Capillary Forces and Structuring in Layers of Colloid Particles

Current Opinion in Colloid & Interface Science 6Ž. 2001 383᎐401

Capillary forces and structuring in layers of colloid particles

Peter A. KralchevskyU, Nikolai D. Denkov

Laboratory of Chemical Physics and Engineering, Faculty of Chemistry, Uniërsity of Sofia, 1 James Bourchier Aënue, Sofia 1164, Bulgaria

Abstract

‘Capillary forces’ are interactions between particles mediated by fluid interfaces. Recent advances in this field have been achieved by experiments and theory on lateral capillary forces, which are due to the overlap of menisci formed around separate particles attached to an interface. In particular, we should mention the cases of ‘finite menisci’ and ‘capillary multipoles’. The capillary-bridge forces were investigated in relation to capillary condensation and cavitation, surface-force measurements and antifoaming by oily drops. The studies on colloidal self-assembly mediated by capillary forces developed in several promising directions. The obtained structures of particles have found numerous applications. ᮊ 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Capillary interactions; Lateral capillary forces; Capillary bridges; Colloidal self-assembly; Arrays of particles; Particulate monolayers

1. Introduction is concave or convex. Attractive forces of this type lead to 3DŽ. three-dimensional aggregation and con- In general, we call ‘capillary forces’ interactions solidation of bodies built up from particulates. A between particles, which are mediated by fluid inter- spontaneous formation of sub-micrometer gas-filled faces. The interest in these forces has grown due to capillary bridges in water seem to be the most their recognised importance for the self-assembly of probable explanation of the hydrophobic surface force. macroscopic and microscopicŽ. Brownian particles and In other cases, each individual particle causes some even of protein molecules and virusesw 1᎐3.ⅷ x perturbation in the shape of a liquid interface or film. In some cases, the liquid phase forms a capillary The overlap of the perturbationsŽ. menisci around bridge between two particles or bodies. Then the two particles gives rise to a lateral capillary force capillary force is directed normally to the planes of between themŽ. Fig. 1b,c,d,e . This force could be the contact lines on the particle surfacesŽ. Fig. 1a . attractive or repulsive depending on whether the The normal capillary-bridge forces can be attractive overlapping menisci, formed around the two particles, or repulsive depending on whether the capillary bridge are similarŽ.Ž say, both concave or dissimilar one is concave and the other is convex. . The attractive lateral capillary forces cause 2DŽ. two-dimensional aggregation and ordering in a rather wide scale of ¨ Abbre iations: 2D, Two-dimensional; 3D, Three-dimensional; particle sizes: from 1 cm down to 1 nm. AFM, Atomic Force Microscope; PDMS, PolyŽ. dimethylsiloxane U Corresponding author. Tel.: q359-2-962-5310; fax: q359-2- Below we first briefly review recent publications on 962-5643. capillary forces. Next we shortly discuss studies in E-mail addresses: [email protected]Ž. P.A. Kralchevsky , which structuring under the action of lateral capillary [email protected]Ž. N.D. Denkov . 1359-0294r01r$ - see front matter ᮊ 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 0 2 9 4Ž. 0 1 00105-4 384 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

Fig. 1. Types of capillary forces:Ž. a The normal capillary forces can be due to either liquid-in-gas or gas-in-liquid capillary bridges, which lead to particle᎐particle and particle᎐wall interactions, the force is directed normally to the contact line. In the case of lateral capillary forces Ž.b,c,d,e the force is parallel to the contact line. The interaction is due to the overlap of interfacial deformations created by the separate particles.Ž. b In the case of flotation force the deformations are caused by the particle weight and buoyancy. In the case of immersion forces Ž.c,d,e the deformations are related to the wetting properties of the particle surface: position and shape of the contact line; and magnitude of the contact angle. When the deformation around an isolated particle is axisymmetric, we deal with ‘capillary charges’, one can distinguish cases of infiniteŽ. c and finite Ž. d menisci, see Eqs. Ž. 5 and Ž 14 . . Ž. e The forces between particles of undulated or irregular contact line can be described as interactions between ‘capillary multipoles’, in analogy with electrostatics; see Eq.Ž. 15 . forces is reported. Comprehensive reviews on capil- surface tension force exerted around the annulus of lary forces and particle structuring can be found in the meniscus: Kralchevsky and Nagayama 2000, 2001w 2ⅷⅷ ,3x . sy␲ ␴ ␪y 2 F␪F␲ FccŽ2r sin rP.Ž0 . Ž.1

2. Normal() capillary-bridge force ␴ Here is the surfaceŽ. interfacial tension, Pc is the difference between the pressures inside and outside 2.1. Definition, measurements and physical importance the bridgeŽ. the capillary pressure , r and ␪ are the radial coordinate and the meniscus slope angle corre- Here we summarise the most important informa- sponding to an arbitrary cross-section of the menis- tion and briefly review recent publications on capil- cus. For example, ␪s␲r2 for a section across the lary-bridge forces. A detailed review can be found in neck of a bridge and then Eq.Ž. 1 can be presented in w ⅷ x sy ␲␴ y Chapter 11 of Kralchevsky and Nagayama 2001 3 . the form Fc 2 r00Ž.1 p , where r is the radius s r ␴ The presence of a liquid bridge between two solid of the neck and p Prc 0 2 is the dimensionless surfacesŽ. Fig. 1a leads to their interaction through a capillary pressure. In general, yϱ-p-qϱ. Accord- capillary force, Fc, owing to the pressure difference ing to the classification of Plateau, with the increase across the curved interface and the action of the of p the shape of the capillary bridge becomes, con- P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 385 secutively, concave nodoid Ž.y ϱ - p - 0, capillary bridge one can use Eq.Ž. 1 , along with some catenoid Ž.ps0 , concave unduloid Ž 0-p-1r2, . appropriate expressions for the meniscus shape. The cylinder Ž.ps1r2 , convex unduloid Ž 1r2-p-1, .contact angle, contact radius and the radius of the sphere Ž.ps1 and convex nodoid Ž 1-p-qϱ .. For neck are connected by simple analytical expressions, - - ᎐ p 1 the capillary-bridge force is attractive Ž.Fc 0, see equations 11.35 11.38 in Kralchevsky and Na- ) ) w ⅷ x whereas for p 1 it becomes repulsive Ž.Fc 0 ; for a gayama 3 . The profile, surface area and volume of s bridge with spherical meniscus we have Fc 0. a bridge can be expressed in terms of elliptic inte- The effect of capillary bridges is essential for the grals, see Table 11.1 in Kralchevsky and Nagayama assessment of the water saturation in soils and the w3ⅷ x . The elliptic integrals can be computed by means adhesive forces in any moist unconsolidated porous of the stable numerical methods of ‘arithmetic᎐geo- media, for the dispersion of pigments and wetting of metric mean’, see Chapter 17.6 in Abramowitz and powders, for the adhesion of dust and powder to Stegunwx 16 . Alternatively, the Laplace equation of surfaces, for flocculation of particles in three-phase capillarity can be solved numerically to determine the slurries, for liquid-phase sintering of fine metal and shape of the bridge and the capillary pressure. For polymer particles, for obtaining of films from latex example, in this way Dimitrov et al.wx 17 estimated the and silica particles, for calculation of the capillary capillary forces between silica particles in amorphous evaporation and condensation in various porous me- monolayers. Likewise, Aveyard et al.wx 18 calculated dia, for estimation of the retention of water in hydro- the liquid bridge profile in a study of the effects of carbon reservoirs and for granule consolidationw 3ⅷ x . line tension and surface forces on the capillary con- The action of capillary-bridge force is often de- densation of vapours between two solid surfaces. tected in experiments with atomic force microscopy Various approximate expressions for Fc are avail- Ž.AFMwx 4᎐6 . For example, Fujihira et al. wx 4 used able for pendular rings, that is a liquid capillary AFM as a friction-force microscope. At higher humid- bridge formed around the point at which a spherical ity in the atmosphere they detected a higher friction, particle of radius R touches a planar surfaceŽ. plate . which was attributed to the presence of an aqueous If the radii of the contact lines are much smaller than bridge due to capillary condensation. R, one can use the formula derived by Orr et al.wx 19 : AFM was also used to measure the interaction fy ␲␴ ␪ q ␪ between a small solid spherical particle and a gas Fc 2 RŽ.cos 12cos Ž.2 bubble attached to a substratew 7᎐10ⅷ ,11x . In fact, ᎐ ␪ ␪ after the particle enters the air liquid interface, the where 12and are the contact angles at the surfaces bubble plays the role of a gaseous capillary bridge of the particle and the plate. If the radii of the between the particle and the substrate. The measured contact lines are not much smaller than R, one can capillary-bridge force is non-monotonic and depends use several alternative expressions for Fc, all of them considerably on the three-phase contact anglewx 7 . In derived in the framework of the so called ‘toroid’ or some experiments a hysteresis of the contact angle ‘circle’ approximation: the generatrix of the bridge was detected; from the measured capillary force one surface is approximated with a circumference, see can determine the advancing and receding contact equations 11.11᎐11.13 in Kralchevsky and Nagayama angles on individual particles and to check whether w3ⅷ x . Using the same approximation, de Lazzer et al. w ᎐ ⅷ x wx there is hysteresis 8 10 . 20 derived analytical expressions for Fc for the cases Capillary bridges between two fluid phases are when the particles are spherical, paraboloidal or coni- found to play an important role in the process of cal. The obtained formulas were verified against the antifoaming by dispersed oil dropsw 12᎐14ⅷ ,15x . When respective exact computer solutions. an oil droplet bridges between the surfaces of an Kolodezhnov et al.wx 21 derived a set of equations aqueous film, two scenarios of film destruction are which provide a convenient way to compute the shape proposed:Ž. i dewetting of the droplet could cause film of the capillary bridge between two identical spherical rupture; andŽ. ii the formed oil bridge could have an particles and to calculate Fc. At the last step numeri- unstable configuration and the film could break at the cal solution was used. The accuracy of the circle centre of the expanding destabilised bridge. The latter approximation was verified against the exact solution mechanism was recorded experimentally with the help for various values of the system parameters. In addi- of a high-speed video camerawx 13 and the results tion, an approximate relationship between the capil- were interpreted in terms of the theory of capillary- lary force and the moisture of a powder was derived bridge stabilityw 14ⅷ x . wx21 . Willett et al. wx 22 obtained closed-form approximated expressions for the capillary-bridge force 2.2. Theoretical calculations of the capillary-bridge force between equal and unequal spheres as a function of the separation distance and for a given bridge volume

