摘要:

Date190719071910191119121913191319131914191419151916191619171917191719181918A918191819191919192019201920192019211921192119211922192219231923192319231923192419241924192419241925192519261926192719271927GENERAL DISCUSSIONS OFTHE FARADAY SOCIETYSubjectOsmotic PressureHydrates in SolutionThe Constitution of WaterHigh Temperature WorkMagnetic Properties of AlloysColloids and their ViscosityThe Corrosion of Iron and SteelThe Passivity of MetalsOptical Rotary PowerThe Hardening of MetalsThe Transformation of Pure LronMethods arid Appliances for the Attainment of High Temperatures in aRefractory MaterialsTraining and Work of the Chemical EngineerOsmotic PressurePyrometers and PyrornetryThe Setting of Cements and PlastersElectrical FurnacesCo-ordination of Scientific PublicationThe Occlusion of Gases by MetalsThe Present Position of the Theory of IonizationThe Examination of Materials by X-RaysThe Microscope : Its Design, Construction and ApplicationsBasic Slags : Their Production and Utilization in AgriculturePhysics and Chemistry of ColloidsEiecrrodeyositlon and ElectroplatingCapillarityThe Failure of Metals under Internal and Prolonged StressPhysico-Chemical Problems Relating to the SoilCatalysis with special reference to Newer Theories of Chemical ActionSome Prdpxtizs of Powders with special reference to Grading byThe Generation and Utilization of ColdAlloys Resistant to CorrosionThe Physical Chemistry of the Photographic ProcessThe Eiecrronic Theory of ValencyElectrode Reactions and EquilibriaAtmospherjc Corrosion.First ReportInvestigation on Oppau Ainmonium Sulphate-NitrateFluxes and Slags in Metal Melting and WorkingPhysicaI and Physico-Chemical Problems relating to Textile FibresThe Physical Chemistry of igneous Rock FormationBase Exchange in SoilsThe Physical Chemistry of Steel-Making ProcessesPhotochemical Reactions in Liquids and GasesExplosive Reactions in Gaseous MediaPhysical Phenomena at Interfaces, with special reference to MolecularAtmospheric Corrosion. Second ReportThe Theory of Strong EieclrolytesCohesion and Related ProblemsLaboratoryElutriationOrientationVoluinrTrans.3367899910101 1121213131314141414151516161616171717171818191919191920202020202121222223232GENERAL DISCUSSIONS OF THE FARADAY SOCIETYDute1928i9291929192919301930193119321932193319331934193419351935193619361937193713%193819391939194019411941SubjectHomogeneous CatalysisCrystal Structure and Chemical ConstitutionAtmospheric Corrosion of Metals.Molecular Spectra and Molecular StructureOptical Rotatory PowerColloid Science Applied to BiologyPhotochemical ProcessesThe Adsorption of Gases by SolidsThe Colloid Aspects of Textile MaterialsLiquid Crystals and Anisotropic MeltsFree RadicalsDipole MomentsColloidal ElecfrolytesThe Strwturc of Metallic Coatings, Films and SurfaceThe Phenomena of Polymerization and CondensationDisperse System in Gases : Dust, Smoke and FogStructure and Molecular Forces in (a) Pure Liquids, and (6) SolutionsThe Properties and Functions of Membranes, Natural and ArtificialReaction KineticsChemical Reactions Involving SolidsLuminescenceHydrocarbon ChemistryThe Electrical Double Layer (owing to the outbreak of war the meetingThe Hydrogen BondThe Oil-Water interfaceThe Mechanism and Cheiiiical Kinetics of Organic Reactions in Liquid'Third Reportwas abandoned, but the papers were printed in the Transactions)Systems1942 The Structure and Reactions of RubberVolume242525252626272829293030313132323333343435353536375138 _ _3Y40414242 A42 €321943 Modes of Drug Action1944 Molecular Weight and Molecular Weight Distribution in High Polymers.(Joint Meeting with the Plastics Group, Society of Chemical Industry)1945 The Application of Infra-red Spectra to Chemical Problems1945 OxidationiY46 Dielectrics1946 Swelling and Shrinking1947 Electrode Processes Disc.11947 The Labile Molecule1947 Surface Chemistry. (Jointly with the Socitt6 de C h d e Physique atBordeaux.) Published by Butterworths Scientific Publications, Ltd.1947 Colloidal Electrolytes and Solutions 1948 The Interaction of Water and Porous Materials Disc. 31948 The Physical Chemistry of Process Metallurgy1949 Crystal Growth1949 Lipo-Proteins1949 Chromatographic Analysis1950 Heterogeneous Catalysis1950 Physico-chemicai Properties and Behaviour of Nuclear Acids1950 Spectroscopy and Molecular Structure and Optical Methods of In-1950 Electrical Double Layer Trans.471951 Hydrocarbons Disc. 101951 The Size and Shape Factor in Colloidal System1952 Radiation Chemistry1952 The Physical Chemistry of Proteins1952 The Reactivity of Free Radicals1953 The Equilibrium Properties of Solutions of Non-Electrolytes1953 The Physical Chemistry of Dyeing and Tanning1954 The Study of Fast Reactions1954 Coagulation and FlocculationTrans. 4345678Trans. 46vestigating Cell Structure Disc. 9111213141516171GENERAL DISCUSSIONS OF THE PARADAY SOCIETYDate195519551956195619571957195819581959195919601960196119611962196219631963196419641965196519661966Subject VolumeMicrowave and Radio-Frequency Spectroscopy 19Physical Chemistry of Enzymes 20Membrane Phenomena 21Physical Chemistry of Processes at High Pressures 22Molecular Mechanism of Rate Processes in Solids 23Interactions in Ionic Solutions 24Configurations and Interactions of Macromolecules and Liquid Crystals 25Ions of the Transition Elements 26Energy Transfer with special reference to Biological Systems 27Crystal Imperfections and the Chemical Reactivity of Solids 28Oxidation-Reduction Reactions in Ionizing Solvents 29The Physical Chemistry of Aerosols 30Radiation Effects in Inorgar,ic Solids 31The Structure and Properties of Ionic Melts 32Inelastic Collisions of Atoms and Simple Molecules 33High Resolution Nuclear Magnetic Resonance 34The Structure of Electronically-Excited Species in the Gas-Phase 35Fundamental Processes in Radiation Chemistry 36Chemical Reactions in the Atmosphere 37Dislocations in Solids 38The Kinetics of Proton Transfer Processes 39Intermolecular Forces 40The Role of the Adsorbed State in Heterogenous Catalysis 41Colloid Stability in Aqueous and Non-Aqueous Media 42For current availability of Discussionvolumes, see back cover

ISSN:0366-9033    

DOI:10.1039/DF966420X001

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

Colloid Stability in Aqueous and Won-Aqueous MediaINTRODUCTORY PAPERBY J. TH. G. OVERBEERvan’t Hoff Laboratory, University of Utrecht, The NetherlandsReceiued 28th July, 1966Colloid stability is determined by the interaction between particles during a (Brownian) en-counter. The forces playing a role in encounters (van der Waals forces, double-layer interaction,interaction between adsorbed molecules, such as surfactants, polymers and small molecules) arediscussed with emphasis on unsolved problems. It is pointed out in which of the papers of thisDiscussion the different problenls are treated.GENERAL ASPECT OF COLLOID STABILITYSince colloidal particles dispersed in a liquid are always subject to Brownianmotion, encounters between the particles occur frequently and the fate of the colloidaldispersion is determined by the interaction between particles during such an en-counter.When attraction predominates the particles will adhere more or lesspermanently and the dispersion will coagulate ; in the case of predominant repulsionthe system will remain in the dispersed state.Van der Waals forces are always present, whatever the composition of thesystem, and it has been proved that such forces always result in attraction betweenparticles of the same material. Therefore, a colloidal suspension can only be stableif a sufficiently strong repulsion counteracts the van der Waals attraction. Thisrepulsion may be based on the interaction of electrical double layers-mainly butnot exclusively important in aqueous systems-or on the interaction of layers ofadsorbed uncharged molecules, including the solvent molecules themselves, amechanism which may act in any solvent.The interaction between particles and adsorbed molecules does not necessarilylead to repulsion.Especially, if the adsorbed molecules are polymeric, one mole-cule may be attached to two particles and thus form a bridge between the particles,enhancing the attraction rather than the repulsion, and leading to sensitizedflocculation.Qualitatively our picture of colloid stability is well established and for severalof the factors entering the picture quantitative or semi-quantitative theories exist.At present we are at a stage of refinement of our understanding and control ofcolloid stability, but much refinement has still to be done before the situation issatisfactory.In this introductory paper, I shall treat the main interaction forcesone by one and try to indicate in each case what critical experiments or improvementsin the theory should be made.TeZak’s contribution to this Discussion, in which he gives a systematic descriptionof all states between the homogeneous solution and the macrocrystal, with a strongemphasis on the variability of the phenomena, has a wider scope than most of theother contributions. It includes and rather stresses such aspects as complex forma-tion, nucleation and crystal growth and reserves only a modest place for colloidalstability in the more restricted sense.8 INTRODUCTORY PAPBRTHE ELECTRICAL DOUBLE LAYERThe structure of the electrical double layer is relatively well established, notin the sense that the value of the surface charge or the surface potential can be pre-dicted from first principles, but that the relation between charge and potential andthe spatial extension of the double layer and the repulsion between overlappingdouble layers are fairly well known-fairly well, but possibly not well enough.Colloid stability is governed by the difference between repulsion and attractionand a relatively small error in one of the two may make our estimate of the stabilitygrossly wrong.The relation between charge and potential difference between the two phasesis dealt with by Levine and Bell, who will discuss a number of refinements to thePoisson-Boltzmann equation, such as the influence of ion-size, dielectric saturation,discreteness of charge, cavity potential, etc.They will also show the influence ofthese refinements on the interaction of double layers and on colloid stability.TeEak lays great stress ori the interaction between individual ions, as opposed tothe collective behaviour of ions in double layers. Lyklema has obtained data oncharge and potential difference at the AgP/water interface at elevated temperatures.Since he finds a more simple, more " Gouy-like " structure of the double layer anda correspondingly simpler behaviour in coagulation, high temperature may wellbecome an important tool in double-layer research.Instead of the potential difference between the two phases the zeta-potential isoften used.It has the advantages that it can be determined in practically all casesof interest, at practically any electrolyte concentration, and that it gives informationon the diffuse part of the double layer. The disadvantage is that the theoreticalrelation between zeta-potential and electrokinetics is far from simple, and as yetthere is no good understanding of where the slipping plane (if it is a plane) is situatedwith respect to the phase boundary. Nevertheless in at least eight of the paperspresented at this discussion (Watillon and Mrs. Joseph-Petit, Hall, Ottewill andShaw, Matijevic, Kratohvil and Stryker, McGown and Parfitt, Romo, Tehk andMicale, Lui and Zettlemoyer) the zeta-potential is used for information on the doublelayer, three being about suspensions in non-aqueous media.In the papers byRomo and by Micale, Lui and Zettlemoyer the influence of trace amounts of wateron the zeta-potential is stressed.The above information deals mainly with single double layers. Direct experi-mental information on the interaction of double layers is much scarcer. I wouldlike to cite the classical work of Bergmann, Low-Beer and Zocher 1 on Schillerlayers, and mention the modern work on black soap films (see Overbeek 2) of whicha good example obtained with a new technique is presented here by Mysels andJones, who find a quite acceptable agreement with the theory for the interaction ofdiffuse double layers.To close my remarks about the double layer I should say that accurate data ofcharge and potential difference for a variety of interfaces especially at low electro-lyte concentrations are still greatly needed and that experiments, in which the doublelayer repulsion is determined as free as possible from other interactions, such asthose mentioned above on Schiller layers or soap films, are extremely valuable.VAN DER WAALS FORCESSince Kallmann and Willstaetter 3 suggested that van der WaaIs forces are re-sponsible for the attraction between colloid particles, much work, both theoreticaland experimental, has been done on these forces.The earlier theories (Tomlinson,J . TH. G . OVERBBEK 9Rradley,s de BoeQ Hamaker 7) treated the forces between atom or molecules asstrictly additive and did not take into account that the forces might be modified bypassage through a dense medium.Lifshitz,s basing his treatment on electromagneticfluctuations in a dense medium, derived an exact expression for the attraction be-tween macroscopic objects (consisting of many atoms or molecules) in terms of themacroscopic dielectric constant and dielectric loss factor, which had to be knownover the complete frequency range of dispersion. This treatment has been extended(Dzyaloshinskii, Lifshitz and Pitaevskii 9) to include even the interaction betweentwo fiat plates of different composition separated by a dense medium. At lowdensities, Lifshitz’ treatment is equivalent to the earlier treatment based on addi-tivity of the forces between pairs of molecules.Unfortunately, the necessary dielectric data are not yet known with sufficientat;curacy to be able to apply Lifshitz’ theory directly.Only for the retarded attrac-tion forces, effective at “ large ” distances (e.g., > 1000 A) between the objects, thesituation is more favourable, since in this case only the “ static ” dielectric con-stant (square of the refractive index extrapolated to long wavelengths) has to beknown. But, although the retarded force may play a role in some colloidal phe-nomena, the non-retarded force is much more important. Independent measure-ments of the van der Waals forces of some accuracy exist only in the retarded region,whereas measurements in the non-retarded range are still highly inaccurate (for areview sce Overbeek and Van Silfhout,lO Van Silfhout 11).In the present situationthe best source of information on van der Waals forces are flocculation experi-ments and experiments on thin liquid films, but to a certain extent this is beggingthe question.In this Discussion the papers by Watillon and Mrs. Joseph-Petit and by Ottewilland Shaw show how the stability of polystyrene latex dispersions can be used to derivevalues for the van der Waals attraction. Use is made of the variation of the stabilitywith particle size, particle charge and electrolyte content, but the resulting valuesfor the van der Waals attraction are not yet internally consistent. The followingfactors should be considered in the search for an explanation of this discrepancy.