Autocorrelation function concentration fluctuations

Fluorescence intensity detected with a confocal microscope for the small area of diluted solution temporally fluctuates in sync with (i) motions of solute molecules going in/out of the confocal volume, (ii) intersystem crossing in the solute, and (hi) quenching by molecular interactions. The degree of fluctuation is also dependent on the number of dye molecules in the confocal area (concentration) with an increase in the concentration of the dye, the degree of fluctuation decreases. The autocorrelation function (ACF) of the time profile of the fluorescence fluctuation provides quantitative information on the dynamics of molecules. This method of measurement is well known as fluorescence correlation spectroscopy (FCS) [8, 9]. 

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-... 

In order to be able to use the fluctuation of the intensity around the average value, we need to find a way to represent the fluctuations in a convenient manner. In Section 5.3b in our discussion of Rayleigh scattering applied to solutions, we came across the concept of fluctuations of polarizabilities and concentration of scatterers and the role they play in light scattering experiments. In the present section, what we are interested in is the time dependence of such fluctuations. In general, it is not convenient to deal with detailed records of the fluctuations of a measured quantity as a function of time. Instead, one reduces the details of the fluctuations to what is known as the autocorrelation function C(s,td), as defined below ... 

First, the autocorrelation function must be computed. In the example plot a strong seasonal effect could be seen in the explanatory variable (nitrate concentration in the feeder stream) as well as in the dependent variable (nitrate concentration in the drinking water reservoir) (Fig. 6-2). The autocorrelation function (Fig. 6-16) has, therefore, the expected exponentially decreasing shape and, because of the seasonal fluctuations, increasing values at x = 12, 24,. .. A better tool for determining the order is the partial autocorrelation function. This function shows the partial correlation between x(t) and x(t - x) and ignores the influences of other variables, e.g. x(t - x + 1). It reveals the order one by the spike at x = 1 in Fig. 6-17. 

Figure 4.13 Concentration fluctuations and the spatial autocorrelation function.

An alternative explanation of the observed turbidity in PS/DOP solutions has recently been suggested simultaneously by Helfand and Fredrickson [92] and Onuki [93] and argues that the application of flow actually induces enhanced concentration fluctuations, as derived in section 7.1.7. This approach leads to an explicit prediction of the structure factor, once the constitutive equation for the liquid is selected. Complex, butterfly-shaped scattering patterns are predicted, with the wings of the butterfly oriented parallel to the principal strain axes in the flow. Since the structure factor is the Fourier transform of the autocorrelation function of concentration fluctuations, this suggests that the fluctuations grow along directions perpendicular to these axes. 

Time- and space-resolved major component concentrations and temperature in a turbulent gas flow can be obtained by observation of Raman scattering from the gas. (1, 2) However, a continuous record of the fluctuations of these quantities is available only in those most favorable cases wherein high Raman scattering rate and/or slow rate of time variation of the gas allow many scattered photons (> 100) to be detected during a time resolution period which is sufficiently short to resolve the turbulent fluctuations. (2, 3 ) Fortunately, in other cases, time-resolved information still can be obtained in the forms of spectral densities, autocorrelation functions and probability density functions. (4 5j... 

The arrival times of fluorescence photons contain information about correlations in fluorescence signals. Eluorescence correlation spectroscopy (FCS) (26) exploits these correlations to measure the magnitude and time scales of fluctuations in fluorescence. These fluctuations contain information about the dynamic time scales of the system and the concentration of fluorescing molecules. Correlations may span time ranges from nanoseconds to milliseconds, which extends the dynamic time window for fluorescence measurements far beyond what is achievable in fluorescence lifetime measurements. The autocorrelation function is calculated as ... 

Polydispersity of simple bile salt micelles can only be assessed by modem QLS techniques employing the 2nd cumulant analysis of the time decay of the autocorrelation function [146,161]. These studies have shown, in the cases of the 4 taurine conjugates in 10 g/dl concentrations in both 0.15 M and 0.6 M NaCl, that the distribution in the polydispersity index (V) varies from 20% for small n values to 50% for large n values [6,146]. Others [112] have foimd much smaller V values (2-10%) for the unconjugated bile salts in 5% (w/v) solutions. Recently, the significance of QLS-derived polydispersities have been questioned on the basis of the rapid fluctuation in n of micellar assemblies hence V may not actually represent a micellar size distribution [167-169]. This argument is specious, since a micellar size distribution and fast fluctuations in aggregation number are identical quantities on the QLS time scale (jusec-msec) [94]. 

In a QELS experiment, the autocorrelation function of the polarized scattered field is measured with K as the scattering vector. The scattered field is proportional to the amplitude of the fluctuations of the local polymer concentration in the gel. These concentration fluctuations are related to the local deformation in the gel. 

Periodic processes show characteristic dependencies as demonstrated in the example on the seasonal variations of sulfur concentrations in Figure 3.22. Periodicities or fluctuations can be recognized and quantified from autocorrelation functions much better than from the time series. 

We measure both the intensity I and the autocorrelation function G(t) of the light scattered by the sample (6). The main contribution to the scattering is due to concentration fluctuations of the droplets. If particle size is assumed to be constant ... 

Also known as quasi-elastic light scattering, this technique monitors the tempord fluctuations in / (q) (Berne and Pecora, 1976 Chu, 1990). These fluctuations result from random thermal motions, which change the instantaneous spatial arrangement of molecules and thus the net scattered intensity. As these random motions result in microscopic concentration fluctuations, a mutual diffusion coefficient can be determined from the time constant of the decay of the time autocorrelation function of Liq, t). Rapid advances in laser and autocorrelator technology during the last two decades have made this experiment a routine characterization and research tool. 

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