Monte Carlo simulation of two interpenetrating polymer networks: Structure, swelling, and mechanical properties

The swelling and mechanical properties of various interpenetrating polymer networks (IPNs) were studied. Six networks made from permutations of a moderately crosslinked polyelectrolyte network (ref), a moderately crosslinked neutral polymer network (net1), and a highly crosslinked polyelectrolyte network (net2) were first swollen in water and structural properties such as end-to-end chain lengths and radial distribution functions were compared with the component networks' equilibrium properties. The swelling of composite IPNs was discussed in terms of a balance between the osmotic pressure due to mobile counterions and the restoring force of the network chains, which act in parallel to counteract the osmotic swelling. For the ref-net2 system, the strong stretching of net2 chains increases the network restoring force and the further swelling due to the counterions is suppressed. The swollen networks were then uniaxially stretched, and equilibrium stress-strain plots were obtained up to high extension ratios. The equilibrium volume decreased upon uniaxial extension, and the elastic moduli of IPNs of the A-A type were slightly greater than that of their respective single networks.     

Rotational diffusion current of multi-charged redox species by means of Monte Carlo simulation

Multi-charged redox species such as dispersed metal nanoparticles and latex particles have exhibited diffusion-controlled currents, which may be caused by not only the conventionally translational diffusion but also by the rotation of the species or random orientation toward the electrode. Rotational diffusion was here taken into account by use of the multiple redox-charged model particle which moves back and force in thin layer cell as well as rotates clockwise and counterclockwise by means of the Monte Carlo simulation. The steady-state current was smaller than the current which might flow if all the charge were to transfer at infinite rotational speed. The current values had a linear relation with the −1/2 powers of the number of the charge per particle. This relation was in accord with the experimental results of the partial charge transfer reaction of the ferrocene-immobilized latex suspension.     

An ab initio simulation on electron beam physical vapor deposition of Gd2Zr2O7 coating by density functional theory and kinetic Monte Carlo

Without any experimental inputs, the electron beam physical vapor deposition (EB-PVD) of Gd₂Zr₂O₇ with much potential for thermal barrier coatings was investigated by use of the kinetic Monte Carlo, after fitting the potential function using lattice inversion method and “coarse-grained” mapping on the cohesive energy calculated by density functional theory, to reveal the effect of critical processing parameters of EB-PVD on the microstructures and porosity of the deposited coating, for example, substrate temperature, deposition rate and incident angle. Based on the lower energy barrier calculated by a nudged elastic band, intra-layer diffusion is easier than interlayer diffusion, attributed to the fewer bonds in the former. Furthermore, the porosity of the coating decreases with the increase of temperature or decrease of deposition rate, with the gradual disappearing large gaps among columnar crystals and filled pores, because of the increase of transition probability and transition times. With the decreasing incident angle, the area of the shadow zone decreases and less particles can be blocked by previously deposited ones, making the columnar crystals disappear gradually, with more like laminated structures.     

外部强制对CO催化氧化动力学影响的Monte Carlo模拟

利用Monte Carlo方法研究了外部强制过程对CO催化氧化反应过程中振荡动力学行为的影响规律。研究结果表明:通过矩形脉冲可以有效地调控振荡的动力学行为,在一定的脉冲振幅和脉冲宽度下,通过改变矩形脉冲的周期,CO催化氧化出现了短周期振荡、双峰振荡等不同的动力学行为。当强制过程即矩形脉冲的周期小于自发振荡的周期时,可以观察到短周期振荡行为,当矩形脉冲的周期大于自发振荡的周期时,可以观察到双峰振荡等动力学行为。振荡动力学的改变主要是因为强制振荡过程使得催化剂表面发生了从氧化态向还原态的转变。     

Magnetic interactions and hysteresis loops study of Co/CoFe2O4 nanoparticles

Co/CoFe₂O₄ nanoparticles with the mean size of 8.8, 10.8 and 16.9 nm were prepared by thermal decomposition of metal salts in the presence of citric acid. The X-ray diffraction patterns and Rietveld refinements confirmed coexistence of Co-ferrite and metallic cobalt phases in the nano-powders. Scanning electron microscope images showed an increase in particles aggregates mean diameter with increasing the annealing temperature. Magnetic hysteresis loops showed a demagnetization jump at low fields, which was attributed to different reversal fields of ferrite and the cobalt phases. Field-dependent behavior of maximum magnetization (M_max), remanence (M_r), squareness (S) and coercivity (H_c) were studied through minor loops measurements. The calculated S value of the loops showed a maximum, between anisotropy and coercive fields. A sharp increase in H_c of larger particles was observed with increasing the applied field when compared to smaller particles. Henkel plots showed that the samples are interacting. Negative deviation of Henkel plots from linear behavior and negative δm plots revealed the dominant role of dipole–dipole interactions in the nano-aggregates.     

