To determine number-average molecular weight

Attempts were made to determine number average molecular weights (Mn) by osmometry (Mechrolab Model 502, high speed membrane osmometer, 1 to 10 g/1 toluene solution at 37 °C), however, in many instances irreproducible data were obtained, probably due to the diffusion of low molecular weight polymer through the membrane. This technique was abandoned in favor of gel permeation chromatography (GPC). 

Vapor Phase Osmometry. A Wescan Model 233 vapor phase osmometer was used to obtain number average molecular weights. The lignin solutions were made up with HPLC grade tetrahydrofuran (THF) and shaken manually until the solutions were clear. The experiments were conducted at 30°C. Number average molecular weights were determined by multistandard calibration (41), a procedure found to greatly enhance reproducibility and accuracy of the results. Experiments were conducted immediately after sample preparation and three days later. 

Carbon-14 labelled co-catalysts have been used on a number of occasions to measure the numbers of active sites. Usually, however, osmotically determined number average molecular weights, were not reported. Thus it was not possible on these occasions to demonstrate unequivocally that nc< l which is a prime requirement for meaningful results. Recently, Ayrey and Mazza (80) have examined the titanium trichloride-triethyl aluminium catalysed polymerization of styrene at 60° and have found values of ne 3—10. They also obtained indirect evidence for the formation of poiyethylene-14C during the preparation of the catalyst. Similar observations have been reported previously (92). On the strength of these observations the use of labelled co-catalysts to measure active centres must be regarded as a somewhat suspect procedure. This conclusion is borne out by the recent kinetic work of Coover et al. (81). 

A chemical method for determining number-average molecular weights involves an analysis of end groups. If the polymer was prepared in such a way that each chain has either one or two labelled ends, then analysis for these ends is equivalent to counting the chains. For example, the ends could be hydroxyl groups or radioactive initiator fragments, and the analysis could involve titration, spectroscopy, or measurements of radioactivity. Chains formed in condensation polymerizations, from A-B monomers... 

Several vapor pressure osmometers are now commercially available. Although they are mainly used for determining number-average molecular weights in aqueous and organic solvents, they can also be employed to evaluate the total osmolality of biological solutions or dissociation and activity coefficients. Each model has its own technical characteristics. However, all are comparable in terms of general measurement procedure and sensitivity. 

The molecular weight obtained by measurement of a colligative property is a number-average molecular weight. Two serious problems need to be addressed in determining number-average molecular weights of humic substances ... 

Membrane osmometry is one of two osmometry techniques that are used to determine molecular weight. The other is vapor-pressure osmometry. The latter requires calibration using samples of known molecular weight, while membrane osmometry is an absolute technique. Only membrane osmometry is described here. The osmotic pressure of a polymer solution is directly related to the number-average molecular weight of the polymer and is useful when Af is less than about 500,000. The basic principle is that if a polymer solution and pure solvent are placed on opposite sides of a semi-permeable membrane, i.e., one that allows solvent to pass but not polymer, there will be a tendency for solvent to flow into the solution, where its chemical potential is lower. If the pressure of the solution is raised above that in the solvent, the chemical potential will be balanced, and the flow will stop when the pressure difference reaches the osmotic pressure, n. The thermodynamic expression required to determine the molecular weight is the van t Hoff equation ... 

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