Thermal Desorption in Pure Hexane and Hexane/Butane Mixtures on Graphite

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1 Thermal Desorpton n Pure Hexane and Hexane/Butane Mxtures on Graphte Cary L. Pnt Department of Physcs Unversty of Northern Iowa Cedar Falls, Iowa USA Receved: November 9, 24 Accepted: November 29, 24 ABSTRACT The results of an extensve study of desorpton n hexane (monolayer and submonolayer) and hexane/butane mxtures ntally adsorbed onto the graphte basal plane s presented. Molecular dynamcs (MD) smulatons are utlzed to carry out atomstc smulatons at temperatures 3 T 7 for all three cases studed. Results from submonolayer and monolayer hexane ndcate that the desorpton energy needed for the system to proceed wth the desorpton process s ndependent of the system s coverage, whch s n good agreement wth expermental results. It s also found that smulatons of desorpton of hexane/butane mxtures yeld a hgh rato of butane molecules beng desorbed from the surface at lower temperatures (3 K), suggestng a strong dependence of the desorpton barrer upon alkane chan length. The results are dscussed and compared to prevous expermental and theoretcal results. I. INTRODUCTION The study of the propertes of the phases and phase transtons of n-alkanes on surfaces has been a rch topc of expermental and theoretcal nterest recently due to advancements n methods to study these systems on a mcroscopc scale (scannng tunnelng mcroscopy and other probng technques) as well as ncreasng ablty of computers to smulate models wth large enough system szes to accurately represent these types of systems. Namely, the famly of n-alkanes s of partcular nterest due to the vast amount of applcatons these molecules provde to ndustry (lubrcaton, adheson, wettng on surfaces, etc). In the past 3 years, consderable progress has been made n understandng the dynamcs of n-alkane adsorpton onto varous types of surfaces. Although, despte ths progress, the studes of n-alkane desorpton from surfaces s stll a topc that s not understood reasonably well, and poses many theoretcal questons. The two molecules that are studed n ths work are prmarly hexane (C 6 H 4 ) and also butane (C 4 H ). Both of these molecules are members of the famly of straght-chaned n-alkanes, whch s a famly of molecules that dffer prmarly n ther length. Butane and hexane are specfcally chosen due to ther balance of ntermedate sze and many degrees of freedom they dsplay as compared to other complex organc molecules. For ths reason, these molecules have been studed extensvely as adsorbates. The surface that s smulated n ths case s graphte. Graphte s arguably the best canddate for a substrate due to ts symmetrc nature, vast avalablty, and strong mechancal stablty. These qualtes, as well as the large amount of expermental and theoretcal work that exsts for systems nvolvng graphte makes t an excellent choce as a substrate n such a smulaton. 25

