Osmometry vapor-pressure

In vapor pressure osmometry, the system ( ) is a droplet of a volatile liquid (1) in which a nonvolatile solute (2) is dissolved. The system ( ) can exchange energy of compression with the gas phase ( ) that consists entirely of the solvent. Further, solvent (1) may move freely from the liquid phase into the gas phase. The gas phase is in contact with a thermostat and a manostat. We address this as a combined system ( ) Thus, the conditions of equilibrium are 

The temperature of the thermostat T and the pressure of the manostat p are constant. We have expressed the chemical potential as a function of intensive variables. Since the chemical potential of the system ( ) consists of a single component, it can no longer be dependent on its composition. Further, we want to keep the temperature and the pressure of the system ( ) constant, therefore 

We cannot make any statement on the temperature of the liquid phase T. We expand as a function of temperature, pressure, and mole fraction and get 

We have to make an assumption what is. This term is the increase of entropy, when 1 mol of solvent enters into the liquid phase. This process is associated with the phase transfer from gaseous to liquid. 

If we think that all the entropy is set free on condensation in the liquid phase, then this expression is the total entropy of condensation, which is just the reverse 

The colligative property shows up also in the vapor pressure of the solution. The vapor pressure p of the solvent above the solution is lower than the vapor pressure p of pure solvent. The vapor phase is nearly ideal. Therefore, the chemical potential of the solvent molecule in the vapor phase is given by pfiT) + k T n p/p°), where p,°iT) is the chemical potential at a reference pressure p°. The vapor-liquid equilibrium for pure solvent is dictated by 

For a solution with a polymer volume fraction at / , the equilibrium is given by 

The second term on the right-hand side is much smaller compared with the first term. Thus, 

This equation gives the principle of vapor pressure osmometry In place of measuring n directly, we can measure the drop in the vapor pressure of the solvent above the solution to estimate II. 

K being a constant which is usually determined experimentally during cell calibration. Lj is the heat of evaporation of the solvent, the density of the solution, and c the polymer concentration. Finally, because the given deviation is valid only for ideal solutions but only real solutions can be studied in practice, the above equation is developed in a power law series with respect to c  

Experimentally, AT is determined for approx, five different polymer concentrations. After several minutes, a constant temperature difference AT of the two drops is reached which is proportional to their initial difference in vapor pressure and thus proportional to the number of dissolved macromolecules in the solution drop. AT can then be determined by measuring the difference in electric resistance of the two thermistors. Then, ATIKc is plotted vs. c (thus the power law series is broken after the linear term in c) and the plotted values are extrapolated to c 0. Mj, is finally calculated from they axis intercept. 

Vapor pressure osmometry is slightly less sensitive than membrane osmometry (M 2 X 10 ) but is not affected by very short chains in the polymer sample which migrate through the semipermeable membrane in the case of membrane osmometry. Therefore, it is in particular valuable for the analysis of oligomeric materials. 

Springer Series in Wood Science Methods in Lignin Chemistry (Edited by S.Y. Lin and C.W. Dence) 

At steady state, according to the hypothesis that AT is proportional to the chemical potential decrease, Aof the solvent, one can write 

Where T is the cell temperature, and AHV the molar latent heat of vaporization of the solvent. 

In the actual determination, AT is measured as a resistance difference, AR, (Bonnar et al. 1958, Lewis and Randall 1961), and can be expressed as 

For polydisperse solutes, M2 is the number-average molecular weight. The calibration constant is commonly determined using a substance of known molecular weight at various concentrations. As a rule, AR is measured at several lignin concentrations a plot of AR/cw against cw is a straight line. If K is known under the same experimental conditions, the intercept at infinite dilution is Mn. 

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Among the techniques employed to estimate the average molecular weight distribution of polymers are end-group analysis, dilute solution viscosity, reduction in vapor pressure, ebuUiometry, cryoscopy, vapor pressure osmometry, fractionation, hplc, phase distribution chromatography, field flow fractionation, and gel-permeation chromatography (gpc). For routine analysis of SBR polymers, gpc is widely accepted. Table 1 lists a number of physical properties of SBR (random) compared to natural mbber, solution polybutadiene, and SB block copolymer. 

