How Strong Is a Covalent Bond?

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Science  12 Mar 1999:
Vol. 283, Issue 5408, pp. 1727-1730
DOI: 10.1126/science.283.5408.1727


The rupture force of single covalent bonds under an external load was measured with an atomic force microscope (AFM). Single polysaccharide molecules were covalently anchored between a surface and an AFM tip and then stretched until they became detached. By using different surface chemistries for the attachment, it was found that the silicon-carbon bond ruptured at 2.0 ± 0.3 nanonewtons, whereas the sulfur-gold anchor ruptured at 1.4 ± 0.3 nanonewtons at force-loading rates of 10 nanonewtons per second. Bond rupture probability calculations that were based on density functional theory corroborate the measured values.

The mechanical stability of covalent bonds has been investigated indirectly in ensemble measurements or by flow-induced chain fracture in liquids (1). The development of nanoscale manipulation techniques (2) has made it possible to directly address single atoms or molecules and probe their mechanical properties. It has been shown that individual polymers may be stretched between the tip of an AFM cantilever and a substrate surface (3–12). In these studies, polymers were coupled either by specific receptor ligand systems, which were covalently attached to the polymers (8), or by nonspecific adsorption to the tip and the substrate (3, 10–12). Force-extension curves that were recorded during stretching and relaxation revealed a wealth of fingerprintlike features, such as conformational transitions or supermolecular rearrangements (3, 6, 8–12). In our study, we used these well-known fingerprints to identify individual molecules that were covalently attached to both the tip and the substrate. We stretched the molecules until one of the covalent bonds in series ruptured (Fig. 1). By analyzing the bond rupture, we were able to identify the bond that failed.

Figure 1

(A) Stretching of a single polysaccharide chain that is covalently attached to the AFM tip and the substrate. (B) Schematics of the covalent attachment of the amylose by carbodiimide chemistry to glass or Au surfaces, which were both functionalized with amino groups.

Upon stretching, polysaccharides such as dextran or amylose undergo a pronounced transition during which the sugar rings switch into a more extended arrangement (3, 8, 12). With amylose, this results in a characteristic plateau at 275 pN with an extension of 0.5 Å per ring unit [Fig. 2A and (12)]. The transition is fully reversible on the time scale of the experiment and thus does not depend on the rate at which the force is increased. Thus, this transition can be used as a molecular strain gauge that can be built into an experiment to report the force that is acting on any point of the molecular bridge. We used this transition to identify those experiments in which only a single polymer is attached between the tip and the substrate. If two or more polymers are stretched simultaneously, the plateau forces add up and either shift the plateau to higher forces or smear it out. Both cases can easily be distinguished from the plateau of a single polysaccharide (13).

Figure 2

(A) Force versus extension curve of amylose covalently bound between an AFM tip and a silicon oxide surface. The indentation force was kept below 0.3 nN for each approach. The control force versus extension was measured without treatment of the amylose with EDC or NHS. (B) Measured force versus extension curve of amylose showing multiple ruptures in the high-force regime. The enlarged curve section of the high-force regime shows multiple small-step ruptures leading to elongations (Δx) of the amylose polymer. All the ruptures observed in the force versus extension curves were plotted in the histogram shown in Fig. 3B.

In the first set of our experiments, carbodiimide chemistry (14) was used to introduce a symmetric covalent attachment of amylose between the substrate and the tip (Fig. 1B). Both silicon oxide surfaces had been functionalized with amino groups beforehand (15). The activated amylose was first coupled to the substrate surface. Then, the tip was slowly brought into contact with the surface, allowing the polymer to bind to the tip (16). In ∼30% of the cases, an individual polymer was attached. In the other cases, either multiple bonds or no bonds occurred. The tip and the substrate were gradually separated while the force was recorded (Fig. 2). The plateau was analyzed by repeatedly stretching and relaxing the polymer through the conformation transition. After confirming that a single molecule was bound, the force was gradually increased until the molecular bridge ruptured.

The rupture of these single-molecule bridges occurred in multiple irreversible steps (Fig. 2B). As shown in the enlarged section of the curve in Fig. 2B, several peaks at variable but discrete spacing (Fig. 3A) precede the final rupture event, after which the force drops to zero. Because only a single polymer is stretched and the molecular bridge between the tip and the substrate remains intact after the individual rupture events, these multiple bond ruptures reflect the stepwise detachment of the polysaccharide from the surfaces. Given the manner in which a polymer interacts with a surface, it is to be expected that the polysaccharide is bound to the surface in loops and trains (17). With increasing force, the bonds of the loops to the surface thus break one by one, whereas the polymer backbone stays intact (see Fig. 1A). After each detachment, the force drops abruptly because the previously unstretched section can take up the slack and thus increase the length of the stretched polymer bridge (18). A quantitative analysis of the bond rupture force is given in Fig. 3B. At the given force-loading rates of 10 nN/s, the histogram peaks at a value of 2.0 ± 0.3 nN (19).