(i) The electrostatic repulsion may have been incorrectly estimated.The in-fluence of this uncertainty can be minimized by comparing sols with different particksizes, but with identical surface charge or potential (at flocculation).(ii) An incorrect estimate of the distance between the phase boundary (wherethe van der Waals constant changes its value) and the plane of the surface charge(from where the distance of repulsion is calculated). Quite often these planes aresupposed to coincide, but this is almost certainly incorrect. It might be advisableto introduce the distance between these planes as a parameter in the theory.(iii) Neglecting the influence of transmission of the van der Wads force througha medium may be a more serious error than is usually assumed. A first estimatecould be obtained by using Lifshitz’ theory with relatively simple models for thedispersion curves.In this connection it is also important to develop Lifshitz’method for more complicated geornetrics (spheres, spheres surrounded by layersof different composition).Further work on the direct measurement of non-retarded van der Waals forces,if possible between objects in a dense medium, is highly desirable. Optical datashould be obtained especially in the far ultra-violet to be used in Lifshitz’ equations.Continued work on the stability of isodispersed sols with careful control of the surfacecharge and wide variation of conditions is desirable. Work on thin films (equi-librium thickness under pressure, light scattering, rate of drainage, etc.) ought tolead to important information10 INTRODUCTORY PAPERPROTECTION AGAINST COAGULATION BY ADSORPTION OF NEUTRALMOLECULESProtective action of hydrophilic colloids on hydrophobic ones has been recog-nized early in the history of colloid science.It was interpreted as the envelopmentof hydrophobic particles by a layer of the hydrophilic colloid making the particlesas stable against coagulation as the hydrophilic colloid. The particles of a goldsol protected by gelatin behave as ‘‘ gelatin particles with a golden heart ”.Later, it was found that the phenomenon is not restricted to aqueous systemsand that protective agents need not necessarily be polymeric. The work of Vander Waarden, Mackor and van der Waals 12-14 on the stabilization of carbon blacksuspensions in a liquid hydrocarbon by adsorbed mixed aromatic-aliphatic mole-cules of modest mass is a good example.In non-aqueous and in particular lion-polar systems repulsion between particlesby electric charge is usually of minor importance.Non-aqueous suspensions,therefore, have to be stabilized by some variant of protective action. Given thetremendous technical importance of non-aqueous suspensions (paints, inks, pig-ments for synthetic polymers, etc.) it is no wonder that in this Discussion muchattention is given to protected colloid systems. Crow1 and Malati and Walbridgeand Waters give some pure examples of stabilization of suspensions in hydrocarbonsby polymeric surfactants. Clayfield and Lumb treat the case of separating carbonfrom metal by a polymeric surfactant.In McGown and Parfitt’s work on thedispersion of rutile in p-xylene by aerosol OT obviously electric charge plays a role.There is no indication that the simple presence of an adsorbed layer of unchargedsurfactant molecules contributes to the protection. Glazman stresses the fact ofprotection in aqueous media by non-ionic surfactants of low and intermediate molarmass. Mrs. Taylor and Haydon point out the parallel between the stability of thinhydrocarbon films in water and colloid stability in non-aqueous media. They con-firm the essential correctness of Mackor and van der Waals ideas, which predicta very steep repulsion for a film thickness equal to twice the length of the stabilizingchains.It is striking that in so many of these cases polymers are used as protectiveagents.They are obviously favourable in several respects. Their standard freeenergy of adsorption is proportionally larger than that of a small molecule of similarchemical nature. Therefore they are more easily adsorbed. Simply on account oftheir size they are expected to form thicker layers, keeping the particles more widelyseparated. Nevertheless, they should not be adsorbed too strongly, ix., at toomany points, because then the layer formed will be thin and the protection inadequate.The detailed chemistry of the adsorption process becomes a point of majorinterest in this field as pointed out by Slater and Kitchener in their paper on theclosely related field of flocculation caused by small amounts of polymers.The theory of protective action is still in a rather primitive state.Mackor andvan der Waals 14 introduced the notion “ entropic repulsion ”, because the loss oftranslafional freedom of the “ wriggling tails ” of the adsorbed molecules when thelayers interpenetrate, leads to a loss of entropy and thus to repulsion. This theoryhas only been worked out for very simple cases.We should try to reach a more complete force-distance relation, using morecomplete statistics for the interpenetrating chains, taking into account that polymermolecules may have several points of attachment to the particles and that thc ad-sorption density itself decreases when the layers interpenetrate. Such a theorywould also be very helpful for a more complete understanding of sensitizationJ .TH. G . OVERBEEK 11SENSITIZATION OF LYOPHOBIC SUSPENSIONS BY SMALL AMOUNTS OFPOLYMERSA polymer molecule, having many points of possible attachment to a surface,can in principle as easily form loops between adsorption sites on one particle as formbridges between sites on different particles. In the last mentioned case, agglomer-ates are formed and flocculation occurs. A low concentration of polymer and a highconcentration of particles will promote this sensitization.Sensitized flocculation cannot simply be treated as an interplay between at-tractive and repulsive force between the particles. The elementary step in thiscase is not the approach of two particles (which, in a stable sol, may be prohibitedby an activation energy of 30 kT or more), but the formation of a single adsorptioncontact (which, even when the adsorbed group is charged, would only have anactivation energy of a few times kT).Once the polymer bridge is made betweentwo particles with single adsorption contacts on each of them, it can be strengthenedand made virtually irreversible by occupying more adsorption sites on each particle.This lack of reversibility does not permit the particles to find the closest packingby sliding along each other and explains the openness of the flocculate.It is evident that the quantitative theory of sensitized flocculation should havemany points in common with the theory of protective action, including consider-ations on the specificity and on the thermodynamics of adsorption of polymer mole-cules.However, as indicated above, for sensitization also kinetic factors andenergies of activation, both for adsorption and desorption, are essential.Several papers in this Discussion deal with sensitized flocculation. In the firstplace we should mention the paper by La Mer, who stresses the different natureof flocculation by polyelectrolytes and that by small ions, and offers the rate ofrefiltration through the flocculate as a tool to distinguish the two types of aggrega-tion. La Mer also proposes to keep the terms coagulation and flocculation sharplyseparated, the former for precipitation by electrolytes (forming dense flocs), thelatter for precipitation by polyelectrolytes (open flocs).It might be useful to spendsome time of the Discussion on this point of nomenclature.Slater and Kitchener also discuss flocculation of aqueous suspensions by poly-mers. Since their theoretical treatment of the phenomenon differs from that byLa Mer in essential points, we may expect an interesting discussion. La Mer andSlater and Kitchener both stress the importance of the specific chemical aspectsin the interactions leading to sensitization.In La Mer’s paper, in that of Hall on the interaction of clay with hydrolyzedaluminium solutions and, although perhaps somewhat less clearly, in the paper byMatijevic, Kratohvil and Stryker, we see the possibility that hydrolyzed polyvalentions form polymers and that charge reversal and flocculation by ‘‘ polyvalent ions ”,as already pointed out by Troelstra and Kruyt,ls, 16 is more akin to sensitizationthan to flocculation by simple compression of the double layer.THE ROLE OF THE SOLVENT AS A PROTECTIVE AGENTUndoubtedly, the structure of a liquid near an interface deviates from its struc-ture in bulk.There is no doubt either that the special structure of water near theinterface with particles dispersed in it will affect their stability by influencing thestructure of the electrical double layer and possibly even by modifying the van derWaals forces. But it is further conceivable that this layer of modified solventaffects the stability in a more direct way, e.g., by increasing the viscosity in theaeighbourhood of the particles or by acting as a protective, impenetrabfe layer12 INTRODUCTORY PAPERAn example of such an influence of small neutral molecules can be found in ahitherto unpublished observation by Mackor.During his work on the influenceof acetone on the electrical double layer at the interface AgI/water 17 he found thatacetone changed the coagulation of AgI by electrolyte in a qualitative way. IfAgI is coagulated in water by the addition of simple salts it has a rather voluminousopen structure and is not easily peptized by washing away the precipitant electro-lyte. In the presence of 5-98 % (vol/vol) of acetone the coagulate is more compactand sandy aiid can be easily and completely repeptized by dilution, which suggeststhat acetone is firmly bound to the surface of the Agl particles and prevents an actualAgl-AgT contact.Whether such an influence of the solvent itself, e.g., of water, occurs more or lessgenerally is still an open question.The arguments for such a role of the solventderive on the one hand from the lack of agreement between experiments and atheory based exclusively on van der Waals forces and double layer interaction(" there must be some additional factor '7, and on the other hand on determinationsof properties of the solvent near an interface such as increased viscosity, nuclearmagnetic resonance, certain interpretations of electrokinetics, etc. Unfortunately,the whole situation is still somewhat ambiguous. The theories of van der Waals+double layer interactions may in themselves be inaccurate. The " additionalfactor " may be just a necessary refinement of these theories.Stigter 18 has calculated from the viscosity of micellar solutions that there isnot a layer of increased viscosity around each micelle.Lyklema, Scholten andivysels 19 concluded from the rates of drainage of soap films that the whole innercore of a soap film has the same viscosity as bulk water. On the other hand,Derjaguin 20 has given examples of changes of viscosity of liquids near interfacesto a very great depth and he pointed out that the thickness of black soap films 21frequently remains thicker than can be explained by double layer repulsion alone.In this Discussion the paper by Derjaguin on the effect of lyophile surfaces onthe properties of boundary liquid films and that by Johnson, Eecchini, Smith,Clifford and Pethica on the stability of polyvinylacetate sols and on the nuclearmagnetic resonance of water in these sols relate to this problem and may hopefullyinitiate an interesting exchange of ideas.The most desirable advance in this field would be a theory which explains theprotective action of the solvent in a mechanistic way and on the other hand moreaccurate experiments connecting stability with " structure " or " adsorption " ofthe solvent.THIN FILMSIt will be clear from some of the above remarks that thin detergent films are animportant source of information for several of the finer points of colloid theories.The combination of a small thickness determined by the interactions, in which weare interested, with a relatively largz area, which makes optical and other observa-tions easy and the applicability of straightforward thermodynamics, are advantages.It is fortunate that several papers in this Discussion on colloid stability are devotedto thin film work.The papers by Mrs. Taylor and Haydon, by Mysels and Jones,and by Derjaguin have been cited earlier. I should also mention here Vrij's paperon fluctuations in the thickness of soap films which may lead to rupture (the equivalentof coalescence in emulsions) and the paper by Corkill, Clunie and Goodman whoobtain consistent values for the thickness of the films using a variety of techniquesand find from their measurements that a water layer of about 20A thickness istenaciously held between the two surfactant layersJ .TH. G. OVERBEEK 13CONCLUSIONThe general framework in which colloid stability can be interpreted appearsto be well established. There are sufficient uncertainties in the quantitative aspectsof the theory and in the detailed interpretation of certain observations, to expecta lively and fruitful discussion.1 Bergmann, Low-Beer and Zocher, 2. physik. Chem. A , 1938, 181, 301.2 Overbeek, J. Physic. Chem., 1960, 64, 11 78.3 Kallmann and Willstaetter, Naturwiss., 1932, 20, 952.4Tomlhson, Phil. Mag., 1928, 6,695.5 Bradley, Phil. Mag., 1932, 13, 853.6 de Boer, Trans. Furaduy SOC., 1936, 32, 10.7 Hamaker, Physica, 1937, 4, 1058.SLifshitz, Doklady Akad. Nauk. S.S.S.R., 1954, 97, 643; 1955, 100, 879; Zhw. Eks. Teor.9 Dzyaloshinskii, Lifshitz and Pitaevskii, Adu. Physics, 1961, 10, 165.10 Overbeek and Van Silf hout, Proc. Symp. InterinoZeculur Forces (Pontifical Academy of Sciences,11 Van Silfhout, Proc. Kon. Neder. Akud. Wetens. B, 1966, 69, 501, 516, 532.12 Van der Waarden, J. Colloid Sci., 1950, 5, 317.13 Mackor, J. Colloid Sci., 1951, 6,492.14 Mackor and van der Waals, J. Colloid Sci., 1952,7,535.15 Troelstra, Thesis (Utrecht, 1941), p. 81.l6 Troelstra and Kruyt, Kulloid Beilzefte, 1943, 54, 251.l7 Mackor, Rec. trav. chini., 1951, 70, 663, 747, 763, 841.l8 Stigter, ZVth Znt. Congr. Surface-Active Substances (Brussels, 1964), no. B IV-2.l9 Lyklema, Scholten and Mysels, J. Physic. Chem., 1965, 69, 116.20Derjagui1-1, Trans. ConJ Colloid Chem. (ed. Acad. Sci. Ukrain, S.S.S.R., Kiev, 1952), p. 26.Karasev and Derjaguin, Colloid J. (Russ.), 1953, 15, 365.21 Derjaguin and Titijevskaja, Disc. Furuday SOC., 1954, 18, 27.Fiz., 1955, 29, 94 ; Soviet Physics JETP, 1956, 2, 73.Rome, April, 18-24, 1966)

