Models are developed to describe sintering of metal crystallites during heat treatment. The growth rate of such crystallites is assumed to depend upon particle migration over the surface of the support as well as on the rate the colliding particles merge (sinter) into a single unit. The theory predicts that the rate of decay of exposed metal surface area S is given as in Equation (1a). The exponent n is related to the assumed size dependence of the diffusion coefficients or of the rate constant of the merging process. It varies from 4 to 8 for diffusion controlled decay and it is less than 3 for sintering controlled decay, that is, when the rate controlling step is the merging of two colliding particles. Diffusion control is associated with strong interactions between the metal and the support, but in sintering control there is a weaker metal‐support interaction.

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where V, i and A,, are the van der Waals volumes and areas of the molecule given by Bondi ( 1968) and where V, , and A,, are the van der Waals volume and area of a standard segment. The choice of a standard segment is somewhat arbitrary. Here it is defined as a sphere such that for a linear polymethylene molecule of infinite length the identity (z/2)(r -9 ) = r -1 (B3) is satisfied. The coordination number z is set equal to 10. The volume of the standard sphere in terms of its radius Rws is given by V, , = 4/3 x Rws3 (B4) and the area by A,, = 4 n Rws2 (B5) The van der Waals volume and area of an n-mer of polymethylene are n times the volume and area of a methylene group as given by Bondi; that is The population balances describing the time dependence of the size distibution can, under some conditions, be transformed by means of a similarity transformation into an ordinary integro-diff erential equation containing two instead of three variables, If there is compatibility between the transformed equation and the constraints given by the total mass conservation equation and the equation for the total number of particles, a self-preserving spectrum of the first kind can be obtained. There are, however, many situations such as the sintering controlled aging of supported metal catalysts, coagulation of colloidal particles in laminar shear flow, and coagulation of colloidal particles in a turbulent flow when the particles are smaller than the size of the smallest eddy for which, although a similarity transformation is possible, the transformed equation has no solution because of incompatibility with the above mentioned constraints. A second kind of self-preserving spectrum is suggested for these situations. The new variables are induced from a particular case for which an analytical result is available.A detailed presentation of the sintering controlled aging of supported metal catalysts is presented.

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