Langmuir 1994,10, 188-196
188
Molecular Dynamics Study of the Self-Assembled Monolayer Composed of S(CH2)14CH3 Molecules Using an All-Atoms Model Wen Mar and Michael L. Klein' Department of Chemistry and Laboratory of Research for the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323 Received August 18,1993. I n Final Form: October 19,199P Molecular dynamics (MD) simulations have been carried out for self-assembledmonolayers (SAMs) of alkanethiol molecules chemisorbed on the Au(ll1) surface using a model with full atomic representation of methyl and methylene groups. The system consisted of flexible alkanethiol chains, S(CH2),$Hs, whose sulfur head groupswere arrangedto form a (d3Xd3)R30° commensuratestructure,withperiodic boundary conditions in the plane of the surface. Various properties of the system have been monitored as functions of temperature. Particular attention is given to the monolayer structure at low temperature. To this end, the configurational energies of several possible crystalline structures have been examined. The present interaction potentials are found to favor a herringbone structure with two moleculesper unit cell, a finding that disagrees with the four-chain per unit cell structure proposed on the basis of recent X-ray and He diffraction data. Among many possible structures with four molecules per unit cell, three are reasonably competitive with the energy of the herringbone arrangement. Although the current study seemsto provide a better description of the SAM than the so-called united-atom model, the disagreement with the X-ray data suggests that more work needs to be done in refining the treatment of the substrate. 1. Introduction
Self-assembled monolayers (SAMs) are a class of molecular assemblies that are prepared by spontaneous adsorption of molecules from solution onto a solid sub8trate.l Systems of current interest include organosilicon on hydroxylated surfaces (glassslides, silicon wafers, etc.),2 alkanethiols or dialkyl disulfides on gold- or silver! and carboxylic acids on aluminum oxide.1° Self-assembly has been shown to provide a viable means of controlling the physical and chemical properties of solid surfaces. The understanding of the underlying interactions that govern the formation and behavior of SAMs will provide answers to questions related to such technologically important areas as adhesion," lubrication,12and wetting of solid surfaces by liquids.7~~J3 The structure of hydrocarbon chains found e Abstract published in Advance ACS Abstracts, December 1, 1993. (1) Ulman, A. An Introduction to Ultra-thin Organic F i l m : From
Langmuir-Blodgett to Self-Assembly; Academic Press, Inc.: San Diego, CA, 1991. (2) (a) Sagiv, J. J. Am. Chem. SOC.1980, 102, 92. (b) Kessel, C. R.; Granick, S.Langmuir 1991, 7, 532. (3) Nuzzo,R. G.; Allara, D. L. J. Am. Chem. SOC.1983,105,4481. (4) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. SOC.1987,109,3559. (5) Chidsey, C. E. D.; Liu, G.-Y.; Rowntree, P.; Scoles, G. J. Chem. Phys. 1989,91, 4421. (6) (a) Chidsey, C. E. D.; Liu, G.-Y.; Scoles, G.; Wang, J. Langmuir 1990, 6, 1804. (b) Camillone, N., III; Chidsey, C. E. D.; Liu, G.-Y.; Putvinski, T. M.; Scoles, G. J. Chem. Phys. 1991, 94, 8493. (7) Bain, C. D.; Troughton, E. B.; Tao, Y.-T.; Evall, J.; Whitesides, G. M.; Nuzzo, R. G.J.Am. Chem. SOC.1989,111,321. (8)(a) Samant, M. G.; Brown, C. A.; Gordon, J. G., I1Langmuir 1991, 7,437. (b) Samant, M. G.; Brown, C. A.; Gordon, J. G.,IILangmuir 1992, 8, 1615. (9) (a) Fenter, P.; Eisenberger, P.; Li, J.; Camillone, N., 111;Bernasek, S.;Scoles, G.; Ramanarayanan, T. A.; Liang, K. S. Langmuir 1991, 7, 2013. (b) Ulman, A. J. Mater. Educ. 1989,11, 205. (c) Laibinis, P. E.;
Whitesides, G. M.; Allara, D. L.; Tao, Y.-T.; Parikh, A. N.; Nuzzo, R. G. J. Am. Chem. SOC.1991,113,7152. (d) Walczak, M. M.; Chung, C.; Stole, S. M.; Widrig, C. A.; Porter, M. D. J. Am. Chem. Soc. 1991,113,2370. (IO)Allara, D. L.; Nuzzo, R. G.; Langmuir 1985,1, 45,52. (11) Zisman, W. A. Handbook of Adhesiues; Skeist, I., Ed.; Van Nostrand Rein: New York, 1977; Chapter 3. (12) (a) Bowden, F. P.; Tabor, D. The Friction and Lubrication of Solids, Part IZ; Oxford University Press: London, 1968; Chapter 19. (b) Chaudhury, M. K.; Owen, M. J. Langmuir 1993,9,29.
