Effects of sulfonated polyether-etherketone (SPEEK)and composite membranes on the proton exchange membrane fuel cell (PEMFC)performanceErce S x engu ¨l a ,Hu ¨lya Erdener a ,R.Gu ¨ltekin Akay a ,Hayrettin Yu ¨cel a ,Nurcan Bac¸b ,_Inc _I Erog ˘lu a ,*a Chemical Engineering Department,Middle East Technical University,06531Ankara,TurkeybChemical Engineering Department,Yeditepe University,34755Istanbul,Turkeya r t i c l e i n f oArticle history:Received 8March 2008Received in revised form 20August 2008Accepted 22August 2008Available online 5November 2008Keywords:PEM fuel cells SPEEKComposite membrane Zeolite betaMembrane electrode assembly (MEA)a b s t r a c tSulfonated polyether-etherketone (SPEEK)has a potential for proton exchange fuel cell applications.However,its conductivity and thermohydrolytic stability should be improved.In this study the proton conductivity was improved by addition of an aluminosilicate,zeolite beta.Moreover,thermohydrolytic stability was improved by blending poly-ether-sulfone (PES).Sulfonated polymers were characterized by posite membranes prepared were characterized by Electrochemical Impedance Spectroscopy (EIS)for their proton conductivity.Degree of sulfonation (DS)values calculated from H-NMR results,and both proton conductivity and thermohydrolytic stability was found to strongly depend on DS.Therefore,DS values were controlled time in the range of 55–75%by controlling the reaction time.Zeolite beta fillers at different SiO 2/Al 2O 3ratios (20,30,40,50)were synthesized and characterized by XRD,EDX,TGA,and SEM.The proton conductivity of plain SPEEK membrane (DS ¼68%)was 0.06S/cm at 60 C and the conductivity of the composite membrane containing of zeolite beta filled SPEEK was found to increase to 0.13S/cm.Among the zeolite Beta/SPEEK composite membranes the best conductivity results were achieved with zeolite beta having a SiO 2/Al 2O 3ratio of 50at 10wt%loading.Single fuel cell tests performed at different operating temperatures indicated that SPES/SPEEK membrane is more stable hydrodynamically and also performed better than pristine SPEEK membranes which swell excessively.Membrane electrode assemblies (MEAs)were prepared by gas diffusion layer (GDL)spraying method.The highest performance of 400mA/cm 2was obtained for SPEEK membrane (DS 56%)at 0.6V for a H 2–O 2/PEMFC working at 1atm and 70 C.At the same conditions Nafion Ò112gave 660mA/cm 2.It was observed that the operating temperature can be increased up to 90 C with polymer blends containing poly-ether-sulfone (PES).ª2008International Association for Hydrogen Energy.Published by Elsevier Ltd.All rightsreserved.1.IntroductionThe increased interest in the potential use of proton exchange membrane fuel cells (PEMFCs)is due to the factthat they can offer high efficiencies with almost zero emis-sion of pollutant gases.Moreover,the quick start-up times and high flexibility to load changes are other advantages.The PEMFC,which uses hydrogen and oxygen (or air)as reactant*Corresponding author .Tel.:þ903122102609;fax:þ903122102600.E-mail address:ieroglu@.tr (_Inc _I Erog˘lu).A v a i l a b l e a t w w w.s c i e n c e d i r e c t.c o mj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /h e0360-3199/$–see front matter ª2008International Association for Hydrogen Energy.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.ijhydene.2008.08.066i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 34(2009)4645–4652gases,is particularly attractive due to high power outputs delivered at low operating temperatures(50–80 C)and pres-sures(1–3atm).The electrochemical reaction occurs in the membrane electrode assembly(MEA),which is considered to be the heart of PEMFC[1].When hydrogen gas is fed to the anode side of the cell,it separates into its protons and elec-trons.The protons are conducted through the membrane electrolyte whereas the free electrons produced at the anode move through an external circuit to the cathode.At the cathode side,oxygen gas combines with the electrons and protons.Thefinal products of such a cell are electric power, water,and heat.They are ideally suited for transportation and other appli-cations.PEM fuel cell stacks operating on hydrogen can be 40–50%electrically efficient and80%system efficient if the heat recovery is included.The research and development of PEM fuel cell stacks based on different materials,structures and fabricating methods are going on[2–4].05pThe key component of PEMFC is the membrane which enables proton transfer between anode and cathode.Current applications prefer NafionÒ(DuPont)which belongs to the perflourosulfonic acid(PFSA)family[5].However,there are two significant drawbacks associated with the use of Nafion membrane.First,the cost of NafionÒmembrane is still too high for commercial applications.Second,it is not possible to operate at high temperatures with NafionÒ.High temperature operation is useful for enhanced reaction kinetics and reduced catalyst poisoning by fuel impurities.Therefore,efforts are concentrated on developing alternate membranes that are capable of operating at higher temperatures.Phosphoric acid doped polybenzimidazole is one of the most successful elec-trolyte membranes[6].Other,the most popular candidates are polyaromatic hydrocarbon polymers,especially PEEK,due to its high thermal and mechanical stability,low price and improvable proton conductivity via post-sulfonation. Although,it is improvable,the conductivity of SPEEK membrane is still lower than that of NafionÒ.Its proton conductivity depends on the degree of sulfonation(DS). However,the mechanical properties tend to deteriorate as the DS increases.Highly sulfonated polymers will swell signifi-cantly at high temperature and humidity[7].2.Experimental2.1.Zeolite synthesis and characterizationZeolite beta crystals were synthesized hydrothermally according to the batch composition2.2Na2O:1.0Al2O3:x SiO2: 4.6(TEA)2O:440H2O at various SiO2/Al2O3ratios[8].In hydrothermal synthesis,an alkaline precursor solution was prepared by dissolving sodium aluminate(52.9wt%Al2O3, 45.3wt%Na2O,Riedel de Hae¨n)in deionized water prior to addition of the structure directing agent,tetraethyl ammo-nium hydroxide(TEAOH)solution(20or35wt%in water, Aldrich).The silica precursor solution,mainly composed of colloidal silica(SiO2),(Ludox40wt%suspension in water, Sigma–Aldrich),was added to the alumina precursor solution and gelation was observed.This gel was poured into Teflon-lined steel autoclaves were kept at constant temperature (150 C)under autogenously pressure for a reaction period of 5–15days.The autoclaves were then taken out of the oven, cooled,filtered,and the zeolite product was dried at80 C. Zeolite beta was calcined at550 C,and then converted into more proton conductive Hþform after acid treatment with 95–98wt%H2SO4(Merck).Synthesized zeolite beta samples were characterized by X-Ray Diffraction(XRD)to confirm beta structure,Thermogravimetric Analysis(TGA)for its thermal stability,Energy Dispersive X-Ray Analysis(EDX)to compare theoretical Si/Al ratio with that in synthesized form,and Scanning Electron Microscopy(SEM)for crystal morphology and average particle size.2.2.Polymer sulfonation2.2.1.Sulfonation of PEEK polymerPEEK polymer