Figure 3

(A) Histogram of the length gain after the events were measured in the force versus extension curves showing multiple ruptures for amylose, which was covalently attached to the silicon oxide surface and the tip. Polymer elongations were measured with an error of ±2 Å. (B) Histogram of rupture forces measured for amylose covalently attached to the silicon oxide surface and the tip. The rupture forces measured for multiple rupture events were also considered in the histogram. (C) The control experiments, where no EDC or NHS was added, revealed that the attachment through nonspecific interaction of polymer ruptures at substantially lower forces. These values are in good agreement with the ones reported for coupling experiments based on noncovalent attachments (3,10). (D) Histogram of rupture forces measured for amylose, which was covalently attached to the Au surface and the tip (multiple rupture events are included). For this experiment, the activated amylose was bound to Au by an aminothiol. The same chemistry as that in the symmetric silicon oxide experiment was used to cross-link the molecule to the AFM tip. (E) For the control experiments, no EDC or NHS was added. The nonspecific adhesion forces are comparable to those in Fig. 3C.

This finding that it is the attachment that ruptures and not the polymer backbone indicates that the measured bond rupture must be attributed to either of the bonds that are part of the attachment and not part of the polysaccharide. In Fig. 1B, the schematics of the chemistry of the attachment are depicted. Four bonds are unique to the attachment: Si–O, Si–C, C–C, and C–N bonds. The C–O bond is found in the attachment and in the amylose backbone. At first, it was difficult to decide which of these four different bonds was breaking in our experiment. We ruled out the rupture of the Si–O bond because three of these bonds hold in parallel at the surface. As a first approximation, we correlated the strength of a covalent bond with the ratio of the dissociation energy and the bond length. Considering the enthalpy for dissociation and the bond length (20), we decided that the Si–C bond was the most likely candidate for rupture in our experiment.

This hypothesis was confirmed by a theoretical investigation of the rupture forces for the different kinds of covalent bonds in the system. One-dimensional potential functions for the covalent bonds of interest were derived from high-level density functional calculations of small model molecules, from which one-dimensional Morse potentials were extracted. Adapting the method outlined in (21), temperature- and force-ramp–dependent bond rupture probability densities were calculated (Fig. 4). Theory corroborates our estimate that Si–C is the weakest of all the bonds in question. The absolute values for the calculated bond rupture forces are slightly higher than the experimental values. This difference may reflect solvent effects that were not considered in our calculations. These theoretical values, as well as the experimental results, compare well to the value obtained by a resistance test on a small polymer specimen [3 nN (1)] or by a flow-induced fracture of single polymer chains [2.5 to 13.4 nN (1)].

Figure 4

Bond rupture probability densities were derived in three steps of theoretical modeling. First, high-level density functional calculations (25) of small model molecules in the gas phase were used to derive potential functions that accounted for the deformations and hybridizations caused by the application of force. Pulling on the terminating H atoms (for example, H3SiCH2-CH3) was simulated by a so-called “relaxed potential energy surface scan.” Starting from a fully optimized geometry, a series of constrained geometry optimizations was performed in which the distancer(H–H) was elongated in steps of 0.1 Å. The energy of the otherwise relaxed molecule was calculated, which yielded a potential for the deformation of the model molecule. The force that corresponds to a certain elongation is the gradient of the potential. For kinetic modeling, the quantum mechanically calculated potential was fitted by a Morse potential (20) V =D e{1 – exp[–b(rr e)]}2, whereD e is the bond dissociation energy, bis chosen so that V has the same maximum slope as the calculated potential, and r e is the equilibrium distance. In the kinetic model, the rupture rate constantn(F) was calculated as a function of the applied force. Under force, V is deformed to the effective potential V eff = VF(rr e) (inset), which in turn yields the parameters for the Arrhenius rate constant law n(F) =A exp(–E A/kT), where A is the Arrhenius A factor,E A is the activation energy, k is the Boltzmann constant, and T is temperature (21). This rate function n(F) was numerically convoluted with a typical experimental load of 10 nN/s, resulting in the bond rupture probability density as a function of force. Results are shown for the model molecules of H3SiCH2CH3, H3SiOCH3, H3CCH2CH3, H3COCH3, and H3CNHCH3. The Si–C bond in H3SiCH2CH3 comes closest to the experimental values of rupture force.

We compared the bond strength of the Si–C bond to the strength of the attachment of the polymer through S to Au (Fig. 3C). The experimental setup and the protocol were identical to the previous experiments, except that the substrate was an evaporated Au surface, which was activated with an aminothiol. The attachment to the tip was unaltered. As seen in Fig. 3D, this replacement resulted in a reduction of the bond rupture force to values of 1.4 ± 0.3 nN. In control experiments, where the polysaccharide was chemically coupled to the Au substrate but not to the tip, the same nonspecific attachment forces of 0.8 ± 0.2 nN were measured as in the silicon oxide control experiments (Fig. 3, C and E). Because the nonspecific interaction between the tip and the polysaccharide was probed in both cases, this agreement was to be expected. This value is also consistent with previously measured values on comparable surfaces (8).

In the symmetric silicon oxide experiment, the measured rupture force could be clearly attributed to the Si–C bond, whereas the S–Au rupture experiments leave room for speculation. Whether this measured value of 1.4 nN represents the rupture of the Au–S bond or the extraction of the S-bonded Au atoms from the metal surface remains unclear.

Although chemical compounds play a dominant role in material sciences, the forces that chemical bonds can withstand could previously not be directly measured in experiments. The experiments reported here demonstrated that the individual chemical bonds can be probed in mechanical experiments. An important feature of such experiments is the mechanical activation of chemical bonds (here in the simplest form as bond rupture), which can now be studied on an individual basis.


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