Supramolecular Structure of the Monolayer Triggers OddâEven Effects

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Supramolecular Structure of the Monolayer Triggers Odd-Even Effects in the Tunneling Rates across Non-Covalent Junctions on Graphene Peng Song, Damien Thompson, Harshini V. Annadata, Sarah Guerin, Kian Ping Loh, and Christian A. Nijhuis J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12949 • Publication Date (Web): 16 Jan 2017 Downloaded from http://pubs.acs.org on February 6, 2017

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The Journal of Physical Chemistry

Supramolecular Structure of the Monolayer Triggers Odd-Even Effects in the Tunneling Rates across Non-Covalent Junctions on Graphene Peng Song,1 Damien Thompson,2 Harshini V. Annadata,1 Sarah Guerin,2 Kian Ping Loh,1,3 and Christian A. Nijhuis*,1,3 1

Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore

117543, Singapore. 2

Department of Physics, Bernal Institute, University of Limerick, V94 T9PX, Ireland.

3

Centre for Advanced 2D Materials and Graphene Research Centre National University of

Singapore, 6 Science Drive 2, Singapore 117546, Singapore.

*To whom correspondence may be addressed. Email: [email protected]

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Abstract: Molecular electronics aims to control charge transport at the molecular level but it is not always clear which factors are important to control because it is difficult to distinguish interface effects from molecular effects. Investigating so-called “odd-even” effects in molecular tunnel junctions provides an opportunity to study molecular effects while keeping the nature of the molecule—electrode interactions unchanged. Odd-even effects in charge tunneling rates have been observed in self-assembled monolayer (SAM) based tunnel junctions with strong covalent molecule-bottom electrode interactions, but it is not clear whether these odd-even effects originate from the intrinsic properties of the SAM or strong molecule-electrode interactions. Herein, we report tunnel junctions based on SAMs that form on graphene through weak non-covalent interactions (i.e., van der Waals interactions) and also form a van der Waals contact with the top-electrode. We found that odd-even effects in charge tunneling rates persist in these junctions with only non-covalent interfaces. AC impedance spectroscopy measurements and molecular dynamics calculations indicate that the odd-even effects of charge transport rates mainly arise from intrinsic properties of the SAM packing and thus these effects should be considered as a general design rule in future SAMbased junctions.

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Introduction Odd-even effects in structure-property relations are widely observed in physical chemistry, surface science, and biology.1-7 Odd-even effects in materials properties are caused by an odd or even number of a repeat unit of the molecule and manifest themselves in myriad ways at both macroscopic and microscopic scales including melting points, surface energies, electron transfer rates, and packing structures of, e.g., polymers,8, 9 self-assembled monolayers (SAMs)1-3, 5, 10-15 and liquid crystals.4, 6 In molecular electronics, odd-even effects in the tunneling rates have been observed in tunneling junctions based on SAMs with alkyl backbones where CH2 is the repeat unit.2, 16-18 In these studies all components of the junctions (electrode material, nature of SAM-electrode interfaces) were kept the same except for the number of the repeat unit and the odd-even effects are believed to be driven by strong molecule–electrode interactions. This belief is at odds with the large body of data showing odd-even effects too in systems that lack interfaces1, 19 and therefore we wish to address the following question: What drives odd-even effects in SAM-based tunneling junctions and are odd-even effects ubiquitous in molecular electronics? In other words, should odd-even effects (and possibly other effects that affect the supramolecular structures of SAMs) be considered as an integral part of the design of all future SAM-based junctions? So far, odd-even effects have only been observed in junctions with SAMs strongly interacting with the bottom electrode via metal–thiolate bonds or monolayers of molecules bound via covalent bonds to Si which set the molecule–electrode bond angles and consequently dictate the orientation of the terminal group of the monolayer (Figure 1).2, 16-18, 20-22

Whitesides et al.2, 16 measured an odd-even effect in the tunneling rates across junctions

of M-SCn//GaOx/EGaIn where SCn is short for S(CH2)n-1CH3, “//” indicates a van der Waals interface, “-” indicates a covalent (-1.7 eV, or 40 kcal/mol, bond energy)23 metal-molecule contact, and “/” indicates the interface of the eutectic alloy of Ga and In (EGaIn) coated with



