Slippery to Sticky Transition of Hydrophobic Nanochannels - Nano

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Slippery to Sticky Transition of Hydrophobic Nanochannels Chirodeep Bakli, and Suman Chakraborty Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b03082 • Publication Date (Web): 15 Oct 2015 Downloaded from http://pubs.acs.org on October 20, 2015

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Slippery to Sticky Transition of Hydrophobic Nanochannels

Chirodeep Bakli and Suman Chakraborty*

Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, INDIA.

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Abstract Contrary to common intuition that hydrophobic surfaces trivially cause water to slip, we discover a slippery to sticky transition in tunable hydrophobic nanochannels. We demonstrate this remarkable phenomenon by bringing out hitherto unveiled interplay between ion inclusions in the water and the interfacial lattice configuration over molecular scales. The consequent alterations in frictional characteristics illustrate that so called hydrophobic nanochannels can be switchable to manifest features that are otherwise typically associated with hydrophilicity, causing water to stick. Our proposition may bear immense consequences towards fluidically functionalizing a hydrophobic interface without necessitating elaborate surface treatment techniques, bringing in far-ranging implications in diverse applications ranging from nature to energy.

Keywords: Slip, stick, wettability, hydrophilization.

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The science of wetting over nanometer scales has given rise to several elusively unresolved anomalies, primarily attributable to possible non-trivial interconnections between the intrinsic surface chemistry, the surface texture, and the incipient flow. Traditionally, it has been believed that hydrophobic effects, omnipresent in natural systems such as self-cleaning lotus leaves1, as well as in engineered nanodevices like carbon nanotubes2, are likely to result in giant augmentations in fluid flow, by promoting boundary slip. Increased fluid flow can further augment the transport of the ionic inclusions in the domain, leading to large scale amplification of current and hence paving the way for economically viable power generation in nanobatteries3–5. Considerations of slippery flow6, thus, have opened up tremendous possibilities of enhancing energy conversion efficiencies of nanofluidic devices7. On the other hand, transport of water at nanoscale itself requires self-actuating mechanisms like capillarity to propel fluid through tortuous confinements. One primary requirement of such surface tension - driven flows in nanofluidic pathways is an inherent ‘sticky-ness’ of the substrate, which is commonly achieved only by surfaces with high intrinsic wettabilities. Is it possible to conceive smart nanofluidic channels that can alternately act as sticky and slippery in flow actuation and ion transport modes, respectively? By questioning the traditionally observed elusively trivial relationship between the contact angle, wettability and slip over nanometer scales, we outline a novel tuning of the ‘effective’ wettabilities8,9 of nanofluidic substrates through a simple exploitation of molecular and ionic arrangements at the interface. Our findings can revolutionize the prevention of fouling in biomolecule separation processes using ultrafiltration membranes10,11. These membranes most commonly employ available hydrophobic material to obtain greater flux at the cost of significant increase in fouling and performance deterioration. Achieving effective hydrophilization of such surfaces would help to flush the walls with water, preventing fouling and at the same time not compromising the inherent wettability advantage. Thus, it may become possible, rather non-trivially, to realize ‘sticky-ness’ over naturally synthesized hydrophobic surfaces, without involving either permanent (expensive) or short-lasting hydrophilization techniques11. Moreover this technique, operating at the length scales of water molecules, does not interfere with the dynamics of biomolecules having larger length scales12 and thus has a wide range of applicabilities in biomedical science and technology.

