Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

Modelling water adsorption on Au(210) surfaces: II. Monte Carlo simulations

Canonical Monte Carlo simulations for the Au(210)/H(2)O interface, using a force field recently proposed by us, are reported. The results exhibit the main features normally observed in simulations of water molecules in contact with different noble metal surfaces. The calculations also assess the influence of the surface topography on the structural aspects of the adsorbed water and on the distribution of the water molecules in the direction normal to the metal surface plane. The adsorption process is preferential at sites in the first layer of the metal. The analysis of the density profiles and dipole moment distributions points to two predominant orientations. Most of the molecules are adsorbed with the molecular plane parallel to surface, while others adsorb with one of the O-H bonds parallel to the surface and the other bond pointing towards the bulk liquid phase. There is also evidence of hydrogen bond formation between the first and second solvent layers at the interface. (c) 2007 Elsevier B.V. All rights reserved.

A new algorithm for Reverse Monte Carlo simulations

We present a new algorithm for Reverse Monte Carlo (RMC) simulations of liquids. During the simulations, we calculate energy, excess chemical potentials, bond-angle distributions and three-body correlations. This allows us to test the quality and physical meaning of RMC-generated results and its limitations. It also indicates the possibility to explore orientational correlations from simple scattering experiments. The new technique has been applied to bulk hard-sphere and Lennard-Jones systems and compared to standard Metropolis Monte Carlo results. (C) 1998 American Institute of Physics.

Structure of acetone and dimethyl sulfoxide from Monte Carlo simulations and MM2 calculations

The structure of acetone and dimethyl sulfoxide in the liquid phase is investigated using Monte Carlo simulations and MM2 calculations. The principal site - site correlations and degree of structure in both liquids have been investigated. The results showed that dimethyl sulfoxide is more structured than acetone. At short distances the dipoles of neighboring molecules are found to be in antiparallel configurations, but further apart the molecules tend to be aligned predominantly as head to tail. In both liquids there is evidence of strong methyl - oxygen interaction, important to the structure of the liquids. The contacts suggest weak hydrogen bonds between methyl hydrogen and oxygen.

A critical investigation of the Tanford-Kirkwood scheme by means of Monte Carlo simulations

Monte Carlo simulations are used to assess the adequacy of the Tanford-Kirkwood prescription for electrostatic interactions in macromolecules. Within a continuum dielectric framework, the approach accurately describes salt screening of electrostatic interactions for moderately charged systems consistent with common proteins at physiological conditions. The limitations of the Debye-Huckel theory, which forms the statistical mechanical basis for the Tanford-Kirkwood result, become apparent for highly charged systems. It is shown, both by an analysis of the Debye-Huckel theory and by numerical simulations, that the difference in dielectric permittivity between macromolecule and surrounding solvent does not play a significant role for salt effects if the macromolecule is highly charged. By comparison to experimental data, the continuum dielectric model (combined with either an approximate effective Hamiltonian as in the Tanford-Kirkwood treatment or with exact Monte Carlo simulations) satisfactorily predicts the effects of charge mutation on metal ion binding constants, but only if the macromolecule and solvent are assigned the same or similar permittivities.

Coil to extended coil transition in polygalacturonic acid: Conductometric titration and monte carlo simulations

The conformational transition from coil to extended coil for polygalacturonic acid has been studied by conductometric titrations and Monte Carlo simulations. The results of conductometric titrations at different polymer concentrations have been analyzed using the model proposed by Manning,1 which describes the conductivity of polyelectrolitic solutions. This experimental approach provides the transport factor and the average distance between charged groups at different degrees of ionization (α). The mean distances between charged groups have been compared with the values obtained by Monte Carlo simulations. In these simulations the polymer chain is modeled as a self-avoiding random walk in a cubic lattice. The monomers interact through the unscreened Coulombic potential. The ratio between the end-to-end distance and the number of ionized beads provides the average distance between charged monomers. The experimental and theoretical values are in good agreement for the whole range of ionization degrees accessed by conductometric titrations. These results suggest that the electrostatic interactions seem to be the major contribution for the coil to extended coil conformational change. The small deviations for α ≤ 0.5 suggests that the stiffness of the chain, associated with local interactions, becomes increasingly significant as the fraction of charged groups is decreased. © 2000 American Chemical Society.

