Abstract

Molecular Dynamics of Topological Barriers on the Crystallization Behavior of Ring Polyethylene Melts with Trefoil Knots

Topological barriers in ring polyethylene (PE) melts of trefoil knots inhibit crystallization due to self-entanglement, as confirmed by united atom molecular dynamics (UAMD) simulations. In this study, we clarified the decrease in the topological barriers of self-entangled knots with increasing polymer chain length (N) and the localization of the knotted segments in the noncrystallized region. In the UAMD simulations, isothermal crystallization processes were performed at T = 300 K for the trefoil knots using a crystallization time t_IC = 200 ns. Here, the trefoil knot gives the simplest nontrivial topology with nonzero crossing number. Crystallization was not observed in trefoil PE knots for N ≤ 120; however, crystallization did take place in the ring PE melt of the trivial knot with trivial topology and zero minimal crossing number. For N = 140, suppression of the growth of a crystalline phase (i.e., the polycrystalline phase) was observed in the trefoil PE melts, whereas such suppression was not detected in the trivial PE melts. In contrast, no significant differences in the crystallization behaviors of the trefoil and trivial PE melts were observed at N = 200. These results indicated that the topological barriers decreased with increasing N. Furthermore, to investigate the relationship between the chain conformation and degree of local crystallization, we developed a new mathematical method for searching the knotted segment of a trefoil knot in a crystallized trefoil PE melt. We found that trefoil knots with large subloops (¡Èlarge-leaves¡É) exhibited localization of the knotted segment. In addition, the large leaves of the localized knots dominated in the crystallized region, and the knotted segments of the localized knots were located mainly in the noncrystallized region.

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Linear response theory-based theoretical approach to structural changes in a polymer induced by β-decay of substituted tritium

Polymers exposed to tritiated water undergo hydrogen defects caused by isotope substitution and subsequent β-decay of substituted tritium, causing structural changes and loss of function in the biopolymers. Here, based on linear response theory, we predict the structural change of tritium-damaged polyethylene using the equilibrium trajectory of undamaged polyethylene to reduce the computation time of molecular dynamics simulations. Specifically, the ensemble average of the change in a physical quantity, such that it represents a structural change before and after damage, was calculated numerically using the time derivative of the total potential energy difference derived analytically and the physical quantity obtained from the simulation of undamaged polyethylene on the basis of linear response theory. A comparison between theoretical and simulation results revealed that the characteristic oscillation behaviors of the structural response of polyethylene can be predicted, whereas the quantitative prediction of the steady-state values over a long period is difficult.

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Rate of double strand breaks of genome-sized DNA in tritiated water: Its dependence on tritium concentration and water temperature

The goal of this study is to establish a simple experimental system to examine the rate of double strand breaks (DSBs) of genome-sized DNA molecules under irradiation of β-rays from tritium under well-controlled conditions for the validation of computer simulation on interactions of biomolecules and ionizing radiation. Irradiation effects were insignificant at tritium concentration of 1300 Bq/cm³, indicating that the effects of β-rays were far smaller than those of oxidation and/or thermal motion at the low dose rate (4.3 μGy/h). Clear increase in DSB rate was observed at tritium concentrations of 3.0-4.0 MBq/cm³. The temperature de-pendence of DSB rate was examined by using the high concentration tritiated water.

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The study on the stability of DNA structure by steered molecular dynamics simul\ ations

The stability of DNA double-stranded structure is examined by pulling atoms using steered molecular dynamics simulations. We use the base sequence to which DNA helicase binds; it acts to separate a double-stranded chain into single-stranded ones. The force is applied to atoms in the middle of the strand and they are pulled perpendicular to the helical axis of DNA. The force profile basically corresponds to the fraction of Watson-Crick hydrogen bonds which shows jumps and plateaus. The work for double-stranded separation can be interpreted in conjunction with the way to break hydrogen bonds. When some hydrogen bonds are broken at once, the bigger force is needed, and it leads to morework.

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A theoretical approach to structural change of a polymer induced by beta decays of substituted tritium based on the linear response theory

Molecular dynamics simulations of the hydrogen-removed polyethylene are carriedout to study the structural change of polyethylene induced by beta decays of substituted tritium. Our simulations show that the folded structure of the hydrogen-removed polyethylene becomes more disordered as the number of removed hydrogen atoms becomes larger. We also propose a theoretical approach to explaining and predicting our molecular dynamics simulation results of hydrogen-removed polyethylene on the basis of the linear response theory. We derive the time derivative of the dynamical quantity, which is conjugate to the force applied as perturbation in the framework of the linear response theory, required to calculate the response function. The dynamical quantity in this study is the total potential energy difference of polyethylene before and after removal of hydrogen. Preliminary results of the response function for the total potential energy of polyethylene after removal of hydrogen are presented.

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Image processing method for automatic measurement of number of DNA breaks

The number of double-strand breaks can be evaluated from the change of average DNA length. The average DNA length is measured by the single-molecule observation method using fluorescence microscope. The measurement of DNA length in the microscope images is done manually by experienced operators and it is time consuming in many experiments. An image processing method using OpenCV library to measure length of DNA in fluorescence microscope images is developed in this paper. An automation of measurement using deep learning is also proposed.

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Evaluation of Solvent-Accessible Surface Area of Backbone Hydrogen in Telomeric DNA Using Molecular Dynamics Simulation Molecular dynamics simulations for structure formation of polymers

Tritiated water is generated under the decommissioning process of the Fukushima Daiichi Nuclear Power Station. The Ministry of Economy, Trade and Industry, Japan (METI) and Tokyo Electric Power Company Holdings (TEPCO) are considering releasing tritium into the ocean. In addition, tritium is planning to use as fuel in fusion power plants, which is expected as a future power generation technology. Therefore, it is important to understand the impact of tritium on biomolecules in living organisms including human in detail. We aim to elucidate the mechanism of DNA damage due to the radioactive decay effect that occurs when light hydrogen in human DNA is replaced with tritium, using molecular dynamics (MD) methods. To understand the decay effect on DNA, first, it is necessary to evaluate the replaceability of light hydrogen to tritium for each hydrogen in DNA. In this study, to evaluate the degree of replaceability of the backbone hydrogen atoms in telomeric DNA of human, solvent-accessible surface area (SASA) is calculated for the data obtained by MD simulation. As a result, it is found that the SASA of H5 hydrogen is large in the hydrogen atoms in the backbone.

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Structural change of damaged polyethylene by beta-decay of substituted tritium using reactive force field

The molecular mechanism of structural change caused by the beta-decay of substituted tritium on DNA or polymeric materials is still being unsolved and it is hard to study the decay effect of tritium solely by experiment. In order to study the structural changes of damaged polyethylene caused by the decay effect of tritium, we randomly removed hydrogen atoms from the polyethylene chain and performed molecular dynamics (MD) simulations using the reactive force field (ReaxFF). We adopted two parameter sets of ReaxFF and evaluated their reliability by comparing the atomic forces with density functional theory calculations. The results of MD simulations at a low temperature of 100 K show that the structure of polyethylene will be less ordered when losing more hydrogen atoms. It is observed that a double bond or a cyclic structure will be formed when two carbon atoms, which are the nearest or next-nearest neighbors, lose hydrogen atoms.

