Frequency sweep curves

The one exception in which phase contrast is not due to the dissipation arises when the tip jumps between attraction phases (>90°) and repulsion phases (<90°). Since sine is a symmetric function about 90°, the phase changes symmetric even if there are no losses in the tip-sample interaction. The relative contribution of the repulsive and attractive forces can be estimated experimentally from the frequency-sweep curves in Fig. lib by measuring the effective quality factor as Qe=co0/Ao)1/2, where Ago1/2 is the half-width of the amplitude curve. The relative contribution of the attractive forces was shown to increase with increasing the set-point ratio rsp=As/Af. Eventually, this may lead to the inversion of the phase contrast when the overall force becomes attractive [110,112]. The effect of the attractive forces becomes especially prominent for dull tips due to the larger contact area [147]. 

Moreover, rotational rheometers can be used in dynamic oscillatory mode, frequency sweep, to assess the elastic G module as well as the viscous G" module and the correlated phase angle 6, as a function of the frequency co. G and G" allow to study the viscoelastic behaviour of HA macromolecules. Fig. (15) shows the frequency sweep curves (G, G", and tg(5) vs. the frequency co) for an HA sample (Mw=1350 kDa, polydispersity index D=1.6, concentration c = 2%) at 20 °C. 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

The exceptionally strong influence of calcium-ions on pectin solutions especially made with HM citrus pectins can be shown by a frequency sweep. The addition of calcium leads to an increase of the complex viscosity. Additionally we can observe a stable trapping of air bubbles in the solution. This effect can not be caused by the increase of viscosity. The frequency sweeps of the solutions give the answer. The storage modulus curves show the significant increase of the elastic shares caused by the addition of calcium-ions. 

Various factors govern autohesive tack, such as relaxation times (x) and monomer friction coefficient (Co) and have been estimated from the different crossover frequencies in the DMA frequency sweep master curves (as shown in Fig. 22a, b). The self-diffusion coefficient (D) of the samples has been calculated from the terminal relaxation time, xte, which is also called as the reptation time, xrep The D value has been calculated using the following equation ... 

Fig. 9.9 CV and frequency-potential curves for the oxidation and re-reduction processes of the electropolymerized polyaniline film [26] (a) in 0.5 M LiCICVAN, and (b) in aqueous 0.5 M NaCl04+HCIO4 (pH = 1). Voltage sweep rate 5 mVs-1, quantity of film deposition 0.4Ccm-2, and SSCE = saturated NaCl calomel electrode.

To obtain as much information as possible on a material, an empirical technique known as time-temperature superposition (TTS) is sometimes performed. This technique is applicable to polymeric (primarily amorphous) materials and is achieved by performing frequency sweeps at temperatures that differ by a few degrees. Each frequency sweep can then be shifted using software routines to form a single curve called a master curve. The usual method involves horizontal shifting, but a vertical shift may be employed as well. This method will not... 

The diagrams in Fig. 1 lb can be obtained by the so-called frequency-sweep method, where the lateral position and the distance Zc are fixed, while the frequency is varied around (O0. The Zc value corresponds to a given set-point ratio of the amplitude in contact to the free amplitude, rsp=Asp/Af. Depending on the tip-sample interaction, both the amplitude and the phase curve shifts in a certain direction. When the overall force is repulsive, the resonance frequency moves to higher values and results in a positive phase shift A(p=90 °-(p>0, where the phase shift of 90 ° corresponds to the free cantilever oscillations at ks=0 in Eq. 12. When the force is attractive the resonance frequency decreases compared to the free cantilever and Acp becomes negative. The situation in Fig. lib corre-... 

Fig. 3.41 Left Frequency sweep in water (silicon nitride lever) right amplitude distance curve recorded in water on a glass sample...

