7. COLLOID AND INTERFACE SCIENCE By G. D. Parfitt (University of Nottingham) THIS review of the 1967 literature is not comprehensive because of the in-evitable delay in receiving translations of papers from the Soviet Union and of delays in receiving certain important journals e.g. the Journal of Colloid and Interface Science. The following topics are not considered in detail: chemistry at electrode surfaces (polarography electrocapillarity etc) ion-exchange chemisorption and heterogeneous catalysis biological interfaces, and polymers biocolloids or polyelectrolytes in solution. Attention is drawn to the papers from four scientific meetings which were published in the literature in 1967; selected papers are included in this review. The meetings were (1) Symposium on ‘Ice’ Pittsburgh U.S.A.March 1966;’ (2) Symposium on ‘Wetting’ Bristol England September 1966 ;2 (3) Dis-cussion on ‘Colloid Stability in Aqueous and Non-Aqueous Media’ Notting-ham England September 1966 ;3 (4) Symposium on ‘Structure of Surfaces’, Durham North Carolina U.S.A. November 1966.4 Characteristics of Solutions of Soaps and Detergents.-The argument as to whether micelle formation should be considered by the law of mass action or as a pseudo-phase change still continues to attract attention. The latter approach has the great merit of simplicity and has been supported by certain experiments. In the phase-separation model the activity of the monomers should be constant above the critical micelle concentration (c.m.c.). Mysels has claimed that recent and more carefully executed ultrafiltration and surface-tension experiments show an increase in monomer activity above the c.m.c.and supports this with dialysis experiments on sodium dodecyl sulphate (SDS) solutions in his paper with Abu-Hamdi~yah.~ The cell they used per-mitted continuous monitoring of the composition of the dialysate and ex-periments were carried out to answer the criticism of their earlier data that the behaviour was concerned with impurities. Dialysis continues at all con-centrations although slower when micelles are present on both sides of the membrane. The data are considered in terms of a simplified mass-action model and fair agreement found. Further evidence in favour of the pseudo-phase separation model is presented ‘ J . Colloid interface Sci.1967,25 129. ’ SOC. Chem. Ind. Monograph 1967 No. 25. Discuss. Faraday SOC. 1966,42 7. Surface Sci. 1967 8 1. M. Abu-Hamdiyyah and K. J. Mysels J . Phys. Chuti. 1967,71 418. E 126 G. D. Parfitt by Nakayama and Shinoda.6 According to this model the Krafft point is the melting point of the hydrated solid surface-activity agent. Furthermore the solubility curve below the Krafft point (the solid-solute equilibrium curve) must intersect with the c.m.c. curve (the liquid-solute equilibrium curve) at the Krafft temperature. In this paper data are presented on the solubility of SDS and potassium perfluorooctanoate as a function of temperature ill the presence of added salts. The solubility is shown to decrease below the Krafft point in accordance with the solubility-product principle in the presence of salt.The c.m.c. decrease is inversely proportional to the 0.6 power of the gegenion concentration (approx.) and the point of intersection of the two curves shifts to a higher temperature on addition of salt as does the Krafft point. The data, the authors conclude therefore support the phase model. Further progress has been made in establishing values of the thermodynamic parameters involved in micelle formation. Emerson and Holtzer7 have estimated the contribution AG& of the hydrocarbon portion of the molecule to the standard free-energy charge AG," for the addition of one more detergent molecule to a micelle which already contains that number of monomers N most probable at the c.m.c. using the relation RTln(c.m.c.) = AG," = AG," + No is Avagadro's number E the magnitude of charge and IJJb the electrostatic potential at the surface of the micelle.Using light-scattering methods the c.m.c. and micellar weight were determined for SDS in NaCl solutions and for the cationics dodecyltrimethylammonium bromide DTAB (in NaBr), chloride DTAC (in NaC1) and nitrate DTAN (in NaNO,). The evaluation of IJJb using the Poisson-Boltzmann equation involved N from light scattering, the micellar radius (from published X-ray data) and the distance of closest approach of the ions to the micelle. Having thus estimated the electrostatic contribution the part played by the hydrocarbon chain was assessed and found for cationics to be independent of ionic strength and approximately independent of supporting electrolyte.For SDS a small dependence of ionic strength was found and the value for AG& (ca. 11 kcal. mole- ') is about 20% higher than that for the cationics. In another paper Emerson and Holtzer' have studied the effects of various additives on the stability of micelles of SDS and DTAB. The additives chosen were materials known to denature proteins (also compounds closely related to these denaturants) so that with the simpler micellar systems it might be possible to obtain information relevant to the disruption of protein structure which is assumed to be asso-ciated at least in part with the breaking of hydrophobic bonds. The tempera-ture-dependence of the c.m.c. in the presence of urea and substituted ureas, dioxan methanol ethylene glycol glycerol and sucrose has been evaluated, from which enthalpy and entropy changes were calculated.Qualitatively a ' H. Nakayama and K. Shinoda Bull. Chem. SOC. Japan. 1967,40 1797. ' M. F. Emerson and A. Holtzer J. Phys. Chem. 1967,71 1898. * M. F. Emerson and A. Holtzer J. Phys. Chem. 1967,71 3320 Colloid and Interface Science 127 correlation was observed between the hydrophobic nature of the additive and its micelle-breaking power but difficulties in interpretation arise when the additives penetrate the micelle i.e. structural changes as well as hydrophobic interactions and dielectric effects must be considered. Some indirect means of distinguishing penetrating from non-penetrating additives are proposed. It was concluded that it is not possible to take the numerical value of the c.m.c.as a single criterion for the hydrophobic bond strength in micelles. The c.m.c. is directly related (as mentioned above) to the standard free-energy change AG," and N is expected to vary with the additive through changes in the electrostatic as well as the hydrocarbon contributions. Qualitative conclusions could be drawn about hydrophobic bonds in micelles but some reservation was expressed about extension to protein denaturation. The effect of urea on the thermodynamics of micellisation of a series of octylsulphinylalkanols (C18H17SO(CH2)n OH with n = 2 3 4) and of alkyl trimethylammonium alkyl sulphates (C,C,SO with x = 10 8 and y = 10 8) has been reported by Corkill et aL9 The first series was used to study the effect of increasing the distance between the two hydrophilic centres while the second series permitted the effect of increasing chain length to be assessed.From surface-tension measurements (for the c.m.c.) and calorimetric data (for the heat of micellisation) the thermodynamic parameters AGO AH" and TAS" were calculated based on a standard state of unit mole fraction. It is shown that urea affects micellisation in two ways the interfacial energy between hydrocarbon and water is lowered thus reducing the free-energy differences between the alkyl chains in the solvent and those in the micelles thereby raising the c.m.c.; also by changing the degree of solvation of monomer it lowers the compensating heat and entropy terms associated with the solvent reorientation accompanying micellisation.The change in the environment of the hydrocarbon chain of a surface-active agent on micelle formation is considered in two papers which adopt rather different approaches to the subject. From measurements reported by Corkill, Goodman and Walker1' of the partial molar volumes above and below the c.m.c. of three series of compounds (n-alkyl trimethylammonium bromides [RN(Me),Br R = 8 10 12 14 and 161 sodium n-alkyl sulphates [RSO,Na, R = 10 12 and 141 and n-alkylsulphinyl alkanols [RSO(CH,),OH R = 6, 8 and n = 2,3 and 41 it was concluded that in the process of micelle formation the hydration of the methylene groups adjacent to the hydrophilic group is retained. Muller and Birkahn" have made use of the significant chemical shift in the I9F n.m.r. spectra when a molecule is transferred from an aqueous to a non-aqueous environment (the shift for hydrogen is much smaller).With a series of fluorinated soaps (CF,(CH,),CO,Na n = 8 10 and l l ) which judged by the c.m.c. are essentially similar to the ordinary alkyl carboxylates, the shifts in the fluorine n.m.r. signal on micelle formation is compared with J. M. Corkill J. F. Goodman S. P. Harrold and J. R. Tate Trans. Faraday SOC. 1967,63,240. l o J. M. Corkill J. F. Goodman and T. Walker Trans. Furaduy SOC. 1967,63 768. l 1 N. Muller and R. H. Birkhahn J . Phys. Chem. 1967,71,957 128 G. D. ParJitt those for CF,(CH,),CF3 in various solvents and show that the CF group in a micelle has characteristics about midway between that in water and hydro-carbon. This suggests considerable penetration of water into the micelle.The data also indicate that the shift is virtually independent of micelle size and added electrolyte. The density hydration shape and charge of micelles of SDS and dodecyl-ammonium chloride (DAC) have been considered by Stigter' in the light of published viscosity light scattering conductance self-diffusion and electro-phoresis data. This paper is an elaboration of a previous suggestion by the author (with Mysels 1955) that micelles have a rough surface. The model of liquid micelles is characterised by four parameters micellar weight micelle density hydration and electric charge (or surface potential). Considering these parameters and existing data Stigter concludes that (1) the shear surface coincides within 1"A with the surface enveloping the heads of the micellised ions (2) about half the total number of counterions are located inside the shear surface and (3) spherical micelles may grow into flexible rods.Further evidence on the binding of counterions to micelles has been obtained from e.m.f. measurements on a number of surface-active materials (potassium caprate laurate and myristrate; sodium caprate and SDS) by Feinstein and Rosano.' Using a cell combining a standard calomel electrode and a cationic glass electrode the activities of K+ or Na' were measured above and below the c.m.c. Assuming that the number of micelles only increased above the c.m.c. and that the number of anions per micelle remained constant values of the apparent degree of dissociation of cations from the micellar unit just above the c.m.c.were estimated and are as follows KClo 0-79 KC, 0.69 KCI4 0.24 Na Cl0 0-57 and SDS 0-14. Doubt still exists about the dependence of micellar weight of ionic surface-active agents on ionic strength as indicated by light-scattering data. Schott's earlier work (1966) with anionics (sodium decane sulphonate and SDS) and non-ionics (two C, ethylene oxide condensates) showed that the dye solubili-sation method gave good agreement with light-scattering and ultracentri-fugation data for the non-ionics and for the SDS in the presence of swamping electrolyte. Apparently one dye molecule was solubilised by each micelle and since in the absence of electrolyte the micellar weight (by light scattering) of SDS is significantly smaller than in excess electrolyte some doubt was cast on the value of the former and on the use of light scattering to determine micellar weight.Now this work has been extended14 to cationics (DTAB and cetyl pyridinium chloride) and to non-ionics with a larger hydrocarbon core [nonylphenol(EO), and C, (EO)18]. The same micellar weights were obtained by light scattering and dye solubilisation (assuming one dye molecule per micelle) for nonylphenol (EO), and DTAB but for the others the light-scattering value was a factor of three larger i.e. these detergents solubilise l2 D. Stigter J . Colloid Interface Sci. 1967 23 379. l 3 M. E. Feinstein and H. L. Rosano J . Colloid Interface Sci. 1967 24 73. l4 H. Schott J . Phys. Chern. 1967,71,3611 Colloid and Interface Science 129 three dye molecules per micelle.Schott therefore concludes that the dye solubilisation method is not an absolute method for determining micellar weights but it can be used to show relative changes on addition of solubilised impurities or electrolytes and provides the lowest possible value for the. micellar weight. Again the results showed little or no effect of added electrolyte on the micellar weight of ionic detergents in contradistinction to light-scattering data. In the light-scattering method for micellar-weight determination of non-ionic systems it is often possible to interpret the data in terms of the formation of micelles whose average molecular weight is independent of concentration and temperature. However the turbidity data at 22 32 and 42" for the octylsulphinylalkanals (the same compounds as discussed earlier) obtained by Corkill Goodman and Walker" show large deviations from ideal behaviour and the Debye plots are such that reliable micellar weights cannot be obtained from the intercepts.Two limiting cases are considered by the authors in their interpretation. The first involves the interactions in a system containing micelles whose size is concentration independent; this is treated using the Flory-Huggins model for a solution in which there is a large difference in the size of the solvent and solute molecules but is not very successful although the possibility of a concentration-independent size is not excluded. However, more success is achieved with a model in which the spherical micelles are assumed to undergo reversible association similar to that of a protein (the Debye plots for these systems and insulin are similar) and some viscosity data show best agreement with this model.Confirmation of the validity of the aggregation model requires further information from transport processes, which are thermodynamically irreversible and therefore do not depend directly on solution non-ideality. Some related information is reported by Ottewill Storer and Walker.16 The micellar weight of dodecyl hexa-oxy-ethylene glycol monoether in D,O has been determined by the Archibald method of approach to sedimentation equilibrium as a function of temperature. The apparent micellar weight remains constant at 5-1 5" at about 50,000 and then increases rapidly with temperature up to 840,000 at 35" in good agree-ment with published results using the light-scattering method.Examination of the system by sedimentation velocity and viscosity experiments suggest that the kinetic unit changes in size with changes in concentration and temperature. It is concluded that the evaluation of true micellar weights requires a know-ledge of the dependence of activity on concentration and temperature. Some comments on the use of dyes to tag micelles for the measurement of transport properties (electrophoresis diffusion and dialysis) have been made by MyseIs.l7 Since the concentration of dye used is so small that micelles seldom contain more than one dye molecule then in principle the tagged and untagged micelles are essentially the same size and have the same transport J.M. Corkill J. F. Goodman and T. Walker Trans. Faraday SOC. 1967,63 759. l6 R. H. Ottewill C. C. Storer and T. Walker Trans. Faraday SOC. 1967,63,2796. I' K. J. Mysels J . Colloid Interface Sci. 1967,23 474 130 G. D. Parfitt properties. But the micelle might swell says Mysels and if the micelles are heterodispersed the effect will be more significant. The thermodynamics of introducing only one dye molecule per micelle is examined and it is shown that the tagged distribution is skewed towards larger micelles so that the number-average micellar weight of the tagged distribution equals the weight-average value for the untagged one. The probability of finding a dye molecule in a micelle is proportional to the number of molecules in the micelle hence larger micelles are more likely to be tagged in proportion to their size and are more frequent in the tagged distribution.Tagging means that diffusion and dialysis will be apparently slower but the effect on electrophoresis depends on whether the zeta potential or the degree of ionisation tends to be constant with size. The entropy change associated with micelle formation in aqueous media is normally associated with the changes occurring in the solvent. Hence it is to be expected that significant effects are observed when the thermodynamic parameters are evaluated in alcohol-water mixtures. Such is the case for dimethyl dodecyl phosphine oxide in ethanol-water mixtures reported by Herrrnann and Benjamin.'* Light scattering is used to determine the c.m.c.and micellar weight and calorimetric data for AH" so that changes in AS" may be evaluated. The c.m.c. increases slightly as the ethanol concentration is changed from %20% (by volume) and then increases markedly at higher ethanol concentration while becoming increasingly less well defined. A significant decrease in micellar weight (550,000-44,000) occurs from 0-10 % ethanol beyond which the decrease is less marked until the value is 170 in pure ethanol (the molecular weight of the monomer is 246). AHo and ASo values decrease considerably over the range %20% ethanol and then at higher concentrations remain almost constant. These data indicate a reduction in the amount of ordered water that is released during micelle formation when ethanol is present and represent weakened hydrophobic bonding.A change in micelle shape is proposed (rodlike or cylindrical to spherical) as the ethanol concentration is increased. These results are consistent with the current picture of the part played by the water in micelle formation. Data on micelle formation of detergents in hydrocarbon solutions are few, and their reliability is a function of the amount of water present. Sharma, Cowie and SiranniI9 have examined the behaviour of a poloxyethylated nonylphenol ether (about 10 moles ethylene oxide per mole of hydrophobe) in hydrous and anhydrous cyclohexane at -45" by light scattering and by vapour pressure in dry solvent at 39.1". Complex behaviour was observed dependent on the relative proportions of detergent and water.Water appears to have a marked effect on the aggregation of the non-ionic in cyclohexane; the aggregation number rises from about 4 (difficult to be accurate with dry solutions) to 8 as the mole ratio of added water is increased to about 0.28 and K. W. Herrmann and L. Benjamin J . Colloid Interface Sci. 1967 23,478, l9 R. K. Sharma J. M. G. Cowie and A. F. Sirianni J . Amer. Oil Chemists' SOC. 1967,44 488 Colloid and Interface Science 13 1 then rises more steeply until phase separation occurs beyond a mole ratio of 2.4. The difference between the weight and number averages is very small in the dry solvent. The relationship between the cloud point and the micellar properties (c.m.c. and micellar weight) of aqueous solutions of polyoxyethylene nonylphenol ethers (n = 10 15 and 20) has been investigated by Arai2' using light-scattering and surface-tension methods.The c.m.c. increases and the micellar weight decreases as the cloud point rises with growing chain length increasing amounts of ethanol or decreasing amounts of sodium sulphate. In the case of the c.m.c. the relationship is almost linear. There has been some discussion in the literature as to whether certain detergents form dimers below the c.m.c. but the evidence has been conflicting and to some extent a function of the technique used. Clunie Goodman and Symons2 have analysed their conductance data for aqueous solutions of members of the homologous series of sodium n-alkyl sulphonates [alkyl chain length n = 2-14 (even nos.)] in terms of the Onsager theory and conclude that only in the case of the tetradecyl salt is their any deviation that might be ascribed to dimerisation of the long-chain ions.The protection provided by organic compounds (in particular n-hexanol) when solubilised in SDS micelles to the precipitation of the detergent by calcium ions has been demonstrated by Pearson and Lawrence.22 A 2% SDS solution containing hexanol in the mole ratio (hexanol):(SDS) of 1.25 can tolerate 0.018~ CaCl without precipitation at 25" but without hexanol the concentration is 0.006~. Measurements of sodium-ion activity in the various systems allowed the contribution of each species to be determined and a mechanism is proposed involving exchange of the sodium ions with calcium at the surface of the micelles which is enhanced when the micelles contain solubilised hexanol.Hexanol is assumed to cause increased ionisation of the micelles leading to salting-in of the sparingly soluble calcium dodecyl sulphate. A second paper by the same describes a study of the relationship between changes in the electrical conductivity of soap solutions on addition of organic additives and the changes in the ionic activity of the detergent. The increases in equivalent conductance with additive (n-aliphatic alcohols with n = 2-7) concentration are correlated with increases in counter-ion activity ; as n increases there is a greater tendency for the alcohol to penetrate into the micelle causing separation of the head groups decrease in repulsion and release of counter-ions. There has been little published on the solubilisation of water in non-aqueous solutions of non-ionic surfactants and in particular the effect of temperature.Shinoda and O g a ~ a ~ ~ describe a study of the solubilisation of water in solu-tions of poloxyethylene nonylphenol ethers ( n = 5.2,6.0,7.4,9.6 and 14.0) in a '() H. Arai J. Colloid Interface Sci. 1967,23 348. " J. T. Pearson and A. S. C. Lawrence Trans. Faraday SOC. 1967,63,488. 