(a) Energy diagram for Eyring model. (b) Conceptual drawing illustrating the activation volumes associated with pressure and shear.
General procedure for obtaining the Eyring model parameters ϕ, Ω, v o , Q, and E * . Dotted lines indicate a path of high uncertainty for v o . In this study v o is obtained from IFA.
IFA data analysis, horizontal shifting provides activation energy information, while vertical shifting provides cooperativity (entropic) information.
(a) Representative friction-velocity master curve of ODPA for a ∼400 nm radius tip as imaged (inset) by transmission electron microscopy. (b) The slope of the corresponding Arrhenius plot of the shift factor ln a T vs T −1 , reveals an activation energy of 46 kJ/mol independent of load. Inset: Chemical structure of ODPA. (c) Ω, ϕ, and Q plots as a function of temperature for a 400 nm tip radius lever, and a constant pressure of 34 MPa Values are averaged over all velocities, and the error bars represent the standard deviation. The Q data is contrasted to E a from IFA (represented by the dashed line).
Shear stress data as a function of temperature for various velocities measured at p = 23 MPa using the large tip (R∼400 nm). Line slopes are –β, and are −0.0086, −0.0135, −0.0177, −0.0246, −0.0320, and −0.0368 MPa/K for 0.5, 1, 2, 5, 10, and 50 μm/s, respectively. (Inset) v o values as a function of log scan velocity calculated from β values and (15) , showing that ln v o = 9.97lnv+143.
Plot of lnv vs 1/T for various ln (va T ) values from ODPA and PtBA master curves. Each data point for ODPA is averaged over six loads. The inset highlights the lnV-intercept data extrapolation with the dotted lines representing high and low deviations from the selected (solid line) value. The corresponding median v o values are provided for ODPA and PtBA.
(a) Master curve for PtBA (see Inset) at a reference temperature of 315 K. (b) Half logarithmic representation of the shift factor a T as a function of inverse temperature and the corresponding WLF fit along with the literature WLF expression for peak values from dielectric spectroscopy measurements (Ref. 33 ). (c) Vertical shift values ΔF F as a function of temperature, reveal the onset of vertical shifting near T g .
Entropic, TΔS*, enthalpic ΔH* = E a-TΔS* and apparent E a energy contributions as function of temperature for PtBA T > T g .
Plot of Ω, ϕ, Q values as a function of temperature for a constant pressure of 99 MPa, error bars represent the standard deviation. The dashed line represents E a from IFA.
(a) For slider-system coupling, the shear stress reveals a peak value, which leads to (b) negative and zero values of θ, and, consequently, (c) unphysical behavior for the Eyring parameters ϕ and Ω in the unextended Eyring model.
IFA master curve for T = 315 K, which corresponds to T o obtained above. Also included are Erying model fits at T = 315 K, where ϕ = 1.5 × 10−27 m3, Q = 35–43 kJ/mol, Ω = 1.92 × 10−28 m3, all of which were obtained by the same procedure as for ODPA mentioned above. A was estimated to be 2.92 × 10−16 m2 assuming JKR contact mechanics (Ref. 26 ). For 315 K, De = 1.0 occurs at a scan rate of 0.1 nm/s.
Erying model results for C 18 monolayers.
Compounded data of IFA and Eyring analysis for ODPA and PtBA.
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