To calculate Fc for a given configuration of the and contact angle. These authors developed also a 386 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 method for measuring the capillary forces arising Capillary bridging between two glass surfaces in a from microscopic pendular liquid bridges. The experi- humid atmosphere was observed by Yaminskywx 24 ; mental force-vs.-distance curves were found to agree the formation of a water bridge by capillary condensa- excellently with the respective theoretical dependen- tion was detected as a discontinuity in the force᎐dis- cies calculated by numerical integration of the Laplace tance dependence. Xiao and Qianwx 25 investigated, equationwx 22 . by AFM, the dependence of the capillary-bridge force on humidity. In the case of less hydrophilic surfaces 2.3. Nucleation of bridges: capillary condensation and they detected an adhesive force, which is independent caïtation of humidity and in agreement with Eq.Ž. 2 . In contrast, between more hydrophilic surfacesŽ enhanced If the length of a capillary bridge is gradually capillary condensation. these authors measured a increased, the bridge becomes unstable and ruptures humidity-dependent capillary-bridge force. The latter at a given criticalŽ. maximum length. Conversely, if means that the simplifying assumptions used to derive the distance between two approaching parallel hy- Eq.Ž. 2 are not satisfied and more complicated theo- drophilic plates in humid atmosphere becomes smaller retical expressions have to be applied to interpret the than the maximum length of the stable water bridges, datawx 25 . then such bridges can spontaneously appear due to Capillary condensation of water bridges was es- ‘capillary condensation’ of vapours. Likewise, if the tablished not only when the ambient mother phase is distance between two parallel hydrophobic plates in a humid atmosphere, but also when this phase is oil water is smaller than the maximum length of the wx26 and even ᎏ a bicontinuous microemulsion wx 27 . stable vapour-filled bridges, then such bridges can With the help of a surface force apparatus, Claesson appear owing to a spontaneous cavitation due to et al.wx 26 detected capillary bridging between mica fluctuational formation and growth of critical surfaces immersed in triolein, which had been pre- ᎐ w ⅷ x bridges nuclei 3 . The maximum length, hmax ,ofa equilibrated with water. With a similar technique stable nodoid-shaped bridge can be estimated by Petrov et al.wx 27 measured the force between two means of the asymptotic expression: mica surfaces immersed in a microemulsion Ž.AOTrdecanerbrine . A contribution of capillary 2␴cos␸ bridge-forces was detected and the force profile was s c Ž.Ž.Њ-␸ - Њ hmax << 70 c 90 3 Pc experimentally obtained on both approach and separation. see equations 11.76᎐11.78 in Kralchevsky and Na- As already mentioned, the capillary-bridge force is w ⅷ x ␸ one of the major candidates for explanation of the gayama 3 , c is the contact angle measured across ␸ attractive hydrophobic surface force. Gaseous bridges the bridge phase; for c out of the above interval a could appear even if there is no dissolved gas in the more complicated expression for hmax is to be used. For a bridge, which is in chemical equilibrium with water phase. The pressure inside a bridge can be as the ambient mother phase, one has: low as the equilibrium vapour pressure of water owing to the high interfacial curvature of nodoid-shaped y bridges, see Eqs.Ž. 3 and Ž. 4 above. Alternatively, the P P0 for vapor-filled bridge <

2 A 6r␴ q s⌬␳gr␴ Ž.for thick films F Ž R .Ž.KqL1 for flotation force Ž.6 Ž.10 2 sy⌸Ј r␴ A␴ 2 q Ž.Žfor thin films . F RK1Ž. qL for immersion force 388 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

In other words, the flotation force decreases, while a ‘sliding particle’ method for determining the coef- the immersion force increases, when the interfacial ficient of surface shear viscosity of surfactant adsorp- ␴ tension increases. Besides, the flotation force de- tion monolayers from the measured fd. Similar exper- creases with the decrease of R much more strongly imental method was applied to measure the yield than the immersion force. Thus, the flotation force is stress of protein adsorption layers, which exhibit elas- negligible for R-5y10 ␮m, whereas the immersion tic and plastic behaviourwx 39 . force can be significant even when Rs2 nm. The Whitesides et al.wx 40᎐42 investigated in detail the latter force is one of the main factors causing the self-assembly of mesoscale objects under the action of self-assembly of small colloidal particles and protein lateral capillary forces. In the case of heavyŽ. or light macromolecules confined in thin liquid films or lipid particles, the flotation capillary force was responsible bilayers; see Kralchevsky and Nagayamaw 2ⅷⅷ ,3x for for the observed interparticle attraction. To estimate details. the force per unit area of the particle contact line The analogy between the capillary and electrostatic these authors applied the Laplace equation for a interactions was discussed in more details by Paunov meniscus of translational symmetrywx 40᎐42 . In some wx37 . This analogy can be extended further: in addition of the studies they used floating hexagonal plates of to the immersion force between ‘capillary charges’ alternatively changing hydrophobic and hydrophilic Ž.monopoles , one can also examine immersion forces edgesŽ. sidesw 41ⅷⅷx . In such cases, the immersion between ‘capillary multipoles’, see below. force between capillary multipoles, in conjunction with the flotation force, is responsible for the observed 3.2. Flotation capillary forces self-assemblyŽ. Section 3.4 .

Here we briefly describe some specific and recent results for the flotation forces. The ‘capillary charge’ 3.3. Immersion force between ‘capillary charges’ for floating particles can be estimated from the ex- pressionw 3ⅷ ,36x As already mentioned, in the case of the immersion 1 force the interfacial deformation is related to the Q f qR23Ž.2y4D q3cos␣ ycos 3␣ , iiiii6 wetting properties of the particle surfaceŽ position and shape of the contact line and magnitude of the Ž.is1,2 Ž. 11 contact angle. , rather than to particle weight and s ␳᎐␳ r ␳᎐␳ ␳ ␳ ␳ buoyancy, Fig. 1c. The asymptotic Eq.Ž. 8 can be used where DiiŽ.Ž.II I II , i, IIIand are the mass densities of the particle and lower and upper to calculate the immersion force only for large inter- fluid phases, respectively. Eq.Ž. 11 allows one to calcu- particle distance L, for which the ‘capillary charges’ ' ␺ late the capillary charge Q directly from the particle Qiir sin iare independent of L. However, for i ␺ ␣ shorter distances both riiand become functions of radius Riiand three-phase contact angle . The convenient asymptotic expressions, Eqs.Ž. 8 and Ž 11 . , L, in such cases one can calculate the immersion can be used to calculate the flotation capillary force capillary force using the procedure described in sec- < ) tion 7.3.2 of Kralchevsky and Nagayamaw 3ⅷ x . There for qRii1 and L 4R . In all other cases one could apply a more accurate computational procedure, one can find computational procedures for various which is described in section 8.1.5 of Kralchevsky and configurations: two spherical particles; two vertical Nagayamaw 3ⅷ x . cylinders; sphere and cylinder; sphere and vertical If a vertical plate is partially immersed in a liquid, a wall, etc. In addition, two types of boundary condi- capillary meniscus is formed in a vicinity of the plate tions are considered:Ž. i fixed contact angle; and Ž ii . Ž.wall . The overlap of the latter meniscus with the fixed contact line, which affects the magnitude of the meniscus around a floating particle gives rise to a immersion capillary force; see section 7.3.4 in w ⅷ x capillary forceŽ. particle᎐wall interaction , which is Kralchevsky and Nagayama 3 . In particular, if the described by equation 8.106 in Kralchevsky and positionŽ. elevation of the contact line is fixed at the ⅷ s s Nagayamaw 3x . If a particle slides along an inclined particle surface, i.e. z hc const., then the energy meniscus, for small Reynolds numbers the capillary of capillary interaction between two equal particles of force is completely counterbalanced by the hydrody- circular contact lines of radius rc Ž.Fig. 1c is given by wx namic drag force and then the velocity of particle the expression 43 : motion is proportional to the capillary forcewx 38 . The coefficient of proportionality gives the hydrodynamic 1 Ž.y Ž. drag coefficient, f , which turns out to be dependent Kqr1 ccqr K0 qL d ⌬ Ž.s ␲␴ 2 2 WL 2 qrcc h q on the type of surfactant and the density of its adsorp- Kqr0 Ž.c KqL0 Ž. tion layer at the interface. Petkov et al.wx 38 developed P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 389

done with micrometer-sized latex spheres encapsu- lated within the bilamellar membrane of a giant lipid vesiclew 49,50ⅷ x . These experiments neatly reveal the film deformation caused by the particles and the related attraction between them. For such systems the meniscus profile around a single particle obeys the equationŽ. for small meniscus slope : Fig. 2. The hydrophobic thickness of an inclusionŽ transmembrane protein.Ž.Ž. can be a greater or b smaller than the thickness, h,of 1 dd␨ the non-disturbed phospholipid bilayer. The overlap of the defor- ␴ r s⌬ Psconst.Ž. 13 mations around two similar inclusions gives rise to attraction rdrž/ dr between themw 3ⅷ ,43x . The interaction energy can be estimated by Ž. means of Eq. 12 , hc is the mismatch between the hydrophobic where ⌬ P is the pressure jump across the meniscus. thicknesses of the inclusion and bilayer. ⌬ P is constant if the effect of the gravitational hydro- static pressure is negligible. The general solution of Eq.Ž. 13 is: KqrŽ. y 1 c Ž.12 KqrŽ. 0 c ␨Ž.r sAqBln rq Ž⌬ Pr4␴ .r 2 Ž.14 where q is defined by Eq.Ž. 6 for liquid interfaces or where A and B are constants of integration. In other films. Eq.Ž. 12 can also be applied to describe the words, Eq.Ž. 13 has no axisymmetric solution which is ªϱ energy of interaction between two inclusionsŽ for infinite at infinity Ž.r , cf. Eqs. Ž.Ž. 5 and 14 . The stance membrane proteins. in a bilayered lipid mem- latter fact implies that the meniscus around a particle 1r2 brane. In the latter case qfw4␭rŽ.h␴ x , where ␭ is must end at a peripheral contact lineŽ. of radius rp , ␨' the shear elastic modulus in the hydrocarbon-chain out of which the film is plane-parallel Ž.0 , see Fig. zone and h is its thicknessŽ. Fig. 2 , for details see 1d. Hence, we deal with a ‘finite’ meniscus. In this Kralchevsky et al.wx 43 and Chapter 10 in Kralchevsky case the overlap of the menisci and the interaction and Nagayamaw 3ⅷ x . Note that the interaction energy, between the particles, begins when they are at a 2 distance L-2r from each other. Such types of in- as given by Eq.Ž. 12 , is proportional to hc, i.e. to the p squared mismatch between the hydrophobic zones of teraction is obviously different from that described by ⌬ A y1r2 the inclusion and bilayer. This interaction can be one Eq.Ž. 7 , which for long distances yields W ŽqL . y of the reasons for aggregation of membrane proteins expŽ.qL . in biomembraneswx 43᎐45 . The problem with the immersion capillary force, F, The immersion capillary force can also be operative in the case of finite menisci was examined theoreti- w ⅷ x between particles captured in a sphericalŽ rather than cally in Danov et al. 50 and in a more detailed planar. thin liquid film or lipid vesiclew 3ⅷ ,46x . In this article by Danov et al.Ž. Langmuir 2001, submitted . case the ‘capillary charge’ characterises the local devi- Both the theory and experiment show that in the ation of the meniscus shape from sphericityŽ rather investigated case F corresponds to attraction, whose N NsN N than from planarity. at the contact line. magnitude, F FLŽ. has a peculiar non-mono- N N Maenosono et al.wx 47 examined experimentally the tonic behaviour: for short distances F increases N N motion of millimetre-sized spheres which are partially with L, then F has a maximum; and decreases immersed in a wetting filmŽ. Fig. 1c . Employing Eq. further. Moreover, the capillary interaction exhibits s Ž.9 to estimate the immersion force, these authors hysteresis: on approach of two particles one has F 0 ) determined the friction coefficientŽ related to the for L 2rp, the interaction begins with a jump when drag force. from the data for the particle law of the two peripheral contact lines touch each other. In motion LtŽ., where t is time. It turned out that the contrast, on separation of the two interacting particles / friction with the substrate is negligible and the main Ž.and of the two overlapping menisci one has F 0 ) hydrodynamic resistance comes from the viscous fric- for L 2rp. With further increases in L the configu- tion in the liquid filmwx 47 . ration of the meniscus becomes unstable and it splits It is worthwhile noting that Eqs.Ž.Ž. 5 ᎐ 9 are valid to two separate menisci around the respective individ- for menisci decaying at infinityŽ. Fig. 1c . However, it ual particles. is possible the particle size is much greater than the film thickness, as shown in Fig. 1d. For example, 3.4. Immersion forces between ‘capillary multipoles’ Velikov et al.w 48ⅷ x observed a strong lateral attraction between latex particles of diameter 2 Rf7 ␮m, The weight of a floating micrometer-sized particle entrapped in a foam film of thickness which is at least is too small to create any surface deformation. How- 100 times smaller. Analogous observations have been ever, surface deformations could appear if the contact 390 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

