Thermal Degradation Kinetics of Polyamide 6,6 Cable Ties by Thermogravimetric Analysis Nabil N. Rammo Dept. of Physics/ College of Education Scientific Departments/ University of Salahaddin Hind A. M. Mahdi Dept. of Physics/College of Education for Pure Science(Ibn Al-Haitham/ University of Baghdad Received in : 20 January 2013 , Accepted in : 17 March 2013 Abstract The thermal degradation of cable ties of polyamide (PA6,6) neat and UV stabilized was investigated by thermogravimetry (TG) and its derivative (DTG) at several heating rates between 5 and 80 oC min-1 in helium atmosphere. High heating rates signal novel peaks in the DTG curves that indicate melting temperature of PA6,6. The kinetic parameters calculated via isoconversion and nonisothermal data using the Flynn-Wall-Ozawa, Kissinger and Coats- Redfern methods showed comparable activation energy values. Exposure of the ties to outdoor environment causes pre-mature stress cracking and brittle failure due to prevalence of crosslinking reaction occurring in the polymer chains. Keywords: Polyamide 6,6 ,Thermal degradation , Kinetic analysis,Thermogravimetric analysis , Activation energy , Cable ties . 199 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Introduction Polyamides such as PA6 and PA6,6 possess a favorable balance of physical and chemical properties, which has been widely used as engineering material [1]. However their thermal stability is hindered by low glass transition temperature posing limit on their high temperature application [2]. Recent usage of PA6,6 in automotive industry has focused on their use for greater fuel economy and weight reduction coupled with the critical requirement of higher continuous use temperature (CUT) and resistance to thermal degradation [3]. Therefore, the knowledge of thermal degradation kinetics of PA6,6 whether photo-oxidized [4] or electron beam irradiated [5] is essential, and for this purpose thermogravimetric analysis (TGA) is widely used because of its experimental simplicity and the wealth of information obtained from a simple thermogram, such as the activation energy in addition to the understanding of thermal degradation mechanism [6]. It has been found that the main route of thermal degradation of PA6,6 is the elimination of the main organic product cyclopentanone and also some hydrocarbons, nitriles and vinyl groups [7,8]. PA6,6 can be crosslinked or degraded as the consequence of their exposure to ionizing radiation in addition that the two processes may compete in the degradation reaction [9,10]. The kinetic analysis of a decomposing material can be done using the dynamic thermogravimetric study, which can be analyzed by the isoconversional method. In this method a series of thermogravimetric curves obtained at different heating rates can be used to calculate the activation energy [11]. The present paper focuses of the thermal degradation kinetic of PA6,6 neat and UV stabilized under dynamic conditions using three methods: Kissinger and Flynn-Wall-Ozawa that utilize heating rate at different levels of conversion, and Coat-Redfern that utilizes ,conversion at different levels of heating rate, to verify the effectiveness of the kinetic analysis method and to shed a light on the thermal degradation mechanism that PA6,6 undergoes when used outdoors for tying cables and pipes. It has been noticed that outdoor use of PA6,6 cable ties fail by stress cracking under its own constant tying load. Kinetic Methods [12] The reaction rate in TG analysis can be defined as the change of degree of conversion (α) with time or temperature and is calculated as: α = mo –mt / mo –mf ……….