23 A. S. C. Lawrence and J. T. Pearson Trans. Faruday SOC. 1967,63,495. 24 K. Shinoda and T. Ogawa J . Colloid Interface Sci. 1967,24 56. J. S. Clunie J. F. Goodman and P. C. Symons Trans. Faraday SOC. 1967,63,754 132 G. D. ParJitt variety of hydrocarbon and halogenocarbons. Solubilisation of water is large at the optimum temperature (when the solubility and cloud-point curves meet) for solutions containing 2-15 % wt.% of detergent in which micelles exist. The effect of chain length and type of solvent and the effect of temperature are reported providing a useful correlation for the selection of a suitable non-ionic surfactant for the solubilisation of water in various solvents. Thermodynamic data for water solubilisation in non-aqueous solutions of polyoxyethylene nonylphenol ethers (n = 6 7 and 8) or Aerosol OT are provided in the paper by Kitahara Ishikawa and Tanim01-i~~ (such data have not been reported previously). By measuring the vapour pressure of water at different tempera-tures the heat of solubilisation (AH,) was determined using cyclohexane, perchloroethylene and benzene as solvents. With increasing solubilisation in the first two solvents AHs decreased for Aerosol OT and increased for non-ionics while in benzene the curves for the non-ionics show a minimum.All the AHs curves approach the latent heat of vaporisation of water and the data explained qualitatively in terms of the forces (non-dipole and hydrogen bonding) involved. The Liquid-Liquid Interface.-An investigation on the effect of molecular structure and unsaturation on the initial spreading pressure (Fh) and initial spreading coefficient (Sb,) on water of numerous pure low-boiling members of the n-alkane 1-alkane n-alkyl benzene and acetylene hydrocarbon series has been reported by Pomerantz Clinton and Zisman.26 It is shown that from F b and the surface tensions of water (y,) and the organic liquid (yb) it is possible to calculate the initial value of the reversible work of adhesion (wba) and the initial interfacial tension (yab) using the relations (derived) The effect of unsaturation and isomerism on Fb (obtained using the piston monolayer method) W and yab is determined and from the data the molar free energy of adhesion of hydrocarbons to water arising from the hydrophilic nature of unsaturated carbon-carbon bonds is assessed.Although the data are not comprehensive values for the molar free energies for the terminal olefinic group (CH2=CH-) and the aromatic double bond of 1030 and 393 cal./mole respectively have been estimated. Such comparisons are not possible with hydrocarbons from surface pressure versus area measurements. A more convenient method of measuring the value of the critical surface tension yc of a liquid a based on a plot of Sb of liquid b on liquid a versus Yb is discussed by Shafrin and Zi~man.~’ The method has two advantages over the preceding methods first it eliminates measuring the contact angle (which presents difficulties) and second it does not require that yc should fall within a range of surface tensions exhibited by the collective members of the series of homologous spreading liquids.A rapid and reliable method for measuring 2 5 A. Kitahara T. Ishikawa and S. Tanimori J . Colloid Znterfnce Scz. 1967,23 243. 26 P. Pomerantz W. C. Clinton and W. A. Zisman J . Colloid Interface Sci. 1967,24 16. 2’ E. G. Shafrin and W. A. Zisman J . Phys. Chem. 1967,71 1309 Colloid and Interface Science 133 S is discussed in the paper mentioned above.25 The value of yc for the water-air interface has been determined using several homologous series of pure hydro-carbon liquids (normal and branched alkanes and alkenes) and the loyest value found was yc = 21.7 dynes/cm.at 20". Since the results are analogous to those already published for solid surfaces it is concluded that the clean surface of water behaves as a low-energy surface with respect to low-polarity liquids, as expected if only dispersion forces are operative between each alkane and water. High resolution n.m.r. spectroscopy has been used to study the molecular interactions and mobility at liquid-liquid interfaces by Zlochower and Schulman.28 Spectra were taken of the various phases (isotropic viscous birefringent and a low-viscosity second isotropic) formed when a concentrated aqueous solution of DTAB is titrated with chloroform.The changes in line width of the long-chain methylene resonance in DTAB reflect the mobility of the chain in the various phases while the broadening of the H,O resonance provides evidence for the binding of the water at the interface. Ion-dipole association between CHC1 and DTAB is indicated by the large downfield shift of the CHC1 resonance. The theory of Vonnegut for the measurement of interfacial tension from the shape of a fluid drop in a horizontal rotating tube filled with a liquid of higher density has been extended by Princen Zia and Mason.29 Numerical solutions based on exact equations are presented from which it is possible to calculate the interfacial tension from the length of the elongated drop along the axis of rotation knowing the values of drop volume speed of rotation and difference in density between the two phases.Previous attempts were seriously limited by the optical correction involved in measuring the drop shape. The authors have developed an experimental method based on the measurement of drop length without the need for optical correction. Results for the system n-hexadecane-glycerol heptane-glycerol (and air-glycerol) show good agreement (within 3 %) with other methods (pendant drop ring tensiometer). Two papers deal with the interfacial tension at the hydrocarbon-water interface. Using the pendant-drop method and an apparatus of new design capable of measuring 0.001 dyne/cm.at high temperature and pressure, Jennings,' has measured the interfacial tension of benzene-water and n-decane-water in the intervals 25-1 76" and 1-8 17 atmospheres. The effect of temperature is much greater than that of pressure and the general equation for the interfacial tension is y = a + a,P + a (t - 25) where t is in degrees centigrade. Values of the constants for the two systems are given. These data are of practical interest because of the increasing depths of new oil discoveries and the injection of heat in low-temperature reservoirs to assist oil recovery. In the second paper Gillap Weiner and Gibaldi consider the linear increase I. A. Zlochower and J. H. Schulman J . Colloid interface Sci. 1967,24 11 5. 29 H. M. Princen I.Y.Z.Zia and S.G. Mason J . Colloid Interface Sci. 1967,23,99. 'O H. Y. Jennings J . Colloid Znterface Sci. 1967,24 323. 31 W. R. Gillap N. D. Weiner and M. Gibaldi J . Amer. Oil Chemists' SOC. 1967,44 71. 134 G. D. Parfitt in interfacial tension at 25" of n-alkane-water [chain length n = 6-16 (even nos.)] systems with the log of the chain length. Contrary to previously published data it is found that the values of @ in the Girifalco and Good equation of yiz0 the dispersion force component for water are not constant but vary in a regular manner with the log of the hydrocarbon chain length. Furthermore the relationship between chain length and interfacial tension is opposite to that predicted by Antonow's rule y12 = /yl + y2/. A model for the interface involving water structure is devised to explain the chain-length dependency of the interfacial properties of the hydrocarbons.A comprehensive set of interfacial-tension data for the adsorption of highly purified SDS from aqueous solutions at the air-water and water-hexane, octane nonane decane heptadecane hexene octene cyclohexane cyclo-hexane benzene butylbenzene and carbon tetrachloride interfaces at 25" is reported by Rehfeld3* (previous data were limited to decane heptane and petroleum ether). The interfacial tension versus log concentration data below the c.m.c. were fitted to a polynomial of the second degree. Organic molecules containing x-electrons give much lower interfacial tensions than the n-alkanes, whereas molecules with dipoles give only slightly lower tensions.The effect of the organic liquid on the c.m.c. and the free energy of micelle formation and the concentration of SDS (evaluated using the Gibbs equation) at each of the organic liquid-water interfaces when the bulk concentration is the c.m.c. are qualitatively correlated with the solubility of the hydrocarbon in the micelles. Electrocapillary curves of oil-water systems containing surface-active agents have been discussed in two papers by Watanabe et a1.,33? 34 using KCl in the aqueous phase and ionic detergents (anionic and cationic) in the oil phase (various polar organic solvents). The interfacial tension was suppressed over the cathodic or anodic polarization range by cationic or anionic agents respectively and using the Lippmann-Helmholtz equation it was concluded that the water side of the interface was charged positively or negatively for the two cases.This charge is assumed to be due to the counterion layer associated with the adsorbed agent on the oil side. In the second paper the effect of cation (or anion) valency of the electrolyte in the aqueous phase is discussed. Over the cathodic branch the suppression of the interfacial tension is greater the larger the crystal radius of the anion and the reverse for the anodic branch. The data demonstrate the applicability of the technique to the study of the oil-water interface under controlled electrical conditions which should lead to a better understanding of the adsorption mechanism at this interface. An investigation of specific adsorption at the mercury-methanol interface is reported by Garnish and parson^.^' The marked difference in behaviour of " S.J. Rehfeld J . Plrys. Chem. 1967,71 738. 3 3 A. Watanabe M. Matsumoto H. Tamai and R. Gotoh Kolloid-Z. 1967. 220 152. 34 A. Watanabe M. Matsumoto H. Tamai and R. Gotoh Kolloid-Z. 1967,221,47. 35 J. D. Garnish and R. Parsons Trans. Faraday SOC. 1967,63 1754 Colloid and Interface Science 135 methanol and water in the capacity curve for the inner layer in the absence of specific adsorption had not previously been adequately explained. By studying the temperature coefficient of the potential at the zero point of charge and the adsorption of di-n-butyl ether it was concluded that when the mercury is uncharged the methanol dipole is oriented with its negative end towards the mercury.From capacity and electrocapillary curves the adsorption isotherms of iodide ions and of thiourea from methanol solutions were determined and found to be associated with a free energy of adsorption which is a linear function of the charge on the metal and a charge-dependent interaction co-efficient. Certain similarities exist in the behaviour of thiourea in methanol, water and formamide ; the two-dimensional second virial coefficients are similar suggesting similar properties of the inner layer in the three solvents, i.e. the effective dielectric constant is similar. Larger differences were found with the iodide ion; the virial coefficient is very large and this is the cause of the absence of adsorption humps in the capacity curves with methanol.The study of the structure and properties of black lipid membranes leads to useful information on various phenomena of biological and technological importance (adsorption colloid stability cell biology etc.). Tien36 has measured, using a new technique (described) the interfacial free energy of black lipid membranes of less than 100 in thickness separating two aqueous solutions, and prepared from cholesterol dissolved in n-dodecane with dodecyl acid phos-phate dioctadecyl phosphite and hexadecyl trimethylammonium bromide (HTAB) as stabilising agents. The ability to form a stable black film is shown to depend on both the interfacial free energy and the c.m.c. of the agent; the forma-tion of stable films is not limited to the use of chemical phospholipids. The electrical properties of cholesterol-n-dodecane-aqueous HTAB system is reported by Tien and Diana,37 and also includes measurements with various neutral electrolytes in addition to the HTAB in the aqueous phase.The trans-verse membrane resistance is dependent both on the electrolyte and the anionic species used the order of the effect of the anion on the decrease in resistance observed being I- > Br- > SO:- > C1- > F-. A qualitative explanation of the effect is proposed in terms of an interaction between the HTA’ and anion at the membrane-water interface. Membrane capacitances were also measured as a function of salt concentration and type and considered qualita-tively in terms of the electrical double layer at the interface. Emulsions. An exact method of solution of Smoluchowski’s equations for the kinetics of the rapid coagulation of emulsions is given by Rice and White-head.38 Smoluchowski’s original theory based on diffusion of the dispersed particles makes a number of assumptions (spherical particles no attractive forces except on contact etc.) and readily gives an expression for the collision rate.The simplifying assumption of Smoluchowski that the product (ri + rj) (r; + r, ’) may be replaced by 4 ri and rj being the radii of any pair of co-36 H. T. Tien J . Phys. Chem. 1967,71,3395. 37 H. T. Tien and A. L. Diana J . Colloid Interface Sci. 1967 24 287. C. L. Rice and R. Whitehead J . Colloid Interface Sci. 1967,23 174 136 G. D. Parfitt agulating particles is discarded in this treatment for emulsions and an exact solution is obtained for the case of particles which on collision coalesce into a third spherical droplet.The time-dependence of the intensity of light scattered by a coagulating emulsion is also analysed. The deviations from Smoluchowski’s original expressions are found to be surprisingly small because the low degree of polydispersion associated with times less than the half-life for the emulsion. It is also indicated how the theory may be modified to take into account mutual forces between droplets incomplete adhesion on collision orthokinetic coagu-lation due to sedimentation delayed coalescence and the breaking up of uncoalesced aggregates. A quantitative study of the role of pepsin as emulsifier in the stability of Niijol in water emulsions has been reported by Prakash and Sri~astava.~’ Particle counts were made haemocytometrically to study the coagulation of the emulsions as a function of pH electrolyte concentration and emulsifier concentration ; the electrophoretic mobility was also measured.Using the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of stability of lyo-phobic colloids the interaction energies have been calculated for different surface potentials and ionic strengths and with classical double-layer theory the charge densities in the Stern and Gouy layers were estimated. The assumption is made that the coagulation sets up a temporary singlet-doublet equilibrium after a time t > a2/D (a = particle radius D = diffusion coefficient). By counting the singlets and doublets the experimental degree of aggregation was calculated and compared with those calculated theoretically using various values of the Hamaker constant A.It is concluded that coagulation into the secondary minimum occurs with A = 6 x erg; the energy barriers are too high for primary minimum coagulation. The factors responsible for the formation of micro-emulsions are considered by Prince.40 Schulman’s theory (1959) for the formation of emulsions stabilised with oleate soaps and long-chain alcohols indicates that the condition for the formation of these small particle (8&800 A diameter) emulsions is that x > yo/w whereas when x c only a macro-emulsion (particles ca. 1 p diameter) would form. Here n is the spreading pressure (n = yo,w - y where y is the total interfacial tension and yo,w that of the oil-water interface in the absence of stabilising agents) in the monolayer of adsorbed species.When n 3 yo,w energy - y dA ( A = surface area) would be available to increase the total surface area hence a micro-emulsion would form. However recent data with mixed films of soaps and alcohols suggest the need for a re-assessment of these factors which Prince has carried out in his paper. The initial negative interfacial tension is now assumed to be due to a large depression of yo, rather than a high x the depression arising from the spontaneous distribution of alcohol molecules between the interface and the oil phase. Rehfeld4’ describes a new method of studying the particle-size distribution 39 C. Prakash and S. N. Srivastava Bull.Chem. SOC. Japan. 1967,40 1756. 40 L. M. Prince J. Colloid Interface Sci. 1967,23 165. 41 S. J. Rehfeld J . Colloid Interface Sci. 1967 24 358 Colloid and Interface Science 137 of mechanically prepared hydrocarbon in water emulsions. This technique has been developed to overcome the problems associated with handling and dilution in the normal microscopic method. A small amount of polymer is dissolved in the hydrocarbon to be emulsified and the hydrocarbon is subse-quently removed by thermal distillation or dilution leaving a polymer dispersion which is counted in a Coulter Counter. The technique was used to study the particle size of benzene in water emulsions as a function of the initial surfactant (SDS) concentration and emulsification time. It is shown that the steady-state particle size decreases with increasing concentration of SDS up to the c.m.c., above which it remains constant.The time to reach the steady-state value increases linearly with increasing surfactant concentration. S h i n ~ d a ~ ~ has correlated the dissolution state of a non-ionic surfactant with the curvature of the adsorbed monolayer of surfactant at the hydrocarbon-water interface and the stability and type of emulsion as a function of tempera-ture. In his analysis he has used such experimental facts as micellar dispersion, the clouding phenomena and the temperature-dependence of the solubilisation of the hydrocarbon (or water) in aqueous (or non-aqueous) surfactant solutions. It is found that the phase-inversion temperature in emulsions corresponds to the temperature at which the hydrophilic-lipophilic property (HLB value) of the surfactant balances for a given hydrocarbon-water system.Hence phase-inversion temperature data are useful in interpreting emulsion behaviour and as a guide for the selection of an emulsifier. The Liquid-Vapour Interface.-A knowledge of the concentration profile of a system containing two fluid phases in direct contact enables the surface excess thermodynamic properties of the system to be determined. Lattice models have been used with a plane interface of several molecular diameters in thickness and the concentration profile is given by the solution of a non-linear second-order difference equation but the computations are laborious and few data are available. Using a computer Lane and Johnson43 have attempted to obtain an exact solution assuming it to be symmetric using a method described by Ono (1947) but without success and propose a method of successive approximations which is an extension of the two-layer interface calculations of Defay and Prigogine.This method provides a well-defined, self-consistent approximate solution without assuming that the final solution is symmetric. By interpreting the internal latent heat (Li) of a liquid as the excess of energy which the surface layer of a liquid removed from the parent liquid possesses over that possessed by an equal mass of the liquid Ramanadha~n~~ has ob-tained the following relation for the thickness of the surface layer 42 K. Shinoda J. Colloid Interface Sci. 1967 24,4.43 1. E. Lane and C. H. J. Johnson Austral. J . Chem. 1967,20,611. 44 M . Ramanadham Indian J. Pure Appl. Phys. 1967,5,369 138 G. D. Parfitt where p" is the density of the surface layer and z its thickness and y is the surface tension of the liquid. The calculated values of z for various liquids are of the order of magnitude usually associated with the dimension of molecules (at 20" z 7-6 A for benzene 1.9 A for water 2.3 A for methyl alcohol etc.) and increase with temperature. Surface tension. Several theories of surface tension of liquids have been published and that of Ree Ree and Eyring (1964) using significant-structure theory gives a simple equation which is approximate but yields good results. However it includes the Lennard-Jones 6-12 potential whose characteristic constants are available only for simple liquids and hence the application of the equation is limited.Lu et aL4' have derived another simple equation of surface tension using significant-structure theory by introducing the approximation that the surface of liquids consists of a monomolecular layer in which the molecule has a sublimation energy different from that for a bulk-liquid mole-cule. The agreement between calculated and observed values for a variety of liquids of monatomic diatomic and polyatomic molecules including liquid metals is overall satisfactory although there are marked exceptions e.g. A controversy has existed as to whether water has a dynamic surface tension, and this has stemmed from the fact that certain dynamic methods notably the oscillating jet leads to a time-dependent surface tension.Either the technique gives erroneous values or water does have a dynamic surface tension and Vandegrift46 has shown which is correct. He measured the surface tension, using the oscillating jet of a liquid having the same physical properties as water but with no association and having nearly the same velocity character-istics (carbon tetrachloride was chosen) and found similar time effects. From this and experiments with different size orifices he concluded that water has no dynamic surface tension in the millisecond range and that any time-dependent effects in this region are probably due to an inadequate mathematical descrip-tion of the process and not to liquid structure effects. The surface tension-temperature relationship for water is described by C l a ~ s s e n .