line on the particle surface is irregularŽ say, undulated contact line could be sufficient to give rise to a as in Fig. 1e. , rather than a perfect circumference. In significant capillary attraction, which may produce 2D this case, instead of Eq.Ž. 5 , the meniscus shape aggregation of colloidal particles attached to a fluid around a single particle is described by the expres- interface, also see Lucassenwx 52 and Chapter 12 in sion: Kralchevsky and Nagayamaw 3ⅷ x . However, in the angstrom scale the fluid interfaces are not smooth: ϱ they are corrugated by thermally excited fluctuation ␨Ž.r,␸ s KqrA Ž.Žcosm␸qB sin m␸ . Ž.15 Ý mm m capillary waves, whose amplitude is typically 3᎐6A.˚ ms1 Hence, one can expect that the effect of the contact- This equation is the respective solution of the lin- line undulations will become significant when their earized Laplace equation of capillarity for small amplitude is greater than the background stochastic meniscus slope, ٌ 2␨sq 2␨, in cylindrical coordinates noise, that is for nanometre and larger amplitudes w ⅷ x ␸ 3. Ž.r, . Here Ammand B are constants of integration. y Ž. Ž. ⌬ A 2 For qr<1 one has K Ž.qr A Ž.qr m and then Eq. Note that both Eqs. 12 and 16 give W hc. m sy Ž.⌬ r Ž.15 reduces to a multipole expansion Ž a 2D analogue With respect to the force, F d W dL, for the of Eq.Ž. 15 in electrostatics . . The terms with ms1, 2, immersion force between two ‘capillary charges’ Ž. A r 3,... correspond to ‘dipole’, ‘quadrupole’, ‘hexapole’, monopoles we have F 1 L, whereas in the case A r 5 etc. In fact, such multipoles were experimentally re- of two quadrupoles the force is F 1 L . In other < alised by Bowden et al.w 40,41ⅷⅷx by the appropriate words, for qr 1, the range of action of the capillary hydrophobization or hydrophilization of the sides of force decreases with the increase of the multipole floating hexagonal plates. order, as it could be expected. Consequently, if capil- Ž. From a theoretical viewpoint, the capillary force lary charges i.e. multipoles of the lowest order are between particles of irregular or undulated contact present, as a rule they dominate the capillary interac- line is a kind of immersion force insofar as it is tion. related to the particle wettability, rather than to the Another difference between the cases of interacting particle weight. Eq.Ž. 5 is the zeroth-order term of the capillary ‘charges’ and ‘multipoles’ is that the interac- expansion in Eq.Ž. 15 . For mG1 the capillary force tion is isotropic for charges, whereas for multipoles Ž.G can cause not only translation, but also rotation of the m 2 its sign and magnitude depend on the particle particles. Theoretical description of this capillary force mutual orientation. For that reason, as sketched in was recently given by Stamou et al.w 51ⅷⅷx for rough Fig. 3a,e, the immersion force between quadrupoles Ž.s colloidal spheres. These authors note that for freely m 2 will tend to organise them in a square lattice, ᎐ floating particles the capillary force will sponta- rather than in a hexagonal one. Particles hexapoles Ž.s neously rotate each particle around a horizontal axis m 3 can be arranged into a hexagonal lattice with Ž. Ž . to annihilate the capillary dipole moment. Therefore, voids Fig. 3c , or without voids Fig. 3b,f . In fact, Ž. the term with ms1 in Eq.Ž. 15 has to be skipped and such lattices hexagonal with voids and square have the leading multipole order in the capillary force been observed in the experiments of Bowden et al. w ⅷⅷx between such two particles is the quadrupole᎐ 40,41 . quadrupole interaction Ž.ms2 ; the respective inter- The angular dependence of the immersion force action energy isw 51ⅷⅷx : between multipoles leads to the conclusion that this force could hardly produce formation of 2D crystals from a mixture of particles with different multipole r 4 ⌬ Ž.sy ␲␴ 2 Ž␸ q ␸ .c Žs . orders m. In principle, it is possible this capillary WL 12 hcABcos 2 2 4 m 2 L interaction is able to induce a ‘phase separation’ of Ž.16 the mixture into ordered domains of particles with the same m. Another possibility, suggested in reference w ⅷⅷx Here hc is amplitude of the undulation of the 51 , is that the particles could form simple linear contact line, whose average radius is rc. The angles aggregates. When two or more modes contribute with ␸ ␸ ABand are subtended between the diagonals of a considerable weight to the multipole expansion, Eq. the respective quadrupoles and the line connecting Ž.15 , the capillary force is expected to be unable to the centres of the two particles. For two particles in cause two-dimensional crystallisation of the respective r s ␸ contact Ž.L rcA2 and optimal orientation, cos Ž 2 particles, because of their inadequate relative orienta- q ␸ s ⌬ sy r ␲␴ 2 w ⅷⅷx 2 Bc.Ž.1, one obtains W 3 4 h . Thus, tions 51 . for interfacial tension ␴s35 mNrm the interaction It is worthwhile noting that Lucassenwx 52 was the energy ⌬W becomes greater than the thermal energy first who developed a quantitative theory of the capil- ) kT for undulation amplitude hc 2.2 A.˚ This result lary forces between particles with an undulated con- is really astonishing: even a minimal roughness of the tact line. He considered ‘rough-edged’ cubic particles P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 391

edge of the cubic particles is equal to ␭. With ␴s40 r ␭s ␮ s ⌬ s mN m, 1 m, hcc100 nm and h 20 nm Eq. f r f r Ž.17 yields Edil124 mN m and E sh 8mN m. The latter values of the surface elasticities are comparable with those for protein adsorption layerswx 53 . How- ever, the predictions of Eq.Ž. 17 have not yet been veriﬁed experimentally.

4. Self-assembly of particles under the action of capillary forces

4.1. Assembly of spherical particles in wetting ﬁlms

The process of formation of well ordered 2D particle arrays in evaporating wetting films was known for many yearswx 54᎐59 . Regular arrays of latex particles were often fabricated by evaporation of drops of suspensions on solid substrates to prepare samples for optical studieswx 54 or for modelling the process of paint dryingwx 55 . In the 1970s the ‘mica spreading technique’ was introduced for preparation of 2D crys- Fig. 3. The 2D arrays formed by capillary quadrupoles Ž.ms2 and tals of viruses and proteinswx 56,57 , which were suit- hexapoles Ž.ms3w 41ⅷⅷ ,51 ⅷⅷx ; the signs ‘q’ and ‘‘y’’ denote, able for structural analysis by electron microscopy. respectively, positive and negative ‘capillary charges’, i.e. convex Yoshimura et al.wx 58 , developed a mercury spreading and concave local deviations of the meniscus shape from planarity at the contact line.Ž. a Quadrupoles of square shape form tetrago- technique and obtained 2D crystals from a dozen of w ⅷ x nal close-packed array, irrespectively of the location of the capillary protein 3 ,59 . chargesŽ.Ž. on the sides or on the corners of the square . b Plates The mechanism and the governing forces of the 2D with a hexagonal shape form a close-packed array only if the particle assembly in evaporating wetting films were charges are located on the corners, whereasŽ. c porous Ž opened . clarified about a decade agowx 60,61 . A two-stage hexagonal array is formed when the charges are located on the Ž. hexagon sides.Ž. d Quadrupoles having the shape of hexagons form process was observed: 1 nucleus formation, under linear aggregatesw 51ⅷⅷx .Ž. e Quadrupoles having circular shape will the action of attractive capillary immersion forces; form square array,Ž. f circular hexapoles can form close-packed andŽ. 2 crystal growth, through convective particle hexagonal array. Note that the aggregate structure depends on both flux caused by the water evaporation from the already the distribution of the capillary charges and the geometrical shape ordered arrayŽ. see Fig. 4a . It was shown that one can of the elementary cell. produce ordered mono- and multilayers of particles by appropriate control of the shape of the liquid film with a sinusoidal contact line. The calculated capillary surface and of the water evaporation ratewx 60 . The force exhibits a minimum: it is attractive at long term ‘convective assembly’ was introducedwx 59 to distances and repulsive at short separations. Any in- identify this mechanism of particle ordering under the terfacial deformation, either by dilatation or by shear, action of capillary immersion force and hydrodynamic will take the particles out of their equilibrium posi- drag force. tionsŽ. at the minimum and will, therefore, be re- During the last few years, the method of convective sisted. As a consequence, the particulate monolayer assembly has found a wide application, see Section will exhibit dilatational and shear elastic properties 4.6. Ordered arrays from various nano- and micron- wx 52 . The respective surface dilatational and shear sized particles were obtainedw 62᎐72ⅷⅷ ,73,74 ⅷ , elastic moduli can be estimated by means of the 75,76ⅷ ,77᎐81x by the method described in Denkov et w ⅷ x expressions 3 : al.wx 60,61 or its modifications. Several research groups suggested new versions of equipment or procedures 2␲ 3␴h3 h2 E f cc, E f2␲␴2 Ž.17 Ž.based on the same principles and governing forces , dil␭⌬22 sh ␭ hc which were aimed at improving the control or at simplifying the procedures for particle array forma- ␭ wx where is the wavelength of the undulations, hc is tion. Thus, Dimitrov and Nagayama 65 developed a ⌬ their average amplitude and hc is the standard set-up which resembles in construction the dip-coat- deviation of the amplitude from its mean value. It is ing apparatus: by appropriate control of the rates of ⌬ < assumed that hcch and that the length of the water evaporation and substrate withdrawal, they suc- 392 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

