*3.4.2. Verification of derivative equation concerning heterogeneous catalysis; electron and photon emission anisotropy*

Eqn. 12 (C = A exp(-*a*y) / cos (*b*y + *d*)) leads to conclusion that the emission of energy (electrons and photons) from the surface of solid body is anisotropic one. Exhaustive literature review revealed that there is no data on the angular distribution of triboemitted electrons, but that existing research works on the emission of electrons from cathodes consistently report anisotropic distributions [7, 11-13]. Highly anisotropic distributions with a maximum in the direction normal to the emitting surface were measured.

Figure. 2. illustrates an example of anisotropic electron emission from sandwich cathodes. At the emission temperature of 300K the measured electrons present a quasi-isotropic characteristic. But at a lower temperature of 80K, the isotropic component vanishes.

**Figure 2.** Examples of EE from sandwich cathodes presenting 2 maxima with a maximum in direction normal to the emitting surface, and highly anisotropic EE: based on Hrach research results [7,13]

References [11-12] allow to make an estimate that at room temperature the narrow maximum around the direction normal to the emitting surface contains approximately 1/3 of the total emission. Further work of Hrach [7,13] was of particular significance as he measured the energy characteristics of emitted electrons at different angles by means of a hemispherical collector and the retarding-grid technique. He found that at room temperature (300K) anisotropic energy spectra of emitted electrons were in the range of 0 and 7eV, but for emission angles closer to the normal to the surface the measured energy was between zero and 4 eV. Figure 3. depicts some of these findings.

54 Tribology in Engineering

protective layer).

*photon emission anisotropy* 

protective layer created in various machines (participation of AW and EP structure in

*3.4.2. Verification of derivative equation concerning heterogeneous catalysis; electron and* 

Eqn. 12 (C = A exp(-*a*y) / cos (*b*y + *d*)) leads to conclusion that the emission of energy (electrons and photons) from the surface of solid body is anisotropic one. Exhaustive literature review revealed that there is no data on the angular distribution of triboemitted electrons, but that existing research works on the emission of electrons from cathodes consistently report anisotropic distributions [7, 11-13]. Highly anisotropic distributions with

Figure. 2. illustrates an example of anisotropic electron emission from sandwich cathodes. At the emission temperature of 300K the measured electrons present a quasi-isotropic

> **Electron emission from sandwich cathodes Electron emission from sandwich cathodes**

At 300K, two maxima. At 300K, two maxima. But at 80K, highly anisotropic But at 80K, highly anisotropic

Narrow maximum contains approximately 1/3 of total emission. Narrow maximum contains approximately 1/3 of total emission.

**Figure 2.** Examples of EE from sandwich cathodes presenting 2 maxima with a maximum in direction normal to the emitting surface, and highly anisotropic EE: based on Hrach research results [7,13]

characteristic. But at a lower temperature of 80K, the isotropic component vanishes.

a maximum in the direction normal to the emitting surface were measured.

**Figure 3.** Typical experimental angular and energy distribution of electrons emitted from Al-Al2O3-Au sandwich cathode structures. Temperature: 300K, applied voltage: 10V [13]

Reference [3] includes more detailed information concerning figures 2 and 3. More recent study [14] was on the angular distribution of thermo-stimulated exoelectron emission (TSEE) from alpha-Al2O3. Anisotropic angular distributions were strongly directed normally to the surface; the energy of the emitted electrons was in the range of 0 to 4 eV. Jablonski and Zemek [8] found highly anisotropic distribution similar to one of electron-type for the photon emission from X-ray-irradiated thin polycrystalline aluminum foils.

#### **3.5. Disscussion on the basic Arrehnius equation**

In Arrhenius equation T equals Ta, (T = Ta) and it relates to ambient temperature of reaction mixture. Conclusions from i model are as follows:

 When catalyst is used ambient energy RTa is less than energy in space near catalysts particles surface = RTs. Ts is the calculated temperature near catalyst surface and it should be higher than ambient temperature of reaction mixture. RTs is real energy acted to the molecules of reactants and this energy should be introduced into Arrhenius equation.

$$\mathbf{k} = \mathbf{A} \exp \left( \mathbf{B} \mathbf{ - E} \sqrt{\mathbf{R} \mathbf{T} \mathbf{s}} \right) \tag{16}$$

A New Attempt to Better Understand Arrehnius Equation and Its Activation Energy 57

of reaction rate constant described by Arrhenius equation and the stream of energy emitted by catalysts surface in angle . This ratio points that to the equation describing reaction rate constant (Arrhenius equation) should be added denominator describing the stream of energy emitted by catalysts surface. The reaction rate constant described by the above ratio leads to another explanation of the mechanism of catalytic effect than, based on Arrhenius

Mechanochemistry is the coupling of the mechanical and the chemical phenomena on a molecular scale and includes mechanical breakage, chemical behaviour of mechanicallystressed solids (e.g., stress-corrosion cracking), tribology, polymer degradation under shear, cavitation-related phenomena (e.g., sonochemistry and sonoluminescence), shockwave chemistry and physics, and even the burgeoning field of molecular machines. Mechanochemistry can be seen as an interface between chemistry and mechanical engineering. A smart method was proposed recently, in order to measure the energy involved during mechanical transformations. Displacement reactions between a metal oxide and a more reactive metal can be induced by ball milling. In some cases the reaction progresses gradually and a metal/metal-oxide nanocomposite is formed. Ball milling may also initiate a self propagating combustive reaction. The information available about these processes is reviewed. It is argued that the gradual or combustive nature of the reaction depends on thermodynamic parameters, the microstructure of the reaction mixture, and the

