Diffusion theory interaction

A final point has to do with the relative Insensitivity of the pore averaged dlffuslvlty on the density structure. Both the LADM and the generalized tracer diffusion theory provide a rational explanation for this fact. The reasons for the Insensitivity may be Identified In the double (triple for the tracer diffusion theory) smoothing Induced by the volume averaging and by the very nature of the molecular Interactions In liquids which makes some type of averaging over the densities In the neighborhood of a certain point necessary. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

Thirion (239a) has suggested that the plateau and terminal regions are the result of diffuse interchain interactions in a viscoelastic medium. He obtains a modified Rouse spectrum by replacing the subchain frictional coefficient by a time dependent micro-memory function. The theory is partly phenomenological since the memory function is not specified. However, reasonable choices lead to forms for G (co) and G"(o>) which are similar to those observed experimentally. 

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. 

However, the theory of Section II in this chapter gives the exact criterion that diffusion theory for the encounter rate is valid when a in Eq. (2.33) is large than unity. For potentials without barriers the factor IF(0)/IF(oo) is close to unity, and the criterion for applicability of the diffusion theory is that the mean free path Dj/C8kT/nfi) be much smaller than the particle size (1 + b)/4-However, for large barriers the criterion is similar to that of Verwey and Overbeek, except that SR is the half-width of the potential barrier at an energy of only kT/2 below the maximum. This is much less than the full width of the barrier, and for reasonable values of the parameters in aqueous solution it can be shown that DLVO theory breaks down for equal-size particles with R, > 150 nm. However, when hydrodynamic interaction between particles is introduced in the formula for in terms of and it is concluded ... 

Vlachos, D.G. Katsoulakis, M.A. Derivation and validation of mesoscopic theories for diffusion of interacting molecules. Phys. Rev. Lett. 2000, 85, 3898-3901. 

Phillies (76,77) has subsequently discussed the empirical extension of this classical diffusion theory to higher terms in the virial expansions. Recently, Batchelor has carried out a more detailed analysis of the intermolecular hydrodynamic interactions contributing to kf and arrived at the conclusion (78) ... 

A number of adhesion theories have been proposed to identify the formation of adhesive forces. The contributed adhesion mechanisms are (1) chemical bonding such as chemisorption theory (2) physical interaction such as polarization, electrostatic, and diffusion theory (3) thermodynamical interpretation such as adsorption theory and (4) mechanical interlocking. No single theory exists to explain the entire property of adhesion oti various substrates and adhesives. However, those theories may provide a guideline to understand the principle of the adhesion as the following details (Fig. 2). 

For longer-range interaction forces, FUCHS uses classical diffusion theory to derive formulas for the flux of particles to a target particle. These formulas were discussed for several monotonic particle interaction potentials and he found that in most cases the role of the interaction force was not significant. 

Thus, when investigating the nature and mechanism of adhesion between an adhesive, coating or polymer matrix and the substrate, it is important to consider the possibility of primary bond formation in addition to the interactions that may occur as a result of Dispersion forces and Poiar forces. In addition to the Adsorption theory of adhesion, adhesion interactions can sometimes be described by the Diffusion theory of adhesion, Electrostatic theory of adhesion, or Mechanical theory of adhesion. Recent work has addressed the formation of primary bonding at the interface as a feature that is desirable from a durability point of view and a phenomenon that one should aim to design into an interface. The concept of engineering the interface in such a way is relatively new, but as adhesives become more widely used in evermore demanding applications, and the performance XPS and ToF-SIMS systems continues to increase, it is anticipated that such investigations can only become more popular. 

Some rubber-based adhesives need vulcanization to produce adequate ultimate strength, and the adhesion is mainly due to chemical interactions at the interface. Other rubber-based adhesives (see Contact adhesives) do not necessarily need vulcanization but need adequate compounding to produce the adhesive joints, mainly with porous substrates. In this case, the mechanism of diffusion dominates their adhesion properties. See Diffusion theory of adhesion and Polymer diffusion reptation and interdigitation. 

Diffusion theory in metals, at its present state of art, is not able to provide a quantitative or even qualitative account for the relative values of the solute diffusivities in rare earth metals. The electrostatic interaction theory, which achieved notable success is accounting for the relative diffusivities of various solutes in the noble metals is not applicable to the polyvalent rare earth solvents (Dariel, 1968). Size effects are probably important in determining relative solute... 

Slab interaction calculations were performed utilizing the albedo reflection options of the diffusion theory code, HFN, and the discrete ordinates code, DTF-IV. Both the HFN and DTF-IV calculations were made using... 

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