Dilute solution behavior

When solute and solvent are very dissimilar chemically, A is large. Therefore, deviations from infinitely-dilute-solution behavior are frequently observed for such mixtures at very small values of x2. For example, solutions of helium in nonpolar solvents show deviations from dilute solution behavior at values of x2 as low as 0.01. On the other hand, since both A and vf are usually positive, it sometimes happens that the last two terms in Eq. (65) tend to cancel each other, with the fortuitous result that Henry s law provides a good approximation to unexpectedly high pressures and concentrations (M3). 

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

The presence of a second type of repeat unit causes the dilute solution behavior to be more complex than that of homopolymers [1], Copyolymer composition and sequence distribution directly effect the intrinsic viscosity. Interactions between unlike chain segments and preferential interaction of solvent molecules with one of the comonomers are also of considerable importance. 

Both modifications affect the analysis of dilute solution behavior, and it is difficult to judge how much the e/e0 term is actually needed. In any case, as the authors themselves point out (41), the e/e0 term makes an entirely negligible contribution to solvent activity in concentrated solutions. For example, simple calculations yield a contribution of approximately l%ina 10% solution of natural rubber in benzene at 30° C (M = 500000, [t/]g = 250, y=0.4). It is therefore clear that thermodynamic measurements can furnish no evidence for or against continued collapse in concentrated solutions. 

A broader study of the dilute solution behavior of ABA copolymers was reported by Beezer et al. 

Dilute Solution Behavior of Sodium Polyacrylate and Quaternized Polyvinylpyridine... 

For dissolved species the standard state is defined as an ideal solution with a concentration of 1 M (this is obtained in practice by extrapolating the dilute solution behavior up to this concentration). A special comment is in order on the standard enthalpies of formation of ions. When a strong electrolyte dissolves in water, both positive and negative ions form it is impossible to produce one without the other. It is therefore also impossible to measure the enthalpy change of formation of ions of only one charge. Only the sum of the enthalpies of formation of the positive and negative ions is accessible to calorimetric experiments. Therefore, chemists have agreed that AH° of H (aq) is set to zero. 

The activity coefficients given by the Debye-Hiickel treatment presumably represent deviations from the dilute solution behavior, i.e., from Henry s law, and are consequently based on the standard state which makes the activity of an ion equal to its mole fraction at infinite dilution ( 37b, III B). In the experimental determination of activity coefficients, however, it is almost invariably the practice to take the activity as equal to the molarity or the molality at infinite dilution. The requisite corrections can be made by means of equation (39.13), but this is unnecessary, for in solutions that are sufficiently dilute for the Debye-Hackel limiting law to be applicable, the difference between the various activity coefficients is negligible. The equations derived above may thus be regarded as being independent of the standard state chosen for the ions, provided only that the activity coefficients are defined as being unity at infinite dilution. 

Khasat, N. Pennisi, R.W. Hadjichristidis, N. Fetters, L.J. Dilute solution behavior of asymmetric three-arm and regular three- and twelve-arm polystyrene stars. Macromolecules 1988, 21, 1100-1106. 

The value of the Henry law constant and concentration range over which this law is valid depends very much on the system. This is easily seen by comparing the behavior of the methanol-water and acetonitrile-water systems (figs. 1.5 and 1.6). In the latter case ideally dilute solution behavior is observed for a lower range of mole fractions of the solute, that is, when x cn is less than 0.03. 

Studies on the dilute solution behavior of sulfonated ionomers have shown these polymers to exhibit unusual viscosity behavior in solvents of low polarity. These results have been interpreted as arising from strong ion pair associations in low polarity diluents. Solvents of higher polarity, such as dimethyl sulfoxide and dimethyl formamide induce classic polyelectrolyte behavior in sulfonate ionomers even at very low sulfonate levels. To a first approximation these two behaviors, ion pair interactions or polyelectrolyte behavior, are a consequence of solvent polarity. Intramolecular association of Lightly Sulfonated Polystyrene (S-PS) results in a reduced viscosity for the ionomer less than that of polystyrene precursor at low polymer levels. Inter-association enhances the reduced viscosity of the ionomer at higher polymer concentrations. Isolation of the intra- and inter-associated species of S-PS has been attempted (via freeze drying). A comparison of selected properties reveals significant differences for these two conformations. 