ISSN:0366-9033    

DOI:10.1039/DF9664200007

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

GENERAL DISCUSSIONProf. M. Mirnik (Zagreb, Yugoslavia) said: Some or all of the difficulties of thetheories of stability and coagulation are removed using the ion-exchange theory.Also the phenomena caused by the interaction of charged elementary particles inthe layer near the solid/liquid interface are explained. Its essential ideas are : (i) Theelectric parameter is the electrostatic potential around the adsorbed discrete consti-tuent ions fixed on the surface ; this decreases with the distance (fig. 1) and replaces theFIG. 1.-Variation of the electrostatic potentials with distance r froni a discrete adsorbed cation atY = 0. 'p+ potential function when the counter ions (anions) are absent, 'p- potential function whenthe statistical distribution of the counter ion remains unchanged when the cation is absent.9 theactual potential function resulting from the equilibrium distribution of counter ions at a mean distancer = 6 determined by the equality of electrochemical potentials of the counter ion in the layer and inthe bulk liquid, i.e., when pM,layer(r = 6) = p ~ ( r + >.surface potential (Psolid- (Pliquid = $0 of the double layer theories. The electrostaticpotential around the discrete adsorbed stabilizing constituent ions is analogous to thepotential of the central ion in the Debye-Huckel theory. The condition of equilibriumis given by the equality of electrochemical potentials of counter ions in the layer andin the solution.(ii) The dependence of the mean electrostatic potential A 9 at which these counterions or a counter ion and a dipole M and M' are statistically exposed in the doublelayer of their adsorbed amounts (= activity) xy and (1 -x)y and their activity a Mand aMt in the liquid is defined by the equations (A'cp is a standard potential)A? = Aoq+(RT/F)[za+ln ( a M / x y ) ] , (1)A(P' = A"q+(RT/F)(z'a +In [ n M p / ( l - x ) y ] ) .( 2 )1GENERAL DISCUSSION 15At equilibrium, Acp = A'cp. Acp corresponds to the potential of the ionic atmosphereof the Debye-Hiickel theory exerted upon the central ion. When aM<a&, Y-)ystaband when aM>ah, y - + ~ ~ ~ ~ ~ . Ystab is greater than Y c o a g due to the high dispersity ofthe stable sols. y is the activity of adsorbed constituent ions, measured on sols ofconstant dispersity as amount adsorbed.(iii) With the aid of these equations, and considering that water molecules are thestabilizing dipoles, equations were derived by which the most experimental results,some of which are summarized by Herak, Despotovib and myself, can be explainedquantitatively .(iv) On the basis of the Smoluchowski equation the reciprocal or the electrokineticpotential 5 or of the measured factor b which is proportional to it, is in the ideal caseproportional to the discrete charges double layer potential A q .The interrelationbetween b or i;, URI. and x is then given by the following equations :or= 1 / C ( U M 4 ) + 1/5, ln (xa&/a,). (3b)11% or l/cs is a constant proportional to RT/F representing the variation of l/b or l/cfor a tenfold variation of aM, when x-+ I .Simultaneously the relationa,(l - x ) / x = a; = ~ O - ' " U ~ ~ (4)is valid. a& = aM,coag is the activity of the counter ion at which x = 1 --x = 0.5,i.e., when 50 % of the stabilizing particles are replaced in the double layer by thecounter ions. It is also assumed to represent the condition for the onset of coagula-tion in the ideal case: a& = aMt. S = 10(z'-z)na~e is a constant of the equation,obtained by extrapolation of experimental values for x = const. or [ = const. toz = 0. Theoretically it is the product of the constant activity of the stabilizingparticle aMt and of the corresponding selectivity coefficient of ion exchange S thatdetermine the equilibrium between the counter ions and the stabilizing dipole mole-cules (H20).In this way the linear formulation of the Schulze-Hardy rule is postu-lated (and experimentally confirmed) in electrokinetics too. Theoretical plots forions of different valencies are shown by fig. 2.1 From eqn. (1) and (2), for twocounter ions, the selectivity coefficient S and the separation factor (equilibriumconstant) of ion exchange can be derived.2Levine claims that silver iodide could not exist if my conclusion were correct.Since silver iodide is chemically stable mathematicians must be wrong when they tryto prescribe postulates which contradict experimental evidence.Overbeek, Derjaguin and others 3-6 have claimed that the DLVO theory has beenconfirmed experimentally in respect of the Van der Waals constant A, the surface Il/oand electrokinetic 5 and potentials respectively, the sixth power formulation of theSchulze-Hardy rule and the particle size.We now appreciate Overbeek's view on thenecessity of including into the theory the influence of solvent molecules on the zetapotentials, on the necessity of replacement of the surface potential and the fact that1 Mirnik, Croat. Chern. Ada, 1963,35, 217.2 Mirnik, unpublished work.3 Overbeek, Disc. Faraday SOC., 1954,18, 184, 186,206,207,210.4 Derjaguin, Disc. Faraday Suc., 1954, 18, 182, 184, 198.5 Reerink, Disc. F'araday SOC., 1954,18,204.6 Reerink and Overbeek, Disc. Favaday Soc., 1954, 18, 7416 GENERAL DISCUSSIONthe problem of Van der Waals attraction forces is not yet solved, and that the electro-static repulsion may have been incorrectly estimated.There has not been a quanti-tative confirmation of the DLVO theory which satisfies the minimum objective criteriato check the original or extended versions of the theory.b'l aM - tog aMFIG. 2.--Theoretical plots for the variation of Acp, 118, 1/6 or l/<(ordinate) against logarithm con-centration of counter ions (abscissa) according to eqn. (3). Upper part : influence of the valency ofcounter ions on the x / ( l - x ) value of eqn. (4).Prof. B. TeZak (Zagreb, Yugoslavia) said: Colloid stability may be interpreted inseveral ways. One is by diagrams of attraction and repulsion forces to give complexfunctions. I would stress other aspects, viz., the physics and chemistry of all essentialcomponents which cannot be independently treated, i.e., (i) the solid or semisolid,usually crystalline colloid particle, (ii) the methorical layer, and (iii) the bulk solution.For an interacting unit, either a simple or complex ion or some other species of thesolution, with constituents or complex groups of the solid phase, the potential may bedivided intofltotal = &hem +&ere0 +&oui +i%ollig./(stereo is responsible for the specific adsorbability and pco11ig is a term giving thecharacteristics of a species with translational degrees of freedom.If the species arecharged, the coulombic interactions should also be taken into account but only as Faras the individuality of the species is preserved. By strong couloinbic or stereochemicalinteractions, new species, such as ion pairs or specific adsorption complexes, may beformed and the new situation should be expressed by the corresponding mass actionequilibria giving other distributions of colligative units in the system.For colloid system of the solid-solution type, the results of such interactions areexpressed by the concentration differences in the neighbourhood of the solid wall(rnethorical layer) and in the bulk solution.Such differences should be responsiblenot only for coagulation, flocculation, stabilization and peptization, but also foGBNBRAL DISCUSSION 17other processes (sensitization, protection, coacervation and other colloid phenomena).The first step for the stability-instability relationship is to ascertain the critical con-centrations, or the critical distances for interacting species of the solution phase fromthe specially distributed species (discrete charges) on the wall of the dispersed phase.Such interactions may be of coulombic character resulting in the formation of ionpairs between a boundary complexoid and oppositely charged counter ion (coagula-tion), or of stereochemical character leading to the specific adsorption of large ions ormolecules of the solute species (flocculation) ; in both cases the changes in stabilityconditions are induced by resulting concentration differences of microcomponents(ions, molecules) between the methorical layer and the bulk solution.These relation-ships are schematically presented in fig. 1.0 I i 3 -4 5 6 -7(-3) (-403 (-501 (-80) I-1001 (-120) (-140)Log.concn [MI(-distance fram the solid wall in A ) 0FIG. 1 .-Schematical presentation of corresponding states of interacting species (ions or molecules)of solution with constituents of solid phase boundary, controlling either coagulation (ion-pairformation), or flocculation-protecting stabilization (specific adsorption).All these circumstances are encountered with preformed sols. If our aim is tounderstand the primary conditions of colloid stability of various systems starting withthe formation of either clusters, or embryos, or nuclei, or primary particles, the rightanswers are given through genetical approaches in which the first orientationalschemes are presented by contours of the precipitation bodies.Prof.J. T. G. Overbeek (vun’t Hoff Lab., Utrecht) (contmuniclzted) : Teiak criticizesthe interpretation of colIoid stability by means of attractive and repulsive forcesbetween colloidal particles and says that these are not reflecting the real cause-effectrelationships. On the contrary the only correct way to understand colloid stabilityis to consider it as the result of the interplay of thermal motion (Brownian motion)or macroscopic shearing motions with the forces between the particles, taking intoaccount that these forces are in principle influenced by all the components of thesystem. I agree that a complete and quantitative formulation of these forces and ofthe Brownian and shearing motions is a complex task, of which only the broad out-lines have been completed and to which much detail still has to be supplied18 GENERAL DISCUSSIONProf.B. V. Derjaguin (Acad. Sci., Moscow) said: The steric mechanism of protec-tive action on the lyophobic sols needs as a supplement some explanation of whyprotective layers do not adhere to one another under the influence of Van der Waalsforces. One explanation is given by Glazman who postulates the formation of solvatelayerson the outer surface of the protective layers. Another is Overbeek's postulate ofthe identity of the Van der Waals constant of the protective layers and the medium.Such identity is very unlikely to be universally realized, so that the solvation hypothesisis preferable.Dr. E. J. W. Verwey (Philips lies. Lab., Eindhoven) said: With respect to theprotective actions as discussed by Overbeek one has the impression that in theliterature there is sometimes a misleading concept of the protective layer.It would betoo simple to imagine that such a layer, if adhering rigidly to the particle, could preventagglomeration by steric hindrance. In that case the effect of such a layer wouldgenerally be that the Van der Waals-London attraction between the particles (includ-ing the adhering layer) is increased. Hence one arrives at the conclusion (perhapssomewhat paradoxical at first sight) that such layers can only give rise to protection ifthey represent structures which deform or break down sufficiently upon interpenetra-tion, because only in that case there will be a repulsive force, acting over a certaindistance, provided by the energy required to demolish these structures.Prof.J. T. G. Overbeek (uatz't HoH Lab., Utrecht) said: Vold has previouslypointed out that when particles are surrounded by a (massive) layer with a Van derWaals constant close to that of the dispersion medium the net Van der Waals attractionis drastically diminished. Consequently such a massive layer may act as a protectiveagent. I believe, however, that the more usual mechanism of protection is based onthe adsorption of molecules with at least one group with a high affinity for the interfaceand with a sufficiently long tail, which is soluble in the dispersion medium and doestherefore not have any tendency to adhere to similar molecules adsorbed on otherparticles. These protecting molecules are not necessarily and perhaps preferably notin close packing.Dr.F. M. Fowkes (Sprague Electric Co., North Adarns, Mass.) said: In myexperience, non-aqueous, especially non-polar, suspensions such as lubricating oils,paints, and inks are normally stabilized by electric charge, and other forms of protec-tive action are seldom required. I disagree with Overbeek that this mechanism is" of minor importance ".Overbeek's remarks on the measurements of van der Waals forces (direct measure-ments of only the retarded forces, and only indirect measurements of the unretardedforces) should have included a mention of calculating Hamaker A constants from thedispersion force contribution to surface free energy (yd).Values of ya are now knownfor a variety of solids and liquids, and use of the approximate equationwhere K1 is the appropriate dielectric constant for the continuous phase, gives excel-lent agreement with many of the Hamaker constants obtained from coagulationkinetics. For example, as mentioned by Watillon and Joseph-Petit, polystyrene(yd = 44) in water (ya = 21.8, K1 = 1-76) is found by experiment to have A - 5 x 10-14 ;the equation gives A = 5x 10-14.Prof. J. T. G. Overbeek (van't HoflLab., Utrecht) said: I have been aware of thepossibility of stabilization of suspensions in non-polar media by an ionic mechanisGENERAL DISCUSSION 19mentioned by Fowkes and I did not want to express more than that in the cases thathave come to my knowledge, stabilization in non-polar media were more frequentlybased on protection rather than on electrostatic repulsion.I am willing to acceptthat for another selection of examples the situation is reversed. At present, themethod based on surface and interfacial tensions and on contact angles to estimatethe Hamaker constant is one of the best, but it suffers from the drawback of beingsensitive to the packing of the molecules near the interface. This packing may differsignificantly from that in the bulk of the phases.Mr. D. W. J. Osmond (Z.C.I. Ltd., Slough) (communicated): I do not think thatthere must be a near identity in the Hamaker constant between the solid polymericmaterial from which the barrier is created and the medium for steric stabilization tooperate.The essential requirement is that the barrier material must have negligibletendency to associate with itself in the medium-i.e., it must be completely soluble.For typical polymeric stabilizing materials, such solubility generally implies a goodmatch between the Hamaker constants of medium and polymer, especially in non-polar media. Where fairly strong short-range polar interactions between mediumand polymer are possible, however, there are cases in which good solubility isachieved despite a substantial mismatch in Hamaker constants. Even in thesesystems, the solution of stabilizing polymer in this medium, which forms the barrier,is not likely to differ greatly in Hamaker constant from the pure medium, whencompletely effective deflocculation occurs.Dr.D. H. Napper (Z.C.Z. Ltd., Slough) (communicated): Overbeek has suggestedthat the terms " flocculation " and " coagulation " should be used synonymously toprevent confusion in reading literature already published. I support, however, thegeneral thesis that a more precise definition of the terms " flocculation " and " coagula-tion " is desirable. Nevertheless, use of the term " coagulation " to describe aggrega-tion in the primary trough and the term " flocculation " to describe bridging aggrega-tion or secondary trough aggregation appears to be semantically clumsy.First, if the particles of a colloidal dispersionaggregate then it is necessary to describe this process by a generic term, usuallybefore it is known how the process occurs.A good analogy to this is the use of thegeneric term sorption to describe gas uptake by a solid before it is known whether thisis specifically adsorption or absorption. The obvious choice for a generic term, ifflocculation and coagulation are reserved for secondary and primary aggregationrespectively, is aggregation. The difficulty with this nomenclature is that, althoughaggregation, flocculation and coagulation are related phenomenologically, the termsare not obviously related semantically as, e.g., are sorption, adsorption and absorption.The second difficulty arises with particles of material A coated with layers ofmaterial B. When such composite particles aggregate, the inner A particles wouldhave to be considered in some instances as flocculated whilst the jackets of material Bwould be coagulated.These difficulties partially disappear if " flocculation " ischosen to be the generic term and the adjectives " primary ", " secondary " and" bridging " (or perhaps " third-body ") are used to differentiate between the parti-cular types of flocculation. The term " coagulation " is thus reserved for flocculationfollowed by coalescence.Prof. B. Teiak (Zagreb, Yugoslavia) said: It seems convenient to apply the namecoagulation to processes and states caused by the formation of ion pairs, whereas foraggregation caused by stereo and chemical forces the name flocculation can be reserved.These are in general accordance with the proposal of La Mer.There are two reasons for this20 GENERAL DISCUSSIONAs to the free energy changes, in complex systems, this consists of different parts,and probably the best solution is to use stepwise and cumulative formation constants,and for the free energy of aggregating systems to use for cumulative functionsAGcum = AHo - TAScUm, where the initial state is a relatively stable colloid solution,and the final one a system with macroscopically separated phases.SENSITIVE STRUCTURAL UNITS OF COAGULATING SYSTEMrncthoiical layer phise/A- - - - I -/ \ . .-\ /3,' \Ae i t h e r o f A ( c r y s t a l l a t t i c e 1, 8 (ionirgenic groilp), o r c (counter ion), or 0 ( s o l v e n t ) , or many of them SimulTaneouslychange in p H may influence t h e sTateFIG. l.-Schematic presentation of points of physical and chemical change for changed substantial orconcentration conditions of colloid system.Prof.B. V. Derjaguin ( A d . Sci., Moscow) said: Overbeek mentioned the paper byMysels concerning the measurements of thickness of free films dragged out of a solu-tion. The thickness of those films coincided within the limits (not very narrow) ofexperimental errors with the theoretical formula when one substitutes in it the vis-cosity value in the bulk of solution. This is reported as a proof that the viscosity ofthin film is the same as in the bulk. This reasoning is not convincing because thethickness of the film dragged from the bulk is controlled not by its own viscosity butby the viscosity of the solution in the place and at a time when it is ready to pass fromthe bulk to the film.In this transient moment the viscosity may still maintain thebulk values. The viscosity may change to some specific thin film value only aftersome lapse of time. But there are direct measurements 1 which have proved thatthe viscosity of liquid changes near a solid interface.Prof. B. V. Derjaguin (Acad. Sci., Moscow) said: In reply to TeZak, the theoryof stability of lyophobic colloids has a certain domain of applicability. Thereforethere is no disagreement between the statement of its validity within this domainand the existence of cases (outside this domain) where the theory is not applicable.TeZak wishes to have a " critical report " concerning the direct experimental determina-tion of the Hamaker constant which was the subject of a lively discussion in 1954.The " vagueness " alluded to by Teiak arose as two mutually contradictory experi-mental papers were presented at the 1954 Discussion.One of these by Sparnaay andOverbeek 2 contained experimental measurements of Van der Waals attraction of twoglass plates that surpassed the theoretical values by more than three orders of1 Derjaguin and Karasev, Proc. 2nd. Int. Congr. Surface Activity, vol. 3 (Butterworths, London,2 Overbeek and Sparnaay, Disc. Farutlay SOC., 1954, 18, p. 22.1957), p. 531GENERAL DISCUSSION 21magnitude. The other paper contained the experimental results of Abrikossova andmyself 1 for quartz lens to quartz plate attraction that are in good quantitative agree-ment with Lifschitz’s theory published later.In subsequent papers by Abrikossovaand myself, results for some other materials 2 were reported (thallium halides and achromium-quartz pair). Those results also agreed with the theory. The experimentswith glass were confirmed by Kitchener,3 De Jongh,4 Black, Jongh,s Overbeek andSpaarnay (after the experimental procedure had been improved). In spite of thiscoincidence, attempts were undertaken again to cast doubt upon the correctness ofthe results presented by myself and Abricossova at the 1954 Discussion and toascribe the agreement of our experiments with theory to an accidental compensationof the errors of digerent origin and nature 6 (Volta potential difference, dust particles,swelling of the quartz surface).These attempts seem unreasonable because theagreement is observed in all our experiments with lenses of diferent materials andcurvature, including those carried out before the appearance of the Lifschitz theory.Therefore, our experiments (but not those of Overbeek and Sparnaay of 1954) are thefirst correct direct measurements of Van der Waals attraction of solid bodies, as afunction of distance. The objections raised in 1954 Discussion by Overbeek7against our method of measurement were refuted by myself at the same discussion 8but in spite of this some of these objections were repeated later.6The only new objection added since is the allegedly possible creation of attractiveforces by the difference in Volta potentials of both plates (or plate and lens). Butto remove this effect we and other authors used the most simple, general, direct andsure means.Namely, we used ionizing agents for securing the electroconductivityof the air in the gap and eliminated the electric contact between the two bodies.Under such conditions the supposition of electric attraction acting through the gapwould be equivalent to the negation of the fundamentals of electrostatics. Thismethod of removing the potential drop across the air gap is familiar to physico-chemists who use it for measurements of the surface potential at air-solution interfaceby means of probe electrode placed in the air.That we (and also Kitchener and Prosser) succeeded in using this method effectivelyis obviously proved by the fact that amongst many hundreds of molecular attractionvalues measured by us 1 9 2 not a single one was abnormally high.This statementembraces also our measurements 2 of attraction between the chromium-quartz pairwhere the difference of contact potentials, were it effective, should surely cause anattraction exceeding the values measured by us by several orders of magnitude.This fact should be compared with the measurements of 1954 of Overbeek andSparnaay, where only abnormally high attraction values were obtained.9 Thisproves objectively that, in the last measurements, ionization of the air in the gap wasnot sufficiently effective.It is also evident that in the absence of air conductivity it is impossible to securesimultaneously the removal of accidental surface charges and of the Volta-effectattraction.1 Derjaguin, Titijevskaja, Abrikossova and Malkina, Disc.Faraday SOC., 1954, 18, 24, § 3 (p.33-37). Derjaguin and Abrikossova, Doklndy Akad. Naitk S.S.S.R., 1953, 90, 1055.2 Derjaguin and Abrikossova, J. Physics Chem. Solids, 1958, 5, 1.3 Kitchener and Prosser, Ngture, 1956, 178, 1339 ; Proc. Roy. SOC. A , 1957, 242, 403.4 De Jongh, Thesis (Utrecht, 1958).5 Black, de Jongh, Overbeek and Sparnaay, Trans. Fwaday SOC., 1960, 56, 1597.6 Sparnaay, Physica, 1958, 24, 751, see espec. p. 756.7 Overbeek, Disc. Firuday SOC., 1954,18, 184.8 Derja,guin, Disc. Faraday SOC., 1954, 18, 184-186; see also p. 182-184.9 Overbeek and Sparnaay, Disc. Faraday SOC., 1954, 18, p. 2222 GENERAL DISCUSSIONThus, summarizing our answer to TeZak’s question we may state : (i) There wereno objective and reasonable grounds to doubt the correctness of our measurements ofretarded Van der Waals forces between identical as well as non-identical bodies.(ii)The vagueness concerning the attraction of macroscopic bodies lies not in our experi-mental procedure and its results but only in the erroneous discussion of possiblesources of errors. (iii) Some sections of the last papers by the Dutch scientists haveincreased this vagueness caused by unsound suppositions that required no specialnew experiments for their refutal. Thus. the statement 1 : “ The present series ofmeasurements appear to have removed all possible doubt about the order of magnitudeof the retarded Van der Waals’ forces ” may be purely subjective. (iv) The directmeasurements of non-retarded Van der Waals forces in liquid media were reportedby Scheludko.1Finally, I mention a misunderstanding connected with the method of comparisonof the theoretical formulae with the experimental results.1 The only statement tomake is : deviations of experimental points from the theory did not exceed the possibleexperimental errors.The range of the values of the variables is too narrow and the errors too high(c 50 %) to justify the attempt to find out from experimental data “ the most probable ”exponent of the force-distance relation. This would have some sense only when it isnecessary to find an empirical formula for molecular attraction. But in the actualcase 12 this procedure is merely an example of an unreasonable use of the theory ofprobabilities.1 Black ef al., Trans. Farahy Soc.? 1960, 56, 1608.2 Scheludko, Doklady Akad. Nauk S.S.S.R., 1958, 123, 1074.3 Black ef al., Trans. Faradar SOC., 1960,56, 1603-1605

