Hydration percolation theory

Application of the percolation theory allows explanation of the changes in the release and hydration kinetics of swellable matrix-type controlled delivery systems. According to this theory, the critical points observed in dissolution and water uptake studies can be attributed to the excipient percolation threshold. Knowledge of these thresholds is important in order to optimize the design of swellable matrix tablets. Above the excipient percolation threshold an infinite cluster of this component is formed which is able to control the hydration and release rate. Below this threshold the excipient does not percolate the system and drug release is not controlled. 

Therefore, the results obtained from the kinetics analysis are in agreement with the release profiles, indicating a clear change in the release rate and mechanism between matrices containing 90 and 95% w/w of drug (5-10% w/w of excipient). The existence of a critical point can be attributed to the excipient percolation threshold. From the point of view of percolation theory, this means that above 10% w/w of FIPMC K4M, the existence of a network of HPMC (able to form a hydrated layer from the first moment) controls the drug release. 

Careri et al. (1986), using the framework of percolation theory, analyzed the explosive growth of the capacitance with increasing hydration above a critical water content (Fig. 14). The threshold for onset of the dielectric response was found to he 0.15 h for free lysozyme and 0.23 h for the lysozyme—substrate complex. In the percolation model the thresh-... 

The use of the percolation model to analyze the d.c. conductivity in hydrated lysozyme powders (Careri et al., 1986, 1988) and in purple membrane (Rupley et al, 1988) introduces a viewpoint from statistical physics that is relevant to a wide range of problems originating in disordered systems. Percolation theory is described in the appendix to this article, for readers unfamiliar with it. Here, we discuss the significance of percolation specihcally for protein hydration and function. 

Water is well known for its unusual properties, which are the so-called "anomalies" of the pure liquid, as well as for its special behavior as solvent, such as the hydrophobic hydration effects. During the past few years, a wealth of new insights into the origin of these features has been obtained by various experimental approaches and from computer simulation studies. In this review, we discuss points of special interest in the current water research. These points comprise the unusual properties of supercooled water, including the occurrence of liquid-liquid phase transitions, the related structural changes, and the onset of the unusual temperature dependence of the dynamics of the water molecules. The problem of the hydrogen-bond network in the pure liquid, in aqueous mixtures and in solutions, can be approached by percolation theory. The properties of ionic and hydrophobic solvation are discussed in detail. 

Proton conductivities of 0.1 S cm at high excess water contents in current PEMs stem from the concerted effect of a high concentration of free protons, high liquid-like proton mobility, and a well-connected cluster network of hydrated pathways. i i i i Correspondingly, the detrimental effects of membrane dehydration are multifold. It triggers morphological transitions that have been studied recently in experiment and theory.2 .i29.i ,i62 water contents below the percolation threshold, the well-hydrated pathways cease to span the complete sample, and poorly hydrated channels control the overall transports ll Moreover, the structure of water and the molecular mechanisms of proton transport change at low water contents. 

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