Gibbs Adsorption Impact on a Nanodroplet Shape: Modification of

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Gibbs Adsorption Impact on a Nanodroplet Shape: Modification of Young-Laplace Equation Mykola Isaiev, Sergii Burian, Leonid Anatolievich Bulavin, William Chaze, Michel Gradeck, Guillaume Castanet, Samy Merabia, Pawel Keblinski, and Konstantinos Termentzidis J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 5, 2018

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The Journal of Physical Chemistry

Gibbs Adsorption Impact on a Nanodroplet Shape: Modification of YoungLaplace Equation Mykola Isaiev1,2*, Sergii Burian2, Leonid Bulavin2, William Chaze1, Michel Gradeck1, Guillaume Castanet1, Samy Merabia3, Pawel Keblinski4, Konstantinos Termentzidis1,5** 1

LEMTA, CNRS-UMR7563, Université de Lorraine, Vandoeuvre les Nancy, F-54500, France

2

Faculty of Physics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Str., Kyiv, Ukraine, 01601 3

Université de Lyon 1, ILM, CNRS-UMR5306, 69621 Villeurbanne, France

4

Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States 5

Univ Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, F69621 Villeurbanne, France

*E-mail: [email protected] **E-mail: [email protected] Abstract We present an efficient technique for the evaluation of the Gibbs adsorption of a liquid on a solid substrate. The behavior of a water nanodroplet on a silicon surface is simulated with molecular dynamics. An external field with varying strength is applied on the system to tune the solidliquid interfacial contact area. A linear dependence of droplet’s volume as a function of the contact area is observed. Our modified Young-Laplace equation is used to explain the influence of the Gibbs adsorption on the nanodroplet volume contraction. Fitting of the molecular dynamics results with the analytical approach allows us to evaluate the number of atoms per unit area adsorbed on the substrate, which quantifies the Gibbs adsorption. Thus, a threshold of a droplet size is obtained, for which the impact of the adsorption is crucial. For instance, a water droplet with 5 nm radius has 3 % of its molecules adsorbed on silicon substrate, while for

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droplets less than 1 nm this amount is more than 10 %. The presented results could be beneficial for the evaluation of the adsorption impact on the physical-chemical properties of nanohybrid systems with important surface-to-volume fraction.

1. Introduction The interfaces between two or more different phases predominate a variety of physical and chemical phenomena, especially at the nanometer scale compared to bulk materials, as the surface-to-volume ratio becomes very high. Interactions between different phases are crucial for the wettability, solubility, chemical reactions etc. The prediction of the interaction of different phases is a key challenge for a wide range of applications in chemical industry, catalysis, material science, microfluidics, pharmacology, medicine, etc. As an example, we can mention, the wetting properties of a liquid droplet on a solid substrate. For the case of nanoscale droplets additionally to the surface tension, the line tension should be considered as it has an important impact on the wetting angle. The free energy excesses between all possible pairs of different phases per unit length should be considered to achieve stability of deformable surfaces. The generalized Young equation taking into account line tension can be presented as follows1–4:

cos =

− − ,

(1)

where is the wetting angle, , , and

are the vapor/solid, liquid/solid, and vapor/liquid

surface tensions respectively, is the line tension, and is the contact radius of the three-phase line. Barisic and Beskok5 have simulated spherical droplets with different volumes located on silicon substrate using molecular dynamics. They measured a wetting angle as a function of the curvature of three phases contact line (1/r). With the use of a linear dependence (Equation (1)),

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they estimated the line tension and they defined several parameters of the interaction between water molecules and silicon atoms with the use of the experimental wetting angles of macrosize droplet as input. Later on, it was shown6 that the simulation of cylindrical droplets is more efficient than this of spherical droplets for the evaluation of the interaction parameters between a droplet and a substrate, due to the zero curvature of the three-phases contact line