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The transformation of a so-called hydrophobic surface to a sticky-one, without affecting any surface treatment, may appear to be a paradoxical situation, since hydrophobic surfaces have been traditionally believed to promote slip13,14, macroscopically because of the inception of a depleted interfacial phase that acts like a intermediate cushion between the solid surface and the bulk liquid. However, it needs to be emphasized that the classification of hydrophobicity and hydrophilicity around the contact angle of 90o is inherent to pure water only. The presence of ionic and colloidal inclusions in water, in effect, may dramatically affect the local dynamic contact angles, letting the classification of hydro(oleo)phobic vs. hydro(oleo) philic surfaces15,16 rather vague, with the possibility of opening up a new window of counter-intuitive slip-stick behavior. Indeed, although there is overwhelming phenomenological and experimental evidence of slip over hydrophobic surfaces13,14, there is no compelling theoretical argument for why the other scenario of sticking behavior on the same may not be the case. Despite significant advancements17–23 on the possible implications of the wetting states associated with surfaces that are either classically classified as hydrophobic or hydrophilic, several recent studies have hinted on certain unanswered questions on the pertinent features. For example, experimental19 and numerical studies17 on droplets sliding over such surfaces have demonstrated a much slower dynamics as compared to that on a homogenous surface with same the same static contact angle. Analogous to such non-intuitive findings on droplet dynamics18,20, experiments on superhydrophobic surfaces with grafted polymers21 have also demonstrated switchability between contrasting slip behavior. These studies hint at the fact that the definition of surface wettability embeds much more than a questionable universal mapping between interfacial slip and the contact angle22. Here we present, through molecular dynamics (MD) simulations, what we believe to be the first evidence of possibility of sticking of liquid water molecules in hydrophobic nanochannels. As evidenced in an earlier work, molecular simulations hold the potential of discovering the molecular signatures of hydrodynamics over a designed surface, since they allow a systematic variation of surface properties, as well as surface-water interaction parameters23. The central result presented herein is the demonstration that contact angle greater than 90° does not necessarily trigger water to slip in nanochannels. Instead, we show that liquid water may also stick to hydrophobic nanochannels, by realizing interplay between the ionic inclusions and 4


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interfacial structure over molecular scales. This, in turn, may create a situation in which even traditionally recognized hydrophobic surfaces present with only isolated attractive adsorption sites that may readily engulf water molecules, bearing far-ranging implications in nature and energy. Fig. 1. depicts the variation of slip length ( a quantitative measure of slip14) of water on a surface with specified static contact angle, with the variation of interparticle distance between wall atoms ( D ). Comparing with the crystal structure of various lattices, it is observed that, energetically more favorable wall structures are obtained for D > 3 . From our results, slip length is observed to decrease monotonically with increase in the interparticle distance, in addition to varying non-trivially with the concentration of a salted solution deployed instead of pure water. To obtain saline solutions, we use sodium chloride as the solute. This selection is based on the fact that sodium chloride (NaCl) in water forms the most common carrier fluid in most biological and electrochemical processes. In the inset, we observe that increase in solute concentration in water also leads to decrease in slip length for different values of static contact angle, with the value of D fixed at 5.5 . The decrease, although monotonic, has an abrupt jump around similar values of concentration for all contact angles. As expected, the slip length is higher for higher values of the contact angle, for both the cases. We analyze the above observations in light of the surface density distribution of water molecules. Fig 2. depicts the variation in surface density of unsalted water molecules as the interparticle distance is varied, for a substrate of contact angle 112o . The contact angles used to represent the graphical data here represent the static contact angle, θ s formed by a sessile saline droplet over an atomically smooth surface with inter-particle distance D = 5.5 . Interestingly, the contact angle variation obtained for changes in the values of D are imperceptible for a hydrophobic surface (see supporting information for details) as opposed to hydrophilic surfaces23. Thus θ s is a good candidate to make the simulation data accessible and reproducible for further theoretical and experimental work. The reduction in the interparticle distance decreases the distance between the wall adsorption sites. Traditionally, the term adsorption site is associated with wetting surfaces. However, irrespective of the intrinsic wettability, all surfaces have an energy landscape (which is a function of D ) causing both attraction and repulsion at the interface. Combining this adsorption-desorption duality of all surfaces with the ionic adsorption 5


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at the interface and corresponding pinning of the hydration water, we continue using the term adsorption site irrespective of the surface wetting properties. The density distribution of water, with nearing of the adsorption sites, changes from evenly distributed surface density maxima to semi-continuous aisles of water number density maxima and finally to connected zones of high water density. This increasing coupling between the high density zones aids the water molecules to flow past from one maximum to another and hence, registers slip over the system scales. More closely interconnected high density zones would essentially implicate that water molecules find it easy to ‘slip’ between the sites and hence, larger slip lengths would be registered. Interestingly, as the solid interparticle distance is reduced, not only the high water density zones tend to move closer, but also the average water density near the surface increases. As evident from fig. 2, with reduction in interparticle distance from 5.5 to 3.5, the density of water next to the surface increases. Such observations are not pertinent for hydrophilic substrates, since the wall-adsorption sites are already saturated with water molecules. Interestingly, the increased near wall density does not impede slip, as it would have intuitively done. The ability of water molecules to switch rapidly between the absorption sites, which are now in closer proximity, would mean larger number of molecules of water slipping on the surface (as compared to the surface with same hydrophobicity but larger D), registering a large value of the slip length. These observations emphasize the fact that the enhancement of slip with the reduction of interparticle distance in a hydrophobic substrate occurs due to two factors. Firstly, nearer adsorption sites mean water molecules can rapidly glide between these sites and secondly, the number of water molecules next to wall that glide between these sites also increases. The surface density plots of water molecules for flow of saline solution of various molarities are shown in fig 3. At low concentration, the salt ions do not drastically modify the distribution of water molecules on the surface as compared to that of pure water. As the solute concentration is increased, the salt ions find a recess to locate themselves near the wall where the density has been depleted due to hydrophobic interactions. These ions coordinate water molecules around them. Thus, at intermediate concentrations, we have two kinds of binding sites at the surface: the surface adsorption sites due to the molecular arrangement of the wall atoms, and the ions residing on the walls acting as centers of hydration. The resulting slip arises from the combination of the freedom of motion of water molecules from one absorption site to another 6