Experiments with latex particles on mercury substrates confirmed the important role of the immersion capillary forces for the convective assembly process and showed that the electrical potential of mercury can be used as another parameter for control of the particle᎐substrate interaction and thereby, of the ordering processw 3ⅷ ,59x . One interesting observation in these studies was the size separation of the particles, when mixtures of particles of various sizes were used wx1,77 : the larger particles always collected in the centre of the close-packed hexagonal cluster, sur- rounded by smaller particles. The reason for this segregation is that the larger particles are pressed by the film surface and start attracting each other by capillary immersion forces before the smaller particles. It was demonstratedwx 78 that another liquid, per- fluorinated oil, can be used as a sub-phase for convective particle assembly. The advantages of the liquid substratesŽ molecular smoothness and mobility of their Fig. 4. Ordering of spherical particles in wetting films on subs- surfaces. were discussed in relation to the quality of trates:Ž. a Main driving forces in the convective assembly process: F the final ordered arrays. The optical-microscope is a lateral capillary immersion force, between particles captured in observationswx 78 showed that the process is governed the thin liquid film. Fd is a hydrodynamic force, which drags the particles suspended in the thicker layers towards the thinner re- by the same forces as in the case of solid substrate: the immersion᎐capillary and hydrodynamic᎐drag gions. FdWis caused by a hydrodynamic flux, J , which compensates the water evaporated from thinner regionswx 60,61 .Ž. b Ordering of forces. particles on patterned solid surfaces. The lateral capillary immer- Several studiesw 48ⅷ ,79᎐81x showed that the convec- sion force, F, acting between particles localised in a given domain, tive assembly method is operative even for particles, focuses these particles towards the domain center. The conventio- Ž. nal method of convective assembly leads to formation ofŽ. c close- which are captured in free-standing foam films. packed mono- and multilayers of particles, whereas the assembly Therefore, the solid or liquid substrates are not a on patterned substrates can be used to fabricateŽ. d small particle necessary component of the assembly process, be- clusters orŽ. e regular arrays of particles with desired lattice shape cause the liquid film itself acts as a 2D matrix for w ⅷⅷxwⅷ x and separation 85 . In Qin et al. 88 the particles are formed particle packing. Following this approach Denkov et in situ in the microdroplets sitting over the hydrophilic domains. al.wx 79᎐81 developed a new procedure for the preparation of vitrified aqueous films, which contain mono- ceeded in obtaining centimetre sized, homogeneous in or multi-layers of particles, suitable for electron cryo- thickness, ordered arrays of latex particles. Other microscopywx 83 . The method was applied to nanome- versions of the method utilise a deposition of the tre sized latex particles and to monodisperse vesicles suspension with a plateŽ. playing the role of a brush made of a lipid᎐protein mixture. or through an extruderw 3ⅷ ,59,68x . In other studieswx 82 , the suspension spreading has 4.2. Self-assembly of particles on patterned substrates or been facilitated by applying the spin-coating tech- in capillary networks niqueŽ. rotating substrate , which is widely used in the polymer industry for casting polymer films. The qual- During the last years, several new approaches to ity of the final ordered array can be improved if the particle self-assembly into complex 2D structures appropriate agitation by sonication is applied during have emerged. One way to fabricate such structures is the film drying processwx 67 . A relatively simple proce- to use a solid substrate, whose surface is chemically dure was introduced by Micheletto et al.wx 66 : a drop patterned, e.g. by the microcontact printing method of suspension was placed on a glass plate, which was wx84 , so that different domains of desired shape and then tilted at an appropriate angle. The array forma- size are formed. Aizenberg et al.w 85ⅷⅷx showed that tion starts at the upper edge of the drop and proceeds micro-patterned substrates, bearing cationic and an- downwards. Jiang et al.w 72ⅷⅷx proposed an efficient ionic regions, can be utilised. The particles preferen- procedure for the formation of large single-crystal tially stick to the domains of the opposite electric colloidal multilayers of silica particles by means of charge. Next, the substrate is rinsed with water, thus controlled evaporation of the disperse medium and removing the non-attached particles. After the rins- the ensuing action capillary forces. ing, one observes that the attached particles are con- P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 393 tained in residual water dropletsŽ. Fig. 4b . Upon which resembles the analogous process in the convec- evaporation of water, each droplet compresses the tive assembly methodwx 60,61 . The term MIMICŽ mi- particles towards the domain centre leaving an or- cro-moulding in capillaries. is used to name this tech- dered cluster after drying is complete. By this proce- niquew 92ⅷⅷx . The latter can be applied to a variety of dure, very well ordered 2D particle arrays of desired liquids, which solidifyŽ or which contain a substance symmetry and lattice constantŽ which could be much able to solidify. upon the appropriate treatment: po- larger than the particle diameter. were produced lymerisation, curing, crystallisation, etc. Thus, a solid w85ⅷⅷx . Furthermore, small clusters of 5 to 7 particles micro-pattern of complex structure can be formed were assembled in the nodes of a 2D periodic lattice from various materials in the capillaries. The removal Ž.Fig. 4d . of the PDMS stamp results in a patterned substrate. It was demonstrated that other types of par- A further chemical or physical treatment can be used ticle᎐surface interactions can be used to induce a to detach the pattern from the support and to obtain deposition of particles onto patterned substrates free-standing structures. Formations of poly- wx r 86,87 . One can conclude that this method for the urethaneŽ free-standing or attached to Si SiO2 subs- formation of complex structures has a big potential trate.Ž , various salts KH24 PO , CuSO 4 , K 3 Fe Ž. CN 6 for further development and applications. An interest- and others. , silica and metals were fabricated by ing modification of this technique was suggested by means of the MIMIC procedurew 92ⅷⅷx . A rich variety Qin et al.w 88ⅷ xwx and Zhong et al. 89 who used of patterns can be produced using this relatively sim- micro-droplets, formed on the hydrophilic domains of ple method. the patterned substrateŽ similar to those described Following a similar idea, Park et al.w 93ⅷ x obtained abovew 85ⅷⅷx. , as micro-crystallisation or micro-chem- large crystalline assemblies of particles by injecting ical reactors, in which the particles were formed in latex suspension, under pressure, in a narrow slit situ, during the drying process. Thus, well ordered between two planar surfaces. Micro-channels were arrays of micro- and nano-particles were formed with made in one of the side-walls of the slit, so that the lattice geometry and spacing, which replicated the fluid was able to flow through these channels under initial pattern. In this technique, the particle size and the action of the applied pressure. The channels were lattice constant can be conveniently controlled by smaller in size than the diameter of the latex parti- varying the domain size and the concentration of the cles, therefore the latter remained captured in the initial suspension. slit. By optimising the applied pressure, water evap- There are experimental indications that the capil- oration rate and intensity of sonication, perfectly or- lary forces play some role in the deposition of mi- dered crystalline assemblies of various thickness were celles on solid surfaceswx 90,91 . Massay et al. wx 90 fabricated. succeeded to orient specially designed core᎐shell mi- Capillary immersion forces could be involved in the celles of a cylindrical shape along nano-sized grooves, observed formation of close-packed arrays of created by electron beam lithography and reactive ion nanoparticles in condensed alkylamine filmswx 94,95 . etching on the surface of a silicon wafer. Thus, nano- The role of the meniscus, mediating the capillary scopic lines of approximately 3 nm in height and 15 interaction, can be played by amphiphilic bilayers, nm in width were formed, which followed the con- which probably form in the structured alkylamine tours of the lithographic grooves. films. A different approach to the formation of complex A comprehensive review on various unconventional 2D and 3D structures of ordered micro-spheres in techniques for fabricating complex nanostructures was pre-formed templates was proposed by Kim et al. recently published by Xia et al.wx 96 . w92ⅷⅷx . First, a PDMS stamp is produced, whose surface has a relief of micro-channels of the desired 4.3. Self-assembly of non-spherical objects into 2D arrays shape and connectivity. This stamp is placed over a solid support and the formed network of micro- In the framework of the so-called meso-scale self- capillaries is set in contact with a suspension of latex assemblyŽ. MESA project, Whitesides et al.w 40,41ⅷⅷ , particles. The capillaries spontaneously suck-in sus- 97᎐102ⅷⅷx developed a new procedure for the fabrica- pension and close-packed 2D and 3D arrays of parti- tion of complex 2D structures from millimetre and cles are found to fill-up the micro-channels under sub-millimetre sized plates floating on the interface appropriate conditions. It should be noted that the between water and perfluorodecalin. The plates were ordering of the latex particles in these experiments is made of PDMS moulds of desired shapeŽ square, not driven by capillary forces. The authors showed hexagon, hexagonal rings, or more complex. and their w92ⅷⅷx that the particles pack in the micro-capillaries side walls were selectively rendered hydrophobic or mainly under the action of a hydrodynamic drag force, hydrophilic. By addition of aluminium oxide to the created by the water evaporation at the capillary exits, PDMS mould, the authors were able to vary the mass 394 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 density of the plates between that of waterŽ 1 grcm3. The MESA approach was successfully applied for and perfluorodecalinŽ 1.9 grcm3. . Depending on the fabrication of complex 3D structures as well. By using mass of the plates and on the hydrophobicityrhydro- the surface of a suspended emulsion dropŽ water-in-oil philicity of their side walls, lateral capillary forces of or oil-in-water. as a template, a self-assembled, virus- different sign and magnitude appear between the like shell was formed from gold hexagonal rings with neighbouring sides of two approaching plates: some of size of approximately 100 ␮mw 103ⅷ x . To prevent the the sides repel, while others attract each other. As a shell disassembly upon drying, the authors deposited result, the plates acquire an optimal mutual orienta- a thin silver layer over the ordered hexagonal rings by tion, which minimises the overall free energy of the using a micro-electrode. The electro-deposition system. A shape selective, lock-and-key mechanism is welded the rings into a spherical assembly, which was imposed in this way. Taking into account the millime- sufficiently robust to withstand the strong capillary tre size of the plates and the different wettability of forces upon drying and to remain intact in air. This is their side walls, one can realise that the lateral capil- one of the most complex tailored procedures, involv- lary forces in these systems presents a combination of ing a stage of particle self-assembly under the action the flotation force, driven by gravityŽ. Fig. 1b , with the of lateral capillary forces, which has so far been immersion force between the ‘capillary multipoles’ realised. A simpler version of this technique was first Ž.Fig. 1e . suggested by Velev et al.wx 104,105 , who ordered mi- By using a mild agitationŽ oscillatory rotation of the crometer sized latex beads on the surface of emulsion container with controlled amplitude and frequency. , drops. the authors were able to balance the capillary interaction with the disrupting hydrodynamic shear force, so 4.4. Formation of balls and rings of structured spherical that well ordered arrays were generated. Whitesides particles et al.w 40,41ⅷⅷ ,97᎐102 ⅷⅷx were able to produce in this way a large variety of complex structures: 2D close- Recently Velev et al.w 106ⅷⅷx developed a new packed or porousŽ. open arrays; linear oligomer- and procedure for assembly of micro- and nano-particles polymer-like aggregates from similar or complemen- into free-standing, millimetre-sized ordered structures tary in shapeŽ. lock-and-key plates; closed rings of of various shapes. Aqueous droplets of colloidal sus- given size and shape; polymer-like branched aggre- pension were placed on the surface of an inert liquid gates; and many othersŽ. Fig. 3a,b,c,d . The observed substrateŽ. perfluoromethyldecalin . The slow evapora- shape-selective recognition and self-assembly were tion of water led to shrinking of the aqueous drops qualitatively explained by the local deformation of the and to a gradual concentration of the suspended meniscus around each side of the plates, which gives particles. Eventually, a compact 3D colloid crystal was rise to lateral capillary forces. A far reaching analogy formed. The shape and size of the final assembly can with the receptor᎐ligand interactions in chemistry be controlled by various factors, such as the size of was drawn and the term ‘capillary bonds’ was intro- the initial drop, particle concentration and presence duced to designate this type of directed capillary of surfactants. The latter affect the interfacial ten- interaction. One can envisage a virtually unlimited sionsŽ. and thereby the shape of the drop and the variety of hierarchical structures that can be obtained appearance of hydrodynamic fluxes, as a result of the by the MESA approach. surfactant-driven Marangoni effect during evapora- The attempts to reduce the characteristic size of tion. By appropriate control of the conditions, Velev the plates down to a micrometer size resulted in less et al.w 106ⅷⅷx obtained spherical, discoidal, dimpled ordered arrays, in which the density of defects was and toroidalŽ. ring-shaped assemblies. Anisotropic as- higherwx 101 . This result was attributed to two main semblies were obtained by using mixtures of magnetic reasons:Ž. i the reduced magnitude of the buoyancy q non-magnetic or plastic q gold particles. This force, which affects the deformation of the fluid inter- method seems rather versatile and can be applied to a face and thereby the flotation force; andŽ. ii the wide variety of inorganic and plastic particles and reduced magnitude of the hydrodynamic shear forces, their mixtures. imposed by the oscillatory motion, for the smaller Rings of particles, deposited on solid substrates, are particles. The second problem could be probably be often observed after drying of suspension drops on overcome by using some other means of system agita- solid substrateswx 60,107᎐109 . The optical observations tionŽ. e.g. sonication . The first problem, however, and the theoretical models have shown that the pre- recalls the necessity for a more rigorous scaling of the vailing force, which determines the particle transport magnitude of capillary forces acting between such and arrangement in these systems, is the hydrody- shaped objects having neither rotational nor transla- namic drag force, caused by the liquid evaporation tional symmetry; a corresponding theory is still miss- wx60,61 . The ring formation in these experiments is ing. explained by the following scenariowx 60,107᎐109 : P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 395

