Molecular Dynamics Simulation of Nanoconfinement Induced

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Molecular Dynamics Simulation of Nanoconfinement Induced Organization of n-Decane Valliappa Kalyanasundaram, Douglas E. Spearot,* and Ajay P. Malshe Department of Mechanical Engineering, University of Arkansas, Fayetteville, Arkansas 72701 Received August 25, 2008. Revised Manuscript Received May 15, 2009 Molecular dynamics (MD) simulations are used to study the behavior of n-decane under sub-10 nm confinement between two gold {111} surfaces. This confinement and dielectric medium are characteristic of those used in nanoscale electromachining (nano-EM) processes; thus, it is important that the behavior of the nanoconfined dielectric medium be investigated for better process understanding. Results obtained via MD simulations indicate that, when confined down to a thickness less than 1 nm, the mechanical boundary conditions trigger organization in the n-decane medium, resulting in two distinct molecular layers. The n-decane chains lie flat on the {111} gold surfaces and show preferred orientation in the close-packed Æ110æ crystallographic directions. A 4-fold increase in the maximum local density as compared with the experimental bulk (liquid) density is observed at the interface between the molecular medium and the gold {111} surfaces, regardless of confinement spacing. Radial distribution function curves are used to quantitatively examine organization of the medium into molecular layers. The deliberate introduction of ledges (atomic steps) on the gold surface triggers a preferred alignment of the n-decane chains toward the boundaries of the ledges.

1. Introduction Controlled removal of material at the nanoscale, particularly in the sub-10-20 nm regime, is a key component in the development of the next generation of 3D nanostructures and nanointegrated systems. In particular, probe-based nanomanufacturing is an area of vital importance for production of consistent nanoscale features with applications such as molecular electronics, correction of photolithographic masks, single DNA detection devices,1 nanovias for Z-axis interconnects in electronic packaging, nanojets for drug delivery, proton exchange membranes for fuel cell applications, and writing of ultradense memory media. Today, the spectrum of techniques for nanoscale material removal includes (but is not limited to) focused ion beam, electron beam lithography, nanoimprint lithography, and X-ray lithography, all of which have serious limitations due to either their complexity, contamination, and cost or their fundamental ability to remove materials in the sub-10-20 nm scale regime. To address this need, nanoscale electromachining (nanoEM) has emerged as a promising approach for sculpting, cutting, and patterning features at the sub-10 nm scale in electrically conducting and potentially semiconducting materials.2-4 This process is simple in application but complex in its physical and chemical understanding and is performed at sub-10 nm scale mechanical, electrical, and chemical boundaries. Specifically, a modified scanning tunneling microscope

*Corresponding author. Telephone: (479) 575-3040. Fax: (479) 575-6982. E-mail: [email protected]. (1) Li, J.; Gershow, M.; Stein, D.; Brandin, E.; Golovchenko, J. A. Nat. Mater. 2003, 2, 611–615. (2) Malshe, A. P.; Virwani, K. R.; Rajurkar, K. P.; Deshpande, D. CIRP Ann. 2005, 54, 175–178. (3) Virwani, K. R.; Malshe, A. P.; Rajurkar, K. P. Phys. Rev. Lett. 2007, 99, 017601-1–017601-4. (4) Virwani, K. R.; Malshe, A. P.; Rajurkar, K. P. CIRP Ann. 2007, 56, 217–220.

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(STM) is used to apply intense mechanical, electrical, and chemical boundary conditions between a nanometrically sharp cathode and an atomically flat anode surface, immersed in an organic liquid medium. Use of the organic molecular medium is found to be a key aspect of the nano-EM process, analogous to conventional electric discharge machining (EDM) processes. It is hypothesized that when the organic molecules are confined in the sub-10 nm scale due to mechanical, electrical, and chemical constraints, bias-assisted self-assembly of these molecules could occur, resulting in a quasi-solid medium. Fundamental understanding of a molecular medium’s behavior under the superimposing mechanical, electrical, and chemical boundary conditions at sub-10-20 nm scale confinement is vital for developing a repeatable and reproducible nano-EM process, and is insufficiently understood scientifically at this time. Nanoconfinement induced organization will have significant impact on the anisotropic dielectric properties of the molecular medium, for example, allowing possible lensing of the electric field, facilitating the experimentally observed machining of features as small as 8 nm in diameter using a 35 nm tip radius. Toward understanding this complex scenario, the objective of this work is to study the first of the three boundary conditions, namely nanoconfinement due to mechanical boundary conditions. Molecular dynamics (MD) simulations are used to study the behavior of n-decane dielectric machining medium in the nano-EM machining interface as a function of physical separation of the electrodes. Although the experimental setup in nano-EM consists of a tungsten (W) or platinumiridium (Pt-Ir) nanotool, the cathode is considered to be gold for all simulations performed in this work to reduce certain complexities in the MD simulations, which will be the goal of a future study. Previous research groups have studied assembly of alkanes, siloxanes, and other molecular fluids on solid surfaces using both