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and from the constraint imposed by the hydration sphere, with an effect of lowering the slip length. At high salt concentration, the ions nearly cover a large part of the surface and the water molecules from the hydration shell are resistant to glide freely over the surface. Such pinned water molecules on the surface can lead to drastic reduction in the slip length. We next simulate saline solutions of various concentrations on surfaces having different wettability and interparticle distance between wall atoms, as shown in fig 4. The slip length is not only drastically reduced at higher values of salt concentration, but also water sticking to the surface is observed for lower interparticle distance. We obtain completely counter-intuitive fluid stick on surfaces having sessile droplet static contact angles of 112o and 120o with D = 3.5 for solutions of molarity 1.5 − 2M . Even for the substrate with static contact angle of 140o , the slip length obtained is extremely low. The reduction in the distance between surface adsorption sites screens the effect of surface hydrophobicity, bringing more water molecules in the proximity of the surface. Introduction of ions, however, prevents these water molecules from moving from one adsorption site to another under the influence of any bulk actuation. With a high density of the water molecules constrained at fixed sites on the surface, the traditionally portrayed hydrophobic surface essentially mimics the density distribution pattern of a conventional wettable surface. It is interesting to note that while reduction in the interparticle distance increases the slip length for pure water, addition of ions completely reverses the dynamics, and slip length reduction is observed. Our observations can also explain qualitatively the experimentally observed slip reduction on hydrophobic surfaces for droplet motion19 and fluid flow21. Fluid sticking or slipping at a solid interface can be attributed to the manifestation of energy dissipation occurring due to the fluid-solid interaction, which primarily involves adsorption and desorption of the fluid molecules on the solid. This forms the essence of the molecular kinetic theory. Abiding by this theory, we can describe fluid molecules jumping between the adsorption sites with a frequency κ o to facilitate interfacial transport, these absorption sites being separated by a distance 2a . Thus, the molecular diffusion coefficient, Dmol is of the order ξU 2 , where the coefficient of molecular friction, ξ is given by ξ =

kBT , k B and T κ o a3

being the Boltzmann constant and absolute temperature respectively, and U being the velocity 7


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scale24. Altering the lattice spacing would essentially alter the distribution of the surface adsorption/ desorption sites.

This change would be reflected in the molecular friction,

culminating in altered molecular diffusion, and finally the macroscopically observed slip. As observed in fig. 2, the adsorption sites would have an increased liquid density in the immediate vicinity. These dense liquid pockets are interspersed by comparatively depleted regions in between, which is the consequence of the hydrophobic effect of the surface. At the molecular level, this transition from a denser zone to a relatively rarified zone can be approximately visualized by means of the existence of an interface between two fluids. This interface may be characterized by an interfacial tension (γ s ) , from a macroscopic sense. The spatial gradient in this surface tension would lead to some additional tangential stress which would either augment or diminish the intrinsic wall shear stress and would according lead to slip or stick. In an effort to review the phenomenon from a macroscopic hydrodynamic perspective, one may first note that the average shear stress at the wall, τ w in the absence of slip, scales as: η

uav H

, H being a characteristic length scale of the fluidic confinement, uav being the

characteristic mean flow velocity, and η being the fluid viscosity. With interfacial slip, it can be suggested τ w scales as η

