Direct and closed form analytical model for the prediction of reaction kinetic of EPDM accelerated sulphur vulcanization

A novel direct model with kinetic base for the prediction of the final vulcanization level of EPDM cured with sulphur is presented. The model bases on a preliminary characterization of rubber through standard rheometer tests and allows an accurate prediction of the crosslinking degree at both successive curing times and different controlled temperatures. Both the case of indefinite increase of the torque and reversion can be handled. The approach proposed bases on a previously presented exponential model, where a calibration of three kinetic constants at fixed temperature by means of non-linear least square fitting was required. Here the exponential model is superseded and kinetic constants are evaluated through simple closed form formulas. The applicability of the approach is immediate and makes the model extremely appealing when fast and reliable estimates of crosslinking density of cured EPDM are required. To show the capabilities of the approach proposed, a comprehensive comparison with both available experimental data and results obtained numerically with the exponential model for real compounds at different temperatures is finally provided.     

A new simple numerical model based on experimental scorch curve data fitting for the interpretation of sulphur vulcanization

Sulphur was the first agent used to vulcanize commercial elastomers (e.g. natural rubber) and allows meaningful cost reductions during the industrial process (production cost ratio between peroxides and accelerated sulphur is around 5). Therefore, accelerated sulphur vulcanization is the most popular technique for the production of polydiene and EPDM elastomers items. At present, crosslinking mechanisms are not analytically known in detail, therefore reticulation kinetic has to be deduced from mechanical properties obtained during standardized tests, as for instance the oscillating disc rheometer. In the present paper, we propose a numerical model to fit experimental rheometer data based on a simple composite three functions curve, able to describe the increase of the viscosity at successive curing times at different controlled temperature to use during the production of thick items vulcanized with sulphur. It is believed that rheometer curve is able to give an indirect information on the rubber reticulation kinetic at different temperatures, to use in a successive step to establish simplified analytical kinetic formulas to adopt in the accelerated sulphur vulcanization of polydiene and EPDM elastomers. In the model, it is necessary to collect rheometer curves at different specimen temperatures, because vulcanization in industrial practice occurs at variable temperatures during curing, with considerable differences from the core to boundary of the item. Once that rheometer curves are suitably collected in a database, they are used to predict the optimal vulcanization of real items industrially produced. Finally, a so called alternating tangent approach (AT) is implemented to determine optimal input parameters (curing external temperature T _n and rubber exposition time t) to use in the production process. Output mechanical property (objective function) to optimize is represented by the average tensile strength of the item. A meaningful example of engineering interest, consisting of a thick 2D EPDM cylinder is illustrated to validate the model proposed.     

硅橡胶新硫化体系的研究

本文介绍一种硅橡胶新硫化体系,即利用Diels-Alder反应使聚硅氧烷进行交联。所用生胶为含乙烯基的高分子量聚甲基硅氧烷,所用交联剂(硫化剂),即双烯体,系含有环戊二烯基的有机硅化合物。所得弹性体的物理机械性能达到高强度硅橡胶水平。     

硅橡胶硫化反应场的数值模拟

以化学反应动力学原理为基础,实验确定了硅氢加成反应的动力学模型;引入 了硫化率增量的概念,获得了全量硫化率和硫化率增量的数值计算式;根据统计理 论,获得了起始分子无规分布时的交联结构参数的数值计算式;介绍了非稳态硫化 反应场的有限元模拟步骤。在此基础上,设计了硅橡胶硫化反应过程的有限元模拟 软件;应用该软件,根据输入的初边值条件,可计算任一空间点在任一时刻的交联 反应参数和交联结构参数,进而可预测制品性能、优化反应参数,或优化设计高分 子材料。最后给出了一个典型算例,并实验验证了该模拟理论及算法的合理性。     

