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𝛤 = 𝐷𝑞2 Equation 4.5 𝑞 = 4𝜋𝑛 𝑠𝑖𝑛 (𝜃) Equation 4.6 𝜆2 where, 𝑞 is wave vector, 𝑛 is refractive index of the dispersant, 𝜆 is the laser wavelength and 𝜃 is the scattering angle. For polydisperse sample, the equation can be written as; 𝐺(𝜏) = 𝐴[1 + 𝐵𝑔1(𝜏)2] Equation 4.7 where, g1(τ) is the sum of all the exponential decays contained in the correlation function. The size from the correlation functions can be obtained by using different algorithms, with the two fundamental approaches being; 1) Cumulants analysis: Use a single exponential to fit the correlation function to obtain the mean size (𝑧-average diameter) and the width of the distribution (polydispersity index). 2) Use multiple exponentials to fit the correlation function to obtain the distribution of particle sizes by using CONTIN or Non-negative least squares. The 𝑧-average diameter is normally used for analysing monodisperse or narrow distributions. Whereas, the multi exponential fit is more appropriate for broader and multi-modal distributions. The size distributions obtained from the multi exponential fit is a plot of the relative intensity of light scattered by different sized particles and therefore called as Intensity Particle Size Distribution (IPSD). If IPSD shows more than one peak, by Chapter 4 – Methods where, τ is the time difference of the correlator. For large number of monodisperse particles in Brownian motion, the correlation function is an exponential decay function of the correlator time delay τ; 𝐺(𝜏) = 𝐴[1 + 𝐵 𝑒𝑥𝑝(−2𝛤𝜏)] Equation 4.4 where, 𝐴 is the baseline of the correlation function, 𝐵 is the intercept of correlation function and 𝛤 is decay constant. 121PDF Image | PRODUCTION AND APPLICATIONS OF GRAPHENE AND ITS COMPOSITES
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