β-Cyclodextrin Host-Guest Complexes Probed under Thermodynamic Equilibrium: Thermodynamics and AFM Force Spectroscopy

Article abstract of DOI:10.1021/ja0383569

The rupture forces of individual host-guest complexes between β-cyclodextrin (β-CD) heptathioether monolayers on Au(111) and several surface-confined guests were measured in aqueous medium by single molecule force spectroscopy using an atomic force microscope, Anilyl, toluidyl, tert-butylphenyl, and adamantylthiolss (0.2-1%) were immobilized in mixed monolayers with 2-mercaptoethanol on gold-coated AFM tips, For all guests and for all surface coverages, the force-displacement curves measured between the functionalized tips and monolayers of β-CD exhibited single, as well as multiple, pull-off events, The histograms of the pull-off forces showed several maxima at equidistant forces, with force quanta characteristic for each guest of 39 ± 15, 45 ± 15, 89 ± 15, and 102 ± 15 pN, respectively. These force quanta were independent of the loading rate, indicating that, because of the fast complexation/decomplexation kinetics, the rupture forces were probed under thermodynamic equilibrium. The force values followed the same trend as the free binding energy ΔG° measured for model guest compounds in solution or on β-CD monolayers, as determined by microcalorimetry and surface plasmon resonance measurements, respectively, A descriptive model was developed to correlate quantitatively the pull-off force values with the ΔG° of the complexes, based on the evaluation of the energy potential landscape of tip-surface interaction.

Full text of DOI:10.1021/ja0383569

Published on Web 01/15/2004
â-Cyclodextrin Host-Guest Complexes Probed under
Thermodynamic Equilibrium: Thermodynamics and AFM
Force Spectroscopy
Tommaso Auletta,† Menno R. de Jong,† Alart Mulder,† Frank C. J. M. van Veggel,†,§
Jurriaan Huskens,*,† David N. Reinhoudt,*,† Shan Zou,‡ Szczepan Zapotoczny,‡,#
Holger Scho¨nherr,‡ G. Julius Vancso,*,‡ and Laurens Kuipers|
Contribution from Supramolecular Chemistry and Technology, Materials Science and
Technology of Polymers, and Applied Optics, MESA+ Institute for Nanotechnology, UniVersity of
Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands, and FOM Institute for Atomic and
Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
Received September 5, 2003; E-mail: j.huskens@utwente.nl; d.n.reinhoudt@utwente.nl; g.j.vancso@utwente.nl
Abstract: The rupture forces of individual host-guest complexes between â-cyclodextrin (â-CD) hep-
tathioether monolayers on Au(111) and several surface-confined guests were measured in aqueous medium
by single molecule force spectroscopy using an atomic force microscope. Anilyl, toluidyl, tert-butylphenyl,
and adamantylthiols (0.2-1%) were immobilized in mixed monolayers with 2-mercaptoethanol on gold-
coated AFM tips. For all guests and for all surface coverages, the force-displacement curves measured
between the functionalized tips and monolayers of â-CD exhibited single, as well as multiple, pull-off events.
The histograms of the pull-off forces showed several maxima at equidistant forces, with force quanta
characteristic for each guest of 39 ( 15, 45 ( 15, 89 ( 15, and 102 ( 15 pN, respectively. These force
quanta were independent of the loading rate, indicating that, because of the fast complexation/
decomplexation kinetics, the rupture forces were probed under thermodynamic equilibrium. The force values
followed the same trend as the free binding energy ∆G° measured for model guest compounds in solution
or on â-CD monolayers, as determined by microcalorimetry and surface plasmon resonance measurements,
respectively. A descriptive model was developed to correlate quantitatively the pull-off force values with
the ∆G° of the complexes, based on the evaluation of the energy potential landscape of tip-surface
interaction.
Introduction
from the measured cantilever deflection according to eq 1.
Short-range interactions determine phenomena such as adhe-
sion, molecular interactions, and molecular recognition. One of
the first examples of direct measurements of surface interactions
dates back to the surface force apparatus (SFA) developed by
Israelachvili and Tabor in the early 1970s.1 The invention of
the atomic force microscope (AFM),2 well-known for its surface
imaging capability, represented a breakthrough in sensitivity for
force measurements as well. AFM spring constants k typically
vary between 10-1 and 102 N/m, and cantilever deflections ∆z
of 0.1 Å can be detected,3 turning the AFM setup into an ex-
tremely sensitive force F measurement apparatus,4 with a de-
tection limit between 10-12 and 10-9 N.5 Forces can be estimated
F ) k∆z
(1)
So-called “chemical force microscopy” (CFM) combines the
resolution available through force microscopy with attractive/
repulsive forces taking place between a functionalized probe
tip and the sample, allowing compositional mapping of surfaces
with different chemical functionalities on the basis of different
adhesion properties.6,7 Furthermore, the possibility to function-
alize individually the tip and surface allows investigation of
(4) (a) Evans, E.; Ritchie, K.; Merkel, R. Biophys. J. 1995, 68, 2580-2587.
(b) Kuo, S. C.; Sheetz, M. P. Science 1993, 260, 232-234 and references
cited herein.
(5) Other techniques utilize magnetic beads, optical tweezers, microneedles,
and biomembrane force probes with typical force ranges of 0.1-100 pN,
0.1-150 pN, >0.1 pN, and 0.5-1000 pN, respectively (see, for example,
Clausen-Schaumann, H.; Seitz, M.; Krautbauer, R.; Gaub H. E. Curr. Opin.
Chem. Biol. 2000, 4, 524-530).
(6) (a) Frisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C.
