Volume 1 Paper 13
A Preliminary Study on the Mechanism of A Passive Metal Corrosion System Using "Stochastic Resonance" Theory
Ding Hongbo, Pan Zhongxiao, Lin Changjian and Renato Seeber
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JCSE Volume 1 Paper 13
Submitted 5 March 1999
A Preliminary Study on the Mechanism of A Passive Metal Corrosion
System Using "Stochastic Resonance" Theory
Ding Hongbo1, Pan Zhongxiao1, Lin
Changjian2 and Renato Seeber3
1Department of Applied Chemistry, University of Science and
Technology of China, 230026,Hefei, P.R.China,
2Dept. of Materials Sci., Ins. Phys. Chem., State Key Lab of Phy.
Chem. of the solid Surf., Xiamen Univ., Xiamen 361005, P.R. China
3Dipartimento di Chimica, Universita di Modena, 41100, Modena,
Author's e-mail: mailto2('hbding','263.net')
Stochastic resonance (SR) is a generic term to describe the
phenomenon which is manifest in nonlinear systems whereby a – generally
feeble – input information (such as a weak signal) can be amplified, and
optimized, by the assistance of noise. In this paper, some basic ideas
concerning a non-coated passive metal corrosion system are discussed, and the
theory of SR is used to interpret the mechanism of the passivity.
Stochastic resonance, corrosion, passivity, noise,
The concept of stochastic resonance was originally put
forward in seminal papers by Benzi and collaborators[1~3] wherein they address
the problem of the periodically recurrent ice ages. A statistical analysis of
continental ice volume variations over the last 106 yr shows that
the glaciation sequence has an average periodicity of about 105 yr.
This conclusion is intriguing because the only comparable astronomical time
scale in earth dynamics known so far is the modulation period of its orbital
eccentricity caused by planetary gravitational perturbations. The ensuing
variations of the solar energy influx (or solar constant) on the earth surface
are exceedingly small, about 0.1%. The question climatologists (still) debate
is whether a geodynamical model can be devised, capable of enhancing the
climate sensitivity to such a small external periodic forcing. Stochastic
resonance provides a simple, although not conclusive answer to this question.
In the model of Benzi et al, the global climate is represented by a
double-well potential, where one minimum represents a small temperature
corresponding to a largely ice-covered earth. The small modulation of the
earth’s orbital eccentricity is represented by a weak periodic forcing.
Short-term climate fluctuations, such as the annual fluctuations in solar
radiation, are modelled by Gaussion white noise. If the noise is tuned
suitably, synchronised hopping between the cold and warm climate could
significantly enhance the response of the earth’s climate to the weak
perturbations caused by the earth’s orbital eccentricity, according to
arguments by Benzi et al.
§4 The processes of corrosion are most complicated, showing
affluent nonlinear phenomena. One example of this is metal passivity. Because
of the appearing of passivity, the corrosion processes of metals are
inhibited. So, it’s worth of the attention for corrosionists to the
phenomenon of passivity.
§5 The most wide-spread and important theories of passivity
are the thin-film theory and the absorption theory. In the thin-film theory,
it is assumed that the cause of passivity is the formation of a thin film on
the surface of metals because of the coherent reaction between metals and its
environment. Lots of experimental evidence has confirmed this kind of
assumption. But, it is also argued that, to promote the corrosion-resistance
of metals, the film must be thorough, completely covering the surface of
metals. On the other hand, some steady metals without film on their surfaces,
e.g. Pt, have also the property of passivity. Then, how to explain this? The
absorption theory, therefore, offers another explanation for passivity
phenomenon. For example, when 6% of the surface area of Pt in HCl solution is
covered with oxygen, its potential moves upwards 0.12V, and its corrosion rate
is reduced to 10% of its original rate.
§6 Unfortunately, there are still questionable points inside
the absorption theory. Scientists failed to give a satisfactory explanation
concerning why so little absorption can lead to complete passivity of a metal.
Modern nonlinear science theory have undergone an extraordinary growth in last
few decades, and this has, in turn, been changing the general views of human
being about the world. Hence, human being has now got deeper and deeper
understanding about the nature of the world. The complexity of corrosion
process requires corrosionists to use modern nonlinear science theory to
explore the inner rules of corrosion process.
§7 In this paper, after the simple description of some basic
ideas of SR theory, the characteristics of corrosion process for a passive
system is discussed, and SR theory is tried to the interpretation of the
mechanism of the passivity along the absorption theory.
§8 Simple Description of SR Theory
The mechanism of SR is simple to explain. Consider a
heavily damped particle mass m and viscous friction ,
moving in a symmetric double-well potential V(x). The particle is subject to
fluctuational forces that are, for example, induced by coupling to a heat
bath. Such a model is archetypal for investigations in reaction-rate
theory. The fluctuational forces cause transitions between the neighboring
potential wells with a rate given by the famous Kramers ratei.e.,
with being the squared angular
frequency of the potential minima at , and the
squared angular frequency at the top of the barrier, located at xb,
ΔV is the height of the potential barrier
separating the two minima. The noise strength D=kB/T is related to
the temperature T.