ISSN:0366-9033    

DOI:10.1039/DF9664200014

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

Possible Mechanism for the Spontaneous Rupture of Thin,Free Liquid FilmsBY A. VRIJvan’t Hoff Laboratory, Sterrenbos 19, Utrecht, The NetherlandsReceived 2nd March, 1966The stability of a free, thin liquid film against small, spontaneous thickness fluctuations is explored.The film is unstable with respect to fluctuations with wavelengths larger than a critical wavelengthA, = [-2-.2y/(d2V/dh2)]4, where y is the interfacial tension and V(h) the free energy of interactionas a function of the film thickness h. V(h) may include van der Waals attraction and double-layerrepulsion. The kinetics of the growing fluctuations is obtained by assuming a laminar liquid flowbetween rigid fiLm surfaces at a constant viscosity. There are stable fluctuation-modes, which growexponentially with time, each with a characteristic time constant T, and modes with certainwavelengths grow faster than all others (T = T~).If the van der Waals forces predominate A, andT, are given by eqn. (4.2) and (4.3) respectively. For A = 10-14-10-12 erg, y = 30 dynelcm andIz = 100-lo00 A, A, ranges from 0.6-600 p and T, from a fraction of a second to several hours. Thelife-time and critical thickness h, of an unstable film are also calculated ; they depend on the timeconstant rrn and on the time of draining. The critical thickness is calculated for microscopic,circular films and compared with measurements of Scheludko and Exerowa. For water andaniline films, the calculated h, are 410 and 750 A respectively, whereas the experimental values are270 and 410 A.Studies on the stability of thin, free liquid films are of importance for an under-standing of colloidal systems, such as foams and emulsions.1-4The life-time of liquid films is determined by two processes, thinning and break-ing.Thinning of a film occurs by draining of the liquid under the influence ofgravity and suction at the Plateau-borders. When the thickness is reduced toabout 1000 A, other forces influence the draining ; van der Waals attraction increasesthe draining rate ; double layer repulsion decreases it. On further thinning-whichoften occurs discontinuously-some films become metastable ; others, however,collapse between 500 and 100 A. Metastability is reached when border suction,van der Waals attraction and double-layer (or other) repulsion equilibrate ; in-stability results when the attraction forces predominate.1Rupturing of metastable films, if it takes place, seems to occur in an irregularmanner because of lack of control over external disturbances such as thermal shocks,vibration, dust, etc.3 Spontaneous rupturing through the formation of a nucleus(hole) requires a high activation energy if the film thickness is larger than lOOAas shown by de Vries 5 ; accordingly, such a process becomes highly improbable.Only for extremely thin films (bimolecular leaflets) may this mechanism becomeimportant.6Unstable films (often called transient films), always rupture spontaneously,often at a characteristic “ critical thickness ”.At present, however, it is still un-known why the critical thickness is usually several lOOA instead of a few 10Anecessary for the spontaneous formation of a hole.Scheludko 7 proposed that, at its critical thickness, the film becomes unstablewith respect to small, spontaneous surface deformations, such that, in spite of an224 RUPTURE OF LIQUID FILMSincrease of the free energy through the increase of surface area, the total free energydecreases because of the van der Waals forces.He associated the wavelength Aof a certain surface deformation with a critical thickness hc, as follows :Here K is a constant proportional to the Hamaker constant : A = 6nK, and y theinterfacial tension. The theoretical value of A could not be calculated, however.Further, he proposed that the sudden formation of black film from a thicker oneoccurs by a similar mechanism.That surface corrugations-due to thermal motion-exist was shown by theauthor 8 from the light scattering a liquid film exhibits when placed in an intenselight beam.From the intensity of the light scattering and its angular dependence,information on surface forces, operating in the liquid film, can be obtained.In this paper the stability of these surface corrugations and the kinetics of theirdiminution and amplification are explored. In an unstable film some of these surfacecorrugations may grow until they rupture the film. The mechanism is analogousto that proposed by Cahn9 fcr the phase separation by spinodal decomposition insolutions.FREE ENERGY OF THE CORRUGATED FILMConsider a free, liquid film (medium 2), with a mean thickness ho, between twomedia 1 and 3.The upper interface (1-2) is in the X-Y plane ; the lower inter-face (2-3) in a plane at a distance tzg beneath it. The free energy increase AP associ-ated with u certain, small corrugation 212 in the interface (1-2) and a corrugation223, in the interface (2-3) is given by 8AF = j J { + m 1 2 1 a x ) 2 +(az,,/aYY +(az231ax>2 +(az2,1aY)21 ++(d2~/dh2)0(Zi2 -z2,)23dxdY, (2.1)where y is the interfacial tension and Y(h) the free energy of interaction per unitarea. The integral is taken over the surface of a square, a2. The first term in eqn.(2.1) is the work associated with the increase of surface area owing to the corruga-tions; the second term is due to interaction forces such as electrostatic repulsionand van der Waals attraction.Eqn.(2.1) may conveniently be separated asAF = AF, +AF,,where we have substituted 212-z23 = h-ho. Thus, the corrugations of the twosingle surfaces, 212 and 223, are replaced by two “normal” corrugations given bythe linear combinations (212 + 223) and (212 - 223). The combination (212 + Z Z ~ ) ,associated with AFl, depicts fluctuations in the bending of the film as a whole,whereas the combination (212 - 2 2 9 , associated with A F 2 , depicts fluctuations intht= film thickness.AFz, however, may become negative if(d2V/dh2)o<O and the second term in eqn. (2.4) predominates. This means thatthe film is always stable with respect to fluctuations of the former type, but mayAFl is always positive when y>OA .VRIJ 25become unstable for some fluctuations of the latter. Because we are only interestedin fluctuations that make the film unstable, we restrict the further discussion tofluctuations in 212-223 = h-ho.To specify such fluctuations further, it is convenient to consider the Fouriercomponents of h(x,y) :4-00 +a,h - h, = c c Hpu exp[ip(px+ OY), (2.5)p = - a @=-mwhere p L== 2nla. Since lz is real the (complex) Fourier coefficients are connectedin pairs by the relations :H-p,-G - * - Hp,; Hp,-u = HTp,G; H-.p,o = Hp*,-=.Each fourier component contributes independently to AF2. For instance, thecomponent Hpo yields the contribution,n 'HP,H:,[+yp2(p2 + 02) + $(d2 Vjdh2)o].tVlien d2V/dh2<0, this component will decrease the free energy ifwh.ereA, is the wavelength of the critical fluctuation.A fluctuation with A<A, will" fluctuate " around a (meta)stable equilibrium. A fluctuation with A>&, how-ever, will grow in amplitude, making the film unstable. Such a fluctuation canElways be found if the dimensions of the film (e.g., a) are larger than&. Thus,a >A,,or with eqn. (2.7),(d2V/dh2)0 < - 27c2y/a2GROWTH OF THICKNESS FLUCTUATIONSTo obtain the kinetics of the fluctuation process, the mechanism of liquid transportthrough the film must be specified. Although the fluctuations may be created througha spontaneous process caused by thermal motion, their average decrease or increasein time may be described by macroscopic laws if A is large with respect to moleculardimensions. Furthermore, eqn.(2.1) is valid only near equilibrium so that theequation to be derived will only describe the kinetics of the initial stage of the growingprocess.For simplicity, we assume a laminar liquid flow parallel to the surfaces of thefilm (of uniform thickness ho) ; this assumption is reasonable if A 9 ho and h - ho < ho.It is further assumed that the liquid in the film has a constant viscosity up to theinterfaces, and that no slip occurs at the interfaces.10 Then we may write for theliquid flux per unit length,llwhere pl is the viscosity of the liquid and AAP is the extra pressure on the film due tothe fluctuation.Q = -(h:/12~) grad AP, (3.1)For AP, one may write 12AP = .AP,,+A(dV/dh).(3 -2)Mere AP is the capillary pressure counteracting this fluctuation whereas A(d V/dh)is due to intermolecular forces in the film. For small fluctuations one may writefor eqn. (3.2),AP = -+y(a2h/ax2 + a 2 h / a y 2 ) + (d2 V/dh2),(h - ho). (3.326 RUPTURE OF LIQUID FILMSTo describe the dependence of h on time we need the law of conservation ofvolume :ahlat = -div Q. (3 04)Combining eqn. (3.1), (3.3) and (3.4) yields the equation of motion :ah/& = (h;/12q)((d2 V/dh2)o(a2h/ax2 + a2h/ay2)-+ ~ ( a ~ h i a ~ ~ + 2a4h/a~2dy2 + a4hpy4)}. (3.5)This equation is formally equivalent to the equation of Cahn,g which describesconcentration fluctuations in solution as a function of tinie.The solution of eqn.(3.5) is 9 :withandEqn. (3.6) is an extension of eqn. (2.5). It describes the thickness fluctuation asthe sum of independent stationary sinewaves, the amplitudes of which are exponentialfunctions of time. Thi: initial amplitudes and phases, represented by the (complex)I$,&) are defined by the initial fluctuation at t = 0.Substitution of the eqn. (2.7) and (2.8) into eqn. (3.8) shows that z<O whenA<& and that z>O when A>&. Thus, fluctuations of thc first kind (z<O) willdecrease exponentially with time and return to metastable equilibrium, whereaA . VRIJ 27fluctuations of the second kind (z>O) will increase exponentially with time and movea way from equilibrium.z depends on k. It shows a sharp minimum at A, -- Ac23; see fig.1. Thisminimum appears because, when A is only slightly larger than Ac, the driving force,and thus also the liquid flow speed, is small, whereas, when A is much larger thanA, the time required to produce the fluctuation is large, because the liquid must betransported over a larger distance. The minimum is equal toZ, = (24yv/h;)(d2V/dh2)i2. (3 -9)Because the amplitudes of fluctuation modes have z in the exponent, the amplitudeof the modes with wavelength Am will grow faster than all others.To visualize the thickness fluctuation (h-ho) of the film we refer to picturesobtained by Cahn.9 He used a computor to calculate the Fourier sum with randomselections of directions, phases and amplitudes. One of these is redrawn and givenin fig.2. It shows a pattern of interconnected ‘‘ hills and gullies ” with dimensionsof the order of A,. It seems reasonable to assume that the rupturing starts alongone of the gullies.STABILITY CONDITIONS AND TIME CONSTANT OF THICKNESSFLUCTUATIONSTo determine values for Am and zm, we need V(h) which is believed to containvan der VC’aals attraction and electrostatic repulsion terms. Graphs of V(h) repre-senting the first two contributions have been discussed elsewhere.1’ 13 Schematicplots of V(h) and also of d2V/dh2 are given in fig. 3(A, B).The stability of the film against thickness fluctuations can now be read fromfig. 3B. According to eqn. (2.10), instability will occur if d2V/d1z2< - h 2 y / a 2 .Large films (for instance, a = 1 cm) are practically unstable in the regions h<OPand h > OQ.For smaller films the unstability region at h> OQ is reduced and forthe smallest ones it will disappear altogether. The instability region at h<OP,however, will remain, although this does not imply that the film can reach suchthicknesses because of the potential barrier in V(h).Let us digress on the important case where the van der Waals forces predominate(at least in some region of h), and formulate V(h) as follows 1 (no retardation) :A is the Hamaker constant. Using this equation to calculate d2V/dh2 and sub-stituting the result into eqn. (2.7) yieldsThis equation is the equivalent of eqn. (1.1) of Scheludko. The numerical con-stant, however, is different because of his approximate treatment.A, as a function of ho is plotted in fig.4 with y = 30 dynes/cm and with A =10-14, 10-13 and 10-12 erg (plot 1, 2 and 3). Applying the stabiliiy conditiona>& (see eqn. (2.9)) it follows that films with n equal to about 0.1 mm should bestable at least down to a thickness of about lOOOA. Much smaller films, for in-stance, those separating oil globules in a creamed emulsion (say, a = IF), shouldbe stable even down to a thickness of about lOOA. For Zm one deduces from theeqa. (3.9) and (4.1) :In fig. 5, Zm is plotted against ho with y = 30 dyneslcm ;10-14, 10-13 and 10-12 erg (plot 1, 2 and 3).V(h) = - A112nh2. (4.1)Ac = hg(4n3y/A)+. (4.2)Z, = 96n2yqh:A-2. (4.3)= 0.01 poise and A 28I I fRUPTURE OF LIQUID FILMSFIG.3.--Schematical graphs of the free energy V(h) of interaction and its secondderivative, d2 Y(h)/dh2,as a function of film thickness h. The stable and unstable regions are marked. y is the interfacialtension and n the linear dimension of the filmA . VRIJ 29510lo"Id7I Qn0 10P3 WI 6'- d10IdTo calculate the time needed for the fluctuations to increase to values aboutequal to ha, i.e., the time needed to break the film, the initial values of the thicknessI3 0 100 3 0 0 1000 l o - - '10fluctuations have to be specified. In the draining film, i.e., a film in which lzo is afunction of t, the breaking time also depends on the draining rate. We considerfirst the simpler case of a stationary film in which ho is constant with time.BREAKING TIME OF A STATIONARY FILMThe breaking time t b of an unstable film will depend on ho, zm and the initialfluctuations of the film at t = 0 : i.e., the values of HpaH&(t = 0).The values ofthese last quantities, however, are generally unknown and different €or differentfilm samples. Therefore one may expect to have not just one value for tb, at a certainho, but a whole distribution of tb, because only one deep gully somewhere in the filmmay lead to breaking. At present, we content ourselves with the calculation of anapproximate, mean vdue for t b , assuming that the initial fluctuations are generatedby thermal motion.To this end let us suppose that the film will break when (h-h@ becomes ofthe nrder nf h, where the;har means an averape over the film area.thus.Substitution of eqn. (3.6) into the integral yieldshi C exp(2t~z)~,,,~~,(t = 0).P 30 RUPTURE OF LIQUID FILMSThis is a rough approximation because eqn. (3.6) was derived for fluctuations whichare small with respect to ho.To obtain an approximate value of this sum we may take advantage of the factthat for t$- only those terms closest to k = km, (k2 = p2(p2+02)), are important.Therefore we replace HpaH&(t = 0) by their average value at km and use, insteadof the full expression for z given by eqn. (3.8), its expansion around the minimumz = zm:where Ak = k-km, and replace the sum by an integral from Ak = - GO to + 00.This yields117 = 1 / ~ , - ( 4 / k ~ ~ , J ( A k ) ~ , (5.3)+a,h i 2i (HH*),, exp(2tlzm) (2nkm/p2) exp - (8t/zmk?)(Ak)'d(Ak), (5 -4)J-a,where (HH*)om is written for H,,H,*,(t = 0 ; k = km).Furthermore, (HH*)m isreplaced by a mean value, to be obtained with the help of the principle of equi-partition that states that the mean free energy of each fluctuation-mode, given byeqn. (2.6), should be equal to kT'2; thusApplication of this equation, at k = km, however, makes HPaHZq <O ; this is im-possible : indeed, eqn. (5.5) becomes invalid at k< k,. To circumvent this difficultywe assume that the interaction forces are " turned on " at t = 0, and drop the term(d2Y/d@)o. Then ( H H * ) h becomesSubstituting eqn. (5.6) into eqn. (5.4) and performing the integration then yieldsSolving this equation for t yields an approximate value for t b .One finds that t bis a small multiple of z, :For instance,franges from 4.5 to 6-9 for ho = 100 to 1000 A, using y = 30 dyneslcm.After a time approximately equal to tb, the unstable film either ruptures or abruptlydecreases its thickness to form a thinner metastable film, depending on the shapeof V(h). This mechanism may explain the sudden formation of black film from amuch thicker one, which is often observed.HpbHp)li6 = a-2[$yk2 +f(d2V/dh2)0]-1(kT/2). (5.5)(HH*),, = 2kT/ykia2. (5.6)(5.7)tb = r m f ( b , y ) (5.8)hi E! ( kT/2ynf)[exp(2 tlz,) Jl(2t/zm)*.LIFE TIME AND CRITICAL THICKNESS OF A DRAINING FILMThe life time tl of a draining film will not only depend on the time of breakinglb, but also on the time of draining.When the film is still thick the draining usuallyproceeds rapidly and the thickness fluctuations grow slowly or not at all. Whenthe film becomes thinner, however, the rate of draining slows down, whereas thestable fluctuations (if present) grow faster and faster until a critical thickness h, isreached at which one of the fluctuations grows so fast that the film breaks.The quantitative treatment of this process is complex because ho depends on tand, in turn, Ac, A, and rm on ho. Where ho decreases with increasing t, there isa corresponding decrease in A,, A m and zm. To take this into account a greaternumber of terms should be included in the sum (5.2) than for the analysis of astationary film, where ho was constant and only the fastest growing fluctuation, atthat ho, had to be included.Therefore, a simplified, graphical treatment is pro-posed which may be applied to films where the dependence of ho on t is relativelA. VRIJ 31simple and known, e.g., the small circular films investigated by Scheludko 7.10. 12.14-16and others.17-19In fig. 6, the breaking time t b and the lime of draining t are plotted, schematically,as a function of ho-within that range of ho for which modes with Am<a exist-for an unstable film (fig. 6A) and for an unstable film thinning to a metastable one(fig. 6B). Also, t + t b is plotted as a function of ho (dashed curve). fb is obtainedfrom eqn. (5.8) and (3.9). For unstable films, eqn. (4.3) for zm may apply1FIG. 6.-Schematical plot of the time t of draining and the time tb of breaking as a function of filmthickness ho.Part A : only van der Waals forces ; part B : both van der Waals forces and double-layer forces. tl is the lifetime of the film, lz, and he the critical and equilibrium thicknesses ; h,, isand, consequently t b will increase continuously with ho (see fig. 6A). For an un-stable film thinning to an equilibrium film with thickness he, V(h) may be of theform displayed in fig. 3A, with he near the minimum and the transient unstableregion at ho>OQ.Now the life time of a draining film with a thickness ho is always smaller thanthe corresponding value of t + t b . For smaller ho, also t+ t b becomes smaller untila minimum is reached at ho = hjn. This minimum value of t + t b is taken equal tothe life-time of the film; thus,is obtained with the relationthe thickness at the minimum in t+fb.vtl = ( t + tb)min.(6.1)(6.2) dtldh + dtb/dh = 0.The critical thickness h, corresponds to the thickness on the drainage line wheret = t l (see fig. 6). According to this procedure it should be considered a minimumvalue. In fig. 6A rupturing takes place at h,; in fig. 6B the thickness suddenlychanges from h, to he, the equilibrium thickness.TEST OF EQUATIONS ON DATA OF MICROSCOPIC FILMSScheludko and Exerowa 7,1*, 14-16 have investigated the draining and rupturingof circular microscopic aniline and water films in air. Some surfactant had beenadded to prevent local thinning (Gibbs-Marangoni effect) in the earlier stages ofdrainage and to allow the films to drain gradually and regularly with the opposin32 RUPTURE OF LIQUID FILMSinterfaces nearly parallel until breaking occurs at a thickness of a few lOOA.Ac-cording to Scheludko 12 the drainage cf the circular free films is governed by theequationwhere P is the pressure applied on the outside of the film mdr is the radius of the film and q the viscosity of the liquid. (For a further discussionof these equations, see Frankel and Mysels 20 and Platikanov.21)dhi2/dt = o ~ P , (7.1)a = 4/3yr2. (7.2)P is equal toP = P()-II,-rl,,. (7.3)(7.4)PO is the capillary suction at the Plateau border, lIw is the contribution of the vander Wads forces, given byand IIel is the electrostatic repulsion between the film surfaces.n,l may be neglectedif double layers are absent or if the electrolyte content is sufficiently high.A useful approximate analytical expression for h, may be obtained if PO andIIe1 are neglected with respect to n,, which is a reasonable approximation for smallho and high salt concentrations. It applies only to the last stage of the drainingprocess. Then one may writeFurther, dlbldh may be obtained from eqn. (5.8) and (4.3). Neglecting the dependenceoff on ho and using (7.5) and (6.2) one obtains :According to this equation, h, does not depend on q. A more general analysis,including the term PO, does not change this conclusion perceptibly. Experimentson films with varying y would show if this conclusion is correct.It is also of interest to calculate the approximate value of Ac at h,.Substitutingeqn. (7.6) into eqn. (4.2) yieldsTakingf = 7, one finds that A, N 0.21r.Scheludko and Exerova measured the ho(t) curve for aniline films stabilizedwith 0-5 % dodecylalcohol and obtained A N 7 x 10-12 erg (Po = 430 dynes cm-2 andr = 10-2 cm). The experimentally obtained critical thickness of aniline filmsstabilized with decylalcohol was about 420 A to within a small variation. Assumingthat the draining rates of films stabilized with dodecyl- and decyl-alcohol are equal,h, is calculated to be 750 using the graphical procedure and y = 39.4 dyneslcmand y = 0.044 poise. Eqn. (7.6) gives the more approximate value 890 A df = 7).From the ho(t) curve for films of 0.1 M aqueous KCl solutions, stabilized with5 x 10-4 % saponin the same authors obtained A N 10-12 erg (PO = 730 dynes cm-2 ;r = 10-2 crn).Critical thicknesses of films containing 0.1 M KCl and stabilizedwith propionic and butyric acid were also measured. They found hc" 270 A. Thedistribution of values of hc, however, was broader than for aniline. Assuming thatthe drainage of these films is the same for all stabilizers, and carrying out the sameprocedure as for aniline with y = 65 dynelcm and q = 0.01 poise, we calculate?I, = 410 A. Eqn. (7.6) yields h, = 485 A (f = 6.5).The analysis shows that the experimental values of h, for aniline and water areabout 1.8 and 1.5 times smaller than the theoretical values. This result seemsreasonable considering the number of approximations that has to be made.TheII, = -dV/dh = - A / 6 ~ h &dh,/dt 21 - A/9nqr2. (7.51h, -N O.222(Ar2/fy)*. ( 7 4A,(h=h,)~0*55rf-'. (7.7A. VRIJ 33discrepancy may be due to additional stabilizing mechanisms not included in thetheory. Any film elasticity will damp fluctuations in h, especially if they tend tobecome larger. Consequently, the thickness at which the film breaks is smallerthan that calculated here because then the van der Waals force outweigh thosearising from the Gibbs-Marangoni effect. Reducing the constant A of aniline bya factor of 8 and that of water by a factor of 3 would also remove the discrepancy.An 8-fold difference for aniline is outside the limit of experimental error, althoughthe reported value of A seems high with respect to that of water.A 3-fold differencefor water, however, is still in the limit of accuracy of which this value is known.The influence of the electrolyte concentration on the breaking process is marked.Scheludko 7 found a continuous draining to the equilibrium thickness with KClconcentrations lower than 10-2 M and a formation of black holes or rupturing atconcentration of about 10-1 M. These facts may be explained qualitatively fromfig. 6B : decreasing the salt concentration decreases 1 -d2l/ldh2[ and thus increasesi b . In the time corresponding to the minimum vdue of t + t b the film has alreadydrained continuously to a thickness close to the equilibrium thickness he, whichmeans that no sudden thinning to the equilibrium thickness occurs.There areindications, however, that the stability of the film against black spot formation orrupturing cannot be explained from the shape of the d2V/dh2 curve only.22The theory given above has been applied to the relatively simple, small, circularfilm. It should be, however, also a valuable starting point for the considerationof more complicated systems such as macroscopic films in a foam, very small filmsin a creamed emulsion, and films on a solid support.The author thanks Prof. Dr. J. Th. G. Overbeek for his encouragement and advice,and Dr. J. W. Vanderhoff for his assistance in the final preparation of the paper.1 Overbeek, J. Physic. Chem., 1960,64, 1178.2 Lyklema, Rec. trau. chim., 1962, 81, 890.3 Kitchener, Recent Progress in Surface Science (Academic Press, New York, 1964), vol. 1, chap. 2.4 Mysels, J. Physic. Chem., 1964, 68, 3441.5 de Vries, Rec. trau. chim., 1958, 77, 392.6Derjaguin and Gutop, Koll. Zhur., 1962,24,431.7 Scheludko, Proc. K. Akad. Wetensch. B, 1962, 65, 87.8 Vrij, J. Colloid Sci., 1964, 19, 1.9 Cahn, J. Chem. Physics, 1965,42,93.10 Scheludko, Proc. K. Akad. Wetensch B, 1962, 65, 76.11 Mysels, Shinoda and Frankel, Soap Films (Pergamon Press, London, 1959), 27.12 Scheludko, Kolloid-Z., 1963, 191, 52.13 Verweyand Overbeek, Theoryof the Stabilityof Lyophobic Colloids (Elsevier, Amsterdam, 1948),14 Scheludko, Kolloid-Z., 1957, 155, 39.15 Scheludko and Exerowa, Kolldd-Z., 1959, 165, 148.16 Scheludko and Exerowa, Kolloid-Z., 1960, 168,24.I7 Platikanov and Manev, Proc. 4th Int. Congr. Surface Actiuity (Brussels, 1964), preprint B/16.18 Sonntag and Klare, KolZoid-Z., 1964, 195, 35.19 Sonntag, Proc. 4th Int. Congr. Surface Activity (Brussels, 19641, preprint B/Vl 14.20 Frankel and Mysels, J. Physic. Chem., 1962, 66, 190.21 Platikanov, J. Physic. Chem., 1964, 68, 3619.22 Scheludko, Exerowa and Platikanov, Koll. Zhur., 1963, 25, 606.p. 106.Note added in proof. Eqn. (7.9, obtained by neglecting Po and 1Ta with respect to IT,, is apoor approximation in the range of ho in which it is applied. Neglection of IIw and Eel with re-spect to Po gives a better approximation. Then eqn. (7.6) becomes hcrtL0-268 (A2$/Pofy)f andcqn. (7.7) h,(h =-. IrJ N O*80(ArsyJ/P$f4)i1r

