Polymer osmotic pressure

Theta conditions in dilute polymer solutions are similar to tire state of van der Waals gases near tire Boyle temperature. At this temperature, excluded-volume effects and van der Waals attraction compensate each other, so tliat tire second virial coefficient of tire expansion of tire pressure as a function of tire concentration vanishes. On dealing witli solutions, tire quantity of interest becomes tire osmotic pressure IT ratlier tlian tire pressure. Its virial expansion may be written as... 

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...

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

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. 

Osmotic pressure experiments provide absolute values for Neither a model nor independent calibration is required to use this method. Experimental errors can arise, of course, and we note particularly the effect of impurities. Polymers which dissociate into ions can also be confusing. We shall return to this topic in Sec. 8.13 for now we assume that the polymers under consideration are nonelectrolytes. 

The limiting reduced osmotic pressure for a sample of polystyrene in chlorobenzene at 25°C is reported to be 257 cm. Account for these units for (n/c2)o and evaluate for the polymer. 

In this section we briefly consider the osmotic pressure of polymers which carry an electric charge in solution. These include synthetic polymers with ionizable functional groups such as -NH2 and -COOH, as well as biopolymers such as proteins and nucleic acids. In this discussion we shall restrict our consideration... 

We consider this system in an osmotic pressure experiment based on a membrane which is permeable to all components except the polymeric ion P that is, solvent molecules, M" , and X can pass through the membrane freely to establish the osmotic equilibrium, and only the polymer is restrained. It does not matter whether pure solvent or a salt solution is introduced across the membrane from the polymer solution or whether the latter initially contains salt or not. At equilibrium both sides of the osmometer contain solvent, M , and X in such proportions as to satisfy the constaints imposed by electroneutrality and equilibrium conditions. 

What makes the latter items particularly important is the fact that the charge and electrolyte content of an unknown polymer may not be known hence it is important to design an osmotic pressure experiment correctly for such a system. It is often easier to add swamping amounts of electrolyte than to totally eliminate all traces of electrolyte. Under the former conditions a true molecular weight is obtained. Trouble arises only when the experimenter is indifferent toward indifferent electrolyte this sort of carelessness can be the source of much confusion. 

As in osmotic pressure experiments, polymer concentations are usually expressed in mass volume units rather than in the volume fraction units indicated by the Einstein equation. For dilute solutions, however, Eq. (8.100) shows that

partial molar volume of the polymer in solution, and M is the molecular weight of the polymer. Substituting this relationship for (pin Eq. (9.9)gives... 

Osmotic Pressure Controlled Oral Tablets. Alza Corp. has developed a system that is dependent on osmotic pressure developed within a tablet. The core of the tablet is the water-soluble dmg encapsulated in a hydrophobic, semipermeable membrane. Water enters the tablet through the membrane and dissolves the dmg creating a greater osmotic pressure within the tablet. The dmg solution exits at a zero-order rate through a laser drilled hole in the membrane. Should the dmg itself be unable to provide sufficient osmotic pressure to create the necessary pressure gradient, other water-soluble salts or a layer of polymer can be added to the dmg layer. The polymer swells and pushes the dmg solution through the orifice in what is known as a push-pull system (Fig. 3). The exhausted dmg unit then passes out of the body in fecal matter. 

Exxon products appear to release via a unique mechanism. Like other polymer-coated technologies, the penetration of water iato the granule is purely by diffusion. However, as water enters the particle, an osmotic pressure is created as the fertilizer is solubilized. This pressure causes an expansion of the elastomeric coating and the particle swells to many times its original diameter. As the particle swells, the coating becomes increasingly thinner to the point where it caimot contain the internal pressure and the nutrient is released. 

As Morawetz puts the matter, an acceptance of the validity of the laws governing colligative properties (i.e., properties such as osmotic pressure) for polymer solutions had no bearing on the question whether the osmotically active particle is a molecule or a molecular aggregate . The colloid chemists, as we have seen, in regard to polymer solutions came to favour the second alternative, and hence created the standoff with the proponents of macromolecular status outlined above. 

From about 1910 onwards, physical chemists began studying the characteristics of polymer solutions, measuring such properties as osmotic pressure, and found them... 

A. Milchev, K. Binder. Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions Monte Carlo simulations of a bead-spring model. Macromol Theory Simul 5 915-929, 1994. 

FIGURE 23.2 Example of separation by high osmotic pressure chromatography. The fraction number is indicated adjacent to each chromatogram. (Reprinted from Tr. Polym, Sci., 5, 258, Copyright 1997, with permission from Elsevier Science.)... 

The partitioning principle is different at high concentrations c > c . Strong repulsions between solvated polymer chains increase the osmotic pressure of the solution to a level much higher when compared to an ideal solution of the same concentration (5). The high osmotic pressure of the solution exterior to the pore drives polymer chains into the pore channels at a higher proportion (4,9). Thus K increases as c increases. For a solution of monodisperse polymer, K approaches unity at sufficiently high concentrations, but never exceeds unity. 

In analytical SEC, the optimal pore size for a given polydisperse polymer is approximately 1/4 < IRJd — 1/2 when a single-pore size column is used (20). In contrast, the pore size needs to be much smaller in HOPC. Small pores are deliberately used in HOPC to exclude nearly all MW components at low concentrations but to allow the entry of low MW components only at high concentrations by the high osmotic pressure (2). Use of the same pore size as used in SEC results in a poor separation. The latter is essentially an overloading in SEC. 

Lactam antibiotics are bicyclic or monocyclic azetidinone ring-containing compounds (Fig. 1). They kill bacteria by preventing the assembly of (4-3) peptidoglycans. These covalently closed net-like polymers form the matrix of the cell wall by which the bacteria can divide and multiply, despite their high internal osmotic pressure. 

E7.12 The following table gives the osmotic pressures as a function of concentration for the polymer polyisobutylene dissolved in benzene at 298.15 K. 

The van t Ho ff equation is used to determine the molar mass of a solute from osmotic pressure measurements. This technique, which is called osmometry, involves the determination of the osmotic pressure of a solution prepared by making up a known volume of solution of a known mass of solute with an unknown molar mass. Osmometry is very sensitive, even at low concentrations, and is commonly used to determine very large molar masses, such as those of polymers. 

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. 

A solution prepared by adding 0.50 g of a polymer to 0.200 L of toluene (methvlbenzene, a common solvent) showed an osmotic pressure of 0.582 Torr at 20.°C. What is the molar mass of the polymer ... 

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