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Wetting and Adhesive Forces on Rough Surfaces – An Experimental and Theoretical Study
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 102 (2015) 45 – 53
The 7th World Congress on Particle Technology (WCPT7)
Wetting and adhesive forces on rough surfaces – An experimental and theoretical study Jörg Fritzschea*, Urs A. Peukera a
TU Freiberg, Institute of Mechanical Process Engineering and Mineral Processing, Agricolastraße 1, 09599 Freiberg, Germany
Abstract
It is well known that wetting plays a crucial role in many processes due to its impact on the emerging adhesive forces. In general, high wetting angles between solid and liquid lead to higher adhesive forces and vice versa. For ideal systems the calculation of these adhesive forces is possible using analytical approaches for van der Waals and polar forces. But there is still a lack of knowledge how to consider impacts like roughness and irregular shape of the solids during the calculation. The present paper aims to show the correlation between wetting behaviour and adhesive forces for non-ideal systems. Therefore, a model system is created wherewith the wetting angle can be changed in a high range. Coated alumina particles are used as solids in this model system. The coating leads to a low surface energy and consequently to a high wetting angle to water of 105°. The wetting angle is reduced by adding ethanol to the aqueous phase and thus the influence of wetting on the adhesive force can be investigated. To correlate the wetting angle with the adhesive force, both of them must be measured. Using a substrate with the same surface coating as the used particles the sessile drop method for the determination of the wetting angle can be applied. Subsequently, the calculation of the interfacial energy, which should be linked up directly to the adhesive force, is possible. The adhesive forces are determined directly by using an atomic force microscope (AFM). Therefore, a coated alumina particle is glued on the end of the cantilever to measure the particle-substrate force directly. The particle and substrate are entirely submerged into the surrounding liquid. As confirmed, measurements of the wetting angle show a decrease with higher ethanol fractions. This is due to the
* Corresponding author. Tel.: +493731392947; fax: +493731392448. E-mail address: [email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS)
doi:10.1016/j.proeng.2015.01.105
46
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
lower surface energy of ethanol compared to water. Furthermore, the results show a selective adsorption of ethanol to the solid surface. This leads to an increased surface saturation of ethanol depending on the concentration in the liquid which can be described with a Langmuir isotherm. AFM measurements show a variation of adhesive forces caused by the high roughness of the substrate. This can be described with statistical distributions. Parameters of this distributions show a correlation to the ethanol saturation. Semi-empirical approaches using van der Waals and polar forces confirm this behaviour. ©©2015 Authors. Published by Elsevier Ltd. This 2014The The Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Selection and under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy Academy ofpeer-review Sciences (CAS). of Sciences (CAS)
Keywords: Adhesive Forces; Wetting; Adsorption; Surface Roughness; Atomic Force Microscope 1. Introduction Interaction forces or energies between particles or particles and a substrate in a liquid are a main influence factor in most fields of process engineering. The prediction of these forces is possible with the aid of the so called extended DLVO (XDLVO) theory which combines disperse, polar and electrostatic forces. Furthermore, especially in poor wetting systems, a capillary bridge occurs due to nano-bubbles which increases the attractive force. Disperse, or van der Waals forces between the materials can be calculated if the geometries are known and the surfaces are smooth. To estimate the influence of roughness several models has been created. Rumpf developed a model in which a small hemisphere is added onto one of the interacting particles. Due to this hemisphere the distance between the particles increases and the attractive forces decrease [1]. The Rabinovich model simulates the roughness by spherical caps at the substrate. These caps can be correlated to the rms-roughness of the substrate which can be measured for example with an atomic force microscope (AFM) [2,3]. The models are able to predict the order of magnitude of the adhesive forces if the roughness is in nanometer scale [4]. Polar forces as described by van Oss can be calculated from the polar parts of the surface energies of the participating materials by given geometry and smooth surfaces [5]. Up to now no analytical models are available to calculate the polar forces at rough surfaces. Capillary bridges due to nano-bubbles at the surfaces of the interacting materials are able to enhance the adhesive forces significantly. At smooth surfaces nano-bubbles can be created by supersaturating of the liquid by temperature change or liquid exchange [6]. Onto rough surfaces, the same mechanism should work similarly to create nanobubbles, but the direct detection with phase-contrast AFM is not possible due to the superposition of the phasecontrast and topography signal [7]. Aim of this paper is the indirect detection of nano-bubbles by the use of force / distance curves measured with an AFM. Furthermore the measured adhesive energies are correlated to the wetting behavior of the solid materials.
