Supporting Information for the Manuscript Entitled
Biodegradable Nanoparticles as Nanomedicines: Are Drug Loading Content and Release Mechanism Dictated by Particle Density?
Caroline A. S. Ribeiro, Carlos E. de Castro, Lindomar J. C. Albuquerque, Carin C. S. Batista and Fernando C. Giacomelli
Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, 09210-580, Brazil.
*Corresponding Author: Fernando Carlos Giacomelli
e-mail.
1. Methods
Dynamic Light Scattering (DLS): In DLS mode, the autocorrelation functions are based on 03 independent runs of 60 s counting time. The data were collected and further averaged by using the ALV Correlator Control software. The correlation functions were analysed using the nonlinear inverse Laplace transformation algorithm CONTIN resulting in distributions of relaxation times - A(t ). The mean relaxation time or relaxation frequency (Γ = 1/τ) is a function of the scattering angle. The diffusion coefficient D of the nanoparticles was calculated by considering the following relation:
(1)
where q is the scattering vector:
(2)
l is the wavelength of the incident laser beam (632.8 nm), n is the refractive index of the sample and q is the scattering angle. The hydrodynamic radius was calculated using the Stokes-Einstein relation:
(3)
kB is the Boltzmann constant, T is the absolute temperature, h is the viscosity of the solvent. The distributions of relaxation times were also converted to distributions of RH by using the Stokes-Einstein equation. The polydispersity of the nanoparticles was accessed by using the Cumulant analysis of the autocorrelation functions measured at 90o as:
(4)
where C is the amplitude of the correlation function and G is the relaxation frequency (t -1). The parameter m2 is known as the second-order Cumulant and was used to compute the polydispersity index of the samples (PDI = m 2 /G 2).
Static Light Scattering (SLS): The SLS measurements were carried out by varying the scattering angle (q ) from 30 to 150° with a 5° stepwise increase. At each angle, the light scattering intensity was measured in triplicate and the average values are reported. The molecular weight (Mw(NPs)) and the radius of gyration (RG) of the biodegradable nanoparticles were determined using the partial Zimm approach as:
(5)
the concentration c is given in mg.mL-1 and K is the optical constant expressed by:
(6)
Rθ (Rayleigh ratio) is the normalized scattered intensity (toluene was used as standard solvent), n is the refractive index of the solvent, NA is the Avogadro’s number and dn/dc is the refractive index increment determined using a BI-DNDC Brookhaven differential refractometer. The values for PCL and PLGA in water were respectively 0.146 mL.g-1 and 0.130 mL.g-1. Hence, measuring Kc/Rθ at a given angular range for one single diluted concentration, the value of RG is estimated from the slope of the curve and as q → 0, the apparent molecular weight (Mw(NPs)) is extracted from the inverse of the intercept.
Additionally, for large spherical particles, the Berry plot provides a better approximation of the form factor than the Zimm approach. This method was applied as the alternative to the Zimm plot for large assemblies (RH > 100 nm) because it led to apparently more reasonable values of Mw and RG.
(7)
Electrophoretic Light Scattering (ELS): ELS measurements were used to determine the average zeta potential (z) of the assemblies. The values of electrophoretic mobility (UE) were converted to values of z-potential (mV) through Henry’s equation:
(8)
where e is the dielectric constant of the medium and h is the viscosity. Furthermore, f(ka) is the Henry’s function, which was calculated through the Smoluchowski approximation f(ka) = 1.5. Each z-potential value reported in the manuscript is an average of 10 independent measurements with repeatability ± 2%.
3. Supporting Results
Figure S1. Time-dependent coumarin-6 release kinetics from PLC nanoparticles produced using THF as starting organic solvent (coumarin-6 feeding: 5.0% w/w). Data are the mean values of 3 independent measurements and the error bars indicate standard deviations.
Figure S2. Model fitting using the Korsmeyer-Peppas approach based on the data given in Figure S1.