Molecular weight distribution skewness

The results in that table are consistent with the picture of chain metalation since the data demonstrate the formation of multiple polystyrene blocks. The grafted polystyrene recovered has a rather broad molecular-weight distribution skewed toward the low-molecular-weight range. The high value of catalyst efficiency as determined in polymers 1 and 3 could result from either limitations in the analysis of molecular-weight distribution or from some form of chain-transfer mechanism. 

Complete description of a molecular weight distribution implies a knowledge of all its moments. The central tendency, breadth, and skewness may be summarized by parameters calculated from the moments about zero U, U[, U 2, and These moments also define the molecular weight averages Mn, and M. Note that A/n and My, can be measured directly wiihoul knowing the distribution but it has not been convenient to obtain A j of synthetic polymers as a direct measurement of a property of the sample. Thus, some information about the breadth of the number... 

It is impossible to manufacture a truly monodisperse polymer in which every molecule has the same value of M. Either the molecular weight distribution (MWD), or statistical averages of the MWD, are measured to characterise polymers. The mean and standard deviation are familiar statistical measures. An equivalent of the mean is used to characterise polymers, but the standard deviation is not used because the distribution shapes are skew rather than normal . 

The distance from the point of injection to the midpoint of the molecular weight distribution curve is a measure of the average molecular weight. If there are peaks in the curve, this suggests a blend of polymers. An initial shoulder in the curve suggests presence of gel, whilst a shoulder at the low end of the distribution suggests addition of some material to the polymer. A skewed distribution indicates a bias towards that end of the molecular weight distribution. 

L/min N2) for the characterization of alcohol (AE) and alkylphenolethoxylates (APE). The authors noted that for those APEs with a low number of ethylene oxide residues, the ELSD skews the molecular weight distribution to higher molecular weights. This is due in part to the volatility of those species (and therefore a lower than expected signal). Conversely, the UV absorptivity must be corrected for the decrease in molar absorptivity as the chain length increases. The latter fact is critical if one pure standard is used for quantitation of all components. Overall, peak shapes were excellent and the authors claimed excellent reproducibility. 

First, the ring-opened tetramethylene bis(trlflate) ester is produced in all cases studied and its behavior as a relatively sluggish THF polymerization initiator causes the otherwise narrow molecular weight distribution to skew toward the low end. Second, at relatively high initial anhydride concentrations,... 

Although there was some skewing towards low molecular weights particularly for the narrowest distribution, these curves were generally well fit by a Gaussian shape. Furthermore, the same was found for the copolymer fractions shown in Figure 16. Results are summarized in Table V. 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

Besides the calculation of average molecular weights, several other means of characterizing the distribution were produced. These include tables of percentile fractions vs. molecular weights, standard deviation, skewness, and kurtosis. The data for the tables were obtained on punched cards as well as printed output. The punched cards were used as input to a CAL COMP plotter to obtain a curve as shown in Figure 3. This plot is normalized with respect to area. No corrections were made for axial dispersion. 

---