(4es) Simple Physical Models of Complex Fluids Analyzed Using Classical Density-Functional Theory and Generalized Langevin Dynamics

Theoretical modeling provides insights into fundamental understanding of many complex systems ranging from functionalized nanoparticle suspensions to biological fluids. Although simple, a suitably chosen coarse-grained description that captures the essential physics of the system can guide the material design for a variety of applications before conducting exhaustive experimental efforts or computational tests of the full complex problem. Here I demonstrate the application of theoretical modeling in two nanoparticle systems.

Nanoparticle-organic hybrid materials (NOHMs) are a new type of complex fluid consisting of 10 nm diameter spherical inorganic core particles surface-functionalized with oligomeric organic molecules with no other solvent. The fluidity is provided by the attached oligomers that mediate the interparticle forces and affect the equilibrium properties and dynamic behavior of the bulk system. The absence of a solvent, the small size of the nanocores and oligomers, and the incompressibility of the tethered oligomeric fluid make the oligomer-mediated interactions non-pairwise-additive. For the first time, we have developed a classical density-functional approach for model hard spheres with tethered bead-spring oligomers that allows us to have a direct description of the system free energy as a functional of the probability densities of cores and oligomers without assuming pairwise additivity. The equilibrium distributions and the static structure factor of NOHMs that can be utilized to characterize experimental systems are obtained from the minimization of the free energy. The theories also predict that the solvent-free homogeneous nanoscale mixture of organic oligomers and inorganic cores can lead to a unique thermodynamic driving force for solute uptake as the solute releases the entropic penalty of the space-filling oligomers, which makes NOHMs a candidate for carbon capture applications. Furthermore, analyzing the rheological behavior of NOHMs through solving the Smoluchowski equation for non-equilibrium probability density suggests that the information regarding the appropriate closure for non-equilibrium many-body interactions can be gained from experimental measurements of the high frequency shear modulus. The significance of this work is that the theories provide a first prediction of how the entropic forces of the tethered fluid in solvent-free conditions influence the experimentally measurable properties of the material. The theoretical approach can be widely applied to design directed self-assembly of colloids and to understand the regulation of cell membranes driven by inter- or intra-cellular forces.

The use of functionalized nanocarriers is gaining translational prominence in targeted vascular drug delivery. Owing to the complexity of the blood flow environment and a wide spectrum of time and length scales that are relevant to nanocarrier-endothelium binding dynamics, a simplified theoretical description that allows us to perform a sensitivity analysis of the parameter space is valuable. To this end, we formulate non-Markovian, generalized Langevin equations for ligand-grafted nanocarrier motion and ligand-receptor (on the endothelium) pair relaxation in the presence of red blood cell-driven marginating potential and particle-wall hydrodynamic forces. While the detailed hydrodynamic interactions of the system can be resolved using direct numerical simulations (DNS) of fluctuating fluids, for a given memory kernel (e.g. Ornstein-Uhlenbeck process) of the viscous drag on the particle the Brownian force can be obtained via continuous-time random-walk simulations satisfying the fluctuation-dissipation theorem. Analyzing the nanocarrier velocity autocorrelation functions and the potential of mean force along a specified reaction coordinate helps quantify the binding affinity in the presence of hydrodynamic interactions. In the future, we plan to integrate DNS and Brownian dynamics simulations to track the nanocarrier motion and binding in a vascular network tree. The broader impact of this approach is that it can be potentially generalized as a versatile multiscale modeling method for hydrodynamics of complex flows.