Inverse Monte Carlo Simulation Research Articles

Role of polydispersity in anomalous interactions in electrostatically levitated colloidal systems

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (sigma), relative range of repulsion (kappa a), and projected interfacial concentration (rho). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (sigma, kappa a, and rho), our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments.

Penetration depth of light for argon laser curing of dental composites

Abstract Polymerization of dental restorative materials as light-activated tooth-colored composites can be done using argon laser light of 488 nm. This study calculates the effective penetration depth of light at 490 nm in different composites and shades in order to gain information for a comparison of the curing properties of the composite resins after argon laser polymerization. Penetration depth was calculated by diffusion theory on the basis of the optical parameters of the composites and shades, as there are the absorption coefficient μ a , the scattering coefficient μ s , and the anisotropy factor g. To determine these optical parameters, a method which includes sample preparation and measurements of transmission and reflectance in an integrating sphere spectrometer followed by inverse Monte Carlo simulations has been used. The calculated penetration depths differ between the investigated composite systems and between the shades. The results are suitable for a relative comparison of different composites and shades. They allow conclusions to be drawn about the expected depth of cure, insofar as a composite with a lower penetration depth of the used curing wavelength will also show a lower depth of cure with a lower degree of conversion compared to a composite with a higher penetration depth of the same curing wavelength.

Differences in optical properties between healthy and pathological human colon tissues using a Ti:sapphire laser: an in vitro study using the Monte Carlo inversion technique

The purpose of the study is to analyze and compare differences in the optical properties between normal and adenomatous human colon tissues in vitro at 630-, 680-, 720-, 780-, 850-, and 890-nm wavelengths using a Ti:sapphire laser. The optical parameters of tissue samples are determined using a double integrating sphere setup at seven different laser wavelengths. The inverse Monte Carlo simulation is used to determine the optical properties from the measurements. The results of measurement show that the optical properties and their differences vary with a change of laser wavelength for normal and adenomatous colon mucosa/submucosa and normal and adenomatous colon muscle layer/chorion. The maximum absorption coefficients for normal and adenomatous human colon mucosa/submucosa are 680 nm, and the minimum absorption coefficients for both are 890 nm. The maximum difference of the absorption coefficients between both is 56.8% at 780 nm. The maximum scattering coefficients for normal and adenomatous colon mucosa/submucosa are 890 nm, and the minimum scattering coefficients for both are 780 nm. The maximum difference of the scattering coefficients between both is 10.6% at 780 nm. The maximum absorption coefficients for normal and adenomatous colon muscle layer/chorion are 680 nm, and the minimum absorption coefficients for both are 890 nm. The maximum difference of the absorption coefficients between both is 47.9% at 780 nm. The maximum scattering coefficients for normal and adenomatous colon muscle layer/chorion are 890 nm, and the minimum scattering coefficients for both are 680 nm. The maximum difference of the scattering coefficients between both is 9.61% at 850 nm. The differences in absorption coefficients between normal and adenomatous tissues are more significant than those in scattering coefficients.

Evaluation of effective ion-ion potentials in aqueous electrolytes.

We present high-accuracy simulation data for ion-ion radial distribution functions in NaCl aqueous electrolyte. From the data we evaluate ion-ion effective potentials via inverse Monte Carlo simulation procedure. Alternatively, we first evaluate effective direct correlation functions and then obtain effective potentials using the hypernetted-chain (HNC) approximation. Both methods are in excellent agreement, indicating that HNC approximation performs well with effective ion-ion potentials in aqueous solutions.

The effect of preparation technique on the optical parameters of biological tissue

The absorption coefficient μa, the scattering coefficient μs, and the scattering anisotropy factor g of porcine liver were studied in vitro using the integrating sphere technique and inverse Monte Carlo simulation in the wavelength range 450 to 700 nm. A reference preparation technique was developed using a dermatome providing specimens of 200 to 800 μm thickness without pre-freezing the tissue. The optical parameters as measured applying the reference preparation were compared to those measured after cryo-homogenisation. We found significant deviations of the scattering coefficient and the anisotropy factor which were compensated when the reduced scattering coefficient μs ′ was calculated. We also compared the effects of freezing reference specimens at -20 °C and at 77 K without homogenisation. For both freezing protocols noticeable deviations were found in all three optical parameters as well as in μs ′. The impact of tissue storage at 4 °C was measured in the range 4 to 48 h post mortem and showed a clear reduction of μa and a significant increase of μs even after 24 h of storage. Short-time storage of the specimens in saline solution reduced all three optical parameters significantly. In conclusion, the tissue preparation must be controlled in order to provide in vitro optical parameters that sufficiently mimic the in vivo situation.

