A Low Temperature Particle Size Effect on the Heat Capacity of Sodium Chloride

Abstract

.in effect of particle sizc upon the heat capacity of socliu~n cl~loricle has been found in the te~mperature range 9' to 21°1C. The euperiments were clone with three NaCl samples of specific surfaces between 38 and 59 sq. meters per gm. 'The observed effect has the temperature dependence predicted by theory but its 111agnitude is three to four times larger than expected. I t is unlil<ely that adsorbed gases have made any significant contribution in the experiments. The accuracy with which the specific heat and surface area differences have been determined is not high enough to show definitely whether or not the surface specific heat is an extensive property of the surface. INTRODUCTIONThe existence of an effect of particle size on the thermodynamic properties of a solid is evident from the Einstein model which considers the solid as an assembly of oscillators identified with the atoms. Atoms on the free surface are less strongly bound than those in the interior so that their frequency is lowered, producing a change in thermodynamic properties which is proportional to the surface area. With the Debye or Born -von Karman models, however, the oscillators are identified with the normal modes of vibration of the whole solid. The effect of free boundaries is then not localized in the frequencies of oscillators associated with the surface but is spread throughout the frequency spectrum. Nevertheless, it may be shown that in particular cases the effect of finite particle size reduces to a contribution t o the thermodynamic quantities which is extensive in the surface area, plus other contributions (e.g. edge contribution) which can ordinarily be neglected.Brager and Schuchowitsky (2, 3), Montroll (8), and Stratton (11) give the following relation (low temperature form) for the heat capacity of small particles of rectangular cross-section and with perfect faces, C, = 464.5 (T/6D)3+B(T/6D)'+ . . . cal./gm. atom deg.[I]where OD is the Debye characteristic temperature and B is a constant proportional to the specific surface area. According t o [I] the surface contribution becomes more important a t low temperatures since it is decreasing as T 2 while the volume contribution does so as T3. If the density of modes in the frequency spectrum is too low, equation [I] breaks down and the specific heat is no longer an extensive property of the surface. This may occur if the particles are too small or if the temperature is too low, i.e. if (hvo/2kT) > (2N/a) (yo is the maximum frequency of the solid lattice and N3 is the number of atoms in the particle). 'ibfanz~script received Seplenzber 16, 1964.

An Experimental Determination of the Surface Enthalpy of Sodium Chloride

“…Morrison and I'atterson (7) have extended the temperature range of the specific heat n~easurements on finely divided sodium chloride previously reported by Patterson, Morrison, and Thompson (8). Their data show a definite particle size effect but it is not simply related to the surface area of the sample and these authors suggest that the excess specific heat over that predicted by the theoretical treatment of Montroll (6) is due to a loosening of the surface structure.…”

The Purity of Small Sodium Chloride Particles Prepared by Electrostatic Precipitation

“…The fine salt used in these experiments was made by electrostatic precipitation of a sodium chloride smoke. Essentially the same method of preparation has been employed by a number of other workers (6,3,11,7). In the course of the surface enthalpy study the following indications of impurities in the fine salt were noted:…”