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Molecular Mechanisms of Solvent-Controlled Assembly of Phosphonate Monolayers on Oxide Surfaces Hanno Dietrich, and Dirk Zahn J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05750 • Publication Date (Web): 04 Aug 2017 Downloaded from http://pubs.acs.org on August 8, 2017

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The Journal of Physical Chemistry

Molecular Mechanisms of Solvent-Controlled Assembly of Phosphonate Monolayers on Oxide Surfaces Hanno Dietrich, Dirk Zahn* Lehrstuhl für Theoretische Chemie / Computer Chemie Centrum Universität Erlangen-Nürnberg Nägelsbachstr. 25 91052 Erlangen Germany E-Mail: [email protected] Keywords: Self-assembled monolayer, growth mechanism, kinetics, molecular simulation.

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Abstract

The explicit role of a series of solvents in octadecylphosphonic acid (ODPA) association and monolayer formation on the (0001) surface of α-aluminum oxide is explored from molecular dynamics simulations. For this purpose, molecule-by-molecule attachment and subsequent relaxation is studied in hexane, THF and 2-propanol, respectively. From a purely structural viewpoint, the simulations show that the packing and ordering of the resulting SAMs closely resembles that of monolayers initially grown in vacuo, followed by immersion into the solvent afterwards. In terms of the formation kinetics, we however find significant dissimilarities which result from solvent structuring at the interface and considerable hindering of surfactant association to the template surface at later stages of SAM growth. This leads to drastic deviation from diffusion-controlled kinetics and calls for a time-dependent picture of SAM formation mechanisms.


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Introduction In recent years, self-assembled monolayers (SAMs) of organic molecules have gained much attention in both academia and industry as they are easily fabricated and have a broad range of possible applications.1–3 SAMs can be used for simple tuning of surface properties such as hydrophobicity and tribology4,5 but may also serve as dielectrics or semiconducting layers in organic electronics and sensors.6–9 The adsorption kinetics and thus the quality of the resulting monolayer, however, depend on many parameters that govern the complex interplay of the interactions between the surfactant, the surface and the solvent. In most experiments, the solvent is chosen merely by the solubility of the surfactant, although even the earliest systematic investigations indicated that the choice of solvent may have a dramatic effect on the formation mechanism and the ordering within the final monolayer.10,11 Despite this important influence, only few studies address the role of the solvent for the self-assembly process and the underlying effects are not very well understood.10,12–16 For endgroup-modified alkanethiols on gold, Danneberger et al. found by means of in situ second-harmonic generation that adsorption is faster in apolar solvents (n-hexane), but the ordering within the layer is better when the SAM is formed in a more polar solvent such as ethanol.15 A better SAM-quality of n-octadecanethiol on copper was also found by Zhang et al. using polar solvents (acetone, acetonitrile, ethanol).17 These authors hypothesize that the apolar solvents (n-hexane, toluene) allow for greater flexibility of the aliphatic chains and thus decrease the ordering. Similar results were obtained by Mekhalif et al., who studied SAM formation of nalkanethiols on polycrystalline nickel surfaces, where adsorption from ethanol was found to be slow but yielded high-quality monolayers, whereas hardly any adsorption was observed in toluene and n-hexane.18,19


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In order to gain detailed insight into the interactions between solvent, surfactant and surface, in situ analysis techniques are necessary, as quenching the assembly process and drying the sample may substantially alter the monolayer structure. However, only few in situ techniques provide a sufficient spatial and time resolution to obtain insight into the growth mechanisms at molecular level. Here, molecular dynamics simulations have proven to be of great avail in explaining experimental observations.7,20–23 We recently presented first steps in this direction by studying the formation of monolayers of octadecylphosphonic acids on α-Al2O3 (0001) in the gas phase.24 To illustrate the solvent effect, snapshots from these simulations were immersed in hexane and 2-propanol, respectively. Relaxation runs showed that both 2-propanol and hexane have a significant ordering effect by filling voids in between the adsorbed surfactants. The effect is much more pronounced in 2-propanol which is fully in line with above mentioned experimental results. Solvent-promoted SAM ordering suggests a better accessibility of the surface for further adsorption and thus faster kinetics of SAM growth. In our previous simulation study the solvent was added after SAM deposition in the gas phase, thus allowing only indirect, structural insights into the solvent effect, whilst its role during individual association steps and kinetics could not be deduced. To overcome this limitation the present study aims to extend our atomistic simulation scheme for the deposition of surfactant molecules on template surfaces to explicit solvent consideration and to discuss the molecular-level mechanisms involved.