M. Science 1994, 265, 2071-2074. (b) Noy, A.; Vezenov, D. V.; Lieber,
C. M. Annu. ReV. Mater. Sci. 1997, 27, 381-421.
(7) For sub-50-nm resolution mapping of functional group distributions in
surface-modified polymers, see: (a) Scho¨nherr, H.; Hruska, Z.; Vancso,
G. J. Macromolecules 2000, 33, 4532-4537. (b) Scho¨nherr, H.; van Os,
M. T.; Hruska, Z.; Kurdi, J.; Fo¨rch, R.; Arefi-Khonsari, F.; Knoll, W.;
Vancso G. J. J. Chem. Soc., Chem. Commun. 2000, 1303-1304. (c)
Scho¨nherr, H.; van Os, M. T.; Fo¨rch, R.; Timmons, R. B.; Knoll, W.;
Vancso G. J. Chem. Mater. 2000, 12, 3689-3694.
† Supramolecular Chemistry and Technology, University of Twente.
‡ Materials Science and Technology of Polymers, University of Twente.
| Applied Optics, University of Twente, and FOM Institute for Atomic
and Molecular Physics.
§ Present address: University of Victoria, Department of Chemistry, P.O.
Box 3065 STN CSC Victoria, BC V8W 3V6, Canada.
# Present address: Jagiellonian University, Faculty of Chemistry, Ingar-
dena 3, 30-060 Krakow, Poland.
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19-38.
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Phys. 1992, 72, 6-12.
9
10.1021/ja0383569 CCC: $27.50 © 2004 American Chemical Society
J. AM. CHEM. SOC. 2004, 126, 1577-1584
1577

A R T I C L E S
Auletta et al.
specific combinations of molecular pairs.8 A wide variety of
examples has been reported, ranging from biological systems,9-11
rupture of covalent bonds,12 and chiral discrimination13 to
rupture forces of individual charge-transfer complexes14 and
cation complexation.15
HG systems are characterized by fast complexation/decomplex-
ation kinetics, and thus, the guest moieties decomplex and rebind
spontaneously many times during the recording of an AFM
force-distance curve as long as the tip stays in close proximity
to the â-CD SAM. Thus, thermodynamic equilibrium, as defined
for our systems including the cantilever, is reached for each
data point of a force-distance curve.
The statistical analysis of the pull-off data for the ferrocene-
â-CD system showed a periodic distribution of forces.24,25 In
accordance with the long timescale of the AFM pull-off
experiments relative to the complexation kinetics and the
thermodynamic equilibrium situation that should result from it,
the force quantum (55 ( 10 pN) attributed to the single HG
complex rupture force was independent of the number of
available guests, the loading rate, and the length of the spacer
between the guest and the surface.24,25
Several studies exist in which the dissociation of molecular
pairs has been theoretically modeled.16-19 Furthermore, several
attempts to correlate the force values measured in single
molecule force spectroscopy with thermodynamic parameters
of molecular recognition or surface adhesion have been
reported.16a,c However, studies on molecular unbinding events
and host-guest (HG) complex rupture forces under thermody-
namic equilibrium conditions remain scarce,20,21 while for far-
from-equilibrium systems the unbinding forces are, depending
on the regime, highly loading rate-dependent,22 as demonstrated
by Evans and co-workers.23
The work presented in this article is a systematic study of
single HG complex rupture forces between â-CD SAMs and
several guest molecules confined onto the surface of gold-coated
AFM tips by adsorption in mixed SAMs. Four different thiol-
modified guests have been used to vary the HG interaction
strength. The complexation constants for model guest com-
pounds in solution or on â-CD SAMs have been determined
by isothermal titration calorimetry (ITC) and surface plasmon
resonance (SPR) measurements. The notion of thermodynamic
equilibrium allows us to correlate quantitatively the measured
pull-off force values with the ∆G° of the complexes using a
newly developed quantitative model that is based on the
evaluation of the energy potential landscape of the tip-surface
interactions.
Previous studies in our groups have been carried out on the
complexation behavior of ferrocene moieties immobilized on
AFM tips and heptathioether â-cyclodextrin (â-CD) self-
assembled monolayers (SAMs) on Au(111).24,25 â-CD is a cyclic
oligosaccharide consisting of seven glucose units linked via
R-1-4 glycosidic bonds that is able to form inclusion complexes
with a variety of neutral and charged organic molecules in
aqueous solutions, mainly via hydrophobic interactions.26,27 Such
(8) For recent reviews, see: (a) Hugel, T.; Seitz, M. Macromol. Rapid Commun.
2001, 22, 989-1016. (b) Zlatanova, J.; Lindsay, S. M.; Leuba, S. H. Prog.
Biophys. Mol. Biol. 2000, 74, 37-61. (c) Janshoff, A.; Neitzert, M.;
Oberdo¨rfer, Y.; Fuchs, H. Angew. Chem., Int. Ed. 2000, 39, 3212-3237.
(d) Samor`ı, B. Chem.-Eur. J. 2000, 6, 4249-4255.
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(b) Moy, V. T.; Florin, E.-L.; Gaub, H. E. Science 1994, 266, 257-259.
(10) Lee, G. U.; Chrisey, L. A.; Colton, R. J. Science 1994, 266, 771-773.
(11) Ros, R.; Schwesinger, F.; Anselmetti, D.; Kubon, M.; Scha¨fer, R.;
Plu¨ckthun, A.; Tiefenauer, L. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 7402-
7405.
Results and Discussion
We have previously reported that the force quantum of 55 (
10 pN, attributed to the rupture of a single inclusion complex
of â-CD heptathioether 1 (Chart 1A) on Au(111) and the
ferrocenylalkanethiol 4 (Chart 1B) immobilized on an AFM tip,
arises from specific HG interactions, as was proven by
systematically leaving out the host or guest from the system
and by competition experiments with a guest in solution.24 This
quantum does not depend on spacer length, loading rate, and
guest concentration on the tip.24,25 Four different thiol-modified
guests, 2, 3, 5, and 6 (Chart 1B), were synthesized to investigate
how changes in the HG motif would affect the rupture force.
