CHAPTER 12
IMPEDANCE SPECTROSCOPY: A GENERAL INTRODUCTION AND APPLICATION TO
DYE-SENSITIZED SOLAR CELLS
Juan Bisquert and Francisco Fabregat-Santiago
12.1 INTRODU C TION
Impedance Spectroscopy (IS) has become a major tool for investigating the properties and quality of dye-sensitized solar cell (DSC) devices. This chapter provides an intro-duction of IS interpretation methods focusing on the analysis of DSC impedance data. It also presents a scope of the main results obtained so far. IS gives access to funda-mental mechanisms of operation of solar cells, for which reason we discuss our views of basic photovoltaic principles required to realize the interpretation of the experi-mental results. The chapter summarizes some 10 years of experience of the authors with regard to modeling, measurement and interpretation of IS applied in DSC.
A good way to start this subject is a brief recollection of how it evolved over the ? rst years. The original “standard” con? guration of a DSC [12.1] that emerged in the early 1990s is formed by a large internal area constituted of a nanostructured TiO 2 semiconductor, connected to a transparent conducting oxide (TCO) and coated with photoactive dye molecules. It is furthermore in contact with a redox I I ?3?/ electrolyte that is in turn connected to a Pt-catalyzed counterelectrode (CE). The DSC was ini-tially developed to be a photoelectrochemical solar cell. Electrochemical Impedance Spectroscopy (EIS) is a traditional method, central to electrochemical science and technology. Electrochemistry usually investigates interfacial charge transfer between a solid conductor (the working electrode, WE) and an electrolyte. This is done with a voltage applied between the WE and CE, with the assistance of a reference electrode (RE), rendering it possible to identify the voltage drop at the interface between the WE and the electrolyte. In addition, the electrolyte often contains a salt that provides a large conductivity in the liquid phase and removes limitations by drift transport in an electrical ? eld. Electrochemistry is thus mostly concerned with interfacial charge transfer events, possibly governed by diffusion of reactants or products. It is with EIS
2 Dye-sensitized
cells
solar
possible to readily separate the interfacial capacitance and charge-transfer resistance, as well as to identify diffusion components in the electrolyte. A good introduction to such applications is given by Gabrielli [12.2].
In solid state solar cell science and technology, the most commonly applied frequency technique is Admittance Spectroscopy (AS). By tradition, AS denominates a special method that operates at reverse voltage and evaluates the energy levels of majority carrier traps (in general, all those that cross the Fermi level) as well as trap densities of states [12.3]. In work on DSCs and other solar cells, we may be interested to probe a wide variety of conditions. Consequently, we generally use the denomina-tion Impedance Spectroscopy (IS) when referring to the technique applied in this context (rather than EIS or AS).
Before the advent of DSC, IS had been largely applied in photoelectrochem-istry [12.4, 12.5]. This is a ? eld widely explored since the 1970s, using compact monocrystalline or polycrystalline semiconductor electrodes for sunlight energy con-version [12.6-12.8]. In these systems, IS provides information on the electronic car-rier concentration at the surface, via Mott-Schottky plots (i.e., the reciprocal square capacitance versus the bias voltage) as well as on the rates of interfacial charge trans-fer [12.9-12.11]. Several important concepts, later to be applied in DSC, where estab-lished at that time, such as the bandedge shift by charging of the Helmholtz layer and the crucial role of surface states in electron or hole transfer to acceptors in solution [12.9, 12.10, 12.12-12.14]. Nonetheless, it was clearly recognized that applying IS in these systems is far from trivial, for example due to the presence of frequency disper-sion that complicates the determination of parameters [12.15]
It was natural to apply such well-established electrochemical methods to DSC and several groups have done so [12.16-12.19]. However, in the early studies, it was necessary to clarify a conceptual framework of interpretation which took several years. On the one hand, the early diffusion-recombination model [12.20] was generally adopted for steady-state techniques and produced very good results when extended to light-modulated frequency techniques [12.21]. In this approach, the only role of the applied voltage is to establish the concentration of electrons at the edge of the TiO2 in contact with TCO [12.20, 12.21]. On the other hand, classical photoelectrochemical methods heavily rest on the notion of charge collection at the surface space-charge layer, while diffusion is viewed as an auxiliary component, at best [12.22]. Thus, in photoelectrochemistry of compact semiconductor electrodes, the main method to describe the system behavior is an understanding of the electric potential distribution between the bulk semiconductor and the semiconductor/electrolyte interface [12.7].
