Chain diffusion coefficient

Lin et al. [60] have tried to reveal the mobility course of PMMA chains in dependence on the distance from the adsorbing surface. They have used the neutron reflectivity measm emerits on the chain diffusion coefficient, PMMA... 

B. Tinland and R. Borsali. Single-chain diffusion coefficient of f-dextran in polyvinyl pyrrolidone/water fluorescence recovery after photobleaching experiments. Macromolecules, 27 (1994), 2141-2144. 

J. Desbrieres, R. Borsali, M. Rinaudo, and M. Milas, xf interaction parameter and single-chain diffusion coefficients of dextran/polyvinylpyrrolidone/water dynamic light scattering experiments. Macromolecules, 26 (1993), 2592-2596. 

Chapter 8 treats single-chain motion including measurements of polymer self-diffusion and tracer diffusion, and measurements that track the motions of individual polymers. It is almost uniformly found that a stretched exponential in polymer concentration and a joint stretched exponential in c, P, and M describe how the single-chain diffusion coefficient depends on matrix concentration and molecular weight and on probe molecular weight. On log-log plots, these functions appear as smooth curves that almost always agree with measurements of D (c, P, M) at concentrations extending from dilute solution to the melt. 

Orientation sometimes leads to lower permeabiHty values (better barrier properties). Orientation can iacrease packing density, which lowers the diffusion coefficient D it can also iacrease the difficulty of hopping or diffusiag ia a direction perpendicular to the film. In the latter case, movement ia general may be fast, but movement through the film is limited. However, mere stretching does not always lead to orientation of the molecular chains. In fact, stretching can lead to void formation, which iacreases permeabiHty. 

The advantage of the simulations compared to the experiments is that the correspondence between the tracer diffusion coefficient and the internal states of the chains can be investigated without additional assumptions. In order to perform a more complete analysis of the data one has to look at the quench-rate and chain-length dependence of the glass transition temperature for a given density [43]. A detailed discussion of these effects is far beyond the scope of this review. Here we just want to discuss a characteristic quantity which one can analyze in this context. 

Tubular reactors are used for some polycondensations. Para-blocked phenols can be reacted with formalin to form linear oligomers. When the same reactor is used with ordinary phenol, plugging will occur if the tube diameter is above a critical size, even though the reaction stoichiometry is outside the region that causes gelation in a batch reactor. Polymer chains at the wall continue to receive formaldehyde by diffusion from the center of the tube and can crosslink. Local stoichiometry is not preserved when the reactants have different diffusion coefficients. See Section 2.8. 

Increasing temperature permits greater thermal motion of diffusant and elastomer chains, thereby easing the passage of diffusant, and increasing rates Arrhenius-type expressions apply to the diffusion coefficient applying at each temperature," so that plots of the logarithm of D versus reciprocal temperature (K) are linear. A similar linear relationship also exists for solubUity coefficient s at different temperatures because Q = Ds, the same approach applies to permeation coefficient Q as well. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

In addition to the environmentally benign attributes and the easily tunable solvent properties, other important characteristics such as low interfacial tension, excellent wetting behavior, and high diffusion coefficients also make SCCO2 a superior medium for the synthesis of nanoscale materials [2]. Previous works on w/c RMs showed that conventional hydrocarbon surfactants such as AOT do not form RMs in scCOi [3] AOT is completely insoluble in CO2 due to the poor miscibility of the alkyl chains with CO2, restricting the utilization of this medium. Recently, we had demonstrated that the commonly used surfactant,... 

Table 5, Average polymer chain concentration (ape), polymer swellability (S), rotational correlation times of TEMPONE (r) and self-diffusion coefficient of methanol (Zf) in the swollen 2,2% Pd catalysts.

The diffusion of U and Th within a solid is, in general, very slow due to their large size and charge (Van Orman et al. 1998). Even at mantle temperatures, it is expected that a solid will not fully equilibrate with the surrounding phases (fluid, melt or other solid phases) if solid diffusion controls the equilibration. As yet, there have been no direct determinations of diffusion coefficients for any other decay chain element. 

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