2 There have been many prevous expermental [-3] and theoretcal [4-] studes of hexane and butane on graphte. In the studes of hexane, a sold commensurate herrngbone structure s observed at low temperatures, followed by a transton nto an ntermedate orentatonally ordered nematc phase, whch s then followed by a transton nto an sotropc flud. In all cases, the phase transtons studed are found to be dependent upon the system s n-plane room (e.g. the ntermedate nematc phase s found to be strctly a result of effects resultng from nplane molecular packng [2]). Smlarly, prevous work that studes butane on graphte [2,4-5,9] fnds a commensurate herrngbone formaton at low temperatures followed by an abrupt meltng transton nto an sotropc flud. There have also been many broad expermental and theoretcal studes of desorpton of n-alkanes on graphte. The frst expermental study of desorpton of hydrocarbons on surfaces was conducted by Zhang and Gellman [3] over a seres of straght chan alcohols on the Ag() surface. Ths work fnds that the desorpton energy ncreases ncrementally by 4.6±.4 kj/mole per methylene group n the hydrocarbon chan. More recently, expermental work has been conducted by Paserba and Gellman [4, 5] that deals wth desorpton over a seres of n-alkanes. The two major conclusons of ths work are () the desorpton energy s ndependent of the surface coverage, and () the desorpton energes ncrease nonlnearly wth ncreasng chan length due to less molecules n the trans confguraton. The theoretcal work that has been done on desorpton of the n-alkanes has been completed by Fchthorn et al [6-8]. In these studes, a molecular dynamcs smulaton of a sngle molecule on a Pt() surface s carred out for varous molecules of dfferng chan length. These studes fnd both a large ncrease of molecules out of ther trans conformatons at longer chan lengths that contrbute to a nonlnear effect on the desorpton energy, and also fnd that calculatons of desorpton rates usng transton-state theory (TST) are n correspondence wth experment. The purpose of ths work s to () study desorpton of hexane on graphte through use of two dfferng denstes (submonolayer and monolayer) to confrm the expermental result that the desorpton barrer s ndependent of coverage; () study the effects on the desorpton process for n- alkane mxtures whch s currently both theoretcally and expermentally unexplored; and () study the desorpton process n these systems through use of larger system szes than were consdered n prevous theoretcal work. II. COMPUTATIONAL DETAILS Ths study s conducted through use of a constant partcle number, planar densty, and temperature (N, ρ, T) molecular dynamcs (MD) method. To model the hexane and butane molecules, a unted atom (UA) model s utlzed whch effectvely approxmates each methyl (CH 3 ) and methylene (CH 2 ) group as a sngle pseudoatom wth an ncreased Van der Waals radus from that of a sngle carbon atom. Ths model reduces the number of force stes that are ncluded n calculatons of forces and neghbor lsts wthn the smulaton, whch tend to be very tme ntensve (e.g. the neghbor lst calculatons scale as N 2, where N s the total number of psuedo-atoms n the smulaton). In all smulatons of hexane, N 672, whch corresponds to 2 hexane molecules, and smlarly n smulatons of hexane/butane mxtures, N 56, whch corresponds to 56 butane molecules and 56 hexane molecules. The two denstes that are studed for hexane correspond to ρ (monolayer completon) and ρ.93 (submonolayer). In the case of the submonolayer densty studed, the computatonal cell s unformly expanded n the y drecton by a factor of na g, where a g s the graphte lattce constant that takes on a value of a g 2.46 Å and n 3 for ths specfc case. The cell sze used n smulatons of monolayer hexane s a Å and b Å, and n the case of submonolayer hexane, a Å and b Å, where a and b correspond to orthogonal drectons parallel to the plane of the substrate. For smulatons of hexane/butane mxtures, the cell sze s a 67 Å and b 67. Å. Perodc boundary condtons are utlzed n the a and b drectons, and free boundary condtons are mplemented n the z drecton. To smulate 26

3 the system at constant temperature, the veloctes are frequently rescaled to satsfy equpartton for the center-of-mass, rotatonal, and nternal temperatures, T INT T T CM ROT 3N k m 3N k j m B B N m N m M T v 2, CM, v t v ω I ω, N m n C v v v v 2 mj ( j, CM ω, CM rj, CM ). 2n 5 C where T CM, T ROT and T INT are the temperatures of the system and the summaton ndex () runs over molecules wle the ndex (j) runs over pseudo-atoms wthn a gven molecule. All varables ndexed wth () are standard and apply to the th molecule and those ndexed wth (j) apply to the j th atom wthn molecule (). A velocty Verlet RATTLE algorthm, wth a tme step of fs, carres out the ntegraton of the equatons of moton. In all cases, the system s ntally started from a sold herrngbone confguraton that s expermentally verfed. The system s then allowed to equlbrate for 8 x 3 steps, whch s found to be suffcent tme to dsrupt the sold confguraton of the system nto a flud and to keep the desorbate under the nfluence of the substrate nteracton. A perod of 3 x 5 steps (3 ps) then follows where the behavor of the system s studed and varous useful averages and dstrbutons are calculated. The system s progressed through a temperature sequence of T3K + n (K), where n, 2, 3, and n 4 for all three cases studed. To model the potental nteractons, both non-bonded and bonded nteractons are used. The frst of the non-bonded nteractons s the molecule-molecule nteracton, modeled by the Lennard Jones par potental u LJ 2 j j ( rj) 4ε. () j σ j r σ j r 6 In equaton (), the Lorentz-Berthelot combnng rules σ + σ j σ j 2 ε j ε ε are appled n order to descrbe mxed nteractons when partcles () and (j) are of dfferent types. The other non-bonded nteracton representng the molecule-substrate nteracton s gven by a Fourer expanson proposed by W.A. Steele [5], and s of the form: u gr E ( z ) + n E n j ( z ) f n ( x, y ), (2) For nformaton on the parameters and quanttes shown n equaton (2), the reader s referred to []. For ths study, there are two types of bonded nteractons nvolved as well. The frst bonded nteracton s bond angle bendng. Ths s a three-body nteracton, wth the bendng potental defned as [6], where u bend b kθ( θ θ 2 ), θ b s the bond angle, (3) θ s the equlbrum bond angle and k s the angular stffness. Smlarly, the other bonded nteracton that s consdered s the dhedral (torsonal) [7,7] bendng, and the bendng potental s defned as: 27