Models and Methods Apolar hexane (εr=1.9, Polarity 0.9%), polar but non-protic tetrahydrofuran (THF, εr=7.6, Polarity 21%) and protic 2-propanol (εr=18.3, Polarity 54.6%) were chosen as solvents for octadecylphosphonic acid (ODPA).25 To explore ODPA diffusion in bulk solution, the three


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solvents were treated in separate runs, each comprising a single solvated ODPA molecule within periodic simulation cells (cubic) of ~7.5 nm in each dimension. After relaxation, constanttemperature, constant-pressure simulations of 50 ns were performed at 300 K and 1 atm, respectively. From this diffusion constants were calculated from the Einstein equation, whilst considering migration along x, y and z directions separately to assess error margins of the approach (Figure S1, see SI). For analysis of the solvation layers at the interface to a 16 × 16 × 1 (6.61 × 76.7 × 1.2 nm3) slab of hydroxyl-terminated (0001) surface of α-Al2O3 as adopted from previous work,24 three parallel model systems were prepared each with a solvent layer of ca. 8.0 nm thickness. As interfacial layers are typically extended over 1-3 nm, this choice ensures a sandwich model comprising at least 2 nm of bulk solution. After relaxation, production runs of density profiles were based on a 5 ns run. An additional nanosecond was sampled with a snapshot every 0.1 ps to analyze the residence times and to confirm convergence of the density profiles. To impose ambient pressure, a custom built 2D-barostat (a stamp on top of the solvent layer) was used to maintain atmospheric pressure as described in previous studies21,26 and implemented for the LAMMPS software package.27,28 Next, the association of a phosphonic acids (PA) to the surface was characterized from welltempered metadynamics simulations29 using the implementation in the Colvars package30 for LAMMPS. To enhance the sampling we focused on the anchoring group by actually investigating the association of a single methylphosphonic acid molecule in each solvent. To that end, the PA molecule was placed on the surface in a 6.5 nm thick layer of solvent over only a quarter of the original slab (8 × 8 × 1 unit cells, 3.30 × 3.82 nm2) in order to save computational effort. As collective variable we chose the z-position of the phosphorous atom rather than the


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PA’s center of mass, since the former also reveals information on the orientation of the molecule on the surface. During metadynamics, repulsive potential hills with a width of 0.1 Å and a weight of 0.01 eV were added every 0.5 ps. The simulations were run until convergence of the respective potential of mean force which was observed at 300 ns, 800 ns and 1100 ns in hexane, THF and 2-propanol, respectively, due the slower diffusion rate and the stronger ordering of contact layers in the polar solvents. Finally, the growth of an ODPA monolayer was studied from molecule-by-molecule deposition, followed by relaxation – based on the Kawska-Zahn technique as described for SAM formation in ref. 24. In each iteration, a new molecule is added 2.5 Å above the solvent layer in (lateral) vicinity of a vacant binding site and is dragged towards the alumina surface by a bias force of 0.83 nN (=50 kJ mol-1Å-1) applied to the phosphonic acid anchor group for at most 100 ps (Figure 1a). If an acidic proton of the anchor then forms a hydrogen bond to a suitable surface hydroxide with a maximum O–H distance of 2.5 Å, the proton transfer is carried out by removal of the resulting water molecule and switching of the phosphonate force-field. Otherwise, the SAM growth iteration is considered as a failed attempt and the procedure is restarted with a new ODPA molecule at a different position (Figure 1b). After successful proton transfer and removal of the water molecule produced, the system is allowed to equilibrate for another 50 ps followed by a 200 ps run for data collection (Figure 1c). The simulation setup is hence essential the same as in our previous work, the only extension being the implementation of solvent layers (and a barostat stamp) on top of the SAM-substrate interface.24 To allow for comparability, we used the same hydroxyl-terminated α-Al2O3 (0001) slab of 16 × 16 × 1 unit cells as in previous work, along with the same combination of the Generalized Amber Force Field and the alumina force field developed by Sun et al.31,32 While the force field


