Poly osmotic coefficient

Fig. 8 Osmotic coefficient as a function of counterion concentration cc for the poly(p-phenylene) systems described in the text. The solid line is the PB prediction of the cylindrical cell-model, the dashed curve is the prediction from the correlation corrected PB theory from Ref. [58]. The full dots are experiments with iodine counterions and the empty dots are results of MD simulations described in ref. [29,59]. The Manning limiting value of l/2 is also indicated...

Deserno, M., Holm, C., Blaul, J., Ballauff, M., and Rehahn, M. The osmotic coefficient of rod-like poly electrolytes Computer simulation, analytical theory, and experiment. European Physical Journal E, 2001, 5, No. 1, p. 97-103. 

Concentration dependence of osmotic coefficient for three poly(a-methylstyrene) samples in toluene at 25 °C. The data corresponding to dilute solutions for these three samples are shown, with lines fit to the lowest concentration data. Data over wider ranges of concentration and chain length are shown in Fig. 5.7 [data from I. Noda, N. Kato, T. Kitano and M. Nagasawa, Macromolecules 16,668(1981)]. 

B. Distribution Functions and Osmotic Coefficient for Salt-Free Poly(p-Phenylene) Solutions... 

TABLE 3 Osmotic Coefficient of the Four Poly(p-Phenylene) Systems from Table T... 

The osmotic coefficient 0 has been measured both in solutions of strongly dissociating poly[2-(methacryloyloxy)ethyl]-trimethylammonium iodide (PMETAI) [48], and weakly dissociating PAA [43] star polymers. 

Fig. 11. Osmotic coefficients 0o of poly(stjrrene sulfonate) with M = 40,000 g/mol plotted against polsmier concentration Cp for salt-free solutions. Darkened and opened circles are for the Na+ and Mg + salts of the poljrmer, respectively. The parameter Zi is the counterion valence. Data are from Refs. 195 and 196.

Vapour pressure determinations in ternary systems with poly (vinylpyrrolidine) [157], 1-al l (butyl-, heptyl- and octyl-)-3-3methylidazolium bromide [161] and poly (ethylene glycol) PEG - 6000 [165] are reasonably consistent with those of the binary NajCit + Hp systems when the vapour-pressure lowerings Ap(7 /w) are considered (Fig. 5.7). However, the agreement when expressed in terms of osmotic coefficients iT m), as will discussed later, is less satisfactoiy. Actually, all reported... 

Table 4 gives a similar sinvey for other polyelectrolytes. Figure 2 shows the influence of the backbone monomer of flie polyelectrolyte on the osmotic coefficient. At crmstant polyelectrolyte concentration (again expressed as the molahty of the repeating units), the osmotic coefficients might differ by, for example, a factor of five. For example, at 25°C, the osmotic coefficient of a 1 mol/kg aqueous solution of monomer groups of poly(sodium ethylene sulfate) (NaPES) is about 0.22, whereas... 

Fig. 4 Influence of counterion on the osmotic coefficient of aqueous solutions of poly(ethylene sulfonates) at 25°C from isopiestic measurements by Ise and Asai [37] open squares N(n 4119)4 open diamonds N(n 3117)4 open triangles N(n 2115)4 times N(n 113)4 open circles N( H3)3 H2 6H5 +, NH4 filled diamonds H closed circles Li closed triangles K...

Figures 3 and 4 show some typical examples of the influence of the nature of the counterion of a polyelectrolyte on the osmotic coefficient. The osmotic coefficient is typically very small for inorganic counterions, but it can be increased by a factor of about 10 by organic counterions, for the same temperature and polyelectrolyte monomer-group molality. Figure 4 shows that the osmotic coefficient of an aqueous solution of a poly (ethylene sulfonate) increases in the counterion series K, Li, H, NH+, N (CH3)3CH2C6H5, N (CH3)4, N (C2H5)4, N ( -C3H7)4, and N>-C4H9)4.

Fig. 15 Osmotic coefficient of aqueous solutions of poly(sodium methacrylate) at 298.2 K with two different molecular masses. Experimental results closed squares NaPMA 6 open squares NaPMA 15. Correlation results solid line NaPMA 6 dashed line NaPMA 15 [116]...

Figure 15 shows a typical example for correlation of experimental results for the osmotic coefficient (on molality scale) of aqueous solutions of poly(sodium methacrylate). 

Predictions from the model for the osmotic coefficient can be made when the binary parameter between nmidissociated repeating units and the counterion of the low molecular weight salt, as well as the influence of that salt on the configurational parameter b are neglected. Figure 16 shows comparisons between experimental data and calculation results for the osmotic coefficient for aqueous solutions of a sodium poly(acrylate) (NaPA 15) and NaCl. The osmotic coefficient (on molality scale) is plotted versus the overall solute molality m, that is defined as ... 

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. 

Figure 15. Electro-osmotic drag coefficients Adras of (a) Nafion 117 (EW — 1100 g/equiv) and (b) sulfonated poly-(arylene ether ketone)s, as a function of the solvent (water and/or methanol) volume fraction 174.212,219,274-281...

Figure 18 shows the temperature dependence of the proton conductivity of Nafion and one variety of a sulfonated poly(arylene ether ketone) (unpublished data from the laboratory of one of the authors). The transport properties of the two materials are typical for these classes of membrane materials, based on perfluorinated and hydrocarbon polymers. This is clear from a compilation of Do, Ch 20, and q data for a variety of membrane materials, including Dow membranes of different equivalent weights, Nafion/Si02 composites ° ° (including unpublished data from the laboratory of one of the authors), cross-linked poly ary lenes, and sulfonated poly-(phenoxyphosphazenes) (Figure 19). The data points all center around the curves for Nafion and S—PEK, indicating essentially universal transport behavior for the two classes of membrane materials (only for S—POP are the transport coefficients somewhat lower, suggesting a more reduced percolation in this particular material). This correlation is also true for the electro-osmotic drag coefficients 7 20 and Amcoh...

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

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,... 

Table 1.2 Reduced osmotic pressures (tt/c)c=o, number average molecular weights Mn and osmotic second virial coefficient A2 for poly(pentachlorophenyl methacrylate) fractions in toluene at 25°C and benzene at 40°C (tt in cm of benzene or toluene) (c in g dl-1). (From ref. [44])...

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