uav − us , where us is the slip velocity, being positive for slip and zero H

or negative for stick. This expression is in agreement with the fact that slippery surface would imply lower viscous stress while a sticky surface means greater interfacial stress. One would be tempted to assert that the van der Waals interactions change with change in interparticle distance and so does the slip velocity. The tangential stress balance equation at the interface of the dense and rare zones of fluid in equilibrium can be written as: (τ d − τ r ) ⋅ nˆ  ⋅ tˆ + ( grad s γ s ) ⋅ tˆ = 0 where τ d

and τ r are the stress tensors for dense and rare phases respectively. nˆ and tˆ are the unit vectors

in directions normal and tangential to the wall respectively, and grad s ≡ ∇ − nˆ (nˆ.∇) is the component of gradient operator in the local plane of interface25. With nearing of the adsorption sites, there are more frequent transitions of the fluid from denser to rarer phases as demonstrated in the cartoon in fig.5. Accordingly, the surface tension gradient contribution to the tangential shear alters, which leads to an altered effective interfacial slip.

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However, the situation becomes dramatically modified with the addition of salt. With the salt ions occupying the interface between the dense and rare phases, the interfacial tension gets modified. The consequent reduction in the interfacial tension can be derived from the corresponding adsorption isotherms, which may be modeled as21: γ s − γ s' = ΓRT where γ s' is the modified surface tension, Γ is the interfacial concentration of solute, R is the universal gas constant, and T is the absolute temperature. In order to obtain deeper insight into the interfacial science portrayed as above, we attempt to characterize the interface in terms of surface adsorption sites and ionic hydration radius. Adsorption sites on a pristine surface can be assumed to be uniformly located as shown in fig. 5. Water molecules would tend to distribute themselves over these adsorption sites, leading to localized circular zones of higher density. The transitions between local density maxima create a pseudo-interface across which a density as well as a surface tension gradient may be obtained. This added surface tension force tends to reduce the drag at the solid-fluid interface. The equation quantifying this assertion can be written as

µ ∆us = ( grad s γ s ) ⋅ tˆ  ∆Aint , where ∆u s is the H

change of slip velocity at the interface and ∆Aint is the change in the interfacial area between the high and low density phases. An estimate of ∆Aint can be obtained by assuming an area ∆A of the substrate containing n

circular zones of distinct water density maxima of radius a (which is determined by the

interparticle distance, D). This approximately gives n =

A π a2

and hence, ∆Aint scales with 2 A / a .

Since the parameter a should be closely related to D , we deduce an inverse proportionality between the interparticle distance and slip length, which is also established from the slip length plot obtained in Fig 2. Dissolution of ions, on the other hand, tends to increase the effective value of a and reduce the value of γ s simultaneously. The combined consequence is a reduction in the slip length. With further increase of salt concentration, the hydration diameter solely decides the liquid slip. This follows from the comparatively more stable residence of water molecules in the hydration shell as opposed to adsorption sites. The linear reduction of slip length is eventually interrupted. Instead, a steeper decrease in the slip length is observed,

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imparting a non-linear dip beyond a threshold concentration, for different values of the contact angle (for additional results and comments, see supporting information). In summary, we demonstrate that it may be possible to switch the surface characteristics of hydrophobic nanochannels from slippery to sticky, exploiting hitherto unraveled interplay between ion-water interactions and the molecular arrangements at the interface. When verified experimentally, our results could lead to advancements of a variety of applications addressing several outstanding problems in microfluidics and nanofluidics. For instance, one may directly use naturally available hydrophobic surfaces for capillarity without necessitating expensive and elaborate hydrophilization (surface treatment) processes. Rather, our consideration of obtaining sticking behavior of water in hydrophobic nanochannels relies on a simple proposition of preventing atomic-scale sliding of molecules which is realized by introducing ionic inclusions of pre-determined concentration and altering the surface interparticle distance at the solid wall (by, for instance maneuvering the interface over atomic scales) simultaneously. Methods Slip length calculation is performed by simulating a nanochannel flow driven by an external body force. The basic simulation unit contains 48204 water molecules in a dimension of

12 ×12 ×10 nm, with the wall atoms organized in FCC lattice in plane. The solute ions are randomly placed in the bulk, representing a saline solution which is electroneutral with concentration values varying from 0.01M − 2.0M .Water is idealized using the simple point charge extended (SPC/E) model

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. The walls atoms and ions are considered to be Lennard-Jones (LJ)

particles. For the wall LJ parameters, we choose, σ ww = 0.35nm , while we vary ε ww from 0.3 to 2kJ / mol to obtain the variation in surface wettability.

