Theory of Critical Opalescence

Einstein returned to the problem of thermodynamic fluctuations, giving a treatment of the density variations in a fluid at its critical point. Ordinarily the density fluctuations are controlled by the second derivative of the free energy with respect to the density. At the critical point, this derivative is zero, leading to large fluctuations. The effect…

Critical opalescence is a phenomenon which arises in the region of a continuous, or second-order, phase transition. Originally reported by Charles Cagniard de la Tour in 1823 in mixtures of alcohol and water, its importance was recognised by Thomas Andrews in 1869 following his experiments on the liquid-gas transition in carbon dioxide, many other examples have been discovered since.

Debye's derivation of the Ornstein-Zernike modification of Einstein's theory of critical opalescence is reviewed. It is shown that Debye's free-energy function leads to a modification of the Landau theory for the width of the Rayleigh line which is equivalent to the results of Fixman, Botch, and Felderhof.

Critical opalescence is a striking light scattering phenomenon, which was elegantly explained by Einstein. In the critical region the light scattering is so large that the substance appears milky whit

For physicists trying to make sense of quantum mechanics, Albert Einstein's thinking remains highly relevant. "This guy saw more deeply and more quickly into the problems that plague us today," one quantum physicist told me.

From 1905, the year he obtained his doctorate, through the 1920s, Albert Einstein made a series of discoveries and formulations that fundamentally changed mankind’s understanding of time, matter and the foundations of reality.

Historians still call the year 1905 the annus mirabilis, the miracle year because in that year Einstein published four remarkable scientific papers ranging from the smallest scale to the largest, through fundamental problems about the nature of energy, matter, motion, time and space.

The distinction between a fluid's liquid and gaseous phases breaks down at a certain temperature and pressure; under these conditions, the fluid looks milky white, like a common opal. Einstein found how this relates to why the sky is blue.

This volume presents Einstein's 49 contributions to Annalen der Physik, together with four introductory essays based on recent historical studies. The first three essays, by David Cassidy, Jürgen Renn, and Robert Rynasiewicz, discuss key aspects of the scientific revolution triggered by the pathbreaking papers of Einstein's annus mirabilis 1905, which changed our understanding of space, time, matter, and radiation.Various ramifications of these papers are worked out in Einstein's subsequent contributions to the Annalen.

Critical opalescence is a phenomenon which arises in the region of a continuous, or second-order, phase transition . Originally reported by Charles Cagniard de la Tour in 1823 in mixtures of alcohol and water, its importance was recognised by Thomas Andrews in 1869 following his experiments on the liquid-gas transition in carbon dioxide , many other examples have been discovered since. The phenomenon is most commonly demonstrated in binary fluid mixtures, such as methanol and cyclohexane . As the critical point is approached, the sizes of the gas and liquid region begin to fluctuate over increasingly large length scales. As the density fluctuations become of a size comparable to the wavelength of light, the light is scattered and causes the normally transparent liquid to appear cloudy. Tellingly, the opalescence does not diminish as one gets closer to the critical point, where the largest fluctuations can reach even centimetre proportions, confirming the physical relevance of smaller fluctuations. In 1908 the Express yourself. Organize your knowledge. Expand your mind. Discover the world. Revolvy connects you with interesting topics, lists and quizzes. Choose from hundreds of quizzes that test your knowledge. Search through millions of topics. Create a your personalized library of topics, and discover topics that others are following.

Marian Smoluchowski was born on May 28, 1872 in Vorderbrühl near Vienna in the family of an important official in the Austro-Hungarian administration.

Albert Einstein was an award winning German-born theoretical physicist who emigrated to U.S. in 1933 due to the rise to power of the Nazis under Hitler. He settled in the U.S., becoming a citizen in 1940. On the eve of World War II, he helped alert President Franklin D. Roosevelt that Germany might be developing an atomic weapon, and recommended that the U.S. begin similar research; this eventually led to what would become the Manhattan Project.