was obtained as pellets(Polyoxy-1,4-pheney-leneoxy-1,4-pheneyelene carbonyl-1,4-phenylene,Aldrich, Mw¼20,800).PEEK pellets were ground to reduce the disso-lution time of the polymer and dried at100 C in vacuum oven prior to post-sulfonation.In the post-sulfonation reaction,the polymer was dissolved in H2SO4to give a dark,viscous solu-tion then the degree of sulfonation(DS)was controlled by changing the reaction times at a constant temperature(50 C) [9].Reaction was stopped by pouring the polymer solution in icy-water and white polymer strings were obtained.The decanted polymer strings were washed with deionized water and dried in vacuum oven.2.2.2.Sulfonation of PES polymerPES polymer cannot be easily sulfonated as PEEK in H2SO4. Therefore chlorosulfonic acid(CSA)was used in the sulfona-tion reaction.The polymer wasfirst dissolved in H2SO4 (usually1/10w/v)then a predetermined amount of CSA was added drop wise into the solution.Reactions were carried out at around5 C by using ice-cold water around reaction vessel to prevent cross linking and decomposition of the polymer chains which may occur above20 C.At the end of the pre-determined reaction time solution was poured into cold ice-water and the precipitate wasfiltered and washed until excess acid is removed and dried at90 C.2.2.3.Determination of DS by H-NMRThe H-NMR spectra were obtained by using Bruker Biospin NMR spectrometer with a resonance frequency of300MHz. Samples were prepared by dissolving10–20mg polymer in DMSO-d6.The degree of sulfonation,DS,was determined by integration of distinct aromatic signals determined quantita-tively by using H-NMR spectroscopy.In H-NMR the presence of sulfonic acid group’s results in a0.25ppm down-field shift of the hydrogen H E compared to H C,H D in the hydroquinone ring[10].The nomenclature of the aromatic protons for the SPEEK repeat unit is given in Scheme1below.The presence of sulfonic acid groups in the structure causes a distinct signal for protons at E position.Estimates for the H E content which is equal to the sulfonic acid group content can be done according to the intensity of this signal[10].The H-NMR signal for sulfonic acid group is difficult since the proton is labile.The ratio of peak area of distinct H E signalsðA HEÞand integrated areas of the signalsi n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y34(2009)4645–4652 4646corresponding to all the other aromatic hydrogen’s ðA H AA 0BB 0CD Þare expressed as:n 12À2n¼A H EPA H AA 0BB 0CD ð0 n 1Þ(1)DS ¼n Â100%(2)2.3.Membrane castingThe SPEEK polymer was dissolved in n-n,dimethyl-acet-amide (DMAc,Merck)and stirred overnight with magneticstirrer.Then,zeolite H þ-beta was added to the solution at certain quantities.The solution was mixed under ultrasonic mixing overnight and then drop-casted onto petri dishes.The membranes were dried in vacuum oven at 60–120 C for 24h.For blend membranes,proportional amounts of sulfonated PEEK and PES polymers were dissolved in DMAc to give a 10wt%polymer solution.The solution was stirred by magnetic stirrer overnight prior to mixing in ultrasonic water bath to obtain a homogenous solution.After mixing,the homogenous solution was cast onto Petri dishes and dried from 60 C to 120 C in 24h.2.4.Proton conductivity analysisThe proton conductivity of the membranes was measured by AC Electrochemical Impedance (EIS)technique over a frequency range of 1–300kHz with an oscillating voltage using GAMRY PCL40Potentiostat system.All measurements were performed in longitudinal direction,under water vapor atmosphere at 100%relative humidity with a 4probe EIS as a function of temperature.The specimens were prepared as 1Â5cm membrane strips and sandwiched into a Teflon Òconductivity cell with Pt electrodes (Fig.1).The specimen and the electrodes were fixed by nuts and bolts.The conductivity,s ,of samples in longitu-dinal direction was calculated in Siemens per cm from the impedance data by using Eq.(3);s ¼L RWd(3)where;L is the distance between the electrodes,W is the width of the membrane,d is the thickness of the membraneand R is the low intersect of the high-frequency semi-circle on a complex impedance plane with the Re(Z )axis.Proton conductivity measurements were performed in a closed jar with water at the bottom in a temperature controlled bath with mechanical stirrer.The temperature and relative humidity (RH)of the vapor inside the jar were measured with a thermocouple and RH meter.Conductivities were measured several times at each temperature until they were constant.2.5.MEA preparationMEAs were prepared from the membranes cast,which resul-ted in good proton conductivities during electrochemical impedance spectroscopy analyses.Gas diffusion layer (GDL)Spraying technique was applied for the preparation of MEAs [10].In the first step,catalyst ink,which is comprised of 20wt%Pt on Vulcan XC-72catalyst (E-Tek),5wt%Nafion Òsolution (Ion Power Inc),distilled water,and 2-propanol,were prepared and mixed in ultrasonic bath for 2h.In order to clean and increase the proton conductivity of the membranes,they were conditioned by boiling in 0.5M H 2SO 4solution and distilled water at 80 C.In order to coat the GDLs with catalyst layer,the anode and cathode side GDLs were fixed on a paper frame.The catalyst ink was sprayed until the desired catalyst loading (0.4mgPt/cm 2for both anode and cathode sides)was achieved.The catalyst loading was controlled by just weighing the GDLs at different times.After the GDLs were loaded with catalyst,they were kept in oven at 80 C for 1h in order to completely remove the liquid components of catalyst ink.Then,they were weighed again.To complete the MEA,the GDLs were hot pressed to the membrane at 130 C [11].2.6.Performance testsPerformances of fabricated MEAs were measured via the PEMFC test station built at METU Fuel CellTechnologyScheme 1–Aromatic protons of PEEK andSPEEK.Fig.1–Proton conductivity cell.i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 34(2009)4645–46524647Laboratory.A single cell PEMFC (Electrochem FC05-01SP-REF)having 5cm 2active area was used in the experiments.The external load was applied by means of an electronic load (Dynaload ÒRBL488),which can be controlled either manually or by the computer.The current and voltage of the cell were monitored and logged throughout the operation of the cell by fuel cell testing software (FCPower Òv.2.1.102Fideris).The fabricated MEA was placed in the test cell and the bolts were tightened with a torque 1.7Nm on each bolt.The cell temper-ature was adjusted and the temperatures of the humidifiers and gas transfer lines were set 10 C above the cell tempera-ture.After the preset temperatures were achieved,hydrogen and oxygen are supplied to the cell at a rate of 0.1slpm.The cell was operated at 0.5V until it came to steady state.After steady state was achieved,starting from the OCV value,the current–voltage data was logged by changing the load.3.Results3.1.Zeolite beta characterizationThe XRD pattern of zeolite beta that was hydrothermally synthesized at SiO 2/Al 2O 3ratio of 20is given in Fig.2a.The characteristic peaks of zeolite beta were observed at 2q w 7.8 and 2q w 22.4 as stated in literature [12].The morphology of the zeolites was explored with SEM and