Self-assembly of diblock copolymer mixtures in confined states: A Monte Carlo study

The self-assembly of diblock copolymer mixtures (A-b-B/A-b-C or A-b-B/B-b-C mixtures) subjected to cylindrical confinement (two-dimensional confinement) was investigated using a Monte Carlo method. In this study, the boundary surfaces were configured to attract blocks A but repel blocks B and C. Relative to the structures of the individual components, the self-assembled structures of mixtures of the diblock copolymers were more complex and interesting. Under cylindrical confinement, with varying cylinder diameters and interaction energies between the boundary surfaces and the blocks, we observed a variety of interesting morphologies. Upon decreasing the cylinder's diameter, the self-assembled structures of the A(15)B(15)/A(15)C(15) mixtures changed from double-helix/cylinder structures (blocks B and C formed double helices, whereas blocks A formed the outer barrel and inner core) to stacked disk/cylinder structures (blocks B and C formed the stacked disk core, blocks A formed the outer cylindrical barrel), whereas the self-assembled structures of the A(15)B(7)/B7C15 mixtures changed from concentric cylindrical barrel structures to screw/cylinder structures (blocks C formed an inside core winding with helical stripes, whereas blocks A and B formed the outer cylindrical barrels) and then finally to the stacked disk/cylinder structures.

Monte Carlo simulation of miscibility of polymer blends with repulsive interactions: effect of chain structure

The effects of the chain structure and the intramolecular interaction energy of an A/B copolymer on the miscibility of the binary blends of the copolymer and homopolymer C have been studied by means of a Monte Carlo simulation. In the system, the interactions between segments A, B and C are more repulsive than those between themselves. In order to study the effect of the chain structure of the A/B copolymer on the miscibility, the alternating, random and block copolymers were introduced in the simulations, respectively. The simulation results show that the miscibility of the binary blends strongly depends on the intramolecular interaction energy ((ε) over bar (AB)) between segments A and B within the A/B copolymers. The higher the repulsive interaction energy, the more miscible the A/B copolymer and homopolymer C are. For the diblock copolymer/homopolymer blends, they tend to form micro phase domains. However, the phase domains become so small that the blend can be considered as a homogeneous phase for the alternating copolymer/ homopolymer blends. Furthermore, the investigation of the average end-to-end distance ((h) over bar) in different systems indicates that the copolymer chains tend to coil with the decrease Of (ε) over bar (AB) whereas the (h) over bar of the homopolymer chains depends on the chain structure of the copolymers.

Monte Carlo simulation of phase behavior of polymer blends with special interactions

Full Paper: The phase, behavior of A-B-random copolymer/C-homopolymer, blends with special interaction was studied by a. Monte, Carlo simulation in two dimensions. The interaction between I segment A and segment C was repulsive, whereas it was attractive between segment B and segment C. The simulation results showed that the blend became two large co-continuous phase domains at lower segment-B component compositions, indicating that the blend showed spinodal decomposition. With an increase of the segment-B component, the miscibility between the copolymer,and the polymer was gradually improved up to being miscible. In addition, it was found that segment B tended to move to the surface of the copolymer phase in the case of a lower component of segment B. On the other hand, if was observed that the average, end-to-end distances ((h) over bar) for both copolymer and polymer changed slowly with increasing segment-B component of the copolymer up to 40%, thereafter they increased considerably with increasing segment B component. Moreover, it was found that the (h) over bar of the copolymer was obviously shorter than that of the homopolymer for the segment-B composition, region from 0% to 80%. Finally, a, phase diagram showing I phase and - II phase regions under the condition of constant-temperature is presented.

Monte Carlo simulation of phase separation of A/B/A-B ternary mixtures

Monte Carlo simulations were used to model A/B/A-B ternary mixtures with different AB diblock copolymer volume fractions for which both the dispersed and continuous phase volume fractions were kept constant. For concentrations of the diblock copolymer below a critical value, the domain size increment of the dispersed phase decreases linearly with the copolymer concentration. This is in agreement with the predictions of Noolandi and Hong. The dependence of the domain size as a function of the copolymer volume fraction can also be fitted by the equation of Tang and Huang. Our simulations indicate, for the first time, that the micelles form before saturation of the interface occurs. This means that the formation of the micelles is not a result of the saturation of the interface.

