Structure factors in granular experiments with homogeneous fluidization

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D fluidized granular experiment, with packing fractions φ ∈ [10%, 40%]. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the "bath" temperature T(b), depending on shaking parameters, and the "granular" temperature T(g) < T(b), which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with φ, after proper rescaling with the mean free path.     

Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).     

Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation

We examine consequences of the non-Boltzmann nature of probability distributions for one-particle kinetic energy, momentum, and velocity for finite systems of classical hard spheres with constant total energy and nonidentical masses. By comparing two cases, reflecting walls (NVE or microcanonical ensemble) and periodic boundaries (NVEPG or molecular dynamics ensemble), we describe three consequences of the center-of-mass constraint in periodic boundary conditions: the equipartition theorem no longer holds for unequal masses, the ratio of the average relative velocity to the average velocity is increased by a factor of [N/(N-1)]1/2, and the ratio of average collision energy to average kinetic energy is increased by a factor of N/(N-1). Simulations in one, two, and three dimensions confirm the analytic results for arbitrary dimension.     

The effect of kinematic parameters on inelastic scattering of glyoxal

The effect of kinematic parameters (relative velocity v(rel), relative momentum p(rel), and relative energy E(rel)) on the rotational and rovibrational inelastic scatterings of 0(0)K(0)S(1) trans-glyoxal has been investigated by colliding glyoxal seeded in He or Ar with target gases D2, He, or Ne at different scattering angles in crossed supersonic beams. The inelastic spectra for target gases He and D2 acquired with two different sets of kinematic parameters revealed no significant differences. This result shows that kinematic factors have the major influence in the inelastic scattering channel competition whereas the intermolecular potential energy surface plays only a secondary role. The well-defined exponential dependence of relative cross sections on exchanged angular momentum identifies angular momentum as the dominant kinematic factor in collision-induced rotationally and rovibrationally inelastic scatterings. This is supported by the behavior of the relative inelastic cross sections data in a "slope-p(rel)" representation. In this form, the data show a trend nearly independent of the target gas identity. Representations involving E(rel) and v(rel) show trends specific to the target gas.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Self-diffusion coefficient of the hard-sphere fluid: system size dependence and empirical correlations

Molecular dynamics simulations have been used to calculate the self-diffusion coefficient, D, of the hard sphere fluid over a wide density range and for different numbers of particles, N, between 32 and 10 976. These data are fitted to the relationship D = D(infinity) - AN(-alpha) where the parameters D(infinity), A, and alpha are all density-dependent (the temperature dependence of D can be trivially scaled out in all cases). The value alpha = 1/3 has been predicted on the basis of hydrodynamic arguments. In the studied system size range, the best value of alpha is approximately 1/3 at intermediate packing fractions of approximately 0.35, but increases in the low- and high-density extremes. At high density, the scaling follows more closely that of the thermodynamic properties, that is, with an exponent of order unity. At low packing fractions (less than approximately 0.1), the exponent increases again, appearing to approach a limiting value of unity in the zero-density limit. The origin of this strong N dependence at low density probably lies in the divergence in the mean path between collisions, as compared with the dimensions of the simulation cell. A new simple analytical fit formula based on fitting to previous simulation data is proposed for the density dependence of the shear viscosity. The Stokes-Einstein relationship and the dependence of D on the excess entropy were also explored. The product Deta(s)p with p = 0.975 was found to be approximately constant, with a value of 0.15 in the packing fraction range between 0.2 and 0.5.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Measurements and quasi-quantum modeling of the steric asymmetry and parity propensities in state-to-state rotationally inelastic scattering of NO (2Pi1/2) with D2

Relative integrated cross sections are measured for spin-orbit-conserving, rotationally inelastic scattering of NO (2Pi1/2), hexapole-selected in the upper Lambda-doublet level of the ground rotational state (j = 0.5), in collisions with D2 at a nominal energy of 551 cm-1. The final state of the NO molecule is detected by laser-induced fluorescence (LIF). The state-selected NO molecule is oriented with either the N end or the O end toward the incoming D2 molecule by application of a static electric field E in the scattering region. This field is directed parallel or antiparallel to the relative velocity vector v. Comparison of signals taken for the different applied field directions gives the experimental steric asymmetry SA, defined by SA = (sigma v upward arrow downward arrow E - sigma v upward arrow upward arrow E)/(sigma v upward arrow downward arrow E + sigma v upward arrow upward arrow E), which is equal to within a factor of -1 to the molecular steric effect, Si-->f identical with (sigmaD2-->NO - sigmaD2-->ON)/(sigmaD2-->NO + sigmaD2-->ON). The dependence of the integral inelastic cross section on the incoming Lambda-doublet component is also measured as a function of the final rotational (jfinal) and Lambda-doublet (epsilonfinal) state. The measured steric asymmetries are similar to those previously observed for NO-He scattering. Spin-orbit manifold-conserving collisions exhibit a larger propensity for parity conservation than their NO-He counterparts. The results are interpreted in the context of the recently developed quasi-quantum treatment (QQT) of rotationally inelastic scattering [Gijsbertsen, A.; Linnartz, H.; Taatjes, C. A.; Stolte, S. J. Am. Chem. Soc. 2006, 128, 8777]. The QQT predictions can be inverted to obtain a fitted hard-shell potential that reproduces the experimental steric asymmetry; this fitted potential gives an empirical estimate of the anisotropy of the repulsive interaction between NO and D2. QQT computation of the differential cross section using this simple model potential shows reasonable agreement with the measured differential cross sections.     

