Membrane osmometry, determination number-average molecular

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). 

Narrow Molecular Weight Triacetate Fractions. Narrow molecular weight cellulose triacetate fractions were obtained by both fractional precipitation and preparative GPC as described above. The number average molecular weight (1 ) of the various fractions and cuts was determined by high speed membrane osmometry. A linear dependence of GPC elution volume on log molecular weight for all cellulose triacetate fractions was found in both methylpyrroli-done and dichloromethane. 

Membrane Osmometry and Viscometry. Number-average molecular weights of PMMA were determined with a Mechrolab model 501 highspeed membrane osmometer in toluene at 60 °C except for samples 122-4 and 122-6 which were determined at 40°C. 

In addition to its major use in determining the number-average molecular weight (Ma) of polymers, osmometry has also been used to determine M of block copolymer micelles. The method involves determining the osmotic pressure (77) across a membrane that is permeable to solvent only. Because osmotic pressure is a colligative property, it depends on the number of particles, and hence yields Ma. It also depends on the interactions between particles, and thus... 

Fig. 18. Plot of apparent number-average molecular weight M , as determined by membrane osmometry, for a cellulose diacetate fraction in tetrachloroethane (TCE) against the temperature of measurement401 O, M in TCE , M in THF...

Membrane osmometry was measured on a few samples to determine the number average molecular weight (Mn). Regenerated cellulose membranes were used, and were found to be highly swollen in NMP, leading to both very long equilibration times and excellent retention of low molecular weights. Table I below shows the results of these and the above measurements for the samples reported here. 

Vapor Pressure Osmometry The VPO became a popular method for the determination of the number-average molecular weight of nonvolatile solutes of less than about 20,000 g/mol and that tend to diffuse across the membrane in MO experiments [91], This method operates on the principle that the vapor pressure of a solution is lower than that of a pure solvent (P°) at constant pressure and temperature. This vapor pressure lowering (AP) is proportional to the molar mass of the solute (polymer) for dilute solutions. As it is known, the vapor pressure of a solvent in dilute solutions obeys the Raoult s law, Pj = Pfxj, where Pj is the partial vapor pressure of the solvent whose mole fraction in the solution is Xj. In terms of the mole fraction of the solute, Pj = P° (l - X2) or AP/pO = -X2. 

Dudley [54] has described in detail the characterization of nylon-66 by SEC. Nylon samples were initially fractionated from a mixed solvent of phenol and water, and the number average molecular weight of the fractions measured by membrane osmometry in m-cresol at 105°C. The intrinsic viscosities of the fractions were also measured, as well as their SEC in m-cresol at 130°C. The chromatograms were analysed using a molecular mass calibration based on polystyrene standards and using a g-factor for nylon-6 6 of 13.9. The Mark-Houwink equation was then determined as... 

The absolute number-average molecular weight (M ) of substituted polyacetylenes can be determined by vapor pressure and membrane osmometry... 

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 ... 

There are other techniques for determining the various molecular-weight averages. Number average, Mn, can be obtained by membrane osmometry or end-group analysis. Weight average, Mw, is determined by... 

---