2.3. Static and Dynamic Light Scattering

The samples were filtered by using 0.22 µm pore size filters into a dust-free quartz cell and kept at 20 °C in the thermostatic cell compartment of a Brookhaven Instruments BI200-SM goniometer. The temperature was controlled within 0.1 °C using a thermostatic recirculating bath. The light scattered intensity and its time autocorrelation function were measured at θ = 90° by using a Brookhaven BI-9000 correlator and a 100 mW solid-state laser (Quantum-Ventus MPC 6000) tuned at wavelength 532 nm. Absolute values of scattered intensity were corrected for the scattering from buffer alone I₀, normalised by the intensity of a toluene standard I_tol and expressed as Rayleigh ratio via:

where n_s and n_tol are the refractive indices of the sample and toluene (n_S  =  1.3367 and n_tol  =  1.4996), and the toluene Rayleigh ratio was taken as 28 × 10⁻⁶ cm⁻¹ at 532 nm. Absolute Rayleigh ratio R(q) is related to the weight averaged molecular mass M_w of particles by the relation R(q)  =  KcM_wP(q), with the instrumental factor K  =  4π²ñ²(dñ/dc)²λ₀⁻⁴N_A⁻¹, where c is the mass concentration, P(q) is the z-averaged form factor, ñ is the medium refractive index, λ₀ is the incident wavelength and N_A is Avogadro’s number [36]. We calculated the average aggregation number M_w/M₀ = R(q) (KcM₀)⁻¹, with M₀ the monomer molecular mass, by taking (dñ/dc) =  (0.18 ± 0.01) cm³ g⁻¹ and P(q)  =  1. The form factor is related to the average shape and size of scatterers. However, it is equal to 1 when the size of solutes is much smaller than q⁻¹ [37].

Due to their Brownian motion, particles moving in solution give rise to fluctuations in the intensity of the scattered light. In a light scattering experiment carried out in dynamic modality, the autocorrelator measures the homodyne intensity–intensity correlation function that, for a Gaussian distribution of the intensity profile of the scattered light, is related to the electric field correlation function:

where A and B are the experimental baseline and the optical constant, respectively. For polydisperse particles, g⁽¹⁾(q,t) is given by:

Here, G(Γ) is the normalised number distribution function for the decay constant Γ = q²D_T, where q = (4πn/λ)sin(θ/2) is the scattering vector defining the spatial resolution with n and D_T being the solvent refractive index and the translational diffusion coefficient, respectively [37]. The hydrodynamic diameter D_H is calculated from D_T through the Stokes–Einstein relationship:

where k_B is the Boltzmann constant, T is the absolute temperature and η is the solvent viscosity. D_H was obtained by the intensity autocorrelation functions by means of the method of cumulants [38].