Nanomedicine, Volume I: Basic Capabilities

© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999


9.2.3 Immersive Adhesion Forces

For hydrophilic particles exposed to high humidity, or immersed and then withdrawn from a fluid, a liquid film can form on the surface of the particle by capillary condensation or by capillary action between particle and surface. For a spherical particle of radius r linked by a liquid bridge to a planar surface of the same material with contact area A, separation zsep, and liquid surface tension g, then the capillary force between sphere and plane is Fcapillary ~ 2 g A / zsep for small contact angles between the liquid and the surfaces.1147 Assuming hydrophilic (wettable) surfaces with wetting coefficient cos(q) as defined in Section 9.2.4 and zsep << r, the capillary force is given approximately by:1146,1147,1149

{Eqn. 9.14}

which has been confirmed experimentally by direct measurement.1149 For the water-air interface, cos(q) ~ 1 and surface tension g = 75.6 x 10-3 N/m at the freezing point (273 K), 72.75 x 10-3 N/m at room temperature (293 K), 70.05 x 10-3 N/m at human body temperature (~310 K), 58.90 x 10-3 N/m at the boiling point at 1 atm (373 K), and 110 x 10-3 N/m for ice at 273 K.763,1149 Thus at room temperature, the capillary force on an r = 0.5 micron particle is Fcapillary ~ 460 nN; an r = 10 nm particle feels Fcapillary ~ 9 nN, a rather substantial force. Liquid bridges containing dissolved substances may evaporate and create solid crystalline bridges. Hydrophobic surfaces are generally unaffected by capillary forces.1146

Eqn. 9.14 also applies to nanorobots that are caught in an air-liquid interface such as the surface of a puddle of water, alveolar fluids in the lung, or an epidermal pool of sweat. However, adding capillary-active solute to a solvent may lower surface tension considerably. For dilute surface concentrations of a solute of molecular area Amol in solvent of surface tension g0 at temperature T, the resulting surface tension of the solution drops to:390

{Eqn. 9.15}

For palmitic or stearic acid (e.g., soap), Amol ~ 0.21 nm2;2178 added to water (g0 = 70.05 x 10-3 N/m) at 310 K, surface tension falls to g = 49.70 x 10-3 N/m. More concentrated solutions further reduce surface tension, nonlinearly with concentration. For example, g ~ 25 x 10-3 N/m for a 0.1 M aqueous fatty-acid solution of hexanoic acid (CH3(CH2)4COOH; MW = 116 daltons), a total of ~6 x 107 molecules, ~0.01 micron3, or ~0.01 picograms of hexanoic acid per micron3 of solution.390 For the aqueous solution-air interface, inorganic electrolytes (e.g., NaCl), organic acid salts, low-MW bases, and certain nonvolatile nonelectrolytes such as glucose and glycerin are capillary inactive.390

Surface tension is reduced even more dramatically by biological surfactants. Lung surfactant, whose activity is largely attributed to the phospholipid palmitoylphosphatidylcholine,996 produces a nonlinear change in surface tension with area. As the lungs fill with air, more-inflated alveoli have higher g's than less-inflated alveoli, serving to stabilize alveoli of different sizes.526 Aqueous solutions of surfactant from mammalian lung extracts show a surface tension reduction to as low as g ~ 0.7 x 10-3 N/m at 20% of maximum film distension.2179 Survanta, an intratracheal pulmonary surfactant commonly used in the treatment of respiratory distress syndrome (aka. hyaline membrane disease) in premature infants, lowers minimum aqueous surface tension to g <~ 8 x 10-3 N/m.2119

Adhesion forces are greatly reduced for particles and surfaces that remain completely immersed in liquid. Surface tension effects are largely eliminated.1146,1147 Electrostatic image forces (Eqns. 9.9 and 9.10), already quite small, are further reduced by a factor of ke-1 ~ 1-2% (ke = 74.3 for pure water at 310 K, usually reduced to ~40 in a hydrophobic environment). Electrostatic contact forces may be greatly reduced because of sorption phenomena which tend to shield the charges (Sections 3.5.1 and 4.7.1). For particles and plates made of the same material, charges generally form the same double layers on both surfaces so that the double layer interactions are repulsive, thus reducing the net adhesive force, by an amount:1146

{Eqn. 9.16}

where k = 0.01381 zJ/K (Boltzmann constant), T is temperature, r is particle radius, cion is the volumetric charge density of ions in the liquid, and xcontact is the double layer thickness. Taking T = 310 K, r = 0.5 micron, cion ~1026 ions/m3 (~1% or 0.15M NaCl aqueous solution, ~human blood), and xcontact ~ 0.8 nm (~Kdh-1; Section 3.5.1), then Fshield ~ 34 nN. (Effective double layer thickness xcontact ~ 1 nm for a 0.1M solution of univalent electrolyte, ~10 nm for a 0.001M solution.1162) While different ions may collect in various alignments at unlike surfaces so that attractive (i.e.,contributing to adhesion) or repulsive shielding forces are possible, in most cases involving nanodevice surfaces that are fully immersed in human body fluids the electrostatic contact forces should be quite small.

The van der Waals force is also moderately reduced in fluids. For example, van der Waals adhesion between two diamondoid nanodevice surfaces fully immersed in water is only half of its vacuum value because the Hamaker constant (Eqn. 9.2) is reduced from 340 zJ to 153 zJ. Blood cells are subject to similar forces. It has been proposed that the ~15 nm gap frequently observed between the surfaces of aggregated red cells represents the position of the potential energy minimum where the forces of electrostatic repulsion (between negatively charged red cells) and the van der Waals attractive forces are equal.1162 Taking H = 5 zJ, rred = 3 microns and zsep = 15 nm in Eqn. 9.7, the net attractive force between red cells is FvdW ~ 0.01 nN.

Surface force experiments have demonstrated molecular control of adhesion at a fine level.1152 According to the commonly-used JKR theory,1155 the mechanical force needed to separate two elastic spheres each of radius r already adhered by molecular contact is:

{Eqn. 9.17}

where Wadhesion is the Dupre reversible work of adhesion (energy per unit area). For example, hydrocarbon rubber spheres display Wadhesion = 71 x 10-3 J/m2 in air but only 6.8 x 10-3 J/m2 in water. When sodium dodecyl sulfate1155 or dodecylammonium chloride3546 is added to the water so the liquid can wet the surface, Wadhesion actually becomes negative -- the surfaces are pushed apart by the intervening fluid. Nonwetting liquids increase adhesion. For instance, polydimethyl siloxane rubber has Wadhesion = 43.6 x 10-3 J/m2 to itself, in air. In water, a nonwetting liquid, adhesion nearly doubles to 74 x 10-3 J/m2; in methanol, a wetting liquid, adhesion is almost eliminated, falling to 6 x 10-3 J/m2.1160 In nanomedical engineering applications where minimization of adhesive forces is an important design objective, adhesion of specific classes of materials may be virtually eliminated by surface modifications that reduce Wadhesion, as is commonplace in biological surfaces and in engineered capillary coatings designed to reduce electroosmotic drag force during capillary zone electrophoresis.1229


Last updated on 20 February 2003