Monte Carlo simulation of the backscatter region in photon-excited energy dispersive X-ray fluorescence spectra

The backscatter region of energy-dispersive X-ray fluorescence spectra obtained by a typical radioisotope system is examined in detail. A Monte Carlo simulation program which incorporates all the information on photon scattering processes including electron momentum distributions in target atoms, form factors and scattering factors for the cross-sections is presented. The program uses extensive variance reduction techniques and has the option of simulating any type of either single or any specified combination of multiple scatters or the complete process as appears in a real detector response spectrum. Based on several simulated spectra various conclusions are reached including that the energy spread of Compton peaks depends mainly on the broadening effect of electron momenta together with detection system resolution, and that the intensity of double scatters is roughly an order of magnitude lower than that of single scatters for thick targets.     

Monte Carlo simulation of electron-ion recombination at high pressure

The Monte Carlo method is applied to the study of electron-ion recombination in CO₂, CH₄ and NH₃ over a wide range of pressures. Dissociative recombination is enhanced by energy transfer to the ambient gas molecules and the recombination rates peak at 11, 2 and 9 × 10⁵ CM³ s^?1, respectively. At very high pressures, the rate approaches the Langevin limit.     

Voxel-based Monte Carlo simulation of X-ray imaging and spectroscopy experiments

A Monte Carlo code for the simulation of X-ray imaging and spectroscopy experiments in heterogeneous samples is presented. The energy spectrum, polarization and profile of the incident beam can be defined so that X-ray tube systems as well as synchrotron sources can be simulated. The sample is modeled as a 3D regular grid. The chemical composition and density is given at each point of the grid. Photoelectric absorption, fluorescent emission, elastic and inelastic scattering are included in the simulation. The core of the simulation is a fast routine for the calculation of the path lengths of the photon trajectory intersections with the grid voxels. The voxel representation is particularly useful for samples that cannot be well described by a small set of polyhedra. This is the case of most naturally occurring samples. In such cases, voxel-based simulations are much less expensive in terms of computational cost than simulations on a polygonal representation. The efficient scheme used for calculating the path lengths in the voxels and the use of variance reduction techniques make the code suitable for the detailed simulation of complex experiments on generic samples in a relatively short time. Examples of applications to X-ray imaging and spectroscopy experiments are discussed.     

A simple Monte Carlo program for simulation of X-ray transport

A Monte Carlo-based program for treatment of photon transport, restricted to photon energies used in medical diagnostics, is developed. Only the photoabsorption and Compton scattering of photons are taken into account, a justifiable assumption for the energies involved. We can simply separate contributions of reflection events with one, two, three, or more successive collisions of X-rays with electrons of the target. This gives us insights and information about photon transport which otherwise would be inaccessible.     

Win X-ray: a new Monte Carlo program that computes X-ray spectra obtained with a scanning electron microscope.

A new Monte Carlo program, Win X-ray, is presented that predicts X-ray spectra measured with an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM) operating between 10 and 40 keV. All the underlying equations of the Monte Carlo simulation model are included. By simulating X-ray spectra, it is possible to establish the optimum conditions to perform a specific analysis as well as establish detection limits or explore possible peak overlaps. Examples of simulations are also presented to demonstrate the utility of this new program. Although this article concentrates on the simulation of spectra obtained from what are considered conventional thick samples routinely explored by conventional microanalysis techniques, its real power will be in future refinements to address the analysis of sample classifications that include rough surfaces, fine structures, thin films, and inclined surfaces because many of these can be best characterized by Monte Carlo methods. The first step, however, is to develop, refine, and validate a viable Monte Carlo program for simulating spectra from conventional samples.     

Need for further inelastic scattering measurements at X-ray energies

With recent improvements in both theory and experiment for scattering of X-rays from atoms, it is possible now to make a more quantitative comparison, and see whether agreement is being obtained within the much more stringent limits set by the present calculations and measurements. Comparing with present theory, measured whole atom Compton scattering cross sections in the photon energy range 11–40 keV using synchrotron X-ray sources demonstrate that a dramatic improvement in the precision of scattering measurements has been achieved. However, circumstances are also identified in which further experimental data is needed in order to test the adequacy of present theoretical approaches.     

