H A N D B O O KO FSurfaceandColloidChemistryThi rd Edi t i onBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page i 14.10.2008 11:27pm Compositor Name: MSubramanian 2009 by Taylor & Francis Group, LLCH A N D B O O KO FSurfaceandColloidChemistryThi rd Edi t i onEdited byK.S. BirdiCRC Press is an imprint of theTaylor & Francis Group, an informa businessBoca Raton London New YorkBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page iii 14.10.2008 11:27pm Compositor Name: MSubramanian 2009 by Taylor & Francis Group, LLCCRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number-13: 978-0-8493-7327-5 (Hardcover)This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint.Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation with-out intent to infringe.Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.comBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page iv 14.10.2008 11:27pm Compositor Name: MSubramanian 2009 by Taylor & Francis Group, LLCDedicationTo LilianBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page v 14.10.2008 11:27pm Compositor Name: MSubramanian 2009 by Taylor & Francis Group, LLCContentsPreface......................................................................................................................................................................................... ixEditor........................................................................................................................................................................................... xiContributors .............................................................................................................................................................................. xiiiChapter 1 Surface and Colloid Chemistry ............................................................................................................................ 1K.S. BirdiChapter 2 Hydrogen Bonding and Nonrandomness in Solution Thermodynamics............................................................ 45Costas G. PanayiotouChapter 3 Surface Waves and Dissipative Solutions Sustained by the Marangoni Effect ................................................. 91Michle Vignes-Adler and Manuel G. VelardeChapter 4 Mobile Subsurface Colloids and Colloid-Mediated Transport of Contaminants in Subsurface Soil .............. 107Tushar Kanti Sen and Kartic C. KhilarChapter 5 Colloidal Systems on the Nanometer Length Scale......................................................................................... 131Mikhail Motornov, Yuri Roiter, Ihor Tokarev, and Sergiy MinkoChapter 6 Colloid Systems and Interfaces Stability of Dispersions through Polymer and Surfactant Adsorption.......... 155P. Somasundaran, Somil C. Mehta, X. Yu, and S. KrishnakumarChapter 7 Chemical Physics of Colloid Systems and Interfaces ...................................................................................... 197Peter A. Kralchevsky, Krassimir D. Danov, and Nikolai D. DenkovChapter 8 Solubilization in Aqueous Surfactant Systems................................................................................................. 379Harald Hiland and Anne Marit BlokhusChapter 9 Solubilization in Surfactant Systems................................................................................................................ 415Clarence A. MillerChapter 10 Controlled Synthesis and Processing of Ceramic OxidesA Molecular Approach....................................... 439Jarl B. Rosenholm and Mika LindnChapter 11 Thermodynamics of Polymer Solutions ........................................................................................................... 499Georgios M. Kontogeorgis and Nicolas von SolmsChapter 12 Thermally Sensitive Latex Particles: Preparation, Characterization, and Applicationin the Biomedical Field .................................................................................................................................... 539Abdelhamid ElassariBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page vii 14.10.2008 11:27pm Compositor Name: MSubramanianvii 2009 by Taylor & Francis Group, LLCChapter 13 Wax Deposition Investigations with Thermal Gradient Quartz Crystal Microbalance ................................... 567K. Paso, B. Braathen, T. Viitala, N. Aske, H.P. Rnningsen, and J. SjblomChapter 14 Bubble-Film Extraction Fundamentals and Application.................................................................................. 585Victor S. GevodChapter 15 Single Bonds and Adhesion in Biological Matter............................................................................................ 631Frederic Pincet and Eric PerezChapter 16 The Surface Properties of Coal ........................................................................................................................ 655Marek PawlikChapter 17 Self-Reproduction of Vesicles and Other Compartments: A Review.............................................................. 681Pasquale StanoChapter 18 Association of Petroleum Asphaltenes and the Effect on Solution Properties ................................................ 703Simon Ivar AndersenChapter 19 Scattering and Absorption of Light by Particles and Aggregates.................................................................... 719C.M. SorensenBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page viii 14.10.2008 11:27pm Compositor Name: MSubramanianviii 2009 by Taylor & Francis Group, LLCPrefaceThe science related to the subject of surface and colloid chemistry has been expanding rapidly in the last decade. This area ofscience is important, especially in such new areas as environmental control, wastewater, nanotechnology, pharmacy, andbiotechnology. In particular, the applications of nanoparticles in pharmacy products are very signicant.This subject initiated over 50 years back when theoretical understanding of surface and colloid systems assumed muchimportance. The information published since then has increased steadily, considering that there are at present some half a dozendifferent specialty journals related mainly to surface and colloids. The application of this subject has developed rapidly in bothindustrial and biological areas. Current energy production and pollution control has provided additional areas where this branchof science is very useful.During the last few decades, many empirical observations have been found to be based on the fundamental laws of physicsand chemistry. These laws have been extensively applied to the science of surface and colloid chemistry. This developmentgave rise to investigations based upon molecular description of surfaces and reactions at interfaces. During the last decade,especially, theoretical analyses have added to the understanding of this subject with increasing molecular detail. Thesedevelopments are moving at a much faster pace with every passing decade.The application area of surface and colloid science has increased dramatically during the last decades. For example, themajor industrial areas have been soaps and detergents, emulsion technology, colloidal dispersions (suspensions and nano-particles), wetting and contact angle, paper, cement, oil recovery, pollution control, fogs, foams (thin liquid lms), the foodindustry, biomembranes, drug delivery (vesicles), membrane technology, and the pharmaceutical industry. New areas ofapplications have developed recently, one of which is synthetic transplants and biological monitors. These trends show theimportance of this eld of science in everyday life.On the basis of these developments, a group of experts from the United States, Europe, and the rest of the world broughtforth the Handbook of Surface and Colloid Chemistry (CRC Press, Boca Raton), which covered this subject extensively in1997 and 2003. However, one nds that in the current literature the number of publications related to surface and colloidscience is very extensive. Accordingly, a new group of experts decided that at this stage there is an urgent need for the thirdedition of this handbook, which should provide easily available theoretical and experimental information on systems related tosurfaces and colloids.The purpose of the third edition is to update the reader on recent developments in this area, and it also includes some newareas of research. Hence, the two editions combined cover a more extensive area of research subjects. In this edition, a unifyingtheme of information on surface and colloid chemistry is presented by a team of international experts. The subject is presentedin such a manner that the reader can follow the physical principles that are needed for application, and extensive references areincluded for understanding the related phenomena. At the same time, the third edition, along with the previous two editions,thus consist of a vast number of literature references. This is very unique in the current literature.As the subject area and the quantity of knowledge are immense, there is always a need for a team of experts to cometogether and compile a handbook. It is therefore an honor for me to be able to arrange and present to the reader the chapterswritten by experts on various subjects pertaining to this science, with bibliographies in excess of 2000.It is most impressive to nd how theoretical knowledge has led to some fascinating developments in the technology. Thepurpose of this handbook is also to further this development. The scope of the third edition is consciously different from that ofany existing volume on the same subject. The molecular description of liquid surfaces has been obtained from surface tension(under static and dynamic conditions), surface waves, and adsorption studies. The thin-lm formation, and emulsion formationand stability are described by the interfacial lm structures. The surfaces of solids are characterized by contact angle andadsorption studies. Foams are described by the bilayer arrangement of the detergent and other amphiphile molecules in the thinlms. The ultimate in interfaces is a molecular lm and molecular self-assemblies (vesicles). Many questions about monomo-lecular lms on solids are answered with the use of modern scanning probe microscopes. The impact of scanning tunnelingmicroscopes and atomic force microscopes is delineated. This has indeed led to such new scientic elds