Nanosurface chemistry 2002 rosoff

The aim of this review is to demonstrate the potential of surface forces measurement as a novel means for investigating surfaces and complex soft systems by describing our cent studies,

This book is printed on acid-free paper.

Headquarters

Marcel Dekker, Inc.

270 Madison Avenue, New York, NY 10016

Copyright © 2002 by Marcel Dekker, Inc All Rights Reserved.

Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit):

10 9 8 7 6 5 4 3 2 1

PRINTED IN THE UNITED STATES OF AMERICA

Tools shape how we think; when the only tool you have is an axe, everything resembles atree or a log The rapid advances in instrumentation in the last decade, which allow us tomeasure and manipulate individual molecules and structures on the nanoscale, have caused

a paradigm shift in the way we view molecular behavior and surfaces The microscopic tails underlying interfacial phenomena have customarily been inferred from in situ mea-surements of macroscopic quantities Now we can see and “finger” physical and chemicalprocesses at interfaces

de-The reviews collected in this book convey some of the themes recurrent in loid science: self-assembly, construction of supramolecular architecture, nanoconfinementand compartmentalization, measurement and control of interfacial forces, novel syntheticmaterials, and computer simulation They also reveal the interaction of a spectrum of dis-ciplines in which physics, chemistry, biology, and materials science intersect Not only isthe vast range of industrial and technological applications depicted, but it is also shownhow this new way of thinking has generated exciting developments in fundamental science.Some of the chapters also skirt the frontiers, where there are still unanswered questions.The book should be of value to scientific readers who wish to become acquaintedwith the field as well as to experienced researchers in the many areas, both basic and tech-nological, of nanoscience

nano-col-The lengthy maturation of a multiauthored book of this nature is subject to life’s tingencies Hopefully, its structure is sound and has survived the bumps of “outrageous for-tune.” I wish to thank all the contributors for their courage in writing It is their work andcommitment that have made this book possible

con-Morton Rosoff

3 Langmuir Monolayers: Fundamentals and Relevance to Nanotechnology 59

Keith J Stine and Brian G Moore

4 Supramolecular Organic Layer Engineering for Industrial Nanotechnology 141

Claudio Nicolini, V Erokhin, and M K Ram

5 Mono- and Multilayers of Spherical Polymer Particles Prepared by

Langmuir–Blodgett and Self-Assembly Techniques 213

Bernd Tieke, Karl-Ulrich Fulda, and Achim Kampes

6 Studies of Wetting and Capillary Phenomena at Nanometer Scale with ScanningPolarization Force Microscopy 243

Lei Xu and Miquel Salmeron

7 Nanometric Solid Deformation of Soft Materials in Capillary Phenomena 289

Martin E R Shanahan and Alain Carré

8 Two-Dimensional and Three-Dimensional Superlattices: Syntheses and CollectivePhysical Properties 315

10 DNA as a Material for Nanobiotechnology 391

Christof M Niemeyer

11 Self-Assembled DNA/Polymer Complexes 431

Vladimir S Trubetskoy and Jon A Wolff

12 Supramolecular Assemblies Made of Biological Macromolecules 461

Nir Dotan, Noa Cohen, Ori Kalid, and Amihay Freeman

13 Reversed Micelles as Nanometer-Size Solvent Media 473

Vincenzo Turco Liveri

14 Engineering of Core-Shell Particles and Hollow Capsules 505

17 Polymer–Clay Nanocomposites: Synthesis and Properties 653

Syed Qutubuddin and Xiaoan Fu

Index 675

Alain Carré Fontainebleau Research Center, Corning S.A., Avon, France

Frank Caruso Max-Planck-Institute of Colloids and Interfaces, Potsdam, Germany

Kwong-Yu Chan Department of Chemistry, The University of Hong Kong, Hong KongSAR, China

Noa Cohen Department of Molecular Microbiology and Biotechnology, Faculty of LifeSciences, Tel Aviv University, Tel Aviv, Israel

Nir Dotan Glycominds Ltd., Maccabim, Israel

V Erokhin Department of Biophysical M&O Science and Technologies, University ofGenoa, Genoa, Italy

Amihay Freeman Department of Molecular Microbiology and Biotechnology, Faculty

of Life Sciences, Tel Aviv University, Tel Aviv, Israel

Xiaoan Fu Department of Chemical Engineering, Case Western Reserve University,Cleveland, Ohio

Karl-Ulrich Fulda Institute of Physical Chemistry, University of Cologne, Cologne,Germany

Suzanne P Jarvis Nanotechnology Research Institute, National Institute of AdvancedIndustrial Science and Technology, Ibaraki, Japan

Ori Kalid Department of Molecular Microbiology and Biotechnology, Faculty of LifeSciences, Tel Aviv University, Tel Aviv, Israel

Achim Kampes Institute for Physical Chemistry, University of Cologne, Cologne,Germany

Kazue Kurihara Institute for Chemical Reaction Science, Tohoku University, Sendai,Japan

Bruce R Locke Department of Chemical Engineering, Florida State University,Tallahassee, Florida

Brian G Moore School of Science, Penn State Erie–The Behrend College, Erie,Pennsylvania

Claudio Nicolini Department of Biophysical M&O Science and Technologies,University of Genoa, Genoa, Italy

Christof M Niemeyer Department of Biotechnology, University of Bremen, Bremen,Germany

Marie-Paule Pileni Université Pierre et Marie Curie, LM2N, Paris, France

Dietmar Pum Center for Ultrastructure Research, Universität für Bodenkultur Wien,Vienna, Austria

Syed Qutubuddin Department of Chemical Engineering, Case Western ReserveUniversity, Cleveland, Ohio

M K Ram Department of Biophysical M&O Science and Technologies, University ofGenoa, Genoa, Italy

Miquel Salmeron Materials Sciences Division, Lawrence Berkeley NationalLaboratory, Berkeley, California

Margit Sára Center for Ultrastructure Research, Universität für Bodenkultur Wien,Vienna, Austria

Bernhard Schuster Center for Ultrastructure Research, Universität für BodenkulturWien, Vienna, Austria

Martin E R Shanahan Adhesion, Wetting, and Bonding, National Centre for ScientificResearch / School of Mines Paris, Evry, France

Uwe B Sleytr Center for Ultrastructure Research, Universität für Bodenkultur Wien,Vienna, Austria

Keith J Stine Department of Chemistry and Center for Molecular Electronics,University of Missouri–St Louis, St Louis, Missouri

Bernd Tieke Institute for Physical Chemistry, University of Cologne, Cologne,Germany

Vladimir S Trubetskoy Mirus Corporation, Madison, Wisconsin

Vincenzo Turco Liveri Department of Physical Chemistry, University of Palermo,Palermo, Italy

Jon A Wolff Departments of Pediatrics and Medical Genetics, University ofWisconsin–Madison, Madison, Wisconsin

Lei Xu Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,California

The problems of chemistry and biology can be greatly helped if our ability to see what we are doing, and to do things on an atomic level is ultimately developed—a development which I think can’t be avoided.