Monte Carlo simulation of equilibrium reactions at vapor-liquid interfaces

Chemical reactions are known to behave differently, depending upon their local environment. While the interactions with neighboring molecules may alter both the kinetics of chemical reactions and the overall equilibrium conversion, we have performed simulations of the latter. The particular environment that we address is the vapor-liquid interface, since only a few, limited studies have explored the influence of an interface on equilibrium reaction behavior. Simple dimerization reactions are modeled, as well as more complex multicomponent reactions, using the reactive Monte Carlo (RxMC) simulation technique. We find that the conversion of a reaction can be markedly different at an interface as compared to the bulk vapor and liquid phases, and these trends are analyzed with respect to specific intermolecular interactions. In conjunction, we calculate the surface tension of the reacting fluids at the interface, which is found to have unusual scaling behavior, with respect to the system temperature.     

Monte Carlo simulation of equilibrium reactions at modified vapor-liquid interfaces

The equilibrium conversion of a chemical reaction is known to be affected by its local environment. Various factors may alter reaction equilibria, including shifts in pressure or temperature, solvation, adsorption within porous materials, or the presence of an interface. Previously, reactive Monte Carlo simulations have been used to predict the equilibrium behavior of chemical reactions at vapor-liquid interfaces. Here, a route is tested for tuning the interfacial conversion of a Lennard-Jones dimerization reaction by adding surfactants to the vapor-liquid interface. Several temperatures are explored as well as several different surfactant models. Even with the addition of a small concentration of surfactants, the simulations predict significant shifts in the conversion at the interface. In general, the shifts in the conversion tend to be related to the values of the interfacial tension.     

Applicability of the condensed-random-walk Monte Carlo method at low energies in high-Z materials

The predictions of several Monte Carlo codes were compared with each other and with experimental results pertaining to the penetration of through gold foils of electrons incident with energies from 128 to 8 keV. The main purpose was to demonstrate that reflection and transmission coefficients, for number and energy, can be estimated reliably with a simple Monte Carlo code based on the condensed-random-walk and continuous-slowing-down approximations.     

Stability of Na-, K-, and Ca-montmorillonite at high temperatures and pressures: a Monte Carlo simulation

Monte Carlo grand canonical molecular simulations on the hydration of Na-, K-, and Ca-montmorillonite show that between 333 and 533 K and 300-1300 bar Na-montmorillonite forms stable one-layer hydrates of d(001) spacings 12.64-12.38 Angstroms, K-montmorillonite of 12.78-12.59 Angstroms, and Ca-montmorillonite of 12.48-12.32 Angstroms. A two-layer hydrate of 14.80 Angstroms occurs for Na-montmorillonite at 533 K and 1300 bar, for K-montmorillonite of 15.32 Angstroms at 533 K and 1300 bar and of 14.74 Angstroms at 533 K and 2000 bar, and for Ca-montmorillonite of 13.83 Angstroms at 473 K and 1000 bar. Three-layer hydrates may possibly form within these same ranges. Outside of them, one-layer hydrates simulate as the only stable hydrates. In sedimentary basins, the two-layer hydrate of Ca-montmorillonite will locate at 6.7 km depth and those of Na- and K-montmorillonite at 8.7 km depth; above and below these depths, the one-layer hydrates are the stable phases.     

Prediction of thermodynamic derivative properties of natural condensate gases at high pressure by Monte Carlo simulation

We have employed Monte Carlo simulation in the isobaric–isothermal ensemble to determine thermodynamic derivative properties of naturally occurring hydrocarbon gas mixtures. Thermal expansivity, isothermal compressibility, heat capacity and Joule–Thomson coefficient have been obtained from a fluctuation method detailed in our previous work [Phys. Chem. Chem. Phys. 3 (2001) 4333]. We have investigated two natural gases using an original method to model hydrocarbon distribution in a representative way with a limited number of linear, branched and cyclic hydrocarbon molecules. The composition used in Monte Carlo simulations was represented by 500 molecules of 20 different types with up to 35 carbon atoms. The two condensate gases are composed of rigid and flexible molecules for which intermolecular potentials have been used without fitting any parameters. Predictions are in good agreement with respect to available molar volumes at high pressure. Joule–Thomson coefficients and the other thermodynamic derivative properties have been then predicted at pressures up to 110 MPa at reservoir temperature, showing a consistent behaviour compared with light hydrocarbon gases. Inversion pressure of the Joule–Thomson effect is obtained within 1.2% compared to experimental value from volumetric measurements.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.