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described above has the advantage that the full charges of +3 and –2 for aluminum and oxygen reflect the strong binding of the deprotonated phosphonates very well (Figure S2, see SI), it certainly overestimates the interactions with non-covalently associated molecules such as the solvent and the fully protonated phosphonic acid molecules. Thus, for these interactions we used the tailor-made CLAYFF model, rather than the GAFF force field. DFT calculations as shown in Figure S2 in the Supporting Information show that physisorption is reproduced better with CLAYFF, whereas the interaction with condensed PAs as needed for the phosphonate SAM growth simulations is much too weak with CLAYFF and best described by GAFF using formal charges on Al3+ and O2- ions. For the molecular dynamics simulations an integration time step of 1 fs was chosen and a cutoff of 12 Å was applied to non-bonded interactions in all of the simulations within this work. Electrostatic interactions were treated with a damped shifted coulomb potential.33 Constant temperature was implemented by the Berendsen thermostat34 using a relaxation time of 0.5 ps.

Results and Discussion Octadecylphosphonic acid (ODPA) migration in solvents of different polarity To characterize ODPA diffusion in the bulk solvent, three simulation runs were carried out each with a single ODPA molecule in a 3D-periodic cubic box of the respective solvent. The diffusivity of ODPA is highest in hexane followed by THF and 2-propanol (Table 1). This reflects the difference in attractive forces both between the solvent and ODPA, and within the solvent itself – which also accounts for different diffusion constant of the respective solvent


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molecules (Table 2). While the interaction in hexane is purely based on weak van-der-Waals forces, the intrinsic dipole moments of THF and 2-propanol are much stronger. In addition, hydrogen bonds significantly impede diffusion. In THF H-bonds can be formed only between the protons of ODPA and the ether oxygen of the THF molecules. Indeed, each proton is stabilized by an average of one hydrogen bond throughout the length of the simulation. The phosphoxyl oxygen (P=O) atom on the other hand is only stabilized by much weaker dipolar interactions in THF. In 2-propanol on the other hand, this atom accepts 1.5 H-bonds on average from the solvent. Surprisingly, only 0.8 H-bonds were found between the hydroxyl oxygen atoms of the ODPA molecule and 2-propanol hydroxyl protons. This can be explained by the bulkiness of the 2-propanol molecules on the one hand and the acidity of the ODPA protons on the other hand. Thus for 2-propanol molecules it is more favorable to stabilize the acidic ODPA protons by accepting H-bonds rather than the oxygen atoms by donating H-bonds. As a total average the PA anchors form 4.3 H-bonds with 2-propanol.

Solvation layer structure at the (0001) interface to alumina The structuring of the solvent at the interface to the (0001) alumina surface was investigated in parallel simulation runs for hexane, THF and 2-propanol, respectively. The density profiles as a function of the distance from the outermost layer of the alumina surface as shown in Figure 2a reveal several discernible solvent layers. Hexane has the lowest degree of ordering forming four clearly visible solvation layers, whereas 2-propanol and THF show six layers each. This is in line with the orientation of the molecular dipoles within the contact solvent layer as illustrated in Figure 2b. In the hydroxyl-terminated alumina surface, the outermost layer of Al3+ ions is separated by more than 4 Å to the solvent and thus no salt bridges are observed. Significant hydrogen bonding of the lowermost solvent layer and alumina was only observed for 2-propanol


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molecules, of which about half form a hydrogen bond with surface hydroxides. In the vast majority of hydrogen bonds to the surface (83%) the 2-propanol acts as H-bond donor. In THF, however, only 4% of the molecules in the first layer form short-lived H-bonds with the hydrogen atoms of the surface hydroxide ions because they preferentially align with the ether oxygen facing away from the surface as dictated by their dipole moment (Figure 2b). To elucidate the implications of solvent layer structuring on SAM growth kinetics, we first investigated the dynamics within the alumina-solvent interface. An estimate for the exchange of solvent molecules within the layers i is given by the residence time correlation function hi (t ) =

1 Ni

Ni

∑ Θ(t ,τ ) n

(1)

n =1

where is the number of molecules in the i-th solvent layer (delimited by the adjacent minima in the density profile), τn the residence time of a given molecule n within the layer and ϴ is the Heaviside step function which is 1 for t ≤ τn and 0 else.35 To discriminate vibrations from true migration steps, the crossing of the z-position with maximum density of an adjacent layer was set as a condition for leaving the initial solvent layer i as exemplarily shown in Figure 2a by the region . All residence time occurrence profiles ℎ can be fitted by an exponential decay function exp (−/) given by first order kinetics. The average residence times τ within the respective solvation layers were fitted from eq. 1 using a time interval of 50 to 500 ps, thus ignoring the first few picoseconds where the population decays is biased as a result of defining the geometric delimiters of the solvent layers. Hexane shows only a relatively small increase of the residence time within interfacial layers as compared to bulk solvent, the largest difference is given by the first solvation layer for which the residence time is increased by a factor of 6.7 (Table 2). Although hardly stabilized by hydrogen