Richard Feynman God created all matter—but the surfaces are the work of the Devil.

Wolfgang Pauli

The prefix nano-, derived from the Greek word meaning “dwarf,” has been applied most

of-ten to systems whose functions and characteristics are determined by their tiny size tures less than 100 nanometers in length (i.e., one-ten-millionth of a meter) are typical innano-technology, which emphasizes the approach of building up from molecules and nano-

Struc-structures (“bottom-up”) versus the “top-down,” or miniaturization, approach Nano- actually

refers not so much to the size of the object as to the resolution at the molecular scale At suchsmall scales, about half of the atoms are in the surface layer, the surface energy dominates,and the surface layer can be considered a new material with properties different from those ofbulk The hierarchy of scales, both spatial and temporal, is represented in the following table:

is important both for a basic understanding of colloidal phenomena and for the creation andmastery of a multitude of industrial applications

ix

The self-organization or assembly of units at the nanoscale to form supramolecularensembles on mesoscopic length scales comprises the range of colloidal systems There is

a need to understand the connection between structure and properties, the evolution and namics of these structures at the different levels—supramolecular, molecular, and sub-molecular—by “learning from below.”

dy-When interaction and physical phenomena length scales become comparable to orlarger than the size of the structure, as, for example, with polymer contour chain length, thesystem may exhibit unusual behavior and generate novel arrangements not accessible inbulk

It is also at these levels (10–500 nm) that nature utilizes hierarchical assemblies in ology, and biological processes almost invariably take place at the nanoscale, across mem-branes and at interfaces Biomolecular materials with unique properties may be developed

bi-by mimicking biological processes or modifying them There is still much to discover aboutimproving periodic arrays of biomolecules, biological templating, and how to exploit thedifferences between biological and nonbiological self-assembly

The linkage of microscopic and macroscopic properties is not without challenges,both theoretical and experimental Statistical mechanics and thermodynamics provide theconnection between molecular properties and the behavior of macroscopic matter Coupledwith statistical mechanics, computer simulation of the structure, properties, and dynamics

of mesoscale models is now feasible and can handle the increase in length and time scales.Scanning proble techniques (SPM)—i.e., scanning tunneling microscopy (STM) andatomic force microscopy (AFM), as well as their variations—have the power to visualizenanoscale surface phenomena in three dimensions, manipulate and modify individualmolecules, and measure such properties as adhesion, stiffness, and friction as well as mag-netic and electric fields The use of chemically modified tips extends the technique to in-clude chemical imaging and measurement of specific molecular interactions Improved op-tical methods complement probe images and are capable of imaging films a single moleculethick Optical traps, laser tweezers, and “nano-pokers” have been developed to measureforces and manipulate single molecules In addition, there is a vast range of experimentaltools that cross different length and time scales and provide important information (x-ray,neutrons, surface plasmon resonance) Nevertheless, there is a further need for instrumen-tation of higher resolution, for example, in the decreased ranged of space and time en-countered when exploring the dynamics and kinetics of surface films

Chapter 1 is a view of the potential of surface forces apparatus (SFA) measurements

of two-dimensional organized ensembles at solid–liquid interfaces At this level, tion is acquired that is not available at the scale of single molecules Chapter 2 describesthe measurement of surface interactions that occur between and within nanosized surfacestructures—interfacial forces responsible for adhesion, friction, and recognition

informa-In Chapter 3, Langmuir–Blodgett films of varying organizational complexity are cussed, as well as nanoparticles and fullerenes Molecular dynamic simulation of mono-layers and multilayers of surfactants is also reviewed Chapter 4 presents those aspects ofsupramolecular layer assemblies related to the development of nanotechnological applica-tions Problems of preparing particle films with long-range two-dimensional and three-di-mensional order by Langmuir–Blodgett and self-assembly techniques are dealt with inChapter 5

dis-The next two chapters are concerned with wetting and capillarity Wetting ena are still poorly understood; contact angles, for example, are simply an empirical pa-rameter to quantify wettability Chapter 6 reviews the use of scanning polarization force

phenom-microscopy (SPFM), a new application of AFM using electrostatic forces, to study thenanostructure of liquid films and droplets The effect of solid nanometric deformation onthe kinetics of wetting and dewetting and capillary flow in soft materials, such as somepolymers and gels, is treated in Chapter 7.

Chapter 8 presents evidence on how the physical properties of colloidal crystals ganized by self-assembly in two-dimensional and three-dimensional superlattices differfrom those of the free nanoparticles in dispersion

or-A biomolecular system of glycoproteins derived from bacterial cell envelopes thatspontaneously aggregates to form crystalline arrays in the mesoscopic range is reviewed inChapter 9 The structure and features of these S-layers that can be applied in biotechnol-ogy, membrane biomimetics, sensors, and vaccine development are discussed

DNA is ideally suited as a structural material in supramolecular chemistry It hassticky ends and simple rules of assembly, arbitrary sequences can be obtained, and there is

a profusion of enzymes for modification The molecule is stiff and stable and encodes formation Chapter 10 surveys its varied applications in nanobiotechnology The emphasis

in-of Chapter 11 is on DNA nanoensembles, condensed by polymer interactions and static forces for gene transfer Chapter 12 focuses on proteins as building blocks for nano-structures

electro-The next two chapters concern nanostructured core particles Chapter 13 provides amples of nano-fabrication of cored colloidal particles and hollow capsules These systemsand the synthetic methods used to prepare them are exceptionally adaptable for applications

ex-in physical and biological fields Chapter 14, discusses reversed micelles from the ical viewpoint, as well as their use as nano-hosts for solvents and drugs and as carriers andreactors

theoret-Chapter 15 gives an extensive and detailed review of theoretical and practical aspects

of macromolecular transport in nanostructured media Chapter 16 examines the change intransport properties of electrolytes confined in nanostructures, such as pores of membranes.The confinment effect is also analyzed by molecular dynamic simulation

Nanolayers of clay interacting with polymers to form nanocomposites with improvedmaterial properties relative to the untreated polymer are discussed in Chapter 17

Morton Rosoff

Molecular architectures are self-organized polymolecular systems where molecularinteractions play important roles [5] They exhibit specific and unique functions that couldnot be afforded by single molecules Molecular architecture chemistry beyond molecules

is not only gaining a central position in chemistry but becoming an important plinary field of science Investigations of molecular architectures by surface forces mea-surement is important for the following reasons

interdisci-1 It is essential to elucidate intermolecular interactions involved in self-organization,whose significance is not limited to material science but extends to the ingenuity of bi-ological systems [5]

