Colloidal gels

Colloidal gels are fundamentally and technologically interesting due to their diverse building blocks, network-supporting attractive forces, and gelation pathways. As a result, they exhibit unusual combinations of properties that would be challenging to realize with other forms of matter. Colloidal gels are structured across a hierarchy of length scales. The building blocks can vary in shape and characteristic size, from nanometers to micrometers, and are linked together in gels to form system-spanning networks. Owing to their porous, disordered structure, gels (unlike superlattices) can readily accommodate mixtures of colloids and linking molecules with different shapes, sizes, or functionalities, allowing for continuous property tunability. The topologies of the stress-supporting particle structures in gels and their spectra of relaxation times can depend sensitively on the nature of physical or chemical links between the building blocks and on the history or applied force. Although equilibrium phase boundaries help establish conditions where homogeneous vs heterogeneous gel networks might be expected to form, universal rules that connect thermodynamic and non-equilibrium behaviors of these materials have proven elusive.

Despite decades of interest in colloidal gels, recent advancements across disciplines—including chemistry, biology, materials science, and physics—are providing fresh opportunities to create gel networks with remarkable properties and gain mechanistic insights needed for materials design. For example, progress in real-space analysis using microscopy¹ and upgrades to beamline facilities and software supporting x-ray photon correlation spectroscopy (XPCS)² are enhancing researchers’ ability to quantitatively probe and interpret non-equilibrium structure formation, aging, and rheology³ of colloidal gels. Simultaneously, new developments in synthetic methods and gelation strategies for nanoparticle-based networks are paving the way for functional nanocrystal gels and aerogels with tunable optical, electronic, and catalytic properties.^4,5 Conceptual and theoretical advances are helping to clarify the role of network valence in establishing the phase behavior, structure, and dynamics of equilibrium gel-forming materials.⁶ 

We organized a three-day symposium on Colloidal Gels at ACS Spring 2022 and were invited to guest-edit this Special Topic on Colloidal Gels in Journal of Chemical Physics. As described below, the 29 articles that appear in this issue shed new light on a wide variety of related topics, including limited valence networks, bridged colloidal networks and coagulant gels, depletant-mediated gels, in situ structural characterization of gel aging, mechanical and rheological properties of colloidal networks, hybrid and deformable particle assemblies, and nanocrystal gels with tunable optical response.

Equilibrium phase diagrams and percolation thresholds constrain possible gelation pathways of colloidal networks and are strongly influenced by the number of bonded neighbors per colloid or valence. Valence can be restricted microscopically (e.g., neighbors link by connecting available surface sites) or macroscopically (e.g., sites on neighbors are linked by secondary molecules). In this special topic, Conrad et al. introduced an emulsion-imaging method for rapidly estimating the boundaries for liquid–liquid phase coexistence of associating macromer solutions in the temperature–concentration plane.⁷ The authors study how valence and salt concentration impact the phase behavior of DNA nanostars, uncovering phase behavior consistent with model patchy-particle gel-formers. In a contribution by Lattuada et al.,⁸ the open space available in low-valence nanostar structures was exploited to design a binary mixture of self-associating DNA nanostars that form interpenetrating equilibrium gel networks. Sequential network formation upon cooling was controlled by the strengths of the bonds formed between nanostar arm tips, encoded by their respective base sequences. Carpenter and Colòn introduced a molecular simulation method to assemble and study similarly open networks of soft porous coordination polymers comprising metal–organic polyhedral nodes and organic linker building blocks.⁹ Analysis of their model networks suggested that experimentally observed pore sizes reflect intercolloid spaces, which depend on building block properties, especially linker flexibility.

Molecular modeling and simulation can help chart the design space for gels of linked- or limited-valence colloids. Using Wertheim theory, Flory–Stockmayer theory, and Monte Carlo simulations, Gouveia et al. explored the rich variety of percolation boundaries in the temperature–concentration plane resulting from binary mixtures of chaining linkers and branching colloids.¹⁰ Kwon et al. studied bonding motifs that produced re-entrant percolation and structural relaxation of polymer-linked patchy colloids using a related theoretical framework and Langevin dynamics simulations.¹¹ The relaxation time of the colloidal self-intermediate scattering function was found to be controlled by the persistence time of linked colloidal pairs, which closely tracked coordination number. Gallegos et al.¹² studied how network formation of patchy colloids is influenced by gravity, performing Monte Carlo simulations to understand how patch surface coverage and gravitational Péclet number affect the phase diagram, clustering, percolation, and gelation.

