Atomic force microscopy (AFM)

The AFM has originally been developed in the 1980s as a tool to study surface topography with atomic resolution.^137,138 Force measurements with the AFM had their breakthrough with the independent publications of Ducker¹³⁹ and Butt¹⁴⁰ in 1991. They proposed a modification of the standard imaging cantilevers which are equipped with a sharp tip.

Instead of the sharp tip a glass sphere of colloidal dimensions (severalµm in diameter) was glued to the front of the cantilever. The such created "colloidal probe" (CP) was used to measure surface forces between the CP and a flat silicon wafer or freshly cleaved mica as a function of ionic strength and pH. Results were compared with DLVO theory.

The advantage of a CP for this kind of studies is obvious: the colloidal sphere provides a well-defined geometry which facilitates modeling and interpretation of the obtained data.

Furthermore, it provides a relatively large contact area and can be modified easilyvia surface chemistry. Finally, it opens the field for studying mechanics and interactions of colloidal particles with the high precision in force and displacement of an AFM. So, it’s not surprising that this technique and modifications thereof have become very popular in colloid and interface science and that Ducker’s article has been cited more than 1,200 times.

Before discussing the different measurement geometries and opportunities of AFM for the characterization of particle mechanics the basic working principles of AFM-instrumented force measurements shall be explained. Figure 2.6 shows a typical setup schematically.

The movement of the cantilever towards the surface is piezo controlled. The deflection of the cantilever is monitored by the deflection of a laser beam which is focused on the

back of the cantilever and reflected to a photodiode. So, the raw signal of a "force"

measurement is voltagePV vs. piezo displacement z. To convert this information into forceF vs. displacement two calibration steps need to be carried out: the determination of the cantilever’s spring constant k and its sensitivity, typically given as the inverted optical lever sensitivity InvOLS.

Figure 2.6. Schematic representation of an atomic force microscope (AFM) probing a particle.

For the determination of k several methods have been developed, of which the most important are: 1) thermal noise method,^141,142 where k is calculated from the thermal resonance peak of the cantilever; 2) Sader method,^143–147 uses the resonant frequency, cantilever dimensions and the density of surrounding fluid; 3) added mass method,¹⁴⁸ evaluates the shift in resonant frequency when masses of defined weight are attached to the cantilever; 4) reference spring method,^149–152 where the cantilever with unknown spring constant is pushed against a calibrated reference.

While, in general, the spring constant only needs to be determined once, theInvOLS has to be determined prior to each measurement (and, to check for consistency, also afterwards). This is due to the fact that it strongly depends on the alignment of the laser spot on the cantilever which will change with each demounting/mounting of the cantilever.

Typically, theInvOLS is obtained as the inverse slope of a voltagevs. displacement curve

resulting from pressing the cantilever against a hard, non-deformable, planar substrate (e.g., a glass slide or silicon wafer). An alternative, non-invasive method has been proposed by Higginset al., who calculate the InvOLS from the known spring constant and resonant frequency.¹⁵³

Knowing the spring constant and theInvOLS the photodiode signal in Volts is converted to force in Newtons in the following way:

F =P V ·InvOLS·k (2.29)

Finally, when examining a compliant sample the displacement needs to be corrected for the cantilever bending to yield the deformation (of the sample) d. This is done like:

d=z−F

k (2.30)

Now, we can obtain a force vs. deformation characteristic as shown exemplarily in fig.

2.7. After the unperturbed approach to the particle surface the cantilever touches and compresses it until a pre-defined trigger point is reached. Upon retraction, the cantilever feels the elastic restoring force of the sample and, in case of adhesive interactions between sample and probe, is deflected to negative values until a minimum is reached (the pull-off force, commonly interpreted as the force of adhesion, F_adh). Additional features might arise, for instance, from attractive or repulsive interactions outside the contact zone. For more details see [154].

The AFM covers a wide reach of forces (pN to µN) and is therefore a useful tool for the mechanical characterization of particles built from a broad range of materials, in particular (bio)polymers and (hydro)gels. Deformations are effected uniaxially which may be ascertained by optic control. In the case of microcapsules the combination with RICM (reflection interference contact microscopy) allows for the observation of change

Figure 2.7. Schematic representation of a deformation experiment with AFM force spectroscopy. 1) Approach: The cantilever is far away from the surface, no interactions with the sample. 2) Compression: The probe is in contact with the sample and deforms it. 3) Withdraw: In case of adhesion between probe and sample, the cantilever bends toward the sample upon retraction. The difference between minimum and baseline equals the adhesion force, F_adh.

of contact area during deformation.^135,155 Moreover, from the interference patterns the three-dimensional shape of the capsule under compression can be reconstructed.^156–159 As said in the beginning, the colloidal probe is often used in force spectroscopy, not only for studying surface or interfacial forces but also to assess materials mechanics (for different probe geometries see fig. 2.8). In the field of particle mechanics first works were published roughly ten years ago.136,71,160,135,155,161 Independently, the Fery and Vinogradova groups studied PEMCs (poly-electrolyte multilayer capsules) whose mechanical properties could be shown to clearly depend on shell thickness, thus confirming theoretical predictions.

In the meantime, mechanics of various particulate systems have been investigated with CP-AFM, among these multilayer capsules,^162–166 vesicles,¹⁶⁷ polymer capsules^55,54,60 and particles.6,8,7,168–170

Figure 2.8. Schematic representation of the different probes/measurement geometries in AFM based force spectroscopy. While a colloidal probe can be chosen such that it has comparable dimensions with respect to the examined particles, the radius of a sharp tip is orders of magnitude smaller, thus probing more local elastic properties. Using a bare cantilever one has to consider its inclination as predetermined by the cantilever holder.

An alternative to CP-cantilevers for the investigation of mechanical properties is the use of standard cantilevers with a tip. This way, however, a decisive advantage of colloidal probes is lost. With a CP of comparable dimension with respect to the examined particles the contact zone is rather extended which minimizes local pressure, thus providing gentle probing of the sample. In contrast, a sharp tip gives a very local information and mechanical pressure is relatively high. Therefore, measurement parameters have to be set with care in order to avoid penetration into the sample, which makes data evaluation difficult due to arising friction or shearing. In addition, sharp tips are not as well defined as colloidal probes; for correct modeling, their actual geometry needs to be determined separately, e.g. with a calibration grating or via SEM. Nevertheless, sharp tips have widely been applied to study particle mechanics, covering polymeric full particles^11,5 and capsules,⁵⁷ inorganic capsules,^56,171 vesicles,^172,173 polymersomes¹⁷⁴ and viral shells.^175,176 Finally, particle deformation experiments can, in principle, also be performed with bare, tipless cantilevers. Yet, one has to be aware of the default tilt of the cantilever in commercial holders (typically 10°). Due to this inclination the axial compression is expected to be accompanied by shear forces and sliding of the particle may occur. Still, this approach has been used for a range of capsule systems.^177–183 In a recent publication on mechanical properties of giant unilamellar vesicles (GUV), Schäfer et al. account for

the inclination of the cantilever by tilting the substrate such that an almost perfectly parallel plate geometry is ensured.¹⁸⁴