Owing to these con? icting approaches, in the DSC area there were many discus-sions concerning the distribution of the applied voltage as internal “potential drops”, the origin of photovoltage, screening, and the role of electron-hole separation at the space-charge region [12.23-12.27]. This is understandable since the DSC is a porous, heterogeneous system, and in models of systems with a complex morphology, it is generally dif? cult to match diffusion control with a precise statement regarding the electrical potential distribution. The key element for progress is to adopt a macro-homogeneous approach and focus in the spatial distribution of the Fermi level. This method emerged in the DSC area [12.24, 12.28-12.30] and eventually led to gener-alized photovoltaic principles based on the splitting of Fermi levels and the c rucial
spectroscopy 3 Impedance
role of selective contacts [12.31-12.34]. Another central concept that appeared in the DSC area was a “conduction band capacitance” [12.26, 12.28, 12.30], later to be generally de? ned as a chemical capacitance [12.35]. This capacitive element is nor-mally absent in classical photoelectrochemistry but is key for the interpretation of frequency-resolved techniques in DSC. Also important was the recognition [12.26, 12.36] that nanostructured TiO2 should be treated as a disordered material, much like the amorphous semiconductors [12.37-12.39], with electronic traps affecting not only the surface events, but any differential/kinetic measurements, including the chemical capacitance [12.35], recombination lifetime and transport coef? cients [12.40].
The passage from established ideas of photoelectrochemistry to those best suited to the DSC have inevitably rendered it necessary to treat the porous-mixed phase structure of the DSC. Electrochemistry was already evolving in this direction for some decades, ? rst with the description of porous electrodes [12.41], and then, with the introduction of truly active electrodes that become modi? ed under bias voltage, such as intercalation metal-oxides [12.42], conducting polymers [12.43] and redox polymers [12.44]. Especially important is the work of Chidsey and Murray [12.44], which shows the modi? cation of the diffusion coef? cient in the solid phase, as well as the capacitance of the solid material as a whole, in opposition to the standard interfa-cial capacitance. In the analysis of these systems, either porous or not, the importance of coupling transport elements with interfacial and/or recombination components for a proper description of IS data was well recognized. Transmission line models pro-vide a natural representation of the IS models and are widely used [12.43, 12.45].
As demonstrated in Figure 12.1, transmission line models incorporating fre-quency dispersion, which is ubiquitous in disordered materials, have been developed and applied to nanostructured TiO2 used in DSC. A very good realization of the model was soon found in the experiment, as shown in Figure 12.2 [12.46]. Later, diffusion-reaction models were solved for IS characterization, and the models where put in rela-tion to both nanostructured semiconductors and bulk semiconductors for solar cells [12.47]. Disorder was included also in generalized transmission lines for anomalous diffusion [12.48]. In addition, the role of macroscopic contacts was analyzed in gen-eralized transmission line models, as shown in Figure 12.1(b) [12.49], and this effect would take relevance as a result of the TCO contribution to the measured impedance [12.50, 12.51].
The calculation of the diffusion-recombination impedance [12.47] opened the way for a direct measurement of conductivity of electrons in TiO2 by IS [12.52], which provided a good validation of the method. Further, the diffusion- r ecombination impedance also naturally reveals [12.47] the chemical capacitance of electrons in nanostructured TiO2 (associated to the rise of the Fermi level), which also appears in measurements of cyclic voltammetry (at slow scan rates) [12.53] and electron lifetime [12.54].
Application of these IS methods and models to DSC [12.51] demonstrated that IS provides a picture of the energetics of TiO2, which is a crucial tool for compar-ing DSC con? gurations [12.55]. It also showed that it was possible to simultane-ously obtain the parameters for transport and recombination at various steady-state conditions of a DSC, which is an unsurpassed power of the technique. The trends of the electron diffusion coef? cient [12.51] where similar to those found previously
Impedance spectroscopy 7and we can also write Eq. (12.1) in terms of V oc
j
j q v v mk T
qv mk T =????sc oc B oc B 11e e ()// (12.3)
Bias voltage is denoted “forward” when it injects charge in the solar cell and induces recombination. Otherwise it is referred to as “reverse”. By changing the illumination intensity Φ0, one can trace curves similar to that in Figure 12.3(a) with other values of j sc and V oc . The values and shape of these curves for a given solar cell allow us to determine the energy conversion ef? ciency of the photovoltaic device, Figure 12.3(b). Another crucial parameter is the ? ll factor (FF), which is the maxi-mum electrical power delivered by the cell with respect to j V sc oc ?, Figure 12.3(b). A high FF requires that the current remains high at the maximum power point. This is obtained if the j-V curve is reasonably “squared” as in Figure 12.3(a).