4 u 5 tors c (cosφ ) d, (4) where φ s the dhedral angle and the c are d constants. For values of parameters used n Equatons (3) and (4), the reader s agan referred to []. For ths study, the use of the RATTLE algorthm [8] provdes a constraned soluton to the equatons of moton to keep the bond lengths fxed at.54 Å. III. RESULTS Many runs were carred out over the temperature regon of 3K T 7K to attempt to classfy the characterstcs of the system as the temperature s ncreased, but also to repress the large statstcal error that s dealt wth when dealng wth desorpton n smaller systems. In fact, the process of desorpton takes place over such large tme scales, t s mpossble to be completely probed through an MD smulaton. Through ths secton, varous quanttes wll be presented to provde a clear pcture of the desorpton process that occurs n both monolayer and submonolayer hexane and compare that to the desorpton process observed n mxtures of hexane and butane. The frst quantty that s of nterest s the tlt angle order parameter. Ths order parameter s defned as OPtlt 2 N m N m 2 (3cos θ ), and s the thermal average of a Legendre polynomal (P 2 ) and takes a value of.5 f the long axs of each hexane molecule s parallel to the (x,y) plane. Ths quantty gves nformaton on the lbraton of the molecules out of the surface plane parallel to the graphte substrate. In the process of desorpton, large values of OPtlt are observed due to the large thermal energes that are present at the hgher temperatures that are needed to conduct smulatons of desorpton. The temperature dependence of OPtlt s shown n Fgure for submonolayer and monolayer hexane. Another useful way to analyze the behavor of the system s to study the behavor of the system s energes. Probably the most sgnfcant of these are the OPtlt Fgure. Temperature dependence of OPtlt for monolayer (sold squares) and submono-layer (sold trangles) hexane. energes that descrbe the moleculemolecule and the molecule-substrate nteracton. The frst of these (the moleculemolecule energy) s gven by the Lennard Jones par potental functon: < U LJ > N m N N u LJ j + ( r ) and s useful when consderng the system s structural behavor ndependent of the graphte substrate. The other s the average lateral Steele corrugaton energy per molecule, gven by: < U v N > En ( r ) N m where the value of <U > vanshes when molecules are randomly samplng postons n the (x,y) plane, and s sgnfcant when the molecules are strongly bound to the graphte surface. The temperature dependence of both of these energes s shown n Fgure 2 for the cases of submonolayer and monolayer hexane. Although these quanttes tell very mportant nformaton, they gve lttle nformaton regardng the process of desorpton. Therefore, the calculatons that were conducted regardng desorpton are shown n Fgures 4-6. Also, n Fgure 3, the desorpton process s llustrated through a seres of snapshots at progressng tmes throughout the smulaton at T 5 K. j 28