COORDINATION CROSSLINKING OF NITRILE RUBBER FILLED WITH COPPER SULFATE PARTICLES

By incorporating copper sulfate(CuSO_4)particles into acrylonitrile butadiene rubber(NBR)followed by heat pressing,a novel vulcanization method is developed in rubber through the formation of coordination crosslinking.This method totally differs from traditional covalent or non-covalent vulcanization approaches of rubber.No other vulcanizing agent or additional additive is involved in this process.By analyzing the results of DMA,XPS and FT-IR,it is found that the crosslinking of CuSO_4 particles filled NBR was induced by in situ coordination between nitrogen atoms of nitrile groups (-CN)and copper ions(Cu~(2 ))from CuSO_4.SEM and EDX results revealed the generation of a core(CuSO_4 solid particle)- shell(adherent NBR)structure,which leads to a result that the crosslinked rubber has excellent mechanical properties. Moreover,poly(vinyl chloride)(PVC)and liquid acrylonitrile-butadiene rubber(LNBR)were used as mobilizer to improve the coordination crosslinking of CuSO_4/NBR.The addition of PVC or LNBR could lead to higher crosslink density and better mechanical properties of coordination vulcanization.In addition,crystal water in CuSO_4 played a positive role to coordination crosslinking of rubber because it decreased the metal point of CuSO_4 and promoted the metal ionization.     

Closed form numerical approach for a kinetic interpretation of high-cis polybutadiene rubber vulcanization with sulphur

A novel mathematical approach to predict the vulcanization degree of high-cis polybutadiene rubber vulcanized with sulphur is presented. The model has kinetic base, it is constituted by four reactions occurring in series and parallel and takes contemporarily into consideration, within a simplified but reliable scheme, the actual reactions occurring during polybutadiene sulphur curing, namely primary crosslinking and possible de-vulcanization. The first order differential equation system obtained is suitably rearranged and a closed form expression for the vulcanization degree is derived, depending the four kinetic constants characterizing the chemistry describing reactions. Instead of using classic least-squares optimization routines to characterize kinetic constants on experimental data, a simplified but reliable approach is proposed, where a system of four non-linear equations is solved with a recursive strategy, allowing estimating kinetic constants that proved to fit well normalized experimental data. The procedure is fast and its reliability is tested on a number of experimental data available, relying into a high-cis polybutadiene rubber cured under different temperatures and accelerators concentrations. Very good approximations of experimental data are obtained, also in comparison with a heuristic numerical approach where optimization is obtained interactively.     

双组份室温加成型硅橡胶口腔印模材料的制备

以自制乙烯基硅油为基胶、自制含氢硅油为交联剂、铂配合物为催化剂、高纯度硅微粉为填料、多乙烯基化合物为抑制剂等,通过实验制得双组份室温加成型硅橡胶口腔印模材料.研究了各组分对硅橡胶印模材料硫化化时间、细微复制、力学性能的影响.并制备了与国外产品性能相当的产品.     

Natural rubber/styrene-butadiene rubber blends prepared by solution mixing: Influence of vulcanization temperature using a Semi-EV sulfur curing system on the microstructural properties

Blends of natural rubber (NR) and styrene-butadiene rubber (SBR) were prepared by solution mixing and vulcanized with sulfur and accelerator in a Semi-EV system at 433 K and 443 K in order to study the vulcanization kinetic and the influence of vulcanization temperature on final structure of the blends. The vulcanization kinetic studied through the variation in rheometer curves was analyzed using the Ding and Leonov model, which takes into account the reversion effect during the cure process. The average free nanohole volume and the fractional free volume of samples with different NR/SBR ratio were estimated using positron annihilation lifetime spectroscopy (PALS). Also, the crosslink density was determined by means of swelling tests in a solvent. For all the compounds, a correlation between the free nanohole volume and the delta torque obtained from the respective rheometer curves was established.     

