Friction scan velocity dependence

Figure 4. Scan velocity dependence of friction at discrete humidities on amorphous...

Figure 8. Time-temperature superposition analysis of frictional data collected on thin PMMA. (a) Temperature dependence offriction at four scan velocities (b) same data inverted, i.e. scan-velocity dependence of friction at multiple temperatures (c) master curve of same data sets as in (b), but shifted by variable multiplicative factors af, (d) plot of shift factors ar versus inverse temperature, with linear fit.

Figure 57 AFM height (a) and friction (b) images on a semicrystalline PVA surface, (c) Comparison of RH dependence of friction on predominantiy amorphous (1) versus highly crystalline (2) surface regions in (b). (d) Scan velocity dependence of friction versus RH on (1). Reprinted with permission from Haugstad, G. Hammerschmidt, J.A. Gladfelter, W. L. In Interfacial Properties on the Submicron Scale, Frommer, J. Ovemey, R. M. Eds. ACS Books Washington, DC, 200f Vol. 781, p 230. Copyright 2005 American Chemical Society.

Velocity / Frequency Relationship. The characteristic temperature-dependent line shapes for each polymer, as determined by bulk dynamic mechanical or dielectric experiments from literature (4), were used as a comparison to our fnctional measurements. For the comparison to be valid the literature data must be adjusted to match the same frequency (time-scale) of the friction experiment. The conversion procedure of scan velocity to frequency has been described in previously (7), whereby a contact diameter was calculated to convert the scan velocity to a frequency by simple division. The contact diameter thus allows a gauge for the time the probe tip affects a point on the polymer surface. For the given radius of curvature of 20 nm, applied load=10 nN, adhesive load=15 nN, and assuming a bulk storage modulus, the contact diameter can be estimated by JKR theory to be 18.7 nm. Thus for a scan velocity of 40 pm/sec the equiv ent frequency of measurement is 2000 Hz and all tabulated tanS data used are scaled accordingly to this frequency for comparison. 

In friction force microscopy (also called lateral force microscopy, LFM), on the contrary, these lateral forces are measured and may yield important insight into friction forces, their dependence on particular phases, and orientation of the underlying polymer or environmental conditions. Due to the difficulties in obtaining truly quantitative friction force data and the dependence of friction forces on load and scan velocity (due to the time-temperature superposition principle) [14], which all require tedious experimental procedures, friction force microscopy is not widely used in the analysis of polymer morphologies. 

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

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