Colligative methods

As noted earlier, certain techniques such as colligative methods, light-scattering photometry, special mass spectrometry (MS) techniques, and ultracentrifugation allow the calculation of specific or absolute molecular weights. Under certain conditions some of these also allow the calculation of the MWD. 

What are colligative methods for measuring molecular weight and what kind of molecular weight do... 

Given the sensitivity of colligative methods to the presence of low molecular weight impurities, particular care was taken to isolate lignin samples free of such foreign contaminants. Thus, for example, the extraction... 

Compared to the colligative methods light scattering can yield information on a possible dissymmetry of the aggregates. For anisotropic particles the direction of the electric field associated with the incident light may not coincide with the shift of the electron cloud. The intensity of light scattered at (usually) 90° from anisotropic aggregates is increased over the value predicted on the basis of isotropy by the Cabannes factor. 

Regular membrane osmometry is not suitable for measurements of below about 30,000 because of permeation of the solute through the membrane. Other colligative methods must be employed in this range, and vapor pressure lowering can be considered in this connection. The expanded virial form of Eq. (2-72) for this property is... 

Da) are even smaller. Considering that the colligative methods are independent of the physical properties of DOM and the noncolligative methods exploit collectively several different physical properties of DOM, the median values in Figure 3 are remarkably consistent. 

The principle involved in a molecular-weight determination by a colligative method is that one determines the mole fraction, molarity, or molality. If the concentration of the solution is known in grams per liter, the molecular weight is easily calculated. 

To a stirred solution of 11.09 gm (71.0 mmole) of methylphenyl phosphinic acid in 600 ml of ethanol is added 7.72 gm (35.5 mmole) of finely divided zinc acetate dihydrate. A white precipitate results and the mixture is stirred for another 2 hr at room temperature. The precipitate is filtered and washed twice with ethanol to give 11.8 gm (95%) after drying at 60°C in a vacuum oven. The TGA of the polymer indicates it is stable to about 400°C in nittogen without weight loss. Weight loss starts at 425°C. The polymer softens below 1(X)°C and is soluble in benzene and chloroform. The molecular weight of the polymer varies between 2500 and 10,000 (colligative methods). 

Hence, any colligative method should yield the number average molar mass M of a polydisperse polymer. Polymer solutions do not behave in an ideal manner, and nonideal behavior can be eliminated by extrapolating the experimental (F/c) data to c = 0. For example, in the case of boiling point elevation measurements (ebullio-scopy) Equation 9.2 takes the form... 

Consequently, virial coefficients can be determined from the concentration dependence of the reciprocal apparent molar mass. But, since the various methods for measuring the molar mass yield various averages of it (see Chapters 8 and 9), the virial coefficients obtained will be average values which vary according to the method used to determine them. Virial coefficients obtained from osmotic-pressure measurements (and all other measurements based on colligative methods) will give the average... 

The field of application of Osmometry is limited to polymers with masses below 100,000, since the precision depends on the mass, and therefore it becomes inaccurate high masse Furthermore, being a colligative method, osmometry yields Mn but not Mw, and therefore it cannot be used to discriminate a narrow MMD from a broad MMD nor a unimodal MMD from a bimodal MMD. 

The type of average which is obtained when attempting to measure the molecular weight of a polymer is a function of the experimental methods which are used. For all colligative methods, the magnitude of the effect which is measured is dependent on the number of molecules in a given volume of solvent, hence... 

The equations could be solved directly, usually by numerical means, to yield the entire distribution of polymer chain lengths. This procedure is quite tedious and lengthy, since the equations form an infinite set. Alternatively, moment equations can be developed from the original set of evolution equations. Inasmuch as colligative methods of analysis yield data related to the moments, it would appear that the solution of a truncated set of moment equations might suffice to give an adequate description of a polymerization. 

Apparatus for determination of molecular weight by colligative methods... 

Colligative methods are those that involve the determination of the numbo of macromolecules present in a polymer sample of given mass it is then easy to deduce the number average molar mass (M ) of the sample analyzed. 

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