Osmotic pressure reduced

Figure C2.1.5. Reduced osmotic pressure FT / (RTc as a function of the weight concentration c of polystyrene (M = 130 000 g mor ) in cyclohexane at different temperatures. At 7"= 35 °C and ambient pressure, tire solution is at tire 0 conditions. (Figure from 1741, reprinted by pennission of EDP Sciences.)...

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 ratio n/c2 is called the reduced osmotic pressure-and can be plotted with or without the RT-and the zero-intercept value (subscript 0) is the limiting value of the reduced osmotic pressure. Quite an assortment of different pressure units are used in the literature in reporting n values, and the units of R in Eq. (8.88) must be reconciled with these pressure (as well as concentration) units. 

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. 

Figure 8.13 shows the reduced osmotic pressure for solutions of polyisobutylene in benzene plotted against C2 at several different temperatures. The... 

The reduced viscosity (I/C2) (77/770 - 1). This is obtained by dividing both sides of Eq. (9.13) by C2 in this sense it is analogous to the reduced osmotic pressure ... 

For this reason, the relationship between the reduced Osmotic pressure p/C and the concentration is generally expressed in the form of virial equation as given below ... 

Fig Reduced Osmotic pressure p/C as a function of the concentration of the solution C (1) polymer solution, (2) ideal solution. 

Figure 2 Plot of the reduced osmotic pressure versus concentration for PS-SO3Li-40, ( O ) in cyclohexane at T = 30°C, ( ) in THF at T = 25 C.

Figure 8 Concentration dependence of the reduced osmotic pressure of PS-S03Li 80 under conditions. The full line represents the model calculations with = 10 9 (mol/1) and N = 11, the dashed line indicates = 6,000.

The quantity ir/c is called the reduced osmotic pressure, and (7r/c)0 the limiting reduced osmotic pressure. Osmotic pressure results are most commonly encountered as plots of reduced osmotic pressure —with or without the R T— versus c. This form suggests that a plot of k/RTc versus c should be a straight line, the intercept and slope of which have the following significance ... 

EXAMPLE 3.1 Molecular Weights from Osmotic Pressure Measurements. To what molecular weights do the limiting reduced osmotic pressures obtained from Figure 3.5 correspond The data in Figure 3.5 are presented in such a way that unit problems do not enter the picture. We are not usually so lucky Consider some possible combinations of units for tt, V, and R that are compatible with the units of the ordinate in Figure 3.5. 

Solution According to Equation (35), the molecular weights of the various polymers are simply the reciprocals of the limiting reduced osmotic pressures in the units that have been used for the ordinate in Figure 3.5, namely, mole g 1, Therefore... 

If the masses (in c) are expressed in g and kg, respectively, in the last two situations, then the units of the ordinate reduce to cm2 s 2 and m2 s"2, respectively, which do not bear much resemblance to molecular weight units. Note, however, that the acceleration of gravity in appropriate units can be factored out of these latter quantities to leave units of cm and m, respectively, for reduced osmotic pressure. ... 

We have already seen that the second virial coefficient may be determined experimentally from a plot of the reduced osmotic pressure versus concentration. Since all other quantities in Equation (99) are measurable, the charge of a macroion may be determined from the second virial coefficient of a solution with a known amount of salt. As an illustration of the use of Equation (99), we consider the data of Figure 3.6 in Example 3.5. 

Describe how this result may be used to facilitate the evaluation of M and B in the event that a plot of reduced osmotic pressure versus c still contains too much curvature to permit a meaningful straight line to be drawn. 

Figure 2.8 Dependence of reduced osmotic pressure on concentration (1) a linear high polymer in a good solvent (2) the same polymer in a poor solvent (3) a globular protein in aqueous solution...

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])...

Figure 3. Reduced osmotic pressure fve. reduced total amphlphllar concentration y. The curves are labeled for various values of the parameter A. The values of the other parameters are o — 4.5, n = 40, and n = 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.

Severe protein-energy malnutrition often occurs after weaning, the transition frcim nursing to the consumption of foods from other sources (i.e.. Solid foods). The marasmus common in Latin America is caused by early weaning, followed by use of overdiluted commercial milk formulas. Kwashiorkor occurs in Africa, where babies arc fed starchy roots, such as cassava, that arc low in protein. It also occurs in the Caribbean, where babies are fed sugar cane. The major symptom of kwashiorkor is edema, mainly of the feet and legs. Edema is the condition produced when water normally held in the bloodstream by osmotic pressure leaks into (jther extracellular spaces. It can result from reduced osmotic pressure in the bloodstream caused by catabolism and depletion of serum albumin. 

Figure 5.7(b) demonstrates that the functional form of Eq. (5.43) reduces osmotic pressure data at various M and 6 (or c) to a universal curve. The limiting scaling laws of II (/> or II are only valid sufficiently far from the overlap concentration. Near (f> (and more generally near any crossover point), a more complicated functional form than a simple power law is needed. For osmotic pressure in a good solvent (and many other examples) the full functional form of Eq. (5.43) is well described by a Simple sum of the two limiting behaviours ... 

The critical micelle concentrations (erne s) were determined with a slightly modified methodology of Floriano et al. (1999). Figure 7 illustrates the concept. The reduced osmotic pressure is obtained from the logarithm of the grand partition function, a quantity which can in turn be determined from the simulations to within an additive constant (Floriano et al., 1999). For the system H2T4 (12), L = 10, we obtain the two curves shown in Fig. 7 at the two temperatures indicated there. There is a clear break, indicating the... 

Fig. 7. Reduced osmotic pressure, 6P /r, versus volume fraction of surfactant for the H2T4 (12) system, L = 10.

Figure 4.6 Reduced osmotic pressure (II/c) versus concentration (c) plots for the same polymer sample in different solvents of increasing solvent power.

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