Nomenclature ܣ ȟܩ ݈ ݎ ܵ ݔ
surface area free energy of interaction minimum distance between the interacting materials radius surface saturation of ethanol at the liquid / solid interface mole fraction of ethanol in the bulk liquid
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
ߛ ߣ
surface or interfacial energy decay length of the polar interactions
2. Material and Methods The force / distance curves where obtained with an AFM XE-100 from Park Systems, South Korea and the colloidal probe technique as described in [8,9]. Thereby a spherical alumina particle is glued onto the end of the cantilever to measure directly the force between the particle and alumina substrate. Figure 1 shows a topography picture of the substrate scanned with the AFM.
Figure 1: 15 μm x 15 μm topography scan of the used rough substrate
Both, the particle and the substrate are coated with the silane Dynasylan F 8261, Evonik Industries Germany, which has a PTFE-like functional group. This decreases the surface energy and creates a poor wetting behavior to water. By the addition of ethanol to the water, the wetting can be improved. This allows the investigation of the influence of wetting on the adhesive force and energy. For each parameter set-up five test run with 256 force / distance curve at several points at the substrate where measured. This is necessary due to the high roughness which leads to a wide-ranged distribution of forces [10]. Afterwards the obtained curves are classified in capillary and non-capillary interactions by several criteria. In the case of capillary interactions caused by gas bridges between the substrate and particle the force / distance curves can show long range snap-ins during the trace which must be caused by a capillary interaction. Also during the retrace a stepwise reduction of force can be seen as shown on the left side in figure 2 which is the major characteristic of capillary interactions at rough surfaces.
Figure 2: Measured force / distance curves in the case of a capillary interaction (left) and non-capillary interaction
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Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
This is due to the pinned contact line of the capillary which leads to local force minima until the contact line moves one step further and the force increases again until the capillary cracks. On the right side only a singular pulloff can be seen which can be interpreted as a non-capillary interaction. Using the pull-off force, defined as the minimum of the reached force in the force / distance diagram leads to the problem, that a capillary interaction has several local minima. One solution of this problem is the numerical integration of the obtained curve which is shown by the hatched areas in the diagrams. This leads to the energy of interaction which is necessary to separate the particle from the substrate. All obtained force / distance curves where analyzed with the aid of a programmed MATLAB routine. Within this routine the numerical integration of the curves is done to determine the adhesive energy. It is also used to split the measured curves in capillary and non-capillary interactions. Therefor the curves where scanned for long-range snapins or multiple force minima during retrace which both indicates capillary interactions. 3. Theory 3.1. Disperse and polar interaction The adhesive energies between two solids immersed in a liquid are strictly connected to the surface energy of the participating materials. The surface energy of a material can be split up in several superimposed parts. (1)
ࢽ ൌ σࢽ
For non-metallic materials the splitting in a disperse ߛ ୢ and a polar ߛ ୮ surface energy is common [11,12], whereby the polar part is calculated as twice the geometric mean of the positive and negative surface energy. (2)
ࢽ ൌ ࢽ ܌ ࢽ ܘൌ ࢽ ܌ ڄඥࢽା ିࢽ ڄ ୮
The disperse ߛୱ୪ୢ and polar ߛୱ୪ interfacial surface energy between the solid and liquid can be calculated with equations (3) and (4). This represents the sum of the cohesion inside the two interacting materials minus the adhesion between them. ࢽ ܔܛ܌ൌ ࢽ ܛ܌ ࢽ ܔ܌െ ڄටࢽܔ܌ࢽ ڄ ܛ܌
(3)
ߛୱ୪ ൌ ʹ ڄቆඥߛୱି ߛ ڄୱା ටߛ୪ି ߛ ڄ୪ା െ ටߛୱି ߛ ڄ୪ା െ ඥߛୱା ߛ ڄ୪ି ቇ
(4)
୮
The surface energies of the materials used in this study are listed in table 1. Table 1: Disperse, polar and overall surface energies of the used materials in mJ/m² taken from [9,13] ߛୢ
ߛା
ߛି
ߛ
Coated Al2O3
19.5
0
1.4
19.5
Water
22.8
25.5
25.5
72.8
Ethanol
18.8
0.019
68
21.1
Material
To calculate the interfacial energy between the solids and the used mixture of ethanol and water, the saturation of ethanol at the solid surface where the interaction takes place has to be known. The saturation of ethanol directly
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above the solid surface can be described in correlation to the bulk concentration using a Langmuir approach (5). Thereby ݔ is the mole fraction of ethanol in the bulk liquid and ܵ the corresponding surface saturation with ܽ ൌ ͶͷǤͶ and ܾ ൌ ͳǤͲʹ as fitting parameters [14]. ࡿ۳ ൌ
ࢇ ࢞ ڄ۳ ࢈ڄ ࢇ ࢞ ڄ۳
(5)
Assuming the Cassie/Baxter model, the surface energy should correlate linearly with the surface saturation of ethanol which leads to equation (6) for the overall surface energy [15]. The same equation is valid for the calculation of the interfacial surface energy between the mixture liquid and solid. ࢽ ܔሺࡿ۳ ሻ ൌ ࡿࡱ ڄሺࢽ۳ െ ࢽ ܅ሻ ࢽ܅
(6)
