Принципы нанометрологии (1027623), страница 45
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As a model,consider the Lennard-Jones potential, which describes the change in intermolecular potential energy (f) that occurs as two particles, such as atoms ormolecules (on tip and sample), are brought closer together. The model gives s 12 s6(7.1)f ¼ 43rrwhere s is approximately the atomic or molecular diameter (distance ofclosest approach), 3 is the minimum value of the potential energy or thedepth of the potential energy well, and r is the separation distance [42].
Asthe particles are brought closer together from relatively distance separations,Table 7.2Examples of surface forces commonly encountered in AFM measurementType of forceDependence of energy on distance (d)Energy (kJ$mol1)Range (nm)Intra-molecular (ionic or covalent)London dispersionH-bondingDipolesElectrostaticVan der WaalsSolvationHydrophobic1/d1/d 61/d 31/d 3ed1/d~ed~ed100s1 to 315 to 205 to 1010 to 1001 to 51 to 101 to 5<10.5 to 50.5 to 30.5 to 310s to 100s5 to 10<510s to 100s193194C H A P T ER 7 : Scanning probe and particle beam microscopythe (1/r)6 term (i.e.
Van der Waals term) describes the slow change inattractive forces. As the particles are brought even closer together, the (1/r)12term describes the strong repulsion that occurs when the electron cloudsstrongly repel one another.The Van der Waals interaction forces are long-range, relatively weakattractive forces. The origin of the Van der Waals forces is quantummechanical in nature; they result from a variety of interactions, primarilyinduced dipole and quadrupole interactions. The Van der Waals forces arenonlocalized, meaning that they are spread out over many atoms. Van derWaals forces for a typical AFM have been estimated to be of the order of 10nN to 20 nN [43].The so-called atomic force (a result of the Pauli exclusion principle) is theprimary repulsive force at close approach.
The magnitude of this force isdifficult to predict without a detailed understanding of surface structure.Several additional forces or interactions must be considered for an AFMtip and sample surface. Capillary adhesion is an important attractive forceduring imaging in air. The capillary force results from the formation ofa meniscus made up of water and organic contaminants adsorbed on to thesurface of the tip and the sample [36] (see Figure 7.7).
The capillary force hasbeen estimated to be of the order of 100 nN or greater. When the tip and thesample are completely immersed in liquid, a meniscus does not form and thecapillary forces are absent. Some tips and samples may have hydrophobicproperties, in which case hydrophobic interactions must also be taken intoconsideration.Water near hydrophilic surfaces is structured [34]. When the tip and thesample are brought into close contact during force microscopy in solution orhumid air, repulsion arises as the structured water molecules on the surfacesof the tip and the sample are pushed away.
In aqueous solutions, electricaldouble-layer forces, which may be either attractive or repulsive, are presentFIGURE 7.7 Schematic illustration of the strong capillary force that tends to drive thetip and sample together during imaging in air.Atomic force microscopynear the surfaces of the tip and the sample. These double-layer forces arisebecause surfaces in aqueous solution are generally charged.Lateral frictional forces must also be taken into account as the sample isscanned beneath the tip. At low forces, a linear relationship should holdbetween the lateral force and the force normal (vertical) to the surface witha proportionality constant equal to the coefficient of friction. This relationship is valid up to an approximately 30 nN repulsive force [44]. Frictionalforces vary on an atomic scale, and with temperature, scan velocity, relativehumidity, and tip and sample materials.7.3.7.1 Tip functionalisationInter- and intra-molecular forces affect a variety of phenomena, includingmembrane structure, molecular recognition and protein folding/unfolding.AFM is a powerful tool for probing these interactions because it can resolveforces that are several orders of magnitude smaller than the weakest chemicalbond, and it has appropriate spatial resolution.
In recent years, researchers havetaken advantage of these attributes to create chemical force microscopy [45].AFM probes (i.e. cantilevers or tips) are functionalised with chemical functionalgroups, biomolecules or living, fully functional cells to make them sensitive tospecific interactions at the molecular to cellular level (see Table 7.3).There are many ways to functionalize an AFM tip or cantilever. Allfunctionalization methods are constrained by one overriding principle – thebonds between the tip/cantilever and the functionalizing substance (i.e. theforces holding the substance of interest to the tip/cantilever) must be muchstronger than those between the functionalizing substance and the sample(i.e. the forces that are actually measured by the AFM).