The motivation of choosing these

particular parameters comes from the fact that an ideal silicon surface is generated with values

σ = 0.35nm and ε = 3.5kJ / mol , so that the interparticle distance in ideal the silicon lattice 5.5σ

( D = 5.5) . Since, treating silicon produces surfaces with a wide range of contact angles,

varying parameters for a silicon surface is physically realistic. While simulating, we do have the freedom to reduce interparticle distance to any degree. However, crystals occurring in the real world would be constrained below a certain interparticle distance. By comparing the lattice parameters of various crystals, we decide D>3 would be realistic and the results are represented 10


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for the same range. The substrate under consideration is further assumed to be non-polar and does not get charged in presence of ions or polar species like water. Since the hydrogen bond network is insensitive to polarizability of the substrate27, a non-polar substrate is capable of representing a general case as well as avoiding the complexities introduced by the zeta potential dependent slip28–31. This assumption helps us to segregate the system hydrodynamics and gives a better understanding of the process that occurs. The values of contact angle of sessile droplets are obtained from MD simulations of saline water droplets on surfaces having identical LJ parameters. Nosé-Hoover thermostat is used to maintain the system temperature at 300 K . We use Leap-frog algorithm to numerically integrate the equations of motions with time step of 0.001 ps and ran for 20 ns. The data is averaged over 50 simulation runs to obtain statistically reliable and robust results. Details of the simulations can be obtained from the supporting information. The velocity profiles are obtained after binning the flow in the channels done by averaging the individual molecular velocities. These velocity profiles form the basis of determining the slip length of water in flow32,33. The extrapolated velocity profile, in accordance with Navier slip considerations, us = ls

du du , gives the slip length ls , dy b dy

being the wall-normal b

velocity gradient.

Associated Content Supporting Information: Further details of simulation methods and additional results are provided in supporting information.

Author Information Corresponding author *Email: [email protected] Present Address

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Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur – 721032, India, Telephone: +913222282990, Fax: +913222282278 Author Contributions C.B. and S.C. conceived the problem. C.B. performed the simulations and analyzed the data. C.B. and S.C. wrote the manuscript. Notes The authors declare no conflict of interest.

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List of Figures

Figure 1. MD data for slip lengths: The variation of slip length plotted for varying interparticle distances at different values of the contact angle. The slip lengths monotonically decrease with increase in interparticle distance irrespective of the contact angle. Inset: Variation of slip length with salt concentration for D = 5.5 at different values of the static contact angle (as in the legend of main figure). Concentrated saline solutions impede slip.

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a

b

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c

Figure 2. Near wall densities for pure water: Surface density variation of water next to a hydrophobic wall having a static sessile droplet contact angle of 112o for interparticle distance values of (a) D=5.5 (b) 4.5 (c) 3.5 Reduction of interparticle distance at the solid wall tends to increase the number density of water molecules at the maxima. This results in maxima aisles coming closer and also increases in the water density next to a hydrophobic wall.

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Figure 3. (Left panel) Surface density variation of water next to a hydrophobic wall having a static sessile droplet contact angle of 112o and D = 5.5 for different values of salt concentration; (a) 0.2 M (b) 0.6 M (c) 1.0 M, (Right panel) The corresponding ion density profiles next to the surface. Presence of ions on the surface disrupts the density distribution pattern formed by the surface adsorption sites.

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Figure 4. Slip lengths with composite variation of solute concentration and interparticle distance. The variation of slip length plotted for varying salt concentration and interparticle distance at the solid wall values at different values of contact angle. The monotonic decrease in slip length with increase of concentration and the abrupt drop in slip length at an intermediate solute molarity can be optimized to obtain fluid stick irrespective of the contact angle. The drop is steeper for lower values of the interparticle distance at the solid wall. For a particular combination of the salt concentration and the interparticle distance, water sticks on a hydrophobic surface.

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Figure 5. A cartoon representing the adsorption sites on a substrate using circles. (a-c) demonstrate the effect variation of the interface between the dense and rarified fluid phases with variation in lattice parameter. An approximate reflection of this effect can be obtained by addition of salt where (d) Pure water (e) for saline water, some of the incoming ions reside on the surface and form hydration shells around which the water molecules generally remain fixed. (f) saline water with high concentration leads to more ions residing on the surface and more water molecules pinned in the hydration shells.

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Slippery to Sticky Transition of Hydrophobic Nanochannels - Nano

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