Structural and dynamical equilibrium properties of hard board-like particles in parallel confinement

We performed Monte Carlo and dynamic Monte Carlo simulations to model the diffusion of monodispersed suspensions composed of impenetrable cuboidal particles, specifically hard board-like particles (HBPs), in the presence of parallel hard walls. The impact of the walls was investigated by adjusting the size of the simulation box while maintaining constant packing fractions, fixed at η = 0.150, for systems consisting of HBPs with prolate, dual-shaped, and oblate geometries. We observed that increasing the distance between the walls led to the recovery of an isotropic bulk phase, while local particle organization near the walls remained stable. Due to their shape, oblate HBPs exhibit more efficient anchoring at wall surfaces compared to prolate shapes. The formation of nematic-like particle assemblies near the walls, confirmed by theoretical calculations based on density functional theory, significantly influenced local particle dynamics. This effect was particularly pronounced to the extent that a modest portion of cuboids near the walls tended to diffuse exclusively in planes parallel to the confinement, even more efficiently than observed in the bulk regions.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Active microrheology of colloidal suspensions of hard cuboids

By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.

Universal Scaling for the Exit Dynamics of Block Copolymers from Micelles at Short and Long Time Scales

The correlation function for the exit of poloxamer copolymers from equilibrated micelles is found to show up to four regimes depending on the chain flexibility: an initial fast reorganization, a logarithmic intermediate regime, followed by an exponential intermediate regime, and a final exponential decay. The logarithmic intermediate regime has been observed experimentally and attributed to the polydispersity of the polymer samples. However, we present dynamic single-chain mean-field theory simulations with chains of variable flexibility which show the same logarithmic relaxation but with strictly monodisperse systems. In agreement with our previous studies, we propose that this logarithmic response arises from a degeneracy of energy states of the hydrophobic block in the micelle core. For this to occur, a sufficiently large number of degenerate conformational states are required, which depend on the polymer flexibility and therefore should not be present for rigid polymers. Experimental results for monodisperse polymeric samples claiming the absence of such a logarithmic response may also lack a sufficient number of hydrophobic blocks for the required number of configurational states for this type of response to be seen. The insight gained from analyzing the simulation results allows us to propose a modified Eyring equation capable of reproducing the observed dynamic behavior. On scaling experimental results from different sources and systems according to this equation, we find a unique master curve showing a universal nature of the intermediate regimes: the logarithmic regime together with the secondary exponential decay. The terminal exponential regime at long times proposed by the standard Halperin and Alexander model is beyond the range of the data analyzed in this article. The universality observed suggests an entropic origin of the short-time dynamic response of this class of systems rather than the polydispersity.

Microrheology of colloidal suspensions via dynamic Monte Carlo simulations

Understanding the rheology of colloidal suspensions is crucial in the formulation of a wide selection of industry-relevant products, such as paints, foods and inks. To characterise the viscoelastic behaviour of these soft materials, one can analyse the microscopic dynamics of colloidal tracers diffusing through the host fluid and generating local deformations and stresses. This technique, referred to as microrheology, links the bulk rheology of fluids to the microscopic dynamics at the particle scale. If tracers are subjected to external forces, rather than freely diffusing, it is called active microrheology. Motivated by the impact of microrheology in providing information on local structure in complex systems such as colloidal glasses, active matter or biological systems, we have extended the dynamic Monte Carlo (DMC) technique to investigate active microrheology in colloidal suspensions. The original DMC theoretical framework, able to accurately describe the Brownian dynamics of colloids at equilibrium, is here reconsidered and expanded to describe the effects of an external force pulling a tracer embedded in isotropic colloidal suspensions at different densities. To this end, we studied the dynamics of a spherical tracer dragged by a constant external force through a bath of spherical and rod-like particles of comparable size. We could extract valuable details on its effective friction coefficient, being constant at small and large values of the external force, but otherwise displaying a nonlinear behaviour that indicates the occurrence of a force-thinning regime. Our DMC simulation results are in excellent quantitative agreement with past Langevin dynamics simulations and theoretical works for the bath of spherical colloids. The bath of rod-like particles is studied in the isotropic phase, and displays an example where DMC is more convenient than Brownian or Langevin dynamics, in this case, in dealing with particle rotation.

