Osmometry, membrane

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  

a plot of nlc) versus c will be more linear than a plot of nk versus c. 

Automatic osmometers are now available that achieve equilibrium very quickly, often within minutes [68]. 

For membrane osmometry, osmotic pressure is measured for a polymer solution of various concentrations. The equation relating osmotic pressure ( ) and molecular 

Usually treatments of membrane osmometry do not refer to the height of a liquid column that brings the pressure to the membrane under gravity. We take care of this aspect. However, we will not deal with capillary effects. We show a possible experimental design for membrane osmometry in Fig. 6.15. The apparatus consists of two subsystems System ( ) is a solvent (1) with a solute (2) that cannot pass the membrane, and system ( ) consists of a pure solvent (1). The systems are separated by a semipermeable membrane. The whole design is embedded in a thermostat and operated in vacuum. We will assume that the solvent has a vapor pressure that does not contribute to the total pressure that is exerted to the membrane by gravity that is pointing downward. 

The pressure exerted due to gravity by the system ( ) is p = p gh, where p is the density of the solution. The back pressure due to the system ( ) is p = p gh , where p is the density of the pure solvent. We have the equilibrium conditions 

Equal temperatures guarantee that there is no entropy flow, and equal chemical potentials guarantee that there is no mass flow across the membrane. We did not make any statement on the pressure. If we would fix the volumes of the two subsystems, then even in the absence of gravity a pressure difference would develop. We must fix the position of the membrane. If we would not fix the position of the membrane, a pressure difference would tend to move the membrane and the volume of the solution would try to increase in the cost of the volume of the pure solute. This process would take place, even when the chemical potentials on both sides of the membrane are equal. Thus, a pressure difference causes a bulk expansion and 

In a quite similar procedure as shown in the section vapor osmometry, we can show that the osmotic pressure Ap is 

Equation (6.77) is known as the van t Hoff equation, who pointed out already the analogy between solutions and gases, because the form resembles much to the ideal gas law [18, 19]. By the way, in this highly interesting paper, van t Hojf points out relations between osmotic pressure, vapor pressure depression, freezing point depression, and boiling point elevation, i.e., what we address nowadays in short as colligative properties. 

Apart from VLE-measurements, membrane osmometry is the next important method that has been used for measuring solvent activities in polymer solutions. This follows from the 

Laboratory designed instruments were developed in the 40 s and 50 s, e.g. by Zimm or by Flory.Later on, high speed membrane osmometers are commercially available, e.g., from Knauer, Hewlett-Packard or Wescan Instruments. External pressures may be applied to balance the osmotic pressme if necessary, e.g., Vink. The principle scheme of a membrane osmometer together with the corresponding 

Some efforts are necessary to keep the osmometer imder appropriate working conditions. This relates mainly to the proper preconditioning and installation of the membrane, the attainment of thermal equilibrium, the caUbration of the electronic output, the adjustment of solvent zero, and to choosing the desired sensitivity. 

The relation between osmotic presstne and solvent activity is to be found from the chemical potential equilibrium condition, taking into account the pressure dependence of t]. From the rules of phenomenological thermodynamics, one obtains  

V1 partial molar volume of the solvent in the polymer solution at temperature T 

When a solution is separated from the pure solvent by a semi-permeable membrane i.e. a membrane that permits the passage of solvent molecules but not of solute molecules, the solvent molecules always tend to pass through the membrane into the solution. This general phenomenon is known as osmosis, and the flow of solvent molecules leads to the development of an osmotic pressure which at equilibrium just prevents further flow. The equilibrium osmotic pressure, n, can be measured using a capillary osmometer such as that shown schematically in Fig. 3.9. 

