Structure and position-dependent properties of inhomogeneous suspensions of responsive colloids

Nonequilibrium relaxation of soft responsive colloids

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations.

External field-driven property localization in liquids of responsive macromolecules

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.

Liquid structure of bistable responsive macromolecules using mean-field density-functional theory

Macromolecular crowding typically applies to biomolecular and polymer-based systems in which the individual particles often feature a two-state folded/unfolded or coil-to-globule transition, such as found for proteins and peptides, DNA and RNA, or supramolecular polymers. Here, we employ a mean-field density functional theory (DFT) of a model of soft and bistable responsive colloids (RCs) in which the size of the macromolecule is explicitly resolved as a degree of freedom living in a bimodal 'Landau' energy landscape (exhibiting big and small states), thus directly responding to the crowding environment. Using this RC-DFT we study the effects of self-crowding on the liquid bulk structure and thermodynamics for different energy barriers and softnesses of the bimodal energy landscape, in conditions close to the coil-to-globule transition. We find substantial crowding effects on the internal distributions, a complex polydispersity behavior, and quasi-universal compression curves for increasing (generalized) packing fractions. Moreover, we uncover distinct signatures of bimodal versus unimodal behavior in the particle compression. Finally, the analysis of the pair structure - derived from the test particle route - reveals that the microstructure of the liquid is quite inhomogeneous due to local depletion effects, tuneable by particle softness.

Active responsive colloids driven by intrinsic dichotomous noise

We study the influence of intrinsic noise on the structure and dynamics of responsive colloids (RCs), which actively change their size and mutual interactions. The colloidal size is explicitly resolved in our RC model as an internal degree of freedom (DOF) in addition to the particle translation. A Hertzian pair potential between the RCs leads to repulsion and shrinking of the particles, resulting in an explicit responsiveness of the system to self-crowding. To render the colloids active, their size is internally driven by a dichotomous noise, randomly switching ("breathing") between growing and shrinking states with a predefined rate, as motivated by recent experiments on synthetic active colloids. The polydispersity of this dichotomous active responsive colloid (D-ARC) model can be tuned by the parameters of the noise. Utilizing stochastic computer simulations, we study crowding effects on the spatial distributions, relaxation times, and self-diffusion of dense suspensions of the D-ARCs. We find a substantial influence of the "built-in" intrinsic noise on the system's behavior, in particular, transitions from unimodal to bimodal size distributions for an increasing colloid density as well as intrinsic noise-modified diffusive translational dynamics. We conclude that controlling the noise of internal DOFs of a macromolecule or cell is a powerful tool for active colloidal materials to enable autonomous changes in the system's collective structure and dynamics towards the adaptation of macroscopic properties to external perturbations.

Active responsive colloids coupled to different thermostats

We introduce a model of active responsive colloids (ARCs) in which an internal degree of freedom (DoF) of a single colloidal particle is "activated" by coupling it to a different thermostat than for the translational DoFs. As for the responsive internal DoF, we consider specifically the size (diameter) of the spherical particles, which is confined by a harmonic parent potential being either entropic or energetic in nature. The ARCs interact via a repulsive Hertzian pair potential, appropriate to model hydrogels or elastic colloids, and are studied for various densities using Brownian dynamics simulations. We tune the internal activity in the nonequilibrium steady state by scanning through a wide range of internal temperatures, both smaller ("colder") and larger ("hotter") than the translational temperature. The results show a rich and intriguing behavior for the emergent property distributions, colloidal pair structure, and the diffusive translational dynamics controlled by the internal activity, substantially depending on whether the internal DoF moves in an entropic or energetic potential. We discuss theoretical thermal limits and phenomenological models which can explain some of the nonequilibrium trends qualitatively. Our study indicates that particle dynamical polydispersity as well as the structure and dynamics of dense macromolecular suspensions can be vastly tuned by internal activity in terms of internal "hot" or "cold" fluctuating states.

Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions

We employ Reactive Dynamical Density Functional Theory (R-DDFT) and Reactive Brownian Dynamics (R-BD) simulations to investigate the dynamics of a suspension of active soft Gaussian colloids with binary interaction switching, i.e., a one-component colloidal system in which every particle stochastically switches at predefined rates between two interaction states with different mobility. Using R-DDFT we extend a theory previously developed to access the dynamics of inhomogeneous liquids [Archer et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75, 040501] to study the influence of the switching activity on the self and distinct part of the Van Hove function in bulk solution, and determine the corresponding mean squared displacement of the switching particles. Our results demonstrate that, even though the average diffusion coefficient is not affected by the switching activity, it significantly modifies the non-equilibrium dynamics and diffusion coefficients of the individual particles, leading to a crossover from short to long times, with a regime for intermediate times showing anomalous diffusion. In addition, the self-part of the van Hove function has a Gaussian form at short and long times, but becomes non-Gaussian at intermediates ones, having a crossover between short and large displacements. The corresponding self-intermediate scattering function shows the two-step relaxation patters typically observed in soft materials with heterogeneous dynamics such as glasses and gels. We also introduce a phenomenological Continuous Time Random Walk (CTRW) theory to understand the heterogeneous diffusion of this system. R-DDFT results are in excellent agreement with R-BD simulations and the analytical predictions of CTRW theory, thus confirming that R-DDFT constitutes a powerful method to investigate not only the structure and phase behavior, but also the dynamical properties of non-equilibrium active switching colloidal suspensions.

Modulating internal transition kinetics of responsive macromolecules by collective crowding

Packing and crowding are used in biology as mechanisms to (self-)regulate internal molecular or cellular processes based on collective signaling. Here, we study how the transition kinetics of an internal "switch" of responsive macromolecules is modified collectively by their spatial packing. We employ Brownian dynamics simulations of a model of Responsive Colloids, in which an explicit internal degree of freedom-here, the particle size-moving in a bimodal energy landscape self-consistently responds to the density fluctuations of the crowded environment. We demonstrate that populations and transition times for the two-state switching kinetics can be tuned over one order of magnitude by "self-crowding." An exponential scaling law derived from a combination of Kramers' and liquid state perturbation theory is in very good agreement with the simulations.

Active binary switching of soft colloids: stability and structural properties

We employ reactive dynamical density functional theory (R-DDFT) and reactive Brownian dynamics (R-BD) simulations to study the non-equilibrium structure and phase behavior of an active dispersion of soft Gaussian colloids with binary interaction switching, i.e., we consider a one-component colloidal system in which every particle can individually switch stochastically between two interaction states (here, sizes 'big' and 'small') at predefined rates. We consider the influence of switching activity on the inhomogeneous density profiles of the colloids confined by various external potentials, as well as on their pair structure and phase behavior in bulk solutions. For the latter, we extend the R-DDFT method to incorporate the Percus test-particle route. Our results demonstrate that switching activity strongly modifies the steady-state density profiles and structural (pair) correlations. In particular, the switching rate interpolates from a near-equilibrium binary colloidal mixture of two states at very low rates to a non-equilibrium, 'one-state liquid' at very high rates characterized by one, average interaction size. The latter limit can be described by an equivalent effective one-component (EOC) equilibrium system, for which the exact analytical expression for the effective pair potential is a diffusion-weighted superposition of the active systems' pair potentials. This leads to the interesting fact that under certain conditions an interacting switching system can behave like a non-interacting (ideal) gas in the limit of high switching rates. Moreover, for colloids that are unstable (i.e., demix) near equilibrium, we demonstrate that phase separation and micro-clustering in both confinement and bulk can be dynamically controlled by the switching rate, and vanish for high rates. All R-DDFT results are in excellent agreement with our R-BD simulations.

