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Nanoscale Insight Into the Mechanism of a HOPG Edge Surface Wetting by “Interferencing” Water Jerzy Wloch, Artur Piotr Terzyk, Marek Wi#niewski, and Piotr Kowalczyk Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02113 • Publication Date (Web): 03 Aug 2017 Downloaded from http://pubs.acs.org on August 8, 2017

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Nanoscale Insight Into the Mechanism of a HOPG Edge Surface Wetting by “Interferencing” Water Jerzy Włoch1, Artur P. Terzyk*2, Marek Wiśniewski2, Piotr Kowalczyk3 [1] Faculty of Chemistry, Synthesis and Modification of Carbon Materials Research Group, Nicolaus Copernicus University in Toruń, Gagarin Street 7, 87-100 Toruń, Poland

[2] Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University in Toruń, Gagarin Street 7, 87-100 Toruń, Poland

[3] School of Engineering and Information Technology, Murdoch University, Murdoch 6150 WA, Australia

(*)Corresponding author: Artur P. Terzyk Tel: (+48) (56) 611-43-71, E-mail: [email protected]

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ABSTRACT: The new Molecular Dynamics simulation results showing the influence of the edge carbon surface atoms on the wettability of a Highly Oriented Pyrolytic Graphite (HOPG) surface with water nanodroplets are reported. The conditions for the occurrence of the Wenzel effect are discussed, and the Cassie to Wenzel transition (CTWT) mechanism in the nanoscale is explored. This transition is detected by the application of a new procedure showing that the CTWT point shifts towards larger values of carbon-oxygen potential well depth with the decrease in the HOPG side angle. It is concluded that the Wenzel effect significantly contributes to contact angles measured for the HOPG surfaces. Wenzel effect is also very important for the “HOPG” structures possessing the disturbed C-C interlayer distance, and its influence on the water nanodroplet contact angles is strongly pronounced. The structure of water confined inside slits and on a HOPG surface is studied using the analysis of the density profiles, the number of hydrogen bonds and, modified for the purpose of this study, structure factor. The detailed analysis of all parameters describing confined water leads to the conclusion about the presence of characteristic interference patterns revealed as a result of long term simulation. A simple model describing this effect is proposed as the starting point for further considerations.

Keywords: contact angle, nanodroplets, HOPG, MD simulations

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INTRODUCTION

Although wetting is one of the most common phenomenon in everyday life, the wetting science is only 200 years old.1 However, during this time very advanced procedures and tools for wetting study have been developed, involving such innovative methods as (for example) advanced optical,2 atomic force,3 transmission electron,4 scanning electron,5 or scanning polarisation force microscopy measurements.6 Wetting phenomena can now be fully controlled by using, for example, biomimetics7 as a tool for the creation of self-cleaning, superhydrophobic, low adhesion and drag reduction surfaces.8 In this field very important is the application of so called "wettability switching techniques" using an external stimuli (of different types, for example: optical, mechanical, magnetic, thermal, chemical etc.) for the switching between hydrophobic and hydrophilic surface properties.9-12 Recently, using the Molecular Dynamics (MD) simulation results, this type of "switchable" HOPG wettability was discussed by the study of water contact angle (WCA) in the nanoscale.13 Remarkable influence of the Wenzel effect on the WCA was observed.13 In 1936 R.N. Wenzel14 proposed the derivation of an equation explaining why the rise in surface roughness factor can change the contact angle (CA) value. In fact, depending on the surface properties, one can observe the Wenzel nonwetting and/or Wenzel partial wetting states.15 However, as it was discussed by Nosonovsky and Bhushan16 also different additional regimes of wetting of a rough surface can occur, due to the presence of a hierarchical roughness. If this type of roughness occurs, the Wenzel, Cassie, Lotus and Petal wetting states can exist. Thus, for a surface with hierarchical roughness a simple consideration of wetting phenomena using only Wenzel and Cassie Baxter approach can be simplification.17 Transition between the both states (called simply Cassie to Wenzel transition - CTWT) has been also widely studied. The CTWT appearing after a surface modification is very important for the superhydrophobic/self-cleaning surfaces.18 Among the recently published reports one can mention (for example) the study reporting new tools for the CTWT characterization19 and the experimental results on the wettability of porous alumina samples.20 Also very important MD simulation study on the role of contact angle hysteresis in the Cassie and Wenzel states21 and on the estimation of the free energy barrier of the CTWT22 have been published. It was also recently shown that the CTWT can exhibit different new properties observed during a liquid drop impact23 and in the case of wetting of super repellent surfaces.24 Interesting experimental results on the CTWT for carbon 3


