Molecular Dynamics Simulation of Oxygen Transport through n

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J. Phys. Chem. B 2009, 113, 456–464

Molecular Dynamics Simulation of Oxygen Transport through n-Alkanethiolate Self-Assembled Monolayers on Gold and Copper Piyush Srivastava,† Walter G. Chapman,*,† and Paul E. Laibinis*,†,‡ Department of Chemical and Biomolecular Engineering, Rice UniVersity, Houston, Texas 77005-1827, and Department of Chemical and Biomolecular Engineering, Vanderbilt UniVersity, NashVille, Tennessee 37235-1604 ReceiVed: August 14, 2008; ReVised Manuscript ReceiVed: October 13, 2008

Molecular dynamics (MD) simulations were performed to investigate the influence of molecular structure on the ability of n-alkanethiolate self-assembled monolayers (SAMs) on gold and copper to act as barrier films against through-film oxygen transport as relevant to the uses of these films in corrosion inhibition. Specific explorations focused on the effects of the packing density of the adsorbates, their chain length, and the size of the diffusing species. The MD simulations showed that the resistances offered by these monolayers against transport of small molecules strongly depend on the penetrant size and that the free volume alignment within these films has a large impact on the diffusivities of oxygen through them. The MD simulations revealed that the barrier for transport through these films increase by ∼0.3 to 0.6 kJ/mol for increases in their thickness of only roughly an angstrom. MD simulations show the existence of a middle section in these SAMs for n g 12 that was more crystalline and dense than the rest of the monolayer. The barrier resistances offered by these films toward oxygen transport, as calculated by the MD simulations, were a function of the crystallinity, density, and thickness of the middle section of the SAMs. Introduction 1-5

Self-assembled monolayers (SAMs) are a popular method for altering the interfacial properties of a surface, with most studies focusing on the structure-property relationships of these systems as they relate to the influences of tail group selection.5-15 The chain length of the adsorbate used to form the SAM can affect these properties as well as others associated with throughfilm processes as a result of changes to the structure, packing density, and crystallinity of the film. SAMs formed by the adsorption of n-alkanethiols [CH3(CH2)n-1SH] onto gold and copper surfaces have been shown to provide barriers for electron transfer7,16-19 and oxygen transport.20,21 This ability to shield the metal surfaces from small molecules such as oxygen has important implications in the fields of corrosion inhibition18-24 and molecular electronics.25 Our motivation for this work comes from various studies that have shown that the barrier properties of n-alkanethiolate SAMs on gold and copper depend strongly on their chain lengths, n.17-22,26,27 Experiments performed using cyclic voltammetry and electrochemical impedance spectroscopy (EIS) have revealed that the coating resistances of n-alkanethiolate SAMs on copper increase dramatically with chain lengths when n g 16 and are negligible in comparison for n e 12.18,26 The rate of oxygen transport through n-alkanethiolate SAMs on copper from XPS measurements was shown to decrease exponentially with the chain length, n, of the monolayer.20,21 Various electrochemical experiments performed on n-alkanethiolate SAMs on gold have also suggested a strong chain length dependence for their barrier properties.17,27 * Corresponding authors. E-mail: [email protected]; paul.e.laibinis@ vanderbilt.edu. † Rice University. ‡ Vanderbilt University.

The experimentally observed chain length changes in the barrier properties of n-alkanethiolate SAMs on gold and copper described above have been attributed to the increase in the crystallinity of the monolayer as the chain length increases, as has been observed by reflectance infrared spectroscopy.2,18,19 The structural information from these techniques provides an overall averaged structural analysis of the SAM, whereas smaller level structural features are likely operative in affecting the transport of species through the SAM. In general, there is a lack of quantitative structural information to firmly establish connections between the crystallinity and the barrier property of a SAM. Moreover, there is a transition region for 12 g n > 16 in n-alkanethiolate SAMs on gold and copper as detected by electrochemical measurements18,21 that signals the onset of superior barrier properties. This transition region indicates a complex interplay between various structural features such as the gauche conformer distribution and the local chain density and cannot be explained by the increase in the averaged crystallinity of the monolayer alone. Also, the experimental results do not elucidate the effect of the size of a penetrant on its transport through these monolayers. Therefore, a better understanding is required of the links between the observed barrier properties of these coatings and molecular level features such as penetrant size, the gauche conformation, and the local densities. We employed MD simulations to examine the issues raised above concerning the transport of oxygen through n-alkanethiolate SAMs on gold and copper. MD simulations have shown to be highly successful in capturing the structural properties of SAMs9,28-33 and for investigating the macroscopic property of wetting32,34 for SAMs. Also, MD simulations have been widely used to study the transport of small molecules through a variety of organic systems including lipid bilayers,35,36 polymers,37,38 and supported monolayers.39 MD simulations can help establish the relationship between the trends exhibited by the barrier

10.1021/jp807288e CCC: $40.75  2009 American Chemical Society Published on Web 12/19/2008

