Bonthuis, Douwe Jan

Loche, Philip

Netz, Roland R.

Schlaich, Alexander

Wolde-Kidan, Amanuel

English

Institutional Repository of the Freie Universität Berlin

Comment on Hydrophobic Surface Enhances Electrostatic Interaction in WaterPhilip Loche,1 Amanuel Wolde-Kidan,1 Alexander Schlaich,2 Douwe Jan Bonthuis,1 and Roland R. Netz11Fachbereich Physik, Freie Universita¨t Berlin, 14195 Berlin, Germany2Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France(Dated: March 17, 2020)In inhomogeneous systems that contain interfaces, thewater dielectric constant becomes anisotropic and posi-tion dependent [1–3]. In their letter, Sato et al. [4] extractperpendicular dielectric constant profiles ε⊥(z) from MDsimulations of water at a planar hydrophobic surface us-ing the expression[ε⊥(z)− 1][2ε⊥(z) + 1]3ε⊥(z)=〈µ2⊥,0(z)〉 − 〈µ⊥,0(z)〉24piε0kBTa3, (1)which is derived for infinite homogeneous systems [5],where kBT denotes thermal energy, ε0 is the vacuum per-mittivity and µ⊥,0(z) is the water dipole moment insidea probe sphere of radius a (subscript 0 denotes zero ex-ternal field). The correct expression for ε⊥(z) in planargeometry looks very different [1],ε−1⊥ (z) = 1−〈m⊥,0(z)M⊥,0〉 − 〈m⊥,0(z)〉〈M⊥,0〉ε0kBT + (〈M2⊥,0〉 − 〈M⊥,0〉2)/V, (2)where m⊥,0(z) is the local perpendicular polarizationdensity, obtained from the local charge density profileρ0(z) via m⊥,0(z) = −∫ z0dz′ρ0(z′), and M⊥,0 is the in-tegral ofm⊥,0(z) over the system volume V . To test thesedifferent expressions for ε⊥(z), we here compare the elec-tric field profile induced by a finite constant displacementfield D⊥, extracted from simulations according to∆E⊥(z) = ε−10 [D⊥ −m⊥(z) +m⊥,0(z)] , (3)with the linear response prediction∆E⊥,lin(z) = ε−10 ε−1⊥ (z)D⊥ , (4)where D⊥ = D′⊥+ (M⊥−M⊥,0)/V contains the explicitdisplacement field D′⊥ and the field due to periodic im-ages [1, 5].Similar to Ref. 4, we simulate water betweentwo frozen neutral nonpolarizable planar hydrophobicgraphene layers at a distance of L = 3 nm. Longrange electrostatics are handled using the smooth par-ticle mesh Ewald (SPME) technique with tin-foil bound-ary conditions (see Ref. 6 for simulation details). Inthe finite-field simulations we apply an external field ofD′⊥/ε0 = 0.25 V nm−1, which is well in the linear regime[2]. The field acts by exerting a supplemental force onall partial dcharges. The simulation time is 500 ns witha time step of 2 fs in the NV T ensemble. Without exter-nal field we obtain in the slab center a dielectric constantof ε⊥ = 69 ± 9 consistent with bulk results [7]. Figure02000ρm/(kgm−3)zGDS ρbulkm0.0 0.2 0.4 0.6 0.8 1.0 1.2z / nm0.00.5∆E⊥/Vnm−1Eqs. (1)+(4) Eqs. (2)+(4) sim., Eq. (3)(a)(b)FIG. 1. (a) Water mass density profile at a graphene layer,the Gibbs dividing surface position is denoted by a red ver-tical line and the bulk density by a horizontal dotted line.(b) Perpendicular electric field profiles: The black line shows∆E⊥(z) directly extracted from a simulation for a finite ap-plied displacement field of D′⊥/ε0 = 0.25 V nm−1, accordingto Eq. (3), the blue and red lines show the linear-responseprediction according to Eq. (4) using Eq. (1) [4] and Eq. (2),respectively.1(a) shows the water mass density profile ρm(z), wherez = 0 is the position of the charge neutral graphene layer,while Fig. 1(b) shows the perpendicular electric field pro-file ∆E⊥(z) calculated using three different routes: Theblack line shows ∆E⊥(z) according to Eq. (3) from sim-ulations with an explicitly applied D′⊥ field, while thelinear-response predictions according to Eq. (4) in con-junction with the expressions for ε⊥(z) from Eqs. (1) and(2) are shown by blue and red lines, respectively. Clearly,the simulated electric field profile agrees perfectly withthe predictions from Eq. (2) and shows oscillatory behav-ior, which is completely missed by the dielectric profilecalculated according to Eq. (1). That a homogenous D⊥field induces locally a change of the electric field thathas an opposite sign as the applied displacement field re-flects the intricate layered water structure at interfaces.We conclude that Eq. (1) is not suitable to treat locallyresolved electrostatic effects at interfaces.We are grateful to D. Mun˜oz-Santiburcio for discus-sions. Support from SFB 765 (DFG) and the EU ITNNanotrans is acknowledged.2[1] H. A. Stern and S. E. Feller, The Journal of ChemicalPhysics 118, 3401 (2003).[2] D. J. Bonthuis, S. Gekle, and R. R. Netz, Langmuir 28,7679 (2012).[3] S. Gekle and A. Arnold, Phys. Rev. Lett. 111, 089801(2013).[4] T. Sato, T. Sasaki, J. Ohnuki, K. Umezawa, andM. Takano, Phys. Rev. Lett. 121, 206002 (2018).[5] M. Neumann, Molecular Physics 50, 841 (1983).[6] P. Loche, C. Ayaz, A. Schlaich, D. J. Bonthuis, and R. R.Netz, J. Phys. Chem. Lett. 9, 6463 (2018).[7] C. Vega and J. L. F. Abascal, Phys. Chem. Chem. Phys.13, 19663 (2011).

Comment on “Hydrophobic surface enhances electrostatic interaction in water”

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Comment on “Hydrophobic surface enhances electrostatic interaction in water”

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