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structures were reported recently by Zhang et al.25 The authors introducing carbonyl surface groups observed the CTWT and the decrease in the WCA value. There has also been the debate in literature about the applicability of the Wenzel theory in the nanoscale.26,27 One of the most important papers concerning the possible Wenzel states on carbon surfaces was published by Leroy and Muller-Plathe.28 The authors discussed water behaviour on defected carbon surfaces concluding, that depending on the degree of heterogeneity, three layers of interfacial water can be observed. The most disturbed layer is located at the distance 9.0 - 11.5 Å, and for this layer the number of formed hydrogen bonds is remarkably smaller than for the bulk water. In this layer water molecules, since located at the vicinity of defected carbon edges, can form only very small number of hydrogen bonds. Thus, the competition between maximization of water-carbon potential energy and the breaking of water-water hydrogen bonds is observed. This finally leads to the linear correlation between the solid-liquid free energy and the roughness contour length. This contour length was defined as the length of the border between two regions. The first region contained water molecules at the vicinity of carbon atoms (water-water hydrogen bonds were not formed). In contrast, the second region was located closer to the centre of surface defects (here the hydrogen bonds were present). The final conclusion from this free energy-length correlation was that the Wenzel theory cannot be applied for the studied systems due to molecular properties of water forming hydrogen bonds (note that for Lennard-Jones systems the reverse conclusion was presented). In contrast to the results presented by Leroy et al.28 our recent study showed that the presence of Wenzel states on carbon surfaces is possible. It was shown that a HOPG edge carbon atoms can induce the Wenzel states in the interfacial water.13 However, the mechanisms of this effect have not been studied yet. Thus, we present the new results considering water-HOPG systems. The complex approach makes a relation between the WCA and the arrangement of HOPG basal surface atoms comprehensive. Moreover, the role of the Wenzel effect, and its influence on WCA on different types of HOPG surfaces is explained in detail. The structure of the interfacial water (at the vicinity of HOPG edge carbon surface atoms) has not been explored yet, and this is also the purpose of this study. This structure was elucidated based on the density plots, the statistics of hydrogen bonds and other important interfacial water characteristics. We also propose the new tool describing interfacial water order, improving the method proposed by Chau and Hardwick29 and Errington and Debenedetti30 for the characterization of bulk tetrahedral configurations. To check how far the 4


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HOPG-induced Wenzel effect changes the WCA, we induce the CTWT of water nanodroplets sitting on studied structures. This CTWT was achieved by changing the values of watercarbon potential well depths. Additionally, we also created the systems possessing larger interlayer carbon-carbon separations (the distance between the centres of carbon atoms across the range of 3.4-8.4 Å was studied) since it is well known that increased interlayer C-C distance can be observed in some graphite intercalated compounds,31,32 graphene oxide membranes33 and graphite oxides.34,35 Summing up, we relate the geometric HOPG surface parameters to the wetting mechanism at the nanoscale trying to explain in what extent the appearance of Wenzel states changes the WCA, and how far this change depends on the type of a HOPG structure. Finally we show, that the results of long term simulation data have shed a new light on the properties of the interfacial water. Namely, it is proved that water molecules reveal characteristic interference patterns. Thus, we propose the fundamentals of a new concept describing density plots of “interferencing” water molecules.

MOLECULAR SIMULATIONS MD simulations and WCA calculations. By means of the MD method the droplets containing 2000 TIP4P/200536 water molecules were simulated for temperature 298 K. The OpenMM toolkit for MD simulation (supported by Python 3.4.537) was used. The details of the simulation technique are provided in Supporting Information. Shortly speaking, the MD simulations were performed for the HOPG models having different angles to the basal surface (x = 15, 30, 45, 60, 75 and 90 degrees, respectively; the samples are labelled as "HOPG-Side-

x˚"), for different values of carbon-oxygen potential well depth (εCO = 0.1, 0.25, 0.35 and 0.45 kJ/mole) and for different “HOPG” C-C interlayer separations (the system HOPG-Side-90˚ was studied for C-C interlayer distance equal to 3.4 Å+d; where: d = 1, 2, 3, 4 and 5 Å, respectively; the systems are labelled as "HOPG-Side-90˚+d"). The initial "flat-surfaced" system is labelled as "Basal plane HOPG". The authors realize that for some of the studied structures the application of “HOPG” abbreviation is not adequate. However, we use it to point out the systematic changes in the structure of studied systems, and to be in accordance with the nomenclature applied previously.13 For some systems additional simulations were performed, especially to define the CTWT point precisely. The WCA values were calculated from the MD data using the

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procedure described previously38 however, modified for the purpose of this study since the "bottom" of the droplet is for some cases undefined (see Supporting Information - Figure S1).