12.2.2 Physical origin of the diode equation for a solar cell
It is important to clarify the physical interpretation of the diode equation. We consider a slab of p-type semiconductor with thickness L . At a position x , n is the density of minority carriers (electrons), and j n the ? ux in the positive x direction. The conserva-tion equation can be written as:
??=+??n t x G x G x J
x x U x ()()()()()Φ??d n
n (12.4)
where G Φ is the rate of optical photogeneration (per unit volume) due to the illumi-nation intensity Φ0 (photons·cm ?2), while G d is the rate of generation in the dark by the surrounding blackbody radiation. U n is the rate of recombination of electrons per volume. A simple and important model is the linear form, with electron lifetime t 0
U n
n =t 0
(12.5)
Eq. (12.4) must hold locally, in equilibrium, therefore, assuming Eq. (12.5), we have
G n d =0
t (12.6)
where n 0 is the carrier density in dark equilibrium. This is due to, the rate of genera-tion in dark equilibrium, by detailed balance principle, equilibrating the recombina-tion rate [12.31]. A similar constraint on G d applies for any recombination model.
The ? ux of electron carriers with the diffusion coef? cient D 0 relates to the gra-dient of concentration by Fick’s law
J D n
x n =???0 (12.7)
Impedance spectroscopy 9
If we restrict our attention to a steady-state condition, Eq. (12.11) reduces to: j qLG qL U G =??Φ[]n d (12.12)
Comparing Eqs. (12.1) and (12.12), the photocurrent generated during short-circuit becomes:
j qLG sc =Φ (12.13)
The total generation per unit area, LG
Φ is proportional to the incident light
intensity, LG ΦΦ=h opt 0, where h opt is an optical quantum yield that depends on the properties of absorption of the radiation by the solar cell. We also obtain that: j qLG d d = (12.14)
Consequently, the dark reverse current corresponds to the extraction of the car-riers generated by the thermal surrounding radiation.
We already appreciate that the ideal diode model of a solar cell states that a constant current is drawn out of the cell, namely j sc + j d , which corresponds to all the electron carriers generated in the semiconductor. In addition, the recombination term produces a current in the opposite direction. At high forward bias the recombination term dominates and bends the j-V curve, as indicated in Figure 12.3(a). Note that this ideal model does not contain any trace of diffusion whatsoever. The only element required in order to obtain the diode model is to state that the contacts are selective, and extract only one carrier at each side, as indicated in Figure 12.4.
Another step for converting the conservation equation into a j -V characteristic is to relate the carrier density, n , to the applied voltage, V , by introducing Fermi levels. We assume the extended states for electrons at the level E c (conduction band edge), with an effective density, N c . With respect to the electron Fermi level E Fn , we have:
n N e E E k T =?c Fn c B ()/ (12.15)
and considering the dark (equilibrium) Fermi level E F0,
n N e E
E k T 0=?c F0c B ()/ (12.16)
we obtain
n n e E E k T =?00()/Fn F B (12.17)
The voltage, V , is measured at the selective contacts, and corresponds to the dif-ference in Fermi levels of carriers at the contacts. If the contacts are ideally reversible
[12.33], each contact separately equilibrates with the Fermi level of electrons, E Fn , and holes, E Fp . This gives:
V E E q =?()/Fn Fp (12.18)
For a p-semiconductor, the holes in the Fermi level remain at the dark equilib-rium level, E E Fp F0=, and Eq. (12.18) can thus be written:
E E qV Fn F0=+ (12.19)
Impedance spectroscopy 11f = v /2p , typically over several decades, i.e., from mHz to 10 MHz, with 5-10 meas-urements per decade. At each frequency the impedance meter must verify that the Z (v ) is stable. At low frequencies, this takes a considerable amount of time, i.e., stabilizing a measurement at f = 10 mHz consumes minutes. Nevertheless, measurements at low frequencies are often important in order to make sure that one is approaching the dc regime, as further explained below. A judicious selection of the frequency window of measurement is therefore necessary, and this is often aided by experience.
