Canada August 2007

Self-Assembled Monolayers: Characterization and Application to Microcantilever Sensors

Brian Seivewright

Department of Chemistry

McGill University, Montreal, Quebec, Canada August 2007

A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

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The assessment of silicon nitride microcantilevers as solution phase sensors and the understanding of the forces at play within these are the principal focus of this thesis. Microcantilevers with different self-assembled monolayers (SAMs) on their top and bottom surfaces were prepared using metal sputtering and thermal evaporation. These dual-coated microcantilevers were shown to be more stable to thermal fluctuations than single-sided microcantilevers. Control of the bottomside surface chemistry of the microcantilevers is shown to be possible with alkylthiolate SAMs. A microcantilever-based liquid cell and a new microcantilever structure were designed, implemented, and characterized. This microcantilever system was assessed as a sensor in solution and was used to investigate the differential surface stress resulting from chemical and physical stimuli.

The stability and reproducibility of 11-mercaptoundecanoic acid SAMs were studied by electrochemical impedance spectroscopy (EIS) and cyclic voltammetry on polycrystalline gold electrodes. The observed voltammetric peak magnitude and position were modeled by accounting for the kinetics of dissociation of the carboxylic acid groups. This surface reaction was then extensively studied in the microcantilever system.

Microcantilevers functionalized with acid-terminated SAMs on one surface and alkyl-terminated SAMs on the other surface are responsive to pH changes.

ii Differential surface stress vs. pH measurements allow for the determination of the surface pKi/2 of acid-terminated SAMs. The pKi/2 of surface-bound acid moieties is shown to be ca. 2 pH units higher than the equivalent solution-phase carboxylic acid. The forces responsible for the observed differential surface stress are evaluated. Although functionalized microcantilevers do respond to pH changes, there remain problems with signal reproducibility and hysteresis. The prospects for development of the microcantilever system into a laboratory tool are discussed.

in Abrege

Cette these traite de revaluation de microcantileviers de nitrure de silicium comme senseurs en solution et de I'etude des forces impliquees autour de cette

utilisation. Des microcantileviers avec differentes monocouches auto-assemblees

(MAA) sur les surfaces inferieures et superieures furent prepares utilisant le

"sputtering" de metaux et I'evaporation thermique. Ces microcantileviers avec doubles-couches sont demontres comme etant plus resistants aux fluctuations thermiques que ceux avec une couche simple. Les proprietes chimiques de la couche inferieure des microcantileviers est demontre avec des MAA d'alkylthiolates. Une cellule liquide ainsi qu'une nouvelle structure de microcantilevier sont developpees, implementees et characterises. Ce systeme de microcantileviers est evalue comme senseur en solution et est utilise pour etudier le stress differentiel de surface cause par differents stimulis chimiques et physiques.

La stabilite et la reproductibilite de MAA de HS-C-12-COOH sont etudiees par spectroscopie d'impedance electrochimique et voltametrie cyclique sur electrodes d'or polycrystallins. La magnitude et la position du pic voltametrique observe sont modelisees en prenant en consideration la cinetique de dissociation des groupes d'acide carboxilique. Cette reaction des surfaces est etudiee en detail a I'interieur du systeme-microcantilevier. Les microcantileviers ainsi fonctionnalises par I'addition de MM avec groupe acide-terminal sur une des surfaces et des MAA avec groupe alkyl-terminal sur

I'autre repondent aux changements de pH.La mesure du stress differential de surfaces et du pH permettent la determination du pKi/2de surface des MAA avec groupe acide-terminal. Le pKi/2 des groupes acides sur surfaces est de ca. 2 unites de pH plus eleve que celui des groupes equivalents en solutions. Les forces responsables du stress differentiel de surface sont mesure. Meme si les microcantileviers fonctionnalises repondent aux changements de pH, il persiste des problemes avec la reproductibilite du signal et I'hysterese. Fianlement, le potentiel de developpement du systeme de microcantileviers comme outil de laboratoire est discute.

V Preface

In accordance with the Thesis specifications of the "Thesis Preparation and

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VI r^. to allow a clear and precise judgement to be made of the importance and originality of the research reported in the thesis.

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8. In no case can a co-author of any component of such a thesis serve as an External Examiner for that thesis."

Contribution of Authors

This dissertation consists of 5 chapters and one final appendix. The first and last

chapters correspond to the general introduction and the conclusions &

suggestions for future work respectively. Chapter 2 introduces the design,

implementation and calibration of the microcantilever system. The experimental

work and the writing for this Chapter were done by me, Brian Seivewright, under

the supervision of Prof. R. Bruce Lennox. Chapter 3 is the verbatim copy of an

vii article published in Langmuir. The experimental work for this publication was performed by me, Brian Seivewright, and Asst. Prof I. Burgess(Dept. of Chem., U. of Sask.). The data analysis and writing were performed by me, Brian

Seivewright, Asst. Prof I. Burgess(Dept. of Chem., U. of Sask.), and Prof. R. B.

Lennox. Chapter 4 assesses doubly-coated microcantilevers for sensor applications in solution. The experimental work and the writing for this Chapter were done by me, Brian Seivewright, under the supervision of Prof. R. Bruce

Lennox. The ferrocenyl probe technique was used in Chapter 4 with the assistance of Lawrence Y. S. Lee.

A communication is in the process of being prepared for Chapter 2 along with a manuscript for publication for Chapter 4. They will be co-authored by my research supervisor Prof. R. B. Lennox.

Fred Kluck machined the liquid cell for the microcantilevers from plans that I had designed. Michel Godin and Vincent Tabard-Cossa(Physics Dept., McGill

University) provided help in getting the project started along with calibration of the microcantilevers. Asst. Prof I. Burgess(Dept. of Chem., U. of Sask.) provided valuable teaching and guidance for the electrochemical experiments. Other than the aforementioned collaborations and assistance, as well as the valued inpu from my research supervisor, Prof. R. Bruce Lennox, the contents of this thesis are the product of the author.

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ix /"•^

I HAAAS| Permissions Letter Ref# 07-23149 DATE: Tuesday, August 21, 2007

TO: Brian Seivewright McGill University 2800B Saint Patrick Apt. 204 Montreal, Qu H3K 3H9 Canada

FROM: Elizabeth Sandler, Rights and Permissions RE: Your request for permission dated 08/18/07

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Permission is valid for use of the following AAAS material only: Fig 1 from Joerg Lahann et al., SCIENCE 299:371-374 (17 January 2003) In the following work only: "DESIGN, CALIBRATION, AND FABRICATION OF A DUAL SAMPLE LIQUID CELL FOR USE WITH D..." published by McGill University in Sept 2007 Thankyoufor writing. If you have any questions please call me at (202) 326-6765 or write to me via fax at /-™ (202) 682-0816. For international calls, +1 is the country code for the United States.

x I hereby give copyright clearance for the inclusion of the following paper, of which

I am a co-author, in the dissertation of Brian Seivewright.

"Electric Field Driven Protonation / Deprotonation of Self-Assembled Monolayers of Acid-Terminated Thiols"

u*.-3Llhl

Prof. R. Bruce Lennox Date

Professor of Chemistry

Department of Chemistry

McGill University

XI I hereby give copyright clearance for the inclusion of the following paper, of which

I am a co-author, in the dissertation of Brian Seivewright.

"Electric Field Driven Protonation / Deprotonation of Self-Assembled Monolayers of Acid-Terminated Thiols"

QJB& -tjMfe" /w**4- 2dr I DrJan Burfjesasm \J Date Assistant Professor of Chemistry

Department of Chemistry

University of Saskatchewan

xii Dedication

This Thesis is dedicated to the following people: Mylene Dandavino, my unborn child, and my Family, Ann Seivewright, Kevin Seivewright, James Seivewright, and Gisele Breton.

xiii Acknowledgements

I thank and recognize the following people who have supported me throughout this journey and for their help in completing my doctoral studies:

Mylene Dandavino, for your love and everlasting encouragement throughout the difficult moments. You have pushed me to persevere and have always believed in me. Thank you so much my love.

Gisele Breton and James Seivewright, my parents, for your patience and moral support. You gave me the confidence to pursue my dreams.

Ann and Kevin Seivewright, my siblings, for the moments we have shared together and the many laughs. I love you both!

My research director, Prof. R. Bruce Lennox, for your guidance and supervision.

Our scientific debates and discussions were always interesting and inspiring.

My colleagues in the Lennox lab, past and present, from whom I have learned a great deal: Vicki, Paul, Bill, Marco, Sam, Valerie, Gerardo, Carl, Aziz, Isabelle,

Simona, Michal, Teddy, Todd, Muriel, Neil, and Vishya. I thank Ian Burgess for his support, laughs, the runs, integrity, and scientific inspiration. Our discussions and arguments were some of the best moments I will carry forward. I owe Lawrence and Jeff so much for their help and scientific discussions. I am grateful to Adil for

xiv the many interesting discussions and for building us a versatile computer network that simplified so many of our tasks.

All of the support staff in the Chemistry Department who have kept everything, including our instruments, running properly, notably: Fred Kluck and Bill Bastian for machining my cell and Rick Rossi for helping me with my electronics problems and my breakout box. I also thank Sandra Aerssen, Chantal Marotte, Renee

Charron, Fay Nurse, Paulette Henault, Carol Brown, Normand Trempe, and

Alison McCaffrey. For financial assistance, I thank Prof. Bruce Lennox, le Fond

Quebecois de la Recherche sur la Nature et les Technologies for a doctoral fellowship, and the National Science and Engineering Council of Canada.

My colleagues who made the journey fun and with whom I shared countless laughs: Claudia Gributs, Shane Pawsey, Owen and Diane Terreau, Andrew

Oliver, Lee Fader, Stephanie Warner, Margaret Antler,

All the scientists with whom I collaborated: Prof. Jacek Lipkowski, Prof. Peter

Griitterfor his fruitful discussions, Michel Godin, Vincent Tabard-Cossa, Robert

Gagnon, and Peter Williams for helping me with my instrumentation.

Last, but certainly not least: Marc, Chantal, Sami, Isabelle, Jean-Francois, Melina,

Nicole, Adrien, Frederic, and Simon for your invaluable friendship. Table of Contents

Contribution of Authors vii Dedication xiii Acknowledgements xiv Table of Contents xvi List of Tables xviii List of Figures xix List of abbreviations and symbols xxvii

Chapter 1 General Introduction 1 1.1 Microcantilever Sensors and Applications 2 The History of Microcantilevers 2 1.2 Modes of Microcantilever Stress 8 1.3 Microcantilever Deflection Detection Schemes 9 Laser Beam Deflection: 10 Embedded Piezoresistance 11 Optical Interferometry 12 Parallel plate capacitor: 13 STM: 14 1.4 Fabrication of Microcantilevers 15 1.5 Microcantilever Applications 16 1.6 Alkylthiolate SAMs on Gold 18 The Gold-Thiolate Bond 23 SAMs with Terminal Groups 27 Alkylthiolate Exchange Reaction 30 1.7 Thesis Objectives: 32

Chapter 2 Design, calibration, and fabrication of a dual sample liquid cell for use with doubly-coated silicon nitride microcantilevers 39 2.1 Introduction 40 2.2 Cell Setup 41 2.3 Fiber Optic Laser Diode 44 2.4 Position Sensing Detectors 45 2.5 Current-to-Voltage Converter 47 2.6 Microcantilevers 48 2.7 Microcantilever Deflection 49 2.8 Determining the microcantilever spring constant: 53 2.9 Calculation of differential surface stress 59 2.10 Metal film deposition 62 2.11 SAM Preparation 64 Passive Deposition: 64 Active Deposition: 65 2.12 Increased microcantilever temperature stability due to dual metal coating. 66 2.13 Discussion of slow microcantilever drift 70 SAM rearrangement: 70 Surface reconstruction: 72 2.14 Conclusions: 72

xvi Chapter 3 Electric Field Driven Protonation / Deprotonation of Self Assembled Monolayers of Acid Terminated Thiols 76 Linking Text 77 3.1 Introduction 78 Overview of Thermodynamic Models of the lonizable Interface 80 3.2 Materials and Methodology 83 3.3 Results 85 Cyclic Voltammetry 85 Electrochemical Impedance Spectroscopy 87 3.4 Discussion 91 Explanation of Experimental EIS Data 91 Derivation of the Protonation/Deprotonation Impedance 93 Nature of the pH Dependence on Voltammetric/EIS Data 101 Determining Surface Acid Dissociation Constants from Electrochemical Data 108 3.5 Conclusions 110 3.6 Acknowledgements 111 3.7 Supporting Information 112 Contribution of the Diffuse Layer Capacity 112

Chapter 4 Assessment of microcantilevers as solution-phase sensors 117 Linking Text 118 4.1 Introduction 119 4.2 Experimental 120 4.3 Results and Discussion 122 SAM stability under solution incubation conditions 122 4.4 Microcantilever Responses 129 The "idealized" response 130 Blank microcantilever response 136 Microcantilever drift 137 Anomalous stress response 139 Nil Response 140 4.5 Origin of differential surface stress - an overview 141 4.6 Lattice Compression/Expansion due to the Geometric Curvature of the Microcantilever 149 4.7 Assessment of the Microcantilever Sensor via Response to pH 152 Determination of the SAM pK1/2 using a SAM-microcantilever system 154 4.8 Conclusions 161 Analysis - Assessment - Overview 162

Chapter 5 Conclusions, Contributions to Original Knowledge, and Suggestions for Future Work 168 5.1 Conclusions 169 5.2 Contributions to Original Knowledge 171 5.3 Suggestions for Future Work 173

Appendices 177 6.1 Software Design 178 6.2 Calculation of Rp and Cp 184 6.3 Microcantilever experiments in NaF solutions 191 6.4 Radius of curvature calculation 180

xvii List of Tables

Table # Text Page # Table 1: Properties and dimensions of the triangular microcantilevers 49 obtained from Veeco Inc.

Table 2: Summary of EIS Fitting Results Using the Equivalent Circuit 113 of Figure 27c. Values are not compensated for the electrode area which was 0.15 cm2.

Table 3: Differential capacitance of an MUA SAM on a gold bead 129 electrode in 50 mM LiCI04. The capacitance was measured using ac voltammetry at 0 mV vs SCE for the SAM, subjected to incubation in pH 3.0 or pH 10.0 buffer for the specified time periods.

xviii List of Figures

Figure # Text Page # Figure 1: The cantilevered beam (black) extends into space from the 4 supporting structure (grey rectangle). The beam is anchored to the structure by a counterweight (grey rounded rectangle) which counteracts the force exerted on the cantilever (arrow). The star indicates the point of the torque on the supporting mount.

Figure 2: a) Veeco Instruments Inc tipless SPM probes NP series, b) 7 Veeco Instruments Inc. calibration SPM probes, CLFC series, c) "Self-Leveling" microcantilever developed by J.L. Corbeil et al. d) IBM Zurich cantilever group artificial nose.

Figure 3: Illustration of compressive stress resulting in a downward 8 deflection of a microcantilever. The perturbation causes the top surface molecules to take up more volume. The resulting compaction of the molecules causes the microcantilever to deflect downward to compensate for compaction of the top-surface molecules.

Figure 4: Piezoelectric cantilever microfabricated on a silicon wafer. 11 Side illustration of the cantilever demonstrates the numerous layers. The cantilever consists of silicon, silicon oxide, gold, chromium, titanium platinum, and a piezoelectric ceramic layer. Figures adapted from C. Lee et. al.1

Figure 5: Interferometer setup for microcantilever deflection detection. 12 The interference between the outbound coherent beam and the reflected beam produces an oscillating intensity output at the 50/50 splitter. The microcantilever deflects A/2 nm per period of the intensity output.

Figure 6: Fabrication steps for the manufacture of Si3N4 16 microcantilevers. A clean Si (100) wafer is first coated with a Si3N4 layer by LPCVT. The Si3N4 film is then lithographically patterned and selectively etched by reactive ion etching. The Si wafer is then etched to free the cantilevers. KOH-based etchants selectively etch through Si (100) planes but effectively stop at Si (111) planes.

xix Figure 7: Lattice structure of a thiolate SAM on a gold (111) crystal 21 plane. Gold atoms are represented by yellow spheres, actual diameter, a = 2.88 A. Sulfur atoms are represented with green spheres and the larger translucent green disc represent the approximate alkyl chain surface area assuming the chains are normal to the surface. Equivalent superlattices c(4x2) and resulting from the chain tilting are illustrated by the blue rhombus and red rectangle respectively.

Figure 8: Illustration of the stripped, low-density phase observed for a 24 tetradecanethiol SAM (9«6.6x10"1° mol/cm2). The alkylthiolates' molecular axes are oriented along the plane of the Au substrate to produce a stable intermediate state. Although this phase consists of low surface coverage, there remains a high degree of correlation between the sulphur tethers.

Figure 9: Schematic of tetradecanethiol SAM formation on gold 28 substrate. The figure illustrates the various phases traversed towards the formation of a complete SAM. Initially the tetradecane thiolate molecules lie parallel to the surface and are highly disordered. As the density of the SAM increases, the chains become more ordered, form a striped pattern, and then eventually align into a commensurate c(4x2) superlattice with upright chains.

Figure 10: Schematic of the place exchange reaction for a CuS-Au 31 SAM in a 16-mercaptohexadecanoic acid solution. Initially place exchange occurs predominantly at surface defects and subsequently occurs at the planar sites until an equilibrium is reached between the surface-bound thiolates and the solution phase thiols.2

Figure 11: Liquid cell made from PCTFE. a) Assembled cell b) Inner 43 compartment of the cell c) input and output ports d) front window e) sample holder f) O-ring.

Figure 12: Lasiris™ pig-tail laser diode model# PTL-635-S-3-1.2mm- 44 5cm. The black housing contains the 635 rjm laser diode, on/off switch, and modulating electronics. The pig-tail laser diode also features a yellow single mode fiber optic coupled with a terminating focusing lens. Image adapted from www.stockeryale.com.

XX Figure 13: On-TRAK 1L10 position sensing detector and a schematic 46 of its operation. Current flow in either electrode is proportional to the proximity of the light spot. Figure adapted from www.on-trak.com.

Figure 14: The op-amp feedback circuit from ON-TRAK Photonics Inc. 47 for calculating the signal position independent of the fluxuations in the light spot intensity.

Figure 15: Schematic of triangular microcantilever and dimensional 48 variables.

Figure 16: Schematic of the cantilever deflection measurement setup. 50 The laser light exits the yellow optical fibre and is focused onto the cantilever tip. The laser light is then reflected onto the PSD. Cantilever deflections, Az, result in a change in position of AS for the impinging laser centroid on the PSD. This diagram is not to scale.

Figure 17: Schematic of the cantilever deflection to determine the 52 angles of reflection and allow for the calculation of Az from known values L and I along with the measured PSD change AS. The red lines represent the laser beam and the black curve represents the cantilever. Note that this diagram is not to scale.

Figure 18: Microcantilever oscillation amplitude vs. frequency. A 55 rectangular microcantilever 200 urn long and 20 urn wide was coated with 5 nm of Ti and 75 nm of Au. Frequency measurements were performed on an atomic force microscope (Park Scientific Instruments, AutoProbe CP).

Figure 19: Simple harmonic oscillator fit (red) on the power spectrum of 57 the rectangular microcantilever (black). The fit is used to determine the quality factor, Q, for the fundamental peak and the resonant frequency, wres of the microcantilever.

Figure 20: Illustration of Au sputtering of microcantilevers within the 64 Edwards Auto 306 sputter chamber. Permanent magnets within the magnetron produce a toroidal field such that the Ar-ion plasma is focused between the sample and the Au target.

xxi Figure 21: CV of an MUA SAM prepared on a gold bead electrode. 66 SAM deposited from 1mM MUA and 50 mM LiCL04 EtOH solution at 200 mV vs SCE for 5 min. CV obtained at a scan rate of 20 mV/s in 50 mM NaF.

Figure 22: a) Differential surface stress plot and overlaid temperature 69 plot for a 320 urn triangular microcantilever coated with 3 nm of Ti and 50 nm of Au on both sides, b) Differential surface stress plot and overlaid temperature plot for a 320 urn triangular cantilever coated with 3 nm of Ti and 50 nm of Au on both sides, c) Temperature sensitivity (differential surface stress vs. temp.) of both microcantilevers during the cooling cycles.

Figure 23: Figure adapted from J. Lahann et. al., Science, 2003, 299, 70 371. Formation of a low density acid-terminated SAM using a bulky end group. Reversible switching of the SAM conformation by potential control.

Figure 24: pH dependent cyclic voltammograms of Au bead electrode 86 coated with MUA SAM. Inset (a) Plot of the anodic CV peak potential vs pH. Inset (b) Plot of maximum anodic peak current vs pH.

Figure 25: Bode plots (phase angle vs frequency) for MUA SAM on 87 polycrystalline Au for potentials E -500 mV < E ^ 0 mV vs SCE. Electrolyte was 50 mM NaF pH adjusted to 8.5.

Figure 26: 3D electrochemical impedance spectra of MUA SAM on Au 90 bead electrode as a function of potential and various pHs.

Figure 27: (a) RC model circuit for a non-ionizing SAM consisting of a 94 solution resistance and a film capacity in series, (b) Model circuit for an ionizing SAM consisting of a generic impedance, Zp, in parallel with the film capacitance, Cc. (c) Model circuit for an acid-terminated SAM consisting of a protonation/deprotonation resistance and capacitance in parallel with the film capacitance.

Figure 28: Fit of equivalent circuit (Figure 27C), solid line, to 102 experimental Nyquist plot of MUA in pH 9.0 at -0.275V vs SCE, square points. Inset: Bode angle plot of MUA SAM in pH 9.0 at -0.275V vs SCE, square points, and equivalent circuit fit, solid line.

xxii Figure 29: Simulated values of Rp(a) and Cp(b) vs pH for potentials 104 corresponding to the maximum protonation/deprotonation current.

Figure 30: Simulated electrochemical impedance spectrum as a 106

function of pH-pKi/2 at the potential corresponding to the maximum protonation/deprotonation current.

Figure 31: (a) Simulated admittance plot vs frequency for pKi/2 107 normalized pHs at the potential corresponding to the maximum protonation/deprotonation current, (b) Simulated admittance plot vs pKi/2 normalized pHs for specific frequencies at the potential corresponding to the maximum protonation/deprotonation current.

Figure 32: Illustration of the closed-loop, flow-through system used to 122 change the cell solution during the experiments. The peristaltic pump circulates the solution between the cell and the solvent reservoir. The solution never contacts any mechanical parts within the pump. The pH is adjusted either by changing the solution in the beaker or by adding spikes of dilute NaOH or HCI. Ar is bubbled into the solution to minimize pH changes caused by C02 dissolution.

Figure 33: Defect labelling of MUA SAMs formed on a gold-bead 124 electrode. Red: CV of an electrochemically deposited (E- dep) SAM (5min @ 200mV vs Ag/AgCI) prior to ferrocenyl labelling. The black curve corresponds to an E-dep MUA SAM probed with FcDDT. The blue curve is the CV of an electrodeposited MUA SAM that was incubated in pH 3.0 phosphate buffer solution for 16 hours, and then assessed with the FcDDT label. The dashed curve is the CV of a passively-prepared MUA SAM (2 hr incubation) followed by assessment with FcDDT label. The % defect labels are values derived from integration of the Fc signals of the CVs, as per the reference.1

xxiii Figure 34: Cyclic voltammograms of an MUA SAM on a gold-bead 127 electrode in 50mM LiCI04 electrolyte. The electrode was immersed in pH 3.0 for the specified time intervals, after which the electrode was rinsed thoroughly with Millipore water (18MQ) and a cyclic voltammogram was measured. The electrode was then re-immersed in the phosphate buffer solution for another specified time period and the process was repeated. After a total of 2 hours, the solution was changed to pH 10 and the process was repeated. After a total of another 20 hours at pH 10, the electrode was returned to the pH 3 buffer solution.

Figure 35: "Idealized" response of an acid-terminated SAM-coated 131 microcantilever to an increase in pH. Deprotonation of the carboxylate moiety results in a compressive stress causing the microcantilever to deflect away from the carboxylate- terminated SAM. Return to low pH returns the microcantilever to its initial position.

Figure 36: Microcantilever surface stress response as a function of pH. 132 Top surface: MHA SAM, bottom surface: Ci2S-Au SAM. Dotted vertical lines correspond to initiation of a pH change.

Figure 37: Microcantilever surface stress response as a function of pH. 134 Top surface of the microcantilever is functionalized with an MUA SAM. The bottom surface is functionalized with a C12S-Au SAM.

Figure 38: Microcantilever coated with 5nm of Ti and 75nm of Au on 135 both the top and bottom surfaces. Top surface is functionalized with an MHA SAM and bottom surface with a Ci2S-Au SAM.

Figure 39: Differential surface stress of microcantilever coated with 136 C12S-AU SAMs on both the top and bottom surfaces vs. pH change of the buffer solution.

Figure 40: Differential surface stress measurement for MPA- 138 functionalized microcantilever displaying substantial drift after >48 h pre-conditioning in buffer solution. The compressive stress and tensile release thereof (pH 8.6 and back to 3.4) is overlaid on a linear drift (red line). Right hand side plot represents the drift-corrected data.

xxiv Figure 41: Differential surface stress vs pH for a bottom-functionalized 140 microcantilever. Top surface coated with a C12S-AU SAM, bottom surface coated with an MUA SAM. Incubating solution is 50mM NaF. The pH was adjusted using dilute HCIO4 or dilute NaOH. The data is corrected for drift. The deflections are in an opposite sense to what was previously observed.

Figure 42: Schematic of how Coulombic repulsion resulting from a pH 145 increase at a carboxylic acid-functionalized microcantilever can result in a deflection. The topside SAM consists of MUA while the bottomside SAM consists of C12S-AU. As the pH increases, the MUA SAM becomes deprotonated and the cantilever deflects in response to the compressive stress of the top-side. The carboxylate anions are represented by red spheres.

