Time-dependent Friction Research Articles

Enhanced diffusion in active intracellular transport.

We show that within a living eukaryotic cell, mean square displacement of an engulfed microsphere shows enhanced diffusion scaling as t(3/2) at short times, with a clear crossover to subdiffusive or ordinary diffusion scaling at longer times. The motion, observed nearby the nucleus, is due to interactions with microtubule-associated motor proteins rather than thermal Brownian motion. We propose that time-dependent friction introduced by the intracellular polymer networks leads to sub-ballistic motion, analogous to subdiffusion observed in passive networks of semiflexible biopolymers.

Colloidal electrolyte friction and sedimentation: A mode-coupling approach

Using a simplified mode-coupling scheme (MCS) for multicomponent Brownian dispersions, we calculate the effect of mobile salt and counterions on the tracer diffusion and sedimentation of a suspended colloidal macroion. In this scheme, potential forces and also the leading far-field hydrodynamic interactions (HI) between macroion and small electrolyte ions forming its ion atmosphere are accounted for on the basis of the many-body Smoluchowski equation. The static pair correlation functions, which are needed as input, are treated in a first step within the Debye–Hückel approximation. In this way, analytical results are derived for the time-dependent friction function, the long-time tracer diffusion coefficient, and the sedimentation velocity of the macroion as functions of the electrolyte concentration, electrolyte ion mobilities, and macroion charge. Onsager’s limiting law for simple electrolytes is recovered from the MCS in the limit of vanishing macroion radius. The results of our theoretical treatment are compared with experimental data on electrolyte friction and predictions of other existing theories. Good agreement with experimental data on tracer diffusion and with Booth’s theory of electrolyte friction is observed. The inclusion of HI between macroion and microions is shown to be essential for a proper description of the electrolyte friction effect.

Influence of ageing on the internal friction of magnesium

The internal friction of cp- (99.8 wt.%) and hp- (99.99 wt.%) magnesium was determined by measuring the logarithmic decrement of free vibrations of bending beams, which were clamped at one end. Independently of the purity and the thermomechanical pretreatment, for all samples the logarithmic decrement increases with increasing strain amplitude. The damping in hp-magnesium is generally higher than in cp-magnesium. This can be explained by the model of Granato and Lücke, assuming that the successive unpinning of dislocation segments between weak pinning points is the reason of the increment of damping with increasing strain amplitude. The weak pinning points are assumed to be solute atoms or vacancies. Based on this model, other effects, found also in time and stress dependent internal friction measurements, can be explained qualitatively. The damping decreases at room temperature with ageing time and annealing temperatures up to 150°C. For higher annealing temperatures the damping increases monotonously with the temperature of the heat treatment. The effect of ageing can also be reverted by dynamic strain in the range of about 10 −4–10 −3, which increases the internal friction of aged samples before they can age again.

The non-separability of “dielectric” and “mechanical” friction in molecular systems: A simulation study

Simulations of the time-dependent friction controlling rotational, translational, and vibrational motions of dipolar diatomic solutes in acetonitrile and methanol have been used to examine the nature of “dielectric” friction. The way in which electrical interactions increase the friction beyond that present in nonpolar systems is found to be rather different than what is anticipated by most theories of dielectric friction. Long-range electrostatic forces do not simply add an independent contribution to the friction due to short-ranged or “mechanical” sources (modeled here in terms of Lennard-Jones forces). Rather, the electrical and Lennard-Jones contributions are found to be strongly anticorrelated and not separable in any useful way. For some purposes, the mechanism by which electrical interactions increase friction is better viewed as a static electrostriction effect: electrical forces cause a subtle increase in atomic density in the solute’s first solvation shell, which increases the amplitude of the force fluctuations derived from the Lennard-Jones interactions, i.e., the mechanical friction. However, electrical interactions also modify the dynamics of the friction, typically adding a long-time tail, which significantly increases the integral friction. Both of these effects must be included in a correct description of friction in the presence of polar interactions.