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Icosahedral order in liquid and glassy phases of cyclohexane

We performed all-atom molecular dynamics simulations for bulk cyclohexane and analysed the short- and medium-range structures in supercooled and glassy states by using the Voronoi tessellation technique. From the analyses of both the potential energy of the system and the radial distribution function of molecules, cyclohexane was found to be vitrified as the temperature decreased. Furthermore, the icosahedral-like local structures are dominant at all temperatures and grow in a supercooled liquid, whereas the face-centred cubic structures do not grow when the temperature decreases. It was also ascertained that the icosahedral-like structure is more dominant than the full-icosahedral one. The network of the distorted icosahedron spreads throughout the system at low temperatures. Our simulation demonstrates the stability of the icosahedral local structure even in a non-spherical molecule such as cyclohexane.

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Molecular dynamics study on DNA damage by tritium disintegration

Using molecular dynamics (MD) simulation, we simulate the structural change of a telomeric DNA by β-decay of substituted tritium to helium-3. he configuration of the telomeric DNA is obtained by removing TRF2 protein from the TRF2-Dbd-DNA complex (Protein Data Bank ID is 3SJM). We assume that hydrogens (H) of guanines in the telomeric DNA are replaced to helium-3. Since this replacement of the H atoms to the 3He atoms changes the charge distribution significantly, the charge distribution used in the MD simulation for the modified guanine is obtained by the density functional theory calculations. We adopt, as the MD simulation, nanoscale molecular dynamics code with CHARMM36 force field using Langevin thermostat and Nosé-Hoover Langevin piston to control the temperature and pressure of the system, respectively. Moreover, changing both the number of replaced guanine N and the temperature of the system T, we calculate the root mean square deviation RMSD to quantify the dependence of the durability of the telomeric DNA on the β-decays. From the MD simulation, it is found that as N or T becomes larger, the RMSD of the DNA becomes also larger. Namely, it denotes that as the intensity of the β-decays becomes arger or as the temperature is increased, the DNA structure becomes more fragile.

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Single-chain folding of a quenched isotactic polypropylene chain through united atom molecular dynamics simulations

The single-chain folding of an isotactic polypropylene (iPP) chain through united atom (UA) molecular dynamics simulations under quenching was investigated using force fields (FFs) based on TraPPE-UA. We estimated the degree of local rigidity of the folded chain along iPP undergoing single-chain folding. To maintain the tacticity of iPP, we introduced improper torsional angle potentials and/or explicit hydrogen atoms bonded to backbone carbon atoms. In the simulation using modified TraPPE-UA FFs with added hydrogen atoms, folded structures were observed. In the cases using modified TraPPE-UA FFs with only improper torsional potentials, folding of the quenched iPP chain was not observed. Moreover, to clarify the folding behavior of the iPP chain, we studied the chirality of a single iPP chain and subsequently observed spontaneous chirality selection during the quenched folding process. We also examined the effect of the angle and torsional potentials of the added hydrogen on the folding behavior of a single iPP chain into local crystals. Therefore, we confirmed that the strength of the angle and torsional potentials contributed to the acceleration of the folding behavior.

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Hydrogen bond analysis of confined water in mesoporous silica using the reactive force field

The structural and dynamical properties of water confined in nanoporous silica with a pore diameter of 2.7 nm were investigated by performing large-scale molecular dynamics simulations using the reactive force field. The radial distribution function and diffusion coefficient of water were calculated, and the values at the centre of the pore agreed well with experimental values for real water. In addition, the pore was divided into thin coaxial layers, and the average number of hydrogen bonds, hydrogen bond lifetime and hydrogen bond strength were calculated as a function of the radial distance from the pore central axis. The analysis showed that hydrogen bonds involving silanol (Si-OH) have a longer lifetime, although the average number of hydrogen bonds per atom does not change from that at the pore centre. The longer lifetime, as well as smaller diffusion coefficient, of these hydrogen bonds is attributed to their greater strength.

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Structural change of tritium-substituted polymeric materials by a beta decay: A molecular dynamics study

The molecular mechanism through which how beta decays in tritium-substituted species damage DNA and polymeric materials is still unknown. Molecular dynamics simulations of hydrogen-removed polyethylene were performed to predict the structural change of the polyethylene chain after the substituted tritium decays. We calculated the potential energy, the global orientational order parameter, and the average number of consecutive trans bonds. The results are that, the greater the number of removed hydrogen atoms, the higher the potential energy and the lower the value of the global orientational order parameter and the average number of consecutive trans bonds. Thus, after losing hydrogen, polyethylene becomes poorer in terms of both thermal and structural stabilities.

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Volume Rendering Method Applied to 3D Edge Impurity Emission in LHD to Produce Projection Image in Arbitrary Plane

Understanding edge impurity transport is one of the important issues for fusion devices to control edge radiation distribution for detachment operation and impurity influx to the confinement region. In LHD, the edge magnetic field structure becomes complex stochastic magnetic field. In order to study relation between impurity transport and the magnetic field geometry, 3D edge impurity emission distributions are obtained by a multichannel spectrometer system and tomography scheme. However, it is difficult to understand the three-dimensional (3-D) structure. Therefore, we propose a visualization system that employs a volume rendering method. With the proposed system, which can be used on a PC or mobile device, the user can observe a 3D structure in an arbitrary plane. To realize this function, we propose a volume visualization system comprising preprocessing and real-time rendering stages. Therefore, the visualization framerate can exceed 30 frames per second on PCs and approximately six frames per second on mobile devices, although the user frequently changes the position and direction of the camera.

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Computational strategy for studying structural change of tritium-substituted macromolecules by a beta decay to helium-3

We propose a computational strategy for investigating structural change of tritium-substituted macromolecules. Effects of radiation on macromolecules such as polymeric materials and DNA are classified into three categories: (1) direct action, (2) indirect action, and (3) decay effect. In this study, we focus on the decay effect exclusively. After a beta decay of substituted tritium in macromolecules to helium-3, the generated inert helium-3 is assumed to be deleted quickly. To get an insight into the decay effect to the damage of macromolecules, we perform molecular dynamics simulations of tritium-deleted macromolecules and analyze their structural change. Preliminary simulation results of decay effect on polymeric materials and DNA are presented.

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Cavitation in Thin Films of Amorphous Polymers from the Static Melt Induced by T hermal Treatment

We discover a new cavitation phenomenon in amorphous polymers sandwiched between two thick slide glasses from the static melt induced by thermal treatment. By quenching atactic polystyrene (aPS) samples from the static melt under the glass transition temperature (T_g) and annealing them above Tg for thick slide glasses, cavities are created to relax the negative pressure. Cavity growth undergoes an Ostwald ripening-like process in cases of large molecular weight, while it undergoes a viscous fingering process in cases of small molecular weight. The induction time for cavity formation is found to decrease with the increase of the annealing temperature and with the decrease of the molecular weight. By contrast, no cavities are observed in an aPS sample between two thin cover glasses because the negative pressure can be relaxed by bending the whole thin cover glasses.