Hydrogen Bond Statistics and Structure Factor calculations. For the calculation of hydrogen bonds number (nhb) from the MD simulation data two main methods are usually used. Both of them are equivalent and give similar results. They differ in the type of used criterions and this can be energetic39 and geometric one.41,42 The first criterion assumes that two water molecules form a hydrogen bond if the interaction energy between them is lower than -9.2 kJ/mole.39,28 The geometrical criterion bases on three assumptions (important for the modified in this study structure factor calculation approach):40 (1) The distance between the position of oxygen atoms of two water molecules forming the hydrogen bond should be no greater than 3.6 Å. It guaranties that they are in the first coordination shell. (2) The distance between the position of oxygen atom of the first water molecule and the position of hydrogen atom of the second one is no greater than 2.4 Å, and (3) the angle between the H-O bond vector of one molecule and the vector connecting positions of oxygen atoms of two considered water molecules is no greater than 30°. In our studies we have used the method based on the geometric criterions due to its simplicity and intuitiveness. Structure factor (SF) was calculated using the procedure proposed by Chau and Hardwick29 and Errington and Debenedetti.30 However, this procedure was modified for the purpose of this study (see below).

RESULTS AND DISCUSSION Nanoscale insight into the CTWT. How the Wenzel states change WCA values? To explore some details of the CTWT in the nanoscale, the density maps were prepared (for water nanodroplets as well as separately for oxygen and hydrogen; a typical map is shown in Figure 1, and in the inset of Figure S2 - see Supporting Information). We have noticed, that with the rise in the εCO value some specific high density regions on the maps appear, and these regions reflect the proceeding wetting process. Based on the analysis of the maps for completely wetted surface (see Figure 1C) it can be concluded, that after the CTWT the maximum oxygen density in some selected regions is the same. Thus, it is clear that the appearance of the CTWT can be related to the differences in the density at selected specific

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points on the density maps. We have chosen two of them as the points for our observation. The first high density region is located at the "bottom" (labelled as "B") and at the vicinity of a structure, whereas the second one on its "ridge" (or on the "top"; it is labelled as "T") (see Figure 1C and Figure S2). As one can observe from the data collected in Figure S2, the density at the B region is usually larger than the density at the T one. Taking into account the density maps for all studied systems it is clear, that the CTWT point can be defined at the intersection of the lines plotted in Figure S2. In this way one can easily obtain the characteristic εCO values (and related density) at the CTWT point (the results are collected in Figure 1A). One can see that for the HOPG-Side structures, the smallest εCO value of the CTWT occurs for the HOPG-Side-90˚ (εCO = 0.162 kJ/mole; this point was assessed arbitrarily because, excepting the smallest εCO, this structure is wetted and in fact no typical CTWT occurs). To induce CTWT in nanodroplets on the HOPG-Side-75˚ and HOPG-Side60˚, the εCO value should be increased by about 35 % (i.e. up to 0.22 kJ/mole). Further increase in εCO is necessary (up to 0.26 kJ/mole) to induce the CTWT of water on the HOPGSide-15˚, HOPG-Side-30˚ and HOPG-Side-45˚. One can also see that the CTWT (Figure 1A) occurs at almost constant density for the HOPG-Side-90˚, HOPG-Side-75˚ and HOPG-Side60˚. For the three remaining systems the density of water at the CTWT increases with the rise in εCO value.

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Figure 1. Insight into the CTWT: the maximum density and the carbon - oxygen potential well depths of the transition plotted for the HOPG - Side structures (A), the same plot for the structures with increasing C-C interlayer distance (B), and selected oxygen density maps (C) for the HOPG-Side-30̊ (εCO = 0.1, 0.25, 0.35 and 0.45 kJ/mole, from the top to the bottom, respectively) and for the HOPG-Side-90˚+3A (εCO = 0.25, 0.35, 0.375 kJ/mole - first row, and 0.4, 0.425 and 0.45 kJ/mole - the second row, respectively). "B" and "T" show the regions selected for the estimation of CTWT point.

Considering the HOPG-Side-90˚+d systems (Figure 1B) one can conclude, that to induce the CTWT the εCO value should systematically increase (with increasing d value) however, if d ≥ 2 Å (i.e. the distance between the centres of carbon atoms forming opposite walls is equal to 5.4 Å) the CTWT occurs at the constant and relatively high interaction energy values (εCO ca. = 0.38 kJ/mole). For the system HOPG-Side-90˚+3A the largest density of the CTWT is observed. It is due to the proximity of the adjacent walls resulting in overlapping of C-O interactions and thus, in the potential well deeper than those in the case of the other systems

