Diffusion theory

This early theory was successfully applied to joints of porous or rough adherends such as wood. The liquid adhesive penetrates the porous and irregular surface and when hardened adds strength to the adhesive joint. Thus, 

The greater the surface irregularity and porosity, the greater is the strength of the joint. 

The joint strength will be proportional to the film strength of the adhesive when the adherend is stronger than the adhesive. 

Some examples in which the mechanical mechanism is important are in the adhesion of polymers (elastomers and rubbers) to textiles. Another example, though somewhat contentious, is the metal plating of a plastic which usually requires a pretreatment to modify the surface topography of the polymer. Usually the increase in adhesion is also attributed to an improved surface force component due to the increased mgosity. 

The bonding of maple wood samples with urea-formaldehyde resins at 5 psi gluing pressure was tested in shear as a result of surface treatment. 

The diffusion theory was first proposed by Borozncui and holds that the mutual cohesion between polymers is caused by mutual diffusion of large molecules on the surface. The diffusion, osmosis, and association of molecular chains of two phases form the interfacial layer. 

The diffusion of the interfacial system is similar to the dissolving process of substances. They are all hybrid processes. The diffusion effect leads to the Interface becoming fuzzy and even disappearing (e.g., solid dissolved in liquid). The diffusion process correlates with molecular weight, flexibility, temperature, solvent, plasticizer, and other factors of the molecular chain. The interface diffusion between the polymer matrix and the filler could improve bonding performance. However, the diffusion theory cannot explain the adhesion phenomenon between the polymer matrix and inorganic reinforced material without interfacial diffusion. 

Researchers studying the interface interaction mechanism also put forward other theories of Interface Interaction, such as electrostatic theory, theory of reversible hydrolysis, the theory of adsorption, and so on. Various theories explain the interfacial interaction from different angles, but no single theory can perfectly explain all kinds of Interfaclal phenomena. With the 

Because we may not always have data available for carrying out dimensional analysis, it is worthwhile to see whether the penetration theory (diffusion model) described in Section 8.5.2 provides a reasonable design. In Eq. 8.170, we assume that Pe 1, and hence, we can use the expression given in Eq. 8.177, which is 

We also assume that the staged efficiency of the film diffusion process is 1 (i.e., Xp = 1.0) as there is no way to obtain this quantity directly (with Xf = 1.0, Pe 1). / (the extraction number) is now 

Substituting the above value back into Eq. 8.199, we can now solve for the unwound channel length required to reduce the amount of MMA to 0.1%  

The dimensional analysis approach with the choice of J/tp as the dimensionless group for determining dynamic similarity seems to be reasonable. 

This value is about 4.6 times the value estimated by means of dimensional analysis and reported by Biesenberger and coworkers (1990). Hence, the theory based on diffusion overestimates the length required to reduce the level of MMA to 0.1%. This is true in spite of the fact that in this case most of the volatiles are predicted to be removed from the melt film and not the pool. 

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Brinkman H C 1956 Brownian motion in a field of force and the diffusion theory of chemical reactions Physica 12 149-55... 

Berezhkovskii A M and Zitserman V Yu 1991 Comment on diffusion theory of multidimensional activated rate processes the role of anisotropy J. Chem. Phys. 95 1424... 

Langhoff C A, Moore B and DeMeuse M 1983 Diffusion theory and piooseoond atom reoombination J. Chem. Phys. 78 1191... 

Diffusion Theory. The diffusion theory of adhesion is mosdy appHed to polymers. It assumes mutual solubiUty of the adherend and adhesive to form a tme iaterphase. The solubiUty parameter, the square root of the cohesive eaergy deasity of a material, provides a measure of the iatermolecular iateractioas occurring within the material. ThermodyaamicaHy, solutioas of two materials are most likely to occur whea the solubiUty parameter of oae material is equal to that of the other. Thus, the observatioa that "like dissolves like." Ia other words, the adhesioa betweea two polymeric materials, oae an adherend, the other an adhesive, is maximized when the solubiUty parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubiUty between adhesive and adherend. The diffusion theory is not appHcable to substantially dissimilar materials, such as polymers on metals, and is normally not appHcable to adhesion between substantially dissimilar polymers. 

The mathematical model most widely used for steady-state behavior of a reactor is diffusion theory, a simplification of transport theory which in turn is an adaptation of Boltzmann s kinetic theory of gases. By solving a differential equation, the flux distribution in space and time is found or the conditions on materials and geometry that give a steady-state system are determined. 