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bonding, the more polar solvent THF adsorbs much stronger to the alumina surface. The average THF molecule residence time in the first solvation layer was found as 0.6 ns and corresponds to a 14.5-fold increase in comparison with the bulk solvent. This can be related to the favorable dipole interaction with the substrate (Figure 2b). Along the same lines, 2-propanol exhibits an even larger residence time of 2.4 ns next to the alumina surface – a more than 21-fold increase as compared to the bulk solvent. This is in line with sum-frequency generation (SFG) spectrographs from Meltzer et al. indicating that 2-propanol forms several ordered layers on alumina.20 Strong interaction with the alumina surface has also been observed for other polar and protic solvents such as ethanol and water.36,37 The mobility of the molecules within each solvation layer was furthermore characterized by the in-plane mean square displacement (MSDxy, whilst a displacement along the z-direction refers to changes between the solvent layers). The MSDxy was analyzed in conjunction with the residence time considering only molecules that are still in the corresponding layer and were fitted with a 2D-diffusion model given by the Einstein relation. The diffusion constants given in Table 2 show that mobility within the layers is slowed down with each layer closer to the surface and, in agreement with the respective residence times, this effect is much stronger in the polar solvents.

Phosphonic acid association to (0001) alumina To characterize the association of phosphonic acids to the alumina surface, we first studied the energetics of de-solvation and physisorption by means of metadynamics simulations. Here, methylphosphonic acid molecule was used as a proxy to accelerate convergence of the free energy profile by focusing on the anchor group-alumina surface distance in absence of alkyl chain rotation and bending. For all three solvents explored, the resulting potential of mean force


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profiles as functions of the z-position of the phosphorous atom are shown in Figure 3. The curves are qualitatively similar, each showing that association is confined to low free-energy barriers (10 kJ/mol or less), but differ for the overall adsorption energy of the phosphonic acid. In hexane, the polar solute is only poorly stabilized and therefore exhibits a particularly high adsorption energy to the alumina surface of about 72 kJ/mol as compared to 36 kJ/mol in THF and 20 kJ/mol in 2-propanol, respectively. The strong difference in adsorption energy between THF and 2-propanol is mainly caused by the lack of donating H-bonds in THF that would stabilize the phosphoxyl oxygen atom. With increasing distance to the surface several energetically favorable conformations can be distinguished which are shown in Figure 3a-d) and marked at their respective position in the potential of mean force curves. The first snapshot (Figure 3a) is taken for the phosphonic acid physisorbed with zero tilt and corresponds to the main energy minimum at z=0. In this state the PA forms three hydrogen bonds with the surface in two of which the PA acts as donor. The second snapshot (Figure 3b) shows the PA lying flat on the surface at a tilt angle of about 90° forming one or two hydrogen bonds with the surface. This configuration reflects an energy minimum only in 2-propanol, while the energy profiles for the other solvents only exhibit a weak shoulder at that position. Another free energy minimum is found for THF and 2-propanol at 2 Å distance from the surface albeit with a much higher energy than the bound state. Here, the PA is still on the surface but in inverted geometry at a tilt angle of almost 180° (Figure 3c). The next energy minimum is again observed for all three solvents. In this configuration, the PA shows no direct contact to the alumina surface and is instead embedded in the second solvation layer (Figure 3d).


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From the series of snapshots in Figure 3 it is evident that the PA molecule, or at least its anchor group, tends to rotates when switching from the first solvation layer to the second. This is also highlighted in the plot of the distribution of the tilt angle for each z-position shown in Figure S7 in the Supporting Information. We hence argue that configurations c and d in Figure 3 would not imply local energy in the potential of mean force curves if computed for PA with long alkyl chains, including ODPA. On the other hand, the overall gain in free energy by PA physisorption is dictated by the anchoring group itself and should show little dependence on the length of the alkyl chain. Combining the free energy profiles and the diffusion dynamics discussed above, the time scales of PA association kinetics can be estimated. For the early stages of SAM formation, PA– PA interactions play a minor role and the underlying the free energy profiles are basically that of the physisorption of the isolated methylphosphonic acid molecule. In absence of large energy barriers hindering penetration of the solvent layers, the early stage of SAM growth is clearly diffusion-controlled. To obtain the average time Δ that it takes for a PA molecule to reach the surface we consider the average volume = ∙ ℎ above the surface A needed per solute molecule at a given PA concentration c. The average diffusion length that must be overcome for each PA association step is then given by h 1 = 2 2⋅ A⋅c⋅ NA