as nanotechnology. Inthe last decade, these developments in the increased sensitivity and innovation in instruments have added much basicknowledge. The colloidal structures and their stability have been found to be of much interest as described extensively inthe second edition of this handbook. The basic theoretical description of colloids and stability is thoroughly described. Thedifferent chapters are arranged such that the information is basically needed for the whole handbook. The chapters are arrangedin such a manner so as to make it easier for the reader to follow the subject, and the tables and gures provide extensive data toachieve the same.Birdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page ix 14.10.2008 11:27pm Compositor Name: MSubramanianix 2009 by Taylor & Francis Group, LLCEditorProfessor K.S. Birdi received his BSc (Hons) in chemistry from Delhi University, Delhi, India, in 1952, and then later traveledto the United States for further studies, majoring in chemistry at the University of California at Berkeley. After graduation in1957, he joined Standard Oil of California, Richmond.Dr. Birdi moved to Copenhagen, Denmark, in 1959, where he joined the Lever Brothers Development Laboratory in 1959as chief chemist. During this period he became interested in surface and colloid chemistry and joined the Institute of PhysicalChemistry (founded by Professor J. Brnsted), Danish Technical University, Lyngby, Denmark, as an assistant professor in1966. He initially did research on surface science aspects (e.g., thermodynamics of surfaces, detergents, micelle formation,adsorption, Langmuir monolayers, and biophysics).During the early exploration and discovery stages of oil and gas in the North Sea, he got involved in Danish ResearchScience Foundation programs, with other research institutes around Copenhagen, in oil recovery phenomena and surfacescience. Later, research grants on the same subject were awarded from European Union projects. These projects also involvedextensive visits to other universities and an exchange of guests from all over the world. Dr. Birdi was appointed as a researchprofessor in 1985 (Nordic Science Foundation), and was then appointed, in 1990, to the Danish Pharmacy University,Copenhagen, as a professor of physical chemistry. Since 1999, he has been actively engaged in consultancy for both industrialand university projects.There has been continuous involvement with various industrial contract research programs throughout these years. Theseprojects have actually been a very important source of information in keeping up with real problems, and helped in the guidanceof research planning at all levels.Dr. Birdi is a consultant to various national and international industries. He is and has been a member of various chemicalsocieties, and a member of organizing committees of national and international meetings related to surface science. He has beena member of selection committees for assistant professors and professors, and was an advisory member (19851987) of theACS journal, Langmuir.Dr. Birdi has been an advisor for some 90 advanced student projects and various PhD projects. He has authored nearly100 papers and articles (and a few 100 citations). In order to describe these research observations and data, he realized that itwas essential to write books on the subject of surface and colloid chemistry. His rst book on surface science was published in1984 (Adsorption and the Gibbs Surface Excess, Chattorraj, D.K. and Birdi, K. S., Plenum Press, New York). This book stillremains the only one of its kind in recent decades. Further publications include Lipid and Biopolymer Monolayers at LiquidInterfaces (K.S. Birdi, Plenum Press, New York, 1989); Fractals, in Chemistry, Geochemistry and Biophysics (K.S. Birdi,Plenum Press, New York, 1994); Handbook of Surface and Colloid Chemistry (1st edn. 1997=2nd edn. 2003; CD-ROM 1999,CRC Press, Boca Raton (Ed. K.S. Birdi); Self-Assembly Monolayer (Plenum Press, New York, 1999); and Scanning ProbeMicroscopes (CRC, Boca Raton, 2002). Surface and colloid chemistry has remained his major interest of research throughoutthese years.Birdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page xi 14.10.2008 11:27pm Compositor Name: MSubramanianxi 2009 by Taylor & Francis Group, LLCContributorsSimon Ivar AndersenHaldor Topse A=SLyngby, DenmarkN. AskeStatoil Hydro ASAStavanger, NorwayK.S. BirdiInstitute of Physical ChemistryTechnical University of DenmarkLyngby, DenmarkAnne Marit BlokhusDepartment of ChemistryCentre of Integrated PetroleumResearchUniversity of BergenBergen, NorwayB. BraathenNorwegian University of Scienceand TechnologyTrondheim, NorwayKrassimir D. DanovLaboratory of Chemical Physicsand EngineeringFaculty of ChemistryUniversity of SoaSoa, BulgariaNikolai D. DenkovLaboratory of Chemical Physicsand EngineeringFaculty of ChemistryUniversity of SoaSoa, BulgariaAbdelhamid ElassariLaboratorie dAutomatique et de Geniedes ProcedesClaude Bernard UniversityVilleurbanne, FranceVictor S. GevodDepartment of Inorganic ChemistryUkrainian State Chemical TechnologyUniversityDnieopetrovsk, UkraineHarald HilandDepartment of ChemistryCentre of Integrated PetroleumResearchUniversity of BergenBergen, NorwayKartic C. KhilarDepartment of ChemicalEngineeringIndian Institute of TechnologyPowai, Mumbai, IndiaGeorgios M. KontogeorgisDepartment of Chemical andBiochemical EngineeringIVC-SEP Research EngineeringCenterTechnical University of DenmarkLyngby, DenmarkPeter A. KralchevskyLaboratory of Chemical Physicsand EngineeringFaculty of ChemistryUniversity of SoaSoa, BulgariaS. KrishnakumarUnilever ResearchEdgewater, New JerseyMika LindnCenter for Functional MaterialsDepartment of Physical Chemistrybo Akademi UniversityTurku, FinlandSomil C. MehtaLangmuir Center for Colloidsand InterfacesColumbia UniversityNew York City, New YorkClarence A. MillerDepartment of ChemicalEngineeringRice UniversityHouston, TexasSergiy MinkoDepartment of Chemistry andBiomolecular ScienceClarkson UniversityPotsdam, New YorkMikhail MotornovDepartment of Chemistry andBiomolecular ScienceClarkson UniversityPotsdam, New YorkCostas G. PanayiotouDepartment of ChemicalEngineeringUniversity of ThessalonikiThessaloniki, GreeceK. PasoNorwegian University of Scienceand TechnologyTrondheim, NorwayMarek PawlikNorman B. Keevil Institute of MiningEngineeringUniversity of British ColumbiaVancouver, British Columbia,CanadaEric PerezLaboratoire de Physique Statistiquede lcole Normale SuprieureParis, FranceFrederic PincetLaboratoire de Physique Statistiquede lcole Normale SuprieureParis, FranceYuri RoiterDepartment of Chemistry andBiomolecular ScienceClarkson UniversityPotsdam, New YorkBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page xiii 14.10.2008 11:27pm Compositor Name: MSubramanianxiii 2009 by Taylor & Francis Group, LLCH.P. RnningsenStatoil Hydro ASAStavanger, NorwayJarl B. RosenholmCenter for Functional MaterialsDepartment of Physical Chemistrybo Akademi UniversityTurku, FinlandTushar Kanti SenDepartment of ChemicalEngineeringCurtin University of TechnologyPerth, Western AustraliaJ. SjblomNorwegian University of Scienceand TechnologyTrondheim, NorwayP. SomasundaranI=UC Research CenterColumbia UniversityNew York City, New YorkC.M. SorensenDepartment of PhysicsKansas State UniversityManhattan, KansasPasquale StanoBiology DepartmentEnrico Fermi Researchand Study CentreUniversity of Roma TreRome, ItalyIhor TokarevDepartment of Chemistry andBiomolecular ScienceClarkson UniversityPotsdam, New YorkManuel G. VelardeInstituto PluridisciplinarUniversidad ComplutenseMadrid, SpainMichle Vignes-AdlerLaboratoire de Physiques des MatriauxDiviss et des InterfacesUniversit Paris-EstMarne la Valle, FranceT. ViitalaKSV Instruments Ltd.Helsinki, FinlandNicolas von SolmsDepartment of Chemical andBiochemical EngineeringIVC-SEP Research Engineering CenterTechnical University of DenmarkLyngby, DenmarkX. YuInternational Specialty ProductsWayne, New JerseyBirdi/Handbook of Surface and Colloid Chemistry 7327_C000 Final Proof page xiv 14.10.2008 11:27pm Compositor Name: MSubramanianxiv 2009 by Taylor & Francis Group, LLC1 Surface and Colloid ChemistryK.S. BirdiCONTENTS1.1 Introduction to Surface and Colloid Chemistry................................................................................................................ 11.2 Surface Tension and Interfacial Tension of Liquids......................................................................................................... 41.2.1 Introduction............................................................................................................................................................ 41.2.2 Parachor (or Quantitative StructureActivity Relationship).................................................................................. 91.2.3 Heat of Surface Formation and Heat of Evaporation.......................................................................................... 111.2.4 Effect of Temperature and Pressure on Surface Tension of Liquids .................................................................. 131.2.5 Corresponding States Theory of Liquids............................................................................................................. 141.2.6 Surface Tension of Liquid Mixtures.................................................................................................................... 211.2.7 Solubility of Organic Liquids in Water and Water in Organic Liquids.............................................................. 251.2.8 Hydrophobic Effect.............................................................................................................................................. 261.3 Interfacial Tension of Liquids (Liquid1Liquid2) ........................................................................................................... 291.3.1 Introduction.......................................................................................................................................................... 291.3.2 LiquidLiquid SystemsWork of Adhesion...................................................................................................... 301.3.3 Interfacial Tension Theories of LiquidLiquid Systems..................................................................................... 