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properties of n-alkanethiolate SAMs on gold and copper and the structural features responsible for them. We selected SAMs on gold and copper for this investigation as these systems have been the subjects of experimental investigations and their structures, albeit related, are different. Specifically, the nalkanethiolates on gold organize to form a hexagonal lattice on a Au(111) surface with a packing density of ∼21.4 Å2/chain, where the chains adopt a 30° tilt from the surface normal.2,3 The molecules on copper adopt a roughly perpendicular orientation (i.e., tilt of ∼0°) and a higher packing density of ∼18.4 Å2/chain.2,5 The differences in packing are likely to influence available free volume space required for through-film transport. In this paper, we have performed MD simulations to explore the effects of penetrant size, chain length, and packing density on the transport of a small molecule through a self-assembled monolayer. These simulations allowed us to (1) calculate the diffusivities, free energy barriers, and the resistances offered by n-hexadecanethiolate SAMs on gold and copper against the transport of the different sized penetrants, (2) obtain quantitative information about the chain length dependence of the barrier properties of n-alkanethiolate SAMs on gold and copper, and (3) compare equilibrium structural features such as gauche population and local density distributions within n-alkanethiolate SAMs on gold and copper having different chain lengths. These MD simulations revealed various connections between the barrier properties of these monolayers and the responsible molecular scale structural features. Simulation Details 1. n-Alkanethiolate SAMs on Gold and Copper. We employed the molecular model for n-alkanethiolate [CH3(CH2)n-1S] SAMs of Hautman and Klein28 that consisted of n + 1 united atoms (a neutral sulfur atom, n - 1 methylene groups, and a methyl tail group) that were connected by rigid bond length constraints. Each united atom was represented by a single interaction site. The bond-bending potential for the united atoms was described by the expression

TABLE 1: Lennard-Jones Parameters for SAMs and Oxygen a

SAMs

O2d

site

σ (nm)

ε (K)

CH3 CH2 Sb S-Sc O2

0.3905 0.3905 0.355 0.425 0.336

88.1 59.4 126.0 200.0 120.0

a

Reference 28. b For the interactions between S and other atoms, except for S-S interactions. c For S-S interactions only. d Reference 41.

TABLE 2: Valence Parameters for SAMsa bond

S-CH2

CH2-CH2

CH2-CH3

rij (nm) angle Kθ (103 K/rad2) θ0 (deg)

0.1812 S-C-C 62.5 114.4

0.1530 C-C-C 62.5 109.5

0.1530

a

Adapted from refs 28 and 49.

TABLE 3: Parameters for the 12-3 Potential Described by Eq 4a CH3 CH2 S O2b

C12 (10-5 K nm12)

C3 (K nm3)

z0 (nm)

3.41 2.81 4.089 2.81

20.8 17.1 180.6 17.1

0.0860 0.0860 0.0269 0.0860

a Adapted from ref 28. b Parameters for the oxygen molecule were assumed to be the same as for the methylene group.

parameters, and rc is the cutoff distance. The intramolecular Lennard-Jones interaction operated only between atoms that were separated by at least three united atoms. United atoms interacted with the underlying metal substrate through a 12-3 potential:

V(z) ) 1 Vb(θ) ) Kθ(θ - θ0)2 2

(1)

where Kθ is a force constant, θ is the bond engle, and θ0 is an equilibrium bond angle. The metal-S-C bond angle was left unrestrained. The torsional potential was described by a series expansion in the cosine of the dihedral angle φ:

Vt(φ) ) a0 + a1 cos(φ) + a2 cos2(φ) + a3 cos3(φ) + a4 cos4(φ) + a5 cos5(φ) (2) where a0 ) 1116 K, a1 ) -1462 K, a2 ) -1578 K, a3 ) 368 K, a4 ) 3156 K, and a5 ) 3788 K for the hydrocarbon chain.28 The united atoms also interacted through a Lennard-Jones potential:

VL-J(rij) )

{

[( ) ( ) ]

4εij 0

σij rij

12

-

σij rij

6

rij e rc

(3)

rij > rc

where rij is the interatomic distance between a pair of united atoms i and j, εij and σij are Lennard-Jones interaction

C12 (z - z0)

12

-

C3 (z - z0)3

(4)

where C3 and C12 are 12-3 interaction parameters, z is the distance from the metal surface, and z0 is a constant. The interaction parameters were assumed to be the same for both gold and copper as the primary difference between the monolayers on the two metals is only in their grafting densities. Values for the parameters used in the simulations are listed in Tables 1, 2, and 3. All simulations were performed in the NVE ensemble. The equations of motion were integrated numerically for 200 ps utilizing the velocity Verlet algorithm with a time step of 0.005 ps. The equilibration period for every simulation was 150 ps, and the velocities were scaled to a temperature of 298 K during that period. The bond lengths in the n-alkanethiol molecules were constrained using the RATTLE algorithm.40 The cutoff distance used for the L-J potentials was 4.5σ, where σ is the segment diameter of the n-alkanethiol chains. For simulation of SAMs on gold, the MD cell consisted of chains arranged in the experimentally observed hexagonal lattice with a nearest-neighbor spacing of 0.497 nm. For SAMs on copper, the exact lattice arrangement is not known. However, preliminary MD simulations performed by us, assuming a hexagonal lattice and a nearest-neighbor spacing of 0.462 nm for SAMs on copper, were successful in capturing the experi-