The synthesis of adsorbate 1 and preparation of SAMs on
gold surfaces have been described elsewhere.28 Compounds 2,
3, 5, and 6 were synthesized by reacting suitable amines with
5-bromopentanoic acid and followed by substitution of the
bromide for thioacetate and subsequent deprotection. Mixed
SAMs of 0.2% or 1% of these guest thiols with 2-mercaptoeth-
anol on gold substrates and on gold-modified AFM tips were
prepared from 1 mM (total thiol concentration) solutions in
ethanol for 16 h at room temperature.
(12) Grandbois, M.; Beyer, M.; Rief, M.; Clausen-Schaumann, H.; Gaub, H. E.
Science 1999, 283, 1727-1730.
(13) McKendry, R.; Theoclitou, M.-E.; Rayment, T.; Abell, C. Nature 1998,
391, 566-568.
(14) Skulason, H.; Frisbie, C. D. J. Am. Chem. Soc. 2002, 124, 15125-15133.
(15) Kado, S.; Kimura, K J. Am. Chem. Soc. 2003, 125, 4560-4564.
(16) (a) Grubmuller, H.; Heymann, B.; Tavan, P. Science 1996, 271, 997-999.
(b) Heymann, B.; Grubmuller, H. Phys. ReV. Lett. 2000, 84, 6126-6129.
(c) Heymann, B.; Grubmuller, H. Biophys. J. 2001, 81, 1295-1313. (d)
Rief, M.; Grubmuller, H. ChemPhysChem 2002, 3, 255-261.
(17) Bell, G. I. Science 1978, 200, 618-627.
(18) (a) Hummer, G.; Szabo, A. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 3658-
3661. (b) Hummer, G.; Szabo, A. Biophys. J. 2003, 85, 5-15.
(19) (a) Seifert, U. Phys. ReV. Lett. 2000, 84, 2750-2753. (b) Seifert, U.
Europhys. Lett. 2002, 58, 792-798.
(20) (a) Rief, M.; Clausen-Schaumann, H.; Gaub, H. E. Nat. Struct. Biol. 1999,
6, 346-349. (b) Essevaz-Roulez, B.; Bockelmann, U.; Heslot, F. Proc.
Natl. Acad. Sci. U.S.A. 1997, 94, 11935-11940.
(21) Tromas, C.; Rojo, J.; de la Fuente, J. M.; Barrientos, A. G.; Garc´ıa, R.;
Penade´s, S. Angew. Chem., Int. Ed. 2001, 40, 3052-3055.
(22) (a) Rief, M.; Gautel, M.; Osterhelt, F.; Fernandez, J. M.; Gaub, H. E. Science
1997, 276, 1109-1112. (b) Fritz, J.; Katopodis, A. G.; Kolbinger, F.;
Anselmetti, D. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 12283-12288. (c)
Marszalek, P. E.; Lu, H.; Li, H.; Carrion-Vazquez, M.; Oberhauser, A. F.
Nature 1999, 402, 100-103. (d) Strunz, T.; Oroszlan, K.; Shafer, R.;
Gu¨ntherodt, H.-J. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 11277-11282.
(e) Evans E.; Ludwig, F. J. Phys.: Condens. Matter 2000, 12, 315-320.
(f) Baumgartner, W.; Hinterdorfer, P.; Ness, W.; Raab, A.; Vestweber, D.
Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 4005-4010. (g) Lee, I.; Marchant.
R. E. Surf. Sci. 2001, 491, 433-443.
(23) (a) Evans, E.; Ritchie, K. Biophys. J. 1997, 72, 1541-1555. (b) Merkel,
R.; Nassoy, P.; Leung, A.; Ritchie, K.; Evans, E. Nature 1999, 397, 50-
53.
Figure 1 shows a schematic representation of the supramo-
lecular single molecule force spectroscopy experiment with an
arbitrary surface-confined guest. Force-displacement curves for
guest surface coverages on the tip obtained from 0.2% and 1%
solutions show single, as well as characteristic multiple, pull-
off events, as shown for 6 in Figure 2A.
(24) Scho¨nherr, H.; Beulen, M. W. J.; Bu¨gler, J.; Huskens, J.; van Veggel, F.
C. J. M.; Reinhoudt, D. N.; Vancso, G. J. J. Am. Chem. Soc. 2000, 122,
4963-4967.
(25) Zapotoczny, S.; Auletta, T.; De Jong, M. R.; Scho¨nherr, H.; Huskens, J.;
van Veggel, F. C. J. M.; Reinhoudt, D. N.; Vancso, G. J. Langmuir 2002,
18, 6988-6994.
(26) (a) Wenz, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 803-822. (b) Chem.
ReV. 1998, 98, 1741-2076. (c) Szejtli, J. ComprehensiVe Supramolecular
Chemistry; Pergamon Press: Oxford, 1996; Vol. 3.
(28) De Jong, M. R.; Huskens, J.; Reinhoudt, D. N. Chem.-Eur. J. 2001, 7,
4164-4170.
(27) Rekharsky, M. V.; Inoue, Y. Chem. ReV. 1998, 98, 1875-1917.
9
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â-Cyclodextrin Host−Guest Complexes
A R T I C L E S
Chart 1. Chemical Structure of â-CD Adsorbate 1 (A), Guest
Molecules 2-6 Immobilized at AFM Tips (B), and Model Guests
7-11 for HG Binding in Solution and at SAMs of 1 (C)
Figure 1. Schematic representation (not to scale) of AFM-based single
molecule force spectroscopy of ferrocene guest 4 immobilized in a hydroxyl-
terminated SAM on an AFM tip and a SAM of 1 on Au(111).