Light-scattering properties of undiluted human blood subjected to simple shear.

An experimental investigation was performed into the effect of simple shear on the light-scattering properties of undiluted human blood. Undiluted human blood was enclosed between two glass plates with an adjustable separation between 30 and 120 microns and with one plate moving parallel to the other. For various shear rates and layer thicknesses, the angular light distribution and the collimated transmission were measured for 633-nm light. For shear rates above 150 s-1, the transmission results directly yielded a total attenuation coefficient of 120 mm-1. At lower shear rates the total attenuation followed an irregular pattern. From the angular intensity distributions, the anisotropy for single scattering was deduced by inverse Monte Carlo simulations. A continuous increase of the average cosine g with the shear rate was observed, with g in the range 0.95-0.975.

Inverse Monte Carlo simulation of the lithospheric thermal regime in the Fennoscandian Shield using xenolith-derived mantle temperatures

Monte Carlo inversion was applied in 2-dimensional conductive steady-state thermal simulation of a 600-km long lithosphere transect in the Fennoscandian Shield. The thermal regime in the mantle was constrained with thermobarometric data derived from kimberlite-hosted mantle xenoliths in eastern Finland, which suggest an average temperature of 1250±50°C at 208 km, but no partial melting down to at least 240 km. A priori models were generated from probability distributions assigned to thermal conductivity and heat production rate values of the 38 domains in the model, as well as the mantle heat flow density used as the lower boundary condition in the simulations. The forward problem was solved with a finite difference code, and the modification of the a priori distributions into a posteriori distributions was done using the Metropolis algorithm as the acceptance rule. The two-stage inversion, first using the measured surface heat flow values as a fitting object, and second, re-sampling the obtained a posteriori models but using xenolith-derived mantle temperature data as a fitting object, results in a considerable improvement in the resolution and average values of temperature and heat flow density in the model. The improvement can be seen in the model results to a distance of about 400 km from the xenolith area. The obtained results support a scheme that mantle heat flow is low in the thickest lithosphere area of the Fennoscandian Shield and about 10±1 mW m −2 at 200 km, and 13±1 mW m −2 in the uppermost subcrustal mantle. The inversion results suggest that there is no partial melt-bearing asthenosphere under the transect at depths shallower than at least 250 km. The seismic lithosphere-asthenosphere boundary is at depths of 110–170 km on the transect and corresponds to about 1100°C temperature in our model. This transition can be related to a zone of rheological weakening but not to the onset of melting. The mantle temperature and heat flow value in the eastern Finland kimberlite province are in agreement with models where small-scale convection (solid state creep) transports heat to the base of the lithosphere at about 250 km depth.

Experimental and theoretical study of the temperature and concentration dependence of the short-range order in Pt-V alloys

We present a detailed theoretical and experimental study of the short-range order in the ${\mathrm{Pt}}_{1\ensuremath{-}c}{\mathrm{V}}_{c}$ system at two concentrations ($c=$$\frac{1}{4}$ and $c=$$\frac{1}{9}$). In situ neutron-scattering experiments were performed in order to measure the short-range-order parameters in the disordered phase. We found a drastic effect of the concentration on the short-range order: in ${\mathrm{Pt}}_{3}\mathrm{V},$ the diffuse intensity is spread along the $(1k0)$ directions with maxima at the (100) positions, despite the stability at low temperature of a ${\mathrm{DO}}_{22}$ phase. In contrast, the diffuse intensity in ${\mathrm{Pt}}_{8}\mathrm{V}$ displays a splitting around the (100) positions with incommensurate maxima. Through inverse Monte Carlo simulations the two experiments yield, within the Ising model, two sets of effective-pair interactions. Despite quite different short-range-order patterns, the interactions seem nearly concentration independent with a dominant first-neighbors interaction ${V}_{1}.$ This concentration independence allows us to predict the ordered states and the ordering temperatures. In particular, at low temperatures, these interactions stabilize a new phase of composition ${A}_{5}B,$ which to our knowledge has not been observed until now. Finally, we analyze the origin and behavior of the incommensurate split peaks in ${\mathrm{Pt}}_{8}\mathrm{V}$ within a high-temperature expansion and show analytically that the splitting is due to a large decrease of the influence of ${V}_{1}$ on the short-range order as the concentration and/or the temperature decreases. This analysis shows also that the splitting distance should decrease with increasing temperature, in agreement with our Monte Carlo simulations, and in contrast with all the other alloys which have already been investigated, either experimentally or theoretically. More generally, we discuss the origin of the temperature behavior of a splitting distance in relation with the location in $q$ space of the incommensurate maxima. Using very simple arguments, we show, provided the restriction that the first-neighbor interactions are dominant, that the splitting distance increases or decreases with increasing temperature depending on whether these maxima lie along the $(1k0)$ axis or not.