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mentally determined structural quantities such as average chain tilt2 and monolayer thickness accurately. As such, we used this spacing in our MD simulations of n-alkanethiolate SAMs on copper. The above-mentioned lattice spacings correspond to grafting densities of 21.4 and 18.5 Å2/chain for n-alkanethiolate SAMs on gold and copper, respectively. As an initial state in our simulations, the chains were arranged in an all trans-zigzag-extended confirmation and stood normal to the surface. Periodic boundary conditions were used in the x and y directions for the SAM, and no periodic boundary condition was used in the z direction. The simulation cell consisted of 90 n-alkanethiolate molecules and a hard wall positioned above the SAM. The size of the simulation box was 11.02σ × 11.45σ × 11.02σ (length × width × height) for n-alkanethiolate SAMs on gold and 10.24σ × 10.66σ × 10.24σ for that on copper. 2. Oxygen Transport through n-Alkanethiolate SAMs on Gold and Copper. We employed the so-called z-constraint algorithm of Marrink et al.35 to compute the diffusivities, free energy barriers, and resistances against the transport of oxygen through the n-alkanethiolate SAMs on gold and copper. The starting chain configurations were obtained by equilibrating n-alkanethiolate SAMs on gold and copper for 300 ps. An oxygen molecule was then inserted and constrained at a particular z location in the monolayer and allowed to move only in the xy plane for 200 ps using a constraining force F(z,t). This process was repeated for different z positions chosen to sample the whole monolayer in equidistant steps. The oxygen molecule was described by a single L-J site.41 The interaction parameters for oxygen are listed in Table 1. The time average of the constraining force 〈F(z)〉t, was used to compute the local free energy barrier, ∆G(z), at a particular z position.

∆G(z) ) -

z 〈F(z')〉t dz' ∫outside

(5)

In eq 5, the constraining force was integrated from an outside distance 2.5σ away from the surface of the monolayer, where interaction forces with the SAM were considered negligible. The local diffusivity value in the z direction, D(z), was calculated using the fluctuation-dissipation theorem.42 In this process, the autocorrelation function, 〈∆F(z,t)∆F(z,0)〉, of the time fluctuations of the instantaneous constraining force, ∆F(z,t), was used to calculate the time-dependent local friction coefficient, ξ(z,t).

ξ(z, t) )

〈∆F(z, t)∆F(z, 0)〉 RT

(6)

The local static friction coefficient, ξ(z), was obtained by integrating ξ(z,t) over time:

ξ(z) )

∫0

∞

ξ(z, t) dt )

∫0∞ 〈∆F(z, t)∆F(z, 0)〉 dt RT

(7)

The local diffusion coefficient in the z direction, D(z), was then calculated using Einstein’s relation:

D(z) )

RT ) ξ(z)

(RT)2

∫0

∞

〈∆F(z, t)∆F(z, 0)〉 dt

(8)

Figure 1. Free energy barrier profiles for the transport of penetrants of 1, 2, and 3.36 Å in diameter through n-hexadecanethiolate SAMs on (a) gold and (b) copper, as calculated from MD simulations. Common Lennard-Jones interaction parameters for oxygen were used for all penetrants.

The overall resistance to permeation,35 R, was obtained using the local free energy barrier, ∆G(z), and the local diffusivity value in the z direction, D(z), by integrating over the entire thickness of the monolayer.

R)

∫outside z)0

( ∆G(z) RT ) dz

exp

D(z)

(9)

Results and Discussion MD Simulations of Transport of Penetrants of Various Sizes through n-Hexadecanethiolate SAMs on Gold and Copper. One factor likely to affect the transport properties of a species through a monolayer film is its size and how well the monolayer can accommodate this species within the film. To address the influence of penetrant size on the through-film transport for these systems, we performed MD simulations to provide comparative quantitative information about the transport of differently sized (σ) penetrants, each with properties similar to those of oxygensi.e., having the same L-J energy parameter (ε) as oxygensthrough both n-hexadecanethiolate SAMs on gold and copper. We selected n-hexadecanethiolate SAM on gold and copper for this study of penetrant size as the chain length of this SAM (n ) 16) is long enough to yield densely packed, well-oriented monolayers.18,32 Figure 1 shows the free energy barrier profiles obtained from MD simulations for the transport of penetrants of similar L-J interaction parameters but different sizes through n-hexadecanethiolate SAM on gold and copper using eq 5. On gold, the free energy barrier offered by the C16 SAM increased from 1.5 to 5.5 kJ/mol when the penetrant size increased from 1 to

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Figure 3. Schematic illustration of n-alkanethiolate SAMs on gold and copper depicting experimentally determined average tilt values of ∼30° and ∼0°, respectively.

Figure 2. Diffusivity profiles (in the z direction) for the transport of penetrants of 1, 2, and 3.36 Å in diameter through n-hexadecanethiolate SAMs on (a) gold and (b) copper, as calculated from MD simulations. Common Lennard-Jones interactions parameters for oxygen were used for all penetrants.