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a self-limiting conductive gallium oxide surface (GaOx),24, 25 and M is the bottom electrode. Their study reports odd-even effects for junctions with Ag bottom electrodes,2 but in a subsequent study using a differently shaped GaOx/EGaIn top electrode the authors found oddeven effects in junctions on Au but not on Ag.16 They argued that the fixed M-S-C and C-C-C bond angles cause the terminal CH3 group to either point towards or away from the top electrode causing an odd-even effect in the SAM//GaOx/EGaIn interaction and, consequently, in the observed tunneling rates. They argued that odd-even effects are more pronounced for SAMs with large tilt angles (~30°) on Au than for SAMs with small tilt angles (~11°) on Ag. Toledano et al. 18 reported odd-even effects in the tunneling rates in junctions of the form of Si-CnPh//Pb (where Ph is a phenyl group) which were rationalised based on the metalelectrode contact angle. By contrast, we recently found that the odd-even effect in the contact resistance in junctions of AgTS-SCn//GaOx/EGaIn is too small to account for the observed odd-even effects in the tunneling rates.17 We proposed that the intrinsic SAM packing structure (an odd-even effect in the twist angles) causes odd-even effects.17, 26 A common thread in these studies is the assumption that a strong SAM–bottom electrode interaction is important to induce odd-even effects. However, this assumption has not been tested and the question remains as to whether or not odd-even effects are unique to a subset of systems. This has the important consequence that we do not yet know if selection of odd vs. even length molecules should be an integral part of the rational design of all molecular electronic devices. Odd-even effects in the melting points of fatty acids date back to 1877.27 Solid molecular materials such as thiols,7 alkanes,19 and fatty acids,28 display odd-even effects in many of their bulk properties yet they do not possess strongly interacting molecule-substrate interfaces. X-ray structures for a broad range of alkane chain lengths19 show that the odd-even effects are the sole result of van der Waals interactions between neighboring CH3 groups. Figure 1b schematically shows how the two terminal CH2CH3 units of each molecule either point in the


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same or opposite directions with respect to the backbone of the molecule. In the solid state, alkanes pack in rows driven by the intramolecular interactions and the odd-even effect in melting points is caused by the odd-even effect in van der Waals interactions between the terminal CH3 groups of neighboring rows: for even-numbered (neven) alkanes both CH3 units at opposite ends of the molecule can interact optimally with neighboring molecules, but for odd-numbered (nodd) alkanes only one end of the CH3 units can interact well because the other points directly to its neighboring CH3 resulting in steric hindrance. Hence, nodd alkanes have lower melting points than neven alkanes. Here we report odd-even effects in SAM-based junctions that consist of only van der Waals interfaces. Long et al.29 showed that SAMs of alkylamines (H2N(CH2)n-1CH3, or H2NCn in short) readily form on graphene and these SAMs were very recently incorporated into EGaIn-junctions.30 These SAMs are long-lived30 and molecular models show that the SAMs form ordered, well-packed monolayers with weak ~220 meV/molecule (5 kcal/mol) van der Waals interactions between the amine anchoring groups and the graphene substrate.29-31 The classical molecular dynamics models (see Methods for details) were validated using the post-Hartree–Fock ab initio Møller–Plesset perturbation theory method. We formed H2NCn SAMs with n ranging from 8 to 16 on graphene freshly grown on copper by chemical vapor deposition32 using previously reported procedures.29 These SAMs were contacted using GaOx/EGaIn top electrodes24, 25 and Figure 1a shows schematics of the tunnel junctions which have the form Cu//graphene//H2NCn//GaOx/EGaIn. The electrical properties of the junctions were investigated using J(V) (current density vs. applied voltage) measurements and impedance spectroscopy to determine the contact resistance (RC, in Ω·cm2), the SAM resistance (RSAM, in Ω·cm2) and capacitance (CSAM, in µF/cm2) using an equivalent circuit (Fig. 1c). We found an odd-even effect in the charge transport across Cu//graphene//H2NCn//GaOx/EGaIn junctions with J(V) measurements and corresponding



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odd-even effects in RSAM and CSAM with impedance spectroscopy. Molecular dynamics calculations indicate that the odd-even effect in the measured charge transport rates has contributions from odd-even effects in SAM-graphene physisorption ∆Eads and in SAM packing energy ∆Epack, and these computed molecular properties are further supported by DFT electronic structure calculations.

