Types of Molecular Weight

Suppose that a protein sample consists of 30% of molecules of mol wt. 20 000, 40% of molecules of mol wt. 30 000, and 30% of molecules of mol wt. 60 000. Calculate the number-average molecular weight. 

The mole fractions are 0.3, 0.4, and 0.3, respectively. Therefore, from equation (3.4), 

Other methods of molecular-weight determination, such as diffusion, sedimentation, flow birefringence, and light scattering (all of which are considered later in this chapter) involve terms related to the size and shape of the molecules and give a 

Since W = NiMi, the weight-average molecular weight can be expressed as 

Using the data given in the previous example, calculate the weight-average molecular weight. 

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Table 1.5 also includes two additional types of molecular weight average besides those already discussed. The following remarks describe some features of these two, the z-average molecular weight, and the viscosity average ... 

One further point might be made here. Although the example illustrates the difference between the two types of molecular weight average, the weight average molecular weight in this example cannot be said to be truly representative, an essential requirement of any measure of central tendency. In such circumstances where there is a bimodal, i.e. two-peaked, distribution additional data should be provided such as the modal values (100 and 100000 in this case) of the two peaks. 

An additional complication arises from the different types of molecular weight averages obtained by different methods. If the polymer comprises a broad range of species differing in chain length, as is usually the case (see Chap. VIII) unless a careful fractionation has been performed, different molecular weight methods will give substantially different values on this account. 

The detailed treatment of the molecular weight analysis of polymers is left to other texts. We should be aware that there are two types of molecular weights, number average and weight average. 

What type of molecular weight average, or M , is based on colligative properties ... 

There are other types of molecular weights based on higher-order moments to the distribution (see Table 1.23), but M and M, are the most widely nsed qnantities. In... 

A variety of tools address the stoichiometry and molecular weight of compounds. The necessary condition that at least two metals be present for multiple metal bond formation is a simple sorting method for initial studies the molecular unit as determined by any type of molecular weight study must correspond to that of at least two metals per molecule. Conductivity measurements supply similar data for ions, and mass spectral data can indicate the presence of at least two metals per molecule. Analytical data with nonintegral ligand-to-metal ratios require that some multiple number of metal centers be present in order to formulate a stoichiometric compound. This array of techniques only eliminates the possibility of metal—metal bonds for mononuclear metal complexes, and further studies are always necessary to confirm the presence of an attractive metal-metal interaction. 

A few very important points have been neglected by some authors in their evaluation of chain transfer constants by means of kinetic measurements. Frequently, a retardation of the overall rate is to be observed in the presence of chain transfer agents. A correct value of the chain transfer constant can result only if the reactions which lead to this retardation are properly considered in the kinetic scheme. In addition, the equation which one must use to calculate the chain transfer constant depends on the type of molecular weight average which is measured. Failure to... 

The first type of molecular weight is the number-average, and is defined by... 

These two types of molecular weight averages are representative of the type called absolute methods, in that well-established thermodynamic equations can be used to convert the experimental data directly into a value of the molecular weight. However, some other methods require calibration. The most important of these indirect methods involves a measurement of the intrinsic viscosity. This quantity is a measure of the extent to which a polymer molecule increases the viscosity of the solvent in which it is dissolved. The viscosity method can be calibrated to yield a viscosity-average molecular weight, defined by... 

If the type of molecular weight distribution of the polymer is known, it is posdble to express 7 as a function of two parameters only, U and a, according to Eq. (65). Thus, for the Schultz-Zimm distribution 33) Eq. (65) yields )... 

Their MWD was determined by GPC. Tables I to IV show the types of molecular weights and distributions obtained when the polymerizations were permitted to proceed to 100 conversion. The following conclusions can be drawn from the data ... 

The polymerization process results in polymer molecules with a variety of chain lengths or molecular weights. Thus, any measurement by experimental means leads to an average value. We should distinguish between two types of molecular weight averages ... 

Notation in parenthesis indicates the type of molecular weight (A/w) where is the weight average molecular... 

Three types of molecular weights (M/i, Mw, and Mz) can be determined from sedimentation data. 

The order of these three types of molecular weight is > M . The distributions of the polymer molecular weight are indicated by polydlspersity The polydlsperslty of the molecular weight of the polymer can be represented by a distribution curve or distribution index. Figure 1.3 is a typical distribution curve of the molecular weight. The relative sizes... 

TYPES OF MOLECULAR WEIGHT 61 Now, the average degrees of polymerization are... 

As a comparison of the types of molecular weight, we let Ni be the number of molecules of kind i (/ being the degree of polymerization) present in the mixture. A/,-be their molecular weight, and Cf be the concentration or weight. Then,... 

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