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experimental and computational techniques.5-39 For example, Gee et al.5 used a surface force apparatus to show that organic liquids of different molecular geometry exhibited solidlike behavior for gap thicknesses below five molecular layers and reported that two confining surfaces are needed for the liquid to become solidlike. Strong layering of n-octane thin films at two to three molecular layers was reported by Ballamudi and Bitsanis,6 although Wang et al.7 in a complementary study found that the system exhibited limited evidence of solidification. Solidlike behavior in experimental studies is typically quantified via viscosity and effective shear moduli increases relative to their bulk values, prolonged relaxation times, and nonlinear responses at low shear rates.8-13 Geometric confinement alone is found to promote these behaviors and not the high compression that can occur under such nanoconfinement.14-16 However, with regard to the nano-EM process, previous work focused on n-decane17-22 does not provide a complete picture of the quasi-solid behavior during mechanical boundary conditions. Specifically, the role of gold as the bounding surface is still unclear, as many previous studies employ either mica or Lennard-Jones (LJ) solids as the confining walls for simplicity. In this work, particular attention is paid to the interfacial layer between the n-decane medium and the gold {111} surfaces, as this layer is expected to be most important in the nano-EM process. Previous MD simulation work reported17 that the density of the (5) Gee, M. L.; McGuiggan, P. M.; Israelachvili, J. N.; Homola, A. M. J. Chem. Phys. 1990, 93, 1895–1906. (6) Ballamudi, R. K.; Bitsanis, I. A. J. Chem. Phys. 1996, 105, 7774–7782. (7) Wang, Y.; Hill, K.; Harris, J. G. J. Chem. Phys. 1994, 100, 3276–3285. (8) Van Alsten, J.; Granick, S. Phys. Rev. Lett. 1988, 61, 2570–2573. (9) Hu, H.-W.; Carson, G. A.; Granick, S. Phys. Rev. Lett. 1991, 66, 2758–2761. (10) Granick, S.; Hu, H.-W. Langmuir 1994, 10, 3857–3866. (11) Granick, S.; Hu, H.-W.; Carson, G. A. Langmuir 1994, 10, 3867–3873. (12) Granick, S.; Demirel, A. L.; Cai, L. L.; Peanasky, J. Isr. J. Chem. 1995, 35, 75–84. (13) Cai, L. L.; Peanasky, J.; Granick, S. Trends Polym. Sci. 1996, 4, 47–51. (14) Klein, J.; Kumacheva, E. Science 1995, 269, 816–819. (15) Klein, J.; Kumacheva, E. J. Chem. Phys. 1998, 108, 6996–7009. (16) Klein, J.; Kumacheva, E. J. Chem. Phys. 1998, 108, 7010–7022. (17) Dijkstra, M. J. Chem. Phys. 1997, 107, 3277–3288. (18) Balasundaram, R.; Jiang, S.; Belak, J. Chem. Eng. J. 1999, 74, 117–127. (19) Zhang, L.; Balasundaram, R.; Gehrke, S. H.; Jiang, S. J. Chem. Phys. 2001, 114, 6869–6877. (20) Pint, C. L. Surf. Sci. 2006, 600, 921–932. (21) Cui, S. T.; Cummings, P. T.; Cochran, H. D. J. Chem. Phys. 1996, 104, 255– 262. (22) Cui, S. T.; Gupta, S. A.; Cummings, P. T.; Cochran, H. D. J. Chem. Phys. 1996, 105, 1214–1220. (23) Granick, S. Science 1991, 253, 1374–1379. (24) Hu, H.-W.; Granick, S. Science 1992, 258, 1339–1342. (25) Demirel, A. L.; Granick, S. Phys. Rev. Lett. 1996, 77, 2261–2264. (26) Thompson, P. A.; Robbins, M. O. Science 1990, 250, 792–794. (27) Thompson, P. A.; Grest, G. S.; Robbins, M. O. Phys. Rev. Lett. 1992, 68, 3448–3451. (28) Bhushan, B.; Israelachvili, J. N.; Landman, U. Nature 1995, 374, 607–616. (29) Gao, J.; Luedtke, W. D.; Landman, U. J. Phys. Chem. B 1997, 101, 4013– 4023. (30) Gao, J.; Luedtke, W. D.; Landman, U. J. Chem. Phys. 1997, 106, 4309– 4318. (31) Rhykerd, C. L.; Schoen, M.; Diestler, D. J.; Cushman, J. H. Nature 1987, 330, 461–463. (32) Diestler, D. J.; Schoen, M.; Cushman, J. H. Science 1993, 262, 545–547. (33) Balasubramanian, S.; Klein, M. L.; Siepmann, J. I. J. Phys. Chem. 1996, 100, 11960–11963. (34) Cui, S. T.; Cummings, P. T.; Cochran, H. D. J. Chem. Phys. 1999, 111, 1273–1280. (35) Cui, S. T.; Cummings, P. T.; Cochran, H. D. J. Chem. Phys. 2001, 114, 7189–7195. (36) Cui, S. T.; McCabe, C.; Cummings, P. T.; Cochran, H. D. J. Chem. Phys. 2003, 118, 8941–8944. (37) Stevens, M. J.; Mondello, M.; Grest, G. S.; Cui, S. T.; Cochran, H. D.; Cummings, P. T. J. Chem. Phys. 1997, 106, 7303–7314. (38) Walley, K. P.; Schweizer, K. S.; Peanasky, J.; Cai, L.; Granick, S. J. Chem. Phys. 1994, 100, 3361–3364. (39) Manias, E.; Bitsanis, I.; Hadziioannou, G.; ten Brinke, G. Europhys. Lett. 1996, 33, 371–376.