0743-7463/94/2410-0188$04.50/0
in the simplest SAMs constitutes an ideal model system for the study of biological membranes and biocompatible materials.14 Potential applications of this new class of materials include chemical modification and functionalization of solid su~faces,~3J5 thin-film nonlinear optical materials,l6 micr~fabrication,'~ and microelectronics.'* In this paper, we are concerned with the properties of one of these systems, namely, alkanethiol molecules chemisorbed on a Au(ll1) substrate. Since its discovery in the early 198Os,3 this system has received enormous attention. Considering the relative ease with which it can be prepared, the structural order it achieves is remarkable. The flexibility in controlling the functional groups exposed at the monolayer-ambient interface makes the thiol-Au system so far the most versatile system yet devised in terms of surface property control and modification. The characterization of this system has been carried out using a variety of techniques. They include transmission electron spectroscopy,lgnormal and Fourier-transformed infrared spectroscopy,20optical ellipsometry,lM helium beam diffraction,516 macroscopic wetting experiments,13 (13) (a) Whitesides, G. M.; Laibinis, P. E. Langmuir 1990,6,87. (b) Evans, S. D.; Sharma, R.; Ulman, A. Langmuir 1991, 7,156. (c) Dubois, L. H.; Zegarski, B. R.; Nuzzo, R. G. J.Am. Chem. SOC.1990,112,570. (d) Folkers, J. P.; Laibinis, P. E.; Whitesides, G. M. Langmuir 1992,8,1330. (14) (a) Lee, J. H.; Kopecek, J.; Andrade, J. D. J.Biomed.Mater. Res. 1989,23,351. (b) Haussling, L.; Ringsdorf, H.; Schmitt, F.-J.; Knoll, W. Langmuir 1991, 7, 1837. (c) Collinson, M.; Bowden, E. F.; Tarlov, M. J. Langmuir 1992, 8, 1247. (15) (a) Chidsey, C. E. D.; Loiacono, D. N. Langmuir 1990,6,682. (b) Bae, I. T.; Huang, H.; Yeager, E. B.; Scherson, D. A. Langmuir 1991, 7, 1558. (16) (a) Prasad,P. N.; Williams,D.J.Zntroduction toNonlinearOptical EffectsinMolecules andpolymers; Wiley Interaciencea: NewYork, 1991. (17) (a) Abbott, N. L.; Folkers, J. P.; Whitesides, G. M. Science 1992, 257,1380. (b) Frisbie, C. D.; Martin, J. R.; Duff, R. R., Jr.; Wrighton, M. S. J. Am. Chem. SOC.1992,114,7142. (18) (a) Sheen, C. W.; Shi, J.-X.; Martensson, J.; Parikh, A. N.; Allara, D. L. J. Am. Chem. SOC.1992, 114, 1514. (b) Bain, C. D. Adu. Mater. 1992, 4, 591. (19) Strong, L. S.; Whitesides, G. M. Langmuir 1988, 4, 546. (20) (a) Nuzzo, R. G.; Fusco, F. A.; Allara, D. L. J. Am. Chem. SOC. 1987,109,2358. (b) Nuzzo, R. G.; Korenic, E. M.; Dubois, L. H. J.Chem. Phys. 1990, 93, 767. (c) Stole, S. M.; Porter, M. D. Langmuir 1990,6, 1199. (d) Evans, S. D.; Goppert-Berarducci, K. E.; Urankar, E.; Gerenser, L. J.; Ulman, A. Langmuir 1991, 7, 2700.
0 1994 American Chemical Society
Langmuir, Vol. 10, No.1, 1994 189
Self-Assembled Monolayer Study STM,21 etc. The consensus that has emerged from these studies is that the sulfur atoms coordinate strongly to the gold surface and, in the case of an ideal Au(ll1) substrate, form a slightly distorted (43x43)R30° triangular lattice. The hydrocarbon tails selforganize into a well-ordered monolayer with chains tilted uniformly toward their next nearest neighbors (NNN). In spite of all these investigations, there still remain many unanswered questions. For instance, a quantitative understanding of the structural changes occurring in the system at various temperatures is lacking, and the nature of the low temperature crystalline structure(s) has yet to be established. Recently low temperature helium diffraction experiments and new synchrotron X-ray diffraction data suggest that at temperatures ranging from 50 K up to room temperature, alkanethiol SAMs adopt a fourchain per unit cell crystalline s t r u ~ t u r e But . ~ ~exactly ~~~ how the four chains are arranged in the unit cell is at present still a matter of speculation. Moreover, the observation of a phase transition a t elevated temperatures seems to indicate that structural defects play a more important role than previously assumed, especially at high temperatures.22 Computer simulation provides a natural complementary method to answer some of these questions and has already made important contribution to the understanding of the processes involved. In earlier attempts to study such systems using MD simulation, Hautman and Klein pointed out that several phases might exist in SAMs over the accessible temperature range?, though the transition temperatures are likely to be higher in the real system than those found in their simulation because of the simplified model used. Siepmann and McDonald conducted a Monte Carlo simulation of a c16 SAM system using a similar and confirmed the essential results of the Hautman-Klein calculations. In this article, we will present results of a new MD study using a more realistic model of the flexible alkyl chains. However, the treatment of the substrate is the same as in the earlier studies. The primary goal is to help rationalize the recently reported four-chain per unit cell structure. For a densely packed hydrocarbon system, experience tells us that hydrogen atoms play avital role in determining the chain packing structure. There have been many discussions concerning the role and the treatment of hydrogen atoms in the simulation of hydrocarbon systems. Early simulations used the so-called united atom (UA) model, which treats methyl (-CH3) andmethylene (-CH2-) groups as pseudoatoms, Le., single interaction sites. Such a model provides a qualitative description of liquid hydrocarbon systems. In the simulation of crystalline n-alkanes, however, the explicit treatment of hydrogen atoms turns out to be indispensable in order to obtain the correct packing structure.26 An alternative method of including the effect of H-atoms has been proposed by Toxvaerd et al. that involves displacing the center of interaction off the carbon atom position.27 The calculated results for the diffusion coefficient of liquid alkanes using ~~
(21) (a) Widrig, C. A.; Alves, C. A.; Porter, M. D.J. Am. Chem. SOC. 1991, 113, 2805. (b) Kim, Y.-T.; Bard, A. J. Langmuir 1992,8, 1096. (22) (a)Fenter, P.; Eisenberger,P.; Liang,K. S. Phys. Rev. Lett. 1993, 70 (16), 2447. (b) Camillone, N., III; Chidsey, C.E.D.; Eisenberger, P.; Fenter,P.;Li, J.; Liang, K. S.;Liu, G.-Y.; Scoles, G. J. Chem.Phys. 1993, 99 (l),744. (23) Hautman, J.; Klein, M. L. J . Chem. Phys. 1989,91, 4994; 1990, 93, 7483. (24) Siepmann, J. I.; McDonald, I. R. MOL Phys. 1993, 79 (3), 457. (26) Camillone, N., III; Chidsey, C. E. D.; Liu, G.-Y.; Scoles, G. J . Chem. Phys. 1993,98 (4), 3503. (26) Ryckaert, J.-P.;McDonald, I. R.; Klein, M. L. Mol. Phys. 1989, 67, 957. (27) Padilla, P.; Toxvaerd, S. J. Chem. Phys. 1991, 94 (a), 5650.