311.3.4 Hydrophobic Effect on the Surface Tension and Interfacial Tension................................................................. 321.3.5 Heat of Fusion in the Hydrophobic Effect .......................................................................................................... 341.3.6 Analysis of the Magnitude of the Dispersion Forces in Water (gD)................................................................... 341.3.7 Surface Tension and Interfacial Tension of OilWater Systems ........................................................................ 351.4 LiquidSolid Systems (Contact AngleWettingAdhesion)........................................................................................... 37References .................................................................................................................................................................................. 401.1 INTRODUCTION TO SURFACE AND COLLOID CHEMISTRYMatter exists as gas, liquid, and solid phases, as has been recognized by classical science. The molecules that are situated at theinterfaces (e.g., between gasliquid, gassolid, liquidsolid, liquid1liquid2, solid1solid2) are known to behave differentlyfrom those in the bulk phase [117]. It is also well-known that the molecules situated near or at the interface (i.e., liquidgas)are situated differently with respect to each other than the molecules in the bulk phase. Especially, in the case of complexmolecules, the orientation in the surface layer will be the major determining factor as regards the surface reactions. Theintramolecular forces acting would thus be different in these two cases. Furthermore, it has been pointed out that, for a denseuid, the repulsive forces dominate the uid structure and are of primary importance. The main effect of the repulsive forces isto provide a uniform background potential in which the molecules move as hard spheres. The attractive forces acting on eachmolecule in the bulk phase are isotropic when considering over an average time length. This means that the resultant net forcein any direction is absent. The molecules at the interface would be under an asymmetrical force eld, which gives rise to theso-called surface tension (ST) or interfacial tension (IFT) (liquidliquid; liquidsolid; solidsolid) (Figure 1.1) [16ac].The resultant force on molecules will vary with time because of the movement of the molecules; the molecules at thesurface will be pulled downward into the bulk phase. The presence of this force at the surface molecules will thus give riseto surface physicochemical analyses for many systems where surfaces are involved. The nearer the molecule is to the surface,the greater the magnitude of the force due to asymmetry. The region of asymmetry plays a very important role. Thus,when the surface area of a liquid is increased, some molecules must move from the interior of the continuous phase to theinterface. The surface of a liquid can thus be regarded as the plane of potential energy. Analogous case would be when the solidis crushed and surface area increases per unit gram. Further, molecular phenomena at the surface separating the liquid and the1Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 1 8.10.2008 7:15pm Compositor Name: VAmoudavally 2009 by Taylor & Francis Group, LLCsaturated vapor are appreciably more complex than those which occur in the bulk homogeneous uid phase. In theseconsiderations, the gels are analyzed as under solid phase.In the case of water, the magnitude of ST is found to decrease appreciably when some specic surface-active substances(soaps, detergents, surfactants, or amphiphiles) are added. Besides the latter property, these substances exhibit other importantproperties in aqueous phase. Especially, some amphiphiles exhibit the self-assembly characteristic [14]. This phenomenon isknown to be the basic building block of many natural assemblies. These assemblies, also called micelles, are found to play avery important role in everyday life. The tendency of the apolar alkyl chains (hydrocarbon, HC) to be squeezed out of theaqueous medium may be considered as the driving force for micelle formation. However, the polar part of the amphiphileexhibits repulsion between the polar groups. At equilibrium between these forces, one obtains a system which corresponds tothe critical micelle concentration and the aggregation number. The decrease of entropy connected with the decrease of thenumber of free kinetic groups is also a factor unfavorable to the micelle formation.The microsize (nanosize) of micelles (varying in sizes of radii from 10 to over 1000 ), Figure 1.2, can carry outchemical reactions both inside and at its surface, reactions which could not be possible otherwise. Micelles are actuallynanoreactor systems. The most important function of micelles is their ability to solubilize organic water-insoluble substances.The role of detergents in many washing applications is well known. Further, the biological phenomena where bile salts(amphiphiles) are necessary for the solubilization and transport of lipid fats, is a very important process in the digestion.Micelle formation is an unique self-assembly property, which is found to be inherent to these amphiphile molecules[13,16,17].The designation colloid is used for particles that are of some small dimension and cannot pass through a membrane witha pore size %106m (micrometer). (Thomas Graham described this about a century ago. The Greek word for glue.). The natureand relevance of colloids is one of the main current research topics [16].Liquid phaseVaporphaseLiquidsurfaceFIGURE 1.1 Intermolecular forces around a molecule in the bulk liquid and around a molecule in the surface layer (schematic).PolaroutercoreApolar coreFIGURE 1.2 Micelle structureinner core (alkane-like) and outer polar region.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 2 8.10.2008 7:15pm Compositor Name: VAmoudavally2 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCThe range of size determines the designation: macrocolloids to nanocolloids. Colloids are an important class of materials,intermediate between bulk and molecularly dispersed systems. The colloid particles may be spherical, but in some cases onedimension can be much larger than the other two (as in a needle-like shape). The size of particles also determines whether theycan be seen with the naked eye. Colloids are neither visible to the naked eye nor under an ordinary optical microscope. Thescattering of light can easily be used to see such colloidal particles (such as dust particles, etc.). The size of colloidal particlesthen may range from 104to 107cm. The units used are as follows:1 mm106m1 (Angstrom) 108cm0.1 nm1010m1 nm109mThe unit Angstrom is named after the famous Swedish scientist, and currently nanometer (109m.) unit is mainly used.Because colloidal systems consist of two or more phases and components, the interfacial area-to-volume ratio becomes verysignicant. Colloidal particles have a high ratio of surface area to volume compared with bulk materials. A signicantproportion of the colloidal molecules lie within, or close to, the interfacial region. Hence, the interfacial region has signicantcontrol over the properties of colloids. To understand why colloidal dispersions can either be stable, or unstable, we need toconsider the following:1. Effect of the large surface area to volume ratio2. Forces operating between the colloidal particlesIf the particle size is larger than 1 mm then the system is called a suspension.There are some very special characteristics that must be considered regarding colloidal particle behavior: size and shape,surface area, and surface charge density. The Brownian motion of the particles is a much-studied eld. The fractal natureof surface roughness has recently been shown to be important [14]. Recent applications have been reported employingnanocolloids [14a]. The new innovations based on nanocolloid technology are becoming very important.The denitions generally employed are as follows. Surface is the term used when considering the dividing phasebetweenGasliquidGassolidInterface is the term used when considering the dividing phase betweenSolidliquidLiquid1liquid2Solid1solid2In other words, the ST (g) may be considered to arise due to a degree of unsaturation of bonds that occurs when a moleculeresides at the surface and not in the bulk. However, the molecules at the surface are easily exchanging with the bulk moleculesdue to kinetic forces.The term ST is used for solidvapor or liquidvapor interfaces. The term IFT is more generally used for the interfacebetween two liquids, two solids, or a liquid and solid.It is, of course, obvious that in a one-component system, the uid is uniform from the bulk phase to the surface, but theorientation of the surface molecules will be different from those molecules in the bulk phase. For instance, one has argued thatthe orientation of water molecules, H2O, at the interface most likely is consistent with the oxygen atom pointing at the interface.This would thus lead to a negative dipole and thus the rain drops would be expected to have a net negative charge (as foundfrom experiments). The question we may ask, then, is how sharply does the density change from that of being uid to that ofgas. Is this a transition region a monolayer deep or many layers deep?Many reports are found where this subject has been investigated [13,14]. The Gibbs adsorption theory considers surface ofliquids to be monolayer. The experiments which analyze the spread monolayers are also based on one molecular layer. Thesubject related to self-assembly monolayer (SAM) structures will be treated extensively [14,16]. However, there exists noprocedure, which can provide information by a direct measurement. This subject will be described later herein. Thecomposition of the surface of a solution with two components or more would require additional comments [15]. InTable 1.1 are given typical colloidal suspensions that are found in everyday life. Colloidal systems are widespread in theiroccurrence and have biological and technological signicance. There are three important types of colloidal systems [16]:Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 3 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 3 2009 by Taylor & Francis Group, LLC1. In simple