Active matter, responsive ("smart") materials and materials under time-dependent load are systems out of thermal equilibrium. To construct coarse-grained models for such systems, one needs to integrate out a distribution of microstates that evolves in time. This is a challenging task. As a preparation to the topic, we recall equilibrium coarse-graining methods, both theoretical and numerical, such as projection operator formalisms, united atom simulations, numerical reconstruction of memory and Markov State Modelling. Then we review recent developments in theoretical approaches to the non-equilibrium coarse-graining problem, in particular, time-dependent projection operator formalisms, dynamic density functional theory and power functional theory, as well as numerical schemes to contruct explicitly time-dependent memory kernels.

Coarse-Grained Modelling Out of Equilibrium

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.

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

Pioneering practical direct sea water splitting via an intrinsically-selective chlorine-phobic nickel polysulphide nanostructured electrocatalyst for pure oxygen evolution

In this work, the effect of pretreatment conditions (10% H2/Ar flow rate 25 mL/min and 400 °C, 3 h or 600 °C, 17 h) on the catalytic performance of 1 wt.% Pd/γ-Al2O3 has been evaluated for hydrogenation of 2-methyl-3-butyn-2-ol in continuous-flow mode. Two palladium catalysts have been tested under different conditions of pressure and temperature and characterized using various physicochemical techniques. The catalytic performance of red(400 °C)-Pd/γ-Al2O3 and red(600 °C)-Pd/γ-Al2O3 are affected by the coexistence of several related factors like the competition between PdH and PdCx formation during the reaction, structure sensitivity, hydrogen spillover to the alumina support and presence or absence of Pd–Al species. High-temperature reduction leads to formation of Pd–Al species in addition to pure Pd. The Pd–Al species which reveal unique electronic properties by decreasing the Pdδ− surface concentration via electron transfer from Pd to Al, leading to a weaker Pd–Alkyl bonding, additionally assisted by the hydrogen spillover, are the sites of improved semi-hydrogenation of 2-methyl-3-butyn-2-ol towards 2-methyl-3-buten-2-ol (97%)—an important intermediate for vitamin A synthesis.

Continuous 2-Methyl-3-butyn-2-ol Selective Hydrogenation on Pd/γ-Al2O3 as a Green Pathway of Vitamin A Precursor Synthesis

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.

/pdf/active-binary-switching-of-soft-colloids-stability-and-200fg7cj0a.pdf

Active binary switching of soft colloids: stability and structural properties.

Electrostatic reaction inhibition in heterogeneous catalysis emerges if charged reactants and products with similar charges are adsorbed on the catalyst and thus repel the approaching reactants. In this work, we study the effects of electrostatic inhibition on the reaction rate of unimolecular reactions catalyzed on the surface of a spherical model nanoparticle using particle-based reaction-diffusion simulations. Moreover, we derive closed rate equations based on an approximate Debye-Smoluchowski rate theory, valid for diffusion-controlled reactions, and a modified Langmuir adsorption isotherm, relevant for reaction-controlled reactions, to account for electrostatic inhibition in the Debye-Huckel limit. We study the kinetics of reactions ranging from low to high adsorptions on the nanoparticle surface and from the surface- to diffusion-controlled limits for charge valencies 1 and 2. In the diffusion-controlled limit, electrostatic inhibition drastically slows down the reactions for strong adsorption and low ionic concentration, which is well described by our theory. In particular, the rate decreases with adsorption affinity because, in this case, the inhibiting products are generated at a high rate. In the (slow) reaction-controlled limit, the effect of electrostatic inhibition is much weaker, as semiquantitatively reproduced by our electrostatic-modified Langmuir theory. We finally propose and verify a simple interpolation formula that describes electrostatic inhibition for all reaction speeds ("diffusion-influenced" reactions) in general.

Electrostatic Reaction Inhibition in Nanoparticle Catalysis.

Electrostatic reaction inhibition in heterogeneous catalysis emerges if charged reactants and products are adsorbed on the catalyst and thus repel the approaching reactants. In this work, we study the effects of electrostatic inhibition on the reaction rate of unimolecular reactions catalyzed on the surface of a spherical model nanoparticle by using particle-based reaction-diffusion simulations. Moreover, we derive closed rate equations based on approximate Debye-Smoluchowski rate theory, valid for diffusion-controlled reactions, and a modified Langmuir adsorption isotherm, relevant for reaction-controlled reactions, to account for electrostatic inhibition in the Debye-Huckel limit. We study the kinetics of reactions ranging from low to high adsorptions on the nanoparticle surface and from the surface- to diffusion-controlled limits for charge valencies 1 and 2. In the diffusion-controlled limit, electrostatic inhibition drastically slows down the reactions for strong adsorption and low ionic concentration, which is well described by our theory. In particular, the rate decreases with adsorption affinity, because in this case the inhibiting products are generated at high rate. In the (slow) reaction-controlled limit, the effect of electrostatic inhibition is much weaker, as semi-quantitatively reproduced by our electrostatic-modified Langmuir theory. We finally propose and verify a simple interpolation formula that describes electrostatic inhibition for all reaction speeds (`diffusion-influenced' reactions) in general.

Electrostatic reaction inhibition in nanoparticle catalysis

The kinetic processes in nanoparticle-based catalysis are dominated by large fluctuations and spatiotemporal heterogeneities, in particular for diffusion-influenced reactions that are far from equi...

Coverage Fluctuations and Correlations in Nanoparticle-Catalyzed Diffusion-Influenced Bimolecular Reactions

Responsive particles, such as biomacromolecules or hydrogels, display a broad and polymodal distribution of conformations and have thus the ability to change their properties (e.g., size, shape, charge density, etc.) substantially in response to external fields or to their local environment (e.g., mediated by cosolutes or pH). Here we discuss the basic statistical mechanics for a model of responsive colloids (RCs) by introducing an additional ``property'' degree of freedom as a collective variable in a formal coarse-graining procedure. The latter leads to an additional one-body term in the coarse-grained (CG) free energy, defining a single-particle property distribution for an individual polydisperse RC. We argue that in the equilibrium thermodynamic limit such a CG system of RCs behaves like a conventional polydisperse system of nonresponsive particles. We then illustrate the action of external fields, which impose local (position-dependent) property distributions leading to nontrivial effects on the spatial one-body property and density profiles, even for an ideal (noninteracting) gas of RCs. We finally apply density-functional theory in the local density approximation to discuss the effects of particle interactions for specific examples of (i) a suspension of RCs in an external field linear in both position and property, (ii) a suspension of RCs with highly localized properties (sizes) confined between two walls, and (iii) a two-component suspension where an inhomogeneously distributed (nonresponsive) cosolute component, as found, e.g., in the studies of osmolyte- or salt-induced collapse or swelling transitions of thermosensitive polymers, modifies the local properties and density of the RC liquid.

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

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Electrostatic Reaction Inhibition in Nanoparticle Catalysis.

Electrostatic reaction inhibition in nanoparticle catalysis

Coverage Fluctuations and Correlations in Nanoparticle-Catalyzed Diffusion-Influenced Bimolecular Reactions

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