Concentration fluctuation correlation

A concentration-fluctuation correlation coefficient, similar to that proposed by Danckwerts (D3, D5), may be defined. 

Near the critical point, the concentration fluctuation correlations contribute significantly to the system state. 

Equation 100 corresponds to the function of the concentration fluctuation correlations ... 

Another important quantity that depends explicitly on the screening length is the concentration-fluctuation correlation function ... 

For values of r less than the screening length, the correlation function should scale as in Equation 6.9, since only intrachain correlations are involved. For distances greater than the screening length, deGennes has proposed that the concentration-fluctuation correlation function scales as ... 

Theoretical approaches for concentration fluctuations - correlation length and random phase approximation 305... 

Komori, S., J. C. R. Hunt, K. Kanzaki, and Y. Murakami (1991b). The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows. Journal of Fluid Mechanics 228, 629-659. 

This effective Q,t-range overlaps with that of DLS. DLS measures the dynamics of density or concentration fluctuations by autocorrelation of the scattered laser light intensity in time. The intensity fluctuations result from a change of the random interference pattern (speckle) from a small observation volume. The size of the observation volume and the width of the detector opening determine the contrast factor C of the fluctuations (coherence factor). The normalized intensity autocorrelation function g Q,t) relates to the field amplitude correlation function g (Q,t) in a simple way g t)=l+C g t) if Gaussian statistics holds [30]. g Q,t) represents the correlation function of the fluctuat-... 

The observation that branches A and B in Fig. 6.25 merge at large Q is consistent with the predictions for and T since 6ti and 18.84 deviate from 16 by less than 15% and statistical errors of the experiment and systematic uncertainties in methods to extract the cumulant exceed this difference. In [325] for both the collective concentration fluctuations and the local Zimm modes the observed rates are too slow by a factor of 2 if compared to the predictions with T (the solvent viscosity) and (the correlation length) as obtained from the SANS data. It is suggested that this discrepancy may be removed by the introduction of an effective viscosity qf that replaces the plain solvent viscosity Finally at very low Q, i.e. 1, branch C should level at the centre of mass... 

This correlation coefficient has properties similar to the one defined by Eq. (96). In particular, a scale of concentration fluctuation may be defined as... 

Surface diffusion can be studied with a wide variety of methods using both macroscopic and microscopic techniques of great diversity.98 Basically three methods can be used. One measures the time dependence of the concentration profile of diffusing atoms, one the time correlation of the concentration fluctuations, or the fluctuations of the number of diffusion atoms within a specified area, and one the mean square displacement, or the second moment, of a diffusing atom. When macroscopic techniques are used to study surface diffusion, diffusion parameters are usually derived from the rate of change of the shape of a sharply structured microscopic object, or from the rate of advancement of a sharply defined boundary of an adsorption layer, produced either by using a shadowed deposition method or by fast pulsed-laser thermal desorption of an area covered with an adsorbed species. The derived diffusion parameters really describe the overall effect of many different atomic steps, such as the formation of adatoms from kink sites, ledge sites... 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

Measurements of static light or neutron scattering and of the turbidity of liquid mixtures provide information on the osmotic compressibility x and the correlation length of the critical fluctuations and, thus, on the exponents y and v. Owing to the exponent equality y = v(2 — ti) a 2v, data about y and v are essentially equivalent. In the classical case, y = 2v holds exactly. Dynamic light scattering yields the time correlation function of the concentration fluctuations which decays as exp(—Dk t), where k is the wave vector and D is the diffusion coefficient. Kawasaki s theory [103] then allows us to extract the correlation length, and hence the exponent v. 

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... 

D. A. Reed and G. Ehrlich, Surface diffusivity and the time correlation of concentration fluctuations, Surf. Sci. 105, 603-628 (1981). 

Here, CA and CB (upper case) denote the mean molar concentrations of reactants A and B while CA and CB (lower case) denote the local concentration fluctuations that result from turbulence. When the species are perfectly mixed, the second term on the right side containing the correlation of the concentration fluctuations, will approach zero. Otherwise, if the species are not perfectly mixed, this term will be negative and will reduce the reaction rate. Estimating this correlation term is not straightforward and numerous models are available. An excellent discussion on this subject was given by Hannon [1],... 

Measurements of the concentration dependence allow one to uniquely separate the dephasing contribution via concentration fluctuations in the solvation layer of the vibrating CH3I molecule, the time scale of which is determined to be 3.2-1.1 ps in the temperature range 242-374 K. Striking deviations from simple exponential relaxation dynamics are reported for the v, mode with correlation times rc > 1 ps, indicating the intermediate case for this relaxation mechanism (46). 

For concentration fluctuations, there is no term corresponding to x-In an ideal solution, there are no correlations in the composition of neighboring molecules. The composition of a solvating molecule can change freely without forcing a compensating change in other solvent molecules. Concentration fluctuations are easy to create. 

According to the general definitions of the coil and the globule241, the macromolecule is in the coil state, if the fluctuations of the monomer concentration within the macromolecule are of order of the monomer concentration itself and the correlation radius of the fluctuations of concentration is of order of the macromolecular dimensions while in the globular state the concentration fluctuations are small compared with the concentration and the correlation radius is considerably smaller than the globular dimensions. 

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