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Experimental Value of the Specific Surface Energy of The crystals Article Experimental Value of the Specific Surface Energy of the Cleavage {10.4} Calcite Rhombohedron in the Presence of Its Saturated Aqueous Solution Emanuele Costa * ID and Dino Aquilano Department of Earth Sciences, Università di Torino, Via Valperga Caluso 35, 10125 Torino, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-347-2281511 Received: 26 April 2018; Accepted: 28 May 2018; Published: 30 May 2018 Abstract: In this study, we describe a method to obtain experimental values of the surface energy of calcite. A zenithal imaging device was used to acquire pictures of droplets of CaCO3 saturated aqueous solution on the surface of a calcite crystal sample. Pictures were used to measure the contact angle between the droplets and the {10.4} calcite surfaces. The method is discussed along with its geometrical ground, as well as the theoretical foundation of the contact angle calculation. A comparison is made with the literature data; a good agreement is found between our experimental values and those obtained from the more recent ab initio calculations. Keywords: calcite; contact angle; surface energy 1. Introduction Measuring the surface energy of calcite is often obtained using methods involving the determination of the contact angle of various liquids in the system: crystal/liquid/air, but also in submerged systems using non-aqueous solvents. Evaluating the contact angle usually requires sophisticated mechanical and optical devices, to ensure perfect co-planarity of the calcite surface and the optical axis of the camera, the absence of parallax error during the image acquisition, and somewhat ability of the operator regarding the determination of the real angle formed between the calcite face and the droplet boundary at the contact interface [1–3]. The use of a simple experimental device for the collection of zenithal pictures of liquid droplets on mineral surfaces could allow to precisely evaluate both the diameter of a drop of known volume and its contact angle. The acquisition of pictures from a vertical perspective eliminates some problems encountered in traditional imaging of droplet profile, and the rapidity of the operation allows the capture of a great number of images, within a simple experiment run, thus improving the statistics of the measurements. Accordingly, it is worth remembering the reliability of a statistical method when dealing with a real crystal surface. Let us consider the {10.4} crystal surfaces of both a cleaved and an as-grown crystal. At a microscopic level, two different situations are found: the cleaved surface is populated by features of micrometric thickness which interrupt the flatness of the ideal (10.4) terraces, like macrosteps, while in the as-grown surfaces, the thickness of the growth steps decreases down to a nanometric level. As an example, we can observe SEM images of calcite cleavage surface or as-grown calcite surface (Figure1). This does not represent a negligible detail, since the contribution of surface steps to the interfacial energy appreciably depends on its height. Consequently, measurements made on a population of droplets settled on different sites of a given crystal surface better represent the interfacial energy value with respect to the one obtained from a single macroscopic drop. Finally, it should not be neglected Crystals 2018, 8, 238; doi:10.3390/cryst8060238 www.mdpi.com/journal/crystals Crystals 2018, 8, x FOR PEER REVIEW 2 of 8 should not be neglected that the corresponding calculated values of the interfacial energy are obtained by considering an ideal flat interface (i.e., the only (10.4) terraces, in our case). When a liquid droplet (in a system solid/liquid/vapor) settles on a solid surface: (i) if the droplet is in mechanical and thermodynamic equilibrium with the substrate and the surrounding vapor phase; and (ii) if the specific adhesion energy between the solid surface and the droplet (βadh) is higher than the specific energy (γlv) of the liquid–vapor interface, then the contact angle (θ) between the droplet and the surface is higher than 90°. This ensues from the coupling of the Young’s (1) and Dupré’s (1) laws [4–6] where we will define γsv as the specific energy of the solid-vapor interface, and γsl as the specific energy of the solid–liquid interface. The latter has been obtained through two independent ways: Crystals 2018, 8, 238 2 of 8 γlv cosθ + γsv = γsl (1) that the corresponding calculated values ofγ thelv + interfacialγsv − βadh = energy γsl are obtained by considering an ideal(2) flat interfaceFrom Equations (i.e., the only (1) and (10.4) (2) terraces, and considering in our case). the constraint: −1 ≤ cosθ ≤ 1, it follows that the adhesionWhen energy a liquid ranges droplet between (in a system two solid/liquid/vapor) limiting values: 0 settles≤ βadh on ≤ a2 solidγlv. The surface: minimum (i) if the (β dropletadh = 0) iscorresponds in mechanical to andthe thermodynamicsituation in which equilibrium the