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(adjacent walls distances). Figure 1C shows the change in oxygen density maps with the rise in εCO value for two arbitrarily chosen systems (HOPG-Side-30˚ and HOPG-Side-90˚+3A). To check in what extent the appearance of Wenzel states can change the WCA values recorded for nanodroplets, in Figure 2 we collect the plots of cos(WCA) for different εCO values. One can see that the rise in εCO leads to the decrease in WCA for all studied systems (Figure 2A). Generally, all structures can be considered as hydrophobic, with exception for larger εCO values (in fact the Basal plane HOPG and HOPG-Side-15˚ become hydrophilic for εCO = 0.35 and 0.45 kJ/mole, respectively). For the lowest εCO the differences between WCA values recorded for different HOPG structures are not large (due to very small droplet substrate interaction energy). In contrast, for larger εCO the state of surface atoms has remarkable influence on the contact process and, as a consequence, the differences between WCA values are strongly pronounced. For all studied εCO values the smallest angles are observed for the Basal plane HOPG sample. The WCA values increase with the side angle up to cutting angle 45°. Above this value slight, but reversal, change is observed. It is in full accordance with previously reported by as results.13 This change of tendency is directly connected with the change of interaction energy (potential well depth) of water molecules with the substrate. In Figure 2B the results for the HOPG-Side-90˚+d structures are collected. It is seen that for the εCO values up to 0.38 kJ/mole the same tendency is observed for all of wall distance values. Similarly to discussed above HOPG-Side structures, the higher C-O interaction energy is, the lower is value of observed WCA. It is also seen that with the rise of the wall distance the WCA also rises. It is due to the fact that, being in the Cassie state droplet, interacts mainly with the upper carbon atoms of the substrate. The number of carbon atoms lowers with the rise of the distance between walls, resulting in the weaker net interaction energy. Observed tendency continues above εCO =0.38 kJ/mole but only for the distance between walls lower than 6.4 Å. It is worth of mentioning that although CTWT can be deduced from density profiles, in the case of WCA such transition seems do not affect the tendency of its change with the εCO variation for HOPG-Side structures, and for distance between walls lower than 6.4 Å. But CTWT is clearly seen in WCA plots for distances between walls equal and larger than 6.4 Å. Namely, very sharp change in the plot direction near εCO =0.38 kJ/mole is observed. CTWT causes the change of the wetting mechanism in these systems. Due to the higher C-O interaction energy water molecules penetrate the inter-wall space, drastically affecting the net droplet-substrate interaction energy. In fact WCA is connected not with 9


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water-carbon atoms interaction only but with water (in droplet)-water (adsorbed between walls) as well. And as the result more steep rise of WCA cosine up to values larger than 0 (WCA lower than 90°) is visible.

Figure 2. Water contact angles on HOPG structures calculated for different values of carbon-oxygen potential well depth. The influence of the HOPG side angle (A) and the interlayer C-C distance (B) is shown. The characteristic εCO and cos(WCA) values for the CTWT are marked by colour circles, thus for a given structure on the rhs of the marked points one can expect water in the Wenzel states.

It should be pointed out that the experimental WCA for the Basal plane HOPG is recovered by the MD simulation for the value of εCO = 0.45 kJ/mole.13 Thus, the fundamental conclusion of this part of our study is that the Wenzel effect significantly contributes to the

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WCA measured on the edge carbon atoms containing HOPG surfaces, irrespective of the side angle value. Summing up. Considering the HOPG-Side-90˚+d structures one can conclude that the value of εCO characteristic for the CTWT increases with d. However, above εCO = 0.38 kJ/mole one can expect the complete filling of the substrate slits below a nanodroplet. The Wenzel nonwetting and Wenzel wetting states occur (see Figure 2) and the influence of the Wenzel effect on the WCA is strongly pronounced for the d values larger than 3Å (i.e. for the slits with diameter larger than 6.4 Å). Above this critical slit width the pore is fully filled by water molecules (having the kinetic diameter around 3Å). The properties of this confined water are discussed below.

The state of water under nanodroplets and the CTWT mechanism in slits. It is well known that water confined in hydrophobic pores can create different more or less ordered forms, like for example ordered liquid (for separation between layers across the range of 4.1 5 Å)42 and mono, bilayer or amorphous ice.43-47 Interesting results were published by Xiu et al. 6 showing the possibility of ice Ih - type structure creation on the surface of mica (below a graphene coating). Li et al. provided a review of recent results exploring the structures and dynamics of water confined between 2D materials and various substrates at the room temperature. It was concluded that ice-like water structures, having different number of layers are formed, especially if water is under graphene confinement.48 Also Johnsston and Molinero49 discussed recently the types of ice and mechanisms of crystallization in water nanodroplets (a hybrid structure of two types of ice was reported in nanodroplets). The TIP4P/2005 model used in this study predicts very small deviations from experimental densities for all types of ice. What is important, this model predicts the best fit to experimental data in comparison to other water models. The model also gives semiqualitative description of the coexistence between different ice polymorphs.36 Zhu et al.47 studied TIP4P/2005 water molecules confined in a graphene nanocapillaries of different diameters. Every water molecule is involved in 4 hydrogen bonds with neighbours - and this is so called "ice rule". Every water molecule is a double donor and donor acceptor of hydrogen bonds. However, these structures were created under high pressures. In our study water nanodroplet is under small saturated vapour pressure, thus the creation of ice is rather not expected. Studied by us systems are similar to widely described "pillared graphite