2 The importance of surface characterization in molecular architecture chemistry and gineering is obvious Solid surfaces are becoming essential building blocks for con-structing molecular architectures, as demonstrated in self-assembled monolayer for-mation [6] and alternate layer-by-layer adsorption [7] Surface-induced structuring ofliquids is also well-known [8,9], which has implications for micro- and nano-tech-nologies (i.e., liquid crystal displays and micromachines) The virtue of the force mea-surement has been demonstrated, for example, in our report on novel molecular archi-tectures (alcohol clusters) at solid–liquid interfaces [10]

en-3 Two-dimensionally organized molecular architectures can be used to simplify thecomplexities of three-dimensional solutions and allow surface forces measurement By

employing this approach, we can study complex systems such as polypeptides andpolyelectrolytes in solutions For example, it is possible to obtain essential informationsuch as the length and the compressibility of these polymers in solutions by systemat-ically varying their chemical structures and the solution conditions [11].

Earlier studies of surface forces measurement were concerned mainly with surfaceinteractions determining the colloidal stability, including surfactant assemblies It hasbeen demonstrated, however, that a “force–distance” curve can provide much richer in-formation on surface molecules; thus it should be utilized for studying a wider range ofphenomena [12] Practically, the preparation of well-defined surfaces, mostly modified

by two-dimensional organized molecules, and the characterization of the surfaces bycomplementary techniques are keys to this approach A similar concept is “force spec-troscopy” [13], coined to address force as a new parameter for monitoring the properties

of materials A major interest in force spectroscopy is the single molecular measurementgenerally employing an atomic force microscope This measurement treats relativelystrong forces, such as adhesion, and discusses the binding of biotin-streptavidin [14] andcomplementary strands of DNA [15] as well as the unfolding and folding of proteins[16] On the other hand, the forces measurement of two-dimensionally organizedmolecules has advantages complementary to those of single molecule force spectroscopy

It can monitor many molecules at the same time and thus is better suited for studyinglong-range weaker forces The measurement should bear a close relevance to real systemsthat consist of many molecules, because interactions between multiple molecules and/ormacroscopic surfaces in solvents may exhibit characteristics different from those betweensingle molecules

The aim of this review is to demonstrate the potential of surface forces measurement

as a novel means for investigating surfaces and complex soft systems by describing our cent studies, which include cluster formation of alcohol, polyion adsorption, and polyelec-trolyte brushes

Surface forces measurement directly determines interaction forces between two surfaces as

a function of the surface separation (D) using a simple spring balance Instruments

em-ployed are a surface forces apparatus (SFA), developed by Israelachivili and Tabor [17],and a colloidal probe atomic force microscope introduced by Ducker et al [18] (Fig 1) Theformer utilizes crossed cylinder geometry, and the latter uses the sphere-plate geometry

For both geometries, the measured force (F) normalized by the mean radius (R) of ders or a sphere, F/R, is known to be proportional to the interaction energy, Gƒ, betweenflat plates (Derjaguin approximation),

III ALCOHOL CLUSTER FORMATION ON SILICA SURFACES

IN CYCLOHEXANE

Surface forces measurement is a unique tool for surface characterization It can directly

monitor the distance (D) dependence of surface properties, which is difficult to obtain by

other techniques One of the simplest examples is the case of the electric double-layer force.The repulsion observed between charged surfaces describes the counterion distribution inthe vicinity of surfaces and is known as the electric double-layer force (repulsion) In a sim-ilar manner, we should be able to study various, more complex surface phenomena and ob-tain new insight into them Indeed, based on observation by surface forces measurementand Fourier transform infrared (FTIR) spectroscopy, we have found the formation of anovel molecular architecture, an alcohol macrocluster, at the solid–liquid interface.Adsorption phenomena from solutions onto solid surfaces have been one of the im-portant subjects in colloid and surface chemistry Sophisticated application of adsorptionhas been demonstrated recently in the formation of self-assembling monolayers and multi-layers on various substrates [4,7] However, only a limited number of researchers havebeen devoted to the study of adsorption in binary liquid systems The adsorption isothermand colloidal stability measurement have been the main tools for these studies The molec-ular level of characterization is needed to elucidate the phenomenon We have employedthe combination of surface forces measurement and Fourier transform infrared spec-troscopy in attenuated total reflection (FTIR-ATR) to study the preferential (selective) ad-sorption of alcohol (methanol, ethanol, and propanol) onto glass surfaces from their binarymixtures with cyclohexane Our studies have demonstrated the cluster formation of alco-hol adsorbed on the surfaces and the long-range attraction associated with such adsorption

We may call these clusters macroclusters, because the thickness of the adsorbed alcohol

layer is about 15 nm, which is quite large compared to the size of the alcohol The ing describes the results for the ethanol–cycohexane mixtures [10]

follow-Typical forces profiles measured between glass surfaces in ethanol–cyclohexanemixtures are shown in Fig 2 Colloidal probe atomic force microscopy has been employed

In pure cyclohexane, the observed force agrees well with the conventional van der Waalsattraction calculated with the nonretarded Hamaker constant for glass/cyclohexane/glass,

FIG 1 Schematic drawings of (a) the surface forces apparatus and (b) the colloidal probe atomic force microscope.

3.1  1021J At an ethanol concentration of 0.1 mol%, the interaction changes ably: The long-range attraction appears at a distance of 35 nm, shows a maximum around

remark-10 nm, and turns into repulsion at distances shorter than 5 nm The pull-off force of the tacting surfaces is 140  19 mN/m, which is much higher than that in pure cyclohexane,

con-10  7 mN/m Similar force profiles have been obtained on increasing the ethanol centration to 0.4 mol% A further increase in the concentration results in a decrease in thelong-range attraction At an ethanol concentration of 1.4 mol%, the interaction becomesidentical to that in pure cyclohexane When the ethanol concentration is increased, therange where the long-range attraction extends changes in parallel to the value of the pull-off force, indicating that both forces are associated with the identical phenomenon, mostlikely the adsorption of ethanol Separation force profiles after the surfaces are in contactshows the presence of a concentrated ethanol layer near and on the surfaces (see Ref 10a).The short-range repulsion is ascribable to steric force due to structure formation of ethanolmolecules adjacent to the glass surfaces

con-In order to understand the conditions better, we determined the adsorption isotherm

by measuring the concentration changes in the alcohol upon adsorption onto glass particlesusing a differential refractometer Figure 3 plots the range of the attraction vs the ethanolconcentration, together with the apparent adsorption layer thickness estimated from the ad-sorption isotherm, assuming that only ethanol is present in the adsorption layer [22] For0.1 mol% ethanol, half the distance where the long-range attraction appears, 18  2 nm, isclose to the apparent layer thickness of the adsorbed ethanol, 13  1 nm This supports ourinterpretation that the attraction is caused by contact of opposed ethanol adsorption layers.Half the attraction range is constant up to ~0.4 mol% ethanol and decreases with increas-ing ethanol concentration, while the apparent adsorption layer thickness remains constant

at all concentration ranges studied The discrepancy between the two quantities indicates achange in the structure of the ethanol adsorption layer at concentrations higher than ~0.4