Table 1. Nonbonded Interaction Parameters
S-S"
SC"
S-Ha CCb C-Hb A (109 kcal) 79.937 81.763 14.565 83.63 8.766 B (k1) 3.18 3.39 3.46 3.60 3.67 C(kcal*Ae) 2002 1066 233.8 568 126
H-Hb 2.654 3.14 27.3
a The potential parameters for the S-S interaction were taken from ref 30. We fitted this potential to exp-6 form by requiring the two potentials to have the samewell depth and long range interaction. Parametersfor S-C and S-H were obtainedthroughthe mixingrule: Aij = (A".Ajj)l/2,Bij = (B" Bjj)/2, and Cij = (Cii42jj)l/%. b These parameters are from ref 29, set N.
+
this so-called anisotropic united atom model is in good agreement with experiments. For SAMs, which closely resemble the crystalline hydrocarbon systems, an all-atoms model seems to be a more natural choice. In section 2, we give a brief account of the model we use and in section 3 we present the simulation results as well as an analysis of the low temperature structure. Our results are, in fact, the completion an earlier attempt,= which showed that the inclusion of hydrogen atoms has a significant impact on the simulation outcome. The article ends with the discussion and conclusion. 2. Review of the Model
The simulation system consisted of either 90 or 100 flexible alkanethiol molecules (SCuHsl) arranged in a rectangular simulation cell, with periodic boundary conditions in the surface plane. The geometry adopted was similar to that used in earlier studies.= The larger system was used to accommodate structures based on four molecules per unit cell. All the atoms, including hydrogen, were represented by sites that interact with one another through potentials of the form V(r)= Ae-& - C/rS. Bond lengths were constrained to the following values: dcc = 1.53 A, dm = 1.82 A, and dcH = 1.040 A. H-C-H bond angles were set equal to the ideal tetrahedral angle, and the methylene hydrogen atoms were constrained so as to follow the motion of the carbon backbone. Nonbonded interactions of the exp-6 form were included between atoms belonging to different chains and between atoms within the same molecule but separated by more than three C-C bonds. Alkyl chain parameters for the H-H, H-C, C-C interactions were taken from studies of alkanes by Williams (parameters set IV)29 and for interactions involving S atoms, from Jorgensen's workam The actual parameters used are listed in Table 1. The S-C-C and the C-C-C bond angles were allowed to vary with a harmonic bending potential
V, = -1k,(B - 0,)' 2 each with the same potential parameters (see Table 2).,l Changes in dihedral angles were subject to the now traditional torsional potential proposed by Ryckaert and Bellemans3,
v, = to + t , COS($) + t, cos2($) + t, cos3($)+ t , c0s4(4)
+ t, COS~W
Terminal methyl group hydrogen atoms were subject to a 3-fold torsional potential ~~~
~~
(28) Hautman, J.; Bareman, J.; Mar, W.; Klein, M. L. J. Chem. SOC., Faraday Trans. 1991,87 (13), 2031. (29) Williams, D. E. J. Chem. Phys. 1967,47,4680. (30) Jorgensen, W. L. J. Phys. Chem. 1986,90,6379. (31) van der Ploeg, P.; Berendsen, H. J. C. Mol. Phys. 1983,49,233. 1978, (32) Ryckaert,J.-P; Bellemans, A. Faraduy Discus. Chem. SOC. 66, 95.
Mar and Klein
190 Langmuir, Vol. 10, No. 1, 1994 Table 2. Intramolecular Potential Parameters; h is the Boltzmann Constant 62542 1116 1462 -1578 -368 3156 3788 14.2 a Angle bending potentialparameter,taken from ref 31. Backbone torsional potential parameters, taken from ref 32. Methyl group torsional potential parameter, taken from ref 33.