Otherwise, thefunctionalizing substance would be ripped from the tip/cantilever duringforce measurements.Table 7.3Various substances that have been linked to AFM tips or cantileversSubstance linked to tip/cantileverLinkage chemistryProteinNucleic acidPolysaccharideGlass or latex beadLiving microbial cellDead microbial cellEukaryotic cellOrganic monolayerNanotubeadsorption, imide, glycol tether, antibody-antigenthioladsorptionepoxysilane, poly-lysinegluteraldehydeepoxy, adsorptionself-assembling monolayer, silaneepoxy195196C H A P T ER 7 : Scanning probe and particle beam microscopySingle, colloidal-size beads, a few micrometres in diameter, can beroutinely attached to a cantilever using an epoxy resin [46]. Such beads maybe simple latex or silica spheres, or more complex designer beads imprintedwith biomolecular recognition sites.
Care must be taken to select an epoxythat is inert in the aqueous solution and that will not melt under the laser ofthe optical lever detection system [47].Simple carboxylic, methyl, hydroxyl or amine functional groups can beformed by self-assembling monolayers on gold-coated tips [45] or by creatinga silane monolayer directly on the tip. Organosilane modification of a tip isslightly more robust because it avoids the use of gold, which forms a relatively weak bond with the underlying silicon or silicon nitride surface of thetip in the case of self-assembling monolayers.
Carbon nanotubes (CNTs) thatterminate in select functional groups can also be attached to cantilever tips[48]. The high aspect ratio and mechanical strength of CNTs creates functionalized cantilevers with unprecedented strength and resolution capabilities. Direct growth of CNTs onto cantilevers by methods such as chemicalvapour deposition [49] will probably make this method more accessible toa large number of researchers.Biomolecules such as polymers, proteins and nucleic acids have beenlinked to AFM tips or deposited directly on the cantilever [50]. One of thesimplest attachment techniques is by non-specific adsorption betweena protein, for example, and silicon nitride. The adsorbed protein can thenserve as a receptor for another protein or ligand.
Virtually any biomoleculecan be linked to a cantilever either directly or by means of a bridging molecule. Thiol groups on proteins or nucleic acids are also useful becausea covalent bond can be formed between sulfulhydrol groups on the biomolecule and gold coatings on a tip. Such attachment protocols have been veryuseful: however, there are some disadvantages. The linkage procedure maydisrupt the native conformation or function of the biomolecule, for example,if the attachment procedure disrupts a catalytic site. It is well known thata protein attached to a solid substrate (a cantilever or tip) may exhibita significantly different conformation, function and/or activity relative to itsnative state within a membrane or dissolved in solution.
Therefore, caremust be taken to design control experiments that test the specificity ofa particular biomolecule as it occurs in its natural state.7.3.8 Tip sample distance measurementTo obtain the distance or separation part of the force–distance curve, a pointof contact (i.e.
zero separation) must be defined and the recorded piezoelectricscanner position (i.e. displacement) must be corrected by the measuredAtomic force microscopydeflection of the cantilever. Simply adding or subtracting the deflection of thecantilever to the movement of the piezoelectric scanner determines thedisplacement. For example, if the sample attached to the piezoelectricscanner moves 10 nm towards the cantilever, and the cantilever is repelled 2nm due to repulsive forces, then the actual cantilever–sample separationchanges by only 8 nm. The origin of the distance axis, the point of contact, ischosen as the beginning of the region of constant compliance, i.e. the pointon the force curve where cantilever deflection becomes a linear function ofpiezoelectric scanner displacement (see Figure 7.6).
Just as it was difficult toconvert photodiode voltage to displacement units for soft, deformablematerials, it is not always easy to select the point of contact because there isno independent means of determining cantilever–sample separation. Fordeformable samples, the cantilever indents into the sample such that theregion of constant compliance may be non-linear and the beginning pointcannot be easily defined. Recent research has developed an AFM with independent measurement of the piezoelectric scanner and the cantileverdisplacements [51].7.3.9 Challenges and artefacts in AFM force measurementsThere are a number of artefacts that have been identified in force curves.Many of these artefacts are a result of interference by the laser, viscosityeffects of the solution or elastic properties of soft samples.
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