Opalescence, critical

The intensity of light scattered from a fluid system increases enormously, and the fluid takes on a cloudy or opalescent appearance as the gas-liquid critical point is approached. In binary solutions the same phenomenon is observed as the critical consolute point is approached. This phenomenon is called critical opalescence.31 It is due to the long-range spatial correlations that exist between molecules in the vicinity of critical points. In this section we explore the underlying physical mechanism for this phenomenon in one-component fluids. The extension to binary or ternary solutions is not presented but some references are given. 

For the purposes of discussing critical opalescence it is useful to define the static density-density correlation function 

This function measures the correlations32 of the fluctuations in the density at two different points of the fluid r,r separated by r — r. As r — r — oo, the density fluctuations dpir) and 8p(j ) should be uncorrelated so that 

In a spatially uniform system G(r,r ) should be invariant to an arbitrary translation a so that G(r + a, r + a) = G(r,r ). This requires that 

Transforming integration variables to R — r — r and r substitution of Eq. (10.7.2) and integration of r over V then gives 

Indeed, the incre2tse in the scattering intensity, when the configurative point approaches the spinodal, is accompanied by a deformation of the polar disigram of the scattered intensity (z 1) and a decrease in the wavelength exponent (Elquation 2.1-92) to n w 2. 

The correlation among density fluctuations is described by special functions of structural element distribution, or by correlation functions. 

Suppose N identical structural elements (eg. atoms) to occupy a volume V. Choose a coordinate system arbitrarily inside the body and draw vectors fl and ri to fix the space elements dV) and dV, which are distant at fi2. In the case of chaotically distributed atoms, the probability for atom 1 to be in the space element dV and for atom 2 to be in the space element dVi simultaneously is equal to the product 

However, if there is a correlation between the atom locations, 

If the origin of the coordinates is placed at atom 1, then the probability of atom 2 being in the spherical layer dr is equal to 

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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. 

As mentioned earlier, the physical properties of a liquid mixture near a UCST have many similarities to those of a (liquid + gas) mixture at the critical point. For example, the coefficient of expansion and the compressibility of the mixture become infinite at the UCST. If one has a solution with a composition near that of the UCEP, at a temperature above the UCST, and cools it, critical opalescence occurs. This is followed, upon further cooling, by a cloudy mixture that does not settle into two phases because the densities of the two liquids are the same at the UCEP. Further cooling results in a density difference and separation into two phases occurs. Examples are known of systems in which the densities of the two phases change in such a way that at a temperature well below the UCST. the solutions connected by the tie-line again have the same density.bb When this occurs, one of the phases separates into a shapeless mass or blob that remains suspended in the second phase. The tie-lines connecting these phases have been called isopycnics (constant density). Isopycnics usually occur only at a specific temperature. Either heating or cooling the mixture results in density differences between the two equilibrium phases, and separation into layers occurs. 

These regions scatter light, and the system has a milky appearance, known as critical opalescence. 

The approach to the critical point, from above or below, is accompanied by spectacular changes in optical, thermal, and mechanical properties. These include critical opalescence (a bright milky shimmering flash, as incident light refracts through intense density fluctuations) and infinite values of heat capacity, thermal expansion coefficient aP, isothermal compressibility /3r, and other properties. Truly, such a confused state of matter finds itself at a critical juncture as it transforms spontaneously from a uniform and isotropic form to a symmetry-broken (nonuniform and anisotropically separated) pair of distinct phases as (Tc, Pc) is approached from above. Similarly, as (Tc, Pc) is approached from below along the L + G coexistence line, the densities and other phase properties are forced to become identical, erasing what appears to be a fundamental physical distinction between liquid and gas at all lower temperatures and pressures. 

We want to compute the fluctuations around c, i.e., we want to compute the mesostate related to the macrostate c. In the situation in fig. 39a that mesostate is identical with the stationary solution Ps of the M-equation because c is the only stationary macrostate. Expansion (X.2.16) is no longer the correct starting point. For, the terms written on the first line of the right-hand member are all zero according to (5.1), and only the (unwritten) term with a5" 0, which is of order 2-1, does not vanish. But that is the term that is responsible for restraining the fluctuations, which are caused by the terms on the second line. The conclusion is that the fluctuations will be proportional to a higher power of Q than anticipated (X.2.9). This is the enhancement of fluctuations near the critical point, as in critical opalescence. 

Let us consider now behaviour of the gas-liquid system near the critical point. It reveals rather interesting effect called the critical opalescence, that is strong increase of the light scattering. Its analogs are known also in other physical systems in the vicinity of phase transitions. In the beginning of our century Einstein and Smoluchowski expressed an idea, that the opalescence phenomenon is related to the density (order parameter) fluctuations in the system. More consistent theory was presented later by Omstein and Zemike [23], who for the first time introduced a concept of the intermediate order as the spatial correlation in the density fluctuations. Later Zemike [24] has applied this idea to the lattice systems. 

As it is known [5], the intensity of the scattered light gives us an information about the system s disorder, e.g., presence therein of pores, impurities etc. Since macroscopically liquid is homogeneous, critical opalescence arises due to local microscopic inhomogeneities - an appearance of small domains with different local densities. In other words, liquid is ordered inside these domains but still disorded on the whole since domains are randomly distributed in size and space, they appear and disappear by chance. Fluctuations of the order parameter have large amplitude and involve a wide spectrum of the wavelengths (which results in the milk colour of the scattered light). 

Omstein-Zemike theory of the critical opalescence which operates also with a linear equation for the joint correlation function. 

Solutions of polystyrene and purified cyclohexane after filtration still exhibited appreciable dissymmetry of scattered intensities at high temperatures where the influence of the critical opalescence was precluded. Therefore all solutions were freed from dust by centrifugation. After a... 

The maximum of the dissymmetry lies at 5-6 wt % of the polymer near the quasi-binary spinodial. All maxima are indicated by arrows in Figure 6. In our opinion polydispersity is the main reason that the maximum of critical opalescence is not found at the critical point. In a system consisting of a polydisperse polymer and a solvent the shape of the spinodial surface may be such that highly unsymmetrical fluctuations may occur in the critical region and give rise to the above mentioned... 

K.W. Herrmann, J.G. Bruchmiller and W.L. Courchene, Micellar properties and critical opalescence of dimethylalkylphosphine oxide solutions, J. Phys. Chem. 70 (1966) 2909-2918. 

Debye P, Kleboth K (1965) Electrical field effect on the critical opalescence. J Chem Phys 42(9) 3155—3162... 

The accuracy of the pressure and temperature measurements was verified by measuring the vapor pressure curves and critical points for pentane and for toluene. Vapor pressures were measured by observing the formation of a liquid phase as pentane or toluene was injected into the constant-volume view cell under isothermal conditions. The observation of critical opalescence was used to determine the critical point. The measured vapor pressures and critical points are given in Table I. Vapor pressures deviate from... 

Phase equilibria and pressure-temperature coordinates of critical points in ternary systems were taken with a high-pressure apparatus based on a thermostated view cell equipped with two liquid flow loops which has been described in detail elsewhere [3]. The loops feed a sample valve which takes small amounts of probes for gas-chromatographic analysis. In addition to temperature, pressure and composition data, the densities of the coexisting liquid phases are measured with a vibrating tube densimeter. Critical points were determined by visual oberservation of the critical opalescence. 

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