It is important to first identify the segmental dynamics of an amorphous polymer melt, and if possible, observe any changes in the amorphous phase mobility during crystallization. As an example of such measurements, changes in the dielectric loss and dielectric constant in the frequency domain as a function of crystallization time at 22°C are presented in Figure 9.10. Short-time frequency sweeps were taken from 100 Hz to 1 MHz (the duration of a frequency sweep is lmin and much shorter than the time-scale of the crystallinity changes occurring). The curve at f = 0 corresponds to the fully amorphous polymer that was quenched prior to crystallization. As crystal-... 

FIGURE 19. Master curve from various frequency sweep data of pressure-sensitive adhesives. 

Interpretation of IC-AFM images is complicated by the fact that the tip-sample force is a nonlinear function of tip-sample separation. The tip-surface interactions in IC-AI have been modeled extensively and have been recently reviewed [109, 143]. Two important conclusions have come from the modeling. First, the nonlinear interaction of the dynamic tip with the surface can lead to two stable oscillation states one that follows a net attractive path and the other that follows a net repulsive path [147, 148]. A hint of this is seen in the phase versus frequency plot (see Fig. 3.32) where the cantilever initially oscillates along an adhesive path and then abruptly transitions to the repulsive path. Simulated amplitude and phase (z-sweep) curves can reproduce those determined experimentally. These have been interpreted in terms of force based interaction models that include the effect of capillary forces and adhesive forces when they are known or can be estimated. The transition between the bistable states depends on a number of factors including the cantilever Q, Ao, and r p, and the drive frequency as well as the surface properties [149]. In general high Q cantilevers or small Ao favor the net attractive path. 

The thermographic activity on the pressure vessel was carried out considering a part of it because of the axial symmetry. Three different partially overlapping area were inspected since it was optically impossible to scan the curved surface of the pressure vessel by a single sweep. The selected areas are shown in fig.7 and the correspondent positions of the thermographic scan unit are also illustrated. The tests were performed with a load frequency of 2, 5 and 10 Hz. 

One of the more useful functions of the DC Sweep is to plot transfer curves. A transfer curve usually plots an input versus an output. A DC transfer curve plots an input versus an output, assuming all capacitors are open circuits and all inductors are short circuits. In a DC Sweep, all capacitors are replaced by open circuits and all inductors are replaced by short circuits. Thus the DC Sweep is ideal for DC transfer curves. The Transient Analysis can also be used for DC transfer curves, but you must run the analysis with low-frequency waveforms to eliminate the effects of capacitance and inductance. Usually a DC Sweep works better for a transfer curve. The one place where a transient analysis works better is plotting a hysteresis curve for a Schmitt Trigger. For a Schmitt Trigger, the input must go from positive to negative, and then from negative to positive to trace out the entire hysteresis loop. This is not possible with a DC Sweep. 

A hysteresis loop can formally be drawn for the interconversion of a photo-chromic substance between two states A and B characterized by two well separated absorption bands as shown in Figure 26 sweeping the frequency up from vc to Va converts the system from state A to B when vc reaches the absorption band of A the system remains in state B if Va goes back to v0 sweeping vc to Vb converts the system from state B to A, where it remains when V goes back to VQ. Such state interconversion curves are also characterized by the non-linearity of the response with respect to scanning the triggering stimulus. 

As is well known, the steady-state behavior of (spherical and disc) microelectrodes enables the generation of a unique current-potential relationship since the response is independent of the time or frequency variables [43]. This feature allows us to obtain identical I-E responses, independently of the electrochemical technique, when a voltammogram is generated by applying a linear sweep or a sequence of discrete potential steps, or a periodic potential. From the above, it can also be expected that the same behavior will be obtained under chronopotentiometric conditions when any current time function I(t) is applied, i.e., the steady-state I(t) —E curve (with E being the measured potential) will be identical to the voltammogram obtained under controlled potential-time conditions [44, 45]. 

Figure 3.11. Frequency distribution profile for an rf pulse of duration (pulse width) tp. The frequencies range from v0 - Av to v0 + Av, where Av equals Mtp. The sweep width can be either half of the curve.

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