Thermal force-distance curves

MEASURING THERMAL CONDUCTIVITY AND THERMAL FORCE-DISTANCE CURVES... 

Equation (7.1) also demonstrates that the amount of heat dissipated to the surface depends on the thermal conductivity of the tested material as AQ-X-RcAT. Of interest is an experiment where the tip starts above the surface of the sample and is then moved toward it until it makes contact, in effect a thermal force-distance curve. The results of this measurement on materials with different thermal conductivity are presented in Table 7.1. Conditions of the experiment were chosen in such a way that the contact radius... 

At the time of writing, there are two major types of probe, both of which are described above the Wollaston and the nanoprobes. The Wollaston probe is very robust, can be used at temperatures of 00 °C, and can provide the calorimetric measurement required for the thermal force-distance curves described above as well as AC and DC thermal imaging. Its disadvantages are that the spatial resolution is of the order of a micro-meter and can be used only in contact mode. 

Since molecular unbinding/unfolding processes are of stochastic nature, rupture forces from many rupture events (typically several hundreds) are compiled in a histogram and multiple curves are plotted. The results can be interpreted e.g. by thermal activation of the rupture [93]. The use of AFM in force distance measurements has emerged from the study of biopolymers and was applied to the field of chemistry several years ago [82]. However, its specific application to the field of supramolecular chemistry is relatively new. 

In addition to understanding the behavior of ceramics exposed to thermal energy, it is important to understand their behavior when they are subjected to an external load or stress. The objective of this section is to interrelate the shape of the energy versus distance curve E r), discussed in Chap. 2, to the elastic modulus, which is a measure of the stiffness of a material and the theoretical strength of that material. To accomplish this goal, one needs to examine the forces F r) that develop between atoms as a result of externally applied stresses. As noted in Sec. 2.4, F r) is defined as... 

All methods based on the capture of individual force-distance, f-d, curves are conceptually similar to this first reported method. The acquisition of f-d data in a pixel-per-pixel fashion is intrinsically slow compared to friction imaging since the tip must be lifted out of contact for each pixel. In liquids the corresponding viscous drag forces limit data acquisition to rates of typically few pixels per second, thus, an image of 64 pixels x 64 pixels takes on the order of 8-12 min. For high resolution work, thermal and instrumental drift may therefore become serious problems. However, these drawbacks are often overcome by a much more straightforward data inter-... 

Figure 5.2 Schematic representations of interparticle potential energy (V) and force (f) versus particle surface to surface separation distance (D). (a) Energy versus separation distance curve for an attractive interaction. The particles will reside at the separation distance where the minimum in energy occurs, (b) Force versus separation distance for the attractive potential shown in (a). (The convention used in this book is that positive interparticle forces are repulsive.) The particles feel no force if they are at the equilibrium separation distance. An applied force greater than a maximum is required to pull the particles apart, (c) Energy versus separation distance curve for a repulsive interaction. When the potential energy barrier is greater than the available thermal and kinetic energy the particles cannot come in contact and move away from each other to reduce their energy, (d) Force versus separation distance for the repulsive potential shown in (c). There is no force on the particles when they are very far apart. There is a maximum force that must be exceeded to push the particles into contact...

As a result of the charges in the relationship between F and x the summed curve shows a maximum at F at a short separation distance. F is an energy barrier. At large distances the energy is a minimum (F J. If the thermal energy of the particles is smaller than F, no interaction will take place and fouling will not occur. The problem is more complex than the simple approach taking only the van der Waals forces and the double layer forces into account, since other interactions are also likely to be present. 

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