the average particle size distribution was found to be around 1micron as shown in SEM Picture below (Fig.2b).Another important characteristicof zeolite beta is its high thermal stability.Thermogravimetric Analyses of zeolite beta crystals showed that the first weight loss was around 465 C as given in Fig.2c and it demonstrates the removal of the structure directing agent (SDA)from the zeolite structure.Thus,zeolite crystals were calcined at higher temperatures to remove SDA completely.The thermal decomposition temperature of zeolite beta particles was around 850 C,this means that the zeolite beta particles are stable up to this temperature.Hence,they are suitable for fuel cell applications.As a result of the EDX analysis it was found that the Si/Al ratio in the structure of the as synthesized zeolite Na-Beta is close to the value of Si/Al ratio in the batch solution (theo-retical)(Table 1).3.2.Sulfonated polymer characterizationsDegree of sulfonation (DS)values of the sulfonated polymers was determined by using H-NMR data as described intheFig.2–(a)XRD pattern of as synthesized zeolite beta (SiO 2/Al 2O 3[20)(b)SEM micrograph of as synthesized zeolite beta (c)TGA of as synthesized zeolite beta.i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 34(2009)4645–46524648experimental section.The signal around7.6ppm chemical shifts corresponds to the aromatic proton H E and its area relative to the other aromatic protons shows the extent of DS (data are not given).The degree of sulfonation is directly related to the reaction time,temperature and the amount of the sulfonation agent used.At higher temperatures the reaction kinetics is enhanced thus higher degrees of sulfonation are achieved. PEEK sulfonation proceeds very slow at room temperature and takes several days to reach a DS above50%.However at around50 C this time decreases to several hours as shown in Fig.3which is consistent with the literature[13].DS of PES was determined similarly as reported in the literature[14].Since sulfonation of PES is more difficult than that of PEEK because of the electrophilic sulfone linkage,DS was around20%.Therefore,conductivity of SPES samples was lower than SPEEK.Since swelling and thermohydrolytic stability strongly depends on DS,SPES membranes showed better stability and low swelling.These properties can becombined by blending these compatible polymers.3.3.Proton conductivity of composite membranesThe objective of introducing zeolite particles into the polymer matrix was to enhance the proton transfer through the membrane by retaining water within the membrane and to create water mediated pathways while contributing their own proton conductivity.The hydrophilic zeolite particles improved the water retention property of the SPEEK membranes.Above60 C,the composite membranes absor-bed too much water and swelling problem was observed above this temperature(Fig.4).Thus,the proton conductivity analyses of composite membranes were limited up to this temperature.The proton conductivities of plain and composite membranes were measured at room temperature before and after treatment with1M HCl.Acid treatment was performed after the casting process,and all the membranes were kept in 1M HCl for2h for complete protonation.Acid treated membranes always result in higher conductivities naturally since all the available ion exchange sites are saturated with protons(–SO3H).All membranes were washed and hydrated with deionized water prior to measurement.As shown in Fig.5,the membranes with higher DS were resulted in better proton conductivities.Proton transfer enhances by increasing the number of acid sites enhances the proton transfer.Moreover,the effect of acid treatment on proton conductivity was explored in Fig.5and improved proton conductivities were observed after the acid treatment of the membranes.Thus,the membranes were treated with 1M HCl and washed with distilled water prior to proton conductivity measurements.Another important observation that could be made in Fig.5is the effect of zeolite particles. The composite membranes containing zeolite Beta have shown improved proton conductivities,for instance,0.11S/ cm was achieved for the composite membranes with74%DS after acid treatment.This is a promising result,since it is comparable with the conductivity of Nafion112membrane (0.1S/cm).Fig.3–Degree of sulfonation with respect to time ofsulfonationreaction.Fig.4–Water uptake capacities of plain and compositeSPEEKmembranes.Fig.5–Proton conductivity of plain and compositemembranes(with10wt%zeolite loading)at roomtemperature and fully hydrated state.i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y34(2009)4645–46524649In order to overcome the swelling problems observed in the pure and composite SPEEK membranes,SPEEK polymer was blended with a more hydrophobic polymer,namely sulfonated poly-ether-sulfone (SPES).The PES polymer was post-sulfonated and blended with SPEEK polymer at pre-determined proportions before membrane casting.However,owing to the poor proton transfer mechanism of SPES poly-mer,lower conductivities were obtained for blend membranes compared to the pure and composite SPEEK membranes.The proton conductivity measurements of pure SPEEK,SPES and blend membranes are given in Fig.6.So a trade-off between mechanical strength and conductivity exists for these blends.3.4.Performance testsFirst of all,the effect of using different catalyst ink solutions on the membrane performance is explored.The MEAs could be either prepared by using Nafion Òsolution or the original SPEEK solution [15].The comparison of two MEAs prepared by both Nafion Òand SPEEK solutions are given in Fig.7.It is apparent that the utilization of Nafion Òsolution in the catalyst ink resulted inhigher performance.Thus,Nafion Òsolution is utilized in the preparation of all MEAs.Second,the effect of operating temperatures on the performances of MEAs prepared by using SPEEK membranes (DS 56%)was examined and the results are given in Fig.8.It was observed that SPEEK based MEAs were not stable at high temperatures and they have punctured above 90 C.The best operating temperature of SPEEK based MEAs was found to be 70 C as demonstrated in Fig.9.The thermal stability of the membranes could be improved by blending with SPES poly-mer.It was noticed that,after the incorporation of 10wt%SPES into SPEEK membrane,the cell operating temperature could be increased up to 90 C without any damage to the membrane.As shown in Fig.9,the highest power output could be obtained at 80 C for SPES–SPEEK blend membranes.In order to understand the effect of sulfonation level on membrane performance,MEAs were prepared by using two membranes with different DS and the test results are displayed in Fig.10.It was not surprising to observe higher performance results for the MEA prepared by using the membrane at higher DS,since the proton transfer facilitates more easily with increased sulfonic acid groupcontents.Fig.6–Proton conductivities of plain and blendmembranes.Fig.7–Comparison of Nafion Òsolution and SPEEK solution for SPEEK based MEAs (cell temperature 708C).Fig.8–Effect of operating temperature on the performance of SPEEK (DS 56%)basedMEAs.Fig.9–Effect of sulfonation level on the performance