Determination of the activation energy of silicone rubbers using different kinetic analysis methods

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1 Determintion of the ctivtion energy of silicone rubbers using different kinetic nlysis methods OU Huibin SAHLI ohmed BAIEE Thierry nd GELIN Jen-Clude FETO-ST Institute / Applied echnics Deprtment, 2 rue de l Epitphe, 25 Besnçon, Frnce Abstrct. The solidifiction of silicone rubbers is crosslinking rection clled vulcniztion. It follows tht the physicl nd mechnicl properties of silicone rubbers increse significntly due to the growth of moleculr weight nd were ffected strongly by the vulcniztion process, such s the tempertures nd times for curing. In this study, the kinetics of the crosslinking rection of silicone rubbers ws investigted by two current techniques: differentil scnning clorimeter (DSC) nd oscillting disk rheometry (OD). From the kinetic experimentl dt, different kinetic nlysis methods were used to determine the ctivtion energy of silicone rubbers, such s the Kissinger, the Ozw, the Friedmn, the Flynn-Wll-Ozw, the Kissinger-Akhir-Sunose nd the integrl methods. The results show the influence of the chemicl composition of silicone rubbers, the current technique used nd the pplied kinetic nlysis methods on the ctivtion energy nd the evolution of ctivtion energy during the cr osslinking rection. 1 Introduction Silicone rubbers is specific ctegory of rubbery mteril, which hve mny interesting physicl nd chemicl properties, such s good therml, chemicl nd mechnicl stbilities, good biocomptibility nd high elsticity [1]. These unique properties hve resulted silicone rubbers to be used in wide vriety of field of ppliction in the industries: eronutic nd erospce, utomotive nd trnsport, electricl nd electronic, helth nd medicl, building nd construction [2]. Silicone rubber is thermoset elstomer, minly bsed on polydimethylsiloxne (PDS) nd solidified exothermlly by crosslinking rection clled vulcniztion. The vulcniztion process hs crucil influence on the performnce nd qulity of the finl product of silicone rubber. A suitble vulcniztion process cn improve the properties of silicone rubbers, such s the ter strength, the elongtion t brek, the hrdness nd the compression modulus [3]. To optimize nd improve the properties of silicone rubbers, the choice of vulcniztion process prmeters is prticulrly importnt, such s the vulcniztion temperture nd time. In this investigtion, two current techniques DSC nd OD were used to chrcterize the evolution of the crosslinking rection of silicone rubbers in different heting cycle. In DSC mesurement, the vulcniztion degree is relted to the het relesed during the crosslinking rection. Otherwise, in OD mesurement, the vulcniztion degree is ttched to the evolution of the elstic modulus. From the experimentl dt, severl kinetic methods were used to determine the ctivtion energy of silicone rubbers following the evolution of crosslinking rection during the vulcniztion process. 2 Theoreticl During the crosslinking rection of silicone rubbers, the rection rte dα/dt is ssumed to be liner function of the rte constnt k(t) nd function of the vulcniztion degree f(α) []: E d k T f k exp f dt where k is the pre-exponentil fctor, E is the ctivtion energy, is the gs constnt nd T is the bsolute temperture. In DSC mesurements, the vulcniztion degree cn be relted to the het relesed during the rection nd clculted by [5]: T (1) Qt (2) Q where Q(t) is the het relesed up to time t nd Q T is the totl het relesed during the crosslinking rection. In OD mesurements, the vulcniztion degree cn be defined s [6]: G'( t ) G' G' G' mx where G (t), G mx, G min re respectively the elstic modulus t time t, the mximum elstic modulus nd the minimum elstic modulus during the rection. min min 3. Kinetic nlysis methods In nisotherml mode, the Kissinger method ssumes tht the rection rte reched the mximum t the pek temperture nd determines the ctivtion energy simply without precise knowledge of the rection mechnism involved: k E T ln 2 ln P E P where β is the heting rte nd T P is the pek temperture. The ctivtion energy cn be determined from the slope of the plot of ln(β/t P ²) ginst P [7]. The Ozw method ssumes tht the rection order is constnt vlue () (3) Corresponding uthor: thierry.brriere@univ-fcomte.fr