2 Å and further increased to 15 kJ/mol for a penetrant the size of oxygen (i.e., 3.36 Å). For n-hexadecanethiolate SAMs on copper, we computed the free energy barriers against transport to be 2.5, 6.5, and 20 kJ/mol for penetrant sizes of 1, 2, and 3.36 Å, respectively. The observed increases in the free energy barrier with penetrant size may be explained by the decrease in the free volume of the monolayer accessible to the penetrant as its size increases. For the same penetrant size, the free energy barrier for transport was generally less for the SAM on gold than for the SAM on copper as the latter has a higher grafting density and a lesser amount of accessible free volume. Figure 2 shows diffusivity profiles in the z direction for different sized penetrants within n-hexadecanethiolate SAMs on gold and copper as calculated from MD simulations by employing eq 8. The z direction diffusivities for the examined penetrants were of the order of 10-8 m2/s, which is an order of magnitude higher than the experimentally determined diffusivity value of 2.5 × 10-9 m2/s for oxygen in bulk hexadecane.43 The values of the diffusivities were found to be greater for smaller penetrants within the SAMs on gold as well as on copper, presumably a consequence of the greater accessible free volume in the monolayers for penetrants of smaller size. For the same penetrant size, the diffusivity value in the z direction was less through SAMs on gold than through SAMs on copper. The observation that penetrants of a same size diffuse faster in the z direction within an n-hexadecanethiolate SAM on copper than through this SAM on gold is intriguing and counterintuitive as the former SAM achieves a higher grafting density and consequently a lower accessible free volume than the latter. This seemingly odd observation may be explained in terms of the differences in the free volume alignment within the n-alkanethiolate SAMs on gold and copper. Figure 3 shows a schematic

Figure 4. Overall resistance to permeation for the transport of penetrants of 1, 2, and 3.36 Å in diameter through hexadecanethiolate SAMs on gold and copper, as calculated from MD simulations. Common Lennard-Jones interaction parameters for oxygen were used for all penetrants.

of n-alkanethiolate SAMs on gold and copper with their respective chain tilts of ∼30° and ∼0°, respectively, from the surface normal. It can be inferred that for SAMs on copper the free volume is more aligned in the z direction as compared to SAMs on gold. This contrast in the free volume alignments appears to be responsible for the trend displayed by the diffusivity values in the z direction for the penetrants of the same size in the n-hexadecanethiolate SAMs on gold and copper. Moreover, the free volume alignment in the z direction for the SAMs on gold and copper seems to explain the higher oxygen diffusivity in the z direction within n-hexadecanethiolate SAMs on gold and copper compared to the experimentally determined oxygen diffusivity in bulk hexadecane. Figure 4 shows the overall resistance to permeation offered by n-hexadecanethiolate SAMs on gold and copper against the transport of different sized oxygen-based penetrants as calculated by MD simulations using eq 9. The overall resistance increased dramatically with increasing penetrant size, likely as a direct result of the decrease in the monolayer free volume accessible to the penetrants. For small penetrants (σ ) 1 and 2 Å), the resistances offered by the n-hexadecanethiolate monolayers on both gold and copper were found to be similar for a particular penetrant size. This similarity in the resistances may be attributed to a lack of sensitivity by these penetrants due to their small size to the differences in the grafting densities of hexadecanethiolate SAM on gold and copper. For a penetrant the size of oxygen (σ ) 3.36 Å), the n-hexadecanethiolate SAM on copper displayed a substantially higher overall resistance against permeation than did the n-hexadecanethiolate SAM on gold. This difference in the resistance provided by the film at this penetrant size shows that an oxygen molecule is large enough for its transport to be sensitive to the differences in the grafting

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Figure 6. Overall resistance to permeation as a function of the chain length (n) for the transport of oxygen through n-alkanethiolate SAMs on gold and copper, as calculated from MD simulations. To facilitate comparison between SAMs having different chain lengths (n) and different canted structures, the resistances in s/m were multiplied by the thickness of the SAMs.

Figure 5. Free energy barrier profiles for the transport of oxygen through n-alkanethiolate SAMs having different chain lengths (n) on (a) gold and (b) copper, as calculated from MD simulations.

densities and the corresponding differences in free volume between n-hexadecanethiolate SAMs on gold and on copper. This penetrant size dependence revealed by MD simulations for transport through SAMs was found to be consistent with related studies performed of differently sized species through lipid bilayers.44-46 MD Simulations of Transport of Oxygen through nAlkanethiolate SAMs on Gold and Copper. To determine the effects of chain length and the associated structural changes to a SAM with chain length on the barrier properties of a SAM, we performed MD simulations to determine the free energy barriers and resistances offered by various n-alkanethiolate SAMs on gold and copper against oxygen transport using the z constraint algorithm (eqs 5-9). Figure 5 shows the free energy barrier profiles for oxygen transport through n-alkanethiolate SAMs of different chain lengths (n) on gold and copper as calculated by MD simulations. The free energy barriers were found to be 10, 14, 15, and 19 kJ/mol for SAMs on gold having chain lengths n of 8, 12, 16, and 20, respectively. The corresponding free energy barriers for SAMs on copper for these chain lengths were computed to be 19, 20, 20, and 22 kJ/mol, respectively. For SAMs on both gold and copper, the free energy barrier was greater for longer chain lengths, except for the region 12 e n e 16 where almost no change was observed. For a particular chain length, the free energy barrier for oxygen transport through the SAM on copper was higher than through the SAM on gold. This difference in the free energy barrier at each chain length reflected the higher grafting density of SAMs on copper as compared to SAMs on gold. In addition to the variations caused by differences in chain length and in substrate, there are several striking features in the free energy barrier profiles in Figure 5 that show some commonality across the different chain lengths. When viewed from a molecule being transported from the outer region to the metal surface, the outer part of the monolayer was responsible