firstly, some of the particles irreversibly stick to the of solvent evaporation and surface forces on the con- substrate at the three-phase contact lineŽ drop peri- ditions for hole nucleation were studiedwx 110 . phery. under the action of normal capillary force. The stuck particles pin the contact line so that the process 4.5. The 2D clusters and foam-like formations of particles proceeds at a fixed contact radius. The liquid evapora- on a fluid interface tion from the edge is compensated by liquid flow from the interior, which drags the suspended particles to- Several studiesw 51ⅷⅷ ,112᎐115 ⅷ ,116 ⅷ ,117,118x re- Ž. wards the drop periphery Fig. 5a . As a result, most ported the formation of 2D clusters and foam-like of the particles get accumulated in the region of the structures from micrometer-sized spherical particles contact line and are compressed there by the liquid on the air᎐water interface. The interparticle spacing meniscus at the final stage of drying. The ring size in in these arrays was about several particle diameters. these experiments is determined by the initial radius The structuring was observed after spreading a drop of the contact line. Therefore, this method can be of suspension over the surface of an aqueous sub- further developed by depositing suspension drops on phase. In some of these studies, the results can be well defined lattice domains on patterned substrates, explained either by pure electrostatic repulsion similar to those described in the Section 4.3 between the particlesw 114,115ⅷ x , or by an interplay of w ⅷⅷ ⅷ x 84,85 ,86᎐88 ,89 . In this way, well ordered arrays the common flotation capillary forceŽ. Fig. 1b with the of rings of given size could be fabricated in a con- van der Waals and electrostatic forceswx 112,113 . trolled manner. Other observationsw 51ⅷⅷ ,116 ⅷ ,117,118x , however, Ohara et al.wx 110,111 studied the formation of required the authors to invoke a very long-range submicrometer rings upon drying of wetting films attraction between the particles. This could be neither containing very small nanoparticlesŽ 3᎐5nmindi- the van der Waals forceŽ which was negligible at such ameter. . A characteristic feature of this system is that separations. nor the flotation capillary force, because the particles are so small, that various surface forces the particles were too small and the respective inter- become operative in the wetting film of thickness action energy was well below the thermal energy, kT. comparable to the particle diameter. These surface It is worthwhile noting that in these experiments the forces may induce film destabilisation and hole for- disperse medium of the suspension, used for spread- mation. Therefore, the authors Ohara and Gelbart, ing of the latex particles, was a methanolrwater mix- and Ohara et al.wx 110,111 have hypothesised that the tureŽ. 9r1 . Stamou et al.w 51ⅷⅷx suggested that the particulate rings in their experiments are formed as a governing, long-range attractive force in the latter result of the nucleation and expansion of holes in the experiments is created by nano-scopic irregularities of wetting film at the final stage of its drying. The rim of the three-phase contact line, i.e. by immersion force the expanding hole drags the particles away and ar- between ‘capillary multipoles’Ž. Fig. 1e and developed ranges them into annular ringsŽ. Fig. 5b . The effects a respective theoretical model. One should note, however, that the observed evolution from 2D foam to 2D clusters in these experiments resembles very much the processes observed when an aqueous suspension of latex particles was spread over liquid perfluorodecalin sub-phasewx 78 . Observations in reflected light of the particle assembly process on perfluorodecalin proved that the latex particles were captured in thin aqueous filmswx 78 and the assembly process was driven by the immersion force between ‘capillary charges’, which is sufficiently strong and long-ranged to explain the observed phenomena. Therefore, it is worthwhile verifying whether some oily filmŽ say from dissolved styrene oligomers. is not generated on the surface of the aqueous sub-phase when spreading the suspension of latex particles in methanol.

Fig. 5. Two possible ways for fabrication of circular particulate rings on substrates:Ž. a by evaporating drops of suspensions; in this 4.6. Applications of 2D particle arrays case the particle transport is driven by a hydrodynamic drag force,

Fd.Ž. b By hole formation and subsequent expansion, which leads to lateral capillary immersion force at the rim periphery. The simulta- Here we brieﬂy overview the main areas, in which neous formation of many holes in the layer leads to formation of the 2D colloidal arrays, assembled with the help of 2D foam-like assembly. capillary forces, ﬁnd application. 396 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

The ordered 2D arrays of monodisperse latex parti- loid monolayer lithography’w 75,76ⅷ x . The use of pat- cles attracted the attention of researchers a long time terned substrates, allows one to obtain 2D crystal ago due to their interesting optical properties symmetries, which are different from the simple w54,62,72ⅷⅷ ,73,74 ⅷ ,119,120 ⅷ ,121᎐123x . When the parti- close-packed hexagonal arrayw 76ⅷ x . cle size and spacing are comparable to the wavelength The process of particle ordering in wetting films is of the illuminating light, a rich variety of optical related to paint coatings. Recent studies showed phenomena, caused by the light diffraction and inter- w134᎐136ⅷ x that the paint layer formation from aque- ference can be observed. Since the lattice constant ous dispersions resembles in some aspects the convec- and the refractive index of the particles can be varied tive assembly process. In many systemsŽ especially in in wide ranges, the optical properties of the arrays those containing surfactants. the drying of the paint can be finely tuned. Therefore, the 2D colloid crystals layer is not uniform but occurs through a moving are studied in the literature as optical elements, such zone, which separates the wetŽ. thicker from the dry as diffraction gratings, interference filters, antireflec- Ž.thinner films ᎏ this ‘compaction’ zone moves in the tion coatings, micro-lenses, etc.w 54,62,72ⅷⅷ ,119x . Along plane of the layer so that the dry regions expand with with these more conventional applications, recent time at the expense of the wet regions. A hydrody- studies were directed to study the application of parti- namic forceŽ. caused by the water evaporation drags cle arrays as basic photonic elements and as photonic the suspended particles from the wet regions towards band-gap crystals, i.e. as periodic dielectric structures, the dry regions, just as in the convective assembly in which the photons behave in a manner similar to methodwx 60,61 . This hydrodynamic flux redistributes that of electrons in semiconductorsw 73,74ⅷⅷ ,120 , also the electrolytes and surfactants, so that the final 121᎐123x . composition of the dry layer is non-uniform in the During the last several years rapid progress was plane of the layerwx 134,135 . The degree of particle achieved in developing procedures for fabrication of ordering in the final layer depends primarily on the regular, highly porous structures from various materi- processes taking place in the compaction zone, where als by using 2D and 3D colloid crystals as templates the capillary forces press the particles against each w124᎐127ⅷⅷ ,128 ,129,130 ⅷ ,131,132x . Such porous struc- other and against the substrate. The capillary bridge tures have been obtained from inorganic oxides, po- forces play a dominant role also in the process of lymers, glassy carbon, semiconductors and metals. particle deformationŽ and to some extent, of particle These structures are of great interest due to their fusion. in the latex layersw 134᎐136ⅷ ,137,138x . unique optical properties and possible applications in Ordered monolayers of particles are used also in catalysis, including the photo- and electro-catalysis. A some biological studies. Thus, Miyaki et al.wx 139 comprehensive overview on this subject can be found studied the interaction of neutrophil-type biological in Holland et al., Jiang et al. and Velev and Kaler cells with particle arrays as a function of the particle w127ⅷⅷⅷ ,128 ,130x . size. They found that the contact of the cells with the Ordered 