This thesis is concerned with the interfacial behaviour of surfactants at solid-
liquid interfaces. The main technique used for the adsorption measurements
during ...
Adsorption of Surfactants at the Solid-Liquid Interface: A Quartz Crystal Microbalance study Johan J.R. Stålgren
Doctoral Thesis 2002
Department of Chemistry, Surface Chemistry Royal Institute of Technology Stockholm, Sweden
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan framlägges till offentlig granskning för avläggande av filosofie doktorsexamen, tisdagen den 29 januari, 2002, kl. 09.00 i Kollegiesalen, Valhallvägen 79, KTH, Stockholm.
Address to the author: Johan J.R. Stålgren Department of Chemistry, Surface Chemistry Royal Institute of Technology SE-100 44 Stockholm Sweden
ISSN 1650-0490 ISBN 91-7283-238-X TRITA YTK-0201
Copyright 2002 by Johan J.R. Stålgren. All rights reserved. No part of this thesis may be reproduced without permission from the author. Other copyrighted material is used with permission Paper I 2001 by the American Chemical Society Paper II 2001 by the Elsevier Science
Abstract This thesis is concerned with the interfacial behaviour of surfactants at solid-liquid interfaces. The main technique used for the adsorption measurements during this thesis work was the Quartz Crystal Microbalance-Dissipation (QCM-DTM). This technique allows both the adsorbed amount, as evaluated as a change in frequency (∆f), and the change in the dissipation factor (∆ D) that is a measure of the energy dissipated in the system, to be determined simultaneously. Methods like null ellipsometry already exist, and they measure the amount adsorbed to a planar, reflecting surface accurately, and the thickness of the adsorbed layer may also be determined. The QCM-DT M technique has, however, some advantages. For instance, the quartz crystal can be coated (physical/chemical) in a large number of ways. In addition, simultaneous measurement of the dissipation factor allows another parameter to be determined, this parameter is a measure of the interaction between the adsorbed surfactant layers and the bulk solution. Further, opaque or even non-transparent solutions can be studied with the QCM-DTM, which is not possible with the ellipsometer. When the project began, an aim was to investigate the visco-elastic properties of polyelectrolytes at different surfaces. This turned out to be more complex than we expected so I decided to use a less complex systems in order to more fully understand the results. Hence, the choice became to study surfactant adsorption, a topic which is well documented before by several other techniques. The choice was based on the surfactants low molecular weight, and the relatively simple distribution of a polar (hydrophilic) and non-polar (hydrophobic) part, and a significant general knowledge about their interfacial behaviour. The methodology for adsorption studies in liquid for the QCM-DTM was only in its infancy, so parameters like temperature dependence, surface roughness, surface modification and cleaning had to be kept under control or developed at the same time. Systematic surfactant adsorption studies from liquids with the QCM technique do not exist. Hence, the aim of this thesis was to achieve an understanding of the information provided by measured shifts in frequency and dissipation factor for such systems, and from this draw conclusions about the interfacial behaviour of both non-ionic and cationic surfactants. Further I aimed to learn how valuable the QCM-DTM technique was for these systems and what pitfalls there are in evaluating the results observed with this technique.
Sammanfattning
Den här avhandlingen handlar om det beteende som uppträder hos tensider, vid gränsytan mellan fast fas och en vätska. Vid adsorptions mätningarna i denna avhandling har huvudsakligen en teknik använts, en kvarts kristall mikrobalans (QCM-DTM). Denna teknik tillåter både den adsorberade mängden, utvärderat genom skiftet i frekvens (∆f), samt förändringen i dissipations faktorn (∆D), som är ett mått på systemets energi dämpning, att uppmätas. Båda dessa faktorer kan uppmätas samtidigt. Metoder som noll ellipsometri existerar redan och de mäter adsorptionen vid en plan, reflekterande yta. Denna teknik kan också bestämma tjockleken hos det adsorberade skiktet. QCM-DTM tekniken har trots allt några fördelar gentemot detta. Till exempel, kan kvarts kristallerna beläggas (fysiskt/kemiskt) på flera olika sätt. En annan fördel är den samtidigt uppmätta dämpnings faktorn som tillåter en parameter till att bestämmas. Dämpnings faktorn, är en parameter som gör att man kan mäta styrkan hos interaktionerna mellan det adsorberade tensid skiktet och bulk lösningen. Även lösningar som ej är genomskinliga kan studeras med QCM-DTM tekniken, detta är inte möjligt med en teknik som till exempel ellipsometri. När projektet började, var vårt mål att studera de viskoelastiska egenskaperna hos laddade polymerer vid olika ytor. Detta visade sig vara mycket mer komplext än vad vi hade förväntat oss, så vi bestämde oss för att använda ett mindre komplext system för att fullständigt förstå våra resultat. Vårt val föll på olika tensid lösningar, ett ämne som är väl dokumenterat sedan innan med flera olika tekniker. Valet grundade sig på tensidernas låga molekylära vikt samt deras relativt enkla distribution av polära (hydrofila) och o-polära (hydrofoba) delar. Dessutom fanns sedan innan en signifikant kunskapsbas om deras beteende vid gränsytan mellan en fast fas och en vätska. Eftersom metodologin för adsorptions studier i vätskor för QCM-DTM var bara i början på sin utveckling behövdes faktorer som temperatur beroendet, ytråhet, ytmodifikation samt rengöring kontrolleras samt utvecklas under tiden. Systematiska studier av tensid adsorption i en vätska finns inte för QCM tekniken. Därav valet på avhandlingens innehåll, en ökad förståelse av informationen för dessa system, genom studier av ändringen i frekvens samt förändringen i dämpning. Samtidigt siktade jag på att lära mig hur värdefull QCM-DT M tekniken var för dessa system, och vilka fallgropar det finns när man utvärderar resultaten från denna teknik.
There are two kinds of scientists, physicists and stamp collectors.