Ukryty punkt krytyczny w mieszaninach binarnych – badania metodami symulacji Monte – Carlo

Wydział Fizyki

Monte Carlo Analysis and Physics Characterization of a Novel Nanoparticle Detector for Medical and Micro-dosimetry Applications

The outcomes for both (i) radiation therapy and (ii) preclinical small animal radio- biology studies are dependent on the delivery of a known quantity of radiation to a specific and intentional location. Adverse effects can result from these procedures if the dose to the target is too high or low, and can also result from an incorrect spatial distribution in which nearby normal healthy tissue can be undesirably damaged by poor radiation delivery techniques. Thus, in mice and humans alike, the spatial dose distributions from radiation sources should be well characterized in terms of the absolute dose quantity, and with pin-point accuracy. When dealing with the steep spatial dose gradients consequential to either (i) high dose rate (HDR) brachytherapy or (ii) within the small organs and tissue inhomogeneities of mice, obtaining accurate and highly precise dose results can be very challenging, considering commercially available radiation detection tools, such as ion chambers, are often too large for in-vivo use.

In this dissertation two tools are developed and applied for both clinical and preclinical radiation measurement. The first tool is a novel radiation detector for acquiring physical measurements, fabricated from an inorganic nano-crystalline scintillator that has been fixed on an optical fiber terminus. This dosimeter allows for the measurement of point doses to sub-millimeter resolution, and has the ability to be placed in-vivo in humans and small animals. Real-time data is displayed to the user to provide instant quality assurance and dose-rate information. The second tool utilizes an open source Monte Carlo particle transport code, and was applied for small animal dosimetry studies to calculate organ doses and recommend new techniques of dose prescription in mice, as well as to characterize dose to the murine bone marrow compartment with micron-scale resolution.

Hardware design changes were implemented to reduce the overall fiber diameter to <0.9 mm for the nano-crystalline scintillator based fiber optic detector (NanoFOD) system. Lower limits of device sensitivity were found to be approximately 0.05 cGy/s. Herein, this detector was demonstrated to perform quality assurance of clinical 192Ir HDR brachytherapy procedures, providing comparable dose measurements as thermo-luminescent dosimeters and accuracy within 20% of the treatment planning software (TPS) for 27 treatments conducted, with an inter-quartile range ratio to the TPS dose value of (1.02-0.94=0.08). After removing contaminant signals (Cerenkov and diode background), calibration of the detector enabled accurate dose measurements for vaginal applicator brachytherapy procedures. For 192Ir use, energy response changed by a factor of 2.25 over the SDD values of 3 to 9 cm; however a cap made of 0.2 mm thickness silver reduced energy dependence to a factor of 1.25 over the same SDD range, but had the consequence of reducing overall sensitivity by 33%.

For preclinical measurements, dose accuracy of the NanoFOD was within 1.3% of MOSFET measured dose values in a cylindrical mouse phantom at 225 kV for x-ray irradiation at angles of 0, 90, 180, and 270˝. The NanoFOD exhibited small changes in angular sensitivity, with a coefficient of variation (COV) of 3.6% at 120 kV and 1% at 225 kV. When the NanoFOD was placed alongside a MOSFET in the liver of a sacrificed mouse and treatment was delivered at 225 kV with 0.3 mm Cu filter, the dose difference was only 1.09% with use of the 4x4 cm collimator, and -0.03% with no collimation. Additionally, the NanoFOD utilized a scintillator of 11 µm thickness to measure small x-ray fields for microbeam radiation therapy (MRT) applications, and achieved 2.7% dose accuracy of the microbeam peak in comparison to radiochromic film. Modest differences between the full-width at half maximum measured lateral dimension of the MRT system were observed between the NanoFOD (420 µm) and radiochromic film (320 µm), but these differences have been explained mostly as an artifact due to the geometry used and volumetric effects in the scintillator material. Characterization of the energy dependence for the yttrium-oxide based scintillator material was performed in the range of 40-320 kV (2 mm Al filtration), and the maximum device sensitivity was achieved at 100 kV. Tissue maximum ratio data measurements were carried out on a small animal x-ray irradiator system at 320 kV and demonstrated an average difference of 0.9% as compared to a MOSFET dosimeter in the range of 2.5 to 33 cm depth in tissue equivalent plastic blocks. Irradiation of the NanoFOD fiber and scintillator material on a 137Cs gamma irradiator to 1600 Gy did not produce any measurable change in light output, suggesting that the NanoFOD system may be re-used without the need for replacement or recalibration over its lifetime.