2 ection rte [/s] ATEC Web of Conferences independent of the heting rte t the pek temperture, nd is represented by the following eqution: 1. 52E ln const (5) By the plot of ln(β) ginst P, the ctivtion energy cn be clculted from the slope [8]. The Friedmn method is probbly the most generl of the differentil techniques nd uses the following nturl logrithmic eqution: E d ln lnkf dt By plotting ln(dα/dt) ginst for constnt vulcniztion degree α vlue, the ctivtion energy cn be obtined from the slope [9]. The Flynn-Wll-Ozw method cn determine the ctivtion energy without knowledge of rection order: k E d 1. 52E f ln ln ln. For given vlue α, the ctivtion energy cn be clculted by the plot of ln(β) ginst [1]. The Kissinger-Akhir-Sunose method is the extension of the Kissinger method, nd is represented by the following eqution: k d E ln ln ln 2 T E f It determine the ctivtion energy by the plot of ln(β/t²) ginst for constnt vlue α [11]. In isotherml mode, the integrl method results in: d lnt,i ln lnk E P (6) (7) (8) (9) f i where t α,i is the time corresponding to degree α for n isotherml rection t the temperture T i. The ctivtion energy cn be obtined by plotting ln(t α,i ) ginst i for given constnt α [6].. Experimentl.1. terils The silicone rubbers studied in this work re originlly liquid nd two-prt, which include three types of Liquid Silicone ubber (LS) provided by Bluestr Silicones nd three types of oom Temperture Vulcniztion (V) silicone rubbers provided by Wcker Chemie. The min properties of these rubber mterils re summrized in Tble 1. L S T V Tble 1. in properties of silicone rubbers studied terils Den sity Hrdn ess Tensile stress [P] Elong tion t brek [%] ix rtio A:B Shore A LS :1 LS :1 TCS : : : :1.2. DSC tests Differentil scnning clorimetry tests were performed on Setrm DSC 92. The mixture of silicone rubbers ws heted from 25 to 2 C t vrious heting rtes from 1 to 2 C/min. The smples were bout 6 mg. The dynmic het flow signls were recorded during the heting cycle..3. OD tests The vulcniztion mesurement of silicone rubbers ws crried out in dynmic mode using rottionl rheometer HAAKE AS III with plte-nd-plte geometry of dimeter 2 mm. The crosslinking rection of silicone rubbers were chrcterized by men of elstic modulus curves obtined under isotherml conditions. Test tempertures used were from 1 to 1 C for LS nd from 7 to 1 C for V. The distnce between the two pltes is.5 mm nd the frequency used in the mesurement is 1 Hz with deformtion of 1 %. 5. esults nd discussion 5.1. Kinetic curves The kinetics curves of rection rte versus temperture t different heting rtes obtined by DSC mesurements for silicone rubber LS35 re shown in Fig. 1. It is cler tht the pek temperture incresed with incresing heting rte C/min 2 C/min C/min 6 C/min 8 C/min 1 C/min 15 C/min 2 C/min Temperture [ C] Figure 1. Kinetic curves t different heting rtes for silicone rubber LS35 obtined by DSC mesurements The evolution of rection degree versus time t different tempertures obtined by OD mesurements for

3 ln(β) ln(β) ln(β/t P 2 ) ln(dα/dt) ection degree NUIFO 216 silicone rubber LS35 re illustrted in Fig. 2. It ppers tht the vrition of vulcniztion time records n exponentil decrese with the incresing temperture for the rubber mterils Figure 2. Kinetic curves t different tempertures for silicone rubber LS35 obtined by OD mesurements 5.2. Activtion energy Time [s] 1 C 11 C 12 C 13 C 1 C From DSC experimentl dt, Kissinger nd Ozw methods were employed to clculte the ctivtion energies of silicone rubbers t the pek temperture, which re shown in Figs. 3 nd. It ppers tht Kissinger nd Ozw methods fit well the results correltion coefficient t lest.985. The vlues of ctivtion energy were obtined from the slope nd summrized in Tble 2. We cn note tht the ctivtion energy of LS re lrger tht those of V LS35 LS37 TCS Tble 2. The vlues of ctivtion energy of silicone rubbers obtined by the Kissinger nd the Ozw methods ubber mterils nd vlues of estimted ctivtion energy [kj/mol] LS 35 LS 37 TCS The Friedmn method, the Flynn-Wll-Ozw method nd the Kissinger-Akhir-Sunose method were lso performed to clculte the ctivtion energy of silicone rubber LS35 with the evolution of rection degree, which re shown in Figs 5, 6 nd 7. The vlues of ctivtion energy were obtined from the slope nd summrized in Fig 8. One cn remrk tht the vlues obtined by the Friedmn method decrese shrply from 1 to kj/mol with the incresing of rection degree. While the vlues obtined by the Flynn-Wll-Ozw method nd the Kissinger-Akhir-Sunose method re round 8 kj/mol for the rection degree vrying from.1 to α=.1 α=.2 α=.3 α=. α=.5 α=.6 α=.7 α=.8 α= Figure 5. Friedmn plot for silicone rubber LS35 in different rection degrees (: K -1 ) P Figure 3. Kissinger plot for silicone rubbers ( p : K -1 ) α=.1 α=.2 α=.3 - α=. α=.5 α=.6 α=.7 α=.8 α= LS35 LS37 TCS Figure 6. Flynn-Wll-Ozw plot for silicone rubber LS35 in different rection degrees (: K -1 ) P Figure. Ozw plot for silicone rubbers ( p : K -1 )

