Self-organization of active matter as well as driven granular matter in non-equilibrium dynamical states has attracted considerable attention not only from the fundamental and application viewpoints but also as a model to understand the occurrence of such phenomena in nature. These systems share common features originating from their intrinsically out-of-equilibrium nature. It remains elusive how energy dissipation affects the state selection in such non-equilibrium states. As a simple model system, we consider a non-equilibrium stationary state maintained by continuous energy input, relevant to industrial processing of granular materials by vibration and/or flow. More specifically, we experimentally study roles of dissipation in self-organization of a driven granular particle monolayer. We find that the introduction of strong inelasticity entirely changes the nature of the liquid-solid transition from two-step (nearly) continuous transitions (liquid-hexatic-solid) to a strongly discontinuous first-order-like one (liquid-solid), where the two phases with different effective temperatures can coexist, unlike thermal systems, under a balance between energy input and dissipation. Our finding indicates a pivotal role of energy dissipation and suggests a novel principle in the self-organization of systems far from equilibrium. A similar principle may apply to active matter, which is another important class of out-of-equilibrium systems. On noting that interaction forces in active matter, and particularly in living systems, are often non-conservative and dissipative, our finding may also shed new light on the state selection in these systems.
We show that a generalized fluctuation-dissipation relation applies upon instantaneously increasing the temperature of a deeply supercooled liquid. This has the same two-step shape of the relation found upon cooling the liquid, but with opposite violation, indicating an effective temperature that is lower than bath temperature. We show that the effective temperature exhibits some sensible time-dependence and that it retains its connection with the partitioned phase space visited in ageing. We underline the potential relevance of our numerical results for experimental studies of the fluctuation…
The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, w…
We present evidence in favor of the possibility of treating an out-of-equilibrium supercooled simple liquid as a system in quasi-equilibrium. Two different temperatures, one controlled by the external bath and one internally selected by the system characterize the quasi-equilibrium state. The value of the internal temperature is explicitly calculated within the inherent structure thermodynamic formalism. We find that the internal temperature controls the relation between the response to an external perturbation and the long-time decay of fluctuations in the liquid.
Symmetry Breaking and Energy Dissipation in the Mechanical Response of Amorphous Solids
North University of China（中北大学）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；The Weizmann Institute of Science（魏茨曼科学研究所）
Minimal models of active and driven particles have recently been used to elucidate many properties non-equilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these non-equilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by the various non-conservative, time dependent forces - this quantifies a violation …
Mechanical inhibition of dissipation in a thermodynamically consistent active solid
Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）
We construct a phase field model including hydrodynamics and elasticity in one-component systems. It can be used to investigate solid-liquid and liquid-liquid phase transitions. Upon first-order phase transition, a velocity field is induced around interfaces in the presence of a density difference between the two phases even without applied shear flow. As applications, we present simulation results on two cases of melting, where a solid domain is placed on a heated wall in one case and is suspended in a warmer liquid under shear flow in the other. We find that the solid domain moves or rotates…
Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials which utilize such properties is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on this challenge. We first demonstrate analytically for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an…
In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient, characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity, involving a non-markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics, leading to superdiffusive motion of the fluctuating wall position.
We have developed a Green-Kubo relation that enables accurate calculations of friction at solid-liquid interfaces directly from equilibrium molecular dynamics (MD) simulations and that provides a pathway to bypass the time-scale limitations of typical nonequilibrium MD simulations. The theory has been validated for a number of different interfaces and it is demonstrated that the liquid-solid slip is an intrinsic property of an interface. Because of the high numerical efficiency of our method, it can be used in the design of interfaces for applications in aqueous environments, such as nano- and…
The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature, in out-of-equilibrium conditions at which the interfacial free energy is ill-defined. Here we draw a connection between the atomistic description of a diffuse solid- liquid interface and its thermodynamic characterization. This framework resolves the ambiguities in defining the solid-liquid interfacial free energy above and below the melting temperature. In …
We discuss the growth process of a crystalline phase out of a metastable over-compressed liquid that is brought into contact with a crystalline substrate. The process is modeled by means of molecular dynamics. The particles interact via the Lennard-Jones potential and their motion is locally thermalized by Langevin dynamics. We characterize the relaxation process of the solid-liquid interface, showing that the growth speed is maximal for liquid densities above the solid coexistence density, and that the structural properties of the interface rapidly converge to equilibrium-like properties. In …
We study the out-of-equilibrium dynamics following a temperature-jump in a model for a strong liquid, BKS-silica, and compare it with the well known case of fragile liquids. We calculate the fluctuation-dissipation relation, from which it is possible to estimate an effective temperature $T_{eff}$ associated to the slow out-of-equilibrium structural degrees of freedom. We find the striking and unexplained result that, differently from the fragile liquid cases, $T_{eff}$ is smaller than the bath temperature.
