Osmotic molecular weight determination

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

In support of the association theory, colloid chemists cited non-reproduceable cryoscopic molecular weight determinations (which were eventually shown to be caused by errors in technique) and claimed that the ordinary laws of chemistry were not applicable to matter in the colloid state. The latter claim was based, not completely without merit, on the ascerta-tion that the colloid particles are large aggregates of molecules, and thus not accessible to chemical reactants. After all many natural colloids were shown to form double electrical layers and adsorb ions, thus they were "autoregulative" by action of their "surface field" (29). Furthermore, colloidal solutions were known to have abnormally high solution viscosities and abnormally low osmotic pressures. 

The osmotic pressure can be measured accurately for colloidal solutes, and one molecular parameter of interest that is readily determined by osmometry is the number average molecular weight of the solute. Molecular weights determined by osmometry are absolute values no calibration with known standards or any assumed theoretical models is required. Even the assumption of solution ideality is not a problem, since results are extrapolated to zero solute concentration before calculations are made. 

We conclude the chapter with a discussion of the Donnan equilibrium and the thermodynamic behavior of charged colloids, particularly with respect to osmotic pressure and molecular weight determination (Section 3.5), and some applications of osmotic phenomena (Section 3.6). 

SIDEBAR 7.13 MOLECULAR WEIGHT DETERMINATION BY OSMOTIC-PRESSURE MEASUREMENTS... 

Synthetic polymers are often produced with a range of degree of polymerization and molecular weight. As shown next, a molecular weight determined for such a polymer by measurement of osmotic pressure is a number-average molecular weight. 

A very different structure has been found for the mannan that is present in yeast. Methylation and hydrolysis67 showed this to be a highly branched molecule. The methylated material was inhomogeneous, the intrinsic viscosity of different fractions varying between 0.062 and 0.212, with corresponding molecular weights (determined by osmotic pressure measurements) between 18,000 and 76,000 (90-830 hexose units). 

Starch acetate solutions, because of their stability, are suited for osmotic pressure measurements and have been employed with considerable success for direct molecular weight determinations. 

Schardinger himself did not attempt molecular-weight determinations of the crystalline dextrins. The first molecular-weight determinations were based on freezing-point depressions in water" or on osmotic-pressure measurements. " " Other measurements were based on dialysis rates or on cryoscopic measurements rvith the acetates," nitrates, and methyl ethers. In some cases microisopiestic methods were used."-... 

Staudinger, H. Schulz, G.V. Highly polymerized compounds. CXXVI. Comparison of osmotic and viscosimetric molecular-weight determinations of polymer-homologous series. Ber. 1935, 68B, 2320-2335. 

Ultracentrifugation experiments yield Mz values. They are used primarily for biological polymers. The random coil conformation of most synthetic polymers in solutions makes it difficult to interpret these data and this method is little used with such materials. Among the absolute methods of molecular weight determination, only the osmotic method and the light scattering method are given primary consideration in this chapter. 

Problem 4.8 Show that the molecular weight determined from osmotic pressure measurements is the number average molecular weight. 

Figure 4.5 Molecular weight determination from osmotic head (/i) and concentration (c) data (Problem 4.9).

By a fractional precipitation a polymer A with most probable distribution (7 = 2.0) and an osmotic molecular weight of 150,000 is separated into two fractions B and C with molecular weights, respectively, 250,000 and 325,000, determined by light scattering. Calculate the weight of B that would be obtained from 200 g of initial polymer A. If both B and C have the same polydispersity, what is the value of the polydispersity index ... 

The amino acid lysine is found, on elemental analysis, to contain 19.17% nitrogen (at. wt. 14.01). A molecular weight determination by the osmotic-pressure method yields an approximate value of 150. Calculate a more accurate value of the molecular weight. 

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