Molar mass Z average

A further but less widely used average is the z-average molar mass, M, defined as ... 

It is rather straightforward to show that proper integration over the cell from the meniscus (rm) to the bottom (rb) yields the weight and z-average molar masses Mw and Mz [12] ... 

Higher molar mass averages sometimes are quoted. For example, certain methods of molar mass measurement (e.g., sedimentation equilibrium) yield the z-average molar mass (Afx) which is defined as follows... 

M v Numeric-, Weight-, Viscosity-, z-Average Molar Masses... 

The z-average molar mass M. is defined as the ratio of the third to the second moments of the number fraction distribution ... 

Knowledge of the concentration c, and weight-average molar mass of each elution volume enables calculation of the weight-average and z-average molar masses ... 

Equations (6.148) and (6.149) provide a way of obtaining weight- and z-average molar masses from size exclusion chromatography. Are they approximate or exact methods If the concentration c, and weight-average molar mass of each elution volume are accurately measured, would the correct and Af, of the whole sample he known ... 

The Z-average molar mass is obtained from sedimentation equilibria experiments. 

For n = 0, Eq. (10.5) reflects the normalization condition. The first moment (n = 1) yields an average value of the distribution function. The second moment (n = 2) contains information about the broadness of the distribution function. The third moment (n = 3) describes the asymmetry of the distribution function. Unfortunately, these moments cannot directly be measured. However, they can be related to quantities accessible by experimental observations. For the characterization of polymers, several average values with respect to molar mass were applied (i.e., number-average molar mass (M ), mass-average molar mass (Mm)-and z-average molar mass (Mz). In polymer thermodynamics, mostly the concept... 

The z-average molar mass can be measured using an ultracentrifuge. Gel permeation chromatography allows the measurement of the complete distribution function and hence the estimation of all average molar masses. 

The Z-average molar mass (Z refers to the German word for centrifuge, i.e., Zentrifuge) is derived from equilibrium sedimentation. It is defined as... 

The third quantity is called the z-average relative molar mass or simply the z-average molar mass denoted and defined as the weighed average of the mass fraction of each macromolecule having a given molecular mass. 

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