Measurement of diffusion constants

It was discussed in Sect. 4.2 that there is a very slow change in the a-dynamics in stacked thin films of P2CS. There may be several possibilities for this slow change. If heterogeneous diffusion in thin polymer layers is an essential process, then direct measurement of diffusion constant of a tracer polymer chain in a thin layer of the... 

Experimentally, the measurement of diffusion constant is done by two methods ... 

Table 1 lists a few pulsed-field-gradient measurements of diffusion constants for some familiar mesophases considered in the text. Extensive data have been collected by Kriiger [24] and by Lindblom and OrMd [25] further more recent references have been summarized by Karger et al. [38]. 

Concentration of Electrolyte Myer and Sievers"" applied the Donnan equilibrium to charged membranes and developed a quantitative theory of membrane selectivity. They expressed this selectivity in terms of a selectivity constant, which they defined as the concentration of fixed ions attached to the polymer network. They determined the selectivity constant of a number of membranes by the measurement of diffusion potentials. Nasini etal and Kumins"" extended the measurements to paint and varnish films. 

If the far exceeds the cylinder length, over which experimental measurements of diffusion distribution of EEPs are taken, then the EEP radiative term found in expression (5.10) may be neglected. If such an approximation cannot be done, then the rate constant of radiative decay should be taken into consideration in processing the experimental data. 

The calculated and experimental curves deviate considerably in shape, and it seems that the simple diffusion model is not adequate to describe the kinetics of the uptake process in this case. Also the value of D (9.25 X 10"9 cm.2/sec.) required to make the two curves coincide at early times seems to be much smaller than expected. The only data available on the diffusion of molybdenum oxide in liquid silicates is from a report by Norman et al. (11), who measured the diffusion constant of... 

Direct measurements of rate constants for quenching of donor triplets by various acceptors in flash experiments indicate that the rates never exceed those of diffusion-controlled reactions. Moreover, the rates are roughly inversely proportional to viscosity.143 Consequently, we infer that transfer occurs at a measurable rate only if the two partners are nearest neighbors in solution. 

There are circumstances in which the simple rules for the partition of intermediates break down. If the acceptor nucleophile reacts with the acylenzyme before the leaving group has diffused away from the enzyme-bound intermediate, the partition ratio could depend on the nature of the leaving group (e.g., due to Steric hindrance of attack, etc.). Also, the measurement of rate constants for the attack of the nucleophiles on the intermediate could be in slight error due to the nonspecific binding effects mentioned above. 

Thus, the results of direct measurements of diffusion rate constants for reactions of etr with acceptors in water-alkaline matrices in the vicinity of the temperature of their devitrification corroborate the conclusion that long-range electron tunneling is the main channel of performing these reactions at low temperatures. 

A recent study has employed the new technique of quasi-elastic light scattering for estimation of diffusion constants (257). The result for the native enzyme at 24° is in close agreement with the data given in the tabulation. The value of D as a function of temperature was measured through the thermal transition. The method was also used to follow the kinetics of the urea-induced transition. 

This index is a measure of the width of the decay rate distribution /(F) and thus the range of diffusion constants (and hence sizes) present in the sample. When 0 = 0, the sample is monodisperse. A nonzero value of Q will, however, not tell one whether the distribution is a broad symmetric distribution, a skewed distribution, or possibly a bimodal distribution since Q models only the width and not the shape of the distribution. 

The properties of the surplus segment probability p and the effective constraint coordination number z are less well established. It seems possible that p will dep d on polymer species to some extent, since loop projection may be easier for a more locally flexible chain. Weak dependences on concentration and temf rature are likely for the same reason. On the other hand, z characterizes the topology on a fairly large scale and therefore may be virtually a universal constant. Diese however are only some speculations. Values of p and z can be established by various experiments, p from the elastic properties of networks and also from the relaxation of star polymers, z from relative relaxation rates of linear and star molecules in liquids and networks and also from measurements of diffusion rates of stars in linear chain liquids. The adequacy of the... 

The determination of frictional ratios from measurements of sedimentation constant or diffusion constant or both, for proteins of known molecular weight. 

Measurements of dielectric constant as a function of frequency. These dielectric dispersion measurements permit the estimation of the relaxation times or rotary diffusion constants which characterize the rotary Brownian movement of the protein molecule. 

Owing to the finite electrolyte volume ofthe nanoliter droplet, the diffusion boundary layer reaches the dimensions of the droplet within seconds, assuming a diffusion coefficient of for example D = 110-5 cm2 s 1. A constant diffusion gradient can not be established because the bulk concentration is reduced. Thus, measurements of diffusion limited currents are not stable over time. The electron transfer reactions discussed below were carried out on anodic oxide layers with maximum current densities 3 to 4 orders of magnitude lower than the diffusion limited current densities, thus ensuring a stable support of consumables over the time of the measurement. In order to prevent evaporation of electrolyte, the ambient was saturated with water vapor. 

Measurement of steady-state compositions y and y after thermal diffusion equilibrium has been established between temperatures T and T" is the most accurate way of determining the thermal diffusion constant. The next-to-the-last column of Table 14.26 pves values of the measured thermal diffusion constant for several binary isotopic mixtures. In all these cases, 7 is positive, which means that the light isotope concentrates at the higher temperature under the experimental conditions listed. 

Most macromolecules when dissolved in salt solutions acquire charges that are shielded by an atmosphere of counterions. This ion atmosphere affects the diffusion coefficient of the macromolecule and hence the light-scattering time-correlation function. Electrolyte solutions are discussed in Chapters 9 and 13. Recent measurements of diffusion coefficients have been made by several groups. Lee and Schurr (1974) have studied poly-L-lysine-HBr. Schleich and Yeh (1973) have performed similar studies on poly-L-proline. Raj and Flygare (1974) have studied bovine serum albumin (BSA) and find that at high ionic strength and low pH the diffusion constant decreases. This they attribute to the expansion of the molecule. 

The work of Vanderslice et al. [142] shows that FIA systems can be used for measurement of diffusion coefficients—provided that the flow geometry of the FIA system is kept constant (preferrably a straight rigid inner polished tube) and calibration can be made by means of a solute with known Dm value. 

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