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surfaces".50-55 However, up to our knowledge, the systems described in this paper have not been studied yet. Some typical results for the HOPG-Side-900+3A are collected in Figure 3. It can be seen, that in fact, for some cases ordered water structures are created under nanodroplets. Figure 3 shows how the wetting at the nanoscale proceeds with the rise in the εCO value. As it was shown in Figure 2 the critical εCO for the CTWT for the HOPG-Side900+3A structure is located at the εCO = 0.375 kJ/mole. This is why for εCO =0.35 kJ/mole (see the lhs of Figure 3) the CTWT is not observed (note that the analysis of snapshots for all studied structures confirms the validity of our CTWT point assignment approach). The rise in εCO up to 0.375 kJ/mole (which is the point of CTWT) starts the transition and wetting, as it is seen on rhs of Figure 3. Further rise in εCO value leads to subsequent filling of the slits by water. Thus, under the nanodroplets created on the HOPG-Side-90˚+3A and HOPG-Side90˚+4A we observe a single ordered water layer inside the slits (see Figure 3 and Figure S3), while for HOPG-Side-90˚+5A two layers of water are created (Figure S4). It can also be seen that in pores the statistical number of hydrogen bonds per water molecule is smaller than in the bulk water (see also below). Thus, it can be concluded that in the case of studied nanodroplets we observe the creation of ordered liquid (and not ice) inside nanopores. This ordered form occurs also on the surface of a HOPG. However, to obtain detailed characteristics of the interfacial water molecules some additional parameters (like a structure factor and the number of hydrogen bonds) should be calculated. This is discussed below.

Figure 3. Water nanodroplets on the surface of the HOPG-Side-900+3A structure formed for different values of carbon-oxygen potential well depth. Right panel shows the structure of

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water in slits under a nanodroplet (top and side view; dashed lines show the direction of hydrogen bonds). This picture was created using the VMD software.56

The modified procedure of confined water Structure Factor calculation. The Structure Factor (SF; called also "Orientational Order") is usually applied to get the information about the spatial arrangement of atoms and/or molecules. It is essential (for example) for investigations of a liquid-solid phase transition possible under particular conditions (e.g. in confined systems). There are various types of SF differing in mathematic formulae. The choice of SF type depends on the nature of spatial arrangement of particular compounds (e.g. the type of crystallographic lattice). Considering solid water - for the normal ice a tetrahedral arrangement is expected. Such arrangement can also appear if water molecules strongly interacts with solid materials (during adsorption, wetting etc.). In these situations for the water spatial arrangement characteristics the SF proposed by Chau and Hardwick29 and Errington and Debenedetti30 is used in the following form:

q = 1−

3 3 4  1 ∑ ∑  cosθ jik + 3  8 j =1 k = j +1 

2

(1)

Summation is done over all possible angles, formed by the lines connecting oxygen atom of a given (i-th) water molecule with that of each of four nearest neighbouring molecules. For the perfect tetrahedral arrangement each addend is equal to zero and thus q=1. In contrast, for the chaotic one, the q value is equal to 0. Calculation of this factor is done over all possible frames, taken from the MD simulations. However, the detailed analysis of eq 1 reveals one serious drawback. In the confined systems the nearest four neighbours not necessary have to form the first coordination shell. It is easy to imagine the situation when a water molecule is near the wetted surface. Even if its nearest neighbours form the perfect ice the value of q is lower than unity. It comes from the fact, that the number of molecules forming the first shell can be lower than four. Hence, the direct use of eq 1 in such situations may lead to erroneous results.

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Thus, for the purpose of this study we propose a new procedure. We propose to modify eq 1, linking it with the calculation of the number of hydrogen bonds (nhb). Firstly the nhb is calculated and the information about the number (N) of water molecules in the first shell (satisfying a first geometrical criterion) is obtained. If it is greater than four, the nearest four molecules are taken into account, and eq 1 is used for the SF calculation. If it is lower or equal to four (but greater than unity) the following formulae is used: 2

3 ⋅ (5 − N )! N −1 N  1 q = 1−  cosθ jik +  , 1 < N ≤ 4 ∑ ∑ 8 3 j =1 k = j +1 

(2)