Synthesis and spectroscopic characterization of a new family of Ni(4) spin clusters

A new family of tetranuclear Ni complexes [Ni(4)(ROH)(4)L(4)] (H(2)L = salicylidene-2-ethanolamine; R = Me (1) or Et (2)) has been synthesized and studied. Complexes 1 and 2 possess a [Ni(4)O(4)] core comprising a distorted cubane arrangement. Magnetic susceptibility and inelastic neutron scattering studies indicate a combination of ferromagnetic and antiferromagnetic pairwise exchange interactions between the four Ni(II) centers, resulting in an S = 4 spin ground state. Magnetization measurements reveal an easy-axis-type magnetic anisotropy with D approximately -0.93 cm(-)(1) for both complexes. Despite the large magnetic anisotropy, no slow relaxation of the magnetization is observed down to 40 mK. To determine the origin of the low-temperature magnetic behavior, the magnetic anisotropy of complex 1 was probed in detail using inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The spectroscopic studies confirm the easy-axis-type anisotropy and indicate strong transverse interactions. These lead to rapid quantum tunneling of the magnetization, explaining the unexpected absence of slow magnetization relaxation for complex 1.     

Monte Carlo simulation of dendrimers in variable solvent quality

We study via lattice Monte Carlo simulation and Flory theory the properties of g=1-6 dendrimers in variable solvent quality. For all the generations studied, we find that the radius of gyration R(g) collapses significantly (factor of 2) going from athermal to extreme poor solvent conditions, indicating that varying solvent quality is an effective means of controlling dendrimer size. We also find that in athermal, theta, and extreme poor solvent conditions, the radius of gyration of dendrimers scales with the total number of monomers roughly as R(g) approximately N(1/3). However, a more careful analysis shows that in athermal and theta solvents, there is, in fact, a small but systematic deviation of R(g) from R(g) approximately N(1/3) scaling and the simulation data is described better by the Flory theory prediction of R(g) approximately N(1/5)[(g+1)m](2/5) in athermal solvents and R(g) approximately N(1/4)[(g+1)m](1/4) in theta solvents. We also find for our simulation data that stronger deviations from constant density scaling are possible, with scaling behavior as shallow as R(g) approximately N(0.26) possible for solvent conditions in between theta and the completely collapsed state. It is evident therefore that dendrimers do not obey (or even approximately obey) R(g) approximately N(1/3) scaling under all solvent conditions. Under all solvent conditions, we find that the intramolecular density is dense corelike (i.e., the density maximum is in the interior of the dendrimer) and terminal groups are delocalized throughout the dendrimer.     

Inelastic hard rods in a periodic potential

A simple model of inelastic hard rods subject to a one-dimensional array of identical wells is introduced. The energy loss due to inelastic collisions is balanced by the work supplied by an external stochastic heat bath. We explore the effect of the spatial nonuniformity on the steady states of the system. The spatial variations of the density, granular temperature, and pressure induced by the gradient of the external potential are investigated and compared with the analogous variations in an elastic system. Finally, we study the clustering process by considering the relaxation of the system starting from a uniform homogeneous state.     

A new spin probe of protein dynamics: nitrogen relaxation in 15N-2H amide groups

(15)N spin relaxation data have provided a wealth of information on protein dynamics in solution. Standard R(1), R(1)(rho), and NOE experiments aimed at (15)N[(1)H] amide moieties are complemented in this work by HA(CACO)N-type experiments allowing the measurement of nitrogen R(1) and R(1)(rho) rates at deuterated (15)N[(2)D] sites. Difference rates obtained using this approach, R(1)((15)N[(1)H]) - R(1)((15)N[(2)D]) and R(2)((15)N[(1)H]) - R(2)((15)N[(2)D]), depend exclusively on dipolar interactions and are insensitive to (15)N CSA and R(ex) relaxation mechanisms. The methodology has been tested on a sample of peptostreptococcal protein L (63 residues) prepared in 50% H(2)O-50% D(2)O solvent. The results from the new and conventional experiments are found to be consistent, with respect to both local backbone dynamics and overall protein tumbling. Combining several data sets permits evaluation of the spectral density J(omega(D) + omega(N)) for each amide site. This spectral density samples a uniquely low frequency (26 MHz at a 500 MHz field) and, therefore, is expected to be highly useful for characterizing nanosecond time scale local motions. The spectral density mapping demonstrates that, in the case of protein L, J(omega(D) + omega(N)) values are compatible with the Lipari-Szabo interpretation of backbone dynamics based on the conventional (15)N relaxation data.     