n n n n Tilt Direction
0 Gold Atom
where cp is the C-C-C-H dihedral angle.33 The potential parameters are listed in Table 2. Following Hautman and Klein, the surface interaction was modeled by 12-3potentials
V(z)= ---c12 (z - z0)"
c3
(z - z0)3
The well depth for sulfur atoms, -28 kcal/mol, was fitted to the experimental thermal desorption energy of methanethiol from a gold surface.20 The curvature at the potential minimum was fitted to the vibrational frequency measured by electron energy loss spectro~copy.~~ A lateral corrugation potential with a large diffusion barrier was used to restrict the sulfur atoms to the 3-fold adsorption site.36 The magnitude of this corrugation (8.4kcal/mol) was chosen, somewhat arbitrarily, so that the barrier between adjacent adsorption site was 30% of the adsorption well depth. Because no explicit substrate relaxation was allowed, the sulfur atoms formed a (d3Xd3)R30° two-dimensional triangular lattice with a surface density of 21.6 A2 per chain. The (substrate)-S-CH~ angle was not subject to any bending potential (model I in ref 23). Microcanonical constant energy molecular dynamics simulations were performed using a timestep of 3.0 fs. The temperature of the system was controlled by scaling the particle velocities in the usual fashion. A typical run of 120 ps takes about 30 h on three IBM RS6000/550 CPUs running in parallel under PVM. To facilitate data processing, runs are subdivided into 3-h (12ps) segments. 3. The Simulation 3.1. Initial Configuration. The system was initially set up with the chains arranged in all-trans configurations, standing normal to the surface and sulfur atoms at the 3-fold adsorption sites. The backbone planes of the chains were randomly oriented. The system was then equilibrated at 300 K for about 200 ps. After a few picoseconds of initial frustration, the chains tilted collectively toward a common direction. At around 20 ps, the system began to settle into a well-defined structure in which the chains tilt away from the surface normal by about 30°, toward one of their next nearest neighbors, a result that accorded well with experiments and previous s t ~ d i e s . ~ ~Avt~this 3 temperature, gauche defects resided mostly at the end of the chains. In the structure prepared in this fashion, the packing of the backbone planes appeared to favor certain distinct patterns. These qualitative observations will be further analyzed in section 3.3. (33) Scott, R. A.; Scheraga, H. A. J. Chem. Phys. 1966,44,3054. (34) This surface model is the same as model I used in ref 23. (35) Sellers, H.; Ulman, A.; Shnidman, Y.; Eilers, J. E. J. Am. Chem. SOC.1993,115,9309.
0 Adsorption site
/
Backbone orientation
Herring-bonestructure for SAM on Au(l11) Figure 1. Sketch of the herringbone packing structure of an alkanethiol SAM on an ideal Au(ll1) surface. The sulfur atoms reside at the 3-fold sites on the gold surface and form a ( d 3 X d 3 ) R30" lattice. The vectors represent the alkyl chain backbone planes and point in the direction of the S-C bond.
Some of the early experiments suggested that a t low temperature this particular SAM system adopts a herringbone structure with two chains per unit cell,20bsuch as shown, schematically,in Figure 1. We constructed such a structure by selecting two chains from the abovementioned MD run which had a mutual herringbone arrangement to form the unit cell. The simulation system was constructed by repeating the unit cell in both the X and Y directions. Random velocities were then assigned to each atom and a trajectory of the system obtained with the temperature held at about 200 K. The initially constructed herringbone arrangement appeared to be stable a t this temperature and, as we will describe below, it remained so up to around room temperature. 3.2. Heating. A series of simulations of the aforementioned systemat various temperatures were performed starting from 200 K. At this temperature the system remained in a well-ordered crystalline phase. There were almost no gauche defects and chains retained their original herringbone orientations over the duration of a MD trajectory spanning several hundred picoseconds. The average chain tilt angle was about 33O. We then progressively scaled the velocities of the particles to reach a higher temperature. A t about 250 K, we observed that 2.2% of the molecules had gauche defects at the last torsional angle of the chain. At 300 K, the defects concentration increased to about 4.4% Up to this point, all the gauche defects were located a t the end of the chain and the interior of the monolayer was essentially defect-free. As the temperature was raised further, gauche defects began to develop in the middle section of the chains as well. Figure 2 shows a plot of percentage of gauche defects vs bond number at various temperatures. For each temperature, the result was obtained by averaging over a period of 200-400 ps, after an equilibration of more than 100 ps. Gauche defects first started to form within the monolayer when the temperature was somewherebetween 300 and 325 K. As we will see later in this section, the formation of gauche defects within the monolayer was actually coupled with the onset of rotational motion of the chains around their long molecular axes. We also noticed an oscillation in the percentage of gauche defects as a function of bond number. This feature can be understoodby noting that a singlegauche defect is unlikely to exist in the middle of the chain because in a densely packed monolayer system, the bend formed by a gauche
.
Self-Assembled Monolayer Study
Langmuir, Vol. 10, No. 1, 1994 191 I
h
'
425
K
395
K
370 K 341
K
332
K
1
-
-
5
10
25
5
10
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20
25
1
h
N
Y
a 10
15
20
25
5
10
-
300
K
250
K
-
200
K
-
15
20
10
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Z (Angstrom)
5
10
15
25
1
395K
5
10
20
1 370K
5
5
15
7
20
25
Z (Angstrom)
15
Bond Number Figure 2. Gauche defect concentrations (in %) as a function of bond number at various temperatures taken from the heating MD run (see text). At 300 K and below, gauche defects exist only in the tail regionof the chain. Gauche defects concentrations increase dramatically, both within the monolayer and at the monolayer-vacuum interface, once the system undergoes a "rotator"phase transition (300-332 K). The alternation in defect concentration along the chain should also be noted. bond in the middle of the chain would be energetically prohibitive. An obvious way to accommodate gauche defects within the layer is to form a "kink", i.e., a pair of gauche defects. Such a conformation, which includes gauche(+) and gauche(-) defects separated by a transbond, can preserve the essential linearity of the molecule. Indeed, almost all of the gauche bonds in the middle section of the chain existed in this form. Another important factor contributing to the observed alternation in gauche concentration was the fact that the first C-C bond (the bond next to the S-C bond) usually had a low gauche defect concentration. This may be due to the nature of the adsorbate-substrate interaction which restricted the motion of sulfur atoms. This chosen potential greatly reduced the number of conformations that the chain head group region could adopt and favored a trans conformation for the first C-C bond. The combination of these effects gives a rationalization of the observed alternation in gauche concentration, as shown in Figure 2. Figure 3 shows density profiles of sulfur and carbon atoms in the direction normal to the surface. At 200 K, the profile clearly shows a doublet pattern characteristic of a herringbone structure in which the C-C bonds take one of two well-defined orientations with respect to the surface normal, i.e., odd-numbered bonds lay almost parallel to the surface and even-numbered bonds were almost perpendicular to the surface. Actually,the presence of these doublets was also an indication that at 200 K there had been no significant reorientational motion of the chain backbone planes around the long axes. Reorientation of the chain backbone planes would cauae C-C bonds to lose their well-defined orientations with respect to the surface normal that they had in the herringbone structure, and the doublets would then disappear, a behavior which can be taken as an indication of the "melting" of the herringbone structure. Indeed, as the temperature was raised further, we started to see broadening of these peaks. The herringbone structure was preserved up to 300 K. Somewhere between 300 and 325 K, the chains started to rotate and, as a result, we see a
Density Profile of C,, Chains a t Different Temperatures
Figure 3. Density profiles of the SAM system along the surface normal. At 300 K and below there is an obvious doubling of the peaks, which is the signature of the initial herringbone packing. The change reflected in the profiles between 300 and 332 K is due to 'rotational melting". At elevated temperatures, the untilting of chains leads to the extension of profiles along the 2-direction.