5 <ULJ> <U> Fgure 2. Average Lennard Jones (top) and average corrugaton energes as a functon of temperature. Agan, the sold squares correspond to monolayer hexane, and the sold trangles correspond to submonolayer hexane. The number of desorbed molecules was montored throughout the smulaton at every tme steps (. ps) to classfy the desorpton actvty as a functon of tme. In Fgure 4, plots of desorbed molecules as a functon of tme are shown for varous temperatures for the three cases of butane/hexane mxtures, submonolayer hexane, and monolayer hexane. These graphs show sgnfcant desorpton actvty throughout the frst porton of the smulaton, wth the actvty becomng less sgnfcant as tme evolves. Smlarly, n Fgure 5a, the temperature dependence of the total number of desorbed molecules s presented for each of the three cases studed, wth the separate cases of desorpton for butane and hexane n the butane/hexane mxture as a functon of temperature shown n Fgure 5b. Another useful way to characterze the desorpton n the system s to analyze the dffuson coeffcent of the molecules. Although one would consder usng the useful Ensten relaton to calculate dffuson coeffcents, due to perodc boundary condtons, the rms dsplacement formula would not gve an accurate representaton of ths quantty. Therefore, the velocty autocorrelaton functon s used n the relaton for the three-dmensonal dffuson coeffcent: D 3 v( t) v() dt where v(t) and v() are the velocty autocorrelatons at tme t and t respectvely. The temperature dependence of D s shown n Fgure 6 for all three cases studed. The trend that s evdent n these plots s generally the same trend that s evdent from the plots n Fgure 5, wth excepton of the dffuson coeffcents for butane/hexane mxtures, where the temperature dependence of D seems to be a lttle more nonlnear than s the case for pure hexane at submonolayer and monolayer coverages. IV. DISCUSSION Ths secton wll be splt nto two subsectons. The frst subsecton wll deal wth comparsons between results of submonolayer and monolayer hexane, and wll compare how the desorpton rate changes as the thermal energy s ncreased n each of these systems, and f the results correspond to expermental work. The second subsecton wll focus on the behavor of butane/hexane mxtures compared to pure hexane, and wll comment on the smlartes and dfferences of the two systems to study the effects of desorpton n mxtures where there are two molecules of dfferng chan length present. a. Monolayer and Submonolayer Hexane In adsorbed systems of monolayer and submonolayer hexane that have been studed prevously, the effects of n-plane room upon the phase transtons brought about a consderably notceable effect at lower temperatures. In ths case, the dfferences between these two systems as they desorb s very mnmal. In Fgure, t s clear that the values of OPtlt for the monolayer case are a lttle greater than the values of OPtlt for the submonolayer case. Ths s consstent wth prevous work monolayer [,2] conducted on 29

6 Fgure 3. Snapshots of system confguratons for monolayer hexane at T6K at (startng from top left and movng left to rght). Top:. ps., 5 ps. Mddle: ps., 5 ps. Bottom: 5 ps., 25 ps. Each ps. s smulaton tme steps. submonolayer and hexane at lower temperatures. However, n Fgure 2, the average Lennard Jones and corrugaton potentals are very nearly the same, wth the same general decreasng trend observed n each. Further, Fgures 4-6 show that the dffuson rates of the molecules n both cases are very nearly dentcal. In Fgure 4, the tme dependence of the desorpton n both cases s very smlar. Ths s also evdent n Fgure 5, where the desorpton barrer (the temperature at whch the molecules have enough energy to desorb from the surface) s at about 4 42 K n both cases, and ncreases lnearly n the same fashon wth ncreasng temperature. Also, the behavor of the dffuson coeffcents of these two systems seems to be very smlar, wthn reasonable statstcal error. These results are strong evdence that the desorpton barrer n ths system of hexane on graphte, s generally 3

7 Fgure 4. Tme dependence on the desorpton process per pseudo-atom for butane/hexane mxtures (left), monolayer hexane (mddle), and submonolayer hexane (rght). The three lnes represent three dfferent temperature ponts: T 4 K (gray), T 55 K (black), and T 7 K (thck black). The vertcal axs on each plot represents the total number of pseudo-atoms ncluded n the smulaton. ndependent of coverage. Therefore, ths means that the energy needed for the molecules to desorb from the surface does not depend on coverage, but rather temperature. Ths result s ndcaton of a frst order process, and has been expermentally labeled as such [4-5]. Ths behavor suggests that n ths mxture, the desorpton process s cooperatve between butane and hexane 56 b. Butane/Hexane Mxtures In contrast to the study of monolayer and submonolayer hexane, the study of the mxture of butane and hexane molecules ntroduces the dependence of the desorpton barrer upon chan length that has prevously been observed n all expermental work 3-5. Ths s clear when consderng the temperature dependence of the number of desorbed molecules after 3 ps, as shown n Fgure 5a. Ths suggests that the desorpton barrer for hexane/butane mxtures s at ~ 3 K, whch s much lower than the 4 42 K as proposed for hexane. Further, from Fgure 5a, t seems as f the desorpton process s lnear wth ncreasng temperature after the desorpton barrer s reached for both cases of hexane. However, Fgure 5b suggests that n a butane/hexane mxture, the desorpton process for each speces as a functon of temperature s not lnear. Although, nterestngly, when consderng the total number of pseudo-atoms desorbed after a perod of 3 ps n the mxture, the result (the sum of the two ndvdual plots for butane and hexane n Fgure 5b) s seemngly lnear wth ncreasng temperature Fgure 5a. Temperature dependence of desorbed molecules for butane/hexane mxtures (top), monolayer hexane (mddle), and submonolayer hexane (bottom). 3