of SPEEK based MEAs (cell temperature 708C).i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 34(2009)4645–46524650Another important parameter affecting the MEA’s perfor-mance is membrane treatment.Since the proton transfer mechanism of both SPEEK and SPES membranes depend on the acidic character of the membranes,the acid treatment influences the membrane performance.The performance curves of both untreated and acid treated SPEEK based MEAs are given in Fig.11.The acid treated membrane showed almost threefold higher power density compared to the untreated membrane.The fuel cell performance of SPEEK membrane was compared with the performance of Nafion Òmembrane as given in Fig.12.The current density of plain SPEEK membrane (DS 56%)was 400mA/cm 2at 0.6V,whereas that of Nafion Ò112membrane was 660mA/cm 2under the same conditions.Although SPEEK membrane possesses lower fuel cell perfor-mance in comparison to the Nafion membrane,the result is promising when the relatively low cost of SPEEK membrane is considered.Moreover,the composite membrane SPEEK-Laponite exhibited better performance than the pure SPEEK membrane [9].Composite membranes prepared with inor-ganic additives such as silica,zeolite 4A and zeolite beta increase the proton conductivity and fuel cell performances of both Nafion Òand SPES-40polymer membrane [16].It should be emphasized that the same technique of MEA fabrication,cell assembling and operating conditions were used in the present work.The significant difference of the obtained performances can be caused by various factors.One of them is the difference in the thickness of the membranes [17].Proton transfer mechanisms are also quite different in Nafion Òand SPEEK membranes.Degree of hydration is the factor that influences the proton conductivity of a membrane.The hydration is dependent on the phase separation between the hydrophobic polymer backbone and hydrophilic side chains [18].Nafion Òand SPEEK polymers both exhibit phase separated domains consisting of an extremely hydrophobic backbone which gives morphological stability and extremely hydrophilic side chains [18].Higher performances could be obtained for the membranes with higher DS values and for composite membranes.4.ConclusionThe development of alternative membranes at relatively low cost for fuel cell applications requires target properties such as suitable thermal and chemical stability,mechanical strength,comparable proton conductivity and fuel cell performance with the commercial PEM fuel cell membranes.In this study,zeolite beta composite membranes and blend membranes were developed.The proton conductivity of SPEEK was improved by addition of an aluminosilicate,zeolite beta.Also thermohydrolytic stability was improved by blending poly-ether-sulfone (PES).The proton conductivity of plain SPEEK membrane (DS ¼68%)was 0.06S/cm at 60 C and the conductivity of the composite membrane consisting of zeolite beta fillers into SPEEK was further increased to 0.13S/cm.Among the zeolite beta/SPEEK composite membranes the best conductivity results were achieved with zeolite beta having a SiO 2/Al 2O 3ratio of 50at 10wt%loading.Single fuel cell tests performed at different operating temperatures indicated that SPES/SPEEK membrane ismoreFig.11–Effect of acid treatment on the performance of SPEEK (DS 56%)based MEAs (cell temperature 708C).Fig.12–The comparison of performances of Nafion Òand SPEEKmembranes.Fig.10–Effect of operating temperature on the performance of blend membranes.i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 34(2009)4645–46524651stable hydrodynamically and also performed better than pristine SPEEK membranes which swell excessively. Membrane electrode assemblies(MEAs)were prepared by gas diffusion layer(GDL)spraying method.The highest perfor-mance,which is400mA/cm2,was obtained for SPEEK membrane(DS56%)at0.6V for a H2–O2/PEMFC working at 1atm and70 C.At the same conditions NafionÒ112gave 660mA/cm2.It was observed that the operating temperature can be increased up to90 C with polymer blends containing poly-ether-sulfone(PES).AcknowledgementsThis study was supported by Turkish Scientific and Research Counsel with Project104M364and Turkish State Planning Organization Grant BAP-08-11-DPT2005K120600.r e f e r e n c e s[1]Barbir F.PEM fuel cells theory and practice.ElsevierAcademic Press;2005.[2]Corbo P,Migliardini F,Veneri O.Performance investigation of2.4kW PEM fuel cell stack in vehicles.International Journalof Hydrogen Energy2007;32:4340–9.[3]Hu M,Sui S,Zhu X,Yu Q,Cao G,Hong X,et al.A10kW classPEM fuel cell stack based on the catalyst-coated membrane (CCM)method.International Journal of Hydrogen Energy2006;31:1010–8.[4]Yan X,Hou M,Sun L,Liang D,Shen Q,Xu H,et al.ACimpedance characteristics of a2kW PEM fuel cell stackunder different operating conditions and load changes.International Journal of Hydrogen Energy2007;32:4358–64.[5]Bıyıkog˘lu A.Review of proton exchange membrane fuel cellmodels.International Journal of Hydrogen Energy2005;30: 1181–212.[6]Li Q,He R,Jensen JO,Bjerrum NJ.PBI-based polymermembranes for high temperature fuel cells–preparation,characterization and fuel cell demonstration.Fuel Cells2004;4(3):147–59.[7]Xing DM,Li BY,Liu FQ,Fu YZ,Zhang HM.Characterization ofsulfonated poly(ether ether ketone)/polytetrafluoroethylene composite membrane for fuel cell applications.Fuel Cells2005;5(3):406–11.[8]Akata B,Yilmaz B,Jirapnogphan SS,Warzywoda J,Sacco Jr A.Characterization of zeolite beta grown in microgravity.Microporous and Mezoporous Materials2004;71:1–9.[9]Chang JH,Park JH,Park G-G,Kim C-S,Park O-O.Proton-conducting composite membranes derived from sulfonated hydrocarbon and inorganic materials.Journal of PowerSources2003;124:18–25.[10]Zaidi SMJ,Michailenko SD,Robertson GP,Guiver MD,Kaliaguine S.Proton conducting composite membranes from polyether ether ketone and heteropolyacids for fuel cellapplications.Journal of Membrane Science2000;173:17–34.[11]Bayrakc¸eken A,Erkan S,Tu¨rker L,Erog˘lu_I.Effects ofmembrane electrode assembly components on protonexchange membrane fuel cell performance.InternationalJournal of Hydrogen Energy2008;33(1):165–70.[12]Holmberg BA,Hwang S-J,Davis ME,Yan Y.Synthesis andproton conductivity of sulfonic acid functionalized zeolitebeta nanocrystals.Microporous and Mesoporous Materials 2005;80:347–56.[13]Huang RYM,Shao P,Burns CM,Feng X.Sulfonation ofpolyetherether–ketone(PEEK):kinetic study andcharacterization.Journal of Applied Polymer Science2001;82: 2651–60.[14]Guan R,Zou H,Lu D,Gong C,Liu Y.Polyethersulfonesulfonated by chlorosulfonic acid and its membranecharacteristics.European Polymer Journal2005;41:1554–60.[15]S x engu¨l E,Erkan S,Erog˘lu_I,Bac¸N.Effect of gas diffusion layercharacteristics and addition of pore forming agents on theperformance of polymer electrolyte membrane fuel cells.Chemical Engineering Communications,2008;196(1–2):161–70.[16]Bac N,Nadirler S,Ma C,Mukerjee S.Inorganic–organiccomposite membranes for fuel cell applications.In:Proceedings international hydrogen energy congress andexhibition IHEC2005Istanbul,Turkey;2005.[17]Grigoriev SA,Lyutikova EK,Martemianov S,Fateev VN.Onthe possibility of replacement of Pt by Pd in a hydrogenelectrode of PEM fuel cells.International Journal of Hydrogen Energy2007;32:4438–42.[18]Hogarth M,Glipa X.High temperature membranes for solidpolymer fuel cells.Johnson Matthey Technology Center;2001 [Crown Copyright].i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y34(2009)4645–4652 4652。