Baláž, et al. [15] investigated the mechanochemical treatment of solids which lead to a positive influence on the solid – liquid kinetics. They used Arrhenius equation for activation energy analysis. The breaking of bonds in the crystalline lattice of solids brings

(ΔE\*) = E - E\* (21)

where E is the apparent activation energy of the non-disordered solid, E\* is the apparent activation energy of the disordered solid, k, R and T stand for the rate constant of leaching for the non-disordered solid, (the pre-exponential factor) gas constant and reaction temperature, respectively; k\* is the rate constant of leaching for the disordered solid. If E > E\*, then exp (ΔE\*/RT) > 1 and thus it follows from Eqn. (18) that k\* > k, i.e., the rate of

Thermodynamic methods are essentially macroscopic by origin and nature. They appear in the analysis of macroscopic engineering systems. They have been reliably validated in numerous macroscopic experiments and observations. Most probably there can be found areas that permit analysis of mechanochemical systems by means of relatively simple

k\* = k exp (ΔE\*/RT) (22)

about a decrease (ΔE\*) in the activation energy and an increase in the rate of leaching

leaching of a disordered solid is greater than that of an ordered mineral.

**3.6. Practical significance of the new (Ea) approach in tribo- and mechano-**

equation, decreasing of the value of activation energy.

way they develop during the milling process.

**chemistry** 

Relation between RTa and RTs is as follows:

$$\exp\left(\text{B - E}/\text{RT}\_2\right) / \exp\left(\text{B - E}/\text{RT}\_2\right) = 1 / \left(\text{e}\_\text{o} \cos\big|\text{y}\right) \tag{17}$$

$$\text{E}\_{\text{\textquotedblleft}} \text{RT}\_{\text{\textquotedblright}} = \text{E}\_{\text{\textquotedblleft}} \text{RT}\_{\text{\textquotedblright}} + \ln \text{ (e}\_{\text{\textquotedblleft}} \cos \text{ \textquotedblright} \text{)} \tag{18}$$

When (eo cos ) > 1 the real energy near catalyst surface is less than ambient energy (RTs < RTa) – reaction inhibition, when (eo cos ) < 1 the real energy near catalyst surface is higher than ambient energy (RTs > RTa) – catalytic effect, for (eo cos ) = 1 there is no catalytic nor inhibitor effect.

In case the same value of reaction rate constant for reaction without and with catalyst is compared using Arrhenius equation, there should be noticed difference between activation energy for reaction with catalyst (Eac) and without catalyst (Ea). The hypothesis based on <sup>i</sup> model is that this difference is equal to energy emitted by solids surface in angle .

$$
\Delta \text{E} = 40 \text{ kJ/mol} = 240 \times 10^{22} \text{ eV/mol} = 4 \text{ eV/molecule}
$$

Empirically determined energy emitted by solid surface is in the range 3 to 7eV and it is the range of value of Ea.

The results of these calculations are in line with hypothesis based on i model saying that catalytic effect is due to energy emission from catalysts surface in the form of electrons / photons stream, additional energy of which makes possible to reach the same reaction rate in lower ambient temperature or increase the reaction rate in the same ambient temperature. This hypothesis is described by C in Eqn. 8: C is the quotient of reaction rate constant described by Arrhenius equation and the stream of energy emitted by the surface of catalyst in angle .

Concluding the general dependence (1):

$$\alpha = \left( \left[ \mathbf{f} \left( \mathbf{b} \right) - \mathbf{f} \left( \mathbf{a} \right) \right] \right) / \left[ \phi \left( \mathbf{b} \right) \cdot \phi \left( \mathbf{a} \right) \right] \right) / \left[ \mathbf{f}' \left( \mathbf{b} \right) / \phi' \left( \mathbf{b} \right) \right] \tag{1}$$

can be shown as follows:

$$\alpha = (\text{L} - \text{L}\alpha) \text{ A } \left[ \exp \left( \text{B} - \text{E}\omega \text{/RT}\_{\text{2}} \right) \right] / \left[ \text{e}\cos(\text{\textgreater}) \right] \tag{19}$$

therefore, it is concluded that:

$$\begin{aligned} & \left( \left[ \mathbf{f} \left( \mathbf{b} \right) - \mathbf{f} \left( \mathbf{a} \right) \right] / \left[ \boldsymbol{\phi} \left( \mathbf{b} \right) - \boldsymbol{\phi} \left( \mathbf{a} \right) \right] \right) / \left[ \mathbf{f}' \left( \mathbf{b} \right) / \boldsymbol{\phi}' \left( \mathbf{b} \right) \right] = \\ & = \left( \mathbf{L} - \mathbf{L} \boldsymbol{\phi} \right) \mathbf{A} \left[ \exp \left( \mathbf{B} - \mathbf{E} \boldsymbol{\phi} \mathbf{R} \mathbf{T} \boldsymbol{\omega} \right) \right] / \operatorname{e} \boldsymbol{\cos} \boldsymbol{\zeta} \boldsymbol{\gamma} \end{aligned} \tag{20}$$

Function f(y) represents the stream of energy introduced into the system, function (y) is connected with catalytic / tribocatalytic reaction critical rate, which is represent by the ratio of reaction rate constant described by Arrhenius equation and the stream of energy emitted by catalysts surface in angle . This ratio points that to the equation describing reaction rate constant (Arrhenius equation) should be added denominator describing the stream of energy emitted by catalysts surface. The reaction rate constant described by the above ratio leads to another explanation of the mechanism of catalytic effect than, based on Arrhenius equation, decreasing of the value of activation energy.
