Molecular number average, definition

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... 

Suppose we have a sample of polymer of weight w grams containing Nq molecules. By definition, the number average molecular weight is given by... 

From a quantitative viewpoint, it is evident that the relative intensities of the resonances from carbons associated with branches and end groups can be compared to the intensity for the major methylene resonance, "n", at 30.00 ppm to determine branch concentrations and number average molecular weight or carbon number. The following definitions are useful in formulating the appropriate algebraic relationships ... 

With the previous definitions, the polymer carbon number and number average molecular weight are given by ... 

Then recall the definition of the number average molecular weight and substitute to obtain an expression for c in terms of this quantity (Equations 12-6) ... 

This is the definition of number average molecular weight M . Equivalent definitions follow from simple arithmetic. Since ... 

This is completely analogous to the definition of number average molecular weight Mn in Eq. (2-6). A number average of aquantity is always the sum of products of values of that quantity times the corresponding fraction of the whole sample which is characterized by the particular value.] Substituting Eq. (7-53) into Eq. (7-55),... 

Mjj Calc, number average molecular weights I see the footnotes in Table I for definitions) are in good agreement. For the third reaction in which R2 is the n-C Hg group, the observed M, was less than half of that expected on the oasis of the monomer-to-initiator mole ratio. 

The distribution we have assumed above is a number distribution, since the record consists of numbers of molecules of specified sizes. If we substitute the proportion of species fi, which have molecular weight Mj, by the corresponding mole fraction m in Eg. (4.2), we obtain the definition of number-average molecular weight Mn representing the number distribution ... 

While Eq. (4.3) gives a simple definition of the number average molecular weight Mn, we can drive other equivalent definitions following... 

Number-average molecular weights around 30,000 were estimated for compounds 123 and 124, by gel-permeation chromatography and vis-cosimetry. Circular dichroism and 1H NMR data in chloroform suggested the presence of definite secondary structures in this solvent. Crystals of both 123 and 124 were obtained upon annealing, and their structures were studied by X-ray diffraction of powders and oriented fibers. Polyamide 123 seemed to adopt a PI triclinic structure as observed for... 

The number-average sequence length of monomer Mi, in a way that is completely analogous to the definition of number-average molecular weight, is... 

From these definitions, the number and weight-average molecular weights, as well as the number average of branches can be written, respectively, as... 

---