Application of reverse Monte Carlo simulations to diatomic molecules. Part 1. Noncomplete radial distribution functions

The reverse Monte Carlo (RMC) method generates sets of points in space which yield radial distribution functions (RDFS) that approximate those of the system of interest. Such sets of configurations should, in principle, be sufficient to determine the structural properties of the system. In this work we apply the RMC technique to fluids of hard diatomic molecules. The experimental RDFs of the hard-dimer fluid were generated by the conventional MC method and used as input in the RMC simulations. Our results indicate that the RMC method is only satisfactory in determining the local structure of the fluid studied by means of only mono-variable RDF. Also we suggest that the use of multi-variable RDFs would improve the technique significantly. However, the accuracy of the method turned out to be very sensitive to the variance of the input experimental RDF. © 1995.

Optimization of x-ray spectra in digital mammography through Monte Carlo simulations

In this work, a Monte Carlo code was used to investigate the performance of different x-ray spectra in digital mammography, through a figure of merit (FOM), defined as FOM = CNR2/(D) over bar (g), with CNR being the contrast-to-noise ratio in image and (D) over bar (g) being the average glandular dose. The FOM was studied for breasts with different thicknesses t (2 cm <= t <= 8 cm) and glandular contents (25%, 50% and 75% glandularity). The anode/filter combinations evaluated were those traditionally employed in mammography (Mo/Mo, Mo/Rh, Rh/Rh), and a W anode combined with Al or K-edge filters (Zr, Mo, Rh, Pd, Ag, Cd, Sn), for tube potentials between 22 and 34 kVp. Results show that the W anode combined with K-edge filters provides higher values of FOM for all breast thicknesses investigated. Nevertheless, the most suitable filter and tube potential depend on the breast thickness, and for t >= 6 cm, they also depend on breast glandularity. Particularly for thick and dense breasts, a W anode combined with K-edge filters can greatly improve the digital technique, with the values of FOM up to 200% greater than that obtained with the anode/filter combinations and tube potentials traditionally employed in mammography. For breasts with t < 4 cm, a general good performance was obtained with the W anode combined with 60 mu m of the Mo filter at 24-25 kVp, while 60 mu m of the Pd filter provided a general good performance at 24-26 kVp for t = 4 cm, and at 28-30 and 29-31 kVp for t = 6 and 8 cm, respectively.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

Monte Carlo Simulations of Novel Scintillator Detectors and Dosimetry Calculations

Monte Carlo (MC) simulation techniques are becoming very common in the Medical Physicists community. MC can be used for modeling Single Photon Emission Computed Tomography (SPECT) and for dosimetry calculations. 188Re, is a promising candidate for radiotherapeutic production and understanding the mechanisms of the radioresponse of tumor cells "in vitro" is of crucial importance as a first step before "in vivo" studies. The dosimetry of 188Re, used to target different lines of cancer cells, has been evaluated by the MC code GEANT4. The simulations estimate the average energy deposition/per event in the biological samples. The development of prototypes for medical imaging, based on LaBr3:Ce scintillation crystals coupled with a position sensitive photomultiplier, have been studied using GEANT4 simulations. Having tested, in the simulation, surface treatments different from the one applied to the crystal used in our experimental measurements, we found out that the Energy Resolution (ER) and the Spatial Resolution (SR) could be improved, in principle, by machining in a different way the lateral surfaces of the crystal. We have then studied a system able to acquire both echographic and scintigraphic images to let the medical operator obtain the complete anatomic and functional information for tumor diagnosis. The scintigraphic part of the detector is simulated by GEANT4 and first attempts to reconstruct tomographic images have been made using as method of reconstruction a back-projection standard algorithm. The proposed camera is based on slant collimators and LaBr3:Ce crystals. Within the Field of View (FOV) of the camera, it possible to distinguish point sources located in air at a distance of about 2 cm from each other. In particular conditions of uptake, tumor depth and dimension, the preliminary results show that the Signal to Noise Ratio (SNR) values obtained are higher than the standard detection limit.