Figure 1. Illustrations of the tunnel junctions, the odd-even effect, and the equivalent circuit. (a) Schematic illustration of the Cu//Graphene//H2NCn//GaOx/EGaIn tunnel junction and (b) the intrinsic odd-even effect of the alkylamines (the arrows indicate the orientation of the top -CH2CH3 unit and bottom -CH2NH2 unit relative to the molecular axis indicated by the dashed lines). (c) The equivalent circuit of the tunnel junctions.

Experimental Section Molecular dynamics computer simulations. The models and simulation protocols are similar to those described previously,30 with more extensive sampling and analyses performed for the models used for the current study as described below. In brief, calculations modelled the self-assembly of 784 molecules (for each SAM of H2NCn with n=8-16) on a single-layer graphene sheet of area 13 nm × 15 nm. Graphene carbons were constrained to 6 ACS Paragon Plus Environment

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their lattice positions throughout the simulations. Each film was relaxed using 20,000 steps of steepest descent minimization with respect to the CHARMM22 force field33 and then brought to room temperature by gradually raising the temperature from 0 to 295 K over 2 nanoseconds of dynamics while simultaneously loosening positional constraints on the SAM non-hydrogen atoms. Each model was then subjected to 50 ns of free dynamics with no constraints on the SAM to allow extensive sampling and quantification of odd-even effects in well-equilibrated, constant-density structures. The computed odd-even effects as given in the main text are robust with respect to the sampling procedure; the same values to within a few percent were obtained from block averages taken over the full 50 ns and from sample sets with the first 10, 20 or 25 ns dropped, and from datasets using structures obtained by sampling every 50, 100 or 200 ps along the MD trajectories. DFT calculations. To calculate Young’s modulus (YM) values from DFT we used simulation cells of single alkylamine molecules in periodic orthorhombic cells (hexagonally packed in the directions normal to the plane of the molecule and well separated in the direction parallel to the plane of the molecule, to reflect the SAM molecule-molecule environment) in the range nc = 8-16. The odd-even effect at each point is the standard deviation of the calculated value away from the expected value for a putative linear YM vs. nc relationship, e.g., at nc = 9 the value plotted is the difference between the YM value calculated for nc = 9 and the average of the YM values calculated for nc = 8 and nc = 10. Positive values at nodd and negative values at neven indicate a larger YM value for molecules with an odd number of carbon atoms. All calculations were carried out using the Vienna Ab initio Simulation Package (VASP),34 using plane wave basis sets and the projector augmented-wave (PAW) method.35 Exchange-correlation effects were treated using density functional theory (DFT) via the Perdew, Burke, and Ernzerhof (PBE) implementation of the Generalised Gradient Approximation (GGA).36 All simulation cells were optimised using 7 ACS Paragon Plus Environment


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conjugate gradient minimisation. A 4 × 4 × 4 gamma centred k point grid was used, with a plane wave energy cut off of 600 eV. A finite differences method was used to calculate the elastic stiffness tensor, with six finite distortions of the lattice being carried out. A 2 × 2 × 2 gamma centred Monkhorst-Pack k-point mesh was used, and the plane wave energy cut off was 1000 eV to allow the stress tensor to converge fully due to the presence of nitrogen atoms. The elastic compliance tensor was then extracted by inverting the stiffness matrix. The Young’s Moduli were calculated using the formula for the inverse modulus of an orthorhombic unit cell (Method I).37 To calculate the dielectric constant, we constructed the amines of the form H2NCn with n = 8-16 in a unit cell. A typical example (n=8) is shown in Figure S3. The values of surface coverage from MD calculations (described above) were used to estimate the area of the square base in the xy plane. There is a vacuum of 15 Å in the z-direction. We performed geometry optimization using DFT as implemented in the SIESTA code.38 Double zeta basis sets with 150 Ry mesh grid, cut-off radius of 0.02 Ry, 3 × 3 × 1 Monkhorst-Pack k-point meshes, Troullier-Martins normconserving pseudopotentials and generalized gradient approximation (GGA) exchange correlation functional of Perdew-Burke-Ernzerhof36 were used for all calculations. The force convergence criterion was less than 0.01eV/Å on each atom. To determine the dielectric constant of substrate-less monolayers, we used Ratner’s model.39 Using this model, a symmetric electric field of ± 5.14 × 108 V/m was applied and the change in the net dipole moment was used to get the value of induced polarization along z-axis. This polarization was used to calculate εDFT. These calculated values of dielectric constant are always higher than the experimental values. Using the same molecular model, we calculated the odd-even effect in YM of the SAMs using a different approach (Method II). Strains of 0.1% to 0.5% were applied on the monolayer along the z axis shown in Figure S3.


