We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory of the glass transition (MCT). Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multi-component calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behaviour is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor, and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantiative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behaviour are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.
The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematical model: It does not rely on assuming a particular distribution function of the particles.
The calculation of discrete or continuous relaxation time spectra from rheometric measurables of polydisperse polymers is an ill-posed problem. In this paper, a curve fitting method for solving this problem is presented and compared to selected models from the literature. It is shown that the new method is capable of correctly predicting the molecular mass distributions of linear polydisperse polymer melts as well as their relaxation time spectra.
Slow dynamics in a fluid are studied in one of the most basic systems possible: polydisperse hard spheres. Monodisperse hard spheres cannot be studied as the slow down in dynamics as the density is increased is preempted by crystallisation. As the dynamics slow they become more heterogeneous, the spread in the distances traveled by different particles in the same time increases. However, the dynamics appears to be less heterogeneous than in hard-sphere-like colloids at the same volume fraction. The particles which move least far in a characteristic relaxation time and, particularly, the partic…
Flow-history-dependent orientational relaxation in dilute polydisperse colloidal rod suspensions
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；University of the Basque Country UPV/EHU（巴斯克地区大学）；University of Cambridge（剑桥大学）
We study numerically the crystallization of a hard-sphere mixture with 8\% polydispersity. Although often used as a model glass former, for small system sizes we observe crystallization in molecular dynamics simulations. This opens the possibility to study the competition between crystallization and structural relaxation of the melt, which typically is out of reach due to the disparate timescales. We quantify the dependence of relaxation and crystallization times on density and system size. For one density and system size we perform a detailed committor analysis to investigate the suitability …
The mechanism behind the $^1$H NMR frequency dependence of $T_1$ and the viscosity dependence of $T_2$ for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies ($f_0 = 0.01 \leftrightarrow$ 400 MHz) and viscosities ($η= 385 \leftrightarrow 102,000$ cP) using $T_{1}$ and $T_2$ in static fields, $T_{1}$ field-cycling relaxometry, and $T_{1ρ}$ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times $T_{1LM} \propto f_0$ and $T_{2LM} \propto…
Standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during to the integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting from a short time approximation of the Smoluchowsky equation, we introduce an algorithm for the simulation of the overdamped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamics interactions and briefly discuss the extension to the case of external drifts.
We study the role of filler concentration and microphysics on the rheology of polydisperse flake-graphite particles suspended in Newtonian mineral oil. Under steady shear, our samples exhibit shear thinning and yielding behaviour is observed for volume fractions $ϕ> 0.18$. Time-temperature superposition was observed using an Arrhenius-type horizontal shift factor, giving a flow activation energy that is dependent on the graphite volume fraction, suggesting concentration-dependent contributions to relaxation processes in the suspensions. The flow curves are fitted by a constraint-based model, i…
We study jammed configurations of hard spheres as a function of compression speed using an event-driven molecular dynamics algorithm. We find that during the compression, the pressure follows closely the metastable liquid branch until the system gets arrested into a glass state as the relaxation time exceeds the compression speed. Further compression yields a jammed configuration that can be regarded as the infinite pressure configuration of that glass state. Consequently, we find that the density of jammed packings varies from 0.638 to 0.658 for polydisperse hard spheres and from 0.635 to 0.6…
The static and the dynamic properties of a size-polydisperse model ionic liquid is studied using molecular dynamics simulations. Here, size of the anions is derived from a Gaussian distribution while keeping cation size fixed, resulting in a system that closely corresponds to IL mixtures with a common cation. We systematically explore the behavior of thermodynamic transition temperatures, spatial ordering of ions and the resulting screening behavior as a function of polydispersity index, $δ$. We observe a non-monotonic dependence of transition temperatures on $δ$, and this non-monotonic behavi…
Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from simulations. In this paper I put the DEFM on firm theoretical ground by deriving it within the framework of dynamical density functional theory (DDFT), in which the relevant part of correlation-induced free energy is approximated by a function of the instantaneous magnetization. The DEFM is generalized to inhomogeneous finite-size samples for which the macroscopic and mesoscopic scale …
A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approx…