ISSN:0366-9033    

DOI:10.1039/DF9664200023

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

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

ISSN:0366-9033    

DOI:10.1039/DF9664200034

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

Direct Measurement of the Variation ofRepulsion with DistanceBY KAROL J. MYSELS" AND MALCOLM N.Double-LayerJONES tChemistry Dept., University of Southern California, Los Angeles, California 90007Received 13th June, 1966Soap films can be subjected to compressive stresses exceeding 1 atm while their thickness ismeasured optically in an apparatus which is described in detail. It permits forming the film withina ring of porous porcelain whose pores communicate to the outside, whereas the film is in an enclosurein which the air pressure can be varied. The applied pressure is balanced primarily by the double-layer repulsion between the monolayers of the film. Hence as the pressure is increased, the filmthickness decreases showing how double-layer repulsion varies with the distance between the mono-layers.The agreement with theory is satisfactory as far as it pertains to the region of low potentialswhich determines the slopes of the distance dependence. The absolute values involve the less certainhigh potential region of the theory as well as assumptions about the structure of the films but canbe brought into reasonable agreement. The effect of van der Waals forces can also be seen at higherionic strengths.The DLVO double-layer theory provides an explanation especially of repulsionsresponsible for the stability of colloidal systems. Rigorous quantitative tests ofthe theory are scarce, because of the usual complexity of the systems used and ofthe difficulty of measuring all the parameters involved.This paper presents ex-ploratory measurements using a technique suggested earlier 1 and designed primarilyto test as directly as possible one part of the theory, namely, the distance dependenceof the repulsion between two charged planes, but it has some relevance to otheraspects of the theory. In this technique, a soap film is formed in a ring of poroussolid which permits the application of large pressure differences between air con-tacting the free surfaces of the film and the bulk liquid in the pores of the solid.Pressures exceeding 1 atm, more than three orders of magnitude larger than thosepreviously accessible,ae 3 can thus be used.For our purposes, it is useful to separate the theory4 into three parts. Thefirst deals with electric properties in the region of high potential close to the chargedsurfaces.Assumptions involving the smeared-out nature of charges, activity co-efficients, ionic sizes and specific interactions are most important here. The secondpart is concerned also with electric properties but in the region of low potentialswhere these assumptions are less questionable. The third part deals with van derWaals forces.The potential +m in the middle between two parallel planes both at potential$ and separated by a distance 2d is 4 given by elliptic integrals but can be approxi-mated by$,,, = (8kTIze)y exp ( - K d ) , (1)* Research Dept., R. J. Reynolds Tobacco, Winston Salem, N.C., USA. t Chem. Dept., University of Manchester, England.4K. J . MYSELS AND M. N. JONES 43wheree is the electronic charge and z the valence of the counterions.The repulsionpressure between the two planes can then be shown 4 to bey = [exp (ze$)/2kT - l]/(exp(ze$)/2kT + 1). (2)+rn0P , = J pd$ = 2nkTCcosh (ze$,/kT- I], (3)where n is the number of counterions per cn13. This can be approximated byP, = nkT(ze$,lkT)2 = 64y2nkT exp (-2ud). (4)The integration in eqn. (3) extends only over potentials lower than t,hna and thefirst part of the theory, dealing with high potentials, enters into the computa-tion of $m only through y which is a constant for a given $. The approximationsleading to eqn. (1) and (4) introduce errors which are negligible in the region oflow potentials corresponding to ~ d > 4 but become important at closer distances.However, these errors tend to cancel so that eqn.(4) is good within 20 % downto ~cd = 0.7. The differences between the approximate and the exact calculationare shown by the dashed lines in the figures.For monovalent electrolytes in water at 25"@, eqn. (4) givesIn P , = In (1.59 x 109y2C)-~d2, ( 5 )where C is the molar concentration and d2 == 2d is the separation of the $ planes.The variation with distance of the double-layer repulsion is therefore given in thisapproximation by-8 In P,/ad2 = IC ( 6 )and is independent of $ and of the absolute value of d2.The third part of the theory involves van der Waals attractive forces which areusually assumed 4 to be dispersion forces resulting in an attractive pressure given byP, = Aa/6nS3, (7)where A is the Hamaker constant, d the thickness of a film or 5 9 6 the separation oftwo thick planes and a a correction factor 7 accounting for the retardation effectswhich become important as the distance becomes comparable to 1, the significantabsorption wavelength.For a soap film at equilibrium, the resultant of these internally generated pressuresmust balance any externally applied hydrostatic pressure Ph so thatPh = P,-P,.(8)When Ph is varied as in our experiment, the thickness of the film must change inorder to satisfy this relation. For thick films corresponding to low ionic strengths,van der Waals forces become negligible andAt higher ionic strengths, however, Pv can become comparable to P, and the hydro-static pressure then corresponds only to the small difference between them.Ph = P,.(9)EXPERIMENTALMATERIALSThe sodium dodecyl sulphate was a sample used in previous investigations 7-9 and thesodium tetradecyl sulphate was of similar purity but contained traces of the correspondin44 MEASUREMENT OF DOUBLE-LAYER REPULSIONalcohol. The sodium chloride was Reagent Grade. Distilled water was used in making upall the solutions.APPARATUSThe essential part of the apparatus is illustrated in fig. 1. It consisted of a cylindricalbrass cell, the top and bottom of which screwed on to the central portion, a seal being madewith neoprene gaskets. Circular windows were cemented into the top and bottom withepoxy resin. The lower window, through which optical thickness measurements were made,was always covered with a layer of liquid to avoid fogging.The porous porcelain disc wascemented with epoxy resin into a Perspex holder. A channel around the circumference of thedisc led into a capillary tube which passed through the top of the cell and was held in positionand sealed with a neoprene O-ring and a screwed plate. There was thus a free passage forliquid from the centre hole in which the film was formed, through the disc, around the channel,Pressure Capillary ,ScrewadDiscFIG. 1.-The apparatus for exerting air pressure upon the surfaoes of a film while allowing freeescape of the liquid.and up the capillary to the outside. The flat faces of the disc were covered with a layer ofcement. The disc itself was 20 mm in diameter and Q inch thick and was obtained from SelasFlotronics, Spring House, Pennsylvania, (microporous porcelain, grade 04 having a statedinaxinzum capillary radius 0.45 p, average capillary radius 0.22 p, bubbling pressure 3 atm).The central hole was drilled with a high-speed carbide-tipped burr drill, care being taken to getit slightly tapered towards the middle and as symmetrical as possibIe.The pressure inside the cell was varied by using compressed air and a bleeder valve.Thepressure was measured with a water manometer for pressures up to 105 dynes cm-2 and apressure gauge above this. Liquid could be pressed in or withdrawn from the disc to formthe film by nieans of an Agla micrometer syringe connected to the capillary with Tygontubing.The cell was mounted on a camera tripod ball and socket fitting so that it could beadjusted easily for focussing.OPTICAL APPARATUSThe optical part of the apparatus was essentially that used in previous work.10 A spotof light 0.8 nun diam. was focussed on the film and the reflection refocussed on a diaphragmleading to a photomultiplier assembly which measured the intensity of the reflected mono-chromatic light. The film was tilted sufficiently to insure that none of the reflection from thelower window or the bulk liquid which covered it entered the intake lens of the photo-mu1 tiplier assembly, so that the optical background wgs always completely negligible. Theangle of incidence of the light was 6"K. 3. MYSELS AND M. N. JONES 45PROCEDUREThe initial filling of the disc with solution was accomplished by immersing the dry discinto the solution contained in a small dish placed inside the brass cell and then increasing thepressure in the cell.Solution was thus forced through the disc around the channel and up thecapillary ; with a little manipulation it was possible to fill the system completely with solution.The same technique was used for flushing the disc between runs.The intensity of the last interference maximum (for which the optical thickness is a quarterwavelength) was determined by forming a film in the hole and applying suction using theAgla syringe, the pressure inside the cell being atmospheric. If the correct amount of suctionwas applied (found by trial and error) and the film was slightly inclined, the film thicknesseswere fairly even and layered and changing slowly enough so that a maximum intensity couldbe measured.The procedure was repeated several times to ensure that the true maximumhad been observed.Once the maximum had been established, the syringe was disconnected and the end ofthe capillary opened to the atmosphere. The pressure inside the cell was then increased to adesired point and the cell isolated with a valve to eliminate small variations of pressureswhich occurred in the compressed air source. The intensity of the reflected light was recordedcontinuously and it was possible to observe when equilibrium was reached. The pressurewas then increased by a further increment and the procedure repeated. No significanthysteresis effects were observed when the measurements were made with increasing or de-creasing pressure.The following two problems in the experiments need special mention.(a) THE KINETIC EFFECT.Fig. 2 shows a schematic plot of intensity against time as thehydrostatic pressure is changed. Provided that the pressure is changed sufficiently slowly insmall increments (104 dynes cm-2) the film thins evenly and equilibrium is always maintained.For large rapid pressure increments, film thickness falls to below its equilibrium value for theTIMEFIG. 2.43che1natic diagram of changes of the intensity of reflected light as a function of time followingchanges of the pressure acting upon the film.pressure concerned and then returns to equilibrium slowly at constant pressure.Thereason for this behaviour is probably that when the film thins rapidly in response to a pressurechange, its surfaces must expand and the surfactant concentration at the interface decreases,thus decreasing the charge density and the potential and hence reducing the double-layerrepulsion. The film thus reaches a momentary equilibrium at a reduced thickness corres-ponding to this lower repulsion and then approaches equilibrium only slowly as surfactantmolecules diffuse back into the surface of the fiIm.If the pressure was raised too abruptly, tne film burst. It sometimes burst also withoutapparent reason. The highest pressure attained without bursting was 1.2 x 106 dynes(1.2 atm) and several other films burst near this value.No systematic attempt was made toinvestigate whether this represents a significant limit as the required gradual increase inpressure becomes very time consuming.(b) THE OSMOTIC EFFECT. The solution used to cover the lower window is at the hydro-static Dressure in the cell whereas the solution in the plateau border round the film and in th46 MEASUREMENT OF DOUBLE-LAYER REPULSIONdisc is open to the atmosphere and is also in equilibrium with the film. As a result, the solu-tion in the base of the cell has a higher free energy and solvent will tend to distil on to thedisc and the film even though the solutions are at the same molar concentration. The cell isakin to an osmometer with a vapour phase membrane. When the difference in pressure is1 atm equilibrium corresponds to a concentration difference of 0.04 M for ideal solutions.If the distillation leading to such an equilibrium were significant, it could vitiate our results4 5 61 I Ifilm thickness, 6,8,FIG.3.-The effect of pressure upon the thickness of films of 0.0025 M tetradecyl sulphate solution.The liquid in the bottom of the cell was water : open symbols ; solution : frlled symbols ; 0.01 MNaCl : crosses. Van der Waals forces are negligible compared to the exact or approximate calculatedelectric forces (dashed lines).or at least greatly increase the experimental difficulty by requiring a change of solution withpressure. Absence of hysteresis suggested, however, that the effect was negligible and toestablish this point, the experiments of fig.3 were performed in which the composition of thesolution over the window was changed from pure water to 0.01 M NaCl. The results showno significant difference. Thus, distillation from the bottom of the cell is too slow to causesignificant changes of concentration in the disc and the film is sufficiently protected by thesurrounding equilibrium liquid in the walls of the hole.COMPUTATION OF THICKNESSESIf the film were to consist only of water, then its thickness d, could be computed from theoptical measurements according to 11I / I o = F sin2 (ndW/2p), (10)where 1/10 is the ratio of the intensity of light reflected from black film to that of the lastinterference maximum, Fis a correction factor accounting for secondary reflections, p = 344n(cos 4), n is the refractive index of the film, A is the wavelength of light (5460 A) and 4 = therefracted angle.To take into account the structure of the film we assume 798 that it is athree-layered sandwich having a core of water ffanked by two monolayers having refractivK. J . MYSELS AND M. N. JONES 47indices of 1.45 and thicknesses of 8.5 and 10A each for the dodecyl and tetradecyl systemsrespectively. This permits calculation 8% 12913 of an optical correction dW-6, amounting to7.25 and 8-25 A for the two systems and gives the material thickness 6 of the film. By sub-tracting twice the monolayer thickness from 6, we obtain the thickness d2 of the aqueous core.The figures show the material thickness 6 of the film and this is used in computing the effectof van der Waals forces with 7 A = 6x 10-13 and A = l O 3 w .The corresponding doublelayer repulsion is calculated using the aqueous core thickness of the film d2.RESULTSThe results obtained for four different solutions are shown in fig. 3-6. Examina-tion of the figures will show that the scatter is much larger between experimentsthan within each. This indicates that methodical errors are present. The two mostlikely sources lie in the difficulty of insuring complete flushing of the disc as solu-tions are changed and in a shift of position of the film in the disc as the pressure?----- I-film thickness, 6,8,FIG. 4.-The effect of pressure upon the thickness of a film of 0.0021 M sodium tetradecylsulphatesolution.Van der Waals forces Pu are negligible conipared to the exact or approximate calculatedelectric forces (dashed lines).changes between the determination of the maximum and the actual thickness measure-ment. The latter is caused by irregularities of the hole in the disc. Two experi-ments which gave completely discordant results, presumably for these reasons, havebeen omitted in the low ionic strength dodecyl system of fig. 4. A few values belowlo3 dyne/crn2 (1 cm H20) are omitted because of the uncertainty introduced bymenisci.DISTANCE DEPENDENCE OF REPULSIONThe figures show the linear double-layer repulsion Pe computed according to theapproximate eqn. (5) for ik =; 100 mV, which is a realistic cstimatc 7 and also fo48 MEASUREMENT OF DOUBLB-LAYER REPULSION$ = 00.The results of an exact calculation also shown differ slightly at higherpressures. The van der Waals pressure Pv is also shown as well as the resultanttotal internal pressure, P, -Pv. Inspection shows that the points have approximatelythe same slopes or curvature as the calculated lines, although the horizontal positiontends to be shifted to greater thicknesses.As deviations from the theoretical straight line are minor for the three systemsof low ionic strength (fig. 3 - 9 , it is meaningful to calculate least4 5 6 7I I I Isquare lines forfilm thickness, 6, 8,FIG. 5.-The effect of pressure upon the thickness of films of 04094 M sodium dodecylsulphatesolutions. Van der Waals forces Po make a significant contribution (heavy line) to the exact orapproximate calculated electric forces (dashed lines).the individual experiments and compare them with the approximate slope.Table 1summarizes the results and shows that in two systems the agreement with theoryis well within experimental error but for the 2-53 x 10-3 M tetradecyl sulphate itis only within 20 %, almost twice the standard deviation. In the system of fig. 3,both the slopes and the abscisse suggest a higher ionic strength.In computing the P, curves and the IC values, the contribution of micelles to theionic strength has been taken as 20 % of the excess surfactant above the c.m.c.This introduces only a minor correction as shown in the table but could accountfor the discrepancy noted if it were a gross underestimate.Interpretatian of the slopes alone is free of uncertainties concerning the ab-solute value of t,b and of its decay in the region of high potential.It is also un-influenced by problems involved in the computation of d:! or 6 and to a considerableextent, even of those in the optical measurements since only changes in thicknessare of importance. Furthermore, II/ may be safely assumed to remain constantsince the filiii is always in equilibriutn with the same bulk solutionK. J . MYSELS AND M. N. JONES 49TABLE THEORETICAL AND EXPERIMENTAL SLOPES OF DOUBLE-LAYER REPULSION IN SODIUMDODECYL (NaLS) AND TETRADECX (NaTS) SULFATE SOLUTIONSsolution effective conc. theor. slope stand. dev.expt. slope and2.53 x 10-3 M NaTS 2 .1 6 ~ 10-3 M 1.53 x 106 1.80 (-16) x 1069-36 x 10-3 M NaLS 8 . 6 ~ 10-3 M 3.05 x 106 2.94 (-35) x 1060.18 M NaCL+2.09 x 10-3 M NaTS 2-09 x 10-3 M 1 . 5 0 ~ 106 1.46 (-)X 1061 . 7 ~ 10-3 M NaLS 0-18 M 1.39 x 109 IABSOLUTE VALUES A N D VAN DER WAALS FORCESThe figures show that the points tend to be to the right of and above the cal-culated 100 mV line and often even beyond the one corresponding to an idmitepotential. Better agreement would be obtained if the potential in the middle ~mwhich determines the magnitude of the double-layer repulsion were higher, e.g.,film thickness, 8, %,FIG. 6.--The effect of pressure upon the thickness of films of a solution 00017 M in sodium dodecyl-sulphate and 0 18 M in NaCI. The contribution of van der Waals forces Po to the calculated approxi-mate or exact electric ones (dashed lines) is shown by the heavy lines.The heavy dashed line showsthe effect assuming thicker monolayers and 4 = 1OOmV.if the decay of potential in the high potential region were slower or of the $ planeswere separated by a lesser distance than assumed. The agreement would also bebetter, if the films were in reality thinner than shown.These last two conditions would be met, if the monolayers were thicker than wehave assumed. Thus, if the small surface area per ion of 36 A2 found by Nilsson * 14by a tracer technique for the dodecyl sulphate ion is used as a base instead of the52 L$2 underlying our calculation,7 the thickness of each monolayer is increased by4 A and the optical correction by 3 A.Hence, the relative position of the line an50 MEASUREMENT OF DOUBLE-LAYER REPULSIONpoints is shifted by 11 A (12 A for the tetradecyl sulphate). Within the scatter ofthe data, this would give reasonable agreement with theory for a high value of $.To illustrate this point the heavy dashed line of fig. 6 has been drawn. It showsthe calculated line in this case for a surface potential of 100 mV taking into account vander Waals forces. The agreement between the curvature produced by van der Waalsforces in the theoretical line and the course of the points is good. This suggeststhat the method should become useful in measuring these forces and in disentanglingthem from the double-layer effects.The computation of thickness used in the figures involves the same assumptionsas in previous experiments 7 ~ 9 performed in the absence of any applied pressure.These gave thicknesses lower than theoretical in contrast to the present results.Whether this is a real effect or an artifact is not clear.However, our results nowsuggest that the monolayers are indeed thicker than was assumed.This work was supported in part by the National Science Foundation undergrant GP-1707. We are also indebted to the Fulbright Commission in the UnitedKingdom for a travel grant to M. N. J.1 Mysels, J. Physic. Chew., 1964, 68, 3441.2 Derjaguin and Titijevskaya, Farday Dis. Soc., 1954, 18, 27.3 Exerowa, Ivanov and Scheludko, Godishnik Sofskiya Univ., Khim. Fak., 1961162, 56, 157.4 Overbeek in Kruyt, Colloid Science (Elsevier Publishing Co., Amsterdam, 1952), chap. IV5 Overbeek, J. Physic. Chem., 1960, 64, 1178.6 Scheludko and Exerowa, Kolloid-Z., 1960,168,24.7 Lyklema and Mysels, J. Amer. Chem. Soc., 1965,87,2539.8 Mysels and Otter, J. Colloid Sci., 1961, 16,462.9 Jones, Mysels and Scholten, Trans. Faraday SOC., 1966, 62, 1336.10 Lyklema, Scholten and Mysels, J. Physic. Chem., 1965, 69, 116.11 Vaiikk, Optics of Thin Films (North-Holland Publishing Co., Amsterdam, 1960).12 Duyvis, Thesis (University of Utrecht, 1962).13 Frankel and Myseb, J. Appl. Physics, 1966,14 Nilsson, J. Physic. Chem., 1957, 61, 1135.* Nilsson is in agreement with Wilson, Epstein and Ross (J. Colloid Sci., 1957, 12, 345) andWeil (J. Physic. Chem., 1966, 70, 133) but Corkill et al. (Trans. Faraday SOC., 1961, 57, 821) find ahigher value.and VI