Monte Carlo simulation of terpolymerization: Optimizing the simulation and post-processing times

Monte Carlo simulations are a useful and easy way to understand a polymerization reaction process properly. However, achieving reliable results with Monte Carlo simulations can also lead to prohibitive computational times and a considerable amount of data to be processed afterward. The present study analyses the Monte Carlo simulation of a steady-state terpolymerization process to reduce the overall computational time of the simulation and the post-processing of its results. Different sorting algorithms (Bubble, Insertion, Selection, and Tim) and Python libraries (Joblib and Numba) were used. The chain composition distribution and the micro-structures resultant of different scenarios were assessed by processing the simulated mechanism results. The simulation time results indicate the Tim sorting algorithm as the best to use in the post-processing step and the Numba library as the best suited for both the simulation and the post-processing step.     

Self-condensing vinyl polymerization in the presence of multifunctional initiator with unequal rate constants: Monte Carlo simulation

Monte Carlo method was applied to simulate self-condensing vinyl polymerization (SCVP) in the presence of multifunctional initiator with unequal reactive rate constants. Simulations showed that, with the increase of reactivity of multifunctional initiator, the molecular weight distribution decreases, the fraction of multi-armed hyperbranched polymers increases, and the best reactivity ratio of multifunctional initiator to inimor is 10/1; the reactivity difference of two active sites in inimer has strong effects on the molecular weight distribution and degree of branching. The branch degree and fraction of branch-points depend on both the conversion of double bonds and reactivity difference of two active centers in inimer, and have no relation with the adding of multifunctional initiator. The density distribution of degree of branching further shows common self-similarity in SCVP.     

动态Monte Carlo模拟蛋白质与微滤膜相互作用及其对微滤过程影响

构建了二维晶格蛋白质-微滤膜疏水相互作用模型，采用动态Monte Carlo方法模拟了微滤膜污染过程及其受膜孔径、蛋白质浓度和蛋白质结构特性等因素的影响。模拟结果显示：微滤过程中膜通量的变化呈现快速下降、缓慢下降和平台期3个阶段。小孔径微滤膜的滤阻从以膜孔阻力为主转变为以饼层阻力为主;而大孔径微滤膜的滤阻则以膜孔阻力为主。提高蛋白质浓度会强化滤阻从膜孔阻力向饼层阻力的转变。在微滤过程中，蛋白质会因疏水相互作用在膜孔内发生构象转换，进而发生不可逆吸附并形成多层堆积，导致膜污染和通量下降，提高蛋白质的构象稳定性可以显著降低其对微滤膜的污染。分子模拟结果与文献报道的实验结果和理论模型相符，所提供的微观信息对于微滤过程优化和微滤膜设计具有参考作用。     

非对称两嵌段高分子在选择性壁面识别吸附的Monte Carlo模拟

采用自由空间的Monte Carlo（MC）方法研究了两嵌段非对称高分子在选择性壁面上的吸附与识别。研究表明;非对称嵌段高分子同对称嵌段高分子一样;在选择性壁面的吸附可分为吸附和识别两个过程。对高分子构型研究的结果发现;无论条纹宽度如何变化;高分子在垂直于z方向的均方回转半径总是小于其垂直另两方向的值。在条纹宽度一定的情况下;尾式构型比率随链节B与白色条纹壁面作用能Ψ ^B-white增加先增加然后趋于不变。在Ψ ^B-white不变的情况下;尾式构型比率则随条纹数的增加而增加。环式构型比率在条纹较宽时会随Ψ ^B-white有一小的下降趋势;而在条纹较窄时下降幅度较大。     

绝氧条件下β-Bi2Mo2O9晶相上丙烯氨氧化反应的Monte Carlo模拟研究

A random walk Monte Carlo （RWMC） simulation model of catalytic particle was established on the basis of the structures of bismuth molybdate catalysts and mechanisms of catalytic reactions with propylene selective oxidation and ammoxidation. The simulation results show that rationality of the RWMC model is proved on the basis of pulse experimental data. One of the most remarkable factors affecting catalytic behavior is the transfer of bulk lattice oxygen, which decides the rate of ammonia-consuming and propylene-consuming. The selectivity of main products reaches the maximum after the reduction of catalysts to a certain degree. It is inferred that catalytic performance improves greatly if the ratio of capacity for dehydrogenation from adsorbed propylene molecule on catalytically active site of molybdenum metal-imido group （Mo=NH） to that on catalytically active site of molybdenum metal-oxo group （Mo=O） becomes much higher.     

