Skiadas C.H., Dimotikalis I. (editors) Chaotic Systems: Theory and Applications
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378
C.
L.
Xapianteris and
E.
Fiiippaki
• The plasma production way, the nature
of
plasma gas, accompanied
with its parameters (plasma density, temperature, pressure ect).
• The kind
of
metal, and its metallurgy.
• The type
of
corossion and the corossion rate which are depended on
the burial environment
of
the objects and on the time
of
their burial.
The purpose
of
the present paper
is
to classify the previous result
s,
to add
new ones from the last experimental results and to draw up a table
of
treatment
methods useful to the restorators.
The paper is organized as following: the new experimental studies are
presented in Sec.2; the precedent results, many
of
which were studied in our
laboratory [5-8], are briefly described
in
Sec. 3 and in SecA treatment tables are
given, the main results are summarised and concluded.
2. New experimental results
Beyond the previous work which has been done during the last five
years, the plasma treatment was extended by the enforcement
of
the d.c potential
on restorated objects. In this way, a d.c current passes both through objects and
plasma, and proves that the Langmuir probe theory which basically
is
valid,
must be modificated.
It
is
known that the
rf
plasma production method gives to the electrons
much more acceleration than the ions because
of
the very small electron mas
s.
Furthermore, the electron energy loss by the collisions with ions or neutrals, is
negligible due to the small value
of
the ratio me / . In this way, the electron
1
m;
temperature increases considerably (10.000-100.000 KO
),
while the ion and
neutral temperature remains at low levels (about
500 KO for ions and 300 KO for
neutrals). Consequently, plasma is not in thermodynamic equilibrium, while the
high electron temperature makes plasma more effective for the oxide reduction.
When none external potential is imposed on the treated objects, the
plasma sheath theory is valid as it was proved
in
an
extented previous work
[7,8]. However,
if
an
external d.c. potential
is
enforced on the objects,
as
in our
experiment, the Langmuir probe theory is valid with the presupposition that the
following thoughts are taken into consideration.
Firstly, when a voltage is applied on the treated object with reference to
the earth, the simple probe with very large surface is formed. From plasma
sheath theory [7,
8]
is
known that the ion current density
to
the object surface,
is
ji =
no
·
e.c
s
(1)
with
no
the plasma number density and C s is the ion sound speed.
It
is possible to approach,
2_
T
e +
T
;_Te_
2
c,
=---=-=V
o
m
i
m
i
where
Vo
is the ion velocity at the sheath edge.
Chaotic Behavior
of
Plasma Surface Interaction 379
Similarly, the electron current density to the
j =
-~
. n . e . c Taking into consideration that
e 4 e
e'
the electron current density is
JlJn
e
)
Yz
e¢(x)
j e = - L
no
. e . (
STe
2.
e
T,
4
JlJn
e
object surface,
e¢(x)
ne
=
no'
e
T,
(2)
IS
and
The current
I to the object (probe)
is
I =
(Ji
+ j
e)'
S where S is the projected
surface area into the plasma.
By substitution
of
ion and electron current density from (1) and (2), the
current
I which is biased to voltage V is
(3)
V
f
is the floating potential, which is equal to the external enforcemed potential,
so
that the current I vanishes. Since the object (probe) dimensions are large
compared to the ion and electron gyro-radii and the Debye length, the area S is
determined
as
following: S =
~
. f B .
is
.
When the probe is biased negatively enough, all ellectrons are repulsed
while what remains is the ion current. This current is not affected by the voltage
and is known as ion saturation current. The ion current is saturated because the
bias potential gathers all ions across the surface sheath and the ion flux is
determined by the flux
of
ions which enter into the sheath at the ion sound
velocity. When the probe potential becomes larger than the plasma potential,
there is no sheath and the electrons strike on the object surface with the thermal
distribution
of
velocities. In this case the electron current is saturated by value
I es =
~
noec
e
. S, with C
e
the electron thermal velocity.