colloids, clear distinction can be made between the disperse phase and the disperse medium, for example,simple emulsions of oil-in-water (o=w) or water-in-oil (w=o)2. Multiple colloids involve the coexistence of three phases of which two are nely divided, for example, multipleemulsions of water-in-oil-in-water (w=o=w) or oil-in-water-in-oil (o=w=o)3. Network colloids have two phases forming an interpenetrating network, for example, polymer matrixThe colloidal stability is determined by the free energy (surface free energy or the interfacial free energy) of the system.The main parameter of interest is the large surface area exposed between the dispersed phase and the continuous phase.Since the colloid particles move about constantly, their dispersion energy is determined by the Brownian motion. The energyimparted by collisions with the surrounding molecules at temperature T 300 K is 3=2 kB T 3=2 (1.38 1023) 300 1020J(where kB is the Boltzmann constant). This energy and the intermolecular forces would thus determine the colloidal stability.The idea that two species should interact with one another, so that their mutual potential energy can be represented by somefunction of the distance between them, has been described in literature.Furthermore, colloidal particles frequently adsorb (and even absorb) ions from their dispersing medium. Sorption that ismuch stronger than what would be expected from dispersion forces is called chemisorption, a process which is of both chemicaland physical interest. It is thus obvious that a colloidal system represents a state of higher energy than that corresponding to thematerial in bulk. Hence, there will be a tendency in the system to move to lower energy state, unless there are other energeticbarriers (such as electrostatic charge repulsion; steric factors; hydration forces) to overcome. Under such conditions, the systemmay be in a metastable state and remain in that state for a long time.These considerations are important in regard to the different systems mentioned above: paints, cements, adhesives,photographic products, water purication, sewage disposal, emulsions, chromatography, oil recovery, paper and print industry,microelectronics, soap and detergents, catalysts, food products, pharmaceutical products, and biology (cell [adhesion andaggregation], virus).1.2 SURFACE TENSION AND INTERFACIAL TENSION OF LIQUIDS1.2.1 INTRODUCTIONThe liquid state of matter is known to play a very important role in everyday life. The liquid surface has a very dominant role inmany of these phenomena. In this context, one may mention that about 70% of the surface of earth is covered by water. Theimportance of rivers and rain drops on various natural phenomena is very obvious. It is therefore important to give a detailedintroduction to the physicochemical principles about ST. The most fundamental characteristic of liquid surfaces is that they tendto contract to the smallest surface area to achieve the lowest free energy. Whereas gases have no denite shape or volume,completely lling a vessel of any size containing them, liquids have no denite shape but do have a denite volume, whichTABLE 1.1Typical Colloidal SystemsPhasesDispersed Continuous System NameLiquid Gas Aerosol fog, sprayGas Liquid Foam, thin lms, frothFire extinguisher foamLiquid Liquid Emulsion (milk)Mayonnaise, butterSolid Liquid Sols, AgI, photography lmsSuspension wastewaterCementBiocolloidsCorpuscles Serum BloodHydroxyapatite Collagen Bone; teethLiquid Solid Solid emulsion (toothpaste)Solid Gas Solid aerosol (dust)Gas Solid Solid foamexpanded (polystyrene)Insulating foamSolid Solid Solid suspension=solids in plasticsBirdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 4 8.10.2008 7:15pm Compositor Name: VAmoudavally4 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCmeans that a portion of the liquid takes up the shape of that part of a vessel containing it and occupies a denite volume, the freesurface being plane except for capillary effects where it is in contact with the vessel. This is observed when one notices raindrops and soap lms, in addition to many other systems which will be mentioned later. The cohesion forces present in liquidsand solids and the condensation of vapors to liquid state indicate the presence of much larger intermolecular forces than thegravity forces. Furthermore, the dynamics of molecules at interfaces are important in a variety of areas, such as biochemistry,electrochemistry, and chromatography.The degree of sharpness of a liquid surface has been the subject of much discussion in the literature. There is strongevidence that the change in density from liquid to vapor (by a factor of 1000) is exceedingly abrupt, that is, in terms ofmolecular dimensions. The surface of a liquid was analyzed by light reectance investigations, as described by Fresnels law.Various investigators indeed found that the surface transition involves just one layer of molecules. In other words, when onementions surfaces and investigations related to this part of a system, one actually mentions just a molecular layer. However,there exists one system which clearly shows the one molecule thick layer of surface as being the surface of a liquid: this is themonolayer studies of lipids spread on water and studied by Langmuir balance [18]. The surface thermodynamics of thesemonolayers is based on unimolecular layer at the interface, which thus conrms the thickness of the surface. The molecules of aliquid in the bulk phase are in a state of constant unordered motion like those of a gas, but they collide with one another muchmore frequently owing to the greater number of them in a given volume (as shown here):Gas phase (molecules in gas)Intermediate phaseLiquid surface (surface molecules)Bulk liquid phase (molecules inside liquid)It is important to notice that the intermediate phase is only present between the gas phase and the liquid phase. Although onedoes not often think about how any interface behaves at equilibrium, the liquid surface demands special comment. Thesurface of a liquid is under constant agitation; there are few things in nature presenting an appearance of more completerepose than a liquid surface at rest. On the other hand, the kinetic theory tells us that molecules are subject to much agitation.This is apparent if we consider the number of molecules which must evaporate each second from the surface to maintain thevapor pressure. At equilibrium, the number of liquid molecules that evaporate into the gas phase is equal to the number ofgas molecules that condense at the liquid surface (which will take place in the intermediate phase). The number of moleculeshitting the liquid surface is considered to condense irreversibly [16a]. From the kinetic theory of gases, this number can beestimated as follows:mass=cm2=s rGkBT2pmm 0:5 0:0583 pvap(Mw=T)(1:1)wherekB is the Boltzmann constant (1.3805 1016erg deg1)mm is the mass of moleculerG is the density of the gasMw is the molecular weightIf we consider water at 208C, the vapor pressure of this liquid is 17.5 mm, which gives 0.25 g=s=cm2from Equation 1.1.This corresponds to 9 1021molecules of water per second. While from consideration of the size of each water molecule,we nd that there are %1015molecules, so that it can be concluded that the average life of each molecule in the surface is onlyabout one eight-millionth of a second (1=8 106s). This must be compounded with the movement of the bulk watermolecules toward the surface region. It thus becomes evident that there is an extremely violent agitation in the liquid surface. Infact, this turbulence may be considered analogous to the movement of the molecules in the gas phase. One observes this vividlyin a cognac glass. In the case of interface between two immiscible liquids due to the presence of IFT, the interface tends tocontract. The magnitude of IFT is always lower than the ST of the liquid with the higher tension. The liquidliquid interface hasbeen investigated by specular reection of x-rays to gain structural information at Angstrom (108cm0.10 nm)resolution [1921].The term capillarity originates from the Latin word capillus, a hair, describing the rise of liquids in ne glass tubes.Laplace showed that the rise of uids in a narrow capillary was related to the difference in pressure across the interface and theST of the uid [2224]:Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 5 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 5 2009 by Taylor & Francis Group, LLCDP g(curvature) g 1radius of the curvature 2g 1radius of the capillary (1:2)This means that when a glass tube of a hair-ne diameter is dipped in water, the liquid meniscus will rise to the very sameheight. A uid will rise in the capillary if it wets the surface, whereas it will decrease in height if it nonwets (like Hg in glasscapillary). The magnitude of rise is rather large, that is, 3 cm if the bore is of 1 mm for water. This equation also explains whathappens when liquid drops are formed at a faucet. Although it may not be obvious here, but the capillary force can be verydominating in different processes. In Figure 1.3, it is found that the ow of liquid takes place due to the DP only, since there ispractically no gravity force present. In porous materials, this capillary force thus becomes the most signicant driving force.The same is found in the case of two bubbles or drops, Figure 1.4, where the smaller bubble or drop (due to lager DP) willcoalescent with the larger bubble or drop.The capillary phenomenon thus means that it will play an important role in all kinds of systems where liquid is in contactwith materials with pores or holes. In such systems the capillary forces will determine the characteristics of liquidsolidsystems. Some of the most important are:. All kinds of uid ow inside solid matrices (ground water; oil recovery). Fluid ow inside capillary (oil recovery; ground water ow; blood ow)It was recognized at a very early stage that only the forces from the molecules in the surface layer act on the capillary rise. Theow of blood in all living species is dependent on the capillary forces. The oil recovery technology in reservoirs is similarlydependent on the capillary phenomena. Actually, the capillary forces become very dominating in such systems. Furthermore,virtually all elements and chemical compounds have a solid, liquid, and vapor phase. A transition from one phase to anotherphase is accompanied by a change in temperature, pressure, density, or volume. This observation thus also suggests that due tothe term DP, the chemical potential will be different than in systems with at surfaces. In a recent study, the cascade of astructure in a drop falling from a faucet was investigated [25]. In fact, uid in the shape of drops (as in rain, sprays, fog,emulsions) is a common natural phenomenon and has attracted the attention of scientists for many decades.A molecular explanation can be useful to consider in regard to surface molecules. Molecules are small objects whichbehave as if of denite size and shape in all states of matter (e.g., gas [G], liquid [L], and solid [S]) [26]. The volumeoccupied by a molecule in the gas phase is some 1000 times larger than the volume occupied by a molecule in the liquid phase,as follows:EquilibriumInitialLiquidFIGURE 1.3 Capillary ow of liquid due to Laplace pressure.Stable stateFIGURE 1.4 Smaller drop (or bubble) will merge into the larger drop due to the difference in the Laplace pressure.