Ernest Rutherford (1871-1937)
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. List of paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.2. Summary of papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1. Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 2.2. Self-Assembled Monolayers (SAMs) . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3. Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4. Silan-coated surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1. Profilometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 3.2. Contact Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3. X-ray Photoelectron Spectroscopy (XPS) . . . . . . . . . . . . . . . . . . . . . .22 3.4. The Quartz Crystal Microbalance-Dissipation (QCM-DTM) . . . . . . . . 23 4. Surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.1. Lipids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .34 4.2. Cationic surfactans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.3. Non-ionic surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.1. Adsorption of emulsion studied with the QCM-DTM . . . . . . . . . . . . . . 39 5.2. Polymer adsorption on phospholipid coated surfaces . . . . . . . . . . . . . 41 5.3. Adsorption of surfactants studied with the QCM-DTM . . . . . . . . . . . . .47 5.4. Counterion effects on sensed mass and energy dissipation . . . . . . . . . 49 5.5. Bound / trapped water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 6. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
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1. Introduction
The Quartz Crystal Microbalance-Dissipation (QCM-DTM) technique is an ultra sensitive weighing device based on the piezoelectric, electromechanical oscillator principle. It consists of a thin single-crystal quartz disk, with one metal electrode deposited on each side. When the electrodes are connected to an electric oscillator, the crystal can be made to oscillate in a very stable manner at its resonance frequency, f. When a mass is adsorbed on one or both of the electrodes, then this leads to a change in the resonance frequency of the quartz crystal, ∆f. If the adsorbed mass is small compared to the mass of the quartz crystal and there is no slip or deformation due to the oscillatory motion, then the resonance frequency decreases proportionally to the mass of the adsorbed film according to the Sauerbrey relation. It is possible to determine very small changes of the resonance frequency and hence very small mass changes. This is possible since the QCM generally has very stable oscillations. In addition to the adsorbed mass, simultaneous measurements of the change in dissipation factor, (∆D), which is a measure of the energy dissipated in the system, is possible. Hence, this parameter is a measure of the interaction between the adsorbed layer and the bulk solution. This thesis is concerned with the interfacial behaviour of surfactants at solid-liquid interfaces. Emphasis is placed on the adsorption / desorption of three different groups of surfactants; cationic, non-ionic, and phospholipid surfactant.
To choose the surfactants to study was not easy, but it had to be surfactants with properties which were well documented before by several different techniques. Further, to be able to systematically vary the surfactant structure was regarded as important. I have used different model surfaces to study the effect of the underlying substrate. The model surfaces also had to be well characterized with several different techniques. The different model surfaces we decided to work with were a metal (gold), silica, methylated silica, and several different selfassembly monolayers on gold substrates. These surfaces had to be thoroughly evaluated to be valuable for the QCM experiments, without adding more unknown parameters to the interfacial study. In chapter 3 all the techniques used for evaluating both the surfaces and the surfactants are discussed.
Systematic adsorption studies of surfactants from liquids using the QCM technique do not exist. Hence, the aim of this thesis was to achieve an understanding of the information 1
provided by the measured shifts in frequency and dissipation factor for such system, and from this draw conclusions about the interfacial behaviour of both non-ionic, cationic and phospholipid surfactants. Last in the summary the main findings during these experiments, and a hopefully valuable discussion of the different results obtained, is presented. More details can be found in the manuscripts that constitute the second part of this thesis.
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List of papers This thesis consists of a summary and six papers. The papers are listed below and are in the summary referred to by their Roman numerals (I to VI).
I
Adsorption of Liposomes and Emulsions Studied with a Quartz Crystal Microbalance. Johan J.R. Stålgren, Per M. Claesson and Torbjörn Wärnheim Advances in Colloid and Interface Science, 2001, 89-90, 383.
II
Adsorption of a PEO-PPO-PEO Triblock Copolymer on Small Unilamellar Vesicles: Equilibrium and Kinetic Properties and Correlation with Membrane Permeability. Markus Johnsson, Nill Bergstrand, Katarina Edwards and Johan J.R. Stålgren Langmuir, 2001,17, 3902.
III
Cationic and Non-ionic Surfactant Adsorption on Thiol Surfaces with Controlled Wettability. Katrin Boschkova and Johan J.R. Stålgren Submitted to Langmuir.
IV
A Correlation between Adsorbed Amount and Frictional Properties of Thin Gemini Surfactant Films - CPP in Relation to Friction. Katrin Boschkova, Adam Feiler, Bengt Kronberg and Johan J.R. Stålgren Submitted to Langmuir.
V
A Comparative Study of Surfactant Adsorption on Model Surfaces using the Quartz Crystal Microbalance and the Ellipsometer. Johan J.R. Stålgren, Jonny Eriksson and Katrin Boschkova Submitted to Journal of Colloid and Interface Science.
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VI
Lubrication in Aqueous Solutions Using Cationic Surfactant – a Study of Static and Dynamic Forces. Katrin Boschkova, Bengt Kronberg, Johan J.R. Stålgren, Karin Persson, and Monica Ratoi-Salagean Accepted in Langmuir.
The papers are reproduced with permission from the publishers.
The author’s contribution to the papers is as follows:
I
Major part of planning, experiments and evaluation.
II
Part of planning, experiments and evaluation.
III
Major part of planning and experiments, part of evaluation.
IV
Part of planning, experiments and evaluation.
V
Major part of planning, experiments and evaluation.
VI
Part of planning, experiments and evaluation.
In all papers, I have been the main responsible for the QCM work and evaluation.
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1.2 Summary of papers Phospholipid adsorption at the solid-liquid interface. The first two papers deal with adsorption of phospholipids at a gold surface, and effects of additives. The results are important for comprehending the data obtained with the Quartz Crystal Microbalance-Dissipation (QCM-DTM), in a useful way.
Paper I deals with adsorption from phospholipid liposome solutions (1.2%) and phospholipid stabilised oil-in-water emulsions (20% purified soybean oil) with the same phospholipid concentration. The main attention in the paper was given to the adsorption process at a gold surface and the effect of repeated injections of the same solution. The second aim was to learn how the dilution of the bulk solution affected the adsorbed layer and to determine what remained on the surface after the dilution step was completed. The adsorption from the liposome solution resulted in formation of a phospholipid bilayer with an additional and incomplete outer layer of liposomes. The outer layer was removed by dilution leaving a bilayer of phospholipids on the surface. The adsorption process observed from the concentrated emulsion solution was considerably more complex. A slow spreading process that also resulted in some expulsion of material from the interface followed the rapid initial adsorption of emulsion droplets. After rinsing with water a phospholipid monolayer was retained on the surface.
