Experimental study of the frequency factor in the Polanyi–Wigner equation: The case of C2H6

Abstract

ElsevierLuna Molina, R.; Millán Verdú, C.; Domingo Beltran, M.; Santonja Moltó, MDC.; Satorre, MÁ. (2015). Experimental study of the frequency factor in the Polanyi-Wigner equation: the case of C2H6. Vacuum. 122:154-160. doi:10.1016Vacuum. 122:154-160. doi:10. /j.vacuum.2015 AbstractFor the first time, an experimental procedure to calculate the frequency factor of the Polanyi-Wigner equation and to study how temperature influences on it is presented. This parameter is necessary to calculate desorption rates for environments where this process occurs. The method presented is based on the analysis of a quartz crystal microbalance signal. In the literature the frequency factor is not experimentally obtained but it is rather assumed as k B ·T/h, proposed by the activated state theory for first order desorption processes, or it is estimated by other methods.Additionally, its variation with temperature is not experimentally explored so far.Two different kind of desorption experiments of zeroth order desorption have been carried out to perform this study. The first experiment, carried out at a constant rate of warming up, is devoted to obtain the desorption energy, which is comparedwith previous values reported in the literature. The second group of desorption Preprint submitted to Elsevier 15 May 2015experiments is performed at constant temperature and is used to calculate and study the frequency factor. Several temperatures have been specifically selected, allowing us to derive the influence of the temperature on this parameter. For ethane, we have calculated an increase of around a 50% for the frequency factor corresponding to an increase in temperature of only 6 K. This result must be taken into account when the Polany-Wigner equation is used for calculation purposes.

Nonlinear desorption activation energy from TPD curves: Analysis of the influence of initial values for the regression procedure

“…The range 10 0 < A ( θ ) < 10 18 , proposed in the following calculations, should be considered as sufficient to explore all the possible numerical solutions with a chemico‐physical meaning. To the best of our knowledge, numerical values greater than the ones considered in this paper have never been reported for samples similar to the ones discussed here for desorption orders equal to 1 or 2 . Then the optimization procedure was performed, for each constant A ( θ ) parameter, by optimizing the coefficient α k of the polynomial Equation , that is, a 0 + a 1 (1 − θ m ) + … + a k (1 − θ m ) k where 1 < k < 7 .…”

“…As discussed in detail by Luna et al, different approaches are reported in the literature to obtain E d ( θ ) by the Polanyi‐Wigner equation. The easiest method considers the dependence of this parameter with respect to the coverage degree as linear and the E d ( θ ) can be calculated from the slope of ln( r des ) vs 1/T ; this simplification, as already discussed, is not suitable for heterogeneous surfaces.…”

Quantum Tunneling Hygrometer with Temperature Stabilized Nanometer Gap

“…This typically is characteristic of a simple first-order desorption process where the absorbed gas-molecule on the surface of the solid simply desorbs back into its gaseous form. The kinetic process is mathematically described by the Polanyi-Wigner equation and is used as the theoretical basis for thermal desorption spectroscopy process [27]. Figure 11 shows the normalized conductance of the sensor as a function of time for one cycle of water-vapor absorption and desorption, where the absorption cycle is curve-fitted with Fick's law of diffusion and the desorption cycle is curve-fitted with the Polanyi-Wigner desorption model.…”

Parametrically Amplified Low-Power MEMS Capacitive Humidity Sensor

“…The performance of the LACM sensor can be effectively modeled as described by Sikame Tagne [50]. The desorption kinetics of the sensor is considered as a gradual desorption of water molecules back into the atmosphere and modeled using the Polanyi-Wigner equation [51]. The curve fitted normalized change in capacitance is shown in Figure 10a.…”