Interface contact resistance

Because a length of metal associated with the connector contact is ordinarily in the path between the contact end to which a wire is terminated and the contact interface, its resistance (bulk resistance) must be added to contact resistance when considering the connector as a circuit element. This overall resistance is sometimes erroneously called contact resistance. 

Around 1936, the existence of a very considerable thermal resistance at the interface between liquid helium and solids was discovered (Kapitza resistance Rk) [50], A similar effect (contact resistance Rc) is present in any contact between two materials. In the presence of a heat flux across the boundary, this thermal resistance causes a temperature discontinuity (see Fig. 4.2). 

Experimental data show that the thermal boundary resistance between solids is poorly reproducible [52-53], The experiments in fact demonstrated that the physical and chemical condition of the interfaces is a critical factor determining the thermal boundary resistance. For this reason, the study of the contact resistance has been carried out on evaporated surfaces in order to reduce the irregularities and make Rc more reproducible. 

In 1959, Little [69] extended the acoustic mismatch model to interfaces between solids. The experiments have revealed that in this case, the thermal contact resistance between solids is higher than that evaluated from the model and that data are less reproducible. 

The different behaviour of contact resistance in the two cases can be examined through the two models the just described acoustic mismatch model and the diffuse mismatch model which suppose that all the phonons are scattered at the interface. Hence these two models define two limits in the behaviour of phonons at a discontinuity. 

Some experiments outlined the frequency dependence of phonon scattering on surfaces [74]. Thus, Swartz made the hypothesis that a similar phenomenon could take place at the interface between solids and proposed the diffuse mismatch model [72]. The latter model represents the theoretic limit in which all phonons are heavily scattered at the interface, whereas the basic assumption in the acoustic mismatch model is that no scattering phenomenon takes place at the interface of the two materials. In the reality, phonons may be scattered at the interface with a clear reduction of the contact resistance value as calculated by the acoustic model. 

Recent developments of materials and devices with structures in nanometer length scales have created new opportunities and challenges in the science of thermal transport. Interfaces play a particularly important role in the properties of nanoscale structures and nanostructured materials [97-98], This is why a renewed interest for contact resistance arose in recent years with studies of nanocomposite, semicrystalline and polycrystalline materials where contact resistances has a controlling role to determine the bulk thermal conductivity of the material [99-100],... 

The small power needed to measure the resistance of the thermometer brings the thermometer at a temperature over that of the support surface. Such overheating is due to the contact resistance at the interface (see Chapter 4). A typical value of the contact resistance is ... 

To rationalize the isothermal assumption, Dykhuizen 39() discussed two related physical phenomena. First, heat may be drawn out of the substrate from an area that is much larger than that covered by asplat. Thus, the 1 -D assumption in the Stefan problem becomes invalid, and a solution of multidimensional heat conduction may make the interface between a splat and substrate closer to isothermal. Second, the contact resistance at the interface is deemed to be the largest thermal resistance retarding heat removal from the splat. If this resistance does not vary much with substrate material, splat solidification should be independent of substrate thermal properties. Either of the phenomena would result in a heat-transfer rate that is less dependent on the substrate properties, but not as high as that calculated by Madej ski based on the... 

Once the plate starts to corrode, many problems appear to affect performance and durability, even serious failure, of fhe fuel cells. For example, fhe interface contact resistance between the corroded metal plates and GDL will increase to reduce the power output. The corrosion products (mainly various cations) will contaminate the catalyst and membrane and affect eir normal functions because the polymer membrane essentially is a strong cation exchanger and the catalyst is susceptible to the ion impurity. Hence, adding a corrosion-resistant coating to the metal plate will almost inevitably assure the performance and long-term durability of a sfack. 

Different complications arise if the selective layer is a solid-state ionic conductor. At such an interface, a net electrochemical reaction, governed by Faraday s law, takes place and the mass transport of the electroactive ionic species within the contact region and formation of a depletion layer must be considered. In general, when the response of the sensor depends on the chemical modulation of the contact resistance by one of the above mechanisms it will be a strongly nonlinear function of concentration. Furthermore, because Rc is always dependent on the applied voltage, the optimization of the response must be done by examining the voltage-current characteristics of the contact. 

Figure 10.4 shows the saturation current at maximum gate voltage for two adjacent sets of transistors, both with 15 jam lines, as a function of 1/L. The results are internally consistent - e.g. maximum on currents scaling roughly linearly with 1/L for a given array of transistors. The one data point outside linear behavior was from a device that had a visible break in one of the source/drain electrodes. The linear dependence extrapolated to zero shows a relatively low contact resistance at the DNNSA-PANI/SWNT pentacene interface [15]. 

Rs (Figure 1.22a). The double layer capacitance is represented by the capacitance C, and Rs is the series resistance of the EDLC, also named the equivalent series resistance (ESR). This series resistance shows the nonideal behavior of the system. This resistance is the sum of various ohmic contributions that can be found in the system, such as the electrolyte resistance (ionic contribution), the contact resistance (between the carbon particles, at the current collector/carbon film interface), and the intrinsic resistance of the components (current collectors and carbon). Since the resistivity of the current collectors is low when A1 foils or grids are used, it is generally admitted that the main important contribution to the ESR is the electrolyte resistance (in the bulk and in the porosity of the electrode) and to a smaller extent the current collector/active film contact impedance [25,26], The Nyquist plot related to this simple RC circuit presented in Figure 1.22b shows a vertical line parallel to the imaginary axis. 

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