O 200
300
400
Temperature (K)
Figure 4. Chain backbone tilt angle variationwith temperature. The open squaresare taken from the heating run, while the fiied hexagons are the results of a cooling run. A hysterisis is seen between 240 and 320 K. The dotted line is a guide to the eye. more uniform distribution of the peaks. At even higher temperature, the peaks broadened further and shifted to higher 2 values, which implies that the chains became more disordered and untilted. Another property we monitored was the average tilt angle of the chains (shown in Figure 4). The tilt decreased linearly with temperature between 200 and 300 K. Then, it dropped abruptly somewhere between 300 and 325 K, when the chains started to rotate. Finally, the trend leveled off a t about 390 K, a t which point the system no longer maintained any uniform tilt. The variation of tilt angle also suggeststhat a phase transition occurred slightly above room temperature. The system thus evolved from a phase in which individual chains were locked in their orientation, to a phase where chains had the freedom to rotate about their long axes. This rotation took the form of discrete jumps at lower temperature (around 330K) and gradually became more of a rotational diffusion a t higher temperature
192 Langmuir, VoZ. 10, No. 1, 1994
Figure 5. Drawing of an adsorbed thiol molecule along with its schematic (stick-ball) representation: B is the tilt angle of the molecule, Rb is the vector (defined in the text) that represents the orientation of the chain backbone, 4t is the chain twist (rotation)angle,and x characterizesthe t ilt direction (precession angle).
(around 360 K) as the chains untilted. At temperatures higher than 370 K, we observed large fluctuations in tilt angle and, occasionally, changes in the tilt direction. At 390 K, there was no longer a collective tilt direction. At any given moment, individual chain might still be tilted to some degree, but over a long period of time, the system precessed around the surface normal, and thus, averaged over time, the system maintained no steady tilt. At temperatures higher than 390 K, the system can be viewed as an array of rods, which are essentially vertical, forming a hexagonal lattice and rotating relatively freely around their long axes. Recent X-ray data on SAMs of varying chain length22 showed that the domain size of a SAM can be dramatically increased through annealing. After annealing at 90 "C, the observed domain size of a C12 SAM (estimated through the X-ray diffraction peak width) increased from 90 to 1000 A. For C14, it increased from 90 to 200 A. This annealingtemperature is close to the temperature (370 K) in our simulation at which the C15 systemstarted to change its tilt direction. This result may not be a pure coincidence since such changes in tilt directions are almost certain to happen when small domains merge to form larger ones. We speculate from this observation that for longer chains, higher annealing temperatures, of course subject to the restriction of thermal stability, are likely needed in order to obtain SAMs with large ordered domains. To study the distribution of backbone-plane orientations, we calculated the distribution of the twist angle, which is defined as angle 4 in Figure 5. The calculated distributions for various temperatures are given in Figure 6. At temperatures below 300 K, the &distribution exhibits two peaks. Again, this reflected the initial setup of herringbone configuration. Clearly, there were very few, if any, chain rotations below 300 K. Starting from 325 K, we saw the emergence of a "four-site" distribution pattern. Early computer simulation studies of LangmuirBlodgett films and crystalline n-alkane systems using a similar intermolecular potential model also revealed such a "four-site" distribution of the twist angle, $.36 The conclusion we could draw from this observation is that the backbones of the chain molecules can take one of four well-defined orientations, with twist angles at h50" and h130". In the next section, we are going to use this result (36)(a) Bareman, J. P.; Klein, M. L. J. Phys. Chem. 1990,94, 5202. (b) Ryckaert, J.-P.; McDonald, I. R.; Klein, M. L. Mol. Phys. 1989,67, 957.
Mar and Klein
-100
0
100
-100
0
100
-100
0
100
$,(deg) Figure 6. Calculated twist angle (&) distributions at various temperatures. The two-peakeddistributionsat 250 K and below reflect the initial perfect herringbone structure. At higher temperatures, chain rotation leads to a four-site distribution,as seen at 332 K. The nearly flat distribution at 395 K is typical for temperatures higher than 370 K, where the chains are almost completely untilted and rotate around their long axes on the time scale of about 5ps. $,(ded
in analyzing the low temperature structure. From the peak position in Figure 6, the estimated twist angle of 50" is in good agreement with experimental results20b Another property we monitored during the heating-up simulation was the chain rotational correlation function, defined as the autocorrelation function of the vector Rb in Figure 5 where we define 12
12
Here, ri is the vector of the ith C-C bond from the sulfur atom, and ri.0is the correspondingbond vector of a perfect all-trans molecule. The correlation function of interest is defined as
where ( ) denotes the average over the simulation trajectory. y ( t ) characterizes the temporal decay of the backbone plane orientation. Figure 7 contains the results for y ( t )a t various temperatures. Below 300 K, we saw no reorientation of the chain backbone planes on the simulation time scale, i.e., several hundred picoseconds. This is consistent with other observations we made about this system. A t 332 K, the chains rotated on a time scale of about 20-30 ps. As the temperature was raised, the reorientation time decreased rapidly so that at 370 K it was only about 6-7 ps. The barrier of reorientation in the rotator phase can be established by assuming that the rotation correlation function, y ( t ) ,decays exponentially with time y(0 = ~ ( 0exp[-t/.rl )
We have estimated T'S a t various temperatures by fitting y ( t ) to this exponential form. We further assumed the
correlation time varies with temperature according the classical transition state theory: T(T)
= 7 0 exp[-Wk,TJ
where AE is the activation energy for rotation and k g is
Langmuir, Vol. 10, No. 1, 1994 193
Self-Assembled Monolayer Study
C""'
t
~ " " " " " " ' " ' " ~
Tilt direction unlocks, almost
--------A
Tilt in nnn direction, chains start to rotate via discrete jumps and have a measurable density of gauche defects.