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Since this is still in the linear range of the stress-strain curve, the slope was used to calculate YM. Growth and characterization of graphene. The copper foil (99.8%, Alfa Aesar, No. 13382) was first electropolished following previously reported methods40, 41 to give a clean and smooth surface. Briefly, the copper foil was used as anode and another copper plate was used as the cathode. The electropolishing solution was a mixture of 500 mL of deionized water (PURELAB, Option-Q, 18.2 MΩ cm), 250 mL of phosphoric acid (Sigma-Aldrich, 85 wt. % in water), 250 mL of ethanol, 50 mL of isopropyl alcohol and 5 g of urea. A constant voltage of 8.0 V was applied using a DC power supply (TEXIO PD18-30AD) and the solution was stirred at a speed of 1000 rpm. The electropolishing was performed for 2 min, after which the copper foil used as the anode was rinsed with deionized water, isopropyl alcohol and dried with N2 flow. The electropolished copper foil was used for chemical vapor deposition of graphene.32 The Cu//graphene substrate was characterized with atomic force microscopy (AFM) and the AFM images were recorded with a Bruker Dimension FastScan AFM (FASTSCAN-A, resonant frequency: 1.4 MHz, force constant: 18 N/m) in tapping mode. Raman spectroscopy was performed using a WITEC alpha300 R Raman system equipped with a 532 nm laser (spot size 1.0 µm2). Formation and characterization of SAMs. SAMs of H2NCn were formed on Cu//graphene substrates by following reported procedures29. Typically, 18 mM solutions of the alkylamine (99%, Sigma-Aldrich) of interest were prepared in a mixture of methanol and tetrahydrofuran (HPLC grade, VWR international, volume ratio: 1:9). The solutions were purged with N2 for 15 min prior to the immersion of Cu//graphene substrates (1.5 × 1.5 cm2) for 18 h. The substrates were rinsed with the solvent mixture (three times, ~3 mL each time) and dried with N2. All chemicals were used as received without further purification. To collect Raman spectra, graphene was transferred onto Si wafer with 300 nm SiO2 using reported method.32 9 ACS Paragon Plus Environment


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SAMs of H2NC11 and H2NC12 were formed on the transferred graphene and the Raman spectra were collected with the WITEC alpha300 R Raman system equipped with a 532 nm laser. Fabrication of the junctions. We used cone-shaped GaOx/EGaIn and PDMS confined microfluidic GaOx/EGaIn top electrodes to fabricate the junctions using previously reported procedures.30, 42 Cone-shaped GaOx/EGaIn top electrodes were formed to contact SAMs on graphene to construct junctions for DC charge transport measurements. The PDMS confined microfluidic GaOx/EGaIn top electrode forms junctions with SAMs simply by placing it gently on the surface. The fabrication of the top electrodes with the GaOx/EGaIn confined in a through-hole in PDMS and the fabrication of the junctions with these electrodes have been described elsewhere42. The geometrical area of the electrode was determined by optical microscopy. Charge transport measurements. We collected the charge transport data of Cu//Graphene//H2NCn//GaOx/EGaIn junctions by following previously reported procedures21. In a typical measurement of one junction (i.e., one contact), we collected the J(V) data of one scan (0 V +1.0 V -1.0 V 0 V in steps of 50 mV), followed by 3 scans, and then a further 20 scans for junctions found to be stable. For each SAM, approximately 20 junctions were fabricated on two to three different substrates and each cone-shaped top electrode was used to measure approximately ten junctions (See Table S1). The data were recorded with Keithley 6430 source meter and processed using home-made code in LabView 2010. Impedance measurements. PDMS confined microfluidic GaOx/EGaIn top electrodes were used to fabricate junctions and J(V) curves were collected between -0.5 and +0.5 V. Stable junctions with electrical characteristics within one log-standard deviation of G were chosen for the impedance measurements, which were performed with a Solartron impedance/gain-phase analyzer (model 1260A with 1296A dielectric interface). By applying 10 ACS Paragon Plus Environment

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a sinusoidal signal (amplitude: 30 mV, frequency: 1 MHz to 1 Hz) at zero bias, five impedance spectra for each junction were recorded with sMaRT (v3.2.1) software with a standard 10 pF capacitor as the external reference. Average data derived from the five spectra were used to fit to the equivalent circuit with EIS spectrum analyzer software.

