Temperature-Dependence of the Contact Angle of Water on Graphite, Silicon, and Gold Kenneth L Osborne III A Thesis Submitted to the Faculty of the Worcester Polytechnic Institute In partial fulfillment of the requirements for the Degree of Master of Science in Physics April, 2009 APPROVED: Dr. Rafael Garcia Dr. Stephan A. Koehler Dr. Alex A. Zozulya Contents 1 Introduction 1 1.1 Theory of Wetting and Wetting Transitions . . . . . . . . . . . . 2 1.1.1 Thin Films and Contact Angles . . . . . . . . . . . . . . . 2 1.2 van der Waals Potential . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 The Sharp Kink Approximation . . . . . . . . . . . . . . . . . . . 5 1.4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Methods 10 2.1 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Cell Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 Preparing the Cell . . . . . . . . . . . . . . . . . . . . . . 12 2.1.3 Cleaning the Cell . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.2 Detailed Description . . . . . . . . . . . . . . . . . . . . . 18 2.3 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Image Preparation . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.3 Mathematical Manipulation . . . . . . . . . . . . . . . . . 25 2.3.4 Program Code for Determining Contact Angles . . . . . . 29 3 Results 34 3.1 H O on Graphite . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2 3.1.1 Stored Water . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.2 New Water . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.3 Two Increased Droplet Size Experiments . . . . . . . . . 39 3.1.4 Charged Droplets . . . . . . . . . . . . . . . . . . . . . . 43 3.2 H O on Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2 3.2.1 Stored Water . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.2 New 17.5 MΩ-cm Water . . . . . . . . . . . . . . . . . . 47 3.2.3 Standard Procedure . . . . . . . . . . . . . . . . . . . . . 48 3.2.4 Stored Water- Revisited . . . . . . . . . . . . . . . . . . . 48 3.2.5 Grounding the Cell . . . . . . . . . . . . . . . . . . . . . 52 3.2.6 Saltwater . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1 3.2.7 Charged Droplet . . . . . . . . . . . . . . . . . . . . . . . 56 3.2.8 Larger Droplet . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3 Water on Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4 Discussion 60 4.1 Theory vs Experiment . . . . . . . . . . . . . . . . . . . . . . . . 60 4.1.1 Water on Graphite . . . . . . . . . . . . . . . . . . . . . . 61 4.1.2 Water on Silicon . . . . . . . . . . . . . . . . . . . . . . . 62 4.1.3 Water on Gold . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2 Experimental Deviation . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.1 Deviations in Water on Graphite . . . . . . . . . . . . . . 67 4.2.2 Deviations in Water on Silicon . . . . . . . . . . . . . . . 67 4.2.3 Water on Gold . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3 Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.1 Temperature Gradients . . . . . . . . . . . . . . . . . . . 73 4.3.2 Adsorption of Water onto Substrate . . . . . . . . . . . . 73 4.3.3 Pinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.4 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . 74 4.4 Interface Charging . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.4.1 A Simple Estimate of the Electrostatic Forces . . . . . . . 76 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.6 Suggestions for Further Work . . . . . . . . . . . . . . . . . . . . 80 2 Abstract The temperature dependence of the contact angle of water on graphite, sili- con and gold was investigated under various conditions to test the Sharp-Kink Approximation. Despitecorrectlypredictingthecontactangleatroomtemper- ature,theidealSharp-KinkApproximationwasnotfoundtoaccuratelydescribe the contact angle’s temperature dependence. The discrepancies from the pre- dicted contact angle were characterized in terms of a correction H(T) to the liquid-solid surface tension. H(T) was found to be linear in temperature and decreasing, and is consistent with electrostatic charge effects. Chapter 1 Introduction This paper is the conclusion to a set of experiments taking place between De- cember 2006andNovember2007. The purpose ofthe experimentswasto make an initial study of the contact angle of water at room temperature and above. A hope was to reproducibly induce what is known as a ‘wetting transition’, a phenomenon wherein it becomes energetically more preferential for a droplet of liquid to spread out in a very thin layer instead of remaining in droplet form. This wetting transition is can be theoretically induced by increasing the tem- perature above a so-called ‘wetting temperature’. This paper surveys the math and physics that lead to the prediction of the wettingtransitionphenomenon,aphenomenonthatmanifestsitselfbyabruptly changingthebehaviorofabulkdropletofwateratthewettingtemperatureT . w Includedinthissurveyaredescpriptionsofwettingvsnon-wettingphenomenon andatool,developedbyMiltonCole[15]andrecastinanespeciallysimpleform by Rafael Garcia [31], called the sharp-kink approximation. Using the sharp-kink approximation it is possible to predict a contact angle for water on different substrates. Following the theoretical introduction to wet- ting and wetting transitions is a survey of recent research in the field, including papers that have used the sharp-kink approximation to accurately predict the contact angle, and thus demonstrating its validity. The survey of recent re- search also serve to present the methods used in past experiments. Then there an overview of the experimentation done in this paper will be presented. 