scholarly journals Regression Methods Based on Nearest Neighbors with Adaptive Distance Metrics Applied to a Polymerization Process

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 547
Author(s):  
Silvia Curteanu ◽  
Florin Leon ◽  
Andra-Maria Mircea-Vicoveanu ◽  
Doina Logofătu

Empirical models based on sampled data can be useful for complex chemical engineering processes such as the free radical polymerization of methyl methacrylate achieved in a batch bulk process. In this case, the goal is to predict the monomer conversion, the numerical average molecular weight and the gravimetrical average molecular weight. This process is characterized by non-linear gel and glass effects caused by the sharp increase in the viscosity as the reaction progresses. To increase accuracy, one needs more samples in the areas with higher variation and this is achieved with adaptive sampling. An extensive comparative study is performed between three regression algorithms for this chemical process. The first two are based on the concept of a large margin, typical of support vector machines, but used for regression, in conjunction with an instance-based method. The learning of problem-specific distance metrics can be performed by means of either an evolutionary algorithm or an approximate differential approach. Having a set of prototypes with different distance metrics is especially useful when a large number of instances should be handled. Another original regression method is based on the idea of denoising autoencoders, i.e., the prototype weights and positions are set in such a way as to minimize the mean square error on a slightly corrupted version of the training set, where the instances inputs are slightly changed with a small random quantity. Several combinations of parameters and ways of splitting the data into training and testing sets are used in order to assess the performance of the algorithms in different scenarios.

2013 ◽  
Vol 33 (9) ◽  
pp. 775-783 ◽  
Author(s):  
Abiola J. Kehinde ◽  
Mohammed A. Usman ◽  
Rasheed U. Owolabi

Abstract Efforts were made to synthesize polystyrene (PS) using free radical solution polymerization. Four common solvents with dissimilar polarities, acetone, chloroform, benzene and toluene, with two different initiators, were selected. The homo-polymerization was conducted in an ace round-bottom pressure flask of diameter 62 mm, with a thermo well, which housed the thermometer. The reaction temperature was maintained at 120°C using a heater with a temperature controller, coupled with a magnetically driven stirrer. One hundred experimental runs of 8 different groups were carried out. Polymerization was conducted in the mass concentration of 0.1 g for each initiator [benzoyl peroxide (BPO) and its blend]. The key parameter considered is the volume ratio of monomer to solvents under different types of solvents, initiators and reaction time. Initially, there was an increase in conversion with the solvent volume and time, until a certain point where there was a gradual decline in monomer conversion. Polymerization rate and monomer conversion were observed to be higher in polar solvents (acetone). Further presented in this study is the macromolecular architecture (molecular weight) and micro-structure of some of the solution polymerized monomer. A kinetic model was also presented to predict the conversion with time profile of the polymerization process. Molecular weight determined were between acceptable ranges while the model presented though with considerable error margin but seems to respond just fairly at extremely low monomer conversion. Similar response was observed from earlier model reported in literature when tested with our experimental data.


2015 ◽  
Vol 1120-1121 ◽  
pp. 615-619
Author(s):  
Hui Yu Jiang ◽  
Mei Hua Zhou ◽  
Ding Pan

Acrylonitrile (AN) and itaconic acid (IA) were used to synthesize UHMWPAN by aqueous suspension method with 2,2’-azobisisobutyronitrile (AIBN) as the initiator and polyvinylalcohol (PVA) as the disperser at different temperatures (55°C~75°C) for different timings (1.0h~3.0h). The usage amounts of AN, IA, AIBN and PVA were also technical polymerization parameters used to obtain the optimal polymerization process. We found that the conversion and the viscosity average molecular weight both achieved the optimum levels when the conditions were as follows: the total monomer concentration (21wt%), the monomer ratio (AN: IA=98:2), the usage amount of the initiator (AIBN, 0.01wt%), the usage amount of the disperser (PVA, 0.1wt%), the polymerization temperature (70°C) and the polymerization time (2h).