ITC, have been reported previously.28 The same approach was
applied to determine the thermodynamics of the HG complexes
of 7 and 8. SPR measurements were employed to determine
the complexation constants on SAMs of 1 only for compounds
9-11, since poor solubility and weak interactions for com-
pounds 7 and 8 prevented reliable measurements. The experi-
mental data for compounds 9-11, obtained by means of the
two independent techniques, show an excellent agreement, as
seen in Table 1. These results are also in agreement with the
observation reported earlier28 that small guest molecules, which
fit into the CD cavity, apparently do not feel the presence of
the alkyl chains of 1, leading to identical binding constants in
solution and at â-CD SAMs. This notion therefore allowed us
to extrapolate the ITC results to the binding parameters on
surfaces of compounds 7 and 8.
Table 1 summarizes the single HG complex rupture force
values determined for the interaction of SAMs of 1 with SAMs
of adsorbates 2-6 and the thermodynamic parameters for HG
complexes of â-CD with compounds 7-11.25 The data clearly
show a correlation of ∆G° and unbinding forces. This result,
together with the loading rate independence of the force values,
strongly supports our view of a process occurring under thermo-
dynamic equilibrium. Therefore, these results open the possi-
bility to investigate the relation between rupture forces and ther-
modynamic quantities, such as the Gibbs free energy of binding,
∆G°.
Expanding on the approach proposed by Hansma and co-
workers for measuring interaction potentials,32 Willemsen et al.
demonstrated that the total potential can be derived from the
probability distribution of the tip position by monitoring the
Brownian movement of an AFM tip in a potential well.33 The
total potential consists of the sum of the harmonic cantilever
potential and the tip-surface interaction potential.
Here we describe a model to correlate ∆G° and the dissocia-
tion force, Fpull-off, for an individual HG pair. It requires: (i)
the generalization and formalization of the tip-surface interac-
tion, which is governed by the HG interaction and is ap-
proximated here using a Lennard-Jones potential (LJP) descrip-
tion, the well depth of which is the guest-specific parameter,
The measured cantilever deflections corresponding to the pull-
off events were translated into force using the independently
determined AFM cantilever spring constants, which were in the
range 0.05-0.12 N/m. All pull-off forces determined from in-
dividually resolved events were plotted in histograms.29 Fast
Fourier transform (FFT) smoothing30 of the force histograms
for tips functionalized with 2, 3, 5, or 6 shows a periodic dis-
tribution of forces, regardless of the bin size, with force quanta
of 39 ( 15, 45 ( 15, 89 ( 15, 102 ( 15 pN, respectively (Fig-
ure 3).31 The loading rate was varied over several orders of mag-
nitude for tips covered with mixed SAMs of 2-mercaptoethanol
containing 1% of guest. In agreement with previous reports,24,25
the quantized force was unaffected by the loading rate for any
of the guests, even for the strongest binding guest 6 (Figure
2B).
ITC and SPR measurements were employed to evaluate the
thermodynamics of complex formation in solution and on
surfaces, respectively, between compounds 7-11 (Chart 1C),
which function as model systems for compounds 2-6, respec-
tively, and â-CD hosts. The solution-binding parameters for
compounds 9-11 with native â-CD in solution, determined by
(29) There appear to be some differences in the probabilities for observing
multiple force quanta, for example, for 3 (Figure 3B), which may arise
from: (i) differences in solubilities and adsorptivities of the guest thiols
leading to different guest-mercaptoethanol ratios on the tip than present
in solution, (ii) different degrees of clustering of guests on the tip, rendering
some guest molecules inaccessible for binding, and (iii) variations in tip
geometry and tip-surface contact areas.
(30) The data in the histograms were treated as described in refs 24 and 25.
(31) Noise levels were ∼15 pN. Plots of peak position from the histograms
versus peak number yielded straight lines, with the force quantum as the
slope (see also ref 25).
(32) Cleveland, J. P.; Scha¨ffer, T. E.; Hansma, P. K. Phys. ReV. B 1995, 52,
R8692-R8695.
(33) Willemsen, O. H.; Kuipers, L.; Van der Werf, K. O.; De Grooth, B.; Greve,
J. Langmuir 2000, 16, 4339-4347.
9
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A R T I C L E S
Auletta et al.
Figure 2. Representative force-distance curve for the interaction of a tip covered with a mixed SAM of 1% of 6 and 2-mercaptoethanol with a SAM of
1 (A) and loading rate dependence for the same system (B).
Figure 3. Histograms for the interaction of tips coated with 1% of 2 (A), 1% of 3 (B), 1% of 5 (C), and 1% of 6 (D) and 2-mercaptoethanol with SAMs
of 1 (bin size 8 pN). The solid lines represent the FFT-smoothed histograms.
Table 1. Force Values, Fpull-off, for Guests 2-6 Measured by Force Spectroscopy, Thermodynamic Data at SAMs of 1 for Model
Compounds 9-11 Measured by SPR, and Solution Data for Model Compounds 7-11 with Native â-CD Measured by ITC
AFM
SPR
ITC
F
∆G°
kcal mol-1
∆G°
kcal mol-1
∆H°
kcal mol-1
T∆S° d
kcal mol-1
pull-off
guest
model guest
pN
2
3
4
5
6
39 ( 15
45 ( 15
55 ( 10b
89 ( 15
102 ( 15
7
8
9
10
11
a
a
-2.3
-3.0
-5.4c
-6.1c
-6.6c
-2.3
-2.7
-6.1c
-5.2c
-5.9c
0.0
0.3
-5.4c
-6.0c
-6.5c
-0.7c
0.9c
0.7c
a
b
Low solubility and weak interactions with the CD SAM do not allow accurate measurements of the thermodynamic parameters for this guest. From
c
d
ref 25. From ref 28. T ) 298 K.