( 1) where m0, mt and mf represent the initial, actual and final mass of material respectively . All kinetic studies assume that the isothermal rate of conversion, dα dt , is a linear function of temperature and is expressed in Arrhenius form as: 𝑑𝛼 𝑑𝑡 = 𝐴(1 − α)𝑛 e−E RT⁄ ⋯⋯ ⋯ ( 2) Where A, n, E, R and T are the pre-exponential factor (min-1), assumed to be temperature – independent of the reaction order, the activation energy (KJ mol-1 ), the gas constant (8.314 J mol-1 K-1) and the absolute temperature (K) , respectively. At constant heating rate β = dT/dt, Eq. (2) may be written as: 𝑑𝛼 𝑑𝑇 = A β (1 − 𝛼)𝑛 e−E RT⁄ ⋯⋯⋯ (3) Kissinger’s method [13] Kissinger’s method is one of the differential methods that has been utilized to calculate the activation energy from plots of the logarithm of the heating rate versus the inverse of the temperature at the maximum reaction rate in constant heating rate experiments. The beauty of this method is that even without a precise knowledge of the reaction mechanism, the activation energy can be determined after taking the logarithm in Eq. (3): Log(β/T2max) = {log AR/E +log[n(1-αmax)n-1]} – E/2.303RTmax ⋯⋯⋯ (4) 200 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 where β, A, R, E, n have their usual significance, Tmax is the temperature indicating the inflection point of the thermal degradation curves which corresponds to maximum rate and αmax is the maximum conversion . From the plot of log(β/T2max) versus 1/Tmax and fitting to a straight line, E can be computed from the slope. Flynn - Wall - Ozawa method This isoconversional integral method is suggested independently by Ozawa [14] and Flynn and Wall [15] uses Doyle approximation [16] of the temperature integral. From Eq. (3) after taking logarithm is: Log β = log (AE/(1-α)n R) - 2.315 - E/2.303RT ………..(5) Thus for α = constant, the plot of logβ versus 1/T gives a straight line with the slope determining the activation energy. Using this method, one can determine the activation energy at different levels of conversion. Coats – Redfern [17] Coats – Redfern method has been used by researchers to determine the activation energy of solid state reactions from plots of the logarithm of conversion versus 1/T. Thus Eq. (3) after integration becomes: log (- log (1-α) /T2 ) = log (AR/βE) – E/2.303RT …..…… (6) Here α is the fraction of sample degradation at temperature T, where T is the derivative peak temperature obtained from DTG curve . Thus a plot of log(-log(1-α)/T2) versus 1/T gives a straight line with the slope determining the activation energy. Using this method one can determine the activation energy at different levels of heating rate. Experimental Samples of polyamide 6,6 were obtained from cable ties (colors: white and black) manufactured by Y.Y. Cable Accessories Co. Taiwan. Samples for the analysis were taken from a sealed pack. Others were outdoor tied on plastic tubes and were failed by stress cracking during one season. Brittleness was obvious on these ties. Thermal degradation was performed on a Perkin Elmer TGA-7 thermogravimetric analyzer at the ibn Sina company / Ministry of Industry and Minerals . The samples were heated from ambient temperature to 850℃ using heating rates of 5, 10, 20, 40 and 80 ℃ min-1 in helium at a gas flow rate of 20 ml min-1 . The initial mass of the sample was 22~38 mg. Results and Discussion Figures 1 and 2 show the variations of the TGA and DTG curves with respect to temperature for various heating rates in helium atmosphere for neat and UV stabilized polyamide 6,6 respectively. It is seen from Figures 1 and 2 that the TG curves for neat and UV stabilized PA6,6 are displaced to higher temperature due to heat transfer lag with increased heating rate and the height of the DTG peaks also increase with the