Diffusion mobility, polymer

In addition to giving conformational information, solid state NMR relaxation experiments can be used to probe the thermal motion of polymers in the hydrated cell wall (5). The motion of the polymers can give us clues as to the environment of the polymer. When there are both rigid and mobile polymers within a composite material, NMR spin-diffusion experiments can be used to find out how far apart they are. 

NMR imaging Diffusion (distribution, mobility) Polymers Food packaging materials... 

Diffusion and permeability are inversely related to the density, degree of crystallinity, orientation, filler concentration, and cross-link density of a polymeric film. Generally, the presence of smaller molecules, such as plasticizers, increases the rate of diffusion in polymers since they are more mobile and can create holes or vacancies within the polymer. The rate of diffusion or permeability is fairly independent of polymer chain length just as long as the polymer has a moderately high chain length. 

Another unique attribute of polymerizations of multifunctional monomers is the dominance of reaction diffusion as a termination mechanism [134,136, 143-146]. Reaction diffusion involves the mobility of radicals by propagation through unreacted functional groups. This termination mechanism is physically different from translation and segmental diffusion termination mechanisms which involve the diffusion of polymer macroradicals and chain segments to bring radicals within a reaction zone before terminating. Whereas normal termination mechanisms are related to the diffusion coefficient of the polymer, reaction diffusion must be considered differently. In essence, reaction diffusion is... 

This is exactly the molecular-weight dependence of conformational relaxation times of polymer in non-entangled state and for the region of diffusive mobility (see equation (4.41), weakly-entangled system). 

The use of these diffusion models to progress the evaluation process of a food packaging plastic will be discussed shortly. In those cases where assessment by mass balance considerations under equilibrium conditions, including partitioning effects, does not provide a clear picture of the plastics conformity status, then the different diffusivities of polymer types and the influence of the migrant molecule size or its molecular weight on its mobility within a plastic can be taken into account to achieve more distinguished views on QM/SML ratios. 

From electron microscope observations, it was found that whisker-like material comes out of coked ZSM-5, indicating that polymers formed within the pores difiuse to the outer surface of the zeolite crystals. Even though the coke formed inside the zeolite crystal are mobile polymers, their diffusion rates are extremely slow in comparison with the reactant molecules and they can be regarded as immobile species On the other hand, the coke formed on the outer surface of the crystal was reported to be carbonaceous materials fi om the observation of TEM spectroscopy (13). 

For mobile polymers, MAS may be enough to narrow the resonances. In such cases, spin diffusion becomes inefficient while the NOE is used to correlate spins. Heffner and Mirau [24] observed 2D NOESY... 

As mentioned earlier, the mechanism of gas separation by non-porous membranes basically is different from the one in microporous membranes. Gas molecules actually dissolve and diffuse in the dense membrane matrix. Differences in permeability, therefore, will result not only from diffusivity (mobility) differences of the various gas species but also from differences in physico-chemical interactions of these species within the polymer, determining the amount of gas that can be accommodated per unit volume of the matrix. 

An ideal inhibited plastic material combines considerable phase and diffusion mobility of Cl with mechanical strength and high barrier characteristics. These contradictory requirements are met when a polymer-solvent system is used as the inhibited plastic base (with high polymer content). The required physical-mechanical parameters in the described systems are promoted by the polymer, while the solvent is either a liquid Cl or its solution (dispersion) in PI. 

Mackle and Meares (24) have modeled diffusion in polymers for the situation where the size of the diffusing molecules are similar to the size of the polymer segments. The mobile polymer segments were considered to act as a physical obstruction to diffusion and the solute was considered to be restricted to the free sites. They arrived at the following functional dependence for Equation 39,... 

Thus, analysis of hydrodynamic properties of native lignins reveals that their behaviour in dilute solutions is different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. Apparently, the macromolecules of soluble lignins are randomly branched chains. Branchings in a chain are known to reduce the hydrodynamic dimensions, (i.e., reduce [q]), and increase the diffusion mobility compared to the linear analog, theoretical value of b, in a 0-solvent is 0.25. The branching of the polymer also reduces the hydrodynamic invariant by 15-20% compared to the standard value 3.2 x 10 erg/(K mol ) and results in anomalous values of the Huggins parameter. 