for the initial slope of the free energy barrier profiles and was similar for all chain lengths for a particular metal substrate. The middle part of the SAM appeared to be the determining factor in the maximum of the free energy barrier eventually achieved by the monolayer against oxygen transport. The middle region for the longer chain lengths appeared to generate a region where the free energy barrier changed little with position, with the average value being greater for longer chain lengths and for systems on copper than on gold. The free energy barrier profiles examining the effects of penetrant size discussed above and displayed in Figure 1 exhibited similar features. Figure 6 depicts the overall resistance to oxygen permeation for n-alkanethiolate SAMs of different chain lengths (n) on gold and copper as calculated by MD simulations. The differences in the free energy barriers between SAMs on copper and gold in Figure 5 translated into roughly 10× greater resistances for SAMs on copper for a given chain length. On both substrates, the resistance plot shows a dramatic (>103×) change over the range of examined chain lengths (n ) 8-22). At the shortest chain lengths (n < 12), SAMs offered poor resistances against oxygen transport. With increasing chain length (n), the resistances improved greatly, showing lesser improvements by SAMs of intermediate chain lengths (12 e n e 16). The SAMs offering the highest resistances to oxygen permeation were those with the longest chain lengths (n > 16), where increases in resistance with chain length were much greater than those of intermediate chain lengths. This less dramatic change in resistance at intermediate chain lengths (12 e n e 16) correlates with the observation of little or no change in the free energy barrier values calculated for SAMs in this region (Figure 5). The differences in behavior for SAMs of shortest, intermediate, and longest chain lengths likely reflect subtle differences in the structure of these SAMs that are examined in detail in a later section. A broader view of the resistance data in Figure 6 is that they show a general exponential trend with chain length. This exponential chain length dependence is in good agreement with the experimentally observed trends for the rate of oxygen transport across n-alkanethiolate SAMs on copper using XPS20 and electrochemical methods.21 In order to further verify the trends displayed by the overall resistances to oxygen permeation as revealed by the MD simulations, we compared them with experimentally determined barrier properties of these coatings obtained by electrochemical

SAMs on Gold and Copper impedance spectroscopy (EIS). This comparison may seem unusual as MD simulations compute the resistance against oxygen transport whereas EIS measures resistance against the transport of ionic species offered by these monolayers. However, despite this difference, resistances against both ion and oxygen transport depend strongly on structural features of the SAMs such as their gauche population and their free volume. As a result, resistances obtained from experiments and MD simulations are expected to show a qualitatively similar chain length dependence. The MD simulations revealed that the coating resistances toward oxygen transport remained poor for nalkanethiolate SAMs on gold and copper of shortest and intermediate chain lengths, n < 16, and that the resistances improved markedly for n > 16 and increased further with increase in the chain length (n) of the monolayer. The experimental observations using EIS revealed that the coating resistances for n-alkanethiolate SAMs on copper were negligible for n < 16 and that there was substantial level of and improvement in the coating resistance for n g 16.18 No experimental data are available for the chain length dependence of the coating resistances of n-alkanethiolate SAMs on gold, but the trend is expected to be similar to that shown by n-alkanethiolate SAMs on copper as the films differ only in their grafting densities. SAMs on gold, owing to their lower grafting density, are expected to have lower coating resistances than SAMs on copper, which was confirmed by the calculated coating resistances from the MD simulations. In general, the trends displayed by the MD simulations were in agreement with the EIS measurements. However, one major difference between the EIS measurements and the results obtained from MD simulations was the chain length at which there is an onset of the superior barrier property coatings. Specifically, the MD simulations predicted that n-alkanethiolate SAMs with a chain length of n ) 16 have barrier properties that are similar to SAMs with chain lengths of n ) 12 and 14, whereas the EIS measurements showed that n-hexadecanethiolate SAMs display markedly better resistances than for monolayers having chain lengths of n ) 12 and 14. This discrepancy may result from experimental challenges associated with preparing high-quality monolayers on copper using shorter n-alkanethiols with chain lengths such as n ) 12 and 142 or to limitations in the potential model used in our MD simulations, which is not exact and could be responsible for this difference. Despite the discrepancy described above, the chain length dependence of the overall resistances offered by n-alkanethiolate SAMs on gold and copper toward oxygen transport as determined by MD simulations were in qualitative agreement with the experimentally observed trends. The MD simulations allow additional comparisons between SAMs of different chain lengths by providing valuable quantitative information about the free energy barriers and resistances for these monolayers. A detailed description of the structure of these coatings, as obtained from MD simulations and their relationship with the barrier properties observed experimentally and computationally, follows below. Equilibrium Structures from MD Simulations of nAlkanethiolate SAMs on Gold and Copper. Although the MD simulations results described above captured the broad trends exhibited by the experimentally determined barrier properties of these coatings, the molecular level origin of these observations is unclear. To provide insight into these connections, we performed MD simulations of n-alkanethiolate SAMs on gold and copper and analyzed their equilibrium structures. Our goal was to extract structural information such as the gauche population and local density for these monolayers and relate

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Figure 7. Profiles of gauche density at bonds along the alkyl chain for different chain lengths (n) of n-alkanethiolate SAMs on (a) gold and (b) copper as obtained from equilibrium MD simulations.