The curvature dependence of interfacial free energy, which is crucial in quantitatively predicting nucleation kinetics and the stability of bubbles and droplets, can be described in terms of the Tolman length δ. For solid-liquid interfaces, however,δ has never been computed directly due to various theoretical and practical challenges. Here we present a general method that enables the direct evaluation of the Tolman length from atomistic simulations of a solid-liquid planar interface in out-of-equilibrium conditions. This method works by first measuring the surface tension from the amplitude of…
We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be weakly dependent on the molecular structures used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.
There has been long-standing debate about the physical state and possible phase transformations of confined liquids. In this report we show that a model confined liquid can behave both as a Newtonian liquid with very little change in its dynamics or as a pseudo-solid depending solely on the {\it rate} of approach of the confining surfaces. Thus, the confined liquid does {\it not} exhibit any confinement induced solidification in thermodynamic equilibrium. Instead, solidification is induced kinetically, when the two confining surfaces are approached with a minimum critical rate. This critical r…
For a deeply supercooled liquid just above its glass transition temperature, we present a simple thermodynamic model, where the deeply supercooled liquid is assumed to be a mixture of solid-like and liquid-like micro regions. The mole fraction of the liquid-like regions controls the thermodynamic properties of the supercooled liquid while that of the solid-like regions controls its relaxation time or viscosity. From the universal temperature dependence of the molar excess entropy for the deeply supercooled liquids, we derive the temperature dependence of the mole fraction of the liquid-like re…
We present single contact friction experiments between a glassy polymer and smooth silica substrates grafted with alkylsilane layers of different coverage densities and morphologies. This allows us to adjust the polymer/substrate interaction strength. We find that, when going from weak to strong interaction, the response of the interfacial junction where shear localizes evolves from that of a highly viscous threshold fluid to that of a plastically deformed glassy solid. This we analyse as resulting from an interaction-induced ``interfacial glass transition'' helped by pressure.
We revisit the fundamental problem of liquid-liquid dewetting and perform a detailed comparison of theoretical predictions based on thin-film models with experimental measurements obtained by atomic force microscopy (AFM). Specifically, we consider the dewetting of a liquid polystyrene (PS) layer from a liquid polymethyl methacrylate (PMMA) layer, where the thicknesses and the viscosities of PS and PMMA layers are similar. The excellent agreement of experiment and theory reveals that dewetting rates for such systems follow no universal power law, in contrast to dewetting scenarios on solid sub…
The effective solid liquid interfacial tension (SL IFT) between pure liquids and rough solid surfaces is studied through coarse grained simulations. Using the dissipative particle dynamics method, we design solid liquid interfaces, confining a pure liquid between two explicit solid surfaces with different roughness degrees. The roughness of the solid phase was characterized by Wenzel roughness factor and the effective SL IFT (γ_sl^') is reported as a function of it also. Two solid liquid systems differentiated from each other by their solid liquid repulsion strength are studied to measure the …
Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the ``exact'' values obtained from their relations to excess energy and pressure. Some consequences, in particular, in the context of the Lindemann's melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.
The Ginzburg-Landau free energy functional for hard-spheres is constructed using the Fundamental Measure Theory approach to Density Functional Theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.
Deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotics. Expanding on this concept, beams can be designed so that the pressure in the channel-network is created directly from external forces acting on the beam, and thus can be viewed as passive solid-liquid composite structure. We obtain a continuous function relating the network geometry to the deformation. This enables design of networks creating arbitrary steady and time varying deformation-fields as well as to eliminate deformation created by external forces.
Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids. We review different approaches to liquids and propose that liquids do not need classifying in terms of their proximity to gases and solids. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This i…
In this supplementary paper we present some details on the solid-liquid interface detection, the deduction of the non-equilibrium free energy, the analysis of the granular temperature and energy per mode, a validation of the small slope approximation, a description of the Langevin dynamics, and the error analysis.
From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and engineering materials. Eshelby's inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a composite's bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelby's theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated droplet's deformation is…
We have given theoretical expressions for the forces exerted on a quasi-2D flat and smooth solid plate immersed into a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. We also revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γ_{SL} and γ_{SV}, and this was verified through the comparison with the SL and SV works of adhesion obtained by the…
A solid withdrawn from a liquid bath entrains a film. In this review, after recalling the predictions and results for pure Newtonian liquids coated on simple solids, we analyze the deviations to this ideal case exploring successively three potential sources of complexity: the liquid-air interface, the bulk rheological properties of the liquid and the mechanical or chemical properties of the solid. For these different complexities, we show that significant effects on the film thickness are observed experimentally and we summarize the theoretical analysis presented in the literature, which attem…
We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations", which grow as the 3/4th power of the mean number. Stable systems also exhibit anomalous rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction pe…
The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several different approaches to explain the thermal conductivities for these systems, for example, the Bridgman's formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to explain the thermal conductivities of liquids and amorphous solids in a unified way. The calculated thermal conductivities using this form…
Soft materials with a liquid component are an emerging paradigm in materials design. The incorporation of a liquid phase, such as water, liquid metals, or complex fluids, into solid materials imparts unique properties and characteristics that emerge as a result of the dramatically different properties of the liquid and solid. Especially in recent years, this has led to the development and study of a range of novel materials with new functional responses, with applications in topics including soft electronics, soft robotics, 3D printing, wet granular systems and even in cell biology. Here we pr…
The paper analyses kinematics and dynamics of internal rotations with spin and their effects on the constitutive relations for uniaxial (nematic) liquids and for weakly elastic nematic solids. It is shown that neglecting the internal rotational inertia terms and effects of director gradient made the stress symmetric. This not only highly simplifies the theories but also allows calculating all the kinematic variables of internal rotations without any additional constants, other than those presented in the simplified theory with symmetric stress.
Compared to nanoscale friction of translational motion, the mechanisms of rotational friction have received less attention. Such motion becomes an important issue for the miniaturization of mechanical machineries which often involve rotating gears. In this study, molecular dynamics simulations are performed to explore rotational friction for solid-state gears rotating on top of different substrates. In each case, viscous damping of the rotational motion is observed and found to be induced by the pure van-der-Waals interaction between gear and substrate. The influence of different gear sizes an…
A sharp phase transition from a crystalline state with the area per molecule A = (17 +/- 1) Angstrom^2 to a liquid state with A = (23 +/- 1) Angstrom^2 at the n-hexane - water interface in a Gibbs monolayer of melissic acid has been revealed in data of X-ray reflectometry with the use of synchrotron radiation.
When a multicomponent liquid composed of particles with random interactions is slowly cooled below the freezing temperature, the fluid reorganises in order to increase (decrease) the number of strong (weak) attractive interactions and solidifies into a microphase-separated structure composed of domains of strongly and of weakly interacting particles. Using Langevin dynamics simulations of a model system we find that the limiting tensile strength of such solids can exceed that of one-component solids.
Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounti…
The structure of the soluble protonated (pH=2) octadecanoic acid film adsorbed on the saturated hydrocarbon (n-hexane) - water and aromatic hydrocarbon (toluene)-water interfaces is studied by X-ray reflectometry using synchrotron radiation. The experimental data demonstrate that a solid phase of a Gibbs monolayer (26 +/- 1) Angstrom thick, in which aliphatic tails are perpendicular to the surface and the area per molecule is A=(18 +/- 2) Angstrom^2, forms in the film at the n-hexane - water interface. The solid monolayer on the toluene - water interface in the adsorbed film melts when tempera…
The capillary forces exerted by liquid drops and bubbles on a soft solid are directly measured using molecular dynamics simulations. The force on the solid by the liquid near the contact line is not oriented along the liquid vapor interface nor perpendicular to the solid surface, as usually assumed, but points towards the liquid. It is shown that the elastic deformations induced by this force can only be explained if, contrary to an incompressible liquid, the surface stress is different from the surface energy. Using thermodynamic variations we show that the the surface stress and the surface …
According to experimental data on X-ray scattering and reflectometry with the use of synchrotron radiation, a two-dimensional crystallization phase transition in a monolayer of melissic acid at the n-hexane - water interface with a decrease in the temperature occurs after a wetting transition.
