Modeling processing of silicone rubber: Liquid versus hard silicone rubbers

The processing of hard and liquid silicone rubbers (LSR) are compared by means of modeling and simulation. The curing process for both, hard and liquid silicone, are modeled using the auto‐catalytic Kamal‐Sourour model and a nonlinear regression method is used to find the kinetic parameters. The fitted kinetic model is then combined with the heat balance equations to simulate real processing conditions. Both resins are compared in terms of process performance and consistency of the final part. The results show that even though hard silicone rubbers are less expensive resins, its processing conditions present several issues of consistency and quality control when compared with LSR. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci 119:1864–1871, 2011     

Cure Kinetic of Poly (alkyltetrasulfide) Using a Rheological Method

The kinetics of the curing of poly (alkyltetrasulfide) was investigated rheologically by evaluating the viscoelastic material functions such as elastic storage modulus, and viscous loss modulus, during the curing process, isothermally. The isothermal kinetic reaction was described using three phenomenological equation based on the Kamal and Sourour model, gel times at various temperatures and a kinetic model developed by Hsich and co-workers. The rate of the reaction was found to be second order. The temperature dependence of the cross-linking rate constant was described by an Arrhenius plot with an apparent activation energy equal to 34 kJ/mol, using the temperature dependence of gel time, which is in reasonable agreement with the value obtained from the Kamal and Sourour and the Hsich models.     

Vulcanization of EPDM rubber compounds with and without blowing agents: Identification of reaction events and TTT‐diagram using DSC data

Vulcanization of industrial‐like ethylene propylene diene termonomer rubber compound is studied using a differential scanning calorimetry (DSC). The analysis starts with DSC information to obtain the total transformation heat, followed by an isothermal‐dynamic temperature ramp that captures diffusion‐controlled reaction kinetics. The vulcanization is modeled by an auto‐catalytic Kamal–Sourour model, complemented with a Kissinger model for the prediction of one energy of activation, DiBenedetto's equation for the glass transition temperature, and adjusted reaction constants to include diffusion mechanisms. Two rubber formulations, with and without blowing agents, containing crosslinking agents, primary and secondary accelerators, activators, promoters, and processing aids are studied. The identification and separation of multiple reaction events, occurring during crosslinking of the compound without a blowing agent, is done through a 2^k design of experiments. Time–temperature–transformation (TTT) diagrams are calculated, integrating the kinetic model, thereby delineating processability windows, providing avenues for optimization, design, and online processing control. According to the kinetics and the TTT diagrams, the blowing agent induces several differences to the vulcanization reaction: decreases reaction temperatures while increasing reaction heats. It eliminates the exothermic peak before vulcanization and decreases the fully cured resin's glass transition temperature. Therefore, the presence of the blowing agent drives a shift in the vitrification line, resulting in a reduced operational window. POLYM. ENG. SCI., 55:2073–2088, 2015. © 2014 Society of Plastics Engineers     

Chemorheological time‐temperature‐transformation‐viscosity diagram: Foamed EPDM rubber compound

Thermal analysis, rheometry, and kinetic modeling are used to generate a comprehensive processability diagram for thermosetting and elastomeric resins. A chemorheological “time‐temperature‐transformation‐viscosity” diagram is proposed to fully characterize curing reactions toward process' on‐line control, optimization, and material design. Differential scanning calorimetry and thermogravimetric techniques are used to measure total reaction heat, degree of vulcanization, and cure kinetics. The viscosity, as a function of temperature and cure degree, is obtained from parallel plate rheometry. The auto‐catalytic Kamal–Sourour model, including a diffusion‐control mechanism, is used to model cure kinetics, while the Castro–Macosko model serves to model the rheological behavior. Non‐linear least‐squares regression and numerical integration are used to find models' parameters and to construct the chemorheological diagram. The usefulness of the proposed methodology is illustrated in the context of an industrial‐like Ethylene Propylene Diene Termononer rubber compound that includes a chemical blowing agent. Even though the rubber formulation contains crosslinking agents, primary and secondary accelerators, promoters, activators, and processing aids, the chemorheological diagram is obtained consistently, validating the proposed methodology to any thermosetting or elastomeric resin. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43966.     