7,8

in the case of cylindrical

droplets. Leroy et al9 have shown recently that the evaluation of the force-fields parameterization using experimental wetting angles of droplet has limitations. They have stated that the dependence of water surface tension on the chosen water model should be taken into account. Thus, additional markers for reliable description of water-solid interfacial properties should be found, such as “work of adhesion”9. Numerous MD studies10–13 of solid-liquid interfaces refer to the density fluctuations of fluids near the solid free surfaces. These fluctuations appear as a result of molecules or atoms absorbed in or adsorbed on the solid substrate. The density of adsorbents strongly depends on how these atoms or molecules interact with the substrate. The density variation can even lead to experimentally perceptible contraction of the volume of the liquid containing nanoparticles14,15. Moreover, the altered structure of confined water near the wall can lead to a drastic change of its physical properties16–19. From all the above-mentioned works a question arises about the scale limitations to which droplet size the macroscopic approaches describes accurately the statistic of nanodroplet. Is there a threshold after which these approaches do not describe the physical phenomena or could these macroscopic approaches be corrected to achieve convergence of dimensions? In the current paper, the influence of the absorbed layer on the droplet shape and droplet volume is analyzed. Silicon first of all is a reference material and it is widely used in different micro3 ACS Paragon Plus Environment


electro-mechanical devices, while the absorbed humidity can affect functional regimes of such devices. Additionally, it should be noted that the surface of crystalline silicon is easy to treat and chemically functionalize. Therefore, the contraction of a nanoscale cylindrical water droplet on a silicon substrate with means of MD is studied. To be able to tune the contact area, an homogeneous external field with varying intensities is applied on the water droplet. We then correlate the shape of a nanoscale droplet modeled and simulated by MD with the one obtained by a macroscopic method of hydrostatic similarity of droplet shape in gravity field. The deviations between the results of the MD simulations and the analytical approach are interpreted. Furthermore, we propose a new model accounting the contraction of the droplet volume due to adsorption phenomena. The proposed model can be also relevant to experimentally observed volume contraction of nanocolloidal solutions14,15 or nanoporous materials filled with liquids20,21. These systems are accessible to experimental measurements and they have high surface/volume ratio.

2. Methods All MD simulations presented here are performed using LAMMPS code (Large-scale Atomic/Molecular Massively Parallel Simulator)22. We have considered cylindrical droplet on a smooth silicon substrate with and without an external force. Additionally, cylindrical droplet without substrate was simulated as reference. We use cylindrical droplets to avoid the influence of line tension on the contact angle, as explained in the introduction. In both cases the dimensions of the simulation box are 108.6 × 217.2 × 200 Å in x, y and z-direction respectively. The initial configurations of the atoms of the droplet without/with substrate are presented in Figure 1a and 1b respectively. Initially, a rectangular crystalline water droplet with size 108.6 × 43.4 × 43.4 Å was built. The total number of water molecules in the droplet is equal to 4 ACS Paragon Plus Environment

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6860. The distance between oxygen atoms of water molecules was set to 3.1 Å, and this corresponds approximately to the density of the bulk water under normal conditions. The surface of the crystalline silicon substrate has (1, 0, 0) orientation of the facet, with lattice constant equal to a0 = 5.43 Å. The silicon slab has dimensions 108.6 × 217.2 × 27.15 Å (40 × 80 × 10 atoms).

Figure 1. Initial (a, b) and after thermostating (c, d) configurations of a cylindrical nanoscale water droplet for the cases of a droplet (a, c) without substrate and a droplet on a silicon substrate (b and d).

The interactions between water molecules are described by the extended simple point charge (SPC/E) water model23, with parameters taken from Orsi24. SPC/E water model was chosen since it represents well bulk density of the water 25 water and it is reasonable concerning the CPU time. The 12-6 Lennard-Jones interatomic potential was used for the interactions between oxygen and silicon atoms, with εSi-O = 15.75 meV and σSi-O = 2.6305 Å6. In our study the interactions between hydrogen and silicon atoms are neglected. The Stilling-Weber potential26 is used for the 5 ACS Paragon Plus Environment


interactions between silicon atoms. Additionally, the harmonic force was applied to silicon atoms of the lower four atomic layers (z

Gibbs Adsorption Impact on a Nanodroplet Shape: Modification of

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