where: N is the number of neighbours in the first shell. This equation is given without proof, but it is equivalent to eq 1. For tetrahedral arrangement it gives 1, independently of the number of neighbours in the first shell. To coefficient multiplier (5-N)! was added in order to get identical results to that drawn from eq 1 that can be checked for any angle value. Given above equation, together with other characteristics (density and the number of hydrogen bonds) can be applied for the description of the properties of interfacial water forming a nanodroplet. To do this one can start from the Basal-plane HOPG system. Figure S5 shows water oxygen and hydrogen densities plotted along the z axis for the Basal plane HOPG system (εCO = 0.45 kJ/mole). One can see that the maxima of oxygen and hydrogen density are located almost at the same z distances, suggesting that H atoms of water molecules are located between O atoms and thus hydrogen bonds along the x,y plane are formed. Further information for this system can be obtained from the data collected on Figure 4. One can observe that at large z distances the oxygen density, nhb and SF tend to 0.87 g/cm3, 3.26 and 0.69 i.e. the values observed for the bulk liquid water.57 However, for smaller z distances the overlapping of maxima on nhb curve at z = 5.2 and 8 Å(with nhb = 3.3) with two minima on oxygen density curves occurs. The rise in SF values is simultaneously observed in these regions leading to the conclusion about the presence of more ordered structure. Surprisingly however these results suggest that if tetrahedral structures are present they are located in the regions of low density. Moreover the lowest SF value in the region close to the basal plane is observed. This means that if any ordered water structures are present in this region they are not tetrahedral ones.

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Figure 4. The comparison of hydrogen bonds number, oxygen densities and structure factors for the basal plane HOPG system (εCO = 0.45 kJ/mole). Inset shows the density profile with marked z distance with (0,0) point located at the top of substrate surface carbon atoms.

For comparison Figure 5 shows the same data as collected in Figure S5 and Figure 4, but for the HOPG-Side-900+3A system. In this case also the maxima of O and H density ale placed closely, and six maxima are observed due to ordering of water inside the slit. 2.4 hydrogen bonds per a molecule are formed due to the fact, that the presence of carbon wall restricts the number of neighbours. Thus, similar restriction of nhb to this reported by Leroy and Muller - Plathe is observed.29 The presence of density of oxygen and hydrogen maxima inside the slit seems to suggest that water molecules are arranged in this region. Lower than for the bulk water SF value shows that if ordered structures of water are present in this region they are not tetrahedral ones as well. Anyway, the above observations suggest the presence of the some kind of ordered water structures, even if they are not “typical” ones. Careful studies of all systems however, do not show the existence of such structures. In fact only liquid state is observed i.e. there no clear arrangement of water molecules is seen even in the case of systems with strongly confined water (see Figure 3, Figure S2 and Figure S3). Summing up, the analysis of the results collected in Figure 4, Figure 5 and in Figure S5, together with similar plots for other systems provide some useful information about the state of water at the vicinity of a HOPG surface. However, as it will be shown below, the more detailed picture emerges from the analysis of the density maps obtained after the long term

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simulation. Namely that the water molecules are ordered but not in a “typical” way, i.e. no phase transition to solid-like state takes place.

Figure 5. Oxygen atoms of water characteristics (densities, number of hydrogen bonds and SF) calculated for the HOPG-Side-900+3A system and for εCO = 0.45 kJ/mole. Inset shows the density profile with marked z distance with (0,0) point located at the bottom of the slit.

“Interferencing” water? In our recent studies we pointed out the importance of longterm simulations for the case of WCA calculation.38,58 It was proved, that only the long term simulations guarantee the final WCA values independent on the starting configuration. Moreover, the dependence between WCA for infinite nanodroplet converges with the values calculated for cylindrical ones.58 Additionally the long term simulations guarantee very small WCA error.38,58 The analysis of the data collected on Figure 6 (oxygen and hydrogen density, SF, and nhb for some selected systems) obtained after the long term simulation, shows the existence of some correlations suggesting the spatial arrangement of water molecules. From the detailed analysis one can conclude that hydrogen atoms are located between oxygen atoms and the arrangement of hydrogen depends on the arrangement of oxygen. Moreover one can see that in fact the first hydrogen density peak can be deconvoluted into four peaks (see Figure S6) and each of them is responsible for the arrangement of hydrogen atoms.

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Figure 6. Oxygen and hydrogen density, structure factor and the number of hydrogen bonds maps for selected systems (εCO = 0.45 kJ/mole). For the system HOPG-Side-900+3A the circle shows overlapping of water oxygen and hydrogen atom densities.

Figure 7. Interference pattern for the oxygen density map created for water molecules on the surface of HOPG - Side-150 (εCO = 0.45 kJ/mole). Inset shows the map generated by the application of the model proposed in this study.

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However, in each case this arrangement is different and apparently correlated with the geometry of the substrate (see also Figures 7,9 and S7). Thus it can be concluded that observed arrangement is the result of water interaction with the surface, and is not caused by any solid-like phase transition. Although observed density patterns are different they have one common feature - they resemble interferometry patterns (Figure 7). In other words, water molecules (or more strictly speaking the averaged values of their positions) behave like waves. To confirm this hypothesis we have elaborated a mathematical test if it is possible to recover density patterns with the use of a wave theory. For this purpose we have used the following equation, that takes into account all necessary properties of examined systems:

()

()

(

)

(

)

r 1 r  r r r r  I R = ∏ Pi R ×  ρ 0 + ∑ D f R − Ri ⋅ H f R − Ri  2 i i  

(3)

where:

ρ 0 - is the initial (unaffected by the interference) oxygen atoms density, r R - oxygen atom position for which interference pattern is calculated,

r Ri - position of an i-th substrate atom,

()

r Pi R - probability of finding of the oxygen atom with respect to i-th substrate atom,

(

)

(

)

r r D f R − Ri - decay function,

r r H f R − Ri - harmonic function.