Figure 43: Lattice compression and expansion of the bottom and top 150 gold films upon deflection of the microcantilever. Black dashed line represents the average microcantilever length; 320 urn. The radius of curvature is obtained from the deflection measurement and the angle 9 is calculated from the average microcantilever length. The green line represents the gold monolayer experiencing the highest lattice expansion whereas the red line represents the gold monolayer experiencing the highest lattice compression. The percent expansion/compression is calculated from the difference in radius of curvature, ie. half the microcantilever thickness or t/2.

Figure 44: Determination of the average differential stress of a 155 microcantilever functionalized with an MUA SAM undergoing a pH titration. The average differential stress was determined from the last 500 s of data before the subsequent pH change. These regions are highlighted with blue striations.

Figure 45: Average differential surface stress vs. pH fit for an MUA- 156 functionalized microcantilever. Red curve is the best fit of equation (4.7) to the data (fit results in box) and the blue curves represent the 95% confidence intervals. Black curve is the theoretical "1-pK" model using a value of f3F_=1.

XXV Figure 46: Fit of equation (4.7) to the average differential surface 159 stress vs pH data for three (a,b,c) MUA-functionalized microcantilevers. Red lines represents the best-fit curve and the blue lines represent the 95% confidence intervals.

Figure 47: Differential surface stress vs pH for MPA and MHA 160 functionalized microcantilevers.

Figure 48: Start-up panel of the LabVIEW data acquisition software. 179 Provides three options: Calibrate the pH meter using buffer solutions, proceed directly to the cantilever deflection acquisition portion of the software, or cancel.

Figure 49: pH calibration panel of the LabVIEW acquisition software. 180 The three pH buffer values are listed in the left column. The measured electrode voltage readings are listed in the right column. The bottom-left plot displays the real-time electrode voltage and the bottom-right plot displays the 3-point calibration.

Figure 50: Data acquisition panel of the LabVIEW software. Buttons 182 along the left-hand side control the laser diode intensity, buffer size, total acquisition time, and data acquisition rate. The large plot displays the real-time non-calibrated laser positions (V) vs time (s). The bottom plot displays the real time solution pH of the solution in the cell.

Figure 51: Graphical code for the LabVIEW data acquisition software 183 used for the microcantilever experiment. The software runs an iterative loop which constantly verifies the state of the experiment along with the entered experimental conditions.

Figure 52: Schematic for determining the radius of curvature of a bent 192 microcantilever. R is the radius of curvature. Az is the microcantilever deflection.

xxvi List of abbreviations and symbols: ac alternating current AFM atomic force microscopy B microcantilever to cell window distance (m) C capacitance CPE constant phase element CV cyclic voltammetry DC direct current E electrode applied potential EIS electrochemical impedance spectroscopy F farads i current IR infrared k (de)protonation rate constant k rate constant K equilibrium constant 1 microcantilever length (m) L microcantilever to PSD distance parallel to microcantilever normal (m) MHA 16-mercaptohexadecanoic acid MPA 3-mercaptoproprionic acid MUA 11-mercaptoundecanoic acid PSD position sensitive detector Q microcantilever quality factor R resistance S distance between reflection spot on microcantilever to SAM self-assembled monolayer SCE saturated calomel electrode SP stylus profilometry STM scanning tunneling microscopy SW Smith and White UHV ultra high vacuum V volts Z impedance a transfer coefficient l~i surface coverage of species i £ relative permitivity n refractive index e fraction of ionized w-functionalized molecules in a SAM A change in surface charge density with change in degree at SAM ionization at constant applied potential. a surface charge density of the electrode

xxvii XXV111 Chapter 1

General Introduction 1.1 Microcantilever Sensors and Applications

The history of microcantilevers

The first microcantilevers were commercially available in the mid-1990s as a result of several coincident developments and ongoing interest in surface science problems. The discovery of the atomic force microscope (AFM) in 1986 and its application to a vast number of areas of materials and surface chemistry hastened the commercial production of microcantilevers. The AFM technique, however, owes its existence to the preceding development of the surface imaging technique of scanning tunnelling microscopy (STM). STM was developed in 1982 by Heinrich Rohrer and Gerd K. Binnig, scientists at IBM's Zurich Research

Laboratory in Switzerland3. Four years later they were awarded the Nobel Prize in

Physics for their work in developing STM. Although these researchers were credited for discovering STM, it should be noted that Russell Young at the

National Bureau of Standards in Washington D.C. proposed the essentials of

STM as far back as 1966. Young published a paper describing the basic design for such an instrument, which he termed the topografiner.4

In 1986 Gerd Binnig, Calvin Quate, and Christoph Gerber developed the first AFM by merging STM with stylus profilometry (SP).5 Although SP had been shown to be applicable to insulating materials it only attained limited lateral resolution. The advantage of AFM is that it provides reasonably accurate 3-dimensional images from the urn to sub-nm range. This technique thus allowed for the imaging of

2 insulating materials under ambient conditions at high resolution. The method was

initially applied to the imaging of ceramics (AI2O3) using a diamond-tipped gold foil

microcantilever. 1 A vertical and 30 A lateral resolution were reported in this

example.5 The detection scheme of the first AFM consisted of an STM probe that

measured the deflections of the gold microcantilever probe. Further

advancements in detection methods and improvements in tip preparation

eventually allowed for the topographical imaging of surfaces at the atomic scale

under room temperature conditions.6,7

The first batch-processed silicon oxide / silicon nitride microcantilevers were

fabricated by T. R. Albrecht, a graduate student in Quate's laboratory at Stanford

University in 1990.8 The microfabrication technique was designed to quickly and

easily produce AFM tips with a sharp tip, a low force constant, and a high

mechanical resonance frequency. The advancements in microfabrication

processes has since allowed AFM to be a commonly used technique in surface

science.

Microcantilevers are common tools used in fields as diverse as surface science and biosensors,9"13 mass sensors,13,14 calorimeters,15 and radiation detectors.16,

17 Before delving into the various types of applications using microcantilever

measurements it is necessary to describe what a cantilever consists of and what the forces acting on a cantilever are. The definition of a cantilever is: "a projecting beam or member supported at only one end: as a: a bracket-shaped member

3 supporting a balcony or a cornice b: either of the two beams or trusses that

project from piers toward each other and that when joined directly or by a

suspended connecting member form a span of a cantilever bridge."18 Because

the beam is attached to the supporting structure, it forms a lever, converting the

loads into torque on the supporting mount. Cantilever designs allow for long

structures without external bracing. Figure 1 illustrates the operating principles of

a simple cantilever.

The extent of bending is dependent upon how elastic the beam is. Some of the

most commonly used cantilevers are the cantilevered wings of commercial

airplanes, cantilevered bridges such as the Quebec City bridge (which is the

a&f

Figure 1: The cantilevered beam (black) extends into space from the supporting structure (grey rectangle). The beam is anchored to the structure by a counterweight (grey rounded rectangle) which counteracts the force exerted on the cantilever (arrow). The star indicates the point of the torque on the supporting mount.

4 longest cantilever span in the world) and many household balconies. All of these function as extended beams tethered to a supporting structure. In principle, these adhere (in terms of their deflections) to the basic principles of Hooke's law, where

AL = -LCT (1.1) E

AL is the distance of extension, £ is the modulus of elasticity of the material, and a is the tensile stress. Microcantilevers however are subject to much smaller loads and forces than conventional cantilevers. The most common forces which must be resolved in cantilever applications are the upward and downward forces applied to the beam. However, torsional forces on microcantilever beams are also studied in experiments involving lateral force microscopy19,20 and micromechanical torque magnotemetry.21,22 In these experiments the twisting of the microcantilever beam is monitored. For the case of coated microcantilevers common terminology refers to a downward deflection of the beam as arising from compressive stress whereas an upward deflection of the microcantilever is described as a tensile stress. Although this may seem counterintuitive, the terminology refers to the overall forces exerted within the coating which cause the corresponding observed deflection. The measurement and calculation of these forces are described in Chapter 2.

5 Since the first report of the batch-process fabrication techniques by Albrecht et al. in 1990,8 microcantilever shapes and materials have evolved dramatically to encompass a diverse range of specific applications and specific needs. Silicon- based microcantilevers with an integrated piezoresistor have been fabricated with internal circuits capable of self-calibrating and transducing beam deflections, thus simplifying the detection method.23,24 Double beam microcantilevers, consisting of one piezoresistive microcantilever and one simple springboard microcantilever are linked via a transmitter. This design minimizes thermal drift due to the resistive nature of the detection method. V-shaped microcantilevers have been designed to minimize torsion and maintain low spring constants. Figure 2 illustrates some of the types of microcantilevers that have been developed. Those displayed in Figure 2a and Figure 2b are commercially available in various formats, sizes, and more importantly, differing spring constants. The microcantilevers shown in Figure 2c are temperature auto-correcting microcantilevers developed by J.L. Corbeil et al. Coated microcantilevers are usually prone to thermal drift due to the bimetallic effect.15,25 However the inner legs of the microcantilever compensate for any thermal drift created in the outer legs thus improving the thermal stability of the system.

6 Finally the microcantilever array shown in Figure 2d were developed by the IBM

Zurich group and has been coined the artificial nose. By coating each microcantilever with a different responsive layer and monitoring the microcantilever responses to specific analytes using a multiplexed laser source, it is envisioned that a neural network analysis could determine the presence and concentration of various analytes in complex solutions.

Figure 2: a) Veeco Instruments Inc tipless SPM probes NP series, b) Veeco Instruments Inc. calibration SPM probes, CLFC series, c) "Self-Leveling" microcantilever developed by J.L. Corbeil et al. d) IBM Zurich cantilever group artificial nose.

7 1.2 Modes of Microcantilever Stress

There are two distinct stress modes that contribute to microcantilever deflection.

In the initial state, assuming that all forces on the microcantilever surfaces are equal, the beam will attain a stable and equilibrium position. When a perturbation occurs resulting in the compaction of the atoms or molecules on the top surface of the beam, then the microcantilever will deflect downward to compensate for the increased proximity of the surface atoms or molecules. This observed deflection is referred to as a compressive stress.

JliillliiiiiiiilllTO Perturbation resulting in compaction of top molecules.

Downward deflection of cantilever beam

Figure 3: Illustration of the compressive stress resulting in a downward deflection of a microcantilever. The perturbation causes the top surface molecules to increase in volume. The resulting compaction of the molecules causes the microcantilever to deflect downward to compensate for this compaction of the top-surface molecules.

8 Similarly, a perturbation resulting in the decrease in volume of each of the atoms or molecules on the top surface will result in an upward deflection to compensate for the void volume created. This is referred to tensile stress. It is important to note that compressive and tensile stresses are relative to a specific microcantilever surface. Therefore, if the bottom surface of the microcantilever is responding to the perturbations, then the tensile and compressive stresses will produce opposite deflection directions. Figure 3 illustrates the effect of compressive stress (topside) on a microcantilever. The initial perturbation in this case causes the top-surface molecules to increase in volume (swell). This change causes the microcantilever to deflect away from the top surface to compensate for the higher compaction of the surface atoms or molecules.

1.3 Microcantilever Deflection Detection Schemes

Several different microcantilever deflection detection methods have been demonstrated, each having advantages and disadvantages. Under certain circumstances, it is impossible to bring any instruments in proximity to the microcantilever, either because the microcantilevers are mounted in a space- limited vacuum chamber or because the medium surrounding the microcantilever must remain uncontaminated and physically unperturbed. In either situation, the microcantilever detection method must perform the measurement either from within the microcantilever or from a distance. In other situations, the microcantilever surroundings are unhindered and it is thus possible to bring an optical fibre or an STM tip within proximity to the microcantilever. Although optical

9 deflection of a focused laser on the microcantilever is generally considered the

simplest detection method, some requirements limit its applicability. The

microcantilever must have a reflective surface and the surrounding medium must

be transparent to the laser wavelength. The following is a summary of some of

the common microcantilever deflection detection methods:

Laser Beam Deflection: This is the most commonly utilized and regularly

implemented detection technique in AFM setups. The method consists of

reflecting a laser beam off the tip of the microcantilever and measuring the

change in position of the reflected beam as the microcantilever is deflecting. (See

Figure 16 for a schematic of the laser beam deflection setup.) The method is

highly sensitive and versatile. With 4-quadrant photodetectors, the reflected beam

position can be monitored in a 2-dimensional plane. This makes the determination

of both the microcantilever normal deflection and torsional deflection possible.

The twisting of the microcantilever is commonly utilized in frictional force

microscopy and lateral force microscopy. However, most other detection methods

cannot monitor microcantilever twisting. Laser beam deflection is also a method of choice because the optical components can be set up at a distance from the

microcantilever. Therefore beam alignment can be performed without the risk of accidentally contacting the microcantilever. The optical components can also be kept outside of the microcantilever environment by using optical windows, thus minimizing contamination risks. Finally, the optical components of this detection method are inexpensive and commercially available. There are however several

10 disadvantages with this method. The surrounding medium must be transparent at the laser wavelength. The microcantilevers must be coated with a reflective film such as Au or Al. In certain sensing experiments, this may not be possible.

Finally, laser alignment and calibration is time consuming and can lead to errors if not performed properly.

Embedded Piezoresistance: This technique has been of limited application but nonetheless has certain advantages. The microcantilevers are microfabricated with integrated circuits and piezoelectric materials. When an ac current is applied,

Figure 4: Piezoelectric cantilever microfabricated on a silicon wafer. Side illustration of the cantilever demonstrates the numerous layers. The cantilever consists of silicon, silicon oxide, gold, chromium, titanium platinum, and a piezoelectric ceramic layer. Figures adapted from C. Lee et. al.1

the microcantilever oscillates at a specific frequency. When the microcantilever approaches a surface, the oscillations are dampened and the piezoelectric output current changes. These microcantilevers have the advantage that when they are produced in a batch process, they will have the same properties and as such calibration and force calculations are trivial after initial characterization. There is

11 no alignment required and changing the microcantilevers simply requires a

reconnection. The measurements can be performed in many types of media and

environments including optically opaque liquids, closed chambers, and

radioactive situations. However, the microcantilevers are complex and must be

prepared in a state-of-the-art microfab facility. The cost of design and fabrication

are thus quite high. In addition, the microcantilevers may be susceptible to

contamination or etching since they consist of advanced layered materials. The

piezoelectric microcantilever shown in Figure 4 consists of 6 different layers.

Optical Interferometry: Optical interferometry is a relatively simple detection

scheme. A coherent single wavelength light source is focused onto the end of the

50/50 Splitter

Single mode optical fibre X~> srgnt -filer Diode

Figure 5: Interferometer setup for microcantilever deflection detection. The interference between the outbound coherent beam and the reflected beam produces an oscillating intensity output at the 50/50 splitter. The microcantilever deflects A/2 nm per period of the intensity output.

12 microcantilever using a proximal single-mode optical fibre that has been divided into two with a 50/50 splitter. The beam reflects off the microcantilever and re enters the optical fibre. As the microcantilever deflects, interference between the incoming and outgoing beams is created. This results in oscillations of the measured intensity at the 50/50 splitter. Therefore, when a wavelength A is being utilized, then the measured oscillating intensity travels one full cycle when the microcantilever has deflected a multiple of A/2 or when the optical path difference is an integral multiple of the wavelength. This detection scheme is illustrated in

Figure 5. By choosing shorter wavelengths the sensitivity of the technique is thus increased. There are nonetheless several problems with this technique. The optical fibre must be positioned within a few microns of the microcantilever tip.

This poses many challenges. Micropositioners must be mounted near the microcantilever, the optical fiber is exposed to the media surrounding the microcantilever, and the medium must be transparent to the laser wavelength of choice. Designing a liquid cell with the following detection scheme poses further challenges. The optical fibre must be accurately positioned within a small volume of liquid. Furthermore, the risk of contacting the microcantilever with the fibre is significant.

Parallel plate capacitor: This technique utilizes the microcantilever as one of the electrodes in a parallel plate capacitor setup. The calibration and measurement are rather simple, considering all measuring components are integrated within the microcantilever and base. However, the microcantilevers are not commercially

13 available and fabricating the microcantilevers requires a sophisticated microfabrication facility. The setup can be quite small and convenient.26,27

However, applying this technique to solution-state sensing is rather complex.

Introducing solution between the two parallel plate capacitors will greatly affect the capacitance and this will complicate the results.

STM: The scanning tunnelling microscope was one of the first cantilever detection methods put to use for microcantilevers. In the development of the first AFM,

Binnig et al. used an STM probe to monitor the motion of a microcantilever scanning over insulating ceramics.5 This development allowed for the topographical imaging of insulating surfaces at the atomic scale. Although the technique is very sensitive, it was proposed that with appropriate cooling, forces below 10"18N, the method requires sophisticated instrumentation and electronics.

STM requires precision positioning of the probe and a constant medium dielectric.

Because a potential is applied between the STM probe and the microcantilever, applying this technique to solution states is extremely complicated. Solution temperature, analytes, and salts can all affect the measured potential and produce erroneous results.

14 1.4 Fabrication of Microcantilevers

Microfabrication techniques have evolved with time through multiple iterations in consideration of specific experimental requirements. Nonetheless, the basic fabrication principles have remained the same while modifying the procedures to batch processing. Experimental limitations such as the force constant, the resonant frequency, the mechanical Q factor, the torsional stiffness, the microcantilever length, and the requirement of a tip or not will alter the fabrication process to a certain extent.8,28 Commercial microcantilevers are produced on Si

(100) wafers using photolithography techniques, thus allowing the formation of several hundred on each wafer. A clean Si wafer is first covered on both sides

29 with a film of either thermally grown Si02 or (a&P)-SJ3N4 grown by low-pressure chemical vapour deposition (LPCVD), to a controlled thickness. The thickness of the Si02 or Si3N4 film dictates the thickness of the microcantilever. This film is then photolithographically patterned. HF acid is used to pattern the Si02 films and reactive ion etching is used to pattern the Si3N4 films. Once the microcantilevers have been patterned, the excess Si is etched away to free the microcantilevers with ethylenediamine/pyrocatechol/water (EDP). This selectively etches Si rapidly in the <100> direction but etches Si slowly in the <111> direction. As a result, regions bound by Si (111) crystal planes remain intact. KOH-based etchants can replace EDP in the case of Si3N4 microcantilevers. The microcantilevers are then coated with a metal film if required. Figure 6 illustrates the fabrication steps in the production of Si3N4 microcantilevers.

15 js/tm/M&gv-

Low Pressure Chemical Vapour Deposition

Lithographic patterning & Reactive Ion Etching

plane

Figure 6: Fabrication steps for the manufacture of Si3N4 microcantilevers. A clean Si (100) wafer is first coated with a Si3N4 layer by LPCVD. The Si3N4 film is then lithographically patterned and selectively etched by reactive ion etching. The Si wafer is then etched to free the cantilevers. KOH-based etchants selectively etch through Si (100) planes but effectively stop at Si (111) planes.

1.5 Microcantilever Applications

Microcantilevers have now been adopted in numerous technologies and applications. As such, several commercial sources are now available for purchasing a wide variety of microcantilevers. Companies such as Protiveris,

16 Veeco, and ThermoMicroscopes provide microcantilevers for various applications

and specific uses. Several groups, such as the IBM Zurich group, are using in-

house microfabrication facilities to design microcantilevers with unique

characteristics and microcantilever arrays. Microcantilevers of almost all shapes,

sizes, and physical properties can be produced with access to microfabrication

facilities.

Microcantilever technology has advanced to its current state because of its wide

applicability and progress in semiconductor devices and technologies.

Microcantilevers are now used in commercial atomic force microscopes, scanning

tunnelling microscopes, lateral and friction force microscopes, and magnetic force

microscopes. In essence, all surface probe microscopes utilise some form of

microcantilever to image the surface. However, each technique requires a unique

microcantilever to transduce the surface topology of interest. For example,

magnetic force microscopy incorporates basic principles of AFM and MRI

imaging.30 The microcantilever is modified with a magnetic tip, thus allowing for

the detection of nuclear and electronic spins on surfaces.31 Other uses of

microcantilevers include mass sensors,13 calorimeters,15 charged particle

detectors,17 and thermocouples.25 Whatever the use, microcantilevers are widely

used in surface science and the techniques for fabricating them are continually evolving. In addition, microcantilevers are becoming applied more commonly to the fields of sensors, whether it be for biological samples or dangerous compounds. Several groups are pursuing the possibility of utilizing

17 microcantilevers as sensitive, portable, and inexpensive analytical devices. For

example, Pinnauduwage et al. recently demonstrated the application of

microcantilevers to the detection of air-borne explosive compounds.32 In addition,

several groups have introduced microcantilevers in the detection of DNA

hybridization experiments.10,33,34 Despite numerous attempts to further apply

microcantilevers to more specific areas, several challenges persist. These are

discussed in the Introduction of Chapter 4.

1.6 Alkylthiolate Self-Assembled Monolayers (SAMs) on Gold

Some of the pioneering self-assembly processes were initially observed as early

as 1946. Zisman and co-workers35 studied the self-assembly of surfactants from

solution onto various metallic and non-metallic substrates resulting in well-

ordered, close-packed monolayers. It was recognized that in order for monolayer

self-assembly to occur, several conditions had to be fulfilled by the candidate

molecule. First, the molecule has to be rod-shaped. Secondly, the molecule

needs to be polar on one end and non-polar on the other.35 Finally, the presence

of van der Waals interactions between neighbouring molecules was noted to be

necessary for higher ordering of the monolayer.36 Important work by Nuzzo and

Allara37 led to the broad application and implementation of alkylthiolate SAMs.

Although they did not understand the nature of the bond at the time, they demonstrated that gold surfaces can easily be functionalized with various

18 disulfides by "spontaneous" self-assembly. In 1992 Alves et al. obtained the first

AFM images of alkylthiolate SAMs on Au(111) under ambient conditions.38

Although it was impossible to determine the exact structure of the alkylthiolate

SAMs, they did confirm the hexagonal periodicity that had been previously observed by diffraction and STM studies. Since then, STM and diffraction experiments have elucidated the exact structure that alkylthiolate molecules adopt; a commensurate fV3xV3) R30° lattice configuration on gold (111) crystal planes.39"42 Several different substrates can be utilized for the formation of SAMs.

However, gold is generally considered to be best and is thus often the standard.

In specific circumstances gold may not however be the metal of choice onto which to prepare SAMs, however, its physical properties make it highly advantageous. Firstly, gold does not oxidize in the presence of O2 under ambient conditions nor does it react with most reagents. This makes it a suitable substrate for preparing samples in dirty conditions, or non-UHV conditions. Secondly, gold is extensively utilized in techniques such as surface plasmon resonance spectroscopy, quartz crystal microbalance, ellipsometry, and photon polarization modulation infrared reflection absorption spectroscopy,43'44 thus enabling the precise characterisation of prepared SAMs. Thirdly, gold substrates can be either prepared or purchased rather inexpensively. Thin films of gold are readily deposited onto various substrates with known thickness, roughness, and crystal grain size by several different techniques such as thermal evaporation, sputter coating, or electrochemical deposition. Masks can be used with these techniques

19 in order to obtain more complex and patterned surfaces. Fourthly, the Au/thiolate bond is, as described later, quite strong and therefore simplifies the process for preparing SAMs on Au substrates. The alkylthiol molecules will remove contaminating molecules physically adsorbed onto the Au surface.45 Finally, bulk gold is non-toxic. Although certain functionalized Au NPs have been shown to be toxic due to their strong interaction with the lipid bilayer,46 bulk Au is not47 and is therefore appropriate for biological studies.

Figure 7 illustrates the lattice structure for an alkylthiolate SAM on a gold substrate. Note however that due to the alkyl chain tilt and rotation about the alkyl chain axis, a larger superlattice is generated with a c(4x2) structure. This is highlighted by the blue rhombus in Figure 7. Similarly, an equivalent 2^3 x3 unit cell is highlighted by the red square in Figure 7.

20 •Jf

k/3a

Figure 7: Lattice structure of a thiolate SAM on a gold (111) crystal plane. Gold atoms are represented by yellow spheres, actual diameter, a = 2.88 A. Sulfur atoms are represented with green spheres and the larger translucent green discs represent the approximate alkyl chain surface area assuming the chains are normal to the surface. Equivalent superlattices c(4x2) and 2v3 x 3 resulting from the chain tilting are illustrated by the blue rhombus and red rectangle respectively.

21 For a fully covered SAM consisting of n-alkylthiolates on gold in the lowest energy state, the chains adopt a linear, all-trans conformation. A chain tilt increases lateral van der Waals interactions and thus minimizes the free energy of the organic layer. Tilt angles of the alkyl chains are defined as a, the angle defined by the chain axis and the surface normal. Similarly chain rotation about the molecular long axis is defined by the angle p. These integral structural properties influence the SAM's interfacial energy, wetting properties, and permeability. Tilt angles vary with the molecular structure of the self-assembling molecule, the surface crystallinity, and the choice of the metal substrate. SAMs on Au(111) substrates generally adopt a 30° tilt angle(a) with a 50° rotation angle(P) about the long axis.48 n-alkylthiols on Au(100) have been shown to have smaller tilt angles, a = 14°, but larger rotation angles, p ~ 70°.42 In the case of bulkier and larger molecules where steric hindrance is relevant (such as p-biphenylthiols and p-terphenylthiols) the resulting SAMs have smaller tilt angles.45 Ultimately the conformation of the resulting SAM will depend on numerous factors including the substrate of choice, the substrate crystal plane, the number of methylene units comprising the alkylthiolate, and the terminal group of the alkylthiolate. Therefore it is important to consider the influence of these factors on the final SAM when selecting a SAM-substrate system for a specific application.

22 The Gold-Thiolate Bond

The gold thiolate bond resulting from the adsorption of alkylthiols onto gold substrates has been extensively studied with several techniques. However a complete understanding of the nature of the bond remains elusive. The results from the multitude of studies have not converged into one concise description.

