Buletinul Ştiinţific al Universităţii “Politehnica” din Timisoara, ROMÂNIA
Seria CHIMIE ŞI INGINERIA MEDIULUI
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
Volume 52(66), 1-2, 2007
A New Mode of Classifying the Medicaments by Using the
Electrochemical Impedance Spectroscopy
N. Bonciocat*, A. Cotarta**
*
**
National Research Institute for Electrochemistry and Condensed Matter, Timisoara , ROMANIA
University “Politehnica” of Bucharest, Department of Applied Physical Chemistry and Electrochemistry, Computer Added
Electrochemistry Laboratory, ROMANIA
- paper presented at Anniversary Symposium “INCEMC – 10 years of existence “, 19 - 20 April 2007, Timisoara, Romania -
Abstract: In this paper an “Electrochemical Impedance Spectroscopy (E I S)” method has been elaborated for classifying
the medicaments (especialy those from the God pharmacy) with respect to their capacitive and inductive properties. The
method uses the following reference dielectrode: Pt | [Fe(CN)6]3- / [Fe(CN)6]4-, KCl (in excess), O2 physically dissolved.
The medicament is introduce in the electrolytic solution of this reference dielectrode, and the Nyquist plots are recorded
according to a schedule described in the paper. Unlike Warburg, we have considered that the interface has both capacitive
and inductive properties. Consequently, we have substituted the Warburg pseudo-capacitance CW , either by a pseudocapacitance CW* put in series with a pseudo-inductance LW*, or by a pseudo-capacitance CW** put in parallel with a
pseudo-inductance LW**. In this way, it was possible to propose a criterion which permits to compare the inductive
properties of two medicaments, and therefore to classify the medicaments with respect to a reference medicament (e.g. the
Sweedish Bitter).
Keywords: Electrochemical Impedance Spectroscopy, pseudo-capacitance, cyclic voltammetry
current densities expressions, it was possible to develop
new methods of direct and cyclic voltammetry, applicable
in aqueous electrolytic solutions or in molten salts [8–18],
new chronoamperometric methods [19, 29] and new
Electrochemical Impedance Spectroscopy methods when
only charge transfer and diffusion limitations are present
[21].
The developments given in this paper are based on the
equations deduced very recently [21, 22] for the Nyquist
plots of redox multielectrodes in the domain of very small
frequencies (round ν = 0.2Hz). These equations are:
1. Introduction
In preceding papers, Bonciocat et al., have shown that
the faradic current density of an electrode redox reaction
occurring with combined limitations of charge transfer and
nonstationary, linear, semiinfinite diffusion, is the solution
of an integral equation of Volterra type [1-7]. To each
electrochemical method used in the experimental
electrochemistry corresponds such an integral equation and
by solving it an expression for the faradic current density
characterizing the respective method. On the basis of these
(
)
Re(P ) = Rsol + γ ∗ Rts∗ +
− Im(P ) −
J 1 [ω (t − τ )]
2π
(γ
∗∗
σ ∗∗ )ω −1 / 2
(1)
J 12 [ω (t − τ )] + J 22 [ω (t − τ )] ∗∗ ∗∗ 2
J [ω (t − τ )] ∗∗ ∗∗ −1 / 2
γ σ ω
Cd = 2
γ σ
2π
2π
(
)
Re and Im represent the real and imaginary part of the
impedance of the measuring cell, i.e., Zcell = Re + Imj,
ω = 2πν
represents the radial frequency of the
alternating current, Rsol the solution resistance, τ the
moment of time when the alternating overtension is
superimposed over the constant overtension applied at t =0
, and t is the time when the Nyquist plot recording ends.
Cd is the double layer capacity, and J 1 [ω (t − τ )] ,
J 2 [ω (t − τ )] =
ω (t −τ )
∫
0
)
ω (t −τ )
∫
0
sin x
dx
x1 / 2
(1’)
(2)
π 2 ≅ 1.253 for sufficiently great
values of the product ω(t-τ). P is a point on the Nyquist
plot, and its coordinates given by eqs.(1 and 1’), depend on
both ω and the product ω(t-τ). In a Nyquist plot, the points
should be enumerated from right to left. Then, considering
a record with 10 points per decade, starting with ν1 = 0.02
Hz and ending at 105 Hz, the first point P1 corresponds to
the radial frequency ω1 = 2πν 1 = 1.256 s −1 , and the second
point P2 to the radial frequency ω2 given by equation
whose values tend to
J 2 [ω (t − τ )] are the Fresnel integrals:
J 1 [ω (t − τ )] =
(
cos x ,
dx
x1 / 2
respective:
90
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
log(ω2 ω1 ) = 0.1 , i.e.,
Volume 52(66), 1-2, 2007
ω 2 = ω1 ·100.1 = 1.582 s-1.
