Vol.2, No.12, 1356-1359 (2010) Natural Science
Copyright © 2010 SciRes. Openly accessible at http:// www. scirp.org/journal/NS/
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: barelko@icp.ac.ru
2 Laboratoire de Physique, Ecole Normale Supérieure de Lyon and CNRS, Lyon, France; alain.pumir@ens-lyon.fr
Received 28 August 2010; revised 30 September 2010; accepted 3 October 2010.
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
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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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
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
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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:
 
  (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
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
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.
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
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
Copyright © 2010 SciRes. Openly accessible at http://www.scirp.org/journal/NS/
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-
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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