(a)–(c) Schemes of the processes involved in apparent height reconstruction in AM AFM as the tip scans over a sample. The tip and the samples are modeled as spheres. In the absence of the sample the force is F tip-sur (tip-surface) while in the presence of the sample the contribution of the tip-sample interaction F tip-sam is added to the net force. In (d)–(e) the effects of the corresponding areas of interaction are illustrated.
Schemes of the deformation of a spherical sample subjected to compression between a spherical tip and a flat surface according the (a) Hertzian contact model and the (b) Tatara modification. In (a) the deformation is assumed to occur on the top hemisphere while in (b) the total deformation is the sum of the deformations occurring on the top and bottom interfaces.
Scheme of the several interactions that might occur in dynamic AFM. These are schemes illustrating snap shots of the interactions occurring at a given separation. (a) The nc interaction regime implies that neither mechanical nor water contact (if water layers are present) ever occur during an oscillation cycle. Thus, only the long range (non-contact) attractive force component Fa acts in the nc interaction regime. (b) In the intermittent water contact ic interaction regime intermittent water contact might occur. This does not exclude nc in parts of the oscillation cycle but excludes intermittent mechanical contact. In the ic regime the acting forces might be Fa, the adhesion vdW force FAD, and the capillary force FCAP. In the scheme in (b) reference is also made to the perpetual water contact regime pc. The only restriction in the definition of this regime is that water contact occurs throughout during an oscillation cycle. (c) In the intermittent mechanical contact mc regime mechanical contact occurs during an oscillation cycle. This regimes might include ic (provided water layers are present) and nc interactions. The attractive and repulsive force regimes (AR and RR) might be included in one or the other interaction regimes. The AR and RR make reference to the net force while the interaction regimes illustrated in Fig. 3 make reference to whether of a particular physical phenomenon, such as water contact or mechanical contact, occurs during an oscillation cycle.
Force distance dependencies (left column) and respective schemes illustrating the physical phenomena (right column). Five cases are presented from Case A in (a) and (b) to Case E in (i) and (j) according to whether water layers are absent (Case A) or present (Cases B–E), and to whether the capillary neck forms on the surface (Case C) on the sample (Case D) or both (Case E). The parameters are: R = 7 nm, γ = 45 mJ, γw = 72 mJ, γsam = 45 mJ, E sur = 60 GPa, Etip = 120 GPa, E sam = 10 GPa, R sam = 1 nm, and h = 0.8 nm.
Simulated amplitude (black lines) and phase (light blue lines) APD distance curves taken (a) below A0 ≈ 15 m, (b) at A0 ≈ 19 m, and (c) above the critical free amplitude A0 ≈ 28 m, where Ac ≈ 18 nm. Approach (dashed lines) and retraction (continuous lines) are shown. The attractive regime (AR) prevails throughout below Ac in (a). At Ac a transition between AR and the repulsive regime (RR) takes places on retraction. Transitions also occur above Ac but the AR only prevails at the largest oscillation amplitudes in this case while the RR prevails elsewhere throughout. The simulation parameters are: R = 6 nm, γ = 10 mJ, γw = 15 mJ, E sur = 70 GPa (elastic modulus of the surface), Etip = 120 GPa (elastic modulus of the tip), Q = 200, k = 4 N/m, f0 = f = 70 kHz, η tip-sur = 18 kPa·s and h = 0.6 nm, expressions (2) and (17)–(24). The curves are reproduced experimentally on a quartz surface in (d)–(f), respectively. Approach and retraction are drawn with red and blue continuous lines, respectively, as it is customary with Asylum Research instrumentation. The experimental value for the critical amplitude is Ac ≈ 24 nm. The experimental parameters are: quartz sample, Q ≈ 200, k ≈ 4 N/m and f0 = f = 74 kHz.
(a)–(e) Predictions of apparent height for the five cases shown in Fig. 4 and for a range of values of free amplitude A0. The normalized apparent height is plotted in the y axis as a function or nomralised amplitude A/A0 in the x axis. A large range of possible values for the apparent height are shown to be predicted according to the interaction and force regimes that prevail. This is particularly so in Case B–E where water layers are present. In (f) experimental evidence of height reversal in a scan of a dsDNA molecule on a mica surface is given. The relative humidity was more than 90% during the scan implying that water layers on the surfaces can have height as large as 1 nm or more. For most of the scan the apparent height is close to zero nm, i.e., the molecule is not resolved topographically and the force regime is AR/AR. The outline of the molecule has been drawn in white next to the real topography to show what the topography should look like. While the AR/AR prevails almost throughout, transitions between force regimes can sometimes be observed. In particular, the AR/RR (see region inside the circle) case can be observed in the figure where height reversal occurs. Sharp phase contrast typically accompanies such behavior (see Fig. 7). Cases B and C in (b) and (c), respectively, predict such behavior in these cases. The data in (f) have been adapted from Ref. 85. The simulation parameters are: Q = 500, k = 40 N/m, f0 = f = 300 kHz, η tip-sur = 10 kPa·s, ηtip-sam = 2 kPa·s, and rest as in Fig. 4. The experimental parameters are: mica surface, dsDNA sample, Q ≈ 500, k ≈ 40 N/m, f0 = f = 300 kHz, A0 = 9 nm, A/A0 ≈ 0.5, Ac ≈ 15nm, and relative humidity ≈95%.
Sequence of topography and corresponding phase contrast scans for a dsDNA molecule imaged on a mica surface at ∼95% relative humidity. In (a) A0 ≈ 3 nm≪Ac ≈ 15 nm. At this point the (z c 2 − z c 1)/2R sam ≈ 0.25 and the prediction is that the nc/nc interaction regime prevails and this water layers are not perturbed; R sam = 1 nm for the dsDNA molecule. The apparent height is minimized in b) 1/2Ac < A0 < Ac, where close to zero values are obtained in the AR/RR regimes and height reversal occurs in the RR/RR case. In (c) the height is recovered to (z c 2 − z c 1)/2R sam ≈ 0.4. In (d)–(f) the corresponding phase contrast images are shown and in (g) and (h) the topography and phase are zoomed in the regions where height reversal occurs in (b) and (e), respectively. Experimental values as in Fig. 6(f). The figures have been adapted from Ref. 85.
Simulation of amplitude curves in the absence (continuous lines) and presence (discontinuous lines) of the sample as a function of the height of the water layers h for 1/2Ac < A < Ac, when the AR/AR regimes prevail. The capillary forms only in the absence of the sample (Case C). Then all the branches shown in the figure correspond to the attractive branch. Note that the x axis stands for the normalized cantilever-surface separation z c /A0 and how the branches shift to the right, i.e., larger separations, as h increases from 0.2 (blue lines) to 0.6 (black lines) and 1 (red lines) nm. The shift for the branch in the absence of the sample, however, occurs faster. Note how the continuous lines shift faster than the discontinuous lines with increasing h. As a result, the apparent height goes from positive for h = 0.2 nm (≈1.4 nm) to negative for h = 1 nm (−0.6 nm). The parameters, other than h, are similar to those used in Fig. 6.
Article metrics loading...
Full text loading...