Influence of reversion on adhesion in the rubber-to-metal vulcanization-bonding process

The vulcanization bonding process is used in a growing number of industrial applications where rubber-to-metal bonded assemblies are needed. The complexity of this process lies in the fact that the vulcanization of the rubber and curing of an adhesive previously coated on the metallic surface have to take place simultaneously during a single molding step.In the present work, we present an instrumented molding device allowing the production of adhesion peeling test samples under well controlled curing temperature cycles. Tests performed on a model natural rubber compound with a commercial adhesive system show that, for high cure temperatures, the quality of the rubber-to-metal bonding obtained is significantly reduced. The decrease of the peeling energy appears to be inversely proportional to the reversion undergone by the rubber during cure. Such a result points out the necessity of taking into account this phenomenon for optimization of the vulcanization bonding process.     

Vulcanization kinetics of graphene/styrene butadiene rubber nanocomposites

This paper presents the influence of graphene on the vulcanization kinetics of styrene butadiene rubber （SBR） with dicumyl peroxide. A curemeter and a differential scanning calorimeter were used to investigate the cure kinetics, from which the kinetic parameters and apparent activation energy were obtained. It turns out that with increasing graphene loading, the induction period of the vulcanization process of SBR is remarkably reduced at low graphene loading and then levels off; on the other hand, the optimum cure time shows a monotonous decrease. As a result, the vulcanization rate is suppressed at first and then accelerated, and the corresponding activation energy increases slightly at first and then decreases. Upon adding graphene, the crosslinking density of the nanocomposites increases, because graphene takes part in the vulcanization process.     

Insight into vulcanization mechanism of novel binary accelerators for natural rubber

A novel TU derivative, N-phenyl-N′-(у-triethoxysilane)-propyl thiourea(STU), is prepared and its binary accelerator system is investigated in detail. Compared to the control references, the optimum curing time of NR compounds with STU is the shortest, indicating a more nucleophilic reaction occurs. The Py-GC/MS results present that the phenyl isothiocyanate fragment still remains in the NR/STU compounds with or without extracting treatment, but no silane segment can be found in the vulcanizate with extracting treatment. Vibrations of C=S, NH and aromatic ring in FTIR experiments and a new methyne carbon peak, as well as the peaks of phenyl group of STU, in the solid state 13C-NMR experiments are found in the NR/STU vulcanizate with extracting treatment. Moreover, the crosslinking density of vulcanizates with STU evolves to lower level, indicating the sulfur atom of STU does not contribute to the sulfur crosslinking. Therefore, a new vulcanization kinetic mechanism of STU is propounded that the thiourea groups can graft to the rubber main chains as pendant groups by chemical bonds during the vulcanization process, which is in accordance with the experimental observations quite well.     

Parabola-Hyperbola P-H kinetic model for NR sulphur vulcanization

A Parabola-Hyperbola (P-H) kinetic model for NR sulphur vulcanization is presented. The idea originates from the fitting composite Parabola-Parabola-Hyperbola (P-P-H) function used by the authors in [1,2] to approximate experimental rheometer curves with the knowledge of a few key parameters of vulcanization, such as the scorch point, initial vulcanization rate, 90% of vulcanization, maximum point and reversion percentage. After proper normalization of experimental data (i.e. excluding induction and normalizing against maximum torque), the P-P-H model reduces to the discussed P-H composite function, which is linked to the kinetic scheme originally proposed by Han and co-workers [3]. Typically, it is characterized by three kinetic constants, where classically the first two describe incipient curing and stable/instable crosslinks and the last reproduces reversion.The powerfulness of the proposed approach stands into the very reduced number of input parameters required to accurately fit normalized experimental data (i.e. rate of vulcanization at scorch, vulcanization at 90%, maximum point and reversion percentage), and the translation of a mere geometric data-fitting into a kinetic model. Kinetic constants knowledge from simple geometric fitting allows characterizing rubber curing also at temperature different from those experimentally tested.The P-H model can be applied also in the so-called backward direction, i.e. assuming Han's kinetic constants known from other models and deriving the geometric fitting parameters as result.Some existing experimental data available, relying into rheometer curves conducted at 5 different temperatures on the same rubber blend are used to benchmark the P-H kinetic approach proposed, in both backward and forward direction. Very good agreement with previously presented kinetic approaches and experimental data is observed.     