T.E. Faber. An Introduction to the Theory of Liquid Metals. Cambridge University Piess (1972). R.A. Swalin. Liquid metal diffusion theory, Acta. Met., 1, 736 (1959). 

Diffusion theory involves the interdiffusion of macromolecules between the adhesive and the substrate across the interface. The original interface becomes an interphase composed of mixtures of the two polymer materials. The chemical composition of the interphase becomes complex due to the development of concentration gradients. Such a macromolecular interdiffusion process is only... 

The mechanisms of adhesion are explained by four main theories mechanical theory, adsorption theory, diffusion theory, and electrostatic theory. 

Fig. 5.12. Q-branch narrowing in classical. /-diffusion theory in strong collision (1) and weak collision (2) models [215], The widths are taken from experimental spectra shown in Fig. 5.11 for systems CO-He ( ) and N2-Ar (o).

As this kind of verification of classical J-diffusion theory is crucial, the remarkable agreement obtained sounds rather convincing. From this point of view any additional experimental treatment of nitrogen is very important. A vast bulk of data was recently obtained by Jameson et al. [270] for pure nitrogen and several buffer solutions. This study repeats the gas measurements of [81] with improved experimental accuracy. Although in [270] Ti was measured, instead of T2 in [81], at 150 amagat and 300 K and at high densities both times coincide within the limits of experimental accuracy. 

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. 

Combining hindered diffusion theory with the diffusion/convection problem in the model pore, Trinh et al. [399] showed how the effective transport coefficients depend upon the ratio of the solute to pore size. Figure 28 shows that as the ratio of solute to pore size approaches unity, the effective mobility function becomes very steep, thus indicating that the resolution in the separation will be enhanced for molecules with size close to the size of the pore. Similar results were found for the effective dispersion, and the implications for the separation of various sizes of molecules were discussed by Trinh et al. [399]. 

For the radical neutrals, boundary conditions are derived from diffusion theory [237, 238]. One-dimensional particle diffusion is considered in gas close to the surface at which radicals react (Figure 14). The particle fluxes in the two z-directions can be written as... 

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... 

To inject a general note it may be pointed out that two very important laws, called Fick s laws, form the basis of diffusion theory. The first law can be expressed in the following form ... 

Topper, L., 1963, A Diffusion Theory Analysis of Boiling Burnout in the Fog Flow Regime, Trans. ASME, J. Heat Transfer 85 284-285. (5)... 

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. 

Hikosaka presented a chain sliding diffusion theory and formulated the topological nature in nucleation theory [14,15]. We will define chain sliding diffusion as self-diffusion of a polymer chain molecule along its chain axis in some anisotropic potential field as seen within a nucleus, a crystal or the interface between the crystalline and the isotropic phases . The terminology of diffusion derives from the effect of chain sliding diffusion, which could be successfully formulated as a diffusion coefficient in our kinetic theory. 

The molecular weight (M) dependence of the steady (stationary) primary nucleation rate (I) of polymers has been an important unresolved problem. The purpose of this section is to present a power law of molecular weight of I of PE, I oc M-H, where H is a constant which depends on materials and phases [20,33,34]. It will be shown that the self-diffusion process of chain molecules controls the Mn dependence of I, while the critical nucleation process does not. It will be concluded that a topological process, such as chain sliding diffusion and entanglement, assumes the most important role in nucleation mechanisms of polymers, as was predicted in the chain sliding diffusion theory of Hikosaka [14,15]. 

There are three kinds of diffusion (i) within the isotropic phase (ii) the interface (between the isotropic and the crystalline phases) and (iii) the crystalline phase. In the case of a polymer system, the topological nature of polymer chains assumes an important role in all three kinds of diffusion, which has been shown in the chain sliding diffusion theory proposed by Hikosaka [14,15]. It is obvious that any nucleus (a primary nucleus and a two-dimensional nucleus) and a crystal can not grow or thicken without chain sliding diffusion. 

The two fundamental theories for calculating the attachment coefficient, 3, are the diffusion theory for large particles and the kinetic theory for small particles. The diffusion theory predicts an attachment coefficient proportional to the diameter of the aerosol particle whereas the kinetic theory predicts an attachment coefficient proportional to the aerosol surface area. The theory... 

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