Solubility-diffusion theory

The solubility-diffusion theory assumes that solute partitioning from water into and diffusion through the membrane lipid region resembles that which would occur within a homogeneous bulk solvent. Thus, the permeability coefficient, P, can be expressed as... 

An alternate strategy is to predict membrane permeability by modeling the physics of membrane permeation. In principle, such models do not require training on existing experimental data and should have a broad domain of applicability. One approach is to model the process based on solubility-diffusion theory, in which the membrane permeability of the permeant is formulated as the reciprocal of the resistance experienced in the permeation process. With the assumption that diffiisional resistance is only contributed by the membrane and there is negligible resistance in the unstirred aqueous layer and the membrane interface, the permeation rate can be estimated from (l) the partition between the aqueous phase and the membrane, (2) the diffusion across the membrane, and (3) the distance of permeation. Common descriptors such as PSA and MW are reasonable surrogates for these properties, but it is possible to obtain more accurate estimates, as described below. 

Diffusion Theory. The diffusion theory of adhesion is mostly applied to polymers. It assumes mutual solubility of the adherend and adhesive to form an interphase. 

Diffusion Theory. The diffusion theory of adhesion is mostly applied to polymers. It assumes mutual solubility of the adherend and adhesive to form a true interpliase. The solubility parameter, the square root of the cohesive energy density of a material, provides a measure of the intemiolecular interactions occurring witliin the material. Thermodynamically, solutions of two materials are most likely to occur when the solubility parameter of one material is equal to that of the other. Thus, the observation that "like dissolves like." In other words, the adhesion between two polymeric materials, one an adherend, the other an adhesive, is maximized when the solubility parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubility between adhesive and adherend. The diffusion theory is not applicable to substantially dissimilar materials, such as polymers on metals, and is normally not applicable to adhesion between substantially dissimilar polymers. 

The same defect thermodynamics and diffusion theory can be applied to ionic crystals with one important proviso, which is the need to account for the charges on the ions (and hence effective charges on the defects), and that the crystal must remain electrically neutral overall. This means that the defects will occur as multiplets to satisfy this later condition. For example, in a MX crystal they will occur as pairs the Schottky pair- a cation vacancy and an anion vacancy the cation-Prenkel pair- a cation vacancy and an interstitial cation and the anion-Frenkel pair - an anion vacancy and an interstitial anion. The concentrations of the defects in the pair are related by a solubility product equation, which for Schottky pairs in an MX equation takes the form ... 

As in the case of hydrophilic (swelling) matrix systems and reservoir (membrane) systems, drug release profiles from insoluble (porous or non porous) systems are most of the time described on a basis of the diffusion theory. This is not true for every situation and we have for example shown that the release from porous matrix systems is dissolution-controlled above the solubility limit of the drug [150]. A simplified equation for the model proposed and for values of kd t > 4, is ... 

For gas separations, solution-diffusion theory leads to the conclusion that gas permeation flux (J) is proportional to the difference in gas partial pressure across the membrane (Ap) J=(P//)Ap. The proportionality constant is equal to the intrinsic permeability (P) for the membrane material divided by the effective membrane thickness (/). In turn, the permeability is equal to the product of a solubility (S) and diffusivity (D) P=D S. The ability to separate two... 

For diffusion of liquid through rubbery polymer composites, Fickian and non-Fickian diffusion theories are frequently used to describe the mechanism of transport, but for gas or vapour, other models have been developed to fit experimental data of diffusion profiles. The models of gas transport include Maxwell s model," free volume increase mechanism," solubility increase mechanism," nanogap hypothesis," Nielsen model, " " Bharadwaj model, ° Cussler model " " and Gusev and Lusti model, " etc. 

The above discussion deals mostly with rubber materials and not with structural adhesives it serves, though, to introduce the subject. From the work of Iyengar and Erickson,it appears that adhesive strength is related to the solubility parameter match of the adhesive to the substrate. In this work the substrate was Mylar (a polyester), which gives some further credence to the diffusion theory of adhesion for materials which can be considered structural members. 

The interdiffusion of the polymer molecules of adhesive and substrate is dependent upon various parameters, such as pressure, time, temperature, molecule size, and, of course, the reciprocal solubility, as shown by the correlation between the compatibility of the polymers and the quality of the bond [21]. Examples of bonds to which the diffusion theory is applicable include the bonding of PVGU adherents to PVC in solvents containing tetrahydrofuran and so-called contact bonding, where the diffusion... 

The diffusion theory explains in some cases the adhesion between pol5mers. This theory postulates that the adhesion is due to the mutoal diffusion of polymer molecules across the interface. This requires that the polymers or their chain segments are sufficiently mobile and that the two substrates are mutually soluble, e.g. they have similar solubility parameters. If the solubility parameters are very different (incompatible polymers), then there is htde chain entanglement and, thus, a very poor joint strength. 

Voyutskii [30-32] is the chief advocate of the diffusion theory of adhesion which states that the intrinsic adhesion of polymers to themselves (autohesion), and to each other, is due to mutual diffusion of polymer molecules across the interface. This requires that the macromolecules, or chain segments of the polymers (adhesive and substrate) possess sufficient mobility and are mutually soluble. This latter requirement may be restated by the condition that they... 

The reluctance to accept the applicability of diffusion theory to adhesion between chemically different polymers was because mutual solubility (emphasized by Voyutskii) was regarded as an essential feature of the mechanism, and most polymer pairs were known to be incompatible. 

Such thermodynamic treatments point to the incompatibility of most polymer/polymer combinations, and practical studies with polymer blends lead to the same conclusion. Mutual solubility, regarded as an essential feature of the diffusion theory, would rarely be achieved, restricting the appKcahflity of the theory to autohesion, and perhaps to adhesion between polymers of closely similar chemical structure. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Thus one must rely on macroscopic theories and empirical adjustments for the determination of potentials of mean force. Such empirical adjustments use free energy data as solubilities, partition coefficients, virial coefficients, phase diagrams, etc., while the frictional terms are derived from diffusion coefficients and macroscopic theories for hydrodynamic interactions. In this whole field of enquiry progress is slow and much work (and thought ) will be needed in the future. 

Emulsion Polymerization. Emulsion polymerization takes place in a soap micelle where a small amount of monomer dissolves in the micelle. The initiator is water-soluble. Polymerization takes place when the radical enters the monomer-swollen micelle (91,92). Additional monomer is supphed by diffusion through the water phase. Termination takes place in the growing micelle by the usual radical-radical interactions. A theory for tme emulsion polymerization postulates that the rate is proportional to the number of particles [N. N depends on the 0.6 power of the soap concentration [S] and the 0.4 power of initiator concentration [i] the average number of radicals per particle is 0.5 (93). 

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