Nonlinear wave mechanisms of very fast chemical and phase transformations in solids. applications to cosmic chemistry processes near to 0 k, to explosive-like decays of metastable solid phases and to catastrophic geotectonic phenomena

doi:10.4236/ns.2010.212165

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Vol.2, No.12, 1356-1359 (2010) Natural Science

doi:10.4236/ns.2010.212165

Nonlinear wave mechanisms of very fast chemical and

phase transformations in solids. applications to cosmic

chemistry processes near to 0 K, to explosive-like

decays of metastable solid phases and to catastrophic

geotectonic phenomena

Viktor Barelko1*, Dmitryi Kiryukhin1, Igor Barkalov1, Galina Kichigina1, Alain Pumir2

1 Institute of Problems of Chemical Physics RAS, Chernogolovka, Russia; *Corresponding Author: [email protected]

2 Laboratoire de Physique, Ecole Normale Supérieure de Lyon and CNRS, Lyon, France; [email protected]

Received 28 August 2010; revised 30 September 2010; accepted 3 October 2010.

ABSTRACT

In the Universe, chemical reactions occur at very

low temperature, very close to 0 K. According to

the standard Arrhenius mechanism, these

reactions should occur with vanishingly small

efficiency. However, cold planets of the solar

system, such as Pluto, are covered by a crust

composed of ammonia and methane, produced

on earth only at very high temperature and

pressure, in the presence of catalysts. This

observation is incompatible with the predictions

of Arrhenius kinetics. Here, we propose a

general mechanism to explain the abundance of

chemical reactions at very low temperature in

the Universe. We postulate that the feedback

between mechanical stress and chemical reaction

provides, through fracture propagation, the

energy necessary to overcome the activation

barrier in the absence of thermal fluctuations.

The notion described in this work can also be

applied to other fields such as explosive-like

solid phase transformations and catastrophical

geotectonics phenomena (earthquak es).

Keywords: Nonlinear Waves;

Coupling between Chemistry and Mech anics;

Combustion at Very Low Temperature;

Geochemistry; Cosmochemistry; Geotectonics

1. NONLINEAR PROPAGATION OF

FRACTURE IN FROZEN REAGENTS

MATRIX: A MECHANISM OF FAST

CHEMICAL EVOLUTION OF MATTER

IN UNIVERSE

Chemical evolution in solid phase occurs in the Uni-

verse, whose temperature is very close to 0 K, at rates

much faster than expected based on standard Arrhenius

considerations. This fact has remained difficult to ex-

plain for many years: how to reconcile the abundance of

certain chemical species, whose synthesis on earth can-

not proceed without very high temperature and pressure

conditions, with the classical picture of chemical reac-

tions occurring as a result of thermal fluctuations over-

coming an activation barrier?

A similar situation has been reported in the case of

cryo-chemical reactions in which the solid reagents were

previously exposed by gamma- or photo-irradiation (see

[1,2] and references therein). The chemical reaction has

been observed to lead to travelling wave, propagating at

very low temperatures in laboratory experiments (4 K in

liquid helium, and at 77 K in liquid nitrogen) at veloci-

ties which can not be explained by traditional Arrhenius

combustion theory.

Explaining these phenomena is the theoretical chal-

lenge that we are addressing in this short review. The

observed phenomena of very fast chemical reactions at

extremely low temperatures can be explained quantita-

tively as resulting from a coupling between chemical

transformation and local brittle fracture propagating over

the frozen sample of reagents, with the following

mechanism. Consider a chemical reaction starting on the

surface. The heat released during the reaction induces

strong strain in the solid matrix, which may lead to brit-

tle fracture close to the region where the reaction started.

The brittle fracture in turn facilitates the reaction in the

neighbourhood of the region where the reaction started.

As a result, reaction propagates, due to the coupling be-

tween mechanical and chemical processes. This sort of

phenomenon has been observed for several classes of

reaction (hydrocarbon chlorination, olefin hydrobromi-

V. Barelko et al. / Natural Science 2 (2010) 1356-1359

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1357

nation, polymerization and copolymerization); it results

from an efficient way of transferring mechanical energy

from the solid matrix into chemical transformation. The

theory developed here thus rests on the assumption that a

mechanical energy accumulated in solid matrix can be

transformed into a chemical energy even at extremely

low temperatures, therefore leading to rates of chemical

transformation larger than predicted by classical Ar-

rhenius factors, by many orders of magnitude. This en-

ergy transformation is a result of self-sustained brittle

disruption (fracture in form of dispersed solid substance)

of solid matrix, resulting in propagation of nonlinear

“tribo-chemical” waves.