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interfacial layer of n-decane on rigid LJ surfaces was independent of gap separation; the universality of this conclusion is evaluated using gold {111} surfaces in this work. Furthermore, a new approach for computing the evolution of density within the nanoconfined volume is presented, along with a first-order analysis of the role of ledges (atomic steps) in the gold {111} surfaces on n-decane organization. Ultimately, the density variation within the nanoscale separation has significant relevance to the nano-EM process; in order to understand the material removal mechanism through potential variation in the dielectric properties of the molecular medium, a quantifiable picture of the density variation within the separation gap is necessary, which is the focus of this manuscript.

2. Molecular Model and Simulation Method Molecular dynamics simulations in this work were performed with the code LAMMPS,40 distributed by Sandia National Laboratories. To study mechanical confinement effects (referred to as physical boundary conditions and both these terms are used interchangeably in the text hereafter), the simulation cell consists of gold atoms as both cathode and anode in the form of rectangular slabs with randomly generated n-decane chains between the surfaces, as shown in Figure 1a. The tools used in nano-EM have a typical end radius of 35 nm ((10 nm); thus, for the simulations here, the cathode is simply assumed to be a rectangular slab orientated so that [110], [111], and [112] crystallographic directions align with the X-, Y- and Z-axes, respectively. The global simulation cell employs periodic boundary conditions in the X- and Z-directions and nonperiodic boundary conditions in the Y-direction. The bottom {111} plane of atoms in the anode is prevented from moving in the Y-direction; all other atoms or molecules are free to move throughout the simulation. The organization of the molecular medium is further investigated by the deliberate introduction of ledges, as shown in Figure 1b. Four different ledge configurations are studied, although only one is discussed in this work as it is representative of n-decane’s behavior under any of these configurations. Table 1 provides a summary of the MD simulations in this work. The united atom (UA) model used by Siepmann et al.41,42 and Mondello and Grest43 is employed in this work for the n-decane molecular medium. In this model, the methylene (CH2) and methyl (CH3) groups are treated as single spherical interaction sites (pseudoatoms) with the interaction centers located at the centers of the carbon atoms. This interatomic potential employs a harmonic form44 for bond stretching, a theta harmonic form45 for angle bending, a cosine polynomial form46 for dihedral angle torsion, and the LJ form47 for nonbonded interactions. The LJ potential is truncated at a cutoff radius, rc = 2.5σij. The mass of the CH2 united atom is taken as 14.027 g/mol and that for CH3 as 15.035 g/mol. The embedded-atom method (EAM)48 potential is used for modeling gold atoms. Lorentz-Berthelot (LB) mixing rules are used for estimating the potential parameters for the

(40) http://lammps.sandia.gov/. (41) Siepmann, J. I.; Karaboni, S.; Smit, B. Nature 1993, 365, 330–332. (42) Smit, B.; Karaboni, S.; Siepmann, J. I. J. Chem. Phys. 1995, 102, 2126– 2140. (43) Mondello, M.; Grest, G. S. J. Chem. Phys. 1995, 103, 7156–7165. (44) Mundy, C. J.; Siepmann, J. I.; Klein, M. L. J. Chem. Phys. 1995, 102, 3376– 3380. (45) Aoyagi, T.; Sawa, F.; Shoji, T.; Fukunaga, H.; Takimoto, J.-I.; Doi, M. Comput. Phys. Commun. 2002, 145, 267–279. (46) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638–6646. (47) Girard, S.; M€uller-Plathe, F. Lect. Notes Phys. 2004, 640, 327–356. (48) Daw, M. S.; Baskes, M. I. Phys. Rev. B 1984, 29, 6443–6453.