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An Accelerated United-Atom Molecular Dynamics Simulation on the Fast Crystallization of Ring Polyethylene Melts

To investigate crystallinities based on trans structures, we determined the differences in the crystallization properties of ring and linear polymers by performing united-atom-model molecular dynamics (MD) simulations of homogenous polyethylene melts of equal length, N, which refers to the number of monomers per chain. Modified parameters based on the DREIDING force field (FF) for the CH₂units were used in order to accelerate the crystallization process. To detect polymer crystallization, we introduced some local-order parameters that relate to trans segments in addition to common crystallinities using neighboring bond orders. Through quenching MD simulations at 5 K/ns, we roughly determined temperature thresholds, T_th, at which crystallization is observed, although it was hard to determine the precise T_th as observed in the laboratory time frame with the present computing resources. When N was relatively small (100 and 200), T_th was determined to be 320 and 350 K for the linear- and ring-polyethylene melts, respectively, while T_th was found to be 330 and 350 K, respectively, when N was 1000. Having confirmed that the crystallization of a ring-polyethylene melt occurs faster than that of the analogous linear melt, we conclude that the trans-segment-based crystallinities are effective for the analysis of local crystal behavior.

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Structure formation of a quenched single polyethylene chain with different force fields in united atom molecular dynamics simulations

The differences in the structure formations of a single polyethylene (PE) chain in united atom molecular dynamics (UAMD) simulations under quenching was investigated with varying force fields (FFs) that included torsional potential. We estimated the crystallinity of the folded structures undergoing local crystallization of the single PE chain. In simulations with DREIDING FF, highly folded structures were observed with fast quenching at the rate of 50 K/ns. From the viewpoint of crystallinity, we clarified that it was easy to achieve folding of the PE chains into local crystals with DREIDING FFs. With recent commonly used general FFs such as OPLS-UA and TraPPE-UA, highly folded structures were observed by quenching at the rate of 1 K/5 ns. In the present paper, we examine the Rigby-Roe (RR) FF optimized by Theodorou and coworkers and Paul-Yoon-Smith (PYS) FF optimized by Rutledge and coworkers. With the RR-Theodorou and PYS-Rutledge FFs, crystallization was observed with quenching at 1 K/ns and 1 K/5 ns, respectively. Consequently, it was relatively easier to achieve folding with the RR-Theodorou FF than with the PYS-Rutledge, OPLS-UA, and TraPPE-UA FFs.

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Dissipative Particle Dynamics Simulation for Self-Assembly of Symmetric Bolaamphiphilic Molecules in Solution

The self-assembly of dissolved symmetric bolaamphiphilic molecules is studied using dissipative particle dynamics simulations. Specifically, we investigate how interactions between the dual hydrophilic ends of the molecules affect the self-assembly process. Simulations show that four types of self-assembled structures (spherical micelles, tubes, vesicles, and wormlike micelles) are obtained from a random configuration of symmetric bolaamphiphilic molecules in solution. We find that the self-assembled structures change from spherical micelles to tubes, then to vesicles, and finally to wormlike micelles as the repulsive interactions between the hydrophilic ends increase. The molecular shapes in vesicles tend to be more rodlike than those in spherical micelles, tubes, or wormlike micelles.

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Dissipative Particle Dynamics Simulation of Self-Assembly in a Bolaamphiphilic Solution

The self-assembly of flexible bolaamphiphilic molecules in a solution is studied by dissipative particle dynamics simulations. In particular, we investigate the effect of the interaction difference, Δa, between the two different hydrophilic end groups on the self-assembly in a bolaamphiphilic solution. Our simulations show that two types of self-assembled structures, spherical vesicles and worm-like micelles, are obtained from a random configuration of bolaamphiphilic molecules in a solution. We find that the worm-like micelles are formed when Δa > 0, whereas spherical vesicles are obtained when Δa ≤ 0. It is also ascertained that the size of the spherical vesicles decreases as Δa decreases.

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An Intuitive Interface for Visualizing Numerical Data in a Head-Mounted Display with Gesture Control

This study aims to create an interface for visualizing numerical data on a head-mounted display (HMD) and introduce functions to allow control of this visualization via hand gestures. HMDs have the advantage of providing a user with a 360-degree field of view without taking up a lot of space. However, it is difficult to control visualized numerical data intuitively with this type of display because the user cannot see his/her own hand. We therefore introduced functions allowing the user to control the virtual scene with visualized virtual hands. We developed a system in which a virtual menu is presented to the users and they can change the visualization method by pushing virtual panels. The user can move freely in the visualized virtual scene. Moreover, to help users share their thoughts, we have introduced a drawing function that enables users to indicate points and areas of interest in the visualized scene.

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Melt memory of a spherulite nucleus formed through a seeding process in the crystal growth of isotactic polystyrene

The melt memory effect on the crystal growth of isotactic polystyrene is investigated using optical microscopy. After a spherulite is melted at a slightly higher temperature than the melting point and completely disappears, a polymer crystal nucleates and grows at the same position as the original spherulite when the temperature is decreased below the melting point. After the melting–recrystallization processes are repeated by raising and lowering the temperature, the melt memory effect becomes weak. This effect completely disappears at ∼40C above the equilibrium melting point when the melt temperature is gradually increased during the melting–recrystallization processes. The formation of spherulite nuclei is promoted by the seeding process, which consists of the following consecutive procedures: quenching a sample to a temperature below the glass transition temperature and annealing the sample slightly above the glass transition temperature. At the initial stage, the number density of spherulites rapidly decreases with the cumulative melting time. After the initial stage, the number density of spherulites exponentially decays with the cumulative melting time and approaches a finite value. This asymptotic value decreases with the melt temperature.

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Molecular Dynamics Simulation of Phase Behavior in a Bolaamphiphilic Solution

The phase behavior of bolaamphiphilic solutions is studied by coarse-grained molecular dynamics simulations of semiflexible bolaamphiphilic molecules with explicit solvent molecules. Our simulations show that six kinds of self-assembled structures (spherical micelles, worm-like micelles, bicontinuous structure, hexagonal structure, plate-like micelles, and lamellar structure) are obtained. It is established that, at low concentrations, a plate-like micelle changes to worm-like micelles, and then to spherical micelles as the hydrophilic interaction increases. Conversely, at intermediate concentrations, a lamellar structure changes to a bicontinuous structure; it then changes to worm-like micelles or a hexagonal structure as the hydrophilic interaction increases. It is also observed that the global orientational order parameter for the end bonds of bolaamphiphilic molecules can be used to clearly distinguish between the randomly-oriented structures (the spherical micelles, the worm-like micelles, and the bicontinuous structure), the lamellar structure, the hexagonal structure, and the plate-like micelles.