For small animal irradiator systems, researchers can deliver a given dose to a target organ by controlling exposure time. Currently, researchers calculate this exposure time by dividing the total dose that they wish to deliver by a single provided dose rate value. This method is independent of the target organ. Studies conducted here used Monte Carlo particle transport codes to justify a new method of dose prescription in mice, that considers organ specific doses. Monte Carlo simulations were performed in the Geant4 Application for Tomographic Emission (GATE) toolkit using a MOBY mouse whole-body phantom. The non-homogeneous phantom was comprised of 256x256x800 voxels of size 0.145x0.145x0.145 mm3. Differences of up to 20-30% in dose to soft-tissue target organs was demonstrated, and methods for alleviating these errors were suggested during whole body radiation of mice by utilizing organ specific and x-ray tube filter specific dose rates for all irradiations.

Monte Carlo analysis was used on 1 µm resolution CT images of a mouse femur and a mouse vertebra to calculate the dose gradients within the bone marrow (BM) compartment of mice based on different radiation beam qualities relevant to x-ray and isotope type irradiators. Results and findings indicated that soft x-ray beams (160 kV at 0.62 mm Cu HVL and 320 kV at 1 mm Cu HVL) lead to substantially higher dose to BM within close proximity to mineral bone (within about 60 µm) as compared to hard x-ray beams (320 kV at 4 mm Cu HVL) and isotope based gamma irradiators (137Cs). The average dose increases to the BM in the vertebra for these four aforementioned radiation beam qualities were found to be 31%, 17%, 8%, and 1%, respectively. Both in-vitro and in-vivo experimental studies confirmed these simulation results, demonstrating that the 320 kV, 1 mm Cu HVL beam caused statistically significant increased killing to the BM cells at 6 Gy dose levels in comparison to both the 320 kV, 4 mm Cu HVL and the 662 keV, 137Cs beams.

Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in S-n rings and chains (n=2-18) (vol 118, pg 9257, 2003)

Density functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of S8 rings, on the interaction between a pair of such rings, and the reaction between one S8 ring and the triplet diradical S8 chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid–liquid phase transition. The results of these simulations will be presented in Part II.

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains [Part I, J. Chem. Phys. 118, 9257 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450less than or equal toTless than or equal to850 K and P=0 starting from monodisperse S-8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T-max that depends on DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(max), because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S-8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S-8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.

Density functional/Monte Carlo study of ring-opening polymerization

Density functional calculations of the structure, potential energy surface and reactivity for organic systems closely related to bisphenol-A-polycarbonate (BPA-PC) provide the basis for a model describing the ring-opening polymerization of its cyclic oligomers by nucleophilic molecules. Monte Carlo simulations using this model show a strong tendency to polymerize that is increased by increasing density and temperature, and is greater in 3D than in 2D. Entropy in the distribution of inter-particle bonds is the driving force for chain formation. (C) 2002 Elsevier Science B.V. All rights reserved.

Monte Carlo simulation of cluster growth in surface defects induced by the tip of a scanning tunnelling microscope

First steps are taken to model the electrochemical deposition of metals in nanometer-sized cavities. In the present work, the electrochemical deposition of Cu atoms in nanometer-sized holes dug on Au(111) is investigated through Monte Carlo simulations using the embedded atom method to represent particle interactions. By sweeping the chemical potential of Cu, a cluster is allowed to grow within the hole rising four atomic layers above the surface. Its lateral extension remains confined to the area defined by the borders of the original defect. (C) 2004 Elsevier B.V. All rights reserved.

Monte Carlo simulation of properties of monolayers and metal islands adsorbed on metallic (111) surfaces

To obtain the surface stress changes due to the adsorption of metal monolayers onto metallic surfaces, a new model derived from thermodynamic considerations is presented. Such a model is based on continuum Monte Carlo simulations with embedded atom method potentials in the canonical ensemble, and it is extended to consider the behavior on different islands adsorbed onto (111) substrate surfaces. Homoepitaxial and heteroepitaxial systems are studied. Pseudomorphic growth is not observed for small metal islands with considerable positive misfit with the substrate. Instead, the islands become compressed upon increase of their size. A simple model is proposed to interpolate between the misfits of atoms in small islands and the pseudomorphic behavior of the monolayer.

Kinetic Monte Carlo study of electrochemical growth in a heteroepitaxial system

Structural and kinetic aspects of 2-D irreversible metal deposition under potentiostatic conditions are analyzed by means of dynamic Monte Carlo simulations employing embedded atom potentials for a model system. Three limiting models, all considering adatom diffusion, were employed to describe adatom deposition. The first model (A) considers adatom deposition on any free substrate site on the surface at the same rate. The second model (B) considers adatom deposition only on substrate sites which exhibit no neighboring sites occupied by adatoms. The third model (C) allows deposition at higher rates on sites presenting neighboring sites occupied by adatoms. Under the proper conditions, the coverage (theta) versus time (t) relationship for the three cases can be heuristically fitted to the functional form theta = 1 - exp(-betat(alpha)), where alpha and beta are parameters. We suggest that the value of the parameter alpha can be employed to distinguish experimentally between the three cases. While model A trivially delivers a = 1, models B and C are characterized by alpha 1, respectively.

