Calculations differential molecular weight

If Mark-Houwink coefficients were supplied at setup time, the chromatogram may be converted into the differential molecular weight distribution of the specimen. Various averages characterizing this molecular weight distribution are then calculated. The molecular weight distribution may be written to a file. 

Fig. 4 Left Fluorescence, MALLS (90°) and RI signals from a CCOA-labeled cellulose sample. Right Differential molecular weight distribution and degree of substitution of carbonyl groups (DSco) as calculated from the detector outputs...

Analytical expressions have been derived for calculating dispcrsitics of polymers formed by polymerization with reversible chain transfer. The expression (eq. 17) applies in circumstances where the contributions to the molecular weight distribution by termination between propagating radicals, external initiation, and differential activity of the initial transfer agent are negligible.21384... 

L is obtained from the first point of inflection on the low-molecular-weight side of the major peak of the molecular weight distribution plot. In practice this is most easily determined from the maxima in a differential plot of the molecular weight distribution, chi (log M)/d log M versus log M, the dotted plot in Fig. 3-12. For this polymerization it is easy to detect not only L. but also Li, L3, and Lj. The detection of several Lt values acts as an internal check on the PLP-SEC method. For Fig. 3-12, the kp values calculated from L, La, and L are within 2% of each other the value from L4 is within 6-7% of the other values. In practice, closeness between kp values from L and L2 are considered sufficient to validate the PLP-SEC method. 

The size exclusion chromatography for this study was done in the routine manner execept for the inclusion of an online viscosity detector called a Differential Viscometer <3> (Viscotek Corp., Porter, Texas, USAl. This instrument together with an RI concentration detector permits the calculation of intrinsic viscosities across the chromatogram. An IBM PC data system with software is also provided (5). The software acquires data from both detectors, and performs calculations of intrinsic viscosity and molecular weight distributions using the Universal Calibration Method. 

Macromolecular properties of grafted cellulosic fibers usually measured are differential solubility in either polymeric or cellulosic solvents, mechanical or physical properties, and abrasion resistances. The molecular weights of the grafted or block polymers and of cellulose, both before and after formation of macrocellulosic radicals, have been determined. The number of grafted or block polymer molecules per cellulose molecule calculated has usually been much less than one. Grafted cellulosic fibers exhibit second order transition temperatures, dependent on the composition of the grafted polymer (3, 4). 

The differential equations used to calculate the evolution in time of the moments of the molecular-weight distribution will be presented in Section 13.6.2. 

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