Summative fractionation

Application of the Summative-Fractionation Method to the Determination of Mw/M for Narrow-Distribution Polymers... 

The Summative-Fractionation Method. To review briefly (8), in the summative-fractionation method one performs a series of small-scale single-step fractional precipitations in which increasing percentages of the total polymer are precipitated. The weight fractions x and average molecular weights Mw of all the precipitates are determined. One calculates and plots against x a parameter... 

Table I. Summative-Fractionation Parameter H for the Poisson Distribution...

Figure 1. The summative-fractionation parameter H (ideal-fractionation assumption) as a function of polydispersity K w/Kln for the Poisson, Schulz-Zimm exponential, Lansing-Kraemer logarithmic-normal, and rectangular...

Figure 2. The summative-fractionation parameter H as a function of polydispersity for the Poisson distribution. H is calculated for the ideal-fractionation assumption while H0.001 and H0 01 we calculated including the Flory-Huggins correction for imperfect fractionation, with the volume ratio R equal to 0.001 and 0.01, respectively.

The summative fractionation is a method of fractionation with the determination of the overall polymer precipitate mass in the second phase (without removing the previously precipitated polymer fractious) ou adding a due portion of non-solvent (or on decreasing temperature). I hus, the degree of phase transformation x is determined at the stage of summative fractionation. 

Spectroturbidimetric titration (STT) of polymer solutions is a version of summative fractionation with optical weighing" of the polymer in the colloid-disperse state. 

Summative fractionation according to Spencer (67) consists of a number of single-step separations, each starting with the whole polymer itself. The temperature, or the amount of non-solvent, is varied so that the size of the fraction in the concentrated phase differs from one separation to another and covers the whole range between 0 and 1. Naturally, Spencer s procedure is much faster than the usual techniques. 

Spencer developed a method for evaluating the distribution from the experimental data obtained with his summative fractionation procedure. His method is bsised on the assumption that the separation according to molecular weight is ideally sharp, i.e. all molecules above a given size are present in the concentrated phase, whereas shorter chains are confined to the dilute phase. This assumption cannot be reconciled with the actual situation, as was pointed out by Billmeyer eind Stock-MAYER (69). 

In all but one of these studies the apparent rate constants of propagation were determined. The observed apparent propagation rate constant (kSPP) is a summ of products of rate constants on various forms of active centers (e.g. free ions, ion-pairs, aggregates) and their fractions in the polymerizing mixture... 

The summative-fractioruition method was extended to apply to narrow-distribution polymers with polydispersity (Mw/ Mn) less than 1.12. A fractionation parameter H, previously defined and calculated for theoretical molecular weight distributions for normal polymers, was computed for narrow-distribution polymers. The calculations were made both with and without correction for fractionation errors, using the Flory-Huggins treatment. The method was applied to a well-characterized anionic polystyrene with Mw = 97,000, for which the polydispersity was estimated by this technique to be 1.02 (in the range 1.014-1.027, 95% confidence limits). 

Fractionation and Bearing on Summative Wood Analysis and on Studies on the Hemicelluloses Pap. Trade J. 1946,122, 35-43. 

CISHC Chem. Safety Summ., 1977, 48, 25 Shaw, A. W., private comm., 1978 During the vacuum fractional distillation of bulked residues (7.2 t containing 30— 40% of the bis(hydroxyethyl) derivative, and up to 900 ppm of iron) at 210—225°C/ 445—55 mbar in a mild steel still, a runaway decomposition set in and accelerated to explosion. Laboratory work on the material charged showed that exothermic decomposition on the large scale would be expected to set in around 210—230°C, and that the induction time at 215°C of 12—19 h fell to 6—9 h in presence of mild steel. Quantitative work in sealed tubes showed a maximum rate of pressure rise of 45 bar/s, to a maximum developed pressure of 200 bar. The thermally induced decomposition produced primary amine, hydrogen chloride, ethylene, methane, carbon monoxide and carbon dioxide. 

Equation (2-42) is the integral equivalent of summative equation (2-4). The number fraction of the distribution with molecular weights in the interval M to M + dM is dx M) =x(M)dM, and the corresponding weight fraction sdw M) = w M)dM. The following expressions are examples of integral equations that are directly parallel to the summative expressions generally used in this chapter ... 

A complete chemical analysis accounts for all the components of the original wood sample. Thus, if wood is defined as part lignin, part carbohydrate, and part extraneous material, analyses for each of these components should sum to 100%. The procedure becomes more complex as the component parts are defined with greater detail. Summative data are frequently adjusted to 100% by introducing correction factors in the analytical calculations. Wise and coworkers (3) presented an interesting study on the summative analysis of wood and analyses of the carbohydrate fractions. The complete analytical report also includes details of the sample, such as species, age, and location of the tree, how the sample was obtained from the tree, and from what part of the tree. The type of wood analyzed is also important i.e., compression, tension, or normal wood. 

Wise L.E., Murphy M., D Addiecco A.A., Chlorite holoceUulose, its fractionation and beating on summative wood analysis and on studies on hemicelluloses, Pap. Trade J., 122, 1946, 35-43. 

Fractionation schemes deviating from the successive procedures are conceivable and have been applied. We shall consider three of them in this study trirngulm fractionation. Spencer s summative procedure and Schulz s, . Spitzenfraklionierung". 

At first sight, the underlying assumption appears to be reasonable. Fig. 11 illustrates this. However, calculated separations for the bimodal function Wg reveal that in this case the fraction distribution at a given ir-value does not always include all of the material covered at a smalla value of X. This explains why the /h (x) function shows a peculiar shape (Fig. 9). A normal behaviour of M as a function of x appears to be conditional for the evaluation of summative date suggested here. 

Wise, L. E., Murphy, M., D Addieco, A. A. Chlorite hollocellulose, its fractionation and bearing on summative wood analysis and on studies on the hemicelluloses. Paper Trade 1946,122, 35 2. 

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