Solutions behavior

One of the first properties of hyperbranched polymers that was reported to differ from those of linear analogs was the high solubility induced by the branched backbone. Kim and Webster [31] reported that hyperbranched polyphenylenes had very good solubility in various solvents as compared to linear polyphenylenes, which have very poor solubility. The solubility depended to a large extent on the structure of the end groups, and thus highly polar end-groups such as carboxylates would make the polyphenylenes even water-soluble. 

Not only good solubility but also solution behavior differs for hyperbranched polymers compared to linear polymers. For example, hyperbranched aromatic polyesters, described by Turner et al. [71,72], exhibit a very low a-value in the Mark-Houwink-Sakurada equation and low intrinsic viscosities. This is consist- 

The size of dendritic polymers in solution has been shown to be greatly affected by solution parameters such as polarity and pH. Newkome et al., for example, have shown that the size of dendrimers with carboxylic acid end groups in water can be increased by as much as 50% on changing the pH [112]. 

The dilution properties of hyperbranched polymers also differ from those of linear polymers. In a comparison between two alkyd resin systems, where one was a conventional high solid alkyd and the other based on a hyperbranched aliphatic polyester, the conventional high solid alkyd was seen to exhibit a higher viscosity [113]. A more rapid decrease in viscosity with solvent content was noted for the hyperbranched alkyd when the polymers were diluted. 

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Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS.

Condensed phases of systems of category 1 may exhibit essentially ideal solution behavior, very nonideal behavior, or nearly complete immiscibility. An illustration of some of the complexities of behavior is given in Fig. IV-20, as described in the legend. 

The qualitative solution behavior becomes more apparent when going to local coordinates, i.e., we rewrite the equations of motion in terms of the center of mass... 

Because the field code POW is also a hierarchical group code (see also Figure 5-17), the solution behavior retrieval POW OR POWIZOG can be abbreviated in the fact editor to simply POW without further specification. 

The constant is not a tme partition coefficient because of difference, — V, includes the soflds and the fluid associated with the gel or stationary phase. By definition, IV represents only the fluid inside the stationary-phase particles and does not include the volume occupied by the soflds which make up the gel. Thus is a property of the gel, and like it defines solute behavior independently of the bed dimensions. The ratio of to should be a constant for a given gel packed in a specific column (34). 

L. V. GaUacher, Solution Behavior of Suf actants-. Theoretical Applications and Aspects, Vol. 2, Plenum Press, New York, 1982, pp. 791—801. 

The ideal solution is a model fluid which serves as a standard to which teal solution behavior can be compared. Equation 151, which characterizes the... 

This equation, known as the Lewis-RandaH rule, appHes to each species in an ideal solution at all conditions of temperature, pressure, and composition. It shows that the fugacity of each species in an ideal solution is proportional to its mole fraction the proportionaUty constant is the fugacity of pure species i in the same physical state as the solution and at the same T and P. Ideal solution behavior is often approximated by solutions comprised of molecules similar in size and of the same chemical nature. 

Liquid solutions are often most easily dealt with through properties that measure their deviations, not from ideal gas behavior, but from ideal solution behavior. Thus the mathematical formaUsm of excess properties is analogous to that of the residual properties. 

Molecular weight determinations of ECH—EO, ECH—AGE, ECH—EO—AGE, ECH—PO—AGE, and PO—AGE have not been reported. Some solution studies have been done on poly(propylene oxide), and these may approximate solution behavior of the PO—AGE copolymer (33,34). 

The ideal gas is a useful model of the behavior of gases and serves as a standard to which real gas behavior can be compared. This is formalized by the introduction of residual properties. Another useful model is the ideal solution, which sei ves as a standard to which real solution behavior can be compared. This is formalized by introduction of excess propei ties. 

Ideal solution behavior is often approximated by solutions comprised of molecules not too different in size and of the same chemical nature. Thus, a mixture of isomers conforms very closely to ideal solution behavior. So do mixtures of adjacent members of a homologous series. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are often based on the concept local... 

