Siegert relations

The Siegert relation is valid except in the case of scattering volumes with a very small number of scatterers or when the motion of the scatterers is limited. We ignore the exceptions, which are rare in common uses of DLS, and consider only autocorrelations of the type shown in Equation (104). As mentioned above, modern DLS instruments use computer-controlled correlators to calculate the intensity autocorrelation function automatically and to obtain the results in terms of the function gi(s,/rf) therefore we only need to concern ourselves here with the interpretation of gi(s,td). 

Assume that the enzyme is roughly spherical and that the instrument constant in the Siegert relation is unity and determine the hydrodynamic radius RH of the enzyme. Given that the partial molar volume V of the enzyme is 0.74 10 3 m3/kg and the molecular weight M is 4.78 102 kg/mol, determine the dry radius Rs for the enzyme and obtain the ratio RH/RS). Can the difference between RH and Rs be attributed to the bound water on the enzyme The viscosity ij of water at 293K may be taken as 0.001 kg/m s. 

Solution The given DLS data can be used to obtain the intensity autocorrelation function g,(s,td) by rewriting the Siegert relation as follows ... 

What is the Siegert relation How is it related to the decay of intensity fluctuations measured in DLS experiments ... 

For self-beating measurements, g(2)(r) is given by the Siegert relation [61], which is... 

The normalized electric field autocorrelation function gift), which can be calculated from the normalized intensity autocorrelation function g2(t) = (1(0) 7(f)) (I(0)/2 according to the Siegert relation [56]... 

In a dynamic light scattering experiment, the measured intensity-intensity time-correlation function g<2)(tc), where tc is the delay time, is related to the normalized electric field correlation function g(1)frc), representative of the motion of the particles, by the Siegert relation [18] ... 

The latter equation, known as the Siegert relation, is valid for a point detector. In practice, the finite area of a photocathode detector [29,42] necessitates a correction factor [13] so that... 

If a homodyne method is used, the measured autocorrelation function (g,x) can be interpreted by using the Siegert relation. Equation 5.454. The translational and rotational diffusion coefficients for several specific shapes of the particles are given in Table 5.9. The respective power spectrum functions can be calculated by using the Fourier transform. Equation 5.449b. 

For a Gaussian distribution of the scattered light intensity profile, the intensity ACF, g(2)(xcorr, 0), is related to the electric field ACF, xcorr, 9), via the Siegert relation ... 

In this section we shall see that the incorporation of polarization into the formulation for PCS enables the shape of the particles to be inferred. This is achieved by a modest augmentation of PCS equipment that facihtates the measurement of the cross-correlation of the scattered intensity that has been resolved into different polarization states. The temporal decay of the polarized intensity cross-correlation function is identical to that of the intensity autocorrelation function used in PCS, however it decays from value less than 2, and the difference from 2 is related to the particles departure from a sphere. Before demonstrating precisely how this occurs, it is first necessary to see how polarization generalizes the Siegert relation. 

Although homodyne is the most used method in PCS, we describe shortly also the heterodyne method, which is widely used for Doppler velocimetry experiments or when the Siegert relation is not applicable. Heterodyning means that we mix in the detector the scattered light with a strong nonscattered signal (named commonly as the local oscillator), that is. 

As proved by Siegert [939] for optical fields with a Gaussian intensity distribution (7.60), the second-order correlation function G x) is related to G x) by the Siegert relation... 

The experimentally accessible quantity is the intensity line correlation function g2(t) which is connected to the theoretically simpler correlation function of the electric field, gi(t) via the Siegert relation... 

In most PCS experiments the intensity autocorrelation function G2(0,t) is measured at one or several scattering angles 0 as a function of time delay x. In the first step of the interpretation procedure G2(0,x) is related to the modulus of the normalized field autocorrelation function gi(0,x) by a Siegert relation ... 

In the double sum, i and j independently pass over all N particles, bi and bj are components of a selected by the incident and scattered polarization vectors, and A is an experimental quantity. Crosignani, et al. s result can also be obtained by invoking Siegert relations. The author urges avoidance of this alternative, which he has never employed, because there is a risk of inadvertently invoking these relations when they are inapplicable. 

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