ISSN:0366-9033    

DOI:10.1039/DF9664200042

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

Stabilization of Thin Films of Liquid Hydrocarbon byAlkyl Chain InteractionBY JANET TAYLOR AND D. A. HAYDONDept. of Colloid Science, University of Cambridge, Free School Lane, CambridgeReceived 13th June, 1966Optically black films in aqueous solutions have been made with aliphatic hydrocarbon solutionsof normal alkyl chain esters. The thickness of the hydrocarbon part of the films has been estimatedfrom measurements of their electrical capacitance. Variation of the chain length of the hydrocarbonsolvent does not, in general, influence the film thickness. On the other hand, between n-CI;? andn-C22 the thickness of the hydrocarbon part of the film is apparently equal to twice the chain lengthof the stabilizing ester molecules. From theoretical consideration of the attractive and repulsiveforces it has been shown that this result is to be expected.In 1950 van der Waarden reported that dispersions 01 carbon particles of 50-1500 A radius could be stabilized in liquid aliphatic hydrocarbon by the additionof alkylated benzenes.1 In order to explain this observation it was suggested byMackor,2 and later by Mackor and van der Waals,3 that the alkyl benzene mole-cules were adsorbed on to the carbon particles through their benzene rings such thattheir chains extended away from the surface, and that the adhesion of the twoparticles was prevented (or at least inhibited) by the steric interference of the alkylchains.Subsequently, there have been further reports of the stabilization of smallparticles in hydrocarbons by adsorbed alkyl chain molecules$* 5 and in neither casehas any alternative to the Mackor and van der Waals hypothesis been put forward.In none of these investigations was there convincing evidence that interactionbetween the adsorbed alkyl chains was responsible for the stability.Thus, in theexperiments of Dawson and Haydon5 on rutile in benzene, the particle size wasevidently far too large for stability to be produced by the fatty acids which never-theless appeared to be effective, and a “loose aggregate” model was proposedto account for the results. In the work of Parfitt and Willis 4 on Graphon particlesin solutions of alkyl benzenes in n-heptane it was concluded that, notwithstandingthe observed stabilization of the suspensions, the alkyl benzenes were adsorbed onto the Graphon with their long axes parallel to the surface, and thus should havebeen incapable of producing stabilization.While the position regarding small particles in liquid hydrocarbons is still un-certain, the essential validity of the Mackor and van der Waals hypothesis can beestablished from studies of free hydrocarbon films in aqueous media.Relativelystable optically black films can be formed under aqueous solutions from solutionsof dialkyl glyceryl phosphatidyl choline in normal aliphatic hydrocarbons such asn-decane.6 From measurements of the electrical capacitance of these films, andan assumption as to the dielectric constant of their hydrocarbon region, the thick-ness of this region was estimated.6 The result is equal, to within a few %, to twicethe length of alkyl chains of the stabilizing molecules.An approximate confirma-tion of this result has been obtained by an optical reflection technique.7-9 Theseexperiments strongly suggest that the interaction of the alkyl chains of the stabiliz-ing molecules is responsible for the film stability. On the other hand, no attempt552 STABILIZATION OF THIN FILMShas yet been made to vary the chain length of the stabilizing molecules and toobserve the influence of this on the film thickness. Neither has it been possibleto determine the adsorption in the film and hence to calculate the probable mag-nitude of the repulsive force.Progress towards these ends using films stabilized by phospholipids is hamperedby the nature of these molecules.Thus, phospholipids which give stable blackfilms are chemically unstable at normal temperatures in presence of water andoxygen. They also associate strongly in non-polar solvents. These two factorsmake it difficult to carry out sufficiently precise interfacial tension and activitymeasurements as to be able to employ the Gibbs equation to estimate the adsorptionat an oil-water interface. Experiments involving chain length variation are alsodifficult to carry out for phospholipids, owing to the present non-availability of suitablematerial.fn an attempt to overcome these problems, various more convenient surfactantshave been examined for their stabilizing properties. The most successful class ofsubstances found so far are the mono-esters of polyhydric alcohols and relatedmolecules.Within the limitations of the present experimental technique, most ofthe pure substances of this type which we have examined give black films which aretoo short-lived for precise measurements of their capacitances and areas to becarried out. However, homogeneous chain length mixtures of substances of thistype, obtained by condensing sorbitol with normal chain carboxylic acids, givemuch more stable films. Measurements on these systems have been used to supple-ment and confirm those made on films of pure substances.EXPERIMENTALMETHODSThe films were formed over a circular hole in the side of a vertical cylindrical Teflonvessel. The vessel was clamped so that the hole was below the surface of an aqueous phasecontained in a square-sided Perspex cell.The films then separated the aqueous phaseinside the vessel from the aqueous phase outside. The films were observed in reflected lightand their electrical properties were measured by means of electrodes inside and outside theTeflon vessel. In order to study films of different areas two Teflon vessels were used havingholes of area - 1 and -4.4 mm2 respectively. Further details of the apparatus are describedin an earlier publication.6 The solutions of the various surfactants in the hydrocarbons wereusually 1 % (wlw), although this concentration was by no means critical for black filmformation.MATERIALSIsosorbide monobrassidate was synthesized from isosorbide and brassidic acid by amethod which will be described elsewhere.The product had a m.p. of 83" and on analysisgave the theoretical C and H to within 0.4 %. The brassidic acid was 94 % pure (by GLC)but 2 % was n-docosanoic acid, and hence the material was 96 % n-C22. Various aspectsof the structure of the ester and the absence of free carboxylic acid were confirmed by theinfra-red spectrum.The glycerol monooleate was obtained from Sigma and was >99 % pure.The sorbitan esters were synthesized by the condensation of d-sorbitol with the appropriatecarboxylic acid, in presence of p-toluene sulphonic acid.10 Infra-red and analytical examina-tion of the products shows that they are mixtures of the mono-esters of sorbitol and anhydrosorbitols.In addition to brassidic acid, palmitoleic and lauric acids were used. Theformer was Sigma grade (>99 %). The latter was 98 % (by GLC). Each of the sorbitanesters is therefore effectively a mixture of mono-esters having equal chain length but differenthead groupsJ . TAYLOR AND D. A . HAYDON 53The commercial sorbitan monooleate (Span 80) was examined by infra-red spectroscopyand, after hydrolysis, the acids were methylated and examined by GLC. The main difference,for present purposes, from the sorbitan esters described above is that the chain lengths of theacids were more heterogeneous. In fact n-Clg chains constituted 73 % and n-C16 10 % ofthe whole. The remainder were shorter chain lengths.The (26, Clo, Cl2 and C14 n-alkanes were obtained from Koch-Light Ltd.and the n-C16was a puriim grade product of Fluka. All these specimens were 299 % pure by gas-liquidchromatography. The 2 : 2 : 4-trimethylpentane was also obtained from Koch-Light Ltd.and was puriss grade. Before use the hydrocarbons were passed through an aIuminacolumn. Their interfacial tensions against water have been given elsewhere.11The sodium chloride was of A.R. grade and was roasted at 700°C to remove organic impuri-ties. The water was twice distilled, first from a commercial still and then from a Pyrex stillfitted with a quartz column, condenser and receiver.RESULTSAfter their initial formation the films drained to the black (or dark grey) statein about 1-2 min. Thereafter the only visible change in the films was a tendency toincrease or decrease in area at the expense of the thick border region.Except underspecial circumstances, mentioned below, the capacitances per unit area at a givenI o310'ncU 310 uI16'frequency (cisec)FIG. l.--Capacitances and conductances of the black h + T e f l o n vessel in Wac1 solutions, as afunction of frequency. A, 10-1 N and 0, 10-3 N NaC1.frequency were independent of time up to the point that the films broke. Thissometimes took several hours (for the Span SO) and sometimes only a few seconds(for the pure isosorbide ester).The capacitances measured were those of the black films in their aqueous en-vironment. These systems were frequency dependent in a way which varied withthe electrolyte concentration. Results for films examined in 10-1 and 10-3 N NaClare shown in fig.1. In 10-1 N the capacitance becomes constant below 1 kc/sec54 STABILIZATION OF THIN FILMSThe curve in lO-3N is shifted to lower frequencies and the limitations of the ap-paratus prevented corresponding information being obtained for this case. Forfilms of given area the variation of electrolyte concentration does not affect the formof the frequency curves. This result was found previously for films stabilized byother substances. 63120o - 6 ]tJ-4----- 15no. of carbon atoms in solventFIG. 2.-The influence of the hydrocarbon solvent on the capacitance of sorbitan monooleate (Span 80)films. For the lower three hydrocarbons the aqueousphase was presaturated with the surfactant and hydrocarbon.For the remainder, this had no0, n-alkanes ; El, 2 : 2 : 4-trimethylpentane.effect on the results.The d.c. conductances of the films on their Teflon suppurts were irreproduciblefrom film to film. ]It has been shown previously, however, that only the lowestvalues show any proportionality to the film area and thus represent true valuesfor the film.13 The others are believed, on circumstantial evidence, to be due toborder leakage. The lowest values for the present films were N 10-9 IR-1 cm-2 andthus we conclude that the true conductances are less than or equal to this value.TABLE 1.capitance (pF/cm2)stabilizer (0-1N NaCI, 1 kclsec)n - Q isosorbide monobrassidate 0.32sorbitan monobrassidate 0.33n-Clg glycerol monooleate 0.39sorbitan monooleate (Span 80) 0.38n-C16 sorbitan monopalmitoleate 0.43n-C14 sorbitan monolaurate 0.57The chain length of the hydrocarbon solvent was varied for the sorbitan mono-oleate and the sorbitan monolaurate films.For the former substance the influenceon the capacitance/cmz is shown in fig. 2. For the latter, only n-decane and 2 : 2 : 4-trimethylpentane were tried and both gave the same result. If the aqueous solu-tions were not presaturated with the hydrocarbon solution of the surfactant, thecapacitances for n-hexane, n-heptane and 2 : 2 : 4-trimethylpentane tended to betime dependent and irreproducible and somewhat higher than normalJ . TAYLOR AND D. A. HAYDON 55For the isosorbide monobrassidate and for the sorbitan monooleate (Span 80)the capacitance/cma was constant over approximately a four-fold range of area.The capacitancelcm2 of the black films was markedly dependent on the lengthof the alkyl chain of the stabilizing surfactant.Results for solutions in n-decaneare shown in table 1. The nature of the polar group of the surfactant does notinfluence the capacitance, and Span 80, which has only 73 % n-Cle chains, givesthe same result as do the other relatively pure n-Cls substances.DISCUSSIONCALCULATION OF THE FILM THICKNESS FROM THE CAPACITANCEThe equivalent circuit for hydrocarbon films supported in the present apparatusis 6 as given in fig. 3, where C' and Gj are the capacitance and conductance of theGm GtFIG. 3 . T h e effective equivalent circuit for film studies.black film and Cm and Gm are the capacitance and conductance of the aqueousphase effectively in series with the black film, and Cs is a frequency-independentstray capacitance.If the complex capacitance of this circuit is writtenthen 6andwhereandC' = C~,+C,+(C~--C,)/(l +02T2),f being the frequency and fo the relaxation frequency of the circuit. We also havethat asand asIn the present systems G& is always small and therefore provided C' and Gf areindependent of frequency a plot of C" against C' should give a semicircle in the com-plex plane.14 When the data of fig. 1 are replotted, this is found to be the case towithin the experimental accuracy (fig. 4). From the values of C' for f,'~ = 0 andflfo + 03 9 C'+ Ch + c , , (8)f/fO--+OY C'-+CI+ c,. (956 STABILIZATION OF THIN FILMSthe value of C8, Cl was found for each system. As Gm& Gf and C'% Cm, eqii.(5)givesThe fact that Cf is evidently independent of frequency shows that at the frequenciesCI = c,. (10)/II 3 0 0\0 \\ \00 1.0 2-0103 c' (PF)FIG. 4.-The Cole-Cole plots for sorbitan monooleate films (+Teflon vessel) in electrolyte solutionsfor constant (but different) film area in each case. (a) 10-1 N NaCl; (b) 10-3 N NaC1. Somefrequencies (kc/sec) are shown on the curves. The dashed line shows the true semi-circle.used the films behave as if they were a single isotropic sheet. Structurally, thefilms are probably best imagined as stratified, with the surfactant polar groupson each side and hydrocarbon in the middle.On this model it is more appropriateto regard the system of the film in aqueous solution as a three-layered dielectricrather than the two-layered one assumed in fig. 3, An analysis of the three-layeJ . TAYLOR AND D . A . HAYDON 57model has been given elsewherep and it has been shown that with dielectric con-stants and specific conductances of the orders of magnitude reasonable for the polargroup region, these regions should make a negligible contribution compared withthe hydrocarbon to the quantities Cl and GI. This conclusion is supported by thefact that the observed film conductances correspond to a specific conductivity ofthe film material of 5 10-15 a-1 cm-1, a value characteristic of hydrocarbons.As in previous ~0rk,13 the present films gave capacitances which were directlyproportional to their area and it was assumed that they were effectively parallelplate condensers.Thus,where A is the black film area and E and d are respectively the dielectric constantand thickness of the hydrocarbon region. The hydrocarbon of the films is madeup of the unsaturated or saturated chains of the surfactants and of the saturatedC f = EA/4nd, (1 1)6C4cnx 5,2cIf/’ P’/‘/- /////-I/[----10 20no. of carbon atoms in stabilizer chainFIG. 5 . T h e thickness d of the hydrocarbon region of the black films as a function of stabilizer chainlength. The dashed line corresponds to a film thickness of twice the chain length of the stabilizer.solvent.n-Octadecene and n-decane were taken as representative of these two com-ponents and following the extensive evidence from micellar systems the interiorsof the films were assumed to approximate to bulk liquid hydrocarbon mixtures.From the adsorption measurements to be published and from the values of E forn-octadecene and n-decane equilibrated with water$ E for the hydrocarbon partof the films was estimated to be 2.00 for the laurate films and 2.07 for the others.Values of the thickness d of hydrocarbon were then calculated from eqn. (1 1). Itis estimated that if the basic assumptions are correct these are likely to be accurateto about Lt, 1.5 A, the largest source of error being probably in the measurement ofA . The results are shown in fig.5.THEORETICAL FILM THICKNESSIt is concluded, from the general lack of dependence of black film capacitanceon the hydrocarbon solvent and an time, that the films drain rapidly to an equi-librium thickness. It is also assumed that in the black films the London-van derWaals forces must give rise to the predominant attractive force. The repulsiveforces could be either electrostatic or steric, although calculations based on thespecific conductance of the film material indicate that the former are likely to b58 STABILIZATION OF THIN FILMSnegligibly small. In consequence, there appears to be nothing to counteract theLondon-van der Waals forces until the films become sufficiently thin for the hydro-carbon chains of the adsorbed esters on the opposing surfaces to interact with eachother.The free energy change for such an interaction has been considered forfilms adsorbed on to solid-liquid interfaces by Mackor and van der Waals.3 Thedetailed treatment of these authors cannot be readily extended to the present systems.Another more empirical approach is, however, possible.For film thicknesses which are larger than twice the chain length of the stabil-izing surfactant molecule, the two interfaces of the film are assumed not to interactsignificantly. For thicknesses less than twice the chain length of the surfactantit is assumed that the alkyl chains of the two adsorbed monolayers tend to interferesterically with each other. The free energy change on interaction is given bywhere SZ is the area of each of the interacting interfaces (assumed constant), (y- y*)is the change of interfacial tension and (pt-p?) the change of chemical potentialof species i on interaction, and ytt is the number of molecules of species i in thesystem.The asterisk is for absence of interaction.( y - y * ) can, in principle, be estimated from the adsorption isotherms andsurface equations of state of the surfactant for the bulk interfaces and thin film.Thus, when a film thins from the very thick to the very thin state, and overlap ofthe two monolayers occurs, the available space for the surfactant (and possiblythe solvent) molecules decreases. We may also expect that the chemical potentialsof the various species will change during this process, giving the second term onthe right-hand side of eqn.(12). This effect has, however, been neglected by pre-vious authors 3 arid is considered to be small in the present systems. Eqn. (12)then reduces to 3F - F* = 2a(y - ~ ' ) ~ i * . (13)At bulk hydrocarbon-water interfaces many non-ionic surfactant moleculesobey, to a close approximation, a two-dimensional van der Waals equation of stateof the form,where N* is the number of adsorbed molecules in area 0, n*( = yo- y*) is thesurface pressure of the monolayer and Ao is the interfacial area per molecule atinfinite surface pressure. .f( aiV*/Q) represents the mutual interaction betweenadsorbed molecules. For a number of types of surfactant f(alV*/0) is negligiblysmal1.16 Provided the surfactant is strongly adsorbed relative to the non-polarsolvent, eqn.(14) is not greatly affected by the precise nature of the solvent.16 Thechain length of the surfactant is similarly unimportant, the molecules behaving toa first approximation as rigid non-interacting rods oriented normally to the interface.16The appropriate adsorption isotherm for the surfactant may be obtained eitherfrom the partition function corresponding to eqn. (14), or by substituting in eqn. (14)for II* from the Gibbs equation and integrating the result. In either case the resultfor dilute solutions in which the surface excess of surfactant may be equated to thesurface concentration is[n*+ f(~tN*lQ)](S2- N"AJ = N*kT, (14)A*-& A0 exp A*-A() A0 = Ka exp {&j01'A4 A*clpr+*)]]where A* = Q/N*, a is, for the present systems, the activity of the surfactant in thehydrocarbon phase and K is an integration constantJ .TAYLOR AND D. A. HAYDON 59We consider an adsorbed monolayer in which the surfactant molecules have auniform cross-sectional area throughout their length and zero mutual interaction.For a given value of N* or A* the surface pressure, 11* (or tension, y*> can becalculated from eqn. (14). If the monolayers were to overlap over the whole lengthof their alkyl chains the free area available to each of the monolayers would beless by NAo and the calculation of the adsorption from eqn. (15) would involve anappropriate allowance for this. The resulting value of A or N could then be putback into eqn. (14) and II (or 7) calculated.(It is assumed that K, which is a functionof the difference in standard chemical potentials in the surface and bulk phases,is the same for an interface in a thin film as one between two bulk phases. Al-though this is not strictly so, the error introduced is unlikely to be serious.) If,on the other hand, the monolayers were to overlap only slightly the free area in theoverlapping region would be (Q-2NAo) and at the outer ends (Q-NAo). Thefree area effectively available is therefore (0 - AN&) where 1 < A <2. For inter-acting monolayers, eqn. (14) therefore becomesand assuming R to be independent of A eqn. (15) becomesII(Q - ANAo) = NkTRAO exp - = Ka. A0A-RAo A-RAoThe adsorption data show that for the various surfactants that have been usedA* G O A2 per molecule.If A0 = 20 per molecule and 3, = 1.1, then F- F* x 0.73erg/cm2. This rise in free energy is large compared with the probable order ofmagnitude of the London-van der Waals energy (x0-015 erg/cmz for a Hamakerconstant of 10-13 erg) and, as R was only 1.1, is achieved for a very small overlap ofthe two monolayers. It is concluded, therefore, that a repulsion sufficient tostabilize the black film comes into operation abruptly when the hydrocarbon regionof the film becomes thinner than twice the chain length of the stabilizing molecules.From this hypothesis we should predict that, provided the alkyl chains of theadsorbed surfactant are fully extended and oriented normally to the interface, thethicknesess of the hydrocarbon parts of the films should be as indicated by thebroken line in fig. 5. The agreement with the experimental results is good.We thank Mr. T. Hayes of Unilever Ltd., and Dr. J. V. Mortimer of The BritishPetroleum Company for carrying out some of the gas-liquid chromatographicanalyses, and Dr. G. Cook for the synthesis of the isosorbide monobrassidate.Dr- Taylor was in tenure of a Medical Research Council Junior Fellowship.1 van der Waarden, J. CoIloid Sci., 1950, 5, 317.2 Mackor, J. Colloid Sci., 1951, 6, 492.3 Mackor and van der Waals, J. Colloid Sci., 1952, 7 , 535.4 Parfitt and Willis, J. Physic. Chern., 1964, 68, 1780.5 Dawson and Haydon, Koltoid-Z., 1965, 203, 133.6 Hanai, Haydon and Taylor, Proc. Roy. SOC. A , 1964,281,377.7 Huang, Wheeldon and Thompson, J. Mol. Biol., 1964, 8, 148.8 Ti Tien, J. Mot. Biol., 1966, 16, 577.9 Thompson and Huang, J. MoE. Biol., 1966,16, 576.10 Nicoud, J . Recherches C.N.R.S., 1950, no. 13, 227.11 Aveyard and Haydon, Trans. Faraday SOC., 1965, 61, 2255.12 Hanai, Haydon and Taylor, J. Theor. Biol., 1965, 9, 422.13 Hanai, Haydon and Taylor, J. Theor. Biol., 1965, 9, 433.14 Cole and Cole, J. Chem. Physics, 1941, 9, 341.15 Hanai, Haydon and Taylor, J. Tlieor. Biol., 1965, 9, 278.16 Haydon, Ann. Reports, in press

