Osmotic pressure membrane osmometry

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. 

First, we consider the experimental aspects of osmometry. The semiperme-able membrane is the basis for an osmotic pressure experiment and is probably its most troublesome feature in practice. The membrane material must display the required selectivity in permeability-passing solvent and retaining solute-but a membrane that works for one system may not work for another. A wide variety of materials have been used as membranes, with cellophane, poly (vinyl alcohol), polyurethanes, and various animal membranes as typical examples. The membrane must be thin enough for the solvent to pass at a reasonable rate, yet sturdy enough to withstand the pressure difference which can be... 

Osmosis is the flow of solvent through a semipermeable membrane into a solution the osmotic pressure is proportional to the molar concentration of the solute. Osmometry is used to determine the molar masses of compounds with large molecules, such as polymers reverse osmosis is used in water purification. 

Practically, polymers with molar masses between 2 x 104 and 2 x 106 g/mol can be characterized by membrane osmometry, but measurements of Mn <104 g/mol have also been reported with fast instruments and suitable membranes [16]. The lower limit is set by insufficient retention of short polymer chains. Above M 2 x 106 g/mol, the osmotic pressure, which is proportional to Mr1, is too low for a reasonable signal-to-noise ratio. An advantage of the low molar mass cut-off is that impurities with a very low molar mass can permeate through the membrane and, hence, do not contribute to the measured osmotic pressure. Their equilibration time may, however, be different from that of the solute, leading to complex time-dependent signals. 

To carry out an osmotic pressure experiment, we need to prepare a solution, find a suitable semipermeable membrane, achieve isothermal equilibrium, and measure the equilibrium pressure. Aside from noting that the pressures produced by colloidal solutes are large enough to be measurable, we have not yet considered any of the experimental aspects of osmometry. This is our present task. 

Osmometry. Measurements were made in tetrahydronaphthalene at 130 °C by using a membrane osmometer (Mechrolab model 502). The plots of osmotic pressures at different concentrations are shown in Figure 5. Comparing the osmotic pressure results with those of GPC (interpretation 1) it appears that molecules larger than A = 50 may have permeated the membrane. If this is the case, the MN by osmometry is too high. 

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... 

Since polymer solutions are markedly non-ideal, osmotic pressure data are taken at low concentrations and are extrapolated to infinite dilution (c — 0). In the case of membrane osmometry, the relevant equation is... 

Osmometry. When a solution is separated from the pure solvent at isothermal conditions by means of a membrane permeable only to the solvent molecules, the osmotic pressure of the solution is defined as the excess pressure which must be placed on it in order to prevent any diffusion of solvent through the membrane. The cause of osmosis is diffusion which arises from a difference in chemical potential. At the same temperature and pressure, the solvent is at a lower chemical potential in the solution than in its own pure liquid, and there is a tendency for it to pass through the membrane in the direction of pure solvent to solution. 

Osmometry is a technique for measuring the concentration of solute particles that contribute to the osmotic pressure of a solution. Osmotic pressure governs the movement of solvent (water in biological systems) across membranes that separate two solutions. Different membranes vary in pore size and thus in their ability to select molecules of different size and shape. Examples of biologically important selective membranes are those enclosing the glomerular and capillary vessels that are permeable to water and to essentially aU small molecules and ions, but not to large protein molecules. Differences in the concentrations of osmoticaUy active molecules that carmot cross a membrane cause those molecules that can cross the membrane to move to establish an osmotic equilibrium. This movement of solute and permeable ions exerts what is known as osmotic pressure. 

The experimental measurement of these averages has largely been performed on polymers in solution (Hunt and James, 1999). Since M depends on the measurement of the number of polymer chains present in a given mass, colligative properties such as vapour-pressure depression AP (measured by vapour-phase osmometry) and osmotic pressure (measured by membrane osmometry) relative to the pure solvent, can in principle provide the molar mass through an equation of the form... 

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. 

Osmometry is an important method of determining the molecular weight of macromolecules such as polymers and proteins. The advantages of this method for macromolecules are that membranes permeable to the solvent but not to the macromolecule are easily found, and the osmotic pressure (or height of the solvent) is large and easily measured. " ... 

A full description of various osmometers and the necessary experimental technique can be found in the book edited by Allen. More-recent types of osmometer have been described, but the outstanding problem in osmometry is still the preparation of suitable semi-permeable membranes. Methods of preparing membranes claimed to be suitable for materials of low molecular weight have been described, and there are several reports of comparisons of the behavior of different types of membranes in osmometryThe problem of correcting observed osmotic pressures for any solute diffusion which may occur has been considered theoretically, - and a suitable technique established. ... 

Membrane Osmometry In this technique a dilute polymer solution and a pure solvent are separately placed in two different chambers that are divided by a tightly held semipermeable membrane through which only solvent molecules can move across. Because the chemical potential of pure solvent is higher than that of the solvent in the solution, the solvent will diffuse across the membrane from the pure solvent to the solution chamber up to the point in which the osmotic pressure equals the hydrostatic pressure created by the volume imbalance between the liquids of the two chambers. The osmotic pressure (k = pgh) at equilibrium (static method) can be calculated from the difference in height (h) between the liquids in the capillaries connected to each chamber. In practice, a dynamic method is used in which a pressure (P) is applied to counterbalance (at t = 0) the osmotic pressure... 

Predict the change in boiling point of toluene (Ti, = 384 K) for a 0.01 g cm" solution of a polyethylene sample with = 10,000 g moL (assume that density of toluene p = 0.862 g cm and A// = 38.06 kJ moLO-A polymer sample was characterized by radioactive end-group analysis and membrane osmometry in acetonitrile at 300 K. The osmotic pressure data are reported below as a function of polymer concentration. 

Osmometry is a straightforward method for the determination of The technique is based on the equilibrium between a solution of the polymer in a suitable solvent and the pure solvent, separated by a semi-permeable membrane, through which only the solvent molecules can diffuse. The polymer solution is diluted to such an extent by diffusion of the solvent through the membrane, that an osmotic pressure, n, is built up. At equilibrium and in the limit of infinite dilution (c - 0), this pressure is given by the following equation ... 

Membrane osmometry (MO) Number average molecular weight Osmotic pressure due to diffusion of solvent through ... 

According to the derivation, Equation (9-23) only applies to solutions at infinite dilution. For finite concentrations, one can, in analogy to the procedure adopted for membrane osmometry measurements, develop a series with virial coefficients. In polymeric solutes, the number-average molar mass is measured in ebulliometry. (The proof is analogous to that given for osmotic-pressure measurements.)... 

Measurements became easier with rapidly equilibrating membrane osmometers with servo pressure control. The instrament senses differences in osmotic pressure based on the mass transport through the membrane. The pressure differential between solvent and solution is then controlled by increasing the solution level to hydrostatically counterbalance the osmotic pressure 71. The success of the osmometry... 

Membrane osmometry (MO) is another absolute method for the determination of M . The osmotic pressure n is related to the molar mass by the equation ... 

Membrane osmometry Measurement of osmotic pressure created by the flow of solvent into polymer solution through semipermeable membrane Mn 5000-1000000... 

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