§9 If we apply a weak periodic forcing to the particle, the
double-well potential is tilted asymmetrically up and down, periodically
raising and lowering the potential barrier. Although the periodic forcing is
too weak to let the particle roll periodically from one potential well into
the other one, noise induced hopping between the potential wells can become
synchronized with the weak periodic forcing. This statistical synchronization
takes place when the average waiting time TK(D)=1/rK
between two noise-induced inter-well transitions is comparable with half
the period TO of the periodic
forcing. This yields the time-scale matching condition for stochastic
2 TK(D)= TO (2)
§10 In short, stochastic resonance in a symmetric double-well
potential manifests itself by a synchronization of activated hopping events
between the potential minima with the weak periodic forcing. For a given
period of the forcing TO, the
time scale matching can be fulfilled by tuning the noise level Dmax
to the value determined by Eq. (2).
§11 In summary, the effect requires three basic ingredients, (i)
an energetic activation barrier or, more generally, a form of threshold; (ii)
a weak coherent input; (iii) a source of noise that is inherent in the system,
or that adds to the input. Given these features, the response of the system
undergoes resonance-like behavior as a function of the noise level; hence the
name stochastic resonance. The underlying mechanism is fairly simple and
robust. As a consequence, SR has been observed in a large variety of systems,
including chemical reactions.
§12 The Tentative Explanation of the Mechanism of Passivity
Phenomenon Using SR Theory
1. The two stable steady-state characteristic of a passive system
For a passive metal corrosion system, the typical anodic
polarization curve can be shown as figure 1.
§13 Fig.1 The typical anodic polarization curve for a passive
metal corrosion system
§14 In figure 1, the Region OA is active dissolution area,
the polarization current increase with the improvement of polarization
potential; Region AB is temporary area, the polarization current decreases
rapidly with the improvement of polarization potential; Region BC is in
passive state, the polarization current shows little increase with the
improvement of polarization potential, the metal shows little corrosion,
almost none; with the further increase of polarization potential, there will
possibly again be some increase of polarization current, so, the Region of
CD can be called as trans-passive area.
§15 In certain circumstance, the determining factor for the
state of a passive metal corrosion system is the cross-point between anodic
polarization curve and cathodic polarization curve. The actual corrosion
system is an typical nonlinear dynamics system. This can be shown as figure
§16 Fig.2 The schematic representation for the corrosion
state of a passive metal corrosion system <Comment from RAC - it is
rather messy using three separate images for these three diagrams - could
you combine them onto one?>
§17 In figure 2 (b), it is shown that, there are three
cross-points between anodic polarization curve and cathodic polarization
curve. This points out that this nonlinear dynamics system has three state,
among them, A and C are steady state, B is unsteady. Because of the
nonlinear characteristic of the system and the inner stochastic force
(electrochemical noise or, ECN)[11~13], the system will not possibly be in
B, so this system is a kind of two stable steady-state nonlinear system, it
has just two possible state: when at A, active dissolving (showing as
figure2a); when at C, passive state (shown as figure 2c).
§18 2. The source of noise[11~13]
From current knowledge, there are possibly three kind of
sources which generated noise: the noise generated by the thermal vibrations
of the equivalent circuit of underlying electrochemical processes of
corrosion; the noise generated by the electrolyte solution; and most
importantly, the noise generated by the process of absorption-desorption
which will generate noise with large enough energy for SR to take place.
§19 3. The source of "signal"
From the discussions above, it is seen that whether the
corrosion system is in the state of passivity or not lies in the shape of
cathodic polarization curve. While, the process of the reduction of
absorbents was controlled by its absorption degree on the surface of metals.
When surface absorption increases, polarization current develops quickly
with polarization potential moving toward cathodic direction. This stands
for a perturbation signal to the two stable steady-state nonlinear system.
§20 Now, we can make some tentative explanations. Although the
absorption degree of absorbents on the surface of metal was very small, this
weak "signal" can be modulated by the two stable steady-state
nonlinear system and the noise, there will be a stochastic resonance response,
a kind of mechanism that noise energy moves on to signal energy, to take
place. Therefore, the corrosion system changes its state from active to
§21 Due to the nonlinear characteristic of corrosion system,
and the inherent stochastic force (ECN) of corrosion process, it is promising
to discover more and understand deeply about the inner rules of corrosion
process with the further study of the effect of stochastic force to the
Passive metal corrosion system can be treated as a two
stable steady-state nonlinear dynamics system. Due to the process of
absorption-desorption of the absorbents, noise with large enough energy can be
produced, and the absorption of reduction agents can also change the shape of
cathodic polarization curve, this equals to a perturbation signal to the
system. Because of the coherent effect among the system, signal and noise,
stochastic resonance may take place. Therefore, the formation of the passive
state of metal corrosion system may be due to this kind of effect.
Experimental verifications are now under considering.
§23 The complexity of the process of metal corrosion tells us
that, there are plenty of nolinear process inside the system, and the process
can produce much stochastic forces (ECN). It is certain that the study of the
effect of stochastic force to the nonlinear system can be a help in the
research of metal corrosion.
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