2D particle monolayers were successfully particle array activated the cell to an extent, which applied as lithographic masks for fabrication of regu- strongly depended on the particle size. Thus, the lar nano-structures on silicon substrates by etching or particle arrays serve as convenient micro-patterned vacuum deposition of metalw 75,76ⅷ ,82,133x . For this surfaces for studying the cell adhesion. The wide purpose, Burmeister et al.w 76ⅷ x further developed the ranges of available particle sizes and compositions, convective assembly method by including several ad- along with the possibility to graft various bio-active ditional steps: The pre-formed dry 2D array of latex molecules onto the particle surface, imply that these particles was reinforced by vacuum deposition of metal studies will expand in the future. or by thermal annealing. These procedures led to shrinking of the openings between the latex beads, without completely closing them. Afterwards, the glass 5. Summary and conclusions substrate was slowly dipped into a water bath and the strengthened particle monolayer floated off onto the The review of publications from the last 2᎐3 years water surface. If a metal deposition is used, the sub- shows that there is a permanent interest in the vari- strate remains covered with a regular array of nano- ous kinds of capillary forces, which often play an metal dots, which replicate the voids between the essential role in fundamental and applied studies. The latex particles in the initial array. However, the float- capillary bridge forcesŽ. Fig. 1a are investigated in ing particle array can be transferred from the water relation to AFM experimentsw 4᎐6,8᎐10ⅷ ,11,32x , stud- surface onto another solid substrate for further exper- ies on capillary condensation and measurements by iments. In this way, a free standing, transportable the surface-force apparatuswx 18,24᎐27 , capillary cavi- lithographic mask was produced. This technique has tation and long-range hydrophobic surface force been termed ‘natural’wx 133 , ‘nanosphere’ wx 82 or ‘col- wx23,28᎐35 , antifoaming action of oily drops P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 397 w13,14ⅷ ,15x . The flotation lateral capillary forceŽ Fig. Chapter 13: two-dimensional crystallisation of particulates and pro- 1b. is employed in surface rheological measurements teins. Chapter 14: effect of oil drops and particulates on the Ž. wx38 and for self-assembly of floating meso-scale ob- stability of foams antifoaming . wx4 Fujihira M, Aoki D, Okabe Y, Takano H, Hokari H. Effect w ⅷⅷ᎐ ⅷⅷx jects 40,41 ,97 102 . The common immersion cap- of capillary force on friction force microscopy: a scanning illary forceŽ. Fig. 1c is reported to take part in the 2D hydrophilicity microscope. Chemistry Letters, 1996:499᎐500. aggregation and ordering of micrometer-sized and Ž.Japan sub-micrometer particles confined in wetting and wx5 Behrend OP, Oulevey F, Gourdon D et al. Intermittent w ᎐ ⅷⅷⅷ contact: tapping or hammering? Applied Physics A free-standing liquid films 54 72 ,73,74 ,75,76 , ᎐ ᎐ x 1998;66:S219 S221. 77 82 . wx6 Suzuki H, Mashiko S. Adhesive force mapping of friction- Systematic presentation of the theory of the afore- transferred PTFE film surface. Applied Physics A mentioned types of capillary forcesŽ. Fig. 1a᎐c was 1998;66:S1271᎐S1274. recently publishedw 2ⅷⅷ ,3x . New theoretical develop- wx7 Fielden ML, Hayes RA, Ralston J. Surface and capillary ments are devoted to the description of the immer- forces affecting air bubble ᎏ particle interactions in aque- ᎐ w ⅷ x ous electrolyte. Langmuir 1996;12:3721 3727. sion force in the case of finite menisciŽ. Fig. 1d 50 wx Ž. 8 Preuss M, Butt H-J. Direct measurement of particle-bubble and the forces between ‘capillary multipoles’ Fig. 1e interactions in aqueous electrolyte: dependence on surfac- w ⅷⅷx 51 . The latter two themes mark directions for tant. Langmuir 1998;14:3164᎐3174. future research, both theoretical and experimental. wx9 Preuss M, Butt H-J. Measuring the contact angle of individ- The studies on self-assembly of colloidal particles, ual colloidal particles. J. Colloid Interface Sci. 1998; 208:468᎐477. mediated by the action of capillary forces, develops wx along the following major directions: improving the 10 Ecke S, Preuss M, Butt H-J. Microsphere tensiometry to ⅷ measure advancing and receding contact angles on individ- w ⅷⅷx procedures for particle assembly in wetting films 72 ual particles. J. Adhesion Sci. Technol. 1999;13:1181᎐1191. w ⅷⅷx or in shrinking drops 106 , structuring on pat- Silanized silica spheres, 4.1 ␮m in diameter, were used. The dis- terned substrates or in capillary networks tance to which a sphere, attached to the AFM cantilever, jumps w85ⅷⅷ ,86᎐88 ⅷ ,89,90,92 ⅷⅷx , and self-assembly of float- into its equilibrium position at the air-liquid interface of a drop or ing non-spherical objects into complex 2D arrays an air bubble was measured. From these distances the contact w ⅷⅷ ⅷⅷx angles were calculated. No hysteresis was measured with micro- 41 ,102 . The obtained ordered structures of par- spheres, whereas a considerable hysteresis was established with ticles have found miscellaneous applications. similarly prepared planar silica surfaces. wx11 Preuss M, Butt H-J. Direct measurement of forces between particles and bubbles. Int. J. Miner. Process. 1999;56:99᎐115. wx12 Aveyard R, Clint JH. Liquid lenses at fluidrfluid interfaces. Acknowledgements J. Chem. Soc. Faraday Trans. 1997;93:1397᎐1403. wx13 Denkov ND, Cooper P, Martin J-Y. Mechanisms of action The authors are grateful to Dr Theodor Gurkov, of mixed solid-liquid antifoams. 1. Dynamics of foam film Ms Petia Vlahovska, Mr Krassimir Velikov, Mr rupture. Langmuir 1999;15:8514᎐8529. wx Stanislav Kotsev, Ms Denitza Lambreva and Mr 14 Denkov ND. Mechanisms of action of mixed solid-liquid ⅷ antifoams. 2. Stability of oil bridges in foam films. Langmuir Alexander Zdravkov, who helped to collect the litera- 1999;15:8530᎐8542. ture sources, as well as to Ms Mariana Paraskova for A new, ‘bridging-stretching’, mechanism of foam destruction by oil preparing the figures. drops was proposed based on systematic experimental investiga- tions. The small oil bridges in foam films are stable, whereas the larger bridges are unstableŽ. few milliseconds lifetime . Initially References and recommended reading stable small bridges could be later transformed into unstable ones due to the thinning of the foam films and the transfer of pre-spread ⅷ of special interest oil. ⅷⅷ of outstanding interest wx15 Denkov ND, Marinova KG, Christova C, Hadjiiski A, Cooper wx1 Yamaki M, Higo J, Nagayama K. Size-dependent separation P. Mechanisms of action of mixed solid-liquid antifoams: 3. ᎐ of colloidal particles in two-dimensional convective self-as- Exhaustion and reactivation. Langmuir 2000;16:2515 2528. wx sembly. Langmuir 1995;11:2975᎐2978. 16 Abramowitz M, Stegun IA. Handbook of mathematical wx2 Kralchevsky PA, Nagayama K. Capillary interactions functions. New York: Dover, 1965. wx ⅷ between particles bound to interfaces, liquid films and 17 Dimitrov AS, Miwa T, Nagayama K. A comparison between biomembranes. Adv. Colloid Interface Sci. 2000;85:145᎐192. the optical properties of amorphous and crystalline An overview, comparison and discussion of recent results, both monolayers of silica particles. Langmuir 1999;15:5257᎐5264. theoretical and experimental, about lateral capillary forces. wx18 Aveyard R, Clint JH, Paunov VN, Nees D. Capillary con- wx3 Kralchevsky PA, Nagayama K. Particles at fluid interfaces densation of vapours between two solid surfaces: effects of ⅷ and membranes: attachment of colloid particles and pro- line tension and surface forces. Phys. Chem. Chem. Phys. teins to interfaces and formation of two-dimensional arrays. 1999;1:155᎐163. Amsterdam: Elsevier, 2001. wx19 Orr FM, Scriven LE, Rivas AP. Pendular rings between Chapters 7᎐9: theory and experiment on lateral capillary forces. solids: meniscus properties and capillary force. J. Fluid Chapter 10: interactions between inclusions in lipid membranes. Mech. 1975;67:723᎐742. Chapter 11: capillary bridges and capillary-bridge forces. Chapter wx20 de Lazzer A, Dreyer M, Rath HJ. Particle ᎏ surface 12: capillary forces between particles of irregular contact line. capillary forces. Langmuir 1999;15:4551᎐4559. 398 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

