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Real time multiple tau autocorrelator and its application in dynamic light scattering : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University
Dynamic light scattering (DLS) has recently been extended from a study of translational diffusion coefficients in dilute solution to a means of obtaining distributions in relaxation times over wide ranges of decay times. Many different data analysis algorithms have been developed to extract information on distribution functions (radius distribution, diffusion coefficient distribution, etc.) from photon correlation functions. Obtaining these distribution solutions usually involves the inversion of the Laplace Transform, and this can lead to ill-conditioned Fredholm integral equations of the first kind. These problems can be minimised by using an optimised time scale for the autocorrelation function. The need to handle such a dynamic range within one correlation function led to the development of the Multiple Tau Autocorrelator. This thesis describes the design and construction of a real time multiple tau autocorrelator and its application in DLS. An introduction to the theory of DLS is given. The theoretical background of the experiments is discussed and DLS techniques are reviewed. Particular emphasis is placed on experimental techniques and experimental data analysis procedures. The relationship among the intensity, amplitude, and photon count correlation functions are discussed. Data analysis methods based on obtaining distributions in relaxation times over wide ranges of decay times are discussed. Different hardware correlator system design techniques are reviewed. A correlator based on multiple tau techniques and symmetric normalisation is discussed. The advantages of using a multiple-instruction-multiple-data (MIMD) system to perform multiple tau autocorrelation is examined. The novel multiple digital signal processor (DSP) architecture for real time implementation of multiple tau autocorrelation is developed based on the task scheduling analysis, interconnection performance, and parallel processing. Detailed explanations of the operation of the Motorola DSP56001 digital signal processor are given, including architecture, addressing modes, instruction sets and peripheral access. The design and construction of the real time multiple tau autocorrelator is described. Detailed descriptions of hardware circuits and software are given. The correlator has proved satisfactory in its applications. The instrument can also works as spectrum analyser or other real time digital signal processing station. Two sets of experiments on ternary polymer solutions were carried out using the multiple tau correlator. The results of dynamic light scattering measurements are discussed within the broad framework of the Borsali-Benmouna theory. Experimental data are analysed using the constrained regularisation method. The interdiffusion coefficient and cooperative diffusion coefficient of PS/PMMA/thiophenol and PS/PMMA/toluene system under "optical tracer" conditions are discussed, and the interesting features of polymer polymer interaction as the temperature is varied are also discussed. Advantages of a multiple tau correlator over a linear correlator in the more complicated ternary polymer solution studies is demonstrated.