Confined KCl Solution between Two Mica Surfaces: Equilibrium and

Sep 8, 2015 - We have simulated the molecular dynamics of a KCl solution confined between two mica surfaces in equilibrium with a reservoir. For compa...
0 downloads 3 Views 5MB Size
Download PDF
Article pubs.acs.org/JPCC

Confined KCl Solution between Two Mica Surfaces: Equilibrium and Frictional Properties Alain Dequidt,*,†,‡ Julien Devémy,†,‡ and Patrice Malfreyt†,‡ †

Clermont Université, Université Blaise Pascal, Institut de Chimie de Clermont-Ferrand, BP 10448, F-63000 Clermont-Ferrand, France ‡ CNRS, UMR 6296, ICCF, F-63171 Aubière, France ABSTRACT: We have simulated the molecular dynamics of a KCl solution confined between two mica surfaces in equilibrium with a reservoir. For comparison, the simulations were also performed with pure water under the same conditions. The relation between normal pressure, lateral pressure in the solution layer, and quantity of water was first investigated. The position and orientation of the chemical species were then determined, showing the local molecular structure. Lastly, we simulated the mechanical response of the system submitted to a constant slip velocity for determining its frictional properties.

■

INTRODUCTION Friction between solid surfaces in relative motion is responsible for energy dissipation and wear. In mechanical systems in general, it is thus necessary to control friction, often to reduce it as much as possible. Usually, a lubricating fluid is inserted between the surfaces in motion, which replaces solid friction by viscous dissipation due to the high shear of the confined fluid. When the thickness of the lubricating layer is very small, an intermediate regime of lubricated friction takes place. Some biological systems like synovial joints show that very low friction and wear can be achieved in this regime.1,2 However, despite their high practical interest, the mechanisms of lubricated friction are not yet understood in general.3−5 The lubrication properties depend on the shape and on the chemical nature of the lubricating fluid.6 It was shown experimentally that confining water does not significantly increase its viscosity, contrary to other liquids like alcanes,7,8 although the dependence of viscosity on the hydrophobicity of the surface is debated.9,10 The viscosity of salt solutions confined between mica surfaces was also shown to be close to their bulk viscosity,11 even down to molecular thicknesses.12 The interest of using a salt solution as a lubricant instead of pure water is that the liquid layer of salt solution supports higher normal pressures, presumably due to hydration layers around the salt ions.2,11,13−15 The structure of adsorbed water on mica surfaces was simulated using Monte Carlo simulations.16 The local structure and dynamics of pure water at mica surfaces and ion-exchanged mica surface were then simulated by Sakuma et al. using molecular dynamics.17−19 The rotation and jump dynamics of water at the interface with a mica surface was also simulated by Malani and Ayappa.20 The understanding of the local structure of salt solutions at the interface with charged surfaces is of high importance in © XXXX American Chemical Society

electrochemical devices and in charged colloidal suspensions. Interfaces of a bulk salt solution with metallic or graphic electrodes or clay or silica particles for instance were studied in the literature, in particular using simulations.21,22 The local structure and molecular mobility of pure water and salt solution confined between mica surfaces was simulated by Leng.23−25 In the latter simulations, the chemical potential of water was kept constant using an explicit liquid vapor equilibrium inside the confined layer. With this method, it is easy to vary the normal pressure and study the corresponding change in the sample thickness.26 However, the salt concentration in the confined liquid varies when the liquid/vapor ratio varies. Also, this kind of system is not homogeneous because of the liquid vapor equilibrium and is not appropriate for shear simulations. Kalra et al. used a water permeable membrane to keep the chemical potential constant,27 but this cannot be done with two mica surfaces. The friction lubricated by a ultrathin water film was simulated by Paliy et al. using Langevin dynamics.28 Their simulations use generic surface models without partial charges on the atoms of the surface. In the present work, we introduce an alternative method for controlling the chemical potential of the confined aqueous solution in simulations of the molecular dynamics. This method is designed to study the local structure inside the liquid layer and to simulate the friction by studying the mechanical response to shear. The paper is organized as follows. In section 2, we introduce the simulated systems and give the details of the simulation procedure. In section 3, we present and comment on Received: July 16, 2015 Revised: September 4, 2015