droplet with does the not substrate wet the and substrate the surrounding (a water vapordroplet phase; on a andhydrophobic (ii) if the specificsurface, adhesionfor instance energy). The between maximum the corresponds solid surface to and the theperfect droplet wetting (βadh (the) is higherdroplet thanspreads the specificonto the energysubstrate (γ lvreaching) of the the liquid–vapor maximum interface,of its contact then area the and, contact consequently, angle (θ) betweenits minimum the ◦ dropletthickness). and In the any surface case, the is higherβadh value than cannot 90 . Thisexceed ensues the value from of the the coupling cohesion ofenergy the Young’s (Kl) of the (1) liquid and Dupritselfé having’s (1) laws recollected [4–6] where that K wel = 2 willγlv. defineIt is worthγsv asto outline the specific that the energy θ angle of the defined solid-vapor in (1) is interface, the angle andcomprisedγsl as the between specific the energy vector of representing the solid–liquid the interfacial interface. Thetension latter γsv has (between been obtained the substrate through and two the independentvapor) and the ways: vector representing the interfacial tension γlv (between the liquid droplet and the vapor); this is to avoid any confusion aboutγlv cos theθ sign+ γsv of= theγsl function cosθ. In other words, the higher(1) the angle θ, the higher the wetting and, hence, the adhesion energy between the droplet and the γlv + γsv − βadh = γsl (2) substrate (Figure 2). FigureFigure 1. 1.SEM SEM images images of of calcite calcite crystal crystal surfaces surfaces showing showing features features at at different different scales. scales. ( A(A)) A A sequence sequence ofof thin thin and and thickthick cleavagecleavage stepssteps on a {10.4} face of of a a calcite calcite crystal: crystal: the the mean mean step step spacing spacing is isclose close toto 50 50μm,µm, while while the the mean mean height height of of thick thick steps steps is is close close to to 1 1 μµm.m. F.O.V. F.O.V. 100 µμmm (by(by courtesycourtesy ofof Dr.Dr. Linda Linda Pastero,Pastero, private private communication); communication); ( B(B)) A A growth growth spiral spiral on on the the {10.4} {10.4} crystal crystal surfaces surfaces of of calcite calcite showing showing monolayeredmonolayered steps steps (height (height = = 0.3 0.3 nm) nm) with with mean mean steps steps spacing spacing of of 30 30 nm. nm. F.O.V. F.O.V. 600 600 nm nm [6 [6].]. From Equations (1) and (2) and considering the constraint: −1 ≤ cosθ ≤ 1, it follows that the adhesion energy ranges between two limiting values: 0 ≤ βadh ≤ 2γlv. The minimum (βadh = 0) corresponds to the situation in which the droplet does not wet the substrate (a water droplet on a hydrophobic surface, for instance). The maximum corresponds to the perfect wetting (the droplet spreads onto the substrate reaching the maximum of its contact area and, consequently, its minimum thickness). In any case, the βadh value cannot exceed the value of the cohesion energy (Kl) of the liquid itself having recollected that Kl = 2γlv. It is worth to outline that the θ angle defined in (1) is the angle comprised between the vector representing the interfacial tension γsv (between the substrate and the vapor) and the vector representing the interfacial tension γlv (between the liquid droplet and the vapor); this is to avoid any confusion about the sign of the function cosθ. In other words, the higher the angle θ, the higher the wetting and, hence, the adhesion energy between the droplet and the substrate (Figure2). Crystals 2018, 8, 238 3 of 8 Crystals 2018, 8, x FOR PEER REVIEW 3 of 8 Crystals 2018, 8, x FOR PEER REVIEW 3 of 8 Figure 2.2. TheThe relationshiprelationship between between the the three three interfacial interfacial tension tension acting acting on the on boundariesthe boundaries between between drop, surfacedrop, surface and air and (Young’s air (Young’s formula). formula). Figure 2. The relationship between the three interfacial tension acting on the boundaries between drop, surface and air (Young’s formula). 2. Materials and Methods 2. Materials and Methods 2.1. Picture Acquisition 2.1. Picture Acquisition To calculate the the contact contact angle angle θθ, ,strictly strictly related related to toβadhβ,adh we, weput puta single a single drop dropof liquid of liquid on a flat on asurface flat surface ofTo the calculate ofchosen the the chosen material.contact material. angle The θ , volumestrictly Thevolume related of the to of dropletβadh the, we droplet putis a singlepriori is a prioridrop constrained, ofconstrained, liquid on using a flat using gas- gas-chromatographychromatographysurface of the syringe, chosen syringe, thatmaterial. thatallows allowsThe to volume put to putdown of down the droplets droplet droplets varyingis a varying priori from constrained, from 10 to 10 100 to 100using microliters microliters gas- in involume, volume,chromatography with with a precision a precision syringe, of ofthatabout about allows half half toa aputmicroliter.
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