Concentration variation of the effective pair interactions measured on the Pt-V system. Evaluation of the gamma expansion method

We present a detailed study of interactions in two alloys, Pt 3V and Pt 8V, and preliminary results on Pt 4V. In situ neutron scattering experiments were performed in order to measure the short range order parameters in the disordered phase for the two concentrations. We will show the drastic effect of the concentration on the short range order (SRO), particularly in Pt 8V, where the diffuse intensity maxima do not peak at special points of the fcc lattice. Using inverse Monte Carlo (IMC) simulations and the gamma expansion method (GEM), two sets of effective pair interactions (EPI) were deduced from the experimental SRO parameters within the Ising model. Surprisingly, despite quite different SRO patterns, the EPI seem nearly concentration independent. We will show, using MC simulation, that the two very different diffuse intensity maps are well reproduced with the same interaction set. The concentration independence of the EPI allowed us to describe also properties of the ordered states and more generally the whole phase diagram. In particular, we predict the existence, at very low temperature, of a new phase of stoichiometry A 5B which has never been observed until now.

Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation

Various models have been published calculating the light transport at the ocular fundus either for interpretation of in vivo reflectance measurements or for the prediction of photocoagulation effects. All these models took the absorption spectra of the pigments located at the ocular fundus, melanin, haemoglobin, xanthophyll, and the photoreceptor pigments, into account. However, light scattering inside the single fundus layers has not been investigated in detail and was, therefore, neglected in the calculations or only considered by very rough approximations. This paper presents measurements on specimens of retina, retinal pigment epithelium, choroid, and sclera using the double-integrating-sphere technique. Absorption coefficients, scattering coefficients, and anisotropy of scattering were calculated by an inverse Monte Carlo simulation from the measured collimated and diffuse transmittance and diffuse reflectance. Conclusions are drawn for the interpretation of fundus reflectance measurements, which are a useful tool in diagnostics and photocoagulation dosimetry.

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.

A First-Principles Study of Short Range Order in Cu-Zn

Recently, measurements of short-range order (SRO) diffuse neutron scattering intensity have been performed on quenched Cu-Zn alloys with 22.4 to 31.1 atomic percent (a/o) Zn, and pair interactions were obtained by Inverse Monte Carlo simulation [1]. These results are compared to SRO intensities and effective pair interactions obtained from first-principles electronic structure calculations. The theoretical SRO intensities were calculated with the Cluster Variation Method (CVM) in the tetrahedron-octahedron approximation with first-principles pair interactions as input. More generally, phase stability in the Cu-Zn alloy system is discussed, using ab-initio energetic properties.

Ordering Mechanism in Ni-Cr Alloys: Theory and Experiment

ABSTRACTRecently, short range order (SRO) parameters have been extracted from the neutron diffuse scattering intensities on Ni-Cr alloys with 11 to 25 at. pct. chromium. These data were analyzed using inverse-Monte Carlo simulations to extract atomic interactions and the results suggested the existence of a well defined, flat sheet of Fermi surface normal to the [110] direction. In this paper, this suggestion is investigated with a series of calculations which are based on the first-principles Korringa-Kohn-Rostoker-coherent-potential-approximation (KKRCPA). We calculate the electronic structure and the Bloch spectral function at the Fermi energy. We then proceed to calculate the effective cluster interactions using the generalized perturbation method (GPM) and compare them with the above-mentioned experimentally deduced interactions. In addition, we present preliminary results of two-dimensional angular correlation of positron annihilation radiation (2D-ACPAR) measurements, which probe the fermiology of this alloy system. The positron experiments demonstrate the existence of well-defined features in the Fermi surface of Ni89Cr11 but our calculations still have not yet established the origin of SRO in this system.