Anomalous Diffusion in Active Intracellular Transport

AbstractThe dynamic movements of tracer particles have been used to characterize their local environment in dilute networks of microtubules, and within living cells. In the former case, 300 nm diameter beads are fixed to individual microtubules, so that the movements of the bead reveal undulatory modes of the polymer. The mean square displacement shows a scaling of t3/4 in keeping with mode analysis arguments. Inside a cell, beads show a more complicated behavior that reflects internal dynamics of the cytoskeleton and associated motors.When placed near the cell edge, 3 micron diameter beads coated by proteins that mediate membrane adhesion are engulfed underneath the membrane and drawn toward the center by a contracting flow of actin. On reaching the region surrounding the nucleus, the beads continue to move but lose directionality, so that they wander within a restricted space. Measurement of the mean square displacement now shows a scaling of t1 up to times of ~1 sec. At longer times the scaling varies between t and t1/2 in the various runs. The data do not fit a crossover between ballistic (t2)and diffusive (t1) behavior. The movement is clearly driven by non-thermal interactions, as it cannot be stopped by an optical trap. Treatment of the cell to depolymerize microtubules restores ordinary diffusion, while actin depolymerization has no effect, indicating that microtubule-based motor proteins are responsible for the motion. Immunofluorescence microscopy shows that the mesh size of the microtubules is smaller than the bead diameter.We propose that the observations are related, and that the non-trivial scaling in the polymer system leads to time-dependent friction in a network, which in turn leads to a generalized Einstein relation operative in the intracellular environment. This results, in the driven system, in sub-ballistic motion at short times and sub-diffusive motion at longer times.

Barrierless Isomerization Dynamics in Viscous Liquids: Decoupling of the Reaction Rate from the Slow Frictional Forces

Many important chemical and biological reactions do not face a sizable activation barrier in their motion along the reaction coordinate. As a result, these reactions often have time constants in the range of a few hundred femtoseconds (fs) only. The existing theories, on the other hand, assume only the viscous, zero frequency frictional response of the solvent, which is clearly inadequate to describe solvent viscosity effects on such ultrafast reactions. In this article, we present a theory of barrierless chemical reactions that includes the bimodal frictional response of the solvent. The generalized theory is based on a non-Markovian Smoluchowski equation, with a time (t) dependent diffusion coefficient (D(t)) to describe the reactive motion along the reaction surface; the reaction itself is described by a coordinate-dependent sink term. This description is reliable for a harmonic reaction potential energy surface. The time-dependent diffusion coefficient can be obtained from the time-dependent friction ...

Time-dependent friction response of plasma-sprayed molybdenum

Plasma-sprayed coatings are used widely for friction and wear control. These coatings are comprised of unique lamellar microstructure and differ considerably from conventional bulk materials. In this work, the friction and wear behavior of sintered and atmospheric plasma-sprayed (APS) molybdenum (PSMo), during sliding contact against an AISI 52100 ball, was studied under 10 N load, 10 mm/s sliding velocity and ambient atmosphere. The hypothesis on the genesis of friction by Suh and Sin [N.P.Suh, H.-C. Sin, Wear 69 (1981) 91–114.] has been examined for applicability to plasma-sprayed coatings. It was observed that plasma-sprayed Mo coatings display a time-dependent friction response similar to that for monolithic iron-based materials as reported in the literature. The initial coefficient of friction (COF) is related to plowing and thereby inversely related to surface hardness. The removal of wear debris from the sliding surfaces leads to a reduction in the COF, establishing that plowing and asperity deformation play a significant role in the genesis of friction during dry sliding contact. The peak in the COF for APS Mo occurs after 9 m of sliding as opposed to 25 m of sliding for sintered Mo due to an early occurrence of sub-surface failure at the inherently weak interlayer bond in plasma-sprayed coatings. This leads to an early onset of increased plowing and asperity deformation in APS Mo as compared to sintered Mo. The above results highlight the time-dependent friction response of thermal-sprayed coatings and distinguish their wear behavior with that of bulk monolithic materials and are significant for affecting improvements in the wear and friction behavior of thermal-sprayed coatings.

The effect of shear load on frictional healing in simulated fault gouge

We report on frictional strengthening (healing) in granular quartz gouge as a function of time of true stationary contact. To distinguish between the slip‐dependent [Ruina, 1983] and time‐dependent [Dieterich, 1979] friction constitutive laws, we designed tests similar to conventional slide‐hold‐slide (SHS) tests except that shear load was completely removed prior to holds. We find large healing values (0.033–0.054 for holds of 10¹–10² s) compared with quasi‐static SHS experiments, and our data indicate time‐dependent weakening in contrast with strengthening observed from SHS tests. Gouge layer compaction increases with increasing hold time, comparable to observations from conventional SHS tests. Our data indicate that purely time dependent processes have a minor influence on healing under the conditions studied and/or that such effects are efficiently erased by particle rearrangement during removal/reapplication of shear load. The data are not adequately described by either the time (Dieterich) or slip (Ruina) dependent state evolution laws.