(ii) a space integration of the HG potential energy to correlate
thus to ∆G°, (iii) a total potential energy description and a
the LJP well depth to the macroscopic stability constant K and
probability distribution for the tip being or not being in contact
9
1580 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

â-Cyclodextrin Host−Guest Complexes
A R T I C L E S
with the sample surface to correlate the LJP well depth to the
(maximum) cantilever deflection at which the pull-off event
occurs and thus to Fpull-off, and (iv) a combination of these
correlations to give a theoretical prediction of Fpull-off as a
function of ∆G°.
The model described below applies in principle only to the
interactions existing between one single guest on the tip and
one â-CD cavity on the surface. Multiple, simultaneous pull-
off events were not taken into consideration. In an earlier
study,25 we showed that the multiple binding events cor-
responded to multiple forces of a single event and that the
fraction of single-rupture events (with the same force quanta)
increased upon lowering the amount of guest on the tip.
Therefore, we assumed that an understanding of a single pull-
off event of a single HG pair sufficed to describe the systems
at hand.
In our system, a potential energy description was used to
model the HG system. Molecular dynamics (MD) calculations
were employed to describe the potential energy of the HG
complex for a linear dissociation pathway, i.e., the guest, in
this case ferrocene, was pulled out of the cavity, and driven by
the tip along the symmetry axis of the â-CD cavity.
The interactions of a â-CD cavity with a guest can be
described by a potential energy well, the shape of which is
approximated by an LJP (eq 2).
since, as stated above, the pull-off trajectory of the guest out of
the cavity can better be assumed to be linear. Therefore, in an
alternative second integration approach, the sampled volume
was restricted to a cylinder defined by the area available for
in-plane movement of the guest in the cavity (ACD ) πr2 with
r ) 2 Å) and the linear trajectory perpendicular to this area
along which the guest dissociated (eq 4).
K ) 2πNav +∞z2 exp[-ULJP(z)/RT] dz
(3)
(4)
∫
-
K ) NavACD +∞ exp[-ULJP(z)/RT] dz
∫
-∞
Employing ∆G° ) -RT lnK led to the following linear
relationships: -∆G° ) 0.93ꢀ - 4.15 and -∆G° ) 0.97ꢀ -
2.79 for the spherical and the cylindrical integrations, respec-
tively, with -∆G° and ꢀ in kcal mol-1. The ∆G° values of the
HG systems studied here varied between -2.3 and -6.4 kcal
mol-1, as determined from ITC and SPR measurements, and
thus ꢀ ranged from -6.6 to -11.4 kcal mol-1 or from -5.3 to
-9.5 kcal mol-1, respectively.
To assess the sensitivity of the geometrical parameter ACD
on the integration step, the relationship between -∆G° and ꢀ
was derived for two other different values of r (r ) 1 Å and r
) 4 Å). From the data it can be observed that changes in the
geometrical parameter ACD did not affect the slope of the curve
of -∆G° vs ꢀ but only modified the intercept (for r ) 1 Å:
-∆G ) 0.97ꢀ - 3.59, and for r ) 4 Å: -∆G ) 0.97ꢀ -
1.99). Therefore, as an approximation, the value of r ) 2 Å
was assumed to hold for all the guests.
To combine tip and HG potentials, the LJP needed to be
modified to include the presence of the alkyl spacer with length
L between the guest moiety and the AFM tip. The alkyl chain
was treated as an infinitely flexible linker until the maximum
elongation was reached, although it could not be stretched
beyond its fully elongated conformation. These considerations
resulted in a total potential energy of the complex Ucomplex(z)
) ULJP(z + L) for z e -L, Ucomplex(z) ) -ꢀ for -L e z e 0,
and Ucomplex(z) ) ULJP(z) for z g 0.
12
6
s
s
ULJP(z) ) 4ꢀ
-
(2)
((
)
(
) )
z + z0
z + z0
Here z represented the distance from the LJP minimum along
the dissociation pathway, z0 was an offset parameter with a value
6
x
of s 2 (ensuring that the well minimum occurred at z ) 0:
ULJP(0) ) -ꢀ and dULJP/dz ) 0), ꢀ was the well depth, and s
determined the width of the well. The MD simulation data for
ferrocene (as a model for guests 4 and 9) were fitted to the LJP
in a least-squares optimization routine (see Supporting Informa-
tion), while varying ꢀ, s, and z0. The width of the well (s )
7.78 Å), which corresponded well to the depth of the cyclo-
dextrin cavity (8 Å), was the only parameter obtained from the
MD simulations that was used in the theoretical description
described below. The z0 parameter was an offset parameter only,
and the well depth ꢀ was varied for all guests depending on K,
as was obtained by a space integration of the potential energy
as described below. For all other guest motifs employed in this
study, we assumed the same well shape, i.e., s was kept constant,
while ꢀ was varied to account for changes in ∆G°.
A space integration of ULJP(z) allowed us to correlate the
depth of the well ꢀ associated with each HG complex to the
corresponding ∆G° value via the complexation constant K. In
a first attempt, a relationship between the HG equilibrium
constant K and the potential energy was applied to simulate
hydrophobic interactions and, thus, molecular recognition.34 This
calculation was based on the space integration of ULJP with a
radial dependence according to eq 3, where Nav was Avogadro’s
number. In our case, the space integration over z g 0 represented
a hemisphere above the â-CD cavity, while z e 0 represented
the cavity interior (repulsive interactions of LJP). This integra-
tion may not describe the 3D interaction dependence correctly
The cantilever potential Utip was described by a harmonic
potential (eq 5)
Utip(z) ) (1/2)k(z - z1)2
(5)
where ∆z ) z - z1 was the cantilever deflection and z1
represented the tip position, i.e., the position of the minimum
of the cantilever parabola potential, which was controlled by
the piezo movement.