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the NPT ensembles are chosen after a series of optimization runs.49 The X- and Z-dimensions of the simulation cell are allowed to expand or contract independently to conform to a pressure of 1.0 atm. In the Y-direction, the cathode (upper slab of gold atoms) is allowed to move vertically during the thermodynamic equilibration portion of the simulation, which is necessary to avoid subjecting the molecular medium to compressive pressures. A velocity-Verlet algorithm54 is used for integrating the equations of motion, and all simulations in this work are performed for 1  106 time steps with a time step size of 1 fs. The equilibrium separation between the gold {111} surfaces is computed after thermodynamic equilibration (data provided in Table 1), making sure to account for the atomic radius of the gold atoms on each side of the nanoconfined region.

3. Analysis Methods Figure 1. Initial configuration (before thermodynamic equilibration) of the n-decane medium. (a) The separation between atomically flat gold {111} surfaces is filled with 680 randomly oriented chains of n-decane. (b) A ledge (step) on the surface of the anode with a height equal to one atomic layer is introduced parallel to the Æ110æ direction.

unlike interactions.21 Parameters for each interatomic potential used in this work are provided in Table 2. The generation of the initial state is one of the most complex aspects of atomistic modeling of noncrystalline molecular systems. The “random order” of the molecular system must be correctly captured in order for atomistic simulations to yield reasonable and relevant results. In general, the criteria for a good configuration are to minimize the potential energy of the system and to create molecules that have realistic structural attributes such as end-to-end lengths, radii of gyration, and distribution of rotational isomeric states. The system should also be well dispersed and have an accurate density at a given temperature and pressure. In this work, the initial configuration of the n-decane molecular medium is generated using a custom-written selfavoiding random walk algorithm.49 Each chain consists of 10 united atoms (8 CH2 UAs in the middle, bounded on both the ends by 1 CH3 UA) constructed on a cubic lattice. Several configurations are generated to ensure that the randomness associated with the different configurations does not have any effect on the dynamical behavior of the system. Prior to MD simulation, the energy of the randomly generated n-decane chains is minimized using a nonlinear conjugate gradient algorithm. Energy minimization techniques do not guarantee that a minimum energy configuration will be found from the randomly generated configurations. However, minimization does bring the high-energy initial configurations to a local minimum energy state, adjusting the initial 90 build angles to the optimal bond angles for n-decane. MD simulations are performed in the NPT ensemble using the equations of motion developed by Melchionna et al.,50 which employ a Nose/Hoover style thermostat.51-53 Most calculations are performed at 450 K, although one set of simulations is performed at 300 K to provide insight into the role of temperature on the diffusion of the molecular medium across the gold {111} surfaces. The temperature and pressure damping parameters for (49) Kalyanasundaram, V. Masters Degree Thesis, University of Arkansas, Fayetteville, Arkansas, 2008. (50) Melchionna, S.; Ciccotti, G.; Holian, B. L. Mol. Phys. 1993, 78, 533–544. (51) Nose, S. J. Chem. Phys. 1984, 81, 511–519. (52) Nose, S. Mol. Phys. 1984, 52, 255–268. (53) Hoover, W. G. Phys. Rev. A 1985, 31, 1695–1697.

