Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

In the present work, a novel kinetic/topology Monte Carlo algorithm is developed for the prediction of molecular, topological and solution properties of highly branched low-density polyethylene (LDPE), produced in a high-pressure multi-zonal tubular reactor. It is shown that the combined kinetic/topology MC algorithm can provide comprehensive information regarding the distributed molecular and topological properties of LDPE (i.e., molecular weight distribution, short- and long-chain branching distributions, joint molecular weight-long chain branching distribution, branching order distribution, seniority/priority distributions, etc.) The molecular/topological results obtained from the MC algorithm are then introduced into a random-walk molecular simulator to calculate the solution properties of LDPE (i.e., the mean radius of gyration, R_g, and the branching factor, g) in terms of the chain length of the branched polyethylene. The validity of the commonly applied approximation regarding the random scission of highly branched polymer chains is assessed by a direct comparison of the average molecular properties of LDPE (i.e., number and weight average molecular weights), calculated by the combined kinetic/topology MC algorithm, with the respective predictions obtained by the commonly applied method of moments (MOM). Through this comparison it is demonstrated that the ambiguous implementation of the random scission reaction in the MOM formulation can result in erroneous predictions of the weight average molecular weight and MWD of LDPE. Finally, the effects of two key process parameters, namely, the polymerization temperature profile and the solvent concentration, on the molecular, topological and polymer solution properties of LDPE produced in a multi-zonal tubular reactor are investigated.     

Experimental simulation of large-scale bioreaetor environments using a Monte Carlo method

Cells grown in production-scale stirred bioreactors experience fluctuating concentrations due to local variations in supply and consumption of oxygen and nutrients. A new method for studying the effects of fluctuations in local conditions on growth and productivity of cells was developed using a Monte Carlo approach to simulate circulation within a fermenter. A small fermenter was driven through cycles of aeration and feeding, with the time of each cycle controlled by a Monte Carlo method to give a log-normal distribution. Experiments with Monte Carlo supply of air to batch and fed-batch cultures of Saccharomyces cerevisiae showed that the method gave reproducible results which were different from both periodic cycling and continuous supply. When substrate was provided to a fed-batch culture of S. cerevisiae according to the Monte Carlo method, the yields of biomass were higher than experiments with continuous feeding or periodic feeding.     

Prediction of hypervariable CDR-H3 loop structures in antibodies

The structure of the most variable antibody hypervariable loop,CDR-H3, has been predicted from amino acid sequence alone. Incontrast to other approaches predictions are made for loop lengthsup to 17 residues. The predictions have been achieved usingartificial neural networks which are trained on a large setof loops from the Brookhaven Protein Databank which have structuressimilar to CDRH3. The loop structures are described by the twobackbone dihedral angles and for each residue. For 21 CDR-H3loops unique to the neural network, the prediction of dihedralangles leads to an average root mean square deviation in theCartesian coordinates of 2.65 Å. The present method, whencombined with existing modelling protocols, provides an importantaddition to the structural prediction of the complementaritydetermining regions of antibodies.     

高分子抑制蛋白质聚集的动态Monte Carlo模拟

抑制聚集是蛋白质产品下游加工特别是制剂过程中的重要问题。本文采用动态Monte Carlo方法和二维晶格HP蛋白质模型,通过建立高分子-蛋白质复合物微观结构和蛋白质构象概率分布来研究高分子对蛋白质聚集行为的影响。结果表明,高分子的疏水性、分子量及其浓度对于蛋白质的聚集行为有显著的影响。当其疏水性适宜时,高分子可富集在蛋白表面疏水位点,强化蛋白质分子在水溶液中的分散,从而抑制聚集。高分子还可缠绕在蛋白质分子表面形成限制性空间从而稳定蛋白质的天然结构。     

Simulations of polycrystalline CVD diamond film growth using a simplified Monte Carlo model

A simple 1-dimensional Monte Carlo (MC) model has been developed to simulate the chemical vapour deposition (CVD) of a diamond (100) surface. The model considers adsorption, etching/desorption, lattice incorporation, and surface migration along and across the dimer rows. The reaction probabilities are taken from experimental or theoretical literature values for standard CVD diamond conditions. Renucleation events believed to be due to reactive adsorbates, such as C atoms or CN groups, were modelled by creating random surface defects which form a critical nucleus upon which to nucleate a new layer. By assuming that migrating C species that encounter these surface defects add to the growing surface by templating either from the underlying layer or from the surface defect, and with suitable colour coding, the evolution of different grains has been modelled. On increasing the probability of creating surface defects, the number of grains increases while their mean size decreases. This simulates the film morphology changing from that of single crystal diamond to microcrystalline, nanocrystalline and finally ultrananocrystalline diamond. With the formation of such defects which can act as renucleation points turned off, but using random seed crystals, the films develop a columnar structure similar to that observed for heteroepitaxial microcrystalline diamond.     