Depending on the technique utilized, whether performed in vacuum or in solution, the results vary significantly due to the contributions from heats of dissolution of the adsorbate. The bond energies obtained from UHV studies are generally accepted as the most accurate representation of the true Au-S bond energy and lie somewhere between 40-50 kcal mol"1.45,49 This relatively strong bond can nonetheless be broken by the recombinative desorption of disulfides from the surface. This phenomenon has also been studied to estimate the Au-S bond energy. Dubois et al. observed that dimethyl disulfide has a binding energy of 28 kcal mol"1 while that of methanethiol is closer to 14 kcal mol"1.50 These values illustrate the variability in observed bond energies using various techniques. The process by which SAMs form on gold has also been the subject of dispute.51

Systems produced from solution phase adsorption are complex and are commonly reported to follow a Langmuir-type adsorption model. Nonetheless, the progression from physisorption to chemisorption and to an eventual organized

SAM structure is assumed to progress as described for gas-phase adsorption models. Gas-phase SAM formation on Au(111) proceeds through several intermediate structures before culminating in the final tightly packed c(4x2) superlattice.52

23 Figure 8: Illustration of the stripped, low-density phase observed for a tetradecanethiol SAM (0«6.6xlO'10 mol/cm2). The alkylthiolates' molecular axes are oriented along the plane of the Au substrate to produce a stable intermediate state. Although this phase consists of low surface coverage, there remains a high degree of correlation between the sulphur tethers.

Alkylthiols initially adsorb onto the surface in a low density striped formation. In this configuration, the alkyl chains lie parallel to the Au substrate as illustrated in

Figure 8. This phase is corroborated by the telltale striped phase observed in

STM images.53 This state is further supported by temperature-programmed SAM

24 desorption measurements. For example, hexanethiol SAMs show two distinct desorption peaks from Au (111) substrates. The first occurs at 305 K while the second occurs at 480 K.54 The peaks have been assigned respectively as the physisorption and chemisorption enthalpies of the SAM. As the alkane chain length is increased, the physisorption energy is observed to increase linearly with the number of carbon atoms.54 Likewise, temperature-programmed desorption measurements demonstrated the physisorption contribution of each methylene unit is ca. 1.5 kcal/mol, that of the terminal methyl groups is 3.7 kcal/mol, and that of the alkylthiol moiety is ca. 8.0 kcal/mol.55

Eventually the c(4x2) superlattice of the SAM, a commensurate solid upright phase, nucleates and grows over the whole substrate. This process involves the increase in the thiol concentration on the surface, conformational changes for the chains from parallel to perpendicular with respect to the surface, and the progression of the metal/thiol bond from physisorbed to chemisorbed via a likely recombinative desorption of H2. The final SAM, although of high density and in a commensurate state, nonetheless consists of many defect sites. Several factors will influence both the extent of SAM uniformity and density. For simple alkylthiolate SAMs, the defect sites will generally originate in the underlying substrate. Step edges, metal film impurities, vacancy islands56 and crystal boundary edges will all result in SAM structure defects. Etch pits also occur due to unknown processes. These are observed as depressions in the SAM film within the terrace areas of the Au (111) substrate. The occurrence of these etch pits has

25 been proposed to be the result of either the dissolution or reconstruction of the Au during thiol adsorption.57 In addition, surface impurities along with SAM crystal edges will produce defects in the c(4x2) superlattice. SAM tilt boundaries and rotational boundaries will generate further disorder in the overall SAM structure.

SAM domain sizes and dispersions have been characterised by He diffraction or

STM imaging.40'58'59

Nonetheless, alkylthiolates self-assemble onto clean gold substrates to produce high quality and reproducible monolayers. Figure 9 illustrates the process by which alkylthiolates are thought to proceed from the physisorbed state to the dense, commensurate chemisorbed state on Au substrates.

Another point of uncertainty concerning alkylthiolate SAMs is the fate of the hydrogen atom during SAM formation. Brust et. al. reported that the hydrogen remains at the gold SAM interface and supported these claims by proton NMR studies of thiol-capped nanoparticles.60 Yates et. al. demonstrated that methanethiol adsorbs to Ag(110) substrates without scission of the S-H bond at room temperature.61 However, it has been shown by temperature-programmed desorption that for longer alkyl chain SAMs the molecules desorb as disulfides,62 thus suggesting that the hydrogen was dissociated in the initial adsorption process. In room temperature experiments, it has been suggested that the hydrogen is removed by either reductive elimination of H2 from the surface, or oxidative conversion to water by dissolved oxygen.45 Therefore it seems most

26 likely that the organic monolayer consists of alkylthiolate molecules for which the hydrogen from the precursor thiol moiety has been desorbed from the surface.

SAMs with Terminal Groups

Thiols with co-functional groups can also form SAMs and their ability to modulate the physiochemical properties of the monolayer is what renders them so interesting for biological and sensing applications. The structure, size, and chemical properties of the functional group will also influence the SAM/Au interaction. In addition to the interchain van der Waals interactions, terminal functional groups can also provide for increased stability by modulating the interfacial properties. Likewise, bulky functional groups can also interfere with

SAM formation, or produce low density SAMs.

27 4^0^^^00: $*!/&&•&&:& &f jii^!i#^lisPN6#sNNj>

I A************ iti«tti«ii*-H***v **»*»*3**»i*?*r SH-HHM*-*** #***i****«*»*s*5r' ^*t*»*r***«*rK /******»***»*f

1 wj*t*t*«*rt, j*?***!*?!* /***»*5>**%^ ^HHHUH M-tHHHH*, *M»WI«V ?#•*•!*>*#»»»*•?> <>)iit)iitW(VV *j*»»»>>4ytf *t»t*r*(***

1 jnvn^Ji^

Figure 9: Schematic of tetradecanethiol SAM formation on gold substrate. The figure illustrates the various phases traversed towards the formation of a complete SAM. Initially the tetradecane thiolate molecules lie parallel to the surface and are highly disordered. As the density of the SAM increases, the chains become more ordered, form a striped pattern, and then eventually align into a commensurate c(4x2) superlattice with upright chains.

28 The sum of all the interactions, including that of the Au/thiolate bond, the interchain interactions, the inter-terminal group interactions, and the terminal group/solution interactions will dictate whether a commensurate or incommensurate SAM on Au substrates are thermodynamically stable. For example, 3, 6, 7, 10, 11-pentapentyloxytriphenylene-terminated SAMs have been prepared and characterised by Schronherr et. a/.63 It was observed that the large terminal group prevents the formation of a commensurate SAM and the resulting monolayer structure formed on gold is dictated by the packing of the bulky terminal groups.

Mixed SAMs, where the SAM consists of two unique thiol molecules with differing terminal groups will often form domains to varying extent depending on the SAM- forming conditions and concentrations.64 It is therefore necessary to evaluate the quality of the SAM when co-functionalised thiols are utilised to prepare SAMs. The packing densities, interfacial properties, and reactivity of the SAMs will be affected by the choice and arrangement of the terminal groups. Because both methyl and carboxylic acid-terminated SAMs are used extensively in this study, their electrochemical properties must be assessed to insure that these are suitable for sensor applications.

29 Alkylthiolate Exchange Reaction

When a SAM is immersed in solution containing different alkylthiols, an exchange reaction between the free alkylthiols in solution and the surface-bound molecules occurs. The rate of alkylthiolate exchange depends on several factors including the density of metal grain boundaries,65,66 SAM disorder,45, and chain length.67 All these parameters influence the rate and extent to which the place exchange reaction occurs. Figure 10 illustrates the process by which the exchange reaction proceeds for a C-u alkylthiolate SAM. The reaction proceeds until equilibrium is attained between the two different alkylthiols both on the Au substrate and in solution. The reaction kinetics have been investigated by various groups using a number of techniques.2,51 However a complete understanding of the kinetics for all systems remains open. For the preparation of double-sided microcantilevers, assembly of the second SAM must proceed without removing the previously assembled SAM. This can be achieved by minimizing the incubation time and applying an electrochemical potential to the substrate favouring monolayer assembly.68 Allowing the assembly process to proceed over extended periods of time will favour thiol exchange and will result in almost complete replacement of the original SAM. This would result in identical SAMs on both the top and bottom surfaces of the microcantilever and render it dysfunctional. The thiol exchange process is of particular importance for this work and is carefully considered in the preparation of the microcantilevers in Chapter 4.

30 Figure 10: Schematic of the place exchange reaction for a Ci4S-Au SAM in a 16- mercaptohexadecanoic acid solution. Oxygen atoms are represented with red spheres. Initially place exchange occurs predominantly at surface defects and subsequently occurs at the planar sites until an equilibrium is reached between the surface-bound thiolates and the solution nhase thiols.2

31 1.7 Thesis Objectives:

The foregoing Thesis explores SAM-functionalized microcantilevers applied to sensor "technologies". By "technology", we mean well-developed and well- understood structures that can be used as tools. This thesis critically examines the state of understanding of the SAM properties and microcantilever responses, and concludes that these are still research problems and not yet technologies.

Some outstanding issues that are evident from the literature even during the execution of this work include:

1. SAM desorption from the substrate69

2. SAM composition, rearrangement, and crystallinity45

3. SAM dynamics and stability51

4. Microcantilever drift/hysteresis70

5. Microcantilever response times71

6. Microcantilever response reproducibility71,72

7. Origin of the microcantilever response73

All sensors require some form of transduction mechanism. Within the realm of chemical reactivity, carboxylic acid (de)protonation reactions are relatively well understood. For this reason, carboxylic acid-terminated SAMs are employed here as chemical transducers of pH changes in solution. The foregoing work describes methodologies for preparing microcantilever sensors with pH responsive SAMs on one surface and non-responsive SAMs on the other surface. The goal here is not to develop a novel pH sensor, but rather to further understand the issues

32 involved in such complex sensor systems. The application of these "technologies" is already being suggested as possible sensors for explosive material detection.74,

75 Because of the significant variability in the published microcantilever sensor responses, we consider the detailed study of the microcantilever architecture,

SAM selection, and chemical response to "simple" chemical stimuli to be essential. An understanding of the various underlying phenomena affecting the response is required to further perfect the microcantilever-based solution sensor.

We thus propose and fabricate a design for a dual-sample liquid cell and improve on current microcantilevers to specifically control both the top and bottom surface chemistries. The stability of the SAMs under the experimental conditions is extensively studied. Electrochemical measurements are employed to determine whether the SAMs desorb and/or rearrange with phi changes. We characterise in detail the response of the microcantilevers to a "simple" chemical perturbation, i.e. change in solution pH. In doing so, we attempt to elucidate the cause of several outstanding issues associated with microcantilever sensors for solution applications. These are fundamental steps in understanding the microcantilever sensor capabilities and limitations.

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38 Chapter 2

Design, calibration, and fabrication of a dual sample liquid cell for use with doubly-coated silicon nitride microcantilevers 2.1 Introduction

At the commencement of this work, no commercial system existed for the simultaneous measurement of two microcantilever samples in close proximity in a liquid flow-through environment. Therefore, to test the feasibility of solution-based microcantilever sensors and assess their physical responses in detail, a novel experimental setup was required. Since then several start-up companies, for example Concentris, have developed commercial systems geared toward microcantilever sensors. However, the immaturity of these systems1 and their design for the broadest of applications with limited software control renders them unsuitable for these studies.

Several considerations were taken into account to optimize the microcantilever deflection measurements and solution flow-through capabilities. Firstly, the cell had to be designed such that the simultaneous measurement of both a reference and working microcantilever deflections could be performed. A simple microcantilever deflection measurement system had to be employed such that realignment with the new samples was trivial and accurate. A small solution volume would minimize differences in solution environments of the two microcantilevers. A system had to be employed to easily and repeatedly change the solution without disrupting the microcantilever deflection measurement system.

40 In addition, a new microcantilever architecture was designed to selectively control the reactivity of both microcantilever surfaces. In most microcantilever experiments, the backside chemistry of the microcantilevers is either ignored or assumed to be insignificant.2"4 Because of much evidence to the contrary,5,6 we have concluded that microcantilevers with controlled chemistries on both the top and bottom surfaces are necessary to produce with high precision and accuracy.

This Chapter describes the cell design, the choice of microcantilever architecture, the fabrication methodologies employed to assemble these, and the overall experimental setup along with the LabVIEW software employed in the development of this solution-based microcantilever sensor. The system is then tested as a whole and the microcantilever deflection measurements are calibrated.

2.2 Cell Setup

The experimental cell was designed over multiple iterations. Several basic requirements guided the design. Firstly, the cell design has to consist of an enclosed cavity with an input and an output port such that positive or negative fluid pressure at either port would create a flow through the cell. The cell has to hold at least two microcantilevers in close proximity in a minimum volume. This condition permits for the possibility of running a blank sample during any experiment while ensuring that both microcantilevers are subject to the same chemical environment. Cell design must allow for optical access to both

41 microcantilever tips. In order to achieve this, the cell is designed with two windows, allowing for dual laser-based microcantilever deflection detection.

Moreover, the cell has to allow for two laser-based microcantilever deflection detection systems in close proximity so that one can monitor both the blank and the sensor microcantilever. The cell also needs to be easily disassembled to access and replace the microcantilevers. Microcantilever clamps were also necessary inside the cell to hold the substrates in position. Finally, the whole cell has to be constructed from an inert material to minimize chemical leaching and minimize impurity contamination. These stringent requirements complicate the cell design process and limit the choice of construction material.

The final cell design consisted of a polychlorotrifluoroethylene (PCTFE) composition with two optical windows on opposite faces of the cell. Like polytetrafluoroethylene (PTFE), PCTFE is a fluorocarbon-based polymer that is highly chemically resistant. However, PCTFE, has better mechanical properties and is more suitable for machining purposes than PTFE. The extra tensile and compressive strength allow it to be machined into smaller components such as screw threads or small substrate clamps. In addition, PCTFE has great chemical resistance, low moisture absorption, and a broad (0-14) pH resistance.7

The internal microcantilever clamps were constructed from PCTFE blocks and fastened with commercially available polyetheretherketone (PEEK) screws. Like

42 PCTFE, PEEK has very good mechanical properties and is commonly employed in the production of inert screws.

The windows were constructed from 1 cm x 1 cm x 1 mm glass microscope slides

(Fisherbrand, plain). Microscope slides have low absorbance in the 634 nm wavelength range, are easily replaced when damaged and thus are highly suitable for cell windows. The input and output ports consisted of threaded holes in the PCTFE cell and commercially available PEEK HPLC fittings. These provide the seal necessary for the pressure changes when pumping solution through the cell while ensuring chemical inertness. The tubing to and from the cell was commercially available PTFE tubing with an outer diameter of 1/16 in. (Cole

Parmer, P/N: 6417-31 20SW). A positive displacement peristaltic pump (Amicon

LP-1 pump, model #: TCF2) was used to flow the solutions through the cell. This mechanical setup allows for a closed loop system without the possibility of any

Figure 11: Liquid cell made from PCTFE. a) Assembled cell b) Inner compartment of the cell c) input and output ports d) front window e) sample holder f) O-ring.

43 mechanical parts contaminating the solutions. Flow through the cell is maintained at a constant rate while either changing the solution or spiking it with an experimental solution. The cell design and components are illustrated in Figure

11.

2.3 Fiber Optic Laser Diode

The laser diode used for all experiments was a commercially available combined laser diode/ fiber optic / focusing lens. The module is produced by Lasiris™ and is model # PTL-635S-3-1.2mm-5cm. The class II laser diode has a wavelength of

635 nm with an output power of 3mW. However the laser power after the coupled fiber optic and focusing lens is ca. 1mW at full power. The laser output is focused

Figure 12: Lasiris™ pig-tail laser diode model# PTL-635-S-3-1.2mm- 5cm. The black housing contains the 635 nm laser diode, on/off switch, and modulating electronics. The pig-tail laser diode also features a yellow single mode fiber optic coupled with a terminating focusing lens. Image adapted from www.stockeryale.com

44 to a dot with a 30 urn diameter at a distance of 5 cm using an adjustable lens.

The lens is attached to the end of the fiber optic with a threaded metal cylinder.

Adjustments to the focal point can be made by repositioning the lens along the thread. Furthermore, the laser diode output can be modulated by applying a voltage to an input BNC connection. Although the laser output can be modulated up to a frequency of 10 kHz, the output of the laser diode was only modulated with a DC signal in the following experiments. The full output power of the diode was not required and the laser output was lowered. Figure 12 illustrates the pig tail laser diode used for the experiments.

2.4 Position Sensing Detectors

The position-sensing detectors (PSDs) were purchased from ON-TRAK Photonics

Inc. U.S.A. and consist of silicon photodiodes that output an analog current that is linearly related to the position of a light spot on the active area. The selected PSD

(model # 1L10) is a 1-dimensional sensor with an active area of 10.0 mm x 2.0 mm. The main advantage of using these sensors over 4-quadrant photodetectors typically employed in AFM microcantilever deflection measurements is that the

PSD is 1-dimensional and will ignore small off-axis variations of the impinging beam. The PSD consists of two biased electrodes separated by a photoresistive surface. The chip has a 14 pin connector, however, only 3 of the pins require connections for proper operation. Pin 1 is connected to the bias voltage while pins

7 and 14 are the two anodes to which current flows with respect to the spot position. The sensors are highly linear with nonlinear drifts of ca. 0.1%, thermal

45 drifts of 20 ppm/°C, and fast response times. Moreover, the position signal is independent of both the spot size and spot intensity. Therefore, small modulations of the laser beam intensity due to solution turbidity, absorption or scattering do not affect the measured spot position. The magnitude of the current output in

Incident Light

Figure 13: On-TRAK 1L10 position sensing detector and a schematic of its operation. Current flow in either electrode is proportional to the proximity of the light spot. Figure adapted from www.on-trak.com.

either of the two PSD electrodes is proportional to the proximity of the impinging beam centroid position. As the beam moves away from one of the terminal electrodes, the current output decreases and vice versa. The PSDs were mounted to the optical table with specially designed and constructed brackets such that the angle of the PSDs remains constant during repositioning. Figure 13 shows both a top view of the PSD active surface and an illustration of the PSD operation. In order to convert the PSD currents into voltages and interface the

PSDs to a computer, high precision current-to-voltage converters were utilized

(ON-TRAK Photonics).

46 2.5 Current-to-Voltage Converter

Two position sensing amplifiers (model # OT-301SL) were purchased from ON-

TRAK Photonics, Inc. to convert the output current from the PSDs into stable voltages. The two circuit boards were mounted in a grounding box and connected to the PSDs through 9-pin serial cables and to the LabVIEW breakout box via

BNC cables and connectors. The printed circuits control the constant bias voltage applied to the PSDs and provide 3 gain multipliers for single axis PSDs. The impinging beam position is calculated by the integrated circuit using the following equation:

X Position LzL. Yl+Y2 [2-1]

where XpOSition is the output voltage directly related to the beam centroid position,

Current-to-Voltage converter Subtraction amplifyer -AAA/ —AAA/

Yr 12V Bias Y1-Y2 Voltage -VW- XI ^_vw_ -AAA/-! Analog Divider -VW- I—WV- -AAAr- = J_i Emm H(— H(—

-AAA^- Yi 4> xt Y1 + Y2 Current-to-Voltage converter Summing amplifyer Figure 14: The op-amp feedback circuit from ON-TRAK Photonics Inc. for calculating the signal position independent of the fluxuations in the light spot intensity.

47 Y1 and Y2 are the two electrode currents, and L is the length of the detector's active area (10 mm in this case).

The electronics allow for further zeroing and calibration of the output voltages.

The output was adjusted such that full scale ranged between +10V to -10V for a total dynamic range of 20V over 10.0 mm.

2.6 Microcantilevers

The microcantilevers were purchased from Veeco Inc., (part# MSCT-NOHW) and have the dimensions listed in Table 1. The silicon nitride microcantilevers with no metal coating are prepared by a batch-wafer process. These are delivered in quantities of 250 on a single wafer. Prior to use, a select quantity of microcantilevers are clipped off the wafer and processed for cleaning and eventual metal deposition. Although the microcantilevers do have a tip, the tips were not utilized for any of the microcantilever-sensor experiments.

Figure 15: Schematic of triangular microcantilever and dimensional variables.

48 Table 1: Properties and dimensions of the triangular microcantilevers obtained from Veeco Inc.

Property Variable Value Length / 320 |Jm Leg Width w 22 ym Base Width b 225 |Jm Intermediate Length U 240 |Jm Sharpness Angle G 19.4° Thickness (uncoated) T 0.6 Mm Spring Constant (uncoated) K 0.01 Nm"1 Resonant Frequency Jres 7 kHz (uncoated)

2.7 Microcantilever Deflection

Microcantilever deflection was measured using a laser diode/PSD deflection

system. Optical interferometry, laser beam deflection, and piezoresistivity9 are

three of the techniques used for monitoring microcantilever deflections. The many

advantages of the laser beam deflection technique make it most suitable for this

application. It does not require unique microfabricated microcantilevers with

integrated circuits and the optical components are setup externally, thus simplifying alignment and assembly, while providing high deflection sensitivity.

Optical interferometry requires the precise repositioning of an optical fibre within proximity of a microcantilever in a closed cell. Although the technique is highly sensitive, the possibility of accidentally striking the microcantilever with the optical fiber and exposure of the optical components to the chemical environment make this technique non-ideal for this setup.

49 Cantilever

Fiber Optic Laser Diode Figure 16: Schematic of the cantilever deflection measurement setup. The laser light exits the yellow optical fibre and is focused onto the cantilever tip. The laser light is then reflected onto the PSD. Cantilever deflections, Az, result in a change in position of AS for the impinging laser centroid on the PSD. This diagram is not to scale.

When immobilized in a closed environment, microcantilevers attain an equilibrium position. However, they bend if the sum of all the forces acting upon the two surfaces is not equal to zero. For example, excess surface stress on either the top or the bottom surfaces of the microcantilever will cause it to deflect. This will

50 happen if the top and bottom surfaces of the microcantilever are coated differently and the medium surrounding the microcantilever is changed. The surface energy of both the top and bottom surfaces will change and this will result in a compensatory microcantilever deflection. Likewise, if either of the microcantilever faces is chemically functionalised to respond to specific analytes, or biomolecules, the microcantilever will bend as a result of the change in surface interactions when the compounds are introduced into the cell. The simplest way to induce a deflection in microcantilevers is to coat a single surface of a microcantilever with a metal film and modulate the temperature. Because of the different expansion coefficients of the metal film and microcantilever material, one of the two materials will expand more and produce a deflection. When using a laser deflection detection scheme, this bending will result in a change of angle of the beam reflected off the microcantilever tip. The microcantilever deflection, Az, must then be correlated to the change in the measured laser beam deflection, AS.

Figure 16 illustrates the measurement scheme along with the different variables influencing the calculated deflection, where / is the microcantilever beam length, L is the microcantilever to PSD distance, AS is the observed change in laser beam position on the PSD, and Az is the microcantilever deflection obtained through calculations.

51 Az

Figure 17: Schematic of the cantilever deflection to determine the angles of reflection and allow for the calculation of Az from known values L and 1 along with the measured PSD change AS. The red lines represent the laser beam and the black curve represents the cantilever. Note that this diagram is not to scale.

From Figure 17 it can be geometrically determined (while accounting for beam curvature) that for a bending microcantilever:

2-Az tan# = (2.1)

52 Similarly, for the laser deflection on the PSD,

tan 20 = — (2.2) L

The approximation that tan 0 « 6 for small angles of 9 and L»Az is used here.

Therefore the microcantilever deflection is

Az = (2.3) 41

2.8 Determining the Microcantilever Spring Constant

The method described by Sader10 was used to calculate the spring constant of rectangular and triangular microcantilevers. Uncoated microcantilevers have a specified spring constant along with a specified confidence interval. However, coating the microcantilevers with thin films of titanium, gold, and an alkylthiolate

SAM on both the top and bottom sides affects both the microcantilever thickness and stiffness. Assuming that the normal spring constant of the coated microcantilevers remains unchanged will result in significant error in the subsequent differential surface stress measurements. Therefore, in order to make precise force measurements a method must be utilized to assess the new spring constant of the coated microcantilevers. Several techniques are available for doing this. However a simple calibration is possible using the Sader method as

53 long as a rectangular reference microcantilever is available. Using the Sader method, it is possible to calculate the new spring constant and quality factor1 (Q) of freshly coated microcantilevers. Having obtained these values it is then possible to calculate the product of the microcantilever Young's modulus and thickness. Because the triangular microcantilevers used here are only one of many on a multi-cantilever chip, including a rectangular microcantilever, it is reasonable to assume that the thickness and elastic properties of all the microcantilevers on the same chip are equivalent. Having obtained the aforementioned product, the spring constant of the other triangular microcantilevers can then be back-calculated.

In order to determine the resonant frequency of the rectangular microcantilever a power spectrum of the microcantilever resonating in air must be acquired. This was performed using a Park Scientific Instrument AFM (AutoProbe CP). The spectrum obtained consists of the oscillation amplitude vs. microcantilever frequency plot. A sample spectrum is plotted in Figure 18.

1 The quality factor(Q) of a microcantilever is a measure of its oscillation frequency relative to the rate at which it dissipates its energy. In other words, it is the ratio of the microcantilever resonant frequency to the width at half maximum of the vibrational energy vs. frequency plot.11 This value is commonly used to ascertain microcantilever sensitivities in the dynamic mode.

54 _j 250- o Amplitud e / a . . 1 c 1 10°: Oscil l o

0- L^^ ,.-...r.,..,.,, , , , , , | , 1 I 1 J "t *'*'lJ -"T"— '" I ' ' ' ' 1 ' ' ' ' 1 10 15 20 25 Frequency / kHz

Figure 18: Microcantilever oscillation amplitude vs. frequency. A rectangular microcantilever 200 um long and 20 um wide was coated with 5 nm of Ti and 75 nm of Au. Frequency measurements were performed on an atomic force microscope (Park Scientific Instruments, AutoProbe CP).