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 6 8.10.2008 7:15pm Compositor Name: VAmoudavally6 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCAs shown above, the volume of 1 mol of a substancefor example, water in the gas phase (at standard temperature andpressure), VG (%24,000 cc=mol)is some 1000 times its volume in the liquid phase, VL (molar volume of water %18 cc=mol).The distance between molecules, D, will be proportional to V1=3such that the distance in the gas phase, DG, will beapproximately 10 (10001=3) times larger than in the liquid phase, DL. The nite compressibility and the relatively high density,which characterize liquids in general, point to the existence of repulsive and attractive intermolecular forces. The same forcesthat are known to be present in the gaseous form of a substance may be imagined to play a role also in the liquid form. Themean speed of the molecules in the liquid is the same as that of the molecules in the gas; at the same temperature, the liquid andgas phase differ mainly by the difference in the density between them.The magnitude of ST, g, is determined by the internal forces in the liquid, thus it will be related to the internal energyor cohesive energy. The ST or capillary phenomena was mentioned in the literature at a very early stage by Leonardo da Vinci[27,28].The phenomena of ST can be explained by assuming that the surface behaves like a stretched membrane, with a forceof tension acting in the surface at right angles, which tends to pull the liquid surface away from this line in both directions(Figure 1.5).ST thus has units of force=length mass distance=time2distance mass=time2. This gives ST in units as mN=m ordyn=cm or J=m2(mN m=m2). As another example, one can imagine a rectangular frame with a sliding wire, EF, tted with ascale pan (Figure 1.6). If the frame is dipped into a soap (or any detergent) solution, a surface lm (denoted as EBCF) will beformed. The ST would give rise to a tendency for the lm to contract, to achieve a minimum in free energy. The weight, wf, thusrequired to balance this force would bewf 2g [EF] (1:3)SurfaceFIGURE 1.5 Tension in liquid surface.wfEEB CFD AFFIGURE 1.6 Stretching of a thin liquid lm.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 7 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 7 2009 by Taylor & Francis Group, LLCThe factor 2 in Equation 1.3 arises from the two sides of the lm. If the lm is stretched to a new EBCF point, the work done onthe system isWork wf [EE0] 2g [EF:EE0] 2g [E0EFF0] 2g (increase in area) (1:4)Gibbs [29] dened ST as the free energy excess per unit area:g G (GaGb)AreaGsurfaceArea (1:5)where G is the free energy of the two-phase system (phases a and b). The liquid and vapor phases are separated by a surfaceregion [2,5,7,13,14,2834].It is also seen that other thermodynamic quantities would be given as [16]Surface energy Usurface UArea (1:5a)Surface entropy Ssurface SArea (1:5b)and from this one can obtaing UsurfaceSsurface (1:5c)Hence, the magnitude of ST is also equal to the work spent in forming unit surface area (m2or cm2). This work increases thepotential energy or free surface energy, Gs (J=m2erg=cm2) of the system. This can be further explained by differentobservations one makes in everyday life, where liquid drops contract to attain minimum surfaces. If a loop of silk thread islaid carefully on a soap lm and the inside the loop is pricked with a needle, the loop takes up a circular shape, which provides aminimum in the energy for the system (Figure 1.7). Indeed, the concept of ST was already accepted around the year 1800. TheVolume per Mole in Gas or Liquid Phase and Distance between Molecules in Gas and Liquid PhasesMolar volume of water (at 208C)Vgasca. 24,000 mL (as gas)Vliquidca. 18 mL (as liquid)RatioVgas: VLiquidca. 1000Distance (D) between molecules in gas (DG) or liquid (DL) phaseRatio DG: DL(VG: VL)1=3(1000)1=310StableFIGURE 1.7 ST causes the equilibrium in the right drawing, where a circular shape is present.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 8 8.10.2008 7:15pm Compositor Name: VAmoudavally8 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCobservations such as a oating metal pin on the surface of water have been a common experience to all youngsters. In fact, agreat many aquatic insects survive by oating on the surface of water in lakes due to surface forces.It is well-known that the attraction between two portions of a uid decreases very rapidly with the distance and maybe taken as zero when this distance exceeds a limiting value, Rc, the so-called range of molecular action. According to Laplace[1,4,35,36], ST, g, is a force acting tangentially to the interfacial area, which equals the integral of the difference between theexternal pressure, pex, and the tangential pressure, pt:g ( pexpt) dz (1:6)The z-axis is normal to the plane interface and goes from the liquid to the gas (Figure 1.8). The magnitude of work which mustbe used to remove a unit area of a liquid lm of thickness t will be proportional to the tensile strength (latent heat ofevaporation) of the liquid thickness. In the case of water, this would give approximately 25,000 atm of pressure (600 cal=g ca.25.2 109erg 25,000 atm). However, different theoretical procedures used to estimate g by using Equation 1.6 have beensubject to much difculty, some of these procedures have been analyzed in a review [37]. In this review, the energetics andhydrostatic forces were analyzed. The change in density which occurs near the interface was also discussed. Further, due to theasymmetry of surface force elds as mentioned herein, the outermost layer of surface molecules in a liquid will be expected tobe highly structured, for example, in the case of water, leading to well-dened structural orientations such as polychair orpolyboat surface networks [38,39]. In the same way, ST can be described by quantitative structureactivity relationship(QSAR) or the so-called parachor (as described briey in Section 1.2.2). QSAR is an analysis by which the molecular structureof a series of molecules is correlated to its major characteristics. It has been known for long time that QSAR approach can beapplied to small molecule series, such as benzene, toluene, ethyl-benzene, etc.1.2.2 PARACHOR (OR QUANTITATIVE STRUCTUREACTIVITY RELATIONSHIP)In all kinds of technology, it is most useful to be able to predict physical property of a molecule from some theoretical criteria.Especially, it is important that one can correlate some molecular property to its structure (both quantitative and qualitative). Incurrent literature, one nds extensive analyses of QSAR as applied to different systems. Many physical properties of moleculesin the bulk phase can be related to their composition and structure [40]. This is very convenient when one needs to be able topredict the properties of any molecule and also from a theoretical viewpoint, which gives one a more molecular understandingof the different forces present in any system. At a very early stage, it was accepted that the same could be expressed for the STand bulk characteristics. The most signicant observation was that the expression relating ST with density (rL and rG: for liquidand gas) was independent of temperature:g1=4( rLrG) Cpara (1:7)The above equation was useful in the determination of molecular properties [41]. After multiplication of both sides by themolecular weight, Mw, the constant, Cpara, is called the parachor (Ppara):Ppara Cpara Mw Mwg1=4( rLrG) (1:8)BzdzACFIGURE 1.8 Pressure gradient in the surface region. (A and B are two parts of uid divided by plane C; dz is an imaginary thin layer inz-axis.) (Schematic)Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 9 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 9 2009 by Taylor & Francis Group, LLCThe parachor quantity, Ppara, is primarily an additive term such that each group of molecules contributes to the same extent in ahomologous series. If one neglects rG in comparison to rL (an error of less than 0.1%), then we getPpara Mwg1=4 rpL Vmg1=4(1:9)where Vm is the molar volume of the liquid. The adaptivity of parachors is thus equivalent to that of atomic volumes measuredunder unit ST, which is regarded to be approximately the same as under equal internal pressures.The atomic and constitutional parachor values are given in Table 1.2. Furthermore, the parachor values for single bond (sb);coordinate bond (cb); double bond (db); triple bond (tb); single-electron bond (seb); 3-, 4-, 5-, 6-, 7-, or 8-membered rings (3r,etc.); and a naphthalene ring (na) were given as follows [4043]:Parachor ValuesSeb sb cb db tb 3r 4r 5r 6r 7r 8r na11.6 0 1.6 23.2 46.6 16.7 11.6 8.5 6.1 4.6 2.4 12.2As an example, the calculated value for tolunitrile, C6H4CH3CN, is found as8 4:8 7 17:1 1 12:5 46:6 3 23:2 6:1 292:9The measured values of parachor are 290.6, 295.5, and 294.4 for the ortho, meta, and compound, respectively. The calculatedvalues for some typical liquids agreed satisfactorily with the measured data (inside brackets):Acetone: 23.35 (23.09)Ethanol: 21.92 (22.03)n-octane: 21.3 (21.32)Parachors in solutions can also be estimated, but it has been reported to be more difcult. This arises from the fact that thecomposition of the surface is different from that of the bulk phase. The present state of analysis is not very satisfactory [4044].Furthermore, the parachor theory for IFT remains to be investigated; therefore, some suggestions will be developed in thisreview. However, some typical data are found in literature where ST for various mixed systems is given along with density,refractive index, and viscosity [45aj]:. Density and ST of aqueous H2SO4 at low temperature [45bj]. Density, viscosity, and ST of sodium carbonate sodium bicarbonate buffer solutions in the presence of glycerin,glucose, and sucrose from 258C to 408C [45bj]. Density, ST, and refractive index of aqueous ammonium oxalate solutions from 293 to 333 K [45bj]. STs, refractive indexes, and excess molar volumes of hexane 1-alkanol mixtures at 298.15 K [45bj]. Densities, viscosities, refractive indices, and STs of 4-methyl-2-pentanone ethyl benzoate mixtures at 283.15,293.15, and 303.15 K, respectively [45bj]TABLE 1.2QSAR for Estimating the Parachor ValuesParachor ValuesC H O F Cl Br I N S P4.8 17.1 20 25.7 54.3 68 91 12.5 48.2 38.2Parachor ValuesCH3 CH2 C6H5 COO COOH OH NH2 NO2 NO3 CONH256 40 190 64 74 30 43 74 93 92Sources: From Birdi, K.S., ed., Handbook of Surface & Colloid Chemistry, CRC Press, Boca Raton, FL, 1997; Birdi, K.S., ed., Handbook of Surface &Colloid Chemistry-CD Rom, CRC Press, Boca Raton, FL, 1997; Handbook of Surface & Colloid Chemistry, 2nd edn., 2002.