Investigating the effect of shape on particle segregation using a Monte Carlo simulation

A Monte Carlo simulation has been used to investigate the segregation potential of a range of particulate systems under conditions in which the particles undergo high amplitude low frequency shaking. These systems involve a wide range of binary powder mixtures in which complex particle shapes have been investigated, including plates and rods which represent the real world materials encountered in pharmaceutical systems such as those which include crystalline components. Previous simulations on the segregation propensity of systems with different shapes were limited to spheres and spherocylinders, with relatively low vibrational amplitude drops. A commercial computer application for particle packing—called MacroPac—has been successfully employed here, as it has been able to model systems that are more complex where the shape variation is much wider. These simulations apply to the case of macroscopic particles, in the absence of air resistance and inter-particle forces. For non-spherical shapes, an ‘effective size’ which relates to the radius of gyration of the particles is determined. Our studies indicate that with high amplitude low frequency shaking, in a mixture of particles with different shapes but with equal volumes, the particles with the larger ‘effective size’, which tend to have a lower packing fraction, segregate to the top.     

Solution of the population balance equation using constant-number Monte Carlo

We formulate a Monte Carlo simulation of the mean-field population balance equation by tracking a sample of the population whose size (number of particles in the sample) is kept constant throughout the simulation. This method amounts to expanding or contracting the physical volume represented by the simulation so as to continuously maintain a reaction volume that contains constant number of particles. We call this method constant-number Monte Carlo to distinguish it from the more common constant-volume method. In this work, we expand the formulation to include any mechanism of interest to population balances, whether the total mass of the system is conserved or not. The main problem is to establish connection between the sample of particles in the simulation box and the volume of the physical system it represents. Once this connection is established all concentrations of interest can be determined. We present two methods to accomplish this, one by requiring that the mass concentration remain unaffected by any volume changes, the second by applying the same requirement to the number concentration. We find that the method based on the mass concentration is superior. These ideas are demonstrated with simulations of coagulation in the presence of either breakup or nucleation.     

Prediction of polymer mixture compatibility by Monte Carlo simulation of intermolecular binary interactions

We have evaluated conformational and orientational averages of binary interaction integrals for pairs of chains constituting atomistic representations of short polymer molecules. By considering A-A, B-B and A-B pairs, we relate these results with the Flory-Huggins parameter for the A-B mixtures. This parameter is commonly accepted as a good indicator of compatibility. Since the method ignores the simultaneous interactions with other molecules in the mixture, the local environment is approximately described by introducing an effective medium dielectric constant whose value is conveniently parameterized. The results for four different real systems are compared with data obtained from experimental neutron scattering data. The method qualitatively predicts the sign and variation with temperature in the four different cases, also showing a reasonable quantitative agreement in some of the cases. Its performance is discussed in comparison with a standard method that evaluates the Flory-Huggins parameter by calculating an average of the intermolecular energy of two molecules in contact, taking also into account their off-lattice Flory-Huggins coordination numbers.     

Prediction of the structures of proteins with the UNRES force field, including dynamic formation and breaking of disulfide bonds

The presence of disulfide bonds is essential for maintaining the structure and function of many proteins. The disulfide bonds are usually formed dynamically during folding. This process is not accounted for in present algorithms for protein-structure prediction, which either deduce the possible positions of disulfide bonds only after the structure is formed or assume fixed disulfide bonds during the course of simulated folding. In this work, the conformational space annealing (CSA) method and the UNRES united-residue force field were extended to treat dynamic formation of disulfide bonds. A harmonic potential is imposed on the distance between disulfide-bonded cysteine side-chain centroids to describe the energetics of bond distortion and an energy gain of 5.5 kcal/mol is added for disulfide-bond formation. Formation, breaking and rearrangement of disulfide bonds are included in the CSA search by introducing appropriate operations; the search can also be carried out with a fixed disulfide-bond arrangement. The algorithm was applied to four proteins: 1EI0 (alpha), 1NKL (alpha), 1L1I (beta-helix) and 1ED0 (alpha + beta). For 1EI0, a low-energy structure with correct fold was obtained both in the runs without and with disulfide bonds; however, it was obtained as the lowest in energy only with the native disulfide-bond arrangement. For the other proteins studied, structures with the correct fold were obtained as the lowest (1NKL and 1L1I) or low-energy structures (1ED0) only in runs with disulfide bonds, although the final disulfide-bond arrangement was non-native. The results demonstrate that, by including the possibility of formation of disulfide bonds, the predictive power of the UNRES force field is enhanced, even though the disulfide-bond potential introduced here rarely produces disulfide bonds in native positions. To the best of our knowledge, this is the first algorithm for energy-based prediction of the structure of disulfide-bonded proteins without any assumption as to the positions of native disulfides or human intervention. Directions for improving the potentials and the search method are suggested.     