MIK Mikhaliov, Yu.M., Ganina, L.V., Kurmaz, S.V., Smirnov, V.S., and Roshchupkin, V.P., Diffusion mobility of reactants, phase equilibrium, and specific features of radical copolymerization kinetics in the nonyl acrylate/2-methyl-5-vinyltetrazole system, J. Polym. Sci. PartB Polym. Phys., 40, 1383, 2002. 

There is evidence now from direct radiotracer measurements and other investigations that metals of low reactivity, in particular Cu, Ag. and Au, diffuse into polymers at elevated temperatures and sometimes form clusters inside the polymer. Diffusion is most pronounced at low deposition rates, where a large number of isolated atoms impinge onto an initially almost metal-free surface. The mobility in the polymer matrix appears to be controlled by the availability of free volume. For reactive metals such as Cr and Ti, which form relatively sharp interfaces, no significant diffusion seems to occur due to strong binding to the polymer. 

It is currently imderstood that the solvent promotes the diffusion of polymer chains from one particle to another. As they cross boundaries they help in the formation of a uniformly built film. Temperature also plays role here as does the polymer stracture. The mobility of polymer chains increases rapidly above the glass transition temperature. It is therefore, a combination of the ambient temperature, the glass transition temperature of... 

Figure 4.23. Mutual diffusion between two polymers of very differing mobilities. The less mobile polymer relaxes by bulk flow, causing the interface position to move Ax towards the side rich in the more mobile polymer.

However, if we can assiune that the non-diffusive relaxation of the less mobile polymers is fast compared with the diffusion of the more mobile chains, we can derive a simple equation relating the mutual diffusion coefficient to the tracer diffusion coefficient and a thermodynamic factor. This equation has been applied to liquid systems, in which context it is known as the Hartley-Crank equation (Tyrell and Harris 1984), and to metals, in which context it is known as the Darken equation (Haasen 1984). The polymer version was first stated by Kramer (Kramer et al. 1984) and is often known as the fast theory . It is most compactly written in the form... 

The homonuclear Overhauser enhancements explained in section 4.2.1 may also in principle be exploited for spatial and conformational information. However, this is only possible when the proton shifts are unusually sensitive to tacticity, because otherwise they cannot be resolved. They can be investigated by either 1-D or 2-D methods. The 1-D method involves selective irradiations, but is relatively quick and easy to quantify. The 2-D method, NOESY [38], is more elegant. In both cases one must take precautions to avoid spin-diffusion if quantitative information is required. Spin-diffusion is discussed in chapters 6 and 7 in the context of solid-state NMR, where its effects are more serious. What happens, in brief, is that the Wq term in (equation 4.6) can become very large for a proton pair, so that spin energy flows freely between most of the protons in the sample. Thus all selectivity is lost. In practice, spin diffusion is not too serious in a typical semi-mobile polymer solution, so that qualitative distance information may easily be obtained. The method is particularly promising for random copolymers, where more resonances are available for selective irradiation, because of the many variations of local sequence, as well as of tacticity. 

Dynamic scattering occurs due to the relaxation of the concentration fluctuations of polymer segments with the scale commensurable with (see subsection 2.1.2). So, the relative contribution of the diffusion mobility of the macromolecules and their internal modes of motion depends on the wave vector q. 

The role of a solvent in the application and reaction of a functionalized resin is complex. An ideal solvent should meet the following requirements, it should (1) interact with the polymer matrix to optimize the diffusion mobility of reagent molecules, (2) have the correct solvating characteristics to aid any chemical transformations being carried out, (3) not limit the reaction conditions which are to be applied, (4) enhance translucence rather than opacity. Certainly, it is difficult to satisfy all these criteria simultaneously and the selection of a solvent often involves compromise. 

Diffusion describes the random motion that transports matter from one part of a system at high concentration to another at low concentration. Mathematically, this process relates the mass-transfer rate of a substance through unit area to the concentration gradient normal to the section by a proportionality constant, D (cmVsec), also referred to as the diffusion coefficient (Crank, 1975). Factors that affect protein diffusion in polymers include properties that alter polymer chain segmental mobility (degree of crystallinity, chain stiffness, degree of cross-linking), deformations that alter the free volume, and factors that can immobilize or denature the protein (Rabek,1980). 

In 1971, P.G. de Gennes wrote a seminal paper on the stochastic diffusion of a long polymer molecule in a strongly crosslinked gel. In this system, the gel network imposes topological constraints on the motion of the mobile polymer chain and can be viewed as forming a tube... 

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... 

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