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 10 8.10.2008 7:15pm Compositor Name: VAmoudavally10 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLC1.2.3 HEAT OF SURFACE FORMATION AND HEAT OF EVAPORATIONAll natural phenomena are dependent on temperature and pressure. As mentioned earlier, energy is required to bring a moleculefrom the bulk phase to the surface phase of a liquid. In the bulk phase, the number of neighbors (six near neighbors forhexagonal packing and if considering only two-dimensional packing) will be roughly twice the molecules at the surface (threenear neighbors, when discounting the gas-phase molecules) (see Figure 1.9).The interaction between the surface molecules and the gas molecules will be negligible, since the distance betweenmolecules in the two phases will be very large. Furthermore, as explained elsewhere, these interaction differences disappear atthe critical temperature. It was argued [7,46] that when a molecule is brought to the surface of a liquid from the bulk phase(where each molecule is symmetrically situated with respect to each other), the work done against the attractive force near thesurface will be expected to be related to the work spent when it escapes into the vapor phase. It can be shown that this is justhalf for the vaporization process (Figure 1.9).The density, viscosity, and ST of liquid quinoline, naphthalene, biphenyl, decauorobiphenyl, and 1,2-diphenylbenzenefrom 3008C to 4008C, have been reported [47].In earlier literature, several attempts were made to nd a correlation between the latent heat of evaporation, Levap, and g orthe specic cohesion, a2co(2g=rL 2gvsp), where rLdensity of the uid and vsp is the specic volume. The followingcorrelation was given [47]:Levap(Vm)3=2a2co 3 (1:10)However, later analyses showed that this correlation was not very satisfactory for experimental data. From these analyses it wassuggested that there are 13,423,656 layers of molecules in 1 cm3of water. In Table 1.3 are given some comparisons of thismodel of a liquid surface as originally described by Stefan [46].AirSurfaceLiquidFIGURE 1.9 Molecular packing in two dimensions in bulk (six near neighbors) and surface (three near neighbors) molecules (schematic).TABLE 1.3Enthalpy of Surface Formation, hs (1014erg=mol),and Ratios of Evaporation, Levap (1014erg=mol),at a Reduced Temperature (T=Tc0.7)Molecule hS hS=LevapNitrogen 3.84 0.51Oxygen 4.6 0.50CCl4 18.2 0.45C6H6 18.4 0.44Diethylether 15.6 0.42ClC6H5 20.3 0.42Methyl formamate 15.4 0.40Ethyl acetate 18.3 0.4Acetic acid 11.6 0.34Water 14.4 0.28Ethyl alcohol 11.2 0.19Methyl alcohol 8.5 0.16Hg 20 0.64Note: See text for details.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 11 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 11 2009 by Taylor & Francis Group, LLCIt has been determined that substances that have nearly spherical molecules have Stefan ratios (g=Levap) of approximately1=2 (three near neighbors at the surface=six near neighbors in the bulk phase). On the other hand, substances with polar groupson one end give much smaller ratios. This suggests that the molecules are oriented with the nonpolar end toward the gas phaseand the polar end toward the bulk liquid phase. At this stage, more detailed analysis is needed to describe these relations in moremolecular detail. This also requires a method of measuring the molecular structure, which is lacking at this stage. In spite ofthis, what one does conclude is that the molecular analysis is valid as regards the surfaces of liquids. Hence, any changes insurface properties would require only molecules at surfaces, as described later below.It is well-known that both the heat of vaporization of a liquid, DHvap, and the ST of the liquid, g, are dependent ontemperature and pressure, and they result from various intermolecular forces existing within the molecules in the bulk liquid. Tounderstand the molecular structure of liquid surfaces, one may consider this system in a somewhat simplied model. Themolecular surface energy, Smse, was dened by Eotovos [48] (in 1886) as the surface energy on the face of a cube containing1 mol of liquid:Smse g(Mwvsp)2=3(1:11)wherevsp is the specic volumeMw is the molecular weightThe molar internal heat of evaporation, Levap, can be given asLevap LerMw(vGvL) (1:12)andg(Mwvsp)2=3 12 Levap (1:13)The correct value for the molar surface energy is probably not the face of a cube representing the molecular volume:Molecular volume Mw(v)2=3(1:14)but rather the area of the sphere containing 1 mol of the liquidMolecular surface area 4p 34p 2=3(Mwv)2=3 4:836 (Mwv)2=3(1:15)The amount of heat required to convert 1 g of a pure liquid into saturated vapor at any given temperature is called the latent heatof evaporation or latent heat of vaporization, Levap. It has been suggested thatLatent heat of evaporation2g Levap2g (1:15a) Area occupied by all molecules if they lie in the surface Amol (1:16)Then we can writeDiameter Amol vsp (1:17)HenceDiameter 2gvspLevap(1:18)Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 12 8.10.2008 7:15pm Compositor Name: VAmoudavally12 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCFor example, for waterLevap 600 g cal(0:15 kg J) 600 42,355 g cm 25,413,000 g cmvH2O ca:1 g=ccgoC 88 dyn=cm 88 mN=m 0:088 N=m(1:19)From this we ndDiameter of water molecule 2 0:088 12,541,300 0:7 108cm 0:7 0:07 nm (1:20)which is of the right order of magnitude.In a later investigation [49], a correlation between heat of vaporization, DHvap, and the effective radius of the molecule, Reff,and ST, g, was found. These analyses showed that a correlation between enthalpy and ST exists which is dependent on the sizeof the molecule. It thus conrms the molecular model of liquids. More investigations are required at this stage before amolecular model can be delineated.1.2.4 EFFECT OF TEMPERATURE AND PRESSURE ON SURFACE TENSION OF LIQUIDSAs already mentioned, all natural processes are dependent on the temperature and pressure variations in the environment. Forexample, the oil reservoirs are found under high temperature (808C) and pressure (200300 atm). The molecular interactions inthe surface (two dimensional) are by one order of magnitude less than in the bulk (three dimensional). As the temperatureincreases, the kinetic energy of the molecules increases. This effect thus provides the means of obtaining information aboutmolecular interactions in different systems and interfaces. Molecular phenomena at the surface separating the liquid and thesaturated vapor (or the liquid and the walls of its containing vessel) are appreciably more complex than those that occur insidethe homogenous liquid, and it is difcult to state much of a rigorous qualitative nature concerning them. The essential difcultyis that from the microscopic standpoint there is always a well-dened surface of separation between the two phases but on themicroscopic scale there is only a surface zone, in crossing which the structure of the uid undergoes progressive modication. Itis in this surface zone that the dynamic equilibrium between the molecules of the vapor and those of the liquid is established.Owing to the attractive forces exerted by the molecules of the liquid proper on one another, only the fast-moving molecules canpenetrate the layer and escape into the vapor; in the process, they lose kinetic energy and, on the average, attain the samevelocity as the molecules in the vapor.Further, the number of molecules escaping cannot, on the average, exceed the number entering from the much rarer vapor.From a statistical point of view, the density of the uid is the most important variable in the surface area; it does not, of course,suffer an abrupt change but varies continuously in passing through the surface zone from its value in the liquid to the generallymuch lower value in the vapor (a decrease by a factor of ca. 1000). In consequence, it is possible to specify only ratherarbitrarily where the liquid phase ends and the gaseous phase begins. It is convenient to some extent to dene the interface as acertain surface of constant density within the surface zone such that if each of the two phases remains homogeneous up to thesurface, the total number of molecules would be the same [7,13].The work required to increase the area of a surface is the work required to bring additional molecules from the interior to thesurface. This work must be done against the attraction of surrounding molecules. Since cohesive forces fall off very steeplywith distance between molecules, one can consider as a rst approximation interactions between neighboring molecules only.There is strong evidence that the change of density from the liquid phase to vapor is exceedingly abrupt, transitional layersbeing generally only one or two molecules thick.Perhaps the most convincing evidence is that derived from the nature of the light reected from the surfaces of liquids.According to Fresnels law of reection, if the transition between air and a medium of refractive index, n, is absolutely abrupt,the light is completely plane polarized if the angle of incidence is the Brucetarian angle. But, if the transition is gradual, the lightis elliptically polarized. It was found [22,50] that there is still some small amount of residual ellipticity in the cleanest surfacesof water and that these scatter light to some extent.The structure of liquid surfaces has been described by using a hybrid approach of thermodynamics and super liquids [20].Even though the ST phenomenon of liquids has been extensively studied, the transition region, where ST is at present has notbeen successfully described.