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Molecular Dynamics Simulation of Micellar Shape Transition in Amphiphilic Solutions

The micellar shape transition in amphiphilic solutions is studied by coarse-grained molecular dynamics simulations of rigid amphiphilic molecules with explicit solvent molecules. Our simulations show that the dominant micellar shape changes from disc to cylinder, and then to sphere as the hydrophilic interaction increases. We find that, as the hydrophilic interaction increases, the potential energy decreases monotonically even during the micellar shape transition, whereas the slope of the potential energy decreases in a stepwise manner in relation to the micellar shape transition. We also ascertained that there exists a wide coexistence region in the intensity of the hydrophilic interaction between a cylinder and a sphere, whereas the coexistence region between a cylinder and a disc is very narrow.

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Nucleation and polymorphism of trans-1,4-polyisoprene containing copper phthalocyanine

The effect of α- or β-copper phthalocyanine (CuPc) as a nucleating agent during the crystallization of trans-1,4-polyisoprene (TPI) was evaluated using polarized optical microscopy (POM), differential scanning calorimetry (DSC) and wide angle X-ray diffraction (WAXD). Pure TPI crystallizes into either a high-melting crystal form (HMF) or a low-melting crystal form (LMF), depending on the cooling condition of the melt. The HMF melts at ∼60C and LMF typically melts at ∼50C. Observation by POM showed that the LMF is generated at the interface between TPI and either α- or β-CuPc, selectively, when crystallized at 38C. In DSC measurements, the TPI composites containing α- or β-CuPc showed a higher crystallization temperature than that of pure TPI during the melt cooling process. Such results provided evidence that the α- or β-CuPc acted as a nucleating agent for TPI. The data obtained from WAXD proved that the HMF was generated mainly when pure TPI was cooled from the melt at a rate of 5C min⁻¹, while the LMF was generated predominantly when the TPI/α- or β-CuPc composites were crystallized under the same cooling conditions as those used for pure TPI. These results led to the conclusion that α- and β-CuPc acted as phase selective nucleating agents for LMF-TPI.

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One-, Two-, and Three-Dimensional Hopping Dynamics

Hopping dynamics in glass has been known for quite a long time. In contrast, hopping dynamics in smectic-A (SmA) and hexatic smectic-B (HexB) liquid crystals (LC) has been observed only recently. The hopping in SmA phase occurs among the smectic layers (one-dimensionally), while hopping in HexB phase occurs inside the layers (two-dimensionally). The hopping dynamics in SmA and HexB liquid crystal phases is investigated by parallel soft-core spherocylinders, while three-dimensional hopping dynamics in inherent glassy states is investigated by systems of Weeks-Chandler-Andersen (WCA) spheres. The temperature dependence of diffusion coefficients of hopping in SmA phase can be described by the Arrhenius equation characteristic of activation process. In HexB LC phase, the diffusion coefficients saturate at higher temperatures. In a system of WCA spheres, the values and temperature dependence of diffusion coefficients depend on the observed states.

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Micellar Shape Change in Amphiphilic Solution: A Molecular Dynamics Study

Micellar shape change in amphiphilic solution after sudden change in the solvophilic interaction is studied by molecular dynamics simulations of coarse-grained, rigid amphiphiles. Our simulations demonstrate that, after sudden increase in intensity of the solvophilicity, the disc micelle transforms into cylindrical or spherical micelles immediately. In contrast, spherical micelles coalesce into a disc micelle in a stepwise manner after sudden decrease in intensity of the solvophilicity.

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Dissipative Particle Dynamics Simulation of Phase Behavior in Bolaamphiphilic Solution

We study the phase behavior of bolaamphiphilic solution performing the dissipative particle dynamics simulations of coarse-grained bolaamphiphilic molecules with explicit solvent molecules. Our simulations show that there are six kinds of phases: isotropic micellar, micellar, rod-shaped micellar, hexagonal, network-structure and lamellar. The network-structure and the lamellar phases disappear when the restoring potential against the bending of bolaamphiphilic molecules in our simulation model is excluded; and the isotropic micellar and the hexagonal phases disappear when the restoring potential is included. This suggests that the bending potential is important in the formation of the higher-ordered structures by the bolaamphiphilic molecules.

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Design Support System with Haptic Feedback and Real-Time Interference Function

When we design and construct a large-scale device, it is very important to confirm the interference among its parts. We might need to confirm not only the interference among the parts that are designed at the start but also the interference with some parts that are added after construction. However, sometimes even on using 3D CAD, we cannot detect the interference or the collision among parts, particularly when these parts form a complex 3D shape. On the other hand, virtual reality devices have been used in various fields such as design support systems; however, real-time collision detection among complex parts has been difficult to achieve. We constructed a system that can detect collision and interference in real time in a virtual reality system. This engine can detect interference between polygons. This enables to calculate more accurately than voxel-based detection engine. Moreover, we propose a dynamic interference vector for removing interference. This vector is defined as a local minimum vector which removes the interference from the same edge where the contact starts. This method enables to prevent an object moves discontinuously, when the interference is removed. Finally, we introduced an example of using this system for assembling parts.

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Molecular Dynamics Simulation of Micellar Shape Change in Amphiphilic Solution

Micellar shape change in an amphiphilic solution is investigated by a molecular dynamics simulation of coarse-grained semiflexible amphiphilic molecules with explicit solvent molecules. Our simulations show that a cylindrical micelle is obtained at small molecular rigidity while a disc-shaped micelle appears at large molecular rigidity. We find that most chains are in an extended conformation at large molecular rigidity whereas the fraction of the chains in a bent conformation becomes large at small molecular rigidity. It is also ascertained that the micellar shape starts to change immediately after sudden increase of the molecular rigidity while an induction time is needed to change the micellar shape after sudden decrease of the molecular rigidity. This result can be qualitatively explained by considering the bond-bending potential energy and the conformational entropy of the amphiphilic molecules.

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Bracelet-shaped thermal display for representing numerical data

A thermal display, a type of haptic display, is effective for providing intuitive information about temperature. In many thermal display studies, users have assumed sitting positions when using these devices. However, their use in a large-scale virtual-reality system requires users to be in a standing position, as they generally observe three-dimensional (3D) objects while standing or walking around. Thus, we developed thermal displays that are suitable for large-scale virtual-reality systems. From another standpoint, in scientific visualization, response time is very important for observing physical phenomena, especially for dynamic numerical simulation. One way to optimize this parameter is to provide two types of thermal information: the rate of thermal change, and the actual temperature. To this end, we propose a bracelet-shaped thermal display with three Peltier elements that can provide both types of information. Finally, we present an example of visualizing and haptizing the result of a molecular dynamics simulation.

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Molecular dynamics simulation for phase behavior of amphiphilic solution

The phase behavior of amphiphilic solution is investigated by molecular dynamics simulation of amphiphilic rigid dimers with explicit solvent molecules. Our simulations show that three kinds of phases (isotropic micellar, hexagonal and lamellar phases) are formed at a lower temperature by quenching from a random configuration of amphiphilic molecules in solution at a higher temperature. It is ascertained that an isotropic micellar phase changes into a hexagonal phase, and then into a lamellar phase as the amphiphilic concentration increases. It is also found that the global orientational order parameter can be used to distinguish these three kinds of phases. From the detailed analyses of the phase behavior, it is concluded that the hydrophilic repulsion plays an important role in the formation of the hexagonal phase while the hydrophobic attraction plays a crucial role in the formation of the lamellar phase.

