Dissolution Phenomena Kinetics of Solubility

Systemic absorption of a drug substance from a particulate form takes place after the compound enters the dissolved state. If the dissolution rate of the substance is less than the diffusion rate to the site of absorption and the absorption rate itself, then the dissolution process will be the rate-determining step. This situation is characteristic of drug substances that have low degrees of aqueous solubility, and therefore low dissolution rates, and it has become an established tenet in pharmaceutics that one method to improve the dissolution rate of a relatively insoluble substance is to reduce the particle size of its component particles. As discussed above, the solubilities of polymorphs, solvatomorphs, and amorphous forms are different, and these differences may lead to differences in the dissolution rate, which in turn could lead to differences in bioavailability.

The mechanism of dissolution was proposed by Nernst (1904) using a filmmodel theory. Under the influence of non-reactive chemical forces, a solid particle immersed in a liquid experiences two consecutive processes. The first of these is solvation of the solid at the solid-liquid interface, which causes the formation of a thin stagnant layer of saturated solution around the particle. The second step in the dissolution process consists ofdiffusion ofdissolved molecules from this boundary layer into the bulk fluid. In principle, one may control the dissolution through manipulation of the saturated solution at the surface. For example, one might generate a thin layer of saturated solution at the solid surface by a surface reaction with a high energy barrier (Mooney et al., 1981), but this application is not commonly employed in pharmaceutical applications.

In the majority of dissolution phenomena, the solvation step is almost instantaneous. The diffusion process is much slower and, therefore constitutes the rate limiting step. Noyes and Whitney (1897) developed an equation based on Fick's second law of diffusion to describe dissolution within the scope of their model, and report the relation:


dt h where dC/dt is the rate of drug dissolution at time t, D is the diffusion coefficient, S is the surface area of the particle, h is the thickness of the stagnant layer, Cs is the concentration of the drug in the stagnant layer (usually taken as the equilibrium solubility), and C is the concentration of the drug in the bulk solvent. According to the Stock-Einstein equation for the small particles, the diffusion coefficient, D, is related to the viscosity of the liquid medium:

6nn r where k is the Boltzmann constant, T is the temperature, n is the viscosity of the solvent, and r is the radius of the particle.

According to the Noyes-Whitney equation (48), the dissolution rate of a drug substance is directly proportional to its equilibrium solubility. However, the nature of the dissolving solid and the dissolution medium also exert strong influences on the dissolution rate. For example, metastable polymorphs will exhibit faster dissolution rates than would the thermodynamically stable poly-morph, and amorphous materials will dissolve faster than any corresponding crystalline forms. Temperature may affect both the solubility and the diffusion coefficient, and in many cases the dissolution rate will increase with increasing temperature. Consequently, as was the case for solubility determinations, evaluation of drug dissolution must be conducted at a fixed and reported temperature.

The effect of particle size and dissolution rate has been known since the pioneering work of Noyes and Whitney (1897), and Hixson and Crowell (1931) subsequently derived a highly useful equation that expresses the rate of dissolution based on the cube root of the weight of the particles. When the Hixson-Crowell model is applied to micronized particles, for which the thickness of the aqueous diffusion layer around the dissolving particles is comparable to or larger than the radius of the particle, the change in particle radius with time is given by:

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