wx21 Kolodezhnov VN, Magomedov GO, Mal’tsev GP. Refined forces: synthesis using the capillary bond. J. Am. Chem. Soc. determination of shape for the free surface of the liquid 1999;121:5373᎐5391. region in analysis of capillary interaction of powder parti- The interactions between floating hexagonal plates, 5.4 mm in cles. Colloid J. Russ. 2000;62:443᎐450. diameter, were experimentally examined. The faces of the plates wx22 Willett CD, Adams MJ, Johnson SA, Seville JPK. Capillary were functionalized to be hydrophilic or hydrophobic; in this way bridges between two spherical bodies. Langmuir 2000; various types of ‘capillary multipoles’ were realized. The strength 16:9396᎐9405. and the directionality of the interactions can be tailored by manipu- wx 23 Attard P. Thermodynamic analysis of bridging bubbles and a lating the geometric size and the pattern of hydrophobization. The quantitative comparison with the measured hydrophobic at- type of 2D lattice of the assemblies was investigated as a function traction. Langmuir 2000;16:4455᎐4466. of the sort of particles. wx 24 Yaminsky VV. Long range attraction in water vapor. Capil- wx42 Grzybowski BA, Bowden N, Arias F, Yang H, Whitesides ᎐ lary forces relevant to ‘polywater’. Langmuir 1997;13:2 7. GM. Modeling menisci and capillary forces from the mil- wx 25 Xiao X, Quian L. Investigation of humidity-dependent capil- limeter to the micrometer size range. J. Phys. Chem. B ᎐ lary force. Langmuir 2000;16:8153 8158. 2001;105:404᎐412. wx 26 Claesson PM, Dedinaite A, Bergenstahl˚ B, Campbell B, wx43 Kralchevsky PA, Paunov VN, Denkov ND, Nagayama K. Christenson H. Interaction between hydrophobic mica sur- Stresses in lipid membranes and interactions between inclu- faces in triolein: triolein surface orientation, solvation forces, sions. J. Chem. Soc. Faraday Trans. 1995;91:3415᎐3432. and capillary condensation. Langmuir 1997;13:1682᎐1688. wx44 Gil T, Ipsen JH, Mouritsen OG, Sabra MC, Sperotto MM, wx27 Petrov P, Olsson U, Wennerstrom¨ H. Surface forces in Zuckermann MJ. Theoretical analysis of protein organiza- bicontinuous microemulsions: water capillary condensation tion in lipid membranes. Biochim. Biophys. Acta 1998; and lamellae formation. Langmuir 1997;13:3331᎐3337. wx 1376:245᎐266. 28 Carambassis A, Jonker LC, Attard P, Rutland MW. Forces wx measured between hydrophobic surfaces due to a submi- 45 Mansfield SL, Gotch AJ, Harms GS, Johnson CK, Larive croscopic bridging bubble. Phys. Rev. Lett. 1998;80: CK. Complementary analysis of peptide aggregation by NMR 5357᎐5360. and time-resolved laser spectrometry. J. Phys. Chem. B ᎐ wx29 Considine RF, Hayes RA, Horn RG. Forces measured 1999;103:2262 2269. wx between latex spheres in aqueous electrolyte: Non-DLVO 46 Kralchevsky PA, Paunov VN, Nagayama K. Lateral capillary behavior and sensitivity to dissolved gas. Langmuir interaction between particles protruding from a spherical 1999;15:1657᎐1659. liquid layer. J. Fluid Mech. 1995;299:105᎐132. wx30 Considine RF, Drummond CJ. Long-range force of attrac- wx47 Maenosono S, Dushkin CD, Yamaguchi Y. Direct measure- tion between solvophobic surfaces in water and organic ment of the viscous force between two spherical particles liquids containing dissolved air. Langmuir 2000;16:631᎐635. trapped in a thin wetting film. Colloid Polym. Sci. wx31 Mahnke J, Stearnes J, Hayes RA, Fornasiero D, Ralston J. 1999;277:993᎐996. The influence of dissolved gas on the interactions between wx48 Velikov KP, Durst F, Velev OD. Direct observation of the surfaces of different hydrophobicity in aqueous media. Part ⅷ dynamics of latex particles confined inside thinning water᎐air I. Measurement of interaction forces. Phys. Chem. Chem. films. Langmuir 1998;14:1148᎐1155. Phys. 1999;1:2793᎐2798. Dynamics of micrometer-sized latex particles confined in thinning wx 32 Yakubov GE, Butt H-J, Vinogradova O. Interaction forces foam films was investigated. The behavior of the particles depend between hydrophobic surfaces. Attractive jump as an indica- on several experimental factors, incl. the type of surfactant. In tion of formation of ‘stable’ submicrocavities. J. Phys. Chem. some experiments the captured particles tended to form small 2D ᎐ B 2000;104:3407 3410. aggregates; the latter were observed to attract each other from wx 33 Ederth T. Substrate and solution effects on the long-range distances, which could reach up to 100 ␮m. This attraction was ‘hydrophobic’ interactions between hydrophobized gold sur- attributed to the lateral immersion force. At higher particle con- faces. J. Phys Chem. B 2000;104:9704᎐9712. wx centration the formation of ‘2D-foam’ structure was observed. 34 Ishida N, Sakamoto M, Miyahara M, Higashitani K. Attrac- wx49 Dietrich C, Angelova M, Pouligny B. Adhesion of latex tion between hydrophobic surfaces with and without gas spheres to giant phospholipid vesicles: statics and dynamics. phase. Langmuir 2000;16:5681᎐5687. J. Phys. II Fr. 1997;7:1651᎐1682. wx35 Ishida N, Inoue T, Miyahara M, Higashitani K. Nano bubbles wx50 Danov KD, Pouligny B, Angelova MI, Kralchevsky PA. on a hydrophobic surface in water observed by tapping-mode ⅷ Strong capillary attraction between spherical inclusions in a atomic force microscopy. Langmuir 2000;16:6377᎐6380. wx36 Chan DYC, Henry JD, White LR. The interaction of col- multilayered lipid membrane. In: Iwasawa Y, Oyama N, loidal particles collected at fluid interfaces. J. Colloid Inter- Kunieda H, editors. Amsterdam: Elsevier, 2001. face Sci. 1981;79:410᎐418. Strong attraction has been experimentally observed between two wx37 Paunov VN. On the analogy between lateral capillary inter- spherical latex particles, which are included in the membrane of a actions and electrostatic interactions in colloid systems. giant spherical phospholipid vesicle. This attraction was interpreted Langmuir 1998;14:5088᎐5097. as a lateral capillary force resulting from the overlap of the menisci wx38 Petkov JT, Danov KD, Denkov ND, Aust R, Durst F. formed around each of the two particles. The theoretical results Precise method for measuring the shear surface viscosity of about the force are in line with the experimentally observed trends. wx surfactant monolayers. Langmuir 1996;12:2650᎐2653. 51 Stamou D, Duschl C, Johannsmann D. Long-range attraction wx39 Petkov JT, Gurkov TD, Campbell BE, Measurement of the ⅷⅷ between colloidal spheres at the air-water interface: the yield stress of gel-like protein layers on liquid surfaces by consequence of an irregular meniscus. Phys. Rev. E means of an attached particle. Langmuir 2001, 17, in press. 2000;62:5263᎐5272. wx40 Bowden N, Terfort A, Carbeck J, Whitesides GM. Self-as- Theory of the interactions between floating spherical particles with sembly of mesoscale objects into ordered two-dimensional undulated contact lineŽ. ‘capillary multipoles’ is developed. A con- arrays. Science 1997;276:233᎐235. venient analytical expression is obtained for the energy of interac- wx41 Bowden N, Choi IS, Grzybowski BA, Whitesides GM. Meso- tion between two capillary quadrupoles. Frustrations of the forma- ⅷⅷ scale self-assembly of hexagonal plates using lateral capillary tion of some types of 2D lattices due to inadequate particle P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 399 orientations are discussed. The theoretical predictions are com- ⅷⅷ colloidal multilayers of controlled thickness. Chem. Mater. pared with experimental data for structuring of latex particles 1999;11:2132᎐2140. spread over the surface of water. A new efficient procedure for assembling silica spheres into single- wx52 Lucassen J. Capillary forces between solid particles in fluid crystal colloid layer, under the action of capillary forces, is de- interfaces. Colloids Surf. 1992;65:131᎐137. scribed. The method relies on a controlled evaporation of the liquid wx 53 Petkov JT, Gurkov TD, Campbell BE, Borwankar RP. Di- from a thin suspension layer spread over smooth solid substrate. latational and shear elasticity of gel-like protein layers on The thickness of the final particulate layer is determined by the r ᎐ air water interface. Langmuir 2000;16:3703 3711. particle concentration in the initial suspension layer. The depen- wx 54 Alfrey Jr. T, Bradford EB, Vanderhof JW, Oster G. Optical dence of the optical properties of the layers on their thickness and properties of uniform particle-size latexes. J. Optical Soc. particle diameter is studied. ᎐ Am. 1954;44:603 609. wx73 Zhao Y, Avrutsky I. Two-dimensional colloidal crystal cor- wx 55 Vanderhoff JW, Bradfod EB, Carrington WK. The transport rugated waveguides. Optics Lett. 1999;24:817᎐819. of water through latex films. J. Polymer Sci. Symp. 1973; wx74 Zhao Y, Avrutsky I, Li B. Optical coupling between 41:155᎐174. ⅷ monocrystalline colloidal crystals and a planar waveguide. wx56 Horne RW. The formation of virus crystalline and paracrys- Appl. Phys. Lett. 1999;75:3596᎐3598. talline arrays for electron microscopy and image analysis. The optical properties of the structure ‘planar wave-guider2D Adv. Virus Res. 1979;24:173᎐221. colloid crystal’ are studied and discussed with respect to possible wx57 Harris JR. The negative staining-carbon film procedure: applications in optical elements. technical considerations and a survey of macromolecular wx75 Burmeister F, Schafle¨ C, Keilhofer B, Bechinger C, Boneberg applications. Micron Microscopica Acta 1991;22:341᎐359. J, Leiderer P. From mesoscopic to nanoscopic surface struc- wx58 Yoshimura H, Matsumoto M, Endo S, Nagayama K. Two-di- tures: lithography with colloid monolayers. Adv. Mater. mensional crystallization of proteins on mercury. Ultrami- 1998;10:495᎐497. croscopy 1990;32:265᎐274. wx76 Burmeister F, Badowsky W, Braun T, Wieprich S, Boneberg wx59 Nagayama K. Two-dimensional self-assembly of colloids in thin liquid films. Colloids Surfaces A 1996;109:363᎐374. ⅷ J, Leiderer P. Colloid monolayer lithography-a flexible ap- wx60 Denkov ND, Velev OD, Kralchevsky PA, Ivanov IB, Yoshi- proach for nanostructuring of surfaces. Appl. Surface Sci. r ᎐ mura H, Nagayama K. Mechanism of formation of two-di- 1999;144 145:461 466. mensional crystals from latex particles on substrates. Lang- Two new, more advanced procedures for application of particle muir 1992;8:3183᎐3190. monolayers as lithographic masks are described and discussed. wx wx61 Denkov ND, Velev OD, Kralchevsky PA, Ivanov IB, Yoshi- 77 Antonietti M, Hartmann J, Neese M, Seifert U. Highly mura H, Nagayama K. Two-dimensional crystallization. Na- ordered size-dispersive packings of polydisperse microgel ᎐ ture 1993;361:26. spheres. Langmuir 2000;16:7634 7639. wx wx62 Dushkin CD, Nagayama K, Miwa T, Kralchevsky PA. Col- 78 Lazarov GS, Denkov ND, Velev OD, Kralchevsky PA, Na- ored multilayers from transparent submicrometer spheres. gayama K. Formation of two-dimensional structures from Langmuir 1993;9:3695᎐3701. colloid particles on fluorinated oil substrate. J. Chem. Soc. wx63 Dushkin CD, Lazarov GS, Kotsev SN, Yoshimura H, Na- Faraday Trans. 1994;90:2077᎐2083. gayama K. Effect of growth conditions on the structure of wx79 Denkov ND, Yoshimura H, Nagayama K, Kouyama T. two-dimensional latex crystals: experiment. Colloid Polym. Nanoparticle arrays in freely suspended vitrified films. Phys. Sci. 1999;277:914᎐930. Rev. Lett. 1996;76:2354᎐2357. wx64 Maenosono S, Dushkin CD, Yamaguchi Y, Nagayama K, wx80 Denkov ND, Yoshimura H, Nagayama K. Method for con- Tsujii Y. Effect of growth conditions on the structure of trolled formation of vitrified films for cryo-electron micros- two-dimensional latex crystals: modeling. Colloid Polym. Sci. copy. Ultramicroscopy 1996;65:147᎐158. ᎐ 1999;277:1152 1161. wx81 Denkov ND, Yoshimura H, Kouyama T, Walz J, Nagayama wx 65 Dimitrov AS, Nagayama K. Continuous convective assem- K. Electron cryomicroscopy of Bacteriorhodopsin vesicles: bling of fine particles into two-dimensional arrays on solid Mechanism of vesicle formation. Biophys. J. 1998;74: ᎐ surfaces. Langmuir 1996;12:1303 1311. 1409᎐1420. wx 66 Micheletto R, Fukuda H, Ohtsu M. A simple method for the wx82 Hulteen JC, van Duyne RP. Nanosphere lithography-a ma- production of two-dimensional, ordered array of small latex terials general fabrication process for periodic particle array particles. Langmuir 1995;11:3333᎐3336. surfaces. J. Vac. Sci. Technol. A 1995;13:1553᎐1558. wx67 Sasaki M, Hane K. Ultrasonically facilitated two-dimen- wx83 Almgren M, Edwards K, Karlsson G. Cryo transmission sional crystallization of colloid particles. J. Appl. Phys. 1996; electron microscopy of liposomes and related structures. 80:5427᎐5431. Colloids Surf. A 2000;174:3᎐21. wx68 Matsushita S, Miwa T, Fujishima A. Distribution of compo- wx nents in composite two-dimensional arrays of latex particles 84 Xia Y, Tien J, Qin D, Whitesides GM. Non-lithographic and evaluation in terms of the fractal dimension. Langmuir methods for fabrication of elastomeric stamps for use in ᎐ 1997;13:2582᎐2584. microcontact printing. Langmuir 1996;12:4033 4038. wx wx69 Picard G. Fine particle 2D-crystals prepared by dynamic 85 Aizenberg J, Braun PV, Wiltzius P. Patterned colloidal thin laminar flow method. Langmuir 1997;13:3226᎐3234. ⅷⅷ deposition controlled by electrostatic and capillary forces. wx70 Du H, Chen P, Liu F, Meng F-D, Li T-J, Tang X-Y. Phys. Rev. Lett. 2000;84:2997᎐3000. Preparation and assembly of nanosized polymer latex. Mater. Chemically micropatterned solid substrates, with cationic and an- Chem. Phys. 1997;51:277᎐282. ionic regions, are used to localize the deposition of charged colloid wx71 Cardoso AH, Leite CAP, Zaniquelli MED, Galembeck F. particles. Direct microscope observations show that the attachment Easy polymer latex self-assembly and colloidal crystal forma- of the particles to wet substrates leads to formation of loose tion: the case of polyw styrene-co-Ž 2-hydroxyethyl methacry- clusters on the oppositely charged regions. The subsequent drying late.x . Colloids Surf. A 1998;144:207᎐217. of the substrate leads to compaction of the particles into well wx72 Jiang P, Bertone JF, Hwang KS, Colvin VL. Single crystal ordered clusters under the action of the immersion capillary force. 400 P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401

