Slow surface integration

Derivations of Equation 4.1 are in the references cited above. One such location is Myerson (2002, pp. 45-46). Theoretical computation of A is given by Nielsen (1964). Predicting diffusion to the surface results in a value of A 10 . Measurements of A for lovastatin by Mahajan and Kirwan (1996) show Nielsen s value to be orders of magnitude too high, presumably because of the slow surface integr ation rate exhibited by many organic molecules. 

This kind of surface imperfections (fissures, shrinkages etc.) damaged the surface integrity of the spheres and may have resulted in the increase in actual surface area as compared to calculated value in Table I and subsequently have increased the surface oil content for large particles. Surface imperfections have been well documented in the literature when slow process of film formation of drying droplets is encountered. 

Kinetically, the occurrence of substrates will, on one hand, lower the nucle-ation barrier, leading to an increase in the nucleation rate on the other hand, it will exert a negative impact on the surface integration. Nucleation on a substrate will reduce the effective collisions of structural units with the surface of clusters (Fig. 4), where the structural units are incorporated into the crystal phase. This will slow down the nucleation kinetics, in contrast to the effect of lowering the nucleation barrier. The latter, called the "shadow effect of the substrate, is described by/"(m) and/(m) appearing in the preexponential term of Eq. 17. 

Equilibration of the interface, and the establislnnent of equilibrium between the two phases, may be very slow. Holcomb et al [183] found that the density profile p(z) equilibrated much more quickly than tire profiles of nonnal and transverse pressure, f yy(z) and f jfz), respectively. The surface tension is proportional to the z-integral of Pj z)-Pj z). The bulk liquid in the slab may continue to contribute to this integral, indicatmg lack of equilibrium, for very long times if the initial liquid density is chosen a little too high or too low. A recent example of this kind of study, is the MD simulation of the liquid-vapour surface of water at temperatures between 316 and 573 K by Alejandre et al [184]. 

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