The first simplest theoretical model of nonlinear

transformation waves in solid-phase cryochemical reac-

tions was proposed in [1,2] and developed in [3]. The

model considered was based on the physical notion that

brittle fracture is induced by thermal strain, induced by

the heat released during the chemical reaction investi-

gated the role of various parameters describing heat-

transfer parameters, sample sizes, as well as the effects

of threshold of “cold ignition”, inducing trans- formation

waves in the frozen reagent matrix. In [1,2] and refer-

ences therein, we study the consequences of the postu-

lated mechanism by investigating the properties of the

wave solutions in different conditions: under uniform

pressure of reagent sample (in compliance with our the-

ory, wave velocity decreased when increasing the solid

matrix strength), waves in thin films (existing of wave

modes under exclusion of heat factor), method of wave

initiation (shock by needle-brittle fracture ignites the

wave, unlike plastic deformation).

The development of the thermal theoretical model has

been recently complemented by taking in account a more

accurate description of the mechanical stress [4]. It has

been shown that travelling wave velocities in the

cryo-chemical systems can reach values with magnitudes

significantly faster than what can be achieved in stan-

dard chemical reactions (deflagration theory in combus-

tion, [5]). The result was experimentally confirmed (see

[6] and cited publications).

To analyze the practical implications of the scientific

concept put forward, we investigated further the

properties of propagating nonlinear transformation waves

of monomer cryo-polymerization with reinforced inert

component [7]. The results of the experiments with the

model systems suggest new technological developments,

in particular concerning polymer composites production

under cryo-conditions (4.2-77 K), using the notion of

nonlinear travelling waves described here, with cosmic

and solar radiation for activation of the frozen monomer

matrix.

2. NONLINEAR FRACTURE TRAVELING

WAVES MECHANISMS OF

EXPLOSIVE-LIKE METASTABLE

SOLID PHASE STATES

TRANSFORMATIONS

We hypothesize that the mechanism identified in the

cryo-chemical context provides the proper framework to

explain the fast cryochemical reactions of cosmic sub-

stances occurring in the Universe. This mechanism

seems particularly appropriate to explain the formation,

from the frozen mixture of elements, of compounds such

as ammonia and methane that are found in appreciable

amounts in crusts of the cold planets of the Solar system.

A model of nonlinear traveling wave [8,9] was devel-

oped to describe the very fast decay of metastable solid

phases (as a rule, amorphous states), for example, in

physics and technology of semiconductors [10], or in the

physical contexts of explosives sensibility to friction and

shock [11], or of “Tempered Glasses” destruction [12].

The explosions of “Prince Ruppert Drops” (also known

as “Batav Tears”) provide a particularly interesting and

impressive example of the class of phenomena studied

here [13].

The model developed in [8,9] describes “gasless

detonation” in solid fractures, and shares several impor-

tant concepts with the models presented in [1-3]. How-

ever, whereas fractures in [1,3] are caused by too strong

a thermal stress (temperature gradient above a threshold),

they are induced in [8,9] by a change of the solid matrix

density during the phase transformation. In addition, a

more precise description of the coupling to the me-

chanical stress leads to the conclusion that the propaga-

tion is supersonic, thus providing a natural explanation

for the extremely fast decays of metastable phases.

The theoretical description proposed here is based on

a reaction-diffusion equation, describing phase trans-

formations, and on the wave equation, describing elastic

perturbations. The simple picture we are proposing is

that the phase transformation and the mechanical proper-

ties of the matrix are coupled. On general grounds, it is

reasonable to expect that the phase transformation in-

duces a change of the matrix properties; we postulate

that the sound velocity depends on the state of the phase

transformation. In the same spirit, we postulate that too

high a strain effectively initiates the decay of metastable

phase. This can be rationalized by arguing that when the

strain exceeds a critical value, the matrix is destroyed,

which in turn facilitates the phase transformation. The

feedback (coupling) considered in this works thus in-

volves 1) A dependence of the sound velocity on the

phase field, and 2) The induction of phase transformation.

V. Barelko et al. / Natural Science 2 (2010) 1356-1359

1358

An exhaustive analytic and numerical study of travelling

waves of fracture reveals the existence of supersonic

wave modes of decay of metastable phases in solids.