Deviations from Raonlt s law in solution behavior have been attributed to many charac teristics such as molecular size and shape, but the strongest deviations appear to be due to hydrogen bonding and electron donor-acceptor interac tions. Robbins [Chem. Eng. Prog., 76(10), 58 (1980)] presented a table of these interactions. Table 15-4, that provides a qualitative guide to solvent selection for hqnid-hqnid extraction, extractive distillation, azeotropic distillation, or even solvent crystallization. The ac tivity coefficient in the liquid phase is common to all these separation processes. 

Experimental reactivity patterns are based on solution behavior which are influenced by interactions between solvent and reacting molecules (especially ions). Compare electrostatic potential maps of 2-methyl-2-propyl cation and dimethylhydroxy cation. Identify sites that might form strong hydrogen bonds with water. Which ion will be better stabilized by its interaction with water ... 

In many process design applications like polymerization and plasticization, specific knowledge of the thermodynamics of polymer systems can be very useful. For example, non-ideal solution behavior strongly governs the diffusion phenomena observed for polymer melts and concentrated solutions. Hence, accurate modeling of... 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

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). 

Deviations in which the observed vapor pressure are smaller than predicted for ideal solution behavior are also observed. Figure 6.8 gives the vapor pressure of. (CHjCF XiN +. viCHCfi at T — 283.15 K, an example of such behavior,10 This system is said to exhibit negative deviations from Raoult s law. 

Therefore, it is a sufficient condition for ideal solution behavior in a binary mixture that one component obeys Raoult s law over the entire composition range, since the other component must do the same. 

When deviations from ideal solution behavior occur, the changes in the deviations with mole fraction for the two components are not independent, and the Duhem-Margules equation can be used to obtain this relationship. The allowed combinations"1 are shown in Figure 6.10 in which p /p and P2//>2 are... 

Figure 6.10 Representative deviations from ideal solution behavior allowed by the Duhem-Margules equation. The dotted lines are the ideal solution predictions. The dashed lines giveP2IP2 (lower left to upper right), and p jp (upper left to lower right).

For ideal solutions, the activity coefficient will be unity, but for real solutions, 7r i will differ from unity, and, in fact, can be used as a measure of the nonideality of the solution. But we have seen earlier that real solutions approach ideal solution behavior in dilute solution. That is, the behavior of the solvent in a solution approaches Raoult s law as. vi — 1, and we can write for the solvent... 

The extent of deviation from ideal solution behavior and hence, the magnitude and arithmetic sign of the excess function, depend upon the nature of the interactions in the mixture. We will now give some representative examples. 

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

Figure 8.21 Effect of pressure on the melting temperatures of. ViCftHft + assuming ideal solution behavior.

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

Assume ideal solution behavior with no solid solutions and constant Afus m and... 

The reason is that classical thermodynamics tells us nothing about the atomic or molecular state of a system. We use thermodynamic results to infer molecular properties, but the evidence is circumstantial. For example, we can infer why a (hydrocarbon + alkanol) mixture shows large positive deviations from ideal solution behavior, in terms of the breaking of hydrogen bonds during mixing, but our description cannot be backed up by thermodynamic equations that involve molecular parameters. 

However, dendrimeric and hyperbranched polyesters are more soluble than the linear ones (respectively 1.05, 0.70, and 0.02 g/mL in acetone). The solution behavior has been investigated, and in the case of aromatic hyperbranched polyesters,84 a very low a-value of the Mark-Houvink-Sakurada equation 0/ = KMa) and low intrinsic viscosity were observed. Frechet presented a description of the intrinsic viscosity as a function of the molar mass85 for different architectures The hyperbranched macromolecules show a nonlinear variation for low molecular weight and a bell-shaped curve is observed in the case of dendrimers (Fig. 5.18). 

Synthesis and mechanical and morphological characterization of (AB)n, ABA and BAB type copolymers of m-phenylene-isophthalamide and polydimethylsiloxane have been reported241 242>. The effect of copolymer type, chemical composition and segment molecular weights on phase separation and the solution behavior of these systems have also been discussed. 

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