Results and discussion Molecular dynamics (MD) simulations. The structures of H2NCn SAMs on graphene for n = 8, 10, 12, 14, and 16 have been reported elsewhere.30 We performed MD simulations to study the SAM-graphene interface and the SAM packing structure in more detail for the full range of SAMs with n = 8-16. The H2NCn molecules assemble into upright SAMs on graphene driven by the van der Waals interactions between the alkyl chains of neighboring molecules and the van der Waals interactions between the amine groups and graphene.29-31 Figure 2 shows the top (Fig. 2a) and side views (Fig. 2b) of computed SAM structures with n = 8, 9, 12, 13, and 16. Figure S1 shows the structure of the other SAMs.29, 30 FigureS3 shows the Raman spectra for graphene with H2NC11 and H2NC12 SAMs. The Raman data with both neven and nodd SAM showed an unchanged D band, blue shifted (~ 7 cm-1) G band and decreased intensity ratio of 2D and G band, i.e., the I2D/IG ratio, from 3.5 to 1.5 upon SAM adsorption, all characteristic of a delocalized π-electron graphene electronic structure that is not perturbed by the presence of the SAM. From these data we conclude that the SAM//graphene interface is non-covalent in nature in agreement with previously reported data.29,30 The MD data in Figure 2 show high-density SAMs formed on graphene. The SAM thickness (d, in nm) increases linearly (with no detectable odd-even effect) by 1.3 ± 0.1 Å and Epack improves by 2.1 ± 0.5 kcal/mol per additional CH2 unit. The surface coverage of the SAMs (Г, in 10-10 mol/cm2) show an odd-even effect of 0.09 ± 0.04 × 10-10 mol/cm2, except



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when n > 14, which may be due to the inherent lowering of order for the very long SAMs as gauche defects build up in the backbone torsion angles. We find small but numerous and persistent odd-even effects in the SAM structure (Fig. 2e and 2f). The pro-odd odd-even effect of 0.13 ± 0.08 kcal/mol in Epack , i.e., molecules with an odd number of carbons pack better than molecules with an even number of carbons, coincides with an opposite (and similarly sized) pro-even effect in Eads of 0.08 ± 0.03 kcal/mol. These small values are in contrast to the odd-even effects of 0.4-0.6 kcal/mol in Epack computed for ferrocene-alkanethiolates on noble metals which give in turn large odd-even dependence on computed film packing energy, molecule flexibilities, and terminal group tilt angle, that were used to rationalize a large measured odd-even effect on the electrical performance of the junctions.21, 22 The MD data in Fig. 2 suggest that the thermodynamic driving forces for SAM assembly are different in physisorbed alkylamine-on-graphene SAMs than in alkanethiolateon-metal SAMs (that have a similar structure but a chemisorbed SAM-electrode contact). The effects are small but examination of the data in Fig. 2 indicates that neven molecules generally exhibit stronger amine-graphene contacts and higher Г. For these physisorbed SAMs with a small NH2 anchoring group the increase in Г for neven SAMs gives a higher population of repulsive sub-5 Å methyl-methyl contacts (Fig.2f), illustrating the subtle effects, and balance of those effects, in molecular, supramolecular and SAM-electrode structure that determine whether a given molecule will perform well in SAM based tunnel junctions. The main conclusion from the MD data is that the non-covalent alkylamine–graphene contact does not dictate the SAM packing (in contrast to alkanethiolates chemisorbed to coinage metals) but instead allows the amine anchoring group to form a large population of inter-amine H-bonds akin to those formed in free-standing non-substrate supported monolayers.31 The mismatch between amine and methylene van der Waals contacts gives the