A

DOI: 10.1021/acs.jpcc.5b06880 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

of 1 ion pair for 15 water molecules. This corresponds to 27.6 g per 100 g of water. This is comparable to, but below, the solubility of KCl (35.5 g per 100 g of water at 25 °C32). The systems were then relaxed during 500 ps in the nPT ensemble at 300 K and 1 atm using a time step of 1 fs. Figure 1 is a snapshot of the simulated system after equilibration.

the simulation results concerning the thickness dependence on pressure, the local structure in the confined layer, and the response to shear. Lastly, we summarize the important results in the conclusion and suggest interpretations.

■

SIMULATION DETAILS The simulated system consists of a mica crystal and a KCl aqueous solution. The mica crystal is of type muscovite-2M1 of formula KAl2(Si3Al)O10(OH)2 with symmetry space group C 2/ c. The crystallographic data was taken from the American Mineralogist Crystal Structure Database.29 The mica crystal was built by replicating the primitive cell 8 times along the a vector, 4 times along the b vector, and 2 times along the c vector, which gives a crystal size around 40 Å in each direction. Then 1/4 of the tetrahedral Si sites were picked randomly and substituted by Al. We ensured that no two substituted sites were direct neighbors. The periodic boundary conditions are applied in the three dimensions and the simulated mica crystal contains 5376 atoms. The CLAYFF force field30 was used for the mica and the ions, together with the SPC water model. All O−H bonds were constrained in length using the SHAKE algorithm. The force field parameters are given in Tables 1 and 2 for completeness. The molecular dynamics simulations were performed using the LAMMPS software.31

Figure 1. Snapshot of the simulation box at the maximum thickness h = 64 Å. The solution contains 3000 water molecules and 200 ion pairs.

Table 1. Non Bonded Force Field Parameters Used in the Simulations;30 (Seea) tetra

Si Altetra Alocta Obridge Osubs−t Ohydroxy Hhydroxy Owater Hwater K+ Cl−

q

σ (Å)

ϵ (kcal mol−1)

2.1 1.575 1.575 −1.05 −1.168 75 −0.95 0.425 −0.82 0.41 1.0 −1.0

3.302 03 3.302 03 4.272 41 3.165 54 3.16554 3.165 54 0.0 3.165 54 0. 3.334 01 4.399 97

1.8405 × 10−6 1.8405 × 10−6 1.3298 × 10−6 0.1554 0.1554 0.1554 0.0 0.1554 0.0 0.1 0.1001

■

RESULTS Thickness. Since the experimental data are available at an imposed normal pressure P⊥, we aim to determine the thickness of the water film under these conditions. Experimentally, the water film is in equilibrium with a reservoir, i.e. at constant chemical potential of the solution. In molecular simulations, it is not easy to impose a constant chemical potential, especially when electroneutrality of the ionic solution has to be preserved. For this reason, we chose to run simulations at constant number of molecules N, in the NPT ensemble. N was varied from 3000 water molecules to 0, by maintaining the KCl:water ratio to 1:15. This was done by deleting 15 randomly chosen water molecules (and 1 ion pair for the KCl solution) every 50 ps. The simulations were run at constant normal pressure of 3 and 1000 atm. After each molecule deletion, the system was allowed to equilibrate at a new smaller thickness. The film thickness h and the lateral water pressure P∥ were computed at each time step and averaged over the last 12.5 ps, which correspond to wellequilibrated configurations. Subsequently, a new molecule deletion is attempted. h is defined here as the difference between the simulation box size in the z direction in the current system and in the initial uncleaved mica crystal. The results are shown in Figures 2 and 3. Figure 2 shows the dependence of the separation distance between the mica surfaces on the number of water molecules for a pure water solution and a salt solution at two different pressures. As expected, the curve shows a monotonic decrease of the thickness with respect to the number of water molecules. This figure shows the formation of discrete layers at small thickness characterized by the presence of plateaux in the curve. In order to deeply investigate this interesting zone, the system was simulated again at small thickness, by deleting only 1 water molecule at each deletion in the case of pure water, and by replicating the system twice in the x and y direction in the case of the KCl solution. We note that the first layer is more marked in

a

q is the electric charge, and the Lennard-Jones energy is defined as ⎛ σ 12 σ 6⎞ ULJ = 4ϵ⎜ r − r ⎟. ⎝ ⎠

