Distribution functions molecular size

For a system of homodisperse molecules, the value of a single decay constant can be determined from equation (13), a single exponential. However, scattering from a solution of polydisperse molecules results in a distribution of exponentials consequently, analysis of DLS data must be made using a probability function which accounts for the distribution of molecular sizes. 

Calculations of the distribution functions of sizes of relaxed structures (Figure 5.11b) show that the starch/silica hydrogel at ft=2.34 g/g is characterized by narrower molecular pockets than that at ft =17.9 g/g. The narrowest pockets (nanopores) are found for hydrogel with gelatinized starch alone. Notice that all distributions show complex structures of pockets (voids) between/inside starch molecules that are in agreement with complex structure of unfolding starch macromolecules. 

Hi) Gaussian statistics. Chandler [39] has discussed a model for fluids in which the probability P(N,v) of observing Y particles within a molecular size volume v is a Gaussian fimction of N. The moments of the probability distribution fimction are related to the n-particle correlation functions and... 

Size exclusion liquid chromatography M) has been widely used to characterize distributions of molecular weights in polymer specimens. This paper describes a package of computer programs for automatic data collection and data reduction in size exclusion liquid chromatography (2). The programs and the environment in which they operate are carefully tailored to emphasize the interaction between the user and his data rather than the Interaction between the user and the computer. The system we describe differs from that described by Koehler et al. (J) in that all functions are performed by a stand-alone system. 

The main statistical characteristic of the chemical structure of a heteropolymer among those pertaining to the first type is the distribution of molecules f( h, 12) for numbers l and h of their constituent monomeric units Mi and M2. In dealing with a high-molecular weight polymer, these numbers may be taken as continuous variables, uniquely specifying chemical size l=l + h and composition f = li/l of a macromolecule. Under such a consideration, it is more convenient instead of function /(Zi, l2) to use the equivalent function of Size-Composition Distribution (SCD) f(l, < ) This is possible to represent... 

A complete theory predicting retention times or volumes as function of molecular size has not yet been formulated for gel permeation chromatography. A specific column or set of columns is calibrated empirically to give such a relationship, by means of which a plot of amount of solute versus retention volume (the chromatogram figure below) can be changed into a molecular-size-distribution curve. Generally commercially available narrow... 

Size exclusion chromatography (SBC) is a separation process by which molecules are fractionated by size on the basis of differential penetration into porous particulate matrices. Blution volume (Vq) of any given molecular species relative to another of different size is dependent on the pore diameter of the matrix, pore-size distribution, pore volume (Vp, interstitial volume (Vq) and column dimensions. Use of SBC to estimate molecular size is achieved by plotting the log of the molecular weight of a series of calibrants against their elution volume. Since Vg is a function of Vg and Vj, its magnitude will be dependent on the geometry of a column. 

The molecular weight distribution in this type of nonlinear polymerization will be much narrower than for a linear polymerization. Molecules of sizes very much different from the average are less likely than in linear polymerization, since this would require having the statistically determined / branches making up a molecule all very long or all very short. The distribution functions for this polymerization have been derived statistically [Peebles, 1971 Schaefgen and Flory, 1948], and the results are given as... 

The molecular size distribution functions for three-dimensional polymers are derived in a manner analogous to those for linear polymers, but with more difficulty. The derivations have been discussed elsewhere [Flory, 1946, 1953 Somvarsky et al., 2000 Stockmayer,... 

In some cases the molecular-weight distribution can be determined by turbi-dimetric titration, a technique which is based on the fractional precipitation. A precipitant is added to a very dilute solution of the polymer, and the resulting turbidity is measured as a function of the amount of added precipitant the preparative separation of the fractions is thereby avoided. If the polymer is chemically homogeneous, the mass distribution function can then be calculated. Tur-bidimetric titration is also suitable as a means for establishing the best fractionation conditions (e.g., choice of solvent/precipitant combination, size of fractions, etc.), before carrying out a full-scale fractionation by precipitation. 

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