~ ~ Data have been analysed by the method of Eotvos (1886) which permits the calculation of extensive surface properties as a function of temperature for an amount of surface that always contains the same number of molecules; the surface layer of molecules is assumed to expand with temperature in the same ratio as does the interior liquid. Thus the extensive surface property of surface free energy AGs of a fixed number of molecules (comprising 1 cm. of surface at 4") is calculated by dividing the surface tension by of the density allowing enthalpy and entropy data to be evaluated. The corrected surface tension is a linear function of temperature and the derived values of the extensive thermodynamic properties (based on 1 cm.2 of surface at 4") are : AGs = +75.74 erg (at O O ) AHs = + 115.42 erg and ASs = +0.1453 erg/% Hg NH,,C6H,.45 Wei-Chen Lu Mu Shik Jhon T. Ree and H. Eyring J . Chem. Phys. 1967,46 1075. 46 A. E. Vandegrift J . Colloid Interface Sci. 1967 23,43. 47 W. F. Claussen Science 1967 156 1226 Colloid and Interface Science 139 which become +2120 cal./mole of surface +3231 cal./mole of surface and + 4-067 entropy units/mole of surface respectively when a hexagonal surface structure is assumed. For binary liquid mixtures a theory of surface tension is proposed by Shere~hefsky~~ leads to a general expression of the form where y yl and y2 are the surface tensions of the mixture and of pure com-ponents 1 and 2 respectively x2 the mole fraction of 2 in the bulk region and AG is the free-energy change in the surface region when solvent (1) is replaced by a mole of solute (2) occupying an area A2/t with t = molecular thickness of the surface region.The equation is applied to seventeen binary liquid mixtures of organic liquids (over the whole range of mole fraction) and the agreement is shown to be good. Values of t derived from the data assuming values of A, are unity in most of the cases (unity corresponds to one molecular diameter of component 2). Those which deviate from unity are interpreted in terms of molecular orientation in the surface layer. Sprow and P r a ~ s n i t z ~ ~ have demonstrated that the surface tensions of mixtures of simple liquids can be predicted satisfactorily from a model based on a regular surface solution with molecules of similar size and dispersion forces predominating.The agreement for such mixtures as carbon tetrachloride-chloroform and neopentane-benzene is within experimental error. For com-plex systems the use of a parameter 01 reflecting the difference in characteristic energy between the bulk liquid and the surface leads to a good fit of the data for a number of associated systems e.g. ethanol-water acetone-chloroform etc. Eberhart’s (1966) equation for the surface tension of liquid mixtures has been shown to fit the data for a variety of systems. The equation involves an empirical constant which Ramakrishna and Suri” show is given by s = exp(y1 - ./2)A2/RT and values of S calculated from the two equations are compared for various liquid mixtures including molten electrolytes and metals.A similar conclusion is reached by S~hmidt.~ The success of the equation is probably because of the validity of the assumption that (f3‘fI)/(f;1,) = 1 where f = activity co-efficient and superscript s refers to the surface phase. Although many values of surface tension of surfactant solutions are reported it is rare that various methods of measurement are compared for one system. Boucher Grinchuk and Zettlem~yer~~ have measured the static surface 48 J. L. Shereshefsky J . Colloid interface Sci. 1967 24 317. 49 F. B. Sprow and J. M. Prausnitz Canad. J. Chem. Eng. 1967,45 25. 5 1 R. L. Schmidt J. Phys. Chem. 1967,71 11 52. 5 2 E. A. Boucher T. M. Grinchuk and A. C. Zettlemoyer J. Colloid Interface Sci.1967 23 600. V. Ramakrishna and S. K. Suri. lndian J. Chem. 5,310 1967 140 G. D. ParJitt tension at 25” of aqueous solutions of sodium chloride and sodium hexyl a-sulphopelargonate using the Wilhelmy plate drop-volume and pendant-drop methods. They conclude that the first two methods give reliable results which differ by no more than 1 5 % . Their pendant-drop apparatus lacked precision but gave values in accord with those of the other methods. For dynamic surface tension the technique used depends on the age of the surface; up to 30 milliseconds old the jet methods are used and for surfaces older than 200 milliseconds the excess bubble-pressure apparatus is convenient. However, for surfaces of ages 30-200 milliseconds there had been no useful method published until Austin Bright and S i m p ~ o n ~ ~ reported their extension of the maximum bubble-pressure technique by use of stroboscopic counting since the limitation in the normal method is the rate at which the bubbles can be counted visually (the limit is about 5 per second).Using the stroboscopic method rates of up to 50 per second were successfully determined. The dynamic surface tensions of Manoxol OT (Aerosol OT) in aqueous and aqueous NaCl solutions are reported. A new equation of state of mixed adsorbed spread or penetration mono-layers is presented by J 0 0 . s ~ ~ and tested for the system sodium laurate and sapoalbin which have very different saturation-adsorption values (previous attempts are applicable to systems for which the saturation values are equal).Agreement between theory and experiment is considered satisfactory. Soapfilms. One method of investigating the properties of the aqueous core of a foam film is the measurement of film conductance parallel to the surface and interpretation of the results in terms of surface conductivity although this method has received little attention. In their paper Clunie et u E . ~ ~ describe simultaneous measurements of thickness and conductivity on foam films drawn from aqueous solutions of the neutral surfactant C,6H33N+Me, (CH2)3SO; (C 6 sultaine) containing NaBr. The surface monolayers are formally uncharged and adsorb inorganic ions to produce an electrolyte excess in the core; the film ruptures when the thickness falls below that cor-responding with the secondary minimum (of the DLVO theory) arising from double-layer overlap between the two monolayers.The zeta potential calcu-lated using Bikerman’s theory of surface conductance decreases with in-creasing electrolyte concentration. Mysels and Joness6 have described a method using soap films for the direct measurements of the double-layer repulsion with distance hence forming a qualitative test of the DLVO theory. A soap film is formed in a ring of porous porcelain whose pores communicate to the outside with the film in an enclosure in which the air pressure can be varied. By applications of large pressure differences between air contacting the free surfaces of the film and the bulk liquid in the pores of the solid the film can be subjected to stresses exceeding ’’ M.Austin B. B. Bright and E. A. Simpson J . Colloid Interface Sci. 1967 23 108. 54 P. JOOS Bull. Soc. chim. belges. 1967 76 591. ’’ J. S. Clunie J. M. Corkill J. F. Goodman and C. P. Ogden Trans. Faraday SOC. 1967,63,505. ’‘ K. J. Mysels and M. N. Jones Discuss. Faraday Soc. 1966,42,42 Colloid and Interface Science 141 one atmosphere. The applied pressure is balanced primarily by the double-layer repulsion between the monolayers of the film so that as the pressure is increased the thickness decreases indicating how the double-layer repulsion varies with distance. SDS and sodium tetradecyl sulphate solutions were used and satisfactory agreement with theory was obtained for the region of low potentials which determined the slopes of the distance function.Reasonable agreement is found in the absolute values the calculation of which make certain assumptions about the high-potential region and film structure. In the thinning of soap films at short distances (10-20 A) the stability is governed by the interaction between solvation layers and any closer approach entails desorption which manifests itself as a rapidly increasing repulsive force as successive solvation layers are removed. This implies that primary-minimum (or Perrin) films are subject to very large pressure differences before they can be further thinned. In an investigation of this effect Clunie Goodman, and Symons5’ have measured film thickness of films from decyl trimethyl-ammonium decyl sulphate solutions containing NaBr as a function of relative water-vapour pressure.The results indicate that a strong repulsive force indeed exists which prevents film collapse at a limiting equilibrium thickness of 40 A corresponding to a thickness of the aqueous core of 12A. The magnitude of this force is of the order of that required for desolvation. A study of the stability of black films drawn from aliphatic hydrocarbon (n = 6 10 12 and 14) solutions of normal alkyl chain esters (n = 14 16 18, and 22) has been made by Taylor and Haydon.’* The film thickness is not determined by the chain length of the hydrocarbon solvent but the hydro-carbon part of the film is equal to twice the chain length of the ester molecules. Theoretical consideration of the force associated with the steric interference of the alkyl chains at the two interfaces on thinning indicates that a repulsion sufficient to stabilise the film comes into operation immediately the film becomes thinner than twice the chain length of the stabiliser.This study provides convincing evidence that interaction between the alkyl chains adsorbed on two approaching surfaces is responsible for the stability. It is generally assumed that the permeation of gases through insoluble monolayers is best described by an energy-barrier theory. The work of Princen, Overbeek and Mason59 suggests that for soluble monolayers the transport is governed by a simple diffusion mechanism which may be through aqueous pores between the surfactant molecules. Previously reported data of the authors on the permeability of very thin soap films (HTAB and NaBr) to various gases (He Ne Ar O, N, H, CO, and N,O) have been re-analysed, and the simple theory explains the results.A new technique for measuring film elasticity is described by Prins Arcuri, and van den Tempel,60 which involves simultaneous measurement of the ’’ J. S. Clunie J. F. Goodman and P. C. Symons Nature 1967,216 1203. ’* J. Taylor and D. A. Haydon Discuss. Faruday Soc. 1966,42 5 1. ” H. M. Princen J. Th. G. Overbeek and S. G. Mason J. Colloid Interface Sci. 1967 24 125. ‘* A. Prins C. Arcuri and M. van den Tempel J . Colloid Interface Sci. 1967 24 84 142 G. D. Parfitt increase in surface tension and the corresponding change in thickness. The measured elasticity of films drawn from aqueous solutions of SDS sodium decyl sulphonate and cetyl trimethylammonium bromide (CTAB) above and below the c.m.c.is compared with the composition and thickness of the films. As predicted by theory the Gibbs elasticity decreases with increasing film thickness and the agreement with theory of the relation between elasticity and composition is satisfactory provided the surfactant is pure. Insoluble monolayers There has been no systematic research published on the retardation of water evaporation by monolayers spread on the water surface of members of the series ofnormal fatty alcohols C 2-C20 which includes the odd members of the series. Noe and Dressler6' have measured the retarda-tion by the nine pure alcohols. A linear relationship exists between per cent evaporation retardation and chain length from 18 % for C12 to 65 % for C,O, with both odd and even alcohols fitting on the same straight line.A theoretical equation of state for monolayers of fatty acids on water has been developed for the liquid expanded state by Smith.62 Previous attempts at describing this state had met with little success. Smith's equation is where II is the surface pressure A the area per molecule n the number of carbon atoms in the chain d the chain diameter and E the minimum Lennard-Jones potential energy. It is based on a simple model with the CH groups acting as a stack of hard discs and the theoretical term for van der Waals cohesion between CH groups is combined with a co-area term developed for two-dimensional hard-disc fluids. The equation is tested with experimental data for a large number of saturated fatty acids.Although there are no adjustable paramerers the equation predicts the experimental variables A n and T to within about 15 % at a given value of II. The equation is also approximately valid for unsaturated fatty acids if n is replaced by 2.5 n where n is the number of carbon atoms to the double bond counting from the ninth carbon atom in the chain. Some attention has been paid to mixed monolayers. Lomonosova and Trape~nikov~~ have studied the temperature variation of the equilibrium surface pressure in monolayers on water of mixtures of straight-chain alcohols with odd numbers of carbon atoms (C and C ,). The mixtures were prepared either by fusing together the components or by normal mechanical mixing. The pressure-temperature curves exhibit breaks which are associated with phase changes.Of particular interest is the behaviour in the temperature range adjacent to the melting point in which 'dips' had been previously observed for the certain single alcohols and substituted alcohols and presumed due to the presence of homologues. Differences were observed between the melts and 6 1 E. R. Noe and R. G. Dressler Ind. and Eng. Chem. (Product Res. and Develapmenr) 1967,6 132. 6 2 T. Smith J . Colloid InterfQce Sci. 1967 23,27. 63 T. A. Lomonosova and A. A. Trapeznikov Zhur.fiz. Khim. 1967,41 384 Colloid and Interface Science 143 mechanical mixtures but no 'dips' were found indicating that these are associ-ated with structural effects. A theory is developed by Joos Vochten and R ~ y s s e n ~ ~ which permits calculation of the surface shear viscosity of a mixed film if the flow parameters of each single component are known.It is assumed that the free energy of viscous flow for the mixture is proportional to the mole fractions of the com-ponents in the surface and to the free energy of viscous flow of the single components. The surface viscosity of mixed adsorbed films of two saponins, digitonin and senegin is measured and used to test the equation; a good fit is achieved. Large deviations were found for the cholesteroldigitonin system suggesting interaction between the two components. The transfer of Langmuir-Blodgett monolayers of 4C-labelled stearic acid on to mica silica glass silver copper platinum and iron has been determined at surface pressures of 30 17.5 and 10 dynes/cm.by S ~ i n k . ~ ~ Using Geiger counting autoradiography electron microscopy and reflection electron diffraction the activity and the nature of the transferred films were determined. Particular interest was shown in the influence of the chemical nature of the substrate on the deposition process ; large-grained polycrystals of silver were used to study the anisotropy of deposition and the influence of surface roughness and lattice defects investigated on thin (1 11) crystals and polycrystalline films of silver condensed on mica and glass. Also the dependence on piston oil pressure pH of the aqueous substrate and the rate of withdrawal of the specimen was examined. The paper contains a number of electron micro-graphs of the deposited layers.The transfer ratio (fraction of close-packed stearic acid monolayer that can be transferred from a water surface) is found to be uninfluenced by the pH between 2 and 6 the piston oil pressure between 10 and 30 dynes/cm. and the rate of transfer between 2.5 and 12.5 mm./min. The stability of the transferred films reflect the competition between water and the acid for the solid surface e.g. they are stable on mica but collapse on silica and glass. For atomically-smooth silver surfaces the transfer ratio may be as low as 0.5 and depends on rate of transfer and crystal orientation; it is least for crystal faces close to (1 11). Further work by the same author66 concerns the rate of desorption of l4C-labe1led stearic acid from Langmuir-Blodgett monolayers in vacuum over the temperature range 2142.5" for mica substrates and 38-80" for thin (1 11) epitaxial silver films on mica (an examination of the stability of the layers is important since these layers are used in studies on lubrication flotation and adhesion).Activation energies of 43.3 and 10 kcal./ mole respectively were obtained. The process is largely zero-order. Again the sensitivity of the process to the structure of the surface on an atomic scale is demonstrated. The Solid-Liquid Interface.-The nature of the liquid phase adjacent to the solid surface continues to be controversial in particular with water. For some 64 P. Joos R. Vochten and R. Ruyssen Bull. SOC. chim. belges. 1967,76,601. 66 J. A. Spink J . Colloid Interface Sci. 1967 24 61. J. A. Spink J . Colloid Interface Sci.1967 23,9 144 G. D. Parfitt years Deryaguin has maintained that surfaces of glass and quartz have the ability to change the physical properties of water and other polar liquids over a relatively large distance. If this is the case then the implications in colloidal problems as well as in biology and medicine are far-reaching. In his most recent paper in English on the subject in relation to the stability of colloidal dispersions Deryaguin6’ has presented experimental evidence for the existence at lyophilic surfaces of thick (500-1000 A) boundary layers of polar liquids that have properties which differ from those of the bulk. He discusses his blow-off method for viscosity measurement the evaluation of shear elasticity modulus of a variety of liquids using piezoquartz the expansion of water in glass capillaries and the formation of ‘anomalous’ water of density and viscosity some 1-2-1-5 times higher than normal water.The paper is basically a review of the work already published in the Russian literature. Some n.m.r. studies of adsorbed water molecules in amounts from 1-15 monolayers on silica surfaces have been made by Clifford and Lecchini68 with particular reference to the effect of porosity surface coverage and temperature on the spin-spin and spin-lattice relaxation times of the water protons. The presence and size of micropores is shown to dominate the effect of silica surfaces both on the freezing behaviour and on both the relaxation times of adsorbed water. The effect of the surface on the spin-lattice relaxation is largely due to a reduction in molecular motion of the adsorbed water while the spin-spin relaxation is dominated by slow exchange with surface hydroxyl groups.The authors review the general principles but conclude that the lack of a satisfactory theory prevents firm conclusions about molecular mobility being drawn from the n.m.r. results. A model system for the study of hydrophobic interactions between water and hydrocarbon is proposed and investigated by with the mechanism of stabilisation of protein structures in mind. Small glass beads treated with dichlorodimethyl silane behave as uniform particles of solid hydrocarbon but with effectively zero solubility in non-polar solvents. In non-polar solvents they remain as individual beads but in ‘ordered’ liquids such as water or formamide they undergo normal hydrophobic interactions and consequently aggregate into clusters.Experiments were carried out to determine the con-centration of additive which must be added to water to cause the change over from clusters to individual beads i.e. to reduce the interfacial tension appropri-ately. The additives include the short-chain alcohols formamide urea SDS, dimethylsulphoxide etc. and form a useful series for comparing the effect on hydrophobic interactions with that on liquid structures. Bailey and Kay7’ have carried Jut a detailed investigation of the influence of vapour liquid and oriented monolayers on the interfacial energy of mica. Using a cleavage technique solid-fluid interfacial energies were measured.In 67 B. V. Deryaguin Discuss. Faraday SOC. 1966,42 109. 6 8 J. Clifford and S. M. A. Lecchini SOC. Chem. Znd. Monograph 1967,25 174. 69 R. Cecil Nature 1967 214 369. ’O A. I. Bailey and S. M. Kay Proc. Roy. SOC. 1967 A . 