Molecular weight skewness

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... 

Calibration of Gel Permeation Chromatograph Polystyrene Calibration. A plot of molecular size in (S) versus elution volume for polysty-rene standards in dichloromethane showed deviation from linearity at about 2,200 which may be attributed to Imperfect column resolution, peak broadening, axial dispersion and skewing. The extensive tailing of the chromatograms of high molecular weight polystyrene standards observed in dichloromethane has also been reported in the literature (23-26). 

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. 

Little is known of the physical properties of guanine aminohydrolase. Elution of rabbit liver enzyme from Sephadex gave a skewed activity peak the estimated molecular weight of the main component was 170,000, a minor shoulder component, 525,000 (60). 

Solubility in Methylene Chloride. The methods described above can show the presence of blocks of DMP and blocks of DPP units, but they do not distinguish between block copolymers and blends of homopolymers. Gel permeation chromatograms of the copolymers are sharp and symmetrical, indicating that they are indeed copolymers rather than blends, but this alone is not conclusive as blends of the homopolymers do not produce binodal or badly skewed curves under the conditions used unless the two polymers differ considerably in molecular weight. A partial answer to this question is provided by the solubility behavior in methylene chloride. Dimethylphenol homopolymer dissolves readily in methylene chloride but precipitates quantitatively on standing for a short... 

Each of the bimodal cases represented a mix of a skewed low molecular weight peak and a higher molecular weight normal peak. The two cases have a three-to-one and a one-to-three ratio of peak areas respectively. The fifth distribution corresponds to a classical free radical polymerization with a number average molecular weight of 50,000 (9). 

For bimodal MWDs none of the methods successfully resolved the two peaks for the case where a majority of the molecules were of low molecular weight (Figure 5). However, CONTIN provided the closest solution. For the case where the skewed low molecular weight peak consisted of only one quarter of the total mass, the GEX fit method gave good results. CONTIN showed three peaks, but the agreement can still be considered fair because of the difficulty in discerning two widely separated peaks of this type. As in the unimodal cases, the subdistribution method showed the poorest fits. 

The critical point is not symmetrically located on the phase boundary but skewed towards the lower-molecular-weight polymer, that is, the PMMA apex (for a discussion of this print see Ref. 36). 

There are various ways of expressing the skewness of statistical distributions. The method most directly applicable to polymers uses the third moment of the distribution about its mean. The extreme molecular weights are emphasized because their deviation from the mean is raised to the third power, and since this power is an odd number, the third moment also reflects the net direction of the deviations. 

---