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alkyl groups only very small tilt angles (below 7°, Figure S2) similar to those of nalkanethiolates on Ag, and triggers an odd-even effect in Epack (as reflected also in alkyl chain flexibilities (root-mean-square fluctuations, RMSF) and populations of methyl-methyl steric clashes (N), Fig. 2f). The computed nodd improvement in SAM packing is counterbalanced by stronger SAM-graphene physisorption (and thus higher Г) for neven. We propose that the SAM-graphene interface stabilization for neven may underlie the experimentally measured improvement in charge transport for devices made with neven molecules (larger J, see below). The effect of switching from a chemisorbed SAM to the physisorbed SAM reduces the SAM order (calculated RMSF values increase 3-4 times relative to chemisorbed alkanethiol-on-Au SAMs43) which we expect will reduce if not remove any odd-even effect in the contact between the methyl hydrogen atoms and the top electrode.16, 17 Rather, the physisorbed contact introduces an odd-even effect in the SAM-bottom electrode interface which would be precluded by the formation of stronger thiol-metal bonds in junctions made using alkanethiolates on coinage metals. The intrinsic packing difference of alkylamine SAMs are further supported by the odd-even effect of calculated Young’s modulus (YM) values of the SAMs (inset of Fig. 2f). The odd-even effect in YM persists across two different calculation methods (Fig. S4 and S5). The pro-odd effect of YM is consistent with pro-odd effect in Epack and RMSF and supports the prediction from MD that nodd molecules form more ordered, less dynamic SAMs. Although differences in the surfaces coverages are difficult to measure experimentally, AFM based friction and nano-indentation experiments can in principle detect the odd-even effects in SAM packing energy and Young’s modulus.44, 45



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Figure 2. Molecular dynamics calculations of the SAMs on graphene. (a) Top views and (b) side views of SAMs with different n on graphene. An approximately 4-5-molecule in radius central region of the SAM is shown for n=8, 9, 12, 13, and 16; the full simulation cells each contain 784 H2NCn molecules assembled on a 13 × 15 nm2 graphene sheet. (c) Calculated SAM height as a function of nC. (d) Calculated surface coverage of SAMs as a function of nC. The estimated error bars are 0.02-0.06 × 10-10 mol/cm2, averaged over hundreds of molecular dynamics snapshots of SAM regions containing hundreds of molecules. The inset shows the odd-even difference (∆Г) of Г. (e) Odd-even difference (∆E) of Epack and Eads. The estimated error bars are 0.05-0.10 kcal/mol. (f) Odd-even difference of RMSF (∆RMSF) and the number of repulsive sub-5 Å inter-methyl contacts (∆N). The estimated error bars for 14 ACS Paragon Plus Environment

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∆RMSF are 0.05-0.12 Å. The estimated error bars for ∆N are 0.08-0.15 contacts per molecule. The inset is the plot of odd-even effect of Young’s modulus (∆YM) estimated from DFT calculations of the molecules (without graphene). All odd-even difference values (∆Г, ∆E, ∆RMSF, ∆N, ∆YM) at each chain length are the deviation of the value at n from the average of values at n+1 and n-1.

Molecular length dependent charge transport. We used graphene on copper as the bottom electrode for our SAM junctions. The graphene was freshly grown by chemical vapor deposition to eliminate transfer of the graphene (which would involve exposure of the graphene to difficult-to-remove polymers and Cu etchant) which in turn avoids contamination and ensures good quality SAMs. The copper substrates were electropolished prior to graphene growth to ensure clean and smooth surfaces (see AFM image in Figure S6).40, 41 The SAMs were formed using a previously reported method29 and we formed the GaOx/EGaIn top contact using a cone-shaped tip of GaOx/EGaIn.17 We recorded and analysed statistically large numbers of J(V) data to determine the log-average J(V) curves following previously reported methods.46 In total, we recorded 4375 J(V) traces (0→1.0 V→1.0 V→0 in steps of 50 mV) for all junctions with an average yield of 92%. For each applied voltage, we determined the Gaussian mean of the values of log10|J|, or G, and the log-standard deviation (σlog) by fitting Gaussian functions to the histograms of log10|J|. Figure S7 shows the histograms, with Gaussian fits, of log10|J(± 1.0)| for all junctions. Figure 3 shows the average J(V) traces (G vs. V) of the junctions as a function of n from which a clear odd-even effect in the value of G is visible: junctions with neven SAMs have higher values of G than junctions with nodd SAMs.



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Charge tunneling through potential barriers imposed by organic molecules can be described by the general tunnel equation (1), where β ( ) is the tunneling decay constant, d is the thickness of SAMs (in units of number of carbons in the alkyl chain, nC), and J0 is the pre-exponential factor (A/cm2). The subscript “even” and “odd” refers to even and odd values of n.