Equation of state and structural properties of the Weeks-Chandler-Andersen fluid

Molecular dynamics simulations have been carried out for the equation of state and percolation properties of the Weeks-Chandler-Andersen (WCA) system in its fluid phase as functions of density and temperature. The compressibility factor Z collapses well for the various isotherms, using an effective particle diameter for the WCA particle which is (in the usual WCA reduced units) sigma(e)=2(16)(1+T)(16), where T is the temperature. A corresponding "effective" packing fraction is zeta(e)=pisigma(e) (3)N6V, for N particles in volume V, which therefore scales out the effects of temperature. Using zeta(e) the simulation derived Z can be fitted to a simple analytic form which is similar to the Carnahan-Starling hard sphere equation of state and which is valid at all temperatures and densities where the WCA fluid is thermodynamically stable. The data, however, are not scalable onto the hard sphere equation of state for the complete packing fraction range. We explored the continuum percolation behavior of the WCA fluids. The percolation distance sigma(p) for the various states collapses well onto a single curve when plotted as sigma(p)sigma(e) against zeta(e). The ratio sigma(p)sigma(e) exhibits a monotonic decrease with increasing zeta(e) between the percolation line for permeable spheres and the glass transition limit, where sigma(p)sigma(e) approximately 1. The percolation packing fraction was calculated as a function of effective packing fraction and fitted to an empirical expression. The local coordination number at the percolation threshold showed a transition between the soft core and hard core limits from ca. 2:74 to 1:5, as previously demonstrated in the literature for true hard spheres. A number of simple analytic expressions that represent quite well the percolation characteristics of the WCA system are proposed.     

Simulations of concentrated suspensions of rigid fibers: relationship between short-time diffusivities and the long-time rotational diffusion

Brownian dynamics simulations of the behavior of suspensions of fibers demonstrate that the scaling of the rotational diffusivity with respect to the number density (nL3) is a sensitive function of the thickness and the parameter L2D(R0)/D(T0), where D(R0) is the rotational diffusivity at infinite dilution, D(T0) is the average center-of-mass diffusivity at infinite dilution, and L is the fiber length. Existing theories for the long-time rotational diffusivities of rigid fibers in the semidilute and concentrated regimes fail to accurately account for the relationship with the dilute values of the rotational and translational diffusivities of the various physical models used to simulate the fibers. The concentration regime studied in this work ranges from a number density of nL3 approximately 0-150, which is below the transition from an isotropic to nematic state. The effect of the fiber thickness was studied by performing simulations of rods with aspect ratios (fiber length over diameter) of 25, 50, and 500, as well as performing projections for infinitely thin fibers. The excluded volume of the rods was enforced through the use of short-range potentials. For a rod with an aspect ratio of 50 with a parameter of L2D(R0)/D(T0)=9, which corresponds to a slender-body model of the individual fibers, the rotational diffusivity (D(R)) scales as D(R)/D(R0) approximately (nL3)(-1.9) in the concentration regime of 70 < or = nL3 < or = 150. Similarly with a parameter of L2D(R0)/D(T0)=4, corresponding to a rigid-dumbbell model, the rotational diffusivity scales as D(R)/D(R0) approximately (nL3)(-1.1) over the same range of concentrations. For rods with aspect ratios of 25, it is observed that a difference in the scaling is seen for L2D(R0)/D(T0) approximately < 8, with higher values of this ratio exhibiting essentially the same scaling. Additional values of the ratio L2D(R0)/D(T0) were investigated to determine the overall behavior of the suspension dynamics with respect to this parameter. These findings resolve discrepancies between simulation results for rotational diffusivities reported by previous investigators and provide new insights for the development of an accurate theory for the diffusivity of rigid rods suspended in solution.     

Does confining the hard-sphere fluid between hard walls change its average properties?