Paper II is devoted to the adsorption of the triblock copolymer F127, poly(ethylene oxide)poly(propylene oxide)-poly(ethylene oxide), EO98P O67EO98 , onto immobilized small unilamellar vesicles (SUVs) of egg phosphatidylcholine (EPC). With the QCM-DTM technique we first showed that SUVs of EPC adsorb on gold to form a monolayer of vesicles. This supported monolayer of vesicles was then used to follow the adsorption of the F127 polymer onto the lipid vesicle membrane surface. The adsorption of F127 was found to be a rapid process and the measured polymer binding isotherm was fitted to a Freundlich type of isotherm. The maximum, or plateau, adsorbed amount was determined to be of a magnitude similar to that found for adsorption of F127 on hydrophobic surfaces. Furthermore, the desorption of the triblock copolymers from the membrane surface was followed after rinsing the SUV monolayer with pure buffer. It was found that the desorption process displayed essentially the same rapid kinetics as the adsorption process, indicating a weak interaction between the polymers and the lipid membrane. The determined polymer binding isotherm was
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used to correlate the adsorbed amount of polymer with the polymer-induced leakage of carboxy fluorescein (CF) from the SUVs. It was found that the membrane permeability was increased severalfold already at low surface coverage, and that the maximum magnitude of the CF release rate was obtained at, or close to, the F127 concentrations giving rise to maximum adsorbed amount of polymer. In addition, the increased membrane permeability induced by the triblock copolymers was compared with the effect of adding a conventional ethylene oxide (EO)-surfactant, Triton X-100, to the SUVs. The result emphasizes the dramatic effect of F127 on the bilayer permeability. Another interesting result was that the stability of the liposomes used in this study was considerably higher compared to those formed by the phospholipids mixtures employed in paper I.
Surfactant adsorption at model surfaces. In papers III-VI we started to modify our surfaces with silica, methylated silica and several different self-assembled monolayers (SAMs). The ionic surfactants used were the cationic, DTAB (dodecyltrimethylammonium bromide), DDAB (didodecyldimethylammonium bromide), and gemini surfactants having the same headgroup and chain length as DTAB but with the additional feature that two headgroups were chemically connected with a spacer of different length. The non-ionic surfactants used were the poly(ethylene oxide) monoalkyl ethers C14EO6 and C12EO8(Octa-(ethylene oxide) mono n-dodecyl ether). In paper III we showed that thiolated surfaces work very well as model substrates in adsorption measurements using the QCM-DTM. Functionalised SAMs were prepared from mixtures of hydrophobic, SH-C 1 6 (thiohexadecane) and hydrophilic, SH-C16OH (thiohexadecanol) terminated thiols, which allowed the interfacial energy of the surfaces to be changed in a systematic way. The prepared thiol surfaces were used as substrates for adsorption of a cationic, DTAB, and a non-ionic, C12EO8, surfactant. The experiments showed that when the fraction of methyl groups at the surfaces was increased, the adsorption of both DTAB and C12EO8 is increased. In particular, there is a transition from a micellar surfactant layer to a surfactant monolayer at 25% to 50% surface coverage of SH-C16 groups with monolayers being formed at higher coverage of SH-C16. In addition, the role of the counterion in the adsorbed surfactant layer for the charged surfactant was discussed in terms of its contribution to the mass and visco-elastic response determined by the quartz crystal microbalance.
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With Paper IV where we used the Gemini surfactants, we showed that by changing the length of the spacer group from 3 to 12 a systematic change in the molecular packing at a gold surface was obtained. Furthermore, the molecular packing was shown to correlate to the frictional behavior of the surfactant film. An increasing length of the spacer group resulted in lower, adsorbed amount and less good frictional properties. This is discussed in terms of the critical packing parameter (CPP) of the surfactant and a relation between CPP and frictional behavior is proposed. The results can be viewed upon either as controlled by the rigidity of the surfactant layer or as a result of defects, holes, in the lubricating film. No correlation between spacer length and viscoelasticity of the adsorbed surfactant layer was detected using the QCM-DTM. This indicates that the resolution of the dissipation factor from QCM-DT M measurements is not sufficient to describe the viscoelastic character of the thin surfactant film. The degree of counterion-binding to charged surfactant films is a difficulty encountered when converting the frequency response of the crystal to packing density. This problem is again highlighted and discussed (see also paper III).
In Paper V we investigated the adsorption behaviour of hexa-ethylene oxide mono ntetradecyl ether (C14EO6), on different model surfaces. This investigation was conducted with two different techniques, the QCM-DTM and the ellipsometer. The adsorbed amount of the non-ionic surfactant was determined both at hydrophilic and hydrophobic surfaces. In particular, the substrates employed were; hydrophilic silica, hydrophobized silica (using dimethyldichlorosilane), hydrophobized gold surfaces (using 10-thiodecane and 16thiohexadecane). We showed that the frequency shift obtained from the QCM-DT M experiments results in an overestimation of the adsorbed mass. This is attributed to two different effects, viz, hydrodynamic coupling of water to the adsorbed surfactant layer and secondly, trapped water within the adsorbed surfactant layer. Furthermore, from the ellipsometry data the adsorbed layer thickness was determined. By combining the thickness information and the dissipation parameter (obtained from the QCM-DTM experiments), we again noted that the dissipation parameter was insufficient in describing the visco-elastic character of thin surfactant films.
Paper VI is devoted to lubrication in aqueous surfactant systems where the surfactants adsorb at surfaces in relative motion forming either a surfactant monolayer or a multi (liquid crystalline) layer. The surfactants were of two kinds, viz., a double chain cationic surfactant,
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didodecyldimethylammonium bromide, DDAB, and a single chain cationic surfactant, dodecyltrimethylammonium bromide, DTAB. Excellent film forming capability was shown for DDAB. We interpret this as being due to good packing of the surfactant molecules at the surfaces, i.e. the inherent ability of these surfactant molecules to form liquid crystalline structures at the surface, results in good load carrying capability. This is also reflected in the bulk properties of the surfactants, where DDAB shows lamellar liquid crystalline phases at concentrations much lower than DTAB, which does not show good lubrication properties. The results were discussed in terms of film stability of a surfactant layer adsorbed at the surface, which in turn is correlated to the critical packing parameter of the surfactant. The systems were characterized using (i) the surface force apparatus determining the interaction forces between the adsorbed layers at the surfaces, (ii) the EHD-rig (Elastohydrodynamic-rig) determining film formation under shear. The adsorption kinetics and composition at the surface were determined by QCM-DTM and X-ray photoelectron spectroscopy.
