Arrhenius Dynamics Research Articles

The thermal response of the ignition and combustion of high-energy material projectiles under the influence of heat

The thermal response of energetic materials involves processes of thermochemical mechanical coupling, which can lead to thermal damage in such materials both before and after ignition, thereby increasing ignition sensitivity and the level of danger. Many studies to date have either neglected or oversimplified the effects of thermal coupling, leading to significant discrepancies between simulated and experimental outcomes. This paper aims to examine the complex processes of ammunition ignition, combustion, and detonation. Employing finite element simulations in conjunction with Arrhenius dynamics and the ignition growth model theory under thermodynamic coupling analysis, it simulates the entire process from the thermal expansion of B explosive prior to ignition, through to combustion and detonation. It establishes the relationship between the damage and fracture state of the shell and the thermal response of the energetic material at varying heating rates. Findings indicate that the severity of the thermal response is determined by the balance between pressure accumulation and the loss of confinement leading to pressure release. Specifically, at heating rates below 0.25 K/min, the shell fractures before combustion of the energetic material; whereas, at rates exceeding 0.375 K/min, the shell fractures after combustion, significantly increasing the risk. The simulation outcomes of this study show strong correlation with experimental results reported in the literature, offering a valuable reference for simulating the ignition and combustion responses of ammunition with similar structural characteristics.

Application of the dynamic Monte Carlo method to pedestrian evacuation dynamics

In this study, we investigate a two-dimensional lattice model for crowd evacuation dynamics by using a dynamic Monte Carlo (DMC) method. This model is built on the microscopic Arrhenius dynamics along with the exclusion rule in which stochastic processes govern the individual movements depending on the relative distance to the room exit. Even though individual decision-making procedures can be complicated during the evacuation in an emergency, our model can quantitatively estimate the time for them to evacuate and predict the emerging patterns of the crowds during the process. The results exhibit the phenomena such that pedestrians spontaneously gather at the exit and form an arched shape close to the door. The DMC simulations and observations agree with the corresponding study in the literature. The DMC algorithm is computationally efficient due to its major property —“rejection-free”, which makes it a suitable tool to simulate evacuation dynamics for a large group of pedestrians.

Deviations from Arrhenius dynamics in high temperature liquids, a possible collapse, and a viscosity bound

Liquids realize a highly complex state of matter in which strong competing kinetic and interaction effects come to life. As such, liquids are more challenging to understand than either gases or solids generally. In weakly interacting gases, the kinetic effects dominate. By contrast, low temperature solids typically feature far smaller fluctuations about their ground state. Notwithstanding their complexity, with the exception of quantum fluids and supercooled liquids, various aspects of common liquid dynamics such as their dynamic viscosity are often assumed to be given by rather simple, Arrhenius-type, activated forms with nearly constant (i.e., temperature independent) energy barriers. In this work, we analyze experimentally measured viscosities of numerous liquids far above their equilibrium melting temperature to see how well this assumption fares. We find, for the investigated liquids, marked deviations from simple activated dynamics. Even far above their equilibrium melting temperatures, as the temperature drops, the viscosity of these liquids increases more strongly than predicted by activated dynamics dominated by a single uniform energy barrier. For metallic fluids, the scale of the prefactors of the best Arrhenius fits for the viscosity is typically consistent with that given by the product $nh$ with $n$ the number density and $h$ Planck's constant. In various fluids that we examined, $nh$ constitutes a lower bound scale on the viscosity. We find that a scaling of the temperature axis (complementing that of the viscosity) leads to a partial collapse of the temperature dependent viscosities of different fluids; such a scaling allows for a functional dependence of the viscosity on temperature that includes yet is far more general than activated Arrhenius form alone. We speculate on relations between non-Arrhenius dynamics and thermodynamic observables.

Relaxation dynamics and growth modes of metastable spin-crossover materials with magnetic interactions

A two-dimensional spin-1 Blume-Emery-Griffiths (BEG) model is used to describe the relaxation dynamics of spin-crossover (SC) compounds with magnetic interactions from a metastable high-spin state by means of Monte Carlo simulations with Arrhenius dynamics. The model comprises temperature-dependent effective spin exchange interaction accounting for spin-phonon interactions. The growth modes of the stable low-spin state domains are singled out in the model parameters' space. For weak magnetic interactions, numerical results indicated a kind of 2D-nucleation with the birth, spread and coalescence of low-spin diamagnetic domains following the Becker-Doering law. A schematic growth phase diagram is presented.