Monte Carlo simulation of chain extension using bisoxazolines as coupling agent

The chain extension using bisoxazolines (OO) as coupling agent was studied by means of the Monte Carlo (MC) method, focusing on the reaction kinetics. A comparison between simulated results and those calculated by an improved kinetic model was made. The coupling efficiency of the chain extender, average molecular weight and molecular weight distributions (MWDs) were investigated. The results show that the biggest coupling efficiency, the highest average molecular weight and the narrowest MWDs can be obtained when the initial concentrations of carboxyl and oxazoline groups are equal. The results indicate that higher activity difference between the oxazoline group in OO and that in blocked CA can lead to higher average molecular weight and narrower MWDs. Those results are in good agreement with the experiments. Besides above factors, diffusion effect and degradation effect are important factors for the average molecule weight and MWDs. And lower reaction kinetics constants of diffusion effect and degradation effect both result in a higher number-average molecular weight . The results also indicate that two peaks, at the different molecular weight, appear in the curve of molecular weight distributions during chain extension reaction. The variation of these two peaks corresponds to different polydispersities.     

Latent mixed Markov modelling of smoking transitions using Monte Carlo bootstrapping

It has been established that measures and reports of smoking behaviours are subject to substantial measurement errors. Thus, the manifest Markov model which does not consider measurement error in observed responses may not be adequate to mathematically model changes in adolescent smoking behaviour over time. For this purpose we fit several Mixed Markov Latent Class (MMLC) models using data sets from two longitudinal panel studies--the third Waterloo Smoking Prevention study and the UWO smoking study, which have varying numbers of measurements on adolescent smoking behaviour. However, the conventional statistics used for testing goodness of fit of these models do not follow the theoretical chi-square distribution when there is data sparsity. The two data sets analysed had varying degrees of sparsity. This problem can be solved by estimating the proper distribution of fit measures using Monte Carlo bootstrap simulation. In this study, we showed that incorporating response uncertainty in smoking behaviour significantly improved the fit of a single Markov chain model. However, the single chain latent Markov model did not adequately fit the two data sets indicating that the smoking process was heterogeneous with regard to latent Markov chains. It was found that a higher percentage of students (except for never smokers) changed their smoking behaviours over time at the manifest level compared to the latent or true level. The smoking process generally accelerated with time. The students had a tendency to underreport their smoking behaviours while response uncertainty was estimated to be considerably less for the Waterloo smoking study which adopted the 'bogus pipeline' method for reducing measurement error while the UWO study did not. For the two-chain latent mixed Markov models, incorporating a 'stayer' chain to an unrestricted Markov chain led to a significant improvement in model fit for the UWO study only. For both data sets, the assumption for the existence of an independence chain did not lead to significant improvement in model fit. The unrestricted two-chain latent mixed Markov model led to a significant improvement of model fit compared to a simple latent Markov model, but this model was overparameterized when the latent transition probabilities and/or response probabilities were assumed nonstationary. For the other models, the manifest/latent transition probabilities and response probabilities (for the four-wave Waterloo study only) were tested to be nonstationary for both data sets.     

Wang-Landau Monte Carlo simulation of capillary forces at low relative humidity in atomic force microscopy

A lattice gas model is used with Wang-Landau Monte Carlo sampling to predict the capillary force between a model of an atomic force microscopy (AFM) probe and a smooth surface as a function of separation, relative humidity (RH), and tip hydrophilicity. Completely wetting AFM tips exhibit a maximum in the capillary force as the RH increases, while the magnitude of the capillary force in the presence of partially wetting and partially drying tips is relatively independent of the RH. Capillary forces can also be significant in low RH environments and should not be discounted in AFM studies involving hydrophilic surfaces.     

Monte Carlo Prediction of Non-Newtonian Viscous Sintering: Experimental Validation for the Two-Glass-Cylinder System

From the Monte Carlo methodology based on a non-discrete potential and developed to model capillary-driven mass transport, a relation between the Monte Carlo step and the physical time has been defined as a function of the viscosity coefficient. The experimental kinetics of the shortening of a unique glass cylinder and the sintering of two-glass cylinders at 950°C then have been compared with the numerically obtained results. The original result indicates that the active sintering mechanism for a glass under the given sintering conditions is not Newtonian viscous flow alone, a finding that corresponds perfectly well with the Monte Carlo simulation.     