FIG 2 Interaction forces between glass surfaces upon compression in ethanol–cyclohexane tures The dashed and solid lines represent the van der Waals force calculated using the nonretarded Hamarker constants of 3  10 21 J for glass/cyclohexane/glass and 6  10 21 J for glass/ethanol glass, respectively.

mix-mol% The structures of the adsorbed ethanol turned out to be hydrogen-bonded clusters,via the study employing FTIR-ATR spectroscopy.

FTIR-ATR spectra were recorded on a Perkin Elmer FTIR system 2000 using a TGSdetector and the ATR attachment from Grasby Specac The ATR prism made of an oxi-dized silicon crystal was used as a solid adsorbent surface because of its similarity to glasssurfaces Immediately prior to each experiment, the silicon crystal was treated with watervapor plasma in order to ensure the formation of silanol groups on the surfaces Obtainedspectra have been examined by referring to well-established, general spectral characteris-tics of hydrogen-bonded alcohols in the fundamental OH stretching region, because ethanol

is known to form hydrogen-bonded dimers and polymers (clusters) in nonpolar liquids [23]

We have also experimentally examined hydrogen-bonded ethanol cluster formation in bulkcyclohexane–ethanol mixtures using transmission infrared spectroscopy

FTIR-ATR spectra of ethanol in cyclohexane at various ethanol concentrations(0.0–3.0 mol%) are presented in Figure 4 At 0.1 mol% ethanol, a narrow negative band at

3680 cm1, a weak absorption at 3640 cm1(free OH), and a broad strong absorption(3600–3000 cm1) with shoulders at 3530 cm1(cyclic dimer or donor end OH), 3450, and

3180 cm1are observed It is known that the isolated silanol group exhibits an absorptionband at 3675–3690 cm1in a nonpolar liquid, e.g., CCl4and when the silanol groups hy-drogen bond with esters, the absorption band shifts to a lower wavenumber (3425–3440

cm1) [24] Thus, the negative absorption at 3680 cm1and the positive shoulder at 3450

cm1should correspond to the decrease in the isolated silanol groups and the appearance

of the silanol groups hydrogen bonded with the adsorbed ethanol, respectively The strongbroad band ascribed to the polymer OH appeared at 3600–3000 cm1together with the rel-atively weak monomer OH band at 3640 cm1 This demonstrated the cluster formation ofethanol adsorbed on the silicon oxide surface even at 0.1 mol% ethanol, where no polymerpeak appeared in the spectrum of the bulk solution at 0.1 mol% ethanol With increasingethanol concentration, the free monomer OH (3640 cm1) and the polymer OH peak (3330

cm1) increased, while the peaks at 3530, 3450, and 3180 cm1remained the same

FIG 3 Plots of half the range of attraction (see Fig 2) and the apparent thickness of the ethanol sorption layer vs the ethanol concentration.

ad-At higher ethanol concentrations, ATR spectra should contain the contribution frombulk species, because of the long penetration depth of the evanescent wave, 250 nm To ex-amine the bulk contribution, the integrated peak intensities of polymer OH peaks of trans-

mission (ATS) and ATR (AATR) spectra are plotted as a function of the ethanol concentration

in Figure 5 The former monitors cluster formation in the bulk liquid, and the latter contains

contributions of clusters both on the surface and in the bulk A sharp increase is seen in AATR

FIG 4 FTIR-ATR spectra of ethanol on a silicon oxide surface in ethanol–cyclohexane binary uids at various ethanol concentrations: 0.0, 0.1, 0.3, 0.5, 1.0, and 2.0 mol%.

liq-FIG 5 Plots of integrated peak intensities of polymer OH (3600–3000 cm1) as a function of the

ethanol concentration Filled circles represent the value obtained from the transmission spectra (A TS),

while filled squares represent those from ATR (A ).

even at 0.1 mol% ethanol, but no significant increase is seen in ATSat ethanol

concentra-tions lower than 0.5 mol% A comparison of ATS and AATRclearly indicated that ethanolclusters formed locally on the surface at concentrations of ethanol lower than ~0.5 mol%,where practically only a negligible number of clusters exist in the bulk The thick adsorp-tion layer of ethanol most likely consists of ethanol clusters formed through hydrogenbonding of surface silanol groups and ethanol as well as those between ethanol molecules

A plausible structure of the ethanol adsorption layer is presented in Figure 6

The contact of adsorbed ethanol layers should bring about the long-range attractionobserved between glass surfaces in ethanol–cyclohexane mixtures The attraction starts todecrease at ~0.5 mol% ethanol, where ethanol starts to form clusters in the bulk phase It isconceivable that the cluster formation in the bulk influences the structure of the adsorbed al-cohol cluster layer, thus modulating the attraction We think that the decrease in the attrac-tion is due to the exchange of alcohol molecules between the surface and the bulk clusters

A similar long-range attraction associated with cluster formation has been found forcyclohexane–carboxylic acid mixtures and is under active investigation in our laboratory.Such knowledge should be important for understanding various surface-treatment pro-cesses performed in solvent mixtures and for designing new materials with the use ofmolecular assembling at the solid–liquid interfaces For the latter, we have prepared poly-mer thin films by in situ polymerization of acrylic acid preferentially adsorbed on glass sur-faces [25]

OPPOSITELY CHARGED SURFACES

The process of adsorption of polyelectrolytes on solid surfaces has been intensively ied because of its importance in technology, including steric stabilization of colloid parti-cles [3,4] This process has attracted increasing attention because of the recently developed,sophisticated use of polyelectrolyte adsorption: alternate layer-by-layer adsorption [7] andstabilization of surfactant monolayers at the air–water interface [26] Surface forces mea-surement has been performed to study the adsorption process of a negatively charged poly-mer, poly(styrene sulfonate) (PSS), on a cationic monolayer of fluorocarbon ammoniumamphiphille 1 (Fig 7) [27].

stud-A force–distance curve between layers of the ammonium amphiphiles in water isshown in Figure 8 The interaction is repulsive and is attributed to the electric double-layer

FIG 6 Plausible structure of the adsorption layer composed of ethanol clusters.

force The addition of 0.7 mg/L PSS (1.4  109M, equivalent to the addition of 0.7 nmol

of PSS, which is close to the amount of the amphiphile on the surface) into the aqueousphase drastically alters the interaction Here, the molecular weight (Mw) of PSS is 5  105.Over the whole range of separations from 5 to 100 nm, the force decreases more than oneorder of magnitude and does not exceed 100 N/m The analysis of the force profile hasshown that more than 99% of the initial surface charges are shielded by PSAS binding The

FIG 7 Chemical structures of fluorocarbon ammonium amphiphile 1 and poly(styrene sulfonate)

(PSS).