wx86 Lin K, Crocker JC, Prasad V et al. Entropically driven hexagonal rod arrays based on capillary forces. J. Colloid colloidal crystallization on patterned surfaces. Phys. Rev. Interface Sci. 2000;224:425᎐428. Lett. 2000;85:1770᎐1773. wx101 Bowden N, Arias F, Deng T, Whitesides GM. Self-assembly wx87 Chen KM, Jiang X, Kimerling LC, Hammond PT. Selective of microscale objects at a liquidrliquid interface through self-organization of colloids on patterned polyelectrolyte lateral capillary forces. Langmuir 2001;17:1757᎐1765. templates. Langmuir 2000;16:7825᎐7834. wx102 Bowden N, Oliver SRJ, Whitesides GM. Mesoscale self-as- wx 88 Qin D, Xia Y, Xu B, Yang H, Zhu C, Whitesides GM. ⅷⅷ sembly: capillary bonds and negative menisci. J. Phys. Chem. ⅷ Fabrication of ordered two-dimensional arrays of micro- and 2000;104:2714᎐2724. nanoparticles using patterned self-assembled monolayers as A systematic experimental investigation of the possible structures templates. Adv. Mater. 1999;11:1433᎐1437. formed by a self-assembly of hexagonal plates at the interface Drops deposited on the hydrophilic domains of a patterned surface between perfluorodecalin and water is performed. All 14 different are used as micro-reactors for confined crystallization or precipita- hexagons that can be made by permuting the number and location tion, so that perfectly ordered 2D arrays of micro- and nano-par- of the hydrophobic and hydrophilic side faces were examined. The ticles are formed on gold substrates. Both the spatial distribution role of the plate mass densityŽ which affects the shape of the and the dimension of the solid particles can be easily controlled. meniscus and thereby the lateral capillary force. is also discussed. wx ⅷⅷ 89 Zhong Z, Gates B, Xia Y. Soft lithographic approach to the Complements referencew 41x . fabrication of highly ordered 2D arrays of magnetic wx103 Huck WTS, Tien J, Whitesides GM. Three-dimensional nanoparticles on the surfaces of silicon substrates. Langmuir ⅷ mesoscale self-assembly. J. Am Chem. Soc. 1998;120: ᎐ 2000;16:10369 10375. 8267᎐8268. wx 90 Massey JA, Winnik MA, Manners I et al., Fabrication of A tailored procedure, including a stage of particle assembly on the oriented nanoscopic ceramic lines from cylindrical micelles surface of an emulsion drop under the action of lateral capillary of an organometallic polyferrocene block copolymer. J. Am. force between multipoles, was applied to produce a closed spherical Chem. Soc. 2001, 123, in press. shell of metal hexagonal ringsŽ. viral-type structure . This assembly wx 91 Spatz JP, Herzog T, Moßmer S, Ziemann P, Moller¨ M. was reinforced by electrodeposition, so that the final aggregate was ᎏ Micellar inorganic-polymer hybrid systems a tool for sufficiently strong to sustain drying and to remain intact in air. ᎐ nanolithography. Adv. Mater. 1999;11:149 153. wx104 Velev OD, Furusawa K, Nagayama K. Assembly of latex wx 92 Kim E, Xia Y, Whitesides GM. Micromolding in capillaries: particles by using emulsion droplets as templates. 1. Mi- ⅷⅷ applications in materials science. J. Am. Chem. Soc. crostructured hollow spheres. Langmuir 1996;12:2374᎐2384. ᎐ 1996;118:5722 5731. wx105 Velev OD, Furusawa K, Nagayama K. Assembly of latex A versatile process for fabricating microstructures of polymers, particles by using emulsion droplets as templates. 2. Ball-like ceramics, metals and microparticles is described. A network of and composite aggregates. Langmuir 1996;12:2385᎐2391. interconnected channels is formed by using a PDMS stamp. An wx106 Velev OD, Lenhoff AM, Kaler EW. A class of microstruc- appropriate precursor liquidŽ. or particle suspension spontaneously ⅷⅷ tured particles through colloidal crystallization. Science penetrates the channels under the action of a capillary suction 2000;287:2240᎐2243. pressure. The solidifying of the material in the channels and the A new method for fabrication of highly ordered, microstructured subsequent stamp removal results in a patterned substrate or in a materials is described. A drop of aqueous suspension, floating on free-standing film with structure complementary to that of the the surface of fluorinated oil, is used as a template, in which stamp. 3D-colloid crystal is formed. The crystallization is induced by the wx93 Park SH, Qin D, Xia Y. Crystallization of mesoscale particles shrinking surface of the aqueous dropŽ as a result of a controlled ⅷ over large areas. Adv. Mater. 1998;10:1028᎐1032. water evaporation. , which imposes a capillary force compressing A new procedure for fabrication of relatively large crystalline layers the particles against each other. Particle assemblies with spherical, of colloid particles is described. The particles are close-packed in a ellipsoidal and toroidal shape were produced. slit formed between two glass plates under the action of a hydrody- wx107 Deegan RD, Bakajin O, Dupont TF, Huber G, Nagel SR, namic drag force. Sonication of the sample is used during the ordering process to improve the crystal quality. Witten TA. Capillary flow as the cause of ring stains from ᎐ wx94 Patil V, Malvankar RB, Sastry M. Role of particle size in dried liquid drops. Nature 1997;389:827 829. wx individual and competitive diffusion of carboxylic acid 108 Uno K, Hayashi K, Hayashi T, Ito K, Kitano H. Particle derivatized colloidal gold particles in thermally evaporated adsorption in evaporating droplets of polymer latex disper- fatty amine films. Langmuir 1999;15:8197᎐8206. sions on hydrophilic and hydrophobic surfaces. Colloid Po- ᎐ wx95 Patil V, Sastry M. Formation of close-packed silver nanopar- lym. Sci. 1998;276:810 815. wx ticle multilayers from electrostatically grown octadecy- 109 Maenosono S, Dushkin CD, Saita S, Yamaguchi Y. Growth laminercolloid nanocomposite precursors. Langmuir 2000; of a semiconductor nanoparticle ring during the drying of a 16:2207᎐2212. suspension droplet. Langmuir 1999;15:957᎐965. wx96 Xia Y, Rogers AJ, Paul KE, Whitesides GM. Unconventio- wx110 Ohara PC, Gelbart WM. Interplay between hole instability nal methods for fabricating and patterning nanostructures. and nanoparticle array formation in ultrathin liquid films. Chem. Rev. 1999;99:1823᎐1848. Langmuir 1998;14:3418᎐3424. wx97 Choi IS, Bowden N, Whitesides GM. Shape-selective recog- wx111 Ohara PC, Heath JR, Gelbart WM. Self-assembly of submi- nition and self-assembly of mm-scale components. J. Am. crometer rings of particles from solutions of nanoparticles. Chem. Soc. 1999;121:1754᎐1755. Angew. Chem. Int. Ed. Engl. 1997;36:1078᎐1080. wx98 Choi IS, Bowden N, Whitesides GM. Macroscopic, hierar- wx112 Onoda GY. Direct observation of two-dimensional dynamic chical, two-dimensional self-assembly. Angew. Chem. Int. clustering and ordering with colloids. Phys. Rev. Lett. Ed. 1999;38:3078᎐3081. 1985;55:226᎐229. wx99 Wu H, Bowden N, Whitesides GM. Selectivities among wx113 Horvolgyi´¨ Z, Nemeth ´ S, Fendler JH. Monoparticulate layers capillary bonds in mesoscale self-assembly. Appl. Phys. Lett. of silanized glass spheres at the water-air interface: 1999;75:3222᎐3224. particle-particle and particle-subphase interactions. Lang- wx100 Oliver SRJ, Bowden N, Whitesides GM. Self-assembly of muir 1996;12:997᎐1004. P.A. Kralche¨sky, N.D. Denko¨rCurrent Opinion in Colloid & Interface Science 6() 2001 383᎐401 401 wx114 Aveyard R, Clint JH, Nees D, Paunov VN. Compression and wx127 Holland BR, Blanford CF, Do T, Stein A. Synthesis of structure of monolayers of charged latex particles at air- ⅷ highly ordered, three-dimensional, macroporous structures water and octane-water interfaces. Langmuir 2000;16: of amorphous or crystalline inorganic oxides, phosphates, 1969᎐1979. and hybrid composites. Chem. Mater. 1999;11:795᎐805. wx115 Aveyard R, Clint JH, Nees D, Quirke N. Structure and Highly ordered, porous oxides of Si, Ti, Zr, Al, W, Fe, Sb, and ⅷ collapse of particle monolayer under lateral pressure at the ZrrY mixture, were produced from metal alkoxide precursors octaneraqueous surfactant solution interface. Langmuir templated around latex spheres, which were assembled in a 3D 2000;16:8820᎐8828. colloid crystal. Depending on the conditions during the subsequent The structure and collapse of particle monolayers, spread on the calcination, amorphous or crystal forms of these oxides were ob- octanerwater interface, is studied in a modified Langmuir trough. tained. Aluminophosphates and silicates, whose surface was grafted It is proven experimentally that the layers collapse by buckling, with organic molecules, were also produced. when the particle-particle repulsive forceŽ. per unit length becomes wx128 Jiang P, Hwang KS, Mittelman DM, Bertone JF, Colvin VL. equal to the tension of the fluid interface. ⅷ Template-directed preparation of macroporous polymers wx116 Ruiz-Garcia J, Gamez-Corrales´ R, Ivlev BI. Foam and clus- with oriented and crystalline arrays of voids. J. Am. Chem. ⅷ ter structure formation by latex particles at the airrwater Soc. 1999;121:11630᎐11637. interface. Physica A 1997;236:97᎐104. A versatile procedure for production of highly porous polymer The formation of 2D foam and cluster structures by latex particles membranes with periodic regular structure, by using silica colloid spread over aqueous sub-phase was reported. The unusual observa- crystals as templates, is described. The optical properties of these tion here was the large interparticle separation, which implies the membranes are studied and their possible applications in optics and presence of a very long-range attractive force. The authors ex- separation technologies are discussed. plained their results with the interplay of electrostatic repulsion wx129 Velev OD, Tessier PM, Lenhoff AM, Kaler EW. A class of and van der Waals attraction, but the theoretical estimates suggest porous metallic nanostructures. Nature 1999;401:548. that probably lateral capillary forceŽ between multipolesw 51ⅷⅷx or wx130 Velev OD, Kaler EW. Structured porous materials via col- ⅷ of immersion typew 48 ,78x. could be involved in this phenomenon. ⅷ loidal crystal templating: from inorganic oxides to metals. wx117 Ruiz-Garcia J, Gamez-Corrales´ R, Ivlev BI. Formation of Adv. Mater. 2000;12:531᎐534. two-dimensional colloidal voids, soap froths, and clusters. A concise and comprehensive review on the various procedures for Phys. Rev. E 1998;58:660᎐663. fabrication of structured porous materials by using colloidal crystals wx118 Ghezzi F, Earnshaw JC. Formation of meso-structures in as templates. The potential applications of these materials are colloidal monolayers. J. Phys.: Condens. Matter 1997;9: briefly outlined. L517᎐L523. wx131 Tessier PM, Velev OD, Kalambur AT, Rabolt JF, Lenhoff wx119 Hayashi S, Kumamoto Y, Suzuki T, Hirai T. Imaging by AM, Kaler EW. Assembly of gold nanostructured films polystyrene latex particles. J. Colloid Interface Sci. 1991; templated by colloidal crystals and use in surface-enhanced 144Ž. 2 :538᎐547. Raman spectroscopy. J. Am. Chem. Soc. 2000;122: wx120 Matsushita SI, Yagi Y, Miwa T, Tryk DA, Koda T, Fu- 9554᎐9555. ⅷ jishima A. Light propagation in composite two-dimensional wx132 Wijnhoven JEGJ, Zevenhuizen SJM, Hendriks MA, Van- arrays of polystyrene spherical particles. Langmuir maekelbergh D, Kelly JJ, Vos WL. Electrochemical assem- 2000;16:636᎐642. bly of ordered macropores in gold. Adv. Mater. 2000;12: 2D colloid crystals, with single fluorescent particles incorporated as 888᎐890. light sources, were produced, and the light propagation inside these wx133 Deckman HW, Dunsmuir JH, Garoff S, Mchenry JA, Peiffer structures was studied. Two modes of light propagation are distin- DG. Macromolecular self-organized assemblies. J. Vac. Sci. guished-one propagating inside the particles and another one, Technol. B 1988;6:333᎐336. caused by the field of the evanescent wave outside the particle wx134 Winnik MA. The formation and properties of latex films. In: surface. The relative contribution of these two modes depends on Lovell PA, El-Aasser MS, editors. Emulsion Polymerization the ratio particle sizerlight wavelength. and Emulsion Polymers. New York: Wiley, 1997:468᎐518. wx121 Yagi Y, Matsushita SI, Tryk DA, Koda T, Fujishima A. wx135 Winnik MA. Latex film formation. Curr. Opinion Colloid Observation of light propagation in single layers of compos- Interface Sci. 1997;2:192᎐199. ite two-dimensional arrays. Langmuir 2000;16:1180᎐1184. wx136 Keddie JL. Film formation of latex. Mater. Sci. Eng. wx122 Park SH, Xia Y. Assembly of mesoscale particles over large ⅷ 1997;21:101᎐107. areas and its application in fabricating tunable optical filters. A comprehensive review on the mechanisms of film formation by Langmuir 1999;15:266᎐273. latex particles with detailed and analytical account of the various wx123 Yamasaki T, Tsutsui T. Spontaneous emission from fluo- experimental methods and results. rescent molecules embedded in photonic crystals consisting wx137 Visschers M, Laven J, German AL. Current understanding of polystyrene microspheres. Appl. Phys. Lett. 1998;72 of the deformation of latex particles during film formation. Prog. Ž.16 :1957᎐1959. Org. Coating 1997;30:39᎐49. wx124 Velev OD, Jede TA, Lobo RF, Lenhoff AM. Porous silica wx138 Du Chesne A, Bojkova A, Stockelmann¨ E, Krieger S, Held- via colloidal crystallization. Nature 1997;389:447᎐448. mann C. Determining the compacting of latex films upon wx125 Velev OD, Jede TA, Lobo RF, Lenhoff AM. Microstruc- drying by interference measurements ᎏ an approach for tured porous silica obtained via colloidal crystal templates. the investigation of film formation. Acta Polym. 1998;49: Chem. Mater. 1998;10:3597᎐3602. 346᎐355. wx126 Holland BT, Blanford CF, Stein A. Synthesis of macrop- wx139 Miyaki M, Fujimoto K, Kawaguchi H. Cell response to orous minerals with highly ordered three-dimensional arrays micropatterned surfaces produced with polymeric micro- of spheroidal voids. Science 1998;281:538᎐540. spheres. Colloids Surf. A 1999;153:603᎐608.