Unveiling Interfacial Li-Ion Dynamics in Li7La3Zr2O12/PEO(LiTFSI) Composite Polymer-Ceramic Solid Electrolytes for All-Solid-State Lithium Batteries

Unlocking the full potential of solid-state electrolytes (SSEs) is key to enabling safer and more-energy dense technologies than today's Li-ion batteries. In particular, composite materials comprising a conductive, flexible polymer matrix embedding ceramic filler particles are emerging as a good strategy to provide the combination of conductivity and mechanical and chemical stability demanded from SSEs. However, the electrochemical activity of these materials strongly depends on their polymer/ceramic interfacial Li-ion dynamics at the molecular scale, whose fundamental understanding remains elusive. While this interface has been explored for nonconductive ceramic fillers, atomistic modeling of interfaces involving a potentially more promising conductive ceramic filler is still lacking. We address this shortfall by employing molecular dynamics and enhanced Monte Carlo techniques to gain unprecedented insights into the interfacial Li-ion dynamics in a composite polymer-ceramic electrolyte, which integrates polyethylene oxide plus LiN(CF₃SO₂)₂ lithium imide salt (LiTFSI), and Li-ion conductive cubic Li₇La₃Zr₂O₁₂ (LLZO) inclusions. Our simulations automatically produce the interfacial Li-ion distribution assumed in space-charge models and, for the first time, a long-range impact of the garnet surface on the Li-ion diffusivity is unveiled. Based on our calculations and experimental measurements of tensile strength and ionic conductivity, we are able to explain a previously reported drop in conductivity at a critical filler fraction well below the theoretical percolation threshold. Our results pave the way for the computational modeling of other conductive filler/polymer combinations and the rational design of composite SSEs.

Dynamic Monte Carlo simulations of inhomogeneous colloidal suspensions

The dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian dynamics or molecular dynamics simulation, DMC is applicable to systems of spherical and/or anisotropic particles and to equilibrium or out-of-equilibrium processes. In this work, we present a theoretical and methodological framework to extend DMC to the study of heterogeneous systems, where the presence of an interface between coexisting phases introduces an additional element of complexity in determining the dynamic properties. In particular, we simulate a Lennard-Jones fluid at the liquid-vapor equilibrium and determine the diffusion coefficients in the bulk of each phase and across the interface. To test the validity of our DMC results, we also perform Brownian Dynamics simulations and unveil an excellent quantitative agreement between the two simulation techniques.

Atomistic Insight into Ion Transport and Conductivity in Ga/Al-Substituted Li7La3Zr2O12 Solid Electrolytes

Garnet-structured Li₇La₃Zr₂O₁₂ is a promising solid electrolyte for next-generation solid-state Li batteries. However, sufficiently fast Li-ion mobility required for battery applications only emerges at high temperatures, upon a phase transition to cubic structure. A well-known strategy to stabilize the cubic phase at room temperature relies on aliovalent substitution; in particular, the substitution of Li⁺ by Al³⁺ and Ga³⁺ ions. Yet, despite having the same formal charge, Ga³⁺ substitution yields higher conductivities (10^-3 S/cm) than Al³⁺ (10^-4 S/cm). The reason of such difference in ionic conductivity remains a mystery. Here, we use molecular dynamic simulations and advanced sampling techniques to precisely unveil the atomistic origin of this phenomenon. Our results show that Li⁺ vacancies generated by Al³⁺ and Ga³⁺ substitution remain adjacent to Ga³⁺ and Al³⁺ ions, without contributing to the promotion of Li⁺ mobility. However, while Ga³⁺ ions tend to allow limited Li⁺ diffusion within their immediate surroundings, the less repulsive interactions associated with Al³⁺ ions lead to a complete blockage of neighboring Li⁺ diffusion paths. This effect is magnified at lower temperatures and explains the higher conductivities observed for Ga-substituted systems. Overall, this study provides a valuable insight into the fundamental ion transport mechanism in the bulk of Ga/Al-substituted Li₇La₃Zr₂O₁₂ and paves the way for rationalizing aliovalent substitution design strategies for enhancing ionic transport in these materials.

