Cure kinetics and modeling the reaction of silicone rubber

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Abstract

The kinetics of the crosslinking reaction of polydimethylsiloxane (PDMS) was studied by differential scanning calorimeter (DSC). The kinetic parameters of the reaction were calculated from the Kissinger, the Ozawa, the Flynn–Wall–Ozawa, and the Friedman methods. The Chang method was also used to determine reaction order and to compare with other methods. To improve the accuracy, the autocatalytic model and the modified-Chang method were introduced. The theoretical heat generation against temperature curves, calculated by the estimated kinetic parameters, well fit the experimental data, which indicated that the analysis method used in this work was valid. The processing time and temperature was predicted by the direct integration of the kinetic equation with the data from isothermal runs. It would give a valuable guide for the thermal processing of silicone rubber.

Introduction

Silicone materials have many applications due to their interesting properties. Silicone rubbers generally, based on polydimethylsiloxane (PDMS), have special properties such as low toxicity, physiological inertness, good blood compatibility, and good thermal, oxidative, and mechanical stabilities, as well as flexibility and reliability over a wide range of temperatures and humidity [1], [2], [3], [4]. These unique properties have allowed silicones to be used in various applications, from aerospace applications to medical devices, such as seals for the automotive industry; artificial skin, blood pumps, drug delivery systems, and implants for medical purposes; packaging and baking pans for the food industry; and connectors and cables for appliances and telecommunications [4], [5], [6], [7], [8], [9], [10].

Silicone rubber is a thermoset elastomer and it is solidified exothermally by a cross-linking reaction called curing [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. To form a cured silicone rubber, peroxide and platinum catalysis are generally used. The cure of liquid silicone rubber is almost exclusively carried out with a platinum-catalyzed hydrosilyation reaction which does not generate by-products [12].

The chemical, physical, and mechanical properties of silicone rubbers are significantly affected by the curing behavior. To achieve the best properties, it is essential to know the optimum temperatures and times for curing. Thus the cure kinetics and mechanisms of silicone rubbers should be fully understood for better control and successful processing of the curing process.

The silicone rubber studied in this work is a thermally curable, addition-curing, two-part, liquid silicone rubber, and is depicted in Scheme 1. A hydrosilylation reaction occurs when sufficient heat is applied. Assuming that each cross-linking can release the same amount of energy, the heat released in curing reactions can be utilized to monitor the curing process [11]. Kinetic models relate the reaction rate to the temperature, and the degree of reaction and kinetic data obtained from DSC are very useful for understanding the cross-linking reaction processes and mechanisms [13], [14], [15]. Mechanistic and phenomenological approaches can be used to characterize a cross-linking reaction [16]. While the former studies the cure process as a series of individual reactions and models each of them, the latter considers it as a whole process. The individual steps of the cure process of silicone rubber can be found in literature [6], [8], but surprisingly, only a few have a kinetic model that describes the whole cure process. Though the n-th order model can describe a mechanism for a number of reactions, it is not good enough for many other cases.

In this study, the cross-linking reaction of silicone rubber was investigated by dynamic DSC. First, four methods were used to carry out the cross-linking reaction kinetics for silicone rubber. Second, we improve the accuracy with modified Chang method and the autocatalytic model with some constraints. Third, the theoretically calculated heat release rate curve produced from the estimated kinetic parameters was compared to the experimental values. Finally, the processing-time prediction at a certain temperature was suggested with an analytical solution.

Section snippets

Theoretical

Generally, the crosslinking reaction of a liquid material can be shown as: A (liquid) + B (liquid)  C (solid) where A and B are the starting materials, C is the different product during the disappearance of A and B. In differential scanning calorimetric measurements, the isothermal reaction rate /dt is assumed to be a linear function of the rate constant, k(T), and a function of the conversion, f(α):dαdt=k(T)f(α)k is the reaction constant, which can be expressed by the Arrhenius equation:k(T)=k0

Nth order reaction models

A Kissinger plot determines the activation energy simply without precise knowledge of the reaction mechanism involved:lnβTp2=lnk0REa+ln[n(1αp)n1]EaRTpwhere β is the heating rate, Tp and αp are the temperature and the peak conversion, respectively. By the plot of ln(β/Tp2) against 1/Tp, the activation energy can be determined from the slope [17], [18]. In an Ozawa plot, it is assumed that the degree of reaction is a constant value independent of the heating rate when a DSC curve reaches its

Model free kinetics

The Friedman method is probably the most general of the differential techniques and utilizes the following natural logarithmic equation:lnβdαdT=ln[k0f(α)]EaRTBy plotting ln [β(/dT)] against 1/T for a constant α value, the value of the −Ea/R can be obtained directly [21]. The FlynnWallOzawa isoconversional method is one of the “model-free” integral methods that can determine the activation energy without knowledge of reaction order:logβ=logk0Eag(α)R2.3150.457EaRT

The activation energy can

Materials

Commercially available silicone reactants were kindly supplied by Bluestar Silicones as a two part system (Silbione LSR 4330) with silica filler. Crosslinking is produced by the addition-cure reaction of vinyl endblocked groups with Sisingle bondH groups. The chemical structures of vinyl-terminated polydimethylsiloxane and methylhydrogen polydimethylsiloxane used are shown in Scheme 1.

Differential scanning calorimetry

Differential scanning calorimetry (DSC) was performed on DSC Q-series (TA, U.S.A.). Samples of about 8 mg were heated from

Results and discussion

Dynamic cure of silicone rubber was studied by determining the heat release rate during heating. Table 1 summarizes the results of DSC for silicone rubber at six different heating rates. While each peak temperature increased with increasing heating rate, the total heat of reaction was nearly constant. This temperature shift might be due to a heat transfer effect similar to pyrolysis [23]. To obtain the rate of cure and the degree of cure, the heat release rates and their running integral were

Conclusions

To investigate the curing phenomena and the processibility during thermal processing of silicone rubber, a cure kinetics study was carried out on dynamic DSC data. The kinetic parameters of the crosslinking reaction were evaluated using five methods. The activation energies calculated from the Kissinger, the Ozawa, the Friedman, the Flynn–Wall–Ozawa and the Chang methods were 109, 109, 103, 104, and 103 kJ/mol, respectively. The average activation energy (Ea), pre-exponential factor (k0), and

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