Osmosis occurs when the pressure, Pq, above the solution and solvent compartments is equal, because the chemical potential, p[, of the pure solvent is higher than the chemical potential, px, of the solvent in the 

The pressure difference (P — Pq) is the equilibrium osmotic pressure re and so Equation (3.87) can be re-written in the standard form 

An equation applicable to dilute polymer solutions can be obtained by substituting the Hory-Huggins expression for (i-e. Equation 

Since the solution is dilute, is approximately equal to the molar volume Vi of the solvent. Also 02 = Jc 2/( i and the total 

Since van t Hoff s law is valid only for infinitely diluted solutions, one develops Iloj/c in power law series (break after the linear term in c) 

the osmotic pressure is first measured at different polymer concentrations, Tlgjc is then plotted vs. c, the values are linearly extrapolated to c 0, and the value of is determined from the y axis intercept. A2 is the second virial 

The chemical potential of the solvent A on the right pa,r is representing chemical potential of pure solvent A. If the solution on the left is dilute enough to be considered ideally dilute, then A,L = / a + RTlaxA, which is less than pa,r = 

Let the equilibrium pressures in the right and left chambers be P and P + II, respectively. The difference in pressures, viz., II, is the osmotic pressure. This extra pressure makes the chemical potential of the solvent (/ta) in solution equal to that in pure solvent. If the solution in the left chamber is dilute enough to be considered as ideally dilute, then at equilibriumpa,r = Pa,l, or 

Considering that liquids are rather incompressible, VI would hardly vary with pressure and we can take VI as practically constant. The integral in Eq. (4.34) then becomes V II and Eq. (4.34) thus gives II = -(i r/V )ln rA- With xa = I -xp, 

Since the solution is quite dilute, we have xg = ng)l nA + ng) ngluA and there- 

Problem 4.5 A solution containing 1.018 g of a protein per 100 g of water is found to have an osmotic pressure of 10.5 torr at 25°C. Estimate the molecular weight of the protein. 

The osmotic pressure is again a colUgative property and leads, thus, to an absolute molar mass and for a distribution of different species, a number-average molar mass, as summarized in Fig. 1.71. The pressure p of the ideal gas Iw is replaced by the osmotic pressure 71, w is the total mass dissolved, so that w/M is the number of moles, n to give the link to pV = nRT. 

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 

The chemical potential of the solvent A on the right pa.r is representing ehemieal potential 

Since is positive, the increase in pressure will increase pa,l until nally equilibrium is reached, that is, pa,l = Pa,r = Pa- (Note that the membrane being impermeable to solute B, there is no equilibrium relation for ps-) 

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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... 

Membrane osmometry. fCapillary isotachophoresis. gFluorescence quenching. 

We report here the results of our recent studies of poly(alkyl/arylphosphazenes) with particular emphasis on the following areas (1) the overall scope of, and recent improvements in, the condensation polymerization method (2) the characterization of a representative series of these polymers by dilute solution techniques (viscosity, membrane osmometry, light scattering, and size exclusion chromatography), thermal analysis (TGA and DSC), NMR spectroscopy, and X-ray diffraction (3) the preparation and preliminary thermolysis reactions of new, functionalized phosphoranimine monomers and (4) the mechanism of the polymerization reaction. 

GPC/SEC, MALDI-MS, membrane osmometry, vapour pressure osmometry, viscometry, light scattering, TDFRS, SAXS, SANS, SEC-HPLC, SEC-MS, SEC-IR, FFF, ultracentrifugation, MALDI-TOF-MS, NMR, capillary electrophoresis... 

Figure 2 Principle of membrane osmometry, p is the solvent density, g the acceleration of gravity, and h the difference between the fluid levels in both chambers.

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. 

Figure 3 Membrane osmometry. Top concentration series with multiple injection of polystyrene (PS, 5,250 g/mol) in toluene. Concentrations 1.07,1.91, 2.94, 4.11, and 5.03 g/L. Multiple solvent injections establish the baseline (subtracted). Inset data evaluation for concentration series of PS (5,250 g/mol) and PS (47,400 g/mol) in toluene. Bottom design of osmometer equipped with flow cell. Reproduced with permission from Lehmann et al. [16]. Copyright 1996 American Chemical Society.