301,47 Colloid and Interface Science 145 this method the work done to cleave a thin strip of mica is determined by measuring the forces required to maintain given separations at the ends of the mica strip. High resolution multiple-beam interference fringes were used to determine the area. The mica was cleaved first in an atmosphere of vapour and then in the corresponding liquid to give the solid-vapour and solid-liquid interfacial energies. Using water and hexane Young’s equation was verified for systems with zero contact angle.For the first time it has been possible to make independent measurements of each of the interfacial energies involved in the equation. The interfacial energies obtained were cleavage in water vapour 182.8 & 0.3 erg/cm.2 in liquid water 107.3 & 1.1 erg/cm.2 in dry hexane vapour 271 f 1 erg/cm.2 and in dry hexane liquid 255 f 1 erg/cm.2 The technique was also used to determine the work done in separating mica surface covered with an adsorbed monomolecular layer of lauric acid ; a value of 37 erg/crn.’ for the surface energy of the acid monolayer on mica was obtained. The interface between ice and silica surfaces is according to Anderson,71 separated by an essentially liquid-like unfrozen interfacial layer of water, the thickness of which varies with temperature.Between 0 and - 5” the thick-ness ranges from 15-45 A but below - 5” to liquid nitrogen temperature the thi’ckness decreases only from 6-3 A. At low temperatures it appears that the mobility of the interfacial water is much reduced and it may assume properties approaching those of the solid. The evidence is obtained from published work on frozen montmorillonite-water systems and from other related observations ; the work of Deryaguin and his collaborators is not discussed. In a second paper by the same author72 the nucleation of ice on clay mineral surfaces is considered with particular reference to the liquid layer discussed above. The conclusion is drawn that it is not ne-cessary for embryos to form by direct attachment to the surface but may originate some distance away in the unfrozen region adjacent to the surface.It is envisaged that various kinds of ordering are brought about in water by interaction with a substrate and one form of the icelike structures might lead to an embryo. Anderson claims that the theory accounts for all the experimental observations so far reported. The effect of liquid in the region between two identical wetted solid spheres in contact on the force of adhesion has been estimated theoretically by Gillespie and S e t t h ~ e r i ~ ~ from the equations of Radushkevich and Melrose for the capillary pressure. Calculated data are presented relating the force of adhesion resulting from the capillary action to the amount of liquid the particle radii, the surface tension and the contact angle.Some experimental data with glass spheres and mineral oil or water are compared with the theoretical results and the agreement is reasonable. Contact ungle. The methods for the measurement of contact angles of liquids on solid surfaces are well known and lead to numerous problems of ’’ D. M. Anderson J . Colloid Interface Sci. 1967 25 174. ” D. M. Anderson Nature 1967,216,563. ” T . Gillespie and W. J. Settineri J . Colloid Interface Sci. 1967 24 199 146 G. D. Parfitt interpretation. Longman and Palmer74 describe two new microscopic methods for determining the contact angle of small droplets of liquid deposited on a surface which involve interference microscopy and either reflected or trans-mitted light. Both methods rely on the resolution of interference fringes and thus the contact angle that enables the fringes to be resolved to the edge of the drop is normally the largest angle that may be measured.These are estimated as 15 and 30" for the reflected and transmitted light methods respectively. The time involved in the experiments is rather longer than for the more usual methods but the accuracy is greater particularly for small angles. For fibres a new technique has been described by Jones and Porter75 which involves a refinement of the light-beam reflection technique for use with filaments and microscope equipment. Previously contact angles were determined from photo-graphs of the liquid-surface silhouette near the point of contact. It is claimed that the new method is rapid and more accurate particularly when small angles are involved.In the measurement of contact angle very little has been said on the way in which the angle changes when the three-phase line of contact moves or is caused to move over the solid surface. Dynamic studies of contact angle bear the same relationship to static equilibrium measurements as does any other kinetic-rate study to the corresponding state of equilibrium and hence they provide information which cannot be obtained from static measurements. Elliott and R i d d i f ~ r d ~ ~ have described an apparatus and procedure for growing a bubble of one fluid with constant radial velocity between parallel solid plates, so displacing a second fluid. By reversing this process both advancing and receding angles can be studied as a function of interfacial velocity.Results are given for the displacement of air by water between two siliconed glass plates at 22 and 42" and between polythene plates at 22". Also of a water-saturated hydrocarbon oil (Bayol D) between siliconed glass plates by oil-saturated water and by an aqueous potassium laurate solution at 22". In all the systems they found a definite dependence of the advancing and receding contact angles on the interfacial velocity except at very low speeds. The contact angle of water on ice has been measured by Knight;77 this is the first reported measurement of the contact angle between the molten and crystalline states of the same material. The experiment was carried out by pouring boiling distilled water onto a copper plate previously cooled to - 70" with dry ice and successive photographs taken of the puddle for a period of several seconds.The intersection lines traversing the surface of the puddle, were observed; the water was forced back by the advancing intersection line (suggesting ysv < ysl + ylv) and maintained a sharp angle with the ice surface. Photographs illustrate the effect. The apparent intersection angle decreases with decreasing freezing rate and a minimum value for the receding contact 74 G. W. Longman and R. P. Palmer J . Colloid Interface Sci. 1967 24 185. 7 5 W. C. Jones and M. C. Porter J . Colloid Interface Sci. 1967 24 1. 76 G. E. P. Elliott and A. C. Riddiford J . Colloid Interface Sci. 1967,23,389. 77 C . A. Knight J . Colloid Interface Sci. 1967,25 280 Colloid and Interface Science 147 angle of water on ice is 12 1” at slightly below 0” at a receding rate of about 1 cm./sec.on a somewhat rough surface. The old problem of contact-angle hysteresis is considered by Dettre and Johnson78 in some studies on the wettability of porous surfaces. An ‘idealised’ model porous surface was generated on the computer and the wettability compared with water contact angles measured on specially prepared porous surfaces of polyethylene polypropylene paraffin wax and a fluoro-carbon polymer using the sessile-drop profile method. The theoretical curves using one adjustable parameter are consistent with the experimental results. This parameter is the ‘drop energy’ which is the smallest energy barrier which the liquid drop is unable to cross. This energy barrier is between any two meta-stable configurations (of which there are many) of the drop on the porous surface i.e.between regions of different contact angles as when the liquid periphery crosses air spaces between the solid regions. Under such circum-stances the familiar equation of Cassie and Baxter does not apply. Wetting. Equations which describe the shape of a bubble or drop resting on an inclined surface have been derived by Larkin” using the capillary equations of Bashforth and Adams (1883) and the solutions tabulated. Application of the results requires a definition of contact angle for interfaces resting on an inclined plane. Experimentally the contact angle varies around the line of solid-liquid-vapour contact and this is shown by the calculations.It is suggested that there is a point on the three-phase line at which the Dupre equation would apply. This point is selected such that the normal to the three-phase line which lies in the inclined surface is perpendicular to the local gravity vector. Drop weights were predicted from advancing and receding contact angles and showed reasonable agreement with experimental values. The free-energy changes associated with wetting and displacement are considered by Melrose.80 The duplex-film hypothesis of Harkins which for spreading conditions is equivalent to both Antonoffs rule and Young’s equation is shown to follow from the analysis due to Gibbs of the stability conditions governing the film adsorbed from the vapour phase. The associated free-energy changes are discussed.A modified form of the Bartell-Osterhof equation is then developed which provides a relationship between the observed wetting parameters displacement and adhesion tensions. This relation is applied to available data for water and n-decane in contact with polytetra-fluorethylene and polyethylene but the problems of contact-angle hysteresis make interpretation difficult. The fundamentals of wetting phenomena in capillary systems are re-examined by Blake Everett and Haynes,8 ’ with particular reference to the use of the Washburn equation to describe two-phase capillary flow and illustrated by some experiments using. a water-benzene interface in a hori-R. H. Dettre and R. E. Johnson SOC. Chem. Ind. Monograph. 1967,25 144. ’’ B. K. Larkin J . Colloid Interface Sci.1967,23 305. 8o J. C. Melrose SOC. Chem. Ind. Monograph 1967,25 123. 81 T. D. Blake D. H. Everett and J. M. Haynes SOC. Chem. Ind. Monograph. 1967,25 164 148 G. D. ParJitt zontally-mounted glass capillary to investigate the velocity-applied pressure behaviour. The results depend strongly on the state of the glass surface. The rate of approach to the equilibrium capillary rise in a vertical uncoated glass capillary using di-n-butyl phthalate against either vacuum or dry argon was also studied. The results demonstrate that the Washburn equation is valid (with exceptions) if it is accepted that the derived dynamic contact angles used are reasonable; The point is made that a complete study of the Washburn equations should be carried out with all the observable parameters studied in the same experiment.Bernett and Zisman82 have discussed the effect of terminal branching and chlorine substitution on the critical surface tension yc of fluorinated carboxylic acids. It had previously been shown by Zisman that a surface rich in covalent florine atoms has a yc which is lower than that containing any other chemical constituent. The lowest value was achieved with a smooth solid surface coated with a condensed monolayer of perfluorododecanoic acid but small departures from adlineation by modifying the structure to prevent close-packing caused significant changes in yc. In this paper the effect on yc of terminal branching and of replacing the terminal fluorine with chlorine is studied for two homologous series of acids (CF3)2CF(CF2),C02H and CF2Cl(CF,)CF(CF2),C02H with n = 11-1 and 9-1 respectively adsorbed on discs of chromium and platinum.Contact-angle measurements on homo-logous series of n-alkanes open-chain polydimethylsiloxanes and various other liquids were carried out to give yc values. In every case yc was increased significantly by branching or terminal chlorine substitution and in most cases (except for the lower homologue acids) the results were independent of the surface. The effect of adsorbed water on the spreading of organic liquids on soda-lime glass is reported by Shafrin and Zi~rnan.'~ Increasing the relative humidity increased the contact angle for many non-hydrophilic liquids on glass; the high-energy glass surface is converted into one that behaves as a low-energy surface i.e.one with a low yc towards non-hydrophilic liquids. Increasing the thickness of the adsorbed water layer leads to a surface with decreasing yc approaching that of bulk water. This work relates to the adhesion of the fibres and the resin binder in the manufacture of glass-fibre-reinforced plastics and is particularly pertinent because of the paucity of experimental data on the effect of thickness of an adsorbed water film on the ability of organic liquids to spread on a hydrophilic solid surface. The thickness of a wetting film which is left when a liquid drains from a smooth plate is discussed by Read and Kit~hener,'~ with experiments carried out on the silica-water system and a theoretical treatment based on Deryaguin's 'disjoining pressure' concept.They explain that disjoining pressures may be calculated by considering four types of physical force namely Born repulsion 8 2 M. K. Bernett and W. A. Zisman J . Phys. Chem. 1967,71,2075. '' E. G. Shafrin and W. A. Zisman J . Amer. Ceram. SOC. 1967,50,478. 84 A. D. Read and J. A. Kitchener SOC. Chem. Ind. Monograph 1967,25,300 Colloid and Interface Science 149 forces permanent-dipole interactions London dispersion forces and electrical double-layer forces. Although the first two may often be neglected this is not the case when dipolar molecules are oriented at the surface leading to ‘auto-phobism’ or when surfaces are ‘hydrophobic’ to highly associated liquids. In the case of thick layers of dilute electrolyte solution (as in this work) the disjoining pressure may be calculated by summing the long-range repulsion with the London energy.An apparatus is described for the measurement of the thickness of the wetting films and compared with that predicted by the theory using the zeta potential and assuming that no electric field passes through the air-water interface i.e. the double-layer structure between the plate and air is exactly equivalent to that in one-half of a plate-water-plate system having double the thickness and the same potential on both plates. The thickness of the wetting films obtained were of the correct order of magni-tude ( lo3 8 and decreasing with electrolyte concentration). Heats of wetting. The thermodynamic relations between quantities obtained from an immersional heat curve and the heats derived from adsorption iso-therms have been examined by Melr~se.~’ It is verified that the immersional heat decrement is an integrated isosteric heat and not related to the film pressure and its temperature coefficient by means of an equation of the Gibbs-Helmholtz type.The interpretation of gas-adsorption data on homogeneous surfaces (e.g. graphitised carbon black) has been successfully carried out but no immersional heat-coverage data have been reported. This paper predicts the form of relationship between heat and coverage namely that a maximum can be expected in the curve prior to the completion of the first layer. Using the theory of additivity of intermolecular forces proposed by Fowkes (1963) the contributions due to dispersion forces polarisation forces and hydrogen bonding to the interaction between Graphon and rutile with organic liquids of varying polarity (n-butyl derivatives) are estimated by Lavelie and Zettlemoyers6 from heats of wetting data.For Graphon the average dispersion-force contribution to the heat of wetting is 110 erg/cm.2 and for rutile 146 erg/cm’. Dispersion forces alone account for the heat liberated in forming the Graphon-organic liquid interface but the rutile value involves a minor contribution due to polarisation of the liquid by the electrostatic field of the solid. Approximately 70% of the interaction energy for heptane on rutile is due to dispersion forces and the remaining 30% due to polarisation of the hydrocarbon by the rutile. For butanol on rutile the major contributor is dipole-dipole interaction with less than 10 % due to hydrogen bonding.An attempt has been made by the Whalen and Wades7 to verify the thermo-dynamic relationships proposed by Melrose (1969 which relate the adhesion energy between a liquid and a solid to the heats of immersion and spreading pressure or to the contact angle and its temperature dependence. In principle a comparison of measured contact angles with adsorption data and/or im-*’ J. C. Melrose J . Colloid interface Sci. 1947 24,416. 86 J. A. Lavelie and A. C. Zettlemoyer J . Phys. Chem. 1967,71,414. ” J. W. Whalen and W. H. Wade J . Colloid Interface Sci. 1967,24 372 150 G. D. Parfitt mersion heats obtained on analogous systems can resolve questions related to the operational validity of contact angles and test the relationship.However, there are uncertainties involved in establishing values for the spreading pressure and immersion heat associated with an adsorbed film at saturation pressure and also in the measurement of the contact angle-temperature relationship. Nevertheless Whalen and Wade considered it worthwhile to establish signs and limited values of magnitudes for the pertinent parameters, and in their study used the low-energy material Teflon-6 and alternate members of the homologous series of n-alkanes from hexane to hexadecane. Because the heat evolved is so small a large number of immersion heats were determined for each hydrocarbon. For the series the adhesion energy is constant at 32 f 2 ergs/cm.’ for Clo and higher and for the lower members the energy increases sharply approaching the liquid-surface energy as a limiting value.It is estimated that the temperature-dependence of the contact angle is negative spreading-pressure terms are negligible for C, and higher and where significant ad-sorption occurs the temperature derivative of spreading pressure is negative. The authors also demonstrate that for many interfacial systems the contact angle can be obtained from a single heat of immersion value. Adsorption at the solid-liquid interface. Two papers have reported potentio-metric studies at the ferric oxide-aqueous solution interface. The work of Atkinson Posner and Quirk88 assumes that the surface charge is determined by the transfer of H+ and OH- ions across the interface. From data in solutions of high ionic strength of indifferent electrolyte (KC1) equations are derived for the net adsorption density ( r H + - r o H - microequivalents per gram) by equating the electrochemical potentials of potential-determining ions and indifferent counterions in the solution and surface phases and neglecting counterions in the diffuse layer.The equations contains interaction constants, and the dependence of these or the parameters on the particle surface area of the various precipitates used is not satisfactorily represented by the Brunauer-Emmett-Teller (BET) nitrogen area. It is concluded that the adsorbed counterions remain solvated and form ion-pairs with only a small proportion dissociating into the diffuse layer. A quantitative study of the time-dependent abstraction of H + and OH- ions from solution by crystalline ferric oxide precipitates is reported by Berube, Onoda and de B r ~ y n .~ ’ The experiment involved potentiometric titration of oxide suspensions with observations of pH drift with time after rapid displace-ment of the pH of the solution initially equilibrated with the solid at the zero point of charge. Also tritium exchange with the tritiated oxide was followed. The pH-drift experiments yielded a diffusion coefficient for protons into or out of the hydrated surface region of cm.2/sec. and an activation energy of 20 kcal./mole. The tritium-exchange experiments also yield a diffusion coefficient of cm.’/sec. and confirm the presence of a hydrated surface layer of thickness not exceeding 26 A (equivalent to four layers of chemisorbed 88 R.J. Atkinson A. M. Posner and J. P. Quirk J . Phys. Chem. 1967,71 550. 89 Y. G. Berube G. Y. Onoda and P. L. de Bruyn Surface Sci. 1967,7,448 Colloid and Interface Science 151 surface water). Comparison with published experimental data on Ti02, ZnO and A1,0 suggests that the diffusion model proposed earlier by the authors is to be augmented by a surface anion exchange between OH- and other univalent inorganic anions derived from the supporting electrolyte to account for the experimental facts. The properties of the zinc oxide-aqueous solution interface have been studied by Healy and Jellett.go Zinc oxide differs from the 'insoluble' oxides that owe their charge to the exchange of H+ and OH- ions in that it is partially soluble in aqueous media yielding hydrolysed species which in turn adsorb the over-all equilibrium again being determined by the activity of the Hf and OH- ions.This paper examines in detail the interfacial reactions of ZnO in water. Coagula-tion and electrophoresis techniques were used to examine the properties of the system as a function of pH and ionic strength. The surface charge at each pH is determined by the concentration and adsorption potential of each hydrolysed (charged and uncharged) 'Zn (11) species. Maximum aggregation occurs at a pH where the electrophoretic mobility is large and negative and this is assumed due to flocculation by polymeric zero-charged Zn (11) hydrolyzed species. No direct correlation between mobility and coagulation was observed. At no pH is the mobility reduced to zero in contrast to the insoluble oxides which exhibit a well-defined zero point of zeta potential.Aleksandrova and Kiselevg' have shown that it is possible to predict with reasonable accuracy for certain cases the adsorption isotherm for a binary liquid mixture on a solid surface. The requirement is strong specific adsorption of one component and non-specific adsorption of the other and the estimate is made in terms of the heats of adsorption of the individual vapours of the components. The equilibrium constant for the system n-octene n-octane, zeolite NaX is estimated using the equation K = exp[Hzr" - H,"~~""]/RT where Ha is the heat of adsorption from the vapour at low coverage and from it the Gibbs adsorption isotherm is determined.Agreement between the pre-dicted and experimental curves is good. Using the thermodynamic treatment of Everett (1964) an analysis of adsorp-tion and heat of immersion data of binary liquid mixtures of benzene and cyclohexane on silica gel was carried out by Lu and Lama.92 The adsorbates were chosen as they are of approximately the same size. Using activity-coeffi-cient data for the bulk phase the activity coefficients for the molecules in the adsorbed phase were determined. For both components the surface-activity coefficients are close to unity over the entire mole-fraction range except for the cyclohexane at low bulk and surface mole fractions. A value of 10.47 was calculated for the thermodynamic equilibrium constant. From published 90 T. W. Healy and V.R. Jellett J . Colloid Interface Sci. 1967 24 41. 