FIG 8 Force–distance dependence for surfaces covered with fluorocarbon amphiphile 1 in pure

water (1) and in aqueous solutions containing 0.7 mg/L poly (styrenesulfonate) (2) and 7.0 g/L poly (styrenesulfonate) (3) The molecular weight of the polymer is 5  10 5 Lines are drawn as a visual guide.

thickness of the adsorbed layer of PSS is in the range of 1.5–2.5 nm (it is less than 1 nm inthe case of PSS of 1  104Mw) These data indicate flat and stoichiometric adsorption ofthe polyelectrolytes onto the monolayer surface (Fig 9a).

Increased concentration of PSS at 7.0 g/L (1.4  105M) leads to an increase in theforce to value seven higher than that between the surfaces of fluorocarbon monolayersalone The origin of this force is electrostatic in nature Recharging of the surface by addi-tional adsorption of PSS should occur as shown in Figure 9b

Our results demonstrate well the complexities of polyelectrolyte adsorption and vide a basis for various surface treatments utilizing polyelectrolytes They especially affordphysical-chemical support for alternate layer-by-layer film formation of polyelectrolytes,which is becoming a standard tool for building composite polymer nano-films in advancedmaterials science

Polypeptides and polyelectrolytes are essential classes of substances because of their portance in such areas as advanced materials science (functionalized gel) and biology (pro-teins, living cells, and DNA) Being polymers with charges and counterions and/or hydro-gen bonding, they exhibit interesting, albeit complicated, properties Two-dimensionallyorganized brush structures of polymers can simplify the complexities of the polyelectrolytesolutions Attempts to investigate polyelectrolyte brushes have been carried out experi-mentally [11,28–32] and theoretically [33,34] Direct measurement of surface forces hasbeen proven useful in obtaining information about the concrete structures of polypeptideand polyelectrolyte brush layers Taking advantage of the LB method, we prepared well-defined brush layers of chain-end-anchored polypeptides and polyelectrolytes [11,28–30]

im-FIG 9 Schematic illustration of adsorption of poly(styrenesulfonate) on an oppositely charged face For an amphiphile surface in pure water or in simple electrolyte solutions, dissociation of charged groups leads to buildup of a classical double layer (a) In the initial stage of adsorption, the polymer forms stoichiometric ion pairs and the layer becomes electroneutral (b) At higher polyion concentrations, a process of restructuring of the adsorbed polymer builds a new double layer by ad- ditional binding of the polymer.

We then investigated them based on the force profiles, together with FTIR spectra and face pressure–area isotherms by systematically varying the polymer chain length, chemicalstructure, brush density, and solution conditions (pH, salt concentrations, etc) When thesurfaces of the opposed polymer layers approach to a separation distance of molecular di-mensions, the steric repulsion becomes predominant and hence measurable By analyzingthem, it is possible to obtain key parameters, such as thickness (length) and compressibil-ity of polyelectrolyte layers, which are difficult to obtain by other methods, and to corre-late them with polymer structures Obtained information should form a basis for elucidat-ing their properties and developing physical models Moreover, it is more likely to discovernew phenomena via a novel approach: We have found the density-dependent transition ofpolyelectrolyte brushes, which we have accounted for in terms of the change in the bindingmodes of counterions to polyelectrolytes [30].

Polypeptides form various secondary structures (

lution pHs We have investigated end-anchored poly(L-glutamic acid) and poly(L-lysine) invarious secondary structures [11,29,35,36], using the analytical method for the steric force

FIG 10 Schematic drawing of surface forces measurement on charged polypeptide brushes

pre-pared by LB deposition of amphiphiles 2 and 3.

in order to examine more quantitatively the structures and structural changes in trolyte layers The elastic compressibility modulus of polypeptide brushes was obtained, toour knowledge, as the first quantitative determination of the mechanical modulus of an ori-ented, monomolecular polymer layer in solvents.

polyelec-Poly(L-glutamic acid) and poly(L-lysine) brush layers were prepared using

am-phiphiles 2 and 3 carrying the poly(L-glutamic acid) (2C18PLGA(n), degree of ization, n 21, 44, 48) and the ply(L-lysine) segment (2C18PLL(n), n 41), respectively(Fig 10) They formed a stable monolayer at the air–water interface in which different sec-ondary structures, such as

polymer-molecular hydrogen bonding, depending on surface pressure and subphase pH They weredeposited onto mica surfaces and subjected to surface forces measurement We used FTIRspectroscopy to study the formation and orientation of their secondary structures

Figure 11a shows a force–distance profile measured for poly(L-glutamic acid) brushes(2C18PLGA(44)) in water (pH  3.0, 103M HNO3) deposited at 40 mN/m from the wa-ter subphase at pH  3.0 The majority of peptides are in the forms of an -helix (38% de-termined from the amide I band) and a random coil Two major regions are clearly seen in

FIG 11 Force profiles between poly(glutamic acid), 2C18PLGA(44), brushes in water (a) at pH

 3.0 (HNO 3 ), (b) at pH 10 (KOH) 1/ represents the decay length of the double-layer force The brush layers were deposited at   40 mN/m from the water subphase at pH  3.0 and 10, respec- tively.

the force–distance profiles At surface separations longer than 35 nm, the interaction is a ical double-layer electrostatic force, with a decay length of 10  1 nm, which agrees wellwith the Debye length (9.6 nm) for 103M HNO3, due to ionized carboxyl groups At sep-arations shorter than ~20 nm, the repulsion is steric in origin and varies depending on thesecondary structures existing in the surface layer In order to examine detailed changes in

typ-the interactions, a force–distance profile is converted to a stress–distance (P-D) profile by differentiating the free energy of interaction Gƒ[Eq (1)] between two flat surfaces as

P   d d G D  f 21d( d F D/R) (2)The stress curve sharply increases when the steric component appears upon compression