Although small harmonic frequencies are usually observed along with random noise peaks, this spectrum is noise-free. The amplitude of the oscillation is then squared in order to obtain a power spectrum. The power spectrum is then fitted to a simple harmonic oscillator function with a white noise baseline included to determine both the Q factor and the resonant frequency of the microcantilever.

55 Equation (2.4) represents the simple harmonic oscillator function used.

' = 4**+ A'f r , (2-4)

where Avhiteis the white noise baseline, aires is the radial resonant frequency, and

Q is the quality factor of the fundamental peak. Figure 19 demonstrates the best curve fit of the simple harmonic oscillator for the above microcantilever. Once these components have been determined for the rectangular microcantilever, its normal spring constant, k, can be calculated using the Sader method.10,12 Note that this method assumes that the length of the microcantilever greatly exceeds its width, that the width greatly exceeds its thickness, and that the quality factor of the fundamental peak is much greater than unity. All three of the aforementioned conditions are met with rectangular microcantilevers obtained from Veeco Inc.

Equation (2.5) describes the relationship between the microcantilever spring constant, the quality factor, and the resonant frequency,

56 70 r, Z5 60

50-1 X CM CD T3 401 U Model: Simple Harmonic Oscillator "Q. lllK I E : Chi2/DoF = 14291860.36275 < 2 c 20-1 R = 0.97062 _g rrT T Ao = 46.35673 ± 7 A = -2411.77034 ±1970 'o 10-1 Q = 39.4 t 3 w ; W = 13825 ±6 O i „—j, 1 1 r •r" -i—i—i i 0 10 15 20 25 Frequency / kHz

Figure 19: Simple harmonic oscillator fit (red) on the power spectrum of the rectangular microcantilever (black). The fit is used to determine the quality factor, Q, for the fundamental peak and the resonant frequency, U)res of the microcantilever.

krecl =0.1906-p-wl, -lrecl .Q-at T{(cores) (2.5)

where krect is the rectangular microcantilever normal spring constant, p is the fluid

3 density, (air in this case, such that) p = \A8kg-m' , wrect and /rect are the

rectangular microcantilever width and length respectively, and /Y is the imaginary

part of the hydrodynamic function which is itself a function of the resonant

frequency and the Reynolds number, Re;

57 p • co -w2 r ^res re (2.6) At]

Where r\ is the viscosity of the surrounding medium, air in this case (rp 1.86x10 kg m"1 s"1). The full hydrodynamic function for microcantilevers is described in detail by Sader.10 The spring constant of the rectangular microcantilever with its power spectrum illustrated in Figure 19 was calculated to be 0.033 N-m"1 using equation (2.5). This is ca. 64% higher than the normal spring constant of the uncoated rectangular microcantilever.

Once the spring constant for the rectangular microcantilever has been calculated, the product of Young's modulus, E, and the microcantilever thickness, f, can be calculated from the following equation;

£-'3=^,-— (2-7) w reel

Continuing with the same rectangular microcantilever, the product of Young's modulus and thickness is equal to 5.3x10"8 N-m. This product is constant for all microcantilevers on the chip, including the triangular microcantilevers. Therefore, it is now possible to calculate the normal spring constant of the triangular microcantilevers. Sader shows that the normal spring constant of triangular microcantilevers using the parallel beam approximation is dictated by:

58 E-t3-w — • cos 0 K- 3 (2.8) 4w 2-/ \+ 3 -(3-cos<9 2)

Where Ef3 is the product calculated above using the rectangular microcantilever, w and / are respectively the beam width and length of the triangular microcantilever, b is the base width, and 6 is the tip sharpness angle. Hence it is possible to determine the spring constant of all triangular microcantilevers using the planar dimensions and the known or measured values of the product of

Young's modulus and thickness. The spring constant for the triangular microcantilevers used in the subsequent experiments is calculated as 0.0140

13 NTTI"1 or a ca. 40% increase in the normal spring constant. Sader et a/. recently demonstrated a scaling law for the stiffness of microcantilevers coated with gold films in a viscous fluid. According to these results, triangular microcantilevers with the specified dimensions have a ca. 39% increase in the normal spring constant when coated with gold films of 150 nm. This is in excellent agreement with the change in normal spring constant of the triangular microcantilevers determined here.

2.9 Calculation of Differential Surface Stress

The differential surface stress of the bent microcantilever is calculated from a modified form of Stoney's equation.14 In its new form, the only parameters required are the microcantilever geometry, spring constant, and Poisson's ratio.

Assuming that the energy stored in the deflected microcantilever is a direct result

59 of surface stress, then the surface stress can be calculated if the microcantilever spring constant is known. Section 2.8 describes in detail the steps required for measuring and calculating the spring constant of coated microcantilevers. The potential energy, Ek, stored in a bent microcantilever is thus equal to:

2 Ek=-l.k-Az (2.9) k 3 2

where the 4/3 term corrects for the bending moment being evenly distributed over the whole surface of the microcantilever whereas Hooke's law assumes a concentrated point force at the tip of the microcantilever. Similarly, the strain energy stored in a deflected microcantilever can be calculated from its elastic properties, the bending moment, and the effective Young's modulus, The elastic energy stored is calculated with the following equation:15

_ :MfJV/jf ''Elastic -l^y]2YI P-10)

where M is the bending moment, / is the area moment of inertia, and Y is the effective modulus in isotropic elasticity and is related to Young's modulus by:16

60 Y = - (2.11) l-v

where E is Young's modulus and v is Poisson's ratio for the microcantilever. The differential equation relating the radius of curvature of the microcantilever, R, to the area moment of inertia and the effective modulus in isotropic elasticity is used for substitution into equation (2.10).

2 d z 1 M (2.12) dy2 R Y-I

In addition, the bending moments of the microcantilevers, Mrect and MA for the rectangular and triangular microcantilevers respectively, are also substituted into equation (2.10).16

AaJVt Mrec, = (2.13)

AaWt for 0 < y < lx

MA = Ao-tb(l-y) (2.14) for l < y < I 21 x

61 Integrating the new form of equation (2.10) and equating it to equation (2.9) we obtain the following equation for the differential surface stress of a bent microcantilever.

A.J^V^L^ (2.15) 3 Wtl,+—(l-L)2

where /CA is the spring constant of the microcantilever calculated in Section 2.8,

Az is the microcantilever deflection, and W, t, h, I, and b are the geometrical dimensions of the microcantilever listed in Table 1. This method of calculating the microcantilever differential surface stress results in a maximum error of 4-7%.14

2.10 Metal Film Deposition

Both the titanium adhesive layers and the gold metal films were deposited by argon-ion sputtering using an Edwards Auto 306 DC sputter coater instrument.

The technique, initially coined spluttering by Sir J. J. Thomson17 and then renamed sputtering by I. Langmuirand K. H. Kingdon18 in the early 1920's, consists in the high-energy bombardment of solid targets with atoms, ions, or molecules to eject atoms from the targets and deposit films onto the substrate. In the following experiments, Ar-ion DC sputtering was used to produce the Ti and

Au films on the microcantilevers. In this case, Ar ions are accelerated within the plasma to the desired kinetic energy with an electric field. The process of atom

62 ejection from the target surface has been likened to a 3-dimensional "billiard game" with atoms replacing the ivory balls.19 As such, the ejection of atoms from a flat metal surface with normal Ar-ion impingement requires a sequence of binary collisions for the momentum vector of the ejected atoms to change by more than

90°. Studies of the ejected particles on Cu(100) targets by Ar-ion sputtering concluded that 99% of the ejected species were either Cu or CU2.19 Approximately

1% of the ejected species were charged. This technique produces films that are essentially indistinguishable from films deposited by other methods.

The system used to prepare the Au and Ti films is thus described. The target holders consist of magnetrons containing permanent magnets forming a toroidal magnetic field to focus the plasma beam between the target and substrates and to increase the ionization efficiency of the ejected electrons. Metal film deposition rates and thicknesses are monitored by a quartz crystal microbalance. The microcantilever substrates are mounted within the deposition chamber onto a water-cooled stage at a distance of ca. 25 cm from the target. Dimensions of the disc-shaped titanium target are 4 cm in diameter and 6.13 mm in thickness.

Titanium(99.99%) was sputtered at 50 W under 2x10"2 Torr of Ar at a rate of ca.

2.2 nm min"1. The dimensions of the gold target are 37.0 mm in diameter and

2mm in thickness with a reported purity of 99.99%. Au was sputtered at 40 W under 2x10"2 Torr of Ar at a rate of ca. 9.0 nm min"1. The sputter-coating setup is illustrated in Figure 20.

63 (. n itilni/er Si.ta«tratp

— Sample Stage

Ar-ion Plasma

Au Target

Figure 20: Illustration of Au sputtering of microcantilevers within the Edwards Auto 306 sputter chamber. Permanent magnets within the magnetron produce a toroidal field such that the Ar-ion plasma is focused between the sample and the Au target.

2.11 SAM Preparation

Passive Deposition: Dodecanethiol SAMs were deposited on Au-coated substrates by immersing the freshly sputtered substrate in a 1 mM dodecanethiol/ ethanol solution for at least 24 hrs. It has been shown that the initial diffusion- controlled adsorption occurs within ca. 1 min while the longer crystallization process can require around 100 min for these thiol concentrations.20 Longer incubation times were chosen to ensure reproducibility and high SAM order. The substrate was then thoroughly rinsed with ethanol to remove excess physisorbed

64 thiols. The samples were generally utilized immediately or stored under argon atmosphere until required. Proper SAM formation under these conditions was verified by performing an identical procedure on Au-bead electrodes and measuring the electrochemical impedance spectra and cyclic voltammograms in

50mM NaF electrolyte. The properties and reproducibility were consistent after 24 hr incubation periods in 1mM dodecanethiol solutions.

11-Mercaptoundecanoic acid (MUA) SAMs were deposited from 1mM ethanol solutions. The deposition times varied depending on both the quality of the SAM required and thiol exchange requirements. Where thiol exchange with the opposite surface of the microcantilever was an issue, the MUA deposition times were reduced to 5 min to minimize thiol exchange with the dodecanethiol SAM.

Thiol exchange studies of dodecanethiol SAMs replaced by polar terminated

SAMs of similar length show that the dodecanethiol exchanged within the 5 min incubation time is minimal (<0.5%).21 For this reason we are confident that MUA exchange with the pre-assembled dodecanethiol SAM is negligible.

Active Deposition: 11-Mercaptoundecanoic acid SAMs were also deposited on

Au-coated substrates by electrochemical deposition. It has been shown that high quality SAMs can be prepared at applied potentials ranging from 200 to 600 mV

(vs Ag/AgCI) in very short time periods.22 The substrates were immersed in 1mM

MUA and 50mM LiCI04 EtOH solutions at 200 mV (vs Ag/AgCI, 20 min). The electrochemical deposition time was varied when the opposite surface of the microcantilever was coated with a different SAM to minimize thiol exchange. The

65 250

200

150-

100

§ 50 < -S 0

$ -50

° -100

-150

-200

-250 ).6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 E/VvsSCE

Figure 21: CV of an MUA SAM prepared on a gold bead electrode. SAM deposited from ImM MUA and 50 mM LiC104 EtOH solution at 200 mV vs SCE for 5 min. CV obtained at a scan rate of 20 mV/s in 50 mM NaF.

substrates were then removed from solution and thoroughly rinsed with EtOH to remove excess physisorbed thiols. The samples were immediately used or stored under argon atmosphere until required. SAM quality and deposition was verified with the CV (Figure 21) and EIS spectra of similarly prepared SAMs on Au-bead electrodes. The results indicate that the SAMs are reproducibly deposited under these conditions.

2.12 Increased Microcantilever Temperature Stability due to Dual

Metal Coating

The microcantilevers were coated on both the top and bottom sides with a titanium adhesion layer and a gold film. Because silicon nitride has a different thermal expansion coefficient (ca. 2x10"6 /K)23 than both gold(14.1x10"6 /K)24 and

66 titanium(8.6x10"6 /K),25 small fluctuations in temperature will cause these materials to expand to different extents and as a result will cause top- or bottom- coated microcantilevers to deflect. This effect has been used to develop sensitive temperature sensors.26,21 Barnes et. al. used bimetallic microcantilevers for calorimetry measurements, attaining sensitivities in the range of 150 fJ or successfully measuring temperature variations of about 10"5 K.26 This clearly illustrates that bimetallic microcantilevers are highly sensitive to the slightest temperature changes. Therefore, coating the microcantilevers with identical metal films on both the top and bottom sides will negate the film's differential thermal expansions. Silicon nitride microcantilevers were prepared with metal films on a single side and with metal films on both the top and bottom sides. The validity of this hypothesis was tested. Two different sets of microcantilevers were prepared.

One set was coated with a 3 nm titanium adhesion layer and a 50 nm gold film on both the top and bottom sides. The other was coated with the same metal film composition and thickness on the bottom side only. The microcantilevers were mounted in a semi-closed cell. A thermocouple was mounted onto the base of the microcantilevers, hooked up to a digital readout, and relayed to a computer. A heating iron was used to heat the microcantilevers to a temperature of ca. 70 °C.

Microcantilever deflections were then monitored while oscillating the temperature over several cycles. Figure 22 a) and b) plot the temperature and differential surface stress of the double- and single-coated microcantilevers respectively. As the temperature is increased, the differential stress of the microcantilevers increases due to the difference in thermal expansion coefficients of the metal

67 films. Figure 22 c) plots the sensitivity of both microcantilevers to temperature variations. The data plotted are subsets of Figure 22 a) and b) selected during the cooling interval. These data were chosen to minimize vibrational effects resulting from the rapid heating of the microcantilevers with the heating iron. Linear regressions were fit to both sets of data. The double-sided microcantilever has a temperature sensitivity of 4.1 mNm"1oC"1 while the single-sided microcantilever has a temperature sensitivity of 25.3 mN-m"1oC"1. The double-sided microcantilever with equivalent metal films on both the top and bottom sides provides a ca. 6 fold improvement in terms of temperature stability relative to single-sided microcantilevers. This confirms the hypothesis that double-sided microcantilevers will provide increased stability for a sensor application.

68 Figure 22: a) Differential surface stress plot and overlaid temperature plot for a 320 um triangular raicrocantilever coated with 3 nm of Ti and 50 nm of Au on both sides, b) Differential surface stress plot and overlaid temperature plot for a 320 um triangular cantilever coated with 3 nm of Ti and 50 nm of Au on both sides, c) Temperature sensitivity (differential surface stress vs. temp.) of both microcantilevers during the cooling cycles.

69 2.13 Origins of Slow Microcantilever Drift

Several reasons are likely for the observed slow, and continuous, drift of the microcantilever signal. Some of these have already been addressed in the literature and are reviewed here to provide a clearer understanding of the complexities involved in utilizing film and SAM covered microcantilevers in solutions.

Mfflta©l»y©r Hydrmy&i& Wanaiwm Mom^ays* Figure 23: Figure adapted from J. Lahann et. al, Science, 2003, 299, 371. Formation of a low density acid-terminated SAM using a bulky end group. Reversible switching of the SAM conformation by potential control.

SAM rearrangement: Several groups have proposed that w-functionalized SAMs can rearrange upon exposure to specific conditions. Lahann etal. performed experiments in which low-density acid-terminated SAMs on gold are reversibly switched from a linear conformation to a bent conformation by potential control of the substrate.28 This resulted in potential-controlled surface properties. The surface becomes highly polar when the acid moiety is in an upright conformation

70 or the surface becomes hydrophobic when the SAM molecules are reorganized into U-conformers by potential control. However, the process required specific

SAM preparation methods. In order for the SAMs to be potentially-controlled, the alkyl segments require sufficient void volume to fold over. This was achieved by initially forming a SAM with a large head group, (2-(chlorophenyl)diphenylmethyl ester), thus creating a low density SAM. The SAM was then rinsed and the bulky headgroup was subsequently cleaved producing an acid-terminated SAM. This low density SAM was then demonstrated to be (reversibly) potential-mediated.

Although the SAMs utilized by Lahann et. al. are very similar to the ones used in this microcantilever sensor study, the requirement that the SAMs be of low surface density (from molecular simulations 6 « 2.6x10"10 mol/cm2) prevents this phenomenon from occurring in many of the microcantilever sensor experiments described here. Capacitance measurements, which are sensitive to the thickness of the SAM of the microcantilever sensor MUA SAMs, clearly show that the capacitance of the film does not change significantly upon extended incubation in pH 3 or pH 10 solutions (Figure 34). This suggests that the SAMs utilized in the proceeding experiments do not undergo the conformational changes as reported by Lahann et. al. when the solution pH is changed.

71 Surface reconstruction:

Bare gold has been shown to have a higher density of gold atoms than the ideal

(111) gold surface.29,30 This arises from the formation of pit-like defects that are created when single gold atoms are ejected from the surface plane and adatoms.

This results in a new superlattice structure with a (23XA/3) arrangement having a

4% contraction relative to the bulk crystal plane.29 When SAMs are deposited on clean gold surfaces, the pit-like defects grow and fuse, eventually leading to surface relaxation and removal of this surface reconstruction. This mechanism has been shown to slow dramatically at room temperature when a full SAM has covered the Au substrate. Annealing the sample to approximately 345 K melts the

SAM and allows for increased rearrangement of both the SAM and the reconstructed layer. It is possible that slow microcantilever drifts are in part due to this phenomenon. Each time the SAMs are perturbed, it is likely that the molecules reorient on the Au surface and in so doing, affect the lattice structure of the Au under-layer. As suggested, this process would be very slow at room temperature and may contribute to, or even cause the observed drifts in the microcantilever deflections.

2.14 Conclusions

A dual microcantilever flow-through liquid cell was designed for solution-phase microcantilever sensor applications. The design of the cell permits for the simultaneous measurement of the differential surface stress of two microcantilevers in solution. The solution pH or the introduction of analytes into

72 the cell is performed via a peristaltic pump. Data acquisition for the differential surface stress measurements are performed via an interfaced data acquisition card using specially designed LabVIEW software.

A novel microcantilever architecture was tested for increased stability and improved control of the microcantilever surface chemistry. Commercially available microcantilevers are coated with gold films on both the top and bottom surfaces.

The top and bottom surfaces of the microcantilevers are then coated with similar or dissimilar SAMs depending on the experimental requirement. Coating both surfaces of the microcantilever with identical metal films greatly improves thermal stability due to the negation of the bimetallic effect. In addition, the self-assembly of alkylthiols on both the top and bottom surfaces allows for integrated referencing of the differential surface stress data or to control the chemistry of the typically unmodified microcantilever bottom side. Finally, the microcantilever deflections are calibrated using the Sader method to obtain accurate differential surface stress measurements (mN/m).

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75 Chapter 3

Electric Field Driven Protonation /

Deprotonation of Self Assembled Monolayers

of Acid Terminated Thiols

76 Linking Text

The previous Chapter describes the, design, construction, and setup of the microfluidic cell along with the optimized microcantilever architecture. The calibration and operation of the system is presented. The Thesis plan describes merging Au-coated microcantilevers with SAMs towards the development of solution-based sensors. The SAM coating chosen, because of its simple chemical transformations, is the carboxylic acid-terminated SAM. However, it became evident at the early stage of this project that the knowledge/understanding of even this "simple" prototype reactive coating is poor.

Thus Chapter 3 is a thorough investigation of the properties of these coatings towards solution sensor applications. The pH response of the acid-terminated

SAM is probed using electrochemical impedance spectroscopy and a model is derived to describe the observed non-faradaic peak in the cyclic voltammograms.

77 3.1 Introduction

Owing to their ability to electrostatically and chemically mediate substrate adhesion, surfaces modified with co-functionalized self assembled monolayers are versatile substrates for anchoring important biomolecules for different applications.1"3 Carboxylic acid terminated thiols are particularly well suited for these purposes because adjusting the pH of the bathing solution can toggle adsorption by switching the surface's hydrophilicity/hydrophobicity or by tuning the electrostatic linkage between a carboxylate terminus and a positively charged substrate.2,4"7 For this reason, carboxylic acid terminated thiol monolayers such as 16-mercaptohexadecanoic acid (MHA),8"1311-mercaptoundecanoic acid

(MUA)14"17 and 3-mercaptopropanoic acid (MPA)18"20 have been used as substrates for protein adsorption and biological sensing purposes. However, these application studies have largely preceded a clear description of the factors that influence the acid/base properties of surface confined monolayers. For example, it is widely known that the surface pKas of acidic monolayer systems are significantly different than the solution state pKgS. These differences may be attributable to effects such as field-dependent (de)stabilization of the acid or base forms. This would be an intrinsic pKa change. Changes in the pKa can also arise from changes in the proton concentration at/near the acid group. This is an apparent pKa shift rather than an intrinsic one. The balance between these two effects is highly system specific and can rarely be separated. Experimental molecular force measurements have determined the surface pKa of MPA to be

78 around 7.7. Shcweiss era/ used streaming potential and streaming current measurements to monitor the adsorption of ions on both MUA and MHA SAMs and obtained values of 5.15 and 5.20 respectively. Using cyclic voltammetry of an electroactive probe, Dai et al determined the pKa of MUA and MHA SAMs to be 7.3 and 7.9 respectively.23 Kakiuchi et al determined the values of MUA and 7- heptanoic acid SAMs to be 10.3 and 9.2 using double-layer-capacitance

24 titrations. The observed variability of the surface pKa of w-acid functionalized

SAMs in the literature is disconcerting and thus calls for a more rigorous understanding of the underlying phenomena.

In many studies employing acid-terminated thiol SAMs, the state of the carboxylic acid group is assumed to be invariant with potential under conditions of constant pH. However, as shown in the elegant model of Smith and White (SW)25 and its refinement by Fawcett and co-workers,26,2? the degree of surface charge on the acid thiol monolayer (i.e. the degree of deprotonation) is dependent not only on the pH of the electrolyte but also on the electric field present at the interface.

Using cyclic voltammetry studies, White et al2S demonstrated that their model qualitatively explained observed experimental data for a mixed decanethiol/MUA

SAM on Ag(111) in that the voltammetric peak attributed to the protonation/deprotonation of the MUA shifted in potential as a function of pH.

However, they unexpectedly observed that the voltammetric peak height was also dependent on the electrolyte pH, a phenomena that is unexplained by either the SW model or the refined model of Fawcett and coworkers. White et al plotted

79 the voltammetric charge passed versus the solution pH and found that the maximal charge corresponded to the pK-1/229 of the MUA self-assembled monolayer. It is important to emphasize that the authors noted that their thermodynamic model offered no theoretical basis for this interpretation and that their assignment of pKi/2 was based solely on the similarity of their pH of maximal voltammetric signal with reported literature pKa values.

The models of SW and Fawcett are based on thermodynamic equilibria and neglect the kinetics of the surface acid protonation/deprotonation. In this paper, we use a kinetic approach to provide an explanation of the dependence of the voltammetric peak height on the electrolyte pH. Furthermore, we derive analytical expressions relating the results of electrochemical impedance spectroscopy (EIS) measurements to the forward and reverse rate constants for the protonation/deprotonation of surface bound acid monolayers. Successful evaluation of these kinetic parameters then makes it possible to determine the surface pKi/2 values as a function of the electrical potential applied to the SAM modified electrode.

Overview of Thermodynamic Models of the lonizable Interface

Using equilibrium conditions to describe the interface of an ionisable monolayer and the bulk solution, Smith and White derived the following relationship between

80 the solution pH, the local electrical potential at the plane of dissociation of the acid headgroups V, and the fraction of ionized molecules in the film;

9 FY log— = pH-pK+ -— (3.1) B\-6 F F ° 2.303RT

where R and T have their usual meanings, 6 is the fraction of ionized molecules

(i.e. TA. /(TA. +r/M) with 77 being the surface coverage of species /) and pKa is

the surface pKa of the bound acid thiol molecules in the absence of any interfacial electric fields. Smith and White assumed that V is equal to the potential drop across the diffuse layer. Fawcett and co-workers extended the SW model to include a more realistic Stern layer26 and accounted for discreetness of charge effects27 which leads to a more complex relation between the potential applied to the electrode and V .

As equation (3.1) is applicable to both models, one can use it to relate pKa to pKi/2 by setting 0 = 0.5,

pKV2 =pKa -FYI23VSRT (3.2)

Both models predict that a positive (negative) shift in the electrode potential causes a positive (negative) shift in V. Consequently, the surface pKa of an

81 ionisable self-assembled monolayer should be dependent on the potential applied to the metal support. The effect of the electrode potential on the surface acid-base properties has been experimentally observed for both carboxylic acid

SAMs,30 amine terminated SAMs31,32 and non-covalently bound adsorbed layers such as benzoic acid and pyridine derivatives on mercury.33"36

In the SW model, the total differential capacity of the interface is divided into contributions from the film, the ionisable headgroups and the diffuse part of the double layer. For simplicity, we will use the equation describing the total interfacial capacity derived by SW rather than Fawcett's more complicated expression, though we note that the latter model more accurately describes experimental data. Smith and White show that

— = —+ l—— (3.3) CT CF Cs + C(0)

where CT is the total interfacial (i.e. experimentally measurable) capacity, CF is the capacity of the alkyl chains of the film, which can be modelled as a Helmholtz capacitor, Cs is the diffuse layer capacity and C(G) is the capacity associated with the plane of dissociation and is therefore a function of the degree of ionization of the acidic headgroups. According to the models of SW and Fawcett, the total differential capacity of the interface should exhibit a peak at potentials close to

82 those where the acidic head groups in the SAM are half-ionized. Furthermore, at constant electrolyte ionic strength, the potential corresponding to the maximum in the total differential capacity should shift cathodically with increasing pH but the maximum value of the capacity should be independent of the acidity of the electrolyte solution.