(
limitations of the interface. Their expressions are:
1
1
1
1
1
;
=∑
= ∑
∗ ∗
∗∗ ∗∗
(γ Rts ) k (γ k Rtsk ) (γ σ ) 2 k (γ k σ k )
)
In eqs.(1,1’) are two unknowns: (γ ∗ Rts∗ ) and γ σ
expressing the charge transfer, respective diffusion,
∗∗
∗∗
(3)
where:
γ k Rtsk =
RT
{β k exp[− β k nk f η k (0)] + (1 − β k ) exp[(1 − β k )nk f η k (0)]}−1
nk F I k0
(4)
respective:
(γ k σ k ) =
⎧⎪
1
exp .[− β k nk f η k (0 )] +
⎨
2
2
2 n k F A ⎪⎩ DOk ⋅ cOk
1
RT
D Rk ⋅ c Rk
⎫⎪
exp .[(1 − β k )nk f η k (0 )]⎬ x
⎪⎭
x {β k exp .[− β k n k f η k (0 )] + (1 − β k ) exp .[(1 − β k )nk f η k (0 )]} ; f =
−1
0
In equations (4, 4’) , I k ,
β k , nk
k
electrode reaction
η k (0) = g m + η − g Nernst,k
RW (P ) ⋅ CW (P ) = RW∗ (P ) ⋅ CW∗ (P ) = RW∗ ∗ (P ) ⋅ CW∗ ∗ (P ) (7)
(5)
where gm represents the mixed potential of the interface,
gNernst,k the equilibrium potential of the electrode reaction
k, and η the constant overtension applied at the initial
moment t=0. A is the free area of the interface and the
other quantities have the usual meanings.
The last term in equation (1) represents the Warburg
diffusion resistance of the interface RW(P), while the last
term in eqution (1’) represents the magnitude of the
capacitive reactance of the interface |XCW(P)|, and is due
to the Warburg pseudo-capacitance of the interface:
1
.
CW (P ) =
(4’)
In this substitution, two conditions must be fulfilled:
- the impedance of the corresponding arrangement (i.e.,
in series, or in parallel) must be equal with the Warburg
pseudo-capacitance impedance.
- of course, these substitutions will change the Warburg
diffusion resistance, but eq.(6) must remain valid, i.e.,
refer to the
electrode redox reaction k , and represent the exchange
current intensity, the symmetry factor, and the number of
electrons participating in the reaction. η k (0) represents the
initial overtension at which the
occurs, and is given by:
F
RT
because the second member of eq.(6) is practically equal to
1 / ω (i.e., is not dependent on these substitutions.
2. Theoretical Section
1. Substitution of the Warburg pseudo-capacitance
CW(P)
a) By a series arrangement
ω X CW (P )
is equivalent with:
Therefore equations (1, 1’) it follows:
J [ω (t − τ )] 1
RW (P )CW (P ) = 1
⋅
J 2 [ω (t − τ )] ω
(6)
The equality of the impedances writes:
The pseudo-capacitance CW(P) has been introduce by
Warburg to explain the phase difference that appears
between the current and the tension.
Unlike Warburg, we shall consider that the interface
has both capacitive and inductive properties.
Consequently, we shall substitute the Warburg pseudocapacitance CW(P), either by a pseudo-capacitance CW*(P)
put in series with a pseudo-inductance LW*(P), or by a
pseudo-capacitance CW**(P) put in parallel with a pseudoinductance LW**(P) .
X C ∗ (P ) = − Im∗ (P ) −
W
X CW (P ) = − Im(P ) −
(8)
⎛
⎞
1
1
⎟j=−
Z ∗ = ⎜ ω L∗W (P ) −
j=Z
∗
⎜
⎟
(P )
ω
C
(
)
ω
C
P
W
W
⎝
⎠
i.e.,
∗
(P ) = X C ∗ (P ) − X CW (P )
ω LW
(9)
(10)
W
where (see eq.(1’)):
J12 [ω (t − τ )] + J 22 [ω (t − τ )] ∗∗ ∗∗ 2
γ σ
Cd
2π
(
)
J12 [ω (t − τ )] + J 22 [ω (t − τ )] ∗∗ ∗∗ 2
γ σ
Cd
2π
(
91
)
(11)
(11’)
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
(
Volume 52(66), 1-2, 2007
)
CW∗ ∗ (P ) = β CW (P ); β>1
2
because the quantity γ ∗∗σ ∗∗ C d is not dependent on the
way the charge transfer occurs.