heating rate due to excesses heat flux. These findings are in agreement with the reported similar observation for polyethylene terephthalate[18] and for styrene butadiene rubber[19]. It is also observed that the residual mass fractions in the neat PA6,6 remain constant after 700℃ and are about 0.1~0.2 for the heating rates 5-80 ℃ min-1 . However, for the UV stabilized PA6,6 the residual mass fractions for the high heating rates namely 40 and 80 ℃ min-1 remain constant after 600℃ and are about 0.2 ~ 0.3, but for the 5, 10 and 20℃ min-1 it remains constant after 750℃ 201 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 for the same residual mass fractions. It is also noticed from the DTG curves in both figures 1(b) and 2(b) the appearance of two peaks near the melting temperature of PA6,6 at the heating rates of 40 and 80 ℃ min-1 ( see Table 1 ). This can be seen as a way of monitoring melting behavior by adapting high heating rate thermogravimetry. Figure 3 shows the plots of 1/T versus log𝛽𝛽 and log (β / T2max) for neat and UV stabilized PA6,6 from which the activation energy is computed for different conversion levels by Flynn-Wall-Ozawa and Kissinger methods. The activation energy values deduced from the plots in Figure 3 by Flynn-Wall-Ozawa and Kissinger methods are shown in Table 2. Figure 4 shows the plots of log(-log (1-α)/T2 ) versus 1/T for neat and UV stabilized PA6,6 from which the activation energy is computed for different heating rates by Coats – Redfern method. The activation energy values deduced from the plots of Figure 4 by Coats-Redfern method are shown in Table 3. The results in Tables 2 and 3 indicated that the activation energy obtained from nonisothermal data (Flynn-Wall-Ozawa and Kissinger methods ) are comparable with the isoconversion data (Coats-Redfern method ) in the low to moderate heating rate range (5 to 20 ℃ min-1 ). It is also noted that the activation energy varies with both kinetic parameters i.e. heating rate and conversion in similar fashion, an indication that the kinetic analysis using the various methods show consistent variations. Table 4 shows the comparison of the activation energy results obtained in this work with the corresponding values reported in the literature for PA6,6 (neat). Effect of environment on degradation The TG and DTG curves of the outdoors used and failed samples of neat PA6,6 show significant changes in the TG curve at the beginning and at the end of the heating cycle. For low conversion of 2.5%, the outdoor sample degrade faster than the unused sample by a wide margin of temperature 230 oC relative to 355 oC. The reason is that exposure to environment has caused pre-mature chain scission reaction especially when the molecular chain endure constant load, which triggers lower temperature degradation. For high conversion of 99.2%, the remaining residue is sustained up to a temperature of 780 oC in the outdoor samples in comparison with 675 oC for the unused samples indicating appreciable build up of crosslinking network in the outdoor samples. This is manifested by the mechanical brittleness endured by the outdoor used samples. The activation energy deduced from Coats-Redfren method for the outdoor samples show an increase relative to the unused samples. A summary of temperatures and activation energy deduced from the TG curves are shown in Table 5. Conclusions Thermal degradation of PA6,6 was studied by dynamic thermogravimetry and the kinetic parameters were analyzed by three analytical methods. Although the route of calculating the activation energy is different within the three methods, comparable results of activation energy were obtained. High heating rates with the conjunction of DTG curves can be useful in monitoring the adaptation of polymer molecules at the boundaries of melting before degradation occurs. Cable ties of PA6,6 exposed in moderate to sever outdoor atmosphere are likely to end up with failure from stress cracking condition by the effect of crosslinking reaction in the polymeric chain. Such observation are likely to be taken for further detail investigation. 