Molecular mass number distribution

Having calibrated the system, the calculation of the molecular mass/weight distribution curve and molecular weight averages requires a number of data treatment steps (Evans, 1973). 

Polymer characterization usually requires a combination of several analytical tools such as NMR and GPC. Today, a number of analytical techniques exist that can provide molecular mass, structure, and composition information, and MALDI-MS is now emerging as a powerful method for polymer characterization. Some demonstrated advantages of the technique include the ability to determine average molecular mass and distributions without the need of polymer standards and with high speed, precision, and accuracy, to analyze polymer mixtures with minimiun sample work-up, and to provide structural and compositional information via... 

An average molecular mass (viscosity average) An average molecular mass (number average) Molecular dimensions and an average molecular mass (weight average) Molecular mass distribution... 

This equation appears to have a number of names, of which the Mark-Houwink equation is the most widely used. In order to use it, the constants K and a must be known. They are independent of the value of M in most cases but they vary with solvent, polymer, and temperature of the system. They are also influenced by the detailed distribution of molecular masses, so that in principle the polydispersity of the unknown polymer should be the same as that of the specimens employed in the calibration step that was used to obtain the Mark-Houwink constants originally. In practice this point is rarely observed polydispersities are rarely evaluated for polymers assigned values of relative molar mass on the basis of viscosity measurements. Representative values of K and a are given in Table 6.4, from which it will be seen that values of K vary widely, while a usually falls in the range 0.6-0.8 in good solvents at the 0 temperature, a = 0.5. 

In the basic molecular mass distribution, N(M), the number N of molecules in a sample is plotted vs. their molecular mass, M. Figure 1.2 presents a sketch of a... 

Figure 1.2. A number molecular mass distribution N (M) of an ideal chain polymer. N (M) is defined for integer multiples of Mm, the monomer mass. The integer factor, P, is called the degree of polymerization... 

Now the function displays the number fraction of molecules with a certain molecular mass. Its integral is 1 by definition. Nevertheless, we still call it the number molecular weight distribution because the factor /N (A/) dM is nothing but a constant. 

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... 

The concentration of the synthase or the number of enzyme copies has been assumed to have an influence on the molecular mass and molecular mass distribution of the synthesized polymer [33],but this has not been confirmed. The only variables found so far to control the molecular mass of the polymer are the initial ratio of substrate to enzyme levels, and the concentration of inducing factors in the culture medium [34-36] cf. also Chap. 9 of this book. 

Example At molecular weights of some 10 u the isotopic distribution of organic ions becomes several masses wide (Fig. 11.20). The minimum resolution for its full separation is always equal to the ion s mass number (Chaps. 3.3.4 and 3.4.3). Lower resolution can only provide an envelope over the distribution. At insufficient resolution, the resulting peak may even be wider than the envelope. [98]... 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

Eq. 2 pKt, inhibition constant Mr, relative molecular mass, log D1A, logarithm of the distribution coefficient at pH 7.4 HBA, number of hydrogen bond acceptors. 

In further studies it was also found that the aromatic fraction of these bitumens as obtained from silica gel chromatography also contained naphthenic sulfides (5) with molecular weight and ring number distribution similar to those of the sulfoxides. Relative abundances versus carbon number as obtained from the field ionization mass spectrum for each ring number series are shown in Figure 4. It is clear from these and... 

When does this process start to play a significant role When the relaxation time of such an elastic deformation exceeds the time scale at which the deformation takes place, which is the reciprocal shear rate 1/f. We have seen before that for a number of similar polymers with the same shape of molecular mass distribution, the deviation from Newtonian behaviour starts with the same value of the shear stress, thus (according to 7= r/p) at values of /which are inversely proportional to the (zero)viscosity p. It seems plausible to suppose that (again with similar mol mass distributions) the relaxation time of the elastic deformation is proportional to the viscosity (see also next section), so that the above mentioned observation is explained. 

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