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To quantitatively characterize the molecular organization of the n-decane medium under nanoconfinement, density profiles are computed within the volume between the gold surfaces. The transition of the confined random molecular medium into an ordered structure can be correlated with an increase in local density as compared with its liquid (bulk) state. The density is computed by a custom-written FORTRAN code using two different methodologies. In the first methodology, the region between gold surfaces is “sliced” into 10 equal partitions to obtain the Yupper and Ylower bound limits for the density computation.18 The global simulation cell limits in the X- and Z-directions are used for Xupper and Xlower and Zupper and Zlower, respectively. In the second methodology, density is computed at 0.1 A˚ increments within the gap, calculated as the average over a 1 A˚ thick slice centered on each data point. Basically, this new method collects more data points portraying a more clear description of the local density variation as compared with the first methodology. To further characterize the organizational behavior of the n-decane medium quantitatively, radial distribution functions (RDFs), g(r), are computed for the terminal-terminal (CH3CH3) (referred to as T-T for further discussion), terminalmiddle (CH3-CH2) (referred to as T-M for further discussion), and middle-middle (CH2-CH2) (referred to as M-M for further discussion) units of the confined molecular medium. The RDF curves are obtained every 25 000 time steps histogrammed into 100 bins over a total distance of 9.7625 A˚ (the maximum cutoff distance for any of the UA type interactions). In the case of crystalline structured materials, since the atoms are regularly arranged, sharp peaks appear at specific positions in g(r). The occurrence of peaks at long-range indicates a high degree of ordering. The peaks are sharp in quasi-solid mediums as well, where atoms remain strongly confined to localized regions within the medium. The peaks become blunt if the medium is not organized or packed in a structural form, wherein atoms might be “locally” packed and/or arranged randomly overall. With increasing interatomic separation, the peaks gradually attenuate and eventually converge to a value characteristic of the average density of the medium. Finally, as a complement to the RDFs, the crystallographic orientation of the molecular medium on the gold {111} surfaces under nanoconfinement is analyzed.

4. Results and Discussion 4.1. Mechanical Confinement. It is found that organization of the n-decane medium as a result of mechanical boundary (54) Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. J. Chem. Phys. 1982, 76, 637–649.

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Kalyanasundaram et al. Table 1. Summary of the MD Simulations in This Work

no. of n-decane chains

gold {111} surface

T (K)

gap spacing at equilibrium (nm)

layers of n-decane at equilibrium

340 340 340 510 595 680 850 1020

atomically flat atomically flat ledge atomically flat atomically flat atomically flat atomically flat atomically flat

450 300 450 450 450 450 450 450

0.9318 0.8958 n/a 1.3158 1.3558 1.4058 1.8158 2.2508

2 organized 2 organized 2/3 organized 3 semiorganized 3 semiorganized 3 semiorganized 4 semiorganized 5 semiorganized

Table 2. Potentials and Parameters Used for the Simulations in This Work type of interaction

interatomic potential

potential parameters

bond stretch between two consecutive united atoms

harmonic: ubond(r) = 1/2k(r - r0)2

r0 = 1.545 A˚ k = 39.0623 eV/A˚2

angle bend between three consecutive united atoms

theta harmonic: uangle(θ) = 1/2k(θ - θ0)2

θ0 = 114.6 k = 5.3944 eV/rad2

bond torsion between four consecutive united atoms

cosine polynomial: utorsion(φ) = Σn=1,5An cosn-1 φ

A1 = 0.2094 eV A2 = 0.007042 eV A3 = -0.2699 eV A4 = -0.0141 eV A5 = -0.02181 eV

nonbonded CH2-CH2

Lennard-Jones: uij(rij) = 4εij[(σij/rij)12 - (σij/rij)6]

εij = 0.007597 eV σij = 3.905 A˚ εij = 0.00512 eV σij = 3.905 A˚ εij = 0.006237 eV σij = 3.905 A˚ εij = 0.01861 eV σij = 3.28 A˚ εij = 0.01861 eV σij = 3.28 A˚

nonbonded CH3-CH3 nonbonded CH3-CH2 nonbonded CH2-Au nonbonded CH3-Au

conditions can be divided into three groups of similar behavior. Figure 2a shows n-decane behavior characteristic of gap separations larger than 1.6 nm at thermodynamic equilibrium, where it is found that the molecular medium remains mostly unorganized as it is not constrained in its degrees of freedom and therefore has sufficient room for random molecular motion. Some n-decane chains in very close proximity to the gold surfaces lie flat. However, the majority of the chains show random and uninhibited motion during the MD simulation. Recall that the properties of fluids within a few monolayers of a solid surface are dominated by the interfacial effects, and hence the nature of the wall (gold)-fluid (n-decane) molecular interaction can have a significant influence on the confined liquid in the interfacial region.6,37-39 Over the course of the simulation, the confined medium remains stable in a mostly disordered state. Figure 2b shows representative n-decane behavior at gap separations between 1.0 and 1.6 nm at thermodynamic equilibrium, where it can be seen that the molecular medium remains in a partially organized state comprising locally organized and unorganized regions. Since the medium is not compactly confined, the chains that are not in close proximity to either gold {111} surface have more “room” for random motion, leading to an unorganized structure. Because of the interfacial interactions of the gold-n-decane medium, a good portion of the confined chains remain attracted to either of the gold {111} surfaces in a state parallel to the surface. Thus, as a combination of all of these effects, it is observed that the confined medium remains stable in a partially ordered state. 7556 DOI: 10.1021/la901285f