()

()

Table 2. Bonded Force Field Parameters Used in the Simulations30 (Seea) r0 (Å) hydroxy

hydroxy

H Hwater

O Owater Hwater Alocta

Owater Ohydroxy

Hwater Hhydroxy

k (kcal mol−1 Å−2)

1.0 1.0 θ0 (deg)

554.135 554.135 kθ (kcal mol−1 rad−2)

109.47 109.47

45.7696 30.0

Ubond = k (r−r0)2, Uangle = kθ (θ − θ0)2. Note that there are no explicit Al−O bonds, but there are Al−O−H angles. The lengths of the OH bonds are constrained using the SHAKE algorithm. a

The mica crystal was first cleaved by stretching the simulation box in the z direction, perpendicular to the a and b lattice vectors. The mica was split at a K+ layer, with one-half of the K+ ions sticking to each surface. Then, either pure water or a KCl solution was inserted in the gap. The aqueous layer comprises 3000 water molecules in both cases and the KCl solution is in the proportion B

DOI: 10.1021/acs.jpcc.5b06880 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 2. Dependence of the thickness of the solution at constant pressure on the number of water molecules.

Figure 4. Snapshot of the pure water solution at the stable equilibrium thickness at 3 atm.

pressure, two stable thicknesses would be possible, the second one between 4 and 5 Å corresponding to 2 water layers. As expected from the usual stability criterion, the higher the normal pressure, the smaller the equilibrium thickness. However, the effect is quite small as compared to the influence of the presence of KCl ions. With KCl ions in the solution, the equilibrium thickness is about 22% higher than in the pure water at 3 atm, while increasing the normal pressure to 1000 atm only decreases the thickness by about 9%. Figure 3 shows that a given thickness, the salt solution leads to a smaller lateral pressure underlining the attractive role of the ions. Structure at the Interface. The number density profiles were determined and plotted as a function of the distance to the mica surface. Since the equilibrium thickness depends on the composition and on the pressure, it is more convenient to compare the structure in the thick films with the same number of water molecules (here 3000 water molecules). In Figure 5, we compare the structure of the interface with and without K+ and Cl− ions. The reference position z = 0 was chosen as the average position of the outer oxygen layer of the mica crystal. First, we

Figure 3. Lateral water pressure P∥ as a function of the thickness of the solution. The equilibrium thickness is such that P∥= Pres = 1 atm. This pressure is indicated by the horizontal line. The equilibrium is stable if the slope of the curve is positive.

the KCl solution, but the influence of the surface seems sensible at a greater distance in the pure water, with thickness oscillations extending farther. Let us now discuss what would happen if the aqueous film could exchange matter with a reservoir at pressure Pres. In experiments, under an imposed normal pressure P⊥, the separation distance changes from a large value (weak compression) to an equilibrium distance corresponding to P⊥. At the beginning, at high thickness h, P∥ > Pres (see Figure 3), so water is expelled out of the film, and h decreases (see Figure 2). The arrows in Figure 3 indicate the spontaneous evolution of thickness. At some point, P∥ drops below Pres, then water is attracted back inside the film, so that h increases again. The stable equilibrium is thus reached when P∥= Pres. This equation has several solutions, but the system choses the first stable one that it encounters, indicated by the black dots. The stability criterion, deduced from the direction of the arrows, can be stated as dP dh

> 0. Note that this stability criterion is opposite to the usual dP

one dh⊥ < 0, requiring that increasing normal pressure should decrease the volume. Figure 3 shows that only one stable equilibrium exists with a water layer if the reservoir is at ambient pressure 1 atm. The corresponding thickness is around h = 2 Å in each case, which corresponds roughly to 1 water layer (see Figure 4). The oscillations of the curves show that at higher reservoir

Figure 5. Density profile close to the mica surface. z = 0 is defined as the average position of the outer oxygens of the mica layer. Dashed lines: pure water, full lines: KCl solution. C