202 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 References 1. Domininghaus, H. (1993) Plastics for engineers, Munich: Hanser Publishers, 363-401. 2. Gu, H. , He, J.M. ; Hu J. and Huang, Y.u. (2012) Thermal degradation kinetics of semi- aromatic polyamide containing benzoxazole unit, J. Therm. Anal. Calorim., 107(3) : 1251- 1257. 3. Wang, X.L. ; Yang, K.K. ; Wang, Y.Z. ; Wn, B. ; Lin ,Y. and Yang, B. (2003) Thermogravimetric analysis of the decomposition of poly (1,4-dioxan- 2-one ) / starch blends, Polym. Degrad. Stab., 81 : 415-421. 4. Singh, R.P. ; Desai, S.M. and Pathak, G. (2003) Thermal decomposition kinetics of photo- oxidized nylon 6,6 , J Appl. Polym. Sci., 87 : 2146-2150. 5. Sengupta, R. ; Sabharwal, S. ; Bhowmick ,A.K. and Chaki T.K. (2006) Thermogravimetric studies on polyamide 6,6 modified by electron beam irradiation and by nanofillers, Polym. Degrade. Stab., 91 : 1311-1318. 6. Park, J.W. ; Oh, S.C. ; Lee, H.T. and Yoo, K.O. (2000) A kinetic analysis of thermal degradation of polymer using dynamic model, Polym. Degrad. Stab., 67 : 535-540 . 7. Ballistresi, A. ; Garozzo, D. ; Giuffrida, M. and Montaudo G. (1987) Mechanism of thermal decomposition of nylon 6,6 , Macromolecules, 20: 2991-2997. 8. Levchik, S.V. ; Costa L. and Camino G. (1994) Effect of the fire – retardant , ammonium polyphosphate on the thermal decomposition of aliphatic polyamides part III- polyamide 6,6 and 6,10, Polym. Degrad. Stab.,43 : 43-54. 9. Dadbin, S. ; Frounchi, M. and Goudrazi, D. (2005) Electron beam induced crosslinking of nylon 6 with and without the presence of TAC, Polym. Degrad. Stab., 89: 436-441. 10. Zaharescu, T. ; Silva, L.G.A. ; Jipa, S. and Kappel, W. (2010) Post-irradiation thermal degradation of PA6 and PA6,6 , Radiat. Phys. Chem., 79: 388-391. 11. Herrera, M. ; Matuschek, G. and Kettrup A. (2001) Main products and kinetics of the thermal degradation of polyamides, Chemosphere, 42: 601-607. 12. Vyazoukin, S. (2000) Kinetic concepts of thermally simulated reaction in solids : a view from a historical perspective, Int. Rev. Phys. Chem., 19: 45-60. 13. Kissinger, H.E. (1957) Reaction kinetics in differential thermal analysis, J. Anal. Chem., 29 : 1702-1706. 14. Ozawa, T. (1965) A new method of analysis thermogravimetric data, Bull. Chem. Soc. Jpn,38 : 1881-1886 . 15. Flynn , J.H. and Wall, L.A. (1966) A quick direct method for the determination of activation energy from thermogravimetric data, Polym. Lett.,4 : 323-328. 16. Doyle, C.D. (1962) Estimating isothermal life from thermogravimetric data, J. Appl. Polym. Sci.,6 : 639-642. 17. Coats, A.W. and Redfern, J .P. (1964) Kinetic parameters from thermogravimetric data, Nature, 201: 68. 18. Hu, S.C. ; Lee, D.G. ; Kwak ,H. and Bae, S.Y. (2006) Combusion kinetics of polyethylene terephthalate, Korean Environ. Eng. Res., 11(5): 250-256. 19. Chen, K.S. and Ye, R.Z. (1997) Kinetics of thermal decomposition of styrene – butadiene 20. Pashaei, S. ; Siddaramaiah, S. ; Souldozi, A. , Seyed, S.U.T. and Syed, A.A. (2011) Investigation on thermal and mechanical behaviors of crysnanoclay incorporated polyamide / nanoclay composites, Int. J. Chem. Tech. Res., 3(3): 1292-1301. 