The total potential energy of the system could now be derived
as the sum of the modified LJP describing the HG complex
and the harmonic potential describing the cantilever potential
(eq 6).
Utot(z) ) Ucomplex(z) + Utip(z)
(6)
Changes in the tip position were reflected in the total potential
energy curve. Initially, when the piezo was not yet moved and
no cantilever deflection occurred (∆z ) 0, -L < z1 < 0), the
positions of the minima of Ucomplex and Utip coincided, and only
one minimum for Utot was observed (Figure 4A, z1 ) 0).
Retraction of the piezo (in our setup, z1 was recorded in steps
of typically 2 Å)35 was translated into a cantilever deflection
(34) (a) Pangali, C. S.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71, 2975-
2981. (b) Jorgensen, W. L. Acc. Chem. Res. 1989, 22, 184-189.
9
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A R T I C L E S
Auletta et al.
Figure 4. Total energy description: Utip (parabola), Ucomplex (black line), and Utot (gray line). The tip position z1 from A to E is 0, 6, 8, 10, and 12 Å,
respectively (ꢀ ) 6 kcal mol-1).
(∆z > 0) with a shift of the parabola potential minimum z1 to
the right, thus raising the minimum observed at z ) 0 for the
total potential energy curve (Figure 4B). Up to a certain point,
only one minimum existed, called “contact”, in which the tip
stayed in contact with the sample, while the HG complex may
rapidly dissociate and reassociate. It can also be seen in Figure
4 that this “contact” minimum stayed at the same position, i.e.,
at z ) 0, because of the larger stiffness of the complex,36 so
that the observed deflection ∆z was equal to z1. Near the point
where a pull-off event takes place, a second minimum, called
“out-of-contact”, appeared and quickly became the predominant
one (Figure 4D). In this minimum, the tip was not in contact
with the surface, and the HG complex was dissociated. In Figure
4B-E, the change in tip position z1 was simulated by four
Figure 5. Plot of pcontact (black line) and ppull-off (gray line) as a function
sequential energy potential curves, with z1 ) 6, 8, 10, and 12
Å, respectively, corresponding to consecutive data points in a
(simulated) pull-off experiment. The plots show the correspond-
ing changes in Utot and describe the transition from the “contact”
to the “out-of-contact” state as the most energetically favorable
situation.
of z1 (ꢀ ) 10 kcal mol-1).
Figure 5 shows pcontact as a function of z1 for ꢀ ) 10 kcal
mol-1, as obtained after numerical integration.37 Here it is seen
that pcontact dropped from 1 to 0 in about 4 Å, i.e., typically
within only two data points. The specific z1 value at which this
occurred obviously depended on ꢀ, but the shape of the curve
hardly changed. A macroscopic pull-off event thus corresponded
to one data point being in the “contact” state, while for the next
data point the “out-of-contact” state was observed. Thus, the
probability ppull-off to observe such a pull-off event can be
defined as in eq 9.
According to Boltzmann statistics, the relative probability p(z)
for the system to exist in situation (z, Utot(z)) is given by eq 7.
p(z) ) exp[-Utot(z)/RT]
(7)
In the case when two minima are present, separated by a barrier
which has a maximum at z ) zbar, the probability for the system
to be in the “contact” state, pcontact, is given by eq 8, which is
a function of z1.
(35) The measured pull-off forces did not vary for nominal spacings of the data
points between 1 and 10 Å.
(36) The stiffness of the complex as a function of ꢀ is described by kcomplex
)
23.81ꢀ [pN Å-1], with ꢀ in kcal mol-1 (see the Supporting Information).
(37) Alternatively, a semianalytical expression can be derived relating pcontact
out-of-contact to the energy difference between the two minima, eliminating
zbar
zbar
p(z) dz
-∞ exp[-Utot(z)/RT] dz
∫
∫
/
-∞
pcontact
)
)
(8)
p
-∞∞p(z) dz
∞ exp[-Utot(z)/RT] dz
the need for the numerical integration (see the Supporting Information).
Here, the interaction potential at the well of the “contact” minimum is also
fitted to a harmonic potential. This analysis shows that the probability
distribution depends only marginally on the “stiffness” of the complex
(which governs the harmonic interaction potential and which is directly
related to the well width s).
∫
∫
-∞
Obviously, pout-of-contact could be obtained from integrating
p(z) for z > zbar, and pcontact + pout-of-contact ) 1.
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â-Cyclodextrin Host−Guest Complexes
A R T I C L E S
molecular species that interacted so weakly with one cyclodex-
trin cavity that the equilibrium complexation constant K was
less than 1.0. For the ferrocene system, we plotted ∆G° data
observed for different Fc model compounds (for compound 9
∆G° ) -5.4 kcal mol-1, while for ferrocenecarboxylic acid
∆G° ) -4.6 kcal mol-1).39
It is necessary at this point to address a certain number of
factors which could affect the value of Fpull-off. As already stated
above, an intrinsic variability of Fpull-off follows from the
probability distribution of ppull-off. Other sources of deviation
can be related to differences in the dissociation trajectories of
the HG system. Different HG complex geometries could
originate from different orientations of the molecular pairs on
the two surfaces (tip and substrate) or could be related to the
granular structure of the gold layer on the AFM tip as well.