The inductive reactance being a positive quantity, it
results from eq.(10), and the meaning of a capacitive
reactance (i.e., X = 1 ):
C
ω L∗W∗ (P ) =
(12)
CW ( P ) − C
(P )
(P )
∗
W
∗
W
ω 2 CW ( P ) C
ω L∗W∗ (P ) =
Equation (12) shows that in a series arrangement, the
pseudo-capacitance CW*(P) is smaller than the Warburg
pseudo-capacitance CW(P). The two equations (12,12’)
may be written in the form:
and
ω L∗W (P ) =
1−α
α
⋅
ω CW (P )
(19)
1
α
α
CW (P ) and
⋅
1
(20)
1 − α ω CW ( P )
2. Relation between the real oscilating period T = 2π/ω
and the Thomson oscilating periods associated to the
two arrangements
a. Series arrangement
From the two equations (13) it follows:
1
T=
2π L∗W (P )CW∗ (P )
1−α
But :
α <1
1
1
⋅
CW∗ ∗ (P ) =
(12’)
CW∗ (P ) = α CW (P );
1
β − 1 ω CW (P )
Taking β= 1/α , one gets:
ωC
ω CW (P )⟩ ω CW∗ (P )
and:
L∗W (P ) =
and
(13)
(21)
TThomson, series = 2π L∗W (P )CW∗ (P )
b. By a parallel arrangement
and thus:
TThomson, series =
b.
is equivalent with:
(21’)
1
1 − α ⋅ T ; ω Thomson, series =
1−α
ω (21’’)
Parallel arrangement
From the two equations (20) it follows:
(14)
T = 1 − α 2π
L∗W∗ (P )CW∗ ∗ (P )
(22)
i.e.,
TThomson, parallel = 2π L∗ ∗ (P )C ∗ ∗ (P ) =
W
W
Then:
1
1
1
;Z =
= ω CW∗ ∗ (P ) j +
∗∗
∗∗
Z
ω LW (P ) j
ω CW (P ) j
1
=
1
X C ∗∗ (P )
W
−
(16)
1
(17)
(23)
ω = ω Thomson, series ω Thomson, parallel
ω L∗W∗ (P ) being positive, eq.(17) leads to the conclusions:
L∗W∗ (P ) = 1 / ω 2 [ CW∗ ∗ (P ) − CW (P ) ]
(22’)
T = TThomson, series TThomson, parallel ;
X CW (P )
ω CW∗ ∗ (P ) ⟩ ω CW (P )
T;
From equations (21’’ and 22’) results a very important
conclusion: the real period (or radial frequency) of the
alternating current is the geometric mean of the Thomson
periods (or radial frequencies) associated to the two
arrangements, i.e.,
it follows:
ω L∗W∗ (P )
1−α
ω Thomson, parallel = 1 − α ⋅ ω
(15)
From the condition:
Z ∗∗ = Z
1
(18)
3. The new expressions of the Warburg diffusion
resistances, and capacitive reactances of the interface
(18’)
a.
Equation (18) shows that in a parallel arrangement, the
pseudo-capacitance CW∗∗ (P ) is greater than the Warburg
Series arrangement
From condition (7) results:
C (P ) 1
RW∗ (P ) = RW (P ) ⋅ W∗
= RW (P )
CW (P ) α
pseudo-capacitance CW (P ) . The two equations (18) may
be written in the form:
(24)
and explicitating the Warburg diffusion resistance (see the
92
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
last term in equation (1)):
∗
W
R
(P ) =
1 J 1 [ω (t − τ )]
α
2π
Volume 52(66), 1-2, 2007