Bulk viscoelastic contribution to the wet‐sliding friction of rubber compounds

The wet‐sliding friction characteristics of rubber compounds made of high cis‐polybutadiene were examined with a British pendulum skid tester at room temperature. Three series of compounds were prepared—unfilled or filled with carbon black at two different levels. The bulk viscoelastic properties as characterized by the bulk glass‐transition temperature for the compounds were systematically adjusted by changing the crosslinking density via sulfur vulcanization. In fact, the dynamic mechanical glass‐transition temperature for the compounds ranges between approximately ?100 and 20 °C. Consequently, the wet‐sliding friction of these rubber compounds is dramatically affected. With increasing compound glass‐transition temperature, the wet‐sliding friction increases to a maximum and then decreases. However, the rate of increase or decrease varies with the amount of filler in the compounds. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 757–771, 2003     

Reaction mechanism of halogenated rubber crosslinking using a novel environmentally friendly curing system

Iron (III) acetylacetonate (Fe (acac)) in the presence of triethanolamine (TEOA) was utilized as a novel crosslinking agent for halogenated diene rubber. Following the assumption that the mechanism of the crosslinking bases on the Heck-type reaction mechanism, which requires the presence of a halogen and an unsaturated carbon-carbon double bond, chloroprene rubber (CR) and brominated butyl rubber (BIIR) were utilized as rubber matrices. The results of FTIR spectra analysis confirm the proposed mechanism and indicate that a Heck-type reaction is feasible for performing a crosslinking of halogenated diene rubbers. The use of the Fe (acac)/TEOA curing system results in a significant torque increase during the vulcanization, which confirms the high activity of those compounds. The elimination of halogen from a rubber macromolecular structure or elimination of a basic environment of the crosslinking reaction results in a deactivation of the new curing system.     

Vulcanization kinetics study of natural rubber compounds having different formulation variables

Vulcanization kinetics of natural rubber (NR) compounds with efficient vulcanization system was studied through phenomenological approach using the experimentally cure data obtained from a moving die rheometer. The cure kinetic parameters were defined using the proposed models by Claxton?CLiska and Deng?CIsayev with the support of curve fitting software. The effects of the amount of accelerators, sulfur and silica in the formulations on the cure characteristics and cure kinetic parameters at high cure temperatures were investigated. Kinetic data results showed that the above two models were able to describe the curing behaviour of the studied compounds satisfactorily. It showed that the fitting of the experimental data with Claxton?CLiska and Deng?CIsayev could provide a good platform to investigate the cure kinetics of the prepared NR compounds.     

Crosslink network evolution of BIIR/EPDM blends during peroxide vulcanization

Crosslink network evolution of brominated butyl rubber (BIIR)/ethylene–propylene–diene-monomer rubber (EPDM) blends during peroxide vulcanization is studied at a meso-scale level. In this work, EPDM is added as a co-agent to increase the crosslink density of BIIR vulcanization. With increasing EPDM content from 0 to 20 phr, the maximum torque of BIIR/EPDM compounds during vulcanization increases by 73%, reaching to 3.40 dNm. Vulcanization kinetic study shows that addition of EPDM favors to the crosslinking of BIIR compound. Meanwhile, the addition of 20 phr EPDM contributes to an increase in the crosslink density of BIIR/EPDM(80/20) vulcanizate, avoiding downward trend at post-cure period in comparison with BIIR only. Crosslink network evolution of BIIR/EPDM blends is divided into three periods during peroxide vulcanization at 150 °C. The role of EPDM in the crosslink network evolution is studied by proton nuclear magnetic resonance, and a “network patching” mechanism is proposed in which EPDM is implied to work as patch on damaged crosslink network resulted from the degradation nature of BIIR.     