4
Figure 1 shows the typical probe characteristic
(I
versus
V),
which
presents three regions: the ion current saturation, the exponential electron
distribution and the electron current saturation.
380
C.
L.
Xaplanteris and E. Filippaki
sma
y-recorder
v
p
ion
saturation
io
eo
V
f
v
p
e
ponential
region
electron
saturation
Figure
1.
The Langmuir probe and its characteristic.
If
plasma is non-magnetized (as the plasma we use to treat corroded
objects), it follows the above simple theory; the characteristic
I - V draws the
two saturation regions with the ratio
of
electron to ion saturation current is equal
to ratio
of
electron thermal velocity to ion sound speed.
However, in our experiment the probe's metallic surface into the plasma
has been replaced with the treated objects, which have much more area than the
probe's one. In spite
of
this big difference the Langmuir probe theory is valid in
a very satisfactory way, and the measurements give currents proportional to the
object area. Figure 2 shows the d.c. current, which passes through the objects
and the plasma.
As
Figure 2 shows, a big ohmic resistance R is necessarely lined at
the circuit to reduce the current
I , which is measured on the value
of
some
Amperes. The negatively charged object (cathode) attracts plasma ions, which
strike on the surface with increased velocity; then, while the ions take free
electrons from the cathode, reductive reactions take place
as
following:
3Fe203
+2H+
=?
2Fe304
+H
2
0
or Fe203
+2H+
=?
2FeO+H
2
0
On the contrary, the positively charged object (anode) attracts the
plasma electrons, which strike on the surface and reduce the oxides as the
reactions show:
6Fe203 +
4e-
=?
4Fe304 + 02
or Fe203 +
2e-
=?
2FeO
+ h
02
Chaotic Behavior
of
Plasma SU/jace Interactioll
381
From the above chemical reactions
it
is obvious that the extemal d.c.
potential makes the plasma much more active and reduce the object oxides to
more stable compounds (magnetite)
as the XRD examination can confirm.
plasma
Figure
2.
The external dc potential circuit during plasma treatment.
3. Previous results
Many inferences have been taked out from the early experimental work
in our laboratory, as the plasma cleaning method is in operation during the last
two decades. An excavated nail fron the Holy Monastery
of
Simonopetra
of
Mount Athos before and after plasma treatment
is
shown in Photo
1.
Photo 1.
An
excavated nail before and after plasma treatment.
The factors and parameters, which affect the plasma cleaning, are too
many and as a
result, it is impossible to mentjon them without the risk
of
forgetting one. The present work has the ambition to start the drawing
of
some
treatment tables in order to achieve the classification
of
the chaotic state. Firstly,
382
C.
L.
Xaplanteris
and
E.
Filippaki
the kind
of
the material used e.g. iron, copper, silver e.t.c. are presented;
secondly, the corrosion depth, which
is
separated in three sizes for practical
reason: lightly corroded, moderately corroded and heavy corroded; the corrosion
depth depends on the time and the environment where the object is being
corroded. Another parameter, which strongly affects the cleaning, is the plasma
gas; gases such as
H
2'
N
2'
CH
4 as combinations
of
various gases were used,
except for
N 2 and
CH
4 due to identification
of
CN-
on the pyrex surface.
Along with the plasma gas, the other plasma parameters, as plasma pressure, the
plasma density, the
rf
absorbed power and the ion temperature, are listed.
Consequently, the treatment time is a remarkable factor; practically, three period
of
treatment times were used, periods
of
lOhours, 1O-20hours and a period that
exceed
20 hours
of
treatment.
4. Summation-elaboration tables
The factors and parameters, which were mentioned in Sec.3 have been
tabulated on cleaning Tables
I,
II and
III.