Quasiclassical trajectory calculations of collisional energy transfer in propane systemsApichart Linhananta and Kieran F.Lim*¤Centre for Chiral and Molecular T echnologies,School of Biological and Chemical Sciences,Deakin University,Geelong,V ictoria3217,Australia.E-mail:lim=.auRecei v ed6th December1999,Accepted27th January2000Published on the Web9th March2000Quasiclassical trajectory calculations of collisional energy transfer(CET)and rotational energy transfer from highly vibrationally excited propane to rare bath gases are reported.The calculations employed atomÈatom pairwise-additive Lennard-Jones,Buckingham exponential and hard-sphere intermolecular potentials to examine the dependence of CET on the intermolecular potential and to establish a protocol for future work on larger alkane systems.The role of the torsional(internal)and molecular(external)rotors in the energy-transfer mechanism were parison of the results with our earlier work on ethane]neon systems(A. Linhananta and K.F.Lim,Phys.Chem.Chem.Phys.,1999,1,3467)suggests that the internal and external rotors play a signiÐcant role in the deactivation mechanism for highly vibrationally excited alkanes.I.IntroductionGas-phase chemical reaction rates are strongly dependent on intermolecular collisional energy transfer(CET).CET is a vital component in any combustion-model and atmospheric-model systems.The only experimental CET quantities for hydrocarbon fuel molecules have been inferred““indirectlyÏÏfrom measurements of pressure-dependent reaction rates.1h3 Despite this,there have been no systematic theoretical dynamics studies of CET of hydrocarbon and halogenated hydrocarbons.In fact,most theoretical studies have been on small molecules.3h14The exceptions are the quasiclassical tra-jectory(QCT)calculations of azulene,toluene,benzene and hexaÑuorobenzene systems.15h23We have recently reported QCT calculations for highly vibrationally excited ethane in neon bath gas.24This and the recent work by Svedung et al. are,to our knowledge,theÐrst theoretical CET studies of an alkane with internal rotors.24,25Comparisons of theoretical and experimental studies of CET show that many of the dominant energy transfer mecha-nisms in small molecules are also present in large mol-ecules.3h6However,there are several di†erences between large-substrate and small-substrate behaviours.A notable example is that in the CET from a““smallÏÏsubstrate to a rare gas collider the trend He[Ne[Ar is observed,26h28 whereas the opposite trend of He\Ne\Ar is observed for ““largeÏÏsubstrates.29h39Theoretical studies of CET on small molecules employing various techniquesÈquantum,semi-classical and classical dynamicsÈall have correctly predicted the small-substrate behaviour.40,41This is not the case for large-substrate systems where QCT simulations incorrectly found the same smallsubstrate trend.15h18The discrepancy may be due to the lack of reliable data on the intermolecular potential surface involving large molecules and is most likely to be manifested in systems with the small collider helium bath gas.42,43¤Lim Pak Kwan.The aforementioned QCT calculations of large-substrate molecules have been on aromatic hydrocarbons because they have been most amenable to experimental studies using spec-troscopic probes.There have been fewer studies28,44h47on alkanes and branched-alkanes,which are the main com-ponents of common combustion fuels,and their halogenated analogues,which are important in ozone and““greenhouseÏÏchemistry.TheÐrst most obvious di†erences between alkanes and aromatics are their shapes,which are expected to a†ect the rotational energy transfer(RET).Since rotation to trans-lation(R]T)energy transfer and vibration to rotation (V]R)energy transfer are often more efficient than vibration to translation(V]T)energy transfer,this can have a strong inÑuence on the overall CET.Another crucial aspect is theÑexibility of alkanes.QCT simulations of alkanes would require the development of an efficient algorithm for sampling conformer space.Related to theÑexibility,as well as to RET,is the role of internal rotors in the CET mechanism.QCT calculations of highly vibra-tionally excited ethane in neon bath gas show that there is an interrelationship between the internal methyl rotors and the external rotation giving rise to V]torsion,R energyÑow in theÐrst collision,resulting in an““enhancedÏÏCET in sub-sequent collisions.24The same e†ect is also observed in experiments on the deactivation of highly vibrationally excited benzene and toluene,where toluene has much larger CET values than benzene.37This e†ect suggests that the torsional rotors in alkanes are important.Since the use of intramolecular torsional potential terms (nine such terms for each additional methylene unit)24plus a sampling of the conformational space may prove to be cost-prohibitive for large(r)alkane systems,there is a need to establish an e†ective protocol for QCT alkane simulations. Use of a hard-sphere potential will reduce a substrateÈcollider collision into a sequence of““sudden-impactÏÏatomÈatom encounters.Furthermore,there is no need to calculate molec-ular interactions at medium-to-large atomic separations.This paper““benchmarksÏÏCET using a hard-sphere potential against the more-commonly used Lennard-Jones andDOI:10.1039/a909614k Phys.Chem.Chem.Phys.,2000,2,1385È13921385This journal is The Owner Societies2000(Buckingham-type exponential-6models,by performing QCT calculations on the propane ]monatomic collider systems.The role of the torsional (internal)and molecular (external)rotors in the energy-transfer mechanism are reported.II.Quasiclassical trajectory calculationsA.Intermolecular potentialThe lack of knowledge of the detailed form of intermolecular potentials has always been a hindrance to quasiclassical mod-elling of CET.This is especially true for large-substrate systems,where there is a paucity of reliable theoretical and experimental data.Previous trajectory calculations of large molecules usually modelled the intermolecular potential by pairwise-additive atom Èatom potentials:7h 24,48h 50the inter-action parameters were usually obtained by semiempirical methods.Collins and coworkers have ““builtÏÏintermolecular potentials by interpolation of ab initio data:51h 53thus far they have only applied their method to relatively small polyato-mics whereas we wish to use a protocol that can be consistent-ly and easily ““scaled upÏÏfor larger alkane systems.Hence in this work three pairwise-additive atom Èatom intermolecular potentials were employed.The Ðrst intermolecular potential was the pairwise-additive Lennard-Jones (LJ)potential with atom Èatom terms given by V ij \4e ijCA p ij r ij B 12[A p ij r ijB 6D,(1)(i \C,H;j \rare gas),where is the atom Èatom centre-of-r ijmass separation,and and are the Lennard-Jones radiusp ij e ijand well depth,respectively.The LJ parameters were chosen by the method of Lim to match empirical values.16,29,54The second intermolecular potential was the pairwise-additive Buckingham exponential (exp-6)potential with atom Èatom terms given byV ij \A ij exp([c ij r ij )[C ij r ij~6,(2)where the parameter determines the repulsive steepness ofc ijthe potential.55The parameters and were chosen toA ij C ijmatch empirical values.16,29,54The last intermolecular potential was a pairwise-additive hard-sphere (HS)potentialV ij \GO ,0,r ij O r ij vdW ,r ij [r ijvdW ,(3)where is the van der Waals radius 56between atoms i andr ijvdW j .This potential is in the spirit of the e†ective mass theory.57The HS potential is tested here to determine if it can be used to derive useful qualitative information:if so then it would be a useful model for simulations of larger alkanes.The intermolecular parameters for propane ]Rg (Rg \rare gases He,Ne and Ar)potentials are given in Table 1.B.Intramolecular potentialA simple harmonic valence force Ðeld,consisting of harmonic stretches,bends and torsions,was used to describe the propane substrate:V intra\;i V stretch,i ];i V bend,i ];iV torsion,i .