91 G. Ya. Aleksandrova and A. V. Kiselev Zhur.fiz. Khim. 1967,41 1197. 92 B. C. Y. Lu and R. F. Lama Trans. Faraday Soc. 1967,63,127 152 G. D. Parfitt heats of mixing data the heats of mixing in the surface phase were evaluated and found to be significantly higher than those for the bulk liquid. A similar study to that just described has been reported by Wrightg3 using benzene + cyclohexane benzene + carbon tetrachloride and carbon tetra-chloride + cyclohexane mixtures with two charcoals as adsorbents. Adsorp-tion and heats of wetting data are reported and the data treated using Everett’s thermodynamic theory to see how far these real systems conform with or deviate from the requirements of perfect and regular surface behaviour.In general these systems approximate to regular surface behaviour (with some exceptions) and also to perfect surface behaviour over a wide concentration range despite the intrinsic non-ideality of the system. It is suggested that the equations may not be sensitive enough to distinguish between regular and perfect behaviour or the systems chosen are intermediate in character and satisfy both situations to some extent. One of the primary difficulties in analysing composite adsorption isotherms for the adsorption of binary liquid mixtures on solid surfaces to obtain isotherms for the individual components is the evaluation of the monolayer values for each component. Using molecular models or vapour-adsorption data is satisfactory when both components adopt the same configuration on the surface, but as Day and Parfittg4 point out difficulties arise in describing the surface layer when the molecules take up different orientations.Using data for alcohol-xylene (or heptanekrutile systems in which it is assumed that the hydrocarbon lies flat and the alcohol adopts a perpendicular orientation it was found neces-sary to include multilayers of hydrocarbon to define the mixed ‘monolayer’ thick film and successful interpretation of the composite adsorption data was then achieved. Comparison between adsorption from liquid mixtures at the liquid-vapour and liquid-solid interfaces is the subject of two papers. Aveyard’Sg5 paper is primarily concerned with the former interface and concerns binary n-alkane mixtures(6 + 16,6 + 14,6 + 12,7 + 16,8 + 16,lO + 16,and 10 + 14)and the applicability of the surface-tension data of the equation of Butler of Hoar and Melford and of Prigogine and Morechal.The equations fit the data well if it is assumed that the molecules lie flat at the surface. Adsorption of the 8 + 16 mixture on Graphon was compared with that derived from the surface-tension data. Octanol is preferentially adsorbed at the vapour interface but on Graphon hexadecane is preferred i.e. the component with the lower surface tension is adsorbed preferentially at the liquid-vapour interface. Nagy Schay and Szekrenyesyg6 classify composite adsorption isotherms for binary liquid mixtures on solid adsorbents into five basic types according to the degree of preferential adsorption of each component.Using the Gibbs adsorption isotherm they have shown that surface-tension data lead to all the five types 93 E. H. M. Wright Trans. Faraday Soc. 1967,63 3026. 94 R. E. Day and G. D. Parfitt J . Phys. Chem. 1967,71,3073. 95 R. Aveyard Trans. Faraday SOC. 1967,63,2728. 96 L. G. Nagy G. Schay and T. Szekrenyesy Acta. Chim. Acad. Sci. Hung. 1967 53,145; Magyar Ktm. Folydirat 1967,73,299 Colloid and Interface Science 153 being encountered at the liquid-vapour interface although there is an essential difference between the adsorption process at the two interfaces. An analysis is made of the conditions which determine each type of isotherm at the liquid-vapour interface in terms of the thermodynamics of the adsorption process. By careful choice of three different adsorbate solutions the total surface area, and the individual contributions of the carbon and hydroxyapatite components of bone char have been determined by Bennett and Abram.97 The total surface was measured by adsorption of Manoxol OT (Aerosol OT) from aqueous solution the carbon surface by CTAB from aqueous solution and the hydroxy-apatite by Manoxol OT from benzene solution.The adsorbates have very different interactions with the hydrophobic and hydrophilic regions according to the solvent used. Samples of bone char were progressively decarbonised to nearly zero and the changes in the individual surface areas measured; in all cases the sum of the carbon and hydroxyapatite areas remained equal to the BET nitrogen area. Based on the diffuse double-layer theory van den Hul and Lyklema'' have demonstrated that the specific surface areas of suspended charged particles may be derived from the measurement of the negative adsorption of co-ions.The advantage of this method is that it requires no molecular cross-section of an adsorbing molecule or ion. The method is illustrated with AgI suspensions with areas between 1 and 5 m.2/gm. and prepared by different methods. The relationship between area and negative adsorption is based on isolated flat double layers (no solution for spheres is available) the deviations from these criteria in the experimental system is shown to be small and the areas calculated are in good agreement with those estimated from double-layer capacity measurements. The Characterisation of Solid Surfaces.-Chemical structure.Investigations of the nature and quantity of hydroxy groups on the surface of oxidic substances continue to make progress as new techniques and more instrumental precision become available. Boehm and Herrmann99 used three methods (deuterium exchange acetylation and reaction with thionyl chloride) for estimating the concentration of surface hydroxy groups on a non-porous anatase sample of area 56 m.2/gm. After outgassing at 150" there are 4.9 hydroxy groups/100 A2 compared with the estimated average of 12-14 for a fully-hydroxylated surface. Thermal decomposition of the surface hydroxy groups occurred at outgassing temperatures below 200" and was apparently complete at 350". On exposure to water vapour at various temperatures up to 290" only half the original number of hydroxy groups were reformed but under liquid water the surface was completely rehydroxylated.For silica surfaces the adsorbed water and the silanol and siloxane were estimated by Kellum and Smith1'' using various techniques. The silicas used included pyrogenic (Cabosils) precipitated and 97 M. C. Bennett and J. C. Abram J . Colloid Interface Sci. 1967 23 513. 98 H. J. van den Hul and J. Lyklema J . Colloid Interface Sci. 1967 23 500. 99 H. P. Boehm and M. Herrmann Z . anorg. Chem. 1967,352 156. loo G. E. Kellum and R. C. Smith Analyt. Chem. 1967 39 341 154 G. D. Parfitt wet-process samples with surface areas 200-600 m.2/gm. A modified Karl-Fischer titration gave rapid and precise determination of adsorbed molecular water in the presence of hydroxy and siloxane groups and compared favourably with results using azeotropic distillation and thermogravimetric analysis.The method of catalytic condensation with boron trifluoride acetic acid and pyri-dine gave values for the water and silanol which compared with those from the thermogravimetric and thermal-condensation (at lO00") methods. Estima-tion of the sum of adsorbed water and strained siloxane rings with reactivity greater than that of hexamethylcyclotrisiloxane was possible by reaction with methanol and conventional Karl-Fischer reagent using a recording biampero-metric apparatus to follow the reaction. The results indicate that a marked decrease in silanol group population with a quantitative increase in strained siloxane occurs at temperatures of 150" and below.Complete removal of surface water (molecular and hydroxy) is only achieved at temperatures in excess of 400". Strained siloxane bridges are stabilized by thermal effects above 150". The surface hydroxy groups on silica alumina and silica-alumina catalysts were determined using a variety of organometallic compounds by Sato et ~ 1 . ' ~ ' Experiments were carried out in a closed system under a nitrogen atmosphere and the volume of ethane produced was measured. To determine the total hydroxy content triethylaluminium is the most convenient ; other compounds show varying reactivity according to the nature of the hydroxy site e.g. tri-ethyl borane does not react with silica-alumina containing a strong Bronsted acid site.The hydroxy groups on the surface of various samples of magnesium oxide (from thermal decomposition of the corresponding hydroxide) have been studied by Faure Fraissard and Imelik,lo2 using diborane trimethylchloro-silane methyl magnesium iodide and by deuterium exchange the latter being the most successful. 1.r.analysis shows a sharp band at 3690 cm.- ' and a less intense band at 3640 cm.-' due to OH-stretching after outgassing at 150"; at higher temperatures a band appears at 2740 cm.-' as a result of some dehydroxylation. Deuterium exchange did not go to completion and indicated that the major part of the total water exists in the bulk of the solid. Hughes and White'03 report a study of the surface structure of decationised Y zeolite by quantitative i.r.spectroscopy. The integrated absorption in-tensities accessibilities relative acidities and hydrogen-bonding characteristics of the hydroxy groups giving 3650 cm-' and 3550 cm-' bands in the i.r. spectrum were studied. These bands are assigned to the hydroxy groups associated with the aluminosilicate portion of the zeolite. Adsorption of piperidine demonstrates that both hydroxy groups are protonic acids and are accessible to molecules in the large intercrystalline channels but the concentration of these sites is much smaller than the ion-exchange capacity. Using pyridine the hydroxy group with a band at 3650 cm-' is shown to be a stronger Bronsted acid than that with 3550 cm-' and experiments with M. Sato T. Kanbayashi N. Kobayashi and Y . Shima J . Catalysis 1967,7 342.T. R. Hughes and H. M. White J . Phys. Chem. 1967,71,2192. lo* M. Faure J. Fraissard and B. Imelik Bull. Soc. chim. France 1967,2287 Colloid and Interface Science 155 t-butanol indicate the lower frequency hydroxy group is strongly hydrogen bonded to other oxygen atoms of the zeolite whereas the other hydroxy group is not. Dehydration at elevated temperatures convert the Bronsted sites to Lewis sites and exposure to water converts some of the Lewis sites to Bronsted sites but not necessarily to the original hydroxy groups. The study of physical adsorption of non-polar gases by decationated zeolites permits a more precise hydroxy band assignment since hydroxy groups on lattice points where they cannot interact with the surroundings will not be affected.White et al.lo4 have determined the shift and change in intensity of the OH-stretching bands of decationated Y zeolite following adsorption of N, O, CH4 Ar and Kr. Bands at 3677 cm-' and 3567 cm-' are assigned to hydroxyls in the supercage and in the cubo-octahedron respectively. The frequency of the shifted bands is almost unaffected by the amount adsorbed suggesting that the hydroxy environment in zeolites is homogeneous (as opposed to silica) hence with a simple electrostatic model it was possible to correlate the shift and intensity change of the 3677 cm- ' band to the dielectric constant of the polarisable adsorbed molecules. Low-energy electron diffruction andfield ion microscopy. Low-energy electron diffraction (LEED) has been widely adopted as a means of studying crystal surfaces but the mechanism of the interaction of low-energy electrons with crystals is not yet well defined.McRae"' has considered the central problem in diffraction theory as approached from the self-consistent multiple-scattering viewpoint of determining the effective wave field incident on each atom in the crystal. In his theory the author treats each atom layer of a model crystal explicitly and shows that the properties of the effective Geld imply the existence of two specific dynamical effects in LEED intensities namely the occurrence of fractional-order peaks in intensity curves and multiple-scattering resonance effects. Experimental evidence for both effects is cited. Future applications of the multiple-scattering approach to the effects of adsorption on intensities to thermal diffuse scattering to Kikuchi effects and to the effect of crystal size are discussed.The most complicated LEED patterns have commonly been explained in terms of single scattering leading to complex two-dimensional surface structures commensurate with the complexity of the diffraction patterns. Bauer1O6 considers this to be a result (in part) of a misconception of the diffraction process and is part of a consequence of the expectation that surfaces have a tendency to form two-dimensional structures. He demonstrates that the certain complex LEED patterns (Ag on Cu C on W etc.) can be interpreted in terms of multiple scattering by superimposed well-known structures. A LEED study of the structures of the clean (lOO) (1 1 l) and (1 10) faces of platinum is reported by Lyon and S~morjai,'~' experiments being carried out J.L. White A. N. Jelli J. M. Andre and J. J. Fripiat Trans. Faraday SOC. 1967 63 461. lo' E. G. McRae Surface Sci. 1967,8 14. E. Bauer Surface Sci. 1967 7 351. lo' H. B. Lyon and G. A. Somorjai J . Chem. Phys. 1967,46 2539 156 G. D. ParJitt in the range 300-1769" (melting point). Two types of surface structure, ordered and disordered were found and both types appear to be the property of the clean platinum substrates. The ordered structures appear during annealing after ion bombardment at <900" and are believed to be due to ordered arrays of vacancies in the substrate plane. The disordered structures appear at high temperatures they are irreversible and can only be removed by ion bombardment.The ratio of lattice parameters assigned to the diffraction rings on each substrate indicate that they can be due to domains of (111) surface structure and this disordered close-packed-hexagonal structure seems to be the stable high-temperature surface phase of platinum. Energy distributions of the electrons 'inelastically' scattered from the tungsten (1 10) surface for primary energies of 5&-250 ev have been obtained by Tharp and Scheibner'08 using a modified LEED system. The information obtained by examining both elastic and inelastic processes rather than from studying diffraction phenomena alone is discussed. In addition analysis of the mass spectra of desorbed species and the Auger peaks in the secondary electron-energy distributions have been used in addition to LEED to study the contamination on and near the surface demonstrating the usefulness of the combination of techniques to detect and identify impurities and to deter-mine their probable surface structures.have demonstrated with a variety of adsorbates (C6H3Br3 GeI, FeCl, ZnI, Br, C, Xe etc.) physically adsorbed on a graphite single crystal that LEED provides a powerful means of studying physisorption and related phenomena. Good patterns however were not obtained with C6H6 eel, C14H10 C6H4(OH) etc. Ordered structures are revealed with evidence for lattice gas and two-dimensional liquid and crystal phases the structure formed depending on the lateral forces. Desorption by the electron beam waiobserved but it was not a serious factor.Muller' lo reports that while ordinarily field ionization of helium in a field-ion microscope ocurs at a field of 450 mv/'cm. only 300 mv/cm. need to be applied when a small amount of hydrogen has been admitted. This promotion effect is shown to be due to adsorption of hydrogen and is explained by a rearrangement of surface charge transferring about to of an electronic charge from a protruding tungsten atom to an adjacently-adsorbed hydrogen atom to form a hydride-like bond. The introduction of hydrogen promotion reduces in many cases the evaporation field so much that the metal no longer yields to the field stress which previously arose because of the extremely high electric field necessary to operate a field-ion microscope. Now it is possible to use the microscope to study Fe Ni and Co and an extensive study of cobalt is reported by Nishikawa and Muller.'" The image quality was found to be satisfactory for viewing stacking faults twin boundaries and phase boundaries between hcp cobalt and fcc cobalt in atomic dimensions.Lander and lo8 L. M. Tharp and E. J. Scheibner J . Appl. Phys. 1967 38 3320. log J. J. Lander and J. Morrison Surface Sci. 1967 6 1 . ' l o E. W. Miiller Surface Sci. 1967 7,462. ' 0. Nishikawa and E. W. Miiller J . Appl. Phys. 1967 38 31 59 Colloid and Interface Science 157 Physical structure. The evaluation of pore-size distribution has attracted attention. Viswanathan and Sastri' '* suggest a simple method for computing the distributions in terms of surface areas instead of pore volumes directly from the low-temperature desorption isotherms of nitrogen.The equation, deduced from a model of the desorption process originally proposed by Wheeler (1955) is simple and does not require the use of a computer. The method when applied to published data obtained on a variety of porous solids gives results which are generally in good agreement with those found by the Brunauer-Emmett-Teller (BET) and Barrett-Joyner-Halenda (BJH) methods as are the distribution plots. The authors suggest that the distribution obtained directly in terms of the surface area is more relevant to catalysts and catalytic activity than the more usual volume-distribution functions. Another simplified approach this time using a modified form of the BET equations, has been proposed by Medema and C~rnpagner.''~ The method is not intended to be a substitute for the more refined methods but is considered to be of value as a quick first-approximation for technological purposes.The adsorption equation is simplified by assuming that the accessible surface areas are taken to be equal only for the first n adsorbed layers and from layer n on they are taken to decrease with a constant factor s < 1 such that = V for i < n and V;. = V si-" for i > n Here 6 is the amount of gas that can be adsorbed in layer i. A general isotherm equation is obtained which involves besides the volume adsorbed and the C constant the two parameters n and s. The capacity of the first layer agrees well with the BET monolayer capacity and the pore-size distributions are in qualita-tive agreement with the results of the more involved procedure associated with the Kelvin equation.All methods employed for pore-structure analysis were based on idealised models for the pore shapes (most assume cylindrical some parallel plate) until Brunauer Mikhail and Bodor' l4 published their analysis for pore volume and surface distributions without assuming any shape. The analysis is made in terms of hydraulic radii instead of Kelvin radii ; the hydraulic radius is defined as V / S where V is the volume of a group of pores and S the surface area of the pore walls. V is obtained in a conventional manner from adsorption or desorption isotherms while S is also obtained from the isotherms but by a new method based on Kiselev's (1958) method of surface-area determination.The volumes surfaces and hydraulic radii thus obtained are properties of the cores of a group of pores the core being defined as the empty part of a pore that contains an adsorbed film on its walls. In fact it is necessary in the calcula-tion to make corrections for the desorption from the walls of the empty pores and in this a shape is required. The authors claim that the corrections add little significant information to that obtainable from the uncorrected values. B. Viswanathan and M. V. C. Sastri J . Catalysis 1967,8 312. J. Medema and A. Compagner J . Catalysis 1967,8 120. 