Critical phenomena temperature

If the temperature is changed the miscibility of the liquids alters, and at a particular temperature the miscibility may become total this is called the critical solution temperature. With rise of temperature the surface of separation between the liquid and vapour phases also vanishes at a definite temperature, and we have the phenomenon of a critical point in the ordinary sense. According to Pawlewski (1883) the critical temperature of the... 

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

An interesting family of polymeric ligands show inverse temperature dependence of solubihty in water, i.e. they can be precipitated from aqueous solutions by increasing the temperature above the so-called cloud point. Typically these ligands contain poly(oxyalkylene) chains, but the phenomenon can be similarly observed with poly(N-isopropyl acrylamide) derivatives (e.g. 132) and methylated cyclodextrins, too. At or above their cloud points these compounds fall off the solution, due to the break-up and loss of the hydration shell which prevents aggregation and precipitation of their molecules. Conversely, upon cooling below this temperature (also called the lower critical solution temperature, LCST) these substances dissolve again. 

The volume change in these gels is not due to ionic effects, but rather to a thermodynamic phenomenon a lower critical solution temperature (LCST). The uncrosslinked polymer which makes up the gel is completely miscible with water below the LCST above the LCST, water-rich and polymer-rich phases are formed. Similarly, the gel swells to the limit of its crosslinks below the LCST, and collapses above the LCST to form a dense polymer-rich phase. Hence, the kinetics of swelling and collapse are determined mostly by the rate of water diffusion in the gel, but also by the heat transfer rate to the gel. 

A direct implication of this hypothesis is that phase transition of the mucus gel should be reversible, and it should exhibit the characteristic features of a critical phenomenon. Studies conducted in isolated giant mucin secretory granules of the terrestrial slug revealed that hydrated mucin gels, released from individual secretory granules, can indeed be recondensed. Recondensation/ decondensation is reversible and exhibits the typical features of a polymer gel phase transition. Namely, it is discontinuous, and is affected by pH, temperature and Ca2 + concentration in a fashion that mimics phase transition in synthetic polymer hydrogels [32, 33] (see Fig. 3). 

There are some similarities between third-phase formation in liquid/liquid extraction and the critical phenomenon of cloud points in aqueous solutions of nonionic polyethoxylated surfactants (12, 91). When a nonionic micellar solution is heated to a certain temperature, it becomes turbid, and by further increasing the temperature,... 

Problem 10 What do you understand by critical temperature and critical pressure in relation to vander Waals equation and critical phenomenon. Calculate the values of critical constants in terms of vander Waals constants. How are the values of critical constants determined experimentally ... 

The importance of the excess entropy of mixing in aqueous mixtures explains why many of these systems show phase separation with a lower critical solution temperature (LCST). This phenomenon is rarer—though not unknown—in non-aqueous mixtures (for an example, see Wheeler, 1975). The conditions for phase separation at a critical temperature can be expressed in terms of the excess functions of mixing (Rowlinson, 1969 Copp and Everett, 1953). 

The linear relation GC°=T observed in Fig. 12 is not sufficient evidence that would unambiguously support Eq. (6) and reveal the interfacial nature of the transition, because a bulk phenomenon may also produce such a temperature dependence. For instance, one might think of melt fracture and write down oc=Gyc that would be independent of Mw where yc would correspond to the critical effective strain for cohesive failure and modulus G would be proportional to kBT. Previous experimental studies [9,32] lack the required accuracy to detect any systematic dependence of oc on Mw and T. This has led to pioneers such as Tordella [9] to overlook the interfacial origin of spurt flow of LPE. It is in this sense that our discovery of an explicit molecular weight and temperature dependence of oc and of the extrapolation length bc is critical. The temperature dependence has been discussed in Sect. 7.1. We will focus on the Mw dependence of the transition characteristics. 

Another type of kinetics pattern currently under discussion is related to the so-called Mode-Coupling Theory (MCT) developed by Gotze and Sjogren [74], In the MCT the cooperative relaxation process in supercooled liquids and amorphous solids is considered to be a critical phenomenon. The model predicts a dependence of relaxation time on temperature for such substances in the form... 

Another solubility phenomenon that may depend partly on H bonding is consolute temperature or critical solution temperature formation in mixtures that have a composition region in which they are im -miscible. The region narrows as the temperature is changed. Above an upper consolute temperature, or below a lower consolute temperature, the components are miscible over the entire composition range. Figure 2-11 shows such loops for 2,4- and 2,5-dimethylpyridine in water, as reported by Andon and Cox (45a). Other pyridine-water systems are... 

Superconductivity is a phenomenon characterized by sudden and complete disappearance of electrical resistance in a substance when it is cooled below a certain tempeSrature, called the critical transition temperature, T. Superconductivity was discovered in 1911 by measuring the resistance of solid mercury (Hg) on cooling with a sharp discontinuity in resistance at about 4.2 K (see Fig. 1). In addition to the total loss... 

On the basis of this brief summary of RPM criticality, one might be tempted to conclude that the problem has been solved all finite-size scaling analysis point towards the Ising universality class. There is, however, one critical phenomenon which does not seem to have been demonstrated unambiguously in the RPM. This is the critical divergence of the constant-volume heat capacity, Cy. Recall that on the critical isochore and close to the critical temperature where the parameter t = (T — Tc)/Tc is small,... 

FIGURE 1 1.37 The critical phenomenon of sulfur hexafluoride. H Below the critical temperature the clear liquid phase is visible, (bj Above the critical temperature the liquid phase has disappeared. (cj The substance is coaled just below its critical temperature. The fog represents the condensation of vapor, (d) Finally, the liquid phase reappears. 

Hot Spot Growth Under a Bubble. When bubbles grow and detach from a nucleation center on a solid surface, evaporation of the liquid layer commonly occurs, separating the bubble from the solid surface. This microlayer evaporation process is particularly important at low pressures When a small zone under the bubble becomes dry as a result of this process, its temperature increases, and this increase can, under certain conditions, be sufficient to prevent rewetting of the surface on bubble departure, leading to a permanent hot spot and onset of the critical phenomenon. 

Stability, systems are intrinsically stable as one homogeneous phase when the temperature is greater than rcnticai- Hence, rcnticai is consistent with the definition of an upper critical solution temperature. Since Sp/SV)t, w, = 0 at rcriacai. small changes in pressure produce enormous changes in density near the critical point. This phenomenon is exploited by physical chemists, who perform lightscattering studies near Tcriticai-... 

---