= , = ,

(1a) (1a)

To derive the values of β and J0 from J(V) data, we fitted eq. 1 to all data by minimizing the absolute values of the error (least absolute deviation fitting, LAD). Compared with the fitting to G (Fig. S8), LAD gives more precise values of β and J0 because it does not rely on any assumption regarding the distribution of the data and uses all values of log10|J|.46 Our analysis of J(-1.0) yields values of βeven = 1.06 ± 0.01 and log10|J0|even = 1.94 ± 0.08 A/cm2 for neven and βodd = 1.02 ± 0.01 and log10|J0|odd = 0.96 ± 0.16 A/cm2 for nodd. All error bars represent 95% confidence levels. Plots of J vs. nC with the value of J(+1.0) (Fig. S9) yield indistinguishable values and indicate that the analysis is robust with respect to choice of negative or positive biases. To determine the statistical significance of the odd-even effects in the values of J0 and β, we calculated the probability (p) of the null hypothesis that log10|J0|odd = log10|J0| even and βodd = βeven,46 which is 1.0 × 10-4 and 2.3 × 10-3, respectively. For both null hypotheses the computed p values are < 0.05 and we thus conclude that log10|J0|odd < log10|J0| even

at the 95% confidence level. We note that the values of log10|J0| are affected by the SAM-

electrode interfaces. The odd-even difference in log10|J0| is larger than that observed in junctions with alkanethiolate SAMs on Ag or Au electrodes by a factor of 2-3, which may be explained by the computed odd-even difference in Eads in the NH2//graphene interface, while the Eads at S-Ag (Au) interface is constant. The S-metal bond strength can be tuned by 16 ACS Paragon Plus Environment

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incorporation of isolated molecules into SAMs, change in pH and change in contact time,47 but is not affected by the chain length in alkanethiol-on-Au SAMs.48 By contrast our data indicates that the weak vdW amine-graphene is affected by chain length, which in turn provides a molecular-level rationale for the measured SAM electrical properties. The values of β are also slightly different in our datasets, and we note that similarly small but signifiant differences in β were also observed in other studies with junctions of organothiolate SAMs.2, 16, 17

Figure 3. Plots of the Gaussian mean of the values of |J| (G) vs. applied bias for junctions with (a) neven and (b) nodd H2NCn SAMs (0→+1.0 V→-1.0 V→0 in steps of 50 mV).



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(c) Plots of all values of log10|J| determined at -1.0 V vs. n with the LAD fits (solid lines) to equation 1 and the corresponding 95% confidence level (dashed lines).

Impedance spectroscopy. To probe the origin of the measured odd-even effect in more detail, we characterized the junctions by impedance spectroscopy following previously reported procedures.25 To collect the impedance spectra, we used GaOx/EGaIn stabilized in microchannels in PDMS (a transparent rubber of polydimethyl siloxane)25, 42 as top electrodes and selected junctions with J(V) characteristics within one σlog of G (Fig. S10). We applied a sinusoidal signal with an amplitude of 30 mV in the frequency range of 1 Hz to 1 MHz and measured the impedance spectra (Fig. S11 shows the Nyquist plots). All impedance data were validated with Kramers-Kronig (KK) transformations (see Fig. S12 for the KK residual plots and Table S2 for χ2KK) and fitted to the equivalent circuit (see Fig. S13 for the residual plots of the fits and Table S2 for χ2fit) following previously reported procedures.49 The electrical response of the SAM to the applied bias in the junction is represented by the equivalent circuit (Fig.1c), which is used to separate “interface effects” (RC) and “molecular effects” (RSAM).17, 30 The value of RSAM is given by equation (2), where RSAM,0 is the pre-exponential factor.

, = ,, (2a) , = ,, (2b) Figure 4 shows all circuit components as a function of d. The values of RC are similar for all junctions (1.2 - 2.5× 10-2 Ω·cm2) but follow a weak odd-even effect in ∆RC of 2.0 ± 1.5 × 10-3 Ω·cm2 indicating that the contribution of contact resistance to the observed odd-even effect in the J(V) data is negligible (Fig. 4a). By contrast, in EGaIn junctions with SCn SAMs on Ag, i.e., SAMs with chemisorbed contacts to the bottom electrodes and a physisorbed


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contact to the top electrode, we found a 2 times larger odd-even effect in RC (but also here RC is

Supramolecular Structure of the Monolayer Triggers OddâEven Effects

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