DOI: 10.1021/acs.jpcc.5b06880 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C note that the K+ ions essentially remain adsorbed at the mica surface and the water profile displays typical oscillations indicating a certain layering of the interface. Since half of the initial K+ ions sticks to each surface, only half of the K+ sites remains occupied and there is empty space accessible to other molecules. In the pure water, the space is occupied by water molecules and mostly by the H atoms. In the KCl solution, many of the holes are filled by K+ ions, which are slightly shifted toward the bulk water, and there is less room for water molecules. The mica surface is thus positively charged, so that the Cl− ions are attracted and form a second layer of opposite charge. A third layer with a slight excess of K+ ions is also visible, and then the concentrations become more or less uniform, although water still displays some layering. We observe that the position of the water layers is the same with and without KCl, only the intensity and width of the peaks being altered. Figure 6 shows the orientation of the water molecules as a function of the distance to the mica surface. The orientation is

Shear Stress. We focus here on the calculation of the response of the system to a relative slip of the mica surfaces. A constant shear rate was applied by deforming the simulation box at velocity v ranging from 2 × 10−4 to 1.0 × 10−3 Å fs−1. The tangential stress σ was then recorded at each time step and averaged during 5 ns, after the stationary regime was established, i.e. after 500 ps. The stress as a function of slip velocity is shown on Figure 7, while Figure 8 shows the stress as a function of normal pressure.

Figure 7. Shear stress as a function of velocity.

Figure 8. Shear stress as a function of pressure at velocity 2.0 × 10−4 Å fs−1, 1.0 × 10−3 Å fs−1 and 5.0 × 10−3 Å fs−1 (from bottom to top). The corresponding friction coefficients averaged over velocities are μKCl = −0.03 and μpure = 0.01, which is extremely small.

The resulting mechanical behavior does not strictly speaking correspond to standard Coulomb friction, because the tangential stress is dependent on the slip velocity.33 The confined solution does not show a Newtonian behavior, because stress is not proportional to shear velocity. Rather, a concave curve is obtained, increasing with the slip velocity, suggesting an Eyringlike behavior of the aqueous film. This is consistent with the shear thinning observed in nanoconfined water.34 Such an Eyring-like behavior was recently observed in lubricated friction experiments between mica surfaces at high normal pressure.2 We did not measure any static friction but we do not exclude that it could exist in these systems. Measuring it precisely would require to run very long simulations at constant shear stress and to detect an onset in the average slip velocity. As for a velocity-

Figure 6. Orientation profile close to the mica surface in the KCl solution. θ is defined for each water molecule as the angle between one of the HO vectors and the normal to the surface, while z is the position of the midpoint of the chosen HO pair. z = 0 is defined as the average position of the outer oxygens of the mica layer. (a) bulk sample, (b) thin film.

measured by the cosine of the angle of an H−O bond of the water with the z direction. It is clear that the water molecules the closest to the surface are very oriented, so that water molecules form H bonds with the outer oxygens of the mica crystal. The distribution of orientation shows a maximum at cos θ = 1 for the bottom surface and at cos θ = −1 for the top surface. There is not much difference with and without K+ and Cl− ions and the situation is also the same in thin and thick water films.

dependent dynamic friction coefficient defined as μ =

∂σ ∂P⊥

, all v

what can be said from our simulations is that it must be “small”, D

DOI: 10.1021/acs.jpcc.5b06880 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C because σ as a function of P⊥ is constant within the error bars. Stress fluctuates a lot during the simulation, with a standard deviation around 500 atm, but the standard error of the mean of stress on long simulations is only a few atm even taking into account time correlations. However, the true uncertainty on σ is greater, and we estimate it from repeatability to a few hundreds of atmospheres. We thus estimate from the simulations that the dynamic friction coefficient μ is in any case less than a few tenths. Regarding friction, the situation is the same with and without KCl in the solution, and more importantly, the stress values in both cases are equivalent within the error bars. The evolution of the density profiles shows that the structure changes slightly on shear (Figure 9). The notable differences are