Table I. Plasma treatment table for iron objects
Iron obJects
Light corroded
Medium corroded Heavy corroded
Gas
H2
H2
H2
Pressure (Torr)
0.8
0.9 0.7
Power
(kW)
0.7 1 to 1.2
0.7
Time
8h-IOh
lOh-20h
more than
20h
Temperature
200°C to 300°C
250°C
to 350°C 200°C
Gas
H
2
,
N2
H
2
,N
2
H
2
,
N2
Pressure (Torr)
0.4,0.2
0.8,0.4
0.4,0.2
Power (kW)
0.8
1.1
to
1.2
0.7
Time
8h-10h
lOh-20h
more than
20h
Temperature 200°C to 300°C 250°C to 350°C
200°C
Gas
N2
N2 N2
Pressure (Torr)
0.7
0.9 0.5
Power
(kW)
0.8 1.0
0.5
Time
more than
20h
10h-20h more than 20h
Temperature
200°C to 300°C
250°C
to 350°C
200T
Chaotic Behavior
of
Plasma Surface Interaction 383
Table II. Plasma treatment table for bronze objects
Bronze objects
Light corroded Medium corroded Heavy corroded
Gas
H2
H2 H2
Pressure (Torr)
0.8 1.2
Power (kW)
0.65
1.0
Time 4h-6h 2h-4h
Temperature
170'C-190'C 230'C-240'C
Table III. Plasma treatment table for silver objects
.
__________________________________________
_
________________________
~!!~~!:_~~J~~_~~
____
__
______________
_
_________________
_
Gas
Pressure (Torr)
Power (kW)
Time
Temperature
Light corroded Medium corroded Heavy corroded
H2
0.8
0.7
2h-4h
21O'C
H2
0.8
0.7
6h-8h
21O'C
H2
0.8
0.7
lOh-12h
21O
'C
It
is obvious, that the above tables need
to
be expanded not only for other kinds
of
material s but also by taking into account other parameters which were
mentioned in section
1,
so
that a useful plasma treatment manual for restorators
will be completed.
From the table
I, which concerns the treatment
of
the iron objects
we
can
see that the state
of
the corrosion
of
the object (light to medium or heavy
corroded objects) is critical for the duration and for the temperature
of
the
plasma treatment. So,
as
far as the light corroded objects concerns, when treated
either with hydrogen or a combination
of
hydrogen and nitrogen, the
temperature varies between
200-300 degrees
of
C and the duration 8-lOhours,
for the medium corroded objects the temperature is between
250-300 degrees
of
C and the duration varies between
1O-20h
. For the heavy corroded objects the
temperature does not exceed
200'C and the duration is more than 20h. The
lower temperature is essential in order to preserve the integrity
of
the object
as
well as the metallographic characteristics
of
the metal itself.
If
the treatment gas
is
nitrogen then the treatment duration is much longer for all the three categories
of
the corrosion state.
The second table concerns bronze objects treated with hydrogen plasma.
The duration
of
treatment varies between 2-4 hours and the temperature between
170 to 240'
C.
As
far as silver objects concerns, the temperature
is
always the
same
21O
'C, while the duration varies between 2-12 hours depending on the
corrosion state
of
the object.
384
C.
L.
Xaplanteris and
E.
Filippaki
Evaluating the above results we assume that
1.
Gas, temperature and time are the key parameters
of
the plasma
process.
2.
The extend
of
the corrosion layer is essential on the plasma duration
and the temperature
of
plasma treatment.
3.
The plasma treatment at all conditions is successful in decreasing the
density
of
the corrosion products and therefore facilitates subsequent
mechanical cleaning. The gradual elimination
of
the chlorine
containing corrosion products in favor
of
the formation
of
more stable
species and sometimes even the complete reduction back to metal is
proportional to the duration
of
the plasma treatment.
It
should be taken
into account that in case
of
heavy corroded objects a longer treatment
in
lower temperature is preferable to a shorter treatment in higher
temperature as it does not make the object too brittle.
References
[I]
Daniels V., Plasma Reduction
of
Silver Tarnish on Daguerreotypes,
Stud. In Conserv, 26,1981.