Surface roughness evolution in a solid-on-solid model of epitaxial growth

The paper presents results from kinetic Monte Carlo simulations of kinetic surface roughening using an important and experimentally relevant model of epitaxial growth—the solid-on-solid model with Arrhenius dynamics. A restriction on diffusing adatoms is included allowing hopping down only at steps of height one monolayer in order to avoid possibly unrealistic events of jumping from arbitrarily high steps. Simulation results and precise analytic expressions representing the time evolution of surface roughness do not depend on the substrate size and clearly put forward the conclusion that for any basic set of parameters, the model approaches in asymptotic limit the usual random deposition process with growth exponent \(\beta =1/2\). At high temperatures, it is preceded by a long transient regime characterized by a smooth surface covered with porous pillars and described by a power law with \(\beta =3/4\).

Depth profile of the segmental dynamics at a poly(methyl methacrylate) film surface

We investigated the segmental mobility distribution at the poly(methyl methacrylate) film surface within the depth of 9.0 nm, by measuring the surface reorganization of fluorinated tracer-labeled PMMA using three different surface-sensitive techniques with various analytical depth capabilities, including contact angle measurements, sum frequency generation (SFG) vibrational spectra and angle-resolved X-ray photoelectron spectroscopy (XPS). The onset temperature of fluorinated chain end reorganization (Tonset) at various depths was identified and is shown to depend on the sampling depth of the techniques. The Tonset was verified to be related to the segmental relaxation of PMMA. Plotting the Tonset against the sensing depth of the corresponding technique, the distribution of surface Tonset within a 9.0 nm depth was obtained. An approximately 2.4 nm surface layer with depth-independent Tonset was found, below which the Tonset increased with increasing depth. The depth profile of Tonset effectively divides a film into three layers: a “surface layer” with Arrhenius dynamics on the uppermost film surface, a “gradient region” layer underneath the top layer transporting “liquid-like” dynamics into the internal film, and the remaining bulk layer. This observed depth profile of the surface dynamics may suggest that the polymer chains near the surface adopt an oblate conformation and have lowered entanglements.

Analysis of long-range interaction effects on phase transitions in two-step spin-crossover chains by using Ising-type systems and Monte Carlo entropic sampling technique

The analysis of two-step spin crossover phenomena in one-dimensional systems is performed in the framework of Ising-type model by using Monte Carlo entropic sampling technique. Both short-range and long-range interactions are considered in the Hamiltonian which also takes into account different degeneracies between the molecular states. The density of states associated to each macrostate is computed by using entropic sampling, via a biased Monte Carlo sampling technique, and the corresponding Ising-type Hamiltonian can thus be solved by using a self-consistent approach. By using this semi-analytical method, the effects of long-range interactions on phase transition driven by temperature variation in spin crossover chains have been investigated. Various types of spin crossover phenomena have been identified from gradual two-step transition to the one accompanied by multiple hysteresis loops, which was also recently observed experimentally. A metastable “plateau” has been observed at a high-spin fraction approximately equal to ½ for intermediate temperature region, but this plateau is not part of the low-to-high spin transition in strong cooperative systems and might be reached only by using special reversal curves or other external factors, such as light or pressure. In addition, a standard Monte-Carlo algorithm with Arrhenius dynamics is applied to this system in order to better understand its molecular behavior during the intermediate phase.

Size dependent thermal hysteresis in spin crossover nanoparticles reflected within a Monte Carlo based Ising-like model

Spin crossover compounds are photo-magnetic bistable molecular magnets with two states in thermodynamic competition: the diamagnetic low-spin state and paramagnetic high-spin state. The thermal transition between the two states is often accompanied by a wide hysteresis, premise for possible application of these materials as recording media. In this paper we study the influence of the system's size on the thermal hysteresis loops using Monte Carlo simulations based on an Arrhenius dynamics applied for an Ising like model with long- and short-range interactions. We show that using appropriate boundary conditions it is possible to reproduce both the drop of hysteresis width with decreasing particle size, the hysteresis shift towards lower temperatures and the incomplete transition, as in the available experimental data. The case of larger systems composed by several sublattices is equally treated reproducing the shrinkage of the hysteresis loop's width experimentally observed.