Colloidal networks formed by nonspecific bridging polymers represent another interesting class of gel formers, although it can be challenging to design dispersible systems with tunable polymer–colloid interactions. Gallegos et al. demonstrated that optically resolvable, core–shell methacrylate-based particles exhibiting pH-sensitive bridging interactions with poly(acrylic acid) could be sterically and electrostatically stabilized, and refractive index- and density-matched to aqueous solvents.¹³ Using dynamic light scattering and confocal microscopy, the authors established that the pH-dependent colloidal structure and dynamics were responsive to changes in polymer and particle concentration, producing fluid, weak gel, and strong gel states. More et al.¹⁴ similarly prepared composite gels comprising hematite pseudocubes and a bridging triblock polymer F127. Gel strength, brittleness, and structure were characterized as a function of temperature and pseudocube composition using linear and nonlinear rheological measurements and confocal microscopy.

Although microscopy has conventionally been used to study dynamics of larger (e.g., micrometer-scale) particles, Williams et al. demonstrated¹⁵ how it can also be leveraged to study gelation of smaller colloids. By doping high-volume fraction dispersions of 130 nm diameter latex particles with larger fluorescently labeled polystyrene tracer particles and bringing them in contact with a coagulant source, the authors visualize and quantitatively characterize coagulant gelation in situ and provide a new understanding about the widely employed industrial-scale dipping process using light microscopy.

Adding macromolecular depletants is another canonical strategy for modifying colloidal interactions, structure, and rheology. Shen and co-workers adopt this approach to study Laponite clay nanoparticle dispersions, using dynamic light scattering microrheology to measure how poly(ethylene oxide) concentration influences the dynamics of probe particles with different sizes.¹⁶ Their results provide microscopic evidence that free polymer chains induce a depletion attraction that delays structural arrest from a flowing dispersion to a repulsive glass or gel-like state. Highlighting the diversity of materials that can form depletion gels, Schmitt and co-workers studied how four different surfactants influenced the structure and rheology of oxidized cellulose nanofibril dispersions.¹⁷ Strain amplitude and frequency sweep measurements of storage and loss moduli were analyzed together with small-angle neutron scattering data to understand how effective interactions depended on the surfactant polar head group. Micelles of anionic or zwitterionic surfactants produced depletion interactions between nanofibrils leading to weak gels, while cationic surfactants adsorbed to the nanofibrils, screening repulsions leading to tough gels or phase separation.

On the modeling side, Carretas-Talamante and co-workers used non-equilibrium self-consistent generalized Langevin equation theory to predict three dynamical arrest scenarios for spherical colloids with competing short-range attractions and long-range repulsions: fluid-to-arrested cluster, arrested-cluster-to-glass, and fluid-to-glass.¹⁸ The predictions suggest that formation of ordered inhomogeneous equilibrium phases previously anticipated for these systems would be interrupted by non-equilibrium dynamic arrest barriers, rendering those phases impossible to observe experimentally. To understand how percolation of correlated structures in model colloids with short-range attractions and long-range repulsions challenge Monte Carlo simulation algorithms, Zheng et al. studied two simplified versions of the axial next-nearest neighbor Ising model.¹⁹ Based on their analysis, the authors proposed two novel cluster algorithms to enhance sampling of the model on a two-dimensional lattice, achieving up to a 40-fold simulation speed-up while laying the foundation for further algorithmic improvements. Finally, Moore et al.²⁰ explored properties of active particles confined in percolating pore network structures mimicking colloidal gels formed due to depletion interactions. Brownian dynamics simulations revealed profound differences in structure, dynamics, and motility-induced phase separation for gel-confined active particles compared with confinement to environments of randomly pinned obstacles.

In situ small-angle x-ray scattering and XPCS measurements on colloidal networks can provide information on scales relevant to their structural and dynamic evolution. In this special topic, Begam and co-workers study how salt ions and temperature influence gelation of egg white protein using ultra-small angle x-ray scattering–XPCS.²¹ Two-step relaxation (structural growth followed by gel aging) was observed. The egg white gels exhibited hyperdiffusive, compressed exponential dynamics, characteristic of materials where structural rearrangements release internal stresses. An XPCS study of gelation of PEGylated gold nanoparticles dispersed in a glycerol–water mixture by Jain et al. revealed a three-step gelation process, where relaxation by stress release accompanied by hyperdiffusive dynamics upon gelation was similarly reported.²² Chen et al. investigated the memory effects due to time-varying attractions in a thermoreversible silica nanocolloid gel using a combination of XPCS and rheological measurements.²³ The observed aging properties, including the behavior resembling the Kovacs effect in glasses, could be rationalized by a model where particles attach and detach to gel strands with coordination number-dependent rates. Kashanchi et al. investigated how pH and colloidal size and concentration affected gelation of preformed silica nanoparticles to understand materials design trade-offs for thermal insulation coating applications.²⁴ By comparing in situ small-angle x-ray scattering with ex situ characterization of dried gels, the authors identified paths for making gels with pore size distributions consistent with improved optical transparency and low conductivity. Finally, in a contribution by Tchakalova and co-workers, small-angle x-ray scattering and rheology were used to characterize the structure and mechanical properties of swollen cubic phase gels, including their structural changes upon incorporation of a fragrance compound and their dispersion into microscopic cubosome particles.²⁵ 

