The Number Average Molecular Mass

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... 

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)... 

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

The formula shows the number average molecular mass and it is a property of function of the number of polymer molecules in a polymer sample. 

The osmotic pressure that a senes of polymer solutions of decreasing concentration produce against pure solvent is dependent on the number average molecular mass of the dissolved polymer. However, if the tendency to flow of a series of solutions is measured and each solution is made from a polymer of higher molecular weight,... 

Plotting A/ versus c M gives the number average molecular mass of the im-imer (intercept) and the association constant (slope). An analogous expression, we get for the weight-average molecular mass when molecule-related open association exists. 

High-temperature SEC finds wide application in polymerization studies, as the molecular mass distribution is an artefact of the various reactions involved in polymerization, initiation, termination, and transfer. It is diagnostic of living systems and random polymerization reactions, such as condensation and radical initiated polymerizations, for which the distributions are Poisson and normal respectively. In the polymerization of ethene and propene by Ziegler-Natta catalysts, the determination of the concentration of active centres as a function of conversion defines catalyst type. Similar studies have been made in the study of chain scission by thermal degradation or by irradiation, in defining the number of molecules produced from the inverse of the number average molecular mass and random chain scission eventually leads to a normal molecular mass distribution, with polydispersities close to 2.0. This has, of course, been widely used to produce narrow from broad molecular mass distribution samples prior to fractionation. 

As pointed out above, dynamic vapor-liquid equilibrium measurement methods are not very suitable for concentrated polymer solutions, especially due to their heavy foaming behavior. For dilute polymer solutions, however, there is continuing application of ebulliometry as an absolute method for the direct determination of the number-average molecular mass M . Dedicated differential ebulliometers allow the determination of values up to an order of 100,000 g/mol. EbuUiometry as a method for molar mass determination was recently reviewed by Cooper, Glover, and Mays and Hadjichristidis. ... 

In this manner, the number average molecular mass (Mn), the mass average molecular mass (M ), the peak molecular mass (Mp), and the polydispersity (M. /Mn) may be calculated. 

Usually the same is observed on a practice. At this, however, the number-averaged molecular mass of the forming polymer proportional to the length of a chain will increase from the illuminated surface to the inside of the layer, thus forming a gradient of the properties of a polymer on the layer. In some cases it can be obtained and be desirable. 

The molecular mass distribution, its number average and mass average and the width of the molecular mass distribution belong to the key parameters of polymeric materials. Let rii be the number of molecules with the molecule mass Mi according to the distribution of the molecular masses in a certain plastic. The number average molecular mass M and the mass average molecular mass can be written as ... 

Figure 2.26. Dependence of the glass transition temperature of polystyrenes of narrow molecular mass distribution on the number average molecular mass (MJM for all samples ranged between 1.01 and 1.12). Heating experiments, with heating rate of 10°C/min. (Menczel, nnpublished results.)...

In other identical conditions, the decrease of monomer initial concentration reduces the number-average molecular mass of polymer. Polydispersity index doesn t practically depend on monomer initial concentration. 

For PMMA, Berry showed that the surface energy was strongly dependent on polymer molecular mass [25], His results (Figure 13.10) fitted an approximately linear dependence of the fracture surface energy on reciprocal molecular mass, such that y = A — B /Mv, where My is the viscosity average molecular mass. Many years previously, Flory [26] had proposed that the brittle strength is related to the number average molecular mass. 

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