(γ
σ
∗∗
∗∗
)ω
−
1
2
(24’)
X C ∗ (P ) = X CW (P ) ⋅
W
W
X CW (P )
= X CW
b)
RW∗ ∗ (P ) = α
(25)
α
X C ∗ ∗ (P )
W
X CW (P )
W
i.e.,
X C ∗∗ (P ) = α
= X CW (P ) ⋅
J 2 [ω (t − τ )]
2π
W
(γ
a)
∗ ∗
Rts
) and (γ
)
∗∗
σ ∗∗ ω −1 / 2
(25’)
J 1 [ω (t − τ )]
2π
(γ
(26)
σ ∗∗ )ω −1 / 2
∗∗
(26’)
Similarly:
and explicitating the magnitude of the capacitive
reactance:
X C ∗ ∗ (P ) = X CW (P ) ⋅
(γ
The same condition (7) leads to:
C (P )
RW∗ ∗ (P ) = RW (P ) ⋅ ∗W∗
= α RW (P )
CW (P )
i.e.,
( ) 1
(P ) ⋅ CW P = X CW (P )
4. Estimation of the unknowns Rsol. +
2π
Parallel arrangement
=
∗
(P )
CW
α
W
As for the magnitude of the capacitive reactance, it is
given by:
X C ∗ (P )
1 J 2 [ω (t − τ )]
X C ∗ (P ) =
∗∗
σ ∗∗
(γ
CW (P )
= α X CW (P )
CW∗∗ (P )
(27)
)
∗∗
σ ∗∗ ω −1 / 2
(27’)
)
By using the equations of the series arrangement
The first parametric equation of the Nyquist plot writes:
[(
Re(P ) = R sol . + γ ∗∗ Rts∗
and may be put in the form:
[(
Re(P ) = Rsol . + γ ∗ Rts∗
)]
∗
+
)]
∗
J 1 [ω (t − τ )]
2π
Let’s introduce the quantity:
[(
Y ∗ (P ) = Rsol . + γ ∗ Rts∗
[(
+ RW∗ (P ) = R sol . + γ ∗ Rts∗
)]
∗
+
(γ
σ ∗∗ )ω −1 / 2 +
∗∗
J 1 [ω (t − τ )]
2π
(γ
σ ∗∗ )ω −1 / 2
∗∗
RW (P )
α
[(
Rsol . + γ ∗ Rts∗
(28)
2π
[γ
σ ∗∗ ]ω −1 / 2
∗∗
(28’)
)
(29)
(32)
)]
∗
(
)
γ ∗∗σ ∗∗
⎛ ω + ω1 ⎞ 1 − α
= Y ∗⎜ 1
⋅
⎟−
1/ 2
α
⎝ 2 ⎠
⎛ ω + ω2 ⎞
2⎜ 1
⎟
2 ⎠
⎝
and finally:
[(
Rsol. + γ ∗ Rts∗
−1 / 2
)]
∗
= −0.42
1−α
α
(γ
σ ∗∗ ) +
∗∗
Re(P1 ) − Re (P2 )⎤
⎡
(33)
+ ⎢Re (P2 ) −
⎥
0.122
⎣
⎦
For α =1 , equation (33) particularizes in the equation
giving the unknown R sol . + γ ∗ Rts∗ :
(31)
Further, one may accept:
⎛ ω + ω2 ⎞
Y ∗ (P1 ) ≅ Y ∗ (P2 ) ≅ Y ∗ ⎜ 1
⎟
⎝ 2 ⎠
and then, equation (31) leads to:
α
Therefore (see equation (29)):
)
= 1.122
1
Re(P1 ) − Re(P2 ) ⎤
⎛ ω + ω2 ⎞ ⎡
Y ∗⎜ 1
⎟ ≅ Re(P2 ) −
⎥
2 ⎠ ⎢⎣
0.122
⎝
⎦
For sufficiently great values of the recording time, one
may consider:
1
(30’)
Re(P ) − Y ∗ (P ) ≅ γ ∗∗σ ∗∗ ω −1 / 2
2
and thus:
Re(P1 ) − Y ∗ (P1 ) ⎛ ω1 ⎞
≅⎜ ⎟
Re(P2 ) − Y ∗ (P2 ) ⎜⎝ ω 2 ⎟⎠
+
1 − α J 1 [ω (t − τ )]
(
(30)
(
∗
1 − α J 1 [ω (t − τ )] ∗∗ ∗∗ −1 / 2
⋅
γ σ ω
α
2π
when equation (28’) takes the form:
Re(P ) − Y ∗ (P ) =
)]
(
(31’)
(
)
Rsol + γ ∗ Rts∗ = Re (P2 ) −
93
)
Re(P1 ) − Re (P2 )
(Ω) (34)
0.122
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
Volume 52(66), 1-2, 2007
Further, equtions (30’ and 32) give:
(γ
Re (P1 ) − Re (P2 ) ⎤ i.e.,
⎥
0.122
⎦
σ ∗∗ ) = 2 ω11 / 2 ⎢Re (P1 ) − Re (P2 ) +
⎡
∗∗
(γ
⎣
σ
∗∗
∗∗
Accepting the approximation:
) ≈ 20.6 [Re(P ) − Re (P )] (Ω s )
1
b.
