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

56 Tribology in Engineering

equation.

When (eo cos

inhibitor effect.

range of value of Ea.

can be shown as follows:

therefore, it is concluded that:

in angle .

Relation between RTa and RTs is as follows:

RTa) – reaction inhibition, when (eo cos

Concluding the general dependence (1):

Ea/ RTs = Ea/ RTa + ln (eo cos

than ambient energy (RTs > RTa) – catalytic effect, for (eo cos

to the molecules of reactants and this energy should be introduced into Arrhenius

exp (B - Ea/ RTs) / exp (B - Ea/ RTa) = 1 / (eo cos

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>

Ea = 40 kJ/mol = 240 x 1022 eV/mol = 4 eV / molecule Empirically determined energy emitted by solid surface is in the range 3 to 7eV and it is the

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

i = {[f ( b ) – f ( a )] / [ ( b ) - (a ) ]} / [f' ( b ) / ' ( b ) ] (1)

i = (L – L0) A [exp (B – Ea/RTa)] / e0cos() (19)

{[f ( b ) – f ( a )] / [ ( b ) - (a ) ]} / [f' ( b ) / ' ( b ) ] =

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

= (L – L0) A [exp (B – Ea/RTa)] / e0cos() (20)

model is that this difference is equal to energy emitted by solids surface in angle .

k = A exp (B - Ea/ RTs) (16)

) > 1 the real energy near catalyst surface is less than ambient energy (RTs <

) < 1 the real energy near catalyst surface is higher

) (17)

) (18)

) = 1 there is no catalytic nor

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 way they develop during the milling process.

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

$$(\Delta \mathbf{E}^\*) = \mathbf{E} \cdot \mathbf{E}^\* \tag{21}$$

$$\mathbf{k}^\* = \mathbf{k} \exp\left(\Delta \mathbf{E}^\*/\mathbf{R}\mathbf{T}\right) \tag{22}$$

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

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 thermodynamic methods. From the purely thermodynamic point of view, the central problem of mechanochemistry is the exchange of energy between the (long-range) elastic energy and the (short-range) energy accumulated in individual bonds.

A New Attempt to Better Understand Arrehnius Equation and Its Activation Energy 59

These kinetic equations used in heterogeneous catalytic reactions description concern no one parameter characterizing catalyst. Consequently the effect of catalyst action can be explained only by the decreasing of activation energy value – the only one calculated parameter in kinetic equations. It is the reason that all theories of catalysts action try explain

The i model, particularly equation (19) describes catalytic and tribocatalytic reactions by

all kinds of energy introduced into the reaction system, including mechanical energy - L

properties of catalyst, explained by energy emitted from its surface to reaction space –

Resulted from the i model concept of the mechanism of heterogeneous catalysis and tribocatalysis, shown above, is confirmed partly by tribochemistry and mechanochemistry. This mechanism should be directly confirmed, particularly by materials engineering, which

Most recent work [19] emphasizes that while the detailed mechanisms by which different mechanochemical phenomena arise are not always well understood, mechanical forces are capable of effecting novel reactivity. Additionally, it strengthens that using force, one can effectively shepherd a chemical reaction down specific reaction pathways, for instance *by selectively lowering the energy of a transition state.* At this point it is of note, that the field of polymer mechanochemistry, has also the potential to change this paradigm by

In recent years the mechanochemistry field approach has found a renaissance, and different techniques have been applied to activate chemical reaction [20-22] and thereby to lower their

i. The i model put forward in this paper attempts to correlate mechanical work performed on a solid with its catalytic activity. This model was worked out on the basis

ii. The analysis of basic dependences resulted from i model lead to the conclusion that the mechanism of catalysis related to tribological processes can be adapted to

iii. The reactants molecules energy resulted from ambient temperature of reaction mixture is enhanced near solid surface by additional energy – emitted electrons / photons. Due

the influence of catalyst surface structure on the electrons / photons emission

revolutionizing the way chemists think about controlling chemical reactions [19].

of tribological tests results and was dedicated to tribochemistry.

heterogeneous catalysis including mechanochemical reactions.

to the additional energy the reaction can reach a critical rate.

the mechanism of activation energy decreasing.

the role of support in catalysts activity,

the possibility of energy storage by different materials

in eqn. (19)

e0 cos .

should explain:

activation energy.

