Lars Onsager

THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES

Introdzution. The shapes of colloidal particles are often reasonably compact, so that no diameter greatly exceeds the cube root of the volume of the particle. On the other hand, we know many coiloids whose particles are greatly extended into sheets (bentonite), rods (tobacco virus), or flexible chains (myosin, various Iinear polymers). In some instances, a t least, solutions of such highly anisometric particles are known to exhibit remarkably great deviations from Raoult’s law, even to the extent that an anisotropic phase may separate from a solution in which the particles themselves occupy but one or two per cent of the total volume (tobacco virus, bentonite). We shall show in what follows how such results may arise from electrostatic repulsion between highly anisometric particles. Most colloids in aqueous solution owe their stability more or less to electric charges, so that each particle will repel others before they come into actual contact, and effectively claim for itself a greater volume than what it actuaily occupies. Thus, we can understand that colloids in general are apt to exhibit considerable deviations from Raoult’s law and that crystalline phases retaining a fair proportion of solvent may separate from concentrated solutions. However, if we tentatively increase the known size of the particles by the known range of the electric forces and multiply the resulting volume by four in order to compute the effective van der Waal’s co-volume, we have not nearly enough to explain why a solution of 2 per cent tobacco virus in 0.005 normal NaCZ forms two phases.

Deviations from Ohm's Law in Weak Electrolytes

The effect of an external electric field on the electrolytic dissociation is computed kinetically from the equations for Brownian motion in the combined Coulomb and external fields. The result is an increase of the dissociation constant, by the factor K(X)/K(0) = F(b) = 1+b+(1/3)b2..., where the parameter b is proportional to the absolute value of the field intensity, and inversely proportional to the dielectric constant. In water at 25°, F(b) = F(1) = 2.395 for a field of 723 kilovolt/cm, while in benzene, the same increase of the dissociation constant is obtained for a field of only 21 kilovolt/cm. The theory is quantitatively confirmed by the deviations from Ohms law which have been observed for solutions of weak electrolytics in water and in benzene. For solutions of salts in acetone, and for solid electrolytes such as glass, mica, celluloid, etc., the observed increments of conductance are smaller than those expected from the theory, but still of the predicted type and order of magnitude. The kineti...

Interpretation of the de Haas-van Alphen effect

(1952). Interpretation of the de Haas-van Alphen effect. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 43, No. 344, pp. 1006-1008.

Diffusion and Relaxation Phenomena in Ice

The underlying mechanisms of several rate processes in ice are examined through cross comparisons of the processes with each other and with experimental observations. The assumption that the migration of orientational defects (Bjerrum faults) is the common origin of dielectric and elastic relaxation leads to a predicted ratio of dielectric‐to‐elastic relaxation time of 32, in close agreement with experiment. The conclusion that a separate process is responsible for diffusion is based on a comparison of diffusion and dielectric relaxation data. The faster diffusive motion controls the thermal equilibration of the proton spins as well as the magnetic resonance linewidths; an interstitial migration appears to be the mostlikely diffusion mechanism.

Surface Specific Heat of an Isotropic Solid at Low Temperatures

The effect of realistic boundary conditions on the computation of the specific heat of an isotropic solid at low temperatures is investigated. Two cases are considered: the surface free of stress and the surface rigidly clamped. The first of these is the one of physical interest. For both cases a term in the specific heat arises which is proportional to the surface area and to T2 and appreciably higher than Montrolls result in the case of the free solid. The effect of approximations introduced during the computation is estimated. Available experimental data are not adequate for a critical test of the theory.

Hopping of ions in ice

The effects of intermolecular tunneling by protons in ice and other protonic semiconductors on thermodynamic and transport properties are estimated on the basis of an idealized model. The model involves a simple tight‐binding Hamiltonian on the infinite‐dimensional set of molecular configurations in the generally proton‐bonded but otherwise disordered structure. The cycle‐poor topology of the state set is approximated by that of a cycle‐free Bethe lattice, i.e., an infinite, homogeneous Cayley tree. For coordination q and hopping matrix element V the distribution of energy levels is given by the function g(u) = g(E/V) = q[4(q − 1) − u2]1/2/2π(q2 − u2), where q = 3 for the set of hopping options available to an ion in ice. The thermal average of the group velocity v = [4(q − 1) − u2]1/2 V d / ℏ on the Bethe lattice with lattice spacings d determines a finite coefficient of diffusion in real three‐dimensional space, where paths on the Bethe lattice are represented by random walks in 3 space with only a fini...

Electrical effects during condensation and phase transitions of ice

Condensation potentials and corresponding electrical currents are observed during the isothermal growth of amorphous, cubic, and hexagonal ice from the vapor phase. Upon heating of the condensate a thermally stimulated current (TSC) spectrum is observed with the application of any external electric field. Current peaks in the TSC spectrum are shown to be of two types: depolarization currents related to dipolar relaxation processes in the condensate and peaks due to phase transitions. Nearly all depolarization (∼90%) occurs in the amorphous phase via relaxation processes. Shifts in the maximum temperature of the peaks are observed for deuterated water for both types of peaks, and are on the order of 5–10 K. Models are proposed for the electrical effects observed during condensation, phase change, and depolarization.

Apparatus for Isotope Separation by Thermal Diffusion

A compact, all‐metal, multi‐stage thermal diffusion apparatus for the separation of isotopes in quantity in non‐corrosive gases at any pressure up to 175 lb/in.2 is described. For a particular gas the proper pressure may be well‐enough calculated in advance as that giving maximum separation factor in the last column only. Operating with neon at 3 atmos. pressure, and using 12 meters of column consuming 4.9 kw for 260 hours, 7 liters of gas with a Ne22 content of 93.4 percent were produced.

Life in the Early Days

The origin and early evolution of life is a matter of more than purely geneological interest; as we grapple with this problem, we expect to gain deeper insight into general aspects of cellular physiology. As yet any effort along these lines must remain somewhat speculative; hut the rewards of a good guess can be great. Even if you dream up a wrong answer to a well-put question, the consolation prize may still be yours when someone else takes a long step forward in the course of demonstrating what a silly notion you had.

Electrons and vortex lines in He II. I. Brownian motion theory of capture and escape

The Brownian motion theory of capture and escape in the form given by L. Onsager in 1934 is applied to the interaction of electrons and vortex lines in He II. Precise results are obtained to lowest order in the external field strength and certain misconceptions are clarified, laying the foundation for a reliable analysis of the available experimental data.