0.6
t.--------
p: V
0.4
Y
0
10
20
30
40
Correlation Time (ps)
Figure 7. Rotational correlation functions y ( t ) at various temperatures. The solid lines correspond to the heating run and the dashed lines are the results of the cooling run in Figure 6 (see text). the Boltzmann constant. The estimated value of AJ3 in the rotator phase is in the neighborhood of 4 kcal/mol. The above results are summarized in the following picture of the system. Below 300 K, the system was in what could be regarded as a crystalline state. Chains tilted toward their next nearest neighbors and were locked in their backbone orientation. There were only a few gauche defects that were located strictly at the end of the chain. Between 300 and 325 K, a "rotator" phase transition brought the system into a state where the chains behaved more or less as "hindered rotators" with gauche defects concentrated at, but not limited to, the end region. From there up to 370 K, we saw chains gradually untilt as a result of rising temperature. The rotation of an individual chain around its long axis changed from discrete jumps between favorable orientations to a more continuous rotational diffusion. Gauche defecta were formed throughout the system, at the ends as well as in the middle section of the chain. At about 370 K, we began to see large amplitude fluctuations in tilt angle coupled with discrete changes in the chain tilt direction. Finally, beyong 390 K, we saw a region where chains untilted completely and rotated nearly freely around their long axes. A phase diagram for the c15 SAM, based on the present MD results, is schematically shown in Figure 8. These results confirm the findings of earlier workers that several phrases exist within the experimentally accessible temperature range.23 3.3. Cooling. Recently, both low temperature He diffraction (between 30and 1 0 0 K Pand room temperature X-ray scattering22experiments revealed clear evidence of superlatticelineswhich have been interpreted asindications of SAM structures based on four chains per unit cell. It is, however, not clear how the four chains are arranged. One possible four-chain unit cell structure has been proposed by Camillone et a1.26 and computer simulations were suggested as a way to differentiate among various possible structures. We therefore constructed their proposed structure in much the same way that we constructed the initial herringbone structure. In this case we used 100 instead of 90 molecules in the simulation box in order to satisfy the requirements of the periodic boundary conditions. The MD results showed that a t 50 K the configurational energy of the proposed structure%is about
t
Next nearest neighbor tilt, molecules are orientationally ordered and free of gauche defects.
Figure 8. Schematic phase diagram for a CISSAM on Au(ll1). Below about 300 K, the system is in a orientationally ordered crystallinephase. Between 300 and 370 K,the system gradually untilts as the temperature increases and the chains behave as hindered rotators. Above 370 K, the chains rotate more freely around their long axes and gauche defects form throughout the system. Precession of chains about surface normal was also seen in this temperature regime.
1.4kcal/mol higher than that of the herringbone structure. Also, the proposed structure began to "melt" at about 150 K (i.e., frequent chain backbone reorientations occurred at this temperature), whereas the herringbone structure, according to our simulation, was stable up to 300 K. Clearly, for our model, the proposed four-chain unit cell structure is not the optimal packing arrangement. In an attempt to find out the most likely low temperature packing configuration of the (216 SAM appropriate to our potential model, we undertook a slow cooling MD run. Local structures resulting from this cooling run were compiled and used to construct possible periodic structures. MD simulations were then carried out on these structures and their energies at 50 K thereby obtained. These studies enabled us to determine a set of efficient chain packing arrangements that were consistent with twoor four-chain unit cell structures. A configuration from the MD run at 425 K (see section 3.2)was chosen as the starting configuration for the cooling run. Then, the temperature of this largely disordered system was scaled down at a rate of about 1 K/20 ps. Thermodynamic properties were monitored at selected temperatures. As shown in Figure 4,the average tilt angles of the system during this cooling run agreed well with those of the first (heating) simulation. However, a hysterisis appeared when the temperature approached the rotational transition temperature of -300 K. This was not surprising considering the rate at which we were cooling the system. The rotational correlation functions for the cooling run, as shown in Figure 7, indicate that the backbone reorientations of individual chains were not frozen out until the temperature was reduced to about 250 K. Following the same procedure as outlined in the previous section, we estimated the barrier for rotation to be about 6 kcal/mol. This value is higher than in the heating run most likely due to residual defects. However, the gauche defects present in the starting configuration did gradually anneal out during the course of the cooling process, and at 250K, the system was almost free of gauche defects. A t this temperature, the chains were tilted uniformly toward their next nearest neighbor, though the structure was orientationally disordered (glassy state). Several favorable local chain packing arrangements emerged a t the end of this MD run and these are summarized in Figures 9 and 10.