Anomalies in supercooled NaCl aqueous solutions: A microscopic perspective

In this work we studied the effect of NaCl on the thermodynamic and dynamic properties of supercooled water, for salt concentrations between 0.19 and 1.33 mol kg(-1), using molecular dynamic simulations for TIP5P∕E water model and ion parameters specially designed to be used in combination with this potential. We studied the isobaric heat capacity (C(p)) temperature dependence and observed a maximum in C(p), occurring at T(m), that moves to lower temperature values with increasing salt concentration. Many characteristic changes were observed at scaled temperature T∕T(m) ∼ 0.96, namely a minimum in the density of the system, a reduction of the slope of the number of hydrogen bonds vs. temperature, and a crossover from Vogel-Tamman-Fulcher to Arrhenius dynamics. Finally, at low temperatures we observed that water dynamics become heterogeneous with an apparently common relationship between the fraction of immobile molecules and T/T(m) for all studied systems.

Anomalous diffusion in heterogeneous glass-forming liquids: Temperature-dependent behavior

In a preceding paper, Langer and Mukhopadhyay [Phys. Rev. E 77, 061505 (2008)] studied the diffusive motion of a tagged molecule in an heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation between heterogeneity and stretched-exponential decay of correlations, and we also confirmed that systems of this kind generally exhibit non-Gaussian diffusion on intermediate length and time scales. Here I extend this analysis to higher temperatures approaching the point where the heterogeneities disappear and thermal activation barriers become small. I start by modifying the continuous-time random-walk theory proposed in Langer and Mukhopadhyay and supplement this analysis with an extension of the excitation-chain theory of glass dynamics. I also use a key result from the shear-transformation-zone theory of viscous deformation of amorphous materials. Elements of each of these theories are then used to interpret experimental data for orthoterphenyl, specifially, the diffusion and viscosity coefficients and neutron-scattering measurements of the self-intermediate scattering function. Reconciling the theory with these data sets provides insights into the crossover between super-Arrhenius and Arrhenius dynamics, length scales of spatial heterogeneities, violation of the Stokes-Einstein relation in glass-forming liquids, and the origin of stretched-exponential decay of correlations.

Dynamics and thermodynamics of water

On decreasing the temperatureT, the correlationtime τ of supercooled water displays a dynamic crossover from non-Arrhenius dynamics (withT-dependent activationenergy) at high T to Arrhenius dynamics (with constant activation energy) at lowT. Simulations for water models show that this crossover occurs at thelocus of maximum isobaric specific heat in the pressure–temperature(P–T) plane. Results of simulations show also that at this locus there is a sharp change oflocal structure: more tetrahedral below the locus, and less tetrahedral above it.Furthermore, in water solutions with proteins or DNA, simulations show thatin correspondence with this locus there is a crossover in the dynamics of thebiomolecules, a phenomenon commonly known as the protein glass transition.To clarify the relation of the dynamic crossover with the thermodynamics ofwater, we study the dynamics of a cell model of water which can be tuned toexhibit: (1) a first-order phase transition line that separates the liquids of highand low densities at low temperatures; this phase transition line terminates ata liquid–liquid critical point (LLCP), from which departs the Widom lineTW(P), i.e. the line of maximum isobaric specific heat in theP–T plane; (2) the singularity-free (SF) scenario, under which the system exhibits water-likeanomalies but with no finite temperature liquid–liquid critical point.We find that the dynamic crossover is present in both the LLCP andthe SF cases. Moreover, on the basis of the study of the probabilitypB of forming a bond, we propose and verify a relation between dynamics and thermodynamicsthat is able to show how the crossover is a consequence of a local relaxation processassociated with breaking a bond and reorienting the molecule. We further find a distinctdifference in pressure dependence of the dynamic crossover between the LLCP and SFscenarios, which may help in resolving which of the scenarios correctly explains theanomalous behavior of water.