The study of the structure reveals that the vacant positions of the K+ surface layer are mostly occupied the cations of the solution. The anions form a second layer, compensating the excess charge. In the absence of ions, the vacant positions are occupied by water. The water layer the closest to the surface is very much oriented, with the hydrogen atoms pointing toward the surface, where they can H-bond to the outer oxygens of the mica. The density profile under shear shows a slight increase of the solution thickness. The friction behavior is very different from solid friction: the shear stress is much more dependent on slip velocity (varied by a factor of 25.0) than on the normal pressure (varied by a factor of 333.0). The velocity-averaged friction coefficient is very low (of the order of 0.01) but could not be determined with a high precision. The presence of salt does not have a significant impact on the shear stress.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Chen, M.; Briscoe, W. H.; Armes, S. P.; Klein, J. Lubrication at Physiological Pressures by Polyzwitterionic Brushes. Science 2009, 323, 1698−1701. (2) Ma, L.; Gaisinskaya-Kipnis, A.; Kampf, N.; Klein, J. Origins of hydration lubrication. Nat. Commun. 2015, 6, 6060. (3) Braun, O. M.; Naumovets, A. Nanotribology: Microscopic mechanisms of friction. Surf. Sci. Rep. 2006, 60, 79−158. (4) Braun, O. M. Bridging the Gap Between the Atomic-Scale and Macroscopic Modeling of Friction. Tribol. Lett. 2010, 39, 283−293. (5) Krylov, S. Y.; Frenken, J. W. M. The physics of atomic-scale friction: Basic considerations and open questions: The physics of atomic-scale friction. Phys. Status Solidi B 2014, 251, 711−736. (6) Braun, O. M.; Manini, N.; Tosatti, E. Role of lubricant molecular shape in microscopic friction. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 195402. (7) Raviv, U.; Laurat, P.; Klein, J. Fluidity of water confined to subnanometre films. Nature 2001, 413, 51−54. (8) Raviv, U.; Perkin, S.; Laurat, P.; Klein, J. Fluidity of Water Confined Down to Subnanometer Films. Langmuir 2004, 20, 5322−5332. (9) Raviv, U.; Giasson, S.; Frey, J.; Klein, J. Viscosity of ultra-thin water films confined between hydrophobic or hydrophilic surfaces. J. Phys.: Condens. Matter 2002, 14, 9275. (10) Li, T.-D.; Gao, J.; Szoszkiewicz, R.; Landman, U.; Riedo, E. Structured and viscous water in subnanometer gaps. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 115415. (11) Raviv, U.; Klein, J. Fluidity of Bound Hydration Layers. Science 2002, 297, 1540−1543. (12) Klein, J.; Raviv, U.; Perkin, S.; Kampf, N.; Chai, L.; Giasson, S. Fluidity of water and of hydrated ions confined between solid surfaces to molecularly thin films. J. Phys.: Condens. Matter 2004, 16, S5437−S5448. (13) Sakuma, H.; Otsuki, K.; Kurihara, K. Viscosity and Lubricity of Aqueous NaCl Solution Confined between Mica Surfaces Studied by Shear Resonance Measurement. Phys. Rev. Lett. 2006, 96, 046104. (14) Perkin, S.; Goldberg, R.; Chai, L.; Kampf, N.; Klein, J. Dynamic properties of confined hydration layers. Faraday Discuss. 2009, 141, 399−413. discussion on pp 443−465 (15) Klein, J. Hydration lubrication. Friction 2013, 1, 1−23. (16) Park, S.-H.; Sposito, G. Structure of Water Adsorbed on a Mica Surface. Phys. Rev. Lett. 2002, 89, 085501. (17) Sakuma, H.; Kawamura, K. Structure and dynamics of water on muscovite mica surfaces. Geochim. Cosmochim. Acta 2009, 73, 4100− 4110.

Figure 9. Density profiles under shear. Top: pure water, bottom: KCl solution. Normal pressure: 3 atm.

(i) the profiles are more symmetric under shear, probably due to a more efficient homogenization, (ii) the film thickness tends to increase under shear.

