Thermodynamic fluctuations, light

The dependence Blue light scatters more than red. (This is often associated with the blue of the sky and the red of the sunset," but other factors are involved here including the fact that in perfectly clean air (no particles) scattering occurs from small, thermodynamic fluctuations in the air density.)... 

The theory of thermodynamic fluctuations in the context of light scattering was introduced first by Smoluchowski and Einstein [12, 13]. Einstein considered that the scattering of light in a solution arises from local density and concentration fluctuations. However, it was only till the late 40s and early 50s that Brinkman and Hermans [14], Stockmayer [15], and Kirkwood and Goldberg [16] adopted this approach in the context of light scattering by poiymer solutions. Here, we summarize only the basic results for a binary mixture. 

Relation of Light Scattering by Polymer Solutions to Thermodynamic Fluctuations... 

Light scattering by particles of small size compared to the wavelength of the incident beam can be described using both electromagnetic particulate and thermodynamic fluctuation approaches. Both are important since the first can be applied... 

The depolarization of light by dense systems of spherical atoms or molecules has been known as an experimental fact for a long time. It is, however, discordant with Smoluchowski s and Einstein s celebrated theories of light scattering which were formulated in the early years of this century. These theories consider the effects of fluctuation of density and other thermodynamic variables [371, 144]. 

Dynamic processes at thermodynamic equilibrium that occur within a time range from sub-microseconds to seconds can be probed without the imposition of a transient disturbance by optical intensity fluctuation spectroscopy. As such, dynamic light scattering (DLS) [155] measures the fluctuation of quasielastic scattering intensity and fluorescence correlation spectroscopy (FCS) [156-158] measures concentration fluctuations of specific fluorescent molecules... 

Statistical Fluctuations. Thermodynamic systems in general present unordered random deviations from equilibrium referred to as statistical fluctuations. Even slight fluctuations are apt to give rise to experimentally accessible effects. Thus, as shown by Smoludiowski, local fluctuations in density in gases and liquids cause light scattering by optically transparent media. Attempts to raise the sensitivity of measuring devices are fmled by... 

Quasi-elastic laser light scattering (also called intensity fluctuation spectroscopy, light-beating spectroscopy or photon correlation spectroscopy) is an accurate method to measure the translational diffusion coefficients of macromolecules. The diffusion coefficient is a parameter, that depends on the size and shape of the macromolecules and on the thermodynamic and hydrodynamic interaction between the macromolecules. 

The current frontiers for the subject of non-equilibrium thermodynamics are rich and active. Two areas dominate interest non-linear effects and molecular bioenergetics. The linearization step used in the near equilibrium regime is inappropriate far from equilibrium. Progress with a microscopic kinetic theory [38] for non-linear fluctuation phenomena has been made. Careful experiments [39] confirm this theory. Nonequilibrium long range correlations play an important role in some of the light scattering effects in fluids in far from equilibrium states [38, 39]. 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems through elastic scattering experiments. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thermodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of thermal fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response theory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thermod5mamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation functions from first principles. This is the subject of section A3.3.2. 

Chapter 13 includes a short introduction to the theory of nonequilibrium thermodynamics. A discussion of frames of reference in the definition of transport coefficients is given and a systematic theory of diffusion is presented. Fluctuations in electrolyte solutions are analyzed, and the parameters measured in electrophoretic light-scattering experiments are related to conductance and to the transference numbers—quantities usually measured in conventional electrochemistry. 

The light-scattering spectrum which is related to 7 (q, /) by Eq. (3.3.3) consequently probes how a density fluctuation <5/ (q) spontaneously arises and decays due to the thermal motion of the molecules. Density disturbances in macroscopic systems can propagate in the form of sound waves. It follows that light scattering in pure fluids and mixtures will eventually require the use of thermodynamic and hydrodynamic models. In this chapter we do not deal with these complicated theories (see Chapters 9-13) but rather with the simplest possible systems that do not require these theories. Examples of such systems are dilute macromolecular solutions, ideal gases, and bacterial dispersions. ... 

Light-scattering experiments are not relaxation experiments like the foregoing but instead, as we have seen, involve fluctuation phenomena and time-correlation functions. In connection with the development of the thermodynamics of irreversible processes, Onsager (1931) proposed the principle that spontaneous fluctuations in A(t, t) regress back to equilibrium according to the same relaxation equations that de-... 

There are five linear hydrodynamic equations containing the seven fluctuations (pi, u x,ii y, uu,pi,si, 7i). The local equilibrium thermodynamic equations of state can be used to eliminate two of the four scalar field quantities (pi, si, Ti, pi). In this chapter we chose the temperature and number density as independent variables, although we could equally well have chosen the pressure and entropy. One useful criterion for choosing a particular set is that the equilibrium fluctuations of the two variables be statistically independent. The two sets (pi = dp, T = ST) and (pi = Sp, si = Ss) both involve two variables that are statistically independent, that is, statistical independence of the two variables simplifies our analysis considerably. It is particularly convenient to chose the set (Pi,Ti) over the set (pi, si) because the dielectric constant derivatives (de/dp)T and (de/dT) are more readily obtained from experiment (other than light scattering) than are (ds/dS)p and (ds/dp)s-... 

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