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Comparison of Hydrogen Adsorption on Diamond and Graphite Surfaces

By a classical molecular dynamics (CMD) simulation with a modified Brenner's reactive empirical bond-order (REBO) potential, we found that graphite with zigzag (1010) and armchair (1120) edge states is destroyed more easily than the other structures, i.e., graphite with (0001) surface, and diamond with the (100), (111), (120), and (110) surfaces. Experimental results indicated that graphite is eroded under hydrogen atom injection with E_in = 0.3 eV, and that diamond is not eroded under the same conditions. Our simulation results are consistent with the experimental results. We also reveal the temperature and saturation dependence of the surface structure of the carbon crystals.

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Haptization of molecular dynamics simulation with thermal display

Thermal display, which is a type of haptic display, is effective in providing intuitive information of temperature. However, in many studies, the user has assumed a sitting position during the use of these devices. In contrast, the user generally watches 3D objects while standing and walking around in large-scale virtual reality system, In addition, in scientific visualization, the response time is very important for observing physical phenomena, especially for dynamic numerical simulation. One solution is to provide two types of thermal information: information about the rate of thermal change and information about the actual temperature. We propose a thermal display with two Peltier elements which can show above two pairs of information and the result (for example energy and temperature, as thermal information) of numerical simulation. Finally, we represent an example of visualizing and haptizing the result of molecular dynamics simulation.

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Effect of Molecular Rigidity on Micelle Formation in Amphiphilic Solution

Micelle formation in an amphiphilic solution is investigated by a molecular dynamics simulation of coarse-grained semiflexible amphiphilic molecules with explicit solvent molecules. Our simulations show that the micellar shape changes from a cylinder to a disc as the intensity of the molecular rigidity increases. We find that the radius of gyration of the cylindrical micelle is larger than that of the disc-shaped micelle for small molecular rigidity, although the radius of gyration is almost steady even during the transition between a cylinder and a disc for large molecular rigidity. This indicates that a cylindrical micelle formed at small molecular rigidity is more anisotropic than the one obtained at large molecular rigidity. We also ascertained that a cylindrical micelle and a disc-shaped micelle coexist dynamically over a certain molecular rigidity range.

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Correlated Anomalous Diffusion - Random walk and Langevin equation -

A random walk model is formulated and examined which gives the correlated anomalous diffusion found in molecular dynamics simulations. The mean square displacement (MSD) shows a logarithmic behavior in one dimension. Corresponding Langevin equation is constructed by solving the inverse problem which gives a procedure to derive random impulse correlation from MSD function.

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Molecular dynamics simulations for structure formation of polymers and self-assembly of amphiphilic molecules

Molecular dynamics simulations were carried out to study the structure formation of polymers and the self-assembly of amphiphilic molecules. In particular, the structure formation of an isolated single polymer chain, isolated short chain molecules, and a single polymer chain in solution, and the spontaneous micelle formation in amphiphilic solution were investigated. From the detailed analyses of the structure formation processes, two characteristic features, the stepwise energy relaxation and the dynamic coexistence, are clarified as those common to the nonequilibrium dynamics in chain-like molecules and amphiphiles systems. We believe that these two findings will provide a key to the research on the universality of the nonequilibrium dynamics.

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Novel Primary Dispersion in Viscoelastic Behavior of Ferroelectric Nylon 6

As-quenched ferroelectric amorphous nylon 6 shows a new intense primary relaxation (α') peak for tan and E" around 300 K. Activation energy of α' relaxation was estimated to be about 150 kcal/mol, ca. three times that of α relaxation. It suggests that loose molecular packing in the ferroelectric amorphous phase makes the large-scale molecular motion possible, when rotational motion of amide groups is activated and D-E hysteresis loops can be observed.

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Molecular dynamics simulation of amphiphilic molecules in solution: Micelle formation and dynamic coexistence

The micelle formation and the dynamic coexistence in amphiphilic solution are investigated by molecular dynamics simulation of coarse-grained rigid amphiphilic molecules with explicit solvent molecules. Our simulations show that three kinds of isolated micelles (disc, cylindrical, and spherical micelles) are observed at a lower temperature by quenching from a random configuration of amphiphilic molecules in solution at a higher temperature. The micellar shape changes from a disc into a cylinder, and then into a sphere as the hydrophilic interaction increases whereas it is not so sensitive to the variation of the hydrophobic interaction. This fact indicates that the hydrophilic interaction plays an important roll in determining the micellar shape in the range of the interaction parameters used. It is also found that, in a certain interaction parameter range, two kinds of micellar shapes coexist dynamically. From the detailed analyses of the dynamic coexistence, it is ascertained that the dynamic coexistence of a cylindrical micelle and a spherical micelle accompanies the coalescence and fragmentation of micelles while that of a disc micelle and a cylindrical micelle does not, but exhibits the continuous change between them.

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Freezing of High-Temperature Phase in Vinylidene Fluoride/Trifluoroethylene Copolymer Crystals on Vacuum-Evaporated Metal Surfaces

Vinylidene fluoride/trifluoroethylene copolymer thin films cast from dilute cyclohexanone solution on vacuum-evaporated Pt, Al, Cu, and Au were annealed at 420K for 1 h. Transmission electron microscopic observation revealed that the hightemperature phase (HP) of the copolymers was frozen even at room temperature with molecular chains normal to the substrate after the annealing. The maximum lattice mismatch was 3.3% between the (001) plane of the HP of the copolymers and the {111} or {110} plane of the Pt crystals. Coulomb¡Çs interaction between the copolymer molecules and metallic atoms is suggested to have an important role in causing such phenomena.

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Superlattice Epitaxy of Vinylidene Fluoride/Trifluoroethylene Copolymer Crystals on Highly Oriented Pyrolytic Graphite

Vinylidene fluoride/trifluoroethylene (VDF/TrFE) copolymer crystals were grown from the dilute solution on cleaved (0001) surface of highly oriented pyrolytic graphite (HOPG). Using transmission electron microscopy, the orientational relation between the copolymer crystals and cleaved (0001) surface of HOPG is clarified, as well as the supperlattice matching. Electron diffraction (ED) patterns with 6-fold symmetry were observed for the copolymer crystals with VDF molar contents of 59, 65, and 71%. It suggests that a rectangular array of (201) plane for the high-temperature phase (HP) of the copolymer crystal faces HOPG(0001) plane, from which the molecular chains tilt by 46.7°. The ED pattern with such 6-fold symmetry is attributed to superposition of diffractions from the HP crystallites with three different orientations on HOPG. Such results suggest that epitaxial growth of HP occurred and it was frozen or stabilized even at room temperature due to epitaxial effect or interaction between copolymer molecules and substrate atoms.

