Mixing spontaneous

The entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

Here, AGeiastic is the contribution due to the elastic retractive forces developed inside the gel and A6mixi g is the result of the spontaneous mixing of the fluid molecules with the polymer chains. The term AGmjXjng is a measure of the compatibility of the polymer with the molecules of the surrounding fluid. This compatibility is usually expressed by the polymer-solvent interaction parameter, xi (Flory, 1953). 

The fundamentals and numerical treatment ot mixing ot two or more liquid components are described in this section. The simplest fundamental explanation is for two miscible liquid components. For example, the spontaneous mixing of two liquid materials is fundamentally controlled by the free energy of mixing ... 

Dispersion spontaneous mixing effected by flow and— only sometimes—by diffusion. 

Mass transfer spontaneous mixing from a system s boundary into its bulk. 

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

Figure 1.12. From Order to Disorder. The spontaneous mixing of gases is driven by an increase in entropy.

In substance spontaneous mixing is a relaxation process and continues until total balance in water composition is reached. For this reason it takes place only when there is a nommiformity in the composition (local contamination, introduction of colorant, meeting of waters with differing... 

The interfacial tension of a stable, two-phase system is always positive, otherwise the two phases would spontaneously mix since they lower their free energy by making more and more interface. Therefore, near the critical point for phase separation, where the two coexisting phases become indistinguishable, one expects the surface tension between the two phases to vanish. The addition of a third interfacially active component to a two-component mixture with a tendency to phase separate can also result in an effectively negative tension (related to the chemical potential of the third component) which can cause the two components to spontaneously form a dispersion with an amount of internal interface related to the amount of the interfacially active component. Such systems are described in Chapter 8. 

Finally, a potential problem with polarity rests in the fact that this term is typically associated with enthalpy. But caution is urged in interpreting the like-dissolves-like rule in terms of enthalpy. It is often stated for example that nonpolar liquids such as octane and carbon tetrachloride are miscible because the molecules are held together by weak dispersion forces. However, spontaneous mixing of the two phases is driven not by enthalpy, but by entropy. 

Compatibility in the polymer blends is defined by either miscibility on the molecular scale or absence of gross symptoms of phase separation. This definition is phenomenological and empirical but no unanimous theoretical scheme for predicting compatibility has been established. Thermodynamics predicts that exothermic mixtures satisfying Equation 5 would spontaneously mix,... 

A Figure 13.1 Spontaneous mixing of two gases to form a homogeneous mixture (a soiution). 

At millimolar concentrations, when MP and Cao are either titrated or spontaneously mixed, NMR studies - C and H - reveal mutually upfield shifts. This clearly indicates the presence of complex formation. Absorption spectroscopy, on the other hand, proved to be insensitive to detect appreciable MP/Ceo interactions, which may lead to the false presumption that the degree of MP/Ceo association might be weak. 

Gases spread out and mix with one another, even without being stirred. If the stopper is removed from a container of ammonia in a room, ammonia gas will mix uniformly with the air and spread throughout the room. The random and continuous motion of the ammonia molecules (assumption 3) carries them throughout the available space. Such spontaneous mixing of the particles of two substances caused by their random motion is called diffusion. 

Spontaneous mixing occurs when AGmix is negative. Exothermic mixtures (AGmix < 0) will mix spontaneously, whereas for endothermic mixtures miscibility will occur only at high temperatures. A plot of AGmix versus is a convex function of the mixture composition, and is represented by a bimodal or spinodal phase with a lower critical solution temperature (LCST) or an upper critical solution temperature (UCST). 

The reason that seawater draws water to itself is related to nature s tendency toward spontaneous mixing, which we discuss in more detail later in this chapter and in Chapter 17. For now, we simply observe that, unless it is highly unfavorable energetically. 

When the barrier is removed, spontaneous mixing occurs, producing a solution of rmiform concentration. 

FIGURE 12.2 The Tendency to Mix (a) Thn-e water and a sodium chloride solution are separated by a barrier, (b) When the barrier is removed, the two liquids spontaneously mix, producing a single... 

---