However, as stated above for the two integration methods and
the theoretical curves reported in Figure 6B, different dissocia-
tion pathways probably play a marginal role in determining the
ppull-off(z1) ) pcontact(z1) × pout-of-contact(z1 + 2) )
pcontact(z1) × (1 - pcontact(z1 + 2)) (9)
The dependence of ppull-off with z1 is shown in Figure 5 as well.
Again, the steep dependence of ppull-off with z1 ensured that the
pull-off event occurred at a specific data point and that no
switching back and forth between the “contact” and the “out-
of-contact” states would be observed in the experimental setup
used here, unless one were to detect data points for relatively
long periods of time at all z1 of a pull-off experiment,38 as was
done and observed recently for another system.33 The curve also
shows that z1, for which the pull-off was observed, had a certain
distribution (approximately (1.5 Å) for an identical HG
complex probed under identical conditions, corresponding to a
force variability of (10 pN.
Once the maximum pull-off probability was determined, the
corresponding tip deflection ∆zmax was converted into the force
exerted by the cantilever according to eq 10, thus determining
the pull-off force value.
Fpull-off
.
As already addressed above, changes in the integration
parameters ACD in eq 4 have been shown to affect only the
intercept of the curve of -∆G° vs ꢀ. This is reflected in the
Fpull-off vs -∆G° curve determining a ∆G° interval of (0.8
kcal mol-1, which is in the same order of magnitude as the
experimental error. Furthermore, considering the physical
dimensions of the guests and of the â-CD cavity, a value of r
) 2 Å represents a reasonable approximation that can be applied
for all different guests.
Fpull-off ) ktip∆zmax
(10)
From the above-described model, it was possible to derive
the dependence of ppull-off and thus the dependence of the pull-
off force with ꢀ. This dependence appeared to be a square root
x
dependence (F ) 31.25× ꢀ-1.75; see Figure 6A).
The relationship between ꢀ and -∆G° described above
allowed us to extend the correlation between energy and force
to the thermodynamics of the HG complex. Figure 6B reports
the derived dependence of pull-off force vs -∆G° for the
spherical and cylindrical integration approaches, F ) 32.60×
Conclusions
Using an atomic force microscope, we determined in aqueous
medium the rupture forces of individual HG complexes between
â-cyclodextrin SAMs and several surface-confined guests. The
analysis of the histograms revealed periodic distributions of
forces with loading-rate independent maxima at integer multiples
of a certain force quantum characteristic of each guest. The
observed force quanta were 39 ( 15, 45 ( 15, 89 ( 15, and
102 ( 15 pN, respectively, and were attributed to the rupture
of a single HG complex. These results, in combination with
previous reports, indicated that the HG complex rupture forces
were probed under thermodynamic equilibrium. Microcalorim-
etry and SPR measurements were employed to investigate the
complex formation for model guest compounds in solution and
on â-CD monolayers. The force quanta and the thermodynamic
parameters of the inclusion complexes followed the same trend.
Finally, a descriptive model based on the evaluation of the
energy potential landscape of tip-surface interaction was
developed to correlate quantitatively the pull-off force values
with ∆G°.
x
x
-∆G+2.39 and F ) 31.76× -∆G+1.03, respectively
(with -∆G° in kcal mol-1 and F in pN). The experimental
values for the five HG complexes investigated are shown as
well.
The theoretically derived square root dependence of Fpull-off
with -∆G° can intuitively be understood from the fact that a
deeper well ꢀ (and thus a linear change in ∆G°) can be
compensated by a square root change in z1 and thus in force,
since the potential energy of the cantilever depends quadratically
on deflection.
In Figure 6B, it can be seen that the fit to the experimental
data improved significantly upon changing the integration
volume from a spherical to a cylindrical type (the average rms
difference between the predicted and experimental force values
amounted to 26 pN for the former and 18 pN for the latter),
with changes in both the slope and intercept with the y axis of
the two curves and lower energy values for the cylindrical
integration. These results thus suggested that the assumption
of a linear dissociation pathway for a guest linked to, and thus
driven by, the AFM tip described more accurately the events
occurring at the molecular level. It must be noted, however,
that although the fit improved, the change in the integration
volume did not severely affect the corresponding force value.
In Figure 6B, it can be observed as well that both curves
possessed an intercept with the x axis at positive ∆G° values.
The model thus predicted a measurable pull-off force for a
Experimental Section
AFM Tip Modification. Standard V-shaped silicon nitride canti-
levers with pyramidal tips (purchased from Digital Instruments (DI),
Santa Barbara, CA) were coated with ca. 2 nm of Ti and ca. 50 nm of
Au by evaporation in high vacuum at SSENS bv (Hengelo, The Neth-
erlands). The tips were functionalized as described previously25 in 1
mM ethanolic solutions containing binary mixtures of 2-mercaptoeth-
anol and a guest adsorbate 2, 3, 4, 5, or 6 (0.2 and 1%), for 16 h at r.t.
(38) This is to monitor multiple times the one datapoint that has a probability
pcontact significantly different from either 0 or 1, and therefore switching
between the “contact” and “out-of-contact” states may be observed.
(39) God´ınez, L. A.; Schwartz, L.; Criss, C. M.; Kaifer, A. E. J. Phys. Chem.
B 1997, 101, 3376-3380.
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1583

A R T I C L E S
Auletta et al.
Figure 6. (A) Dependence of Fpull-off on ꢀ. (B) Experimental pull-off forces vs -∆G° (∞) and calculated square root functions for spherical (eq 3) (black
solid line) and cylindrical integration (eq 4) (gray solid line). For ferrocene, two -∆G° values are reported with the same force value due to different ∆G°
measured for different model compounds (for details, see text).