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Molecular dynamics simulation of micelle formation in amphiphilic solution

The micelle formation in amphiphilic solution is investigated by molecular dynamics simulation of coarse-grained rigid amphiphiles with explicit solvent molecules. In our simulation model, the intensity of the hydrophilic interaction and the hydrophobic interaction can be varied independently. Our simulations show that various kinds of micellar structures are formed at a lower temperature by quenching from a random configuration of amphiphilic molecules in solution at a higher temperature. The micellar shape changes from a disc (bilayer) into a cylinder, and then into a sphere as the intensity of the hydrophilic interaction increases. It is also found that the micelle formation proceeds in a stepwise fashion through the coalescence of smaller micelles. From the analysis of the orientational order for the amphiphilic molecules, it is concluded that the orientational order parameters can be used to distinguish the micellar shapes clearly.

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Molecular dynamics simulation of self-organization in amphiphilic solution

The micelle formation in amphiphilic solution is investigated by means of a molecular dynamics simulation of coarse-grained amphiphilic molecules with explicit solvent molecules. A random configuration of amphiphilic molecules in solution at high temperature is quenched to a lower temperature. Our simulations show that the micellar shapes change from a cylindrical micelle to a planar bilayer as the number density increases. At higher densities, we also find the following characteristic features: (1) The potential energy relaxes in a stepwise manner. (2) The radius of gyration R_g of the largest micelles increases with time in a stepwise fashion. (3) The sharp bumps in R_g occur during coalescence of micelles.

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Molecular Dynamics Simulation for Structure Formation of Single Polymer Chain in Solution

The structure formation of a single polymer chain in solution with explicit solvent molecules is investigated by molecular dynamics simulation. The orientationally ordered structure is formed at a low temperature by quenching from a random conformation at a high temperature. The growth of the global and local orientational order proceeds in a stepwise manner at T 350 K, whereas it proceeds in a gradual manner at T = 300 K. From the detailed analyses of the parallel ordering process, it is found that a conformational change of the polymer chain occurs at first, and then parallel ordering starts to take place. In comparison with the simulation results of an isolated polymer chain in vacuum, it is ascertained that the stem length of the orientationally ordered structure formed in solution becomes 2-3 times longer than that formed in vacuum.

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Thermal, Structural and Ferroelectric Properties of Amorphous Phases in Quenched Nylon 6 Film

Three types of amorphous phases (ferroelectric metastable phase A with large remanent polarization, ferroelectric metastable phase B with small remanent polarization and paraelectric stable phase C) are identified in as-quenched and/or annealed nylon 6 films on the basis of the thermal data obtained by light-modulated differential scanning calorimetry (LMDSC) as well as X-ray data, which show different glass transition temperatures and d-spacings. The irreversible exothermic anomaly at 328 K observed through heating process in the conventional DSC is attributed to transition from phases A and/or B to nematic phases. The transition from phase A to phase B is considered to complete after 15 min anneling at 320 K on the basis of the LMDSC data, which corresponds to abrupt diminution of the remanent polarization by the correspondent anneling condition. Such results suggest that ferroelectricity of nylon 6 film is mainly attributed to phase A (frozen state of the melt) formed in quenched nylon 6 thin film.

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Phase Transition in Even-Even Nylon Crystals

Temperature dependence of crystal structures is examined with X-ray diffraction at normal pressure or elevated pressures for solution-grown nylons with octamethylene moiety between amino or carboxy groups (nylons 82, 410, 610, 810). Although octamethylene moiety between amino groups has the potential to cause the phase transition, the low melting point veils the transition appearance. Considering this comprehensively with previous results, it is concluded for all even-even nylons, that the phase transition in the two-dimensional methylene layer system can be experimentally observed only in nylon 6Y () crystals at normal and/or high pressures, where the hexamethylene moiety between amino groups plays an intrinsic role. The so-called `Brill transition' widely reported for melt-crystallized nylons is not a phase transition but an abrupt thermal expansion.

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Gradient Pattern Analysis of Structural Dynamics: Application to Molecular System Relaxation

This paper describes an innovative technique, the gradient pattern analysis (GPA), for analysing spatially extended dynamics. The measures obtained from GPA are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. By means of four gradient moments it is possible quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. The GPA technique is applied for the first time in 3D-simulated molecular chains with the objective of characterizing small symmetry breaking, amplitude and phase disorder due to spatio-temporal fluctuations driven by the spatially extended dynamics of a relaxation regime.

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Structure Formation of a Single Polymer Chain in Solution: A Molecular Dynamics Study

Molecular dynamics simulations are carried out to study the structure formation of a single polymer chain in solution. A random conformation of a polymer chain in solution at high temperature (550 K) is quenched to several lower temperatures (300, 350, and 400 K). Our simulations show the following characteristics: 1) At lower quenching temperature (300 K), local orientationally ordered domains are formed first, and they grow to be a folded orientationally ordered structure. 2) At a higher quenching temperature (400 K), a toroidal structure can be formed. 3) At an intermediate quenching temperature (350 K), a toroidal structure can be formed before a folded orientationally ordered structure is formed. The last characteristic indicates that an intermediate toroidal structure at 350 K is in a metastable state. We also find that it depends on the initial conformation of a polymer chain, whether a toroidal structure is formed or not.

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Molecular dynamics simulation of a single polymer chain in vacuum and in solution

Molecular dynamics simulations are carried out to study the structure formation of a single polymer chain in vacuum and in solution. We find that, in both cases, the folded orientationally ordered structure is formed at a low temperature by quenching from a random configuration at a higher temperature. It is also found that the stem length of the folded orientationally ordered structure formed in solution is longer than that formed in vacuum. This result is caused by the fact that the persistence length of a polymer chain in solution becomes longer than that in vacuum.

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Dynamics of orientationally ordered domains in a short chain-molecule system: Size dependence of domain oscillation

It was reported, in our previous works, that two orientationally ordered domains of short chain molecules move collectively as if they were rigid bodies in spite of the non-bonded short-range interaction potential (Lennard-Jones potential) among chain molecules. In this paper, in order to investigate the rigidity of the domain of short chain molecules in further detail, molecular dynamics simulations are performed for the following four case combinations of domains: the case I, II, III and IV are (61+29), (61+61), (124+61) and (124+124) chain molecule combinations, respectively. From these simulations, the size dependence of the domains' motion is demonstrated. Estimating an oscillation period for each case, it is found that . This relation is a peculiar property of orientationally ordered domains in a short chain-molecule system.

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Molecular dynamics study of structure formation of a single polymer chain by cooling

Structure formation of a single polymer chain with 500 methylene groups is investigated by means of a molecular dynamics simulation. We find that the folded orientationally ordered structure is formed at a low temperature by gradual stepwise cooling or by quenching from a random configuration at a higher temperature. It is also found that the global orientational order grows in a gradual manner in the case of gradual stepwise cooling, whereas it grows in a stepwise manner in the case of quenching.

