Osmometry, membrane vapor phase

The practical range of molecular weights that can be measured by membrane osmometry is approximately 30,000 to one million. The upper limit is set by the smallest osmotic pressure that can be measured at the concentrations that can be used with polymer solutions. The lower limit, on the other hand, depends on the permeability of the membrane toward low-molecular-weight polymers. For measurements of Mn less than 30,000 another technique known as vapor-phase osmometry described next is more suitable. 

The practical range of molecular weights that can be measured by membrane osmometry is approximately 30,000 to one million. For measurements of M less than 30,000 another technique known as vapor-phase osmometry described next is more suitable. 

Fig. 6.15 Design for membrane osmometry. The bent arrow suggests a transfer of solvent via the vapor phase instead through the membrane...

Equation Eq. (6.82) conforms to Eq. (6.79). Thus, we can conclude that via the vapor phase the same equilibrium would be established than via the membrane. In other words, the membrane is not neeessary, if the solvent is sufficiently volatile. We call this procedure the altibaric method. In practical measurements, the establishment of the equilibrium via the membrane is much faster than the establishment via the gas phase. Therefore, elassieal membrane osmometry is still preferred. 

Equations applicable to membrane osmometry, as also in the case of ebulliometry, cryoscopy, and vapor phase osmometry, can be rigorously derived from the second law of thermodynamics in the form... 

Thus, in order to determine the molar mass of a partially permeating solute, the solution is first dialyzed with the same membrane as is to be used for osmometry. The nondialyzing part is then studied by membrane osmometry, and the dialyzing part is then studied by, for example, vapor phase osmometry. The molar mass of the original sample is then calculated from the mass fractions and molar masses of both the dialyzing and the nondialyzing parts. 

Vapor-pressure osmometry is, from its name, compared with membrane osmometry by considering the vapor phase to act like the semipermeable membrane, however, from its principles it is based on vapor pressure lowering or boiling temperature elevation. Sinee the direct measure of vapor pressure lowering of dilute polymer solutions is impractieal because of the extreme sensitivity that is required, VPO is in widespread use for oligomer solutions (Mn less than 20,000 g/mol) by employing the thermoeleetrie method as developed by Hill in 1930. In the thermoelectric method, two matched temperature-sensitive thermistors are placed in a chamber that is thermostated to the measuring temperature and where the atmosphere is saturated with solvent vapor. If drops of pure solvent are placed on both thermistors, the thermistors will be at the same temperature (zero point ealibration). If a solution drop is placed on one thermistor, a temperature differenee AT oeeurs whieh is caused by condensation of solvent vapor onto the solution drop. From equilibrium thermodynamics follows that this temperature increase has its theoretical limit when the vapor pressure of... 

Colligative properties of dilute solutions—polymer solutions particularly—directly result from the variation of the chemical potential of the solvent into which a solute is added. Such properties can be assessed by measuring the osmotic pressure (membrane osmometry), the decrease of the vapor pressure (vapor phase osmometry) or of the freezing point (cryometry). Contrary to the titration of the terminal functional groups, colligative methods do not require a prior knowledge of the polymer structure and depend exclusively on the number of solute molecules. 

Vapor-phase osmometry is also a colligative method and is based on the decrease of the vapor pressure, due to the addition of a solute into a pure solvent (Figure 6.4). Like osmotic pressure this property depends exclusively on the number of molecules of solute introduced and thus gives access to the number average molar mass. The disadvantage of VPO is its lack of sensitivity, due to the very small variations of the vapor pressure exhibited by dilute polymer solutions. It is, in fact, well suited to the analysis of low molar mass samples (<2 x 10 g mol ) and is thus complementary to membrane osmometry. Because it is easier to measure small variations in temperature than those in vapor pressure, a thermoelectric device is used to transform the increase of vapor pressure in a VPO experiment into a variation of temperature. Thus, two thermistors are placed in a closed chamber containing a pure solvent at a given temperature. If a pure solvent drop is placed on each of the two thermistors, they will indicate the same temperature. On the other hand, if a drop of a dilute polymer solution is placed on one of the two thermistors, a variation in temperature will result, caused by the condensation of pure solvent on this thermistor due to the difference in chemical potential between the drops. 

Vapor-pressure osmometiy is, from its name, compared with membrane osmometry by considering the vapor phase to act like the semipermeable membrane, however, from its principles it is based on vapor pressure lowering or boihng temperature elevation. Since the direct measure of vapor pressure lowering of dilute polymer solutions is impractical... 

Second Virial Coefficient (A) All absolute methods for the determination of molar masses may be used most commonly applied are membrane osmometry and static light scattering. Less frequently used are vapor phase osmometry and sedimentation equilibrium. Absolute methods that depend on specific solvent behaviour caimot be applied examples are cryoscopy and ebullioscopy. Measurements must be performed at sufficiently low polymer concentrations in order to avoid effects of third virial coefficients. 

We emphasize that vapor pressure osmometry is highly analogous to membrane osmometry from the view of thermodynamics. The difference to membrane osmometry is that in the latter case instead of a barrier of thermal energy, a barrier of volume energy is built up. Further, the transfer of the solvent is not accompanied with a phase transfer. 

Isopiestic [33] experiments also offer access to chemical potentials. This method monitors the conditions under which the vapor pressures above different solutions of nonvolatile solutes (like polymers or salts) in the same solvent become identical, where one of these solutions is a standard for which the thermodynamic data are known. These experiments can be considered to be a special form of differential osmometry (cf. Sect. 3.2) where the semi-permeable membrane, separating two solutions of different composition, consists of the gas phase. 

Because polyelectrolytes are nonvolatile, the most important thermodynamic property for vapor + liquid phase equilibrium considerations is the vapor pressure of water above the aqueous solution. Instead of the vapor pressure, some directly related other properties are used, e.g., the activity of water a, the osmotic pressure 71, and the osmotic coefficient < . These properties are defined and discussed in Sect. 4. Membrane osmometry, vapor pressure osmometry, and isopiestic experiments are common methods for measuring the osmotic pressure and/or the osmotic coefficient. A few authors also reported experimental results for the activity coefficient y i of the counterions (usually determined using ion-selective electrodes) and for the freezing-point depression of water AT p. The activity coefficient is the ratio of activity to COTicentration ... 

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