3.2 Materials and Methodology

The working electrodes in these experiments were polycrystalline gold beads formed by melting gold wire (99.99% Alfa Aesar) with a propane torch. The gold bead, at the end of the gold wire, was immersed in aqua regia (3:1 HCI: HNO3) to remove surface impurities and then remelted. This procedure was repeated iteratively until the molten gold displayed no visible contaminants. The electrodes were then electrochemically polished in 50 mM KCIO4 (Aldrich, x2 recrystallised) by cycling through the surface oxidation / oxide stripping peaks (-0.8V < £ <

1.25V vs SCE). Electrochemical measurements were performed in an all glass, sealed cell, which was connected to an external reference electrode (SCE) via a salt bridge. All glassware was heated in a mixture of H2S04 and HNO3 (2:1 by volume) and then copiously washed with Millipore water (Millipore > 18.2 MO) prior to every daily experiment. The counter electrode was a loop of flame annealed gold wire. The electrolytes were prepared from NaF (Aldrich 99.99%),

KOH (Sigma, 99.99% Semiconductor Grade), and HCIO4 (70%, Aldrich). The aqueous electrolyte solution was thoroughly degassed with argon for a minimum

83 of 30 minutes before the experiments were performed. An argon blanket was maintained over the electrolyte throughout the duration of the experiments to ensure an oxygen free environment.

Prior to every experiment, the electrodes were cleaned in Piranha solution (3:1

H2S04:H202), rinsed, flame annealed, and quenched in Millipore water. These bare gold surfaces were then electrochemically characterized in 50 mM NaF to ensure their cleanliness. Self assembled monolayers were electrochemically deposited, 0.2 V vs SCE for 15 minutes, in a separate cell from an aqueous solution of 1 mM MUA, (Aldrich, 97%) and 0.1 M NaF. The pH of the 0.1 M NaF solution is approximately 9 which is sufficient to solubilize MUA.

Electrochemical experiments (cyclic voltammetry and EIS) were performed using a Solartron 1287 potentiostat and a 1255B Frequency Response Analyzer. Cyclic voltammograms were recorded using CorrWare software (Scribner Associates) and the impedance measurements using ZPIot/ZView (Scribner Associates). The supporting electrolyte for these experiments was 50 mM NaF (pH -8.7), the pH of which was adjusted using dilute solutions of KOH and HCIO4. The pH of the electrolyte was monitored using a pH meter (Accumet 910). For the EIS measurements, the range of frequencies of the 5mV rms amplitude, ac perturbation was 3000 Hz to 0.5 Hz. Higher frequencies were avoided due to the stray capacitance of the salt bridge. Using an internal reference electrode alleviated this problem but introduces the possibility of chloride contamination in

84 the working cell. Fitting of the experimental EIS data and simulation of EIS curves was performed using ZView/ZPIot.

3.3 Results

Cyclic Voltammetry

Figure 24 shows the results of the pH dependence of cyclic voltammograms of an MUA SAM on polycrystalline gold. The results closely correspond to those reported by White et al for a mixed decanethiol/MUA SAM on Ag(111). We observe that the peak attributed to the protonation/deprotonation shifts cathodically with increasing pH. As shown in inset (a) of Figure 24, the peak position shifts linearly with pH at a rate of 67 mV/decade. From equation (3.1) the expected slope of the line should be 59 mV/decade. The measured value is close to that predicted by SW's equation and the discrepancy may arise from the fact that we are plotting the applied electrode potential rather than the local potential, f. Inset (b) in Figure 24 plots the voltammetric peak current versus pH and displays a maximum value at pH ~ 8.9.

This is in very good agreement with White et al who reported a maximum voltammetric peak signal at pH ~ 8.5 for a mixed MUA/C12S- on Ag(111). To reiterate, Smith and White's model (and Fawcett and co-workers' refinement) explain the potential shift in the voltammetric peak with changing pH but does not account for the dependence of the peak height on pH. Below we present an explanation for this latter observation based on kinetic considerations.

85 Figure 24: pH dependent cyclic voltammograms of Au bead electrode coated with MUA SAM. Inset (a) Plot of the anodic CV peak potential vs pH. Inset (b) Plot of maximum anodic peak current vs pH.

86 Electrochemical Impedance Spectroscopy

To further characterize the interface, we performed EIS measurements with DC potentials ranging from -500 mV < £ < 0 mV. According to both the SW and

Fawcett models, the equivalent circuit describing the interface should consist of a solution resistance in series with a capacitor to describe the total interfacial capacitance (see equation (3.3)). Figure 25 presents the results of EIS studies on an MUA monolayer formed on a polycrystalline gold electrode as a function of the

T 1—l""l [""I"T"| 1 1 P—I I I"TT| 1 1 1—II I I I | 1 1 1—1"'|'|""|"|"| 1 1 1—TT

J 1—I Mill 1 I I I I I I I I ' ' ' I 1 I • ' I i i I I I I I I I I I I L_L 1 10 100 1000 Frequency/Hz Figure 25: Bode plots (phase angle vs frequency) for MUA SAM on polycrystalline Au for potentials E -500 mV<£<0raVvj SCE. Electrolyte was 50 mM NaF pH adjusted to 8.5.

87 applied DC potential. The pH of the electrolyte was 8.5. The EIS data is rendered in a Bode phase angle diagram which plots the negative of the phase angle, -

Figure 25 for E < -300 mV and E > -200 mV. In our fitting analysis, a constant phase element (CPE) was used rather than a pure capacitor.

a The impedance of a CPE is a power law-dependent capacity, ZCPE =A(ja>y and accounts for the roughness of solid electrodes which leads to frequency dispersion. The closer the value a approaches unity, the more the element behaves as an ideal capacitor.37 In all our fitting analyses the values of a were

0.98 or larger for this CPE. As expected, the fitting of the EIS curves with a simple model of an R-CPE series circuit gives excellent fits (see Table 2 in

Supporting Information) for E < -300 mV and E > -200 mV. In contrast, in the region of DC potentials close to the observed peak in the cyclic voltammetry (-

300 mV < £ < -200 mV), the Bode phase angle plots display a characteristic "dip" at intermediate frequencies (ca. 1Hz < f < 100Hz) where the phase angle is significantly lower than 90°. The dip is most strongly pronounced at potentials

88 that correspond to the formal peak potential in the CV. Thus the interface cannot be modelled as simple R-CPE series circuit at the protonation/deprotonation potentials.

The influence of pH on the EIS data is as pronounced as it is for the CV data.

Figure 26 displays three dimensional plots of the phase angle as function of potential and frequency for different solution pH values. At both high and low pH, the dip is completely absent, indicating that the interface mimics an R-CPE series circuit. It is only when the acidity of the electrolyte is close to pH 9 and the DC potential applied to the electrode corresponds to the peak observed in the voltammetry that the characteristic dip is apparent in the Bode phase angle plots.

89 pH 10.0 ___

i Ll-i4-rrn4-+T^-.-*.

pH 9.50 pH 8.50 ri"'.:'*sEaifl^si!i

0.5 -\< 05 0.0 0.0 \Pi ^i^ 0.0 0.0 \fft

pH 9.00 pH 7.75 90 ~p ."1 U-H 85 -|

4 «-.„•<"

Figure 26: 3D electrochemical impedance spectra of MUA SAM on Au bead electrode as a function of potential and various pHs.

90 3.4 Discussion

Explanation of Experimental EIS Data

An explanation of the observed EIS data for DC potentials corresponding to the peak in the cyclic voltammetry is given below. Consider the reaction

H+ + A" <=^=> HA Reaction 1 where HA denotes surface bound, protonated molecules and A" represents the bound, conjugate base. The degree of charge at the plane of dissociation plus the excess charge in the diffuse part of the double layer will be balanced by the surface charge density, om, on the electrode. At constant pH, om is a function of both the applied potential (E) and the degree of ionization of the carboxylic acid functionalities {&). The relationships between these variables can be written in terms of a complete differential.

f{E,e)

rda^ (da da„ dE + dO (3.4) ydE j 30 JB

Differentiating equation (3.4) with respect to time provides an expression for the current flowing through the interface

91 (da-_\ dE_ (da„\ d6 I = (3.5) ydE j dt ydO JE dt

The first term in equation (3.5) describes the capacitive current arising from charging the interface under conditions of constant composition whereas the contribution to the total current due to the rate of change in the degree of ionization is provided by the second term. Thus the total current can be divided into a purely charging current and a current due to the kinetics of the surface acid chemistry described in Reaction 1. The current that arises due to the protonation/deprotonation reaction under the condition of constant total coverage is

. ,d6 (3.6) " dt

where A is (dam/dO)E. Although A is closely related to the electrosorption

rd*^ valency, 38 y = — , it should not be confused with the charge flowing to the v ar, JE electrode per adsorbed MUA molecule because the partial derivative in equation

(3.6) is with respect to the fractional coverage of the acid and not the surface coverage f.

92 In instances where there is no change in the degree of ionization of the SAM, (i.e. dOjdt = 0) the protonation/deprotonation current does not exist and the observed current arises solely from the capacitive charging of the interface. This occurs at

DC potentials far removed from the peak in the CV and/or at pHs well-removed from the pK-i/2. Under these conditions, one should be able to successfully model the interface as a capacitor, Cc, in series with the electrolyte resistance, Rs (see

Figure 27a) which is what is observed experimentally. On the other hand, when dQjdt is appreciable, a generic parallel impedance, Zp, associated with the protonation/deprotonation must be introduced (see Figure 27b).

Derivation of the Protonation/Deprotonation Impedance

The derivation of the protonation impedance follows in an analogous fashion to the derivation of the faradaic impedance for a surface redox reaction given by

Gabrielli et a/39 from which we borrow heavily. We strongly note that this impedance is not due to any faradaic reaction such as hydrogen evolution, but rather stems from the change in the electrode's surface charge density due to changes in the degree of ionization at the plane of dissociation.

We start with the assumption that reaction 1 follows a Langmuir isotherm

93 a) •VWAr

b) Rs Cf 4Mr

c) Rs

Mwvw Rr Cr

Figure 27: (a) RC model circuit for a non-ionizing SAM consisting of a solution resistance and a film capacity in series, (b) Model circuit for an ionizing SAM consisting of a generic impedance, Zp, in parallel with the film capacitance, Cc. (c) Model circuit for an acid- terminated SAM consisting of a protonation/deprotonation resistance and capacitance in parallel with the film capacitance.

94 d6 ^ = K{i-e)-kfe[n^ (3.7) dt

where kf and kbare the rate constants for the forward (protonation) and reverse

(deprotonation) reactions. It is further assumed that for constant electrolyte pH, the reaction is controlled by the applied potential (as shown by White, Fawcett and Figure 24 of the current work) and the relationship between the applied potential, E, and the measured rate constants (kf and kb) is given by a modified form of the Tafel equation.40

kf=k°fexp[-bf(E-E°) (3.8)

kb=k°exp[bb(E-E°j (3.9) where,

(3.10) RTr and

{\-a)X h = (3.11) RTR,

95 The parameter A/(RTriol) (where rtot = TA_ + rm) represents the number of charge units transferred to the electrode in the protonation/deprotonation reaction and a is the transfer coefficient (0 < a < 1). This modified Tafel equation has been previously used by Parsons41 to describe the chemisorption of a redox- inactive adsorbate on Ag(111). The parameters £° and k°b are the rate constants for a chosen reference potential, E°, and have units of M"1s"1 and s"1 respectively.

The current that flows due to the protonation/deprotonation reaction is arrived at by combining Equations (3.6) and (3.7).

+ ip=Jl(kb(\-0)-kfe[H ]) (3.12)

In the steady state, the forward reaction balances the backward reaction and by setting the left hand side of Equation (3.7) equal to zero we achieve

6, = r \ (3.13)

where the subscript s denotes the steady state conditions.

96 Now consider a small perturbation, dE(f), being superimposed upon the steady state potential £s. The effect of this perturbation is to induce a corresponding fluctuation in the degree of ionization which causes a change in the protonation/deprotonation current.

0(t) = es+d9(t) E(t) = E,+dE(t) (3.14)

ip(t) = i„+dl(t)

Inspection of Equations (3.7)-(3.11) reveals that

dp) ~ = f(0,E) (3.15)

where

o o + o o f = (l-0)k exp[bb(E-E )y0[n ]k exp[-bf(E-E )} (3.16)

and similarly

ip = g{0,E) (3.17)

where

97 o o + o o g = Ai(l-0)k exp[bb(E-E )y0[H ~\k exp[-bf(E-E )J> (3.18)

We can relate the quantities 9, E, ip by taking the full derivatives of equations

(3.15) and (3.17)

r w\ Ue\ (df^ dE(t)+ — dO(i) (3.19) \dt) \dEj

dg^ rag\ «'>iHm"HUM® (3.20)

Explicitly evaluating the partial derivatives of equations (3.16) and (3.18) provides the following;

Ue^ d = {o\dE(t)-{b}de(t) (3.21) \dt j

d(ip(t)) = A[{a}dE(t)-{b]d0(t)] (3.22)

where

+ a = (l-0)kbbb+0[u ~\kfbf (3.23) and

98 + b = kb+[R ~\k/ (3.24) the former of which can be rewritten using equation (3.13) to yield

*A[H+] + •[V*/] (3.25) kf[n ]+kb

If d6{co), dV(co), dip(a>)are the Fourier transforms of

dO(t), dV(t), dip (t) respectively, then the Fourier transforms of equations (3.21) and (3.22) are as follows;

jcod 9(o)) = {a}dV\a)-{b}dO{a>) (3.26)

dip{ca) = X \{a}dV (a>)-{b}d~0(co) (3.27)

Finally, by combining equations (3.26) and (3.27) to eliminate dd(co)\Ne arrive at an expression for the impedance of the protonation/deprotonation reaction.

dV(co)_ 1 *» = 1 + - (3.28) je>

99 Equation (3.28) demonstrates that the protonation impedance consists of both a real valued quantity and an imaginary quantity which corresponds to a series combination of a resistor and a capacitor. Explicit expressions for the values of

Rp and Cp are readily obtained by substituting equations (3.24) and (3.25) into 28

+ kf[a ]+kb Re[Z] = *,=i + (3.29) A kfkb[H ][bb+bf]

and recalling that Z.tor=l/ja>C

lmg[Z] = Cp = + (3.30) RP(kb+kf[H ])

Figure 27c shows the equivalent circuit needed to model the interface at conditions where the protonation/deprotonation reaction is appreciable. The generic protonation/deprotonation impedance has been replaced with a series combination of a resistor and a capacitor. Jovic and Parsons used an equivalent circuit identical to Figure 27c to model the adsorption of acetate ions on

Ag(111)42 implying that the protonation/deprotonation of acid thiol SAMs is fundamentally equivalent to the partial transfer concept used to treat the specific adsorption of anions on metal electrodes. We tested the adequacy of our model by fitting the EIS spectra shown in Figure 25, as well as the EIS bode phase

100 angle curves that displayed the "dip" in Figure 26 to the equivalent circuit of

Figure 27c. As shown in Figure 28, other than having to replace the pure capacitors with CPEs, our equivalent circuit provides excellent fits to the experimental data. Parameters of the best fit results are shown in Table 2 of supporting information.

Nature of the pH Dependence on Voltammetric/EIS Data

The expressions for the protonation/deprotonation resistance and capacitance can be used to provide insight into the apparent pH dependence of the voltammetric peak and the "dip" in the EIS. We do this by simulating the EIS spectra at the potential corresponding to the protonation/deprotonation at different values of the pH. At this potential we choose kf to have a value of 109 M"

1 s"1, set kb = 1 s"1 and note that, as defined by reaction 1, the equilibrium constant for the surface deprotonation, K?/2, is equal to kh/kf so that the values we have chosen correspond to a SAM with a surface pKi/2 of 9.

101 i 1 1 i 1 I 1 I 1 ) 1 I 1 I 1 ' ' ""1 'III Hill 1 1 1 1 Hill 1 1 1 1 Hill 350 - - - 7 80 - . /*"*\ 300 1 \ r \ _ 5 J S \ / \ / -o \ P \ / - 250 / 0 \ i \ g70 - i TO / \ / V 200 / 85 - H TO Q. \ / I • N / \ J \ / 1 150 m 60 »" 1 • - i i - A r\r\ 100 - 1 10 100 1000 P Frequency/Hz 50 jt 0 f i i i . i . i . i , i 0 50 100 150 200 250 300 350 ReR/kH

Figure 28: Fit of equivalent circuit (Figure 27C), solid line, to experimental Nyquist plot of MUA in pH 9.0 at -0.275V vs SCE, square points. Inset: Bode angle plot of MUA SAM in pH 9.0 at -0.275V vs SCE, square points, and equivalent circuit fit, solid line.

The value selected for A was 10 uC-crrf2 and is assumed to be constant with potential. This value was estimated from some preliminary chronocoulometric experiments which we describe in detail in a follow-up publication. We further assume that the energetics of the reaction are symmetric, i.e. a = 0.5 and that rtot

10 2 = 8.0 x 10" moles cm" . We used these values to simulate the values of Rp and

Cp as a function of pH using Equations (3.29) and(3.30), the results of which are shown in Figure 29. The value of Rp is shown to increase rapidly with increasing

102 pH, ranging from a value of ~ 20 kQ at pH 6 to 2 MQ at pH 11. In contrast, Cp displays a peak dependence on the pH of the electrolyte, reaching a maximum value when the pH equals the pKi/2 (pH = 9 in our example). We proceed further by using the values of Rp and Cp and the equivalent circuit of Figure 27c, to construct simulated EIS bode phase angle plots for the protonation/deprotonation potential as a function of pH.

We chose a value of 100Q for the electrolyte resistance and a value of 2 uF cm"2 for the charging capacitance, Cc. The latter value is obtained from the equation of a Helmholtz capacitor

Cc-^f- (3.31)

where s is the relative permitivity of the hydrocarbon core of the SAM (~3), s0 is the permitivity of vacuum (8.85 x 10"12 C2 J"1 m~1), and d is the thickness of the hydrocarbon layer (estimated to be ca. 1.3 nm based on Tanford's empirical equation43). For convenience, we assume an electrode area of 1 cm2. We note that the contribution to the total interfacial capacitance from the diffuse part of the double layer has been purposely omitted as its contribution to the total capacity is negligible in the presence of such a low value of Cc even at the potential of zero charge (see supporting information).

103 n a

CO O 0.1V X c

0.01

pH-pK 1/2

Figure 29: Simulated values of Rp(a) and C^b) vs pH for potentials corresponding to the maximum protonation/deprotonation current.

104 Figure 30 shows a three dimensional plot of the phase angle as a function of both the log of the ac perturbation frequency and the pKi/2 normalized pH. The simulation reveals that the most pronounced phase angle "dip" occurs when the pH = pKi/2. At pHs far removed from the pKi/2 the magnitude of the dip has been greatly attenuated. Qualitatively, the simulated results are in excellent agreement with the experimental results shown in Figure 25 and Figure 26. The simulated data can also be used to explain the voltammetric behaviour of the MUA films as a function of pH. The admittance modulus of the interface is given by the reciprocal of the impedance modulus |y| = \z\~1 and is therefore directly proportional to the peak current in the cyclic voltammetry experiment.

105 Figure 30: Simulated electrochemical impedance spectrum as a function of pH-pKl/2 at the potential corresponding to the maximum protonation/deprotonation current.

Figure 31a shows the admittance as a function of frequency for different pK^ normalized pHs. One can use the admittance data to simulate the cyclic voltammetric peak height dependence on pH by plotting the admittance versus the pKi/2 normalized pH for one particular frequency. Examples shown in Figure

31b for frequencies 1 Hz, 0.5 Hz, and 0.1 Hz correspond to CV sweep rates of 20 mV/s, 10 mV/s, and 2 mV/s respectively. The peak shape dependence of the simulated voltammetric response on electrolyte pH, Figure 31b, corresponds to the experimental voltammetric peak heights of inset b in Figure .

106 1E-3 11"| ' i 1—fx-r-rri'i r-™r—• i-r-rrn | T i i "i" i i 11[

! a)

1E-4 2 3 1E-5 c CO —v-- pH-pKi/2= -1 —o-- pH-pKi/2= -0.5 3 1E-6 —*-- pH-pKi/2= 0 — D-- pH-pKi/2= 0.5 —A- - pH-pKi/2= 1

1E-7 _J i i..,i„J,.i.iil _j *'•'•••• « ' i i i. ml 0.01 0.1 10 Frequency/Hz

Figure 31: (a) Simulated admittance plot vs frequency for pKi/2 normalized pHs at the potential corresponding to the maximum protonation/deprotonation current, (b) Simulated admittance plot vs pK1/2 normalized pHs for specific frequencies at the potential corresponding to the maximum protonation/deprotonation current.

107 Interestingly, we note that the simulated voltammetric admittance does not necessarily reach its maximum value when the solution pH equals the surface pKi/2. According to Figure 31b the pH corresponding to the maximum peak is dependent on the voltammetric sweep rate. Rendering our experimental impedance results as an admittance plot (figure not shown) reveals qualitatively similar features to those of Figure 31a. However, constructing the equivalent plot to Figure 31b with the experimental data does not reveal a discernable frequency dependence on the position of the maximum admittance. A possible explanation for this apparent discrepancy might be that the influence of the sweep rate on the experimental admittance maximum is less than the pH increments studied. This observation highlights a cause for caution when using a single sweep rate to estimate pK-i/2 values when using DC voltammetry.

Determining Surface Acid Dissociation Constants from

Electrochemical Data

Based on the simulated data shown in Figure 30, it is tempting to infer that the greatest "dip" in experimentally measured Bode phase angle plots occurs when the pH of the electrolyte corresponds to the surface pKa of the self-assembled monolayer. There are several subtle reasons why we hesitate to make this assertion. First, it is important to restate that the quantity evaluated is pKi/2 not pKa, the two being related by Equation (3.2). The former is clearly a function of the potential applied to the SAM covered electrode while the latter is specific to

108 the condition of zero electric field at the plane of acid dissociation. The potential

30 32 dependence of pKi/2 has been previously reported for SAMs. " Secondly, in

Figure 30 we simulate the EIS data for potentials corresponding to the voltammetric peak as a function of pH and assume pH-independent rate constants such that pKi/2 equals 9. However, Figure 24 clearly shows that the voltammetric peak potential is a function of pH. Combining this observation with

Equation (3.8), it becomes evident that the rate constants must be dependent on pH. Finally, the value ofA,(dcrm/d0)E, has also been assumed to be invariant with potential and/or pH. This may or may not be true and it is unclear how a variable value of A affects the simulations shown in Figure 30.

109 We believe that a more exact means of evaluating pKi/2 values would be to use experimentally measured values of Rp and Cp and Equations (3.29) and (3.30) to directly evaluate the forward and reverse rate constants. A particularly appealing feature of this approach is that the influence of the potential on pKi/2 can be readily determined as long as Rp and Cp are extractable from the EIS data. This may be problematic if the rate constant for the protonation, kf, is large enough that the reaction is diffusion controlled. In such a case, the value determined from the EIS data will be an apparent rate constant that is less than the true protonation rate constant. Slevin and Unwin have recently used induced desorption mode SECM to determine a protonation rate constant of 2.5 x 107 M"1 s"1(after unit conversion) for stearic acid Langmuir monolayers.44 The rate constant for diffusion-limited proton transfer in water is on the order of 1010 M"1 s"1.45 Accurate determination of the protonation/deprotonation rate constants should be possible if the magnitudes of these variables extend to the current system.

3.5 Conclusions

We have derived an analytical expression for the impedance of the protonation/deprotonation reaction of a surface bound acidic self assembled monolayer. Our treatment of the interface includes a contribution to the total current due to the kinetics of the change in the degree of dissociation of the

COOH groups. To test our model, we have simulated the EIS spectra for the

110 interface and the results are in excellent, qualitative agreement with our experimental results on an 11-mercaptoundecanoic acid SAM on polycrystalline gold. Our model successfully predicts the observed pH dependence on the voltammetric peak height attributed to the electric field driven protonation/deprotonation of the MUA SAM which could not be accommodated by previous thermodynamic models. This work demonstrates that electrochemical techniques, particularly EIS, can be used to determine the surface pKi/2 of acidic organic films on conductive surfaces. Unlike other techniques, it should be possible to use EIS to extract the rate constants for the surface acid chemistry.

We know of no reports of these physical parameters for acid thiol SAMs. An important quantity which needs to be evaluated before this is possible is the value of/. We are currently performing chronocoulometric and surface IR experiments toward this end, allowing us to extract the values of kf, kb, and Km from EIS measurements as a function of potential. Finally, we wish to note that although we have demonstrated the use of this approach for acidic monolayers, the formalism of the mathematics should be identical for monolayers containing basic functionalities.

3.6 Acknowledgements

IB would like to thank both NSERC Canada and the Tomlinson Foundation of

McGill for post-doctoral funding. BS thanks FQRNT for provision of a doctoral fellowship. NSERC and FQRNT provided funding for this research.

Ill 3.7 Supporting Information

Contribution of the Diffuse Layer Capacity

Strictly speaking, the capacitance of the interface in the absence of any protonation/deprotonation reaction is given by the serial combination of the film capacity and the diffuse layer capacity, Qi.

111 , n — = — + — (a-1) c c c

In the Guoy-Chapman [refj model of the electrical double layer, the diffuse layer capacity is given by s Cdl =ss0Kcosh 'e(Af~ )/2kT~\ (a-2) where, for 1:1 electrolytes (i.e. z = 1), the inverse Debye length, A: is

(~. 2 2 oY/2 K- 2e z n (a-3) V ££okT j

of the electrolyte cations. The minimum value of C<# occurs when A^2"s is equal to zero.

Using a value of 78.5 for ss, the diffuse layer capacity minimum for 50 mM NaF is equal to ~50 uF cm"2. Substitution of the values for Cp (2 uF cm"2) and the minimum value of

Cdi (uF) into Equation (a-1) clearly demonstrates that the contribution of the diffuse layer capacitance is negligible.

112 Table 2: Summary of EIS Fitting Results Using the Equivalent Circuit of Figure \17c. Values are not compensated for the electrode area which was 0.15 cm2. CPE-1* CPE-2* ENvs X PH Rs/Q Rp/kD \ 4 SCE (x10 ) CF/MF a* CP/MF a* -0.300 161 (±2) 0.303 (±0.002) 0.98 168.6 (±4.4) 0.171 (±0.003) 0.92 1.6 8.5 -0.250 164 (±2) 0.297 (±0.002) 0.98 107.7 (±1.3) 0.329 (±0.003) 0.93 1.0 -0.200 165 (±2) 0.291 (±0.002) 0.99 162.1 (±3.8) 0.153 (±0.003) 0.95 1.6 -0.300 159 (±3) 0.308 (±0.003) 0.98 96.5 (±1.8) 0.367 (±0.004) 0.90 1.8 8.75 -0.250 164 (±2) 0.298 (±0.002) 0.98 96.0 (±1.4) 0.402 (±0.004) 0.92 1.6 -0.200 167 (±3) 0.288 (±0.003) 0.99 193 (±8.0) 0.138 (±0.004) 0.93 3.7 -0.300 158 (±2) 0.311 (±0.003) 0.98 61.4 (±0.7) 0.706 (±0.005) 0.90 1.3 -0.280 160 (±2) 0.309 (±0.003) 0.98 57.6 (±0.6) 0.752 (±0.005) 0.90 1.3 9.0 -0.250 165 (±3) 0.297 (±0.002) 0.98 78.1 (±0.9) 0.507 (±0.004) 0.92 1.4 -0.200 165 (±5) 0.288 (±0.005) 0.99 175 (±14) 0.136 (±0.007) 0.91 9.0 -0.325 175 (±2) 0.292 (±0.002) 0.98 268 (±6.3) 0.185 (±0.003) 0.92 1.8 -0.300 176 (±2) 0.288 (±0.002) 0.99 354 (±10) 0.135 (±0.003) 0.94 2.3 9.5 -0.250 178 (±2) 0.285 (±0.002) 0.99 713 (±74) 0.05 (±0.003) 0.91 4.3 -0.200 165 (±5) 0.288 (±0.005) 0.99 175.3(±14) 0.136 (±0.007) 0.91 9.0

CPE denotes "constant phase element". To account for frequency dispersion, CPEs were used in the fitting analyses rather than the pure capacitors shown in Figure 27c. ^rror less than ±0.01.

113 References

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2. Jordon, C. E.; Frey, B. L.; Kornguth, S.; Corn, R. M. Langmuir 1994,10, 3642-8.

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4. Frey, B. L.; Jordan, C. E.; Kornguth, S.; Corn, R. M. Anal. Chem. 1995, 67, 4452-7.

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9. Wang, H.; Castner, D. G.; Ratner, B. D.; Jiang, S. Langmuir 2004, 20, 1877-87.

10. Clark, R. A.; Bowden, E. F. Langmuir 1997,13, 559-65.

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12. Tarlov, M. J.; Bowden, E. F. J. Am. Chem. Soc. 1991,113, 1847-9.

13. Song, S.; Clark, R. A.; Bowden, E. F.; Tarlov, M. J. J. Phys. Chem. 1993, 97, 6564- 72.

14. Kasmi, A. E.; Wallace, J. M.; Bowden, E. F.; Binet, S. M.; Linderman, R. J. J. Am. Chem. Soc. 1998,120, 225-26.

15. Arnold, S.; Feng, Z. Q.; Kakiuchi, T.; Knoll, W.; Niki, K. J. Electroanal. Chem. 1997,438,91-97.

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19. Li, J.; Cheng, G.; Dong, S. J. Electroanal. Chem. 1996, 416, 97-104.

114 20. Zhao, Y.-D.; Pang, D.-W.; Hu, S.; Wang, Z.-L.; Cheng, J.-K.; Dai, H.-P. Talanta 1999,49,751-56.

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24. Kakiuchi, T.; Iida, M.; Imabayashi, S.-i.; Niki, K. Langmuir 2000,16, 5397-401.

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28. White, H. S.; Peterson, J. D.; Cui, Q.; Stevenson, K. J. J. Phys. Chem. B 1998,102, 2930-34.

29. In an effort to avoid confusion we wish to clearly define the difference between surface pKa and pKi/2. Both of these terms describe acidic monolayers and represent the pH of a solution in which the concentration of deprotonated surface species is equal to the concentration of protonated surface species (i.e. 0 = Vi). The difference arises in that pK.1/2 corresponds to a film in the presence of an interfacial potential whereas surface pKa is a unique instance of pK.1/2 when ¥=0.

30. Sugihara, K.; Shimazu, K.; Uosaki, K. Langmuir 2000,16, 7101-05.

31. Cao, X.-W. J. Raman Spectrosc. 2005, 36, 250-56.

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115 38. IUPAC prefers using the other notation "formal partial charge number" and the symbol /.

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116 Chapter 4

Assessment of microcantilevers as solution-

phase sensors

117 Linking Text

Chapter 2 & Chapter 3 independently describe the two components to be

assessed in this research: the dual-coated microcantilever and the

alkylthiolcarboxylate SAM. In this Chapter we merge the two components, ie

microcantilever based transduction systems functionalized with specific SAMs on

both surfaces to assess whether these systems are viable sensor platforms. The

now-understood chemical reaction of acid (de)protonation is used to test the

response of the functionalized microcantilevers to pH changes. The

microcantilever responses are critically analyzed for reproducibility and accuracy.

The microcantilever-based sensor functionalized with SAMs on both the top and

bottom surfaces is used to determine the surface pK1/2 of acid-terminated SAMs.

Finally, the practical application of SAM-functionalized microcantilever sensors is discussed.

118 4.1 Introduction

Several research groups have proposed using Si and SiNx microcantilevers in sensor applications.2"4 Attempts to detect DNA hybridization and single base-pair mismatches have been performed with a range of outcomes.5,6 Some reports present a series of successful experiments, while others have described problems with reproducibility and non-specific responses.7,8 Understanding the response of derivatized microcantilevers to specific analytes can be so complex that some researchers have resorted to using artificial neural network models9 to decipher the responses. Principal component analysis, for example, was used to distinguish between a number of small molecular weight analytes. This statistical interpretation does not, however, consider the nature of each of the response of the microcantilevers. In an other example, the responses of acid-functionalized microcantilevers were treated with ANOVA statistics to reject responses having significant variance.10 Other researchers have used surface-modified microcantilevers to detect metal ions via surface complexation11 or for pH determination.10,12 However most of these data are plagued by significant noise and significant microcantilever drift. The overall outcome is a literature with contradictory results and a crisis in confidence that the microcantilever system can be used as a sensor platform. For these reasons, this Chapter sets out to determine whether microcantilevers in solution-phase can in fact serve as sensor devices. In order to serve as sensor devices, several criteria must be met: (i) the signal response must be reproducible (ii) there must be minimal or controlled interference from undesired analytes (iii) the signal must be stable in the

119 observation time frame (iv) the sensor must be sensitive within the concentration range required for the analyte in question. To this end, this Chapter presents a derivatized microcantilever preparation method which attempts to optimize each of these criteria. The method involves the preparation of microcantilevers with gold films on both the top and bottom surfaces. Each surface is then functionalized with a different SAM-forming molecule. The differential-surface coating method provides independent control of the surfaces. Sensitivity to pH of the doubly-coated microcantilevers was used as a trial chemical reaction, so as to test the microcantilever response to external stimuli in solution. Drift, hysteresis, response time, and reproducibility were monitored throughout prolonged experiments held at ambient (solution) conditions and under challenges of changing pH. Parenthetically, we note that there are many pH sensors with much better sensitivity, faster response time, and instrumental simplicity than the microcantilever system. The pH experiments reported here are not explicitly pH detection, but instead are used for calibration and mechanistic purposes. These pH experiments test and prioritize the many factors which influence the response of microcantilevers in solution.

4.2 Experimental

Deflection measurements of functionalized microcantilevers were performed using the system described in Chapter 2. The preparation of the differentially- coated microcantilevers involves a sequential process. Microcantilevers are first prepared by sputter deposition of Ti on one of the microcantilever surfaces (Ti

120 serving as a gold adhesion layer) and then a Au metal film on the Ti film. The Au

coatings were then coated with an acid-terminated (11-mercaptoundecanoic acid

(MUA), 3-mercaptoproprionic acid (MPA), or 16-mercaptohexadecanoic acid

(MHA)) SAM. The metal films were then deposited onto the opposite

microcantilever surface. This surface was coated with a dodecanethiol (C12S-AU)

SAM. Surface stress was monitored as a function of the extent of protonation and

(de)protonation of the carboxylic acid-terminated SAM. Reference

microcantilevers were prepared by coating C12S-AU on both microcantilever

surfaces. The resulting coated microcantilevers were immersed in buffer for 24hrs

prior to pH cycling. This wait time allowed the SAM to attain a steady state described as a surface crystallization.13 A custom LabVIEW program was used for data acquisition and analysis. Flow of analyte was maintained at a constant rate of 1mL min"1 using a peristaltic pump and a closed-loop system (Figure 32). The

pH of the solution was changed by replacing the buffer solution in the reservoir of the closed-loop system. The pH was monitored using a pH electrode immersed in the solvent reservoir that was linked to a computer for continuous data acquisition.

121 =fs

Pel iiidhn: Pump ^^ • I 9

k!""°*>5S

Figure 32: Illustration of the closed-loop, flow-through system used to change the cell solution during the experiments. The peristaltic pump circulates the solution between the cell and the solvent reservoir. The solution never contacts any mechanical parts within the pump. The pH is adjusted either by changing the solution in the beaker or by adding spikes of dilute NaOH or HC1. Ar is bubbled into the solution to minimize pH changes caused by C02 dissolution.

4.3 Results and Discussion

SAM stability under solution incubation conditions

The stability of the surface stress signal of microcantilevers coated with acid- and

methyl-terminated SAMs was studied in detail. The purpose of these experiments was to determine if all or part of a microcantilever response results from chemical

and/or physical changes in the SAMs formed on the gold films. In particular,

changes in coverage were studied as a function of critical SAM preparation conditions and storage conditions. These experiments also probe whether the

122 response originates from changes in the gold film itself. A complication in this configuration is the extent to which the initial SAM may not fully cover the gold surface, and instead leaves gold atoms exposed to the analyte/buffer. This is a significant factor in the microcantilever response of SAM-coated microcantilevers as has been recently demonstrated.14 In order to determine the degree to which the surface coverage of an alkylthiolate is < 1.00, the recently described ferrocenyl label method was used.1,15 Electrochemical quantification of the ferrocenyl label is a versatile method in that it quantifies and classifies the small but important coverage defects in alkylthiolate SAMs. This method provides a defect number density and reports whether the defects are the size of individual alkylthiolate molecules or are clustered in nature.

123 In order that we might understand what the coating conditions create in terms of a

SAM, cyclic voltammograms (20 mV/s) of MUA-coated electrodes were obtained in 1 M HCIO4 using a Ag/AgCI reference electrode. The electrodes were subsequently rinsed with water and ethanol and incubated for 5 s in a 2 mM 12- ferrocenyl-1-dodecanethiol (FcDDT) solution. This sequence is optimized for

_u-lu' Passive SAM (2hrs) E-dep SAM, 16Hrs in pH3 PBS -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 E/Vvs. Ag/AgCI Figure 33: Defect labelling of MUA SAMs formed on a gold-bead electrode. Red: CV of an electrochemically deposited (E-dep) SAM (5min @ 200mV vs Ag/AgCI) prior to ferrocenyl labelling. The black curve corresponds to an E-dep MUA SAM probed with FcDDT. The blue curve is the CV of an electrodeposited MUA SAM that was incubated in pH 3.0 phosphate buffer solution for 16 hours, and then assessed with the FcDDT label. The dashed curve is the CV of a passively-prepared MUA SAM (2 hr incubation) followed by assessment with FcDDT label. The % defect labels are values derived from integration of the Fc signals of the CVs, as per the reference.'

124 ferrocenyl labelling of defect sites in SAMs.15 The resulting electrode was thoroughly rinsed with water and ethanol and another cyclic voltammogram was

obtained. The pH was maintained for specific periods of time, after which the electrodes were assessed using the ferrocenyl label methodology. Both

passively-prepared and electrodeposited MUA SAMs (black curves, Figure 33) were assessed by the ferrocenyl label method.

The electrodeposited MUA SAM maintained at pH 3.0 was assessed with the ferrocenyl label (Figure 33). Verification of the areal defect density before and after (16 h) incubation at pH 3.0 establishes that the extent of SAM surface coverage is not affected. MUA SAMs stored either pH 3.0 or pH 10.0 (118 h)

undergo very small changes in the surface defect density of the SAM: 0.1 % change at pH 3.0 and 0.3 % change at pH 10.0. MUA SAMs prepared by electrodeposition and passive-preparation are therefore stable to desorption at both pH 3.0 and pH 10.0. As little as 0.1% change in SAM coverage is detectable using the ferrocenyl label method. If the MUA SAM had deteriorated or partially desorbed from the surface during these prolonged storage conditions, a greater quantity of ferrocenyl label would have been deposited and detected.

Gold-coated microcantilevers cannot be reproducibly used in quantitative cyclic voltammetry because of the variability in the active gold area. Gold bead electrodes were therefore used as substrates for testing the SAM stability under conditions resembling those which the microcantilevers are exposed to. Unlike

125 microcantilever electrodes, the response of polycrystalline gold electrodes has been extensively used in SAM electrochemical studies.16"18 Both the HO2C-C11S-

Au SAM and the C12S-AU SAM were produced by incubation of freshly annealed gold-bead electrodes in 1 mM ethanolic thiol solution for 24 hrs. The electrodes were then thoroughly rinsed with ethanol to remove physisorbed thiols.

SAM capacitance provides an estimate of SAM thickness and density.19,20

Because the capacitance of an electrode immersed in an electrolyte solution is dependent on both the thickness and the dielectric constant of the film coating the electrode, the capacitance measurements are best used to assess changes in film thicknesses and composition. The capacitance, C, of a film on a metal electrode in an electrolyte solution is given by:

C = e~ (4.1) d where C is the capacitance (F), A is the area of the electrodes (m2), d is the distance between the capacitor plates (m), (i.e. between the electrode surface and the electrolyte solution), and e is the permittivity of the insulator film (F/m).

Changes in the SAM thickness or the SAM permittivity will therefore change the

SAM capacitance. The capacitance of a "blocking" SAM can be obtained from a cyclic voltammogram (CV). The capacitance is the average of the absolute values of the anodic and cathodic currents, ia, divided by the scan rate, v.

126 -PH3.02 140 -I pH 3.02 1/2 hr later - pH 3.02 1 hr later 120 - pH 3.02 2 hrs later pH 10.0 - pH 10.0 1/2 br 100- pH 10.0 1 hr -pH 10.0 20hrs 80- pH 3.02 after pH 10.0 -pH 3.02 1/2 hr after pH 10.0 60 40 H c 20 0^ o -20 -40- -60- -80 pH 3.02

I I | ,T""T,"1 I | 1—r ""I "!' | I 1 !»'|"'| IT T I p»rraT T" T f I "T'T I"" | ' I t r'T \ 1 I I "1 " |' "I I' I1 T'f'T'ir l'| -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 E / V vs SCE Figure 34: Cyclic voltammograms of an MUA SAM on a gold-bead electrode in 50mM LiC104 electrolyte. The electrode was immersed in pH 3.0 for the specified time intervals, after which the electrode was rinsed thoroughly with Millipore water (18MQ) and a cyclic voltammogram was measured. The electrode was then re-immersed in the phosphate buffer solution for another specified time period and the process was repeated. After a total of 2 hours, the solution was changed to pH 10 and the process was repeated. After a total of another 20 hours at pH 10, the electrode was returned to the pH 3 buffer solution.

(4.2) d v

The capacitance of a SAM at pH 3.0, pH 10.0, and then pH 3.0 again was determined from CVs. The capacitance remains constant at each pH value over prolonged times (<20 h) and multiple CV sweeps (Figure 34). The differential capacitance of the SAMs can also be directly measured through ac voltammetry.

This method assumes that the SAM-coated electrode and the cell can be accurately represented with an RC equivalent circuit.21 Table 3 lists the

127 capacitance data of an MUA SAM after incubation in buffer for the specified time

intervals. The differential capacitance at pH 10.0 is 24% greater than at pH 3.0. A

change in SAM permittivity due to the (de)protonation state of the terminal

carboxylate is the likely origin of this change.22 Both CV-derived and differential

capacitance-derived data establish that the MUA SAMs as prepared are stable to

surface coverage changes within the pH range of interest.

This conclusion is particularly important when the potential is scanned between

-500 and 400 mV (vs SCE) because MUA SAMs have been reported to undergo

a very specific type of reversible coverage change. Under very specific conditions, the acid terminal group is believed to fold over and interact with the gold surface, resulting in both the thiolate and the carboxylate binding to the gold.23 Sum frequency generation spectroscopy at specified applied potentials for

low density acid-terminated SAMs suggests that this "fold-back" process is reversible. The possibility that the SAMs, as used here, undergo a similar chain fold-back phenomenon must therefore be considered. This is important because such a process must then be accounted for in any description of the origins of stress in these microcantilevers. The observation of invariant CVs as a function of pH suggests that the densely packed MUA SAMs used here are not in fact prone to this "fold-back" process.

128 Table 3: Differential capacitance of an MUA SAM on a gold bead electrode in 50 mM LiC104. The capacitance was measured using ac voltammetry at 0 mV vs SCE for the SAM, subjected to incubation in pH 3.0 or pH 10.0 buffer for the specified time periods.

Elapsed Incubating Diff. Cap. Time (h) Solution (uF/cm2) + 0.02 0 pH3.0 1.74 0.5 pH3.0 1.71 1 pH3.0 1.76 2 pH3.0 1.78 0 pH 10.0 2.13 0.5 pH 10.0 2.17 1 pH 10.0 2.16 2 pH 10.0 2.20 0 pH3.0 1.77 0.5 pH3.0 1.76

4.4 Microcantilever Responses

The foregoing experiments established that the MUA SAMs prepared on both gold beads and gold-coated microcantilevers do not undergo alkylthiolate surface coverage changes and are resistant to surface density changes when cycled between pH 3.0 (protonated state) and pH 10.0 (deprotonated state). This conclusion is limited, of course, by the sensitivity and specificity of both the ferrocenyl label technique (Figure 33) and the capacitance measurements.

Estimates of accuracy are ±0.1% of the surface coverage. The microcantilever response under equivalent pH conditions, on the other hand, is quite complex.

Although many of the experimental parameters are well controlled, the surface stress response of the functionalized microcantilevers to pH change is clearly more complex than has been implied in the literature.10,12,24 Despite the methodical and consistent preparation procedures employed here for the SAM-

129 modified microcantilevers the responses span a large range. Stress value magnitudes vary widely and the response times vary by a factor of about 4. For these reasons, it was decided that an in-depth analysis of the SAM-modified microcantilever response to the pH experiment is required. The following is a methodical categorization and analysis of the different types of microcantilever response to pH change.

The "idealized" response

We begin by discussing the "idealized" SAM-coated microcantilever response to pH changes. A compressive stress is expected to develop within an MUA SAM at pH 10.0 from repulsive electrostatic (Coulombic) forces. Deprotonation of the carboxylic acid will create sufficient surface charge and electrostatic repulsion to cause the microcantilever to deflect towards the neutral, pH unresponsive CH3- terminated SAM (Figure 35). The process should be reversible and a return to pH

3.0 will lead to a return to the initial surface stress value.

130 * >H s-s • •&30 H _ * cOO H s \ t tOOH >A* m ^COOH - CCXW -'— COOH ft1-caw * 'LOOM •W-1MOI I rnon F."C M

Figure 35: "Idealized" response of an acid-terminated SAM-coated microcantilever to an increase in pH. Deprotonation of the carboxylate moiety results in a compressive stress causing the microcantilever to deflect away from the carboxylate-terminated SAM. Return to low pH returns the microcantilever to its initial position.

A representative experimental test of this "idealized" response hypothesis is shown in Figure 36. The bottom surface is Ci2S-Au coated (24 h passive

incubation in 1mm C-|2SH) and the top surface is MHA-Au coated (1 h passive incubation in 1 mm MHA). Once a constant stress signal (12 h) was achieved, the microcantilevers were exposed to alternating pH 3.0 and pH 10.0 challenges.

The tensile or compressive nature (directional sense) of the stress change is as per expected for an "idealized" response. However, the magnitude of the

131 response is not. The microcantilever does not return to its previous position after

a complete pH cycle. This hysteresis persists when the pH is cycled through

several periods.

Several other features of the stress/pH response are noted. Firstly, the time

required to attain a steady microcantilever position is very long (>1 h). Given that

the (de)protonation reactions studied proceed with rate constants for diffusion-

limited proton transfer in water on the order of 1010 M"1 s"1,25 the slow response of

the microcantilevers must arise either from processes within the SAM (such as

0.06-,

E 0.04 -\

CO to i_ 0.02

(D O 0.00 H -0.02

pH3.0 -0.04

T 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 2000 4000 6000 8000 10000 12000 14000 16000 18000 Time/ s Figure 36: Microcantilever surface stress response as a function of pH. Top surface: MHA SAM, bottom surface: C^S-Au SAM. Dotted vertical lines correspond to initiation of a pH change.

132 chain packing and reorientation) or processes in the underlying gold substrate.

Several complex combinations of these factors might be envisaged. For example,

changes produced within the SAM because of the deprotonation/protonation will

significantly alter the open circuit potential of the microcantilever. A slow

reorganization of the SAM as well as a potential-induced reconstruction of the

gold surface atoms may ensue. Relaxation times for these types of surface

reconstructions are on the order of minutes.26 Half-life (t-1/2) values for the

attainment of steady states for the microcantilever responses in Figure 36 are

1400, 460, and 950 s.1 These are all very long on the timescale of the

(de)protonation reaction and span a fairly large range. An MUA-functionalized

microcantilever exhibits similar response features (Figure 37); ti/2 values of

1100 s and 500 s are observed.

1 Note that the reaction half-life is used here as a simple indication of the timescale and reproducibility of the measurement. Neither 1st nor 2nd order-like kinetics are implied by determining the half-lives.

133 pH3.0

T 1 1 1 1 1 10000 15000 20000 25000 Time / s Figure 37: Microcantilever surface stress response as a function of pH. Top surface of the microcantilever is functionalized with an MUA SAM. The bottom surface is functionalized with a C12S-Au SAM.

For otherwise identically prepared microcantilevers, the differential surface stress can differ from that presented in Figure 36. The differential stress for the

MUA/Ci2S-Au-functionalized microcantilever (Figure 37) undergoes a stress change of 80 mN-m"1 upon switching between pH 10.0 and 3.0. An identical microcantilever from a previous experiment however undergoes a 3-fold larger stress change (Figure 38). The average U/2 value (pH 6.54, 7.53, 8.40, and 9.16) is 505 ± 30 s. The Un value is less when small pH increments are used compared to large pH increments. This is important evidence that a change in the organic film is dominating the form (kinetics, extent) of the surface stress change. Clearly

134 the microcantiiever response is governed by kinetic and not thermodynamic factors. A batch of several microcantilevers prepared under identical conditions gives response times (ti/2) ranging from 430±170 s to 710±300 s to 1050±300 s.

u.oo-

E 0.30^

0.25-|

0.20- co O O (D C\| O s CD s~ O . CO •*r •ST" iri / X I X X X Q. •e 0.15-j Q. Q. Q. O CD w / ^ 00 oi X X '•4-cJ 0.10- Q. Q. a (D CD r b 0.05-J r /

0.00- 1 p r ' p "I ' 1 r "' ' "1 • 1 • •" i • • • 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Time / s Figure 38: Microcantiiever coated with 5nm of Ti and 75nm of Au on both the top and bottom surfaces. Top surface is functionalized with an MHA SAM and bottom surface with a Ci2S-Au SAM.

135 Blank microcantilever response

A second class of microcantilever experiment studied here is referred to as the

"blank" microcantilever configuration. In this case, microcantilevers were coated

with identical C12S-AU SAMs on both the top and bottom surfaces. If the top and

bottom surface coatings (gold and alkylthiolate) are identical, any challenge

presented to these surfaces should yield a null response.

In fact, such microcantilevers are found to be nonresponsive to pH changes. It is

significant, however, that many of these "blank" microcantilevers also display

considerable drift during the measurement process. An illustrative differential

0.08 . • 0.06 z - pH 10.0 pHIO.O pH3.0 pH3.0 CO 0.04 CO CD 1— CO 0.02 CD O 0.00 rf a 3 CO /•j.^V-1 -0.02 j**rvrv\~/

"c+Jo CcD i_ -0.04 CD a= b -0.06 . _, , , ,—i 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 1 0 5000 10000 15000 20000 Time / s> Figure 39: Differential surface stress of microcantilever coated with C^S-Au SAMs on both the top and bottom surfaces vs. pH change of the buffer solution.

136 surface stress plot (microcantilever coated with C12S-A11 SAMs on both surfaces)

is shown in Figure 39. No discernable signal change is observable upon changing the pH from 10.0 to 3.0. There is, however, constant drift in the measured

differential surface stress throughout the experiment. The surface stress value slowly changes by as much as -25mN/m over a time period of 5 hrs. This drift

associated with ostensibly identically-coated (top and bottom surfaces)

microcantilevers is a serious complication which has not, to date, been reported in the literature.