them to the coating resistance trends shown by simulations and experiments. The gauche population density of a monolayer is an indication of its crystallinity.19 A monolayer having a low gauche population density can be considered well ordered or crystalline and is likely to exhibit better barrier properties than those having higher gauche populations. Figure 7 shows the gauche density profiles for n-alkanethiolate SAMs of different chain lengths (n) on gold and copper as calculated by MD simulations. A dihedral angle, φ, defined by the configuration of four sequential carbon atoms in the alkyl chain, was considered gauche for cos φ g 0.5. The profiles in Figure 7 reveal that the gauche conformers present in a SAM are concentrated at the chain ends for chain lengths of n g 12, in good agreement with previous studies.30,32 The percentage of gauche conformers decreased with increasing chain length for SAMs on gold and copper, indicating a greater level of crystallinity within these monolayers. For a particular chain length (n), SAMs on copper had a lower percentage of gauche conformers than did SAMs on gold, reflecting the higher grafting density and consequently higher crystallinity of the former system. An interesting feature displayed by these gauche profiles was the appearance of a middle section along the chain that had a substantially lower gauche population than the terminal regions for monolayers having chain lengths of n g 12. This middle part became progressively longer and more ordered or crystalline for SAMs having chain lengths of n g 12. For SAMs formed from the longest n-alkanethiols (n > 18) on copper, the gauche percentage was near zero along more than half of the chain. The local density of a monolayer is a measure of its local free volume. A monolayer having a higher local density or a lower local free volume would be expected to display better barrier properties against transport. Figure 8 depicts the average local densities for n-alkanethiolate SAMs on gold and copper

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Figure 9. Fraction of dihedral angles along the chain backbone having fewer than 1% of their average configurations as gauche as a function of the chain length (n) of the SAM. Results were obtained from equilibrium MD simulations of n-alkanethiolate SAMs on gold and copper.

Figure 8. Average local density around each segment number (m) of the chain as obtained from equilibrium MD simulations of nalkanethiolate SAMs on (a) gold and (b) copper having different chain lengths (n). In the figure, m ) 1 denotes the sulfur atom and m ) n + 1 denotes the terminal methyl group of the SAM.

as a function of the segment number, m, where m ) 1 denotes the sulfur atom and m ) n + 1 denotes the terminal methyl group of the monolayer. The reciprocal of local densities were obtained by calculating the differences in the average z positions of alternate chain segments (zm+2 - zm) in a SAM as a function of the segment position, m, from equilibrium MD simulations and then multiplying them by the average chain area. These calculations using MD simulations revealed that the SAMs were able to pack themselves to remarkably higher densities (>1 g/cm3) as compared to crystalline polyethylene and polypropylene (∼0.95 g/cm3).47 The densities for n-alkanethiolate SAMs were also considerably higher than the corresponding nalkanethiols and n-alkanes in the bulk.48 These densities computed by using MD simulations compared favorably with a density value of ∼1 g/cm3 calculated for n-hexadecanethiolate SAM on gold, by assuming the experimentally determined grafting density of 21.4 Å2/molecule, a 100% coverage, and a measured ellipsometric thickness of 20 Å. The local densities around the sulfur headgroup were substantially higher than the rest of the monolayer, demonstrating the effect of the strong anchoring provided by the metal-sulfur bonding. Additionally, the local densities around the methyl tail group were marginally higher than that for the preceding methylene segment due to their higher relative mobility and the effect of surface reorganization events at the chain ends. SAMs on copper displayed higher densities as compared to SAMs on gold, reflecting the tighter chain packing in the former system. The density of the SAMs was found to increase with increases in the chain length (n) on both gold and copper, similar to the trend observed in densities for n-alkanethiols and n-alkanes in the bulk.48 In Figure 8, the middle part of the chain exhibits appreciably higher local densities than for the rest of the monolayer for SAMs having chain lengths of n g 12. Moreover, this middle part becomes longer and undergoes enhanced compaction in the monolayers

with increasing chain lengths. This suggestion of increased structuring by the middle part of the chain in these SAMs is compatible with that observed in the gauche profiles (Figure 7), where regions of lower gauche densities were observed to form in the middle section of the longer chained SAMs. Figures 7 and 8 suggest that a part of the SAM is present within the chain with a highly dense and well-ordered structure and that its extension depends on the chain length of the SAM. To quantify the extent of the SAM in this more ordered state, Figure 9 plots the fraction of dihedral angles within a SAM with gauche populations of less that 1% as a function of the chain length (n) of the n-alkanethiolate SAMs on gold and copper. This gauche population fraction may be considered as a measure of the relative crystallinity of the monolayers having different chain lengths. The cutoff value of 1% was chosen arbitrarily and had no effect on the general shape of the curves. The trends in Figure 9 show that the monolayers become progressively more crystalline as the chain length increases and that SAMs on copper contain chains with a higher fraction of trans-extended configurations than for SAMs on gold of a common chain length. The trends displayed by the gauche profiles, the local density profiles, and the relative crystallinity (Figures 7, 8, and 9, respectively) obtained from MD simulations of n-alkanethiolate SAMs on gold and copper indicate that the chains consist of distinct regions of better packed and less packed structures. The relative fraction of the chain in these states depends on the chain length of the n-alkanethiol and the metal support. Longer chain lengths and metal supports that produce higher chain grafting densities lead to greater regions and fractions of the chain in a more crystalline state. These variations in structure can be used to explain the trends observed in Figure 6 in the dependence of the overall resistance of a SAM to its chain length. Figure 10 illustrates the structural differences that exist between SAMs on copper of increasing chain lengths. At the shortest chain length (n ) 8) on copper, the SAM is packed less densely (Figure 8) and with lesser organization (Figure 7) than for the other SAMs on copper. Increases in the chain length from n ) 8 to n ) 12 lead to reductions in the levels of gauche conformers (Figure 7), resulting in dramatic improvements in film resistance with increasing chain lengths (Figure 6). Further increases in chain length from n ) 12 to n ) 16 show slight decreases in gauche densities along the chain; however, continuous chain segments of near-zero gauche density do not appear for these SAMs (Figure 7). As the gauche density change little

