Molecular weight variance

Traditionally, column efficiency or plate counts in column chromatography were used to quantify how well a column was performing. This does not tell the entire story for GPC, however, because the ability of a column set to separate peaks is dependent on the molecular weight of the molecules one is trying to separate. We, therefore, chose both column efficiency and a parameter that we simply refer to as D a, where Di is the slope of the relationship between the log of the molecular weight of the narrow molecular weight polystyrene standards and the elution volume, and tris simply the band-broadening parameter (4), i.e., the square root of the peak variance. 

This, in turn, reduced the number of polymer particles (the loci of reaction) and hence the reaction rate fell. However, this explanation is at variance with the results reported in Figure 12 where the molecular weight (weight-average) clearly increases with increasing Reynolds number. It seems more likely that the turbulent flow results could be explained by a decrease in the effective initiator concentration. This low concentration would also explain why there is no further reaction after a period of about one hour as contrasted with the batch reactions where the reaction is still proceeding after two to three hours. The current absence of corroborating evidence makes this explanation very tentative. 

Curve G, Figure 20, (sample G in Table V) shows the results of adding columns to GPC 1 (resulting in Code A4, Table I). Now the variance for NBS7( has been reduced by 1/3 with a notable loss of the high molecular weight tail. 

Mjj and My or [q] for the broad MWD standard are taken as known quantities. Fy(v) is the normalized chromatogram for the broad MWD standard obtained with a mass detector. D2 is the slope of the molecular weight calibration curve at the peak position of the chromatogram (the equation of the tangent is given by M(v) = Dj exp(-D2v). is the variance of the single-species chromatogram... 

M tris-HCl buffer solution (pH 7.94) was used as mobile phase. The peak separation obtained with a three column set (G 3000 PW + 2 G5000 PW) is comparable to the peak separation obtained in the present study for the molecular weight range, 120,000 to 3.6 X 10. Peak broadening appeared to be appreciable although no calculations of single-species variance were done. 

The overall objective of the system is to map from three types of numeric input process data into, generally, one to three root causes out of the possible 300. The data available include numeric information from sensors, product-specific numeric information such as molecular weight and area under peak from gel permeation chromatography (GPC) analysis of the product, and additional information from the GPC in the form of variances in expected shapes of traces. The plant also uses univariate statistical methods for data analysis of numeric product information. 

This can be shown ly plication of the error propagation equation (Equation 11). If the error in the peak molecular weight M is represented by the error variance, s and we let... 

Number Protein spots selected spots are indicated in Fig. 3 condition. Protein sample mouse liver lysate 2.3 pg, Number of tested times 5, The values shown in the table are coefficient of variance (CV) (%). The data are summarized in pJand molecular weight (M. W.) directions... 

Molecular weight information is especially useful since variances in molecular weight are shown to impact adhesion and brittleness properties (Kroschwitz, 1990), solubility (Flory, 1970), and sorption and mass transfer characteristics of organic solutes (Kilduff and Weber, 1992). The impacts of varying molecular weight on polymer crystallinity, solubility, and, to a lesser extent, the glass transition temperature are discussed in the following sections. 

The variance measures the absolute breadth of the distribution, but properties that depend on the width of the distribution would depend on the width relative to the average. For this reason the dispersion index is defined as the ratio of the weight to the number average molecular weight, which is related to the variance as follows ... 

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