'I4 S. Brunauer R. Sh. Mikhaii and E. E. Bodor J . Colloid Interface Sci. 1967,24,451 158 G. D. ParJitt By small sacrifices in accuracy Lester"' has demonstrated that the time required (ca.40 hours) for the experiments and calculations in the determina-tion of pore-size distributions of catalysts from nitrogen-adsorption isotherms, may be reduced by about one-third. Only 12-15 experimental points are taken (usually 40 or more) and the regions between data are analysed using a modified form of the Halsey equation log (p/p,,) = - A / f l ; A and n are deter-mined by the two adjacent real data points. The agreement between computed and actual points is within experimental error. The calculation of the pore-volume size distribution then follows the method of Cranston and Inkley (1957) assuming cylindrical pores. Little accuracy is lost considering the time and effort saved. The evaluation of physical structure of the surface of porous solids using the t method (based on a standard adsorption isotherm for a non-porous surface) proposed by de Boer (1965) has been extended by Broekhoff and de Boer'16 to include open cylindrical pores.A combination of the t plot and characterisation of the hysteresis loop in the nitrogen-adsorption isotherm often leads to a clear picture of the pore system present. However there is some ambiguity with respect to the calculation of pore distributions from the adsorption branch. For isotherms exhibiting the A type of hysteresis loop, open cylindrical pores may be assumed but here the adsorption branch is only metastable with respect to the desorption branch and the Kelvin equations may not be applied. The authors have used simple thermodynamic arguments to show that the equation of Cohan (1938) for capillary condensation in open cylinders is not suitable for quantitative work.By introducing the universal t curve a model for the occurrence of hysteresis is given and quantitative relations are derived for the spontaneous filling of pores during adsorption as well as for the evaporation of capillary condensate on desorption in terms of the pore radius. It is shown that the thickness of the adsorbed layer in a cylindrical pore is expected to be different from that on a flat surface at the same pressure. With increasing pressure the adsorbed film in an open cylindrical pore becomes unstable at a certain pressure leading to spontaneous filling of the pore by capillary condensation. After filling hysteresis is found during desorption by the presence of a different form of meniscus capillary evapora-tion during desorption taking place at a lower relative pressure.Application of the equations requires a mathematical expression for the t curve in terms of RT In (pdp) as a function of t and this is derived in the second paper by Broekhoff and de Boer."' Numerical values for the radii of pores spontane-ously filling with capillary condensate at a given relative pressure are given, with which the pore distribution may be calculated. The results are shown to be a major improvement over the results obtained using the Cohan equation for capillary condensation. G. R. Lester J . Catalysis 1967,8,283. J. C. P. Broekhoff and J. H. de Boer J . Catalysis 1967,9 8.J. C. P. Broekhoff and J. H. de Boer J . Catalysis 1967,9 15 Colloid and Interface Science 159 Use has been made of the t plot by other workers. Day and Parfitt'18 show that the t method reveals the presence of micropores (cracks) in the surface of a pure rutile of surface area of about 30 m.2/gm. and that the standard BET method is not applicable for the determination of the specific surface for such material. Horlock and Anderson' l9 have studied beryllium oxide powders prepared by the thermal decomposition of P-Be(OH) in vacuo and contain a substantial volume of pores < ca. 6 A and < ca. 3 A. t plots give information on the micro-structure which is amplified by adsorption of molecules of various sizes and nature (He H20 and CCI,). With aluminium hydroxide gels Bye, Robinson and Sing'20 suggest that the t plot is a useful way of recognising the onset of reversible capillary condensation but emphasise that caution must be exercised in the applications to microporous solids and this is also illustrated in papers by Bye and Sing,'" and by Sing.'22 Surface area.The surface area and structure of a commercial activated alumina has been examined by Bowen Bowrey and Malin'23 by direct observa-tion using an electron microscope. From electron micrographs (shown in the paper) it was concluded that the sample contained regions of well-ordered pores approximately cylindrical in cross section with a mean diameter of 27 1 A and arranged hexagonally and other regions of random pores without characteristic size or shape between the particles.Some estimates of the proportion of the total BET surface (of 275 m.2/gm.) due to pores is given. A t plot suggests the existence of large macropores in which no condensation occurs and contributing an area of 18 m.2/gm. and these are assumed to lie between particles in the granules. Surface areas of 0.1-0.5 m.2/gm. have been determined using Kr-85 by Beurton Bussiere and Imelik.I2 Using a scintillation counter the pressure of the gas was determined as well as the amount adsorbed by direct measure-ment of the radioactivity of the sample and the area estimated by the BET method. A reproducibility of 10 % is claimed using various solid materials. Rootare and Pren~low'~' consider that no previous serious effort had been made to use the mercury porosimeter as a reliable surface-area measuring device and they show that surface areas can be calculated directly from stand-ard porosimeter pressure-volume curves without assuming a particular pore geometry.The results for 20 different powders with areas in the range 0-1-1 10 m.'/gm. compare favourably with those from BET measurements provided porosimeter pressures are high enough to force mercury into the smallest pores and that the mercury does not wet the powder (low-energy surfaces). The surface area and particle structure of Teflon-6 has been studied by 1 1 * R. E. Day and G. D. Parfitt Trans. Faraday Soc. 1967,63,708. lZo G. C. Bye J. G. Robinson and K. S. W. Sing J . Appl. Chem. 1967,17 138. lZ2 K. S. W. Sing Chem. and Znd. 1967 829. I f 3 3. H.Bowen R. Bowrey and A. S. Malin J . Catalysis 1967 7 209. lZ4 G. Beurton P. Bussiere and B. Imelik Bull. SOC. chim. France 1967 1793. 125 H. M. Rootare and C. F. Prenzlow J . Phys. Chem. 1967,71,2733. R. F. Horlock and P. J. Anderson Trans. Faraday SOC. 1967,63 717. G. C. Bye and K. S. W. Sing Chem. and Znd. 1967 1139. 160 G. D. Parfitt Whalen Wade and Porter'26 using nitrogen and argon isotherms. No linear BET region was observed for this low-energy surface and areas estimated from the isotherm show considerable discrepancy depending on the adsorbate and isotherm region selected. Electron-microscope areas were found to be significantly greater than the estimated maximum nitrogen BET area but in reasonable agreement with that using argon. It appears that Teflon-6 granules consist of fundamental particles connected by a filament network each particle being a two-phase system.The interior phase may consist of ordered polymer chains while the surface phase of lower density may consist of disordered, random-length polymer chains. The availability of a large number of data on the cross-sectional areas of molecules adsorbed on solid surfaces which have appeared since the last examination carried out by Livingston in 1949 have led McClellan and Harn~berger'~~ to re-examine the subject. Data for the adsorption of two or more gases measured on the same solid are collected and these values for 106 compounds (1 88 references) are tabulated as are cross-sectional areas calculated from molecular models critical constants or liquid density.It is concluded that the size of the adsorbed molecule is not constant but varies with the adsorbent temperature of adsorption and choice of reference sub-stances. Recommended values for cross-sectional areas are N (- 195") 16-2A2, n-C,H, (0') 44.4 81'. The calculated values tend to be lower than those from adsorption measurements. Surfaceenergy. Using published contact angles of water drops on solid noble-metal plates ThelenI2* has calculated using Fbwkes' theory (1964), the dispersion energies of the metals with the following results Ag 84.95, Au 121.63 Pd 129.86 and Pt 18956 ergs/cm.'. These values are shown to correlate with cohesive energy densities (C.E.D.) (hence to the energies of vaporisation) and with total surface free energy calculated from Cottrell's approximate equation (1964), Ar ( - 195 - 183") 13.8 .8L2 Kr (- 195") 20.2 A' C6H6 (20") 43.0 A' and ys = r (C.E.D.) - TS where r is the atomic radius and S the surface entropy (taken as 0.4 erg/cm.' deg.).Application of fundamental and statistical-mechanical principles to the terrace-ledge kink model of crystalline surfaces leads to a two-parameter theory of the anisotropy of surface tension (specific surface free energy) reports Gruber and M~llins.''~ Previous treatments of the surface free energy as a function of crystallographic orientation has been confined to absolute zero and the effect of a finite temperature on the free energy arising from configura-J. W. Whalen W. H. Wade and J. J. Porter J . Colloid Interface Sci. 1967 24 379. ''' A.L. McClellan and H. F. Harnsberger J . Colloid Interface Sci. 1967,23 577. ''* E. Thelen J . Phys. Chem. 1967 71 1946. E. E. Gruber and W. W. Mullins J . Phys. and Chem. Solids 1967,28 875 Colloid and Interface Science 161 tional entropy has been little discussed. The authors take into account this entropic effect and thus calculate the energy at a finite temperature ; the entropy term is shown to contribute significantly to the ledge free energy. Examples of the predicted anisotropy of surface tension are given for copper. Adsorption of Gases on Solids.-A generalised potential theory of adsorption is developed by Kuhn13' by deriving first the expression of the possible course of adsorption without the pressure variable and then completing this for the pressure-dependence of equilibrium by applying Polanyi's adsorption potential concept.The equation derived is when k and 6 are constants for a given temperature y is the power of the variation of potential with distance from a given adsorption site and p is provisionally the pressure corresponding to a supposed static-adsorption equilibrium with points of maximum surface potential. A different adsorption potential is assumed for each site and also a hemispherical loop is assumed to be formed on each site as the relative pressure increases. The equation is capable of representing all general forms of adsorption isotherms and contains four adjustable constants. Conventionally the calculation of the thermal-accommodation coefficient a associated with the energy transfer between a beam of gas molecules and a solid is based on the model of harmonic oscillation of the surface atoms and usually studies based on this model lead to a values much smaller than the observed data.Interaction-potential parameters are then adjusted rather than applying a more realistic model. Shin13 has assessed the effect of removing the approxima-tions of harmonic oscillation and using data for helium and neon on tungsten, nickel and iron shows that there is a large range of values of the ratio of the a values calculated with and without assuming harmonic oscillation. The author concludes that the logical step to improve the theory is to consider the an-harmonic behaviour of the surface atom. In general anharmonicity increases the probability of energy transfer over the model for simple-harmonic oscilla-tion.The dependence of adsorption properties on surface structure for bcc substrates is considered by Neustadter and Ba~igalupi,'~~ by applying the Lennard-Jones 6-12 atom-interaction potential to the calculation of the adsorption energy of an atom on to as many as 132 sites on a unit-cell surface area for each of the eight highest surface-density planes of a bcc substrate. A normalised adsorption energy is plotted as a function of position on a unit-''' I. Kuhn J. Colloid interface Sci. 1967 23 563. 131 H yung Kyu Shin J. Phys. Chem. 1967,71 1540. ''' H. E. Neustadter and R. J. Bacigalupi Surface Sci. 1967,6,246 162 G. D. Parfitt cell area of each plane for various adsorbate-adsorbent combinations and normalised values of maximum adsorption energies and minimum-surface diffusing-activated energies are obtained.The results are compared with data for the adsorption for variety of adsorbates (inert gases alkali metals and alkaline-earth metals) on transition-metal substrates and found to be in good agreement. The (1 10) surface is found to be the lowest energy configuration for the bcc crystal. Such a study of adsorption on an atomic scale is considered essential now that the field-ion microscope and the field-emission microscope have shown that the adsorption properties are strongly dependent on the atomic arrangement of the substrate. Adsorption in micropores is discussed by Dubinin. 133 Radical differences between adsorption phenomena taking place in micropores (effective radius from 5 4 to 13-14 A) and those on the surface of intermediate pores (15-16 to 1000-2000 A) or on non-porous adsorbents demand different theoretical approaches to describe and interpret the behaviour.Dubinin discusses the basic principles of adsorption in micropores associated with his 'theory of volume filling of micropores' and the new trends which involve empirical methods for calculating adsorption equilibria. Two extensions to the Ross and Olivier (1964) theoretical model for physical adsorption on heterogeneous surfaces are suggested by Hoory and Prausnitz. 134 In this model the surface is visualised as a collection of homogeneous patches, and variation in the adsorption potential from patch to patch are taken into account. However the model neglects possible variations in translational, rotational and vibrational energies and entropies of the molecules at the different patches.In this paper the effect of the variation of vibrational energy on the adsorption isotherm at low coverage is analysed. Furthermore the statistical distribution function of the adsorption potential over the different patches is considered not as previously with a Gaussian distribution but the log-normal distribution is proposed. Both extensions are tested on published data for adsorption of argon on a heterogeneous carbon black (black pearls). Apparently the effect of including vibrational-energy changes is small and no significantly large effects are caused if the complete Gaussian distribution is replaced by log-normal distribution.Hoory and P r a ~ s n i t z ' ~ ~ have also derived a systematic treatment for mobile monolayer adsorption of gas mixtures on homogeneous surfaces. By defining a surface fugacity for each component non-ideality of mixing in the monolayer is related to constants in the two-dimensional equation of state. The results are extended to heterogeneous surfaces using the surface-patch concept of Ross and Olivier; the theory is a generalisation to mixtures of the Ross and Olivier theory for pure gases. For this system three heterogeneity parameters were required two being the variances of the adsorption potential distributions for the pure components while the third is their covariance. 133 M. M. Dubinin J . Colloid Interface Sci. 1967,23,487. 134 S . E.Hoory and J. M. Prausnitz Surface Sci. 1967,6,377. S. E. Hoory and J. M. Prausnitz Chem. Eng. Sci. 1967,22 1025 Colloid and Interface Science 163 For non-polar chemically-pure gases good estimates of mixed-gas adsorption on heterogeneous surfaces using only data for the pure component are shown to be possible. Computed results for adsorption of ethane-ethylene mixtures on charcoal agree well with experimental data. Adsorption on oxides. The displacement of the i.r. absorption band due to free surface hydroxy groups as a result of their interaction with adsorbed molecules is associated with the energy of this interaction and the change in intensity gives further information on the effect. Galkin Kiselev and L ~ g i n ' ~ ~ report data on the interaction of a variety of molecules with Degussa Aerosil.The intensity ratio of the bands due to perturbed and free hydroxyls increases until a monolayer is reached. For a series of molecules of similar electronic structure (benzene and its alkyl derivatives) there is a linear frequency shift and intensity ratio with increase in total heat of adsorption and decrease of ionisation potential. A simple relationship of this kind does not exist for mole-cules of different electronic structure because of the different contributions of specific and non-specific interactions to the total heat of adsorption. An approximately-linear relation exists for such molecules when the difference between the heats of adsorption on hydroxylated and dehydroxylated surfaces is taken as the energy of the specific interaction with the surface hydroxyls.Precise gravimetric data extending down to p / p = 10- has been obtained by Whalen137 for nitrogen and benzene on two characterised silica surfaces, with a view to establishing the applicability of the BET method to both weakly and strongly interacting adsorbates on variable-structure surfaces of constant area. Both adsorbates are shown to interact with the surface in a manner dependent upon the substrate structure which was varied by outgassing at temperatures up to 400". The surface areas derived from nitrogen-adsorption data using the BET equation depends only slightly on the nature of the surface, and justifies the value of nitrogen for routine surface-area measurement (although gross differences may lead to larger variations).Benzene does not form complete monolayers or statistically-equivalent multilayers in the region of BET applicability and the adsorption is strongly dependent on the detailed chemical nature of the surface. Apparent compliance of the benzene data to the BET model is considered fortuitous. The Adamson-Ling treatment (1961) is used to obtain site energy-distribution functions from the adsorption isotherms. For nitrogen two peak functions are obtained which vary in accord-ance with the established oxide-hydroxide character of the surface but in contrast the spectrum of interaction energies for benzene is quite wide. These results are consistent with the known surface structures and with specific adsorbate interaction. The decrease 0 in surface free energy for adsorption of a gas on a solid surface is usually evaluated by application of the Gibbs adsorption equation to the observed isotherm such that 136 G.A. Galkin A. V. Kiselev and V. I. Lygin Zhur.jz. Khim. 1967,41 40. 137 J. W. Whalen J . Phys. Chem. 1967,71 1557 164 G. D. ParJitt P c$ = RTSn,dlnp 0 where n is the number of moles of gas adsorbed at pressure p. The evaluation of this integral presents a number of problems and since no general relation exists between n and p for more than a limited range of the isotherm it is usual to evaluate the integral by graphical methods involving different extrapolations. Glossman and Corrin' 38 have used the Dubinin-Radushkevich approach (1947) to describe data in the very low-pressure region as an aid to the extra-polation to zero pressure for their data on the adsorption of argon on anatase (the Harkins and Jura sample) at 76-91 and 89.39"~ down to relative pressures of ca.lop7. The data fit the Dubinin-Radushkevich equation at adsorption potentials greater than 2-2 x lo3. Differential and integral thermodynamic-adsorption functions were calculated and show that at a coverage of about 12 % of the BET monolayer a pseudo-monolayer effect is observed (maximum in the enthalpy functions and a minimum in the entropy functions). It is concluded that the anatase sample is composite with patches of high-energy sites occupying about 12 % of the total area. It is not often that the rate of physical adsorption or desorption of gases on solids is studied partly due to experimental difficulties and partly to a lack of theoretical basis (this is not the case with chemisorption).Micale and Zettle-moyer'39 have measured the rate of desorption of water from the rutile surface at 25 40 80 and loo" and using the Elovich equation modified so that the rate approached zero as the reversible water on the surface approached zero, obtained values of the rate constants. The modified form where b and P are constants q the amount adsorbed or desorbed at time t and A is the initial concentration of desorbable gas on the surface is empirical and the physical significance of the constants is not clear. The heat of desorp-tion varied from 8.0 to 5.9 kcal./mole with decreasing surface coverage but the small decrease does not appear to be significant and the values cannot be explained at the present time.The physical adsorption of nitrogen on ice powder prepared at 7 7 " ~ , reported by Adamson Dormant and Orem,14' indicates a fairly uniform and not highly polar surface. Annealing at - 70" leads to adsorption behaviour characteristic of a non-polar surface such as Teflon and surface inertness towards nitrogen reaches an extreme in the case of snow samples collected from two locations in California and Colorado. Ideas on the surface structure which follow from the data are discussed and the authors suggest that water and probably ice near its melting point exhibit an apparently heterogeneous surface the molecules in the surface rearranging to permit strong interactions 13* N. Glossman and M. L. Corrin J .Colloid Interface Sci. 1967,23 237. 