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J. Phys. Chem. B, Vol. 113, No. 2, 2009 463

Figure 10. Structural overview of the regions present within n-alkanethiolate SAMs on copper as a function of their chain length (n). At shortest chain lengths (n < 12), the density of gauche conformers is at its greatest, with films decreasing in gauche content with increasing chain lengths. At intermediate chain lengths (12 e n e 16), chain ends have the highest density of gauche conformers. At longest chain lengths (n > 16), the interior region resembles a dense, highly crystalline state with outer regions containing some gauche conformers. The size of this crystalline domain increases with chain length and provides a dominant resistance to transport through the film. The lightest shading denotes regions of highest gauche density, the medium shading denotes regions of lower gauche density, and the darkest shading denotes regions that resemble crystalline hydrocarbon chains that contain almost no gauche conformers.

Figure 11. Number of dihedral angles along the chain backbone having fewer than 1% of their average configurations as gauche as a function of the chain length (n) of the SAM. Results were obtained from equilibrium MD simulations of n-alkanethiolate SAMs on gold and copper. The inset shows the coating resistances in MΩ cm2 as measured by EIS for n-alkanethiolate SAMs on copper as a function of the chain length (n) of the SAM.18

and the chain does not yet transition to forming extended regions in a highly no-gauche structure, the resistance of the film of these chain lengths show only slight differences (Figure 6). At the longest chain lengths (n > 16), the SAM contains a middle region devoid of gauche conformers (Figure 7) in a highly compacted state (Figure 8). With increasing chain length, a longer span within the monolayer adopts this highly ordered structure that may be reasoned to be nearly crystalline. The barrier properties of these crystalline regions are superior to those present at the lower chain lengths, and SAMs having n > 16 show greater improvements in resistance with chain length than for those with n < 16 (Figure 6). An overall view of the structure of the SAM is one that is not fully ordered for n > 16, but instead one that contains an inner ordered alkyl region that increases in size (thickness) with increases in chain length (n) (see Figure 10). As a result, above n ) 16, SAMs on copper exhibit substantial improvements in their barrier properties that improve further with increases in n. The above discussion suggests that the coating resistance of a SAM on copper is related to length of the chain present in a highly crystalline state. Figure 11 plots the absolute number of dihedral angles with gauche populations less that 1% for various n-alkanethiolate SAMs on gold and copper as a function of their chain length (n). The inset shows coating resistances for

n-alkanethiolate SAMs on copper as a function of their chain length as determined by EIS measurements.18 Figure 11 shows that the number of bonds in a predominantly trans configuration increases linearly with the chain length of the monolayer. We note that our choice of 1% in Figure 11 as a cutoff in gauche population is arbitrary, and other values yield similar trends. Each of these crystalline segments within the SAMs may be considered as a resistor in series, with each offering equal resistance toward transport through the monolayer. As the chain length of the SAM increases, the total resistance provided by the monolayer will tend to increase linearly due to the linear increase in the number of the crystalline segments. Further, as a certain chain length is required before segments can adopt the requisite crystalline state for providing high levels of resistance, this linear relationship should not begin at the origin. Together, these factors yield a trend (Figure 11) that is mirrored by the coating resistances obtained through EIS measurements18 of n-alkanethiolate SAMs on copper (see inset). We note that SAMs with chain lengths of n < 16 gave EIS coating resistances that were negligible (Figure 11, inset), in contrast with the linear progression predicted by MD simulations for all chain lengths from n ) 8 to 22. This difference may be attributed to difficulties in preparing fully covered, defect-free monolayers on copper from shorter chain length (n < 16) n-alkanethiols,2 an assumption that is implicit in our MD simulations. The results from the equilibrium MD simulations firmly establish the crucial role that molecular level structural features such as the gauche conformations and the local densities have in determining the barrier properties of these monolayers. The degree of crystallinity, the extent of compaction, and the thickness of a more organized inner region within the SAMs on gold and copper appear to be the key factors responsible for the computationally and experimentally observed trends. Conclusions We performed MD simulations to investigate oxygen transport through n-alkanethiolate SAMs on gold and copper. The MD simulations showed that the diffusivities, free energy barriers, and resistances for these monolayers are strongly affected by attributes of the penetrant and structural features of the SAMs. The free volume alignment within these systems plays an important role in determining the diffusivities of species through these films. Structural variations in the films, as affected by the grafting density of chain to the substrate as well as the

