Polymerization distribution

Although carbohydrates/polysaccharides exist in such huge amounts, their industrial processing is expensive due to enormous quality fluctuations of succeeding raw material batches. The reason for these fluctuations is a high variability on the molecular level, particularly in the degree of polymerization distribution, in branching characteristics, and in complex interactive properties. 

Differences between molar and mass degree of polymerization distribution of a partially hydrolized starch... 

Degree of polymerization distribution of a plant fructan (inulin) at increasing physiological age of the source remarkable performance of S-200 in the low dp range degree of polymerization distribution obtained from bad (P-6) and good (S-200 / P-6) resolution of high dp components... 

On-line changing of solvent from DMSO to H2O for a starch glucan establishing an absolute calibration function characteristics of mass and molar degree of polymerization distribution for a broad distributed starch sample... 

The selective separation range of the S-500/S 1000-system for glucans is shown for hybrid starch Triticale T22. This mixture of scb and nb/lcb glucans contains components in the range between approximately dp 50-300,000 glucose monomers (Fig. 16.11). The degree of polymerization distribution obtained from dextran-based calibration was computed as well in terms of... 

FIGURE 16.13 Degree of polymerization distribution (m dpD d) for synthesized amylose -type nb/lcb glucans calculated from dextran-calibrated — amylose-converted calibration of S-SOO/S-IOOO dp. = SSI [glucose units]. 

Briefly summarized, S-1000 shows better resolution in the high dp range, whereas the CL 2B system resolves low dp components better. Due to these differences in separation performance, the degree of polymerization distribution and degree of polymerization average values for the same sample obtained from broad scb— nb/lcb-transformed dextran calibration yielded dp = 29,900 glucose units for the S-1000 system and dp = 21,100 glucose units for the CL 2B system (Fig. 16.18). 

FIGURE 16.19 Degree of polymerization distribution (m dpD d) of wild-type potatoe starch ( ), a nb/lcb fraction ( amylose -type A)- s b fraction ( amylopectin"-type ) of the native starch ... 

Consequently, inappropriate (P-6) and appropriate (P-6/S-200) separations yield significantly different results for the degree of polymerization distribution and average values of degree of polymerization (Fig. 16.27). In a first and qualitative evaluation, dp distribution achieved from P-6/S-200 differs significantly in symmetry from the dp distribution of P-6. In particular, differences in separation performance become obvious for high dp components. In a... 

FIGURE 16.27 Degree of polymerization distribution (m dpD d) computed utilizing system calibra-... 

In these experiments, simultaneous DRI (mass) and FALLS detection is applied to obtain absolute information about molecular weight (degree of polymerization) distribution and average values of degree of polymerization. 

M NaCl eluent. Because of the good performance of the TSK PW system in the low dp range, DMSO was shifted outside the selective separation range > 50 ml) and aqueous eluent-dissolved starch components could he analyzed in terms of absolute degree of polymerization distributions (mass m ... 

Figure I 6.34 Degree of polymerization distribution molar distribution ( ) with number average degree of polymerization (dp = 140 glucose unimers) mass distribution ( ) with weight average degree of polymerization dp = 1242 glucose unimers.

Fractional extraction242 (dissolution) may also be employed, as was demonstrated for a polyxylose, using batchwise extraction with aqueous ethanol.141 A more convenient procedure would involve adsorption of the polyglycose onto an inert, solid support (such as cellulose), followed by extraction using a procedure already described.243 The continuous nature of this process, the opportunity for solvent to reach all particles of the polymer, and the possibility of using gradient elution make this method attractive, particularly if the examination of a range of polymeric distributions is desired. 

The quantity v is then used for calculating the sol fraction, degree of polymerization distribution and averages of the sol, the number or concentration of elastically... 

Hence, molecular weight, which is handled as molar mass distribution (MWD) or degree of polymerization distribution (dpD), is an important characteristic of polysaccharides (Fig. 6A). For practical purposes, molar mass distributions are expressed in either differential form ( d), with mass fractions [Eq. (2a)] or molar fractions [Eq. (2b)j represented by the normalized area (1.0), or integral form ( i), with accumulated percentages represented by the normalized height (maximum height = 1.0). 

Furthermore, sulfur has been written in the diatomic form S2, although there is actually a distribution of polyatomicity at the temperatures of interest. Mauras has also calculated the equilibria between the species S2, S4, S6, and S8 At 1 atm total pressure and temperatures above 1000°F, he showed that equilibria calculated using the polymeric distribution of sulfur do not differ from those based on diatomic sulfur. 

Instead of determining the complete degree of polymerization distribution, it is often considered to be sufficient to measure various moments of the distribution, that is, various degree of polymerization averages. The relationships between the various moments or averages are also characteristic of the distribution type. 

For the differential molar degree of polymerization distribution, the Poisson distribution gives... 

A numerical example may clarify these ratios. Assume there are three fractions A, B, and C, which are mixed together according to their mass fractions Wi. Each fraction also has a degree of polymerization distribution which is characterized by individual number, mass, andz averages (Table 8-1). The number, mass, andz averages of the mixture are, according to Equations (8-44)-(8-46),... 

The equilibria discussed presume that all reaction partners are in equilibrium with each other. The degree of polymerization distribution is then given by the probabilitypi of finding a molecule of degree of polymerization i ... 

As can be seen from the numerical example (Table 18-4) for a kinetic chain length = 10, the degree of polymerization distribution is exceptionally narrow. Since the mass-average degree of polymerization Xw is obtained from Xw = Xwii, this gives, with Equation (18-45) and X = p I... 

It is not unusual for polymers to have p = 0.999 and average length (k) = 1000. Figure 4.1 shows that this simple model predicts well an experimental polymerization distribution. 

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