By using
arrangement
the
equations
of
the
parallel
[(
Re (P ) = R sol + γ R
∗
ts
)]
∗∗
∗∗
W
+R
[(
)]
∗∗
[(
+ α RW (P )
[(
)]
∗∗
+ (α − 1)
+
Y
(P ) = Rsol + [(γ
∗
∗
ts
R
(
)
= 0.42 (1 − α ) γ ∗∗σ ∗∗ +
− Re (P ) ⎤
) + ⎡⎢Re(P ) − Re(P0).122
⎥
1
2
2
⎦
J 1 [ω (t − τ )]
2π
2π
)] + (α − 1) ⋅
(γ
(γ
σ ∗∗ )ω −1 / 2
∗∗
J 1 [ω (t − τ )]
2π
Re(P1 ) − Re(P2 ) ⎤ (Ω) (42) ≡ (34)
⎡
Rsol . + γ ∗ Rts∗ = ⎢Re(P2 ) −
⎥
0.122
⎣
⎦
σ ∗∗ )ω −1 / 2 +
(
∗∗
(γ
σ
∗∗
(36’)
∗∗
)ω
(γ
−1 / 2
⎞
⎟⎟
⎠
(
Re (P1 ) − Re(P2 ) ⎤ (43)
⎥
0.122
⎦
σ ∗∗ ) ≅ 20.6 [Re(P1 ) − Re(P2 )] (Ωs-1/2) (44) ≡ (35)
∗∗
3. Experimental Section
In a very recent paper[25] it has been proved that the
interface of the dielectrode:
(39)
)
⎡
⎣
(γ
−1 / 2
= 1.122
σ ∗∗ ) = 2ω11 / 2 ⎢Re(P1 ) − Re(P2 ) +
∗∗
i.e.,
equation (36’) takes the form:
J [ω (t − τ )] ∗∗ ∗∗ −1 / 2 1 ∗∗ ∗∗ −1 / 2
(γ σ )ω ≅ 2 (γ σ )ω
Re (P ) − Y ∗∗ (P ) = 1
2π
(38)
and thus:
Re(P1 ) − Y ∗∗ (P1 ) ⎛ ω1
≅⎜
Re(P2 ) − Y ∗∗ (P2 ) ⎜⎝ ω 2
)
As for the expression of (γ** · σ**), it is obtain from eqs.
(38 and 40):
(37)
(
)
Pt K 3 Fe(CN)6 10 −3 M , K 4 Fe(CN)6 10 −3 M , KCl (0.5M), O2 physically dissolved
)
(
)
Pt K 3 Fe(CN )6 10 −3 M , K 4 Fe(CN )6 10 −3 M , KCl (0.5M ), 50ml Swedish Bitter, O2 physically dissolved
Respective:
Pt K 3 Fe(CN )6 10 −3 M , K 4 Fe(CN )6 10 −3 M , KCl (0.5M ), 20ml Energotonic Complex, O2 physically dissolved
(
)
(
(45)
upon the electrochemical properties of the reference
dielectrode [45]. These medicaments have been introduced
in the electrolytic solution of the reference dielectrode[45],
maintaining the total volume of the solution at V= 300ml.
The two electrochemical systems that have been
analyzed are:
has only capacitive properties, and for explaining them
suffice to introduce the Warburg pseudo-capacitance in the
Faraday impedance of the interface.
In this paper, one analyzes the effect that two
medicaments, namely the Sweedish Bitter, original
Schweden Tropfen, BANO, and the Energotonic
multivitamin complex Plant Extrakt- Radaia , Cluj, have
(
(41)
and for α = 1:
J 1 [ω (t − τ )]
∗∗
∗∗
⎣
With the aid of the quantity:
∗∗
)]
(36)
and may be put in the form:
Re(P ) = Rsol . + γ ∗ Rts∗
(40)
R sol + γ ∗ Rts∗
(P ) =
= R sol + γ ∗ Rts∗
Re(P1 ) − Re(P2 ) ⎤
⎛ ω + ω2 ⎞ ⎡
Y ∗∗ ⎜ 1
⎟ ≅ ⎢ Re(P2 ) −
⎥
2 ⎠ ⎣
0.122
⎝
⎦
and further:
The first parametric equation is now
∗
(39’)
one gets:
(35)
−1 / 2
2
⎛ ω + ω2 ⎞
Y ∗∗ (P1 ) ≅ Y ∗∗ (P2 ) ≅ Y ∗∗ ⎜ 1
⎟
⎝ 2 ⎠
)
(46)
(47)
plots have been recorded, corresponding to four values of
the time τ , i.e., 0s, 10s, 100s, and 1000s. In this way, 12
Nyquist plots have been obtained, for each medicament,
and from each Nyquist plot, the coordinates of the two
points P1 and P2 have resulted. These coordinates have
The concentrations are given with respect to the same
total volume of V= 300ml.
To perform the experiments, three values of the
constant overtension η have been used, namely 0.00V; 0.05V and 0.05V and for each overtension, four Nyquist
94
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
Volume 52(66), 1-2, 2007
The resulted values are given in Table 1.
served to estimate, by means of equations (34 and 35), the
values of R sol +
(γ
∗
(
)
)
Rts∗ , respective γ ∗∗σ ∗∗ .
