High-frequency viscosity and generalized Stokes-Einstein relations in dense suspensions of porous particles

Size control over metal-organic framework porous nanocrystals

Porous nanocrystals of metal-organic frameworks (MOFs) offer greater bioavailability, higher surface-to-volume ratios, superior control over MOF membrane fabrication, and enhanced guest-sorption kinetics compared to analogous bulk phases, but reliable synthesis of uniformly sized particles remains an outstanding challenge. Here, we identify the smallest and most probable sizes of known MOF nanocrystals and present an exhaustive comparative summary of nano- versus bulk-MOF syntheses. Based on critical analysis of reported size data and experimental conditions, an alternate to the LaMer model is proposed that describes nanocrystal formation as a kinetic competition between acid-base and metal-ligand reactivity. Particle growth terminates when ligands outcompete metal-ion diffusion, thereby arresting polymerization to produce kinetically trapped particle sizes. This model reconciles disparate trends in the literature and postulates that minimum particle sizes can be achieved by minimizing the relative ratios of metal-to-linker local concentrations. By identifying conditions that disfavor small nanocrystal sizes, this model also provides routes towards macroscopic MOF single crystals. A universal "seesaw" relationship between nanocrystal sizes and the concentrations of acidic surface-capping ligands provides a roadmap for achieving precise synthetic control. Best practices in synthesis, characterization, and data presentation are recommended for future investigations so that MOF nanocrystals may achieve their full potential as advanced nanomaterials.

Effective temperatures and the breakdown of the Stokes-Einstein relation for particle suspensions

The short- and long-time breakdown of the classical Stokes-Einstein relation for colloidal suspensions at arbitrary volume fractions is explained here by examining the role that confinement and attractive interactions play in the intra- and inter-cage dynamics executed by the colloidal particles. We show that the measured short-time diffusion coefficient is larger than the one predicted by the classical Stokes-Einstein relation due to a non-equilibrated energy transfer between kinetic and configuration degrees of freedom. This transfer can be incorporated in an effective kinetic temperature that is higher than the temperature of the heat bath. We propose a Generalized Stokes-Einstein relation (GSER) in which the effective temperature replaces the temperature of the heat bath. This relation then allows to obtain the diffusion coefficient once the viscosity and the effective temperature are known. On the other hand, the temporary cluster formation induced by confinement and attractive interactions of hydrodynamic nature makes the long-time diffusion coefficient to be smaller than the corresponding one obtained from the classical Stokes-Einstein relation. Then, the use of the GSER allows to obtain an effective temperature that is smaller than the temperature of the heat bath. Additionally, we provide a simple expression based on a differential effective medium theory that allows to calculate the diffusion coefficient at short and long times. Comparison of our results with experiments and simulations for suspensions of hard and porous spheres shows an excellent agreement in all cases.

Structural response of polyelectrolyte dendrimer towards molecular protonation: the inconsistency revealed by SANS and NMR

Polyamidoamine (PAMAM) dendrimers and their charged state in deuterium oxide have been investigated with proton pulsed field gradient diffusion nuclear magnetic resonance (PFG-NMR) and small-angle neutron scattering (SANS) techniques. NMR measurements suggest that significant variation of the hydrodynamic radius, calculated by the Stokes-Einstein relation with appropriate surface conditions, is observed upon increasing the molecular protonation. However, a comparative SANS experiment indicates little dependence of the dendrimer global size, in terms of its radius of gyration, on molecular protonation. The inconsistency indicates the necessity of incorporating the effect of molecular interface modification and molecular porosity provided by dressed counterions, when dynamical measurements are used for the determination of the structural characteristics of ionic soft colloids even in dilute suspensions.

Short-time diffusion of charge-stabilized colloidal particles: generic features

Analytical theory and Stokesian dynamics simulations are used in conjunction with dynamic light scattering to investigate the role of hydrodynamic interactions in short-time diffusion in suspensions of charge-stabilized colloidal particles. The particles are modeled as solvent-impermeable charged spheres, repelling each otherviaa screened Coulomb potential. Numerical results for self-diffusion and sedimentation coefficients, as well as hydrodynamic and short-time diffusion functions, are compared with experimental data for a wide range of volume fractions. The theoretical predictions for the generic behavior of short-time properties obtained from this model are shown to be in full accord with experimental data. In addition, the effects of microion kinetics, nonzero particle porosity and residual attractive forces on the form of the hydrodynamic function are estimated. This serves to rule out possible causes for the strikingly small hydrodynamic function values determined in certain synchrotron radiation experiments.