An analysis of the influence of the accelerator/sulfur ratio in the cure reaction and the uniaxial stress–strain behavior of SBR

Vulcanized styrene butadiene rubber (SBR) with different cure systems was prepared and analyzed by using the model of rubber elasticity based on the tube concept, applied to the treatment of the stress–strain measurements. Samples with several ratio accelerators to sulfur, Λ, between 0.22 and 3.0 cured at 433 K were studied. The network chain density and the crosslink density of the samples were evaluated. By means of normalized rheometer curves, the kinetics of cure of these samples were evaluated by considering the model of isothermal curing proposed by Kamal and Sourour. In this frame, the parameters of the kinetics model were obtained. A correlation between the order of the kinetic equation, n, and the network chain density of the cure samples was established. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2601–2609, 2004     

Effect of carbon nanotubes content on the vulcanization kinetic in styrene–butadiene rubber compounds

Styrene–butadiene rubber compounds reinforced with commercial multiwall carbon nanotubes (MWCNT) in amounts between 0.5 and 10 parts per hundred of rubber (phr) were mixed in a two‐roll mill. A compound with 40 phr of carbon black (CB) was prepared as reference. From rheometric curves at five different temperatures (between 140°C and 180°C), a similar maximum torque and vulcanization time values in the samples reinforced with 10 phr of MWCNT and 40 phr of CB were obtained. The Kamal–Sourour model was used to analyze the influence of the MWCNT content and the vulcanization temperature on the cure rate and induction time. Then, through an Arrhenius plot, it became evident the effect of the reinforcement content on the activation energy of the vulcanization process. Mechanical properties of normalized sheets vulcanized at 160°C indicate that content between 5 and 10 phr of MWCNT are enough to reach a similar performance to that sample with 40 phr of CB. SEM analysis exhibits a good dispersion of MWCNT. Swelling experiments point out a similar absorption degree of toluene in the compounds with 5 phr of MWCNT and 40 phr of CB. POLYM. ENG. SCI., 59:E327–E336, 2019. © 2019 Society of Plastics Engineers     

The effect of pre-curing UV-irradiation on the crosslinking of silicone rubber

A recent work made use of selective pre-curing UV-irradiation and its effect on the kinetics of reaction of heat-cure silicone elastomers to spatially tune its viscoelastic properties and design architected solid membranes. The present study adds to the possibility of controlling the local properties of spatially graded materials by exploring the effect of key processing parameters such as the UV dose and the silicone mix thickness on the vulcanization kinetics. Dynamic Differential Scanning Calorimetry measurements have been performed showing that, over the conditions explored, the higher the UV dose, the slower the kinetics reaction. Additionally, complete crosslinking was always reached. Companion modeling effort using the Kissinger reaction model is attempted and the effects of processing parameters on the apparent activation energy are discussed. This work is a crucial first step towards the control of the processing settings needed to design architected silicone rubber membranes with spatially controlled mechanical property gradients obtained from a unique macromolecular network.     

Method for time–temperature–transformation diagrams using DSC data: Linseed aliphatic epoxy resin

A novel method to generate time–temperature–transformation (TTT) diagrams from Differential Scanning Calorimetry (DSC) data is presented. The methodology starts with dynamical DSC information to obtain the total transformation heat, followed by an isothermal‐dynamic temperature ramp that allows the inclusion of diffusion‐controlled reaction kinetic. The cure kinetics is modeled using an auto‐catalytic Kamal–Sourour model, complemented with a Kissinger model that allows the direct prediction of one energy of activation, DiBenedetto's equation for the glass transition temperature as a function of the cure degree and adjusted reaction constants to include diffusion mechanisms. The methodology uses a nonlinear least‐squares regression method following J.P. Hernández‐Ortiz and T.A. Osswald's methodology (J. Polym. Eng. 2004, 25, 23). A typical linseed epoxy resin (EP) presents two different kinetics control mechanisms, thereby providing a good model to validate the proposed experimental and theoretical method. TTT diagrams for EPs at two different accelerator concentrations are calculated from direct integration of the kinetic model. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40566.     