Molecular mechanisms of liquid slip

It is now well-established that the liquid adjacent to a solid need not be stationary – it can slip. How this slip occurs is unclear. We present molecular-dynamics (MD) simulation data and results from an analytical model which support two mechanisms of slip. At low levels of forcing, the potential field generated by the solid creates a ground state which the liquid atoms preferentially occupy. Liquid atoms hop through this energy landscape from one equilibrium site to another according to Arrhenius dynamics. Visual evidence of the trajectories of individual atoms on the solid surface supports the view of localized hopping, independent of the dynamics outside a local neighbourhood. We call this defect slip. At higher levels of forcing, the entire layer slips together, obviating the need for localized defects and resulting in the instantaneous motion of all atoms adjacent to the solid. The appearance of global slip leads to an increase in the number of slipping atoms and consequently an increase in the slip length. Both types of slip observed in the MD simulations are described by a dynamical model in which each liquid atom experiences a force from its neighbouring liquid atoms and the solid atoms of the boundary, is sheared by the overlying liquid, and damped by the solid. In agreement with the MD observations, this model predicts that above a critical value of forcing, localized slipping occurs in which atoms are driven from low-energy sites, but only if there is a downstream site which has been vacated. Also as observed, above a second critical value, all the liquid atoms adjacent to the wall slip. Finally, the dynamical equation predicts that at extremely large values of forcing, the slip length approaches a constant value, in agreement with the MD simulation results.

Field-driven solid-on-solid interfaces moving under a stochastic Arrhenius dynamics: Effects of the barrier height

We present analytical results and kinetic Monte Carlo simulations for the mobility and microscopic structure of solid-on-solid (SOS) interfaces driven far from equilibrium by an external force, such as an applied field or (electro)chemical potential difference. The interfaces evolve under a specific stochastic dynamics with a local energy barrier (an Arrhenius dynamics), known as the transition dynamics approximation (TDA). We calculate the average height of steps on the interface, the average interface velocity, and the skewness of the interface as functions of the driving force and the height of the energy barrier. We find that the microscopic interface structure depends quite strongly on the barrier height. As the barrier becomes higher, the local interface width decreases and the skewness increases, suggesting increasing short-range correlations between the step heights.

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

We study the microscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (electro)chemical potential. We use an analytic nonlinear-response approximation [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] together with kinetic Monte Carlo simulations. Here we consider interfaces that move under Arrhenius dynamics, which include a microscopic energy barrier between the allowed Ising/lattice-gas states. Two different dynamics are studied: the standard one-step dynamic (OSD) [H.C. Kang and W. Weinberg, J. Chem. Phys. 90, 2824 (1992)] and the two-step transition-dynamics approximation (TDA) [T. Ala-Nissila, J. Kjoll, and S.C. Ying, Phys. Rev. B 46, 846 (1992)]. In the OSD the effects of the applied force and the interaction energies in the model factorize in the transition rates (a soft dynamic), while in the TDA such factorization is not possible (a hard dynamic). In full agreement with previous general theoretical results we find that the local interface width under the TDA increases dramatically with the applied force. In contrast, the interface structure with the OSD is only weakly influenced by the force, in qualitative agreement with the theoretical expectations. Results are also obtained for the force-dependence and anisotropy of the interface velocity, which also show differences in good agreement with the theoretical expectations for the differences between soft and hard dynamics. Our results confirm that different stochastic interface dynamics that all obey detailed balance and the same conservation laws nevertheless can lead to radically different interface responses to an applied force.

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers.

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.

Coarse-grained microscopic model of glass formers.

We introduce a coarse-grained model for atomic glass formers. Its elements are physically motivated local microscopic dynamical rules parameterized by observables. Results of the model are established and used to interpret the measured behaviors of supercooled fluids approaching glass transitions. The model predicts the presence of a crossover from hierarchical super-Arrhenius dynamics at short length scales to diffusive Arrhenius dynamics at large length scales. This prediction distinguishes our model from other theories of glass formers and can be tested by experiment.