TABLE I. Estimation of the quantities Rsol + (γ*·Rts*) and (γ**·σ**) characterizing the charge transfer an diffusion limitations of the
electrochemical systems (46) and (47)
Swedish
Bitter
Energotonic
complex
η
τ
(V)
0
0
0
0
-0.05
-0.05
-0.05
-0.05
0.05
0.05
0.05
0.05
0
0
0
0
-0.05
-0.05
-0.05
-0.05
0.05
0.05
0.05
0.05
(s)
0
10
100
1000
0
10
100
1000
0
10
100
1000
0
10
100
1000
0
10
100
1000
0
10
100
1000
Re(P1)
(Ω)
Re(P2)
(Ω)
(Ω s-1/2)
γ**·σ**
Rsol + (γ*·Rts*)
4236
4297
4419
4595
6495
6559
6559
6527
5676
5946
5946
5838
1358
1325
1287
1263
2525
2525
2535
2535
1912
1926
1933
1946
3791
3851
3932
4054
5676
5707
5739
5739
4973
5243
5243
5135
1273
1240
1197
1178
2323
2313
2333
2354
1771
1785
1798
1805
9173
9194
10039
11152
16883
17563
16903
16244
14492
14492
14492
14492
1752
1752
1855
1752
4164
4370
4164
3731
2907
2907
2783
2907
143
195
-60
-380
-1037
-1277
-982
-720
-789
-519
-519
-627
576
543
459
481
667
575
677
870
615
629
691
649
The fact that in the case of Energotonic multivitamin
complex the values obtained for Rsol + (γ*·Rts*) and
(γ**·σ**) are all positive and mutual compatible for each
value of the overtension η , shows that the electrochemical
system [47] must be considered as having only capacitive
properties. Consequently, in the case of the system
containing the Energotonic complex, the Warburg pseudocapacitance CW(P) accounts for its electrochemical
properties, and there is no need to introduce something else
in its Faraday impedance.
As for the negative values resulted for Rsol + (γ*·Rts*)
in the case of the system [46], they are unacceptable and
shows that the Swedish Bitter has transformed the
reference dielectrode [45] in a multielectrode whose
electrochemical properties may not be explained by a
Faraday impedance containing only a capacitive
reactance.
To account for this transformation, we have considered
that the Faraday impedance must contain a Warburg
pseudo-inductance too.
The values of CW (ω1 ) , CW
∗∗
(Ω)
The results given in Table 2, show that a substitution
of the Warburg pseudo-capacitance CW(P) by a parallel
arrangement: C ∗ ∗ (P ) = 1 C (P ) in parallel with a Warburg
W
W
α
α
1
pseudo-inductance
(see
L∗W∗ (P ) =
1 − α ω 2 CW ( P )
equations (20)), leads to acceptable values for Rsol +
[(γ*·Rts*)]**.
The value of α has been chosen taking into account
the condition:
0.42 (1-α )17563 > 1277
(48)
which gives α < 0.827. To be not far away from α =1,
when the substitution of the Warburg capacitance is not
necessary, we have chosen the value α =0.8. The
∗∗
corresponding values CW
(ω1 ) and
L∗W∗ (ω1 ) are given
in Table 3.
(ω1 ) and L∗W∗ (ω1 ) have been obtained by means of the formulae:
CW (ω1 ) =
1
ω1 X C (ω1 )
W
=
2π
(
J 2 [ω1 (t − τ )] γ σ
∗∗
∗∗
)ω
−1 / 2
1
⋅
1
ω1
≅
(γ
2
σ
∗∗
∗∗
)ω
1/ 2
1
(49)
respective:
CW∗∗ (ω1 ) =
1
;
CW (ω1 ) ; L∗W∗ (ω1 ) = α ⋅ 2 1
α
1 − α ω1 CW (ω1 )
and 1H(henry) = 1Ωs.
