Dynamics of equilibrium linked colloidal gels

Colloids that attractively bond to only a few neighbors (e.g., patchy particles) can form equilibrium gels with distinctive dynamic properties that are stable in time. Here, we use a coarse-grained model to explore the dynamics of linked networks of patchy colloids whose average valence is macroscopically, rather than microscopically, constrained. Simulation results for the model show dynamic hallmarks of equilibrium gel formation and establish that the colloid-colloid bond persistence time controls the characteristic slow relaxation of the self-intermediate scattering function. The model features re-entrant network formation without phase separation as a function of linker concentration, centered at the stoichiometric ratio of linker ends to nanoparticle surface bonding sites. Departures from stoichiometry result in linker-starved or site-starved networks with reduced connectivity and shorter characteristic relaxation times with lower activation energies. Underlying the re-entrant trends, dynamic properties vary monotonically with the number of effective network bonds per colloid, a quantity that can be predicted using Wertheim's thermodynamic perturbation theory. These behaviors suggest macroscopic in situ strategies for tuning the dynamical response of colloidal networks.Comment: 25 pages, 9 figure

Intrinsic Optical and Electronic Properties from Quantitative Analysis of Plasmonic Semiconductor Nanocrystal Ensemble Optical Extinction

The optical extinction spectra arising from localized surface plasmon resonance in doped semiconductor nanocrystals (NCs) have intensities and lineshapes determined by free charge carrier concentrations and the various mechanisms for damping the oscillation of those free carriers. However, these intrinsic properties are convoluted by heterogeneous broadening when measuring spectra of ensembles. We reveal that the traditional Drude approximation is not equipped to fit spectra from a heterogeneous ensemble of doped semiconductor NCs and produces fit results that violate Mie scattering theory. The heterogeneous ensemble Drude approximation (HEDA) model rectifies this issue by accounting for ensemble heterogeneity and near-surface depletion. The HEDA model is applied to tin-doped indium oxide NCs for a range of sizes and doping levels but we expect it can be employed for any isotropic plasmonic particles in the quasistatic regime. It captures individual NC optical properties and their contributions to the ensemble spectra thereby enabling the analysis of intrinsic NC properties from an ensemble measurement. Quality factors for the average NC in each ensemble are quantified and found to be notably higher than those of the ensemble. Carrier mobility and conductivity derived from HEDA fits matches that measured in the bulk thin film literature

Tuning Nanocrystal Surface Depletion by Controlling Dopant Distribution as a Route Toward Enhanced Film Conductivity

Electron conduction through bare metal oxide nanocrystal (NC) films is hindered by surface depletion regions resulting from the presence of surface states. We control the radial dopant distribution in tin-doped indium oxide (ITO) NCs as a means to manipulate the NC depletion width. We find in films of ITO NCs of equal overall dopant concentration that those with dopant-enriched surfaces show decreased depletion width and increased conductivity. Variable temperature conductivity data shows electron localization length increases and associated depletion width decreases monotonically with increased density of dopants near the NC surface. We calculate band profiles for NCs of differing radial dopant distributions and, in agreement with variable temperature conductivity fits, find NCs with dopant-enriched surfaces have narrower depletion widths and longer localization lengths than those with dopant-enriched cores. Following amelioration of NC surface depletion by atomic layer deposition of alumina, all films of equal overall dopant concentration have similar conductivity. Variable temperature conductivity measurements on alumina-capped films indicate all films behave as granular metals. Herein, we conclude that dopant-enriched surfaces decrease the near-surface depletion region, which directly increases the electron localization length and conductivity of NC films