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2. Surfaces
A controlled surface/environment is required when studying interfacial properties of surfactant molecules. Otherwise it is impossible to interpret the experimental results. Model surfaces, where chemical and structural properties can be controlled, are not readily found and in most cases one has to prepare and characterize them oneself. Surfaces can be characterized and classified in many different ways. The surface topology allows classification into “rough” and “smooth” as quantified by e.g. the root mean square roughness, Rq. Other classifications can be based on the chemical composition of the surface, the surface energy, or the wetting properties. The latter classification is particularly suitable when studying surfactant adsorption from aqueous media. The wetting properties can also very conveniently be quantified by the contact angle, θ, of the liquid on the solid, i.e. cosθ = (γSV - γSL) / γ LV. The cosine of the contact angle is thus given by the difference in surface energy between the solid-vapour (γSV ) and solid-liquid (γSL) interface, normalized by the liquid-vapour interfacial tension (γLV). Generally, high energy solids have by definition a high value of γ SV, and in most cases, a much lower interfacial tension against water due to the hydrogen bonding capability and high dipolar moment of the water molecule. The contact angle of water on such surfaces is low. Based on the contact angle one can classify a given liquid on a given surface as completely wetting θ = 0, partly wetting (0 < θ ≤ 90°) or nonwetting (θ ≥ 90°). When the liquid is water one normally talks about hydrophilic and hydrophobic surfaces, but there is no general agreement about what contact angle the surface is required to have in order to be classified as “hydrophilic” or “hydrophobic”. In this thesis we use the general term “hydrophilic” for surfaces having a low contact angle, and “hydrophobic” for surfaces with high contact angle. The quantitative measure of the wetting behaviour is provided by the contact angle. We note that the contact angle is extremely sensitive to the surface composition and sub monolayer adsorption of hydrophobic compounds is easily detected. In fact, in many cases simple contact angle measurement is a more sensitive probe of adsorption than sophisticated XPS (X-ray Photoelectron Spectroscopy) analysis. However, of course, the contact angle does not give the same chemical information as the XPS-spectra.
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In this work we have varied the wetting properties from that of hydrophilic silica to that of hydrophobic alkane thiol SAM on gold surfaces. Some of the properties of these surfaces are described more extensively below. The wetting properties of the surfaces have been characterized using contact angle measurement; the surface composition has been determined employing x-ray photoelectron spectroscopy (XPS, ESCA). The topological character of the surfaces has been determined by the profilometer for surface roughness effects and for some surfaces, the scanning electron microscope (SEM) looking for eventual defects. Some data can be found in table 1, where we have summarized the characteristics of our model surfaces.
Surface
Ra [nm]
Rq / Ra
θ
1.3 ± 0.1
1.5 ± 0.3
< 20°
Dimetyldichlorosilaneellipsometer 1.1 ± 0.2
1.5 ± 0.5
101° ± 1°
SilicaQCM
1.3 ± 0.2
1.5 ± 0.3
< 20°
DimetyldichlorosilaneQCM
1.0 ± 0.1
1.4 ± 0.3
101° ± 1°
GoldQCM
1.4 ± 0.1
6.0 ± 3
≈ 30° ± 5°
ThiohexadecaneQCM
1.2 ± 0.1
3.0 ± 1.0
103° ± 3°
ThiodecaneQCM
1.2 ± 0.1
3.0 ± 1.0
91° ± 3°
ThiohexadecanolQCM
1.2 ± 0.1
3.0 ± 1.0
20° ± 2°
Silicaellipsometer
Table 1: Characteristics of our model surfaces, where silicaellipsometer means a silica surface for ellisometry studies and silicaQCM means a quartz crystal coated with silica for measurements with the QCM.
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2.1 Gold.
The electrodes on the quartz crystal are made of gold, and in many cases this has been a suitable surface to conduct some of our adsorption studies with. The water contact angle on the gold surface obtained after cleaning (see table 1) was low indicating a low degree of contamination, and this surface will henceforth be classified as “ hydrophilic gold” to distinguish it from a gold surface that has been exposed to air for a prolonged time and appears hydrophobic due to adsorption of contaminants. Gold is a material that has a partly filled electron band in its ground state. This means that it has both empty states and electrons in the valence band. The electronegativity1 for gold is 2.41, which is very high for being a metal. The electronic configuration for gold is:
1s22s22p63s23p63d104s24p64d105s25p64f145d106s1
The 6s electrons move around freely in the gold crystal, whereas the 5d electrons are tightly bound to the nucleus. These 6s electrons play a major role for the chemical bonding to gold atoms in the surface layer. In the ideal crystalline structure of gold, the atoms are located themselves in a face centered cubic (fcc)1 lattice, which means that the unit cell consists of a cube with one atom in each corner and one at the centre of each side. Each atom is thus in contact with 12 others. The fcc structure provides maximum number of nearest neighbours and is thus the preferred structure of crystalline materials of spherical molecules or individual atoms. However, the bulk order has to end somewhere near the surface, for gold it prefers to end in a structure called the (111) surface1 of an fcc crystal. It gives the closest packing of atoms in the surface layer. Each surface atom has 6 neighbours on the surface. Gold are in practice a polycrystalline material2, where a lot of small single crystals are joined together, and the borders between the crystals are very far from the perfect (111) surface. At a hydrophilic gold surface, there are a lot of unpaired electrons, and they are highly reactive2. This leads to a fast contamination of a clean surface exposed to air. To keep the surface clean you can either store it in ultra-high vacuum and never let it come in contact with contaminations (solid-gas), or you could clean it in-situ under clean solvent conditions (solidliquid). Since we are doing all our experiments at the solid-liquid interface, we have chosen to clean our surfaces in-situ, and keep the exposure to air contaminants to a minimum This is very demanding since you have to keep all other surfaces in the experimental setup equally
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clean and exposed to a liquid that is as pure as the liquid in contact with the cleaned gold surface to prevent a contamination transport from the other surfaces to the clean (highly reactive) gold surface. It exists several other techniques to clean surfaces, but most of them are still dependent on the environment you do your cleaning and experiments in.
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2.2 Self-Assembled Monolayers (SAMs).