[2]
Veprek, S., Patscheider,
J.
and Elmer, J., Restoration and Conservation
of
ancient artifacts: A new area
of
application
of
plasma chemistry,
Plasma Chern. Plasma process, Vol. 5(2), 1985.
[3]
Patscheider,
J.
and Veprek, S. Application
of
low pressure Hydrogen
plasma to the conservation
of
ancient iron artifacts, Stud.
In
Consern.,
Vol.
31,1986.
[4]
Veprek,
S.
, Eckmann, Ch. ,and Elmer,
1.
Th., Recent progress in the
restoration
of
archaeological metallic artifacts by means
of
low-pressure
plasma treatment
Plasma Chern. Plasma process. Vol. 8 (4), 1988.
[5]
Kotzamanidi I., Sarris Em., Vassiliou P.,Kollia
c.,
Kanias G.D., Varoufakis G.l.
Filippakis S.E., Corrosion behavior
of
oxidized steel treated
in
reducing plasma
environment-Chloride ions removal, British Corrosion Journal, 34(4), 285-29
I,
( 1999).
[6]
Kotzamanidi, I. Vassiliou,
P.
Sarris, Em. Anastasiadis, A., Filippaki,
E., Filippakis,
S.:
Anti-corrosion methods and materials, Vol 49, No 4,
2002.
[7]
Xaplanteris,
c.,
Filippaki,
E.
Plasma -surfaces interaction and
improvement
of
plasma conservation system by application
of
a d.c.
electrical potential. Topics on Chaotic Systems, Selected
Papers from
CHAOS 2008 International Conference, pp. 406-415, 2009.
[8]
Xaplanteris, C., Filippaki,
E.
Mechanical and chemical results
in
the plasma-
surface contact.
An
extended study
of
sheath parameters. (to be published).
385
Simulation
of
Geochemical Self-Organization: Acid
Infiltration and Mineral Deposition in a Porous
Ferruginous Limestone Rock
Farah Zaknoun, Houssam EI-Rassy, Mazen AI-Ghoul,
Samia AI-Joubeily, Tharwat Mokalled, and Rabih Sultan
Department
of
Chemistry, American University
of
Beirut
P.O. Box 11-0236, 11072020 Riad EI-Solh, Beirut, Lebanon
(e-mail:
rsultan@aub.edu.lb)
Abstract:
The phenomenon
of
Liesegang banding finds its most striking natural
similarity in the band scenery displayed in rock systems. Whereas theoretical
modeling studies are extensive in the literature to simulate the reaction-transport
dynamics
of
the medium, experimental simulations in-situ are very scarce. We carry
out an empirical observation
of
the evolution
of
a deposition pattern embedded in a
rock. A sulfuric acid solution is infiltrated into a porous ferruginous limestone rock by
means
of
an
infusion pump. This acidization causes the dissolution
of
the calcite
(CaC0
3
)
mineral and deposition
of
calcium sulfate in the form
of
anhydrite (CaS04)
and mainly gypsum (CaS04'2H20), behind the advancing dissolution front. We
observe the growth
of
such a deposition pattern and investigate the extent
of
its
resemblance with the well-known Liesegang patterns obtained
in
the laboratory. The
composition
of
the seemingly banded zones
is
analyzed by powder X-ray diffraction,
both qualitatively and quantitatively. The irregular shape
of
the band zone boundaries
seems to be
of
fractal nature.
Keywords: Liesegang, acidization, acid-infiltration, banding in rocks, ferruginous
limestone, fractals.
1.
Introduction
In this paper,
we
shed light on the similarities between the band formation in
rocks and the well-known Liesegang banding phenomenon [1,2]. Liesegang
precipitation bands are obtained when co-precipitate ions interdiffuse in a gel
medium due to a cycle
of
supersaturation, nucleation and depletion [3],
coupled to the on-going diffusion process. Beautiful bands
of
precipitate
appear
as
a result
of
this complex physico-chemical scenario. Representative
specimens
of
colorful banded Liesegang patterns are displayed in Fig.
1,
for a
variety
of
precipitate systems.
