Compared with other types of polymerization, the molecular weight and its distribution (MWD) of equilibrium ring‐opening polymerization (EROP) are complicated and have not been extensively studied. By using statistic method, a series of equations based on polymerization mechanism is established to describe numbers of rings, chains, and active centers. Using this new model, the predicted results of polydimethylsiloxane synthesized by EROP agree well with experimental results. This model has advantages in molecule number, calculation speed, and stability when compared with the Monte Carlo simulation. It also has the potential to replace Monte Carlo simulation in MWD prediction. 相似文献
To understand the fundamental aspects of the polycondensation reaction of hydrolyzed tetraethoxysilane (TEOS) and silanol‐terminated poly(dimethylsiloxane) (PDMS), we modeled the reaction system as a step‐growth polymerization of A4 and polydisperse A2, assuming the reactivities of all functional groups are equal. The analytical solution for the weight‐average molecular weight is developed, and in addition, a Monte Carlo simulation is conducted to investigate the detailed structural development. It was found that as long as the molecular weight of PDMS is much larger than TEOS, the apparent behavior is significantly different from usual gelling systems. The gel point is relatively insensitive to the weight fraction of crosslinker (TEOS), the polydispersity index may decrease during polymerization before the rapid increase to infinity, and the molecular weight distribution profile may not show a significant broadening toward gelation. Even though the present model assumes a complete random reaction process among functional groups, formation of a heterogeneous structure in which a tight core consisting of TEOS‐based molecules is surrounded by soft PDMS chains was observed in the Monte Carlo simulation. 相似文献
The polycondensation of hyperbranched polymers, based on AB2 type monomers, was simulated using an off‐lattice Monte Carlo method in order to investigate the polymerization kinetics and microstructures of hyperbranched polymers. The effects of temperature and activation energy of reaction on the conversion rate seem qualitatively acceptable, indicating that our simulation model properly describes the polymerization reaction of hyperbranched polymers. Number average degree of polymerization and polydispersity index were calculated as a function of conversion and compared with Flory's expectation. Fractions of dendritic, linear and terminal unit were also determined from simulation and compared with theoretical predictions. As the hyperbranched polymer grows, it is observed that the molecular shape changes from a regular fan‐shape structure to an edge‐curled up structure. 相似文献
In this paper, we developed two types of programs in order to simulate the polymerization reaction of a fully deuterated crystal of diacetylene 2,4‐hexadiynylene bis(p‐toluenesulfonate) (pTS‐D). The first simulation is based on a modification of Baughman's model, a classical model for simulating the polymerization of diacetylene crystals. The agreement between the simulated and experimental results concerning the reaction kinetics is satisfactory. With this simulation algorithm, we take into account the experimental observation that the polymerization of pTS‐H and pTS‐D crystals is really a random process of formation of polymer chains along the crystallographic axis b . The second simulation is based on the Monte Carlo method, which permits not only to simulate the kinetics of the reaction, but also the chain‐length distribution in the hydrogenated and deuterated compounds. These two types of simulations were already developed for the hydrogenated crystal of diacetylene, named pTS‐H. Two main modifications are applied in the case of pTS‐D for taking into account experimental results: in the first the rate constants of chain‐terminating microscopic processes are different in pTS‐H and pTS‐D which must be considered. The second modification concerns the evolution of the lattice deformation during the course of polymerization. The experimental variation of the b parameter as a function of polymer content X in pTS‐D is different from that in pTS‐H; this result is important to consider when calculating the activation energy of the initiation and propagation microscopic processes. 相似文献
A Bayesian modeling and Markov Chain Monte Carlo simulation was developed for a kinetic study of homopolymerization and copolymerization systems at the molecular scale. Two copolymerization models – the terminal unit model and the penultimate unit model – were considered. Prior estimates of the kinetic parameters were obtained by L1‐norm robust statistics. Using the structure of experimental data through a likelihood function, Bayesian modeling was employed to update the prior estimates. The joint posterior probability regions and shimmer bands were calculated for updated reactivity ratios. A method for assessing the power of experimental data in discrimination between copolymerization models is presented. This method was validated for free radical polymerization in binary systems. The evolution of species and radical populations during the course of polymerization were determined. The computational time was considerably decreased by calculating the propagation step from lifetime of the polymer chain and local monomer concentration. To avoid inaccuracies in the results caused by poor choice or false computation of the time step, the time step between successive Monte Carlo events was adapted to the time scale of the fastest reaction. The simulation algorithm is exact, in the sense that it takes full account of the fluctuations and correlations.
