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

Andrzej Kulczycki and Czesław Kajdas

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54503

### **1. Introduction**

46 Tribology in Engineering

381-390

Abrasion. Wear 12(1968) 35-53

Trans., 7A(1976) 1833-1839

ASME, Vol: 104 91-101, 1982.

and Design 27 (2006) pp: 173–181

Arnold, London. 1992.

65(1981) 359-373.

[9] Rabinowicz, E. and Mutis, A., Effect of Abrasive Particle Size on Wear. Wear, 8(1965)

[10] Larsen-Badse, J., Influence of Grit Size and Specimen Size on Wear during Sliding

[11] Moore, M. A. and Douthwaite, R. M. Plastic deformation below worn surface, Metall.

[12] Hutchings, I. M., Tribology: "Friction and Wear of Engineering Materials", Edward

[13] Misra, M., and Finnie, I., On The Size Effect in Abrasive and Erosive Wear, Wear,

[14] Rabinowicz, E., "Penetration Hardness and Toughness Indicators of Wear Resistance", Int. Conference, Tribology-Friction, Lubrication and Wear, Volume 1, pp: 197-204, 1987.

[16] Misra, A., Finnie, I., A Review of the Abrasive Wear of Metals, Transactions of the

[17] Sevim I., Dry sliding wear of 332.0 unaged Al-Si alloys at elevated temperatures,

[18] Sevim I., Eryurek B. Effect of fracture toughness on abrasive wear resistance of steels

[19] Sevim I., Eryurek B. Effect of abrasive particle size on wear resistance in non-heat-

[20] Sevim I., Eryurek B. Effect of abrasive particle size on wear resistance in steels Materials

[15] Khruschov, M., M., Principles of Abrasive Wear, Wear, 28(1974) Pp: 69-88.

treated steels, Kovove Materialy-Metallic Materials 43(2005), pp:158-168

Kovove Materialy-Metallic Materials 44(2006), pp:151-159

Materials and Design 27 (2006) pp:911–919

Activation energy (Ea) is strictly combined with kinetics of chemical reactions. The relationship is described by Arrehnius equation

$$\mathbf{k} = \mathbf{A} \exp(-\mathbf{E}\_2 \mathbf{/RT}) \tag{1}$$

where k is the rate coefficient, A is a constant, R is the universal gas constant, and T is the temperature (in Kelvin); R has the value of 8.314 x 10-3 kJ mol-1K-1, Ea is the amount of energy required to ensure that a reaction happens. Common sense is that at higher temperatures, the probability of two molecules colliding is higher. Accordingly, a given reaction rate is higher and the reaction proceeds faster and, the effect of temperature on reaction rates is calculated using the Arrhenius equation. Further reaction rate enhancement is promoted by catalysis. Catalysis is the phenomenon of a catalyst in action. Catalyst is a material that increases the rate of chemical reaction, and for equilibrium reactions it increases the rate at which a chemical system approaches equilibrium, without being consumed in the process [1]. It is applied in small amounts relative to the reactants. Chemical kinetics, based on Arrhenius equation assumes that catalysts lower the activation energy (Ea) and the presence of catalyst results higher reaction rate at the same temperature. In chemical kinetics Ea is the height of the potential barrier separating the products and reactants. Catalytic reactions have a lower Ea than those of the thermally activated. This fact enables a chemical reaction not only to proceed faster but also at a lower temperature than otherwise possible. The solid heterogeneous catalyst mechanism that would lower activation energy is still under discussion. It is known that the effect of catalysts is intrinsically connected to the material surface states. However, the connection of catalysts material states to their action is not yet fully clear and specific stimulators of this action are unknown. Few years ago [2] a new approach to Ea was proposed and a first indirect confirmation was made [3]. Dante et al. [4]

© 2013 Kulczycki and Kajdas, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Kulczycki and Kajdas, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

supported the new approach to Ea by theoretical considerations based on irreversible thermodynamics.

A New Attempt to Better Understand Arrehnius Equation and Its Activation Energy 49

The main assumption of i model, described in detail in [9] introduced the **new measure – <sup>i</sup> coefficient** of reagent/lubricating oil or additive **properties / structure** influence on its **reactivity** related to **reaction conditions**. This model was worked out on the bases of the results of tribochemical investigations of different lubricating oils. In relation to tribological processes, **tribochemical reaction conditions** depend on the work done on tribological system - L. The work L is the function of applied load P, which can be treated as the only one variable y – L = f(y). The reagents **reactivity** is described by the second function of variable y - ( y ). Basing on Cauchy theorem the relation between two functions of the

 i = {[f ( b ) – f ( a )] / [ ( b ) - (a ) ]} / [f' ( b ) / ' ( b ) ] (3) where *a* and *b* are values of y parameter. For different reagents value *b* is the only one variable (assumption of Cauchy theorem) and *a* is constant. Variable *b* was related to tribological process conditions – for example applied load P. In i model P is critical value and it relates either to seizure load or weld load. Consequently work done on the system

Work done on tribological system can be related to thermodynamic description of tribological process. In the consequence reactivity can be related to the internal energy

Since it is difficult to define relationship u= (P) because u is not linear dependence of the applied load P, we can use the first low of thermodynamics L to express it as a function of

Q is energy dissipated by system during tribological process; mainly it is a dissipated heat, which in relation to tribological process can be described by the following dependence:

Assuming that both average specific heat capacity and Tb are constant for different oils, Q

Tb – temperature of lubricant out of friction area, Tot – temperature of environment.

L = Pvt; - friction coefficient; v – speed; t – time; P – applied load (test result);

i = [ (L – Lo) / (u–uo) ] x (d u/ d L ) (4)

L = Q + u (5)

Q = ch (T – Tot) (6)

T = Tb + A P0,5 (7)

**3. Thermodynamic interpretation of i model** 

means the work needed to achieve the seizure or weld.

change u, and Eqn. (4) can be written as follows:

where: ch - average specific heat capacity,

can be expressed as

**3.1. Theoretical information** 

same one variable y is as follows:

where: Lo = f(a), u0 = (a)

u:

Heterogeneous catalysis provides the link between reactants and products on a reaction pathway which involves simultaneous motion of several to very many atoms [5]. Predictability of the outcome of catalytic reactions is controlled by their molecular mechanisms. Thus, the importance of the activation energy better understanding can not be overestimated. Some forty years ago, work [6] demonstrated that a "chemically stimulated" exo-electron emission (EEE) occurs simultaneously during the partial oxidation process of ethylene. It was also found that the emission rate was proportional to the rate of ethylene oxide formation. Therefore, discussing heterogeneous catalytic reactions, EEE process should also be taken into account, because they involve electro physical phenomena. Additionally, such electrons are of low-energy and are produced from the excited active catalytic surfaces.