Several studies (6, 13) of the solution behavior of sulfonate ionomers have provided additional insight on the nature of the ion pair aggregation. The polarity of the solvent environment has been shown to have a major influence on the dilute solution behavior of these polymers. In the course of these studies it has been observed with selected systems that both melt viscosity values and solution behavior can vary according to the history of sulfonate ionomers. This study provides some data and provides one rationale for such differences. 

Recently the study of the dilute solution behavior of polymacromonomer, a limiting case of graft copolymer where each repeat unit carries a grafted chain, has been initiated. The main interests are focused on the dependence of conformation and size of the whole molecule on factors such as nature of the backbone and side chain, molecular weight of backbone and grafts, solvent interactions with respect to both components, and chain stiffness induced on the backbone due to the high grafting density and its dependence on the aforementioned factors [310-313]. 

The HMHECs used in these experiments provided good examples of an associative thickener, in that clear evidence of a critical aggregation concentration was seen from the dilute-solution behavior. Although some limited molecular aggregation may occur below this concentration, once this concentration is achieved, a three-dimensional network starts to form. This network formation leads to a significant enhancement of adsorption onto polymer latex particles from which the surfactant has been removed. The adsorption density is high for a cellulosic polymer of the equivalent molecular weight. 

MUM Mumick, P.S., and McCormick, C.L., Water soluble copolymers. 54 V-isopropyl-acrylamide-co-acrylamide copolymers in drag reduction Synthesis, characterization, and dilute solution behavior, Polym. Eng. Sci., 34, 1419, 1994. 

An investigation of the dilute solution behavior of a polymer can provide useful infonnation about the size and shape of the eoil, the extent of polymer-solvent inter-aetion, and the molar mass. Deviations from ideahty, as we have seen in Chapter 9,... 

Studies of the dilute solution behavior of polymers with a specific stereostructure have revealed that the unperturbed dimensions may depend on the chain configuration. 

Bauer, B.J., Fetters, L.J., 1978. Synthesis and dilute-solution behavior of model star-branched polymers. Rubber Chem. Technol. 51 (3), 406-436. 

Simha, R., Utracki, L. A., Dilute solution behavior of block polymers, pp. 107-122 in Block Polymers, Aggarwal S. L., Editor, Pergamon Press, New York (1970). 

As in previous chapters, synthesis, morphology, and physical and mechanical behavior will be considered. In addition, dilute solution behavior and kinetics of single crystal formation will be treated, also using PS/PEO block copolymers as models, since these block copolymers have been investigated the most thoroughly. 

Poly(dlmethyl siloxane) 4-200 Kx measured dilute solution behavior and RIS treatment discussed. [84]... 

We want to use the Henryan standard state, which is a state in which the solute exhibits dilute solution behavior. That is, no matter what the actual concentration, the solute behaves as if there is absolutely no solute-solute interactions - each solute molecule thinks it is alone in the solvent. It is a state which obey s Henry s law, which at real concentrations is obviously a hypothetical state, and it lies anywhere on the Henry s law tangent. In 8.3.4 we saw that we could choose a point on this tangent having X = 1, or we could choose any other point. What the other points on this slope mean depends on what concentration scale we are using - if we use a weight percent scale we can choose a weight percent standard state, and if we use a molality scale we can choose a molal standard state. 

Figure 1 illustrates the dilute solution behavior of a series of HTP in toluene at 25°C. Compared to the relative viscosity (Hrel) curve of the non-neutralized PBD (Hycar CTB), that of the neutralized polymer increases more or less abruptly with concentration. Ultimately a gelation phenomenon occurs, which is the obvious consequence of the intermolecular interactions of the ion pairs that the metal carboxylate end-groups form in toluene at 25°C. In the alkaline-earth cations series (Ba, Ca, Mg), the sharp increase of the relative viscosity appears at decreasing concentrations as the cation size decreases (Figure 1). As already mentioned, the smallest alkaline earth cation (Be) exhibits systematically a phase separation at high dilution which prevents significant measurements in that range with a capillary viscometer. These results can be explained by the equation (eq. 2) relating the attractive force between anion and cation to their charge (e and eQ, respectively), the square of their distance (r) and the dielectric constant (c) of the medium, respectively.

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