In addition to scanning the frequencies, it is usually very important to deter-mine the IS parameters at various conditions of steady state. This is the key approach in order to relate the measurement to a given physical model. At each steady state the Z (v ) data is related to a model in the frequency domain, which is usually represented as an equivalent circuit. By modifying the steady state, the change in impedance parameters (resistances, capacitances, etc.) can be monitored in relation to the physi-cal properties of the system. Since the impedance measurement takes a considerable amount of time, the steady state often changes along the impedance measurement, and precautions should be taken to avoid a serious drift of the parameters. In par-ticular, care should be taken with unintentional changes of temperature in solar cells, since this introduces additional and unwanted variations of the parameters.
Note that, at each steady state, a full scan of frequencies is necessary. Thus many steady state points imply a long measurement, perhaps over an entire day. However, data that do not cover different steady states may in some cases be of little value, particularly if there is uncertainty regarding the meaning of the parameters. It is also important to verify the true signi? cance of parameters by material varia-tions of the samples, e.g., to con? rm the correlation of a transport resistance with the reciprocal length of the sample. The extent to which these approaches must be judiciously realized depends on the preliminary knowledge and experience of the particular system.
12.3.1 Steady state and small perturbation quantities
As an example of the relationship between the ac impedance and steady-state quan-tities, we discuss a characteristic experiment on a solar cell using the ideal model outlined in Figures 12.3 and 12.4. We choose a certain point of bias voltage, V 0, with the associated current density, j 0. At this point, a small displacement of voltage ?()V 0 implies a change of current ?()j 0. The value v
= 0 in parenthesis indicates that the
displacement is in? nitely slow, i.e., ?()V 0 and ?()j 0 attain a value that is independent of
time. The displacement of the current and voltage is indicated in Figure 12.3(a) with arrows.
For a solar cell with area A , the quotient of the small quantities gives:
Z V Aj Adj
dV R 0001
()=()()=??????=???dc (12.23)
In other words, the small quantities provide a derivative of the voltage with respect to the current. This is the reciprocal of the slope of the j -V curve, which is in turn the dc resistance of the solar cell R dc (per area) under those particular conditions.
Impedance spectroscopy 15
voltage acting on them is identical. Using Kirchhoff rules, we add the impedances for two elements in series and the resulting impedance is an equivalent description of the initial connection (under an applied voltage, it produces the same current as the combination that it replaces). For elements in parallel, we add the admittances (or the complex capacitances) to form the equivalent impedance.
A ? rst example of an equivalent circuit is the R 1C 1 series combination. From the impedance
Z R i C ()v v =+
11
1
(12.31)
we obtain the complex capacitance
C C i *()v v =+1
1
1t (12.32)
Table 12.6 Impedance representations.
Denomination De? nition* Real and imaginary parts Impedance Z (v ) Z = Z ′ + iZ ″
Admittance Y Z ()()v v =1
Y = Y ′ + iY ″
Phase angle tan d =Z Z ″
′
Complex capacitance C i Z *()()v v v =1
C * = C ′ + iC ″
Conductivity s *()()v v =L
AZ s * = s ′ + i s ′, s ′(0) ≡ s
Complex dielectric constant e *(v ) = LC*(v )/A e * = e ′ + i e ″
s * = i ve *
Complex electric modulus M *()()v v =1
e M * = M ′ + iM ″
*L is the length of the sample, A is the area.
Table 12.7 Basic ac electrical elements.
Denomination Symbol Scheme Impedance Resistance R R Capacitance C 1
i C
v Inductor L i v L Constant phase element (CPE) Q n ()i Q n
n
v ?
16 Dye-sensitized solar cells
Here, the relaxation time is de? ned as
t = R 1C 1 (12.33)
Let us look more closely at the meaning of the relaxation time, t 1, in relation to the response of the system in the time domain. We consider the type of measurement commented before, in which a change of voltage, ΔV , is applied at time t = 0, and for which the subsequent evolution of the electrical current is monitored. In the frequency domain, the step voltage ?()()V t V u t =?Δ has the expression:
?