Assembly of colloidal nanocrystals into open networks

Inorganic nanocrystals exhibit a wide variety of optical, electronic, chemical, and electrochemical functionality that is synthetically tunable based on their size and composition. Their properties and emerging methods for functionalizing their surfaces with specific chemical agents pose the exciting prospect to program the assembly of nanostructured materials whose properties depend intimately on both the characteristics of the building blocks and the mesoscale organization of these in the assembly. In this presentation, I describe novel strategies for assembling optically active nanocrystals into organized gel networks. In particular, theoretical frameworks predict open gel architectures when the extent of inter-particle bonding (i.e. valence) is constrained.[1] To achieve a chemically tunable valence, we functionalized semiconductor nanocrystals with highly charged chalcogenidometallates clusters that induce long range repulsive interactions.[2] The addition of controlled amounts of a cationic crosslinking agent determines the assembly of the nanocrystals into a low volume fraction gel. In another assembly strategy, short range attractive forces are induced between charge-stabilized nanocrystal colloids by the introduction of oligomeric polyethylene glycol (PEG). At low PEG concentrations, it can crosslink nanocrystals into a gel. At higher concentrations, PEG effectively passivates the nanocrystal surfaces, yet excess PEG can induce gel network assembly through the depletion attraction. The organization of the gel networks is characterized by small angle X-ray scattering, from which the fractal dimension that describes the gel topology is determined. We present an integrated approach leveraging theory, synthesis, characterization, and simulation to predict, realize, and analyze the formation of low volume fraction gels from colloidal nanocrystals with unusual optical properties in the visible and infrared spectral ranges. References: [1] BA Lindquist, RB Jadrich, DJ Milliron, TM Truskett, “On the Formation of Equilibrium Gels via a Macroscopic Bond Limitation,” J. Chem. Phys. 145 (2016), 074906. [2] A Singh, BA Lindquist, GK Ong, RB Jadrich, A Singh, H Ha, CJ Ellison, TM Truskett, DJ Milliron, “Linking Semiconductor Nanocrystals into Gel Networks through All-Inorganic Bridges,” Angew. Chem. Int. Ed. 54 (2015), 14840-14844

Wertheim’s thermodynamic perturbation theory with double- bond association and its application to colloid–linker mixtures

We extend Wertheim’s thermodynamic perturbation theory to derive the association free energy of a multicomponent mixture for which double bonds can form between any two pairs of the molecules’ arbitrary number of bonding sites. This generalization reduces in limiting cases to prior theories that restrict double bonding to at most one pair of sites per molecule. We apply the new theory to an associating mixture of colloidal particles (“colloids”) and flexible chain molecules (“linkers”). The linkers have two functional end groups, each of which may bond to one of several sites on the colloids. Due to their flexibility, a significant fraction of linkers can “loop” with both ends bonding to sites on the same colloid instead of bridging sites on different colloids. We use the theory to show that the fraction of linkers in loops depends sensitively on the linker end-to-end distance relative to the colloid bonding-site distance, which suggests strategies for mitigating the loop formation that may otherwise hinder linker-mediated colloidal assembly.This research was primarily supported by the National Science Foundation through the Center for Dynamics and Control of Materials: an NSF MRSEC under Cooperative Agree- ment No. DMR-1720595, with additional support from an Arnold O. Beckman Postdoctoral Fellowship (Z.M.S.) and the Welch Foun- dation (Grant Nos. F-1696 and F-1848).Center for Dynamics and Control of Material

Gelation of Plasmonic Metal Oxide Nanocrystals by Polymer-Induced Depletion-Attractions

Gelation of colloidal nanocrystals (NCs) emerged as a strategy to preserve inherent nanoscale properties in multiscale architectures. Yet available gelation methods still struggle to reliably control nanoscale optical phenomena such as photoluminescence and localized surface plasmon resonance (LSPR) across NC systems due to processing variability. Here, we report on an alternative gelation method based on physical inter-NC interactions: short-range depletion-attractions balanced by long-range electrostatic repulsions. The latter are established by removing the native organic ligands that passivate tin-doped indium oxide (ITO) NCs while the former are introduced by mixing with small polyethylene glycol (PEG) chains. As we incorporate increasing concentrations of PEG, we observe a reentrant phase behavior featuring two favorable gelation windows; the first arises from bridging effects while the second is attributed to depletion-attractions according to phase behavior predicted by our unified theoretical model. The NCs remain discrete within the gel network, based on X-ray scattering and high-resolution transmission electron microscopy. The infrared optical response of the gel is reflective of both the NC building blocks and the network architecture, being characteristic of ITO NC LSPR with coupling interactions between neighboring NCs