The self-assembly of molecules at the solid-liquid interface has been an area of growing interest. There are different combinations of surfaces and molecules that form SAMs and many of them rely on the strong interaction between one part of the assembling molecules and the surface, in addition to the interaction between the molecules within the monolayer. Longchain organosulphur compounds on noble metals, such as silver, platinum and in our case gold, can be used for forming SAM coated surfaces with stable monomolecular (monolayer) films. It is a versatile preparation technique, and SAM coated surfaces have served as model systems in a number of applications, such as for biosensors, biomaterials, anti-corrosion agents and lubrication1-2. In 1983 Nuzzo and Allara3 published the first observations of organic disulphides that formed monolayers on gold from solutions as studied with infrared spectroscopy. The general picture for the chemisorption of alkane thiols on gold is that the thiol moiety adsorbs in a three-fold hollow site at the Au(111) lattice whereupon it loses its hydrogen atom to become a thiolate. This gives an area of 21.4 Å2 per thiol molecule. SAM coated surfaces have been studied with a number of techniques, including x-ray photoelectron spectroscopy (XPS, ESCA), infrared spectroscopy, scanning tunnelling microscope (STM), electrochemistry, ellipsometry, contact angles and various diffraction methods, see for instance the review by Ulman1. The experimental findings4-5 strongly support the model proposed for the structure of SAMs, and so do theoretical calculations6. However, the detailed quantum mechanical processes are not completely understood. The structure of SAMs has been determined by infrared reflection absorption spectroscopy (IRAS). The distance between the sulphur atoms on the gold surface is slightly larger than the closest possible separation between two alkyl chains, allowing an approximately 28-30° tilt of the chains in the layer to increase van der Waals interaction between the chains, as confirmed both experimentally7 and theoretically8. Whereas the adsorption of molecules on the surface is fast (minutes) the self-assembling process into an ordered monolayer is quite slow (hours)9. After a few minutes alkane thiol molecules forming an almost fully covered layer have been adsorbed, but the order in the layer is low. For one of the thiols used by us, the SH-(CH2)15CH3 thiol, different groups have obtained very different kinetics for forming a well ordered SAM, ranging from seconds to hours 10. The concentration of the thiol in the liquid from which the SAM is formed is, of course, important to take into account when investigating SAM kinetics. At low
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concentrations a diffusion limited adsorption kinetics has been observed4, whereas at high concentrations the time limiting step in the process is the actual surface attachment1. The stability of alkane thiol SAMs when immersed in a solution containing the SAM molecules is excellent. It is a stationary system, i.e. there is a continuous exchange of molecules from the monolayer at the surface to the bulk solution. If the bulk solution contains another alkane thiol, the surface monolayer will be exchanged by the new alkane thiol from the bulk solution. This exchange could take from hours to days depending on which SAMs that are involved10. Even though molecules in the SAM can be exchanged for other SAMs, the desorption of the SAM in contact with a SAM-free solution is very slow due to the interaction with the surface and within the tightly packed layer. It is very easy to prepare mixed SAMs by just mixing the adsorbing species in the solution (see paper III). The surface composition will be highly dependent on properties like chain length, terminal functionality and solubility11. The preparation procedure of thin monolayers of alkanethiols on surfaces is relatively easy. One dissolves the film forming molecules in an appropriate solvent (in our case ethanol) to a rather low concentration, for our SH-C16 a 1mM concentration is enough. A previously cleaned gold surface is then immersed in the solution for approximately 24 hours. When the surface is withdrawn from the solution it is rinsed and then put into pure solvent for approximately a week in order to dissolve any loosely bound, physisorbed, molecules that might be attached to the monolayer.
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2.3 Silica.
The gold coated quartz crystals used in the QCM can be further modified with an evaporated 100 nm thick layer of SiO2. The roughness and contact angle is well defined, as described in table 1. Silica has been widely used the last decade as a model for a hydrophilic surface. The chemistry of silica is rather complex, and a more detailed description can be found elsewhere1. SiO2 surfaces consist of two very different surface groups, relatively hydrophobic siloxane (Si2O), and more hydrophilic silanol groups (SiOH). The silanol group is amphoteric1, which means that it can act both as a base and an acid. Hence, when the silica surface is exposed to water solution the surface charge is determined by the density of silanol groups on the surface and both the ionic strength of the solution and its pH. This forced us to perform all our experiments with SiO2 under controlled pH and electrolyte concentration, and preferably keeping them constant. In order to increase the number of silanol groups at the surface (making it more hydrophilic) and to remove eventual contaminations, we treated the surface with surfactants (Hellman ExTM) followed by plasma cleaning as described in detail in paper III. Yaminsky et al2 have an explanation to the instability of SiO2 surfaces in water. The surface decomposition of SiO2, into polysilicic acids may result in the formation of a diffuse silica gel layer. This gel is probably the main reason for instability of our SiO2 surfaces in water, which are shown as a small drift in the frequency, but not in the dissipation factor. This is contrary to ellipsometric studies using silica surfaces where instabilities could be seen at the gas-solid interface but not at the liquid-solid interface3.
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2.4 Silan coated silica.
The silanol groups present at the surface of silica crystals allow a surface modification by reactions with different types of silanes. Surfaces can for instance be made more or less hydrophobic by reaction with different alkylchlorosilanes1-2. For all our measurements (QCM and ellipsometry) we used a dimethyldichlorosilane to modify our silica crystals/wafers in order to obtain a small surface roughness and a reproducible hydrophobicity. This silane does not form large hydrophobic islands as probed by profilometry, whereas this was found to occur when for instance dimethyloctylchlorosilane (DMOS) was used. When surfaces coated with DMOS were used in surface force experiments, a long-range attractive force was observed2. This may be a direct consequence of these silane islands present on the surface. When two surfaces of DMOS are brought together for the first time, capillary condensation immediately starts3 and drops of DMOS are formed. The reason for the long-range attraction seen in the surface forces experiment was suggest to be is the coalescence of these drops between the surfaces. The dimethyldichlorosilane does not show this behaviour, probably due to the strong cross-linking between the dimethyldichlorosilanes in the hydrophobic layer and no hydrophobic islands are formed. We note however, that a long-range attraction has also been observed for silica surfaces coated with dimethyldichlorosilane6 despite that we do not see any islands of silane on such surfaces. The reason may be that air-bubbles are attached to the surface and it is the coalescence of these bubbles that gives rise to the attractive force. This mechanism was first suggested by Parker et al. for other silane coated surfaces7. For a further discussion on long-range attractive forces between non-polar surfaces in water we refer the reader to a recent review 9 . It has been shown that correctly prepared dimethyldichlorosilane coated surface are surprisingly stabile over several days, as long as they are kept in Milli-Q water or in clean organic solvents4. Such good stability has not been found for DMOS, which likely is due to the lack of crosslinking in the hydrophobic layer, leading to a hydrolyse of the silanol-silane bond in water. This indicates that the silanes are kept at the surface partly by the low solubility, and that they are only partly stabilized by chemical reaction with silanol groups5.
The preparation of the silane surface is a process that easily can go wrong, because of that a precise experimental protocol needs to be used. The method described below has shown to have the highest success rate.
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The SiO2 surfaces were cleaned in a mixture of 25% NH4OH, 30% H2O2 and H2O (1:1:5, by volume) at 80° C for 10 min, followed by cleaning in a mixture of 25% HCl, 30% H2O2 and H2O (1:1:5, by volume) at 80° C for 10 min. In between and after the cleaning procedures by the two mixtures, the substrates were rinsed in water. The substrates were then immediately put into a reactor and exposed to vapours of dimethyldichlorosilane for 24 hours. Afterwards these substrates were rinsed in toluene, ethanol and water, followed by heating to 200°C for 1 hour. All substrates were stored in ethanol until use.
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3. Methods
When positioned at one of the interfaces between chemistry and physics, called surface science, you relatively soon realize that surface chemists are lacking in the knowledge of how to characterize physical (mechanical), properties and surface physics are lacking in knowledge about the basic chemical properties. Hence, in this chapter a number of analytical methods that can be used to study thin surface layers and surface structures are described. I will mainly discuss the Quartz Crystal Microbalance-Dissipation (QCM-DTM) technique. However, also some of the other techniques that I have been using, and which I consider being the most valuable ones for the characterization of my model surfaces, will be briefly presented.
3.1 Profilometer. The surface roughness analysis was carried out using a Zygo View 5010TM, which is a noncontacting technique (see figure 1 for a schematic illustration). It is a precision vertical scanning transducer and a camera put together to generate a three dimensional interferogram of the model surface. This is processed by the software (Metro Pro PCTM) in the computer and transformed using frequency domain analysis to give a quantitative 3-D image. The vertical resolution is 1 Å, independent of microscope magnification and the lateral resolution is at best 0.3 µm. The model surfaces are characterized using the average surface roughness, Ra, which is the average deviation of all points from a plane fit to the test surface. The standard deviation of the profile heights Rq (rms) is also given. For a gaussian surface the ratio between Ra and Rq is close to 1.3. Both Ra and Rq (rms) can be found in table 1 (see chapter 2) for all our model surfaces. Ten measurements were made on random spots on each model surface. The measurement area was 0.18 mm * 0.13 mm, which gives an area of 0.0234 mm2. All measurements were carried out in ambient atmosphere.
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Light Source
Camera
PZT Stack
Interference Microscope Objective
Reference Surface Sample
Figure 1: The Zygo View 5010TM, a precision vertical scanning transducer and a camera put together.
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3.2 Contact angle.
Contact angle measurements were conducted with a Fibro DAT 1100 system. This instrument is used for fast absorption and wetting studies for contact angles above 20°. The application of the droplet from the syringe onto the test surface was computer controlled; giving a controlled drop volume (4 µl). The syringe used was a Teflon syringe in order to avoid any liquid remaining onto the tip. The spreading process was recorded using a CCD camera connected to an image analyser. The images were analysed with respect to base width and height in terms of contact angle and drop volume. The drop volume starts to decrease due to evaporation after 10 s of spreading time. These data are discarded in the evaluation of contact angles. As this simple method is a sensitive measure of the interfacial properties it is widely used to characterize surfaces. The surfaces tension γ [J/m2] are only one of many properties, but also estimates of surface roughness and chemical heterogeneity can be obtained from spreading experiment. It is a simple and reliable method to use as a quality control of the self-assembly monolayer formation process and general cleanliness of for instance silica and gold or other hydrophilic materials (in general contaminations are of hydrophobic nature). The contact angel α is related to the involved surface tensions, in this case there are three, the solid-vapour, γSV , solid-liquid, γ SL , and finally liquid-vapour, γLV , surface tension. This relation is described by the Young’s expression (see equation 1).
cos(α ) =
γ SV − γ SL γ LV
(1)
Whereas the Young-Dupre equation (see equation 2) relates to the adhesion energy per unit areas of the solid (S) and liquid (L) adhering in the medium gas/liquid in our case vapour (V),
∆WSLV [J/m2] . γ LV (1+ cosα ) = ∆W SLV
(2)
Different chemical or structural components on a surface produces a heterogeneous surface. Cassie suggested a way to calculate the contact angle of a heterogeneous multicomponent model surface (see equation 3).
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cosα = Σχ i cosα i
(3)
where, χi is the fraction of the i:th component on the surface and cosαi is its contact angle on that type of surface1. In 1989, Israelachvili2, derived a revised version for the contact angle on a heterogeneous surface (see equation 4).
(1 + cosα ) 2 = Σχ i (1 + cosα i ) 2
(4)
Israelachvili’s assumptions are that the work of adhesion/cohesion is proportional to the square root of the interaction forces involved, and again adding the works of adhesion/cohesion to give the overall work of adhesion/cohesion. This equation claims to account for the heterogeneity that is likely to occur in patches of molecular/atomic dimensions.
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3.3 X-ray Photoelectron Spectroscopy (XPS).
XPS is in the chemistry society often called, Electron Spectroscopy for Chemical Analysis (ESCA). It is described in detail in references 1-5. Photons with energy hv from an X-ray source are irradiated at the surface under study and adsorbed by the atoms. As a direct consequence of this irradiation, emissions of electrons with lower binding energy, the ionisation energy (Eb), than the energy of the incoming photons will occur. As a consequence of the law of energy conservation, the emitted photoelectron obtains a kinetic energy (EK) that is characteristic for the type of atom, the shell of the electron and its chemical environment. The photoelectrons are separated by their kinetic energy before they reach the detector. By the uniqueness of the kinetic energies of the photoelectrons emitted from the atoms an elemental analysis can be conducted. In Albert Einstein’s equation (see equation 1) for the photoelectric effect all this is described, for his work in this area Einstein got the Nobel Prize in 1921. E K = hv − E b − φ
(1)
where, φ is a correction for the spectrometer work function. The photoelectrons, having kinetic energy up to around 1500 eV (if the AlKα electrode is used), do not move more than a few nanometers in the solid material until they collide and loose all or part of their kinetic energy. The average distance that photoelectrons move within the solid material before they collide inelastically is mainly a function of the density of the material and the kinetic energy. The inelastic mean free path λ(EK) describes this process. A fraction of 1/e, about 37 %, of the photoelectrons move the distance λ before being scattered, about 5 % moves as far as 3λ before they get scattered inelastically. The mean free path is often referred to as sampling escape depth or sampling depth. It is around 0.5-2 nm for a metal and 1.5-4 nm for oxides, these values are typical mean free paths2 for photoelectrons having a kinetic energy of 1000 eV. Hence, XPS is truly a surface sensitive technique for chemical analysis. The equipment employed is a Kratos, AXIS HS X-ray photoelectron spectrometer (Kratos Analytical, Manchester, UK). The X-ray emitted in our case comes from an MgKα (1253.6 eV) source. There are other sources available, one of them is the energetic AlKα (1486.6 eV) source that produces more energetic photoelectrons, and due to this in some cases is more useful.
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3.4 The Quartz Crystal Microbalance-Dissipation (QCM-DTM).
The Quartz Crystal Microbalance (QCM) is by no means a new technique1-2. In vacuum physics for instance it has existed for decades, providing film thickness measurements for metal film deposition3. However, lately numerous advancements have been made in the measurement of the frequency factor of the QCM. Among these is the new Quartz Crystal Microbalance-Dissipation (QCM-DTM) instrument from Q-Sense, Gothenburg, Sweden (see figure 2), which we have used for our experiments4. This new setup has two advantages. First, an improved resolution of the frequency factor in aqueous solutions. In fact, it is hard to find any comparable non-vacuum QCM setup5-6. Secondly, this instrument also measures the socalled dissipation factor, which is a measure of the damping of the crystal as will be discussed later. Hence, the QCM technique has only recently become a potentially useful tool for the surface scientists concerned with “wet” surface chemistry. The possibility to monitor the interfacial processes quantitatively in real time opens up new windows of opportunity. The QCM principle is based on evaluating a change in frequency of the oscillating crystal, ∆f [Hz], due to the change occurring on or adjacent to its electrodes. This frequency change is most often interpreted as being due to the change in surface mass loading. In this work we have used the QCM as a “probe”, in order to characterize physical changes at interfaces occurring as a result of surfactant addition7-8. Such effects may arise due to adsorption or different phase changes9-11. This chapter will describe the basic operational parameters of the QCM, and the focus will be on its operation in liquids, even though its use is more widely documented for the gas phase system. We note that not so many studies have explored the use of the QCM for studying solid-liquid interfaces in surfactant solutions12-14. However, a much more extensive literature on surfactant films deposited onto surfaces via the air-solution interface with monolayers of insoluble surfactants is available. A discussion of this extensive literature is beyond the scope of this thesis. The interested reader is referred to reference 12.
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Figure 2: The Quartz Crystal Microbalance-Dissipation (QCM-DTM).
The Quartz crystal. Most QCMs consist of a thin wafer of piezoelectric material, usually quartz, sandwiched between a pair of thin metal electrodes (see figure 3), usually gold. Quartz is a piezoelectric crystalline form of silicon dioxide (SiO2). For oscillating systems the α-quartz is the preferred choice because of its thermodynamic stability at temperatures up to 846° K. The other form, the β-quartz, is metastable at room temperature and it is not piezoelectric15. Piezoelectricity1 is literally “pressure electricity”, the prefix piezo- being derived from the Greek word “to press”. The direct piezoelectric effect refers to the electric polarisation of certain materials by mechanical stress. The converse effect refers to the deformation of the same material by an electric field. Electrostriction is a property of all dielectric materials; it means that when they are placed in an electric field they deform. The difference between piezoelectric materials and purely electrostriction materials is that the piezoelectric deformation is much larger than the ordinary electrostriction deformation and the piezoelectric deformation is reversible. As an example, a rod of quartz is cut in such a way that an applied field causes an elongation of the rod. Reversing the direction of the field will cause the rod to contract in a piezoelectric material, whereas in a non-piezoelectric material, whatever deformation is caused will be independent of the direction of the field. The piezoelectric effect being reversible gives that it is also anisotropic, which means that the mechanical deformation and the electric field (see below) in the material depends on the
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direction within the material. Such materials cannot have a centre of symmetry; with a centre of symmetry the reversal of an applied field would have no effect on the materials internal structure. Lord Kelvin gave the first explanation of the origin of the piezoelectric effect1 in terms of molecular structure; the assumption he made is useful as a qualitative and heuristic guide to understand piezoelectricity.
The electrode. The electric field is in almost all quartz crystals applied via electrodes deposited at the quartz surface in a key hole pattern, as shown in figure 3. In general gold electrodes give a considerably more chemically stable surface compared to other electrode materials16 such as silver (Ag) and aluminium (Al), which both tend to oxidize in aqueous solutions. Although it has been suggested that the gold electrodes of the QCM may also be subject to minor oxidation. This is certainly the case when they are treated with UV/ozone (AuO3, is the product from the UV/ozone treatment17). For the gold and silver electrodes a thin adherent layer (2.5-5 nm) made of chromium (Cr) or titanium (Ti) are used to improve the adhesion of the electrodes to the quartz crystal. The disadvantage of this thin adherent layer is the increased stress in the electrodes, which can influence the output frequency.
Figure 3: The Quartz crystal, with its gold electrode in a characteristic “keyhole” pattern.
