Spontaneous shrinking of soft nanoparticles boosts their diffusion in confined media

Abstract

Improving nanoparticles (NPs) transport across biological barriers is a significant challenge that could be addressed through understanding NPs diffusion in dense and confined media. Here, we report the ability of soft NPs to shrink in confined environments, therefore boosting their diffusion compared to hard, non-deformable particles. We demonstrate this behavior by embedding microgel NPs in agarose gels. The origin of the shrinking appears to be related to the overlap of the electrostatic double layers (EDL) surrounding the NPs and the agarose fibres. Indeed, it is shown that screening the EDL interactions, by increasing the ionic strength of the medium, prevents the soft particle shrinkage. The shrunken NPs diffuse up to 2 orders of magnitude faster in agarose gel than their hard NP counterparts. These findings provide valuable insights on the role of long range interactions on soft NPs dynamics in crowded environments, and help rationalize the design of more efficient NP-based transport systems.

Fig. 1

Dynamics of soft and hard nanoparticles in pure water at volume fractions ϕ < 0.1%. a DDM intermediate scattering functions extracted from g(q,τ) functions using Eq. (1), showing the dynamics over a large sample of q. b Intermediate scattering functions as a function of the spatial-frequency-scaled time for hard NPs (blue triangle, q = 0.37 μm⁻¹, red triangle q = 0.57 μm⁻¹) and soft NP (orange triangle, q = 0.63 μm⁻¹). c Relaxation time τ_R vs q for different soft and hard NPs radii. Data shows the typical scaling relation between τ_R vs q with an exponent of −2. d Comparaison of the hydrodynamic radius obtained from DDM (r⁰_H) and DLS (R⁰_H). The red line is a linear least square fit to the data (slope = 0.972 ± 0.012) with its corresponding R² value. Numerical values for hydrodynamic radius are provided in Supplementary Table 1

Fig. 2

Diffusion of hard and soft NPs in agarose. Diffusion is compared at different concentrations of agarose (C_ag = 0.05, 0.1, 0.5, 1% w/w) versus the hydrodynamic radius r⁰_H measured in water by DDM. Solid lines are guides to the eye, while the grey area shows the region below the detection limit, also indicating NP immobilization. Each point is presented with an error bar that corresponds to an average of 5–7 DDM measurements on one sample and its standard deviation

Fig. 3

Experimental reduced diffusivities and theoretical prediction using Kang et al. model. a Data for hard NPs; b Reduced diffusivity of soft NPs. The theoretical curves were produced considering no change in particle size (r_H = r⁰_H). Also presented are different simulated curves, using Eq. (4), fallen into the highlighted areas calculated for different values of Z_f to demonstrate that electrostatic interactions alone cannot account for the increased diffusivity of soft NPs. c Reduced diffusivity of soft NPs (dotted lines) calculated assuming r_H = αr⁰_H. Data points and their error bars correspond to the average of 5–7 DDM measurements on one sample and their standard deviation

Fig. 4

Electrostatic interactions in the EDL.Theoretical reduced interaction potential, V_R/k_BT, between a sphere and a fibre (left axis) and experientally measured NPs shrinking ratio, α, (right axis) as a function of the surface-to-surface distance H. Experimental values for α were collected at different agarose concentrations C_ag, which were used to calculate H (see Supplementary Notes 6). The different colors used for the symbols (circles refer to α) and curves (which refer to V_R/k_BT) correspond to different values of r⁰_H (red: r⁰_H = 25 nm, orange r⁰_H = 40 nm, blue r⁰_H = 45 nm, green r⁰_H = 50 nm)