■

CONCLUSION We simulated a confined film of water between two mica surfaces at equilibrium and under shear. By computing the lateral pressure tending to expell the molecules outside the film, we could determine the equilibrium thickness of the aqueous film. The equilibrium thickness is very thin and corresponds to one or two water layers. The presence of ions in the aqueous film significantly increases the equilibrium thickness (Figure 3) and delays the contact between the mica surfaces because the first layer is more stable (Figure 2). On the other hand, the following water layers are more stable without salt maybe due the screening of the electrostatic interaction between the water and the mica surface. E

DOI: 10.1021/acs.jpcc.5b06880 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C (18) Sakuma, H.; Kawamura, K. Structure and dynamics of water on Li +-, Na+-, K+-, Cs+-, H3O+-exchanged muscovite surfaces: A molecular dynamics study. Geochim. Cosmochim. Acta 2011, 75, 63−81. (19) Sakuma, H.; Kondo, T.; Nakao, H.; Shiraki, K.; Kawamura, K. Structure of Hydrated Sodium Ions and Water Molecules Adsorbed on the Mica/Water Interface. J. Phys. Chem. C 2011, 115, 15959−15964. (20) Malani, A.; Ayappa, K. G. Relaxation and jump dynamics of water at the mica interface. J. Chem. Phys. 2012, 136, 194701. (21) Wang, J.; Kalinichev, A. G.; Kirkpatrick, R. J.; Cygan, R. T. Structure, energetics, and dynamics of water adsorbed on the muscovite (001) surface: a molecular dynamics simulation. J. Phys. Chem. B 2005, 109, 15893−15905. (22) Dewan, S.; Carnevale, V.; Bankura, A.; Eftekhari-Bafrooei, A.; Fiorin, G.; Klein, M. L.; Borguet, E. Structure of Water at Charged Interfaces: A Molecular Dynamics Study. Langmuir 2014, 30, 8056− 8065. (23) Leng, Y.; Cummings, P. T. Fluidity of Hydration Layers Nanoconfined between Mica Surfaces. Phys. Rev. Lett. 2005, 94, 026101. (24) Leng, Y.; Cummings, P. T. Hydration structure of water confined between mica surfaces. J. Chem. Phys. 2006, 124, 074711. (25) Leng, Y. Hydration Force between Mica Surfaces in Aqueous KCl Electrolyte Solution. Langmuir 2012, 28, 5339−5349. (26) Leng, Y.; Xiang, Y.; Lei, Y.; Rao, Q. A comparative study by the grand canonical Monte Carlo and molecular dynamics simulations on the squeezing behavior of nanometers confined liquid films. J. Chem. Phys. 2013, 139, 074704. (27) Kalra, A.; Garde, S.; Hummer, G. Lubrication by molecularly thin water films confined between nanostructured membranes. Eur. Phys. J.: Spec. Top. 2010, 189, 147−154. (28) Paliy, M.; Braun, O. M.; Consta, S. The friction properties of an ultrathin confined water film. Tribol. Lett. 2006, 23, 7−14. (29) Richardson, S. M.; Richardson, J. W. Crystal structure of a pink muscovite from Archer’s Post, Kenya: implications for reverse pleochroism in dioctahedral micas. Am. Mineral. 1982, 67, 69−75. http://rruff.geo.arizona.edu/AMS/amcsd.php. (30) Cygan, R. T.; Liang, J.-J.; Kalinichev, A. G. Molecular models of hydroxide, oxyhydroxide, and clay phases and the development of a general force field. J. Phys. Chem. B 2004, 108, 1255−1266. (31) Plimpton, S. J. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1−19. (32) Lide, D. R. CRC handbook of chemistry and physics, 89th ed.; CRC Press: Boca Raton, FL, 2008. (33) Braun, O. M.; Peyrard, M. Dependence of kinetic friction on velocity: Master equation approach. Phys. Rev. E 2011, 83, 046129. (34) Kapoor, K.; Amandeep; Patil, S. Viscoelasticity and shear thinning of nanoconfined water. Phys. Rev. E 2014, 89, 013003.

F

DOI: 10.1021/acs.jpcc.5b06880 J. Phys. Chem. C XXXX, XXX, XXX−XXX