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Hydrodynamic corrections to contact resonance atomic force microscopy measurements of viscoelastic loss tangenta)
a)Contribution of NIST, an agency of the US government; not subject to copyright in the United States.
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10.1063/1.4812633
/content/aip/journal/rsi/84/7/10.1063/1.4812633
http://aip.metastore.ingenta.com/content/aip/journal/rsi/84/7/10.1063/1.4812633

Figures

Image of FIG. 1.
FIG. 1.

Fluid damping effects that must be considered in CR spectroscopy. and are the natural frequency and quality factor of the cantilever measured far from the sample surface, and are the natural frequency and quality factor of the cantilever measured near to the sample surface, and is the natural frequency of the cantilever when in contact with the sample surface. (a) Surface proximity effects. The quality factor decreases as the cantilever is brought closer to the surface. (b) Frequency dependence of fluid damping. Because > , estimations of the fluid damping made at do not accurately portray the real fluid damping at .

Image of FIG. 2.
FIG. 2.

Added mass and damping effects. (a) Damping term and added mass term gap height at the first free natural frequency of the cantilever ≈ 75 kHz and 5 . (b) Damping term and added mass term frequency at = ∞. should not be confused with the actual quality factor . is inversely proportional to the damping experienced by the system at a particular frequency and gap height and is equal to in special cases.

Image of FIG. 3.
FIG. 3.

Flowchart of the hydrodynamic correction procedure.

Image of FIG. 4.
FIG. 4.

Contact resonance results for tan δ of polystyrene sample obtained for the first three flexural modes with use of different inputs for the fluid damping estimation. “Far” represents tan δ values calculated with and , “Near” represents tan δ values calculated with and , and “Hydrodynamic” represents tan δ values calculated with and .

Image of FIG. 5.
FIG. 5.

Here, we have assigned values of (tan δ) (x-axis) and sample stiffness normalized by cantilever stiffness α. We use the measured values of , γ, and the calculated values of for each mode. We assume that is the actual fluid damping of the system, and compute the percent difference, ε, between (tan δ) calculated with the damping measured close to the surface, , and the prescribed theoretical values of (tan δ). (a) Results for α = 60. (b) Results for α = 240.

Tables

Generic image for table
Table I.

Experimental results for the cantilever's natural frequency and quality factor . and are measurements taken with the cantilever ∼1 mm from the sample surface. and are measurements taken with the cantilever tip ∼250 nm from the sample surface. and are measurements taken with the tip in contact with the polystyrene test sample.

Generic image for table
Table II.

Values of tan δ calculated from the data in Table I with Eq. (5) . (tan δ) is the viscoelastic loss tangent calculated with the values of and as inputs. (tan δ) is calculated with the values of and , while (tan δ) is calculated with the values of and . Δ is the percent difference between (tan δ) and (tan δ) as defined in the text, and Δ is the percent difference between (tan δ) and (tan δ).

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/content/aip/journal/rsi/84/7/10.1063/1.4812633
2013-07-09
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hydrodynamic corrections to contact resonance atomic force microscopy measurements of viscoelastic loss tangenta)
http://aip.metastore.ingenta.com/content/aip/journal/rsi/84/7/10.1063/1.4812633
10.1063/1.4812633
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