AFM Measurements and Analysis. The AFM measurements were
carried out on a NanoScope III multimode AFM (DI) utilizing a 10
µm (E) scanner and a DI liquid cell on SAMs of 1 on atomically smooth
Au(111).40 The cantilever spring constants k (in the range of 0.05-
0.12 N/m) of the gold-coated tips were calibrated using the reference
method described by Tortonese and Kirk41 and by the thermal noise
method.42 Force-displacement (f-d) curves were acquired sequentially
in Milli-Q water at different positions on the sample surface. The
loading force was kept below 500 pN, and the loading rate was varied
between 3.5 × 103 pN/s and 8.8 × 105 pN/s. The quantitative analysis
of the observed individual pull-off events was performed as described
previously.25
the charge template method, and excess charge was smoothed over
nonpolar carbons and hydrogens. The ferrocene was treated as a rigid
body by having large harmonic potentials applied between all carbon-
iron pairs. The iron atom had a charge of +2 and the two cyclopen-
tadenyl ligands had a charge of -1. The ferrocene was placed
“manually” in the cavity of the cyclodextrin, followed by ABNR
minimization until the root-mean square of the energy gradient was
e0.001 kcal mol-1 Å-1. This complex was placed in the center of a
cubic box of TIP3P water of 30 Å,44 as implemented in CHARMm).
The ferrocene was translated along the quasi 7-fold axis of the
cyclodextrin in steps of 0.5 Å. Overlapping waters were removed (on
the basis of heavy-atom interatomic distances of e2.3 Å). The positions
of the carbon atoms of the cyclodextrin bearing the CH2OH groups
and the Fe were constrained. Before the MD simulations were run, the
system was minimized by steepest descent for a maximum of 1000
steps or until a root-mean square of the energy gradient of e1 kcal
mol-1 Å-1 was reached. The system was heated to 300 K in 5 ps,
followed by equilibration of 10 ps, after which the MD (NVE ensemble,
no systematic deviation from 300 K) was run for 100 ps. During the
simulation, the nonbonded list was updated every 20 time steps with a
cutoff of 14 Å. The van der Waals interactions were treated with a
switch function between 10 and 13 Å, whereas the shift function was
applied to the electrostatic interactions (cutoff 13 Å). The time step
was 1 fs, with the SHAKE algorithm placed on the hydrogens.45
Coordinate sets were saved regularly and used for subsequent data
analysis. The interaction energy between the cyclodextrin and ferrocene
was averaged over all data sets.
Isothermal Titration Calorimetry. Titrations were performed at
25 °C using a Microcal VP-ITC titration microcalorimeter. Sample
solutions were prepared using Milli-Q water. Titrations of guests 9,
10, and 11 were performed by adding aliquots of a 1 mM â-CD solution
to a 0.1 mM guest solution,28 while 50 mM solutions of compounds 7
and 8 were titrated to â-CD solution 5 mM. The titrations were analyzed
using a least squares curve-fitting procedure. Control experiments
involved addition of â-CD to water and addition of water to a guest
solution.28
Surface Plasmon Resonance. SPR measurements were performed
in a two-channel vibrating mirror angle scan setup based on the
Kretschmann configuration, described by Lenferink et al.43 Light from
a 2 mW HeNe laser was directed onto a prism surface by means of a
vibrating mirror. The intensity of the light was measured with a large-
area photodiode. This setup allowed determination of changes in
plasmon angle with an accuracy of 0.002°. The gold substrate with the
monolayer was optically matched to the prism using an index matching
oil. A Teflon cell, placed on the monolayer via an O-ring to avoid
leakages, was filled with 800 µL of Milli-Q water. After stabilization
of the SPR signal, titrations were performed by removing an amount
of water and adding the same amount of 0.1 mM stock solution of
guest 9, 10, or 11.28 Between each addition the cell was thoroughly
washed with Milli-Q water (700 µL of water 5 times). SPR measure-
ments were repeated 3 times for each monolayer guest system.
Acknowledgment. This research has been supported finan-
cially by the Council for Chemical Sciences of The Netherlands
Organization for Scientific Research (CW-NWO; T.A. Grant
No. 97041), the European Union (project Polynano), the
Technology Foundation STW, and MESA+ Institute for Nano-
technology.
Supporting Information Available: Full experimental details,
XPS data, electrochemistry data for monolayer characterization,
MD simulation data and fit to LJP, and derivation of analytical
expression of pcontact (PDF). This material is available free of
charge via the Internet at http://pubs.acs.org.
Molecular Dynamics. Coordinates for the native â-CD were derived
from an X-ray structure, and the water molecules were removed. All
calculations were done with Quanta/CHARMm 24.0 and referred to
an unsubstituted ferrocene molecule. The cyclodextrin was charged with
JA0383569
(40) Scho¨nherr, H.; Vancso, G. J.; Huisman, B.-H.; van Veggel, F. C. J. M.;
Reinhoudt, D. N. Langmuir 1999, 15, 5541-5546.
(41) Tortonese, M.; Kirk, M. Proc. SPIE 1997, 3009, 53-60.
(42) (a) Hutter, J. L.; Bechhoefer, J. ReV. Sci. Instrum. 1993, 64, 1868-1873.
(b) Sader, J. E. J. Appl. Phys. 1998, 84, 64-76.
(44) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein,
M. L. J. Chem. Phys. 1983, 79, 926-935.
(45) Berendsen, H. J. C.; Postma, J. P. M.; Dinola, A.; Van Gunsteren, W. F.;
Haak, J. R. J. Chem. Phys. 1984, 81, 3684-3690.
(43) Lenferink, A. T. M.; Kooyman, R. P. H.; Greve, J. Sens. Actuators, B 1991,
3, 261-265.
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1584 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004