The molecular weights and molecular weight distributions (MWD) of phenolic oligomers have been evaluated using gel permeation chromatography (GPC),23,24 NMR spectroscopy,25 vapor pressure osmometry (VPO),26 intrinsic viscosity,27 and more recently matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS).28... 

ADMET polymers are easily characterized using common analysis techniques, including nuclear magnetic resonance ( H and 13C NMR), infrared (IR) spectra, elemental analysis, gel permeation chromatography (GPC), vapor pressure osmometry (VPO), membrane osmometry (MO), thermal gravimetric analysis (TGA), and differential scanning calorimetry (DSC). The preparation of poly(l-octenylene) (10) via the metathesis of 1,9-decadiene (9) is an excellent model polymerization to study ADMET, since the monomer is readily available and the polymer is well known.21 The NMR characterization data (Fig. 8.9) for the hydrogenated versions of poly(l-octenylene) illustrate the clean and selective nature of ADMET. 

Membrane osmometry, vapor pressure osmometry, gel permeation chromatography, light scattering, and intrinsic viscosity measurements have been used to... 

However, because of the high price, MALDI-TOF mass spectrometers have not come into wide use. Vapor pressure osmometry (VPO), an old and traditional method for estimating molecular weight, is useful in the field of CPO chemistry. The experimental error of this measurement is approximately 10% however, the obtained data are sufficiently useful to estimate the number of porphyrins in a molecule. 

Vapor Pressure Osmometry - The number average molecular weights of polymers with Mn < 20,000 were determined using "Model 232A Molecular Weight Apparatus, Wescan Instruments, Inc., 3018 Scott Blvd., Santa Clara, CA 95050". Toluene was used as solvent and the instrument was calibrated using polystyrene of Mn 9,000 and 20,400. 

The degrees of polymerization determined by mass spectroscopy are corroborated by vapor pressure osmometry and gel permeation chromatography studies (21). 

Larabee, C.E., Jr. and Sprague, E.D. (1986) Aggregation of sodium undecanoate and sodium 10-undecenoate in water at 37 °C vapor pressure osmometry. Journal of Colloid and Interface Science, 114 (1), 256-260. 

Vapor pressure osmometry in principle, should produce valid results at moderate molalities (a few hundredths to a few mol kg-- -) but the real accuracy and precision of this method have not yet been properly demonstrated and/or documented (Goldberg, Nuttall, and Staples, 1979). 

Bisphthalonitrile monomers were cured neat, with nucleophilic and redox co-reactants, or in combination with a reactive diluent. Dynamic mechanical measurements on the resulting polymers from -150 to +300°C turn up several differences attributable to differences in network structure. Rheovibron results were supplemented with solvent extraction, differential scanning calorimetry (DSC), vapor pressure osmometry, and infrared spectroscopy to characterize the state of cure. 

In this work, bis-phthalonitrile networks (1, 2) were examined by dynamic mechanical and dielectric methods, supplemented with infrared measurements of state of cure, DSC, vapor pressure osmometry, and solvent extraction. For resins cured with 4,4 -methylene dianiline as co-reactant, a simple network model rationalizes the data. 

Molecular weights of the products as measured with vapor pressure osmometry were in good agreement with the calculated ones. Interestingly, resins based on hexahydrophthalic anhydride and diisopropanolamine with tertiary amines as functional groups are soluble in water without quaternization of the... 

Grams monomer/mole initiator Vapor pressure osmometry Light scattering... 

GPC was calibrated with polystyrene standards. M was also determined by vapor pressure osmometry (VPO) on a Wescan model 233 molecular weight apparatus at a current setting of 50pamp in toluene... 

The association number of Li amides, such as LrN(SiMe3)2, organolithium compounds bound at the a-position to S or Se atoms, such as LiCH2SePh, and various transition metal complexes was determined at 0°C in THF or at —35°C in Et20, by differential vapor-pressure osmometry. The method allows handling compounds sensitive to autooxidation, moisture and temperature . ... 

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