95
α = 0.8,
ω1 = 1.256 s −1
(50)
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
Volume 52(66), 1-2, 2007
TABLE 2. Estimation of the quantities Rsol + [(γ*·Rts*)]**, characterizing the charge transfer limitations of the electrochemical
system[46], α = 0.8
η
(V)
0
0
0
0
-0.05
-0.05
-0.05
-0.05
0.05
0.05
0.05
0.05
γ**·σ**
(Ω s-1/2)
9173
9194
10039
11152
16883
17563
16903
16244
14492
14492
14492
14492
τ
(s)
0
10
100
1000
0
10
100
1000
0
10
100
1000
0.42· (1-α) ·( γ**·σ**)
(Ω)
771
772
843
937
1418
1475
1420
1364
1217
1217
1217
1217
Rsol + (γ*·Rts**)
(Ω)
143
195
-60
-380
-1037
-1277
-982
-720
-789
-519
-519
-627
Rsol + [(γ*·Rts*)]**
(Ω)
934
967
783
557
381
198
438
644
428
698
698
590
TABLE 3. Estimation of the components of the parallel arrangement by which one may explain the inductive effect of the Swedish Bitter
η
(V)
0
0
0
0
-0.05
-0.05
-0.05
-0.05
0.05
0.05
0.05
0.05
τ
(s)
0
10
100
1000
0
10
100
1000
0
10
100
1000
γ**·σ**
(Ω s-1/2)
9173
9194
10039
11152
16883
17563
16903
16244
14492
14492
14492
14492
103 · CW(ω1)
(s/ Ω)
0.195
0.194
0.178
0.160
0.106
0.102
0.106
0.110
0.123
0.123
0.123
0.123
103 · CW**(ω1)
(s/ Ω)
0.244
0.243
0.223
0.200
0.133
0.128
0.133
0.138
0.154
0.154
0.154
0.154
103 · LW**(ω1)
TTh,p
(s)
11.19
11.19
11.19
11.18
11.20
11.20
11.20
11.20
11.19
11.19
11.19
11.19
13.01
13.07
14.25
15.85
23.92
24.86
23.92
23.05
20.62
20.62
20.62
20.62
T = 1 − α TTh , p
(s)
5.00
5.00
5.00
5.00
5.01
5.01
5.01
5.01
5.00
5.00
5.00
5.00
L∗W∗ (P )
1
α2
,
=
⋅ 2 2
∗∗
CW (P ) 1 − α ω CW (P )
To verify the correctness of the values obtained for
C (ω1 ) and L∗W∗ (ω1 ) in the last two columns are given
∗∗
W
the Thomson periods corresponding to the parallel
arrangement and the values resulted for the real time T =
2π / ω1 =5s, by applying the first equation (22’).
α = 0.8.
may be used to compare the inductive properties of two
medicaments; indeed the fact that the Energotonic
multivitamin complex has practically only capacitive
properties, must be reflected in a much smaller value of the
ratio (51). Therefore, a criterion for comparing the
inductive properties of two medicaments may be the
quotient:
4. Conclusions
The Energotonic multivitamin complex transforms the
reference redox dielectrode(45), which has only capacitive
properties, in the mutielectrode(47), having practically only
capacitive properties too. The Farady impedances of both
systems have only Warburg capacitive reactances.
The Swedish Bitter transforms the reference redox
dielectrode (45) in the multielectrode (46), having both
capacitive and inductive properties. To account for these
properties, it was necessary to substitute the Warburg
pseudo-capacitance CW(P) by a parallel arrangement:
1
CW∗ ∗ (P ) = CW (P ) in parallel with a Warburg pseudoα
1
inductance L∗ ∗ (P ) = α ⋅
,
α = 0.8.
W
2
1 − α ω CW (P )
The ratio:
(51)
⎡ L∗W∗ (P ) ⎤
⎥
⎢ ∗∗
⎣ CW (P ) ⎦ B
/ ⎡⎢ L (P ) ⎤⎥
∗∗
W
∗∗
W
⎣C
(P ) ⎦ E
But, from eq.(49) it results;
[C
[C
2
W
2
W
(P )]E
(P )]B
(
(
=
[C
[C
⎡ γ ∗ ∗σ ∗ ∗
= ⎢ ∗∗ ∗∗
⎣γ σ
2
W
2
W
)
)
(P )]E
(P )]B
⎤
⎥
E ⎦
(52)
2
B
(52’)
and thus, the criterion we are looking for, may be:
(
(
⎡ γ ∗ ∗σ ∗ ∗
Q = ⎢ ∗∗ ∗∗
⎣γ σ
)
)
⎤
⎥
E ⎦
B
2
(53)
In Table 4, are given the values of this criterion for the
two medicaments; B= Swedish Bitter and E= Energotonic
complex.
96
Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
Volume 52(66), 1-2, 2007
medicament is introduce in the electrolytic solution of this
reference dielectrode, and the Nyquist plots are recorded in
the way shown in this paper. From each Nyquist plot, the
coordinates of the points P1, P2 , (corresponding to ω1 =
1.256s-1 and ω2 = 1.582s-1) are obtained. This coordinates
permit to get the values of the unknowns Rsol + (γ*·Rts*)
and (γ**·σ**).
The values resulted for this criterion show that the
Swedish Bitter has much greater inductive propertie than
the Energotonic multivitamin complex.
Of course, this criterion may be used for classifying
the medicaments (especialy those from the God pharmacy)
with respect to their capacitive and inductive properties, by
using the Electrochemical Impedance Spectroscopy. The
method uses the reference dielectrode (45). The
TABLE 4. The values of the criterion Q proposed for comparing the inductive properties of the two medicaments investigated.