Advances in theory and simulation help refine how we understand gel network formation and its implications for mechanical and rheological properties. In their contribution to this special topic, Vinutha and co-workers used computer simulations to demonstrate that force chains in colloidal gels emerge from stress–stress correlations in much the same way that they do in granular solids.²⁶ By using simulation to monitor bond dynamics during yielding of model depletion gels, Mangal et al. established that bonds with high network centrality rupture most readily, suggesting a structural predictor of network failure.²⁷ Employing adaptive Brownian dynamics simulations, Sammüller and co-workers found that a model gel of colloids interacting via a modified Stillinger–Weber potential exhibited a pronounced non-equilibrium structural and flow response to a steady sinusoidal external potential.²⁸ The resulting inhomogeneous shear dynamics were qualitatively different from those of a simple fluid and could be reproduced and interpreted using power functional theory. In a contribution from Diaz Maier and Wagner, schematic mode-coupling theory was applied to predict experimentally measured temperature- and linker-concentration-dependent viscosities and viscoelastic moduli of poly(N-isopropylacrylamide) hydrogels.²⁹ Suman and co-workers analyzed the experimentally measured linear and nonlinear rheology of a synthetic clay at the critical gel state using an integral constitutive equation, exploring the intracycle stress response and the transition to nonlinearity.³⁰ Finally, based on results from extensive simulations of stress transmission, Gadi Man et al. proposed a constitutive model for soft colloidal gels and provided evidence that their mechanical response is controlled by a subtle balance of compressive and tensile forces at particle contact.³¹ 

Mechanical forces in gel assemblies produce distinctive responses when the building blocks are soft and deformable. In a contribution from Nickel and co-workers, small-angle neutron scattering with contrast variation, small-angle x-ray scattering, and Monte Carlo simulations were combined to study how ellipsoidal hollow nanogels adapt their size and shape, self-healing to match the particles composing the surrounding matrix.³² Lee et al. demonstrated that embedding nanoparticle superlattices into a polymer gel matrix stabilizes against disassembly due to chemical or thermal stresses, while allowing for controllable dynamical perturbations of the hybrid nanoparticle-gel network.³³ 

Gel assemblies also offer opportunities for materials with widely tunable optical properties. Rusch et al. demonstrated the synthesis of ZnS-tipped CdSe/CdS dot/rod nanocrystal gel and aerogel networks.³⁴ By controlling the ZnS tip lengths, networks with tunable band structures were realized. In their contribution, Kang and co-workers used a thermoreversible linking approach to assemble mixed gels of plasmonic metal oxide nanocrystals with different doping levels, sizes, and shapes. The resulting networks featured optical properties that differ from those of the building blocks or the corresponding close-packed structures and are predictable using the mutual polarization method.³⁵ 

The articles of this special topic reflect the vibrant ongoing research activity in the field of colloidal gels where theoretical, simulation, and experimental techniques are often used together to help uncover new structure–property relations paired with a mechanistic understanding. Several contributions demonstrate how this knowledge can help integrate building blocks with new material compositions or functionality to create network-based materials with distinctive properties. Moving forward, we envision opportunities on many fronts, including developing soft, processable gels with the kinds of electronic or optical properties typically engineered into solid-state materials, fueled gel assemblies capable of rapidly transforming between states with differentiated structures and properties, and colloidal gels with synthetic peptide- or peptoid-based building blocks and phase behavior mimicking biomolecular{ }condensates.

We thank those researchers who authored contributions featured in this special topic highlighting fundamental research on colloidal gel networks. We are grateful to the Journal of Chemical Physics editors Francesco Sciortino, Mark Ediger, and Carlos Vega; editor-in-chief Tim Lian; journal manager Jenny Stein; and editorial assistant Olivia Zarzycki.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.