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Dynamical Process of Coalescence of Domains in a Short Chain-molecule System

As the fundamental process of structure formation for short chain molecules, the coalescence of two orientationally ordered domains are investigated by numerical simulation. Each domain consists of 61 chain molecules, each of which consists of 20 CH₂ groups. One domain is tilted against another one with a certain angle. Then, the potential energy excited by tilting makes each domain rotate gradually. In this process, it is demonstrated that domains move collectively as if they were rigid bodies in spite of the non-bonded short-range interaction potential (Lennard-Jones potential) among chain molecules. From analysis of oscillation period of each potential well, it is concluded that the rigidity of domain derives its origin from the fact that the Lennard-Jones potential interaction of the unit hexagonal cell is strengthened to the order of the bonded interaction by packing.

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Virtual reality system to visualize and auralize numerical simulation data

One of the most practical objectives to use the virtual reality (VR) system in science is to make it easy to intuitively percept complex physical phenomena. We developed a VR system, called CompleXcope, which can represent "real" 3D visual and aural environment. Since attractive physical phenomena are often so complex and tangled, the VR system with 3D-sound functions is really useful for the quick comprehension of phenomena. We also show an example of visualizing and auralizing the molecular dynamic simulation results.

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Rigidity of Orientationally Ordered Domains of Short Chain Molecules

By molecular dynamics simulation, discovered is a strange rigid-like nature for a hexagonally packed domain of short chain molecules. In spite of the non-bonded short-range interaction potential (Lennard-Jones potential) among chain molecules, the packed domain gives rise to an apparent global moment of inertia. Accordingly, as two domains encounter obliquely, they rotate so as to be parallel to each other keeping their overall structures as if they were rigid bodies.

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Structure formation of a single polymer chain. I: Growth of trans domains

Molecular dynamics simulations are carried out to study structure formation of a single polymer chain with 500 CH₂ groups. Our simulations show that the orientationally ordered structure is formed at a low temperature both by gradual stepwise cooling and by quenching from a random configuration at a higher temperature. The growth of the global orientational order proceeds in a gradual manner in the case of gradual stepwise cooling, whereas it proceeds in a stepwise manner in the case of quenching. The latter feature endorses the previously proposed hypothetical grand view of self-organization [e.g. T. Sato, Phys. Plasmas 3, 2135 (1996)]: when a system is driven far from equilibrium, it will evolve to a more stable state in a stepwise fashion irrespective of its fundamental interaction forces. From the microscopic analysis of the structure formation process, we find the following characteristic features: (i) In the case of gradual stepwise cooling, the global orientational order grows gradually through the incorporation of small trans domains and the surrounding trans segments into the largest trans domain. (ii) In the case of quenching, the growth of the orientational order is either due to the incorporation of small trans domains and the surrounding trans segments into the largest trans domain or due to the elongation of the trans segments in the largest trans domain.

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Aural-Visual Virtual Representation System for Numerical Simulation Data

One of the most practical objectives to use the virtual reality system in science is to make it easy to intuitively percept complex physical phenomena. We developed a virtual reality system, called CompleXcope, which can represent "real" 3D visual environment. Since attractive physical phenomena are often so complex and tangled, the virtual reality system with 3D-sound functions is really useful for the quick comprehension of phenomena. We have recently added a sound function to the CompleXcope. In this paper we present examples produced by this aural-visual virtual reality system "CompleXcope".

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Molecular Dynamics Simulation of Chain-molecule Systems
--- Distribution of Conformational Defects ---

Molecular dynamics simulations are carried out to study the conformational defects in the orientationally ordered structures of short chain molecules and a single polymer chain. Our simulations show that the orientationally ordered structure is formed from a random configuration by cooling. There exist no fold surfaces in the orientationally ordered structure of short chain molecules while fold surfaces exist in the ordered structure of a single polymer chain. From detailed analyses of the conformational defects, we find that, in the case of short chain molecules, the double gauche defects with the same sign (...tg⁺g⁺t...) are predominantly located at the chain ends and the kink defects (...tg⁺tg^-t...), which do not cause serious deformation of chain molecules, can exist even at the chain interiors. On the other hand, in the case of a single polymer chain, several types of the conformational defects which give rise to large deformation of a polymer chain, such as the double gauche defects with the opposite sign (...tg⁺g^-t...), can be observed in the fold surfaces.

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Structure Formation in a Short Chain-molecule System: A Molecular Dynamics Study

The structure formation of 100 short chain molecules, each of which consists of 20 CH₂ groups, is investigated by means of a molecular dynamics simulation. The orientationally ordered structure is formed at a lower temperature by a sudden cooling from a random configuration at a higher temperature. It is also found that the growth of the local ordered clusters proceeds in a stepwise fashion.

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Molecular dynamics simulation of structure formation of short chain molecules

Molecular dynamics simulations are carried out to study the structure formation of 100 short chain molecules, each of which consists of 20 CH₂ groups. Our simulations show that the orientationally ordered structure is formed from a random configuration by quenching. The global orientational order starts to increase suddenly after a certain duration and grow in a stepwise fashion afterwards. This behavior is also found in the growth process of the local orientationally-ordered domains. It is found from the microscopic analysis of the structure formation process that parallel ordering of chain molecules starts to occur after the chain molecules stretch to some extent. From the analysis of the obtained orientationally ordered structure and the molecular mobility, we also find the following characteristic features: (i) The chain molecules are packed hexagonally at 400 K and the transition from the hexagonal phase toward the orthorhombic phase takes place as the temperature decreases. (ii) The gauche bonds in the same chain molecule tend to form gauche pairs. The gauche pairs with the same sign form the double gauche defects and those with the opposite sign form the kink defects. (iii) In the hexagonal phase, the chain molecules become longitudinally mobile. This result, which is obtained by the microscopic analysis of the chain motion, is the microscopic evidence to confirm the existence of the chain sliding diffusion in the hexagonal phase which underlies the sliding diffusion theory of polymer crystallization proposed by Hikosaka [Polymer 28, 1257 (1987); 31, 458 (1990)].

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MOLECULAR DYNAMICS STUDY OF THE STRUCTURAL FORMATION OF SHORT CHAIN MOLECULES: STRUCTURE AND MOLECULAR MOBILITY

By carrying out the molecular dynamics simulations of 100 short chain molecules, each of which consists of 20 CH₂ groups, we show that the orientationally ordered structure is formed at low temperature by a sudden cooling from a random configuration at high temperature. The essentially extended chains form a monolayer structure. The ratio of the lattice constants a/b takes the hexagonal value 3^1/2 at 400 K and decreases as the temperature decreases. From detailed analysis of the local orientational order, it is found that the growth of the local ordered clusters proceeds in a stepwise fashion. From the analysis of the molecular mobility, we find that the longitudinal chain motion increases dramatically with increasing temperature while the transverse chain motion is not so sensitive to the temperature variation.

