Lateral capillary force

We will describe two mesoscale, self-assembling systems in which the interactions between objects are based on capillary forces. The first is based on polyhedral polydimethylsiloxane (PDMS) objects at a perfluorodecalin (PFD)/H20 interface. These objects have their faces patterned to be either hydrophobic or hydrophilic, and they assemble via lateral capillary forces that originate from interactions between these faces (Fig. 4. la). The second system uses polyhedral objects that are suspended in water and have selected faces covered with a water-insoluble liquid - either a hydrophobic organic liquid or a liquid metal solder these objects assemble via capillary forces into three-dimensional (3D) structures (Fig. 4.1b). 

Figure 4.1. Systems in MESA (a) the self-assembly of two objects at the PFD/H20 interface through lateral capillary forces, and (b) the self-assembly of two objects in water with a hydrophobic liquid coating one face on each. In both systems, the objects may initially come into partial contact lateral movement of the faces increases the area of contact. The thick lines indicate hydrophobic faces, and the thin lines indicate...

Lateral capillary forces have several useful characteristics. First, the characteristic length for decay of the menisci (from a face several millimeters in width and height) is of the order of a millimeter. Objects of this size are easy to fabricate and to observe. Second, capillary forces are well understood. Their description by the Laplace equation is clear, although often mathematically intractable [ref. 2], Third, capillary forces are comparable in strength to shear... 

An advantage of using capillary forces in MESA is that they can be used at a variety of size scales. In previous work lateral capillary forces have been used to cause the assembly of objects ranging from millimeter-sized PDMS objects, to micron-sized polystyrene beads, to nanometer-sized proteins, into 2D arrays [refs. 7, 32, 33]. Although not all of the assemblies have taken place at a PFD/H20 interface, it should be possible to do so. 

A hydrophobic mismatch between a membrane protein and the surrounding lipids may create a lateral force that would pull membrane proteins together. A general theoretical description of this force, referred to as a lateral capillary force, has been presented by Kralchevsky and co-workers (Kralchevsky, 1997 Kralchevsky and Nagayama, 2000). Although experimental verification of this force for membrane proteins in a bilayer has not been demonstrated, the force can be observed in larger systems, such as 1.7 fim latex beads at an air/water interface, and would be expected to operate on membrane proteins (Kralchevsky, 1997). 

Fig. 6. Lateral capillary forces can assist protein-protein associations. A meniscus is formed around each TM protein when the hydrophobic regions of the protein (black regions) are not the same length as the hydrophobic regions of the membrane. The unfavorable deformation can, in part, be relieved by the lateral association of two proteins, which reduces the surface area the proteins expose to lipids.

N. Bowden, l.S. Choi, B.A. Grzybowski, G.M. Whitesides, Mesoscale Self-Assembly of Hexagonal Plates Using Lateral Capillary Forces Synthesis Using the Capillary Bond , J. Am. Chem. Soc., 121, 5373 (1999)... 

Lateral Capillary Forces between Particles Attached to Interfaces... 

FIGURE 5.17 Flotation (a, c, e) and immersion (b, d, f) lateral capillary forces between two particles attached to fluid interface (a) and (b) are two similar particles (c) is a light and a heavy particle (d) is a hydrophibc and a hydrophobic particle (e) is small floating particles that do not deform the interface (f) is small particles captured in a thin liquid film deforming the interfaces due to the wetting effects. 

In the case of interactions between inclusions in lipid bilayers (Figure 5.19) the elasticity of the bilayer interior must also be taken into account. The calculated energy of capillary interaction between integral membrane proteins turns out to be of the order of several Hence, this interaction can be a possible explanation of the observed aggregation of membrane proteins. The lateral capillary forces have been calculated also for the case of particles captured in a spherical (rather than planar) thin liquid film or vesicle. ... 

Lateral capillary forces between vertical cylinders or between spherical particles have been measured by means of sensitive electromechanical balance, piezotransducer balance,and torsion microbalance. Good agreement between theory and experiment has been established. 

FIGURE 5.20 Special types of immersion capillary forces (a) The contact line attachment to an irregular edge on the particle surface produces undulations in the surrounding fluid interface, which give rise to lateral capillary force between the particles, (b) When the size of particles entrapped in a hquid film is much greater than the nonperturbed fihn thickness, the meniscus surfaces meet at a finite distance, r in this case, the capillary interaction begins at L < 2rp. 

Two types of boundary conditions at the wall are analyzed theoretically fixed contact fine (Figure 5.21) or, alternatively, fixed contact angle. In particular, the lateral capillary force exerted on the particle depicted in Figure 5.21 is given by the following asymptotic expression... 

N. Bowden, F. Arias, T. Deng, and G. M. Whitesides, Self-assembly of microscale objects at a liquid/liquid interface through lateral capillary forces. Langmuir 17 p. 1757-1765 (2001). 

Rothemund. P.W.K. Using lateral capillary forces to 27. compute by self-assembly. Proc. Natl. Acad. Sci. U. S. 

Fluidic forces are also exerted on solids at a fluid/fluid interface. Lateral capillary force causes failure of many microstractures during fabrication and release. Constructively, lateral capillary force can be used to assemble large number of identical parts in repeated array. 

Velev OD, Denkov ND, Paunov VN, Kralchevsky PA, Nagayama K (1993) Direct measurement of lateral capillary forces. Langmuir 9 3702... 

The immersion force appears not only between particles in wetting films (Figure 4.21b and d), but also in symmetric fluid films (Figure 4.21f). The theory provides the following asymptotic expression for calculating the lateral capillary force between two particles of radii / , and / 2 separated by a center-to-center distance L [37,288-293] ... 

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