Monte Carlo simulation of sequential structure control of AN-MA-IA aqueous copolymerization by different operation modes

The regulation of polyacrylonitrile (PAN) copolymer composition and sequence structure is the precondition for producing high-quality carbon fiber high quality. In this work, the sequential structure control of acrylonitrile (AN), methyl acrylate (MA) and itaconic acid (IA) aqueous copolymerization was investigated by Monte Carlo (MC) simulation. The parameters used in Monte Carlo were optimized via machine learning (ML) and genetic algorithms (GA) using the experimental data from batch copolymerization. The results reveal that it is difficult to control the aqueous copolymerization to obtain PAN copolymer with uniform sequence structure by batch polymerization with one-time feeding. By contrary, it is found that the PAN copolymer with uniform composition and sequence structure can be obtained by adjusting IA feeding quantity in each reactor of a train of five CSTRs. Hopefully, the results obtained in this work can provide valuable information for the understanding and optimization of AN copolymerization process to obtain high-quality PAN copolymer precursor.     

Monte Carlo simulation on the adsorption properties of carbon tetrachloride, neopentane, and cyclohexane in MCM-41

The adsorption properties of carbon tetrachloride, neopentane, and cyclohexane in MCM-41 with heterogeneous and cylindrical pores have been studied by using grand canonical ensemble Monte Carlo simulation. The adsorption isotherm, average potential of adsorbate, isosteric heat of adsorption, and number density of molecules in MCM-41 were calculated. The simulated isotherms were compared with experimental ones. Also, different adsorption behaviors in MCM-41 with pore diameter of 2.2 and 3.2 nm were discussed. The capillary-condensation pressure increased for a given adsorbate with an increase in pore diameter. The average densities of carbon tetrachloride, neopentane, and cyclohexane in the two different pores above the capillary-condensation pressure were smaller than the corresponding liquid densities by about 12%. The adsorbate molecules did not form the multilayer in pore below the capillary-condensation pressure. The number of adsorption layers of molecules was constant in a given pore for the three adsorbates above the capillary-condensation pressure. Carbon tetrachloride molecules in pore were also ordered along the pore axis.     

Monte Carlo simulation of hydrogen absorption in palladium and palladium–silver alloys

A modified Monte Carlo (MC) simulation was performed to investigate the hydrogen absorption behavior in Pd and Pd–Ag alloys of the composition Pd_xAg_1−x (x=0.7–0.8) under H₂ pressure (0.1 MPa) at different temperatures. The present method employed can consider the dissociative adsorption of hydrogen molecule and the subsequent absorption of hydrogen atom by formalizing the relationship between the pressure of hydrogen molecule and hydrogen atom. The potential parameters were determined to reproduce the solution enthalpy of hydrogen in pure metals. The results are in good agreement with experimental findings as well as previous theoretical studies. We confirmed that our method is useful to simulate the absorption of hydrogen in metals and alloys.     

Monte Carlo simulation of the compatibility of graft copolymer compatibilized two incompatible homopolymer blends: Effect of graft structure

Compatibility of graft copolymer compatibilized two incompatible homopolymer A and B blends was simulated by using Monte Carlo method in a two‐dimensional lattice model. The copolymers with various graft structures were introduced in order to study the effect of graft structure on the compatibility. Simulation results showed that incorporation of both A‐g‐B (A was backbone) and B‐g‐A (B was backbone) copolymers could much improve the compatibility of the blends. However, A‐g‐B copolymer was more effective to compatibilize the blend if homopolymer A formed dispersed phase. Furthermore, simulation results indicated that A‐g‐B copolymers tended to locate at the interface and anchor two immiscible components when the side chain is relatively long. However, most of A‐g‐B copolymers were likely to be dispersed into the dispersed homopolymer A phase domains if the side chains were relatively short. On the other hand, B‐g‐A copolymers tended to be dispersed into the matrix formed by homopolymer B. Moreover, it was found that more and more B‐g‐A copolymers were likely to form thin layers at the phase interface with decreasing the length of side chain. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Modeling and Monte Carlo simulation on photothermal effect in Gd3Al3Ga2O12:Ce3+/Y3Al5O12:Cr3+ layered composite ceramic

Layered composite ceramics have wide application in solid-state lasers. However, the photothermal effect in the layered ceramics has not been clarified, due to the interface effect between layers. In this work, the model of photon propagation and thermal distribution in the Gd₃Al₃Ga₂O₁₂:Ce³⁺/Y₃Al₅O₁₂:Cr³⁺ layered ceramics are established. The property of photon absorption, reflection, transmission, and thermal distribution are studied by combining the Monte Carlo method and the convolution method. It is found that the photon absorption distribution and thermal distribution of this layered ceramics show the gradient change. Furthermore, this change is strongly dependent on the type, beam width, and power of laser. The temperature of layered ceramics induced by Gaussian beam is higher than that induced by flat circular beam. This work provides a useful research method for the design of layered ceramic materials with excellent scintillation performance.     