η
(V)
τ
(s)
(γ**·σ**)B
(Ω s-1/2)
(γ**·σ**)E
(Ω s-1/2)
Q=[(γ**·σ**)B / (γ**·σ**)E ]2
0
0
0
0
-0.05
-0.05
-0.05
-0.05
0.05
0.05
0.05
0.05
0
10
100
1000
0
10
100
1000
0
10
100
1000
9173
9194
10039
11152
16883
17563
16903
16244
14492
14492
14492
14492
1752
1752
1855
1752
4164
4370
4164
3731
2907
2907
2783
2907
27.41
27.54
29.29
40.52
16.44
16.15
16.48
18.96
24.85
24.85
27.12
24.85
If among the values of Rsol + (γ*·Rts*) are also negative
values, it is a prove that the Warburg pseudo-capacitance
must be substituted by a parallel arrangement CW**(P) ,
LW**(P) , and the corrected quantities Rsol + [(γ*·Rts*)]** are
obtained by adding to the values of Rsol + (γ*·Rts*), the
values 0.42 · (1-α) · (γ**·σ**). In doing this, the value of α
results from the condition Rsol + [(γ*·Rts*)]** >0.
In this way, the unknowns [(γ*·Rts*)]** and (γ**·σ**),
characterizing the charge transfer and diffusion limitations
of the reference dielectrode in whose electrolytic solution is
introduced the medicament, are estimated.
Further, repeating the experiments with a second
medicament, results new values for (γ**·σ**), and therefore,
the inductive properties of the two medicaments may be
compared by means of the criterion (53).
Choosing, e.g., the Swedish Bitter as a reference
medicament, the proposed “Electrochemical Impedance
Spectroscopy“ method permits to classify the other
medicaments, by using the criterion (53).
7. Bonciocat N., Alternativa Fredholm in Electrochimie, Editura
MEDIAMIRA, Cluj-Napoca, 2005, 28-39.
8. Adina Radu(Cotarta), Ph.D. These, Institut National Polytechnique de
Grenoble, 1997.
9. Bonciocat N., Cotarta A., A new approach based on the theory of
variational calculus in studying the electrodeposition process of chromium
in the system Cr0/CrCl2, LiCl-KCl”, Contract Copernicus 1177
“Utilisation de sels fondus en metallurgie”, Final Report of European
Community, july 1998.
10. Bonciocat N., Papadopol E., Borca S., Marian I.O., A new theoretical
approach to the voltammetry with linear scanning of the potential. I. The
ordinary differential equation of the voltamograms and its solutions in the
case of irreversible and reversible electrode redox reactions”, Rev. Roum.
Chim. 45, 2000, 981-989.
11. Bonciocat N., Papadopol E., Borca S., Marian I.O., A new theoretical
approach to the voltammetry with linear scanning of the potential. II.
Comparison with the standard approach given in the literature”, Rev.
Roum. Chim. 45, 2000, 1057-1063.
12. Marian I.O., Sandulescu R., Bonciocat N., Diffusion coefficient (or
concentration) determination of ascorbic acid using carbon paste
electrodes, in Fredholm alternative, J. Pharm. Biomed. Anal., 23, 2000.,
227-230.
13. Bonciocat N., Papadopol E., Borca S., Marian I.O., A new theoretical
approach to the voltammetry with linear scanning of the potential. III
Method of determining the diffusion coefficients of the electrochemical
active species participating in a reversible electrode reaction O + e ↔R,
Rev. Roum. Chim., 46, 2001, 3-8.
14. Bonciocat N., Papadopol E., Borca S., Marian I.O., A new theoretical
approach to the voltammetry with linear scanning of the potential IV.
Method of determining the standard exchange current densities of the
electrode redox reactions, Rev. Roum. Chim., 46, 2001, 481-486.
15. Bonciocat N., Papadopol E., Borca S., Marian I.O., A new theoretical
approach to the volammetry with linear scanning of the potential. V
Method of determining the symmetry factors of the electrode redox
reactions, Rev. Roum. Chim., 46, 2001, 991-998.
16. Marian I.O., Bonciocat N., Sandulescu R., Filip C., Direct
voltammetry for vitamin B2 determination in aqueous solution by using
glassy carbon electrodes” J. Pharm. Biomed. Anal. 24, 2001, 1175-1179.
17. Bonciocat N., Cotarta A., Bouteillon J., Poignet J.C., The
electrodeposition of chromium from molten alkali chlorides. The effect of
the direct voltammetry on the quality of an initial deposit of Cr0, J. of
High Temperature Material Processes, 6, 2002, 283-304.
18. Bonciocat N., Marian I.O., Sandulescu R., Filip C., Lotrean S., A new
proposal for fast determination of vitamine B2 from aqueous
pharmaceutical products, J. Pharm. Biomed. Anal. 32, 2003, 1093-1098.
19. Bonciocat N., Radovan C. , Chiriac A., Chronoamperometric method
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Chem. Bull. "POLITEHNICA" Univ. (Timişoara)
Volume 52(66), 1-2, 2007
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98