The initial thickness of a deformed layer is equal to be half the distance D0obtained by

ex-trapolating the sharpest initial increase to stress zero The value D0is 21  1 nm, which isclose the thickness of two molecular layers (19.2 nm) of the -helix brush, calculated us-ing the CPK model and the orientation angles obtained by FTIR analysis We have calcu-

lated the elastic compressibility modulus Y,

to be 38  8 MPa from the steepest slope of the stress–distance curve This value is one totwo orders of magnitude larger than the elasticity measured for a typical rubber (1 MPa).Figure 11b shows a profile at pH 10, measured between the 2C18PLGA(44) LB sur-faces prepared at 40 mN/m from the aqueous KOH subphase (pH 10) In this sample, two-thirds of the carboxylic acid groups dissociate; therefore, it behaves as a simple polyelec-trolyte The initial thickness of the deformed layer is 35  2 nm, which is close to twice thelength of 2C18PLGA(44) in the extended form, 37 nm The elastic compressibility modu-lus is 0.2  0.1, which is even smaller than the value for a typical rubber Unexpectedly,the ionized layers are easily compressed Counterion binding to the ionized chain shouldplay an important role in decreasing the stress for compression by reducing the effectivecharges through the shielding and charge-recombination mechanisms

Similar measurements have been done on poly(L-lysine) brushes Table 1 lists a part

of our data, which display specific features: (1) The value D0depends on the polymer chain

TABLE 1 Effective Length and Compressibility Modulus of Polypeptide Brushes Determined

length as well as the secondary structures; thus it is a good measure for determining thethickness (length) of the polypeptide (or polyelectrolyte brush); (2) the compressibilitymodulus is sensitive to changes in the kind of secondary structures; (3) the moduli of -he-lix brushes are one order of magnitude larger for poly(L-glutamic acid) than for poly(L-ly-sine), which is likely due to interchain hydrogen bonding between the carboxylic acidgroups of neighboring poly(glutamic acid) chains; (4) the moduli of ionized chains areidentical for poly(L-glutamic acid) and poly(L-lysine).

The stress–distance profile measured by the surface forces apparatus thus providesinformation on structural changes in polymers and polyelectrolytes in solvents One ad-vantage of our approach is that a model calculation is not necessary to extract physical pa-rameters involved in the structural changes One may note that the mechanical propertiesdiscussed here reflect not only the intrinsic flexibility of polypeptide chains but also othereffects, such as the osmotic pressure of counterions present within charged brush layers.Such knowledge is essential for the theoretical understanding of polyelectrolytes andpolypeptides Our work employing surface forces measurement opens the door to studies

on a wide range of structural changes of polymers in solvents, including proteins and electrolyte networks in water The complexities of their solution properties can be reduced

poly-by aligning them in a two-dimensional manner Very recently, polyelectrolyte brushes havealso begun to attract attention as a novel molecular architecture for nanotechnology [37].The forces measurement should also provide valuable information for effectively design-ing such materials

The ionized forms of polypeptides exhibit many characteristics in common; therefore, wehave studied them under various conditions The most interesting observation is the transi-tion of a polyelectrolyte brush found by changing the polyelectrolyte chain density Thebrush layers have been prepared by means of the LB film deposition of an amphiphile,2C18PLGA(48), at pH 10 Mixed monolayers of 2C18PLGA(48) and dioctadecylphos-phoric acid, DOP, were used in order to vary the 2C18PLGA(48) content in the monolayer.Surface force profiles between these polyelectrolyte brush layers have consisted of along-range electrostatic repulsion and a short-range steric repulsion, as described earlier.Short-range steric repulsion has been analyzed quantitatively to provide the compressibility

modulus per unit area (Y) of the polyelectrolyte brushes as a function of chain density ( ) (Fig

12a) The modulus Y decreases linearly with a decrease in the chain density , and suddenlyincreases beyond the critical density The maximum value lies at  0.13 chain/nm2 When

we have decreased the chain density further, the modulus again linearly decreased relative to

the chain density, which is natural for chains in the same state The linear dependence of Y on

in both the low- and the high-density regions indicates that the jump in the compressibilitymodulus should be correlated with a kind of transition between the two different states

To examine this peculiar behavior, we have converted the elastic compressibility

modulus, per unit area, Y (Fig 12a), to the modulus per chain, Y 18 (Fig 12b)

The elastic compressibility modulus per chain is practically constant, 0.6  0.1 pN/chain,

at high densities and jumps to another constant value, 4.4  0.7 pN/chain, when the sity decreases below the critical value The ionization degree, , of the carboxylic acid de-termined by FTIR spectroscopy gradually decreases with increasing chain density due tothe charge regulation mechanism (also plotted in Fig 12b) This shows that does not ac-count for the abrupt change in the elastic compressibility modulus

den-The density-dependent jump in the properties of polyelectrolyte brushes has alsobeen found in the transfer ratio and the surface potential of the brushes [38], establishingthe existence of the density (interchain distance)-dependent transition of polyelectrolytes insolutions.

The transition of the compressibility, and other properties of the polyelectrolytebrushes, is most likely accounted for in terms of the transition in the binding mode of thecounterion to the polyelectrolytes, from the loosely bound state to the tightly bound one,which reduces inter- and intrachain repulsive interactions The following supports this ac-count: (1) At the critical density, c 0.20 chain/nm2, the separation distance between poly-

electrolyte chains, d, is 2.4 nm This distance is close to the sum, 2.6 nm, of the chain

diam-eter, 1.3 nm, and the size of two hydrated Kcounterions, 1.32 nm, indicating that the abruptchange in the compressibility modulus should be closely related to the counterion bindingmode (2) The critical distance satisfies the energy requirement for the tight binding of coun-terions (coulombic interaction between two unscreened elementary charges is equal to thethermal energy) (3) The stress profiles can be fitted to the theoretical equation derived based

on the assumption that the stress of deformation arises from the osmotic pressure of the terions The analysis revealed that the osmotic coefficient in the high-brush-density region

coun-is one order of magnitude larger than that in the low-density region (4) At the critical chaindensity c 0.2 chain/nm2, we have found that the distance between the ionized chargesbecomes close to twice the Bjerrum length [39] Therefore, counterions must bind strongly

to the polyelectrolytes at densities greater than the critical density

In polyelectrolyte solutions, the counterion condensation on linear polyelectrolytechains is known to occur when the charge density along the chain exceeds the critical value[40] Our work indicates the existence of a critical value for the separation distance betweenchains, where the interchain interaction changes drastically, most likely due to the transi-tion in the binding mode of the counterions (see Fig 13) Many peculiar forms of behav-ior, which are often interpreted by the cluster formation or the interchain organization ofpolyelectrolytes, have been reported for high concentrations of aqueous polyelectrolytes

FIG 12 Plots of elastic compressibility modulus (a) per unit area, Y; and (b) that per chain, Y

2C18PLGA(48) brushes as a function of chain density The ionization degree of the carboxylic acid group, , is also plotted in part b.

