Osmotic pressure , polymer solutions

The bulk segment concentration affects the distributions of the electrostatic potential and osmotic pressure in solution. Fig. 6 shows that as the bulk segment concentration increases, the force becomes less attractive and at large distances and, for high bulk polymer concentrations, it becomes slightly repulsive. 

Problem 4.10 Measurement of osmotic pressure for solutions of two polymers A and B in the same solvent (benzene) at 27°C yielded the following data ... 

Example You are required to calculate the molecular weight of a polymer by measurements of its osmotic pressure in solution. At infinite dilution, measured graphically from your experiments, the equation below applies ... 

The second virial coefficient can be obtained from the slope of the straight line portion of the (II/c) versus c plot by removing the terms in Eqs. (4.41)-(4.43). When plotted according to Eq. (4.41), the osmotic pressures of solutions of the same polymer in different solvents should yield plots with the same intercept (at c = 0) but with different slopes (see Fig. 4.5), since the second virial coefficient,... 

The osmotic pressure for solutions of polymers, proteins, and other large molecules increases strongly with concentration, as shown in Figure 9.12 for whey proteins. This can make An a significant portion of AP even when the osmotic pressure of the feed solution is negligible. 

Figure 12.12 Concentration dependence of osmotic pressure of solutions of polystyrene in toluene at 30°C. Numbers on each curve denote polymer molecular weights. (From Flory, P.J., Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953. With periwsslon.)...

Ohta and Oono (1982) applied the method of conformational space renormalization to calculate the osmotic pressure of solutions and the sizes of macromolecules in. semidilute solutions of polymers. 

Osmotic pressure measurements of solutions of a polymer in a solvent can be employed to determine the molecular weight of the polymer. After approximately one hour the osmotic pressure of solutions of poly-a-methylstyrene in toluene becomes practically constant. From this osmotic pressure and the concentration of the polymer in solution it is possible to calculate the number-average molecular weight of the polymer from the following relationship ... 

Figure 2.12 presents measurements of osmotic pressures for solutions of polystyrene in cyclohexane, carried out under variation of the weight fraction of the dissolved polymer, Cm, and of the temperature. As can be seen, A2 vanishes at 35 °C, which therefore represents the theta-point of this system. As indicated by the positive values of A2, for temperatures above 35 °C the repulsive forces become dominant. On the other hand, we observe negative values of A2 for T < 35 °C, indicative for the actual presence of effective attractive forces between the monomers. On further cooling, the attractive forces then lead to a separation of solvent and solute, and the sample becomes turbid. 

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... 

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. 

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. 

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. 

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. 

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 ... 

Acrylic resins are polymeric materials used to make warm yet lightweight garments. The osmotic pressure of a solution prepared by dissolving 47.7 g of an acrylic resin in enough water to make 500. mL of solution is 0.325 atm at 25°C. (a) What is the average molar mass of the polymer ... 

---