Probability function can be essentially of any sigmoidal form, giving the values: 0 for the direct vicinity of a substrate atoms, and 1 for distance running to infinity. The best choice however, seems to be the use of the error function, since it is frequently used in probability calculations:

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r r   R − Ri − Rc   1   Pi = 1 + erf    2 ∆   

(4)

where: Rc - distance to the substrate atom at which probability of finding oxygen atom is equal 0.5, ∆ - erf function distribution width.

The harmonic function has been borrowed from the quantum mathematics, and it takes the form:

r r   R − Ri − Rs  H f = exp i ⋅ 2π   λ   

    

(5)

where: Rs - is the phase shift of wave,

λ - the wave length.

Thus, we have:

r r r r   R − Ri − Rc     R − Ri − Rs r 1  r r    ×  ρ + D R − R ⋅ exp i ⋅ 2π  I R = ∏ 1 + erf  f i      0 ∑  2 i  ∆ λ i      

()

(

)

       

(6)

The choice of the form of probability and harmonic functions seems to be obvious. The choice of the form of a decay function is a little bit problematic, since the theory (to the 19


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best of our knowledge) of observed phenomenon is unknown. In fact any function whose value that tends to 0 with a distance to the substrate atoms can be used for fitting. Fortunately, necessary information can give the MD calculation itself. The form of this function should be related to the form of the Lennard-Jones (L-J) equation, used for the calculation of O-C dispersive interaction energy. The simplest is the power function of the form:

 σ r r D f R − Ri = A ⋅  r r  R−R i 

(

)

   

Z

(7)

This function has two adjustable parameters A, and Z. The first one is connected with the energy of interaction of oxygen atoms with the substrate (the stronger is this interaction, the larger A value is expected). The value of σ is introduced for compatibility with the L-J function and was fixed (equal to 3.19 Å for C-O dispersive interaction) since it is mathematically connected with the parameter A. The final equation used in this study has six adjustable parameters and takes the form:

r r  R − Ri − Rc r 1  I R = ∏ 1 + erf   2 i  ∆  

()

     × ρ + A ⋅  r σ r  R−R    0 ∑ i i    

Z r r    R − Ri − Rs  ⋅ exp i ⋅ 2π     λ   

    (8)    

In order to find the values of the parameters the following procedure was used. Firstly the density curve (which should be fitted) was obtained from the MD calculations of wetting of a Basal plane HOPG surface. From these calculations the matrix of oxygen density by the projection of oxygen atoms position on the x, z plane was obtained. Mean values of density were calculated along the axis z, perpendicular to the substrate. In this way the plot of the density dependence on the distance to the surface of graphite is obtained (Figure 4). Theoretical curve, based on the eq 8 was obtained in the similar manner. Appropriate density matrix was calculated and averaged similarly to that obtained from MD simulations. Obtained

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curve was fitted, until satisfactory results were obtained (Figure 8, red line). Obtained optimal parameters are listed in the Table 1 (second column).

Table 1. Parameters of the wave model (eq 8) used for interferometry patterns calculation.

Parameter For eq 7 Rc[Å] ∆[Å] ρ0 A σ[Å] Z(Z1) Z2 Rs[Å] λ[Å] Rd[Å]

3.2 0.25 0.87 1 3.19 4 ---0.6 3.26 ----

For eq 9 3.2 0.55 0.87 7 3.19 6 16 0.4 3.2 6.5

As can be seen, proposed by us description gives similar results to that obtained from MD simulations. To check if there is a better form of decay function we have also used a bit more complicated power form - piecewise one:

(σ / R )Z 2 + Ds , R < Rd r r  D f R − Ri = A ⋅  (σ / R )Z 1 , R ≥ Rd 

(

)

(9)

where:

r r R = R − Ri , Rd - additional adjustable parameter, dividing subdomains,

Ds = (σ / Rd ) − (σ / Rd ) - shift value necessary to obtain continuous curve. Z2

Z1

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It occurred, that such a form of decay function much better reflects the change of density, that can be seen in Figure 8 (gray line). Parameters of this improved form are listed in the Table 1, third column.

Figure 8. The fit of experimental oxygen density with the model proposed in this study for the Basal-plane HOPG system (εCO = 0.45 kJ/mole), for two types of the decay function given by eq 7 and eq 9. Inset shows the behaviour of Df.

Selected interference patterns, that are seen in Figure 9 (top left corners) and Figure S7 are calculated with use of this form of decay function.