In the case of a non-capillary interaction, the free energy of interaction ȟ ܩis the superimposition of disperse and polar energies. The disperse free energy of interaction for two spheres of the same material immersed in a liquid can be calculated using the van der Waals approach (7). ઢࡳ ܌ൌ െ ڄ ܔܛ܌ࢽ ڄ ࣊ ڄ כ࢘ ڄ
(7)
Thereby, ݈ is the minimum distance between the two solids which can be estimated with ݈ ൌ ͲǤͳͷ for an unknown system [13,16]. The polar free energy of interaction is calculated by equation (8) whereby ߣ is the characteristic decay length and can be approximated for water with ߣ ൎ ͳ [13,17]. ܘ
ઢࡳ ܘൌ െ כ࢘ ڄ ࣅ ڄ ܔܛࢽ ڄ ࣊ ڄ
(8)
In both equations כ ݎis the mean radius of the interacting system calculated with equation (9). ݎଵ and ݎଶ are the radii of the two interacting spheres. In the case of an interaction between a sphere and a plate, one radius is infinite and the mean radius is twice of the sphere radius. ࢘ כൌ
࢘ ڄ ࢘ ڄ ࢘ ࢘
(9)
3.2. Capillary interaction The calculation of the free energy of capillary interactions can be done using the energetic approach [18]. With it the free energy of interaction is calculated from the amount of energy which is needed to create new surfaces as illustrated by figure 3.
Figure 3: Scheme of the capillary interaction in contact (left) and in non-contact (right) state.
The dashed line represents the area ܣୗ of the spherical cap which gets wetted by the surrounding liquid during the retrace of the particle. At the same time, the lateral surface of the capillary meniscus ܣେ is formed to a nano-bubble with the new surface ܣ represented by the dotted lines.
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ઢࡳ۱ ൌ ࢽ ܁ ڄ ܛ ࢽ ڄ ܔ۱ െ ࢽ ܁ ڄ ܔܛെ ࢽۼ ڄ ܔ۰
(10)
The calculation of the required areas in equation (10) can be found elsewhere in literature and will not be explained in this paper [18,19]. 4. Results Due to the high roughness of the used substrate wide-ranged distributions as shown in figure 4 are obtained. The dashed line represents the overall distribution in pure water as surrounding liquid. The capillary and non-capillary distributions are obtained by the division of the overall curve. One can see that non-capillary interactions lead to lower adhesive forces compared to capillary interactions. It also shows a large area where the distributions overlap which illustrates that - within a certain probability - a non-capillary interaction can have a higher adhesive energy than a capillary interaction.
Figure 4: Adhesive energy distributions calculated from the measured force / distance curves for pure water.
Figure 5 represents the probability of occurrence of the capillary and non-capillary kind of interaction correlated to the cosine of the wetting angle. In the case of pure water, the cosine of the wetting angle is ൎ െͲǤʹͷ and the probability of occurrence for non-capillary interaction is about 45 %. By the addition of ethanol to the surrounding liquid, the cosine is increased which leads to an increasing of non-capillary interactions which corresponds to theoretical considerations. Due to better wetting conditions the energetic driving power for the creation of nanobubbles, which are required for capillary interactions decreases. The correlation of the probability of occurrence to the cosine of the wetting angle seems to be linear which allows an empirical description within the measured range.
Figure 5: The probability of occurrence of non-capillary and capillary interaction in correlation to the cosine of the wetting angle
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
One possible approach for the calculation of the adhesive energies in the case of non-capillary interactions is shown in figure 6. The red circles represent the mean values of the measured adhesive energy distributions for noncapillary interactions correlated to the surface saturation of ethanol at the interface. If a log-normal distribution is
Figure 6: Measured and calculated adhesive energies correlated to the surface saturation of ethanol
used to describe the measured adhesive energies, the lower (black squares) and upper (blue triangles) bound of the standard deviation can be calculated. The dashed lines represent the theoretical calculation of these statistical values. Therefor the radius ݎଶ is used as fitting parameter which represents the radius of an asperity at the substrate surface. For the mean adhesive energy a radius of ݎଶ ൌ ͳǤʹͳɊ is obtained. The lower bound of the standard deviation leads to a radius of ݎଶ ൌ ͲǤʹɊ while the upper bound results in ݎଶ ൌ ͺǤͷɊ. Related to the used substrate the calculated radii seem to be feasible but a direct correlation to the topography profile is not done yet. Figure 7 shows the statistical values of the adhesive energy distributions in the case of capillary interaction correlated to the surface saturation of ethanol. The dashed lines represent an exponential fitting of the statistical values of the measured adhesive energies. Below a surface saturation of ethanol of 50 % a good agreement can be achieved. At higher saturation levels a deviation between the fitting model and measurements occurs. A direct prediction of the obtained behavior is up to now not possible due to the high number of influence factors. Both, the surface energy of the liquid and the interfacial energy between the liquid and solids depend on the mole fraction of ethanol in the surrounding liquid. Changes in the mole fraction of ethanol have an effect on the size and occurrence of nano-bubbles at the surface before the contact happens. Furthermore the topography, roughness and inhomogeneity of the substrate and particle surface influence the size of nano-bubbles.
Figure 7: Adhesive energies of capillary interactions correlated to the surface saturation of ethanol
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To validate the measured adhesive energies of the capillary interactions, a calculation of the nano-bubble size is possible. Therefore equation (10) is used with the following assumptions: x x x x
Equal volume of the meniscus and nano-bubble Radius of the meniscus and nano-bubble stay constant at the substrate Radius of the meniscus has a circular shape Nano-bubble has the shape of a spherical cap
Figure 8 illustrates the statistical values of the calculated nano-bubble radii. In general the calculated radii agree with radii reported in literature [20–22]. It also shows a decrease of the radius by an increasing surface saturation of ethanol. This is in contrast to literature where the size of nano-bubbles increase with higher ethanol fractions in the liquid [23]. The authors explain this behavior with coalescence of the nano-bubbles at higher ethanol concentrations which is not possible if a highly rough substrate is used. In this case, the contact line of the bubble is pinned at edges and inhomogeneities of the surface. This will suppress the coalescence and the size of nano-bubbles stay constant.
Figure 8: Radius of nano-bubbles at the substrate calculated from the measured adhesive energy
5. Conclusion The study shows the occurrence of capillary and non-capillary interactions at highly rough surfaces in correlation with the wetting behavior. It illustrates that improved wetting leads to a decrease of capillary and an increase of noncapillary interactions. In general the adhesive energy of both kinds of interaction will decrease with an increased surface saturation of ethanol which is similar to an improved wetting behavior. In the case of non-capillary interactions, the adhesive energy can be calculated by the use of disperse and polar energies regarding the van Oss theory. In contrast, the adhesive energy of capillary interactions cannot be predicted by a theory up to now due to the higher number of influence factors. Acknowledgements The authors would like to thank the German Research Foundation (DFG) for supporting the investigations in the subproject B04, which is a part of the Collaborative Research Center CRC 920. References [1] [2]
H. Rumpf, Die Wissenschaft des Agglomerierens, Chemie Ing. Techn. 46 (1974) 1–11. Y.I. Rabinovich, J.J. Adler, A. Ata, R.K. Singh, B.M. Moudgil, Adhesion between Nanoscale Rough Surfaces, Journal of Colloid and
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
Interface Science 232 (2000) 10–16. Y.I. Rabinovich, J.J. Adler, A. Ata, R.K. Singh, B.M. Moudgil, Adhesion between Nanoscale Rough Surfaces, Journal of Colloid and Interface Science 232 (2000) 17–24. O. Laitinen, K. Bauer, J. Niinimäki, U.A. Peuker, Validity of the Rumpf and the Rabinovich adhesion force models for alumina substrates with nanoscale roughness, Powder Technology 246 (2013) 545–552. C.J. van Oss, M.K. Chaudhury, R.J. Good, Interfacial Lifshitz-van der Waals and polar interactions in macroscopic systems, Chem. Rev. 88 (1988) 927–941. M.A. Hampton, A.V. Nguyen, Nanobubbles and the nanobubble bridging capillary force, Advances in Colloid and Interface Science 154 (2010) 30–55. M. Rudolph, K. Bauer, U.A. Peuker, Phasenkontrast-Rasterkraftmikroskopie für die Charakterisierung der Verteilung von Nanopartikeln in Verbundwerkstoffen., Chemie Ing. Techn. 82 (2010) 2189–2195. F. Heuzeroth, J. Fritzsche, U.A. Peuker, Raster-Kraft-Mikroskopie zur Evaluation der Abscheideeffizienz bei der Metallschmelzefiltration, Chemie Ingenieur Technik 86 (2014) 874–882. J. Fritzsche, J. Teichmann, F. Heuzeroth, G.K. van den Boogaart, U.A. Peuker, Impact of Wetting to the Agglomeration of Dispersed Particles in an Aqueous Medium, Adv. Eng. Mater. 15 (2013) 1299–1306. M. Götzinger, W. Peukert, Particle Adhesion Force Distributions on Rough Surfaces, Langmuir 20 (2004) 5298–5303. F.M. Fowkes, F.L. Riddle, W.E. Pastore, A.A. Weber, Interfacial interactions between self-associated polar liquids and squalane used to test equations for solid—liquid interfacial interactions, Colloids and Surfaces 43 (1990) 367–387. C.J. van Oss, M.K. Chaudhury, R.J. Good, Monopolar surfaces, Adv Colloid Interface Sci 28 (1987) 35–64. C.J. van Oss, Interfacial forces in aqueous media, 2nd ed., Taylor & Francis Ltd, Boca Raton, Fla, 2006. J. Fritzsche, U.A. Peuker, The Influence of Particle Agglomeration on the Filtration Efficiency of Ceramic Foam Filters, in: Filtech Exhibitions Germany (Ed.), Filtech 2013. Content: Full Papers, 2013. A.B.D. Cassie, S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40 (1944) 546. J.C. Berg, Wettability, M. Dekker, New York, 1993. C.J. van Oss, Long-range and short-range mechanisms of hydrophobic attraction and hydrophilic repulsion in specific and aspecific interactions, J. Mol. Recognit. 16 (2003) 177–190. B.P. Binks, T.S. Horozov, Colloidal particles at liquid interfaces, Cambridge Univ. Press, Cambridge [u.a.], 2006. H.-J. Butt, M. Kappl, Normal capillary forces, Advances in Colloid and Interface Science 146 (2009) 48–60. B.M. Borkent, S. de Beer, F. Mugele, D. Lohse, On the Shape of Surface Nanobubbles, Langmuir 26 (2010) 260–268. J.R.T. Seddon, D. Lohse, Nanobubbles and micropancakes: gaseous domains on immersed substrates, J Phys Condens Matter 23 (2011) 133001. A.C. Simonsen, P.L. Hansen, B. Klösgen, Nanobubbles give evidence of incomplete wetting at a hydrophobic interface, Journal of Colloid and Interface Science 273 (2004) 291–299. A.V. Nguyen, J. Nalaskowski, J.D. Miller, H.-J. Butt, Attraction between hydrophobic surfaces studied by atomic force microscopy, International Journal of Mineral Processing 72 (2003) 215–225.
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ScienceDirect Procedia Engineering 102 (2015) 45 – 53
The 7th World Congress on Particle Technology (WCPT7)
Wetting and adhesive forces on rough surfaces – An experimental and theoretical study Jörg Fritzschea*, Urs A. Peukera a
TU Freiberg, Institute of Mechanical Process Engineering and Mineral Processing, Agricolastraße 1, 09599 Freiberg, Germany
Abstract
It is well known that wetting plays a crucial role in many processes due to its impact on the emerging adhesive forces. In general, high wetting angles between solid and liquid lead to higher adhesive forces and vice versa. For ideal systems the calculation of these adhesive forces is possible using analytical approaches for van der Waals and polar forces. But there is still a lack of knowledge how to consider impacts like roughness and irregular shape of the solids during the calculation. The present paper aims to show the correlation between wetting behaviour and adhesive forces for non-ideal systems. Therefore, a model system is created wherewith the wetting angle can be changed in a high range. Coated alumina particles are used as solids in this model system. The coating leads to a low surface energy and consequently to a high wetting angle to water of 105°. The wetting angle is reduced by adding ethanol to the aqueous phase and thus the influence of wetting on the adhesive force can be investigated. To correlate the wetting angle with the adhesive force, both of them must be measured. Using a substrate with the same surface coating as the used particles the sessile drop method for the determination of the wetting angle can be applied. Subsequently, the calculation of the interfacial energy, which should be linked up directly to the adhesive force, is possible. The adhesive forces are determined directly by using an atomic force microscope (AFM). Therefore, a coated alumina particle is glued on the end of the cantilever to measure the particle-substrate force directly. The particle and substrate are entirely submerged into the surrounding liquid. As confirmed, measurements of the wetting angle show a decrease with higher ethanol fractions. This is due to the
* Corresponding author. Tel.: +493731392947; fax: +493731392448. E-mail address: [email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS)
doi:10.1016/j.proeng.2015.01.105
46
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
lower surface energy of ethanol compared to water. Furthermore, the results show a selective adsorption of ethanol to the solid surface. This leads to an increased surface saturation of ethanol depending on the concentration in the liquid which can be described with a Langmuir isotherm. AFM measurements show a variation of adhesive forces caused by the high roughness of the substrate. This can be described with statistical distributions. Parameters of this distributions show a correlation to the ethanol saturation. Semi-empirical approaches using van der Waals and polar forces confirm this behaviour. ©©2015 Authors. Published by Elsevier Ltd. This 2014The The Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Selection and under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy Academy ofpeer-review Sciences (CAS). of Sciences (CAS)
Keywords: Adhesive Forces; Wetting; Adsorption; Surface Roughness; Atomic Force Microscope 1. Introduction Interaction forces or energies between particles or particles and a substrate in a liquid are a main influence factor in most fields of process engineering. The prediction of these forces is possible with the aid of the so called extended DLVO (XDLVO) theory which combines disperse, polar and electrostatic forces. Furthermore, especially in poor wetting systems, a capillary bridge occurs due to nano-bubbles which increases the attractive force. Disperse, or van der Waals forces between the materials can be calculated if the geometries are known and the surfaces are smooth. To estimate the influence of roughness several models has been created. Rumpf developed a model in which a small hemisphere is added onto one of the interacting particles. Due to this hemisphere the distance between the particles increases and the attractive forces decrease [1]. The Rabinovich model simulates the roughness by spherical caps at the substrate. These caps can be correlated to the rms-roughness of the substrate which can be measured for example with an atomic force microscope (AFM) [2,3]. The models are able to predict the order of magnitude of the adhesive forces if the roughness is in nanometer scale [4]. Polar forces as described by van Oss can be calculated from the polar parts of the surface energies of the participating materials by given geometry and smooth surfaces [5]. Up to now no analytical models are available to calculate the polar forces at rough surfaces. Capillary bridges due to nano-bubbles at the surfaces of the interacting materials are able to enhance the adhesive forces significantly. At smooth surfaces nano-bubbles can be created by supersaturating of the liquid by temperature change or liquid exchange [6]. Onto rough surfaces, the same mechanism should work similarly to create nanobubbles, but the direct detection with phase-contrast AFM is not possible due to the superposition of the phasecontrast and topography signal [7]. Aim of this paper is the indirect detection of nano-bubbles by the use of force / distance curves measured with an AFM. Furthermore the measured adhesive energies are correlated to the wetting behavior of the solid materials.
Nomenclature ܣ ȟܩ ݈ ݎ ܵ ݔ
surface area free energy of interaction minimum distance between the interacting materials radius surface saturation of ethanol at the liquid / solid interface mole fraction of ethanol in the bulk liquid
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
ߛ ߣ
surface or interfacial energy decay length of the polar interactions
2. Material and Methods The force / distance curves where obtained with an AFM XE-100 from Park Systems, South Korea and the colloidal probe technique as described in [8,9]. Thereby a spherical alumina particle is glued onto the end of the cantilever to measure directly the force between the particle and alumina substrate. Figure 1 shows a topography picture of the substrate scanned with the AFM.
Figure 1: 15 μm x 15 μm topography scan of the used rough substrate
Both, the particle and the substrate are coated with the silane Dynasylan F 8261, Evonik Industries Germany, which has a PTFE-like functional group. This decreases the surface energy and creates a poor wetting behavior to water. By the addition of ethanol to the water, the wetting can be improved. This allows the investigation of the influence of wetting on the adhesive force and energy. For each parameter set-up five test run with 256 force / distance curve at several points at the substrate where measured. This is necessary due to the high roughness which leads to a wide-ranged distribution of forces [10]. Afterwards the obtained curves are classified in capillary and non-capillary interactions by several criteria. In the case of capillary interactions caused by gas bridges between the substrate and particle the force / distance curves can show long range snap-ins during the trace which must be caused by a capillary interaction. Also during the retrace a stepwise reduction of force can be seen as shown on the left side in figure 2 which is the major characteristic of capillary interactions at rough surfaces.
Figure 2: Measured force / distance curves in the case of a capillary interaction (left) and non-capillary interaction
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Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
This is due to the pinned contact line of the capillary which leads to local force minima until the contact line moves one step further and the force increases again until the capillary cracks. On the right side only a singular pulloff can be seen which can be interpreted as a non-capillary interaction. Using the pull-off force, defined as the minimum of the reached force in the force / distance diagram leads to the problem, that a capillary interaction has several local minima. One solution of this problem is the numerical integration of the obtained curve which is shown by the hatched areas in the diagrams. This leads to the energy of interaction which is necessary to separate the particle from the substrate. All obtained force / distance curves where analyzed with the aid of a programmed MATLAB routine. Within this routine the numerical integration of the curves is done to determine the adhesive energy. It is also used to split the measured curves in capillary and non-capillary interactions. Therefor the curves where scanned for long-range snapins or multiple force minima during retrace which both indicates capillary interactions. 3. Theory 3.1. Disperse and polar interaction The adhesive energies between two solids immersed in a liquid are strictly connected to the surface energy of the participating materials. The surface energy of a material can be split up in several superimposed parts. (1)
ࢽ ൌ σࢽ
For non-metallic materials the splitting in a disperse ߛ ୢ and a polar ߛ ୮ surface energy is common [11,12], whereby the polar part is calculated as twice the geometric mean of the positive and negative surface energy. (2)
ࢽ ൌ ࢽ ܌ ࢽ ܘൌ ࢽ ܌ ڄඥࢽା ିࢽ ڄ ୮
The disperse ߛୱ୪ୢ and polar ߛୱ୪ interfacial surface energy between the solid and liquid can be calculated with equations (3) and (4). This represents the sum of the cohesion inside the two interacting materials minus the adhesion between them. ࢽ ܔܛ܌ൌ ࢽ ܛ܌ ࢽ ܔ܌െ ڄටࢽܔ܌ࢽ ڄ ܛ܌
(3)
ߛୱ୪ ൌ ʹ ڄቆඥߛୱି ߛ ڄୱା ටߛ୪ି ߛ ڄ୪ା െ ටߛୱି ߛ ڄ୪ା െ ඥߛୱା ߛ ڄ୪ି ቇ
(4)
୮
The surface energies of the materials used in this study are listed in table 1. Table 1: Disperse, polar and overall surface energies of the used materials in mJ/m² taken from [9,13] ߛୢ
ߛା
ߛି
ߛ
Coated Al2O3
19.5
0
1.4
19.5
Water
22.8
25.5
25.5
72.8
Ethanol
18.8
0.019
68
21.1
Material
To calculate the interfacial energy between the solids and the used mixture of ethanol and water, the saturation of ethanol at the solid surface where the interaction takes place has to be known. The saturation of ethanol directly
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above the solid surface can be described in correlation to the bulk concentration using a Langmuir approach (5). Thereby ݔ is the mole fraction of ethanol in the bulk liquid and ܵ the corresponding surface saturation with ܽ ൌ ͶͷǤͶ and ܾ ൌ ͳǤͲʹ as fitting parameters [14]. ࡿ۳ ൌ
ࢇ ࢞ ڄ۳ ࢈ڄ ࢇ ࢞ ڄ۳
(5)
Assuming the Cassie/Baxter model, the surface energy should correlate linearly with the surface saturation of ethanol which leads to equation (6) for the overall surface energy [15]. The same equation is valid for the calculation of the interfacial surface energy between the mixture liquid and solid. ࢽ ܔሺࡿ۳ ሻ ൌ ࡿࡱ ڄሺࢽ۳ െ ࢽ ܅ሻ ࢽ܅
(6)
In the case of a non-capillary interaction, the free energy of interaction ȟ ܩis the superimposition of disperse and polar energies. The disperse free energy of interaction for two spheres of the same material immersed in a liquid can be calculated using the van der Waals approach (7). ઢࡳ ܌ൌ െ ڄ ܔܛ܌ࢽ ڄ ࣊ ڄ כ࢘ ڄ
(7)
Thereby, ݈ is the minimum distance between the two solids which can be estimated with ݈ ൌ ͲǤͳͷ for an unknown system [13,16]. The polar free energy of interaction is calculated by equation (8) whereby ߣ is the characteristic decay length and can be approximated for water with ߣ ൎ ͳ [13,17]. ܘ
ઢࡳ ܘൌ െ כ࢘ ڄ ࣅ ڄ ܔܛࢽ ڄ ࣊ ڄ
(8)
In both equations כ ݎis the mean radius of the interacting system calculated with equation (9). ݎଵ and ݎଶ are the radii of the two interacting spheres. In the case of an interaction between a sphere and a plate, one radius is infinite and the mean radius is twice of the sphere radius. ࢘ כൌ
࢘ ڄ ࢘ ڄ ࢘ ࢘
(9)
3.2. Capillary interaction The calculation of the free energy of capillary interactions can be done using the energetic approach [18]. With it the free energy of interaction is calculated from the amount of energy which is needed to create new surfaces as illustrated by figure 3.
Figure 3: Scheme of the capillary interaction in contact (left) and in non-contact (right) state.
The dashed line represents the area ܣୗ of the spherical cap which gets wetted by the surrounding liquid during the retrace of the particle. At the same time, the lateral surface of the capillary meniscus ܣେ is formed to a nano-bubble with the new surface ܣ represented by the dotted lines.
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ઢࡳ۱ ൌ ࢽ ܁ ڄ ܛ ࢽ ڄ ܔ۱ െ ࢽ ܁ ڄ ܔܛെ ࢽۼ ڄ ܔ۰
(10)
The calculation of the required areas in equation (10) can be found elsewhere in literature and will not be explained in this paper [18,19]. 4. Results Due to the high roughness of the used substrate wide-ranged distributions as shown in figure 4 are obtained. The dashed line represents the overall distribution in pure water as surrounding liquid. The capillary and non-capillary distributions are obtained by the division of the overall curve. One can see that non-capillary interactions lead to lower adhesive forces compared to capillary interactions. It also shows a large area where the distributions overlap which illustrates that - within a certain probability - a non-capillary interaction can have a higher adhesive energy than a capillary interaction.
Figure 4: Adhesive energy distributions calculated from the measured force / distance curves for pure water.
Figure 5 represents the probability of occurrence of the capillary and non-capillary kind of interaction correlated to the cosine of the wetting angle. In the case of pure water, the cosine of the wetting angle is ൎ െͲǤʹͷ and the probability of occurrence for non-capillary interaction is about 45 %. By the addition of ethanol to the surrounding liquid, the cosine is increased which leads to an increasing of non-capillary interactions which corresponds to theoretical considerations. Due to better wetting conditions the energetic driving power for the creation of nanobubbles, which are required for capillary interactions decreases. The correlation of the probability of occurrence to the cosine of the wetting angle seems to be linear which allows an empirical description within the measured range.
Figure 5: The probability of occurrence of non-capillary and capillary interaction in correlation to the cosine of the wetting angle
Jörg Fritzsche and Urs A. Peuker / Procedia Engineering 102 (2015) 45 – 53
One possible approach for the calculation of the adhesive energies in the case of non-capillary interactions is shown in figure 6. The red circles represent the mean values of the measured adhesive energy distributions for noncapillary interactions correlated to the surface saturation of ethanol at the interface. If a log-normal distribution is
Figure 6: Measured and calculated adhesive energies correlated to the surface saturation of ethanol
used to describe the measured adhesive energies, the lower (black squares) and upper (blue triangles) bound of the standard deviation can be calculated. The dashed lines represent the theoretical calculation of these statistical values. Therefor the radius ݎଶ is used as fitting parameter which represents the radius of an asperity at the substrate surface. For the mean adhesive energy a radius of ݎଶ ൌ ͳǤʹͳɊ is obtained. The lower bound of the standard deviation leads to a radius of ݎଶ ൌ ͲǤʹɊ while the upper bound results in ݎଶ ൌ ͺǤͷɊ. Related to the used substrate the calculated radii seem to be feasible but a direct correlation to the topography profile is not done yet. Figure 7 shows the statistical values of the adhesive energy distributions in the case of capillary interaction correlated to the surface saturation of ethanol. The dashed lines represent an exponential fitting of the statistical values of the measured adhesive energies. Below a surface saturation of ethanol of 50 % a good agreement can be achieved. At higher saturation levels a deviation between the fitting model and measurements occurs. A direct prediction of the obtained behavior is up to now not possible due to the high number of influence factors. Both, the surface energy of the liquid and the interfacial energy between the liquid and solids depend on the mole fraction of ethanol in the surrounding liquid. Changes in the mole fraction of ethanol have an effect on the size and occurrence of nano-bubbles at the surface before the contact happens. Furthermore the topography, roughness and inhomogeneity of the substrate and particle surface influence the size of nano-bubbles.
Figure 7: Adhesive energies of capillary interactions correlated to the surface saturation of ethanol
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To validate the measured adhesive energies of the capillary interactions, a calculation of the nano-bubble size is possible. Therefore equation (10) is used with the following assumptions: x x x x
Equal volume of the meniscus and nano-bubble Radius of the meniscus and nano-bubble stay constant at the substrate Radius of the meniscus has a circular shape Nano-bubble has the shape of a spherical cap
Figure 8 illustrates the statistical values of the calculated nano-bubble radii. In general the calculated radii agree with radii reported in literature [20–22]. It also shows a decrease of the radius by an increasing surface saturation of ethanol. This is in contrast to literature where the size of nano-bubbles increase with higher ethanol fractions in the liquid [23]. The authors explain this behavior with coalescence of the nano-bubbles at higher ethanol concentrations which is not possible if a highly rough substrate is used. In this case, the contact line of the bubble is pinned at edges and inhomogeneities of the surface. This will suppress the coalescence and the size of nano-bubbles stay constant.
Figure 8: Radius of nano-bubbles at the substrate calculated from the measured adhesive energy
5. Conclusion The study shows the occurrence of capillary and non-capillary interactions at highly rough surfaces in correlation with the wetting behavior. It illustrates that improved wetting leads to a decrease of capillary and an increase of noncapillary interactions. In general the adhesive energy of both kinds of interaction will decrease with an increased surface saturation of ethanol which is similar to an improved wetting behavior. In the case of non-capillary interactions, the adhesive energy can be calculated by the use of disperse and polar energies regarding the van Oss theory. In contrast, the adhesive energy of capillary interactions cannot be predicted by a theory up to now due to the higher number of influence factors. Acknowledgements The authors would like to thank the German Research Foundation (DFG) for supporting the investigations in the subproject B04, which is a part of the Collaborative Research Center CRC 920. References [1] [2]
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