13' F. J. Micale and A. C. Zettlemoyer J . Colloid interface Science 1967,24,464. I4O A. W. Adamson L. M. Dormant and M. Orem J . Colloid Interface Sci. 1967,25 206 Colloid and Interface Science 165 with the adsorbate. Freezing a clean surface at liquid-nitrogen temperatures so that no rearrangement can occur means that the surface retains its non-polar and essentially homogeneous nature. Measurement of the dielectric behaviour of gas molecules adsorbed on a solid surface by measuring the capacitance change of a test condenser filled with the adsorbent leads by application of the Clausius-Mosotti equation (or other equations) to the polarisability of the molecules in the adsorbed phase. However there are difficulties in the application of the equation but GrObnerl4l has demonstrated a method for the evaluation of relative polarisabilities for two gases by comparing the appropriate capacity changes and these relative values are shown to yield valuable information.His study includes N2 COz C2H2 CC12F2 and l,l-F,C,H on alumina (120 m.2/gm.). The capacitance change was non-linear for large surface con-centrations and it is considered that the polarisability a depends on the number of molecules adsorbed per unit surface i.e. a = A[1 - (N/S)B] where A and B are constants N is the number of molecules and S the surface area. B has the dimension of a surface area per molecule and defines an average distance at which the interaction of neighbouring molecules affects their polarisability.Adsorption on carbons. Graphite and the graphitised carbon blacks are popular adsorbents because of their characteristic surfaces and in particular the graphitised blacks provide ‘homogeneous’ surfaces for fundamental studies. Harris Hudson and Ross’42 describe a technique for the measurement of physical adsorption of gases at pressures as low as 10- lo torr on small solid samples of very low surface area (a few cm.2) whose structure can be charac-terised independently by X-ray diffraction and electron microscopy. The method is a variation on the ‘flash-filament’ technique and was used to study the adsorption of krypton (at liquid nitrogen and oxygen temperatures) on annealed pyrolytic graphite the surface of which was studied by means of electron microscopy.Over the pressure range 10- torr the isosteric heats vary from 5-6-3.5 kcal./mole. The results suggest a high degree of surface heterogeneity and that adsorption at low coverage takes place in interlamellar crevices less than 10 8 wide. In view of the strongly anisotropic properties of graphite the boundary surfaces of graphitic solids should present two arrays of adsorption sites one in the basal planes and the other in the prism faces of the graphite crystal. Different specimens of graphite should vary in surface properties according to the proportion of basal plane and prism faces that are present. This assumes that the anisotropic properties of the crystal extend into the boundary surface. D e i t ~ ’ ~ ~ has suggested that the high-temperature (OO) physical adsorption of C02 at low pressure (below 1 torr) provides sufficiently low coverage to discriminate between the adsorption sites.The adsorption isotherms presented 0. Grobner J . Chem. Phys. 1967,46,4381. L. B. Harris J. B. Hudson and S. Ross J . Phys. Chem. 1967,71 377 143 V. R. Deitz J . Phys. Chem. 1967,71 830 166 G. D. Parfitt in the paper for mineral graphite and annealed pyrolytic graphite a graphitised carbon black and a heat-treated coconut charcoal show two distinct regions of surface coverage separated by a wide plateau. At very low pressures (<Om01 torr) the adsorption is compatible with high-energy adsorption on one array of carbon atoms in the prism faces and at higher pressures the adsorption is on the more abundant basal planes. The similar behaviour for graphite graphitised carbon black and charcoal is significant.Some calculations based on the different electronic environment to which the adsorbed molecules are subjected (dispersion interaction) on the two types of sites leading to different interaction energies are published by Meyer and D e i t ~ ' ~ ~ and show that anisotropy has a definite influence on the adsorptive properties of graphite. Low-pressure isotherms (down to lop4 torr) for benzene toluene thiophene, cyclohexane and n-hexane are reported by Pierce and E ~ i n g ' ~ ' for graphitised Sterling MT (3100"). Usually isotherms are concave to the pressure axis at low coverage for a non-uniform surface and convex for a uniform surface; the convex shape is due to lateral interactions which cause an increase in the beat of adsorption as the coverage increases.Benzene isotherms below the freezing point are concave to the pressure axis at low coverage have a heat of adsorption equal to the heat of vaporisation during filling of the first layer show no change in V (monolayer volume) with temperature and show no lateral interactions at any coverage. These properties are explained in terms of strong localisation of benzene at lattice sites due to similarity of the aromatic nucleus hexagon to lattice hexagons of graphite. Toluene shows the same effect but the other adsorbates give normal convex isotherms. Concave isotherms for benzene on a graphitised carbon black (and convex for water) over the range 30-100" are reported by Beldjakova Kiselev and K0va1eva.l~~ Gas phase chromatography was used based on the method of Glueckauf (1945).Isosteric heats of adsorption were calculated and the results show good agreement with those obtained by static methods. Xenon adsorption isotherms (using Xe-133) for Sterling MT (3100") and Grapkon at surface coverages ranging from 10-'o-0.9 are reported by Cochrane et aE. 147 The small degree of heterogeneity associated with both adsorbents is confirmed. For Sterling MT Henry's law is closely obeyed for coverages 10-10-10-6 and for both carbons the adsorbed phase at high coverages is interpreted as a two-dimensionally mobile layer with adsorbate-adsorbate interactions. The homogeneity of the surface is considered the cause of the difference between the surface area from t plots and the BET values for graphitised carbon blacks and the former is considered to be correct by de Boer and co-workers.148 Stepped isotherms are normally obtained with graphitised carbon blacks, 144'E. F. Meyer and V. R. Deitz J . Phys. Chem. 1967,71 1521. 145 C. Pierce and B. Ewing J . Phys. Chem. 1967,71,3408. 146 L. D. Beldjakova A. V. Kiselev and N. B. Kovaleva Bull. SOC. chim. France 1967 285. 147 H. Cochrane P. L. Walker W. S. Diethorn and H. C. Friedman J . Colloid InterfuceSci., 148 J. H. de Boer J. C. P. Broekhoff B. G. Linsen and A. L. Meijer J . Catalysis 1967,7 135. 1967 24 405 Colloid and Interface Science 167 the steps corresponding to the filling of successive layers. In addition to the need for a homogeneous surface it is considered necessary that there must be strong lateral interactions between adsorbed molecules and that the tempera-ture must be such that thermal agitation of the adsorbed molecules does not erase the discontinuities between the filling of adsorbate layers.The work of Bassett Boucher and Z e t t l e m ~ y e r ' ~ ~ confirm that stepped isotherms are possible at room temperature if the saturation pressure is in the range 1-10 torr (as predicted by Pierce 1966). Isopropyl alcohol adsorption on Graphon at 0 and 25" has been investigated and it is concluded that the temperature needed to show steps is related to the characteristics of the adsorbate. The reduced temperature is a better guide. Strong lateral interactions coupled with relatively weak adsorbate-adsorbent interactions enhance step-wise adsorption and alcohols on carbon fit these requirements.Adsorption of gases on other surfaces. Some difficulties have been experienced in the past in the characterisation of the surface of silver iodide in terms of its interaction with water vapour partly because of contamination resulting from the preparation (aqueous precipitation) and partly because interpretation is made difficult by three-dimensional clustering of the adsorbate molecules in the adsorbed phase. In the investigation reported by Edwards and Corrin"' these difficulties have been removed by using methanol as adsorbate and a sample of AgI (surface area about 1 m.2/gm.) prepared by direct reaction between metallic silver and iodine followed by treatment with ammonia. The isotherms did not fit the Brunauer classification and their shapes indicate absence of three-dimensional clustering.Isosteric heats calculated from measurements at 9.77,19.79 and 30.02" over the pressure range 0.24-10.8 mm., indicate that the surface has a dual nature. About 12% of the heterogenetic surface consists of high-energy sites located patchwise over the surface. The adsorption of n-pentane by a NaX zeolite at 180 200 230 250 and 270" has been studied by Garkavenko and c o - ~ o r k e r s . ' ~ ~ (At temperatures lower than 180" the adsorption is so strong that reversibility etc. at low coverage when the voids of the zeolites are filled is difficult to assess). The isotherms are Langmuirian and log K varies almost linearly with the reciprocal of the temperature ( K is the equilibrium constant).Theoretical isotherms calculated from the Langmuir equation using this temperature-dependence of K agree well with the experimental curves. Isosteric heats are practically independent of the amount of pentane adsorbed and are close to the 12-3 kcal./mole calculated from the temperature-dependence of K and also to published calorimetric data. Entropy calculations indicate that as the voids become filled the mobility of the n-pentane molecules decreases and over a wide range is less than in the liquid state. The surface of cavities in X-type zeolite cationated by small-radius covalent D. R. Bassett E. A. Boucher and A. C. Zettlemoyer J . Phys. Chem. 1967,71,2787. H. W. Edwards and M. L. Corrin J . Phys. Chem. 1967,71,3373. L.G. Garkavenko 0. M. Dzhigit A. V. Kiselev K. N. Mikos and G. G. Muttik Zhur.Jiz. Khim. 1967,41. 244 168 G. D. Parfitt cations is homogeneous to non-specific adsorbates due to the crystalline struc-ture and on such surfaces adsorbate-adsorbate interactions are clearly defined. Adsorption isotherms have a wave-like form first convex to the pressure axis and an inflection point near half-monolayer coverage; heats of adsorption increase with coverage cf graphitised carbon blacks. For the zeolites Kr Xe, C2H6 n-C5Hl, and n-C6Hl show this behaviour. The adsorption of krypton and xenon at temperatures in the range - 30 to - 90” is discussed in detail in a paper by Aristov Bosacek and Kiselev.lS2 Simple equations are deduced to take approximate account of adsorbate-adsorbate interactions in the adsorbed phase and adsorption values and isosteric heats are predicted which are in agreement with the experimental data.The electrical coriductivity of a semiconductor may increase or decrease according to the nature of the gas adsorbed on the surface as demonstrated with copper and zinc oxides. The reverse of this process in which the quantity of adsorbed substance might be influenced by appropriate manipulation of the density of electrons within the solid is considered by R o ~ h o w ’ ~ ~ and if an alternating field is applied he defines the possibility of alternately seizing and releasing the adsorbed gas as ‘alternosorption’ which is shown to be reversible in principle. Application to heterogeneous catalysts is discussed. Spectra of adsorbed species.Although LEED and field emission studies give information on the form of the adsorbed phase on a single crystal of a metal or semiconductor they give only very indirect evidence as to what species are present. The application of i.r. spectroscopy has obvious merits, but there are certain difficulties both experimental and in interpretation. It is necessary to optimise the experimental parameters and to have a theory for the interpretation of the vibrational spectrum for a regular moiiomolecular film chemisorbed on clean oriented single-crystal metallic or semimetallic sub-strates. The spectrum is discussed in the harmonic-oscillator approximation by Smith and Eckstrom,’ 54 and it is concluded that optical modes must be totally symmetric with respect to translation and be of an appropriate symmetry species under the unit cell ( N factor) group.The implications of anharmonicity, quadrupolar-induced transitions and non k = 0 processes are discussed and the theory applied to the case of CO and H (or D2) adsorbed on the (loo), (110) and (111) surfaces of nickel. Some agreement is found although present experimental data were not obtained under optimum conditions. An e.s.r. study of chlorine atoms adsorbed on a silica-gel surface at 77”K, reported by Gardner,”’ indicates that the orbital degeneracy has been re-moved as a result of the electrostatic interaction with the surface. The author states that this is the first example of detection of trapped halogen atoms. An estimate of 2.7 x 1017 v/cm.2 has been made for the electric-field gradient at the position of the chlorine atom.1 5 2 B. G. Aristov V. Bosacek and A. V. Kiselev Truns. Faraday SOC. 1967 63 2057. l S 3 E. G. Rochow J . Inorg. Nucleur Cheni. 1967,29,65. 155 C. L. Gardner J. Chem. Phys. 1967,46 2991. W. H. Smith and H. C. Eckstrom J . Chem. Phys 1967.46. 3657 Colloid and Interface Science 169 Substrate absorption limits the use of i.r. spectroscopy to the high-frequency modes of vibration of the adsorbate whereas Raman spectra should provide an effective alternative method for covering a wide frequency range. The use of a conventional laser Raman spectrometer has been investigated by Hendra and Loader,156 using CCl, Br, CS, and trans-C,H,Cl adsorbed on silica gel and spectra recorded over the range 150-3400 cm- '.This is a preliminary investigation which looks promising. The i.r. and e.s.r. spectra of silica (Aerosil) y-alumina rutile titanium dioxide, and of these oxides with adsorbed gases have been studied by Kiselev and Uvarov.lS7 On the clean oxide e.s.r. signals were only detected with alumina and rutile. Adsorbed n-hexane benzene diethyl ether acetone diethylene-triamine pyridine and acetic acid were studied by i.r. and anthracene by e.s.r. spectroscopy. In addition to the specific interactions of the oxygen and nitrogen containing molecules on all three oxides there is chemical interaction with the aprotonic acid centres of alumina and rutile. Similarly with anthracene for which charge transfer takes place and ion radicals emerge. Such effects were not observed with silica suggesting the absence of aprotonic electron-acceptor centres on the silica surface.In the characterisations of solid surfaces and adsorbed species by i.r. spectro-scopy almost no spectra have been obtained at elevated temperatures yet most catalytic reactions of practical importance occur at high temperatures. The paper by EberlyI5* describes a new high-temperature i.r. cell which he has used to record spectra at temperatures up to 650" and pressures from lo-' mm.-760 mm. A study of the interaction of the various ion-exchanged faujasites (Y zeolites) with hexene-l and other olefins at 90-427" is described. Three different hydroxy groups were found with hydrogen faujasite at 427" and these groups readily exchange with deuterium gas.Hexene-1 adsorbed at 93" with the loss of double-bond character; at higher temperatures polymer-isation and dehydrogenation processes occur. On other ion-exchanged forms the main reaction involved the loss of double-bond character. Sols.-Particle size. The use of a simple small-angle scattering device attached to a commercial X-ray diffractometer (Philips) for determining particle size distribution of thoria sols is described by Stoecker,lS9 and shows that simple equipment of low resolution is adequate for a system of particles having a scattering curve that can be approximated by a Gaussian distribution (or by a composite of several Gaussian distributions). Each thoria sol investi-gated had its own characteristic scattering curve the shape of which was un-changed by dilution and the average particle diameter agreed with that deter-mined by line broadening.Besides the inherent difficulties in the electron-microscopic examination of sols that are associated with the preparation of the sample for analysis there 156 R. J. Hendra and E. J. Loader Nature 1967,216,789. l S 7 A. V. Kiselev and A. V. Uvarov Surface Sci. 1967,6,399. lS8 P. E. Eberly J . Phys. Chem. 1967,71 1717. W. C. Stoecker Analyt. Chem. 1967,39,628 1 70 G. D. Parfitt always arises the uncertainty of defining exactly the shape and character of particle aggregates from electron micrographs. A new geometrical method of analysis has been described by Medalia.16' The silhouette is treated as a plane figure from which are calculated the radii of gyration about the two central principal axes in the plane.The ratio of these radii is taken as the anisometry of the figure and other parameters are also calculated including the area and bulkiness as well as a 'structure factor' which expresses the excess area swept out by the figure as it rotates. To relate the two-dimensional projection to the three-dimensional aggregate flocs are generated by computer simulation. Similarity is demonstrated between the appearance of the simulated flocs and of actual electron micrographs of carbon blacks. Using recent values of the refractive index of selenium Danchot and Watillon16' have computed with the Mie equations the extinction coefficients of selenium sols as a function of wavelength (240-1100 mp) for particle diameters in the range 0 ( x 20)-500 mp.The computation was limited when the contributions of both the nth electric and magnetic partial waves were smaller than the 10-4th part of the extinction coefficient. The maxima appearing in the extinction curves are related to the contribution of various electric and magnetic partial waves and all the maxima shift towards the i.r. with increasing particle size. The influence of a normal particle-size distribution on the extinc-tion coefficients is analysed and the data afford a simple and accurate method for the simultaneous determination of particle diameter and size distributions. The first comprehensive study of the optical behaviour of dilute aqueous dispersions of carbon black has been carried out by Donoian and Medalia.I6' Both absorption and scattering (Zimm plot and angular-dependence) were studied and the relative importance of each to the extinction of light through the suspensions assessed.For most blacks the extinction is due mainly to absorption with subsequent conversion into heat but for the less-jet furnace blacks extinction due to scattering contributes at least 20% of the total. Both forward and total scattering increasz monotonically with particle size in the larger particle size range of blacks as does the diffuse reflectance from opaque pastes. Using the optical parameters obtained from measurements on the dilute sols the diffuse reflectance of concentrated systems was estimated but quantita-tive agreement with experiment is poor but a qualitative correlation is evident.Stability. Much fundamental work has been done on the stability of silver halide sols prepared by the 'classical' method of mixing reagents in a controlled manner ; however such sols are not monodisperse and the desirability of using sols with narrow particle-size distributions for comparison with theory is obvious. Methods of preparation involving homogeneous precipitation or decomposition of soluble complexes lead to sols of too low concentration to be useful but Weiss Ericson and her^'^^ have developed a procedure for 160 A. I. Medalia J . Colloid Interface Sci. 1967 24 393. 16' J. Dauchot and A. Watillon J . Colloid Interfuce Sci. 1967 23 62. 16' H. C. Donoian and A. I. Medalia J . Paint Technology 1967,37 716. 