8 Butane Hexane Fgure 5b. Temperature dependence on the desorpton of butane (left) and hexane (rght) n smulated butane/hexane mxtures. In contrast to 5a, the vertcal axs both of plots shown here ndcate the total number of molecules of each type consdered (butane and hexane). molecules. Ths means that regardless of the fluctuatons n the desorpton of butane or hexane molecules specfcally wthn the mxture, the net effect of desorpton of molecules n the system as a functon of temperature s lnear, and the therefore the molecules wthn the system cooperate to produce ths temperature-drven lnear desorpton effect. a. Other Comments It should be mentoned that error bars were not used n any plots to gve ndcaton of statstcal error present due to the large number of temperature ponts that were run and plotted. Also, n all cases of butane/hexane mxtures, the system had the same qualtatve behavor for OPtlt, <U >, and <U LJ > as was observed for hexane, so the author found t unnecessary to nclude plots of these. V. CONCLUSIONS The conclusons of ths work are () desorpton n the system of hexane on graphte s ndependent of coverage, and therefore exhbts frst-order lke transton propertes, and () desorpton n systems of hexane on graphte and butane/hexane mxtures on graphte produce a lnear trend n desorpton as a functon of temperature. In the case of butane/hexane mxtures, ths trend s non-lnear for each ndvdual speces, but the net effect s stll seemngly lnear, whch s evdence that the desorpton Fgure 6. Temperature dependence of the three-dmensonal dffuson coeffcent for butane/hexane mxtures (top), monolayer hexane (mddle), and submonolayer hexane (bottom). The numercal value on the vertcal axs s dentcal and arbtrary for all plots shown. 32

9 process s cooperatve between speces n mxtures of alkanes of dfferent chan length. ACKNOWLEDGEMENTS The author s ndebted to Dr. Paul Gray and the UNI Computer Scence department for nvaluable use of CPU tme that allowed ths research to be carred out. Also, a specal thanks s extended to Dr. Mchael Roth for contnuous support n all current projects and deas the author s currently workng on. REFERENCES. J. Krm, J. Suzanne and H. Shechter, R. Wang and H. Taub, Surf. Sc. 62 (-3) 446 (985). 2. Newton, dssertaton under H. Taub, unpublshed. 3. H. Taub, Vol. 228 of NATO Advanced Study Insttutes, Seres C: Mathematcal and Physcal Scences, edted by G. J. Long and F. Grandjean (Kluwer, Dordrecht, 988), pp Flemmmg Y. Hansen and H. Taub, Phys. Rev. Lett., 69 (4), 652 (992). 5. Flemmmg Y. Hansen, J.C. Newton and H. Taub, J. Chem. Phys., 98 (5), 428 (993). 6. E. Velasco and Gunther H. Peters, J. Chem. Phys., 2 (2) 98 (995). 7. G.H. Peters and D.J. Tldesley, Langmur (996). 8. Gunther H. Peters, Surf. Sc., (996). 9. K. W. Herwg, Z. Wu, P. Da, H. Taub, and F. Y. Hansen, J. Chem. Phys. 7, (997).. M. Krshnan and S. Balasubramanan, S. Clarke, J. Chem. Phys., 8 () 582 (23). M.W. Roth, C.L. Pnt, and Carlos Wexler, Phys. Rev. B, (submtted) 2. Cary Pnt and M.W. Roth, (to be submtted) 3. R. Zhang and A. Gellman, J. Phys. Chem., 95, 7433 (99) 4. K. Paserba and A. Gellman, Phys. Rev. Lett., 86, 4338 (2) 5. K. Paserba and A. Gellman, J. Chem. Phys., 5, 6737 (2) 6. D. Huang, Y. Chen, and K. A. Fchthorn, J. Chem. Phys,, 2 (994) 7. J.S. Raut and K. A. Fchthorn, J. Chem. Phys., 8, 626 (999) 8. K. A. Fchthorn and R.A. Mron, Phys. Rev. Lett., 89, 963 (22) 9. W.A. Steele, Surf. Sc. 36, 37 (973). 2. Marcus G. Martn and J. Ilja Sepmann, J. Phys. Chem., 2, 2569 (998) 2. P.Padlla and S. Toxværd, J. Chem. Phys (99). 22. M. P. Allen, D. J. Tldesley, Computer smulaton of lquds, Clarendon Press, New York, NY,

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