Dynamics of a creep-slip model of earthquake faults

Starting off from the relationship between time-dependent friction and velocity softening we present a generalization of the continuous, one-dimensional homogeneous Burridge–Knopoff (BK) model by allowing for displacements by plastic creep and rigid sliding. The evolution equations describe the coupled dynamics of an order parameter-like field variable (the sliding rate) and a control parameter field (the driving force). In addition to the velocity-softening instability and deterministic chaos known from the BK model, the model exhibits a velocity-strengthening regime at low displacement rates which is characterized by anomalous diffusion and which may be interpreted as a continuum analogue of self-organized criticality (SOC). The governing evolution equations for both regimes (a generalized time-dependent Ginzburg–Landau equation and a non-linear diffusion equation, respectively) are derived and implications with regard to fault dynamics and power-law scaling of event-size distributions are discussed. Since the model accounts for memory friction and since it combines features of deterministic chaos and SOC it displays interesting implications as to (i) material aspects of fault friction, (ii) the origin of scaling, (iii) questions related to precursor events, aftershocks and afterslip, and (iv) the problem of earthquake predictability. Moreover, by appropriate re-interpretation of the dynamical variables the model applies to other SOC systems, e.g. sandpiles.

Generalized Langevin dynamics simulations of NaCl electrolyte solutions

The stochastic simulation method called generalized Langevin dynamics has been employed in the study of NaCl aqueous solutions at several ionic concentrations. Only the ion pairs have been considered explicitly in the simulations. Every ion follows a generalized Langevin equation in which the total acceleration has a stochastic term, an integral time-dependent friction term, and a deterministic part that takes into account the interaction with the other ions in the system. Different solvent-averaged potentials and memory kernels have been tested in order to obtain a realistic behavior of the systems. The screening of electrostatic forces between ions has been analyzed too. The electric field around Na+ and Cl− ions has been calculated and the screening has been analyzed in terms of the structural features of the ionic surroundings.

Rotational dielectric friction and molecular relaxation at metal-solvent interfaces

Dynamical properties of dipolar liquids near metal surfaces are investigated by means of molecular dynamics simulations. The dipolar molecules are characterized by the well-known Stockmayer potential (Lennard-Jones plus point dipole interaction) and the metal is treated by employing a jellium model. The metal potential is calculated self-consistently by using density functional theory. The relaxation of angular velocity autocorrelation function, time and frequency dependent rotational dielectric friction and dipole orientational correlation function are calculated for interfacial and bulk dipolar molecules. The dynamics of solvation of a newly created ion in the vicinity of metal surface is also investigated. These studies provide useful information on metal field induced modifications of dielectric friction and molecular relaxation in dipolar liquids near metal surfaces.

Effects of ion atmosphere relaxation on dipole isomerization reactions in electrolyte solutions

A theoretical study of the effects of ion atmosphere relaxation on the rate of a model dipole isomerization reaction in electrolyte solutions is presented. The time-dependent ion atmosphere friction is calculated by using a molecular hydrodynamic theory which properly includes the static and dynamic interionic correlations through ionic structure factors and van Hove functions. The rate constant is determined by employing the well-known Grote-Hynes theory. Numerical results are obtained for the time-dependent ion atmosphere friction and for the rate of isomerization reaction in electrolyte solutions of varying ion concentration and dielectric constant. It is found that the ion atmosphere friction can have significant effects in reducing the rate of isomerization below the prediction of equilibrium solvation transition state theory.

Stick-slip vibrations induced by alternate friction models

In the present paper a simple and efficient alternate friction model is presented to simulate stick-slip vibrations. The alternate friction model consists of a set of ordinary non-stiff differential equations and has the advantage that the system can be integrated with any standard ODE-solver. Comparison with a smoothing method reveals that the alternate friction model is more efficient from a computational point of view. A shooting method for calculating limit cycles, based on the alternate friction model, is presented. Time-dependent static friction is studied as well as application in a system with 2-DOF.

The normal stress effect and equilibrium friction coefficient of articular cartilage under steady frictional shear

During creep or stress relaxation, articular cartilage exhibits a time-dependent friction coefficient which has been shown to reach an equilibrium value, μ eq , as the tissue deformation equilibrates. This study investigates the frictional properties of articular cartilage explants under steady frictional shear and constant compressive strain after the tissue reaches stress-relaxation equilibrium. The two parameters measured are the normal force and frictional torque, from which the friction coefficient was then calculated. It is shown in this experimental study that: (1) Under a prescribed infinitesimal compressive strain, cartilage supports higher compressive normal stress under steady shear than it does in the absence of frictional shear. Furthermore, the normal stress increases with increasing sliding velocity, resulting in a velocity-dependent value of μ eq . The observed normal stress effectively increases the compressive stiffness of cartilage by a factor up to 3.1. (2) Under a prescribed steady frictional shear both the normal stress and frictional shear stress increase, though not proportionally, with increasing compressive strain, producing a decreasing friction coefficient. (3) This velocity-dependent normal stress effect is also shown to result, at least partly, from intrinsic properties of cartilage. The normal stress effect has not been previously reported for articular cartilage, and represents an intriguing mechanical response not commonly encountered in solids, though common in non-Newtonian fluids.