Simulation Analysis of the Kinetic Exchange of Copolymer Surfactants in Micelles

The exchange of surfactants in micelles involves several processes that are difficult to characterize experimentally. Microscopic simulations have the potential to reveal some of the key activities that occur when a surfactant spontaneously exits a micelle. In this work, we present a quantitative analysis of the kinetic exchange process over a large range of time. This study is based on a dynamic version of single-chain mean-field theory using a coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems. The kinetics described in our simulations involves three different regimes. After a fast initial rearrangement of the labeled chains, the system undergoes a logarithmic relaxation, which has been experimentally observed. Contrary to what has been reported in previous analyses, our simulations indicate that this regime is caused by the intrinsic physical behavior of the system and is not due only to the polydispersity of the samples. Finally, the terminal regime is characterized by an exponential decay. The exit rates predicted by our simulations are in good agreement with the values reported experimentally. In addition, we address the sequence of microscopic conformational changes undergone by the surfactants when leaving the micellar aggregates. We found a subtle variation in the radius of gyration of the hydrophobic block, which challenges the image of either a complete collapse or a full stretching commonly accepted in the current theoretical and experimental literature.

Logarithmic Exchange Kinetics in Monodisperse Copolymeric Micelles

Experimental measurements of the relaxation kinetics of copolymeric surfactant exchange for micellar systems unexpectedly show a peculiar logarithmic decay. Several authors use polydispersity as an explanation for this behavior. However, in coarse-grained simulations that preserve microscopic details of the surfactants, we find evidence of the same logarithmic behavior. Since we use a strictly monodisperse distribution of chain lengths such a relaxation process cannot be attributed to polydispersity, but has to be caused by an inherent physical process characteristic of this type of system. This is supported by the fact that the decay is specifically logarithmic and not a power law with an exponent inherited from the particular polydispersity distribution of the sample. We suggest that the degeneracy of the energy states of the hydrophobic block in the core, which is broken on leaving the micelle, can qualitatively explain the broad distribution of energy barriers, which gives rise to the observed nonexponential relaxation.

Mean-field coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems

The microscopic modeling of surfactant systems is of the utmost importance in understanding the mechanisms related to the micellization process because it allows for prediction and comparison with experimental data of diverse equilibrium system properties. In this work, we present a coarse-grained model for Pluronics, a trademarked type of triblock copolymer, from simulations based on a single-chain mean-field theory (SCMF). This microscopic model is used to quantify the micellization process of these nonionic surfactants at 37 °C and has been shown to be able to quantitatively reproduce experimental data of the critical micelle concentration (CMC) along with other equilibrium properties. In particular, these results correctly capture the experimental behavior with respect to the lengths of the hydrophobic and hydrophilic moieties of the surfactants for low and medium hydrophobicities. However, for the more highly hydrophobic systems with low CMCs, a deviation is found which has been previously attributed to nonequilibrium effects in the experimental data (Garcı́a Daza, F. A.; Mackie, A. D. Low Critical Micelle Concentration Discrepancy between Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 2027-2032).

Low Critical Micelle Concentration Discrepancy between Theory and Experiment

Experimental measurements for a variety of surfactants unexpectedly show that the critical micelle concentration (CMC) becomes constant with respect to increasing the size of the hydrophobic tail. This observation disagrees with theoretical models where it is expected to continue to decrease exponentially. Because of the lack of a satisfactory explanation for such a discrepancy from theory, we have studied these systems using a coarse-grained model within the single-chain mean field (SCMF) theory combined with relevant micellar kinetic effects. In particular, a microscopic model for poly(ethylene oxide) alkyl ether was applied to describe a series of nonionic gemini surfactants. When kinetic effects are used to correct the equilibrium CMC values from the SCMF scheme together with the loss of surfactants due to adsorption on the experimental recipient, it is possible to reproduce the correct order of magnitude of the experimental CMC results. Hence it appears that the experimental values disagree with the theoretical predictions because they are not true equilibrium values due to the fact that the time scales for these low CMC values become astronomically large.