4 ln(t α,i ) Activtion energy [kj/mol] ln(t α,i ) ln(β/t 2 ) ATEC Web of Conferences obtined by OD mesurements in isotherml conditions re lmost identicl to those obtined by DSC mesurements in nisotherml conditions α=.1 α=.2 α=.3 α=. α=.5 α=.6 5 α=.7 α=.8 α= Figure 7. Kissinger-Akhir-Sunose plot for silicone rubber LS35 in different rection degrees (: K -1 ) Figure 8. Evolution of the vlues of ctivtion energy s function of rection degree for silicone rubber LS35 obtined by the Friedmn, the Flynn-Wll-Ozw nd the Kissinger- Akhir-Sunose methods, from the kinetic curves obtined by DSC mesurements Figure 9. Isotherml integrl plot for silicone rubber LS35 in different rection degrees ( i : K -1 ) From the OD experiment results in isotherml conditions, the integrl method ws pplied to determine the ctivtion energy of silicone rubber by plotting ln(t α,i ) ginst i for rection degree vrying from.1 to.9, Fig. 9. It shows tht the stright lines re prllel for the different rection degree nd hve correltion coefficient over.99. In Tble 3, the verge vlues of ctivtion energy were clculted nd compred for the six types of silicone rubbers by the Friedmn, the Flynn-Wll-Ozw, the Kissinger-Akhir-Sunose nd the isotherml integrl methods. We cn find tht the vlues of ctivtion energy of LS silicone rubbers re lwys lrger thn those of V silicone rubbers. In dditions, the verge vlues Friedmn Flynn-Wll-Ozw Kissinger-Akhir-Sunose ection degree i α=.1 α=.2 α=.3 α=. α=.5 α=.6 α=.7 α=.8 α= Figure 9. Isotherml integrl plot for silicone rubber LS35 in different rection degrees ( i : K -1 ) Tble 3. The vlues of ctivtion energy of silicone rubbers obtined by the different kinetic nlysis methods ubber mterils nd vlues of estimted ctivtion energy [kj/mol] LS 35 LS 37 TCS (ethod: 1 Friedmn, 2 Flynn-Wll-Ozw, 3 Kissinger- Akhir-Sunose nd Isotherml Integrl) 6. Conclusions The curing kinetic study ws crried out by DSC nd OD mesurements in isotherml nd nisotherml conditions in order to investigte the crosslinking rection of silicone rubbers. From the kinetic curves obtined, the kinetic prmeters of ctivtion energy were determined by six methods. The Kissinger nd the Ozw methods show tht the mximum ctivtion energies were reched t the pek temperture in nisotherml mode. In dditions, the isotherml integrl method lmost gives the sme vlues of ctivtion energies s the Flynn-Wll-Ozw nd the Kissinger-Akhir-Sunose methods. At the end, the vlues of ctivtion energy of LS silicone rubbers were lrger thn those of V silicone rubbers studied in this investigtion. eferences i α=.1 α=.2 α=.3 α=. α=.5 α=.6 α=.7 α=.8 α=.9 1. L. Wng, Q. Liu, D. Jing, S. Zhou, L. Sho, Journl of Dentistry, Progress in Orgnic Cotings, 2, (21), W. Brchczek, 77, (21), X. Ye, H. Liu, Y. Ding, H. Li, B. Lu, icroelectronic Engineering, 86, (29), 3113,.. I.K. Hong, S. Lee, vol. 19, pp. 2-7, J.P. Hernández-Ortiz, T.A. Osswld, Journl of Applied Polymer Science, 119, (211),

5 6. E. Leroy, A. Souid, A. Srd,. Deterre, Polymer Testing, 32, 213, H.E. Kissinger, ection kinetics in differentil therml nlysis, Anlyticl Chemistry, 29, (1957), T. Ozw, Journl of Therml Anlysis, 2, (197), 312, 9. H.L. Friedmn, Journl of Polymer Science Prt C, 6, (196), J.H. Flynn, Journl of Therml Anlysis, 27, (1983), T. Akhir, T. Sunose, eserch report, Chib Institute of Technology, Journl of Science Eduction nd Technology, 16, (1971), 221. NUIFO 216

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Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl