Institute of Semicon-ductor and Solid State Physics Supervisor Univ. Prof.in Dr.in Alberta Bonanni Co-Supervisor Christopher Allgaier, MSc February 2021 JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, ¨Osterreich www.jku.at DVR 0093696
Experimental
study
of
wetting phenomena for
fuel-cell use
Master Thesis
to obtain the academic degree of
Diplom-Ingenieur
in the Master’s Program
Ich erkläre an Eides statt, dass ich die vorliegende Masterarbeit selbstständig und ohne fremde Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt bzw. die wörtlich oder sinngemäß entnommenen Stellen als solche kenntlich gemacht habe.
Die vorliegende Masterarbeit ist mit dem elektronisch übermittelten Textdoku-ment identisch.
Linz, Februar, 2021
Zuallererst möchte ich mich bei meiner Betreuerin Alberta Bonanni bedanken, die sich dazu bereit erklärt hat meine Masterarbeit zu betreuen, was diese in Zusam-menarbeit mit der Robert Bosch GmbH erst ermöglicht hat. Danke, dass du mich trotz deiner vielen anderen Verpflichtungen immer produktiv unterstützt und zum erfolgreichen Studienabschluss gebracht hast.
Seitens der Robert Bosch GmbH möchte ich mich bei Ingo Brauer und Christopher Allgaier bedanken, die mir die Chance gegeben haben meine Masterarbeit in ihrer Abteilung zu schreiben. Vielen Dank Christopher, dass du mich während der Zeit bei Bosch immer unterstützt und mir genügend Freiraum bei der Ausarbeitung gegeben hast. Ich bin jeden Tag gerne ins Büro gekommen.
Ohne die Unterstützung der vielen Kolleg*innen bei Bosch wäre die Arbeit niemals möglich gewesen. Sie sind: Michael Rittmann, Gerhard Hüftle, Alexander Markov, Holger Pfeiffer, Veronika Kraemer, Alexander Eifert, Lea Haus, Andre Theile, Alexander Braun und Dennis Hierath.
Für die Unterstützung beim Mikroskopieren möchte ich mich bei Margherita Matzer und Michael Steiner aus der QMAG bedanken.
Das Physikstudium war nicht immer eine angenehme Zeit. Es gibt aber seit Beginn des Studiums eine Hand voll, anfangs Studienkollegen – jetzt enge Freunde, die die Zeit erträglich bis gar unvergesslich gemacht haben und ohne die ich die ersten Semester nicht überstanden hätte. Vielen Dank an Klemens Dösinger, Andreas Erber, Thomas Ömer, Markus Detter, Oliver Maier und Gerald Schwödiauer für eure Kameradschaft. Gemeinsam ist man immer stärker.
Abseits vom Studium kann ich mich glücklich schätzen Freunde aus ganz frühen Tagen, dem Gymnasium, Auslandssemester oder der Zeit in Stuttgart zu haben. i
Vielen Dank an Dominik Dorfhuber, Michael Miesgang, David Jobst, Caro Eis-feld, Tobias Lechner, Andreas Schuhböck, Christian Kuska und Thomas Braun. Manchmal vergisst man wie privilegiert man ist, wenn man Freunde hat, die für einen da sind, auf die man sich verlassen kann, mit denen man die Zeit seines Lebens hat und vor allem, mit denen man gemeinsam durchs Leben geht.
Because of you, I never walk alone.
Vielen Dank an meine Großeltern Helga und Franz Thalhammer, die mich immer auf meinem Weg unterstützt und mir diesen geebnet haben. Ohne euch hätte ich mich nicht voll und ganz auf mein Studium konzentrieren können.
Der finale und auch größte Dank gilt meinen Eltern Gabriele und Günther Kratzer. Es ist sowas von nicht selbstverständlich und schön zu wissen, dass es da jemanden gibt, der sich freut, wenn man nach Hause kommt - egal ob man auf der anderen Seite der Welt war, oder nur im Oberdorf. Danke, dass ihr mir nach all den Jahren noch immer ein zu Hause gebt und mich wissen lasst, wo meine Wurzeln sind. Nur durch eure unermüdliche Unterstützung und Akzeptanz kann ich meinen eigenen Weg gehen und den Kurs auf Erfolg stellen.
Auf eine gesunde, erfolgreiche, erfüllte, finanziell freie und glückliche Zukunft – ich kann’s kaum erwarten.
One of the efforts to reduce, at least locally, the carbon dioxide emission of cars relies on the development of hydrogen fuel cells (HFC), whose only exhaust gas is steam. A safety sensor located in the exhaust pipe of the HFC has to detect non-reacted hydrogen gas in the exhaust gas. A thin tube made from polybutylene terephthalate (PBT), leads the exhaust gases towards the sensor element. Since the exhaust gas is steam, droplets can condense on the walls of the thin tube and potentially clog it. A comprehensive understanding of the wetting behaviour of liquids on substrates in various environmental conditions is still wanted. In the perspective of contributing to this open discussion, a systematic study of double distilled water on PBT as a function of the surface roughness is summarized in this thesis. One raw and seven grinded PBT samples, with root mean square surface roughnesses Rq in the range of (0.19 − 5.02) µm are prepared. On each of these samples, droplets with volumes in the range of (10 − 50) µl have been investigated. To be able to measure static, advancing and receding contact angles, as well as critical sliding angles, an according experimental setup has been built. With increasing surface roughness, the static and advancing contact angles gener-ally increase and the receding contact angle decreases. The critical sliding angles of droplets increase with increasing roughness independent of the droplet volume and decrease on every surface with increasing droplet volume. Droplets with 10 µl remain pinned at every surface and on the roughest surface, no droplets slide off. A dimensionless ratio P K is introduced in order to deduce the critical sliding angle for different PBT-surface-roughness-to-droplet-volume combinations based on the measurements of this work. The findings of this work provide guidelines on how to design the dimensions of the hydrogen sensor’s tube in order to prevent a blockage due to the formation of condensed water droplets.
Eines der Bestreben, den Kohlendioxidausstoß von Autos zumindest lokal zu re-duzieren, setzt auf die Entwicklung von Wasserstoff-Brennstoffzellen (HFC), deren einziges Abgas Wasserdampf ist. Ein Sicherheitssensor, der sich im Abgasrohr der HFC befindet, soll nicht reagiertes Wasserstoffgas im Abgas erkennen. Ein dünnes Röhrchen aus Polybutylenterephthalat (PBT) leitet die Abgase in Rich-tung des Sensorelements. Da es sich bei dem Abgas um Wasserdampf handelt, können Tropfen an den Wänden des dünnen Röhrchens kondensieren und dieses möglicherweise verstopfen. Ein umfassendes Verständnis des Benetzungsverhal-tens von Flüssigkeiten auf Substraten unter verschiedenen Umgebungsbedingungen wird noch erforscht. Mit der Perspektive, einen Beitrag zu dieser offenen Diskus-sion zu leisten, wird in dieser Arbeit eine systematische Untersuchung von dop-pelt destilliertem Wasser auf PBT in Abhängigkeit von der Oberflächenrauigkeit durchgeführt. Es wurden eine rohe und sieben abgeschliffene PBT-Proben mit mit-tleren quadratischen Oberflächenrauigkeiten Rq im Bereich von (0.19 − 5.02) µm hergestellt. Auf jeder dieser Proben wurden Tropfen mit Volumina im Bereich von (10 − 50) µl untersucht. Um Gleichgewichts-, Advancing- und Receding Kon-taktwinkel sowie kritische Abrollwinkel messen zu können, wurde ein entsprechen-der Versuchsaufbau aufgebaut. Mit zunehmenentsprechen-der Oberflächenrauigkeit steigen die Gleichgewichts und Advancing Kontaktwinkel generell und der Receding Kontak-twinkel nimmt ab. Die kritischen Abrollwinkel der Tropfen nehmen mit zunehmender Rauigkeit unabhängig vom Tropfenvolumen zu und nehmen auf jeder Oberfläche mit zunehmendem Tropfenvolumen ab. Tropfen mit 10 µl bleiben an jeder Ober-fläche haften und auf der rausten OberOber-fläche rollen keine Tropfen ab. Es wird ein dimensionsloses Verhältnis P K eingeführt, um den kritischen Abrollwinkel für verschiedene
PBT-Oberflächen-Rauigkeit-Tropfen-Volumen-Kombinationen basierend auf den Messungen dieser Arbeit abzuleiten. Die Ergebnisse dieser Arbeit liefern Richtlin-ien, wie die Abmessungen des Röhrchens des Wasserstoffsensors zu gestalten sind, um eine Verstopfung durch die Bildung von kondensierten Wassertropfen zu ver-hindern.
Cover sheet a Eidesstattliche Erklärung c Danksagungen i Abstract iii Kurzzusammenfassung v Contents vii 1 Introduction 1 2 Fundamentals 5 2.1 Surface energy . . . 5
2.2 Smooth and chemically homogeneous surfaces . . . 7
2.2.1 Derivation of Young’s equation . . . 7
2.2.2 Line tension . . . 10
2.3 Heterogeneous surfaces . . . 11
2.3.1 Change of apparent static contact angle . . . 11
2.3.2 Microscopic view of the static contact angle and Gibbs en-ergy curve . . . 15
2.3.3 Contact angle hysteresis . . . 19
2.3.4 Adhesion force . . . 23
2.4 Microscopy . . . 24
2.4.1 Atomic force microscopy . . . 24
2.4.2 Optical microscopy . . . 25
3 Sample fabrication and characterisation 29
3.1 Sample fabrication process . . . 29
3.2 Characterisation using optical microscopy . . . 31
3.3 Characterisation using atomic force microscopy . . . 39
4 Experimental setup 41
5 Contact angle measurements and analysis 45
5.1 Measurement plan . . . 45
5.2 Test sequence . . . 45
5.3 Evaluating video recordings and measuring contact angles . . . 47
6 Experimental results 51
6.1 Static contact angle measurements . . . 51
6.2 Critical sliding angle measurements . . . 56
6.3 Contact angle hysteresis measurements . . . 60
7 Synopsis and outlook 67
One of the greatest challenges humans have to face nowadays is climate change. Besides industry and farming, commercial, as well as private transport are the most relevant energy consuming sectors [1]. Energy is mostly provided through fossil fuels and with the continuously increasing demand for energy, the carbon dioxide emission from burning fossil fuels, steadily increases likewise. Since car-bon dioxide emission is the driving force behind climate change, it is of paramount importance to provide the required energy using regenerative energy sources. In a reduced frame, fuel cell (FC) stacks are a way to generate energy in an emission free fashion, at least locally, provided that the fuel is produced using regenerative energies. Fuel cell stacks are future-oriented alternatives to traditional combus-tion engines used in e.g., deep sea shipping/transport, trains, planes, commercial trucks, buses and also private cars, depending on the development status of the respective infrastructure.
This work is a collaboration between the Robert Bosch GmbH headquarters in Stuttgart, Feuerbauch, Germany and the Quantum Materials Group (QMAG) of the Institute of Semiconductor and Solid State Physics at the Johannes Kepler University - JKU Linz. The Robert Bosch GmbH is strongly investing in fuel cell technology, particularly in collaboration with Nikola, a manufacturer for fuel cell powered trucks and with Ceres Power, a company developing solid-oxide fuel cells. Since Bosch is the greatest automotive supplier world-wide, the company is also working on hydrogen fuel cells in cooperation with Powercell Sweden. At the time of writing, one consumer car hydrogen fuel cell stack consists of 400 single fuel cells and can deliver up to 120 kW of power [2]. Depending on how much power is needed and how much space is available, multiple stacks can be combined. One of the relevant accompanying components for the automotive market is the exhaust 1
hydrogen sensor, which allows measuring the percentage of non-reacted hydrogen gas in the exhaust gas of the fuel cell. Through this monitoring, the sensor is able to detect fuel cell stack aging and possible failures, making the sensor a safety al-ready required by legislation. The exhaust gases are guided to the sensor through a thin tube made from polybutylene terephthalate (PBT), a thermoplastic. Since the exhaust gas of the hydrogen fuel cell is steam, the steam condenses below a certain temperature, which depends on ambient temperature and humidity and thus forms droplets. These droplets then possibly clog the pipe, leaving the sensor unable to measure the hydrogen gas percentage in the exhaust gas. Since the sen-sor is a safety feature, a possible malfunction from blockage must be prevented. The goal of this thesis is to establish the size limit of water droplets inside a verti-cal PBT tube of given diameter. To lay the foundation for further investigations, the wetting properties of double-distilled water on PBT, depending on surface roughness and droplet volume, are investigated in a phenomenological approach, in this work. In particular, eight PBT sample plates are prepared and seven of them are grinded with abrasive papers with grit sizes 120, 240, 320, 800, 1200, 2400 and 4000. An untreated raw plate is additionally investigated. To obtain the root mean square (RMS) surface roughness Rq each sample is scanned us-ing a confocal microscope. Additionally, the raw plate is investigated by means of atomic force microscopy (AFM). An experimental setup is built to determine the static, advancing and receding contact angles of the droplets on the differently rough surfaces. The experimental setup is able to tilt, so that the critical tilt angle, at which droplets slide off of the surfaces, can be measured. These critical sliding angles are recorded for five different droplet volumes, namely 10 µl, 20 µl, 30 µl, 40 µl and 50 µl. Each droplet volume is investigated on each surface roughness. This work consists of six chapters, with the current one as introduction. In chap-ter 2the theoretical basics are provided, e.g., how a static contact angle is formed or how the static contact angle changes depending on surface roughness. Fur-thermore, information is provided on advancing and receding contact angles on a microscopic level, on the adhesion force and the microscopy techniques employed in this work are introduced. Chapter 3 gives information on how the samples are grinded and provides the surface scans. In chapter 4 the experimental setup is
presented. The experimental process and contact angle evaluation are described in chapter 5. The experimental results are discussed in chapter 6. In the final chapter 7, the conclusions to this work and an outlook for further investigations are given.
In this chapter, the theoretical aspects and concepts of static contact angles on rough and chemically heterogeneous surfaces, as well as advancing and receding contact angles are provided. Furthermore, the working principles of confocal and atomic force microscopes are presented.
2.1 Surface energy
Attractive interactions are at the origin of the condensed phases of matter [3, 4]. In a fluid, the resulting force acting on a molecule is−F→R = 0 on average, since each
molecule is equally surrounded and therefore attracted by other molecules. In contrast, molecules on the surface experience a resulting force −F→R 6= 0. The forces
exerted by neighbouring molecules cannot be compensated, due to the missing molecules outside of the liquid [5]. These two different situations are sketched in fig. 2.1. The net force acting inwards prompts the surface to contract towards
Figure 2.1: Inside a fluid the total force−F→Ron molecules is zero in contrast to what happens
at the surface of the liquid [5].
the shape of a sphere with minimum volume and therefore also minimum surface, as it can be observed in e.g., water droplets. A perfect sphere with minimum volume represents the energetically most favourable state, as here all net forces are equally distributed and compensate each other leaving the droplet at equilibrium [6]. Energy ∆E is needed to lift a molecule from the inside of the liquid to its surface and thus expand the surface by ∆A. The specific surface energy is defined as γ = ∆E/∆A. A U-shaped pipe with a movable crossbar is used to measure the surface tension σ, as shown in fig. 2.2. Based on the tendency of liquids to
Figure 2.2: Experimental setup to measure the surface tension σ [5].
minimise their surface, a force −→F needs to be exerted on the crossbar with width L in order to enlarge the liquid’s surface by 2L· ∆S. The factor 2 accounts for
the front- and backside of the liquid film, i.e. its non-monoatomic nature. Since
γ = ∆E/∆A, W = F · ∆S, σ = F/2L and W = ∆E, the specific surface energy γ
is equal to the surface tension σ [5].
Surface tension further causes a pressure inside the liquid and thus a pressure discontinuity at the liquid-vapor interface. This pressure difference ∆p is the Laplace pressure and is calculated using the Young-Laplace’s equation [7]:
∆p = σ 1 R1 + 1 R2 ! (2.1)
where σ represents the surface tension of the liquid and R1 and R2 the radii of curvature of the liquid’s surface.
2.2 Smooth and chemically homogeneous surfaces
2.2.1 Derivation of Young’s equation
A reformulation of the thermodynamic principle of maximum entropy yields the principle of minimum free energy. Through a Legendre transformation, the internal energy U of a physical system can be transformed into the Gibbs free energy [8]:
G= U − T · S + p· V (2.2)
where T represents the temperature, S the entropy, p the pressure and V the volume. This specific thermodynamic potential is chosen, since it accounts for the whole energy of a multiparticle system including the mechanical and thermal interactions of the system with the environment [9]:
dG= −SdT + V dp +X i µidNi+ X i γidAi (2.3)
where µ represents the chemical potential, N the number of particles, γ the specific surface energy and A the surface area. Ideally, T , p and N are constant and:
dG=X
i
γidAi (2.4)
For a droplet on a surface, dG only depends on the changes of surface energy. The energetical contribution when changing the surface by dALV is γLVdALV at
the liquid-vapor interface. Similarly, γSLdASL is the contribution at the solid
and liquid interface and γSVdASV is the contribution at the solid-vapor interface.
The entries γLVdALV and γSLdASL are of positive sign, since energy is needed to
generate the respective surfaces. On the other hand, γSVdASV contributes with a
is formed. Equation 2.4 therefore becomes [3, 10]:
dG= (γSL− γSV) dASL+ γLVdALV (2.5)
Through geometric considerations [3] eq. 2.5 is rewritten as:
dG= 2πa (γSL− γSV) da + 2πaγLV cos (θ) da (2.6)
with a the radius and θ the static contact angle of the droplet on the surface. The radius a of the solid-liquid interfacial area is related to the radius of curvature R of the droplet’s surface via a = R cos (θ), as illustrated in fig. 2.3. At the equilibrium
Figure 2.3: Droplet on a surface with curvature radius R, radius of interfacial area a, height
h and contact angle θ [3].
state of the droplet, dG/da equals zero, turning eq. 2.6 into Young’s equation: cos (θY) =
γSL− γSV
γLV
(2.7) The surface tensions σSV, σSL and σLV act tangentially to the respective interfaces
and are visualised in fig. 2.4.
If the internal interaction between the molecules of a substance, i.e. the cohesion, is greater than the interaction between two different substances, such as a liquid and a solid surface, i.e. the adhesion, an obtuse or vice versa an acute contact angle forms [3]. According to eq. 2.7, the formation of an acute or obtuse contact angle depends on whether γSL or γSV dominates, respectively. Practical examples
Figure 2.4: Droplet on a surface with solid-vapor σSV, solid-liquid σSL and liquid-vapor
σLV surface tensions as well as static contact angle θ; adapted from ref. [11].
are given by liquid droplets on a surface or menisci of liquids in tubes, as seen in fig. 2.5. A droplet forms an acute contact angle on a hydrophilic surface, whereas obtuse contact angles emerge on hydrophobic surfaces. Obtuse contact angles greater than 150◦ are formed on superhydrophobic surfaces. Mercury has a convex meniscus in a glass tube, as the contact angle is obtuse. Water, on the other hand, adapts an acute contact angle on glass and therefore forms a concave meniscus in a glass tube.
(a) (b)
Figure 2.5: Visualisation of acute and obtuse contact angles: (a) Droplets on surfaces with different specific surface energies; adapted from ref. [12]; (b) Menisci of liquids with different specific surface energies inside tubes; adapted from ref. [13].
The work necessary to separate two materials has been defined by P. Dupré [11]:
W12 = γ1+ γ2− γ12 (2.8)
where γ1 and γ2 represent the specific surface energies of materials 1 and 2, re-spectively and γ12 is the specific surface energy between the two materials. By combining eq. 2.8 with 2.7, the Young-Dupré equation is obtained:
WSL = γLV (1 + cos (θ)) (2.9)
where WSL represents the work needed to separate a droplet from a solid surface,
γLV the specific surface energy between liquid and vapor and θ the static contact
angle of the droplet on the surface [14].
2.2.2 Line tension
Energy is needed or released when generating or shrinking an interface between two different materials or phases. Similarly, energy is needed or released when expanding or reducing a three-phase contact line (TPCL). In the case of a droplet on a surface this is the line resembling the circumference of the droplet’s inter-face with the surinter-face. Gibbs [15] found, that the Young’s equation needs to be complemented with an additional term representing the interactions at the TPCL.
cos (θ) = γSL− γSV − τ /a
γLV
(2.10) where τ represents the line tension and a the radius of the drop’s solid-liquid interfacial area [16]. However, extensive research and discussions show, that line tension contributions are only relevant when dealing with nano-scale droplets [17]. When line tension can be neglected, the static contact angle θ of a droplet on a surface only depends on the surface tensions. Therefore, in the case of macroscopic droplets, which this thesis exclusively deals with, eq. 2.10 reduces to eq. 2.7 [18].
2.3 Heterogeneous surfaces
2.3.1 Change of apparent static contact angle
Having reviewed the case of smooth and chemically homogeneous surfaces, it is now necessary to consider heterogeneous surfaces and how imperfections affect their wetting properties. J. J. Bikerman [19] assumed that on every infinitesimally small surface section of rough surfaces, the contact angle of a droplet is given by the Young’s equation 2.7. An example is sketched in fig. 2.6. Here, a sinusoidal surface with contact angle 90◦ is assumed and the TPCL of the droplet is located in a valley. If the assumption made by J. J. Bikerman is valid, the two other possible locations of the droplet contour, indicated left and right with respect to the valley, also have a contact angle of 90◦, according to the Young’s equation. One consequence of this assumption is, that the macroscopic/apparent contact
Figure 2.6: Different locations of the TPCL of a droplet on a sinusoidal surface with a 90◦
contact angle [19].
macro-scopic/apparent contact angle is the contact angle detected by a microscope or by the observer’s eye.
The change of the apparent contact angle due to surface roughness has been de-scribed by R. N. Wenzel [20]. He postulated, that based on the Young’s static contact angle θY, the apparent contact angle θW on a defined, chemically
homo-geneous and periodically rough surface, can be calculated according to:
cos (θW) = r· cos (θY) (2.11)
where r is the ratio between the actual rough, wetted surface and the 2D projec-tion of said rough surface onto the surface plane. In the Wenzel state, the droplet wets the underlying surface completely, as sketched in fig. 2.7 b). However, using
Figure 2.7: Different states of a droplet wetting a solid surface: a) Cassie-Baxter-state: Partial wetting with air entrapped between solid and liquid surfaces; b) Wenzel-state: Complete wetting; c) Mix of Cassie-Baxter-state and Wenzel-state [21].
the Wenzel’s equation, the calculated contact angles generally do not match the experimental data. The Wenzel’s equation ascribes the dependence of the contact angle to the solid-liquid interface. In the calculation, an average roughness value across the whole interface is used, implying an unrealistic constant roughness. The assumption, that wetting depends on the solid-liquid interface has been primarily used by researchers in this field until L. Gao and T. J. McCarthy [22] questioned it. They considered a smooth surface with a rough spot of diameter d, as seen in fig. 2.8. A droplet with diameter D > d fully covers the rough spot and adapts the contact angle to the smooth area, in contrast with the Wenzel’s equation. When a droplet with D < d is placed on the rough spot and its volume is increased
Figure 2.8: Rough/Hydrophilic spot with diameter d on an otherwise smooth/hydrophobic surface. A droplet with diameter D fully covers the rough/hydrophobic spot [22].
continuously, the contact angle changes abruptly when the TPCL crosses the bor-der between the two differently rough areas. Afterwards, the droplet lies on the smooth part of the surface and adapts its contact angle, as depicted in fig. 2.9. In this way L. Gao and T. J. McCarthy showed that wetting does not depend
Figure 2.9: A droplet on a plate with either a spot of different roughness or chemical properties at the centre, marked with dashed lines. From left to right the volume of the droplet increases. When the TPCL crosses the border onto the outer area of the sample with different surface properties the contact angle changes abruptly [23].
on the solid-liquid interface, but on the interactions at the TPCL. It has to be noted here, that the ratio between the surface roughness and the droplet size is significant. The larger the droplet is compared to the surface’s roughness it lies on, the more accurate the calculated θW and the measured contact angles match
the calculated θW is comparable to the measured contact angles. This is to be
ex-pected, as this surface structure follows Wenzel’s aforementioned assumptions of a constant roughness [16].
Besides surface roughness, the other main parameter that impacts the static con-tact angle and modifies it with respect to the Young’s concon-tact angle, is the chemical heterogeneity of a sample surface [23]. A. B. D. Cassie and S. Baxter [10] postu-lated an equation that is also based on an averaging principle like the Wenzel’s equation. According to them, the apparent contact angle θCB can be calculated
according to:
cos (θCB) = f1cos (θ1) + f2cos (θ2) (2.12) where θ1 and θ2 represent the contact angles on pure, smooth materials 1 and 2, and f1,2 = material1,2−liquid contact areatotal interf acial area with f1+ f2 = 1. Thus, the weighted average contact angle of the two materials is adapted according to A. B. D. Cassie and S. Baxter. In the case of a rough, and chemically homogeneous surface, the Cassie-Baxter state refers to droplets partially wetting the underlying surface with air entrapped in the roughness gaps between solid and liquid. This state is sketched in fig. 2.7 a). In this case, material 2 is air. Thus θ2 in eq. 2.12 becomes 180◦ and
f2 = air−liquid contact areatotal interf acial area . Therefore θCB for the Cassie-Baxter state becomes [21]:
cos (θCB) = f1(cos (θ1) + 1) − 1 (2.13) If complete wetting occurs, f2 = 0 and thus the Cassie-Baxter’s equation reduces to the Wenzel’s equation [24]. However, also the Cassie-Baxter’s equation was formulated under the assumption of a defined surface with periodic chemical het-erogeneity, and therefore may not be generalised [25]. The averaging assumption was proven to be not appropriate [26]. A surface with a hydrophilic spot of di-ameter d on an otherwise hydrophobic sample has been considered, as sketched in fig. 2.8. A droplet of diameter D fully covering the hydrophilic spot and its TPCL positioned on the hydrophobic area adapts the contact angle of the hydrophobic area, in contrast with the Cassie-Baxter’s equation. When increasing the volume until the droplet crosses the border from the hydrophilic spot onto the hydropho-bic surface, a sudden change in contact angle is observed, as depicted in fig. 2.9.
Thus, the formed contact angle does not depend on the solid-liquid interface, but on the interactions at the TPCL. However, it has been found that for a surface with concentric rings with alternating contact angles, if the TPCL is exactly at the border between two rings, eq. 2.12 yields correct results [16, 27].
It is also possible for droplets to wet a solid surface in a mix of Cassie-Baxter and Wenzel states, as sketched in fig. 2.7 c). Here, some parts of the surface are completely wetted and some parts have air trapped in between the solid and liquid surfaces. A mixed state always has to be considered when dealing with real, undefined surfaces.
On these issues there is still a debate going on among researchers, as proven by the numerous publications in the recent years and by the fact that, there is no final answer or comprehensive theoretical description of these phenomena [28].
2.3.2 Microscopic view of the static contact angle and Gibbs
energy curve
Having discussed the change of the apparent/macroscopic contact angle due to surface heterogeneities, this subsection now focuses on how the contact angle be-haves at the microscopic level. When considering a sinusoidal and axisymmetric, but chemically homogeneous surface and a spherical droplet, the thermodynamic equilibrium condition for the static apparent contact angle is given by:
θapp = θY + α (2.14)
where θapp represents the apparent contact angle and α the inclination angle of the
surface location at which the TPCL lies [16, 29]. A sketch is provided in fig. 2.10. As discussed in subsec. 2.3.1 for every infinitesimally small surface section, the contact angle of a droplet on a surface is given by the Young’s equation. Therefore, to be able to calculate the apparent/macroscopic contact angle, α must be added. For a negative slope of the surface, α is taken as negative, for a positive slope, α is positive.
macro-Figure 2.10: Microscopic (left) and macroscopic (right) view of the contact angle of a droplet on a surface; adapted from ref. [17].
scopic thermodynamic equilibrium condition is given by the Cassie-Baxter’s equa-tion.
Back to a rough, but chemically homogeneous surface, eq. 2.14 as a standalone equation gives a spectrum of solutions for θapp ranging from θY to θY +α. Without
further restraints, the TPCL should be able to lie at any position on the surface with any inclination angle α, which is not the case. Thus, the condition of constant volume needs to be considered. This condition forces the droplet’s TPCL to lie at a position on the surface with an inclination angle α fitting the droplet’s volume and solid-liquid interfacial area. This narrows the spectrum of solutions for eq.
2.14 down to a discrete set, leaving only few options for the TPCL to lie on a surface. An example for this discretisation is sketched in fig. 2.11. A sinusoidal-axisymmetric surface is considered with a droplet lying on it and θY = 90◦ and
θapp = 45◦, as sketched in fig. 2.11 1. If the droplet’s solid-liquid interfacial area
is now slightly enlarged, so that the TCPL lies at the next possible location where eq. 2.14 yields θapp = 135◦, as sketched in fig. 2.11 2, the droplet’s volume would
have to increase abruptly in order for the droplet to maintain its sphericity. Since, however, the droplet’s volume is constant, the TCPL cannot be located at the sketched position in fig. 2.11 2. In order for the droplet to be able to lie on the surface and θapp = 135◦, the droplet’s solid-liquid interfacial area would have to
decrease. Therefore, a finite number of solutions exists for eq. 2.14, i.e. only certain positions are available for the droplet on the surface [16].
Figure 2.11: Abrupt change of volume from droplet 1 to droplet 2 or vice versa if macro-scopic contact angle increases due to a change of location on the surface; adapted from ref. [30].
The Gibbs energy curve as a function of the apparent contact angle is sketched in fig. 2.12. This curve has the form of a distorted parabola with an overlying oscillation whose amplitude decreases with the distance from the minimum of the parabola [31]. Each aforementioned discrete position of the TPCL and therefore each possible θapp is represented by a local minimum, and thus by a metastable
state, of the droplet in the Gibbs energy curve. These local minima are separated by energy barriers. The most stable θapp and therefore the equilibrium state of the
droplet is represented by the global minimum of the curve. The energy barriers can be understood by considering the process of moving the contact line from one metastable state across a low or high point on the surface to the next metastable state. Hereby, the droplet’s surface close to the solid surface has to be modified in order to fulfil the constraint of Young’s contact angle and constant volume. Since however, liquid surfaces tend to assume a perfectly spherical surface, a deviation from the spherical shape results in a deviation from the droplet’s minimum energy state, i.e. in an increase in the system energy [32]. This deviation is illustrated in fig. 2.13, where the solid line represents the original position of the droplet at point A and the dashed lines show the evolution across the non-equilibrium states to the next metastable position at point A’. Furthermore, it has been shown, that for an axisymmetric, sinusoidal and chemically homogeneous surface, the apparent
Figure 2.12: Characteristic Gibbs energy curve over the apparent contact angle with multi-ple metastable minima separated by energy barriers and one global minimum, as well as theoretical (T) and practical (P) advancing (AD) and receding (RC) contact angles (CA) respectively; adapted from ref. [17].
contact angle that corresponds to the global minimum of the Gibbs energy curve is close to the contact angle predicted by the Wenzel’s equation [16, 31].
The actual contact angle of a droplet depends on the kinetic energy of the droplet, related to the way of dispensing it, as well as on the vibrational energy depending on the surroundings of the droplet in combination with the height of the energy barriers. Different contact angles are obtained, depending on the speed, with which a droplet falls onto a surface or the rate with which a droplet is dispensed onto a substrate. Depending on how significant the deviation from the droplet’s most stable θapp and thus how significant the energy difference between the droplet’s
current state and its most stable state is, i.e. how significant the contortion en-ergy is, the droplet tends to adapt to the most stable θapp. If an energy barrier
is higher than the droplet’s contortion energy, the advancement towards the equi-librium state stops, leaving the droplet at a contact angle different from its most stable θapp. From there on, the energy barriers can be overcome by making the
Figure 2.13: Different contortion stages of a droplet on a solid surface moving from metastable equilibrium state A to the next one at A’ [33].
equilibrium state at the global minimum of the Gibbs energy [17, 31, 34].
Due to the energy barriers, i.e. to the non-monotonic nature of the Gibbs energy curve, it is challenging to measure the contact angle corresponding to the global minimum of the Gibbs energy curve, i.e. the most stable contact angle [16, 17].
2.3.3 Contact angle hysteresis
Contact angle hysteresis (CAH) is the difference between the advancing and the receding contact angle values of a liquid droplet on a solid surface, i.e. CAH =
θA− θR. The advancing contact angle describes the contact angle at the advancing
side of a droplet just before or while rolling off a surface, either through tilting the surface or due to airflow. The contact angle on the receding end of the droplet just before or while rolling off a surface is the receding contact angle. These two angles are schematically shown in fig. 2.14. Additionally, advancing and receding contact angles can be observed when adding or removing liquid to or from a droplet, respectively, as sketched in fig. 2.15. When adding liquid to a droplet, the contact angle increases, while the TPCL remains pinned at first. At the advancing contact angle, the solid-liquid interface starts to expand. During the expansion, the contact angle does not change. When removing liquid from
Figure 2.14: Advancing θAand receding θRcontact angle of a droplet on a surface, inclined
by an angle α; adapted from ref. [35].
a droplet, its contact angle decreases, while the TPCL remains pinned at first. When the receding contact angle is reached, the solid-liquid interface decreases, while the contact angle remains constant. It has to be noted, that under non-idealised experimental conditions, θA and θR do not remain constant while the
TPCL moves. Only in first approximation θA and θR can be assumed constant
during the increase or decrease of interfacial area. This is visualised in fig. 2.16, where the solid line represents the realistic behaviour of θA and θR and the dashed
line the idealisation. R. Shuttleworth et al. [29] defined θA and θR, i.e. the
respective advancing and receding contact angles, as follows:
θA = θY + αmax (2.15)
θR= θY − αmax (2.16)
with αmaxthe angle of maximum inclination of the surface at which the TPCL lies.
For better understanding, θA and θR are also shown in fig. 2.17. From this it can
be seen, that θA and θR do not necessarily have to be distributed equally around
the Young’s contact angle, as the maximum surface inclination can be different at different surface locations.
In fig. 2.12 it is shown, that at the theoretical advancing (TADCA) and theoreti-cal receding contact angle (TRCA), the energy barriers in the Gibbs energy curve are zero. However, due to unavoidable environmental vibrations, the practical advancing (PADACA) and receding contact angles (PRCA) are located further
Figure 2.15: a) Adding and b) removing liquid to and from a droplet lying on a solid surface while the TPCL remains pinned and the contact angles change. When in a) the advancing contact angle θA and in b) the receding contact angle θR is
reached, the solid-liquid interfacial area increases or decreases respectively while the contact angles stay constant; adapted from ref. [36].
towards the global minimum in the Gibbs energy curve than their theoretical values. The PRCA and PADCA are located at a lower energy in the Gibbs en-ergy curve than their theoretical values, since environmental vibrations allow the droplets to overcome energy barriers that are smaller than the energy contained in the environmental vibrations. Therefore, CAH decreases the smaller the energy barriers or the greater the environmental vibrations are [31]. The addition or re-moval of liquid to or from a droplet or tilting the substrate leads to an increase in the system energy and thus to a higher Gibbs energy which, when energy barriers can be overcome, eventually leads to the displacement of the droplet.
A complete and comprehensive theoretical description of CAH is still wanted. Since it is challenging to measure the equilibrium contact angle, efforts have been made to determine the most stable contact angle from the measurable advancing and receding contact angles. However, a satisfactory way of deducing the
equilib-Figure 2.16: Dependence of the contact angle θ on the droplet’s sliding velocity V . The advancing and receding contact angles θA and θR are adapted when wetting
and dewetting take place, respectively. The dashed line represents the ide-alised case in which θAand θRstay constant while the TPCL moves; adapted
from ref. [37].
Figure 2.17: Droplet on a tilted, rough surface with advancing, receding and Young’s equi-librium contact angles θA, θR and θ0 respectively; adapted from ref. [38].
rium contact angle from the advancing and receding ones has still to be found [17]. In a recent paper by L. Makkonen [39] efforts have been made towards develop-ing formulas to calculate advancdevelop-ing and receddevelop-ing contact angles. No experimental verification has been reported so far.
2.3.4 Adhesion force
When tilting, by an angle α, a substrate with a droplet on it, the component −−→
FG,k = −F→G·sin (α) of the gravitational force acting parallel to the surface and
forcing the droplet to slide increases with increasing α. A corresponding sketch is shown in fig. 2.18. A first approach to quantify the retention force that keeps a
Figure 2.18: Components of the gravitational force −F→G on a body lying on a substrate,
tilted by an angle α, parallel−−→FG,kand vertical
−−→
FG,⊥ to the substrate’s surface;
adapted from ref. [40].
droplet pinned on a tilted surface until the critical sliding angle αcrit is reached,
has been proposed by C. Furmidge [41]. He postulated that the adhesion force F is proportional to γLVD(cos (θR) − cos (θA)), with D the diameter of the droplet’s
solid-liquid interfacial area. It is assumed, that it takes more energy to dewet a surface than to wet it and that the length of the TPCL directly influences the adhesion force’s magnitude. Another model was developed by approximating the TPCL with an ellipse and by considering an empirical found function that describes the contact angle dependence on the location along the TPCL [42]. The resulting formula is:
F = 24
π3γLVD(cos (θR) − cos (θA)) (2.17) Equation 2.17 was extended with the introduction of the same solid-liquid surface fraction parameter f1 [43] as in the Cassie-Baxter’s equation to yield:
F = 24
The critical sliding angle thus is expressed as: α = 180 ◦ π ! arcsin−1 24 π3 γLVDf1 ρgV (cos (θR) − cos (θA)) ! (2.19) with ρ the density of the liquid, g the gravitational acceleration and V the droplet volume. As the gravitational force parallel to the surface is proportional to the third power of the droplet radius and the adhesion force is proportional to the first power of the droplet radius, droplets roll eventually off, when the substrate is sufficiently tilted or the droplets’ volume is high enough. However, there is an exception at CAH = 90◦, where the adhesion force equals the gravitational force parallel to the surface and thus the droplet cannot slide off, regardless of its radius and of the tilting angle [44].
For α (V ) an arcsin
c/x2/3 dependence is expected, with c a constant, since D ∝ √3
V, D/V ∝ 1/V2/3 in eq. 2.19. Due to the unknown dependence of the
CAH on f1, it is challenging to establish a trend for α (f1).
2.4 Microscopy
2.4.1 Atomic force microscopy
In order to characterise the substrates’ surfaces, atomic force microscopy is em-ployed. At the end of a cantilever, a sharp tip is located, hovering over the surface of a sample. Depending on the distance between the tip and the sample surface, the tip experiences changing attractive or repulsive forces. To generate an image of the surface, the tip scans the surface either in constant force, constant distance, contact or tapping mode. The first of the four modes varies the distance of the tip from the sample surface, so that the force exerted on the tip is kept constant. The second mode of operation keeps the distance between the tip and the sample surface constant and records the changing forces experienced by the tip. In con-tact mode the tip is in constant concon-tact with the surface. However, in situations where the substrate’s surface must not be scratched by the tip, the tapping mode is suited. There, the tip rapidly taps the surface and is not dragged over it. The
deviation of the cantilever due to forces or surface roughness directly is monitored by a laser beam, reflected from the back of the cantilever onto a photodiode, as seen in fig. 2.19. This reflection data is eventually translated into a topographic map of the surface [45]. In the current work a Veeco Dimension 3100 AFM [47]
Figure 2.19: Schematic representation of the working principle of an AFM [46].
is used in tapping mode to avoid altering the sample surface by scratching it. Hereby, the cantilever is made to oscillate by a piezo actuator. Depending on the change in oscillation frequency while tapping the sample surface due to the changing surface-tip interaction, a topographic map is produced.
2.4.2 Optical microscopy
For generating substrate surface topographic maps, optical microscopy can as well be used. Since one single image contains a shallow depth of field, only a layer of limited height is in focus. To compensate that, multiple images are captured at different focal heights. This is achieved by moving the lens in vertical direction using a motor, with the focus of the lens remaining unchanged. The image stack is then merged to provide a topographic map of the surface. This technique is em-ployed in the Keyence VHX-7000 [48] digital microscope used in this work. With it, a vertical resolution of 0.1 µm can be achieved at 50x magnification.
To obtain higher resolutions, e.g., a confocal microscope can be used. The working principle of a confocal microscope is sketched in fig. 2.20. A laser is focused onto
Figure 2.20: Working principle of a confocal microscope with a laser light source [49].
the substrate through an array of lenses. The reflected light is then deflected onto a detector by a beamsplitter. In front of the detector, a pinhole is located which only lets the light reflected from the in-focus plane impinge onto the detector. Thus, all light from out-of-focus planes is blocked by the pinhole, which enhances vertical resolution compared to a regular optical microscope. The generation of topographic surface maps is again achieved by focus stacking multiple images of different focal heights. In this work, a nanofocus µsurf custom [50] confocal micro-scope has been used. With it, a vertical resolution of 0.011 µm can be achieved at 50x magnification. The motor that moves the lens when focus stacking is replaced
by a piezo drive in the nanofocus µsurf custom.
From the recorded topographic surface maps the RMS surface roughness Rq is obtained. It is defined as Rq = q
1
L RL
0 Z2(x) dx, with Z (x) the recorded height profile of the surface and L the total length of the height profile [51].
characterisation
In this chapter, the grinding of the samples and their characterisation by means of a confocal and of an atomic force microscope, are summarised.
3.1 Sample fabrication process
The considered hydrogen sensor’s tube is manufactured from uncoloured PBT by the BASF SE. In order to investigate the wetting properties of PBT, seven
(60x60x2) mm3 BASF sample plates have been grinded with abrasive papers of grits from P120 to P4000. Since PBT and polytetrafluoroethylene (PTFE, Teflon) are both thermoplastics, the investigation of the CAH on PTFE depending on roughness done by J. Wang et al. [52] has been used as point of reference for the sample preparation. In the mentioned work, the goal RMS sample roughnesses were Rq = (5 ∼ 20) µm. In this work, for the preparation of the PBT, a Buehler Beta Grinder/Polisher disc grinding machine at 300 rpm with wet-grinding SiC abrasive paper of 200 mm diameter has been used. The grinding duration differs for different abrasive paper grits. The pressure applied onto the sample during the grinding process is kept constant within the possibility of the operator. During grinding, the samples are continuously rotated, in order to ensure a homogeneous lapping.
Since the abrasive effect of the papers differs depending on the substrates, a base set of samples has been prepared with grit sizes 800, 1200, 2000, 2400 and 4000 to gain information on the resulting surface roughnesses. Additionally, one plate has been prepared using polishing paste with grains of diameter of 3 µm. Due to the 29
limited number of the uncoloured samples available for this work, the roughness testing for optimising the final preparation of the uncoloured PBT has been done using black PBT, provided by BASF. The roughnesses of the base set of samples are investigated using a Keyence VHX-7000 [48] digital microscope at the QMAG of the Institute of Semiconductor and Solid State Physics at the JKU Linz. For the generation of a 3D image of the substrate’s surface the microscope scans the surface at different focal heights with a vertical resolution of 0.2 µm at a magnifi-cation of 50x. From the scans, it can be seen that for the 1200 and 4000 abrasive papers, the pressure with which the samples are pressed onto the abrasive paper during grinding, is insufficient to completely grind the surface of the raw material. In the case of the polished sample, it is visible to the observer’s eye, that paste residue leaves an uneven layer on top of the surface, resembling an orange skin. Therefore, polishing has been ruled out for further preparations. The RMS rough-ness Rq = 0.56 µm of the sample prepared with the 800-grit abrasive paper, has further led to the conclusion that abrasive papers of lower than 800-grit need to be included in order to achieve roughnesses in the single-digit micrometre range. Due to these challenges, a completely new set of samples has been prepared. For the second set of samples, abrasive papers with grits 120, 240, 320, 800, 1200 and 2400 have been used. The modus of grinding has been changed for this set. Instead of directly using the abrasive paper with the targeted grits on the samples, as done for the first set, this time the grit level has been gradually increased, until the targeted grit had been achieved. For samples with target grit sizes greater than 320, an additional 600-grit abrasive paper iteration has been made to bridge the gap between the 320 and 800-grit abrasive paper. For this set and for all the follow-ing ones the roughness investigations have been performed at the BOSCH plant in Stuttgart, Feuerbach using a nanofocus µsurf custom [50] optical microscope with a vertical resolution of 0.022 µm at 50x magnification. From the analysis of the surface, it has been deduced, that for the sample prepared with up to the 2400-grit abrasive paper, the abrasive effect of the 2400-grit is negligible to further reduce the roughness obtained by previous, coarser grits. This is confirmed by the roughness measurements, which yield Rq = 0.28 µm for the 2400-grit sample prepared using the iterative process and Rq = 0.07 µm for the sample treated with
the 2400-grit directly. Therefore, a third set of samples has been prepared.
For the third set of samples, the grinding modus has been changed back to direct use of the target grits on the substrates. Thus, samples have been grinded using abrasive paper grits 120, 240, 320, 800, 1200, 2400 and, in addition, 4000. During the preparation of the 2400 and 4000-grit samples it is found that after 5 min of grinding and multiple renewals of the abrasive paper, a surface with the same, homogeneous roughness across the grinded area has not been achieved. In con-trast, the sample thickness is reduced by half when grinding a sample for 30 s with the 120-grit abrasive paper. Through the injection moulding production of the PBT, the plates show an overlying macroscopic texture that the 1200-grit can still grind and even out, but the 2400 and 4000-grit cannot. For the latter two grits, the surface is left with spots of different roughnesses, i.e. spots of grinded and non-grinded areas. Even though the spots grinded with 2400 and 4000-grit abra-sive paper show an RMS roughnesses as low as Rq = 0.07 µm and Rq = 0.05 µm, respectively, the samples are not suitable for the droplet experiments. Spots of dif-ferent roughness influence the wetting behaviour of droplets on the sample, which is not desired in this work. To compensate that, the targeted 2400 and 4000-grits have been prepared using the same iterative process as described for the second set of samples with a starting grit of 1200. The requirement of preparing all samples of the set in the same way has been compromised to obtain the reduced roughnesses reachable with the 1200-grit.
3.2 Characterisation using optical microscopy
For each grinded sample of the third set, as well as for one raw plate, (300x300) µm2 and (800x800) µm2 scans have been recorded and shown in 2D and 3D represen-tations in figs. 3.2 to 3.5. The relevant samples are named PBTXit, with X the grit of the abrasive paper used to grind the surface and it indicating the iterative grinding. The RMS roughnesses acquired from the (300x300) µm2 scans of all grinded plates and the unprocessed one - referred to as PBTraw - including the according figures are given in tab. 3.1. In fig. 3.1 the Rq over the used abrasive paper is sketched. The surface roughness decreases exponentially with decreasing
Sample name Rq in µm from (300x300) µm2 scans Figure PBT120 5.02 3.2 a) - d) PBT240 1.88 3.2 e) - h) PBT320 0.95 3.3 a) - d) PBT800 0.57 3.3 e) - h) PBT1200 0.47 3.4 a) - d) PBTraw 0.32 3.4 e) - h) PBT2400it 0.28 3.5 a) - d) PBT4000it 0.19 3.5 e) - h)
Table 3.1: RMS roughnesses Rq of the investigated samples with corresponding figures.
grit size. The sample PBT120 shows an RMS roughness of Rq = 5.02 µm. The
Figure 3.1: RMS roughnesses Rq of the investigated samples from tab. 3.1.
related scans in figs. 3.2 a) - d) prove the significant abrasive effect of the 120-grit abrasive paper compared to the higher-grit ones. The scans show a uniform grind-ing direction, which leads to the conclusion that the abrasive effect is so high, that no grooves of previous grinding directions are visible. Only the grinding direction of the last contact to the abrasive paper before the end of the grinding process
remains. Furthermore, several single high-spots can be seen in the scan, which can be traced back to the abrasive paper not only grinding the surface, but also tearing off parts of the surface. After grinding the sample for 30 s, the sample thickness has been reduced by half, which further gives measure for the high abrasive effect of the 120-grit abrasive paper and the softness of the PBT.
The sample PBT240 has an RMS roughness of Rq = 1.88 µm. From the scans in figs. 3.2 e) and f) it can be seen, that the abrasive effect is not sufficient to com-pletely remove the grooves from previous grinding directions. This is only visible in the (800x800) µm2 scans in figs. 3.2 e) and f) but not in the (300x300) µm2 scans in figs. 3.2 g) and h), which show a uniform grinding direction.
The RMS roughness for PBT320 is Rq = 0.95 µm. Figures 3.3 a) and b) show that now, even more than in PBT240, grooves of different grinding directions are visible, which fits with the higher grit number employed. In the (300x300) µm2 scans in figs. 3.3 c) and d) the softness of PBT is again continued: the grooves of previous grinding directions are washed out rather than clearly defined.
Measuring the roughness of PBT800 yields Rq = 0.57 µm. In figs. 3.3 e) and f) grooves from different grinding directions can be seen. However, when considering the (300x300) µm2 scans in figs. 3.3 g) and h), fine, evenly distributed grooves of one grinding direction are detected. These are a result of the inevitable fill-up, during the grinding, of the abrasive paper with ablated material. By adding water during the grinding process, the fill-up can be slowed down, but not prevented. The spacing between the grains is filled up, i.e. the abrasive paper becomes finer over time. This means, that the abrasive paper cannot remove the deep grooves produced at the beginning of the grinding process.
The same fill-up effect is visible for PBT1200 in figs. 3.4 c) and d). The deeper grooves cannot be removed by the filled-up abrasive paper, which leaves finer grooves towards the end of the grinding process. Figures 3.4 a) and b) present (800x800) µm2 scans which show grooves of different grinding directions. The RMS roughness of PBT1200 is Rq = 0.47 µm.
In the case of PBTraw the RMS surface roughness is Rq = 0.32 µm. Due to the injection moulding, figures3.4e) - h) show a surface morphology which differs from the one of the grinded samples. The finite viscosity of the hot, liquid PBT when
filling it into moulds, prevents a completely uniform and even surface. Further-more, the moulds themselves have a finite surface roughness, of which the negative counterpart is manufactured when moulding the liquid PBT.
The first of the two samples prepared with the iterative procedure is PBT2400it, with RMS roughness Rq = 0.28 µm. The corresponding scans are shown in figs.
3.5 a) - d). Compared to the surfaces grinded with the coarser abrasive papers, this surface shows fewer deep grooves and more uninterrupted, flat areas between the grooves.
For PBT4000it, the RMS roughness is Rq = 0.19 µm. The surface scans of PBT4000it are presented in figs. 3.5 e) - h). Even less deep and also shorter grooves are visible on PBT4000it than on PBT2400it. Furthermore, the grooves are oriented in various directions resulting from different grinding angles with re-spect to the rotation direction of the grinding disc.
(a) PBT120 - (800x800) µm2 scan - 2D (b) PBT120 - (800x800) µm2 scan - 3D
(c) PBT120 - (300x300) µm2 scan - 2D (d) PBT120 - (300x300) µm2 scan - 3D
(e) PBT240 - (800x800) µm2 scan - 2D (f) PBT240 - (800x800) µm2 scan - 3D
(g) PBT240 - (300x300) µm2 scan - 2D (h) PBT240 - (300x300) µm2 scan - 3D
(a) PBT320 - (800x800) µm2 scan - 2D (b) PBT320 - (800x800) µm2 scan - 3D
(c) PBT320 - (300x300) µm2 scan - 2D (d) PBT320 - (300x300) µm2 scan - 3D
(e) PBT800 - (800x800) µm2 scan - 2D (f) PBT800 - (800x800) µm2 scan - 3D
(g) PBT800 - (300x300) µm2 scan - 2D (h) PBT800 - (300x300) µm2 scan - 3D
(a) PBT1200 - (800x800) µm2scan - 2D (b) PBT1200 - (800x800) µm2 scan - 3D
(c) PBT1200 - (300x300) µm2scan - 2D (d) PBT1200 - (300x300) µm2 scan - 3D
(e) PBTraw - (800x800) µm2 - 2D (f) PBTraw - (800x800) µm2 - 3D
(g) PBTraw - (300x300) µm2 - 2D (h) PBTraw - (300x300) µm2 - 3D
(a) PBT2400it - (800x800) µm2 - 2D (b) PBT2400it - (800x800) µm2 - 3D
(c) PBT2400it - (300x300) µm2 - 2D (d) PBT2400it - (300x300) µm2 - 3D
(e) PBT4000it - (800x800) µm2 - 2D (f) PBT4000it - (800x800) µm2 - 3D
(g) PBT4000it - (300x300) µm2 - 2D (h) PBT4000it - (300x300) µm2 - 3D
3.3 Characterisation using atomic force microscopy
The raw sample plate has been investigated using AFM. With (50x50) µm2 scans, the AFM allows for a 36-time higher magnification than the (300x300) µm2 scans of the confocal microscope. The AFM scans of two different areas on the surface are shown in 2D and 3D representations in fig. 3.6. Here, the same surface characteristics for the injection moulded raw PBT emerge, when comparing the AFM scan to the optical microscopy scans in figs. 3.4 e) - h). Random grooves are formed due to the fact that the liquid PBT has a finite viscosity, i.e. not all interspaces are filled. Furthermore, the topography of the mould is printed onto the PBT surface as a negative.(a) Area 1 - 2D (b) Area 1 - 3D
(c) Area 2 - 2D (d) Area 2 - 3D
Figure 3.6: PBTraw (50x50) µm2 AFM surface scans of two different areas a), b) and c),
An experimental setup has been built to measure the contact angles of a droplet on a tilted substrate and is shown in fig. 4.1. The centrepiece of the setup is
Figure 4.1: Experimental setup.
represented by the tilting stage. The knob on the housing of the stage is connected to a threaded worm which intermeshes with a cogwheel fitted to the stage. Thus, the stage can be tilted by turning the knob. An advantage of this arrangement is that the tilt angle can be adjusted continuously and the stage stays at the chosen angle when the knob is left off. The inclination angle of the stage can be read, 41
with a precision of ±0.5◦, from a scale on the side of the stage housing. Since the stage only allows for a maximum tilt angle of 60◦ in both directions, the stage housing is positioned at a 45◦ angle, as shown in fig. 4.2. Thus, a full tilt range of (0 − 90) ◦ can be achieved. For this and all other mounts, aluminium profiles
Figure 4.2: Stage housing tilted at 45◦.
are used. To ensure that the droplet is not excluded from the image frame during tilting, the stage’s centre of rotation needs to lie inside the droplet. Since this is generally not the case, an inlay has been custom CNC milled to fit the cylindrical hole in the stage. This hole in the stage allows to efficiently change the stage’s setup. The custom inlay offers the possibility to precisely adjust, with a grub screw, the height, at which the PBT plate is located. Thus, the droplet can be placed in the stage’s centre of rotation. The PBT plates are mounted to the stage by spring loaded arms screwed into the custom inlay, as shown in closer detail in fig. 4.3. Droplets are dispensed vertically onto the surface using a syringe and a tip with an opening diameter of 0.25 mm. The tip is held and thus stabilised by a mounting arm to eliminate shaking while dispensing the droplets, as seen in fig. 4.1. A Leventhuk DTX 90 [53] USB microscope camera is employed to record sideview videos of the process, from dispensing the droplets to their sliding
Figure 4.3: Closeup of the tilting stage.
off. The camera is positioned in such a way, that a straight line of sight onto the droplet is ensured. A closeup of one dispensed droplet is shown in fig. 4.4. For the later analysis of the contact angles, it is necessary to have a bright and
homogeneously lit background, so that the droplets’ contours are set off through contrast. This is achieved by shining light with a torchlight onto a piece of white acrylic glass, as reported in fig. 4.5. The tilting process from 0◦ to 90◦ involving
Figure 4.5: Torchlight shining on white acrylic glass to produce a bright homogeneous droplet background.
a dispensed droplet sliding upon tilting of the stage, is shown in fig. 4.6.
analysis
In this chapter the experimental sequence and procedure are described. Addition-ally, details on how the contact angles are evaluated are provided.
5.1 Measurement plan
The goal of this work is to record the static, advancing and receding contact angles as well as critical sliding angles of droplets of five different volumes on eight substrates of different roughness. The different volumes are achieved by dispensing up to five single droplets merging onto the surface. Therefore, e.g., the droplet with the greatest volume consists of five single droplets. Twelve sets of data for each of the aforementioned angles have been recorded for each of the five droplet volumes on each of the eight substrates.
5.2 Test sequence
The droplets are manually dispensed onto the sample by the operator using a syringe. The syringe is held in place by a mounting arm, as shown in fig. 4.4. A possible tilt angle of the syringe-tip, shaking of the operator and the velocity at which the droplet leaves the tip, i.e. the pressure the operator applies to the plunger rod, affect the volume and thus the weight of the dispensed droplet. Without further developments, the droplet randomly detaches from the syringe tip at different volumes. The first two sources of random error can be eliminated by the mounting arm, which helps to dispense the droplets from a steady and 45
vertical tip. The latter source of error is reduced, by the operator developing a subjective criterion of how much pressure is applied to the plunger rod or vice
versa, to keep the droplet dispensing rate as constant as possible. To measure the
droplet weight, a scale with a precision of 10 mg has been used. From five sets of 50 droplets each, a single droplet weight of (10 ± 1) mg has been determined. To eliminate unknown influence of contamination in regular tap water, double distilled water is used for all measurements. Since PBT does not provide the minerals that distilled water tends to bind after the distillation process, distilled water does not modify the PBT surface. Thus, there is no need to place the droplets at different positions on the surface every time. For the measurements of the equilibrium contact angle, the tilting stage remains horizontal. The pictures are taken after dispensing the droplets, since the contact angle changes over time due to time-dependent wetting. To measure the advancing and receding contact angles, as well as the critical sliding angle, the stage is tilted. The tilt rate is kept constant, within the operators possibilities, at ∼ (5 − 10) ◦
/s. It has been found, that the criterion to establish when a droplet starts to slide off cannot be defined precisely. Therefore, an uncertainty on the critical sliding angle of ±3◦ is estimated. After the contact angles are measured, the tilting stage is set back to 0◦ and the surface is prepared for the next measurement. To ensure that no residual water is left on the surface, i.e. to ensure that the surface is not pre-wetted before the next experiment, the droplets are soaked up with a paper towel and the surface is heated for 10 s with a hot air gun at ∼ 100◦. After vaporising possible residual water, the surface is cooled back down with compressed air for 15 s to recover the same starting conditions for every experiment. It is acceptable to use compressed air for cooling, since it is ensured that the air is clean, especially of oil, which would pollute the surface. A pre-wetted surface lowers the critical sliding angle of a droplet, because the droplet does not have to wet as much surface as without the residual water. This effect has been observed in a test. The whole test sequence is repeated for every measurement.
5.3 Evaluating video recordings and measuring
contact angles
From the recorded videos of the droplets being dispensed and sliding off, screen-shots have been extracted to measure the contact angles. In the case of static contact angle measurements, images of one droplet have been considered since the larger droplets with a volume of 20 µl, 30 µl, 40 µl and 50 µl generally do not show the equilibrium state of one single droplet. This is due to the fact, that the addi-tion of droplets to an existing droplet may cause the added droplet to roll off of the underlying droplet at first before coalescing. The result is then a 20 µl, droplet but with a non-circular contact line and therefore varying contact angle depending on the location at the TPCL. Even if the added droplet coalesces with the underlying droplet at the first interaction, there is the possibility that the solid-liquid inter-facial area of the underlying droplet does not expand equally around the droplet’s centre with added volume. This is due to the differently strong pinning of the TPCL at different locations on the non-defined surface. This results in varying contact angles along the TPCL, which are not necessarily representing the equi-librium contact angle.
For the measurement of advancing and receding contact angles, images of 40 µl droplets have been analysed. Droplets with a volume of 50 µl slide off with a velocity that is too high to allow the 13 fps framerate of the USB microscope to generate sharp images without motion blur. It has been found, that the sliding velocity of 30 µl droplets is not as constant as the sliding velocity of 40 µl droplets. Since a single droplet remains pinned at one location for every surface roughness and a 20 µl droplet only slides off from the two surfaces with the lowest rough-nesses, 40 µl droplets have been chosen for the measurement of advancing and receding contact angles.
The DropSnake [54] software tool used for the measurements is provided by A. F. Stalder et al. [55]. It is freely available as a plugin for the free image-processing program ImageJ [56]. DropSnake’s working principle is based on parametric spline curves which consist of polynomial segments, linked at breakpoints [55]. For the plugin to work properly, an ImageJ version no newer than v1.46 including a Java