2021 ◽  
Author(s):  
Pegah Khazraei Karimi Fard

Free radical (co-)polymerization of low-density polyethylene (LDPE) is carried out commonly in high pressure autoclaves or tubular reactors. The severe thermodynamic conditions of the process hinder ethylene from going to full conversion. One remedy to improve the monomer conversion is to investigate the effectiveness of initiators, such as difunctional organic peroxides. In the present work, a kinetic model based on a postulated reaction mechanism for free radical ethylene (co-) polymerization initiated by difunctional initiators is applied to analyze the dynamic behavior of a continuous LDPE isothermal autoclave reactor and a non-isothermal tubular reactor. The model describes the rates of initiation, propagation and the population balance equations. It predicts variations of the initiator and monomer concentrations and reaction temperature as well as molecular weight distribution of reactive macromolecular species. Variations of the pressure, velocity and transport/physical properties of the reacting mixture were accounted for in the tubular reactor. Model predictions are compared to experimental data collected from literatures for one monofunctional (dioctanoyl) and two difunctional initiators namely, (2,2-bis(tert-butylperoxy)-butane and 2.5-dimetyl hexane-2t-butylperoxy-5perpivalate). In comparison with dioctanoyl peroxide, polymerization with difunctional initiators requires a lesser amount of initiators and gives higher ethylene conversion in a shorter time. The modeling of LSPE with difunctional initiators was then extended to ethylene copolymerization with vinyl acetate and butyl acrylate. The model helps to determine the influence of reactivity ratio on the end-use product properties. Details of modeling a multiple feed LSPE tubular reactor are included for both homo- and co-polymerization reactions. The effect of monomer and initiator injections on the productivity and (co)polymer rheology and composition are investigated as well. Finally, an optimization method was applied to determine the optimal values of control variables via maximization of an objective function expressed in terms of monomer conversion, number average molecular weight, polydispersity and final desired composition of copolymer product. The results show that we can obtain a polymer with desired characteristics by proper manipulation of the control variables.


2021 ◽  
Vol 18 (38) ◽  
pp. 27-37
Author(s):  
Eldar N. MIFTAKHOV ◽  
Svetlana A. MUSTAFINA ◽  
Ildus Sh NASYROV ◽  
Azat Kh DAMINOV

Background: the polymer product obtained in the presence of microheterogeneous catalytic systems is characterized by fairly molecular weight distribution (MWD), resulted from kinetically nonequivalent active centers (ACs) in the system that initiate the polymerization process. The nature and composition of ACs are determined by setting and solving an inverse problem on the formation of MWD. This problem is acute because revealing the nature of the kinetic heterogeneity explains changes in the molecular and consumer parameters of the product for different catalyst compositions and propagation modes in polymerizations. Aim: This study aimed to develop methods and algorithms for interpreting gel chromatograms to analyze the kinetic heterogeneity of a polymer product obtained industrially in microheterogeneous catalytic systems. Methods: the solution method is based on the assumption that the formed MWD is a superposition of distributions inherent in each type of ACs. Since the problem in the final formulation refers to the Fredholm integral equations of the first kind, the regularization method of A. N. Tikhonov is used for its numerical solution, with the original problem being preliminary discretized. This methodology and the developed software algorithms were used to determine the kinetic heterogeneity of titanium- and neodymium-containing catalytic systems. Results and discussion: The MWD analysis revealed two types of ACs with an average molecular weight of ATi-lnM = 11.3 and BTi-lnM = 13.2 in the titanium catalyst and three types of ACs ANd-lnM = 11.1, BNd-lnM = 12.7 and CNd-lnM = 14 for the neodymium catalyst, respectively. Conclusions: repeated computational experiments under different polymerization conditions and requirements for the preparation of a catalytic system make it possible to reveal a relationship with the resulting heterogeneity of ACs. It allows us to set and solve problems of controlling the molecular characteristics of the resulting polymer product.


2010 ◽  
Vol 148-149 ◽  
pp. 1661-1667
Author(s):  
Kai Gu ◽  
Xiao Di Xu ◽  
Ming Zhao

In this paper, Polymer Plus of Aspen Tech Inc. is used to establish a styrene-butadiene rubber (SBR) polymerization process model; the sensitivity analysis method is used to analyze concentration of the initiator, reaction temperature and other factors which influence production and molecular weight of product. It is concluded that increasing amount of initiator can improve production, while the molecular weight would increase at first and then decline; and along with the increasing temperature, weight-average molecular weight would lower and production of polymer PBS would increase; molecular weight of polymer and production of polymer would magnify along with increase of amount of emulsifier and volume of the reactor.