Differential model accounting for reversion for EPDM vulcanized with peroxides

One of the main drawbacks of EPM/EPDM rubber vulcanization by peroxides is the lack of selectivity, which leads to a number of side reactions. The reaction mechanisms at the base of peroxides crosslinking are generally known and include the formation of alkyl and allyl (in the EPDM case) macro-radicals through H-abstraction from the macromolecular chains and the combination of these macro-radicals, which macroscopically is known with the term “vulcanization”. In the paper, a simple but effective mathematical model having kinetic base, to predict the vulcanization degree of rubber vulcanized with peroxides, is presented. The approach takes contemporarily into consideration, albeit within a simplified scheme, the actual reactions occurring during peroxidic curing, namely initiation, H-abstraction, combination and addition, and supersedes the simplified approach used in practice, which assumes for peroxidic curing a single first order reaction. After a suitable re-arrangement of the first order system of differential equations obtained from the actual kinetic system adopted, a single second order non-linear differential equation is obtained and numerically solved by means of a Runge–Kutta approach. Kinetic parameters to set are evaluated by means of a standard least squares procedure where target data are represented by experimental values available, i.e. normalized rheometer curves or percentage crosslink density experimentally evaluated by means of more sophisticated procedures. In order to have an insight into the reliability of the numerical approach proposed, two cases of technical interest are investigated in detail: the first is an EPDM crosslinked with two different peroxides, whereas the second is a compound with high level of unsaturation, showing reversion at medium-high vulcanization temperature ( $175^\circ \text{ C}$ ).     

Computer simulation and control for product quality in injection molding

The use of computers in plastics processing has continued to grow in parallel with rapid expansion of computer availability and computing power. One of the main areas of application is in computer simulation of the injection molding process where more demanding applications relate to the simulation of molding of complex-shaped moldings. Recent development include the use of boundary fitted curvilinear coordinates, the incorporation of fountain flow, and the coupling of crystallization kinetics within the transport equations. Applications in computer control relate to the control of pressure and temperature throughout the injection molding process, self-tuning control, physically-based dynamic models, and the control of properties of the molding, e.g. the weight of the article. Recent developments relate to the application of inverse modeling. An example is given of the use of inverse modeling of thermal stresses to predict or optimize thermal or pressure history during molding.     

Synergistic effect of 4,4′‐bis(maleimido) diphenylmethane and zinc oxide on the vulcanization behavior and thermo‐mechanical properties of chlorinated isobutylene–isoprene rubber

It is well known that the vulcanization of chlorinated isobutylene–isoprene rubber (CIIR) with ZnO alone is very slow and the resulting vulcanizate shows low crosslinking density as well as poor mechanical and thermal properties. For these problems to be addressed, 4,4′‐bis(maleimido) diphenylmethane (BMDM) has been applied along with ZnO to cure CIIR. The curing behavior was investigated using oscillating disk rheometer and differential scanning calorimetry analysis. The crosslinking densities, mechanical, dynamic mechanical, and thermal properties of the vulcanizates were also evaluated as a function of BMDM content. From the rheometer and differential scanning calorimetry analysis, it has been confirmed that the rate of curing, as well as the extent of curing between CIIR and ZnO, has remarkably increased in the presence of BMDM. The Diels–Alder reaction between the in situ formed conjugated diene butyl from CIIR/ZnO with the maleic moieties of BMDM has been identified as a primary reason for the higher rate and state of cure. The crosslinking densities of the vulcanizate CIIR/ZnO have significantly increased with increase in the content of BMDM. As a result, the compression set of the vulcanizate was remarkably decreased at elevated temperature. Moreover, the vulcanizates contain BMDM that has exhibited high thermal degradation temperature and good retention of the mechanical properties even after 7 days of thermal ageing. Copyright © 2016 John Wiley & Sons, Ltd.