Figure 2. Snapshot of n-decane under nanoconfinement using (a) 850 chains, (b) 510 chains, and (c) 340 chains after 1 ns of thermodynamic equilibration. The chains are colored based on their chain number, and only 50 chains are shown in (a-c) for visual clarity. The separation distance between the gold surfaces at thermodynamic equilibrium for each case is provided in Table 1. Significant organization of the n-decane medium is observed at the gap spacing corresponding to 340 n-decane chains, as all of the chains lie flat on the gold {111} surfaces. (d) Top view showing the preferred orientation of n-decane molecular medium using 340 chains at 450 K. Langmuir 2009, 25(13), 7553–7560

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Figure 3. Density profile of n-decane molecular medium under nanoconfinement obtained by two different computational methodologies: (a) 340 chains, (b) 680 chains, and (c) 1020 chains. Two distinct layers are identified for gap separations associated with 340 chains, while at larger gap separations more liquidlike behavior is observed in the center of the gap separation.

Figure 2c shows representative n-decane behavior at gap separations less than 1.0 nm at thermodynamic equilibrium, where it is observed that the molecular medium is more organized, transitioning from a liquid to a solidlike state. Since the medium is confined at a thickness of approximately two molecular layers, the chains remain in close proximity to the gold {111} surfaces having a more densely packed state resembling a quasi-solid structure. Because of the strong nature of the gold-n-decane interaction and the related geometric effects, all of the confined chains remain attracted to either of the {111} surfaces in a state parallel to their respective gold surface. This clearly demonstrates the effect of severe nanoconfinement on the organization of the molecular medium. Clearly, under the physical boundary conditions alone, the ordering of n-decane medium gradually increases as the gap separation decreases. Similar behavior is reported for studies of water molecules under nanoconfined spaces.55 Cui et al.35 have observed similar behavior for dodecane (C12H26) films of thickness between three and eight molecular layers confined between mica surfaces at ambient temperature and pressure. They observed a dramatic transition from an unorganized liquidlike to an ordered solidlike structure when the confined film thickness was reduced from seven to six molecular layers. Thus, the present results match remarkably well with the observed behavior of n-alkanes under nanoconfinement in the literature. 4.2. Density Profiles. Figure 3 shows representative density profiles for the n-decane medium under nanoconfinement corresponding to gap separations at thermodynamic equilibrium of 0.932 nm (340 chains), 1.406 nm (680 chains), and 2.251 nm (55) Jung, D. H.; Yang, J. H.; Jhon, M. S. Chem. Phys. 1999, 244, 331–337.

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(1020 chains). Density profiles are approximately symmetric about the center axis, indicating an equilibrated distribution of n-decane within the nanoconfined volume. Density is computed using two different methodologies as discussed previously in section 3. Maximum density corresponds to the molecular layer that is closest to either of the gold {111} surfaces. The maximum local density of the molecular medium is approximately four times larger than the experimental bulk (liquid) density, indicating a more “close-packed” structure within the layer closest to the gold {111} surface during the nanoconfinement. Interestingly, the maximum local density does not appear to be influenced appreciably by the number of n-decane molecules within the gap, implying that molecular organization at the gold-n-decane interface is dominated by the strength of the nonbonded molecular interactions, and less impacted by the geometric details of the nanoconfinement (gap separation). This is consistent with previous simulations performed using LJ solid surfaces.17 Note that the two different methodologies for computing density produce different maximum local densities, although both follow the same pattern of density variation. The second methodology clearly provides a more complete picture of the density variation, indicating that methods used previously18 to compute density variation during nanoconfinement may not be sufficient. Particular attention must be drawn to minima and intermediate density oscillations as well. Figure 3 indicates that the local organization of the n-decane medium decreases gradually from the gold {111} surface toward the center of the nanosized gap; intermediate peaks indicate partially ordered local structure of the medium. Specifically, in the model with 1020 n-decane chains, shown in Figure 3c, the magnitude of each density peak decreases DOI: 10.1021/la901285f

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Figure 5. Crystallographic orientation of n-decane molecular medium on {111} gold anode surface using 340 chains at 450 K. The majority of the chains are oriented along close-packed Æ110æ crystallographic directions.