()V s V
s =Δ (12.34)
and the electrical current can be written:
?()?()()()()
I s V s Z s V sZ s V
R s ===+ΔΔt t 1111 (12.35)
By inverting Eq. (12.35) to the time domain, we obtain:
I t V R e t ()/=?Δt 1
(10.36)
In general, the process described by Eqs. (12.32) or (12.36) is an elementary relaxation with the characteristic frequency:
v 1111
1
1
=
=t R C (12.37)
The plot of the complex capacitance is shown in Figure 12.8(a). The capaci-tance displays an arc from the dc value C *(0) = C 1 to the high frequency value. The top of the arc occurs at the characteristic frequency of the relaxation v 1. The impedance, shown in the complex plane in Figure 12.8(b), forms a vertical line. This is a “blocking” circuit, since the impedance of a capacitor is ∞ at low frequency, which effectively constitutes an open circuit connection, thus preventing the dc cur-rent from ? owing. However, the impedance of the capacitor decreases as the fre-quency increases, and at very large frequencies, with respect to v 1, the capacitor indeed becomes a short-circuit. Consequently, there remains only the resistance R 1. The impedance of a resistor is the same at all frequencies, hence the vertical line in Figure 12.8(b). The arc in Figure 12.8(a) is a manifestation of an elementary relaxa-tion process that corresponds to an exponential decay in the time domain, indicated in Eq. (12.36).
Another important example of an equivalent circuit is the RC parallel combina-tion, depicted in Figure 12.9. The admittance of the combination is here:
Y R i C 11
11
()v v =+ (12.38)
20 Dye-sensitized solar cells
respect to the frequency, Figure 12.10(c), usually reveals a great deal of information. In Figure 12.10(c), we observe two plateaus of the real part of the capacitance which clearly indicate two distinct relaxation processes. These relaxations are manifested in the peaks of the loss component of the capacitance, C ′. When increasing the frequency, each peak of C ′ indicates the occurrence of a relaxation and a consequent decrease of the capacitance [12.72]. Such features can also be observed in the complex capacitance plot in Figure 12.10(a), demonstrating separate arcs for the two relaxations.
Let us consider in more detail how to obtain the parameters of a given IS data set. The main method consists in ? tting by least squares methods using an equivalent circuit software that is available in many kinds of measuring equipments. However, the ? tting process requires the assumption of a given equivalent circuit, and sometimes, in addition, the input of reasonable trial parameters. As we have mentioned before, the inspection of the data set in several complementary representations usually provides a good hint of the equivalent circuit structure, at least in the less complex cases. Another useful approach is to read the parameter values directly from the data representation, e.g., resistances and capacitances of separate contributions. How to perform this has already been discussed in the examples of Figures 12.9(b) and 12.10(c). However, the values of capacitance or impedance in a certain frequency domain can be in? uenced by the whole equivalent circuit. So, to obtain the circuit parameters, there is often no substitute for integral data ? tting. Separately treating part of the spectral data is a valuable resource, but one that should be used with care.
For instance, in Figure 12.9(a) we observe that the impedance displays a verti-cal line when approaching the dc limit. Therefore, at low frequency, Figure 12.9(a) can be simply described by RC parallel combination. The low frequency resistance is clearly given by R dc . But what should be used as the low frequency capacitance C lf ? It cannot be C 1, otherwise the arc would ? nish at the origin of Figure 12.9(a), which it does not. In general, it is very useful to obtain the impedance formula in a restricted frequency domain, and the method is demonstrated with this example.