Recycling of silicone rubber waste: Effect of ground silicone rubber vulcanizate powder on the properties of silicone rubber

The silicone rubber vulcanizate powder (SVP) obtained from silicone rubber by mechanical grinding exists in a highly aggregated state. The particle size distribution of SVP is broad, ranging from 2 µm to 110 µm with an average particle size of 33 µm. X‐ray Photoelectron Spectroscopy (XPS) and Infrared (IR) Spectroscopy studies show that there is no chemical change on the rubber surface following mechanical grinding of the heat‐aged (200°C/10 days) silicone rubber vulcanizate. Addition of SVP in silicone rubber increases the Mooney viscosity, Mooney scorch time, shear viscosity and activation energy for viscous flow. Measurement of curing characteristics reveals that incorporation of SVP into the virgin silicone rubber causes an increase in minimum torque, but marginal decrease in maximum torque and rate constant of curing. However, the activation energy of curing shows an increasing trend with increasing loading of SVP. Expectedly, incorporation of SVP does not alter the glass‐rubber transition and cold crystallization temperatures of silicone rubber, as observed in the dynamic mechanical spectra. It is further observed that on incorporation of even a high loading of SVP (i.e., 60 phr), the tensile and tear strength of the silicone rubber are decreased by only about 20%, and modulus dropped by 15%, while the hardness, tension set and hysteresis loss undergo marginal changes and compression stress‐relaxation is not significantly changed. Atomic Force Microscopy studies reveal that incorporation of SVP into silicone rubber does not cause significant changes in the surface morphology.     

The kinetics of B‐a and P‐a type copolybenzoxazine via the ring opening process

The structure of benzoxazines is similar to that of phenolic resin through thermal self‐curing of the heterocyclic ring opening reaction that neither requires catalyst nor releases any condensation byproduct. These polybenzoxazine resins have several outstanding properties such as high thermal stability and high glass transition temperature. To better understand the curing kinetics of this copolybenzoxazine thermosetting resin, dynamic and isothermal differential scanning calorimetry measurements were performed. Three models, the Kissinger method, the Flynn–Wall–Osawa method, and the Kamal method, were used to describe the curing process. Dynamic kinetic activation energies based on Kissinger and Flynn–Wall–Osawa methods are 72.11 and 84.06 KJ/mol, respectively. The Kamal method based on an autocatalytic model results in a total order of reaction between 2.66 and 3.03, depending on curing temperature. Its activation energy and Arrhenius preexponential are 50.3 KJ/mol and 7959, respectively. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 730–737, 2005     

Thermal stability and kinetics analysis of rubber‐modified epoxy resin by high‐resolution thermogravimetric analysis

A dynamic heating rate mode of high‐resolution thermogravimetric analysis was used to study the thermal and thermal‐oxidative stability, as well as kinetics analyses, of a model liquid rubber‐modified epoxy resin, Ep/CTBN, made up of bisphenol A diglycidyl ether‐based epoxy and carboxyl‐terminated butadiene acrylonitrile rubber (CTBN). Results show that the thermal degradation of Ep/CTBN resin in nitrogen and air consists of two and three independent steps, respectively. Moreover, Ep/CTBN has a higher initial degradation temperature and higher activation energy than those of pure epoxy resin in both gases, indicating that the addition of CTBN to epoxy can improve the thermal and thermal‐oxidative stability of pristine epoxy resin. Kinetic parameters such as activation energy, reaction order, and preexponential factor of each degradation step of both Ep/CTBN and pure epoxy resins in air and nitrogen were calculated. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3594–3600, 2003     

Shape-stable phenolic/polyethylene glycol phase change material: kinetics study and improvements in thermal properties of nanocomposites