Monte Carlo simulations of Potts glasses

A complete understanding of the glass transition isstill a challenging problem. Some researchers attributeit to the (hypothetical) occurrence of a static phasetransition, others emphasize the dynamical transitionof mode coupling-theory from an ergodic to a non ergodicstate. A class of disordered spin models has been foundwhich unifies both scenarios. One of these models isthe p-state infinite range Potts glass with p>4, whichexhibits in the thermodynamic limit both a dynamicalphase transition at a temperature T_D, and a static oneat T_0 < T_D. In this model every spins interacts withall the others, irrespective of distance. Interactionsare taken from a Gaussian distribution.In order to understand better its behavior forfinite number N of spins and the approach to thethermodynamic limit, we have performed extensive MonteCarlo simulations of the p=10 Potts glass up to N=2560.The time-dependent spin-autocorrelation function C(t)shows strong finite size effects and it does not showa plateau even for temperatures around the dynamicalcritical temperature T_D. We show that the N-andT-dependence of the relaxation time for T > T_D can beunderstood by means of a dynamical finite size scalingAnsatz.The behavior in the spin glass phase down to atemperature T=0.7 (about 60% of the transitiontemperature) is studied. Well equilibratedconfigurations are obtained with the paralleltempering method, which is also useful for properlyestablishing static properties, such as the orderparameter distribution function P(q). Evidence is givenfor the compatibility with a one step replica symmetrybreaking scenario. The study of the cumulants of theorder parameter does not permit a reliable estimation ofthe static transition temperature. The autocorrelationfunction at low T exhibits a two-step decay, and ascaling behavior typical of supercooled liquids, thetime-temperature superposition principle, is observed. Inthis region the dynamics is governed by Arrheniusrelaxations, with barriers growing like N^{1/2}.We analyzed the single spin dynamics down to temperaturesmuch lower than the dynamical transition temperature. We found strong dynamical heterogeneities, which explainthe non-exponential character of the spin autocorrelationfunction. The spins seem to relax according to dynamicalclusters. The model in three dimensions tends to acquireferromagnetic order for equal concentration of ferro-and antiferromagnetic bonds. The ordering has differentcharacteristics from the pure ferromagnet. The spinglass susceptibility behaves like chi_{SG} proportionalto 1/T in the region where a spin glass is predicted toexist in mean-field. Also the analysis of the cumulantsis consistent with the absence of spin glass orderingat finite temperature. The dynamics shows multi-scalerelaxations if a bimodal distribution of bonds isused. We propose to understand it with a model based onthe local spin configuration. This is consistent with theabsence of plateaus if Gaussian interactions are used.

Monte Carlo simulations of nucleation of colloidal crystals

A crystal nucleus in a finite volume may exhibit phase coexistence with a surrounding fluid. The thermodynamic properties of the coexisting fluid (pressure and chemical potential) are enhanced relative to their coexistence values. This enhancement is uniquely related to the surface excess free energy. rnA model for weakly attractive soft colloidal particles is investigated, the so called Asakura-Oosawa model. In simulations, this model allows for the calculation of the pressure in the liquid using the virial formula directly. The phase coexistence pressure in the thermodynamic limit is obtained from the interface velocity method. We introduce a method by which the chemical potential in dense liquids can be measured. There is neither a need to locate the interface nor to compute the anisotropic interfacial tension to obtain nucleation barriers. Therefore, our analysis is appropriate for nuclei of arbitrary shape. Monte Carlo simulations over a wide range of nucleus volumes yield to nucleation barriers independent from the total system volume. The interfacial tension is determined via the ensemble-switch method, hence a detailed test of classical nucleation theory is possible. The anisotropy of the interfacial tension and the resulting non-spherical shape has only a minor effect on the barrier for the Asakura-Oosawa model.