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95) A catalytic model?

Ludwik Kowalski (August 13, 2003)
Department of Mathematical Sciences
Montclair State University, Upper Montclair, NJ, 07043

Catalysts are atoms or molecules affecting rates of reactions. These atoms or molecules may be independent, as in a gas, or be parts of structures, as in solids. In what follows no distinction is made between single atoms and groups of atoms. The term particle will refer to both a single atom or a group of atoms.

To simplify, let me assume that a catalyst is a gas A mixed with two reacting gases, B and C. In the absence of gas A one can imagine a reaction B+C --> BC. The number of B and C particles decreases in time while the number of BC particles increases. But at what rate does this happen? The answer depends on initial and final energies. If the energy of BC is higher than the energy of B+C then the reaction is called endothermic; such reaction will not take place spontaneously, even when a catalyst is present. The reaction rate is zero, unless energy is supplied.

On the other hand, if the energy of BC is lower than the energy of B+C then the reaction is exothermic and it can occur spontaneously. But the rate of an exothermic reaction depends not only on initial and final energies; it also depends on how potential energy changes with the distance between reacting particles. A typical situation is schematically represented below.

   potential energy
^ I I top I - I - - I - - I - - B+C I - ------ I BC - I ----- I I I I---------------------------------------------> distance
Note that although the potential energy of B+C is higher than that of BC it increases when the particles approach each other. We say that a potential barrier exists between the initial state (B+C) and the final state (BC). The height of the barrier (between the top and the B+C in the above figure) is called the activation energy. In general, the rate of an exothermic reaction depends on the activation energy; the rate is slow when the activation energy is high, and vice versa. Explosive reactions have very low activation energies. The role of a catalyst is to provide a path along which the barrier is lower. How can this happen?

In the presence of catalyst A our idealized reaction can proceed in steps, such as:
           A+B --> AB       followed by        AB+C --> A+BC
Note that A does participate in the reaction; it disappears in step one and it reappears in step two. The net result is consumption of B and C, accumulation of BC, and a constant number of A particles. The rate of A+B-->BC, in the presence of a catalyst A, may increase when the activation energies in step one and two are lower than for the single step reaction (without a catalyst)..

What does all this have to do with cold fusion? I had to refresh my understanding of catalytic reactions after I noticed the word catalyst in several cold fusion papers. It is common knowledge that two D+ ions repel each other electrically. But they attract each other strongly when the distance is very small. A cold fusion reaction, D+ + D+ -->He++, was said (in 1989) to be theoretically impossible because its activation energy is of the order of one million of eV. That is why extremely high temperatures (tens of millions of K) are necessay to observe thermonuclear reactions in gases. But cold fusion seems to be happening on surfaces of some metals, such as Pd, Ti, Ni, etc.
Accordin to Storms, certain spots on such surfaces might act as catalysts facilitating fusion of deuterium ions.

The mechanisms of catalytic processes facilitating cold fusion are not clear. But one aspect is undeniable; the energy of BC (in this case He++) is much lower than the energy B+C (in this case D++D+). The difference between B+C and BC, about 24 million eV, is much larger that the activation energy (about 1 million eV). One is tempted to think that the energy to “climb the hill” is somehow borrowed from the energy available in the “downhill fall.” This would be impossible in the independent single-step reactions (as in hot fusion) because released energy escapes in the form of 24 MeV photons. But in a system of millions of interacting atoms (a crystal catalyst) the borrowing may perhaps be possible. Instead of producing a 24 MeV photon, as in thermonuclear fusion, the energy released during each cold fusion event might go into the crystal and be subsequently used to promote another fusion. Conceptually this can be compared to a banking operation; borrowing on credit, paying back later and making profit. Many successful companies (exothermic events) must be involved to make this possible. Banks are social catalysts.

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