2013 ◽  
Vol 787 ◽  
pp. 241-244
Author(s):  
Jia Hui ◽  
Yan Shi ◽  
Zhi Feng Fu

Well defined polychloroprene has been synthesized by reversible addition fragmentation chain transfer (RAFT) polymerization with 2-(ethoxycarbonyl) prop-2-yl dithiobenzoate (EPDTB) as RAFT agent, AIBN as initiator, Chloroprene as monomer. Polymerization with two different feed ratios of monomer to RAFT agent were carried out. The sampling products at different reaction times were characterized using GPC and 1H-NMR. The GPC results demonstrated the molecular weight distributions (Mw/Mn) were narrow, and the number average molecular weight (Mn) was developed linearly with monomer conversion. All the characteristic signals of polychloroprene with the EPDTB as terminal groups were clearly observed in the 1H-NMR spectrum. In addition, the chain-extended polymers were also obtained successfully using the macro-RAFT agent, which indicated the active nature of the chain end.


2021 ◽  
Author(s):  
Pegah Khazraei Karimi Fard

Free radical (co-)polymerization of low-density polyethylene (LDPE) is carried out commonly in high pressure autoclaves or tubular reactors. The severe thermodynamic conditions of the process hinder ethylene from going to full conversion. One remedy to improve the monomer conversion is to investigate the effectiveness of initiators, such as difunctional organic peroxides. In the present work, a kinetic model based on a postulated reaction mechanism for free radical ethylene (co-) polymerization initiated by difunctional initiators is applied to analyze the dynamic behavior of a continuous LDPE isothermal autoclave reactor and a non-isothermal tubular reactor. The model describes the rates of initiation, propagation and the population balance equations. It predicts variations of the initiator and monomer concentrations and reaction temperature as well as molecular weight distribution of reactive macromolecular species. Variations of the pressure, velocity and transport/physical properties of the reacting mixture were accounted for in the tubular reactor. Model predictions are compared to experimental data collected from literatures for one monofunctional (dioctanoyl) and two difunctional initiators namely, (2,2-bis(tert-butylperoxy)-butane and 2.5-dimetyl hexane-2t-butylperoxy-5perpivalate). In comparison with dioctanoyl peroxide, polymerization with difunctional initiators requires a lesser amount of initiators and gives higher ethylene conversion in a shorter time. The modeling of LSPE with difunctional initiators was then extended to ethylene copolymerization with vinyl acetate and butyl acrylate. The model helps to determine the influence of reactivity ratio on the end-use product properties. Details of modeling a multiple feed LSPE tubular reactor are included for both homo- and co-polymerization reactions. The effect of monomer and initiator injections on the productivity and (co)polymer rheology and composition are investigated as well. Finally, an optimization method was applied to determine the optimal values of control variables via maximization of an objective function expressed in terms of monomer conversion, number average molecular weight, polydispersity and final desired composition of copolymer product. The results show that we can obtain a polymer with desired characteristics by proper manipulation of the control variables.


2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Vincent G Gomes ◽  
Ibrahem S Altarawneh ◽  
Mourtada H Srour

Accurate control of product properties through the manipulation of transfer agents can be of great benefit to industry in producing targeted polymeric materials. In this work we developed experimental protocols and mathematical models for understanding and characterising semi-batch emulsion polymerization in the presence of a xanthate-based transfer agent. Zero-one kinetics was employed with population balance equations to predict monomer conversion, molecular weight (MWD) and particle size (PSD) distributions in the presence of xanthate-based reversible addition-fragmentation chain transfer (RAFT) agents. The effects of the transfer agent (AR), surfactant, initiator (KPS) and temperature were investigated. Monomer feed rate was found to strongly affect conversion, MWD and PSD. The polymerization rate (Rp), number average molecular weight (Mn) and particle size () decreased with increasing AR. Rp increased with increase in SDS and KPS; while with increase in temperature, Mn decreased, Rp increased and increased. With semi-batch mode, Mn and increased with monomer flow rate.


e-Polymers ◽  
2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Gang Wang ◽  
Xiulin Zhu ◽  
Cheng Zhengping ◽  
Jian Zhu

AbstractHeterogeneous atom transfer radical polymerization (ATRP) of styrene initiated by 2-bromo-2-nitropropane in bulk was carried out with CuCl/2,2′-bipyridine as the catalyst. The kinetics was first order in monomer and the numberaverage molecular weight of the polymer increased linearly with monomer conversion, indicating the ‘living’/controlled nature of the polymerization. However, the number-average molecular weight was usually higher than the theoretical one. The nitro group might react with the Cu complex, resulting in insufficient initiation. The amount of catalyst has no effect on the controllability of this catalyst system for the ATRP of styrene. The presence of a halide end group in the obtained polymer was confirmed by both 1H NMR and chain-extension reaction.