Microcantilever drift

It is frequently observed that pH-induced stress changes are significantly smaller than the changes in background (drift). This problem is characteristic of freshly prepared microcantilevers subjected to the pH-change experiment immediately after SAM preparation. Some microcantilevers reach a steady state surface stress value in hours while others are still changing after 24 h in the phosphate buffer solution. For example, a microcantilever (Figure 40) that had been pre conditioned in buffer for >48 h exhibits large changes (ca 0.05 mN/m) superimposed on the surface stress resulting from a pH change. The pH-related stress changes are almost completely obscured by the large background drift.

Correcting for the drift (Figure 40) establishes that the compressive stress on going from pH 3.4 to 8.6 is reversed (ie. is in the tensile direction) when the pH is returned to pH 3.4. However the microcantilever has not yet reached a steady-

137 stress-state after the elapsed time intervals (ca. 0.5 h). The microcantilever drift is

thus a significant issue affecting microcantilever differential surface stress

measurements. This drift limits the reproducibility of the experiment and

confidence in the meaning of the analytical signal. Although incubating

functionalized microcantilevers in buffer solution prior to the experiment greatly

lessens the observed drift, perhaps by means of SAM rearrangement and

organization,27 the drift problem is by no means resolved by use of a backside

"reference" coating, as is shown in Figure 40. There is no question that the drift

problem described here is intrinsic to the SAM/gold/SiNx system as highlighted in the "blank" configuration described in the previous section.

V 0.10- E z ~~ 0,08- / to c6 3 X te o.oe- I / 1 o. / 1 o €O 0.04 - 3 (/} 0,02 • 1 / 1 I o.oo. H, - f ^ CO V l <5 X X Li !E -0.02- a. a. \ Q

—1 r-l 1 ]— -i—i—' -1 1 1 1 . 1 2000 4000 6000 8000 10000 12000 14000 16000 0 2000 4000 6000 3000 10000 12000 14000 16000 Time / s Time / s

Figure 40: Differential surface stress measurement for MPA-functionalized microcantilever displaying substantial drift after >48 h pre-conditioning in buffer solution. The compressive stress and tensile release thereof (pH 8.6 and back to 3.4) is overlayed on a linear drift (red line). Right hand side plot represents the drift-corrected data.

138 Anomalous stress response

In addition to the compressive stress observed with a pH 3.0 tolO.O change, in a

number of experiments a tensile response is also observed. An illustrative

example (Figure 41), a C12S-AU (top) / MUA-Au (bottom)-functionalized

microcantilever exhibits a tensile differential surface stress on going from pH 3 to

pH 10.0. Instead of a compressive stress as the pH is increased and a tensile

stress as the pH is lowered, the opposite is observed. This phenomenon is

attributed to the use of a NaF electrolyte solution which results in HF etching of

2 the SiNx substrate. NaF electrolyte solutions were abandoned once the HF

etching of the microcantilevers was realized at low pH values. This is discussed in further detail in Section 6.3 of the Appendix.

: 28 The pKa of HF is 3.17. HF is thus generated in NaF solutions at pH 3.0.

139 0.00 £

c/> -0.05 A pH 10.0 CO

.1—*

CO _

-0.15H

-0.20 T • T T ' 1 ' 1 ' 1 2000 4000 6000 8000 10000 12000 14000 16000 Time / s Figure 41: Differential surface stress vs pH for a bottom-functionalized microcantilever. Top surface coated with a C^S-Au SAM, bottom surface coated with an MUA SAM. Incubating solution is 50mM NaF. The pH was adjusted using dilute HC104 or dilute NaOH. The data is corrected for drift. The deflections are in an opposite sense to what was previously observed.

Nil Response

In addition to the types of responses described above, some MUA- and d2S-

(backside) functionalized microcantilevers were non-responsive to pH changes.

Although the microcantilever and SAM preparation procedures were identical to those exhibiting responses, microcantilevers occasionally do not deflect with pH change. These microcantilevers were obtained from the same SiNx wafer and were coated alongside the functional ones in the sputter chamber. Similar, if not

140 identical, metal films are expected to be deposited on all the microcantilevers thus prepared. The SAMs were generally prepared simultaneously using the same alkylthiol solutions, whether by passive incubation or electrochemical deposition and many times on several microcantilevers at once. The SAM preparation methods used are highly reproducible, as assessed by the ferrocenyl label and capacitance methods (Figure 33 and Figure 34). Some of the microcantilevers apparently have intrinsic structural defects which produce nil changes in the stress measurements. The microcantilevers can be of variable robustness, and it is interesting to note that several microcantilevers were broken by simply immersing them in solution. The surface tension of the solution, especially aqueous solutions, was sometimes sufficient to crack one or both of the triangular microcantilever legs. For this reason, the microcantilevers were always checked for cracks with an optical microscope and by scanning the laser beam up and down the microcantilever. However, it is possible that this superficial inspection process did not screen out all the cracked or defective microcantilevers.

4.5 Origin of differential surface stress - an overview

A measured differential surface stress can arise from several sources localized at the microcantilever surface. Electrostatic forces are a likely contribution to the differential stress signals. As the pH increases and the MUA SAM becomes deprotonated, the carboxylate anions located at the SAM-solution interface generate increasing electrostatic interactions as the average distance between

141 proximal charges decreases. Coulombic forces of isolated ions decrease with distance as 1/r2. However, in the case of solvated ions shielded by counterions, the field is shielded and decays exponentially with distance.29 An intermediate stage during the deprotonation has been speculated upon, where hydrogen bonding would produce a net tensile stress within the MUA SAM, as neighbouring carboxylate anions and carboxylic acid moieties form in-plane attractive hydrogen bonding.10 However, no tensile stress was observed in any of the pH 3 to 10 microcantilever experiments performed here. Indeed, it is highly likely that the observation described by Watari et. al. is an artefact resulting from the pH- dependent changes at the uncoated, backside silicon surface of the

12 microcantilever. Ji et. al. have shown that both the underivatized S\ZUA and SiC>2 surfaces of the microcantilevers are sensitive to pH and deflection results on changing the pH. Increasing the solution pH produces a finite compressive stress within the silicon oxide layer as the pH is increased from pH 3 to 6. The tensile stress described by Watari et. al. is thus unlikely to be a result of hydrogen bonding within the carboxylate monolayer, but instead is a Si02 response overwhelming the acid-terminated SAM response. Double-coating microcantilevers with SAM-coated gold films as described in this work were in fact undertaken to specifically avoid this problem. By coating both the top and bottom surfaces with Au films, microcantilever bending caused by the bimetallic effect is minimized. In addition, the chemistry of both microcantilever surfaces can be controlled with the appropriate selection of SAM. Passivation of one surface with a chemically unresponsive SAM and fixation of a responsive surface on the

142 opposite surface is a logical approach to reducing backside interference. For the experiments undertaken here, where need be, one of the microcantilever Au- coated surfaces is passivated with respect to a pH change by using a C12S-AU

SAM.

Stress changes in the MUA system may also arise from the interaction of the carboxylate anion with the underlying gold surface. This would require chain folding or bending. An increase in film hydrophobicity reported as a function of applied potential may have parallels in the differential stress of the microcantilever. 23,3° However, this phenomenon is unlikely to be responsible for the deflections reported here for several reasons. Firstly, Lahann et al. only observed this phenomenon for low density SAMs (from molecular simulations 9 ~

2.6x10"10 mol/cm2) prepared from a sterically-demanding thiol. Densely-packed

SAMs (from molecular simulations 0 « 6.6x10"10 mol/cm2) did not show the same switching behaviour. The acid-terminated SAMs used here (MUA, MHA) adopt a straight, unfolded conformation at open circuit potential when embedded in a densely-packed SAM. Because the acid-terminated SAMs used for this study were of relatively high density and were studied at open circuit potential, there is low likelihood that this conformational change has an effect on the microcantilever surface stress. Moreover, because the voltammetry and the differential capacitance results suggest that the MUA SAMs are stable to thiol loss on repetitive pH cycling, there is little likelihood that these SAMs have been converted to low density (coverage) forms during the experimental procedure.

143 Coulombic repulsion between carboxylate anions might be a source of differential surface stress. The electrostatic force between point charges is proportional to the magnitude of both charges and inversely proportional to the distance between them, Equation (4.3).29 The force generated by the carboxylate anions at the

SAM/solution interface can create a compressive stress within the SAM, and if transmitted to the underlying gold, can produce a deflection (Figure 42).

4=7^^, (4-4) 4ns„s • r

Where zi and Z2 are the acted upon and acting ionic valencies, e is the

19 elementary charge (1.602x10" C), r is the distance between the two charges, E0 is the permittivity of free space (=8.854 * 10"12 C2J"1m"1), e is the relative permittivity of the medium(for water £=78), and r21 is the unit vector between charges z2 and z-i.

144 Figure 42: Schematic of how Coulombic repulsion resulting from a pH increase at a carboxylic acid-functionalized microcantilever can result in a deflection. The topside SAM consists of MUA while the bottomside SAM consists of Ci2S-Au. As the pH increases, the MUA SAM becomes deprotonated and the cantilever deflects in response to the compressive stress of the top-side. The carboxylate anions are represented by red spheres.

145 The total Coulombic repulsion along the length of the microcantilever can be calculated for the case of a microcantilever with a fully deprotonated carboxylic acid-terminated SAM. Assuming that the carboxylate-terminated SAM forms a well packed c(4x2) lattice similar to that of alkylthiolates on gold, then the spacing between adjacent carboxylate anions can be determined for the unbent microcantilever. For a rectangular microcantilever 320 urn long and 22 urn wide in water, the total Coulombic repulsion along the length of the beam due solely to the nearest-neighbor carboxylates parallel to the length of the beam is ca. 380 mN. This is a conservative approximation that ignores additional forces arising from the double layer counterions, hydrogen bonding, and the complex nature of permittivity. It also ignores the latent neutralization of the calculated point charges by their counterions. In addition, this calculation does not calculate the surface energy of the surface nor the surface stress but this calculation nonetheless illustrates that the force generated in a deprotonated SAM is significant.

Counterions are likely to affect the net differential stress. Cations will be closely associated with the carboxylate SAM/solution interface. Changing the concentration, size, and charge of the counterions in solution should have a direct impact on the differential surface stress. Experiments with Ca2+ explored the ability of the ions to chelate two carboxylates simultaneously. This would significantly counteract the Coulombic repulsions and possibly result in a net tensile stress when the pH is increased. However, these experiments were

2+ inconclusive due to the precipitation of Ca as CaP04. The counterion

146 concentration for the case of non-specific ion associations is partially described

by the Gouy-Chapman-Stern (GCS) model.31 However, the SAM situation is more

complex than is accommodated by the GCS model. The SAM/solution interface is

permeable and some quantity of counterions may reside in the SAM itself.

Nonetheless, high concentrations of counterions increase the shielding of the

Coulombic repulsions of the carboxylate anions.32 Experiment however shows

that the differential stress is equally sensitive to a change in electrolyte

concentrations at low and high extents of SAM ionization (ie. low and high pH).

Decreasing the solution ionic concentration increases the Debye screening length

and thus is expected to increase the surface compressive force. However

lowering the ionic concentration has been shown to have the opposite effect.10

This may be a result of ion adsorption on the metal film and charge transfer

across the metal-electrolyte interface. This would have a significant effect on the

surface stress of the microcantilever.26

Another significant factor affecting the microcantilever differential surface stress is the surface stress generated within the underlying gold film as a result of

adsorbate binding and/or the SAM density. A clean gold surface has shorter

interatomic distances than does bulk gold. The surface atoms rearrange to

minimize the surface energy. Au (111) has been shown to contract into a

22x V3j lattice at the surface or a ca. 4.3% contraction along the (lIo\ axis.26

Upon adsorption of an adsorbate onto the clean surface (i.e. an alkanethiol molecule) the surface stress of the gold film will change. The electron

147 donating/withdrawing nature of the adsorbate is important. The adsorption of alkanethiol onto clean gold produces a compressive stress within the gold film33,34 due to the electronegativity of the sulfur atom and the resulting positive charge in the gold. This results in a lifting of the reconstructed (22x^3) gold surface.35 An analogous process occurs for the adsorption of ions onto a clean gold surface.

For example, adsorption of chloride ions onto gold results in a charge transfer.

This relieves some of the accumulated tensile stress of the clean surface.26 It is therefore noteworthy that the adsorption of ions, electrolytes, and impurities onto the gold surface during the microcantilever experiment will affect the surface stress. This phenomenon is likely to be contributing factor to the long response times required to attain steady-state in the pH experiments.

Finally, the net forces produced within the SAM due to solution pH changes likely result in slow molecular rearrangements of the SAM and possibly even a top-layer

Au restructuring. IR reflection-absorption spectroscopy studies have demonstrated that the crystallinity of carboxylic acid-terminated SAMs varies with the degree of film protonation.36 The degree of disorder (gauche defects) within the SAMs are shown to reversibly increase upon deprotonation of the terminal carboxylic acid. Subsequent immersion of the SAMs into acidified solutions regenerates the highly ordered states. This illustrates that changes in the charge of a SAM's terminal moiety are sufficient to cause the SAM to reorient and reorganize. These processes can take on the order of hours to days.37,38 The long times(Figure 36) required to reach a steady state stress values after a pH

148 change thus suggest that this slow SAM reorganization is a source of stress change.

4.6 Lattice Compression/Expansion due to the Geometric

Curvature of the Microcantilever

The geometric curvature of a bent microcantilever results in a finite lattice compression/expansion within the metal coating film. An estimate of this change is required to ascertain the stress produced upon the films when the microcantilevers deflect. Lattice compression/expansion of the gold film may result in a slow lattice rearrangement and gold reconstruction.

149 320 um" w 71 il ±. \ I 1 \ / 1 \ / I \ / 1 K Rl / \ I / \ I / 1 /

i / i/ i/ Figure 43: Lattice compression and expansion of the bottom and top gold films upon deflection of the microcantilever. Black dashed line represents the average microcantilever length; 320 um. The radius of curvature is obtained from the deflection measurement and the angle 0 is calculated from the average microcantilever length. The green line represents the gold monolayer experiencing the highest lattice expansion whereas the red line represents the gold monolayer experiencing the highest lattice compression. The percent expansion/compression is calculated from the difference in radius of curvature, ie. half the microcantilever thickness or t/2.

A 0.75 um thick, 320 um long, double-sided, gold-coated microcantilever

undergoing a 220mN/m differential surface stress experiences a lattice compression (or expansion) of 0.00087%. This change is insignificant w.r.t. the contraction of the gold lattice associated with the Au(111) reconstruction (ca,

4.3%) to a (22xV3) lattice.26 This calculation is performed as follows. Assuming that the average length of the microcantilever does not change, then the surface compression/expansion can be calculated from the Euclidean arc equation;

150 Having determined the radius of curvature, R, from the microcantilever deflection measurement, the angle 9 is determined from the average length of the microcantilever. The compression and expansion of the gold film is then calculated from the same angle 8 obtained in Equation (4.5) and the difference in radius of curvature, R, due to the thickness of the microcantilever. Figure 43 illustrates the regions of the microcantilever experiencing the most lattice compression/expansion. The green curve represents the gold monolayer with a radius of curvature of R+t/2 and the red line represents the gold monolayer with a radius of curvature of R-t/2. The maximum compression/expansion occurring in the outermost monolayers of the gold films for a microcantilever experiencing a differential surface stress of 220 mN/m is 0.00087%. The calculated contraction is also not comparable to the height modulation of the surface gold atoms, 0.2 A,26 arising from the top interlayer attraction. The lattice compression/expansion resulting solely from the microcantilever deformation is thus minimal compared to other processes involving surface reconstruction of bare gold surfaces.

151 4.7 Assessment of the Microcantilever Sensor via Response to

To examine the feasibility of using functionalized microcantilevers as chemical sensors, it is essential to understand the origin of the surface stress generated by interaction of an analyte with the surface. Acid-terminated SAMs offer an excellent test system for studying the origin of microcantilever surface stress changes caused by chemical stimuli. The acid-base reaction is reasonably well understood and has the opportunity to probe the mechanism(s) in play at a microcantilever surface. Several groups have reported results of acid- functionalized SAMs on microcantilevers. The conclusions from these studies have been both contradictory and incomplete. Other groups have reported significant drift.10,39 These studies do not use a reference microcantilever and/or overlook the effects of reactions at the microcantilever backside.12,40 The backside of silicon nitride microcantilevers, if left uncoated, will respond to pH

12 changes after slow hydrophilic conversion to SiOx. The double-sided coating system described in the foregoing allows one to study the acid-functionalized microcantilever while ensuring that the backside chemistry is either controlled or annulled.

C12S-AU SAMs formed on the backside serve to minimize silicon nitride and silicon oxide pH effects. This is a key point because SiNx slowly hydrolyzes to from SiOH, which in turn is pH-sensitive.12 In addition, this configuration serves to

152 minimize thermal drift effects arising from the bimetallic effect and functions as an internal referencing system. Other studies have left the SiNx/SiOx backside of the microcantiievers exposed to the experimental solution, leading to drift and pH- sensitivity.2,10,12 The microcantiievers used in the studies reported here are coated with identical gold films on both surfaces with a backside Ci2S-Au SAM.

This SAM minimizes non-specific interactions shown to occur on the underside of the microcantiievers. Removing (or as shown in the following, reducing) these effects has allowed for the analysis of microcantilever deflections to determine the surface pKi/2of the acid-terminated SAMs without interference from other sources of surface stress. Functionalized microcantiievers exhibiting stable baselines and minimal pH-associated hysteresis were used in the following studies.

153 Detemination of the SAM pK1/2 using a SAM-microcantilever system

Microcantilevers functionalized with an MUA SAM on the top surface and a C12S-

Au SAM on the bottom surface were used to determine the surface pK-|/2 of the

SAM carboxylic acid. This study is used to identify characteristics of the SAM-Au- microcantilever experiment that might, or might not, be conventional. In particular, these experiments serve to establish whether the response to chemical stimuli of a modified microcantilever is thermodynamically or kinetically controlled. The pH of the incubating solution was incrementally increased from low pH to high pH with phosphate buffers. The microcantilevers were monitored for ca. 1800 s after each pH change. The differential surface stress value at each pH was calculated as the average of the last 500 s of data before the next pH change was initiated

(Figure 44).

154 0.35

7 U.4U-^ z 0.35-

(/> 0.30- • J8= CO 0.25- • 8 0.20- 53 • CO 0.15-

1 0.10- • tO~J 0.05- • • • Diff e a> 0.00- D> • ro -0.05 • —i 1 —i ' 1 0 2000 4000 6000 8000 1000012000140001600018000 10 Time / sec pH Figure 44: Determination of the average differential stress of a microcantilever functionalized with an MUA SAM undergoing a pH titration. The average differential stress was determined from the last 500 s of data before the subsequent pH change. These regions are highlighted with blue-striped squares.

Fitting of the stress-pH data requires the assumption that the total surface concentration of surface carboxylate and carboxylic acid molecules remains constant throughout the experiment. This assumption is likely to be valid given the stability of the SAMs (Section 4.3) reported using differential capacitance measurements and the ferrocenyl probe method. The Henderson-Hasselbalch equation

[RCOCT] pH = pKy + log Surface (4.6) [RCOOH] iSurface

allows one to determine the surface pKV2 via equation:

155 (pH-^) 10 Constant [RCOO"] =Baseline + (4.7) L J Surface Pii-pKy^j 1 + 10

This equation is an approximation of the carboxylate anion surface concentration because it ignores several significant factors/Firstly, this equation does not take into account the electrostatic repulsion effects that become significant at higher pH. Such an effect would, in the higher pH regime, serve to make the extent of deprotonation per pH increment lesser than in the low pH regime. Secondly, it

7 0.40 n E ChiA2/DoF = 0.00061 Z 0.35- R*2 = 0.97009 w Baseline =0.030 ±0.013 0.30- pKa =6.99 ±0.20 Constant =0.264 ±0.021

Stre s 0.25-

/9J7 / 0.10- irentia l £ 0.05- •^ • b 0.00- • __^-"~

rag e -0.05- 1 1 (D 1 I ' t 1 ' \ i • i > \ 4 5 6 7 8 9 10 < pH Figure 45: Average differential surface stress vs. pH fit for an MUA functionalized microcantilever. Red curve is the best fit of equation (4.7) to the data (fit results in box) and the blue curves represent the 95% confidence intervals. Black curve is the theoretical "1-pK" model using a value of (3E=1.

156 assumes that the carboxylate anions are all in equivalent environments, similar to that of bulk solution acid/base reactions. However, surface-bound carboxylic acids involved in acid/base reactions are not necessarily exposed to identical environments. The ease of carboxylic acid deprotonation will vary with the ionization state of the nearest neighbours. The experimental microcantilever differential stress data vs. pH data fitted to equation (4.7) (Figure 45) yields a titration curve where the pK-1/2 of the carboxylic acid corresponds to the inflection point in the average microcantilever differential surface stress vs. pH curve. The surface pK-1/2 of the MUA SAM determined by fitting equation(4.7) to the data

(using nonlinear least squares fitting) yields a value of 7.0+0.2. The "1-pK" model41,42 takes into account the electrostatic repulsions at the surface yields the following relationship between [RCOO"] and pH:

pH-pK = \og± 4 + T-^-1 FJ ^ (4.8) [RCOOH] 2303([RCOOH] + [RCOO-])

where pK is the intrinsic pK value in the absence of electrostatic repulsions,

/3=1/RT, and £ is the potential of mean force due to the electrostatic interaction between a carboxylate anion and its surroundings. The theoretical fit (the black curve in Figure 45) closely approximates the observed differential stress. The 1- pK model cannot, however, be applied to the experimental data using a nonlinear least squares fitting, and is compared to the experiment by overlaying a theoretical curve onto the data. It therefore cannot be used to precisely determine

157 the surface pKi/2 of the SAM. Nonetheless, the comparison illustrates that equation (4.7) approximates the data well and yields an appropriate surface pKi/2 value. The pKi/2 value thus determined for the MUA SAM, being ca. 2 pH units

43 greater than the solution pKa of an alkylcarboxylate of ca. 4.8, is in agreement with several literature reports44"46 as well as our recent impedance-based results

47 (Chapter 3). The increased pK-i/2 value arises from several factors. The first is solvent dielectric in origin48 and is likely to be contributing a small amount (<0.3

units) to the observed change. Secondly, the alkylchains of the organic monolayer

present a non-polar medium which disfavours acid dissociation. 45 Thirdly, due to classical electrostatics, H+ and OH" surface concentrations are altered by the developing negative surface potential of the SAM.48 The titration curve of the surface carboxylic acid SAM is notably broader (extending between 5.5 and 8.5) than the equivalent titration of similar carboxylic acids in solution. This broadening is attributable to the surface charge effects. As the SAM becomes progressively deprotonated, the activation barrier for the deprotonation of the remaining carboxylic acids increases due to the excess surface charge. This resistive effect causes the remaining carboxylic acids to require higher pH to be deprotonated and thus results in a broader titration curve. Both the increased surface pKi/2 value and broadening of the surface acid titration curve are in good agreement with reported measurements on carboxylic acid-terminated SAMs.44,47

158 E 0.08 Chi"2/DoF = 0.00002 • z R*2 • 0.99006 in 0.07- --;-"" in Baseline =-0.0006 ±0.0024 0.06 pKa = 6.85 ±0.11 55 Constant = 0.0737 ±0.0037 0) 0.05 o •g 0.04 • w 0.03' /• Ij 0.02 • / / // / i 0.01 • 0.00 " , V a) -0.01 • I pH

E 0.08- • CI#2/DoF = 0.00003 A R 2 * 0.97492 // V 0} 0.06- Baseline 0.0046 ±0.0029 ' } pKa 7.77 ±0.14 Constant 0.0722 ±0.0056 \ / '

W 0.04

OJ 0.02 b »•""' .,.-••"'' . • ""* b)

0.18- • Chi"2/DoF -0.00014 0.16- R*2 " 0.9784

0.14- Baseline 0.0137 ±0.0061 pKa 7.74 ±0.13 to 0.12- Constant 0.160 ±0.011 0.10- 0.08- /// 0.06-

0.04- /// „.»•" 1 0.02- • --''' 0 00- * ^ «>

1 0.02- • 1 • 1 - 1 •- 10 PH Figure 46: Fit of equation (4.7) to the average differential surface stress vs pH data for three (a,b,c) MUA-functionalized microcantilevers. Red lines represents the best-fit curve and the blue lines represent the 95% confidence intervals.

159 Differential surface stress vs pH measurements on similar microcantilevers functionalized with an MUA SAM yields similar results in terms of surface pKyz and broadening of the titration curve. However the magnitude of the differential surface stress change observed varies significantly from microcantilever to microcantilever. Plots of sample average differential stress measurements vs pH for three MUA functionalized microcantilevers illustrates this situation (Figure 46).

The average calculated surface pK-1/2 value is 7.45 ± 0.07. An incremental return to low pH reproduces a similar titration curve contaminated with the previously described hysteresis effect. The surface pKi/2 value appears to be a constant of this SAM system and the range of pKi/2 values observed is related to the measurement process of the microcantilever experiment.

0.10 E • 3-Mercaptoproprionic acid SAM • Z • 16-Mercaptohexadecanoic acid SAM w 0.08- 2 / aCZ CO // 0) /ml 0 0.06- / /* CO To 0.04- c /* / fe 0.02- Q 1J J 0 ca •— =*^ fc 0.00- > < 1 1 ' 1 1 1 • 1 ' 1 • 1 1 1 • 1 • ! 3 4 5 6 7 8 9 10 pH

Figure 47: Differential surface stress vs pH for MPA and MHA functionalized microcantilevers.

160 Similar experiments with SAMs of differing chain lengths were performed. These experiments addressed whether the chain length affects the differential surface stress values. Microcantilevers were prepared with 3-mercaptoproprionic acid(MPA) and 16-mercaptohexadecanoic acid (MHA) SAMs to complement the

MUA studies described in detail in the above. MPA SAMs are known to be particularly unstable compared to MUA and MHA SAMs. Large differences in the absolute differential surface stress observed in repeat experiments makes it impossible to establish a relationship between chain length and response.