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Frequency. A quartz crystal used in the QCM is normally cut at an angle θ ≈ 35° from the ZX-plane, this is known as an AT-cut18, this cut angle makes the quartz crystal less sensitive to temperature drifts as compared to the large temperature drifts in the original X-cut quartz crystal (quartz crystals cut normal to the x-axis) where the temperature drifts are as large as 30 ppm / °K. In the AT-cut case the temperature drift could be as small as 2 ppm. / °K. Another improvement from the original X-cut is that when applying an electrical field across an AT-cut crystal, a shear strain will be induced instead of the induced strain in the thickness direction in the Xcut case. Consequently, an alternating electric field onto an AT-cut quartz crystal will induce shear waves. Of all the vibrational modes that may exist in a quartz crystal, only those that can be driven by an alternating electrical field are relevant in the context of this thesis. Mechanical resonance begins when the thickness of the quartz crystal contains an integral number n of half wavelengths of the extensional wave or longitudinal waves. The quartz crystal’s surfaces will be the anti-nodes of vibration from a standing wave within the plate. When n is even the vibrational modes of the two surfaces are in phase (destructive), and in anti-phase (constructive) when n is odd (n=1 being the fundamental mode, n = 3 is called the first overtone, and so forth). The resonance frequency condition is (equation 1):
f =
nv 2 tq
(1)
Where v is the velocity of the extensional waves, (v/f) is the wavelength, tq is the thickness of the quartz crystal and n is an odd integer (1,3,5,…). Sauerbrey1 9 was the first to show that any mass, ∆ m, deposited on one or both of the electrodes of a QCM crystal, induces a shift in the frequency, ∆ f, that is proportional to the added mass. If the mass is deposited evenly over the electrode(s), and ∆ f is much smaller than f, then the frequency shift versus mass relationship is:
∆m = −
ρ q tq ∆f nf 0
=−
ρ qν q ∆f 2 nf 02
=−
ρt C∆f ⇒C= q q n f0
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(2)
Where ρ q and ν q are the specific density and the shear-wave velocity in quartz, respectively, tq is the thickness of the quartz crystal, f0 the fundamental resonant frequency and n is the shear wave number. With ρ q = 2648 kg/m3, ν q = 3340 m/s, tq = 0.33 mm, and f0 = 5 MHz, C is 17.7 ng cm-2 Hz-1. For the relation to be valid, Sauerbrey assumed that the added mass should be much smaller than the mass of the quartz crystal, and it should be rigidly attached to the electrode(s), with no slip or inelastic deformation in the added mass due to the oscillatory motion. Pulker later confirmed equation 2 by experimental data up to mass loadings (madsorbed / mcrystal ) of approximately 2 %. There are various models or converting the frequency shift to mass loadings up to approximately 5 %, and they all behave similarly21. Another property, probably the most important to have under control, is that the surface area should be smooth. The QCM surface area is approximately the same as the projected geometrical area for low Ra values, and this roughness effect will be discussed later.
The use of QCM in liquid media. In 1980, Nomura showed that a quartz crystal could be completely immersed in a liquid and still be excited to stable oscillations22, after this theories had to be worked out. In 1985 Kanazawa and Gordon published a theory23 on the QCM behaviour in the liquid phase. They were totally unaware of the theory that Stockbridge24 had published already in 1966. This paper was concerned with the gas pressure effect on the QCM oscillations, and it turned out to be exactly the same as the Kanazawa and Gordon theory. The relationship derived describes the change in oscillation frequency of the quartz crystal in contact with a fluid in terms of material parameters of the fluid and the quartz. This relationship is shown below (equation 3).
∆f = −
f0 2 tq ρ q nπ
ρ fηf
(3)
Where ρ f and ηf are the specific density and the absolute viscosity of the film, respectively, tq is the thickness of the quartz crystal, f0 the fundamental resonant frequency of the dry crystal,
ρq is the specific density of quartz and n is the shear wave number. With ρ q = 2648 kg/m3, tq = 0.33 mm, and f0 = 5 MHz. This relation is obtained from a simple physical model, which
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couples the shear wave in the quartz crystal, to a damped shear wave in the fluid. The shear wave extension or, as it is more commonly called, the decay length, is given by equation 4.
δ=
4 πη f
(4)
fn ρ f
where, δ is the decay length of the shear wave, ηf is the absolute viscosity of the film, fn the resonant frequency of the dry crystal in mode n and ρq is the specific density of quartz. The decay length is the distance into the liquid where the amplitude of the shear wave has fallen by a factor of e, and for a 5 MHz quartz crystal oscillating in water this decay length is approximately 250 nm at 20° C.
Roughness properties. Martin, Frye and Wessendorf examined the frequency response of smooth (low surface roughness, Ra < 10 nm) and textured surfaces (high surface roughness, Ra > 100 nm) on quartz crystals in liquids in 199425. Smooth quartz crystals, which viscously entrain a layer of contacting liquid, exhibited a response that depends on the square root of the product of liquid density and viscosity. Textured-surface quartz crystals, which also trap liquid in surface crevices, pores, etc., exhibit an additional response that depends linearly on liquid density alone. The resulting modification to the Stockbridge and Kanazawa equation 4, is shown in equation 5.
∆f = ∆f v + ∆f t = −
f0 2 tq ρ q nπ
ρ fηf −
fn tf ρ f tq ρ q
(5)
Where ∆fv is the induced frequency shift due to the liquids viscosity and density over a uniform crystal. ∆ft is the induced frequency shift due to trapped liquid with an average thickness of tf , ρ f and ηf are the specific density and the absolute viscosity of the film, respectively, tq is the thickness of the quartz crystal, fn the resonant frequency of the dry crystal, ρ q is the specific density of quartz and n is the shear wave number. The liquid 28
entrained by the oscillating smooth surface is described as viscously coupled. This liquid does not move synchronously with the surface, but undergoes a progressive phase lag with increasingly distance from the surface. The textured-surface also traps a quantity of fluid in excess of that viscously entrained by a smooth surface. The perpendicular character of the texture-surface constrains this trapped liquid to move synchronously with the surface, rather than undergoing a progressive phase lag. This trapped liquid can be viewed as an added mass, contributing to an areal mass density, ρtf, where ρ is the absolute density of the liquid and tf is the effective thickness of the perpendicular features of the surface. The frequency shift measured in an adsorption experiment is relative to the frequency of the crystal immersed in water. Under the conditions we have used the instrument, i.e. relatively low solute concentrations, no measurable effects due to changes in bulk viscosity or density is expected. Hence, the measured frequency shift in our experiments is due to changes occurring close to the surface. Most importantly adsorption including bound water. Martins addition to Gordon’s and Kanazawa’s equation is valid under the condition that the effective thickness h, of trapped liquid is small compared to the liquid decay length δ. In such a case the relative response due to liquid trapping is small, compared to the frequency shift due to viscous entrainment and may be neglected. This defines a criterion for hydrodynamic smoothness29: h