We consider the thermal relaxation of a particle in a piecewise-constant potential landscape subject to thermal fluctuations in the overdamped limit. We study the connection between the occurrence of the Mpemba effect, the presence of metastable states, and phase transitions as a function of the potential. We find that the Mpemba effect exists even in cases without metastable states. In the considered physical system, the borders of the areas where the effect happens correspond to either eigenvector changes of direction or to phase transitions. Finally, we discuss the topological aspects of th…
Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored -- especially how chains of different lengths affect the dynamics of one another in a mixture. This study explored the dynamics of bidisperse polymer melts using molecular dynamics and a bead-spring chain model. Binary mixtures between a moderately entangled long-chain species and an unentangled or marginally entangled short-chain species were investigated.…
We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a perturbed velocity distribution toward the equilibrium Maxwellian solution. We work out the cases of discrete as well as continuous distributions of masses, as found in dilute fluids of mesoscopic particles such as granular matter and colloids. On the basis of analytical and numerical evidence, we formulate a dynamical equipartition principle that leads to the resu…
Using molecular dynamics simulations we study the static and dynamic properties of spherical nanoparticles (NPs) embedded in a disordered and polydisperse polymer network. Purely repulsive (RNP) as well as weakly attractive (ANP) polymer-NP interactions are considered. It is found that for both types of particles the NP dynamics at intermediate and at long times is controlled by the confinement parameter $C=σ_N/λ$, where $σ_N$ is the NP diameter and $λ$ is the dynamic localization length of the crosslinks. Three dynamical regimes are identified: i) For weak confinement ($C \lesssim 1$) the NPs…
Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs. We describe the structural relaxation of a tagged molecule as a coupled process of cage-scale dynamics and collective molecular rearrangement beyond the first coordination shell. The coupling between local and non-local dynamics behaves distinctly in different substances. Theoretical calculations for the structural relaxation time, glass transition temperature, and dynamic fragility are carried out over twenty-two amorphous drugs and polymers. Numerical results have a qua…
The relaxation dynamics of a polymer wound around a fixed obstacle constitutes a fundamental instance of polymer with twist and torque and it is of relevance also for DNA denaturation dynamics. We investigate it by simulations and Langevin equation analysis. The latter predicts a relaxation time scaling as a power of the polymer length times a logarithmic correction related to the equilibrium fluctuations of the winding angle. The numerical data support this result and show that at short times the winding angle decreases as a power-law. This is also in agreement with the Langevin equation prov…
We study a relaxation behavior of an Ornstein-Uhlenbeck (OU) process with a time-dependent and fluctuating diffusivity. In this process, the dynamics of a position vector is modeled by the Langevin equation with a linear restoring force and a fluctuating diffusivity (FD). This process can be interpreted as a simple model of the relaxational dynamics with internal degrees of freedom or in a heterogeneous environment. By utilizing the functional integral expression and the transfer matrix method, we show that the relaxation function can be expressed in terms of the eigenvalues and eigenfunctions…
We study the dynamics of a suspension of magnetic nanoparticles. Their relaxation times are strongly size-dependent. The dominant mode of relaxation is also governed by the size of the particles. As a result the dynamics is greatly altered due to polydispersity in the sample. We study the effect of polydispersity on the response functions. These exhibit significant changes as the parameters characterizing polydispersity are varied. We also provide a procedure to extract the particle size distribution in a polydisperse sample using Cole-Cole plots. Further the presence of attractive interaction…
Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface…
An advance was made by Guiselin et al. [arXiv:2103.01569 (2021)] in molecular dynamics simulations of the equilibrium dynamics of supercooled liquids near the experimental glass transition by utilizing the giant equilibration speedup provided by the swap Monte Carlo algorithm. The found emergence of a power law in relaxation spectra at lower temperatures on the high frequency flank of the alpha-loss peak in analogy to the excess wings observed experimentally in molecular glass-formers. Their remarkable finding leads to the question of where the excess wing is located relative to the alpha-loss…
We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory. By invoking a high temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron scattering measurements. In contrast, in the same format strongly non-universal behavior is found for the activation barrier that controls lo…
Finite-inertia effects in Langevin dynamics of a lopsided elastic dumbbell using exponential-time differencing schemes
State Key Laboratory of Fluid Power and Mechatronic Systems and Department of Engineering Mechanics, Zhejiang University（浙江大学流体动力与机电系统国家重点实验室和工程力学系）；Zhejiang Key Laboratory of Intelligent High Speed UAV Technology（浙江省智能高速无人机技术重点实验室）；Innovation Center of Yangtze River Delta, Zhejiang University（浙江大学长三角创新中心）；Department of Mechanical Engineering, National University of Singapore（新加坡国立大学机械工程系）；Mekong University (MKU)（湄公河大学）
The adsorption of single colloidal microparticles (0.5--1 $μ$m radius) at a water-oil interface has been recently studied experimentally using digital holographic microscopy [Kaz \textit{et al., Nat. Mater.}, 2012, \textbf{11}, 138--142]. An initially fast adsorption dynamics driven by capillary forces is followed by an unexpectedly slow relaxation to equilibrium that is logarithmic in time and can span hours or days. The slow relaxation kinetics has been attributed to the presence of surface "defects" with nanoscale dimensions (1--5\,nm) that induce multiple metastable configurations of the c…
