Chemical Force Microscopy - Force of Adhesion (tensile Testing)

Force of Adhesion (tensile Testing)

This is the simpler mode of CFM operation where a functionalized tip is brought in contact with the surface and is pulled to observe the force at which separation occurs, Fad (see Figure 2). The Johnson-Kendall-Roberts (JKR) theory of adhesion mechanics predicts this value as

(1)

where WSMT = γSMTMST with R being the radius of the tip, and γ being various surface energies between the tip, sample, and the medium each is in (liquids discussed below). R is usually obtained from SEM and γSM and γTM from contact angle measurements on substrates with the given moieties. When the same functional groups are used, γSM = γTM and γST = 0 which results in Fad = 3πRγSM, TM. Doing this twice with two different moieties (e.g. COOH and CH3) gives values of γSM and γTM, both of which can be used together in the same experiment to determine γST. Therefore, Fad can be calculated for any combination of functionalities for comparison to CFM determined values.

For similarly functionalized tip and surface, at tip detachment JKR theory also predicts a contact radius of

(2)

with an “effective” Young's modulus of the tip K=(2/3)(E/(1-ν2)) derived from the actual value E and the Poisson ratio ν. If one knows the effective area of a single functional group, AFG (e.g. from quantum chemistry simulations), the total number of ligands participating in tension can be estimated as . As stated earlier, the force resolution of CFM does allow one to probe individual bonds of even the weakest variety, but tip curvature typically prevents this. Using Eq 2, a radius of curvature R<10 nm has been determined as the requirement to conduct tensile testing of individual linear moieties.

A quick note to mention is the work corresponding to the hysteresis in the force profile (Figure 2) does not correlate to the bond energy. The work done in retracting the tip is, approximated due to the linear behavior of deformation with Fmax being the force and Δx being the displacement immediately before release. Using the results of Frisbie et al., normalized to the estimated 50 functional groups in contact, the work values are estimated as 39 eV, 0.25 eV, and 4.3 eV for COOH/COOH, COOH/CH3, and CH3/CH3 interactions, respectively. Roughly, intermolecular bond energies can be calculated by: Ebond=kTB, TB being the boiling point. According to this, Ebond = 32.5 meV for formic acid, HCOOH, and 9.73 meV for methane, CH4, each value being about 3 orders of magnitude smaller than the experiment might suggest. Even if surface passivation with EtOH were considered (discussed below), the large error seems irrecoverable. The strongest hydrogen bonds are at most ~1 eV in energy. This strongly implies that the cantilever has a force constant smaller than or on the order of that for bond interactions and, therefore, it cannot be treated as perfectly rigid. This does open an avenue for increasing the usefulness of CFM if stiffer cantilevers can be used while still maintaining force resolution.

Read more about this topic:  Chemical Force Microscopy

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