ISSN:0366-9033    

DOI:10.1039/DF9664200051

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

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

ISSN:0366-9033    

DOI:10.1039/DF9664200060

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

Modified Poisson-Boltzmann Equation and Free Energy ofElectrical Double Layers in Hydrophobic ColloidsBY S. LEVINE* AND G. M. BELL?Received 21st June, 1966Corrections are obtained to the Poisson-Boltzrnann (P.B.) equation for the potential distributionin the diffuse part of the electric double layer for an aqueous medium. In addition to effects ofion-size, variation in dielectric constant and self-atmosphereimage terms, these corrections include theeffect of medium compressibility and so-called cavity potentials. Numerical integration of thecorrected P.B. equation for a single plate and for two parallel plates shows that the potential dropsmore rapidly with distance from a plate surface than is predicted by the P.B. equation. The freeenergy of the double layers with the modified P.B.equation is determined, in the absence of specificadsorption of counter-ions.1. INTRODUCTIONThe numerous publications (see ref. (1)) on corrections to the Poisson-Boltzmann(P.B.) equation for the potential in the diffuse part of the electric double layer fallinto two broad categories. The more fundamental approach, based on statisticalmechanics 2-6 has been limited in its scope because of the mathematical difficulties.Although it has been indicated that owing to ion-size effects the classical P.B. equationceases to be an acceptable approximation in 1-1 electrolytes for concentrationsexceeding roughly 0-1 M, the approximations made in these studies appear tomake this result inconclusive.16 Most of the investigations are in the second category,which is based largely on the method of local thermodynamic balance.In arecent paper (to be referred to as paper I) we have extended this work to includeimage-self-atmosphere potentials? the important so-called cavity potentials (both ofwhich, although treated approximately, are based on statistical mechanics) and alsothe effect of Compressibility of the dispersion medium. In this paper, we presentsome numerical solutions of the modified P.B. equation for a single charged plateand for two equal charged parallel plates, immersed in al a ~ g e volume of aqueous 1-1electrolyte. For simplicity, no account is taken of tire Stern inner region con-taining adsorbed counter-ions. A brief discussion of previous work is imluded.The determination of the double-layer Helmholtz free energy, with all thecorrections considered in this paper, is lengthy, particularly since it may be expressedin a number of equivalent and physically meaningful forms.17 Here we quote withoutproof one particular form for the free energy for a single plate and two parallelplates immersed in a large volume of dispersion medium and give some numericalresults.2.NOTATION AND PRELIMINARY RELATIONSe, k, N, T proton charge, Boltzmann’s constant, Avogadro’s number, absolutetemperature T = 298°K.* Department of Mathematics, University of Manchester, Manchester.f Department of Mathematics, Chelsea College of Science and Technology, London, S.W.3.670 FREE ENERGY OF ELECTRICAL DOUBLE LAYERSx distance measured from (i) plate wall for a single plate (ii) medianplane for two parallel plates.2h separation of two plates at x = kh.el charge on ion of speciesj(j = I , .. ., p ) ; el = e, e2 = - e for 1-1electrolyte type.nj,n(?),ng volume number densities of ion j or of solvent (water) ( j = 0) atposition x, at median plane and in electrolyte bulk (at x = KI forsingle plate) respectively; np = n; = n for 1-1 electrolyte; c =concentration in molesll. of 1-1 electrolyte.+ = $(x) mean electrostatic potential at x ; for single plate $0 = $(O) is platepotential and $(a) = 0 ; for two plates $0 = $( & h) and t,hm = $(O)is potential at median plane.v = e$/kT, V m = e$mlkT, ~0 = e$o/kT,s = sinh (q/2), s, = sinh (q,,,/2), (2.1 )k = exp (-urn), 0 = arc sin (exp (- (y - ym)/2)),EO dielectric constant of bulk electrolyte,KO Debye-Hiickel parameter for bulk electrolyte, given byPj = 1IC: = (4n/sokT) nge? = 8nne2/&,kT (1-1 type), (2.2)1-1 type) (2.3) I rc0x = In [tanh (go/4)/tanh (q/4)],KOX = k3[F(k,z/2)- F(k,@)],are solutions of P.B.equations for one plate and two plates respectively,where F(k, CD) is elliptic integral of the first kind ; when = yo, CD = CD0,x = h, half-plate separation.is the density of ion j at x and at median plane by P.B. equation.v j = ng exp (- ej$lkT), vy) = nj. exp (- ej@,/kT), (2.4)E = d$/dx, electric field at x.are the electric fields for one plate and two plates respectively in P.B.approximation.4n 8nne2K 2 =- C v.e? = - cosh qEokTj=l I EokT (1-1 type)for the local K at x in P.B.approximation.unit volume) no, nl, . . ., np of solvent andp ion types.bulk electrolyte; hj = uS/u& ratio of partial volumes.x(nj) logarithm of the number of configurations available to numbers (peruj, j = 0, 1, . . ., p , partial volume of solvent molecule or ion j ; u j = u? iS . LEVINE AND G . M. BELLis volume fraction statistics formula of Flory-Huggins.P l Px(nj) = xo(no)- C n j ( h n j - 1 ) - - C C ( ~ z ~ - n ~ ) ( n ~ - n I t g ) v ~ ~ (2-9)j = 1 2 i = l j = 1is a formula based on imperfect gas theory; for hard-sphere model ofhydrated ions, exclusion volume u ~ j = 4na$3, where aif = distanceof nearest approach between ions i and j . Comparison of (2.8) and(2.9) gives vij = hihpvo.A fraction of actual ion charge in Debye-Hiickel fictitious chargingprocess.~ o ( u 0 ) Helmholtz free energy per molecule of pure solvent at molecularvolume VO.{;(uo) Helmholtz free energy of interaction of ion j with the immediate solventneighbourhood ; a separate coupling parameter A', distinct from dand equal to 1, is assumed in the interaction energy between an ion andmolecules in its hydration shell.n(2.10)is the Helmholtz free energy per unit volume in completely dischargedstate d = 0.is the corresponding contribution to chemical potential of solvent orion i.Pj = Op*(nj) = -f*+ C njp7 (2.12)is the local pressure at x in the completely discharged state ;1 = 0.q - v ; = hi(Pi/Po)(vo-v~), i = 1 , .. ., p (2.13)gives the relation between partial volumes based on the assumptionthat ratio of compressibilities of a hydrated ion pi and a water mole-cule PO is constant ; PO = 0.46 x 10-10 c.g.s.units(2.14)is the self-atmosphere-image (Debye-Huckel) potential at ion i, chargeel( = h i ) , at position x and charging stage A. For a single plate (of infinitethickness)#IDH) = 41DH)(e; ,A) = - (ef /Eo)g(Arc,x)(2.15)for small or large values of E ~ / E O ; d, common distance of nearestapproach between two ions; E ~ , dielectric constant of plate medium(Ep = 10);f = (EO- E ~ ) / ( E o + gp) reflection coefficient in electrostatic imaging72 FREE ENERGY OF ELECTRICAL DOUBLE LAYERSg(rC0) = q / ( l + ~ o a ) value of g in bulk electrolyte.For two plates, if q(u) = exp ( - ~ K ' u ) / u ,( 2 - ( m - n ) 2 ) f "+"q(mh-x+nh+x) (2.16)- -1 03n = l r n = n , n f ldescribes multiple screened image reflections.is the mean charge density at x and stage A.4 c a v ( 4 = - (2.a21&o>P(4 (2.17)is the main term in the so-called cavity potential, due to removal ofdiffuse layer charge distribution from spherical exclusion volume of ion.+fav(A) = (47ca3/3&O)p(l)g(l~,~) (2.18)is an additional term in the cavity potential, due to the reduction ineffective charge of ion by an amount (4nd3/3)p(A).(2.19)is the standzrd Debye-Hiickel local free energy density associated withthe potential (2.14) ; integration is carried out at constant nj.(2.20)(2.21)gives the condition of self-consistency implied in the method of localthermodynamic balance and satisfied by (2.14).is a particular form of condition of self-consistency with +cav(A), sincethis potential is independent of ei ; the self-consistency condition is notsatisfied by &&).(2.23)are parts of the self-atmosphere potential and corresponding free energydensity which satisfy the self-consistency condition.a f c a v ( 2 ) l a n i = ei#cav(n) (2.22)#LA> = $f""(~eiJ> + 4cav(R), feI(1) = fDH(2) + fcav(A>(2.24)is a pressure term associated with self-atmosphere-cavity potential atR = 1 .(2.25)(2.26)n(nj> = Pel(nj) + ~ " ( n j).PE = cO+ C (nj-ng)(aeidng)ni,.=o-aE2j = S.LEVINE AND G . M. BELL 73gives the dependence of dielectric constant of medium at x on ion con-centrations and electric field ; dielectric saturation parameter a - 3 x 10-7e.s.u.7(2.27)is the energy of polarization of a hydrated ion or solvent moleculefor moderate field E.(2.28)is the form of E equivalent to (2.26) for 1-1 electrolyte,8 where as-suming a variation of E with concentrations at constant pressure,4nkT 4nkTJ I - h l J o = --6,(s2-si), J2-h2J0 = -- 6,(s2 - s:).(2.29)EON EONHere we assume 61 = 8 2 = lO36,6 = - 7.5.t = d In &;Id In PO; PO, density and dielectric constant of pure solvent ;t = 1.34.9noJo m -4nkTt(s2-s2) (1-1 type).is the (electro-)chemical potential of ion i at stage A, which is uniformthroughout diffuse layer ; pLp(A) chemical potential in bulk electrolyte.Po = A+ Jo (2.31)is the chemical potential of solvent.I = -hE4"(2.32)r0 = (1/8n)(&E2+I)- n j J j - I ? ( n j ) + I I ( n ~ ) ) -j = Ois the first integral of the modified P.B.equation for system of twoparallel plates, obtained from (2.30)-(2-31) in paper I for a single plate,where n(n(7)) is replaced by rI(n;) and limits of integration (0,x) bySo = e2/&kTa (2.34)z(x) = 3Eln (1 + x) - x + +x2]/x3. (2.35)S = Jcosh q, S m = Jcosh q,, V = 1 + K o a S , V , = 1 + KOaSm. (2.36)G(V, v,) = $( v 4- v:) -$( v3 - v:) i- 3( v2 - V:) - 4( V - V,) + In (VlV,). (2.37)3 ( S 2 - s:,2 (I -I- uoa)'H(S,S,) = S 3 ~ ( S x o a ) - S:z(S,lcoa) - - (2.38)l(q) = Ag(xoS,x) sinh q/rco f, A g ( d , x ) = g(rc',x) - d / ( l + d a ) (2.39)where x is regarded as a function of g, given by the solution of the modified P.B.equation74(2.40)(2.41)(2.42)where x is held constant in the integration.3.SOLUTION OF MODIFIED P.B. EQUATIONEqn. (2.33) can be expressed in a form suitable for numerical integration, viz.In arriving at (3.1) from (2.33), it is assumed that the electrolyte is sufficiently dilute(&q<no) and that the difference between the ion densities y1i given by the refinedtheory and the densities vi given by the P.B. equation are small compared withvi. The equation for a single plate corresponding to (3.1) was derived inpaper I. A first integral of the P.B. equation is recovered by retaining the firstterm only on the right-hand side of (3.1). The second, third, fourth and fifth termsrepresent respectively the corrections due to (ii) volume (ion-size) effect (iii) depend-ence of dielectric constant on ion concentration and contribution of polarizationenergy of ions to electro-chemical potentials, (iv) dielectric saturation and (v) com-pressibility effect of medium, PO being the compressibility of the pure solvent.Theseventh term is due to the self-atmosphere-image (Debye-Hiickel) potential and thesixth and last terms account for the two cavity potentials $cav and $La", respectively.Considering a 1-1 electrolyte, we choose the Flory-Huggins formula (2.8) andwrite hl = hz such that hTvo equals the exclusion volume 4na3/3, which is the samefor all three types of ion-pairs. Then (3.1) can be expressed asPj = S . LEVINE AND G . M.BELL 75In the two integrals yl(q,qm), ~2(q,qm) defined by (2.40) and (2.41), x can be treatedas a function of y and it is sufficient to assume the solution of the P.B. equation,as given by the second relation in (2.3). For a single plate we need to put qm = 0and therefore Sm = 0, Sm = 1, Vm = 1 +Kod and we substitute the first relationin (2.3) for x as a function of q in yl(y1,0) and yz(q,O). If we use (2.9), then differentdistances of nearest approach between ion pairs can be assumed. For example,writing u11 = 2122 = 2012 = 8na3/3, the third term on the right-hand side of (3.2)is replaced by72-Because the expressions (2.8) and (2.9) for the configuration function x(nj) startfrom different premises concerning the structure of the solvent, it is possible that3 -l -4 \ 0.5\ 40.41 I 1 1 I0 5 10 15 20 25x(&FIG.1.-Potential-distance (-q-x) plots for single plate for equal exclusion volumes for the threeion-pair types in 1-1 electrolyte ; a = 4 A, 30 = 4. Modified P.B. equation-curves A,C ; P.B.equation-curves B,D ; concentration c = 0.1 M, curves A,B ; c = 0.01 34, curves C,D. Ratio ofslopes (plate charge densities) at intersection point of A,B (-q = 3, xo = 3-89A) equals 1.25;that of C,D (3 = 3.5, xo = 3-87 A) equaIs 1-08. Plots of C(X), curves A1,Cl. Fs/Fip-B.l = 1.112,1.044 for curves (A,B), (C,D) respectively. On scale used curves C and D are almost coincident andD is drawn broken to indicate that it lies above C.the compressibility term in (3.2) will also be altered when (2.8) is replaced by (2.9).Since we have not investigated this problem, we shall retain the compressibilityterm based on (2.8).Fortunately this term is small.Typical numerical solutions of the eqn. (3.2) for the potential in the diffuse layeras a function of distance have been obtained for a single plate and for two parallelplates. For a single plate (fig. 1, Z), numerical integration of (3.2) is initiated byintroducing the solution of the P.B. equation at large x at a specified wall potential( q g ) and then step-by-step integration by a Runge-Kutta technique proceeds towardssmaller x until a distance XO, say, slightly less than 4A, is reached from the platewall; xo is treated as the distance of nearest approach of the hydrated ions to th76 FREE ENERGY OF ELECTRICAL DOUBLE LAYERSwall.For comparison, the solution of the P.B. equation is included with the samepotential at x = XO. If we write (3.2) in the formthen, because (3.4) is a first integral of the P.B. equation when C(x) = 0, C(x) isa convenient function to describe the difference between the modified P.B. equationand the P.B. equation; and this is also plotted. It is observed that the potentialderived from (3.2) and (3.3) drops more quickly with distance x than the P.B.potential. This is consistent with the conclusions reached from cluster theoryconsiderations.2-5 In contrast, Sparnaay 10 and Steinchen-Sanfeld, Sanfeld and(dtf/dx)2 = 4ti;(s2 -~:)(1+ C(X)) (3 *4)i t I5 I0 15 2 0 Lx(&FIG. 2.-Similar plots to fig.1, with volume effect given by (3.3). Curves A,B, c = 0.1 M, ratioof slopes = 1-16 at intersection 3 = 2.8, xo = 3.82A; TO = 4. Curves C,D, c = 0.01 M; ratioof slopes = 1-20 at intersection 7 = 5.0, xo = 3-95A; 30 = 6. Plots of C(x), curves At,C1.FJF$P-B.) = 1-069, 1.078 for curves (A,B), (C,D) respectively.Hurwitz,ll calculate corrections to the P.B. equations which have the oppositesign. The reason for this disagreement is that they have omitted the self-atmosphere-image and cavity terms,* which dominate the sign of C(x) ; e.g., these terms contributeto C(x0) the amounts 0-46 and 0.40 in curves A, of fig. 1 and 2 respectively. Further-more, our calculations suggest that even at 1-1 electrolyte concentrations c = 0.1 Mand potentials -50-75 mV, the corrections to the P.B.equation in the diffuse layerare not excessive, because of partial cancellation among the various effects. Ap-parently trustworthy information on the range of validity of the P.B. equation inthe diffuse layer requires simultaneous treatment of all the corrections to this equa-tion. Also, the suggestions2-5 that the P.B. equation is only adequate at verylow electrolyte concentrations are not borne out by the present work. However,since our treatment of certain corrections, e.g., the volume effect, probably shouldbe modified very close to the plate wall 12 we cannot claim conclusive evidence thatthe P.B. equation is a reasonable approximation at concentrations as high as 0.1 Min 1-1 electrolytes. Potential-distance plots for 2 parallel plates are shown in* see note added in proofS.LEVINE AND G . M. BELL 77fig. 3. A value is chosen for the potential at the median plane and the distance 2 hbetween the plates is fixed from the solution (2.3) of the P.B. equation by choosingthe wall potential yo at a given concentration c. Step-by-step integration of (3.2)from the median plane to a wall proceeds until a value xo just less than h, is reached.The corresponding solutions of the P.B. equation (curves B and D) are shown for4 i I I I I'3 -I -I 1 I0 2 4 6 8 10--I ----I__ L--- 112FIG. 3.-PotentiaLdistance plots for 2 parallel plates with volume effect given by (3.3); ym = 1.5,yo = 4, K o h = 1.23. Modified P.B. equation, curves A,C; P.B. equation, curves B,D.CurvesA,B, c = 0.1 M ; ends of curves nearest wall xo = 10 8, (~0x0 = 1.04, h-xo = 1-78 A) and 11-07 A(~0x0 = 1.12) respectively withcommony = 3.54, wheresloperatio = 1.12. Curves C,D, c = 001 M ;ends of curves nearest wall xo = 34A ( ~ 0 x 0 = 1.12, h-xo = 3.27A) and 353A (KOXO = 1-16)respectively with common q = 3-59, where slope ratio = 1.03.0.2n-0.1 3 ucomparison in fig. 3. If the latter curves are shifted in such a way that they inter-sect at xo with the corrected curves (A and C respectively), then again we find thatthe P.B. solution drops less rapidly with distance from the wall than does themodified solution.FREE ENERGY OF THE DOUBLE LAYERSIn an earlier paper 13 (paper II), we described a general method of obtaining thefree energy of the electric double layers of two or more colloidal particles of arbitraryshape situated in the dispersion medium.The electrical part of the free energyFe was determined by means of the Debye-Hiickel charging process, carried out atconstant temperature, volume and surface density of ions on the surfaces of theparticles. The volume (ion-size) effects and dielectric saturation were consideredin paper 11. In a later treatment of two parallel plates, Sparnaay 14 included theeffect of the dependence of dielectric constant on electrolyte concentration. Herewe include the additional corrections due to self-atmosphere-image and cavitypotentials and to compressibility of the dispersion medium. For simplicity, weignore the presence of an inner Stern region and assume that the charge on th78 FREE ENERGY OF ELECTRICAL DOUBLE LAYERSplates is due to adsorbed ions which are identical in type with one of the latticeions constituting the plate medium.The total free energy which concerns us isobtained by adding to Fe the so-called chemical free energy Fc, i.e., the free energyof the colloidal system in the completely discharged state ;1 = 0. As the volumeof the dispersion medium becomes infinitely large, Fe + Fc -+a. We therefore sub-tract the free energy that the system would have if no ions were adsorbed on thecolloidal surfaces and the systems were homogeneous up to these surfaces. Ignoringthe outer faces of the parallel plates, the resulting free energy per plate per unitarea of its inner face is given byFs =If we put E = EO, I I ( r z j ) = k T 2 q and retain only the first and third terms in (4.1),then Fs reduces to the Verwey-Qverbeek free energy.15The last term in (4.1) differs from the others in that integration with respect to;I has not been carried out.This is basically owing to the fact that the potentialq5LaV(jl) defined by (2.18) does not satisfy the self-consistency condition discussedin $2. To carry out computations with a 1-1 electrolyte it is convenient to express(4.1) in a form which corresponds to (3.2). This readsj = 1nPo% UokT --4n ( ) [ (s2 + ( s2 - si)t> (s2 - ( s2 - s i ) t I - $1 +It is possible to express a number of the integral terms in (4.2) in terms of ellipticintegrals by a method of successive approximations and use of the P.B.equation.14, 15Again, (3.3) can be substituted for the third term in the integrand when weassume different distances of nearest approach between ion-pairs. If the P.B.equation is assumed, then the first term only in the integrand is retained.Integration with respect to x then gives the Verwey-Overbeek expression for thefree energy, which we denote by Fip.B.), in terms of elliptic integrals. For a singleplate we put qm = 0, 12 = and (4.2) reduces toBecause of electrostatic imaging and ion-size, the potential at the limit of the diffuselayer ( ~ ( x o ) ) is less than the P.B. potential ( ~ 0 ) at the wall. Values of the ratioFs/FLp.B.) for the various examples of a single plate illustrated in fig.1 and 2 areincluded in the legends. The ratio is somewhat greater than 1, whereas Sparnaay 14obtained a value less than 1 because he omitted the self-atmosphere-image-cavitypotentials. Since his potential-distance curves diminished with distance from theplate walls more slowly than predicted by the P.B. equation, Sparnaay also calculateS. LEVINE AND G . M. BELL 79an increase in the double-layer repulsion between two parallel plates at a givenseparation, resulting from his corrections to the P.B. equation. From our presenttreatment of these corrections, we would expect, however, a decrease in repulsion;numerical computations of the complicated integrals in (4.2) for this case are stillin progress. The small departure from the P.B. solution obtained here suggeststhat in 1-1 electrolytes, modifications in diffuse layer theory will not greatly alterpresent-day stability theory of hydrophobic colloids.We are indebted to Manchester University Computing Service for facilities on theirAtlas electronic computer.1 Bell and Levine, Chemical Physics of Ionic Solutions (ed.Conway and Barradas (Wiley and2 Stillinger and Kirkwood, J. Chem. Physics, 1960, 33, 1282.3 Stillinger and Buff, J. Chem. Physics, 1962, 37, 1 ; 1963, 39, 191 1.4 Krylov and Levich, Zhur. Fiz. Khim., 1963, 37, 106.5 Krylov, Electrochim. Acta, 1964,9, 1247.6 Martynov and Derjaguin, Dokl. Akad. Nauk S.S.S.R., 1963, 152, 767; Martynov, Research7 Malsch, Physik. Z., 1928, 29, 770 ; 1929, 30, 837. * Hasted, Ritson and Collie, J.Chem. Physics, 1948, 16, 1.9 Jacobs and Lawson, J. Chem. Physics, 1952,20, 1161.10 Sparnaay, Rec. trav. chim., 1958, 77, 872.11 Steinchen-Sanfeld, Sanfeld and Hunvitz, (a) Kon. Acad. Wetens, Belg. A, 1966, 66, 41 ; (b)12 Levine and Bell, J. Physic. Chem., 1960, 64, 1188.13 Bell and Levine, Trans. Faraday SOC., 1957, 53, 143.14 Sparnaay, Rec. trav. chim., 1962, 81, 395.15 Verwey and Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier Publishing Co.,16 Bell and Levine, Conference on Statistical Mechanics, International Union of Pure and Applied17 Bell and Levine, 2. physik. Chem (Lpg.), 1966, 231, 289.18 Huckel and Krafft, 2. physik. Chem., 1955,3, 135.19 Sparnaay, 2. physik. Chem., 1957,10, 156.20 Kirkwood and Poirier, J.Physic. Chem., 1954, 58, 591.21 Loeb, J. Colloid Sci., 1951, 6, 75.22 Williams, Proc. Physic. SOC. A , 1953, 66, 372.Sons, 1966), pp. 409-461.in Surface Forces (ed. Derjaguin) (1966) (Consultants Bureau, New York), 2, 75.Electrochim. Acta, 1964,9, 929.Amsterdam, 1948).Physics, Copenhagen, July, 1966 (Benjamin).Note added in proofSparnaay has brought to our attention that in their extension of the Debye-Huckel theoryof electrolytes, Huckel and Krafft 18 obtained corrections which correspond to the cavitypotentials and 4Lv defined by (2.17) and (2.18), and which were interpreted as such byhim.19 In this case the cavity effect is due to the displacement of an ion’s self-atmospherecharge, rather than the diffuse layer mean charge, by the finite volume of a second ion.Theseauthors therefore preceded Buff and Stillinger 3 to whom we had attributed the concept ofcavity potentials in ref. (1) although these were later neglected by Sparnaay 10 in his theory ofthe diffuse layer. Also, the cavity effect described by is implicit in the work of Kirkwoodand Poirier 20 on strong electrolytes, as well as in the statistical mechanical treatment of ion-size effect in diffuse layer theory in ref. (2)-(6). Comparison of our results with those ofHuckel and Krafft can be illustrated by means of eqn. (3.4) for a single plate at large x.This reads(dq/dx)2 = 4k-;s2( 1 + C( GO)),where, for the particular unequal exclusion volumes treated above80 FREE ENERGY OF ELECTRICAL DOUBLE LAYERSto which Huckel and Krafft’s more general form reduces. The first term, which dominatesfor KO a< 1 , is due to the cavity potential &cav, the second is due to &iaV and the third to thevolume effect ; the last-named contribution is absent if the exclusion volumes for the threetypes of ion-pairs are equal. (We have made the reasonable assumption that the radius aof the exclusion volume 2112 for an oppositely charged ion pair equals the Debye-Hiickel‘‘ a ”.) The cavity potential which determines the (positive) sign of C( a), lowers theenergy of a counter-ion in the diffuse layer, but raises that of a co-ion. Thus the populationof counter-ions is increased, whereas that of co-ions is decreased. Because (in a 1-1 electro-lyte) the number of counter-ions exceeds that of co-ions, the net effect is an increase in the totalion concentration in the diffuse layer. Assuming equal exclusion volumes and neglectingthe self-atmosphere-image terms (our potential (2.14)) and consequently $cav, Stillinger andKirkwood 2 obtained an expression for the surface potential of a single plate, which corres-ponds at small IcOa to our C(m) = H#oca)2 when expanded in powers of q a . In paper 1 weshowed how an extension of the work of Loeb 21 and Williams 22 on the self-atmosphere-image effects of point ions in the diffuse layer leads naturally to cavity potentials when theion-size effect is included. The Loeb-Williams theory was mentioned by Sparnaay 10 andapplied in more detail by Hurwitz, Sanfeld and Steinchen-Sanfeld.llb In their more recentresults on the modified P.B. equation at a single plate, these authors lla introduced a meanactivity coefficient for ions in the diffuse layer to account very roughly for the Loeb-Williamsterm. The cavity potentials, however, are absent in their work

ISSN:0366-9033    

DOI:10.1039/DF9664200069

出版商:RSC    

年代:1966

数据来源: RSC

摘要:

Electrical Double Layer on Silver IodideInfluence of Temperature and Application to Sol StabilityBY J. LYKLEMAAgricultural University, Laboratory for Physical and Colloid Chemistry,De Dreyen 6, Wageningen, NetherlandsReceived 9th June, 1966Results on the double layer charge and capacitance on AgI previously obtained have been im-proved and extended to include the temperature dependency between 5 and 85°C. At room tem-perature, alkali ions adsorb specifically on negative AgI, which gives rise to a marked ion specificityin the double layer capacitance and which is responsible for the lyotropic sequence in the coagulationconcentrations. With increasing temperature, charge and capacitance decrease, with a concurrentdecrease in specificity. At 65°C and above, the double layer is predominantly diffuse and non-specific.The lyotropic sequence in the coagulation concentrations is then also lost. There is someevidence for a phase transition around 50°C in the adsorbed water layer.The electrical double layer at the mercury/solution interface is doubtless theone most thoroughly studied.1-4 Some of its merits are the well-defined interfacialgeometry, the large potential range that can be covered and the possibility of workingwith expanding surfaces, thus minimizing contamination hazards.Double-layer studies on other metals and on nun-metals are scanty and muchmore difficult to perform and analyze. The advantages of the mercury system donot generally apply. However, some of these materials can be dispersed to givestable sols and the prospect of comparing sol stability with the properties of theelectrical double layer can outweigh the practical disadvantages.In this study, results obtained with the AgI/aqueous solution interface are re-ported. Among the systems other than mercury, AgI has attractive features, e.g.,the potential-determining mechanism is known, the surface potential can be con-trolled because stable AgI electrodes exist ; there is much information availableon the stability of the AgI sol (e.g., ref.(5)) and the surface area problem is nowsolved.6 In this paper, double layer and stability data are combined and exploitedto gain more insight in both double-layer structure and sol stability. The tem-perature is included as another controlled variable. Special attention is paid tolyotropic effects.Finally, from a comparison between the double layer propertieson mercury and on AgI insight can be gained about the idhence of the nature ofthe charge-carrying material on the properties of the electrical double layer.EXPERIMENTALTHE BASIC TECHNIQUE is essentially a potentiometric titration of suspended AgI withpotential-determining electrolyte. We followed the procedure described by Lyklema andOverbeek 7 with the following modifications. The temperature was varied between 5 and85°C and controlled within 0.05 deg. (0.2 deg. at 5") by immersion of the cell in an ultra-thermostat. A closed cell was used to prevent evaporation. The cell consisted of twoparts, a Pyrex titration beaker and a stainless steel set-up for electrodes, stirring, etc.Both parts were jointed by a Viton (copolymer of hexafluorpropylene and vinylidene fluoride882 DOUBLE LAYER ON SILVER IODIDE17.'16151413I2Du Pont) gasket ring which after prolonged extraction with hot water gave no surface-activeor conducting material. As the calomel electrode cannot be used at elevated temperatures *a special high-temperature TlCl glass-electrode (Electrofact, Netherlands) was chosen as thereference.Its potential was kept constant with a 10-3 M phthalate buffer (PH -4 at 25°C).Thus, liquid junctions are avoided. Potentials were measured with a Vibron pH-meter(Electronic Instruments, England). Readings were taken when the mean potential of fivedifferent electrodes changed less than 0.02 mV/15 min.The titration finally yields 7 thesurface charge 00 (pC/cm2) as a function of the potential $o(mV) across the interface, bothwith respect to the zero point of charge (zpc). If desired--e.g., for comparison with thedouble layer on mercury-the ao(q0) curves can be differentiated to give the differentialdouble-layer capacitance C.'''I " " " " '5 15 25 35 45 55 65 75 85OCTFIG. 1 .-Zero point of charge PI" and negative logarithm of the solubility product pL of AgI againsttemperature ; salt : 10-3 M KH phthalate+O099 M KN03.AgI SUSPENSIONS were prepared from 0.1 M AgN03 and 0.1 M KI solutions and aged for3 days at 80" without drying. As the application of the B.E.T.-method is open to doubt 6surface areas were determined from negative adsorption and double layer capacitance whichmutually agreed within 10 %.Areas of 1-15 m2/g were found.The reproducibility of the surface charge determination, using different samples of AgIis 1-3 %. The absolute accuracy depends mainly on the accuracy of the surface area andzpc and is difficult to assess. All adsorption isotherms reported (except at 15°C) are theaverage result of at least 4 independent titrations on different samples.THE ZPC can, e.g., be determined from the intersection points of the ao(&-J curves atdifferent ionic strengths. Van Laar,9 using this procedure at 25" found in 10-3 and 10-1M KNO3 p1 = 10-58 and 10.27 respectively. We repeated these experiments and extendedthem to the temperature range 5445°C.Results in 10-3 M K biphthalate-tO.099 M KNO3are given in fig. 1. As these results are not yet confirmed by independent methods (likeelectrokinetics) they are provisional. At room temperature, van Laar's and our values differslightly, presumably due to specific adsorption of phthalate in our caseJ . LYKLBMA 83ACTIVITY COEFFICIENTS of 1- in KNO3 solutions appeared to be only slightly dependent onT which agrees with the generally observed trend 11 in not too concentrated solutions.STABILITY. Flocculation concentrations were determined in the classical way (using aseries of flocculation tubes with sol and varying salt content 12) with the modification thatthe turbidity after flocculation was observed instrumentally rather than visually.13 Asexpected, this method gives lower results than the kinetic method of Reerink and Overbeek.14RESULTS AND DISCUSSIONDOUBLE LAYER AT 25°Cao($o) graphs at four ionic strengths are given in fig.2. The mutual positionof the four isotherms is fixed by the titration but the zero point of charge is differentfor the four ionic strengths (i.e.? a given PI corresponds to different $0 for differentionic strengths). In order to show the mutual position all curves are drawn withrespect to the zpc in 10-1 solution (fig. 1). The 10" curve intersects the zero axisa few mV to the right which might be the result of specific adsorption of NO,' ions.The 10-2 and 10-3 curves have also their zpc shifted towards more negative poten-tials, which perhaps may be interpreted as the result of competitive specific ad-sorption of the biphthalate ion which here contributes relatively strongly to theionic strength.In the potential range - 50 >$o > -250 mV the results of fig.2 agree within 5 %(7 % for the 10" curve) with the corresponding curves given in ref. (7), (15). Atthe outer right the curves tend to attain a constant slope (i.e., the differential capacit-ance tends to become constant) whereas previously a definite levelling-off wasobserved. Due to specific adsorption of biphthalate the present curves differsomewhat from the previous ones around the zpc and at positive potentials.The solubility product of AgI can be calculated from the standard cell potential.Its value in 10-3 M K biphthalate+0.099 M KNO3 is also plotted in fig.1 as pL =-log CAg+CI- against temperature. As far as data at lower salt content wereavailable, extrapolation to zero electrolyte concentration gave results which agreedwithin 0-3 % with those of Owen and Brinkley 10 (measurements up to 45"). Thequotient pIo/pL decreases gradually from 0.650 at 5" to 0.588 at 85", i.e., the zpcbecomes more symmetric at elevated temperatures.The iduence of the nature of the counterion is illustrated by fig. 3. This figureshows that at fixed negative $0in M/10 solutions. Flocculation concentrations reported by KlompC and Kruyt 12for RbN03, KN03 and LiN03 are 126, 135 and 165 mmole/l. respectively (i.e.,about 10-1 mole/l.). Hence the lyotropic series in the flocculation concentrationsis reflected by the double-layer charge.Around PI = 4 the specificity (i.e.? thedifference between Li+ and Rb+) is about the same for both cases, viz., around30 %. The salt in which the charge (at given PI, i.e., at given $0) is relatively high(RbNO3) is at the same time the most efficient flocculant. This indicates specificadsorption, increasing in the order Li+ < K+ < Rb+. The relatively high degree ofoccupancy of Rb+ in the Stern layer leads automatically to a relatively low potentialt,bs of the diffuse part of the double layer and hence to a relatively low stability.The alkali-ion specificity in the double layer on mercury 16 is only about a tenthof that on AgT 17; it can be explained without recourse to specific adsorption.16p 18Reasoning by analogy we may predict that a Hg sol will show no lyotropic sequencein the flocculation concentration.oo(Rb+) > ao(K+) > oo(Li+84 DOUBLE LAYER ON SILVER IODIDEUsing the curves of fig.2 the ionic components of charge can be calculatedfrom 15where a+ and CT- represent the charge (pC/cm2) attributable to cations and anions10 O10- 110-210-3-100 -200 -300mV +looFIG. 2.-Surface charge against potential at 25°C. Ionic strength : 10-3 M K biphthalate, with KNO3added to value indicated in the figure. $0 applies to 10-1 curve, corresponding values for othercurves are obtained after accounting for shift in zpc.FIG. 3.--Surface charge against potential at 25°C ; ionic strength 10-1 ; influence of the nature ofthe counterion.respectively, 10 is the Faraday, ps the chemical potential of the salt and K an integra-tion constant which is physically equivalent to the adsorption of the ion underconsideration at the zpc, also expressed in pClcrn2. The results of this analysisare shown in fig.4. The constant K is taken as zero at the zpc of the ionic strengthconsideredJ . LYKLEMA 85A striking difference between this figure and the m e given in ref. (15) is thatthe negative adsorption of co-ions 0- does not pass through a maximum. Theimplications of such a maximum in terms of the discreteness-of-charge theory havebeen discussed by Levine et a1.19 The absence of the maximum as we have nowfound after improvement of the experimental technique means probably that thedistance between the surface and the inner Helmholtz plane (location of specificallyadsorbed cations) is large.This, in turn, agrees with the picture that the alkali-ions are physically adsorbed rather than chemisorbed (see below).+3+2+ I0-4- IFIG. 4.-Charge attributable to cations and anions. Salt : 10-3 K biphthalate, with KNo3 addedto the ionic strength indicated ; T = 25°C ; $0 applies to 10-1 curves.The dashed line in fig. 4 gives the contribution of the negative adsorption to thecountercharge, calculated from the data of fig. 2 assuming absence of specific ad-sorption. Tbe real negative adsorption is lower, which means that the contributionof the cation to the countercharge must be greater than as calculated under theassumption of absence of specific adsorption.This again supports the idea thatalkali-ions adsorb specifically on negative AgI.The general trend of (r- against $0 agrees both with the directly measured negativeadsorption 6 and with the prediction of the diffuse dcuble layer theory,where E is the dielectric constant of the medium, and n the salt concentration inmolecules/cm3. For monovalent anion (z = - 1) and sufficiently negative potentials86 DOUBLE LAYER ON SILVER IODIDEThe calculated limiting value in 10-3 solution is indicated by an arrow. The goodagreement with experiment presumably means that the assumption K = 0 in thezpc is correct, although a fortuitous compensation of a high K in the zpc and asomewhat incorrect surface area cannot a priori be excluded.TEMPERATURE INFLUENCE AND DOUBLE LAYER AT 85°CThe influence of the temperature on the double layer charge constitutes anothervariable that is useful to our insight in counterion adsorption and double-layerstructure, especially if combined with stability experiments.For AgI a markeddecrease in surface charge (and hence in differential capacitance) with increasingtemperature is found, see fig. 5. (The fact that the curves tend to become shorterwith enhanced temperature is due to- 5 JJc/cm* i - L -- 3 -- 2-the increased solubility of AgI.)FIG, 5.-Temperature dependence of the doublelayer charge. Salt : 10-3 M K biphthalate+0.099 KNO3 ; all curves plotted with respect to their own zpc.In analyzing the curves of fig.5, then under the conditions of the measurementsthe double layer is essentially non-diffuse. The value of the temperature coefficientof the double-layer capacitance can then be used as a criterion for specific adsorptionbecause in the presence of specific adsorption it is much higher than in its absence.20On slightly negative mercury with non-specifically adsorbed alkali-ions (X/BT)#,,amounts to about 0.07-0-08 pF cm-2 deg.-WY 22 The corresponding value for AgIis, depending on 60, a factor of 3-6 higher. This again fits well the idea that alkaliions do adsorb specifically on negative AgI.The decrease in charge with increasing temperature may thus be interpreted asdue to a gradual desorption of specifically adsorbed cations. In other words, thehigher the temperature the more diffuse the double layer.One feature of theGouy-Chapman theory is that it is non-specific. Consequently we must expect amore or less gradual decrease in specificity, going from 5 to 85". As at 85" we coulddetect no significant difference between Li+ and Rb+, neither in the charge nor inthe flocculation concentrations, we conclude that the thermal desorption processi s complete at 85" and that the double layer is now purely diffuse. ao(ll/o) curvesat 85" are shown in fig. 6, again at three ionic strengths with K+ as the cationJ . LYKLEMA 87The corresponding graphs for Li+ and Rbf are indistinguishable (within a few %).If eqn. (1) is used to find the ionic components of charge 0- and G+ the graphs appearto be within the accuracy of the method identical to the corresponding graphs,calculated from the Gouy-Chapman theory, as expected.t+2FIG. 6.4urface charge against potential at 85°C ; ionic strength, 10-1, 10-2, 10-3; cation : Li+, K+or Rbf.EVIDENCE FOR SURFACE PHASE TRANSFORMATIONA feature of fig.5 is that the mutual distance between the 45 and 65" isotherm isrelatively small. This effect is well beyond experimental error and was reproducedseveral times. It is more clearly shown in fig. 7 where the differential capacitanceis plotted against T, revealing a definite point of inflection around T = 50-55°C.This irregularity is typical for Agl ; on mercury, C falls off continuously with T.21Analysis of the double layer on mercury has led to the conclusion that somestructure formation takes place in the aqueous layer(s) adjacent to the metal surface(sometimes referred to as " icelike " layer).The effect of an increase in T wouldthen be a gradual melting of this " ice ". If a similar structure formation occursin the double layer on AgI-and there is much circumstantial evidence for it-theresults of fig. 7 suggest that in this case the " melting " does not proceed graduallybut more or less abruptly around T = 50". The subsequent increase in dielectricconstant of the Stern layer could, e.g., partially compensate the general downwardtrend and thus give rise to the observed inflection points.Two experimental facts support a phase transition. A DTA experiment con-ducted by Dr. van der Plas of the Agricultural University showed a phase transitionaround 50°C with wet AgI.On dry AgI no phase transition could be detected.This proves that the transition is a property of water adjacent to AgT. The otherexperimental evidence stems from stability experiments. If around 50°C a moreor less sudden breakdown of the structural layer occurs, then the specificity in thedouble layer properties should also disappear suddenly around this temperature,at least if the specificity at low temperature is partly or completely due to this struc-tural layer. To investigate this point we performed stability measurements at varioustemperatures. In fig. 8 ratios of flocculation concentrations are plotted againstT ; these ratios drop (resp. increase) abruptfy to one between 45 and 65", whichconfirms the presumed phase transition.The precise nature of the structural layer on AgI at room temperature is not known,but conceivably is analogous to the " icebergs " which form around hydrophobicmolecules in water and which give rise to the " hydrophobic bonding ''-23 Thefact that butyl-alcohol adsorbs with the 4ydrophobic part of its molecule toward88 DOUBLE LAYER ON SILVER IODIDEa AgI surface 24 shows that Agl is-at least in this sense-" hydrophobic ".Similarevidence follows from water vapour adsorption on AgI.25 The study of this struc-tural layer is of great importance for colloidal stability, the interpretation of electro-kinetic potentials and the mechanism of ice nucleation by AgI.boo--095-201918171 6151413121 1109I - - - - - - -A /8 RbN03CT1 I ITI5 15 25 35 45 55 65 75 85OCFIG.7.-Variation of double-layer capacitance with temperature at fixed potential ; ionic strength, 10-1.The properties of the structural layer will not only depend on T but also on 00,because the double layer field tends to orient the water dipoles. In fig. 7 there is aslight indication that the phase transition at -200 mV is less pronounced than aJ . LYKLEMA 89the zpc. This could mean that at -200 mV the structure is partially broken down,perhaps because the first molecules orient strongly towards the surface, thus makingthe attachment possibilities for molecules in subsequent layers less favourable,which in turn leads to a higher degree of disorder in these layers.26 Indeed, iffrom (aoo/aT),, the surface entropy q = (aS/aO)p, T, ,+ is calculated along the linesof Hills and Payne,zz q increases with increasing negative potential, which configura-tionally can be interpreted as due to increased disorder.This picture is also cor-roborated by n.m.r. experiments.27SPECIFIC ADSORPTION POTENTIAL AT 25°CIt is impossible to subdivide o+ of fig. 4 into a diffuse part ad+ and a non-diffusepart a,+ because $a is not known. This precludes the calculation of the specificadsorption potential 4. However, as we have concluded that at 65 and 85" thedouble layer is purely diffuse we can exploit this fact to calculate $a at 25°C indirectly.The procedure is described elsewhere.13 The principle is that first at 65 or 85"from 00 and the coagulation concentration the Hamaker-van der Wads constantA is calculated, using the DLVO theory.Values of 2-4 x 10-13 erg are found, ingood agreement with other results on AgT (e.g. ref. (28)). Assuming A to be inde-pendent of T, this value is substituted in the flocculation equation at 25"; from themeasured flocculation concentration od is found and subtraction gives then om+.Application of a Langnmir-type equation finally gives 4. For Li+, Kf and Rbfat $0 = -220 mV values of 2-1, 2.5 and 2.9 kT are found respectively at degreesof coverage from 20 to 30 %. Although high in comparison with other specificadsorption potentials for cations 29 the adsorption is well within the physical rangewhich agrees with the picture that the counterions are not very close to the surface.It is a pleasure to acknowledge the collaboration of Miss A.C. Korteweg whoperformed the greater part of the experiments. Preliminary standardizationexperiments have been performed by Miss F. H. van der Voort.1 Grahame, Chem. Rev., 1947,41,447.2 Parsons, in Modern Aspects of Electrochemistry, ed. Bockris and Conway (Butterworths,3 Frumkin, ibid., 1964, 3, 149.4 Devanathan and Tilak, Chem. Reo., 1965,65, 635.5 Kruyt, Colloid Science (Elsevier, Amsterdam, Houston, New York, London 1952), vol. 1.6van den Hul, Thesis (State University of Utrecht, 1966); van den Hul and Lyklema to bepublished. Preliminary note : 4th Int. Congr. Surface Active Substances (Brussels, 1964),BVI, 22.London), 1954,1, 103.7 Lyklema and Overbeek, J.Colloid Sci., 1961, 16, 595.8 Clerc, gtefanac and Simon, Helv. chim. Acta, 1965,4$, 54.9 van Laar, Thesis (State University of Utrecht, 1952) ; see also Overbeek in ref (9, p. 160.10 Owen and Brinkley, J. Amer. Chem. Soc., 1938,60,2237.11 Harned and Owen, Physical Chemistry of Electrolyte Solutions (Reinhold, New York, London,12 Klomp6, Thesis (State University of Utrecht, 1941) ; Klompt5 and Kruyt, Kolluidchem. Beilz.,13 Lyklema, IZI Znt. Vortragstagung iiber grenzflachenaktive Stofe, (Berlin, 1966).14 Reerink and Overbeek, Disc. Faraday Soc., 1954, 18,74.15 Lyklema, Trans. Farcrday Soc., 1963, 59, 418.16 Grahame, J. Electrochem. SOC., 1951, 98, 343.17 Lijklema, Kulluid-Z., 1961, 175, 129.18 Steinchen-Sanfeld, Sanfeld and Hurwitz, Colloquium over grenslaugve~schijnselen (Symp.inter-19 Levine, Mingins and Bell, 4th Int. Congress Surface-Active Substances (Brussels, 1964), BII/3.3rd ed., 1958), tabulations.1942,54,484.facial phenomena) (Royal Flemish Acad. Sci., Brussels, 1965), p. 4190 DOUBLE LAYER ON SILVER IODIDE20 Mott, Parsons and Watts-Tobin, Phil. Mqq., 1962, 7, 483.21 Grahame, J. Amer. Chem. SOC., 1957, 79, 2093.22 Hills and Payne, Trans. Faraday Soc., 1965,61, 326.23 Nkmethy and Scheraga, J. Chern. Physics, 1962, 36, 3382, 3401 ; J. Physic. Chem., 1962, 66,24 Bijsterbosch, Thesis (State University of Utrecht, 1965). Bijsterbosch and Lyklema, J. Colloid25 Tcheuekdjian, Zettlemoyer and Chessick, J. Physic. Chem., 1964, 68, 773.26 Scheraga, private suggestion.27 Fawcett, Parfitt and Smith, Nature, 1964, 204,775.28 Mathai and Ottewill, Trans. Faraday Soc., 1966, 62, 759.29 Davies, Proc. 3rd Int. Cungr. Surface Activity (Cologne, 1960), B 310.1773.Sci., 1965, 20, 665

ISSN:0366-9033    

DOI:10.1039/DF9664200081

出版商:RSC    

年代:1966

数据来源: RSC