464 J. Phys. Chem. B, Vol. 113, No. 2, 2009 chain length of the n-alkanethiol comprising the SAM, result in differences in the resistance of these films toward oxygen transport. Specifically, longer chain lengths result in SAMs that contain greater regions within the film that are characterized by achieving high local densities and low levels of gauche conformers. The structural state within the SAM is not uniform, but instead varies along its thickness, with chain ends providing regions that offer the least resistance for transport and inner regions that offer the most. It is the state of this inner region and its extension within the SAM that are responsible for the dramatic changes in film resistance that occur with changes in chain length. Acknowledgment. We gratefully acknowledge the financial support of the Dow Chemical Company and the NSF Center for Biological and Environmental Nanotechnology at Rice University (CBEN, EEC-0118007). This work was supported in part by the Rice Terascale Cluster funded by NSF under Grant EIA-0216467, Intel, and HP. References and Notes (1) (a) Allara, D. L.; Nuzzo, R. G. Langmuir 1985, 1, 52–66. (b) Nuzzo, R. G.; Allara, D. L. J. Am. Chem. Soc. 1983, 105, 4481–4483. (c) Bain, C. D.; Troughton, E. B.; Tao, Y.-T.; Evall, J.; Whitesides, G. M.; Nuzzo, R. G. J. Am. Chem. Soc. 1989, 111, 321–335. (2) Laibinis, P. E.; Whitesides, G. M.; Allara, D. L.; Tao, Y.-T.; Parikh, A. N.; Nuzzo, R. G. J. Am. Chem. Soc. 1991, 113, 7152–7167. (3) Ulman, A. Chem. ReV. 1996, 96, 1533–1554, and references therein. (4) Laibinis, P. E.; Palmer, B. J.; Lee, S.-W.; Jennings, G. K. In Thin Films: Self-Assembled Monolayers of Thiols; Ulman, A., Ed.; Academic Press: New York, 1998; Vol. 24, pp 1-41. (5) Love, J. C.; Estroff, L. A.; Kriebel, J. K.; Nuzzo, R. G.; Whitesides, G. M. Chem. ReV. 2005, 105, 1103–1169, and references therein. (6) (a) Bain, C. D.; Whitesides, G. M. Angew. Chem., Int. Ed. Engl. 1989, 28, 506–512, and references therein. (b) Whitesides, G. M.; Laibinis, P. E. Langmuir 1990, 6, 87–96, and references therein. (7) Chidsey, C. E. D.; Loiacono, D. N. Langmuir 1990, 6, 682–691. (8) (a) Dubois, L. H.; Zegarski, B. R.; Nuzzo, R. G. J. Am. Chem. Soc. 1990, 112, 570–579. (b) Nuzzo, R. G.; Zegarski, B. R.; Korenic, E. M.; Dubois, L. H. J. Phys. Chem. 1992, 96, 1355–1361. (9) Hautman, J.; Bareman, J. P.; Mar, W.; Klein, M. L. J. Chem. Soc., Faraday Trans. 1991, 87, 2031–2037. (10) (a) Prime, K. L.; Whitesides, G. M. Science 1991, 252, 1164–1167. (b) Mrksich, M.; Whitesides, G. M. Annu. ReV. Biophys. Biomol. Struct. 1996, 25, 55–78, and references therein. (c) Sigal, G. B.; Mrksich, M.; Whitesides, G. M. J. Am. Chem. Soc. 1998, 120, 3464–3473. (d) Chapman, R. G.; Ostuni, E.; Takayama, S.; Holmlin, R. E.; Yan, L.; Whitesides, G. M. J. Am. Chem. Soc. 2000, 122, 8303–8304. (e) Ostuni, E.; Chapman, R. G.; Liang, M. N.; Meluleni, G.; Pier, G.; Ingber, D. E.; Whitesides, G. M. Langmuir 2001, 17, 6336–6343. (f) Holmlin, R. E.; Chen, X.; Chapman, R. G.; Takayama, S.; Whitesides, G. M. Langmuir 2001, 17, 2841–2850. (g) Qian, X.; Metallo, S. J.; Choi, I. S.; Wu, H.; Liang, M. N.; Whitesides, G. M. Anal. Chem. 2002, 74, 1805–1810. (11) Laibinis, P. E.; Whitesides, G. M. J. Am. Chem. Soc. 1992, 114, 1990–1995. (12) Laibinis, P. E.; Bain, C. D.; Nuzzo, R. G.; Whitesides, G. M. J. Phys. Chem. 1995, 99, 7663–7676. (13) (a) Kim, H. I.; Koini, T.; Lee, T. R.; Perry, S. S. Langmuir 1997, 13, 7192–7196. (b) Lee, S.; Puck, A.; Graupe, M.; Ramon Colorado, J.; Shon, Y.-S.; Lee, T. R.; Perry, S. S. Langmuir 2001, 17, 7364–7370. (14) Aizenberg, J.; Black, A. J.; Whitesides, G. M. J. Am. Chem. Soc. 1999, 121, 4500–4509. (15) Lee, S.; Puck, A.; Graupe, M.; Colorado, R., Jr.; Shon, Y.-S.; Lee, T. R.; Perry, S. S. Langmuir 2001, 17, 7364–7370. (16) Zamborini, F. P.; Crooks, R. M. Langmuir 1997, 13, 122–126.

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