(2)

where NA is the Avogadro number. Assuming a PA concentration of c=1 mM (adopted from the SAM formation experiments of Meltzer et al.20 and Koutsioubas et al.38, respectively) our model (A=50.5 nm2) implies a diffusion length of 16 nm. This is far beyond the dimensions of the attractive regime in the potential of mean force for PA association (Figure 3) and the


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1-dimensional Einstein relation based on the bulk diffusion coefficient D may be used for estimating the required time scales: 2

h   1 2 D = Dz = 2 ∆t diff

∆t diff =

1 2 8 D ⋅ (A ⋅ c ⋅ N A )

(3)

(4)

For our nm-sized simulation model the kinetics of PA association are hence given by physisorption attempts after diffusion from the bulk within average time scales of ∆tdiff = 0.1, 0.3 and 3.6 µs in hexane, THF and 2-propanol, respectively. This is two to three orders of magnitudes slower than the time scales needed for solvent layer penetration as listed in Table 2, thus supporting the picture of diffusion-controlled kinetics during the early stage of SAM formation. We also argue that proton transfer to a hydroxide ion on the alumina surface occurs on much faster scales than ∆tdiff thus leading to practically identical kinetics of PA physisorption and phosphate chemisorption.

Growth of ODPA-SAMs Considering the µs scales of single PA molecule association events, it is impractical to study SAM formation from brute-force molecular dynamics simulations. We hence focus explicit MD simulations to the ps scales of PA/SAM relaxation after each association event using our previously described molecule-by-molecule deposition technique. Along this line, we also account for defect-free, dense packing as a consequence of long-termed relaxation processes by implementing PA grafting on idealized lattices. As in previous work,24 different lattices of ODPA on the (0001) alumina surface were imposed, namely the (1 × 1) and 2⁄√3 ×


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2⁄√3 !30° lattice of α-Al2O3 allowing for a maximum coverage of 3.80 and 5.07 nm-2, respectively. This was compared to one simulation run with no restrictions towards the binding sites other than the exclusion of already occupied sites. The latter type of simulation runs was only applied to the most polar solvent considered, 2-propanol, as it exhibits the most drastic difference with respect to our earlier study performed for SAM formation in vacuum.24 The growth simulations in vacuum indicated that the use of pre-defined lattice has little influence on the SAM morphology whilst saving considerable computational efforts. An overview of the SAM formation runs performed in the present work is given in Table 3. The role of the different polarity of the studied solvents during SAM formation is illustrated in Figure 4. Moreover, a quantification of the SAM ordering is given in Figure 5a,b which plots of the average tilt angle and the number of gauche defect per molecule as functions of the monolayer density. The snapshots are both taken at a coverage of 1.50 nm-2, from the growth simulations in 2-propanol and hexane with the (1 × 1) lattice, leading to a final density of 5.07 nm-2, iPrOH5.07 and Hex5.07, respectively. In 2-propanol, the space between the phosphate anchors is occupied by solvent molecules oriented in favor of hydrogen bonding to the alumina surface. As a consequence, the alkyl chains of ODPA are more or less stretched out towards the solvent phase. In hexane, on the other hand, the alkyl chains of both ODPA and the solvent have similar affinity to the surface. In absence of driving force to interface structuring, the forming SAM appears more disordered and tangled with several chains lying flat on the surface. In addition, the amount of gauche defects marked in green in Figure 4 is considerably higher in hexane solution. This difference has also been observed in our previous work, where the two solvents were added to monolayers initially grown in vacuum and then exposed to solvent as a