Storage, transformation, and absorption of energy play effective roles in application and performance of heat and thermal energy beneficiary. Phase change materials (PCMs) are substances with high heat of fusion which can be utilized to design thermal protective and thermal energy storage systems. However, PCM leakage in phase changing process is a well-known disadvantage of the PCM containing systems. One of the approaches to avoid PCM leakage is to prepare shape-stabilized PCM in polymeric composites. In this study, polyethylene glycol (PEG), as a PCM, was shape-stabilized with low leakage in the novolac colloidal structure with no solvent and through a sol–gel in situ polymerization process. Supercooling is a negative associate phenomenon in these systems, which may occur due to the low rate of nucleation and nucleation growth. Nanoclay was used to avoid supercooling of PEG. PEG supercooling significantly decreased when 2.5 wt% of nanoclay was incorporated. This is due to the role of nanoclay particles as the crystal nuclei. The sol–gel polymerization kinetics of novolac resin in the presence of nanoclay and molten PEG was also studied using the Kamal–Sourour model. Results showed that 85 wt% of PEG was preserved with leakage less than 3.5 wt% by shape stabilization encapsulated with colloidal structure of the phenolic resin. Nanoclay improved the thermal properties of the system and reduced the supercooling about 20%. Moreover, based on Kamal–Sourour model, polymerization kinetics could suggest a lower novolac curing rate in the presence of molten PEG and nanoclay.     

Development of a bubble growth model for natural rubber-based foams

The modeling of bubble growth was employed as a technique to control the cellular structure and by taking the equations of bubble growth and rubber curing into account simultaneously, the instantaneous radius of cells as a function of time was predicted. Side-by-side solves of the Kamal–Sourour kinetic model, as well as the heat transfer equation, led to the development of temperature variation function. Also, the predictions of the employed model concerning the effects of different parameters like the temperature of the foaming process, the level of foaming agent, and various physical attributes such as viscosity, gas diffusion coefficient, thermal conductivity, density, and surface tension on the bubble growth and radius alterations were analyzed. Based on the obtained scanning electron microscopy image from the cellular structure, there was only a 15% disparity between the predicted and experimental data about the bubble radius. Contrary to temperature, viscosity, and thermal conductivity, an increment in the level of foaming agent, diffusion coefficient, and density caused a rise of bubble radius. Also, the surface tension had an insignificant impact on the volume of the bubbles. Based on the findings, the applied model has proper credibility and can predict the influences of the abovementioned factors with satisfying accuracy.     

等温DSC法研究液态橡胶改性环氧树脂固化动力学

用等温差示扫描量热法(DSC)在三个不同的固化温度下研究了不同含量端羧基液态橡胶(CTBN)改性环氧树脂的等温固化过程,考察了不同CTBN含量对环氧树脂固化动力学的影响。通过Kamal方程对不同含量CTBN改性环氧树脂固化过程数据进行拟合,得到反应速率常数k1、k2及反应级数m、n,计算得到反应活化能的值,结果表明CTBN质量分数由0%到20%,k1、k2逐渐增大,反应前期活化能由67.34kJ/mol增加到80.31kJ/mol,增加了19.26%,反应后期活化能由94.19kJ/mol增加到180.07kJ/mol,增加了91.18%。     

Model for a solid‐liquid airlift two‐phase partitioning bioscrubber for the treatment of BTEX

BACKGROUND: Airlift solid–liquid two‐phase partitioning bioreactors (SL‐TPPBs) have been shown to be effective for the treatment of gas streams containing benzene, toluene, ethylbenzene and o‐xylene (BTEX). The airlift SL‐TPPB is a low‐energy system that utilizes a sequestering phase of solid silicone rubber beads (10%v/v) that will uptake and release large amounts of BTEX in order to maintain equilibrium conditions within the system. This increases mass transfer from the gas phase during dynamic loading periods and improves degradation performance. This study discusses the development and analysis of a steady‐state, tanks‐in‐series mathematical model, arising from mass balances on BTEX and oxygen in the gas, aqueous and polymer phases to predict the performance of the airlift SL‐TPPB over various gas flow rates and BTEX loadings. RESULTS: An estimability analysis on model parameters determined that the parameters to which model output is most sensitive are those that affect biological activity, which were targeted for estimation. The developed tanks‐in‐series model was able to predict the removal of BTEX components and dissolved oxygen concentrations over various inlet loadings (20, 60 and 100 mg L^?1 h^?1) and gas flow rates (2,3 and 4 L min^?1) that resulted in a range of system performance from effective BTEX treatment to oxygen limiting conditions. CONCLUSIONS: The model developed, with estimated parameters, provides a valuable tool to determine operating conditions that will result in favourable performance of the airlift SL‐TPPB. Copyright © 2009 Society of Chemical Industry     