Nonetheless, the short MPA and longer MHA acid-terminated SAMs exhibit sigmoidal surface stress titration curves and similar surface pK-i/2 values (6.5±0.2 and 7.2±0.2 respectively) (Figure 47).

4.8 Conclusions

Carboxylic acid-functionalized microcantilevers respond to pH changes. The electrostatic repulsion of the carboxylate anions is sufficient to produce a compressive stress within the SAM which then causes the microcantilever to deflect. Coating the microcantilevers with metal films on both surfaces minimizes differential surface stress effects resulting from the bimetallic effect. Furthermore, coating the second surface with an alkyl-terminated SAM allows for the control of backside chemistry and/or function as an internal reference.

SAM-functionalized microcantilever sensors still require further investigation due to the shortcomings described herein. Microcantilever responses vary significantly

161 and the magnitude of the differential surface stress show important discrepancies for similarly prepared microcantilevers. Film adhesion to the silicon nitride substrate and the possibility of micro fissures within these will have to be studied to determine if these may be responsible for the observed unresponsiveness of certain microcantilevers.

Analysis - Assessment - Overview

The following itemized list summarizes the main conclusions ascertained from the microcantilever pH experiment and the subsequent analysis of the data.

1. The kinetics of the microcantilever response as a function of pH change are

3 such that the ti/2 of the responses are on the order of ca. 10 s. Because the

rate constant for (de)protonation in solution of carboxylates is on the order of

1010 M"1 s"1,25 it is evident that the microcantilever responses are not

reporting the (de)protonation event. Instead the microcantilevers are

reporting a combination of effects occurring within both the organic film and

the gold film.

2. The surface pKi/2 of the MUA-functionalized microcantilever is 2-3 units

higher than that of the analogous acid in bulk aqueous solution. The surface-

tethered carboxylates behave classically relative to surface carboxylates.

The measured surface pKi/2 is higher and the surface force titration curve is

significantly broadened due to several factors discussed in Section 4.7.

162 3. Hysteresis in the microcantilever response is important and affects most of

the microcantilever pH experiments. This implies that the SAM on gold

surface has rearranged in some fashion after a solution pH change and

requires a long relaxation/reorganization time to reach a steady state.

Incremental pH changes (ca. 1 pH unit steps covering 7 pH units) vs. large

pH 3.0 to 10.0 jumps yield different responses. While the surface pK-i/2

appears to be a thermodynamically controlled change, both the pH

increment and pH reversal experiments clearly show that these are

kinetically controlled phenomena in which the structural changes in both the

SAM and gold determine the measured differential surface stress.

4. Gold film rearrangement likely plays a significant role in the slow response

times of the pH induced differential stress changes. Coulombic repulsion

within the SAM may produce sufficient stress on the gold film to cause a

slow rearrangement of the surface gold atoms, thus contributing to both

hysteresis and long Un values.

The results of responsive microcantilevers demonstrate that the microcantilever sensor functions in solution and is sensitive to Coulombic repulsions resulting from the (de)protonation of the SAM. The surface pK1/2 values of MUA, MPA, and,

MHA SAMs were determined and corroborate the literature observations that the

163 surface pK-1/2 of these SAMs are shifted ca. 2 pH units higher than the equivalent

acids in bulk aqueous solution.

In response to the original query posed by this investigation, we do not believe

that the microcantilever sensor, in its current state, will be developed into a lab-

grade tool. Reports suggesting that such systems will eventually be converted

into portable systems capable of possibly identifying DNA base-pair mismatches

or identifying contaminants in miniscule amounts from liquid samples do not

agree with our observations. The system setup and detection mechanism are

highly complex and sensitive to many forms of noise and interferences.

Microcantilever preparation methods require meticulous attention that will otherwise affect reproducibility. Even with this attention to detail, using a range of

improvements in instrumentation and microcantilever preparation methods, drift and hysteresis signal contamination are persistent. For these reasons, the

microcantilever sensor will only become a tool for solution analysis when the fundamentals of microcantilever preparation are worked out to a much greater

level of reproducibility.

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8. Yue, M.; Lin, H.; Dedrick, D. E.; Satyanarayana, S.; Majumdar, A.; Bedekar, A. S.; Jenkins, J. W.; Sundaram, S. J. Microelectromech. S. 2004,13, 290-99.

9. Bailer, M. K.; Lang, H. P.; Fritz, J.; Gerber, C.; Gimzewski, J. K.; Drechsler, U.; Rothuizen, H.; Despont, M.; Vettiger, P.; Battiston, F. M.; Ramseyer, J. P.; Fornaro, P.; Meyer, E.; Guntherodt, H. J. Ultramicroscopy 2000, 82, 1-9.

10. Watari, M.; Galbraith, J.; Lang, H.-P.; Sousa, M.; Hegner, M.; Gerber, C; Hortonan, M. A.; McKendry, R. A. J. Am. Chem. Soc. 2007,129, 601-09.

11. Ji, H.-F.; Dabestani, R.; Brown, G. M.; Britt, P. F. Chem. Comm. 2000, 457-58.

12. Ji, H. F.; Hansen, K. M.; Hu, Z.; Thundat, T. Sens. Actuators, B 2001, B72, 233-38.

13. Ulman, A. Chem. Rev. 1996, 96, 1533-54.

14. Monga, T. Surface Stress at the Solid-Liquid Interface: Alkanethiol Monolayers on Gold. McGill University, Montreal, 2006.

15. Lee, L. Y. S.; Lennox, R. B. Langmuir 2006, 23, 292-96.

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17. Luo, L.-Q.; Cheng, Z.-L.; Yang, X.-R.; Wang, E.-K. Chin. J. Chem. 2000,18, 863- 67.

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167 Chapter 5 Conclusions, Contributions to Original Knowledge, and Suggestions for Future Work

168 5.1 Conclusions

Microcantilevers with different self-assembled monolayers (SAMs) on the top and

bottom surfaces were prepared to assess the double-coated microcantilever as a

solution-phase sensor in the static-deflection mode. Silicon nitride

microcantilevers were functionalized differentially on the top and bottom surfaces

using self-assembled monolayers (SAMs). A C12SH SAM was deposited onto

one of the gold-coated surfaces. This "backside" functionalization serves both as

an internal reference and a control of the chemistry of the non-responsive

surface. The opposite surface of the microcantilevers was then functionalized

with a carboxylic acid-terminated SAM. The response of the functionalized

microcantilevers to pH changes was then studied. The microcantilevers respond

reversibly to solution pH change. Incremental pH changes produce surface force

titration curves similar to that of the analogous acid dissolved in aqueous

solution. However the titration curves are significantly broader and the pK-|/2 of

the terminal carboxylate is several {ca. 2) pH units higher as expected for

surface-bound reactions.

The double-coated microcantilever functions as a solution-phase sensor.

However several obstacles are noted that prevent the practical implementation of these microcantilever-based solution sensors. Firstly, the response of the

microcantilevers, as shown here and in several prior reports, suffers severely from drift. This phenomenon is attributed to several factors, notably the slow

169 surface reorganization of the SAM and the change in the surface free energy of the underlying gold with the adsorption of ions and impurities. In addition, the response of the microcantilevers, although reversible in gross features, is contaminated by significant hysteresis. The pH changes lead to long response half lives. Finally, although the system in itself (including the optical setup, liquid cell, and software) is reasonably straightforward, the microcantilever preparation procedures and alignment of the optical components requires extreme care and meticulous attention. Small variations in the coating procedures, uniformity of the gold films, and/or the manipulation of the microcantilevers have important consequences for the response of the microcantilevers. For these reasons, the practical implementation of the solution-based microcantilever sensor is unlikely at present.

The pH-dependence and potential-dependence of the non-faradaic cyclic voltammetry peak of an 11-mercaptoundecanoic acid (MUA) SAM was studied. A model was derived to describe the electrochemical impedance spectroscopy

(EIS) response of the MUA SAM as a function of pH. This technique illustrates that EIS data can be used to determine the surface pKi/2 of acid- and base- terminated SAMs.

170 5.2 Contributions to Original Knowledge

The development of microcantilever-based sensors is in its early stages. The push for applied applications has left a void in the understanding of the mechanism of chemistry-related responses in these systems. This Thesis describes in detail the obstacles and issues facing current microcantilever architectures using a surface reaction exhaustively studied via EIS. In doing so, the following contributions to original knowledge have been presented:

i. Doubly-coated microcantilevers are more stable (than are singly-coated ones) to thermal drift effects caused by the negated bimetallic effect. This method also allows for "controlled" chemistry of the microcantilever unresponsive surface.

By coating both the bottom and top surfaces of the microcantilevers with equivalent gold films, thermal drift resulting from the differential expansion coefficients of gold and silicon nitride are significantly reduced. In addition, coating the microcantilevers with gold films on both surfaces of the microcantilever allows for the deposition of a chemically responsive SAM on one surface and a non-responsive SAM on the opposite surface.

ii. A sequential procedure for the preparation of doubly-coated microcantilevers has been developed. Microcantilevers are coated with gold films and SAMs (same or different) on both surfaces. The deposition of the second

171 SAM is performed under potential control to minimize thiol exchange and

desorption of the initial SAM.

iii. A model has been derived describing the non-faradaic peak of

11-mercaptoundecaoic acid SAMs on polycrystalline gold electrodes. The

intensity and position of the peak are attributed to the kinetics of proton exchange

from the SAM/solution interface. It is shown that the rate constants for the

(de)protonation reaction along with the pKi/2 of the acid can be determined

electrochemically if the value for>A can be evaluated. The required term, A, is the

change in surface charge density with change in degree of SAM ionization at

constant applied potential

iv. The surface pK1/2 of carboxylic acid-terminated SAMs is obtained from the

differential surface stress measurement of doubly-coated, self-referencing

microcantilevers. An incremental change in pH produces a differential surface

stress titration curve from which it is possible to extract the pK-i/2 of the surface-

bound acid.

v. Several issues with the current state of microcantilever-based solution

sensors are evaluated. Signal drift, hysteresis, and long response times continue

to hinder the development of these sensors into practical devices. The limitations

of such systems and possible causes for these difficulties are discussed.

172 5.3 Suggestions for Future Work

i. Rather than exploring microcantilevers applied to solution-phase sensors for

complex mixtures, further studies aimed at understanding the fundamentals and origins of surface stress for the existing systems are required. Otherwise, the lack of response reproducibility will deter researchers from adopting the method.

Existing pH, DNA hybridization, and ion-chelation microcantilever experiments

require strict operating conditions and drift issues persist. This is rarely, if ever, adhered to in the literature. Instead of pursuing more complex environments of interest, stepping back and studying the system under "simpler" conditions may resolve several issues.

ii. Further studies should be undertaken to develop microcantilevers with responses having little or no drift and minimal hysteresis artefacts. One possible route may be to further simplify the microcantilever architecture and remove the gold films. This would help establish if the surface chemistry of the gold and ion- dependent events are the cause of the slow response times and hysteresis.

Functionalization of the microcantilevers would thus require SAMs of a different kind, possibly tethered to the surface using silane chemistry.1,2 However the

173 preparation of high quality alkyltrichlorosilane SAMs is complicated and results in

incomplete monolayers or polymer-coated surfaces.3 Differential functionalization

of each surface of the microcantilever would also be complicated. A photo-

induced covalent binding of the SAM to the surface might provide a viable route

towards differentially modifying both surfaces of the microcantilever. Moreover,

covalent bonds between the microcantilever material and the responsive SAM

should alleviate many of the response issues discussed here.

iii. As was suggested, in order to determine the surface pK-i/2 of acid-

terminated SAMs on gold electrodes using the model derived in Chapter 3,

X = {dam/dO)E, must first be evaluated. The combination of potential-modulated

infrared reflectance spectroscopy (PM-IRRAS) and chronocoulometric

experiments on the acid-terminated SAM on gold electrodes may be able to

provide a value for A. Initial experiments to this end have been attempted,

however limited instrument time and low signal-to-noise prevented an accurate

determination. More in-depth studies under varying conditions are required to

calculate A and eventually determine the surface pKi/2 of base- and acid-

terminated SAMs.

iv. Adopting a novel microcantilever architecture may resolve many of the

issues described here. The main reason for using static deflection mode and not

dynamic mode measurements in solution is that the Q factor of the

174 microcantilever is greatly decreased in solution. A recently reported microcantilever operates under vacuum and is imbedded with microchannels.4 It allows for the use of the microcantilevers in the dynamic mode while flowing solutions within the microcantilever. Although the design of the microcantilever does not currently facilitate the measurement of differential surface stress, functionalizing the inner top and bottom surfaces of the microcantilever channels with differing SAMs may eventually permit the direct measurement of differential surface stress. This would allow for the monitoring of the differential surface stress effects in both the dynamic and static modes.

175 References

1. Ji, H. F.; Hansen, K. M.; Hu, Z.; Thundat, T. Sens. Actuators, B 2001, B72, 233-38.

2. Fadeev, A. Y.; McCarthy, T. J. Langmuir 1999,15, 7238-43.

3. Ulman, A. Chem. Rev. 1996,96, 1533-54.

4. Burg, T. P.; Mirza, A. R.; Milovic, N.; Tsau, C. H.; Popescu, G. A.; Foster, J. S.; Manalis, S. R. J. Microelectromech. S. 2006,15, 1466-76.

176 Appendices

177 6.1 Software Design

Software was designed in order to perform data acquisition for the microcantilever differential stress measurements. To automate and simplify repeat data measurements, LabVIEW6i (a visual programming platform) was employed to construct software that would acquire data, average the results, and control specific portions of the experiment. The program was designed to achieve the following.

a. Control of laser intensity

The software initially prompts the user for a selected laser applied voltage. This voltage is applied to the laser diode through a BNC connection to modulate the intensity of the laser. Once the value is selected, the applied voltage is maintained throughout the duration of the experiment.

b. Data acquisition

Voltage measurements, corresponding to the laser spot positions on both position sensitive detectors (PSDs), are performed in a continuous fashion at a rate of 200

Hz and collected as separate data sets. The voltages are acquired using a

National Instruments data acquisition card (DAQ) connected to the current-to- voltage converter, model # OT-301SL, described in Section 2.5, through a BNC

178 connector box. The data is then averaged such that one point/sec is displayed and saved for each PSD. The LabVIEW software is designed such that the averaged data is saved and displayed concurrently while the experiment is running. This was a precaution taken to prevent loss of data in the event of a buffer overflow and "freezing" of the software. The graphical display of the data is also designed such that specific sections of the data may be isolated and/or emphasized for further study, without affecting the data acquisition. Once the specifiec data acquisition time has expired, the software checks if the "Turn off lasers after acquisition" controllers were depressed during the course of the experiment. If so, the software outputs 5 V through the National Instrument digital- to-analog converter to shut off the lasers. The program then terminates. The

Cantilever EApteriments with pH Measurement

STOP

Figure 48: Start-up panel of the LabVIEW data acquisition software. Provides three options: Calibrate the pH meter using buffer solutions, proceed directly to the cantilever deflection acquisition portion of the software, or cancel.

179 startup panel of the software is displayed in Figure 48.

The initial panel provides the user with the option to either calibrate the pH meter that is interfaced to the LabVIEW software or to proceed directly to the microcantilever deflection acquisition portion of the software. If the user selects to calibrate the pH meter, the software calls the panel displayed in Figure 49.

Once the pH calibration window has been accessed, the user may then perform a

i> pi I talih 61.vi ItllQpCl File Edit Operate lools |ro' PI • (Hi pH Calibration j QVT]^™

; Calibration Solution =*1 ' v4.00 167 pH : mV jeading channel (0) !$rhanrai2" " pi- J n„' 2 116?'~ "' Calibration Solution -2 , .'J7.00 :-l

intercept mse Calibration Solution n3 \ ;.';10.00 ;.';-16p fss-sT. aw 17 J Wtib I

pH ;a-bratain Graph 200.0

MO |5G0 2C0 0 253 0 3QC 0 3bC 0 Trno *2J u7:\ Figure 49: pH calibration panel of the LabVIEW acquisition software. The three pH buffer values are listed in the left column. The measured electrode voltage readings are listed in the right column. The bottom-left plot displays the real-time electrode voltage and the bottom-right plot displays the 3-point calibration.

180 three point calibration. The selected buffers are first entered and the corresponding voltage readings from the pH meter are entered. If the meter has an analog recorder output for the electrode millivolt reading, it can be interfaced directly to the software through channel three of the DAQ card. With this configuration, the electrode potentials are read directly through the software under the indicator "pH:mV reading". The software then calculates a best fit line for the calibration, calculates the slope, intercept, and standard error. Having completed the pH calibration, the user must then select the "Done" button to return to the start-up interface. There, the user proceeds by selecting the "Run

Experiment" button as shown in Figure 48 to initiate the data acquisition. The data acquisition interface is illustrated in Figure 50.

181 Ole gbit Operate lools groi "'•; (fill

Total time for run (Hours)

Number of points to average o

Scan rate (samples/sec)

Input buffer size

L«irAppMVott»g«- DoNOTcrntigtonc* tcqunitiort II itirtad. i El

Y- coord, Delta yb/w of cursor 1 cursors £,59Etrj! Y-coord.

hnyo lU.ODQ IIP.71 MBA

Lai Figure 50: Data acquisition panel of the Lab VIEW software. Buttons along the left-hand side control the laser diode intensity, buffer size, total acquisition time, and data acquisition rate. The large plot displays the real-time non-calibrated laser positions (V) vs. time (s). The bottom plot displays the real-time solution pH of the solution in the cell.

The data acquisition panel contains two separately controllable graphical interfaces. The top one displays the laser spot positions of PSDs 1 and 2 in volts with the green and white lines respectively. The y-axis is set in units of volts and ranges between ±10V. The x-axis on both graphical displays has units of seconds and auto scales as the experiment proceeds. The lower display plots the real-time

182 solution pH. Both of the graphical displays can be controlled during the experiment to focus select data or view the entire experiment using the tools

located above and below the plots.

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r,"""ii.*!ftii;'~"[+>- • ipj|Di 0- =[>>...

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jjlgpgf Intercept] >number to read each tlme> m^.^Ji^UJ™-

[Stops Acq in case 1 ToP error I •a ; \-^

jp->nunnbof to check for last read>— d*> is> s> o rn

^u!jLmjiusuiaia50gOiOMJ^«iimDip:orQaKU?tmj55i LsJ ^2 Figure 51: Graphical code for the Lab VIEW data acquisition software used for the microcantilever experiment. The software runs an iterative loop which constantly verifies the state of the experiment along with the entered experimental conditions.

183 6.2 Calculation of Rp and Cp

This is the derivation of the explicit expressions of the resistor and capacitor for the (de)protonation reaction of Chapter 3.

The forward (protonation) and backward (deprotonation) rate constants for the

+ reaction H + A" <—> HA can be represented as kf and kb respectively.

bf{E E0) kf=k°/e- - (6.1)

aX bf = Where RTr<°< (6.2)

H-HQ (6.3)

Where RTr<°< (6.4)

Therefore, the rate of change in the degree of ionization is written as

+ ^ = kb(l-0)-kf0[U ] dt (6.5)

Thus the current due to the (de)protonation reaction is

+ ip=A(kb(l-0)-kf0[H ]) (66)

184 X = (dajde\ Where (6.7)

And am is the surface charge density.

Therefore, for small perturbations

0{t) = 0s+d0(t)

E(t) = Es+dE(t) i t i +di t P{ ) = P, { ) (6.8)

k,0 [IT] = k (l-0,) M b (6.9)

k 0 [H+] = k -k e f s b b s (6-10)

0 (k [H+} + k )=k s f b b (6.11)

0S= ^ k,[H+] + kb (6.12)

Both the degree of ionization and (de)protonation currents are functions of the degree of ionization and applied potential.

d0 f E) Tr ^ iP-g{o,E) (6.13)

$0 dE(t)- d0(t) ydty dE (6-14)

f = k (l-0)-k 0[H+] Note: b f (6.15)

185 f = k eW^(l-0)-k~M^W+e-'W0[H+1] So o o (6.16)

b {v K) + = -k/^-k0e- ' - [H ] \d9jv (6.17)

+ = -kb-kf[H ] (6.18)

Av K) + : k/^°) (x-e)bb + koe-" - 0[H ]bf ydVj (6.19)

+ kb(\-0)bb+kf0[H ]bf (6.20)

+ + • (-kb-kf[H ])d0 + (kb(l-0)bb + kf0[H ]bf)dV dt . (6.21)

+ + A^y(-kb-kf[H ])A0 + (kb(\-0)bb+kf0[H ]bf)AV (6.22)

a = k (\-0)b +k 0[H+]b Let b b f f (6.23)

-b = -k -k [H+] b f (6.24)

'dd^ = a-AV(t)-b-A9(t) So ydt j (6.25)

p AK(0 + [—I -A0(O Similarly \dV 80 (6.26)

186 g = x{koe^v-^(l-B)-ko0[H+yb^-v")} Where (6.27)

b v ) + b Vo) = X\k°-(l-0)-bbe ^- " + k°-b£[H ]e' ^- KdVj (6.28)

Substitute equations (6.1) and (6.3) into equation (6.28)

+ |M =A.{kb-(l-0)-bb+kf-bf[H ]-0} (6.29)

Substitute equation (6.23) into equation (6.29)

d ^ g X{a] dV (6.30)

fdg\ :X{-k°eh(V-v°)-k\H+}e-bf(v-v°)} (6.31)

r dg} + = A{-kb-kf[H ]} \dOjv (6.32)

Substitute equation (6.24) into equation (6.32)

= A{-b} \d0Jv (6.33)

AI =A[a-AV(t)-b-A0(t)] So p (6.34)

Find the Fourier Transform of (6.25) and (6.34)

Note: The Fourier Transform of a derivative is ik x f(k)

187 So

j-co- A0O) = a • AV(co) - b • A0(co) (6.35)

AI {o)) = A\a-AV{cD)-b-Ae{co)^ p (6.36)

. . . a-AV(a>) A0{co)-s — ' Thus j-co + b (637)

From equation (6.36)

AI (w) f • = a-AV{m)-b-A0(co) (6.38)

AIAoj) a-AV(co)— /v A0((o) = ^— Thus b (6.39)

188 Therefore by combining equations (6.37) and (6.39) we obtain

a-AV(co)_a-AV(co) AIjco) A6(co) •• j-co + b b b-X (6.40)

Multiply both sides by b

b-a-AV(co) AIjco) = a-AV{co)- j-co + b X (6.41)

Subtract «Aj7(^)

b-a AIjco) AV{co) --a j-co + b X (6.42)

Rearrange the impedance

AV{a>) 1 jco + b jco + b AI(co) X ab - ajo) — ab -ajco (6.43)

AV(co) 1 J

AV(co) 1 1 + - AI(co) a-X J°>. (6.45)

From equations (6.23) and (6.12) we obtain

+ _ "•/"•kfkb[H* t ] a + (bb+bf) k,[H ] + kt (6.46)

189 Therefore replacing equation (6.46) into equation (6.45) we obtain the impedance for the (de)protonation reaction. This consists of two parts, which corresponds to a series combination of a resistor and a capacitor.

+ AVjco) = 1 kf[H ] + kb Lb' AI(t»)~ Ak k [H+](b +b ){ + jco f b b f (6.47)

The resistance (Rp) is the real portion of equation (6.47)

+ 1 kf[H ] + kb R Ak k [H+](b +b ) So f b b f (6.48)

~* Capacitor And since JoCp then

— = RpP -b C. (6.49)

C„ " R -b p (6.50)

190 6.3 Microcantilever Experiments in NaF Solutions

Several experiments were carried out without the use of phosphate buffers. NaF was used as a solution electrolyte and the solution pH was varied using dilute solutions of NaOH and perchloric acid. Fluoride ions, perchlorate ions, and sodium ions are commonly used in gold electrochemistry because of their low binding affinities to gold.1,2 The solution pH values were adjusted in real time while maintaining a constant flow rate through the cell using the peristaltic pump.

Experimental results with these systems generally suppported the phosphate buffer experiments but displayed extreme microcantilever drift, especially at the lower pHs. The microcantilevers were observed to be functional, but for only short time periods. It was eventually observed that the gold films on these microcantilevers was being irreversibly damaged. The reflected laser beam off the tip of the microcantilever was initially specular but soon became diffuse after cycling the solution pH. Further examination of the gold surface by optical microscopy confirmed the presence of cracks and scaling of the gold films. It was

3 concluded that under the low pH conditions, enough HF was present (pKa= 3.17 ) in solution to etch away at the silicon oxide on the microcantilevers. Although the microcantilevers are silicon nitride, a small oxide layer is always present at the surface, upon which the titanium adhesion layer and the gold film are deposited. It is likely that HF slowly etched the edges of the microcantilevers that remain

191 uncoated and seeped under the gold film to cause the film to degrade. For this reason, this experimental approach for testing the microcantilevers was abandonned.

6.4 Radius of Curvature Calculation

Calculation of the radius of curvature for a bent microcantilever is done as follows.

This calculation applies to the calibration of the microcantilever deflection for

Chapter 2. For a microcantilever with a small deflection (Figure 52), Az, such that

Figure 52: Schematic for determining the radius of curvature of a bent microcantilever. R is the radius of curvature. Az is the microcantilever deflection.

192 Az «l, where I is the microcantilever length, then the radius of curvature can be determined from the following.

R = \la +b = + — « 2Az 2 2Az

By using the following: a = R-Az and b = l-Ay»l since l»Ay.

193 References

1. Lipkowski, J.; Shi, Z.; Chen, A.; Pettinger, B.; Bilger, C. Electrochim. Acta 1998, 43, 2875-88.

2. Haiss, W. Rep. Prog. Phys. 2001, 64, 591.

3. Christian, G. D., Analytical Chemistry. 5 ed.; John Wiley and Sons, Inc.: New York, 1994;p 812.

194