2007_01_12_15_38_07.pdf2007_01_12_15_39_29.pdfCHAPTER 70 CONTRASTS BETWEEN INTERMOLECULAR, INTERPARTICLE AND INTERSURFACE FORCES 10.1 SHORT RANGE AND LONG-RANGE EFFECTS OF A FORCE We are told that when an apple fell on Newton's head it set in motion a thought process that eventually led Newton to formulate the law of gravity. The conceptual breakthrough in this discovery was the recognition that the force that causes apples to fall is the same force that holds the moon in a stable orbit around the earth. On earth, gravity manifests itself in many different ways: in determining the height of the atmosphere; the capillary rise of liquids, and the behaviour of waves and ripples. In biology it decrees that animals that Jive in the sea (where the effect of gravity is almost negligible) can be larger than the largest possible land animal; that heavy land animals such as elephants must have short thick legs while a man or a spider can have proportionately long thin legs; that larger birds must have progressively larger wings (e.g., eagles and storks) while smaller birds, flies and bees can have relatively small light wings; that only small animals can carry many times their own weight (e.g., ants), and much else (Thompson, 1968). But beyond the immediate vicinity of the earth's surface and out to the outer reaches of space this same force now governs the orbits of planets, the shapes of nebulae and galaxies, the rate of expansion of the universe, and, ultimately, its age. The first group of phenomena-those occurring locally on the earth's surface --may be though t of as the short-range effects of the gravitational force, while the second and very different types of phenomena occurring on a cosmological scale may be thought of as the long-range effects of gravity. Intermolecular forces are no less versatile in the way the same force can have very different effects at short and long range, though here 'short range' usually means at or very close to molecular contact « I nm) while 'long-range' forces are rarely important beyond 100 nm (0.1 11m). In Part I we saw that the properties of gases and the cohesive strengths of condensed 152 CONTRA' phases are det, contact w(o-), For example, t is at least 64 tir compared to 1/ in that the ener However, in a of the Coulo! electroneutralit We may thel properties of ~ binding forces molecular coni distance depen A very diffe macroscopic p, the molecules i: energy is prop energy can be more, and (ii) the separation macroscopic b molecules even case. Furthermofi repulsive) then form of the I illustrated in F of Fig. 10.la. interaction, be properties of 2 be determined adhesion eneq two molecules small compan each other sine circumstances though the ulti We thus enl particle intera, in some kinetic that prevents tINTERPARTICLE j it set in motion a e the law of gravity. recognition that the rolds the moon in a lays: in determining >, and the behaviour ; that live in the sea rger than the largest ;lephants must have >rtionately long thin ngs (e.g., eagles and elatively small light eir own weight (e.g., e immediate vicinity pace this same force ae and galaxies, the e. The first group of ce---may be thought Ihile the second and nological scale may , the same force can ;h here 'short range' act « 1 nm) while 1 (0.1 ,um). In Part I engths of condensed CONTRASTS BETWEEN INTERMOLECULAR. INTERPARTICLl AND INTERSURFACE FORCFS 153 phases are determined mainly by the interaction energies of molecules in contact w(J), i.e., molecules interacting with their immediate neighbours. For example, the van der Waals pair energy of two neighbouring molecules is at least 64 times stronger than that between next nearest neighbours (l / (J6 compared to 1/(2<5)6). Only the Coulomb interaction is effectively long ranged in that the energy decays slowly, as 1/r, and remains strong at large distances. However, in a medium of high dielectric constant such as water the strength of the Coulomb interaction is much reduced as is its range due to electroneutrality and ionic screening effects (Chapter 12). We may therefore conclude that apart from ionic crystals (Chapter 3) the properties of solids and liquids are determined mainly by the molecular binding forces, i.e. by the strength of the interactions at or very near molecular contact, the long-range nature of the interaction (e.g., the exact distance dependence of the force law) playing only a minor role. A very different situation arises when we consider the interactions of macroscopic particles or surfaces, for now when all the pair potentials between the molecules in each body is summed we shall find (i) that the net interaction energy is proportional to the size (e.g. radius) of the particles, so that the energy can be very much larger than kT even at separations of 100 nm or more, and (ii) that the energy and force decay much more slowly with the separation. All these characteristics make the interactions between macroscopic bodies effectively of much longer range than those between molecules even though the same basic type of force may be operating in each case. Furthermore, if the force law is not monotonic (not purely attractive or repulsive) then all manner of behaviour may arise depending on the specific form of the long-range distance dependence of the interaction. This is ill us trated in Fig. 10.1. For example, consider the purely attractive interaction of Fig. 10.la. If both molecules and particles experience the same type of interaction, both will be attracted to each other, and the thermodynamic properties of an assembly of molecules in the gas or condensed phase will be determined by the depth of the potential well at contact, as will the adhesion energy of two particles. However, for the energy law in Fig. 10.1 b two molecules will still attract each other since the energy barrier is negligibly small compared to kT, but two macroscopic particles will effectively repel each other since the energy barrier is now too high to surmount. Under such eircumstances particles dissolved in a medium will remain dispersed even though the ultimate thermodynamic equilibrium state is the aggregated state. We thus encounter another important difference between molecular and particle interactions, namely, that particles can be (and often are) trapped in some kinetic or