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Molecular Dynamics Simulation of Structural Formation of Short Polymer Chains

Molecular dynamics simulations are carried out to study the structural formation of 100 short polymer chains, each of which consists of 20 CH₂ groups. Our simulations show that the orientationally ordered structure at low temperature is formed from a random structure at high temperature by a sudden cooling. The essentially extended chains form a monolayer structure with a hexagonal packing. From detailed analyses of the local and global orientational order, it is found that the formation of the global orientational order as well as the growth of the local ordered regions proceeds stepwise.

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Molecular dynamics simulations of structural formation of a single polymer chain: Bond-orientational order and conformational defects

The structural formation of a single polymer chain with 500 CH₂ groups is studied by the molecular dynamics simulations. Our simulations show that the bond-orientationally ordered structure at low temperatures is formed from a random-coil structure at high temperatures by a gradual stepwise cooling. From the radii of gyration and the bond-orientational order parameters, it is found that the anisotropy of a polymer chain also grows during the growth of the bond-orientational order. In the bond-orientationally ordered structure at low temperatures, 16 stems form a structure with deformed hexagonal symmetry and the stems in the outer layer have a tilted configuration. Furthermore, the gauche states are localized in the fold surface and the conformational states in the fold surface change more readily than those in the orientationally ordered reagion.

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Model of anomalous relaxation in supercooled liquids: random walk in fractal space and time

Anomalous structural relaxation observed in the supercooled liquids has been one of the most exciting problems for the last decade. Toward the full understanding of this phenomenon from the microscopic viewpoints, we report in this article the results of our studies on the several random walk models, i.e., random walk on fractal and non-fractal structures and the fractal time random walk model. It is found that the relaxation becomes of the Cole-Cole type, a famous empirical law, when the models have the fractal nature while the stretched-exponential type relaxation is observed in non-fractal structures. This work indicates that the concept of `fractal' introduced with mathematical mind has important relevance to realistic physical systems.

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Anomalous relaxation in fractal and disordered systems

Anomalous relaxation was studied by the Monte Carlo, MC, simulations of a random walk in fractal and disordered structures. The calculations of the relaxation functions and the complex susceptibilities show that the anomalous relaxation is of the Cole-Cole type in fractal structures while it is of the stretched-exponential type in non-fractal disordered structures, both types of which are empirical laws of anomalous relaxation known so far. Moreover the MC simulations of correlated random walks indicate that an inertia of a particle does not have influence on the long-time behavior of the anomalous relaxation.

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Complexity in plasma: From self-organization to geodynamo

A central theme of ``Complexity'' is the question of the creation of ordered structure in nature (self-organization). The assertion is made that self-organization is governed by three key processes, i.e., energy pumping, entropy expulsion and nonlinearity. Extensive efforts have been done to confirm this assertion through computer simulations of plasmas. A system exhibits markedly different features in self-organization, depending on whether the energy pumping is instantaneous or continuous, or whether the produced entropy is expulsed or reserved. The nonlinearity acts to bring a nonequilibrium state into a bifurcation, thus resulting in a new structure along with an anomalous entropy production. As a practical application of our grand view of self-organization a preferential generation of a dipole magnetic field is successfully demonstrated.

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Anomalous relaxation in fractal and disordered structures

For the purpose of clarifying the mechanisms of the anomalous relaxation, we carry out the Monte Carlo simulations of random walks in fractal and disordered structures. From our calculations of the relaxation functions and the complex susceptibilities, we find that the anomalous relaxation is of the Cole-Cole type in fractal structures while it is of the stretched-exponential type in non-fractal disordered structures. A most interesting aspect indicated by the results of our work is that the concept of fractal, originally introduced from purely mathematical point of view, is shown to play important roles in understanding some properties of realistic physical systems.

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Molecular Dynamics Simulations of Anomalous Relaxation in a Binary Lennard-Jones System

The anomalous relaxation in normal and supercooled liquids is studied by molecular dynamics (MD) simulations of a simple Lennard-Jones binary mixture for various temperatures and wave numbers. Our MD simulations show that the anomalous structural relaxation of a stretched-exponential type appears not only in a supercooled liquid region but also in a normal liquid region. This fact indicates that the anomalous relaxation is not a feature characteristic of supercooled liquids alone, but rather it is a phenomenon to be found in broader categories of disordered systems.

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Monte Carlo Simulations of Anomalous Relaxation in Percolating Systems

By Monte Carlo simulations of random walks in percolating systems, we show that the anomalous relaxation observed in disordered systems can be ascribed to the restricted geometry allowed for diffusion. In the fractal region corresponding to the concentration p=p_c, the relaxation function has scaling properties and becomes the Cole-Cole type, while, in the nonfractal disordered region corresponding to p>p_c, the relaxation function becomes the stretched-exponential and Cole-Cole type, respectively, when and . From detailed analyses, we give a microscopic explanation for these two types of relaxation functions known so far only as the empirical laws.

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Anomalous Relaxation in Fractal Structures

For the purpose of studying some interesting properties of anomalous relaxation in fractal structures, we carry out Monte Carlo simulations of random walks on two-dimensional fractal structures (Sierpinski carpets with different cutouts and site-percolation clusters in a square lattice at the critical concentration). We find that the relaxation is of the Cole-Cole type [J. Chem. Phys. 9, 341 (1941)] which is one of the empirical laws of anomalous relaxation. Scaling properties are found in the relaxation function as well as in the particle density. We also find that, in structures with almost the same fractal dimension, relaxation in structures with dead ends is slower than that in structures without them. This paper ascertains that the essential aspects of the anomalous relaxation due to many-body effects can be explained in the framework of the one-body model.

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Slow dynamics in supercooled liquids: molecular dynamics simulations

The relaxation processes in supercooled liquids were studied by molecular dynamics simulations of simple systems such as a simple Lennard-Jones binary mixture. Our simulations show (1) the existence of three stages of relaxation (microscopic, β and α-relaxation), (2) the scaling behavior of the susceptibility at the minima in the intermediate frequency region and the α-relaxation peak in the low frequency side, and (3) that the mechanisms of α- and β-relaxation are related to each other and independent of temperature. Although these features have only been observed experimentally so far in complex fluids, our results indicate that simple systems reveal the essential features of anomalous relaxation.

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Monte Carlo simulations of anomalous relaxation in a-Si ---random walk in spaces of fractal dimension ---

By carrying out Monte Carlo simulations of random walks in structures of fractal dimension, we show that the anomalous relaxation observed in amorphous systems including a-Si is ascribable to the restricted space allowed for diffusion in disordered systems. We calculate the mean square displacement as well as the exponent and relaxation time of the stretched-exponential decay in the Fourier components of the density. Discussion is given about the relations between the time dependences of these quantities and the fractal dimension.

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Stochastic transport model for diffusive properties in amorphous systems

The diffusive properties in amorphous systems are studied by Monte Carlo simulations of a continuous time random walk on a one dimensional lattice. When the probability distribution for the time interval between jump events satisfies the power law t^−1−α, the relaxation becomes anomalous of a stretched-exponential type when α<1, while transport phenomena similar to normal diffusion are observed when α>1. Scaling properties both in real and reciprocal space are ascertained.

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