Number average molecular mass

End group quantification is thus a useful method for number average molecular mass determination. Also, if the end group concentration is higher than the value calculated from an independent Mn determination, chain branching can be deduced and quantified. 

The obvious definition of the number average, Mn, of the distribution is the position on the M-axis that divides the area under the n (A/)- curve in equal parts (cf. Fig. 1.3). Because of the fact that n M) is normalized to 1, each of the subareas is equal to 0.5. As 50% of all the molecules are shorter than Mn, the other 50% are longer than Mn. Bearing in mind the normalization, the number average molecular mass is... 

Figure 1.3. The number average molecular mass, M , is the position that divides the area under the corresponding distribution in equal parts... 

D (7y notation employed for block copolymers, where the subscripts (w and y) denote the composition in weight percent and the superscripts (x and z) the number-average molecular mass in kilograms per mole. In the case of PPDX-fr-PCL diblock copolymers, the letter D is used for PPDX and the letter C for PCL... 

Fig. 21 Representative microfluidic device and resulting data from ATRP on a chip a image of a microfluidic device (dimensions 25 mm x 75 mm) fabricated from UV curable thiolene resin between two glass slides b reaction data for ATRP of HPMA synthesized on a chip showing the correlation of flow rate (or residence time) to reaction time and resulting conversion of monomer (M) to polymer (ln([M]o/[M]) c comparison of number average molecular mass (M ) and poly-dispersity for -butyl acrylate prepared in a traditional round bottom flask ( Flask ) and on a chip ( CRP Chip ). (Reproduced with permission from [102])...

Molecular weight measured by GPC (polystyrene standard). Mw is weight-average molecular mass and Mn is number-average molecular mass. 

From eqn. (148) an important relation can be derived between the number average molecular mass of the product and catalyst yield, 0, equal to mP/nK (Mn = PM)... 

This generic name is commonly, but improperly, used to designate a family of copolymers obtained from unsaturated hydrocarbons of petroleum refinery C4 fractions, and the products obviously must not be confused with the crystalline isotactic 1-polybutene obtained through Ziegler-Natta catalysis. The commercial polybutenes are clear, water-white, odorless, oily to highly viscous liquids, with number-average molecular masses ranging from about 300 to 2500. 

The number-average molecular mass M expressed in g/mol is given by the formula ... 

Another known procedure for the measurement of number-average molecular mass is based on membrane osmometry. This can be done using van t Hoff equation ... 

Figure 6.21 (a) Idealised distribution of molecular mass of a pol)rmer (M = number average molecular mass ... 

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