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post-processing step.24 For the SAM grown from THF solution, we find a degree of ordering in between the two other solvents at same monolayer density. We find that tilting and the amount of defects both decline with increasing number of surfactants. This is also reflected in the radial pair distribution functions of the terminal methyl groups in the SAM depicted in Figure 6 for the (1 × 1) systems. In 2-propanol, the nearestneighbor peak is already present at coverages of 0.5 nm-2, whereas for THF and hexane the peak emerges only at around 1 nm-2 and 1.5 nm-2, respectively. A long range order with peaks for second- and third-nearest neighbors can be found starting from around 2 nm-2 for all three solvents. To allow comparison of our modelling data with experimental characterization using SFG spectroscopy, we also calculated the SFG intensities of the CH2 and CH3 vibrational modes for all solvent setups and at different stages of SAM formation, respectively. Trajectory analyses using a cancellation algorithm for the dipole vectors of the CH2/3 groups as described in ref. 20 show the development of the average z-component of the dipole moment as a function of SAM coverage (Figure 5c). In line with experimental data obtained by Meltzer et al.,21 the CH2 intensity initially rises sharply with increasing coverage and then slowly decays due to the cancellation of opposing dipole moments within the ordered alkyl chains. Again, the curves indicate the best ordering in 2-propanol followed by THF and hexane, as evidenced by the higher signal intensity in the latter cases. The stronger signal for the less polar solvents can be attributed to a combination of both higher tilt angles (and thus greater z-component of the CH2 dipole moments) and a higher concentration of gauche defects, which entails less cancellation of opposing dipole moments. The curves for CH3 intensity on the other hand are almost identical and show a steady increase of signal intensity, which is caused primarily by the adsorption of


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new ODPA molecules and in small parts also by a steady reduction of the tilt angle (see also Figure 5a). In conclusion, all structural analyses confirm the trend of higher ordering in SAMs grown from polar solvents and weaker ordering in less polar solution. Along the same lines, SAM formed in vacuum (the ultimately unpolar environment) show poorest ordering. With increasing number of deposited ODPA molecules, however, the differences diminish and the final ordering is determined by the ratio of anchor group packing and the space demand of the alkyl chains. Thus, the role of solvent in SAM formation is essentially of kinetic nature. Our molecule-by-molecule deposition simulation method primarily reflects diffusioncontrolled kinetics, mimicking long range migration processes by a steady influx of solutes towards the alumina surface. To this end, the average time scale ∆tdiff as given by eq. 4 may be associated to each growth attempt. This is reasonable up to a coverage of about 1 nm-2 as our simulations indicate that practically every association attempt leads to successful ODPA deposition. However, a signature of different formation kinetics, other than purely diffusioncontrolled, is given by the increasing number of failed association attempts observed at later stages of SAM formation. Figure 5d shows the total number of deposition attempts required as a function of SAM density. At a coverage of more than 1 nm-2 SAM growth is subject to increasing numbers of failed deposition attempts, again depending on the polarity of the solvent, however in the opposite manner as the structural analyses of the SAMs would suggest. The predominant effect of kinetic hindering is indeed not the permeation of the forming layers of alkyl chains, but the removal of interfacial solvent molecules from the alumina surface – which is least feasible for polar solvents. This effect gets increasingly significant at mature stages of SAM formation, as solvent


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molecules that block a potential site of ODPA association need to be pushed through the increasingly dense SAM embedding this site. The drastic increase in the number of deposition attempts needed for SAM growth is found at around 40-50% of the maximum coverage for 2propanol, whilst the corresponding regime in THF and hexane is observed at 60-70% and 7080%, respectively. Finally, our growth runs were stopped when the acceptance rate of attempts to SAM growth dropped below 1%. Assessing the kinetics of SAM growth beyond diffusion-controlled growth (coverage < 1nm-2) is far from trivial. From a qualitative viewpoint, the sharp increase of the number of failed deposition attempts is in agreement with the observed degree of SAM coverage at which experimentally found growth rates show sharp changes in growth rate.12,38,39 However, to associate time scales to our molecule-by-molecule deposition models, it is not sufficient to simply multiply ∆tdiff by the number of attempts required for a successful deposition step. To boost the acceptance rate of ODPA deposition, we were bound to apply an additional attractive force Fdrag towards the alumina surface. This gives rise to an enhanced influx of ODPA jboost according to Fick’s first law: jboost =

D c ⋅ N A ⋅ Fdrag k BT

(5)

We thus boosted the beforehand diffusion-controlled ODPA association process, leading to much shorter time scales ∆tboost needed for each association attempt. For the given surface area A of our simulation model, we instead find

jboost =

1 A ⋅ ∆t boost

(6)


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∆tboost = ∆t diff ⋅ 8 ⋅ c ⋅ A ⋅ N A

k BT = 824 ∆t diff Fdrag

Page 18 of 34

(7)

In conjunction with the number of failed attempts reaching one hundred this calls for an estimated average scale of 105 times the µs scales of diffusion-controlled ODPA deposition steps. While error control prohibits extrapolation of our simulation data over five orders of magnitude, this consideration still illustrates how deposition rates change to molecules per seconds upon late stages of SAM growth. The need for boosting ODPA association is clearly connected to the number of failed deposition attempts. We hence suggest that the tremendous raise in time scales is linked to the same degrees of SAM coverage for which we observed the sharp increase of rejection rate in Figure 5d.

