Self-beating

The spectrum of scattered light contains dynamical information related to translational and internal motions of polymer chains. In the self-beating mode, the intensity-intensity time correlation function can be expressed (ID) as... 

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

Up to now, we have given a general theoretical development of the self-beat technique. As a practical illustration of the experimental apparatus used to detect autocorrelation functions in scattering experiments, the equipment currently used in our laboratory will now be described. While our treatment of the autocorrelation function has been in terms of an analog signal, the computer that measures this function is actually a digital device. This is based on the fact that it is also valid to count the scattered photons in order to calculate Ci(r) as the optical intensity signal is essentially determined by the number of photons that strike the photocathode per unit time. We have then... 

In the detection of the autocorrelation functions in self-beat spectroscopy, solution polydispersity can lead to a non-exponential form. If we assume that there are no contributions to the autocorrelation function except those from translational diffusion for the different types of molecules, we can consider two simple cases a continuous distribution of solute particle sizes and several distinct components in a solution. We shall approach the two cases by determining their effect on the observed correlation function. 

It is to be noticed that knowledge of KD and b is required to interpret correlation functions in terms of Mw and z. The quantities KD and b may be determined from separate experiments or possibly found in the literature. Thus a single measurement of the self-beat spectrum is adequate to give both the weight-average molecular weight (Mw) and the width of the weight distribution (2). 

From the description presented here, it can be seen that self-beating spectroscopy as a technique for measuring the diffusion coefficient of... 

It appears noteworthy that it is in principle possible to obtain information on rotational diffusion coefficients from the self beating spectrum (the most frequently applied technique). In this case it is necessary to observe a (usually small) polarized component of the scattered light perpendicular to that of the normal scattering. Mazer, Benedek et al.143,144,145 in the US, Corti and Degiorgio29 in Italy have pioneered this method regarding its application to micellar phenomena in aqueous solutions. 

In dynamic LLS [45,46], the intensity-intensity time correlation function G(2 t, q) in the self-beating mode was measured. For a Poisson distribution of the number of photons, G 2)(f, q) can be related to the normalized first-order electric field time correlation function g (f, q) as [46]... 

Dynamic Light Scattering. The measured single clipped photoelectron count autocorrelation function for the self-beating experiment has the form (5)... 

Preheating of the air bath of the adiabatic self-heating process recorder and the choice of a nominal 7, in the adiabatic self-beating test performed for 2 cm of TBPB charged in the open-cup cell... 

A c mperatuce t which a diethyl ether solution ofMNTS was found to self-beat at a rale of 0.044 K/min in an ARC set... 

Equations 5.446 and 5.450 are applicable in the so-called homodyne method (or self-beating method), where only scattered light is received by the detector. In some cases, it is also desirable to capture by the detector a part of the incident beam that has not undergone the scattering process. This method is called heterodyne (or method of the local oscillator) and sometimes provides information that is not accessible by the homodyne method. It can be shown that if the intensity of the scattered beam is much lower than that of the detected nonscattered (incident) beam, the detector measures the autocorrelation function of the electrical held of the scattered light, dehned as... 

Time Correlation Function. The measured, self-beating intensity correlation function can be expressed as... 

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