Poly osmotic pressure

Figure C2.1.8. Reduced osmotic pressure V l(RTc as a function of the polymer weight concentration for solutions of poly(a-metliylstyrene) in toluene at 25 °C. The molecular weight of poly(a-metliylstyrene) varies...

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

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... 

The solute molecular weight enters the van t Hoff equation as the factor of proportionality between the number of solute particles that the osmotic pressure counts and the mass of solute which is known from the preparation of the solution. The molecular weight that is obtained from measurements on poly disperse systems is a number average quantity. 

Table 9.3 lists the intrinsic viscosity for a number of poly(caprolactam) samples of different molecular weight. The M values listed are number average figures based on both end group analysis and osmotic pressure experiments. Tlie values of [r ] were measured in w-cresol at 25°C. In the following example we consider the evaluation of the Mark-Houwink coefficients from these data. 

The results of osmotic pressure measurements are shown in Fig. 145 for poly-(4-vinyl-N-butylpyridinium bromide) in alcohol, and for the parent uncharged polymer, poly-(4-vinylpyridine), likewise in alcohol. The value of /c for the former (note difference in scales) is much larger than for the latter, and it increases with dilution. The... 

Fig. 145.—Osmotic pressure-concentration ratios ( in g./cm and c in g./lOO ml.) for poly-(4-vinylpyridine) in alcohol, O, coordinates left and below poly-(N-butyl-4-vinylpyridinium bromide) in alcohol, coordinates right and above and the same polymer in alcoholic 0.61 N lithium bromide, 3 coordinates left and below. °> ...

If 0.6 N lithium bromide is added to the solution of the polyelectrolyte and also to the solvent on the opposite side of the osmometer membrane, the lowermost set of points in Fig. 145 (lower and left scales) is observed. The anion concentration inside and outside the coil is now so similar that there is little tendency for the bromide ions belonging to the polymer to migrate outside the coil. Hence the osmotic pressure behaves normally in the sense that each poly electrolyte molecule contributes essentially only one osmotic unit. The izjc intercept is lower than that for the parent poly-(vinylpyridine) owing to the increase in molecular weight through addition of a molecule of butyl bromide to each unit. 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

Itou et al. [60] determined 0II/0C for isotropic solutions of poly(n-hexyl isocyanate) (PHIC) and dichloromethane (DCM) from sedimentation equilibrium data on narrow distribution PHIC samples. Figure 3 shows their results, where the ordinate Mw(0II/0c) represents the osmotic pressure increment on the molar concentration scale. 

The osmotic pressure of solutions of a fractionated, atactic poly(isopropylacrylate) solution was measured at 25°C with the following results ... 

The swelling behavior of poly(N-isopropylacrylamide) has been studied extensively [18,19]. It has been shown that this gel has a lower critical point due to the hydrophobic interaction. Such a swelling curve is schematically illustrated in Fig. 9. The gel is swollen at a lower temperature and collapses at a higher temperature if the sample gel is allowed to swell freely in water. The volume of the gel changes discontinuously at 33.6°C. The swelling curves obtained in this way correspond to the isobar at zero osmotic pressure. On the other hand, the friction coefficient is measured along the isochore, which is given in Fig. 9,... 

Fig. 9. The swelling curve of the poly(/V-isop-ropylacrylamide) gel is schematically shown. The isobar curve (thick line) corresponds to the zero osmotic pressure. The dotted line indicates the experimental path at which the volume is fixed at the initial volume V0 (the volume at which the gel is prepared)...

The occurence of power laws is not the only universal feature. Rather those laws just are limiting forms of more general scaling laws, which state that physical quantities depend only on certain scaling combinations of their variables. To give an example, the osmotic pressure 11 a priori depends on chain concentration chain length n. temperature T and chemistry of poly-... 

The following osmotic pressures were measured for solutions of a sample of poly isobutylene in benzene at 25°C ... 

The osmotic pressure function tt in benzene at 40°C is independent on polymer concentration c. This result is a proof that this solvent is a - solvent (A2 = 0) for poly(pentachlorophenyl methacrylate). The results are shown in Figure 1.5 for three fractions. 

Fig. 1.5 Variation of the reduced osmotic pressure tt/c, (tt in cm of solvent, c in g dl ) with the concentration c for three poly(pentachlorophenyl methacrylate) fractions in benzene solutions at 40° C ( -solvent). (From ref. [44])...

Table 1.3 Reduced osmotic pressures (tt/c)c=0, number average molecular weights M and osmotic second virial coefficient A2 for fractions of poly(l,l,3,3-tetramethylbutylphenyl methacry-late)(la) in toluene at 25°C. (From ref. [50])...

Fig. 6. Reduced osmotic pressure vs. reduced concentration, plotted on a log-log scale, measured through osmometry by Noda el al. (1981). Symbols denote various molecular weights of poly(a-methylstyrene) in toluene at 25 C. The solid line has a slope of 1.32.

Monodisperse microgels based on poly(acrylamide-methacrylic acid) copolymer [P(AAm-co-MAAc)] crosslinked by BIS with a sharp pH-induced volume transition were prepared in ethanol [68], Osmotic pressure and deformation of crosslinked polymer network were considered to be the two dominant factors influencing the... 

Shiomi et al. (1980) provide osmotic pressure poly(dimethylsiloxane) (PDMS) system at 293.15 K. 

Concentration dependence of osmotic pressure data for five poly(a methyl styrene)s in the good solvent toluene at 25 °C. (a) Raw data—the data below c for the lowest three molar masses are... 

In dialysis, size exclusion is the main separation mechanism, while osmotic pressure and concentration difference drive the transport across two typically aqueous phases. While dialysis is used in some analytical separations, dialysis for the removal of toxins from blood (hemodialysis) is the most prominent application for hollow fiber technology in the biomedical field. The hemodialyzers are used to treat over one million people a year and have become a mass produced, disposable medical commodity. While the first hemodialyzers were developed from cellulosic material (Cuprophane, RC, etc.), synthetic polymers such as polyacrylonitrile, poly(ether) sulfone, and polyvinyl pyrrolidone are increasingly used to improve blood compatibility and flux. Hemodialyzer modules consist of thousands of extremely fine hollow fibers... 

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