1 1.1 Theory of Wetting and Wetting Transitions The experiments reported on in this paper examine droplets that are small enough that capillary effects are negligible. Such small droplets, look like small truncated spheres when placed on the surface of a substrate. Given a droplet of a liquid of constant volume, a sphere’s height off The truncated spheres form an angle with the substrate at the liquid-substrate interface, which is known as the ‘contact angle’. The equations predicting contact angle require knowledge of the surface tensions at the liquid-gas interface σ , the surface tension at the lg solid-liquid interface σ , and the surface tension at the gas-solid interface σ . sl gs Because σ and σ have yet to be determined for most interfaces, including sl gs all such interfaces utilized in this experiment, it is hard to predict the contact angle based on this theory. Thus, until relatively recently when Cole et al published their paper [15] on thesharp-kinkapproximationitwasalmostimpossibletopredictthebehaviorof contact angles. The sharp-kink approximation predicts the contact angle from just the liquid-gas surface tension σ , the difference in density between the lg liquid and vapor, and the van der Waals potential describing the net preference of the adsorbate water for wetting the substrate instead of forming a droplet. This preference is determined from equations modeling intermolecular forces. After study, it is found that the sharp-kink approximation upholds quali- tatively the long-standing prediction that there is a ‘wetting temperature’ T , w which varies depending on the three surface tensions at the three pairs of inter- faces. AbovethetheoreticalT awaterdropletwillhaveacontactangleofzero w degrees [15]. The sharp-kink approximation has be experimentally validated by predicting pre-wetting transitions at low temperatures [2], but the theory has notbeentestedatroomtemperature. Assuch,thisexperimentwasdonetotest the validity of the sharp-kink approximation at room temperature, by testing if the sharp-kink approximation correctly predicts the contact angle of water on graphite and gold. 1.1.1 Thin Films and Contact Angles One of the assumptions that is made about the system is that there is only a microscopicallythinfilmofliquidwhichadsorbsonthesurfaceofthesubstrate. This thin filmis assumed for the purposes ofthis experiment to beof 1-2 layers uniform thickness and moreover is uniformly present everywhere on the sub- strate. This is different than the bulk-like liquid droplet which is localized to a small section of the substrate. Attheplacewherethethreeinterfaces(liquid,vapor,andsolidsurfacewith thin film) meet, called the ‘three-phase contact line’, or TCL, the water-air interface forms an angle with the substrate, see Figure 1.1. This angle, called the contact angle is an observable manifestation of the interactions of the three surface tensions. Depending on the contact angle the droplet is characterized as completely wetting, non-wetting, or completely non-wetting. Figure 1.2 shows droplets in 2 Figure 1.1: The ring around the droplet where liquid, vapor and solid surfaces meet is called the TCL. At the TCL the droplet makes a contact angle θ with the substrate. all three stages of wetting. When a liquid is wetting a surface, the liquid has a 0 degree contact angle. Furthermore the droplet spontaneously spreads out in a thin sheet on the substrate surface. When a liquid is completely not wetting a substrate, a droplet the liquid restsontopofthesubstrate,witha180degreecontactangleatthethree-phase contact line. A side view shows that the completely non-wetting droplet looks like an untruncated sphere resting on the substrate surface. The intermediate case is the that where the droplet is partially wetting the surface. This is the case where the contact angle is above 0 but less than 180 degreesatthethree-phasecontactline. Thedropletlookslikeaspherethathas been truncated, resting on top of the substrate. Figure 1.2: a) The droplet has completely wet the substrate, and hence, is spread across the surface of the substrate and has a contact angle of 0 degrees. b)Thedropletisnotwettingthesurface, butthecontactangleisstilllessthan 180degrees. c)Thedropletrestsonthesurfaceofthesubstratewiththeliquid- solid interface at an angle of 180 degrees with respect to the substrate surface. The droplet looks like a sphere on the surface of the substrate. 