Constant-release diffusion systems, rate

A monolithic system is comprised of a polymer membrane with dmg dissolved or dispersed ia it. The dmg diffuses toward the region of lower activity causiag the release of the dmg. It is difficult to achieve constant release from a system like this because the activity of the dmg ia the polymer is constantly decreasiag as the dmg is gradually released. The cumulative amount of dmg released is proportional to the square root of time (88). Thus, the rate of dmg release constantly decreases with time. Again, the rate of dmg release is governed by the physical properties of the polymer, the physical properties of the dmg, the geometry of the device (89), and the total dmg loaded iato the device. 

Buccal dosage forms can be of the reservoir or the matrix type. Formulations of the reservoir type are surrounded by a polymeric membrane, which controls the release rate. Reservoir systems present a constant release profile provided (1) that the polymeric membrane is rate limiting, and (2) that an excess amoimt of drug is present in the reservoir. Condition (1) may be achieved with a thicker membrane (i.e., rate controlling) and lower diffusivity in which case the rate of drug release is directly proportional to the polymer solubility and membrane diffusivity, and inversely proportional to membrane thickness. Condition (2) may be achieved, if the intrinsic thermodynamic activity of the drug is very low and the device has a thick hydrodynamic diffusion layer. In this case the release rate of the drug is directly proportional to solution solubility and solution diffusivity, and inversely proportional to the thickness of the hydrodynamic diffusion layer. 

Another important consequence of the constant rate of release diffusion model is that it mimics many of the features that have commonly been attributed to surface reaction (matrix dissolution) control. If one were to account for changes in surface area over time, the predicted long-term dissolution rate due to surface reaction control would also yield constant element release. In surface reaction controlled models, the invariant release rate with respect to time is considered to be the natural consequence of the system achieving steady-state conditions. Other features of experiments commonly cited as evidence for surface reaction control, such as relatively high experimental activation energies (60-70 kJ/ mol), could be explained as easily by the diffusion-control model. These findings show how similar the observations are between proponents of the two models it is only the interpretation of the mechanism that differs. 

The study of the release kinetic profiles of naproxen from microcapsule compressed as well as matrix tablets using a combination of water-insoluble materials (like beeswax, cetyl alcohol, and stearic acid) with hydrophilic polymers was investigated. The ethylcellulose/HPMC combinations, contributing to an increase in hydrophilic part of blend system, rationally increased the release rate, kinetic constant, and diffusion coefficient thereby, whereas HPMC/beeswax, HPMC/cetyl alcohol, and HPMC/stearic acid combinations, contributing an increase in hydrophobic part of the blend system, caused a substantial reduction of release. ... 

The latter device, developed by Alza Corp., Palo Alto, California, is a diffusion unit consisting of a drug reservoir (e.g., pilocarpine HCl in an alginate gel) enclosed by two release-controlling membranes made of ethylene-vinyl acetate copolymer, and enclosed by a white ring which Slows positioning of the system in the eye. The Pilo-20 Ocular Therapeutic System has a release rate of 20 mg/hr for 7 days, and the Pilo-40 system a release rate of 40 mg/hr for 7 days. The former releases a total of 3.4 mg in 7 days, the latter 6.7 mg. In order to maintain constant release of tog, and in accordance with the principles of diffusion, there... 

Membra.ne Diffusiona.1 Systems. Membrane diffusional systems are not as simple to formulate as matrix systems, but they offer much more precisely controlled and uniform dmg release. In membrane-controlled dmg deUvery, the dmg reservoir is intimately surrounded by a polymeric membrane that controls the dmg release rate. Dmg release is governed by the thermodynamic energy derived from the concentration gradient between the saturated dmg solution in the system s reservoir and the lower concentration in the receptor. The dmg moves toward the lower concentration at a nearly constant rate determined by the concentration gradient and diffusivity in the membrane (33). 

The performance of the dmg dehvery system needs to be characterized. The rate of dmg release and the total amount of dmg loaded into a dmg dehvery system can be deterrnined in a dissolution apparatus or in a diffusion ceU. Typically, the dmg is released from the dmg dehvery system into a large volume of solvent, such as water or a buffer solution, that is maintained at constant temperature. The receiver solution is weU stirred to provide sink conditions. Samples from the dissolution bath are assayed periodically. The cumulative amount released is then plotted vs time. The release rate is the slope of this curve. The total dmg released is the value of the cumulative amount released that no longer changes with time. 

Since the left side of Eq. (7) represents the release rat of the system, a true controlled-release system with a zero-order release rate can be possible only if all of the variables on the right side of Eq. (7) remain constant. A constant effective area of diffusion, diffusional path length, concentration difference, and diffusion coefficient are required to obtain a release rate that is constant. These systems often fail to deliver at a constant rate, since it is especially difficult to maintain all these... 

Owing to this large concentration of OH relative to O and H in the early part of the reaction zone, OH attack on the fuel is the primary reason for the fuel decay. Since the OH rate constant for abstraction from the fuel is of the same order as those for H and O, its abstraction reaction must dominate. The latter part of the reaction zone forms the region where the intermediate fuel molecules are consumed and where the CO is converted to C02. As discussed in Chapter 3, the CO conversion results in the major heat release in the system and is the reason the rate of heat release curve peaks near the maximum temperature. This curve falls off quickly because of the rapid disappearance of CO and the remaining fuel intermediates. The temperature follows a smoother, exponential-like rise because of the diffusion of heat back to the cooler gases. 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

Exchange of trace components The equations for adsorption (diffusion) can be equally applied in the case of isotopic exchange (exchange of isotopes) with minor changes. The same equations can be also be used in the case of the exchange of trace components of different valences (Helfferich, 1962). This is the case where the uptake or release of an ion takes place in the presence of a large amount of another ion in both the solid and liquid phase. In such systems, the amounts removed ate so small that the concentrations in both phases are practically constant, and thus in turn the individual diffusion coefficients also remain unaffected. Moreover, the rate-controlling step is the diffusion of the trace ion. 

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