The solid-liquid phase-diagram of charge-stabilized colloidal suspensions is calculated using a technique that combines a continuous Poisson-Boltzmann description for the microscopic electrolyte ions with a molecular-dynamics simulation for the macroionic colloidal spheres. While correlations between the microions are neglected in this approach, many-body interactions between the colloids are fully included. The solid-liquid transition is determined at a high colloid volume fraction where many-body interactions are expected to be strong. With a view to the Derjaguin-Landau-Verwey-Overbeek theo…
We study the interface between a solid trapped within a bath of liquid by a suitably shaped non-uniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields or a surface template. We study a two dimensional case where a thin strip of solid, created in this way, is surrounded on either side by a bath of liquid with which it can easily exchange particles. Since height fluctuations of the interface cost energy, this interface is constrained to remain flat at all length scales. However, when such a solid is stressed by altering the depth of the…
We study experimentally the pressure drop needed to push a bubble train in a millimetric channel, as a function of the velocity. For dry liquid foams, the influence of the amount of liquid and of the bubble size is pointed out and we predict theoretically that this influence is closely related to the power law obtained for the force/velocity relation. This model is in fair agreement with our experimental data and provides a new interpretation of previous results.
We apply microcanonical ensemble considerations to suggest that, whenever it may thermalize, a general disorder-free many-body Hamiltonian of a typical atomic system has solid-like eigenstates at low energies and fluid-type (and gaseous, plasma) eigenstates associated with energy densities exceeding those present in the melting (and, respectively, higher energy) transition(s). In particular, the lowest energy density at which the eigenstates of such a clean many body atomic system undergo a non-analytic change is that of the melting (or freezing) transition. We invoke this observation to analy…
We have studied the slip length of confined liquid with small roughness of solid-liquid interfaces. Dyadic Green function and perturbation expansion have been applied to get the slip length quantitatively. In the slip length, both effects of the roughness of the interfaces and the chemical interaction between the liquid and the solid surface are involved. For the numerical calculation, Monte Carlo method has been used to simulate the rough interfaces and the physical quantities are obtained statistically over the interfaces. Results show that the total slip length of the system is linearly pro…
We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the total free energy from the interface contribution, performed a finite-size scaling analysis and obtained for the (100)-interface $γ=0.591(11)k_{B}Tσ^{-2}$.
Solid/liquid interfaces control various processes of technological relevance in the process industry and many fundamental physicochemical phenomena. This work examines the link between the atomistic description of mass transfer at solid/liquid interfaces out of equilibrium and the constitutive mass transfer equations typically used to model these processes at the mesoscale. In our analysis, we discuss the microscopic inconsistencies apparent in simplified models of mass transfer whenever non-idealities dominate the liquid phase in the proximity of solid/liquid interfaces. Using CμMD - a molecu…
The surface free energy, or surface tension, of a liquid interface gives rise to a pressure jump when the interface is curved. Here we show that a similar capillary pressure arises at the interface of soft solids. We present experimental evidence that immersion of a thin elastomeric wire into a liquid induces a substantial elastic compression due to the solid capillary pressure at the bottom. We quantitatively determine the effective surface tension from the elastic displacement field, and find a value comparable to the liquid-vapor surface tension. Most importantly, these results also reveal …
We calculate the energy and heat capacity of a liquid on the basis of its elastic properties and vibrational states. The experimental decrease of liquid heat capacity with temperature is attributed to the increasing loss of two transverse modes with frequency $ω<1/τ$, where $τ$ is liquid relaxation time. In a simple model, liquid heat capacity is related to viscosity and is compared with the experimental data of mercury. We also calculate the vibrational energy of a quantum liquid, and show that transverse phonons can not be excited in the low-temperature limit. Finally, we discuss the implica…
Single-run determination of the saturation vapor pressure and enthalpy of vaporization/sublimation of a substance undergoing successive solid-solid and solid-liquid phase transitions: the case of $N$-methyl acetamide
