THERMAL CONDUCTIVITY EFFECTS IN THE DIFFERENTIAL THERMAL ETC. 233 ductivity of a bed of disc shaped particles would be expected to be higher than that of a bed of spherical particles. Similarly, the pressure under which a particulate bed is packed will affect the thermal conductivity since, for a given particle shape, increased packing pressures will distort the contact points and so tend to produce increased areas of contact. The pattern of packing will also influence the overall thermal con- ductivity since for spherical particles in cubical array the number of contact points per particle is eight whereas in the closest form of packing the number of contact points is twelve. In the foregoing discussion the influence of powder characteristics for a single material only have been considered but in the case of a sample com- posed of a mixture of powdered materials further factors enter the problem. For a mixture of two component powders, and if the two materials are of widely differing thermal conductivities, the ratio of particle sizes of the two components could well be important. Thus, for example, if one com- ponent consists of large particles of low thermal conductivity and the second material is composed of small particles of high thermal conductivity, then it is reasonable to expect the smaller particles to pack into spaces between the larger particles. In this situation, the larger particles would, in effect, form an insulating layer around the fine particles, and so a compact of low thermal conductivity would be formed. The converse would be the case if the larger particles were of higher thermal conductivity. For a mixture of powdered materials the degree of uniformity of mixing might also enter the problem since a non-uniform mixture would produce signi- ficant variation in the thermal conductivity and specific heat throughout the particulate bed. Thus, although differential thermal analysis is a satisfactory technique for many purposes, if accurate quantitative analyses of powdered materials are to be consistently achieved, further investigation is necessary both into the factors which affect the thermal properties of particulate beds and into the effect of these thermal properties upon the results of differential thermal analyses. (Received: 11th February 1969) REFERENCE (1) Rose, H. E. and English, J. E. The effect of particle size characteristics on the differential thermal analysis of powdered materials. Brit. Chem. Engng., 1111 1135 (1008).

234 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS DISCUSSION MR. P. J. LLo¾I): I am not very familiar with the technique of differential thermal analysis, but is it true that the samples are heated under normal pressure? THE LECTURER: In this case, yes. MR. P. J. LLO¾I): We have been working for some years on the thermal con- ductivity of powders, both under atmospheric pressure and under vacuum, and it is fairly clear from this work that the thermal conductivity of the material plays little part in the overall thermal conductivity of the compact or loose powder this really depends upon the thermal conductivity of the air. The air trapped within the walls of the crucible, between the particles, will form approximately 40% of the total volume of the sample and I would have thought that this would have a big effect on the overall thermal conductivity of the sample. T•E L•c'ru•R: In considering the best method of evaluating the thermal con- ductivity of a powdered sample, various equations which have been derived from experiments by other workers were considered, and these included Rayleigh's equation for the thermal conductivity of a powdered compact. Rayleigh's equation takes into consideration the thermal conductivity of the air trapped between the particles of the sample and also the bulk density of the material. Calculations based upon this equation of the thermal conductivities of the quartz, nickel and copper mixtures used in the present work produced values which did not differ significantly from that of air at the same temperature. Thus, these results would appear to be in agreement with your statement that the thermal conductivity of a powdered material is largely dependent only upon the thermal conductivity of the air. The results of the present work, however, show that this is not the case, since for each of the powdered samples of quartz, copper and nickel the only difference between the samples is the thermal conductivity of the mixture and the area of peak of the thermogram has been shown to vary with the variations in the proportions of copper and nickel powder in each sample. Thus in the absence of any other information, the weighted mean of the thermal conductivities of the components was chosen as being a reasonable estimate of the overall thermal conductivity of the mixture. I would agree, however, that much more research is necessary into the relationship between the thermal conductivity and the particulate properties of a powder taking into consideration the effect of the air in the spaces between the particles. D•. ]. E. P. MiL•s: In an age where the continuous processing of powdered materials is becoming increasingly important, what do you feel about this instrument being developed, say, for production control analysis. Do you think that there is any chance that it could be used to control the composition of powdered materials in a continuous process? THE I,F. CTUREm I do not think it likely that this technique, as such, will be de- veloped as a continuous method for quality control, simply because it is necessary to heat the material to a temperature at which there is a reaction within the material which in turn will give rise to a peak on the differential temperature curve. If, however, as part of a process a materi:41 were heated to a temperature at which