(4)The Ðrst two terms have been deÐned previously.15,58,59The harmonic stretching and bending force constants were obtained by the empirical prescription of Lindner:60k str,CC\4.705]102J m ~2,J m ~2,k str,CH \4.702]102k bend,CCH\6.67]10~17J rad ~2,and J rad ~2.k bend,HCH\5.61]10~17The Ðnal term in eqn.(4)is a 3-fold methyl torsional potential,which was assumed to be:V torsion,i \V 0n ;j /1n cos 2A 3qij 2B.(5)The torsional angles are the nine H ÈC ÈC ÈH or H ÈC ÈC ÈCq ijdihedral angles for each of the i th C ÈC bonds.Each carbon centre was assumed to have perfect tetrahedral geometry with C ÈC and C ÈH bond lengths of 0.1543nm and 0.1093nm,respectively.To study the e†ect of the torsion,the torsional barrier parameter was taken to be 0(free rotors)and 13.8V 0kJ mol ~1(experimental barriers).61The direction of the bond vectors was deÐned so that the staggered conformer has the lowest-energy geometry.The free-rotor model has apparent harmonic torsional ““vibrationalÏÏfrequencies of 9.2and 9.3cm ~1while the hindered-rotor model has apparent harmonic torsional ““vibrationalÏÏfrequencies of 167.4and 186.3cm ~1.These fre-quencies arise from the numerical normal mode analysis and are used in the selection of initial conditions.58,59,62The other 25vibrational frequencies compare favourably with experi-mental group frequencies of putational detailsTrajectory calculations were performed using program MARINER 58which is a customised version of VENUS96.59The LJ and exp-6potential models,selection of initial condi-tions,and general methodology are standard options in program MARINER/VENUS96.58,59,62The initial impact energy was chosen from a 300K thermal distribution.InE transthe majority of cases,the initial rotational angular momentum of propane was chosen from a thermal distribution at 300K.The rotational temperature was varied from 100to 1500K to investigate the RET of propane ]argon by the HS model.The initial vibrational phases and displacements were chosen from microcanonical ensembles at E @\41000,30000or 15000cm ~1,where E @is the rovibrational energy above the zero-point energy.These initial conditions are appropriate for comparison with the Ðrst few collisions in time-resolved infra-red Ñuorescence and ultraviolet absorption experi-ments.3h 6,29h 38,64Note that experiments measure the CET values of a cascade of collisions.The rovibrational energy dis-tribution of subsequent collisions will not be microcanonical,Table 1Intermolecular potential parametersLJ model exp-6model HS model p (e /k B )Aij Cij c ij r vdW /nm/K /kJ mol ~1/10~6kJ mol ~1nm 6/nm 1/nm H ÉÉÉHe 0.28258.0882294712479.945.50.325C ÉÉÉHe 0.291517.6931859254179745.60.345H ÉÉÉNe 0.293817.00103476168.5345.70.305C ÉÉÉNe 0.302034.156********.6945.90.325H ÉÉÉAr 0.306628.87140033519.240.80.335C ÉÉÉAr0.321658.025809650187641.00.3551386Phys .Chem .Chem .Phys .,2000,2,1385È1392but the CET behaviour of these subsequent collisions can be inferred 18,65,66from the microcanonical values.For the models employing the LJ and exp-6intermolecular potentials,trajectories were initialised with a centre-of-mass separation of 1.2nm and the classical equations of motion were integrated by the Adams ÈMoulton algorithm 58,59,62until the distance between the monatomic collider and the closest hydrogen exceeded a critical value of 1.0nm,at which point the trajectory was terminated.The initial impact param-eter b was chosen with importance sampling 16,17,58,59,62for values between 0nm and nm (He and Ne)or 0.9nmb m\0.8(Ar).These initial and Ðnal conditions were chosen by per-forming preliminary runs which showed that an insigniÐcant amount of energy was transferred at larger distances.For the HS interaction model,there is no intermolecular interaction until the point of impact,when the propane sub-strate is still described by a (near)microcanonical putationally,this is achieved by initialising trajectories as above,but translating the colliders to the point of initial contact without altering the rovibrational phases and orienta-tion.The translation was performed using an algorithm devel-oped by Alder and Wainwright 67,68to model hard-sphere Ñuid systems.After this initial point of contact,the trajectory was propagated normally.At each time step,the interatomic distances between the rare gas collider and every propane atom were checked for overlap.If an atom Èatom encounter occurred,the trajectory was projected back to the point of impact and the impulsive momentum transfer was calcu-lated.68The process was repeated until another encounter occurred or until the distance between the monatomic collider and the closest hydrogen exceeded a critical value,at which point the trajectory was terminated.Program MARINER 58was altered to implement the HS potential and trajectory-propagation algorithms.The short-ranged HS interaction per-mitted critical values as low as 0.4nm.Since the equations of motion are integrated for a comparatively short period,the HS model required much less computing time than the LJ and exp-6models.For E @\15000and 30000cm ~1,the integration time step was chosen to be 0.085fs,which is sufficient to conserve total energy to within 0.5cm ~1.This is approximately four times larger than the time step used in our previous ethane trajec-tory calculations.24Propane has less excitation per vibra-tional mode and hence energy can be conserved by larger time steps.For E @\41000cm ~1,it was necessary to employ a time step of 0.075fs to conserve energy.The numerical insta-bilities associated with the inversion of the methyl group(s)previously observed in simulations of ethane 24and toluene 16,17were not observed here.The calculations were performed on a DEC Alpha 3000/300LX workstation and an SGI Power Challenge Super-computer.In calculations that employed the LJ or exp-6intermolecular potentials,batches of 3000trajectories required approximately 60CPU hours for He collider and 100CPU hours for Ar on the workstation.The HS model decreased the required CPU time by a factor of 10:this reduction will be very signiÐcant in the study of larger alkanes.CPU time was reduced by a factor of about 4on the supercomputer.D.Rotation energy and torsional angular