Fulcher transition

The vibrational population in the excited state n(v ) is determined by the vibrational population in the ground state n(v), if the electron impact excitation from the ground state is the most dominant excitation mechanism. The application of the Franck-Condon principle for electron impact excitation allows a calculation of n(v ) from n(v) based on the Franck-Condon factors between ground and excited state. Figure 4.2 illustrates this scheme for the three states involved in the Fulcher transition upper and lower state, d3nu and a3A)] respectively, in the triplet system and the ground state... 

In a first step, the vibrational population in the ground state is characterized by a Boltzmann distribution, i.e., n v )/ n v = 0) depends on TVib X). The left column of Fig. 4.3 shows relative vibrational populations in the ground state (X1 ) and in the upper state of the Fulcher transition (d377u) with Tvib(X) as parameter, assigned to the 15 vibrational levels of H2, i.e., v = 0-14. The right column shows the relative vibrational population in the excited state as a function of 7 vib(X) for H2 and D2. Due to the usage of vibrationally resolved excitation rate coefficients a dependence on electron temperature is obtained. Te = 4eV is chosen in Fig. 4.3. 

On the other hand, polymeric materials show universal aspects of glass transition behavior, just like other materials. For instance, the classical Vogel-Fulcher behavior... 

In spite of the problems associated with the static structure, the coarsegrained model for BPA-PC did reproduce the glass transition of this material rather well the self-diffusion constant of the chains follows the Vogel-Fulcher law [187] rather nicely (Fig. 5.10),... 

To interpret the cooling rate dependence of the glass transition temperature, one can use the Vogel-Fulcher law discussed in the section on the... 

The non-Arrhenius temperature-dependence of the relaxation time. It shows a dramatic increase when the glass transition temperature region is approached. This temperature dependence is usually well described in terms of the so called Vogel-Fulcher temperature dependence [114,115] ... 

Viscosity temperature dependence in ILs is more complicated than in most molecular solvents, because most of them do not follow the typical Arrhenius behavior. Most temperature studies fit the viscosity values into the Vogel-Tammarm-Fulcher (VTF) equation, which adds an additional adjustable parameter (glass transition temperature) to the exponential term. 

In order to directly study hydrogen molecule behavior in divertor plasmas, hydrogen molecular line emission has recently been observed [5]. Figure 5.2 shows Fulcher (d3IIu —> a3S+ ) lines observed near the divertor plates in an attached divertor plasma. The Q branches for the v = 0 — 0, 1 — 1 and 2 — 2 transitions are identified. The vertical lines indicate the line intensities calculated on the assumption that Trot(0) = 0.040eV, Trot(l) = 0.057eV, Trot(2) = 0.046eV, n(l)/n(0) = 0.76, and n(2)/n(0) = 0.60. Here, Trot(w) and n(v) are the rotational temperature and the population of the vibrational... 

Fig. 5,2. Fulcher lines observed near the divertor plates in an attached divertor plasma in JT-60U [7], Calculated Q-branch line intensities for the v = 0 — 0,1 — 1,2 — 2 transitions are also shown as vertical lines. The electron temperature and density measured with a Langmuir probe near the separatrix strike point were 20 eV and 0.7 x 1019 m-3, respectively...

Fig. 6.11. The Fulcher-band system of D2 observed in front of a gas inlet. The first lines of each Q-branch of the visible diagonal transitions are marked ( 91181-86)...

It appears, however, that the mode-coupling theory is not able to explain some of the most significant slow-relaxation processes of these more complex glass formers. In particular, it cannot explain the success of the Vogel-Fulcher-Tammann-Hesse (VFTH) equation for the temperature-dependence of the relaxation time near the glass transition. The mode-coupling theory predicts instead a power-law dependence of the longest relaxation... 

Keywords glass transition, dynamics, Vogel-Fulcher-Tammann counterparts, negative pressures, fragility... 

Trachenko, K. (2008) The Vogel-Fulcher-Tammann law in the elastic theory of glass transition J. Non-Cryst. Solids 354, 3903-3906. 

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