Continuum estimates of rotational dielectric friction and polar solvation

Dynamical solvation data recently obtained with the probe solute coumarin 153 are used to test the reliability of dielectric continuum models for estimating dielectric friction effects. In particular, the predictions of the Nee–Zwanzig theory of rotational dielectric friction are examined in some detail. The analysis undertaken here uncovers an error made in virtually all previous applications of the Nee–Zwanzig formalism. The error involves neglect of the solvent’s electronic polarizability when calculating dielectric friction constants. In highly polar solvents the effect of this neglect is shown to be minor, so that the results of past studies should not be appreciably altered. However, in weakly polar and especially in nondipolar solvents, the proper inclusion of electronic polarizability terms is essential. The equivalence between the Nee–Zwanzig theory of dielectric friction and more general continuum treatments of polar solvation dynamics is also demonstrated. This equivalence enables the use of solvation data to test the reliability of the Nee–Zwanzig description of electrical interactions between a solute and solvent that form the core of this and related continuum theories of dielectric friction. Comparisons to experimental data show that, with the important exception of nondipolar solvents, such continuum treatments provide reasonably accurate (±40%) predictors of time-dependent solvation and/or dielectric friction.

Simulation of Stick-Slip Friction in Control Systems

An analysis is developed for the simulation of stick-slip friction between lubricated surfaces at low sliding velocity. The simulation shows the time-dependent motion and unsteady friction force. The simulation is based on a fundamental dynamic friction model which considers the hydrodynamic forces as well as the friction due to direct contact between the surface asperities. In addition, the Dahl effect which demonstrates presliding displacement is considered. The analysis considers a system of a motor driving a journal with inertia through a flexible shaft. The journal is supported by hydrodynamic journal bearing where slick-slip friction can be generated in the mixed friction region. This problem is equivalent to a closed-loop proportional control of the angular rotation of a rigid shaft. The stick-slip is simulated and the physical phenomena are elucidated. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in San Francisco, California, October 13–17, 1996

General theory of tracer-diffussion in colloidal suspensions

In this work we derive a generalized Langevin equation that describes the translational Brownian motion of a tracer particle which interacts with other diffusing particles in the system. The direct interactions of the tracer with these other diffusing particles give rise to memory effects described by a time-dependent friction. The main result of this work is a general and exact expression for this friction function which admits the possibility that the tracer is non-spherical, and that the particles diffusing around it are not of a single species, although they are assumed spherical.

Memory effects on stochastic resonance

We study the phenomenon of stochastic resonance (SR) in a bistable system with internal colored noise. In this situation the system possesses time-dependent memory friction connected with noise via the fluctuation-dissipation theorem, so that in the absence of periodic driving the system approaches the thermodynamic equilibrium state. For this non-Markovian case we find that memory usually suppresses stochastic resonance. However, for a large memory time SR can be enhanced by the memory.

Brownian motion of interacting nonspherical tracer particles: General theory.

A general theoretical framework is developed to describe the tracer-diffusion properties of nonspherical Brownian tracer particles that interact with the other particles in a multicomponent colloidal suspension of generally nonspherical particles, in the absence of hydrodynamic interactions. Here we present the derivation of the generalized Langevin equation (GLE) for the linear and angular velocity describing the Brownian motion of the tracer particle. In addition to the dissipative plus the random force and torque exerted by the solvent, this GLE contains the dissipative plus random force and torque due to the direct interactions with the other particles. An exact and general expression is derived for the time-dependent friction tensor that embodies the effects of the latter. Using a generalized Wertheim-Lovett's relation, this expression is cast in two alternative but equivalent forms. The long-time and short-time limits (in reference to the structural relaxation time ${\ensuremath{\tau}}_{\mathrm{I}}$) are also discussed.

A quantitative theory of linear chain polymer dynamics in the melt. III. Dependence of quantities on bead location along the chain contour

The dependence of the bead mean squared displacement on the position of the bead along the chain backbone is considered within the lateral motion model for the dynamics of linear chain polymer melts. The bead position dependence has been ignored in the previous development of this theory. In the lateral motion model, the effective bead friction coefficient increases as the bead mean squared displacement increases, due to the greater interchain correlations that result because of the noncrossability of the chain backbones. In this work, a position dependent model is considered for this bead friction coefficient. The resulting equations of motion for the chain have the form of a generalized Rouse model with a position and time dependent bead friction coefficient. These equations are solved numerically. It is found that the time dependence of the center bead mean squared displacement has the same form as predicted by the simpler theory, in which the dependence of quantities on the position of the bead along the chain backbone is ignored. The scaling of the terminal time and the center of mass diffusion constant on chain length are also found to be unchanged by the inclusions of the bead position dependence of the friction coefficient. The mean squared displacement, averaged over all beads in the chain, shows a stronger time dependence than the same quantity for the center bead. The predictions are in excellent agreement with the results from previous numerical simulations.