Diffusion of a polymer chain

V. Yamakov, A. Milchev. Diffusion of a polymer chain in a porous medium. Phys Rev 55 1704-1712, 1997. 

Whenever the polymer crystal assumes a loosely packed hexagonal structure at high pressure, the ECC structure is found to be realized. Hikosaka [165] then proposed the sliding diffusion of a polymer chain as dominant transport process. Molecular dynamics simulations will be helpful for the understanding of this shding diffusion. Folding phenomena of chains are also studied intensively by Monte Carlo methods and generalizations [166,167]. 

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 jamming effect, i.e., the slowing down of the longitudinal diffusion of a polymer chain by the head-on collision with other chains, can be treated by a model similar to that proposed by Cohen and Turnbull [112] for self diffusion of small molecules in a fluid. This model assumes that if at least one surrounding polymer chain exists within the critical hole ahead of a test chain, both collide, and this prevents the test chain from diffusing longitudinally. With this assumption, we express the longitudinal diffusion coefficient Dp of the test chain as... 

It is possible that equilibrium morphology is not obtained because the movement of the polymer chains is not fast enough to reach that equilibrium within the time-frame of the reaction this is kinetic control of morphology. The kinetic parameters influence the rate of formation of a certain morphology [27, 28], which is basically determined by the interfacial tensions [29]. The parameters of importance are the rate of formation of the polymer (parameters are propagation rate coefficient, and the local monomer and radical concentrations) and the rate of diffusion of the polymer chains (parameters are viscosity in the locus of polymerization, molar mass and topology of the polymer chain). Both the rate of formation and the rate of diffusion of a polymer chain are, for example, affected by the mode of addition of the monomer and initiator. An increased rate of addition of the monomer will lead to a lower instantaneous conversion and thus a lower viscosity in the particle, which in turn increases the rates of diffusion and leads to different morphologies. 

There are a number of factors, both thermodynamic and kinetic, which control the concentration at the interface see Table 12.9 (76). One of the more complicated kinetic aspects involves diffusion of a polymer chain through already adsorbed polymer layers. It is assumed diffusion follows reptation motions. However, the fraction of remaining available bonding sites becomes important when the chain actually reaches the surface. 

D represents the diffusion of a polymer chain due to Brownian or thermal motion, while is a coefficient that characterizes the relaxation of a concentration gradient being present in a solution. At zero percent conversion, these two diffusion coefficients are identical. 

The mechanism of adhesion to various substrates has not been fully explained. Brauer Stansbury (1984b) consider that bonding to composite resins occurs by the diffusion of methacrylate polymer chains into the resin. Bonding to base metals is, perhaps, by salt or chelate bridges. Here it is significant that ZOE cements do not bond, so perhaps bonding is due to the action of free EBA on the substrate. The adhesion to porcelain is surprising. Porcelain is inert so that the attachment can hardly be chemical. Also, it would be expected that if a cement adheres to porcelain then it should adhere to untreated enamel and dentine, but this is not so. 

It is well known in the case of self-diffusion of a linear chain polymer within the melt that Dm is in proportion to the power of M,... 

Rearrangement of the two chains so that the two radical ends are sufficiently close for chemical reaction, which occurs by segmental diffusion of the chains, that is, by the movement of segments of a polymer chain relative to other segments... 

The process by which a thermoplastic matrix composite consolidates to form a laminated structure has been attributed to autohesive bond formation at the ply interfaces. Autohesive bond formation is controlled by two mechanisms (1) intimate contact at the ply interfaces, and (2) diffusion of the polymer chains across the interface (healing). The rate of autohesive bond formation and hence the speed of the composite consolidation process is directly related to the temperature-pressure-time processing cycle. 

Almost all of these examples involve diffusion of a chemical species measuring diffusion rates has long been a specialty of NMR spectroscopy. The studies of KBr and drawn polyethylene produced unique information in the latter case, the known orientation of the deuterium electric field gradient in C-D bonds is used to determine the orientation, with respect to the magnetic field, of a polymer chain of a uniaxially ordered polyethylene fiber. The real time imaging of the polymerization of methyl methacrylate is very interesting and may represent a major direction for NMR imaging applications to polymer science. 

The configuration of a polymer chain is analogous to the path r(s) of a diffusing particle with the segment rank s replacing time. At equilibrium, configurations follows the Boltzmann distribution... 

The kinetic scheme with constant reaction of the polymer/monomer droplet increases fairly quickly with conversion, and the mobility of the polymer chains rapidly falls below the mobility of the monomer. The reduced diffusion of live polymer chains in the droplet will reduce the rate of termination of polymerization. The associated increase in the number of radicals will cause a rapid increase in the polymerization rate. This phenomenon is well known as the Trommsdorf or gel effect [8,9]. The gel effect causes a growth of the polymer chain length and widening of the molecular weight distribution (Figure 9.5). 

The path integral technique was first proposed by Feynmann (Feynmann Hibbs, 1965). The purpose of this technique was to deal with questions in quantum mechanics. It has been applied to the study of the statistical mechanics of polymer systems (Kreed, 1972 Doi Edwards, 1986) and liquid crystalline polymers as well (Jahnig, 1981 Warner et al, 1985 Wang Warner, 1986). The path integrals relate the configurations of a polymer chain to the paths of a particle when the particle is undergoing Brownian or diffusive motion. 

Stacked thin film is required. Recently, an alternative measurement of the diffusion constant of a polymer chain has been proposed [74], Such measurements could be applicable for the present case. 

The diffusion motion of a polymer chain is the translational behavior of its center of mass Rc(f) defined by... 

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