Interface-induced hysteretic volume phase transition of microgels: simulation and experiment

Thermo-responsive microgel particles can exhibit a drastic volume shrinkage upon increasing the solvent temperature. Recently we found that the spreading of poly(N-isopropylacrylamide) (PNiPAm) microgels at a liquid interface under the influence of surface tension hinders the temperature-induced volume phase transition. In addition, we observed a hysteresis behavior upon temperature cycling, i.e. a different evolution in microgel size and shape depending on whether the microgel was initially adsorbed to the interface in expanded or collapsed state. Here, we model the volume phase transition of such microgels at an air/water interface by monomer-resolved Brownian dynamics simulations and compare the observed behavior with experiments. We reproduce the experimentally observed hysteresis in the microgel dimensions upon temperature variation. Our simulations did not observe any hysteresis for microgels dispersed in the bulk liquid, suggesting that it results from the distinct interfacial morphology of the microgel adsorbed at the liquid interface. An initially collapsed microgel brought to the interface and subjected to subsequent swelling and collapsing (resp. cooling and heating) will end up in a larger size than it had in the original collapsed state. Further temperature cycling, however, only shows a much reduced hysteresis, in agreement with our experimental observations. We attribute the hysteretic behavior to a kinetically trapped initial collapsed configuration, which relaxes upon expanding in the swollen state. We find a similar behavior for linear PNiPAm chains adsorbed to an interface. Our combined experimental - simulation investigation provides new insights into the volume phase transition of PNiPAm materials adsorbed to liquid interfaces.

Soft Particles at Liquid Interfaces: From Molecular Particle Architecture to Collective Phase Behavior

Soft particles such as microgels can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. To date, experimental efforts have predominantly provided phenomenological links between microgel structure and resulting interfacial behavior, while simulations have not been entirely successful in reproducing experiments or predicting the minimal requirements for the desired phase behavior. Here, we develop a multiscale framework to link the molecular particle architecture to the resulting interfacial morphology and, ultimately, to the collective interfacial phase behavior. To this end, we investigate interfacial morphologies of different poly(N-isopropylacrylamide) particle systems using phase-contrast atomic force microscopy and correlate the distinct interfacial morphology with their bulk molecular architecture. We subsequently introduce a new coarse-grained simulation method that uses augmented potentials to translate this interfacial morphology into the resulting phase behavior upon compression. The main novelty of this method is the possibility to efficiently encode multibody interactions, the effects of which are key to distinguishing between heterostructural (anisotropic collapse) and isostructural (isotropic collapse) phase transitions. Our approach allows us to qualitatively resolve existing discrepancies between experiments and simulations. Notably, we demonstrate the first in silico account of the two-dimensional isostructural transition, which is frequently found in experiments but elusive in simulations. In addition, we provide the first experimental demonstration of a heterostructural transition to a chain phase in a single-component system, which has been theoretically predicted decades ago. Overall, our multiscale framework provides a phenomenological bridge between physicochemical soft-particle characteristics at the molecular scale and nanoscale and the collective self-assembly phenomenology at the macroscale, serving as a stepping stone toward an ultimately more quantitative and predictive design approach.

Structure and dynamics of responsive colloids with dynamical polydispersity

Dynamical polydispersity in single-particle properties, for example a fluctuating particle size, shape, charge density, etc, is intrinsic to responsive colloids (RCs), such as biomacromolecules or microgels, but is typically not resolved in coarse-grained mesoscale simulations. Here, we present Brownian dynamics simulations of suspensions of RCs modeling soft hydrogel colloids, for which the size of the individual particles is an explicitly resolved (Gaussian) degree of freedom and dynamically responds to the local interacting environment. We calculate the liquid structure, emergent size distributions, long-time diffusion, and property (size) relaxation kinetics for a wide range of densities and intrinsic property relaxation times in the canonical ensemble. Comparison to interesting reference cases, such as conventional polydisperse suspensions with a frozen parent distribution, or conventional monodisperse systems interacting with an effective pair potential for one fixed size, shows a significant spread in the structure and dynamics. The differences, most apparent in the high density regimes, are due to many-body correlations and the dynamical coupling between property and translation in RC systems, not explicitly accounted for in the conventional treatments. In particular, the translational diffusion in the RC systems is surprisingly close to the free (single RC) diffusion, mainly due to a cancellation of crowding and size compression effects. We show that an effective monodisperse pair potential can be constructed that describes the many-body correlations reasonably well by convoluting the RC pair potential with the density-dependent emergent size distributions and using a mean effective diffusion constant.