The depletion thickness of a solution of semi-flexible polymers reaches a maximum as a function of chain stiffness in the semidilute concentration regime.

Nanoparticle gradient materials combine a concentration gradient of nanoparticles with a macroscopic matrix. This way, specific properties of nanoscale matter can be transferred to bulk materials. These materials have great potential for applications in optics, electronics, and sensors. However, it is challenging to monitor the formation of such gradient materials and prepare them in a controlled manner. In this study, we present a novel universal approach for the preparation of this material class using diffusion in an analytical ultracentrifuge. The nanoparticles diffuse into a molten thermoreversible polymer gel and the process is observed in real-time by measuring the particle concentrations along the length of the material to establish a systematic understanding of the gradient generation process. We extract the apparent diffusion coefficients using Fick’s second law of diffusion and simulate the diffusion behavior of the particles. When the desired concentration gradient is achieved the polymer solution is cooled down to fix the concentration gradient in the formed gel phase and obtain a nanoparticle gradient material with the desired property gradient. Gradients of semiconductor nanoparticles with different sizes, fluorescent silica particles, and spherical superparamagnetic iron oxide nanoparticles are presented. This method can be used to produce tailored nanoparticle gradient materials with a broad range of physical properties in a simple and predictable way.

We present a simple mean-field theory to describe the polymer-mediated depletion attraction between colloidal particles that accounts for the polymer’s chain stiffness. We find that for fixed polymer radius of gyration and volume fraction, the strength of this attraction increases with increasing chain stiffness in both dilute and semidilute concentration regimes. In contrast, the range of attraction monotonically decreases with chain stiffness in the dilute regime, while it attains a maximum in the semidilute regime. The obtained analytical expressions for the depletion interaction were compared with numerical self-consistent field lattice computations and shown to be in quantitative agreement. From the interaction potential between two spheres, we calculated the second osmotic virial coefficient B2, which appears to be a convex function of chain stiffness. A minimum of B2 as a function of chain stiffness was observed both in the numerical self-consistent field computations and the analytical theory. These findings help explain the general observation that semiflexible polymers are more effective depletants than flexible polymers and give insight into the phase behavior of mixtures containing spherical colloids and semiflexible polymers.