1.2 van der Waals Potential ThevanderWaalspotentialdescribestheattractionofindividualmoleculesthe substrate that they are resting on, and to other molecules. In the specific case where V is a Lennard-Jones 3-9 potential, with a well depth D and a van der Waals coefficient C, the van der Waals Potential is given as 4C3 C V (z)= − (1.1) 27D2z9 z3 3 Here V =V −V describes the net preference of the adsorbate molecule for s l wettingthesubstrateinsteadofformingadroplet,duetointermolecularforces. In the definition of V, V is the potential energy of the adsorbate molecule due s tothesubstrateandV isthepotentialenergyoftheadsorbatemoleculeduetoa l hypothetical puddle of bulk liquid at the same location as the substrate. These terms include both attractive van der Waals forces and repulsive forces that result from the excluded volume of the adsorbate molecule, as seen in Figure 1.3. Figure 1.3: A 3-9 van der Waals potential. When D is sufficiently large, there is a minimum in the energy graph at z . The radius r of a molecule is min comparable length corresponding to the forbidden section of the van der Waals potential in the sharp kink approximation. The integral is taken over the thickness of the droplet starting from the minimum of the van der Waals potential of the near the surface z . This is min done because z is assumed to coincide with the position of the first layer of min molecules on the surface. The thickness of the bulk droplet is assumed to be infinite, because it is a great number of atomic lengths away. From the equation for V (z) it is possible to find the distance from the substrate surface at which water molecules will adsorb. Setting dV/dz = 0 shows that z = (2C/3D)1/3. After having solved for z we can now min min integrate V dz in order to find I = 0.600(cid:0)CD2(cid:1)1/3. In accordance with the sharp-kink approximation, the first layer of atoms coincides with the minimum ofV, whichisagoodapproximationwheneverDissufficientlydeepthatatoms 4 behave as they would in the classical limit. 1.3 The Sharp Kink Approximation Underthesaturatedvapor-pressureconditionsdiscussedinThinFlmsandCon- tactAngle,thecontactangleθisrelatedtothesurfacetensionsonthegas-solid, gas-liquid, and liquid-solid layers by the Young Eq. 1.2 σ =σ +σ cos θ (1.2) gs ls lg This equation is only valid in the case where the droplet is not completely wetting the substrate. An equivalent form that is more useful is σ −σ =−σ cos θ (1.3) ls gs lg Alargeproblemwiththisequationisthatσ andσ ,andtheirtemperature- gs ls dependences,ingeneral,cannotbedeterminedexperimentally. Atpresent,there hasonlybeenoneexperiment[]toindependentlydetermineallfourparameters in Eq. 1.2. The van der Waals potential models the attraction of individual atoms in the bulk liquid, and their attraction to the substrate. In a moment it will be shown that the difference σ −σ can be modeled by integrating the ls gs van der Waals potentials of all atoms in the bulk liquid The ‘sharp-kink’ approximation assumes that the atoms that reside at the minimum energy of the van der Waals potential form the first layer of liquid atoms of the liquid layer. This assumption showed to be a good approximation by Dietrich [9] because the radius of an atom is comparable to the distance z , which means that the first layer of atoms in the droplet almost touches min the layer of atoms on the substrate. A typical van der Waals 3-9 potential is shown in Figure 1.3. The poten- tial has an excluded region, that atoms are classically forbidden from entering. Beyond the excluded region is z , the minimum of the potential. Classically, min theatomswouldstarttofillthispotentialatthepoint,andasfillingcontinued, some of the atoms would fill part of the classically forbidden space as seen in Figure 1.4 (top) [31]. To simplify the problem, we assume that the atoms fill the van der Waals potential like Figure 1.4 (bottom) shows that ρ sharply changes from its ρ to g ρ atz [31]. Theactualdensityprofileshowsthatdensityisonlyfractionally l min greater than the bulk density z , and beyond a few atomic radii away, the min densityofatomsthatwouldfillavanderWaalsmatchesthebulkdensity. This shows Dietrich’s approximation to be sensible. Coleetal[15]noticedthatiftheaboveapproximationsweremadeabout∆ρ, then σ could be broken into three different sections, as shown in Figure 1.5. sl In the Figure the substrate and liquid are separated by a distance z which min is greater than the radius of an atom, while there is a gas section between. Cole et al used Dietrich’s descriptions of the sharp-kink approximation to showthatσ canbethoughtofasasysteminwhichthereisathinlayerofgas ls 5 Figure1.4: (top)CalculateddensityprofileinavanderWaals3-9potential[9]. (bottom) Density profile using the sharp kink approximation [9]. The sharp- kink approximation also assumes ρ is does not vary with distance, and remains at the bulk value beyond z . min 6