Hardness relationship with diffusivity

This study indicates that drug release from these formulations is by a matrix-diffusion-controlled process. The release rate constant shows an inverse relationship with the concentration of carbomer only. For all the formulations, release rate constants were independent of tablet hardness. 

Stokes-Einstein Relationship. As was pointed out in the last section, diffusion coefficients may be related to the effective radius of a spherical particle through the translational frictional coefficient in the Stokes-Einstein equation. If the molecular density is also known, then a simple calculation will yield the molecular weight. Thus this method is in effect limited to hard body systems. This method has been extended for example by the work of Perrin (63) and Herzog, Illig, and Kudar (64) to include ellipsoids of revolution of semiaxes a, b, b, for prolate shapes and a, a, b for oblate shapes, where the frictional coefficient is expressed as a ratio with the frictional coefficient observed for a sphere of the same volume. 

In a simple case the diffusion coefficients of spheres can be determined via the Stokes-Einstein relationship see Section 12.6.4. While such a relationship was originally derived with hard spheres in mind, it can also be used with globular proteins such as bovine serum albumin (59). Dynamic light-scattering can be used to study aggregation, adsorption, and structural changes as well as chain dynamics. 

Figure 17.21. Variation of the normalized collective Dc/Do) (A) and long-time self-diffusion (D /A)) ( ) coefficients with the hard-sphere volume fraction 0hs- All filled symbols refer to microemulsion data (taken from ref. (17)). The A/Do data, shown as open triangles correspond to silica spheres, taken from ref. (26), while the T>s/A) data, shown as open circles, correspond to the self-diffusion of traces of silica spheres in a dispersion of poly(methyl methacrylate) spheres (data taken from ref. (27)). The dashed line represents the equation, Dc/Dq = 1 + 1.30HS, while the continuous line represents the relationship. A/A) = (1 — 0hs/O-63) ...

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