We use grand canonical transition-matrix Monte Carlo and discontinuous molecular dynamics simulations to generate precise thermodynamic and kinetic data for the equilibrium hard-sphere fluid confined between smooth hard walls. These simulations show that the pronounced inhomogeneous structuring of the fluid normal to the confining walls, often the primary focus of density functional theory studies, has a negligible effect on many of its average properties over a surprisingly broad range of conditions. We present one consequence of this insensitivity to confinement: a simple analytical equation relating the average density of the confined fluid to that of the bulk fluid with equal activity. Nontrivial implications of confinement for average fluid properties do emerge in this system, but only when the fluid is both (i) dense and (ii) confined to a gap smaller than approximately three particle diameters. For this limited set of conditions, we find that "in-phase" oscillatory deviations in excess entropy and self-diffusivity (relative to the behavior of the bulk fluid at the same average density) occur as a function of gap size. These paired thermodynamic/kinetic deviations from bulk behavior appear to reflect the geometric packing frustration that arises when the confined space cannot naturally accommodate an integer number of particle layers.     

Visualizing the dose distribution and linear energy transfer by 1D and 2D ESR imaging: a potassium dithionate dosimeter irradiated with C6+ and N7+ ions

We report the application of one- and two-dimensional (1D and 2D) spectral-spatial electron spin resonance imaging (ESRI) for visualizing the dose distribution and linear energy transfer (LET) in a potassium dithionate, K2S2O6 (PDT), dosimeter irradiated with the heavy ions C(6+) and N(7+). The ESR spectrum in the irradiated PDT consists of a superposition of two isotropic signals assigned to two *SO3(-) radicals, R1 and R2, with no hyperfine splittings and slightly different g values. The 1D ESRI profiles clearly indicate the spatial penetration of the beams and the location of the sharp maximum dose, the "Bragg peak", detected for each beam. The depth penetrations are different: approximately 2.3 mm for C(6+) and approximately 1.8 mm for N(7+) beams, +/-0.1 mm; beyond these limits, no radicals were detected. 2D spectral-spatial ESRI images reflect both the dose distribution and the spatial dependence of the relative intensities of radicals R1 and R2, an effect that is assigned to the depth variation of the LET. This study has demonstrated that ESRI is a promising new method for dose and LET determination. Of particular interest are applications in the field of radiotherapy with heavy ions, because in this case the Bragg peak is pronounced and the dose can be focused at specific depths while the surrounding areas are protected.     

MnIII2 (5-Rsaltmen)2NiII(pao)2(L)]2+: an S(T)=3 building block for a single-chain magnet that behaves as a single-molecule magnet

Mn(III)-Ni(II)-Mn(III) linear-type trinuclear complexes bridged by oximate groups were selectively synthesized by the assembly reaction of [Mn2(5-Rsaltmen)2(H2O)2](ClO4)2 (5-Rsaltmen2-=N,N'-(1,1,2,2-tetramethylethylene) bis(5-R-salicylideneiminate); R=Cl, Br) with [Ni(pao)2(phen)] (pao-=pyridine-2-aldoximate; phen=1,10-phenanthroline) in methanol/water: [Mn2(5-Rsaltmen)2Ni(pao)2(phen)](ClO4)2 (R=Cl, 1; R=Br, 2). Structural analysis revealed that the [Mn(III)-ON-Ni(II)-NO-Mn(III)] skeleton of these trimers is in every respect similar to the repeating unit found in the previously reported series of 1D materials [Mn2(saltmen)2Ni(pao)2(L1)2](A)(2) (L(1)=pyridine, 4-picoline, 4-tert-butylpyridine, N-methylimidazole; A=ClO4-, BF4-, PF6-, ReO4-). Recently, these 1D compounds have attracted a great deal of attention for their magnetic properties, since they exhibit slow relaxation of the magnetization (also called single-chain magnet (SCM) behavior). This unique magnetic behavior was explained in the framework of Glauber's theory, generalized for chains of ferromagnetically coupled anisotropic spins. Thus, in these 1D compounds, the [Mn(III)-ON-Ni(II)-NO-Mn(III)] unit was considered as an S(T)=3 anisotropic spin. Direct-current magnetic measurements on 1 and 2 confirm their S(T)=3 ground state and strong uniaxial anisotropy (D/k(B) approximately -2.4 K), in excellent agreement with the magnetic characteristic deduced in the study on the SCM series. The ac magnetic susceptibility of these trimers is strongly frequency-dependent and characteristic of single-molecule magnet (SMM) behavior. The relaxation time tau shows a thermally activated (Arrhenius) behavior with tau0 approximately 1x10(-7) s and Delta(eff)/k(B) approximately 18 K. The effective energy barrier for reversal of the magnetization Delta(eff) is consistent with the theoretical value (21 K) estimated from |D| S2T. The present results reinforce consistently the interpretation of the SCM behavior observed in the [Mn2(saltmen)2Ni(pao)2(L1)2](A)2 series and opens new perspectives to design single-chain magnets.