利用Monte Carlo方法预测精馏塔板上气泡尺寸分布及相界面积

精馏塔板上气泡尺寸分布是计算精馏塔板效率以及设计和操作精馏塔的关键参数，但对它的预测受到理论不完善、实验测试手段落后及求解计算困难等方面的限制。本文以Kolmogoroff各向同性湍流理论为基础并结合格率理论，利用计算机图形处理技术对气泡的尺寸分布现象进行观察，分析气泡的聚并和破裂机理。通过已建立的气泡破裂和聚并速率模型，得到精馏塔板上气泡粒数衡算方程。针对气泡粒数衡算方程求解的复杂性，本文采用了Monte Carlo模拟技术来简化气泡粒数衡算方程的求解。求解结果与实验数据相吻合并显示气泡尺寸分布为对数正态分布，这与其他研究者的结论相一致。由所求得的气泡尺寸分布可以进一步计算出气泡的Sauter平均直径以及气液相界面积。     

Monte Carlo simulation of the response of ferromagnetic polymer chain to external magnetic field

The response of ferromagnetic Ising polymer chain in dilute solution to external magnetic field is investigated using Monte Carlo technique. It is found that both magnetic and spatial conformational properties are dependent on the external field, chain length, and temperature. They behave differently at temperatures below and above the zero-field critical temperature T_c⁰. Simulation results indicate that the model chain is a possible candidate for recording material and molecular mechanism.     

Modelling of acoustic agglomeration processes using the direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is applied to simulate acoustic agglomeration in travelling sound waves; orthokinetic and hydrodynamic mechanisms are considered as well as Brownian coagulation. The method is based on the constant-volume Monte Carlo approach combined with a modified full-conditioning algorithm of Gillespie, and is proved accurate by simulating only Brownian coagulation. Using the DSMC method, the validities of the classic Mednikov orthokinetic kernel, the König hydrodynamic kernel and the Song's orthokinetic and hydrodynamic models are examined by simulating acoustic agglomeration with only individual kernels. The predictions obtained by applying simple additive combinations of Song's orthokinetic model with the König equation and Song's hydrodynamic model are validated against experimental data in the literature. It has been found that the individual Song's models and the two combinations yield fairly good agreement with the measurements in some experimental cases, but all have limitations in covering a wide range of experimental conditions. This suggests that the present modelling needs further improvement to correctly describe the coupled contributions of two or more mechanisms.     

优化温度相关力场预测正构烷烃热力学性质

为了实现不同温度下正构烷烃及其混合物热力学性质的准确预测,以正构烷烃（n-C₄~C₁₀）为训练集,通过对全原子OPLS-AA力场中非键相互作用参数（ε）的模拟优化,得到了ε与对比温度（T_r）以及正构烷烃碳原子个数（N_C）的经验关系式。利用该关系式计算出不同温度不同种类的正构烷烃的ε值,预测了正构烷烃纯物质及其混合物的黏度、密度、扩散系数等物性,并将新力场模拟计算值与理论估算值以及实验值进行比较。结果表明,采用优化温度相关力场预测烷烃及其混合物的物性与实验值最为吻合。密度、黏度和扩散系数的预测值与实验值的相对偏差分别小于2%、5%和10%,显著优于目前的理论方法和原OPLS-AA力场模拟计算的预测值。上述温度相关力场参数的确立,对于利用分子动力学模拟方法准确地预测正构烷烃及其混合物的热力学性质具有重要的实际应用价值。     

Modeling of aggregation kernel using Monte Carlo simulations of spray fluidized bed agglomeration

The present work attempts to consider the microscopic mechanisms of spray fluidized bed agglomeration while modeling the macroscopic kinetics of the process. A microscale approach, constant volume Monte‐Carlo simulation, is used to analyze the effects of micro‐processes on the aggregation behavior and identify the influencing parameters. The identified variables, namely the number of wet particles, the total number of particles, and the number of droplets are modeled and combined in the form of an aggregation kernel. The proposed kernel is then used in a one‐dimensional population balance equation for predicting the particle number density distribution. The only fitting parameters remaining in the population balance system are the collision frequency per particle and a success fraction accounting for the dissipation of kinetic energy. Predictions of the population balance model are compared with the results of Monte‐Carlo simulations for a variation of significant operating parameters and found to be in good agreement. © 2014 American Institute of Chemical Engineers AIChE J, 60: 855–868, 2014