Authors: Isabelle Largillière | D. E. Sullivan | Michel Meunier
Source: Small (article, 2024-09-24)
Field: Chemistry — Physical and Theoretical Chemistry

Diffusion Coefficients of Coated Plasmonic Nanoparticles in Viscous Environment The Stokes-Einstein relationship (SER) is not valid anymore in polymeric solutions for nanoparticles. It is thus important to characterize their diffusion properties to get a finer understanding of their behavior and to better tune their attributes for biomedical applications. The diffusion of gold and silver nanoparticles with citrate, hyaluronic acid, methyl-polyethylene glycol, and antibody-polyethylene glycol coatings is studied in hyaluronic-based viscous solutions. The diffusion coefficient D is estimated from the Brownian motion thanks to a cost-effective side-illumination device. It is determined that the nanoparticles (hydrodynamic radius r<sub>h</sub>: 30-135 nm) diffuse up to 4-5 times faster than expected using the SER with a macroscopic viscosity from 1 to 30 mPa·s. It is shown that the adapted Huggins equation is a good model to describe the diffusion behavior of nanoparticles using an effective viscosity η<sub>eff</sub> given by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>l</mml:mi> <mml:mi>n</mml:mi> <mml:mspace></mml:mspace> <mml:mrow><mml:mo>(</mml:mo> <mml:mfrac><mml:msub><mml:mi>η</mml:mi> <mml:mrow><mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi></mml:mrow> </mml:msub> <mml:msub><mml:mi>η</mml:mi> <mml:mi>s</mml:mi></mml:msub> </mml:mfrac> <mml:mo>)</mml:mo></mml:mrow> <mml:mo>=</mml:mo> <mml:mspace></mml:mspace> <mml:mi>k</mml:mi> <mml:msup><mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mspace></mml:mspace> <mml:mfrac><mml:msub><mml:mi>R</mml:mi> <mml:mrow><mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi></mml:mrow> </mml:msub> <mml:mi>E</mml:mi></mml:mfrac> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> <mml:mi>a</mml:mi></mml:msup> </mml:mrow> <mml:annotation>$ln\ ( {\frac{{{{\eta }_{eff}}}}{{{{\eta }_s}}}} ) = \ k{{( {\ \frac{{{{R}_{eff}}}}{E}} )}^a}$</mml:annotation></mml:semantics> </mml:math> where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mrow><mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi></mml:mrow> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msubsup><mml:mi>r</mml:mi> <mml:mi>h</mml:mi> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> <mml:mspace></mml:mspace> <mml:mo>+</mml:mo> <mml:msubsup><mml:mi>R</mml:mi> <mml:mi>h</mml:mi> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> <mml:annotation>$R_{eff}^{ - 2} = r_h^{ - 2}\ + R_h^{ - 2}$</mml:annotation></mml:semantics> </mml:math> where E is the polymer correlation length, R<sub>h</sub> the polymer hydrodynamic radius and η<sub>s</sub> the solvent viscosity. The values of k and a are given and allow to obtain D with an error of 10-20%. The impact of chemical interactions on the model parameter values are also highlighted, especially due to electrostatic interactions between the polymer and the nanoparticles. Nanoparticle ; Viscosity ; Materials science ; Diffusion ; Brownian motion ; Polymer ; RADIUS ; Hydrodynamic radius ; Polyethylene glycol ; Nanotechnology ; Thermodynamics ; Chemistry ; Composite material ; Dynamic light scattering ; Physics ; Organic chemistry Electrostatics and Colloid Interactions ; Surfactants and Colloidal Systems ; Gold and Silver Nanoparticles Synthesis and Applications