Monte Carlo simulation of gas phase polymerization of 1,3‐butadiene. Part II: Kinetics optimization and confirmation

Studies on the deactivations and initiations of gas phase polymerizations of 1,3‐butadiene have been achieved by Monte Carlo simulation. Initiation and deactivation control the reaction before and after the peak of the polymerization rate, respectively. The influence of polymerization temperature has been studied. Monte Carlo modeling of polymerization kinetics and mechanism was confirmed by the agreement of experimental data and simulation results of polymerizations run with a temporary evacuation of monomer. The balance of catalysts and active chains is established by both initiation and chain transfer reactions with cocatalyst, which causes a ‘pseudo‐stability’ stage. © 2003 Society of Chemical Industry     

Effect of Ni2+ substitution on structural,magnetic, dielectric and optical properties of mixed spinel CoFe2O4 nanoparticles

Nanoparticles of Co_1−xNi_xFe₂O₄ with x=0.0, 0.10, 0.20, 0.30, 0.40 and 0.50 were synthesized by co-precipitation method. The structural analysis reveals the formation of single phase cubic spinel structure with a narrow size distribution between 13–17 nm. Transmission electron microscope images are in agreement with size of nanoparticles calculated from XRD. The field emission scanning electron microscope images confirmed the presence of nano-sized grains with porous morphology. The X-ray photoelectron spectroscopy analysis confirmed the presence of Fe²⁺ ions with Fe³⁺. Room temperature magnetic measurements showed the strong influence of Ni²⁺ doping on saturation magnetization and coercivity. The saturation magnetization decreases from 91 emu/gm to 44 emu/gm for x=0.0–0.50 samples. Lower magnetic moment of Ni²⁺ (2 µ_B) ions in comparison to that of Co²⁺ (3 µ_B) ions is responsible for this reduction. Similarly, overall coercivity decreased from 1010 Oe to 832 Oe for x=0.0–0.50 samples and depends on crystallite size. Cation distribution has been proposed from XRD analysis and magnetization data. Electron spin resonance spectra suggested the dominancy of superexchange interactions in Co_1−xNi_xFe₂O₄ samples. The optical analysis indicates that Co_1−xNi_xFe₂O₄ is an indirect band gap material and band gap increases with increasing Ni²⁺ concentration. Dispersion behavior with increasing frequency is observed for both dielectric constant and loss tangent. The conduction process predominantly takes place through grain boundary volume. Grain boundary resistance increases with Ni²⁺ ion concentration.     

Monte Carlo simulation of molecular weight distribution and copolymer composition in transamidation reaction of polyamides

Melt mixing of polyamides results in exchange reaction and generation of copolymers. In this work, Monte Carlo method is used to simulate the time evolution of molecular weight distribution (MWD) and copolymer composition during the exchange reaction process between polyamides with AA and BC structure. The influences of initial composition and molecular weight have been investigated. Decrease in the difference between the average molecular weight of two kinds of polyamides results in faster approach of the MWD toward Flory's distribution and higher probability of producing copolymers. When the ratio between the numbers of initial molecules of two homopolymers is increased, the number of generated copolymers is reduced and the wider MWD is obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Study of tablet-coating parameters for a pan coater through video imaging and Monte Carlo simulation

The movement of tablets in a pan coater and the exposure of different surfaces of tablets for deposition of coatings by spray-coating have been studied by video imaging and Monte Carlo simulation techniques. A representative variety of tablets of different shapes and sizes were used at different pan loads and at various pan speeds. A single “tracer” tablet was used to track the motion of tablets and coating variables such as circulation time, surface time, projected surface area and surface velocity of a tablet were determined from the video imaging experiments. The coating uniformity is described in terms of the coating variation from tablet to tablet CV(tt) and a new parameter CV(st) the coating variation on a single tablet. The effect of shape of tablets on coating uniformity was analyzed by introducing a “sphericity” of tablet (φ_s) into the CV models. The methodology, new models and the analysis developed here incorporating the additional parameters will help users to optimize the coating process in pan-coating operations.