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The physical nature of the critical opalescence.

Francis. E. Murray

Published Jan 1, 1953• 0 citations
Publisher

Abstract

The phenomena associated with the phase transition at the liquid-vapor critical point and at the consolute point in a binary liquid mixture have been investigated. Photo-electric measurements of turbidity were used to determine vertical density gradients within 0.2° C of the condensation point. The turbidity, determined either by measuring transverse light scattering, or transmission, was observed at fixed temperatures, as a function of the density, or composition in the case of a binary liquid system.

DOI
10.82308/21694

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The phenomena associated with the phase transition at the liquid-vapor critical point and at the consolute point in a binary liquid mixture have been investigated. Photo-electric measurements of turbidity were used to determine vertical density gradients within 0.2° C of the condensation point. The turbidity, determined either by measuring transverse light scattering, or transmission, was observed at fixed temperatures, as a function of the density, or composition in the case of a binary liquid system.
We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte Carlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.
Quantum liquid, in the form of a self-bound droplet, is stabilized by a subtle balance between the mean-field contribution and quantum fluctuations. While a liquid-gas transition is expected when such a balance is broken, it remains elusive whether liquid-gas critical points exist in the quantum regime. Here, we study the quantum criticality in a binary Bose mixture undergoing the liquid-gas transition. We show that, beyond a narrow stability window of the self-bound liquid, a liquid-gas coexistence persists, which eventually transits into a homogeneous mixture. Importantly, we identify two distinct critical points where the liquid-gas coexistence terminates. These critical points are characterized by rich critical behaviors in their vicinity, including divergent susceptibility, unique phonon-mode softening, and enhanced density correlations. The liquid-gas transition and the critical points can be readily explored in ultracold atoms confined to a box potential. Our work highlights the thermodynamic approach as a powerful tool in revealing the quantum liquid-gas criticality, and paves the way for further studies of critical phenomena in quantum liquids.
Here, in brief outline, is the run of the chapter. Section 16.1 presents two experiments to introduce the topic of “critical phenomena,” as that phrase is used in physics. The next section illustrates the mathematical behavior of certain physical quantities near a critical point. Section 16.3 constructs a theoretical model: the Ising model. The following two sections develop methods for extracting predictions from the model. The last three sections draw distinctions, outline some general results, and collect the chapter's essentials. Achieving a sound theoretical understanding of critical phenomena was the major triumph of thermal physics in the second half of the twentieth century. Thus the topic serves admirably as the culmination of the entire book. Experiments Liquid–vapor We begin with an experiment that you may see as a lecture demonstration, performed either with carbon dioxide or with Freon, a liquid once used in refrigerators. A sealed vertical cylinder contains a carefully measured amount of CO 2 (say) under high pressure. To begin with, the system is in thermal equilibrium at room temperature, as sketched in part (a) of figure 16.1. A distinct meniscus separates the clear liquid phase from the vapor phase above it. Now heat the system with a hair dryer. The meniscus rises (because the liquid expands), and gentle boiling commences. Next the meniscus becomes diffuse, and then it disappears. The CO 2 has become spatially homogeneous in density, as illustrated in figure 16.1 (b).
Introduction In this chapter we provide a comprehensive and unified treatment of the physical concepts and quantities relevant to phase transitions and critical phenomena. Some of these concepts and quantities have already been discussed in the particular contexts of magnetism (Chapter 7), or liquid crystals (Chapter 9, We conclude the chapter with a brief reference to the application of renormalisation group ideas to critical phenomena. The resulting reconciliation of the predictions of classical theories with experiments and exact or quasi-exact solutions of model systems is a major triumph of twentieth-century physics. Phases and phase transitions Thermodynamics habitually deals with equilibrium systems that are uniform on the macroscopic scale – i.e., where the structure, density and composition are the same throughout the bulk of the system, which is many times greater than a single atom or molecule. Because the system is in equilibrium, intensive thermodynamic variables such as the temperature or chemical potential are also spatially uniform. Such a system is said to consist of a single phase – it is a one-phase system. Phases are what used to be called the states of matter. Solids, liquids, gases and plasmas are four commonly occurring phases – they correspond to the four elements of Aristotelian physics: earth, water, air and fire, respectively. There are, however, many other, less easily identified phases, some of which we have already encountered in this book, such as the ferromagnetic, antiferromagnetic, nematic or superconducting phases. On varying the temperature, pressure and chemical potential(s) of a system, properties such as its structure, density, composition, compressibility, specific heat, etc., in general change smoothly. Yet under certain conditions the changes may be abrupt – some of these properties may exhibit discontinuities, or even divergences, at a phase transition . Phase transitions are among the most spectacular phenomena of nature. Consider, for instance, the phase sequence of water on heating: from ice, an opaque, slippery, rock-like solid; to colourless, incompressible, liquid water, which nevertheless easily flows under gravity; to water vapour, an invisible and very low-density (greenhouse!) gas, hence of ill-defined volume.
A first-principles theory for the description of critical phenomena in mixtures is presented. This is a natural extension of the hierarchical reference theory of fluids, which has proven useful and accurate in the treatment of the critical region of one-component fluids. The case of a binary mixture is studied in detail. Near the critical point, the theory develops a renormalization-group structure that allows the identification of several possible critical behaviors corresponding to different fixed points. For a generic binary mixture, the most stable fixed point gives rise to the same critical exponents as are predicted by the well-known phenomenological approach, providing a microscopic mechanism for such behavior. The competition between two fixed points is identified as the mechanism leading to the strong corrections to scaling seen experimentally. Explicit expressions for the most interesting universal quantities are evaluated to O(4-d). This theory is then applied to a few simple models of mixtures in three dimensions. As a first step, the mean-field phase diagram is reproduced and the stability of this solution is determined. The physical nature of the relevant order parameter and the one-loop correction to mean-field results are also calculated within our approach.
The effect of the 1.5-scattering mechanism on the time and temperature behavior of the electric field autocorrelation function for the light wave scattered from fluids has been studied for the case where the order-parameter fluctuations obey the diffusion-like kinetics with spatially-dependent kinetic coefficient. The leading contributions to the relevant static correlation functions of the order-parameter fluctuations were obtained by using the Ginzburg-Landau model with a cubic term, and then evaluated with the use of the Gaussian uncoupling for many-point correlation functions and the Ornstein-Zernicke form for the pair correlation function. It is shown that the presence of the 1.5-scattering effects in the overall scattering pattern may be detected in the form of a small but noticeable deviation from exponential decay of the total electric field autocorrelation function registered experimentally near the critical point. Obtained with the standard methods of analysis, the effective half-width of the corresponding spectrum can reveal a stronger temperature dependence and a multiplicative renormalization as compared to the half-width of the spectrum of the pair correlator.