[41] Our observation should be important in understanding these properties of trolytes in solutions and perhaps in gels.

The nanometer level of characterization is necessary for nanochemistry We have learnedfrom the history of once-new disciplines such as polymer science that progress in synthe-sis (production method) and in physical and chemical characterization methods are essen-tial to establish a new chemistry They should be made simultaneously by exchanging de-velopments in the two areas Surface forces measurement is certainly unique and powerfuland will make a great contribution to nanochemistry, especially as a technique for the char-acterization of solid–liquid interfaces, though its potential has not yet been fully exploited.Another important application of measurement in nanochemistry should be the characteri-zation of liquids confined in a nanometer-level gap between two solid surfaces, for whichthis review cites only Refs 42–43

REFERENCES

1 JN Israelachivili Intermolecular and Surface Forces 2nd ed London: Academic Press, 1992.

2 F Ohnesorge, G Binnig Science 260:1451, 1993.

3 PC Heimenz, R Rajagopalan Principles of Colloid and Surface Chemistry New York: Marcel Dekker, 1994.

4 AW Adamson, AP Gast Physical Chemistry of Surfaces 6th ed New York: Wiley, 1997.

5 J-M Lehn Supramolecular Chemistry Weinheim, Germany: VCH, 1995.

6 B Alberts, D Bray, J Lewis, M Raff, K Roberts, JD Watson Molecular Biology of the Cell 3rd

ed New York: Garlaud, 1994.

7 G Decher Science 277:1232, 1997.

8 J Israelachvili, H Wennerstrom Nature 379:219, 1996.

9 G Reiter, AL Demiral, S Granick Science 263:1741, 1994.

10 (a) M Mizukami, K Kurihara Chem Lett: 1005–1006, 1999; (b) M Mizukami, K Kurihara Chem Lett 248, 2000.

11 T Abe, K Kurihara, N Higashi, M Niwa J Phys Chem 99:1820, 1995.

12 K Kurihara Adv Colloid Sci 71–72:243, 1997.

FIG 13 Schematic drawing of possible binding modes of counterions to polyelectrolyte chains Counterions loosely bind and form a cloud around the polyelectrolyte chains when the interchain dis-

tance (d) is greater than 2.4  0.5 nm, while they strongly bind to form nearly neutral polyelectrolytes

at smaller distances (d 2.4  0.5 nm).

13 NA Burnham, RJ Colton In: DA Bonnel, ed Scanning Tunneling Microscopy and troscopy New York: VCH, 1993, p 191.

Spec-14 VT Moy, EL Florin, HE Gaub Science 266:257, 1994.

15 GV Lee, LA Chrisey, RJ Colton Science 266:771, 1994.

16 M Rief, J Pascual, M Saraste, HE Gaub J Mol Biol 186:553, 1999.

17 JN Israelachivili, GE Adams J Chem Soc: Faraday Trans 74:975, 1978.

18 WA Ducker, TJ Senden, RM Pashley Langmuir 8:1831, 1992.

19 K Kurihara, T Kunitake, N Higashi, M Niwa Thin Solid Films 210/211:681, 1992.

20 JL Parker, P Claesson, P Attard J Phys Chem 98:8468, 1994.

21 H Okusa, K Kurihara, T Kunitake Langmuir 10:3577, 1994.

22 M Mizukami, K Kurihara, manuscript in preparation.

23 U Liddel, ED Becker Spectrochim Acta 10:70, 1957.

24 AK Mills, JA Hockey J Chem Soc, Faraday Trans 71:2398, 1975.

25 S Nakasone, M Mizukami, K Kurihara 78th JCS Spring Annual Meeting: 2PA175, 2000.

26 M Shimomura, T Kunitake Thin Solid Films 132:243, 1985.

27 P Berndt, K Kurihara, T Kunitake Langmuir 8:2486, 1992.

28 K Kurihara, T Kunitake, N Higashi, M Niwa Langmuir 8:2087, 1992.

29 K Kurihara, T Abe, N Higashi, M Niwa Colloids Surfaces A 103:265, 1995.

30 T Abe, N Higashi, M Niwa, K Kurihara Langmuir 15:7725, 1999.

31 Y Mir, P Auroy, L Auvray Phys Rev Lett 75:2863, 1995.

32 P Goenoum, A Schlachli, D Sentenac, JW Mays, J Benattar Phys Rev Lett 75:3628, 1995.

33 SJ Miklavic, SJ Marcelja J Phys Chem 92:6718, 1988.

34 P Pincus Macromolecules 24:2912, 1991.

35 T Abe PhD thesis, Nagoya University, Nagoya, 1997.

36 S Hayashi, T Abe, K Kurihara manuscript in preparation.

37 RR Shah, D Merreceyos, M Husemann, I Rees, NL Abbott, CJ Hawker, JL Hedrick molecules 33:597, 2000.

Macro-38 S Hayashi, T Abe, N Higashi, M Niwa, K Kurihara MCLC: in press.

39 T Abe, S Hayashi, N Higashi, M Niwa, K Kurihara Colloids Surfaces A 169:351, 2000.

40 GS Manning, Ber Bunsen-Ges Phys Chem 100:909, 1996.

41 H Dautzenberg, W Jaeger, J Kotz, B Philipp, Ch Seidel, D Stscherbina Polyelectrolytes New York: Hanser, 1994.

42 JN Israelachvili, PM McGuiggan, AM Homola Science 240:189, 1988.

43 H-W Hu, S Granick Science 258:1339, 1992.

44 C Dushkin, K Kurihara Rev Sci Inst 69:2095, 1998.

Adhesion on the Nanoscale

SUZANNE P JARVIS Nanotechnology Research Institute, National

Institute of Advanced Industrial Science and Technology, Ibaraki, Japan

I ADHESION OVERVIEW

Sticky, one of our earliest childhood experiences and probably one of the first words to

en-ter our vocabulary, is familiar to scientists and nonscientists alike However, does our rect experience of stickiness, or scientifically speaking, adhesion, have any relevance at thenanoscale? How can adhesion be measured, how can it be manipulated, and what role does

di-it play both in technological applications and intrinsically in nature? These are the tions that I will try to address in this chapter

ques-The adhesion of surfaces on a macroscopic scale is usually associated with speciallydesigned glues or tapes, which are a prerequisite for holding two dry, solid surfaces to-gether Exceptions to this tend to be very smooth surfaces with small amounts of moisturebetween them, such as two sheets of glass or a rubber sucker on a bathroom tile Intuitivelythen, even on a macroscopic scale, it is apparent that surface roughness and environmentplay a critical role in adhesion Similarly, for many years scientists have realized that as thesurfaces approach nanoscale dimensions, the surface roughness and the area of contactreach comparable dimensions, such that the apparent and true contact areas become ap-proximately equal, as shown in Figure 1 This significantly increases the importance of ad-hesion in the interaction between the two surfaces Ultimately it becomes necessary to con-sider the materials as ideal systems with properties no longer limited by defects, impurities,and contamination, which dominate for bulk materials When considering the material on

a near-atomic level, there are a number of attractive forces that can act between two faces brought into contact that can cause them to adhere to each other The force required

sur-to separate the two surfaces is then known as the adhesive force or pull-off force The

mag-nitude of this force depends on the true contact area and the nature of the attractive forcesholding the surfaces together These forces could include, for example, van der Waals, cap-illary, or electrostatic forces An excellent text explaining intermolecular and surface forces

in detail is that of Israelachvili [1]