the further each peak is away from the gold {111} surface. As compared with the experimental density of 0.6136 g/cm3 and maximum bulk density of 0.725 g/cm3 for n-decane,56 the maximum local densities obtained here clearly indicate increased organization of the medium upon nanoconfinement. For very small gap separations, such as that associated with 340 n-decane molecules, the minimum local density obtained is zero, in agreement with visual evidence of the molecular organization in Figure 2c. The n-decane molecules are ordered into two distinct layers and cannot access the spaces in between the well-defined layers. For larger gap separations, such as that associated with 1020 n-decane molecules, the minimum local density does not reach zero and oscillates around the experimental bulk liquid density, implying that molecules are only semiorganized into separate layers and still primarily in the liquid state. Note that, in the model with 340 n-decane chains, density profiles are shown only for the simulation performed at 450 K; the density profile at 300 K follows a very similar pattern. 4.3. Radial Distribution Functions. Figure 4a shows that, for small gap equilibrium separations (filled with 340 n-decane chains), the M-M and T-M peaks are sharp indicating that atoms are positioned in an organized structure analogous to that of a solid. The first and second M-M and T-M RDF peaks are pronounced relative to the long-range peaks, indicating a quasisolid atomic arrangement. As expected, at higher temperature (450 K), the M-M and T-M peaks are comparatively broad,

indicating increased thermal vibration, while at low temperature (300 K) they are more sharp. At equilibrium gap separations between 1.0 and 1.6 nm, the M-M and T-M profile peaks become slightly blunt, as shown in Figure 4b relative to Figure 4a, but still appear at the same values of the interatomic separation distance as in Figure 4a, indicating that an organized structure is still maintained, although not uniformly throughout the system. The first and second M-M and T-M peaks are very similar in magnitude, indicating an intermediate state where the medium is neither completely solid nor completely liquid. This indicates that both phases coexist in the system under this level of nanoconfinement. In contrast, at large equilibrium gap separations, such as that associated with 1020 chains, an obvious change in the RDF is observed (although not explicitly shown for brevity). The M-M and T-M profile peaks are blunt comparatively with the other cases discussed, indicating there is less tendency toward molecular organization. In addition, the first M-M and T-M peaks are reduced in magnitude as compared to the second, indicating the packing structures closely resemble a pattern typical of amorphous solutions.57 The secondary peaks appear to indicate a maximum due to the formation of particle aggregates, and they are more blunt than the primary peaks, implying that the atoms are more scattered and randomly arranged. In all the cases, the first peaks of the M-M and T-M profiles of g(r) occur at similar interatomic separation distances; the distribution of the nearest neighbor distance (secondary peaks) is about the same, while long-range structures are different. Also, a number of obvious peaks appears in all cases indicating that atoms pack around each other in “packets” of neighbors but in varying numbers. In summary, these results indicate that at very small separations between the gold {111} surfaces (less than 1 nm) the n-decane molecular medium becomes organized in its structure even though it is liquid in the bulk. 4.4. Orientation Results. Investigation of preferential orientation of the n-decane molecular medium on the gold {111} surfaces provides more insight on the anisotropy induced in the nano-EM interface. Recall Figure 2c where it is shown that, for very small equilibrium gap separations (less than 1 nm), the

(56) Nielsen, S. O.; Lopez, C. F.; Srinivas, G.; Klein, M. L. J. Chem. Phys. 2003, 119, 7043–7049.

(57) Tsuchiya, Y.; Hasegawa, H.; Iwatsubo, T. J. Chem. Phys. 2001, 114, 2484– 2488.

Figure 4. Radial distribution function (RDF) curves for the terminal-terminal (CH3-CH3), terminal-middle (CH3-CH2), and middle-middle (CH2-CH2) units of n-decane molecular medium corresponding to (a) 340 chains at 300 K and (b) 680 chains at 450 K.

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Figure 6. (a) Top view of the gold {111} surface showing the organization of the n-decane molecular medium in the presence of a ledge. The gap separation is filled with 340 chains. (b) The gold {111} surface is removed from view to better illustrate the structure of the n-decane medium near the ledge. (c) Density profile of n-decane within the gap showing the nonuniform distribution of molecular medium due to the presence of the ledge.