A framework based on the Monte Carlo/random‐pore polymeric flow model is proposed to simulate both single‐particle and continuous slurry reactor industrial polymerizations. The Sanchez–Lacombe equation of state describes the distributions of components in the different phases of these systems. The developed process model is applied to describe heterogeneously catalyzed polymerizations of ethylene in n‐hexane diluent with or without 1‐hexene as a comonomer, but the proposed methodology is applicable to any ethylene/1‐olefin copolymerization in slurry reactors. In addition to the effects of catalyst particle size and reactor residence time distributions, the proposed hybrid model is used to investigate the impact of several catalyst characteristics under different process conditions on polymer yield and microstructure. Particular attention is paid to the catalyst fragmentation process and active center distribution through the particle. These simulations demonstrate the versatility and thoroughness of combining Monte Carlo simulation with single‐particle models to analyze and predict the behavior of commercial polyolefin reactors. 相似文献
Two different modeling techniques, the method of moments and Monte Carlo simulation, were compared for propylene polymerization with coordination catalysts including a new mechanistic step, site transformation by electron donors. We used the models to show how the molecular weight and tacticity distributions of several poly(propylene) chain populations were affected by changing the concentration of hydrogen, electron donor, and propylene in the reactor, under steady‐state or dynamic operating conditions. The Monte Carlo simulation describes the molecular weight and tacticity distributions for the whole polymer and chain populations with distinct microstructural characteristics. We have also applied the Monte Carlo model to simulate the pentad sequence distributions and its equivalent 13C NMR spectra.
By use of a Monte Carlo method the course of crosslinking without cyclization was simulated. For the simulated case the following was determined: number-average molecular weight and degree of polymerization of the system; weight-average molecular weight and degree of polymerization of the system; number of molecules of a given degree of polymerization; quantity of gel; number-average degree of polymerization of sol and branching. The values obtained by simulation were compared with some equations published to date. It was shown that the dependence of weight-average polymerization degree and, consequently, of the weight-average molecular weight on time and the dependence of the number of molecules of a given polymerization degree on time is probably more complicated than hitherto supposed. 相似文献
The formation of long‐chain branches (LCBs) during ethylene polymerization with a combination of catalysts was studied by Monte Carlo simulation. The model describes polymerization with a non‐branching catalyst that produces linear macromonomers, and a branching catalyst that produces linear and branched macromonomers. The LCBs are formed when the branching catalyst incorporates a macromonomer. The discussion is based on the three types of chain topology obtained during the synthesis: linear, comb‐branched, or hyperbranched. Simulation results show how the chain length distribution and the number of LCBs change according to the ratio between the two catalysts present in the reactor. The ratio hyperbranched/comb‐branched is defined to evaluate the system composition and the contribution of each catalyst. 相似文献
A novel, parallelised approach to Monte Carlo simulations for the computation of full molecular weight distributions (MWDs) arising from complex polymerisation reactions is presented. The parallel Monte Carlo method constitutes perhaps the most comprehensive route to the simulation of full MWDs of multiple chain length polymer entities and can also provide detailed microstructural information. New fundamental insights have been developed with regard to the Monte Carlo process in at least three key areas: (i) an insufficient system size is demonstrated to create inaccuracies via poor representation of the most improbable events and least numerous species; (ii) advanced algorithmic principles and compiler technology known to computer science have been used to provide speed improvements and (iii) the parallelisability of the algorithm has been explored and excellent scalability demonstrated. At present, the parallel Monte Carlo method presented herein compares very favourably in speed with the latest developments in the h‐p Galerkin method‐based PREDICI software package while providing significantly more detailed microstructural information. It seems viable to fuse parallel Monte Carlo methods with those based on the h‐p Galerkin methods to achieve an optimum of information depths for the modelling of complex macromolecular kinetics and the resulting microstructural information.
We developed an analytical solution to describe how the CLD of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerization times before the CLD becomes completely developed. We compared the analytical solution with a dynamic Monte Carlo model for validation, obtaining excellent agreement. Our analytical solution can be used to determine when the steady‐state hypothesis, commonly used in polymerization models, becomes valid as a function of polymer chain length. We also extended our model to describe polymerization with multiple‐site‐type catalysts. Depending on the polymerization kinetic parameters of the different site types on the catalyst, the fully developed CLD is reached through very different intermediate CLDs. This modeling approach, although rather simplified, can be used to interpret results from short polymerization time experiments such as the ones done in stopped‐flow reactors.
Pulsed‐laser polymerization (PLP) has been adopted by IUPAC as the method of choice for the determination of propagation rate constants (kp). However, the method has failed in the polymerization of alkyl acrylates at temperatures above 30 °C. In this work, the PLP experiments were analyzed by simulation using a Monte Carlo algorithm. It was found that the experimental difficulties encountered to accurately determine kp at temperatures above 30 °C were caused by extensive intramolecular chain transfer. This mechanism is not operative at lower temperatures because of its high activation energy.
Pulsed‐laser polymerization of BA in bulk at temperatures between −41 and +40 °C: Simulated MWD trace. 相似文献