TTT‐diagram for epoxy film adhesives using quasi‐isothermal scans with initial fast ramps

The characterization of film adhesives is challenging because they required freezer storage, contain an inseparable filler—thermoplastic knit or fiber‐reinforcement, and are heat activated systems with a pre‐cure and unknown chemistry. A testing protocol that eliminates these sources of error is proposed. This study presents a method to generate time–temperature‐transformation (TTT) diagrams of epoxy film adhesives via differential scanning calorimetry (DSC). Non‐isothermal and isothermal DSC scans are used to capture the reaction and the glass transition temperature. The use of an initial fast ramp—up to 500 K/min—in the isothermal scans is explored for the first time. This technique shows the potential to produce a quasi‐isothermal cycle, eliminating the loss of data in the initial stage of the reaction. The total heat released, the activation energy, and the fractional kinetic parameter, are estimated via model‐free methods. The Kamal–Sourour model and the formal kinetic model are fit to model the rate of cure. The simplest model that accurately captures the reaction, a parallel two‐step model, A , is outlined. The glass transition temperature is modeled via DiBenedetto's equation to include the diffusion‐controlled mechanism. The TTT‐diagrams of two commercial adhesives, DA 408 and DA 409, are shown with an analysis of processing optimization. The use of quasi‐isothermal scans with initial fast ramps combined with the correction for filler, moisture, and pre‐curing history can be applied to characterize fast curing thermosets, complex B‐stage resins, and thermosetting composites. The modeling results can also be used in numerical studies of residual stresses and dimensional stability in the manufacturing of thermosetting composites. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45791.     

Effects of polymethylvinylsilicone oil with side tetraphenylphenyl groups on the radiation resistance of addition‐type silicone rubber

Polymethylvinylsilicone oil with side tetraphenylphenyl groups (called C₂ gum for short) as a low molecular additive was used in two kinds of addition‐type silicone rubber, polymethylvinyl silicone rubber and poly (dimethyl‐diphenyl) silicone rubber, and the radiation resistance of silicone rubbers obtained was investigated by γ‐rays radiation with the dose rate of 117 Gy/min at doses up to 350, 500, and 850 kGy, respectively. Moreover, the average molecular weight between crosslinks and mechanical properties of silicone rubbers after irradiated in air and N₂ were determined by toluene‐swelling method and on a XLS‐A rubber test instrument, respectively. The results show that C₂ gum can effectively improve the radiation resistance of silicone rubber. When C₂ gum is used in poly(dimethyl‐diphenyl) silicone rubber, phenyl groups and tetraphenylphenyl groups may have synergistic effect, and the radiation resistance is improved greatly. The suitable amount of C₂ gum used in silicone rubber is 10– 14 phr. The crosslinking density of vulcanizates irradiated in N₂ is higher than that of vulcanizates irradiated in air because of the oxidative degradation. The radiation protection mechanism of C₂ gum was also discussed. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 4144–4148, 2007     

Adhesion properties and thermal degradation of silicone rubber

Silicone rubber is suitable for the thermal insulator of the rocket motors owing to its heat resisting properties as well as its excellent elasticity and restoring force. However, the adhesion properties of the silicone rubber should be improved greatly to be used as the thermal insulator because of its poor adhesiveness coming from the low surface tension. Functional groups were incorporated through copolymerization to the silicone rubber to induce chemical reaction with the functional groups in the propellant/liner components to enhance the adhesion properties. Peeling tests results disclosed that the incorporation of amine groups was the most efficient for the adhesiveness enhancement and that addition of carbon black improved the adhesiveness still more. Stability against thermal degradation of the silicone rubber was examined by measuring the activation energy through the thermogravimetric analysis. The results revealed that the compounding of the Cloisite® clays boosted up the thermal stability of the silicone rubber much more greatly than that of carbon black. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2782–2787, 2007