Singularity spectra of rough growing surfaces from wavelet analysis

We apply the wavelet transform modulus maxima method [A. Arneodo, N. Decoster, and S. G. Roux, Phys. Rev. Lett. 83, 1255 (1999)] to the analysis of simulated surfaces grown by molecular-beam epitaxy. In contrast to the structure function approach commonly used in the literature, this method permits an investigation of the complete singularity spectrum. We focus on a kinetic Monte Carlo model with Arrhenius dynamics, which in particular takes into consideration the process of thermally activated desorption of particles. We find a wide spectrum of Holder exponents, which reflects the multiaffine surface morphology. Although our choice of parameters yields small desorption rates (<3%), we observe a dramatic change in the singularity spectrum, which is shifted toward smaller Holder exponents. Our results offer a mathematical foundation of anomalous scaling: We identify the global exponent alpha(g) with the Holder exponent that maximizes the singularity spectrum.

Nonuniversality in models of epitaxial growth.

Kinetic roughening in two variants of a solid-on-solid model of epitaxial growth, a ``toy'' relaxation model and a collective diffusion model, is studied and compared, using extensive computer simulations in different spatial dimensions. We have studied the Wolf-Villain (WV) model and its modifications, and a full diffusion (FD) model with Arrhenius dynamics. The WV model shows nonuniversal features and its asymptotic behavior switches between the Edwards-Wilkinson type and a morphological instability, depending on the spatial dimension, a lattice coordination, or a minor modification of the model rules. The results for the FD model in 1+1 and 2+1 dimensions are not consistent with any of the continuum equations proposed to describe epitaxial growth; in particular, we observe too low values of the roughness exponent measured from the height-difference correlation function. In 1+1 dimensions, the results obtained for both models are very similar for more than ${10}^{6}$ monolayers deposited with an ``incorporation'' radius in the WV model corresponding to the substrate temperature in the FD model. Such a close correspondence is not found in 2+1 dimensions. Asymptotic behavior of the WV and FD models is different in all spatial dimensions. Both FD and WV models show anomalous scaling in all dimensions studied. The anomalous scaling in the FD model is very weak (logarithmic) in the physically relevant case of 2+1 dimensions. \textcopyright{} 1996 The American Physical Society.

Hydrogen bond dynamics in benzoic acid dimers as a function of hydrostatic pressure measured by nuclear magnetic resonance

The dynamics of hydrogen atoms in the hydrogen bonds of benzoic acid dimers have been studied as a function of hydrostatic pressure to pressures in excess of 4 kbar. This paper is primarily concerned with results up to 3.3 kbar. The temperature dependence of the correlation time for the motion at a series of pressures has been investigated using measurements of the proton spin–lattice relaxation time. Strong non-Arrhenius behavior is exhibited and the data are in good agreement with a model which invokes phonon assisted tunneling at low temperature and thermally activated Arrhenius dynamics at high temperature. The parameters in the model include the asymmetry of the double minimum potential experienced by the hydrogen atoms and dynamical variables relating to the tunneling and hopping processes. The rate of phonon assisted tunneling is observed to increase exponentially with increasing pressure and this is attributed to the increase in the tunneling matrix element which occurs as the distance between the potential wells is decreased and the overlap of the localized eigenstates beneath the barrier increases. We also observe a decrease in the asymmetry of the potential with increasing pressure which is attributable to modifications to the interdimer contributions to the potential. There is evidence in the nuclear magnetic resonance (NMR) data for two phase transitions below 4 kbar and one of these may be correlated with the reduction in asymmetry of the potential.

Vibrational control of systems with Arrhenius dynamics

A nonlinear system with S-shape steady state characteristic is referred to as a system with Arrhenius dynamics. The negative slope part of the S-shape curve represents a set of unstable steady states. Using two examples of Arrhenius systems (catalytic reactor and continuous stirred tank reactor), it is shown that introduction of sufficiently fast oscillations in the parameters of the system generates a new Arrhenius system, the steady state characteristic of which has a smaller negative slope part. Results of analytical investigation as well as numerical simulation are presented. It is shown that vibrational stabilization of Arrhenius systems gives an increase in productivity of the plants.