There are a number of industrial and technological areas in which nanoscale adhesion

is important One of the earliest fields concerned with adhesion on this scale was colloidscience Colloid particles lie in the intermediate region between macro and nano, with di-mensions typically of the order of hundreds of nanometers up to a few microns This meansthat their true contact areas lie well within the nano-domain and are influenced by interac-tions on this length scale Adhesion between such particles is important, due to its influence

on mineral separation processes and on the aggregation of powders, for example, on thewalls of machinery or in the forming of medical tablets In an extraterrestrial context, such

processes are also important, because cosmic dust aggregation plays a role in planet mation.

for-As physical structures used in technological applications have been reduced in size,there has been an increasing need to understand the limiting processes of adhesion and totry to minimize them For example, adhesion due to humidity is known to have a major ef-fect on the durability and friction forces experienced at the recording head/disk interface.Microelectromechanical systems (MEMS) are also detrimentally affected by nanoscale ad-hesion, with their motion being perturbed or prevented

On a molecular level there are a number of aspects of adhesion that are important.Preventing the infection of biocompatible materials by preventing bacterial adhesion isvery important in the medical industry, particularly for artificial heart valves as well as themore commonly used contact lenses and dentures A wider understanding of adhesion will

be required to support the current boom in biotechnology, with particular regard to ular motors and drug delivery systems Adhesion and its manipulation may also lie at theheart of many biological functions and recognition processes

Various continuum models have been developed to describe contact phenomena betweensolids Over the years there has been much disagreement as to the appropriateness of thesemodels (Derjaguin et al [2–4] and Tabor [5–7]) Experimental verification can be complexdue to uncertainties over the effects of contaminants and asperities dominating the contact.Models trying to include these effects are no longer solvable analytically A range of mod-els describing contact between both nondeformable and deformable solids in various envi-ronments are discussed in more detail later In all cases, the system of a sphere on a plane

is considered, for this is the most relevant to the experimental techniques used to measurenanoscale adhesion

1 Nondeformable Solids

(a) In Vacuum. For smooth, ideal, rigid solids, the Derjaguin approximation [8]

relat-ing the force law between a sphere of radius R and a flat surface to the energy per unit area

W(D) between two planar surfaces separated by a distance D gives:

FIG 1 Real and apparent contact areas (a) macroscopic surfaces; (b) at the nanoscale.

This equation is useful in that it is applicable to any type of force law so long as the range

of interaction and the separation are much less than the radius of the sphere Thus the force

to overcome the work of adhesion between a rigid sphere and a flat surface written in terms

of the surface energy  is:

Fpull-off 2R  where   sphere flat interface (Dupré) (2)

If the sphere and the flat surface are the same material, then:

interface 0 and sphere flat s⇒ Fpull-off 4R s (3)This assumes that the only source of adhesion is the solid–solid contact

(b) Forces Due to Capillary Condensation. For experiments conducted in air, the hesive force acting between the two bodies may be dominated by the presence of capillarycondensed water These additional forces due to capillary condensation may be calculatedfor smooth, ideal, rigid solids For a sphere and a flat surface joined by a liquid bridge the

ad-force F due to the Laplace pressure within the meniscus is given by [9]:

where LVis the surface tension of the liquid in the condensate and  is the contact angle

of this liquid on the solid

(c) Nondeformable Solids in Condensable Vapor. The capillary forces just discussedact as an additional force; thus the force needed to separate a rigid sphere and a flat surface

of the same material joined by a liquid bridge is given by:

Fpull-off  4R LVcos   4R SL (5)

2 Deformable Solids

The foregoing models considered incompressible bodies; however, this is never the case inpractice The following section discusses models that specifically consider contact betweendeformable solids

(a) Hertz. For deforming solids, Hertzian analysis [10] gives the simplest tion, for adhesive forces are ignored, i.e., no pull-off force and zero contact area for zero

approxima-applied load Given an approxima-applied force, P, and a tip radius, R, the contact diameter, 2a, is 2a  2  43R E P*1/3

(6)where

2a  2  43E R (P  3R  * 6RP(3R)2) (7)

where  is the work of adhesion This is related to the force required to separate the sphere

and the flat surface after contact (known as the adhesive force) Fpull-offby the followingequation:

The model is found to be most appropriate for contact between low-elastic-modulimaterials with large radii when the work of adhesion is high In comparison, the followingmodel assumes that the surface forces extend over a finite range and act in the region justoutside the contact It is found to be more appropriate for systems with small radii of cur-vature, low work of adhesion, and high modulus [12]

(c) Derjaguin, Muller, and Toporov (DMT). Derjaguin, Muller, and Toporov [2] sume that under the influence of surface forces, the sphere will deform in the contact region

as-in accordance with the Hertzian model Sas-ince the deformation is taken as Hertzian, the faces do not separate until the contact area is reduced to zero At this instant, the pull-offforce is predicted to be:

(d) Maugis, Dugdale. Maugis [13] included a surface force, which acts both inside andoutside the contact perimeter The attractive interaction is assumed to be constant up to a

separation of ho, at which point it falls to zero abruptly The value of hois defined such thatthe maximum attractive force and the work of adhesion correspond to a Lennard–Jones po-tential, the Dugdale approximation [14] The error of this somewhat arbitrary approxima-tion is only apparent at low values of the elastic parameter lambda, ,

 o

29w

R E*2

1/3

(12)

where ... R Rajagopalan Principles of Colloid and Surface Chemistry New York: Marcel Dekker, 1994.

4 AW Adamson, AP Gast Physical Chemistry of Surfaces 6th ed New York: Wiley, 1997.... method) and in physical and chemical characterization methods are essen-tial to establish a new chemistry They should be made simultaneously by exchanging de-velopments in the two areas Surface... Surface forces measurement is certainly unique and powerfuland will make a great contribution to nanochemistry, especially as a technique for the char-acterization of solid–liquid interfaces, though