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 13 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 13 2009 by Taylor & Francis Group, LLC1.2.5 CORRESPONDING STATES THEORY OF LIQUIDSTo understand the molecular structure of liquid surfaces, it is important to be able to describe the interfacial forces as a functionof temperature and pressure. As temperature increases, the kinetic energy increases due to the increase in the molecularmovement. This effect on the change in ST gives information on the surface entropy. Although a large number of reports arefound in the literature at this stage, complete understanding of surface energy and entropy has not been achieved. In thefollowing, some of these considerations are delineated. The magnitude of g decreases almost linearly with temperature within anarrow range [14,36,40]:gt go(1 kot) (1:21)whereko is a constantt is the temperature (8C)It was found that the coefcient ko is approximately equal to the rate of decrease of density (r) with rise of temperature:rt ro(1 kdt) (1:22)Values of constant kd were found to be different for different liquids. Furthermore, the value of kd was related to Tc (criticaltemperature) and Pc (critical pressure) [1].The following equation relates ST of a liquid to the density of liquid, rL, and vapor, rV [51]:g( rLrV)4 Cmc ca: 3 (1:23)where the value of constant Cmc is only nonvariable for organic liquids, while it is not constant for liquid metals.The effect of temperature (at constant pressure) on ST is different for different uids (Table 1.4) [5]. This is the surfaceentropy, ss (dg=dT). Thus, we can obtain much useful information from this as regards thermodynamics and the molecularinteractions. As shown later, the effect of temperature can also give information about the surface orientation of the molecules.These data are given here merely to indicate how ST is characteristic for a given uid, as one can estimate from the effect oftemperature. One clearly observes the range in g and the variation in ss for the various types of uids. At the criticaltemperature, Tc, and the critical pressure, Pc, rc of liquid and vapor is identical; the ST, g, and total surface energy, like theenergy of vaporization, must be zero.The critical point of the equilibrium of two phases corresponds to the limit of their coexistence. The tension of the interface(ST) decreases as one approaches the critical point and g becomes zero at this state.At critical temperature, Tc, and critical pressure, PcdgdT T!Tc,P!Pc 0 (1:24)In current literature, erroneously, the term Pc is omitted in this equation [51a]. It also needs to be emphasized that Tc and Pcexist simultaneously, by denition.TABLE 1.4Typical Data of Variation of ST with Temperature of Different LiquidsFluid T (K) g (mN=m) (dg=dT)a(dyn=cm=K)H2O 293.2 72.8 0.16NaCl 1076 114 0.07Zn 693.2 782 0.17Hg 235.2 498 0.2Sources: From Birdi, K.S., ed., Handbook of Surface & Colloid Chemistry, CRC Press, Boca Raton,FL, 1997; Birdi, K.S., ed., Handbook of Surface & Colloid Chemistry-CD Rom, CRCPress, Boca Raton, FL, 1997; Handbook of Surface & Colloid Chemistry, 2nd edn., 2002.adg=dT is the surface entropy.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 14 8.10.2008 7:15pm Compositor Name: VAmoudavally14 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCAt temperatures below the boiling point, which is 2=3 T, the total surface energy and the energy of evaporation are nearlyconstant. The ST, g, variation with temperature is given in Figure 1.10 for different liquid n-alkanes with a number of carbonatoms [52]. These data clearly show that the variation of g with temperature is a very characteristic physical property of a givenliquid, analogous to other bulk properties such as boiling point, heat of vaporization, density, viscosity, compressibility, andrefractive index. In other words, the molecules at the surface of the alkanes exhibit dependence on chain length which can berelated to some of these bulk properties. The surface entropy is almost a linear function of nC (Table 1.5). These data providevery useful information about the molecular structures at the surface. This observation becomes even more important whenconsidering that the sensitivity [13,14] of g measurements can be as high as ca. 0.001 dyn=cm (mN=m). It is seen that themagnitude of the extrapolated value of g at T08C increases with alkane chain length, nC. This means that g increases withincreasing van der Waals interactions between chains, analogous to heat of vaporization, melting point, and other molecularproperties. The data thus show how such useful physical measurements can be related to the molecular property of ahomologous series of molecules. This allows one to predict data for more complex molecules. These data clearly show thatC5C10C1630100 100 Temperature (C)Surface tensionFIGURE 1.10 Variation of ST versus temperature for nC for n-alkanes. (n-pentane; n-decane; n-hexadecane)TABLE 1.5Linear Equation a for Data of g versus Temperature for n-AlkanesAlkane (nC) Ao Bs,s (dg=dT) Extrapolated Value of gb5 18.25 0.1102 776 20 0.1022 757 22.10 0.098 768 23.52 0.0951 759 24.72 0.0935 7510 25.67 0.092 7511 26.46 0.0901 7512 27.12 0.08843 7513 27.73 0.0872 7514 28.30 0.0869 7515 29 0.08565 7516 29 0.0854 7517 29 0.0846 7518 30 0.08423 7519 30 0.0837 7520 31 0.0833 75Note: See text for details.ag Ao BS,S T, where T is in degree Celsius. Magnitude of Ao is the extrapolated value of g atT 08C.bAt T 5408C (see text).Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 15 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 15 2009 by Taylor & Francis Group, LLCthe magnitude of g is proportional to the chain length of the alkanes, nc. This is to be expected based on the previous relationgiven by Stefan on the dependence of the magnitude of g on the heat of evaporation. The data of ST versus temperature can beanalyzed as follows. It is well-known that the corresponding states theory can provide much useful information about thethermodynamics and transport properties of uids. For example, the most useful two-parameter empirical expression thatrelates the ST, g, to the critical temperature is given as [4]g ko(1 T=Tc)k1(1:25)where ko and k1 are constants. van der Waals derived this equation and showed that the magnitude of constant k13=2,although the experiments indicated that k1ca. 1.23. Guggenheim [53] has suggested that k111=9. Moreover, the quantityko(Vc)2=3=Tcwas suggested [54] to have a universal value of ca. 4.4; however, for many liquids, the value of k1 lies between6=5 and 5=4. Thus, the correct relation is given asg (Vc)2=3Tc(1 T=Tc)k1(1:26)It is thus seen that ST is related to Tc and Vc. van der Waals [14,36,40] also found that ko was proportional to (Tc)1=3(Pc)2=3.The above equation, when t to the ST, g, data of liquid CH4, has been found to give the following relation [55a]:gCH4 40:52(1 T=190:55)1:287(1:27)where Tc,CH4190.55 K. This equation has been found to t the g data for liquid methane from 918C to 1908C, with anaccuracy of 0.5 mN=m. Although the theory predicts that the exponent is valid only asymptotically close to the critical point,the ST corresponding states theory with additional expansion terms has been shown to be valid for many pure substances overtheir entire liquid range [55a].In a different context, the ST of a uid, ga, can be related to that of a reference uid, gref, as follows [55b]:ga(T) Ta,cTref,c Vref,cVa,c 2=3grefTref,cTa,c (1:28)whereT is the temperatureTa,c and Va,c are the critical temperature and volume of uid under consideration, respectivelySimilarly, the terms Tref,c and Vref,c refer to the reference uids critical temperature and volume, respectively. This procedurewas found to predict the temperature dependence of g of various uids and mixtures (such as CO2, ethane, butane, hexane,octane, hexane ethane, hexane CO2). The variation of g of a mixture of hexane ethane was almost linear with the molefraction of hexane, xC6:gC6C2 0:64 17:85xC6 (1:29)This means that one can estimate the concentration of dissolved ethane from such g measurements. Similar analyses ofC6CO2 data gives almost the same relationship as for C6C2H6. This indicates that in a mixed system the addition of a gasto a uid simply reduces the magnitude of g in the mixture, since the extrapolated plot tends toward almost zero at a molefraction of the uid equals zero. That the magnitude of g of uids can be measured with a very high accuracy [14] suggests thatthe solubility of gas (or gases) can be investigated by the g change. A change in mole fraction by 0.1 unit will give a change in gof the solution of ca. 2 mN=m. This quantity can be measured with an accuracy of 0.001 mN=m, suggesting a gas solubilitysensitivity of 104. Further, this method is most useful in those cases where gas is not available in large quantity. This arisesfrom the fact that very small amounts of liquid are needed for g measurements.The variation of g of a large variety of liquids (more than a hundred) is available in literature [52]. The different homologseries will provide information about the stabilizing forces in these uids. For instance, while alkanes are stabilized by mainlyvan der Waals forces, the alcohols would be mainly stabilized by both van der Waals forces and hydrogen bonds, the latterbeing stronger than the former.To analyze such thermodynamic relations of different molecules, we take the model system to be a homologous series ofnormal alkanes and alkenes, since very reliable and accurate data are available in the literature. Linear HC chains, n-alkanes, areamong the most common molecular building blocks of organic matter. They form part of the organic and biological moleculesBirdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 16 8.10.2008 7:15pm Compositor Name: VAmoudavally16 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCof lipids, surfactants, and liquid crystals and determine their properties to a large extent. As major constituents of oils, fuels,polymers, and lubricants they also have immense industrial importance. Accordingly, their bulk properties have beenextensively studied. The measured variation in g with temperature data, near room temperature, was almost linear withtemperature for all the alkanes with carbon atoms, nC, from 5 to 18. This means that the magnitude of surface entropy isconstant over a range of temperature. Similar observation was made from the analyses of other homolog series of organic uids(over 100 different molecules):1. Alkenes [52]2. n-alcohols [52]3. CO2 in liquid state [55]The g data of alkanes were analyzed by using Equation 1.25. The constants, ko (between 52 and 58) and k1 (magnitude rangingbetween 1.2 and 1.5), were found to be dependent on the number of carbon atoms, nC; since Tc is also found to be dependent onnC, the expression for all the different alkanes which individually were t to Equation 1.29 gave rise to a general equation whereg was a function of nC and T [14]:g Function of T, nC 41:41 2:731 nC0:192 n2C0:00503 n3C (1:30)1 T273 99:86 145:4 ln (nC) !17:05 ln n2C k1(1:31)wherek1 0:9968 0:04087 nC0:00282 (nC)20:000844 (nC)3(1:32)The estimated values from the above equation for g of different n-alkanes were found to agree with the measured data within afew percent: g for n-C18H38, at 1008C, was 21.6 mN=m, both measured and calculated (Table 1.6). Using such analyses onedoes not need to apply tables, since computer memory can assist in the estimation of ST of any alkane at a given temperature.This shows that the ST data of n-alkanes ts the corresponding state equation very satisfactorily. In these analyses, the pressureTABLE 1.6Calculatedag and Measured Values of Different n-Alkanesat Various Temperaturesn-Alkane Temperature (8C) g (Measured) g (Calculated)C5 0 18.23 18.2550 12.91 12.8C6 0 20.45 20.4060 14.31 14.3C7 30 19.16 19.1780 14.31 14.26C9 0 24.76 24.7050 19.97 20.05100 15.41 15.4C14 10 27.47 27.4100 19.66 19.60C16 50 24.90 24.90C18 30 27.50 27.50100 21.58 21.60Sources: From Birdi, K.S., ed., Handbook of Surface & Colloid Chemistry, CRC Press,Boca Raton, FL, 1997; Birdi, K.S., ed., Handbook of Surface & ColloidChemistry-CD Rom, CRC Press, Boca Raton, FL, 1997; Handbook of Surface& Colloid Chemistry, 2nd edn., 2002.aFrom Equation 1.3.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 17 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 17 2009 by Taylor & Francis Group, LLCis assumed to be constant. Furthermore, by using this relationship we do not need any elaborate tables of data. Especially byusing a simple computer program one can nd g values rapidly and accurately, as a function of both nC and T. However, theeffect of pressure must not be considered as negligible, as delineated later. More studies are needed on similar homolog seriesof liquids, to understand the relation between molecules and ST.The physical analyses of the constants ko and k1 have not been investigated at this stage. Further, since QSAR models canpredict relations between molecular structures and boiling points [5658], it should be possible to extend these models to STprediction based upon the above relation. A general and semiempirical correlation between the alkane chain length and ST hasbeen described [59].It is worth mentioning that the equation for the data of g versus T for polar (and associating) molecules such as water andalcohols, when analyzed by the above equation, gives magnitudes of ko and k1 which are signicantly different than those foundfor nonpolar molecules such as alkanes, etc. This observation therefore requires further analysis to understand the relationamong g, surface entropy, and Tc (as well as Pc and Vc).The critical constants of a compound are of both fundamental and practical interest. Furthermore, sometimes the criticalconstants are not easily measured, due to experimental limitation. In Table 1.7, the estimated data for gt 0 (at t 08C) and themagnitude of dg=dT (surface entropy) for a variety of liquids are given. For a very practical approximate estimation of Tc onecan use these data asTc gt0(dg=dT) (1:33)where T is in 8C. The calculated value for water is Tc75.87=0.1511 273 502 K. This compares with the measured valueof 647 K. The data for C6H6 gives Tc,C6H6226.48C (499 K), as compared to the measured value of 561 K. The estimatedvalues are lower as expected.In the case of n-alkanes, the linear part (Figure 1.10) was extrapolated to g 0 to estimate Tc (and P1 atm). The analysesof the alkane data from C5 to C20 is of much interest in this context, from both a theoretical and practical point of view. If onemerely extrapolates the linear part of the measured data (at 1 atm) then the estimated Tc, 1 atm is found to be somewhat lower(ca. 10%, dependent on nC) than the directly measured values (Table 1.7). It is observed that the magnitudes of Tc for thesealkanes can be very high. This may lead, in some cases, to decomposition of the substance if measurements are made directly.On the other hand, if one can use the present ST data to estimate Tc then it can provide much useful information.The difference between the estimated Tc (lower in all cases) and the measured Tc (range measured from 2008C to 5008C atPc) per carbon atom is found to be 68. This gives values of estimated Tc within a 5% error for alkanes with nC from 5 to 20. Thisnding is of great signicance.TABLE 1.7Comparison of Measured and EstimatedaValues of Tc, 1atm at g0 for Different n-AlkanesbnC Tc, g 0 (8C) (Estimated) Tcc,at Pc (Measured) DcD=ndC Pc=Bar (Measured)5 166 197 31 6 336 200 234 34 6 307 216 267 51 7 278 240 296 56 7 259 260 320 60 7 2310 279 344 65 6.5 2111 294 364 70 6.3 2012 307 385 78 6 1913 318 403 85 6 1714 326 420 94 6 1415 336 434 98 6 1516 342 449 107 6 1417 350 460 110 6 1318 356 475 119 6 1219 361 483 121 6 1120 367 494 127 6 11aFrom g versus T data to g 0.bExtrapolated from data for g versus T.cTc,g > o Tc,estimated.dTc,g > o Tc,estimated=nC.Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 18 8.10.2008 7:15pm Compositor Name: VAmoudavally18 Handbook of Surface and Colloid Chemistry 2009 by Taylor & Francis Group, LLCOne of the most important consequences is that, in the case of uids that are unstable at high temperatures, one need onlymeasure the variation of ST with temperature, from which one can estimate the value of Tc. The correction required arises fromthe effect of Pc on g.One can thus show from these data that for n-alkanes:Tc,g0 TcnC6 (1:34a)Or, one can rewriteTc Tc,g0nC6 (1:34b)This shows convincingly that an increase in pressure gives rise to an increase in ST, that is, dg=dP (i.e., positive).However, the need for this correction is expected; if we consider the fact that at the critical point the pressure is not 1 atm but Pc,then a correction would be needed. For example, the Tc and Pc for alkanes of nC equal to 12 and 16 are 658 K and 18 atm and722 K and 14 atm, respectively. In fact, all the relations as found in literature which neglect critical pressure are inadequate.To modify the data of g versus T at 1 atm to include the effect of pressure, Pc, then this would give an increase in ST, sincethe quantity dg=dP is positive for liquids [16]. In other words, the analyses of ST versus temperature data must be reformulatedto include the effect of Pc on the ST data, as shown below (Figure 1.11). The measured g data is obtained at 1 atm.The extrapolated line is moved from 1 atm to Pc and moved up by a value which corresponds to dg=dP (positive). It is thuspossible to estimate the magnitude of dg=dP from such data.The correction required based on the above is as follows:Tc (gt,ref sstref)ss6(nC) (1:35)wheregt,ref is the ST at a given temperature (and at 1 atm)ss is the surface entropyThe correction term, second on the right-hand side, arises from the correction necessary to obtain g at Tc at pressure equal to Pc.Previous studies have shown that an increase in the hydrostatic pressure over gaswater systems can produce marked changesin the ST by virtue of enhanced adsorption of the gaseous component at the interface.It is obvious that when more systematic ST data becomes available, a more detailed molecular description of thesignicance of this observation can be given. For example, there exist no such analyses of alkane mixtures (of two or morecomponents). These latter systems are of much interest in enhanced oil-recovery processes (EOR).The g versus temperature data for the homologous series n-alkanes and n-alkenes show some unique characteristics. Thedata for alkanes, on extrapolation to a hypothetical supercooled region, converge at Tscca. 5408C, and gsc75 mN=m[1a,b].The calculated values of gsc are given in Table 1.8 for a homologous series of alkanes. The magnitude of gsc is estimated as ca.75 mN=m in all cases. This shows that the alkane molecules in their hypothetical supercooled state at Tsc (5408C2(2738C)exhibit the same ST (gsc75 mN=m) regardless of chain length. To analyze this in more detail, the ST data ofalkenes were investigated [16]. These data also exhibit a supercooled temperature, Tsc ( 5408C), where all the alkeneTc, 1 atmTc, PcPcPressureTemperatureSurfacetensionFIGURE 1.11 Variation (schematic) of ST versus temperature (T) and pressure (P).Birdi/Handbook of Surface and Colloid Chemistry 7327_C001 Final Proof page 19 8.10.2008 7:15pm Compositor Name: VAmoudavallySurface and Colloid Chemistry 19 2009 by Taylor & Francis Group, LLCmolecules have the same gsc (75 mN=m). This characteristic property can be ascribed to the fact that long molecule axes will tendto lie along a preferred direction at the interface. This is well recognized in such structures as liquid crystal phases. Thus, at thesupercooled state at Tsc (5408C), the attractive forces and the repulsive forces in different alkanes exhibit a supercooled statewhere the dependence on nC disappears. In other words, all alkanes behave as pseudomethane. Another possibility could be thatthe holes in the alkanes are all lled at a supercooled state, Tsc, as expected from Eyrings [60a] theory for liquids.From these observations,