As for the case of membrane osmometry, non-ideality is accounted for by a virial expansion (Equation (28)). 

Experimental considerations Sample preparation and data evaluation are similar to membrane osmometry. Since there is no lower cut-off as in membrane osmometry, the method is very sensitive to low molar mass impurities like residual solvent and monomers. As a consequence, the method is more suitable for oligomers and short polymers with molar masses up to (M)n 50kg/mol. Today, vapour pressure osmometry faces strong competition from mass spectrometry techniques such as matrix-assisted laser desorption ionisation mass spectrometry (MALDI-MS) [20,21]. Nevertheless, vapour pressure osmometry still has advantages in cases where fragmentation issues or molar mass-dependent desorption and ionization probabilities come into play. 

Membrane osmometry measurements were carried out with the capillary osmometer shown in Figure 3. Owing to the short equilibration time of the instrument and the low cut-off molar mass of the membrane, solute permeation through the membrane, which would show up as a drift of the baseline, did not cause problems even for the lowest molar mass fraction. M was obtained from... 

Table 3 Light scattering (Mw, (Rp ), membrane osmometry (M ), and viscosity ([>/]) data for the nine poly(p-phenylene) fractions P1-P9...

Endlinked PDMS. Linear polydimethylsiloxanes with vinyl endgroups were supplied by Dow Corning Corporation. Three different molecular weight ranges were employed. Membrane osmometry yielded values for Mj, of 16,000, 24,000, and 37,000 g/g-mole. Endgroup analysis using mercuric acetate (5) gave vinyl contents of 0.47 0.03, 0.24 0.02, and 0.15 0.02 per cent, corres-... 

Randomly - Crosslinked PDMS. The polydimethylsiloxane (PDMS) used to make random networks was obtained from General Electric. Membrane osmometry showed to be 430,000 g/g-mole. The polymer was mixed with various amounts of a free-radical crosslinking agent, dicumylperoxide (Di-Cup R, Hercules Chemical Co.). Samples were then pressed into sheets and crosslinking was effected by heating for 2 h at 150°C in a heated press. Mc values were calculated using equation 2, and are included in Table I. 

Table 2. Intramolecular crosslinking of PVS [217], Reaction conditions PVS concentration = 0.975 mass % AIBN concentration = 1.65X10 3 M temperature = 70 °C n-butylmercaptan (chain transfer agent) concentration = 20 mL/L reaction time = 25 min. The Mw and Mn were measured by light scattering and membrane osmometry respectively.

In membrane osmometry the two compartments of an osmometer are separated by a semi-permeable membrane only solvent molecule can penetrate through the semi-permeable membrane which is closed except for capillary tubes. The polymer solute remains confined to one side of the osmometer and the activity of the solvent is different in the two compartments. Because of the thermodynamic drive towards equilibrium a difference in liquid level in the two capillaries results. 

Table Apparent Molecular weights of Branched Polyethylene by Membrane Osmometry...

Of the preponderance of small ions, the colligative properties of polyelectrolytes in ionising solvents measure counterion activities rather than Molecular weight. In the presence of added salt, however, correct Molecular weights of polyelectrolytes can be measured by membrane osmometry, since the small ions can move across the membrane. The second virial coefficient differs from that previously defined, since it is determined by both ionic and non-ionic polymer-solvent interactions. 

Analytical procedures The molecular weights of the polyisobutylenes (Systematic name poly(l,l-dimethylethylene) and of the polynorbornadienes (Systematic name poly(3,5-tricyclo[2.2.1.02, b]heptylene) were determined by membrane osmometry in toluene solution and those of the polystyrenes were determined by vapour-pressure osmometry in chloroform. 

Membrane osmometry Absolute small sample size reasonable range of mol. wt. (2 x 104 - 1 x 106) Several concentrations necessary 5... 

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