Mar and Klein
194 Langmuir, Vol. 10, No. I , 1994
I
Favorable :
Unfavorable :
tilt direction
n
IJi
1 Chain Der unit cell
-
(a) E -21.615 kcalimol
I
tilt direction
(b) E = -21.207 kcal/mol
2 Chain oer unit cell
(dl
Figure 9. Possible packing arrangementsfor chains belonging to different rows. Favorable patterns result from careful annealing. The unfavorable pattern was shown to be unstable by direct simulation starting from the arrangement. Favorable :
I
tilt direction
n n Unfavorable :
n
t, (CI
Figure 10. Possible packing patterns for alkyl chains belonging to the same row (see text). From the twist angle distribution shown in Figure 6, we concludedthat at temperatures relevant to the experiments (30-100 K for He diffraction and around room temperature for the X-ray experiment), the chain backbone planes tend to take on one of the four well-defined orientations. This observation forms the basis of our analysis of possible crystalline structures. Since the chains are predominantly in an all-trans conformation at these temperatures, we can use a vector (in this caae, the S-C bond vector) to characterize the backbone plane orientation of a molecule in the annealed structure. Figure 9 shows local arrangementa for chains in neighboring rows. A row of molecules is defined to be along the direction that is perpendicular to the chain tilt direction. In parts a and b of Figure 9, chains in neighboring rows are perpendicular to each other. This is basically the herringbone packing arrangement, while the S-C bonds can orient either along or opposite to the tilt direction. In parts c and d of Figure 9, chains have their backbone planes parallel to one another. In Figure 9c, the chains have their first S-C bonds oriented in the same way so that the zigzag backbones of the two molecules will interlock. This turns out to be an effective way for the two molecules to maximize their contact and minimize the intermolecular interaction energy. On the other hand, when the two S-C bond vectors are pointing toward each other, as shown in Figure 9d, the repulsion
(c) E = -21.891 kcallmol
(d) E = -212 4 1 kcaWmol
-
(e) E -21.197 kcalimol
Figure 11. The specific systems with one or two molecules per unit cell that were considered. Their total energies at SO K are given. The herringbone structure seems to be the most efficient in terms of chain packing. between the two chains makes this configuration unfavorable. For hydrocarbon chains within the same row, the relative orientation of their backbone planes can be either parallel or near perpendicular, as shown in Figure 10. The parallel alignment, as shown in Figure loa, is stable and was often observed in the final (quenched) MD structure. In the case of near perpendicular alignment, chains prefer to have S-C bonds pointing in the direction indicated in Figure lob so as to avoid a ‘head-to-head” repulsion. Such repulsion between the two molecules makes the configuration in Figure 1Oc unstable. With the above observations in mind, we began to construct crystalline structures with one-, two-, and fourchains per unit cell. Structures with one- and two-chains per unit cell were included just for completeness. We allowed each chain in the unit cell to adopt four possible orientations. Unfavorable local configurations shown in Figures 9 and 10 were used to eliminate those configurations that were unlikely to be the candidates for stable crystalline structures. However, we did not attempt a systematic study of all possible structures. Thus, certain structures were excluded either for symmetry considerations or because we had reason to believe their energy would be higher than some of the other structures. A total of 11 structures were selected for detailed MD analysis. They included two structures with one cbain, three with two chains, and six with four chains per unit cell. For the case of one chain per unit cell, we examined two distinct structures, as shown in Figure lla,b, whereas for two chains per unit cell systems, we only considered the case where chains were tilted toward their next nearest neighbors with the tilt direction along one of the unit cell axes. A total of 4 X 4 = 16 possibilities were examined. After applying the criteria of Figures 9 and 10, we ended up with only three distinct candidates (Figure llc-e) for further studies. MD simulations of these structures a t 50 K were carried out. Their total internal energies, E, are listed in the figures, along with the unit cell structures.
Langmuir, Vol. 10, No. 1, 1994 195
Self-Assembled Monolayer Study
I I
E
direction
90"tilt direction
direction 4 Chains Der unit cell
I
-
au- Ill1
/
-20.478 kcallmol (proposed)
I
I
I
I
-
E -20.991 kcallmol
-
(b)E = -20.857
(a) E -20.478 kcaUmol (proposed)
kcal/mol
Figure 12. Effect of changing the tilt directionfrom 90' to 30'. This causes the structure proposed in ref 25 to be transformed into a structure that has one of the lowest energies among those with four molecules per unit cell. The herringbone structure has the lowest energy among all the cases considered. By comparing the energies of Figure 11(a and b, c and e),we concluded that of otherwise similar structures, the one that has the lower energy is the one whose S-C bonds are pointing along the tilt direction. This energy difference comes primarily from the surface dispersion interaction. By pointing the S-C bond along the tilt direction, the first methylene groups are closer to the substrate and thus lower the surface energy. Our estimation for this energy difference is about 0.29 kcall mol. The dominant factor determining the structure is thus the chain-chain interaction, which is around 20 kcall mol for the C15 system. The most stable crystalline structure is thus the one that gives the most efficient packing of the chains under the constraint of the imposed specific head group lattice. The four chain per unit cell structures deserve careful analysis since experiments seem to favor such a structure.22325Up to this point, the analysis has considered only cases where chains tilted along one of the unit cell axes (Le., a 90° tilt direction). It is also important to consider the case where chains tilt toward the NNN direction but not along the unit cell axis (e.g., 30°, rather than 90°, tilt direction; see Figure 12). After examining carefully all the possible combinations using the above local packing rules and symmetry arguments, we decided to further study a total of six structures. These are shown in Figure 13. Four have a 90° tilt direction and two a 30' tilt direction. The structure proposed from the helium diffraction e ~ p e r i m e n t shown , ~ ~ in Figure 13a, actually contradicts one of the earlier observations for local packing, i.e., chains within the same row should avoid a "head-tohead" repulsion. Thus, it came as no surprise that it did not have the lowest energy among the four chain per unit cell structures. The Figure 13b structure was a variation of the proposed structure. With two chain backbone planes flipped by 180°, it avoids the energetically costly chain arrangements. We initially hoped the structure shown in Figure 13d, which retained the basic herringbone type arrangements, would be an efficient way to pack the molecules. But it turned out to have a rather unfavorable energy, which was about 2.0 kcal/mol higher than that of the herringbone packing structure. This difference can be understood by the following qualitative arguments. To minimize the intermolecular interaction energy, the optimal separation between two methylene groups is about 4.5-5 A. In the herringbone structure, molecules in the same row are oriented in the same way and the distance between corres onding methylene groups in neighboring molecules is 5 i f(the nearest neighbor distance), which is about at the energy minimum. By flipping the backbone