**4. Conclusions** 

dependence concerning parts, which quantitatively characterizes:

There is no clear theory which could be adapted to mechanochemistry, however the most recent approach [16] should be mentioned here. The i model applied for tribochemical applications can also be adapted to mechanochemistry. This model can be helpful in general dependences formulation, related to kinetics of mechanochemical reactions and to mechanical forces used for reactions activation. The theory based on i model assumes that mechanical energy introduced into solid body – reagent or catalyst, is accumulated in it and then emitted as low energy electrons or photons of energy equal or higher than activation energy of the reaction. The general Eqn. (19) can be used to determine quantitatively relationship between mechanical stress (L), the possibility of solid body to accumulate and then emit energy (e0 cos ) and kinetics of mechanochemical reaction.

Mechanochemistry, especially results of investigations shown above can be explained by hypothesis based on i model. On the other hand the positive effect of mechanical stress on catalyst efficiency confirms this hypothesis. However the reason of this effect can be mechanically (eg. during milling) produced changes of catalysts surface.

Rodriguez et al. [17] found out the influence of ultrasound radiation on catalysts effectiveness. They tested a new advanced method for dechlorination of 1,2,3-, 1,2,4-, and 1,3,5-trichlorobenzenes in organic solvent catalysed by palladium on carbon support and solid hydrazine hydrochloride yields benzene in short reaction times. The catalyst system can be efficiently reused for several cycles. Ultrasound radiation of the heterogeneous catalyst reaction increases remarkably the rate of dechlorination. Moreover, Rodriguez found that there is optimum energy of ultrasound radiation which results maximum catalysts efficiency. This effect is not seen when ultrasound radiation act liquid reactants. Rodriguez results confirm thesis that energy, in this case of ultrasound radiation is useful in reaction rate increasing when solid body – particles of catalyst are present in reaction mixture. This energy is cumulated by catalyst and emitted to the space near catalyst surface, what is the reason of reaction rate increasing. This effect can not be explained by the changes of the structure of catalysts surface, like in other mechanochemical effects (eg. during milling) so the only one probably mechanism is emission of cumulated in solid catalyst energy to reaction space.

The concept of mechanochemistry to modify molecular reactivity has a rich history for a long time. For instance Kauzmann an Eyring as early as 1940 [18] suggested that the mechanical perturbation of diatomic molecules could alter the reaction coordinates combined with their homolytic dissociation.

The chemical kinetic quantitatively describes homogenous reactions, where the rate of reaction depends only on heat introduced to reaction system. Kinetic equations concern reagents concentration, and according to Arrhenius equation: temperature of reaction mixture as well as activation energy.

These kinetic equations used in heterogeneous catalytic reactions description concern no one parameter characterizing catalyst. Consequently the effect of catalyst action can be explained only by the decreasing of activation energy value – the only one calculated parameter in kinetic equations. It is the reason that all theories of catalysts action try explain the mechanism of activation energy decreasing.

The i model, particularly equation (19) describes catalytic and tribocatalytic reactions by dependence concerning parts, which quantitatively characterizes:


Resulted from the i model concept of the mechanism of heterogeneous catalysis and tribocatalysis, shown above, is confirmed partly by tribochemistry and mechanochemistry. This mechanism should be directly confirmed, particularly by materials engineering, which should explain:


Most recent work [19] emphasizes that while the detailed mechanisms by which different mechanochemical phenomena arise are not always well understood, mechanical forces are capable of effecting novel reactivity. Additionally, it strengthens that using force, one can effectively shepherd a chemical reaction down specific reaction pathways, for instance *by selectively lowering the energy of a transition state.* At this point it is of note, that the field of polymer mechanochemistry, has also the potential to change this paradigm by revolutionizing the way chemists think about controlling chemical reactions [19].

In recent years the mechanochemistry field approach has found a renaissance, and different techniques have been applied to activate chemical reaction [20-22] and thereby to lower their activation energy.