Conclusions The effect of solvent polarity on growth of SAMs of ODPA on the (0001) surface of α-alumina was studied by means of molecular dynamics simulations with the three solvents hexane, THF and 2-propanol. Simulations with pure solvent on the surface revealed a strong ordering effect of the substrate with up to six discriminable solvation layers in THF and 2-propanol. As expected, the effect is strongest in 2-propanol where the residence time increases by a factor of 26 in the contact layer as compared to the bulk while the in-plane diffusivity drops to 46% of the bulk value. Despite solvent structuring at the interface, the potential of mean force for physisorption of phosphonic acids to plain alumina surfaces show only shallow barriers, if at all.

In the very early stages of SAM formation the kinetics are hence driven by ODPA diffusion and the deposition of each molecule may be related to the µs time scales (∆tdiff = 0.1, 0.3 and 3.6 µs in hexane, THF and 2-propanol, respectively). To this end, our simulation scheme of


18

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molecule-by-molecule deposition could be interpreted as a kinetic Monte-Carlo approach. The latter mimics ODPA influx indirectly and uses 250 ps runs for molecular relaxation after placing the ODPA in proximity of the alumina surface – which saves 3 order of magnitudes in computational efforts compared to brute-force molecular dynamics simulation. However, at later stages of SAM growth, the association of further ODPA is sterically hindered by solvent molecules trapped between the already deposited SAM molecules. To allow efficient moleculeby-molecule deposition (taken as less than 100 failed attempts per successful growth step), we therefore applied an additional attractive force to the newly incoming ODPA molecule. While this allows studying SAM growth towards densities close to ideal packing for unpolar solvents (hexane). For more polar reaction media, we find that solvent molecules trapped at ODPA association sites are increasingly slowing SAM formation. The underlying kinetics then change from µs to seconds scale, depending on the polarity of the solvent. In our simulations, this may be monitored from a drastic increase in the number of failed deposition attempts in hexane solution when reaching 70-80% of the maximum SAM density, whilst the corresponding degree of packing in THF and 2-propanol is only 60-70% and 40-50%, respectively.

It is interesting that the observed kinetics are contrary to the intuitive picture one would get by focusing on SAM structure only. Indeed, SAMs grown in polar solution appear nicely ordered and seemingly should grow fastest. This effect, however, is more than compensated by entrapped solvent molecules that hinder PA association as discussed above. The impact of solvent on the adsorption of various phosphonic acids (PAs) on indium tin oxide surfaces has been investigated by Chen et al. In line with the observations from our simulations, these authors obtained SAMs


19


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Page 20 of 34

with higher grafting density by using solvents with low dielectric constants for the same immersion time.13


20

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Figure 1. Scheme for the working principle of the molecule-by-molecule deposition. a) A new ODPA molecule (blue alkyl chain) is added above the forming SAM in vicinity of a vacant site and dragged through the solvent (here: 2-propanol) and the sub-monolayer towards the OHterminated α-Al2O3 (0001) surface by a constant force Fz. b) Example for a failed attempt as occurred at a coverage of 3.70 nm-2. The anchor cannot reach the surface, as a 2-propanol molecule blocks the vacant binding site (OH– highlighted in pale blue) and would have to escape on virtually the same route as the oncoming anchor. The chains of PA molecules surrounding the narrow channel are marked in olive green. c) Example for a successful attempt defined by ODPA donating an H-bond to the surface hydroxide.


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Figure 2. a) mass density profile and b) charge density profile for hexane (green), THF (red) and 2-propanol (blue). Depending on solvent polarity, up to 6 layers of solvent structuring are observed at the interface to the alumina surface. $% and are an example for the regions used for calculating the residence time and the mean square displacement as described in the main text. c) Histograms of the z-component of molecular dipole moments of hexane, THF and 2-propanol shown for different solvation layers, respectively.