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Figure 9. Interferometric model at work. Oxygen density profiles from MD simulation (large images) and from our model (insets), (εCO = 0.45 kJ/mole).

Finally we show how our model works in details. On Figure 10 we present images describing the interference method used by us. For the sake of clarity arbitrary parameters are used. This method can be divided into 5 separate steps:

a) Everywhere in the 2D space the initial value ρ0=0.87 (like oxygen density in the bulk water) is given (Figure 10 A).

()

r I a R = ρ0

(10)

b) The positions of the substrate atoms are set (here represented by 3 points for simplicity). These positions are taken from projection on the x, z plane of those used in MD simulations (Figure 10 B). c) Substrate atoms generate waves. The following equation gives pattern represented by Figure 10 C.

r r   R − Ri − 0.3   3 r   I c R = ρ 0 + ∑ 0.1⋅ exp i ⋅ 2π     3 . 3  i =1   

()

(11)

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d) But waves decay with distance to substrate atoms (Figure 10 D): 3 r r   3.19   R − Ri − 0.3   3 r      ⋅ exp i ⋅ 2π I d R = ρ 0 + ∑ 2.0 ⋅ r r      3.3  R − Ri i =1     

()

(12)

e) There is no water molecules in the vicinity of substrate atoms (Figure 10 E):

3 r r r r   R − Ri − 3.2     3.19   R − Ri − 0.3   3 r 1 3           (13) I e R = ∏ 1 + erf ρ + 2.0 ⋅  r r  ⋅ exp i ⋅ 2π      0 ∑   2 i =1  0.2 3 . 3  R − Ri i =1           

()

Figure 10. Schematic representation of the interference method. Perfect distribution of oxygen atoms of water molecules in a 2D space (A), three substrate atoms (B), waves generated by a substrate atoms (C) are decaying with distance (D). Substrate atoms occupy a space excluded for water molecules (E).

Of course we are aware, that presented above attempt of the mathematical description of wave nature of oxygen density distribution is the arbitrary one. But it seems to be apparent, that in most cases it gives very similar patterns to those obtained from the MD simulations. For some of them differences are seen only (see Figure S7). Explanation for this discrepancy is relatively simple - proposed by us description is simplified. But the wave nature and interference behaviour of water molecules seems to be proven. Hence presented attempt should be called as the hypothesis rather than the theory. This means, that the proper description (theory) should be developed with consideration of the following hints:

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1. Wave form of description of molecular simulations should be used - presumably DFT one. 2. It is worth of consideration the influence of local density maxima, observed near the substrate atoms on other regions of the molecular system. Proposed hypothesis hardly gives such pattern. 3. Due to very long calculations in 3D space interference patterns were calculated in 2 dimensions. Along the y axis everywhere is the same density value. Such assumption is valid, since such tendency is observed. But perhaps calculations in 3D space can give more accurate results.

We leave this opportunity to the readers however, since the essential reason of use the wave theory and interference had one goal, namely that the observed discrete distribution of density is not caused by any kind of liquid-solid phase transition but by the shape of the substrate and its influence on the behaviour of interacting with it water molecules.

CONCLUSIONS

Proposed by us the new procedure of the CTWT point assessment shows that this transition strongly depends on the type of HOPG surface atoms arrangement. The CTWT point shifts towards larger εCO values with the decrease in the HOPG side angle. For the structures possessing the side angle across the range of 15-45˚, the εCO values of CTW transition are similar. Above the εCO close to ca. 0.27 kJ/mole the Wenzel nonwetting as well as Wenzel wetting (for the HOPG-Side-15˚ above εCO = 0.35 kJ/mole) states of water on a HOPG-Side surface occur. Since experimental WCA was recovered from the MD simulation for εCO = 0.45 kJ/mole13 one can conclude that the Wenzel effect significantly contributes to the WCA measured on the edge carbon atoms containing HOPG surfaces, irrespective of the side angle value. Thus the contamination of the Basal plane HOPG surface with some edge carbon atoms containing surfaces can drastically change the WCA by the induction of the Wenzel states. For the HOPG-Side-90˚+d structures the value of εCO characteristic for the CTWT increases with the d value. Above εCO = 0.38 kJ/mole one can expect the complete filling of

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the substrate slits below a nanodroplet. The influence of Wenzel effect on the WCA is strongly pronounced for the d values larger than 3Å (i.e. for the slits with diameter 6.4 Å). Above this critical slit width the pores are filled by water molecules. The structure of water inside slits as well as interfacial water resembles the ordered liquid, and this was proved by the analysis of density profiles, number of hydrogen bonds and modified for the purpose of this study structure factors. Finally it is shown that the analysis of all parameters describing the confined water leads to the conclusion about the presence of characteristic interference patterns. Simple model describing this effect is proposed as the starting point for further considerations.

ASSOCIATED CONTENTS Supporting Information The Supporting Information is available free of charge on the ACS Publications website.

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