We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more rece…
Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as $t^α$ for some $α<1$ until the terminal relaxation time $τ$ of the polymer. Beyond time $τ$ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts…
The biological properties of proteins are uniquely determined by their structure and dynamics. A protein in solution populates a structural ensemble of metastable configurations around the global fold. From overall rotation to local fluctuations, the dynamics of proteins can cover several orders of magnitude in time scales. We propose a simulation-free coarse-grained approach which utilizes knowledge of the important metastable folded states of the protein to predict the protein dynamics. This approach is based upon the Langevin Equation for Protein Dynamics (LE4PD), a Langevin formalism in th…
Based on a microscopic system reservoir model,where the associated bath is not in thermal equilibrium, we simulate the nonstationary Langevin dynamics and obtained the generalized nonstationary fluctuation dissipation relation (FDR) which asymptotically reduces to the traditional form. Our Langevin dynamics incorporates non-Markovian process also, the origin of which lies on the decaying term of the nonstationary FDR. We then follow the stochastic dynamics of the Langevin particle based on the Fokker-Planck-Smoluchowski description, in ratchet potential to obtain the steady and time dependent …
The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature $β$ and the particle density $ρ$. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small $β$ and $ρβ$ constant. The one-loop result can also be re-summed using a semi-phenomen…
The binary Voronoi mixture is a fluid model whose interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the structural relaxation of this mixture in the supercooled-liquid regime. From the simulations we determine the time- and temperature-dependent scattering functions for a large range of wave vectors, as well as the mean-square displacements of both particle species. We perform a detailed analysis of the dynamics by comparing the MD results with the first-princip…
We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore significantly slows-down the molecular dynamics when increasing the pressure. We quantitatively determine the temperature and pressure dependence of the structural relaxation time. To validate our model, dielectric spectroscopy experiments for three rigid and non-polymeric supramolecules are carried out at ambient and elevated pressures. The numerica…
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 theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulation. An external pressure restricts local motions of a single molecule within its cage and triggers the slowing down of cooperative mobility. While the ECNLE theory and simulation generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulation indicates a decrease of fragility as pressure above 10…
We propose a simple approach to investigate the structural relaxation time and glass transition of amorphous drugs. Amorphous materials are modeled as a set of equal sized hard spheres. The structural relaxation time over many decades in hard sphere fluids is theoretically calculated using the Elastically Collective Nonlinear Langevin Equation theory associated with Kramer's theory. Then, a new thermal mapping from a real material to an effective hard sphere fluid provides temperature-dependent relaxation time, which can compare to experiments. Numerical results quantitatively agree with previ…
We generalize the force-level Nonlinear Langevin Equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cag…
A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres. Effects of nearest-neighbor interactions and cooperative motions of particles on glassy dynamics are quantified through a local and collective elastic barrier calculated using the Elastically Collective Nonlinear Langevin Equation theory. Inserting two barriers into Kramer's theory gives structural relaxation time. Then, we formulate a new mapping based on the t…
The dynamics of glass-forming liquids display several outstanding features, such as two-step relaxation and dynamic heterogeneities, which are difficult to predict quantitatively from first principles. In this work, we revisit a simple theoretical model of the $β$-relaxation, i.e., the first step of the relaxation dynamics. The model, first introduced by Cavagna et al., describes the dynamics of the system in the neighborhood of a saddle point of the potential energy surface. We extend the model to account for density-density correlation functions and for the 4-point dynamic susceptibility. We…
We use a microscopically motivated Generalized Langevin Equation (GLE) approach to link the vibrational density of states (VDOS) to the dielectric response of orientational glasses (OGs). The dielectric function calculated based on the GLE is compared with experimental data for the paradigmatic case of two OGs: Freon 112 and Freon 113, around and just above $T_g$. The memory function is related to the integral of the VDOS times a spectral coupling function $γ(ω_p)$, which tells the degree of dynamical coupling between molecular degrees of freedom at different eigenfrequencies. The comparative …
Multiscale Prediction of Polymer Relaxation Dynamics via Computational and Data-Driven Methods
Faculty of Materials Science and Engineering, Phenikaa University（菲尼卡大学材料科学与工程系）；Phenikaa Institute for Advanced Study, Phenikaa University（菲尼卡大学高级研究院）；Center for Materials Innovation and Technology, VinUniversity（Vin大学材料与技术创新中心）