2007 ◽  
Vol 26 (1_suppl) ◽  
pp. 115-127 ◽  

Polyethylene is an ethylene polymer used for a variety of purposes in cosmetics as an abrasive, adhesive, binder or bulking agent, an emulsion stabilizer, a film former, an oral care agent, and as a nonaqueous viscosity-increasing agent. Polyethylene is also used in food packaging materials and medical products, including prosthetics. The molecular weight of Polyethylene as used in cosmetics varies over a wide range. The lowest reported molecular weight is 198 Daltons and the highest is 150,000. In any given polymer preparation, there can be a broad range of molecular weights. Cellular and tissue responses to Polyethylene, determined as part of implant biocompatibility testing, include fibrous connective tissue build-up around the implant material that varies as a function of the physical form of the implant material. Specific assays for osteoblast proliferation and collagen synthesis demonstrated a reduction as a function of exposure to Polyethylene particles that is inversely related to particle size. The effect of Polyurethane particles on monocyte-derived macrophages, however, had a stimulatory effect, prolonging the survival of these cells in culture. The LD50 for Polyethylene, with an average molecular weight of 450, in rats was > 2000 mg/kg. For Polyethylene with an average molecular weight of 655, the LD50 was > 5.0 g/kg. Toxicity testing in rats shows no adverse effects at Polyethylene (molecular weight not given) doses of 7.95 g/kg or at 1.25%, 2.50%, or 5.00% in feed for 90 days. Dermal irritation studies on rabbits in which 0.5 g of Polyethylene (average molecular weight of 450) was administered in 0.5ml of water caused no irritation or corrosive effects; Polyethylene with an average molecular weight of 655 was a mild irritant. Polyethylene (average molecular weight of 450) did not cause dermal sensitization in guinea pigs tested with 50% Polyethylene ( w/w ) in a rachis oil BP. Polyethylene, with a molecular weight of 450 and a molecular weight of 655, was a mild irritant when tested as a solid material in the eyes of rabbits. Rabbit eyes treated with a solution containing 13% Polyethylene beads produced minimal irritation and no corneal abrasions. No genotoxicity was found in bacterial assays. No chemical carcinogenicity has been seen in implantation studies, although particles from Polyethylene implants can induce so-called solid-state carcinogenicity, which is a physical reaction to an implanted material. Occupational case reports of ocular irritation and systemic sclerosis in workers exposed to Polyethylene have been difficult to interpret because such workers are also exposed to other irritants. Clinical testing of intrauterine devices made of Polyethylene failed to conclusively identify statistically significant adverse effects, although squamous metaplasia was observed. The Cosmetic Ingredient Review (CIR) Expert Panel did not expect significant dermal absorption and systemic exposure to large Polyethylene polymers used in cosmetics. The Panel was concerned that information on impurities, including residual catalyst and reactants from the polymerization process, was not available. The Panel considered that the monomer unit in Polyethylene polymerization is ethylene. In the United States, ethylene is 99.9% pure. The other 0.1% includes ethane, propylene, carbon dioxide, carbon monoxide, sulfur, hydrogen, acetylene, water, and oxygen. The Panel believed that the concentration of these impurities in any final polymer would be so low as to not raise toxicity issues. Safety tests of cosmetic-grade Polyethylene have consistently failed to identify any toxicity associated with residual catalyst. Although it was reported that one process used to cross-link Polyethylene with an organic peroxide, this process is not currently used. In addition, cosmetic-grade Polyethylene is not expected to contain toxic hexanes. The Panel was concerned that the only genotoxicity data available was nonmammalian, but taking this information in concert with the absence of any chemical car-cinogenicity in implant studies suggests no genotoxic mechanism for carcinogenicity. The solid-state carcinogenicity effect was not seen as relevant for Polyethylene as used in cosmetics. The available data support the conclusion that Polyethylene is safe for use in cosmetic formulations in the practices of use and concentrations described.


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