4 ± 53.7 [56] FePt Poly(diallyldimethylammonium check details chloride) 30-100 [57] NiO Cetyltrimethyl ammonium bromide 10-80 [58] Fetal bovine serum 39.05 [59] Not specified 750 ± 30 [60] CoO, Co2O3 Poly(methyl methacrylate) 59-85 [61] CoFe Hydroxamic and phosphonic acids 6.5-458.7 [62] The underlying principle of DLS The interaction of very small particles with light defined the most fundamental observations such as why is the sky blue. From a technological perspective, this interaction also formed the underlying working principle of DLS. It is the purpose of this section to describe the mathematical analysis involved to extract size-related
information from light scattering experiments. The correlation function DLS measures the scattered intensity over a range of scattering angles θ dls for a given time t k in time steps ∆t. The time-dependent intensity I(q, t) fluctuates around the average intensity I(q) due to the Brownian motion of the particles [38]: (1) where [I(q)] represents the time average of I(q). Here, it is assumed that t k , the total duration of the time step measurements, PR-171 datasheet is sufficiently large such that I(q) represents average of the MNP system. In a scattering experiment, normally, θ dls (see
Figure 1) is expressed as the magnitude of the scattering wave vector q as (2) where n is the refractive index of the solution and λ is the wavelength in vacuum of the incident light. Figure 2a illustrates typical intensity JNK inhibitor solubility dmso fluctuation arising from a dispersion of large particles and a dispersion of small particles. As
the small particles are more susceptible to random forces, the small particles cause the intensity to fluctuate more rapidly than the large ones. Figure 1 Optical configuration of the typical experimental setup for dynamic light scattering measurements. The setup can be operated at multiple angles. Figure 2 Schematic illustration of intensity measurement and the corresponding autocorrelation function in dynamic light scattering. The figure illustrates dispersion from composed of large and small particles. (a) Intensity fluctuation of scattered light with time, and (b) the variation of autocorrelation function with delay time. The time-dependent intensity fluctuation of the scattered light at a particular angle can then be characterized with the introduction of the autocorrelation function as (3) where τ = i ∆t is the delay time, which represents the time delay between two signals I(q,i Δt) and I(q,(i + j) Δt). The function C(q,τ) is obtained for a series of τ and represents the correlation between the intensity at t 1 (I(q,t 1)) and the intensity after a time delay of τ (I(q,t 1 + τ)). The last part of the equation shows how the autocorrelation function is calculated experimentally when the intensity is measured in discrete time steps [37].