momentum It is well documented that rotational energy transfer is an effi-cient pathway for CET.3,24,65,66,69However,while angular momenta are well-deÐned,rovibrational coupling gives rise to an ambiguity in the deÐnition of rotational energy.Previous quasiclassical simulations employed several di†erent methods to decouple the rotational and vibrational energies.One method 11deÐnes the rotational energy asE rot \1(JI ~1J ),(6)where I and J are,respectively,the instantaneous moment of inertia and angular momentum.In a second method isE rotapproximated by the instantaneous angular momentum,but the moment of inertia is taken to be the equilibrium geometry value.11Both deÐnitions give rotational energies that oscillate with time.There is an alternative deÐnition that is valid for symmetrical top rotors:65E rot \1B effJ 2,(7)where J is the magnitude of the rotational angular momentum and is an e†ective rotational constant.This deÐnitionB effdecoupled the rovibrational energy so that the rotational energy includes only the ““adiabatic partÏÏ,whereas the ““activeÏÏpart is included with the vibrational energyE V \E [E rot,(8)where and E are,respectively,the vibrational and totalE Vinternal energies.Eqn.(7)is a valid approximation for sym-metrical top molecules.70The main advantage of this deÐni-tion is that,classically,it is a conserved quantity.The equilibrium Cartesian principal moments of inertia of propane are kg m 2,kgI xx \1.11]10~45I yy\9.7]10~46m 2and kg m 2.Hence,propane is a goodI zz\2.97]10~46approximation of a symmetrical top and it is possible to deÐne the rotational energy by eqn.(7),with the approx-imationB eff \12hc (I xx I yy I zz)~1@3.(9)It was shown in our previous work on ethane 24that the coupling between external and internal rotors enhances the overall CET.Hence the torsional angular momentum of propane was also monitored in this work.Whereas ethane has only one torsional rotor which lies along its molecular axis,propane has two distinct and unparallel torsional rotors.The deÐnition of the torsional angular momentum introduced for ethane is generalised by calculating the rotational angular momentum of the methyl group and the associated ethyl groupJ methyl \;i /H,H,Hr i ]p iJ ethyl\;i /C,H,Hr i ]p i,(10)where is the angular momentum of the methyl groupJ methyland is the angular momentum of the associated ethylJ ethylrotor.Note that for consistency with eqn.(5),only the six atoms directly bonded to each torsional C ÈC bond have been included in the summation in eqn.(10).The torsional angular momentum is then deÐned asJ tor \o (J methyl [J ethyl)Éa o ,(11)where is a unit vector parallel to the CC torsional axis.The a CET to/from the torsional rotors was monitored by calcu-lating the average torsional angular momentum change*J tor \J tor (Ðnal)[J tor(initial).(12)E.Data analysisTrajectory data were analysed by a bootstrap algorithm 71,72in program PEERAN.16,73Some 3000È5000trajectories were performed for each potential model.This was sufficient to obtain average energy-transfer quantities with statistical uncertainties of about 10%.However,the uncertainties for the average rotational energy transfer were about 20%,due to the initial rotational-energy Boltzmann distribution (rather than an initial microcanonical distribution).Trajectory averagesPhys .Chem .Chem .Phys .,2000,2,1385È13921387deÐned by (for both overall CET and RET)S*E n TtrajS*E n T traj \1N ;i /1N bi bm(*E i )n(13)are related to experimentally obtained quantities S*E n T by ratio of collision cross-sectionsS*E n T \p b m 2p p LJ2X (2,2)RS*E n T traj (14)where is the LJ collision cross-section and is thep LJ 2X (2,2)R b mmaximum impact parameter in the trajectory simulation.This normalisation removes the ambiguity related to the elastic scattering at high impact parameter.74The input LJ param-eters were obtained from ref.29.At 300K,the LJ collision cross-section values of nm 2,0.4834nm 2p LJ2X (2,2)R \0.3976and 0.6945nm 2for propane ]He,propane ]Ne and propane ]Ar,respectively,were obtained using the program COLRATE.75This corresponds to the LJ collision frequencies of m 3s ~1,328.58]10~18m 3s ~1Z LJ,coll\523.29]10~18and 382.37]10~18m 3s ~1,respectively.In this paper,we have reported both the Ðrst and second moments of the trajectory data since the Ðrst moment is usually more useful for comparison with experiment,but the QCT second moment is statistically more reliable.74Some experiments can determine both the Ðrst and second moments of the CET probability.3,5III.Results and discussionA.The e†ect of the torsional barrierFigs.1and 2show the CET values,[S*E T and S*E 2T 1@2,and the RET values,as functions of energy E @aboveS*E RT ,zero-point energy for propane ]neon.One set of results areFig.1Dependence of energy-transfer quantities on torsional barrier for deactivation of vibrationally excited propane by neon bath gas:)Hindered-rotor (LJ);Free-rotor (LJ);Hindered-rotor (exp-6);L +…Free-rotor (exp-6).Fig.2Dependence of rotational energy transfer on torsional barrier for deactivation of vibrationally excited propane by neon bath gas:)Hindered-rotor (LJ);Free-rotor (LJ);Hindered-rotor (exp-6);L +…Free-rotor (exp-6).for the free-rotor model the other for the hindered-(V 0\0),rotor model kJ mol ~1).These results are for the LJ(V 0\13.8and exp-6intermolecular potentials.The overall deactivation,[S*E T and S*E 2T 1@2,is larger for the hindered-rotor model,similar to results for ethane ]neon.24The torsional angular momentum transfer is shownS*J torT in Fig.3.Note that for the hindered-rotor modelsS*J torT with both LJ and exp-6intermolecular potentials are virtually identical:the reason for this is unclear.Overall,S*J torTdecreases,but remains positive,with the presence of a barrier In contrast,for ethane ]neon changes from posi-V 0.S*J torT tive to negative over a similar range of values.24This di†er-V 0ence is probably due to the higher torsional moment of inertia for propane torsion compared to ethane(CH 3ÈCCH 2)This means that propane torsion has higher(CH 3ÈCH 3).density of states and can more readily gain torsional excita-tion than ethane torsion,explaining why is positiveS*J torT for propane,but negative for ethane.In ethane,the torsion acts like a vibration providing an efficient torsion ]T pathway.24The increase in [S*E T and S*E 2T 1@2(Fig.1)for the hindered-rotor model suggests that propane torsions play the same role in the CET mechanism.The RET is smaller for the propane free-rotor modelS*E RT than the hindered-rotor model (Fig.2),contrary to the ethane results.24For ethane,the torsion is aligned along the molecu-lar axis,hence any increase in methyl-rotor angular momen-tum contributes to both (internal)torsional excitation S*J torTand (external)rotational excitation The propane free-S*E RT .rotor model has Ðve (three external and two internal)indepen-Fig.3Dependence of torsional angular momentum change on tor-sional barrier for deactivation of vibrationally excited propane by neon bath gas:Hindered-rotor (LJ);Free-rotor (LJ);)L +Hindered-rotor (exp-6);Free-rotor (exp-6).Note that the two sets …of hindered-rotor results are almost identical.1388Phys .Chem .Chem .Phys .,2000,2,1385È1392dent rotors,none of which have coincident axes.The extra