With the physical ideas explained above, we introduce,

in 1-dimension the concentration field, C, which de-

scribes the phase transformation (C = 0 in the metastable

state, and C = 1 in the transformed state), and the me-

chanical field (, describing the deformation, the stress

being proportional to



). The evolution equations are

written as:



txx

uVu

 









(1)





cfcDcwu



  (2)

Eq.1 is simply the equation that describes mechanical

perturbation in the solid matrix, whereas Eq.2 is a sim-

ple reaction-diffusion equation that describes phase

transformation. The unperturbed state is defined (arbi-

trarily) by the variable c = 0, whereas the fully trans-

formed state is given by c = 1. The kinetic term f(c) is

nonlinear, describing a chain branch reaction (f(c) = 0 in

the initial phase, C = 0). Whether the state is unstable or

metastable does not affect the main predictions of the

model. The coupling between the chemical and the me-

chanical fields is provided by the term in

Eq.1,

which physically expresses that the phase transformation

is initiated by stress. More precisely, we assume that

is zero, and turns on when the stress exceeds a

certain limit c and remains at a value W0 for a

time τ after this threshold has been reached. The velocity

of sound is also assumed to increase monotonically as

the phase transformation proceeds –V = V(C).













The physical picture is that the stress field induces the

phase transformation, through the coupling term







This phase transformation in turn leads to mechanical

perturbation, which propagate ahead of the zone under-

going phase transformation. The phase transformation

studied here depends crucially on the coupling with me-

chanical perturbations, which propagate at the speed of

sound. This leads to fronts of phase transformation that

propagate at velocities much larger than what is typically

obtained in standard reaction-diffusion cases. A full

analysis of steadily propagating fronts [8,9] confirms

that front propagation occurs at a supersonic velocity,

thus demonstrating our claim that the model leads to

much higher front propagation velocity than expected on

theory of standard combustion (reaction-diffusion) they.

As a consequence, in contrast to the prediction of reac-

tion-diffusion theory, the front velocity does not depend

crucially on the diffusion coefficient D: the analysis [8,9]

was carried out for values of D very close to zero (diffu-

sion mobility in solid states has a very small value), and

the velocity was found to be of the order of the sound

velocity.

The physical picture presented here is reasonable on

simple physical grounds, and provides a general descrip-

tion of some interesting phenomena observed in nature.

It would be clearly very important to check the tenets

postulated here. At a dynamical level, one needs to fol-

low the evolution of a wave of transformation propagate-

ing at a velocity of the order of the sound velocity in a

solid (~1000 m/s). A temporal resolution of the order of

1 ms would be necessary to resolve the evolution of the

wave in systems such as described in [13]. The available

fast cameras enable a time resolution of ~0.01 ms, which

still makes the detection of the travelling waves very

challenging, even with the best equipment currently

available. In the same spirit, it would be interesting to

carry out systematic studies of the materials involved in

these reactions under very high strain conditions, very

close to conditions leading to rupture. Experiments nec-

essary to substantiate the hypotheses presented here thus

require state-of-the-art techniques, which should become

available in the coming years.

3. APPLICATION OF THE TRAVELLING

WAVE CONCEPT TO CATASTROPHIC

GEOTECTONIC PHENOMENA AND

EARTHQUAKES

We make the hypothesis that the mechanism [8,9] of

explosive-like metastable solid phases decays presented

above may be applied to describe theoretically the proc-

esses of initiation and dynamics of propagation of geo-

tectonic phenomena and earthquakes.

The underlying postulate to apply the theory devel-

oped here to geotectonic phenomena in earthquakes is

based on the first observation that numerous metastable

phases have been identified in rocks in the earth crust.

Many transitions have been found between them, in-

duced by pressure or temperature changes. It is thus en-

tirely plausible that changing the state of strain may lead

to a transformation of the rock, analogous to the phase

(or chemical) transformations postulated above. The

dynamics of these phase transformations remains very

difficult to study, in view of the extreme conditions

where these transformations occur. Our work thus pro-

poses a few simple feedbacks between mechanical and

phase transformations, known to happen simultaneously

during earthquakes. A bifurcation approach to modeling

of the geological phenomena is proposed in the present

work.

An understanding of the mechanisms of initiation

(“ignition”) and propagation of earthquakes has poten-

tially very important consequences for society in general.

Results of the model developed in [8,9] are in general

V. Barelko et al. / Natural Science 2 (2010) 1356-1359

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agreement with some works of geophysicists [14,15] in

which a phase transformation concept was used to ex-

plain certain aspects of earthquakes. The theory however

remains to be tested in more detail on real systems.

Laboratory experiments devoted to the explosive de-

composition of “Prince Ruppert drops” should provide a

good testing ground. We mention in this context that the

existence of an explosive decay of the “Prince Ruppert

drops”, with supersonic velocities (“gasless detonation”)

had been established in [13]. Moreover, the decomposi-

tion of amorphous silicate glasses is expected to provide

important hint concerning the decomposition of rocks,

thus providing a connection to the physics of earth-

quakes.

In conclusion of the short review we argue that the

proposed models are fundamentally new objects in the

theory of nonlinear traveling wave processes. The mod-

els presented here require improvements at several levels,

and confrontation to experimental study. They provide a

reasonable first step to understand a broad class of phe-

nomena, which certainly deserve increased attention.

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