Two-temperature model

Figure 3.43. The time dependent electronic temperature Te, lattice temperature Tq. and adsorbate temperature defined as Tads = [EH /2kB following a 130 fs laser pulse with absorbed laser fluence of 120 J/m2 centered at time t = 0. The bar graph is the rate of associative desorption dY/dt as a function of t. Te and T are from the conventional two temperature model and 7 ads and dY/dl are from 3D first principles molecular dynamics with electronic frictions. From Ref. [101].

The optical excitation of electron-hole pairs represents a non-equilibrium state. The subsequent relaxation processes from the initial state includes both carrier-carrier interactions and coupling to the bath phonons. In some treatments, there is a distinction made between carrier-carrier and carrier-phonon interactions in which the latter is referred to as thermalisation. A two-temperature model is invoked in that the carrier-carrier scattering leads to a statistical distribution that can be described by an elevated electronic temperature, relative to the temperature characterising the lattice phonons (Schoenlein et al, 1987 Schmuttenmaer et al, 1996). This two-temperature model is valid only if the carrier-carrier energy redistribution occurs on time scales much faster (>10 times) than relaxation into phonons. This distinction has limited value when there is not a sufficient separation in time scale to make a two-temperature model applicable. The main emphasis in this section is on the dynamics of the energy distribution of the carriers as this is most relevant to energy storage applications. 

What is the physical basis of the two-temperature model (TTM) describing the cooling of photonically heated gold nanoparticles ... 

Bogoliubov, Shotkin (28) numerically studied centers and limit cycles in the two-temperature model. Fourier-series techniques were recently applied to the same model in two interesting papers (29, 30). 

Second, the initial thermal nonequihbrium between electrons and phonons during ultrafast laser heating of nanoparticles requires special attention. A two-temperature model [75] describing the particle can be used to account for the electron-phonon relaxation time of the particle. Here, the electrons and the lattice of the particle are treated separately and the coupling-that is, the heat transfer from electrons to the lattice-is realized through the electron-lattice couphng factor, g. 

The two-mode model has two characteristic cross-over temperatures corresponding with the freezing of each vibration. Above = hcoo/2k the dependence k(T) is Arrhenius, with activation energy equal to... 

Students of professor R. G. Anthony at College Station, TX used a mechanism identical (by chance) to that in UCKRON for derivation of the kinetics. Yet they assumed a model in which the surface reaction controls, and had two temperature dependent terms in the denominator as 13,723 and 18,3 16 cal/mol. Multiplying both the numerator and the denominator with exp(-15,000) would come close to the Ea,/R about 15,000 cal/mol, with a negative sign, and a denominator similar to that in the previously discussed models. 

The two-phase model is used mostly to check very exothermic or endothermic reactions, to calculate the temperature difference between catalyst and gas at extreme conditions, or when accounting for changes in both phases is needed. This model was applied to the two-phase counter-... 

The basic phenomenon was observed in modeling studies by Bjoreskov and Slinko (1965) that sudden increase in inlet temperature caused a transient drop of the peak temperature. The wrong-way response name was given by Mechta et al (1981) after they experienced the opposite a sudden of inlet temperature resulted in an increase of the peak temperature (which may eventually cause a runaway.) The work used a pseudo-homogeneous reaction model and explained the phenomenon by the different speeds of transient response in gas and solid. The example in the last part of Chapter 7.4 explained the speed difference by the large difference in heat capacity of gas and solid phases. For this a two-phase model is needed and spatial and time changes must be followed. 

At high temperature, the conductivity was found to increase linearly with temperature and the observed high-temperature MR was positive. In fact, by fitting the data using a simple two-band model] 17] the authors obtained the theoretical curve in Fig. 4 (a). The fitting parameters showed that the ratio Op/ct, where Op and are the partial conductivities of holes and electrons, respectively, decreases with increasing tern-... 

Fig. 4. (a) Magnetic field dependence of the high- and low-temperature MR, respectively. The solid lines are calculated using a simple two-band model for (a) and the 2D weak localization theory for (b) (after Song et o/.[16]). 

Fig. 5. Electrical resistance as a function of the temperature at the indicated magnetic fields for a single microbundle of carbon nanotubes. The solid line is a fit using the two-band model for graphite (see inset) with an overlap A = 3.7 meV and a Fermi level right in the middle of the overlap (after Langer et at. l9 ).

Two-zone models are especially useful for stratification and zoning strategies because of the typical vertical accumulation of heat, contaminants, or water vapor within these strategies. The level of the boundary between the lower and the upper zone is usually determined on the level of the highest temperature or/and concentration gradient. 

Mundt presents a two-zone model for the calculation of temperature gradient within a stratification strategy. 

FIGURE 8.33 Two-zone temperature model ol the zoning strategy. 

Figures 8.33 and 8.34 describe a two-zone model application of the zoning strategy where all the main variable parameters are presented. Figure 8.33 (temperature model describes the accumulation of heat and Fig. 8.34 (concentration model) the accumulation of contaminants. After solving for the temperatures, heat flow s, and airflows, contaminant concentrations can lie calculated. The models are here determined for stationary loads, airflow rates, and indoor/outdoor conditions, but they can be developed also for dynamic simulations.

---