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Figure 3. Characteristic configurations and potentials of mean force profiles for the adsorption of a methylphosphonic acid to the (0001) surface of sapphire from hexane (green), THF (red) and 2-propanol (blue). The configurations showing “flipped” anchor arrangements c and d should be disfavored for longer alkyl chains hence diminishing the small barriers to association even further.


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Figure 4. Top and side view of systems iPrOH5.07 in 2-propanol (left) and Hex5.07 in hexane (right) both deposited on (1 × 1) lattice at a coverage of 1.50 nm-2. Alkyl chains are shown in blue, whilst the gauche defects are highlighted in green.


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Figure 5. Progress of key parameters of the different systems in the course of SAM formation. a) Average tilt angle 〈'〉, b) number of gauche defects per molecule, c) expected SFG signal intensity according to the CH2 and CH3 bond vector analysis, d) number of required deposition attempts. Gray: Growth in vacuum with 2⁄√3 × 2⁄√3 !30° lattice. Black: Growth in vacuum with (1 × 1) lattice. Cyan: Growth in 2-propanol without pre-defined lattice (iPrOHrand). Light blue: Growth in 2-propanol with 2⁄√3 × 2⁄√3 !30° lattice (iPrOH3.80). Dark blue: Growth in 2-propanol with (1 × 1) lattice (iPrOH5.07). Orange: Growth in THF with 2⁄√3 × 2⁄√3 !30° lattice (THF3.80). Dark red: Growth in THF with (1 × 1) lattice (THF5.07). Green: Growth in hexane with (1 × 1) lattice (Hex5.07).


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Page 26 of 34

Figure 6. Pair distribution functions of the terminal methyl groups of the phosphonic acids at different coverage for systems Vac5.07 (black), Hex5.07 (green), THF5.07 (red) and iPrOH5.07 (blue). The reflexes indicated as gray lines mark the positions and relative intensities of the ideal

(1 × 1) superlattice. The dashed gray curve is calculated from these reflexes with a Gaussian standard deviation of 1 Å.

Table 1. Dielectric constant )* , number of accepted (++ ) and donated (,$ ) hydrogen bonds between ODPA and the respective solvents and diffusion coefficient of ODPA in bulk solution.

)* 25

++

,$

-./01 [10-5 cm2/s]

Hex

1.9

0

0

1.31

THF

7.6

0

1.9

0.46

iPrOH

18.3

2.3

2.0

0.04


26

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Table 2. Residence times and lateral diffusion coefficient -2 for each solvent layer at the interface to OH-terminated α-Al2O3 (0001).

[ps]

-2 [10-5 cm2/s]

Layer Hex THF iPrOH Hex THF iPrOH bulk

25

44

112

4.58

2.40

0.43

7

–

40

111

–

2.31

0.41

6

–

41

110

–

2.25

0.37

5

–

43

109

–

2.18

0.32

4

24

45

133

4.09

2.20

0.26

3

28

61

182

4.10

1.94

0.24

2

42

117

390

3.96

1.68

0.19

1

167

638

2403

3.38

1.43

0.20

Table 3. Overview of the investigated simulation models for SAM growth. System

Solvent

Binding Sites

iPrOHrand

2-propanol

no restriction

iPrOH3.80

2-propanol

2⁄√3 × 2⁄√3 !30°

iPrOH5.07

2-propanol

(1 × 1)

THF3.80

THF

2⁄√3 × 2⁄√3 !30°

THF5.07

THF

(1 × 1)

Hex5.07

Hexane

(1 × 1)


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Page 28 of 34

Acknowledgement We gratefully acknowledge funding from the Deutsche Forschungsgemeinschaft via the Excellence Cluster EXC 315.

Abbreviations MD, molecular dynamics; ODPA, Octadecylphosphonic acid; PA, phosphonic acid; SAM, selfassembled monolayer.

Supporting Information Figure S1: Plots and fits of the MSD of ODPA in each solvent. Figure S2: Comparison of energy profiles for PA chemisorption with different force fields and DFT. Figure S3: Plots and fits of the residence time correlation functions for solvent molecules. Figure S4: Plots and fits of the in-plane MSD for solvent molecules. Figure S5: Radial pair distribution functions for solvent molecules. Figure S6: Plot of the collective variable vs. time in metadynamics simulations. Figure S7: probability for tilt angle as a function of z-position in metadynamics simulations. Figure S8: Scheme for the working principle of the molecule-by-molecule deposition with snapshots of the system.

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TOC Figure


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