Negative deviation behavior

Liquid crystalline polymers (LCPs) added to high Tg polymers can often significantly reduce the viscosity of the high Tg polymer at very low LCP addition levels [269-272]. An example of this is shown in Fig. 6.22 for polyamide/liquid crystalline polymer blends. The significant negative deviation behavior was observed with a minor amount of LCP addition. 

If the molecular species in the liquid tend to form complexes, the system will have negative deviations and activity coefficients less than unity, eg, the system chloroform—ethyl acetate. In a2eotropic and extractive distillation (see Distillation, azeotropic and extractive) and in Hquid-Hquid extraction, nonideal Hquid behavior is used to enhance component separation (see Extraction, liquid—liquid). An extensive discussion on the selection of nonideal addition agents is available (17). 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

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. 

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. 

Either a negative deviation or a positive deviation is regularly observed. In any phase diagram, composition is plotted against temperature. In this way, we can see how the interactions between phases change as the temperature changes and the behavior as each solid phase then melts. Either two-phase or three phase systems can be illustrated. This is shown in the following ... 

Figure 1.9 Vegard s law relating unit cell parameters to composition for solid solutions and alloys (a) ideal Vegard s law behavior (b) negative deviation from Vegard s law and (c) positive deviation from Vegard s law.

Such behavior occurs when the two components either form an ideal mixture or are immiscible. Before drawing conclusions concerning molecular interactions (12, 13), it is clearly important to establish that homogeneous mixed films have been formed. Any deviation from line LM is, of course, indicative of both mixing and nonideality. In discussing such effects, we define any negative deviation from LM as a "condensation and any positive deviation as an "expansion. Our results fall into three distinct categories. 

In all the above discussions regarding liquid-vapor equilibria we have assumed that our representative systems were ideal, that is, there are no differences in attractions between molecules of different types. Few systems are ideal and most show some deviation from ideality and do not follow Raoult s law. Deviations from Raoult s law may be positive or negative. Positive deviations (for binary mixtures) occur when the attraction of like molecules, A-A or B-B, are stronger than unlike molecules, A-B (total pressure greater than that computed for ideality). Negative deviations result from the opposite effects (total pressure lower than that computed for ideality). A mixture of two liquids can exhibit nonideal behavior by forming an azeotropic mixture (a constant boiling mixture). 

Deviations from log-linear behavior can still occur even if none of the above explanations is valid for your system [71-74], Deviations are typically at low and/or high concentrations of cosolvent. Typically, negative deviations are observed at low cosolvent concentrations and positive deviations are observed at high cosolvent concentrations. In Rubino and Yalkowsky s [72] review of this topic, deviations could not be consistently attributed to physical properties of the cosolvent-water mixtures or alterations in the solute crystal. They concluded that changes in the structure of the solvent play a role in deviation from expected log-linear solubilities. 

In true chemical solutions mixing on the molecular level leads to substantial increases in the entropy of the system and, consequently, negative deviations from the linear relationship between composition and the free energy of the solution (Raoult s law). If this is the only deviation from the Henry s law behavior of equation 3.1, then the solution is referred to as being ideal. 

Figure 1 Positive and negative deviations for ideal behavior.

The results are plotted in Fig. 3. As can be seen, with the Raoult s law reference, the acetone-chloroform system shows negative deviation from ideal behavior. This is unusual and is due to there being some tendency to form hydrogen bonds between acetone and chloroform. Note that as the system approaches either of the pure components, the vapor-pressure curve of that component becomes tangent to its Raoult s law line. 

In systems with negative deviation from ideal behavior, maximum-boiling-point azeotropes can occur. This is illustrated in Fig. 8 for the chloroform-acetone system, treated in Example 1. This system shows negative deviation from ideal behavior due to the possibility of hydrogen bonds between chloroform and acetone, which cannot occur with the pure components. 

Show that the Gibbs-Duhem equation requires that in a binary solution, both solvent and solute must show positive deviation from ideal behavior or must both show negative deviation from ideal behavior. 

This behavior requires positive deviations from Raoult s law over part of the composition range and negative deviations over the remainder. Thus a plot of GE vs. x starts and ends with GE = 0 at A i = 0 and X] = 1 and shows positive values over part of the composition range and negative values over the remainder, with an intermediate crossing of the Xi axis. Because these deviations are usually quite small, the vapor pressures P 1 and P2sat must not be too different, otherwise the dewpoint and bubblepoint curves cannot exhibit extrema. 

If the attraction between the A and B molecules is stronger than that between like molecules, the tendency of the A molecules to escape from the mixture will decrease since it is influenced by the presence of the B molecules. The partial vapor pressure of the A molecules is expected to be lower than that of Raoult s law. Such nonideal behavior is known as negative deviation from the ideal law. Regardless of the positive or negative deviation from Raoult s law, one component of the binary mixture is known to be very dilute, thus the partial pressure of the other liquid (solvent) can be calculated from Raoult s law. Raoult s law can be applied to the constituent present in excess (solvent) while Henry s law (see Section 3.3) is useful for the component present in less quantity (solute). 

TV. Neel temperature (N.O. means not observed). Td. Temperature below which departures from Curie-Weiss law become noticeable. 0. Weiss constant, fiett. Effective moment. b Below about 160° K. linearity of 1/fi vs. T is only approximate for these two samples. The data between 75° and 160° K. show small but significant systematic negative deviations from the straight line which represents the results well above 160° and between 40° and 75° K. The cause of these deviations is unknown but TbH2.4o is known to be a two-phase mixture of the di- and trihydrides. TbH2l2i is close to the phase boundary and it, too, may be two-phase (see 9). The anomalous magnetic behavior may in these cases be due to the fact that they are mixtures. 

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