163 G. R. Weiss R. H. Ericson and A. H. Herz J .Colloid Interface Sci. 1967 23 277 Colloid and Interface Science 171 producing concentrated dispersions of monodisperse AgBr crystals. Using gelatin solutions monodisperse halide dispersions were formed by controlled mixing of reagents and then the gelatin was destroyed with enzymes. The zero point of charge of these and the classical sols is at pAg 5.3 f 0-2 and this is independent of crystal size and size distribution. Mere dilution of the sols to lo-% AgBr lowered the zero point of charge to pAg 2-4. The Smoluchowski theory of rapid coagulption does not take into account the attractive forces between the particles and therefore values of the stability ratio W calculated using the Fuchs theory (1934) may be less than unity i.e. the actual rate of coagulation is greater than the theoretical rapid rate.For adequate comparison with experiment W c 1 is untenable. McGown and Parfitt'64 have derived a simple equation to take account of the attractive forces in the derivation of a theoretical value for W Deryaguin and M ~ l l e r ' ~ ' have estimated the effect of the viscous resistance of the aqueous medium between coagulating particles which is normally assumed to remain constant and is expressed by the Stokes formula. They conclude that including a term to allow for changes in viscous resistance leads to a negligible effect on W and therefore differences between theory and experiment cannot be explained in this way. The successful application of the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of colloid stability to dispersions in non-aqueous media has been demonstrated by several workers.The coagulation kinetics of rutile in hydrocarbon solutions of Aerosol OT reported by McGown and Parfitt'66 show excellent agreement with the theory over a wide range of zeta potential. The magnitude and sign of the charge on the rutile particles is a complex function of the concentration of surfactant and the quantity of water in the system. Provided the water content of the solution is below 60 p.p.m. the ionic mechanism is operative and experiment agrees with theory. At higher water concentrations deviations are observed as shown in a further paper by the same a ~ t h 0 r s . l ~ ~ An increase in the amounts of water added leads to an increase in stability but a maximum in zeta potential.It is suggested that water adsorbed on the rutile surface leads to an increase in the effective particle (aggregate) size which compensates for the decrease in potential and maintains the stability. A similar correlation between the zeta potential and dispersion stability is demonstrated by Romo'68 for alumina and aluminium hydroxide in n- and iso-C, C, and C5 alcohols. Changes in sign of charge (negative to positive) were observed on addition of small quantities of water to alumina dispersions but the correlation was maintained. For the positively-charged hydroxide dispersions the stability increased with addition of water with no reversal of charge. Crowl' 69 has studied the stability of dispersions of mixed pigments (phthalo-16' B. V. Deryaguin and V.M. Muller Doklady Akad. Nauk. S.S.S.R. 1967,176,869. D. N. L. McGown and G. D. Parfitt J . Phys. Chem. 1967,71,449. D. N. L. McGown and G. D. Parfitt Discuss. Faraday SOC. 1966,42,225. D. N. L. McGown and G. D. Parfitt Kolloid-Z. 1967,220 56. L. A. Romo Discuss. Farad. SOC. 1966,42 232. 'Iy V. T. Crowl J . Oil Colour Chemists' Assoc. 1967,50 1023 172 G. D. Parfitt cyanines and titanium dioxide) in non-aqueous solutions of alkyd resins and similar media in an attempt to explain the flocculation flotation and flooding behaviour of alkyd and alkyd/amino paints. The degree of flocculation of the phthalocyanine pigments correlated with differences in particle-size distribu-tions of the pigments those with the greatest amount of fine particles showing the least flocculation.In general the stability was related to the nature and thickness of the adsorbed layer and although by electrophoresis a surface charge was found in some cases the effect of this charge was shown to be insufficient to explain the behaviour. Flotation effects are most pronounced with the finer sized pigments except where co-flocculation of the two pigments occurred. Flooding of the oxide pigment is associated with polar material in the alkyds. The removal of colloidal particles adhering to a solid surface by a non-aqueous surfactant solution has been studied by Clayfield and Lumb.”’ Particles of carbon black were deposited from a dispersion in a non-polar hydrocarbon oil surface of a metal powder bed and the removal attempted with hydrocarbon solutions of polyisobutene-succinic anhydride/tetraethylene-pentanine block copolymers of molecular weights in the range 600-120,000.Considerable detachment on the solid particles occurred with minimum hydrodynamic-displacement action and is explained in terms of the ‘secondary minimum’ adhesion concept and an entropic mechanism of polymer detergent action. The mechanism of flocculation by various water-soluble polymers (non-ionic anionic and cationic) has been investigated by Slater and Kitchenerl’l using aqueous fluorite suspensions. The influence of molecular weight the open structure of the flocs in contrast to those resulting from electrolyte coagulation and other data are accounted for qualitatively by the ‘bridging’ mechanism but the quantitative theory of Smellie and La Mer (1958) of refiltration curves is shown to be invalid.The adsorption of polymer on the ionic fluorite crystal surface is considered to be non-ionic and associated with a dipole interaction of non-ionic groups with the electrostatic field of the lattice. The part played by water structure around colloidal particles is considered by Johnson et in an attempt to explain marked deviations from the DLVO theory which the authors had observed with arachidic acid sols e.g. they are stable at zero zeta potential. The experiments reported are of measure-ments of the most rapid rate of coagulation of monodisperse polyvinylacetate sols at different temperatures and the rates compared with those predicted by the classical Smoluchowski theory based solely on diffusion.The experimental rates are lower than the theoretical values supporting the water-structure postulate and further evidence is provided from relaxation times of the water 170 E. J.Clayfield and E. C. Lumb Discuss. Faraday SOC. 1966,42,285. ”’ 172 G. A. Johnson S. M. A. Lecchini E. C. Smith J. Clifford and B. A. Pethica Discuss. Farday R. W. Slater and J. A. Kitchener Discuss. Faraday SOC. 1966,42 267. Soc. I966,42 120 Colloid and Interface Science 173 in the system as a function of temperature and particle concentration using spin echo n.m.r. techniques. The evidence presented would appear to support the views of Deryaguin on the long-range structuring of boundary layers of water. have studied the kinetics of coagulation by barium nitrate of a series of monodisperse polystyrene latex dispersions (600-4230 A) and compared log W versus log electrolyte-concentration curves with those predicted by the DLVO theory.The theory predicts an increase of slope with particle size but the experimental slopes showed little change with an increase in particle radius over nearly an order of magnitude a discrepancy yet to be explained. Estimated values of the Hamaker constant range from 1.03 x 10- l4 -1.10 x 10- l 3 erg. Similar experiments by Watillon and Joseph-Petit' 74 lead to a constant between 4 x and 7 x erg. Using a turbidity technique for the evaluation of stability ratios Daluja and Srivastava'75 have carried out a quantitative study (the first ever) of the coagulation of negative antimony sulphide sols on addition of mono-(Na' , K') di-(UOi + Mn2+ Ba2 +) tri-(A13 +) and tetra-(Th4+) valent cations.The critical electrolyte concentrations decrease in the order Na+ > K+ > UO;' > Th4+ > Mn2+ > Ba2+ > A13+ and show a marked deviation from the Schulze-Hardy rule. Using the DLVO theory with the zeta potential the authors have estimated values for the effective Hamaker constant varying from 2.4 x 10-l2 and 1-8 x erg according to the method of analysis. Rapid rate constants are lower than the theoretical (Smoluchowski) values by a factor of ca. 20. It is generally assumed that the effect of similions (those ions of the same sign of charge as the particles) on colloid coagulation is small and very little work has been done on the magnitude and nature of the effect.Lindfors and co-w o r k e r ~ ' ~ ~ have used the 'in statu nascendi' technique to investigate the critical electrolyte concentration of sodium counterions associated with various anions for negatively-charged silver bromide sols. The critical con-centration shows a linear dependence on the Stokes radius of the anion and there is a marked dependence on the charge of the similion the concentration being considerably larger for di- and tri-valent anions. The effect is still small compared with that of the counterion. Large organic cations (strychnine quinine etc.) are known to coagulate negative lyophobic colloids at concentrations considerably lower than simple inorganic ions of the same charge but before the work reported by Matijevic and K01ak'~~ there had been no previous studies containing sufficient in-formation to correlate the charge size configuration and chemical composition of the complex counterion with its effect on colloid stability.Their paper contains the results on the interactions of silver bromide sols with a number of Ottewill and 173 R. H. Ottewill and J. N. Shaw Discuss. Faraday Soc.,'l966,42 154. 174 A. Watillon and A. M. Joseph-Petit Discuss. Faraday SOC. 1966,42 143. 175 K. L. Daluja and S. N. Srivastava Indian J . Chem. 1967,5 262. 176 K. R. Lindfors D. X. West G. L. Blackmer and L. M. Carson J . Phys. Chem. 1967,71,3057. 177 E. Matijevic and N. Kolak J . Colloid Interface Sci. 1967,24,441 174 G. D. Parfitt metal (Ni Co Cr) chelates which permit variations in the size and nature of ligand and also with the same ligands variation of central ionic charge.The ‘in statu nascendi’ method was used to determine the critical stabilization concentration or critical coagulation concentration and significant enhance-ment of the coagulation power and charge-reversal ability of the metal ions by chelation is demonstrated. The remarkable effects are discussed in terms of the stability size and hydration of the chelate counterions. Electric double-layer and electrokinetic phenomena. In their paper on the discrete-ion effect in ionic double-layer theory Levine Mingins and Bell178 have reviewed the present state of the theory and concluded that only the hexagonal lattice model the cut-off disc approach and the Buff-Stillinger model are self-consistent. However the Buff-Stillinger model can break down at non-metallic interfaces and the lattice model is only valid at high surface charge densities.To cover all cases the authors suggest a ‘middle-of-the-road’ approach which might be provided by a cut-off disc of varying radius or by a more elaborate model based on a lattice liquid theory of the adsorbed phase, or by a calculation of the correlation function for relative ionic distributions on the inner Helmholtz plane. The paper also includes a discussion of certain experimental ‘anomalies’ in terms of the discrete-ion effect namely the Esin-Markov effect the maximum in the potential at the outer Helmholtz plane, certain aspects of colloid stability (e.g. the slope of log W versus log electrolyte-concentration plots) mutual antagonism of electrolyte mixtures in coagulation behaviour and certain effects at the mercury-electrolyte solution interface and with ionized monolayers.The relation between the surface charge density of stabilising ions and surface potential for a model which represents the silver iodide-aqueous 1 1 electrolyte solution interface with or without specific cation adsorption is examined by Levine and Matije~ic”~ in connection with the criticism of Mirnik of current electric double-layer theory. It is shown that the general behaviour can be reproduced by the theory and the authors claim than Mirnik’s proposal that the condition of thermodynamic equilibrium between AgI and the aqueous phase with respect to stabilising (I-) ions implies log charge density being proportional to surface potential is essentially incorrect.Mirnik’s ion-exchange theory of coagulation is also discussed and arguments given which are claimed to show that the theory is invalid. Mirnik,I8’ however, suggests that the derivation of Levine and Matijevic does not assume equality of the chemical potentials of the I- ions in the double layer and in solution, and claims that their approach is not physically significant. Furthermore he suggests that the objections to his ion-exchange theory are not valid. Corrections to the Poisson-Boltzmann equation for the potential distri-bution in the diffuse part of the electric double layer are considered by Levine ”’ S. Levine J. Mingins and G. M. Bell J . Electroanalyt. Chem. Interfacial Electrochem., 1967, 17’ S .Levine and E. Matijevic. J . Colloid Interface Sci 1967. 23. 188. 13 280. 180 M . M. irnik J . Colloid Interface Sci. 1967 24 282 Colloid and Interface Science 175 and Bell" in terms of ion-size variation in dielectric constant self-atmosphere effect the effect of medium compressibility and cavity potentials. Some numerical solutions of the modified equation for a single charged plate and for two equally charged parallel plates immersed in large volumes of aqueous 1 1 electrolyte are presented. No account is taken of the Stern layer containing adsorbed counterions. The potential drops more rapidly with distance from the surface than predicted by the unmodified equation but the corrections even at 0 . 1 ~ and potentials ca. 50-75 mv are not excessive.For two double layers the correction is such as to lead to a decrease in repulsion but the magnitude of the effect is not sufficient to affect the currently accepted stability theory of hydrophobic colloids. The influence of temperature on the electric double layer at the silver iodide-aqueous solution interface and the application to sol stability has been reported by Lyklema. 182 The technique involved a potentiometric titration of suspended AgI with potential-determining electrolyte and experiments were carried out at 5-85". At 25" alkali ions adsorb specifically on negative AgI, which gives rise to marked ion specificity in the double-layer capacitance leading to the lyotropic sequence in coagulation concentrations. With in-creasing temperature charge and capacitance decrease with a concurrent decrease in specificity and at 2 65" the double layer is predominantly diffuse and non-specific with absence of lyotropic sequence.Some evidence is presented (definite point of inflection in the differential capacitance versus temperature plot) for a phase transition at about 50" in the water layer adjacent to the particles. It is usual to describe the electrical behaviour of the non-polarisable interface between solids such as AgI and electrolyte solutions with the assumption of permanent equilibrium conditions i.e. of surface charge and potential difference between solid and solution being completely determined by the solution composition. However when rapid changes occur such as in collisions between particles in Brownian motion or changes in the double layer due to sudden changes in electrolyte concentration the assumption must be only an approxi-mation.Frens Engel and O ~ e r b e e k ' ~ ~ have considered the situation that arises when the inert electrolyte is added to a AgI surface in contact with an electrolyte solution. The double-layer capacity is changed and since double-layer capacities are adjusted in short times (ca. 10- ' sec.) it takes high exchange currents (10 A/cm.2) to maintain equilibrium. Exchange currents depend on the potential-determining ion concentration and conditions may be such that they are of the order of pA/cm.2 when equilibrium would be restored seconds after addition of inert electrolyte. Experiments are described in which the transient changes in e.m.f.of a galvanic cell containing a AgI electrode and reference electrode after adding the inert electrolyte. The effect vanishes at the zero point of charge. It is concluded that the exchange current fails to S. Levine and G. Bell Discuss. Faraday SOC. 1966,42,69. J . Lyklema Discuss. Faraday Soc. 1966,42 81. lE3 G. Frens D. J. C. Engel and J. Th. G. Overbeek Trans. Faraday Soc. 1967,63,418 176 G. D. Parfitt maintain equilibrium conditions during the rapid process even at the non-polarisable AgI-solution interface. The technique provides a new method of establishing the zero point of charge. Electrokinetic studies on oxidised aluminium surfaces by Morfopoulos and Parreira18 show that the behaviour of aluminium oxidised in air or water is intermediate between that of aluminium metal and pure alumina.The zero points of zeta potential obtained at constant ionic strength range from pH 6-9 depending on the extent of surface oxidation and permit correlation of electrokinetic parameters with corrosion phenomena. Adsorption isotherms for simple and complex ions were deduced from the measurements. Aerosols.-The work reported by Matteson and Stober' 8 5 was initiated to determine how the particle size distribution and quantity of dispersed material in aerosols generated from salt solutions varies with the concentration of the solution and the nature of the electrolyte. Several strong electrolytes (CuSO,, MnSO, ZnSO, MnCl, NaC1 and Th(NO,),) were dispersed from 0.1-10.0 weight per cent solutions with a modified Dautrebande-type generator and the particles examined by electron microscopy and the aerosol concentration determined by drawing through a membrane filter and analysing titrimetrically.For a given dispersant concentration in solution the concentration of electrolyte in the aerosol and the mean-volume diameters (from log normal size distri-bution) increased approximately in the same order namely Th(NO,), NaCl, CuCl, ZnSO, MnSO, and CuSO,. This is attributed to the variation in resistance to particle agglomeration by surface charges on the mist droplets. Estimated electrical field intensities at the external drop surface are in quali-tative agreement with the order of particles sizes. For a given electrolyte the mean-volume particle size increased with an average of 0.45 power of dis-persant concentration for electrolytes with polyvalent cations and with the 0.28 power for NaCl.A constant size was achieved at a certain concentration according to the electrolyte and above this concentration the number of particles increased. Some experiments were carried out with methanol solu-tions ; these gave relatively higher aerosol concentrations an effect related to the solvent surface tension. By analysis of the angular distribution of the polarisation of the scattered light from aerosols of solid spheres of vanadium pentoxide Jacobsen Kerker, and Matijevic' 8 6 have compared the particle size distributions at different wavelengths; this aerosol has a high optical absorption in the lower wave-length part of the visible spectrum comparable to that of metals but at higher visible wavelengths there is very little absorption (comparable to dielectrics).Hence the characteristics of the scattered light depend on the wavelength. The very different scattering data were analysed to give size distributions which agreed with each other and the uniqueness of the results was established with the aid of error contour maps. la4 V. C. P. Morfopoulos and H. C. Parreira Corrosion Sci. 1967,7 241. Ins M. J. Matteson and W. Stober J . Colloid Interface Sci. 1967,23,203. R. T. Jacobsen M. Kerker and E. Matijevic J . Phys. Chem. 1967,71,514 Colloid and Interface Science 177 Sulphuric acid aerosols consisting of droplets of narrow size distributions have been prepared by Coutarel et al.,I8' and the particle size distribution determined by light scattering. Particle size increased with increasing boiler temperature and decreased sharply with flow rate. These aerosols could be grown by passing over dilute solutions of the acid when the droplets absorb water until their vapour pressure reach that of the master solution; the rate of growth is proportional to the particle volume. Takahashi and Iwai188 have calculated the size distribution of various aerosols (linoleic acid triphenylphosphate stearic acid) containing very small particles (0.064.3 p) by means of polarisation ratio and/or dissymmetry of scattered-light measurements at various wavelengths. The values of these parameters were calculated for various size distributions assuming a log normal distribution. Estimated values of geometric mean size and standard deviation were confirmed with values obtained by electron microscopy. The polarisation ratio at 90" is shown to be very sensitive to size and polydispersity, while dissymmetry is essentially insensitive to polydispersity. Using both parameters it is possible to determine the mean size and standard deviation of polydispersed small aerosol particles within an error of about 10 % or less. The reproducible preparation of aerosols and their accurate characterisation by light scattering have been described in the literature and with such progress it should now be possible to follow coagulation by light scattering. Willis, Kerker and Matije~ic'~' have calculated the size distribution at various times of a dispersion of spherical aerosol particles undergoing coagulation as a result of Brownian motion for two initial distributions having a model radius of 0.25 p and zeroth-order logarithmic-breadth parameters of o0 = 0.1 and 0.3. For this distribution the angular variation of the polarisation ratio of the scattered light is calculated for h = 5460 and m = 1-50. Light scattering is shown to be useful for following the coagulation of the narrower of the two distributions up to about 1.4 half-lives. Using the equations of Smoluchowski modified to include a feed term, Mockros Quon and Hjelmfelt ' have calculated the particle size distributions of an aerosol that is being continually reinforced by the introduction of particles while coagulation under Brownian motion is proceeding. The dependence of the size distribution on the coagulation and feed rates and on the nature of the feed is discussed. la' J. Coutarel E. Matijevic M. Kerker and Chao-Ming Huang. J . Colloid Interface Sci. 1961, 24,338. K. Takahashi and S. Iwai J . Colloid Interface Sci. 1967,23 113. E. Willis M. Kerker and E. Matijevic J . Colloid Interfie Sci. 1967 23 182. L. F. Mockros J. E. Quon and A. T. Hjelmfelt J . Colloid Interface Sci. 1967 23,90