Atomic ordering in nano-layered FePt: Multiscale Monte Carlo simulation

Nano- and meso-scale simulation of chemical ordering kinetics in nano-layered L1(0)-AB binary intermetallics was performed. In the nano- (atomistic) scale Monte Carlo (MC) technique with vacancy mechanism of atomic migration implemented with diverse models for the system energetics was used. The meso-scale microstructure evolution was, in turn, simulated by means of a MC procedure applied to a system built of meso-scale voxels ordered in particular L1(0) variants. The voxels were free to change the L1(0) variant and interacted with antiphase-boundary energies evaluated within the nano-scale simulations. The study addressed FePt thin layers considered as a material for ultra-high-density magnetic storage media and revealed metastability of the L1(0) c-variant superstructure with monoatomic planes parallel to the (001)-oriented layer surface and off-plane easy magnetization. The layers, originally perfectly ordered in the c-variant, showed discontinuous precipitation of a- and b-L1(0)-variant domains running in parallel with homogeneous disordering (i.e. generation of antisite defects). The domains nucleated heterogeneously on the free monoatomic Fe surface of the layer, grew inwards its volume and relaxed towards an equilibrium microstructure of the system. Two

A Monte Carlo model of DNA double-strand break clustering and rejoining kinetics for the analysis of pulsed-field gel electrophoresis data

In studies of radiation-induced DNA fragmentation and repair, analytical models may provide rapid and easy-to-use methods to test simple hypotheses regarding the breakage and rejoining mechanisms involved. The random breakage model, according to which lesions are distributed uniformly and independently of each other along the DNA, has been the model most used to describe spatial distribution of radiation-induced DNA damage. Recently several mechanistic approaches have been proposed that model clustered damage to DNA. In general, such approaches focus on the study of initial radiation-induced DNA damage and repair, without considering the effects of additional (unwanted and unavoidable) fragmentation that may take place during the experimental procedures. While most approaches, including measurement of total DNA mass below a specified value, allow for the occurrence of background experimental damage by means of simple subtractive procedures, a more detailed analysis of DNA fragmentation necessitates a more accurate treatment. We have developed a new, relatively simple model of DNA breakage and the resulting rejoining kinetics of broken fragments. Initial radiation-induced DNA damage is simulated using a clustered breakage approach, with three free parameters: the number of independently located clusters, each containing several DNA double-strand breaks (DSBs), the average number of DSBs within a cluster (multiplicity of the cluster), and the maximum allowed radius within which DSBs belonging to the same cluster are distributed. Random breakage is simulated as a special case of the DSB clustering procedure. When the model is applied to the analysis of DNA fragmentation as measured with pulsed-field gel electrophoresis (PFGE), the hypothesis that DSBs in proximity rejoin at a different rate from that of sparse isolated breaks can be tested, since the kinetics of rejoining of fragments of varying size may be followed by means of computer simulations. The problem of how to account for background damage from experimental handling is also carefully considered. We have shown that the conventional procedure of subtracting the background damage from the experimental data may lead to erroneous conclusions during the analysis of both initial fragmentation and DSB rejoining. Despite its relative simplicity, the method presented allows both the quantitative and qualitative description of radiation-induced DNA fragmentation and subsequent rejoining of double-stranded DNA fragments. (C) 2004 by Radiation Research Society.

Monte Carlo radiation hydrodynamics:Methods, tests and application to Type Ia supernova ejecta

In astrophysical systems, radiation-matter interactions are important in transferring energy and momentum between the radiation field and the surrounding material. This coupling often makes it necessary to consider the role of radiation when modelling the dynamics of astrophysical fluids. During the last few years, there have been rapid developments in the use of Monte Carlo methods for numerical radiative transfer simulations. Here, we present an approach to radiation hydrodynamics that is based on coupling Monte Carlo radiative transfer techniques with finite-volume hydrodynamical methods in an operator-split manner. In particular, we adopt an indivisible packet formalism to discretize the radiation field into an ensemble of Monte Carlo packets and employ volume-based estimators to reconstruct the radiation field characteristics. In this paper the numerical tools of this method are presented and their accuracy is verified in a series of test calculations. Finally, as a practical example, we use our approach to study the influence of the radiation-matter coupling on the homologous expansion phase and the bolometric light curve of Type Ia supernova explosions. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.