n-decane chains lie flat on the gold {111} surfaces with their axis parallel to the surface. Only at that separation does the medium consistently resemble an organized structure regardless of the temperature at which the system is simulated. Hence, the anisotropy and order in the molecular arrangement for this case is evaluated by the topographical information of organized molecules and analyzing their crystallographic orientation on the gold {111} surfaces. Figure 2d shows the top view of one of the layers of n-decane molecules organized on the anode surface after 1 ns of thermodynamic equilibration, showing the preferred orientation of n-decane chains in certain crystallographic directions. It is found that the majority of n-decane chains are oriented in the Æ110æ direction on the {111} gold surface; the distribution of chain orientations is shown in Figure 5. One such example of a group of n-decane chains organized in Æ110æ directions is shown in Figure 2d. Other low-index orientations, such as Æ112æ and Æ123æ, are also observed. Of course, the Æ110æ direction represents the close-packed direction for the {111} oriented gold’s FCC structure, and the remaining directions represent the next preferred orientations for n-alkane chains as shown previously during studies of adsorption of longer n-alkane chains on unconfined gold surfaces.58-60 Thus, the molecular medium (58) Marchenko, A.; Xie, Z. X.; Cousty, J.; Pham Van, L. Surf. Interface Anal. 2000, 30, 167–169. (59) Baxter, R. J.; Teobaldi, G.; Zerbetto, F. Langmuir 2003, 19, 7335–7340. (60) Zhang, H.; Xie, Z.; Mao, B.; Xu, X. Chem.;Eur. J. 2004, 10, 1415–1422.

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organizes such that a greater number of chains can fit within the region, providing further evidence that quasi-solid behavior is achieved under nanoconfinement. 4.5. Influence of Surface Ledges. Four different ledge configurations (differentiated by orientation) are introduced deliberately on the gold {111} anode surface. Figure 6 shows a representative result of n-decane organization in the presence of a surface step; it is observed that the ledge indeed forms a constraint for the n-decane chains in their molecular motion with a noticeable effect on its organization. The chains are attracted toward the ledge boundaries, likely due to the increased ability of the chains to interact with the gold surface at the defect. Figure 6b shows only the molecular medium in the ledge region. It is observed that several chains lie with their axis parallel to the ledge axis under these conditions. However, the medium does not have the overall organization behavior as observed in the case without ledges, as is evident from the density profile shown in Figure 6c. The ledge creates a nonuniform spatial distribution of the molecular medium within the gap, with respect to the X- and Z-directions. This observation has profound relevance on the nano-EM process, as this nonuniformity likely plays a very strong role in the atomic accuracy of the material removal mechanism. The RDF curves for this case show that the M-M and T-M profile peaks are comparatively blunt, indicating a structure neither completely solid nor completely liquid, but a tendency favoring the solidlike state. DOI: 10.1021/la901285f

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5. Summary of Primary Conclusions The organization and behavior of n-decane in the nano-EM machining interface have been studied thoroughly using MD simulations. Three different ordering behaviors are observed under nanoconfinement: states of unorganized randomly oriented n-decane chains (at equilibrium gap separations of 1.6 nm or more), partially organized n-decane chains (at equilibrium gap separations between 1.0 and 1.6 nm), and quasi-solid n-decane chains organized into two distinct molecular layers (at equilibrium gap separations less than 1.0 nm). To characterize this organizational behavior quantitatively, the density distribution within the gap is computed showing a 4-fold increase in the maximum local density at the interface between the n-decane medium and the gold {111} surfaces. This maximum local density does not appear to be influenced by the number of chains or the size of the nanoconfined volume. Radial distribution functions also indicate that nanoconfinement triggers a change in the structure of the medium with more ordering observed for decreasing gap separation between the gold surfaces, with preferred

orientation toward the close-packed and other low-index directions on the gold surface. The deliberate introduction of ledges causes several n-decane chains to orient themselves parallel to the axis of the ledge. Simulations in this work provide significant evidence that, through the physical boundary conditions alone, the n-decane molecular medium undergoes a structural transformation from a bulk liquid to a quasi-solid under nanoconfinement. Further ordering is expected when subjected to the electrical field boundary conditions during nano-EM.61,62 This knowledge will pave the way for a thorough understanding of the nano-EM process mechanism and the machining protocol. It is hypothesized that the above observed organization of nanoconfined molecular medium has an impact on nano-EM by masking the work function of the cathode material as shown previously using Paschen curves.63 Ultimately, anisotropy in the dielectric function of the molecular medium and in the characteristics of diffusion within the machining interface will further determine nano-EM process speed and efficiency.

(61) Vegiri, A.; Schevkunov, S. V. J. Chem. Phys. 2001, 115, 4175–4185. (62) Ueda, K.; Iizumi, N.; Sakomura, M. Bull. Chem. Soc. Jpn. 2005, 78, 430– 434. (63) Kalyanasundaram, V.; Virwani, K. R.; Spearot, D. E.; Malshe, A. P.; Rajurkar, K. P. CIRP Ann. 2008, 58, 199–202.

Acknowledgment. The authors thank the National Science Foundation (NSF) for the financial support extended for this research through the CMMI Grant No. 0423698.

7560 DOI: 10.1021/la901285f

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