Liesegang systems share a great deal
of
similarity with natural systems
displaying striped patterns and ripple morphology, notably in Biology and
Geology. Biological rhythmic patterns are manifest in the stripes on tigers
and zebras, belts
of
bacteria colonies [4,5], gallstones
[6]
and cysts. In
Geology, agates and banded rocks present a typical example
of
rhythmic
patterns [7-13], and are perhaps the closest widespread natural phenomenon
to the Liesegang stratification, because they directly involve precipitation and
386
F.
Zaknoun et al.
mineral deposition. Pictorial scenes
of
periodic banding in real natural
geological systems are displayed in Fig.
2.
Figure
1.
Liesegmlg precipitation patterns grown in gel for a variety
of
precipitate systems.
Between the rapid growth
of
bacterial colonies and the tremendously slow
formation
of
rock patterns, we realize that self-organization can take place on
a huge range
of
time scales (minutes
to
millions
of
years).
a.
b.
c.
Figure 2. Patterns
of
bands in natural stone systems (geology). a. Liesegang stone,
a highly silicated banded rhyolite; b. an agate
of
malachite, hydrous copper
carbonate; c. donut agate.
In the present study, we investigate the phenomenon
of
band formation in
rocks by simulating one possible scenario that would take place in a real,
rock medium. Instead
of
focusing on the study
of
existing, "ready made"
banded patterns in rock specimens, we force and steer the band deposition
inside a rock bed, by simulating the physico-chemical processes which lead
to
such deposition, thus exactly mimicking the real natural scenario. This is
done by infiltrating a ferruginous limestone rock with sulfuric acid, causing
the dissolution
of
the bare rock calcite
(CaC0
3
)
medium, followed
by
the
deposition
of
anhydrite (CaS04) or gypsum
(CaS0
4'2H20
),
behind the
dissolution front:
Cae0
3
(s) +
2W
(aq)
~
Ca
2
+ (aq) + CO
2
(g) + H
2
0
(l)
(1)
Simulation
of
Geochemical Self-Organization 387
Ca
2
+ (aq) + sol-(aq)
~
CaS04 (s) (2)
Thus, we carry out our experiments in-situ, spanning long times as required
by the appearance
of
the desired patterns. To our knowledge, no investigator
tackled this approach to geochemical self-organization before. The study
would rather routinely be based on the analysis
of
existing rock specimens
displaying parallel bands, or essentially, on theoretical modeling and
numerical simulations. The mechanism involves diffusion and percolation
of
the infiltrating solution, coupled to chemical reactions driving dissolution,
porosity changes and precipitation. The mineral deposition requires a
collective scenario
of
nucleation,
as
well as competitive growth
of
both
nuclei and larger particles
of
precipitate. A representative schematic picture
of
the dynamical events is illustrated (in reduced form) in the following
scheme, and portrayed in Fig.
3:
A
~---PAO
space
Figure
3.
Moving dissolution front
of
mineral A, infiltrated by aqueous species
X,
and producing the banded deposition
of
mineral
B.
A + 2X
~
Y (3)
Y + Z
k2)
B (4)
where A respresents a solid mineral (here calcite,
CaC0
3
),
Y the dissolved
salt material (Ca
2
+),
from the reaction with X (acidic water,
H+),
Z the
counter-ion from the infiltrating solution (here
SOl-)
which reacts with Y to
form precipitate
B (CaS04). Thus this scheme (also illustrated in Fig. 3) is a
simplified form
of
chemical reactions 1 and
2.
kJ
and
k2
are rate coefficients
used in the numerical solution
of
the mathematical model adopted in Ref. 14.
2. Experimental Section
2.1. Acid-Infiltration Experiments
A red brown, porous, ferruginous limestone rock is used in the experiment. A
relatively high porosity is an advantage
in
our experiments as less time is
required for the acid percolation inside the rock. The acid was infiltrated into
the rock by means
of
an infusion pump (M361 Multi-rate Infusion Pump).