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2008, 112, 7359–7362 Published on Web 05/30/2008
Rupture Force of Single Supramolecular Bonds in Associative Polymers by AFM at Fixed Loading Rates Anika Embrechts, Holger Scho¨nherr,* and G. Julius Vancso* Faculty of Science and Technology, MESA+ Institute for Nanotechnology, Department of Materials Science and Technology of Polymers, UniVersity of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands ReceiVed: April 15, 2008; ReVised Manuscript ReceiVed: May 16, 2008
Atomic-force-microscopy-based single-molecule force spectroscopy (AFM-SMFS) was used to study the bond strength of self-complementary hydrogen-bonded complexes based on the 2-ureido-4[1H]-pyrimidinone (UPy) quadruple H-bond motif in hexadecane (HD). The unbinding force corresponding to single UPy-UPy dimers was investigated at a fixed piezo retraction rate in the nonequilibrium loading rate regime. The rupture force of bridging supramolecular polymer chains formed between UPy-functionalized substrates and AFM tips in the presence of a bis-UPy derivative was found to decrease with increasing rupture length. The rupture length was identified as the chain length of single, associating polymers, which allowed us to determine the number of supramolecular bonds (N) at rupture. The rupture force observed as a function of N was in quantitative agreement with the theory on uncooperative bond rupture for supramolecular linkages switched in a series. Hence, the value of the dimer equilibrium constant Keq ) (1.3 ( 0.5) × 109 M-1, which is in good agreement with previously estimated values, was obtained by SMFS of supramolecular polymers at a single loading rate. Introduction The investigation of the spontaneous self-assembly processes governed by supramolecular interactions on the molecular level has received growing attention.1 Also, within the rapidly developing fields of nanotechnology and nanoscience, as well as molecular level biochemistry and biophysics, knowledge regarding molecular stability and bond strengths on a singlemolecule level becomes crucial.2 Using atomic-force-microscopybased single-molecule force spectroscopy (AFM-SMFS),3,4 optical tweezers,5 or the biomembrane force probe (BFP),6 bond strengths can now be measured accurately at a single-molecule level.7–9 By contrast, traditionally only ensemble averaged thermodynamics could be probed.10 These experimental studies are complemented by advanced density functional theory (DFT) calculations that allow one to predict interaction energies.11 Our research is focused on the investigation of H-bonded complexes on a single-molecule level. One central motivation is the important role of H-bonds in biological, as well as synthetic, supramolecular systems.12 Previously, we employed AFM-SMFS to unravel the bond strength of a self-complementary hydrogen-bonded system based on the 2-ureido-4[1H]-pyrimidinone (UPy) quadruple H-bond motif in hexadecane (HD).13 Using the Evans model (eq 1),2,6 the decrease of the most probable rupture force (f*) as a function of the force loading rate (rf) the chain experiences provided the bond lifetime in the absence of any externally applied force, toff(f ) 0), of 5-7 s, which corresponds to a dimer equilibrium constant of Keq ∼ 109 M-1 (hexadecane, * Corresponding authors. Phone: ++31 53 489 3170 (H.S.); ++31 53 489 2967 (G.J.V.). Fax: ++31 53 489 3823 (H.S.); ++31 53 489 3823 (G.J.V.). E-mail:
[email protected] (H.S.); g.j.vancso@ tnw.utwente.nl (G.J.V.).
10.1021/jp803260n CCC: $40.75
T ) 301 K).13a The UPy motif was previously also studied by Guan et al.14
() ( ) (
f * ) fβ · ln
rf
rf0
)
kB · T rf · toff(0) · ln xβ fβ
)
(1)
Here, fβ denotes the thermal force, r0f is the thermal scale for the loading rate, kB is the Boltzmann constant, and xβ is the distance of the energy barrier that needs to be overcome for unbinding from the energy minimum along the direction of the applied force (for a more detailed treatment of the theory, the reader is referred to refs 2 and 6). To obtain the thermal force fβ and thus the dimer equilibrium constant Keq using this model, f* is usually measured for various rf. Here, we report on a new, alternative approach to obtain toff(f ) 0) and Keq of dimeric complexes from measurements (at a single piezo retraction rate) of N bonds switched in series such that they fail uncooperatively under load. According to Evans and Williams,15 uncooperative bond rupture in series leads to a decrease of f* with the number of linkers N, as shown in eq 2, which provides access to fβ and all desired parameters.
f * ) fβ[ln(rf) - ln(N)] ) f *single - fβ ln(N)
(2)
Thus, in our experiments, the rupture forces of supramolecular, associative polymers12,13,16 formed between two UPy motifs attached to gold-coated substrates and tips were studied in the presence of bis-UPy derivative 3 in HD (Figure 1).17 The observed rupture forces were analyzed according to eq 2 to yield toff(f ) 0) and Keq for UPy-UPy dimers for one data set at a single loading rate. 2008 American Chemical Society
7360 J. Phys. Chem. B, Vol. 112, No. 25, 2008
Letters taken directly from solution followed by rinsing with pure solvent. The cantilever spring constant (k ) 0.187 ( 0.02 N/m) was determined in liquid via the thermal tune method.20 Loading rates were determined as the slope of the force versus time trace of the force-extension curves (∼20 data points) close to the rupture event. All experiments were performed in a saturated solution of 3 in anhydrous hexadecane at T ) 303 ( 2 K (concentration ) (3.2 ( 0.4) × 10-5 M). Results and Discussion
Figure 1. Scheme of a supramolecular polymer formed in hexadecane between substrate and AFM tip both functionalized with a layer of PEG-terminated disulfide 1, which has been reacted with UPy-isocyanate 2, in the presence of bis-UPy derivative 3.
Experimental Section Materials. Anhydrous hexadecane (purity g99%, water
