Solute polydisperse

This result should be vahd for sufficiently high density 0 where correlations, brought about by the mutual avoidance of the chains, are negligible. Due to the recombination-scission process a polydisperse solution of living polymers should absorb or release energy as the temperature is varied. This is reflected by the specific heat Cy, which can be readily obtained from Eq. (9) as a derivative of the internal energy U... 

For a polydisperse solution—the hallmark of solutions of polysaccharides—s (and s ) will be a weight average [30,38,39]. If the solution contains more than one discrete (macromolecular) species—e.g. a mixture of different polysaccharides, the polydispersity will be manifested by asymmetry in the sedimenting boundary or, if the species have significantly different values for S2o,w. discrete boundaries are resolved (Fig. 2b [29]). 

In a more realistic case of a polydisperse solution, gd)(T) will be a sum of exponentials (one for every molecular weight species present) and Equation (51) becomes... 

This choice describes a polydisperse solution, in equilibrium with respect to a fictitious reliction of breaking and recombining chains ... 

In this contribution, the experimental concept and a phenomenological description of signal generation in TDFRS will first be developed. Then, some experiments on simple liquids will be discussed. After the extension of the model to polydisperse solutes, TDFRS will be applied to polymer analysis, where the quantities of interest are diffusion coefficients, molar mass distributions and molar mass averages. In the last chapter of this article, it will be shown how pseudostochastic noise-like excitation patterns can be employed in TDFRS for the direct measurement of the linear response function and for the selective excitation of certain frequency ranges of interest by means of tailored pseudostochastic binary sequences. 

Tg versus degree of polymerization was linear.254 Similarly, for a series of commercial starch hydrolysis products (polydisperse solutes), there was a linear relationship between Tg (Tg of the maximally freeze-concentrated solute glass) and 1/MW.270... 

For polydisperse solutes, M2 is the number-average molecular weight. The calibration constant is commonly determined using a substance of known molecular weight at various concentrations. As a rule, AR is measured at several lignin concentrations a plot of AR/cw against cw is a straight line. If K is known under the same experimental conditions, the intercept at infinite dilution is Mn. 

Expression (1.88) is valid for very low concentrations (c < c ) or for noninteracting molecules. In a polydisperse solution, each speciesy with molar mass Mj contributes KcjMj to the Rayleigh ratio. Therefore, the total Rayleigh ratio for a polydisperse system is given by the sum-------------... 

In polydisperse solutions, the decay of the autocorrelation function is not a single exponential and it is challenging to extract the distributions of diffusion coefficients and sizes from the non-exponential decay of the intensity correlations. In the case of a bidisperse distribution with diffusion coefficients that differ by at least a factor of 2, it is possible to fit the decay of the intensity correlations by a sum of two exponentials and obtain the corresponding sizes and relative concentrations of the two components -----------------------------------------------------------... 

It is therefore highly desirable to develop more quantitative methods for characterization of pore structures. The results of recent investigations, including ultrafiltration (water flux and rejection of a polydisperse solute), high-resolution SEM and nitrogen sorption/desorption analysis, are described below. 

Homogeneous polydisperse solute mean form function... 

However, there are other types of experimental tests of the theory of polymers in solution these are experiments in which the chemically homogeneous solute is a mixture of two (or more) samples whose polymer chains have very different average sizes. However, we cannot test the theories of strongly polydisperse solutions as we did in the weakly polydisperse case i.e. by referring to a monodisperse solute of molecular mass equal to the average molecular mass of the sample. Polydispersion here becomes an essential parameter. 

For polydisperse solutions, the corrections become rather complicated at high concentrations. Let us consider only the limit of very low concentrations. 

Further discussion of polydisperse solutions is given in Section 8.10 in connection with light-beating experiments. 

In Section 8.5, the effects of polydispersity on integrated spectra of polydisperse solutions were discussed. It was shown, for instance, that weight-average molecular weights... 

With a polydisperse solute, the molar mass Mi that occurs in Equation (9-6) is the number-average molar mass of the solute. In a multicomponent system, the observed osmotic pressure II is given as the sum of all the osmotic pressures II, ... 

Polymer samples used for coil—globule transition studies must be as close to monodispersity as possible. When a polydisperse solution is cooled to a certain temperature below 9 its part containing high-molecular-weight fractions enters two-phase regions while the rest still maintains homogeneity. Behavior of such a system cannot be analyzed by the theory of uniform solutions. 

Given f P), these q I equations can, in principle, be solved for Tp, ", and f Py as functions of . The resulting relation between Tp and gives the cloud-point curve, while that between Tp and " gives a line called the shadow curve. The latter cannot be determined experimentally, since the second phase is too small in volume to be analyzed for the composition. It can be shown that the cloud-point and shadow curves coincide with the conjugate coexistence curves when and only when the solution is strictly binary. This fact is important, because some authors make no distinction between cloud-point curve and coexistence curve in describing phase equilibria of polydisperse solutions. 

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