Clunie, Goodman and Ogden, Nature, 1966,209, 1192.11 Dasher and Mabis, J. Physic. Chem., 1960,64, 77.12 Clunie and Mabis, J. Physic. Chem., 1967, in press.13 Parrish and Wilson, International Tables for X-ray Crystallography, vol. I1 (The Kynoch Press,14 Bikerman, 2. Physik. Chem. A , 1933, 163, 378.Press, London, 1959).Birmingham, 1959)