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π(π») = ππ΅π Equation 4.2 3πΕπ· Where, π(π») is hydrodynamic diameter, π· is translational diffusion coefficient, ππ΅ is Boltzmannβs constant, π is absolute temperature and π is viscosity of solvent. The hydrodynamic diameter is the diameter of a hard sphere that has the same translational diffusion coefficient as the particle. Figure 4.10: Hypothetical dynamic light scattering of larger and smaller particles along with its typical intensity fluctuations with time and typical correlogram showing the signal decay.343 When a light hits particles, the light scatters in all the directions. Different size particles move at different speeds resulting in different scattering intensities. In DLS, a digital autocorrelator is used to analyse the intensity fluctuations with time and a correlation function as a function of delay time is derived by fitting the intensity fluctuations. Larger the particle, slower the Brownian motion hence slower intensity fluctuation and longer correlation time as shown in Figure 4.10. The correlation function G(Ο) of the scattered intensity from the correlator is given by; πΊ(π) =< πΌ(π‘). πΌ(π‘ + π) > Equation 4.3 120 Chapter 4 β MethodsPDF Image | PRODUCTION AND APPLICATIONS OF GRAPHENE AND ITS COMPOSITES
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