I
-
I
(d) E = -19.612 kcal/mol
(c) E -19.792 kcallmol
30" tilt direction
I
(e) E = -20.991 kcallmol
I
(f) E = -21.004 kcal/mol
Figure 13. Four chains per unit cell structures that we have considered. The first four cases have a 90° tilt direction and the remaining two have a 30' tilt direction. Their total energies at 50 K are given. plane of one molecule, the zigzag backbones of the neighboring molecules will become mismatched and the separation of the corresponding methylene groups will become larger. This larger separation reaulted in an increased total energy of the system. Parts e and f of Figure 13 were configurations with 30' tilt direction. Within the statistical uncertainty, they had the same energy and were the lowest among four chain per unit cell structures. Based on the above results, it seems to us that the structure proposed (Figure 13a) in the recent helium diffraction experiment25is unlikely to be the most efficient chain packing that is consistent with the observation of a four-chain unit cell. Indeed, it proved to be relatively unstable upon heating. Apparently, the energy of the system can be lowered either by rearranging the chain orientations in the unit cell (Figure 13b) or by changing the chain tilt direction (Figure 13e,f). It is difficult to make a choice between possible structuressolely based on the present simulation results since we employed a rather simplified model for the surface chemisorption potentials, which does not allow relaxation of the substrate structures. 4. Conclusion
A molecular dynamics study of self-assembled monolayer systems on Au(ll1) has been carried out using an alkyl chain model with full atomic detail. In contrast to
196 Langmuir, Vol. 10, No. 1, 1994 the nearest neighbor (NN) tilt and 90° twist angle found when using the so-called united-atom the present all-atoms model gave a SAM with next nearest neighbor and a tilt angle (NNN) tilt, an average twist angle of No, of about 30° at room temperature. Our MD simulations confirmed the results of an earlier that upon heating, the system undergoes a transition to a “rotator” phase. However, a recent X-ray experiment22seems to rule out the possibility of such a “rotator” phase. In addition, the new X-ray data show that the tilt direction varies as a function of the chain length. The differences between the simulation results and the experimental observations may, to a large degree, reflect the role that the substrate plays in determining the monolayer structure and highlights the inadequate treatment of the surface potential in our model. Features that may be relevant but which were not treated in our model of the substrateadsorbate interactions include the substrate relaxation upon chemisorption and an angle bending potential for M-S-CH2, where M is the adsorption site. According to the recent quantum mechanical calculation by Sellers et a1.,36 there are indeed two equilibrium positions for the bending around the sulfur atom, with minima at angles of 104O and 180° separated by a 2.5 kcal/mol barrier at 123O. Such a barrier is accessible at room temperature and should have ita impact on the SAMstructure. Another factor that might also contribute to the observed discrepancies between the present simulation and the latest experiments is the role of structural defects.24922b In fact, the periodic boundary conditions in our model will tend to inhibit the formation of such defects. On the other hand, experiment indicates that the formation of a SAM may well be a kinetically limited process and hence structural defects are likely to play a role, especially in the solution phase deposition processes. In an attempt to identify the most stable crystalline structure, a slow cooling MD run was performed starting from a disordered high temperature model configuration. Several favorable local chain packing arrangements were derived from the resulting quenched (glassy) low temperature structure. These observations, in conjunction
Mar and Klein with symmetry considerations, enabled us to determine likely candidates in the ground-state crystalline structure. Experiments have shown strong evidence of a four-chain unit cell structure.n However,our MD simulations suggest that the stable crystalline structure is the herringbone (two-chain unit cell) structure. Of the many possible fourchain unit cell structures, the real (experimental) one is likely to be one of those which are consistent with the observed local packing rules. By comparing the energy of various hypothetical structures, we recommended three as possible candidates for four-chain unit cell structures. As stated before, our focus has been on the chain packing. Hence, the structures recommended are favored for their efficient chain arrangements. However, the adsorbatessubstrate interaction must also contribute to the overall energetics in real SAM systems. Due to the limited information available at this moment on the nature of the adsorbates-substrate interaction, we are unable to distinguish between the three most likely crystalline structures with four-chain unit cells. In our simulations the herringbone structure gives the most favorable packing structure. But clearly it does not satisfy the observed four-chain per unit cell requirement. Thus, the adsorbates-substrate interaction and/or the substrate relaxation22likely conspire to make the herringbone structure less favorable. To resolve this question, further experimental and theoretical investigations focusing specifically on the role of the substrate are warranted. Acknowledgment. We thank Joe Hautman, Jim Bareman, and John Shelley for their assistance in setting up the calculations and many stimulating discussions. We also thank Gang-yu Liu, Paul Fenter, and Giacinto Scoles for encouragement to pursue more realistic modeling of SAMs. John Shelley is also thanked for the graphics progam that has been used in this project. This work was supported by generous grants from the NSF and NIH. Some of the calculation described herein made use of the facilities at CNSF funded under an grant of the NSF Grand Challenge Project. Others utilized facilities provided by the Penn MRL.