rotors mean that there is less energy available to the external rotors in any V ]torsion,R energy redistribution.Noteworthy is the fact that the di†erences between the free-rotor and hindered-rotor models persist up to E @\41000cm ~1.For ethane ]neon,there is an onset of near-free-rotor behaviour at E @\30000cm ~1:at E @\41000cm ~1there is no signiÐcant di†erence between the free-and hindered-rotor models.However,the larger number of vibrational modes in propane,which decreases the excitation per torsional mode,ensures that the di†erences remain even at very high excita-tion.Hence correct theoretical treatments of internal rotors become even more essential for larger molecules.B.Trajectory results for LJ and exp-6modelsThe CET results for the deactivation of highly excited propane by helium,neon and argon are shown in Fig.4,where the intermolecular interactions have been modelled by the LJ and exp-6potentials.Three important features are:(1)Energy transfer increases with increasing E @and is in accord with theoretical and experimental studies on the deac-tivation of highly vibrationally excited molecules.(2)The LJ potential results in larger CET values than the exp-6model,since the LJ potential has a much harder repul-sive part than the exp-6potential.There are numerous works which concluded that CET depends mainly on the repulsive part of the intermolecular potential and that,in general,a harder repulsive part results in larger energy transfers.9,16,17(3)The deactivator efficiency shows the trend He [Ne [Ar which,unfortunately,is in discord with experi-mental trends for Ñuorinated alkane systems.28To our knowledge,there has been no experimental study of CET in propane ]rare gas systems.““IndirectÏÏstudies of related systems include 2-bromopropane ]Ne ([S*E T \130cm ~1for E @\17000È21000cm ~1)76andFig.4Energy-transfer quantities for deactivation of vibrationally excited propane by rare gases:Helium (LJ);Neon (LJ);)K |Argon (LJ);Helium (exp-6);Neon (exp-6);Argon (exp-6).+=>isotopically-substituted cyclopropane ]He (S*E 2T 1@2\200È400cm ~1for E @D 22000cm ~1).2These CET quantities were not directly measured,but were inferred from pressure-dependent thermal reaction rates at elevated temperatures.Some more recent studies using time-resolved optoacoustic spectroscopy include ([S*E T \114cm ~1atC 3F 8]Ar E @\15000cm ~1and [S*E T \300cm ~1at E @\40000cm ~1).46These studies reveal no information about RET nor the role of torsional modes.These experimental CET quan-tities correlate well with our present calculations (Fig.4)but also indicate a need for fresh experimental studies.The decreasing trend with collider He [Ne [Ar has been observed in many other QCT studies.9,15,18,77Although the lack of qualitative agreement with experiment is disappoint-ing,these studies and the present work have used very crude intermolecular potential models.Given the lack of detailed information about polyatomic intermolecular potential sur-faces,the intention in the present and other studies has been to use a set of consistent and transferable potentials,16much in the spirit of molecular mechanics force Ðelds.Experience with simulations on other systems would suggest that the exp-6model potentials predict ““betterÏÏCET values than the LJ potentials.17Fig.5plots the RET of propane ]rare gas systems.For Ne and Ar,monotonically increases with E @,whereas forS*E RT He,it initially increases but decreases at higher excitation energy.In all cases,RET is larger for the LJ model which is in accord with the CET behaviour.Clary and Kroes 78and others 16,17,40have observed that RET is larger for heavier colliders because the collision duration is closer to the rota-tional period of the molecular substrate.Fig.6plots the torsional angular momentum transfer as a function of E @.is largest for He and smal-S*J tor T S*J torT lest for Ar,which is the same trend as for CET.This implies that,in addition to the external rotor gateway,the torsional rotor is a gateway for facile CET via V,torsion ]torsion,T.24An interesting feature of Fig.6is that seems to beS*J torT Fig.5Rotational energy transfer for deactivation of vibrationally excited propane by rare gases:Helium (LJ);Neon (LJ);)K |Argon (LJ);Helium (exp-6);Neon (exp-6);Argon (exp-6).+=>Phys .Chem .Chem .Phys .,2000,2,1385È13921389Fig.6Torsional angular momentum change for deactivation ofvibrationally excited propane by rare gases:Helium(LJ);Neon)K(LJ);Argon(LJ);Helium(exp-6);Neon(exp-6);Argon|+=>(exp-6).insensitive to the intermolecular potential.However,the factthat it depends on the type of bath gas indicates a dependenceon the mass of the deactivator.This suggests that isS*JtorTinsensitive to theÐne details of the intermolecular potentialand can be modelled by either LJ or exp-6potentials.C.Trajectory results for hard-sphere modelLJ and exp-6potentials have long-range attractive terms andare computationally expensive.Since HS is a short-rangepotential,it is computationally cheaper in terms of computertime than other potential models by an order of magnitude.Inthis section we compare the results of the short-range HS withthe longer-range potentials.Fig.7shows S*E T and S*E2T1@2for the HS model.Fig.8shows the RET for the HS model.The qualitative behavioursare the same as for the LJ and exp-6models but the energy-transfer values are several times larger than for the LJ andexp-6model.This is not surprising in view of the““hardnessÏÏof the HS potential.9,16,17Another important feature is thatS*E T and S*E2T1@2for He are several times larger than forNe and Ar.This is also true for the LJ model(Fig.3)whichindicates that the HS and LJ models tend to give CET valuesthat are much too high for helium colliders.Table2lists the average number of encounters per collision,for He,Ne and Ar colliders.This average includes onlyNC,trajectories in which collisions have occurred.As expected NCTable2Average number of atomÈatom encounters NcE@/cm~1150003000041000Propane]He 1.967 1.884 1.847Propane]Ne 3.145 2.952 2.852Propane]Ar 3.753 3.501 3.400Fig.7Energy-transfer quantities for deactivation of vibrationallyexcited propane by rare gases for the HS model:Helium;Neon;+=Argon.>is largest for Ar and smallest for He due to their reducedmasses.also decreases with increasing E@which suggestsNCthat a more highly excited substrate imparts more energy perencounter to the deactivator,reducing the collision duration.Fig.9shows S*E T,and for propane]argonS*EVT S*ERTsystems at rotational temperatures300,1000andTROT\100,1500K.In these simulations,initial excitation wasÐxed atE@\15000cm~1and the initial translational temperaturewas K.It can also be seen that RETTtrans\300S*ERTdecreases with increasing the magnitude of the vibra-TROT;tional energy transfer also decreases with increasingS*EVTThis implies that rotationally cold systems exhibitTROT.V]R,T energy transfer,whereas rotationally hot systemsexhibit V,R]R,T.It can be seen that the overall[S*E T islarger for larger which agrees with the hypothesis thatTROTthe external rotation is a facile CET path.This behaviour hasFig.8Rotational energy transfer for deactivation of vibrationallyexcited propane by rare gases for the HS model.Helium;Neon;+=Argon.>1390Phys.Chem.Chem.Phys.,2000,2,1385È1392。