203 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Table No. (1) : Melting and decomposition temperatures of neat and UV stabilized PA6,6 obtained from DTG curves at various heating rates Decomposition ( oC ) Melting ( oC ) Heating rate ( oC min1) UV Neat UV Neat max. on-set max. on-set 428 324 425 342 - - 5 438 346 437 369 - - 10 444 351 455 375 - - 20 449 376 474 396 253 266 40 489 409 501 420 263 272 80 Table No.( 2): Activation energy of neat and UV stabilized PA6,6 obtained using Flynn- Wall- Ozawa and Kissinger methods Activation Energy (kJ mol-1) Conversion (%) Kissinger Flynn-Wall-Ozawa UV Neat UV Neat - 101 - 105 2.5 151 113 141 121 5 159 134 164 144 10 183 152 192 164 20 Table No.(3):Activation energy of neat and UV stabilized PA6,6 obtained using Coats- Redfern method Activation Energy ( kJmol-1) Heating rate (oC min-1) UV Neat 152 113 5 173 129 10 204 165 20 216 200 40 229 226 80 204 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Table No.( 4): Summary of the activation energy obtained for neat PA6,6 in this work and the ones reported in the literature by various analytical methods Range of Activation Energy (kJ mol-1) References Other Coats- Redfern Kissinger Flynn-Wall- Ozawa 182 175 166 Gu et al. [2] 51-112 Singh et al. [4] 180 148 Sengupta et al. [5] 91 Herrera et al. [11] 257 Pashaei et al. [20] 113-165 101-152 105-164 This work Table No.( 5): Comparison between thermal behavior of outdoor loaded neat PA6,6 cable ties with unused ones analyzed at β = 10 oC min- Outdoor + loaded Unused Conversion α = 1% 140 oC 160 oC α = 2.5% 230 oC 355 oC α = 99.2% 780 oC 675 oC Activation energy(KJmol-1) (Coats-Redfern) 144 129 205 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 (a) (b) Figure No.( 1): TG (a) and DTG (b) curves of neat PA6,6 at various heating rates 206 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 (a) (b) Figure No.( 2): TG (a) and DTG (b) curves of UV stabilized PA6,6 at various heating rates 207 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 (a) (b) Figure No.( 3): Plots of 1/T versus log β (Flynn-Wall-Ozawa) and log (β/T²max) (Kissinger) at different levels of conversions for neat (a) and UV stabilized (b) 208 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 (a) (b) Figure No.( 4): Plots of 1/T versus log (-log (1- α ) / T² ) (Coats-Redfern) at different heating rates for neat (a) and UV stabilized (b) -7.9 -7.6 -7.3 -7 -6.7 1.32 1.4 1.48 1.56 1.64 lo g ( - lo g (1 -α ) / T ² ) 1000/T (K-1) 5 oC / min 10 oC / min 20 oC / min 40 oC / min 80 oC / min -7.9 -7.6 -7.3 -7 -6.7 1.32 1.38 1.44 1.5 1.56 lo g ( - lo g (1 -α ) / T ² ) 1000/T (K-1) 5 oC / min 10 oC / min 20 oC / min 40 oC / min 80 oC / min 209 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 بوساطة التحلیل 6,6حركیات التفكك الحراري لرابطات الكابل نوع بولي اماید الحراري التفاضلي نبیل نعیم رمو كلیة التربیة ، جامعة صالح الدین ھند عبد المجید مھدي جامعة بغداد / )ابن الھیثم(للعلوم الصر فة قسم الفیزیاء/ كلیة التربیة 2013آذار 17، قبل البحث في 2013كانون الثاني 20أستلم البحث في : الخالصة النظیف و المستقر لالشعة فوق 6,6درس التفكك الحراري لرابطات الكابل نوع بولي اماید عند معدالت تسخین DTGو مشتقتھا TGالبنفسجیة بوساطة منحنیات التحلیل الحراري الوزني 80و 40م لكل دقیقة في جو الھیلیوم . لوحظ أن معدالت التسخین المرتفعة ( ˚ 80 – 5مختلفة بین . 6,6التي تشیر الى درجة انصھار البولي اماید DTGم/دقیقة) تبین وجود قمم فریدة في منحنیات ˚ Coats and Redfern and Kissingerالمعلومات الحركیة المحسوبة من البیانات المتضمنة تساوي , Flynn-Wall-Ozawa و تباین الحرارة باستخدام طرائق تبین قیم متقارنة لطاقة التنشیط . التحویل تسبب تعرض الرابطات الى بیئة خارجیة في تكسر اجھادي مسبق االوان وفشل ھش لالنموذج جراء سیادة تفاعل التشابك الحاصل في سالسل البولیمر. ، تفكك حراري ، تحلیل الحركیات ، التحلیل الحراري الوزني ، 6,6: بولي اماید مفتاحیةالالكلمات طاقة التنشیط ، رابطات الكابل . 210 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013