First, from the expression of the impedance in Eq. (12.39), we ? nd the low frequency limit, which gives:
Z R R i R C ()v v =++1212
1 (12.40)
This last equation does not correspond to any recognizable combination of cir-cuit elements. In fact, we seek a parallel combination, which should provide a good description of the data in Figure 12.9(a) at low frequencies. Consequently, we trans-form Eq. (12.40) to the admittance, maintaining the ? rst order approximation in v , with the result:
Y R R i R R R C ()()v v =+++11212
122
1 (12.41)
In Eq. (12.41), we readily recognize the parallel RC admittance formula. The low frequency capacitance is:
C R R R C lf =+12
122
1() (12.42)
电化学阻抗谱的应用及其解析方法 交流阻抗法是电化学测试技术中一类十分重要的方法，是研究电极过程动力学和表面现象的重要手段。特别是近年来，由于频率响应分析仪的快速发展,交流阻抗的测试精度越来越高，超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步，对阻抗谱解析的自动化程度越来越高，这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的诱发、发展、终止以及活性物质的吸脱附过程。 阻抗谱中的基本元件 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R ，纯电容C ，阻抗值为1/j ωC ，纯电感L ，其阻抗值为j ωL 。实际测量中，将某一频率为ω的微扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应所引起的阻力均视为电阻，则等效电路如图1所示。 图1. 用大面积惰性电极为辅助电极时电解池的等效电路 图中A 、B 分别表示电解池的研究电极和辅助电极两端，Ra 、Rb 分别表示电极材料本身的电阻，Cab 表示研究电极与辅助电极之间的电容，Cd 与Cd ’表示研究电极和辅助电极的双电层电容，Zf 与Zf ’表示研究电极与辅助电极的交流阻抗。通常称为电解阻抗或法拉第阻抗，其数值决定于电极动力学参数及测量信号的频率，Rl 表示辅助电极与工作电极之间的溶液 电阻。一般将双电层电容Cd 与法拉第阻抗的并联称为界面阻抗Z 。 实际测量中，电极本身的内阻很小，且辅助电极与工作电极之间的距离较大，故电容Cab 一般远远小于双电层电容Cd 。如果辅助电极上不发生电化学反映，即Zf ’特别大，又使辅助 电极的面积远大于研究电极的面积（例如用大的铂黑电极），则Cd ’很大，其容抗Xcd ’比串 联电路中的其他元件小得多，因此辅助电极的界面阻抗可忽略，于是图1可简化成图2，这也是比较常见的等效电路。 图2. 用大面积惰性电极为辅助电极时电解池的简化电路 Element Freedom Value Error Error %Rs Free(+)2000N/A N/A Cab Free(+)1E-7N/A N/A Cd Fixed(X)0N/A N/A Zf Fixed(X)0N/A N/A Rt Fixed(X)0N/A N/A Cd'Fixed(X)0N/A N/A Zf'Fixed(X)0N/A N/A Rb Free(+)10000N/A N/A Data File: Circuit Model File:C:\Sai_Demo\ZModels\12861 Dummy Cell.mdl Mode: Run Fitting / All Data Points (1 - 1) Element Freedom Value Error Error %Rs Fixed(X )1500N/A N/A Zf Fixed(X )5000N/A N/A Cd Fixed(X ) 1E-6 N/A N/A Data File: Circuit Model File:C:\Sai_Demo\ZModels\Tutor3 R-C.mdl Mode: Run Simulation / Freq. Range (0.01 - 10000Maximum Iterations: 100 B
电化学曲线极化曲线阻抗谱分析 一、极化曲线 1.绘制原理 铁在酸溶液中，将不断被溶解，同时产生H2，即：Fe + 2H+ = Fe2+ + H2 (a) 当电极不与外电路接通时，其净电流I总为零。在稳定状态下，铁溶解的阳极电流I(Fe)和H＋还原出H2的阴极电流I(H)，它们在数值上相等但符号相反，即：(1) I(Fe)的大小反映Fe在H+中的溶解速率，而维持I(Fe)，I(H)相等时的电势称为Fe／H+体系的自腐蚀电势εcor。 图1是Fe在H+中的阳极极化和阴极极化曲线图。图2 铜合金在海水中典型极化曲线 当对电极进行阳极极化(即加更大正电势)时，反应(c)被抑制，反应(b)加快。此时，电化学过程以Fe的溶解为主要倾向。通过测定对应的极化电势和极化电流，就可得到Fe／H+体系的阳极极化曲线rba。 当对电极进行阴极极化，即加更负的电势时，反应(b)被抑制，电化学过程以反应(c)为主要倾向。同理，可获得阴极极化曲线rdc。 2.图形分析 （1）斜率 斜率越小，反应阻力越小，腐蚀速率越大，越易腐蚀。斜率越大，反应阻力越大，腐蚀速率越小，越耐腐蚀。 （2）同一曲线上各各段形状变化 如图2，在section2中，电流随电位升高的升高反而减小。这是因为此次发生了钝化现象，产生了致密的氧化膜，阻碍了离子的扩散，导致腐蚀电流下降。 （3）曲线随时间的变动 以7天和0天两曲线为例，对于Y轴，七天后曲线下移（负移），自腐蚀电位降低，说明更容易腐蚀。对于X轴，七天后曲线正移，腐蚀电流增大，亦说明更容易腐蚀。 二、阻抗谱 1.测量原理 它是基于测量对体系施加小幅度微扰时的电化学响应，在每个测量的频率点的原始数据中，都包含了施加信号电压（或电流）对测得的信号电流（或电压）的相位移及阻抗的幅模值。从这些数据中可以计算出电化学响应的实部和虚部。阻抗中涉及的参数有阻抗幅模（| Z |）、阻抗实部（Z,）、阻抗虚部（Z,,）、相位移（θ）、频率（ω）等变量，同时还可以计算出导纳（Y）和电容（C）的实部和虚部，因而阻抗谱可以通过多种方式表示。
锂离子电池的电化学阻抗谱分析 1. 锂离子电池的特点 锂离子电池充电时，正极中的锂离子从基体脱出，嵌入负极；而放电时，锂离子会从负极中脱出，嵌入正极。因此锂离子电池正负极材料的充放电容量、循环稳定性能和充放电倍率等重要特性均与锂离子在嵌合物电极材料中的脱出和嵌入过程密切相关。这些过程可以很好地从电化学阻抗谱（EIS ）的测量与解析中体现出来。 2. 电化学阻抗谱的解析 2.1. 高频谱解析 嵌合物电极的EIS 谱的高频区域是与锂离子通过活性材料颗粒表面SEI 膜的扩散迁移相关的半圆（高频区域半圆），可用一个并联电路R SEI /C SEI 表示。 R SEI 和C SEI 是表征锂离子活性材料颗粒表面SEI 膜扩散迁移过程的基本参数，如何理解R SEI 和C SEI 与SEI 膜的厚度、时间、温度的关系，是应用EIS 研究锂离子通过活性材料颗粒表面SEI 膜扩散过程的基础。 2.1.1. 高频谱解析R SEI 和C SEI 与SEI 膜厚度的关系 SEI 膜的电阻R SEI 和电容C SEI 与SEI 膜的电导率、介电常数ε的关系可用简单的金属导线的电阻公式和平行板电容器的电容公式表达出来 S l R SEI ρ = (1) l S C SEI ε= (2) 以上两式中S 为电极的表面积，l 为SEI 膜的厚度。倘若锂离子在嵌合物电极的嵌入和脱出过程中ρ、ε和S 变化较小，那么R SEI 的增大和C SEI 的减小就意味着SEI 厚度的增加。由此根据R SEI 和C SEI 的变化，可以预测SEI 膜的形成和增长情 2.1.2. SEI 膜的生长规律（R SEI 与时间的关系） 嵌合物电极的SEI 膜的生长规律源于对金属锂表面SEI 膜的生长规律的分析
电化学阻抗谱解析与应用 交流阻抗发式电化学测试技术中一类十分重要的方法，是研究电极过程动力学和表面现象的重要手段。特别是近年来，由于频率响应分析仪的快速发展,交流阻抗的测试精度越来越高，超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步，对阻抗谱解析的自动化程度越来越高，这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的诱发、发展、终止以及活性物质的吸脱附过程。 1. 阻抗谱中的基本元件 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R ，纯电容C ，阻抗值为1/j ωC ，纯电感L ，其阻抗值为j ωL 。实际测量中，将某一频率为ω的微扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应所引起的阻力均视为电阻，则等效电路如图1所示。 Element Freedom Value Error Error %Rs Free(+)2000N/A N/A Cab Free(+)1E-7N/A N/A Cd Fixed(X)0N/A N/A Zf Fixed(X)0N/A N/A Rt Fixed(X)0N/A N/A Cd'Fixed(X)0N/A N/A Zf'Fixed(X)0N/A N/A Rb Free(+)10000N/A N/A Data File:Circuit Model File:C:\Sai_Demo\ZModels\12861 Dummy Cell.mdl Mode: Run Fitting / All Data Points (1 - 1) Maximum Iterations:100Optimization Iterations:0Type of Fitting: Complex Type of Weighting: Data-Modulus 图1. 用大面积惰性电极为辅助电极时电解池的等效电路 图中A 、B 分别表示电解池的研究电极和辅助电极两端，Ra 、Rb 分别表示电极材料本身的电阻，Cab 表示研究电极与辅助电极之间的电容，Cd 与Cd ’表示研究电极和辅助电极的双电层电容，Zf 与Zf ’表示研究电极与辅助电极的交流阻抗。通常称为电解阻抗或法拉第阻抗，其数值决定于电极动力学参数 及测量信号的频率，Rl 表示辅助电极与工作电极之间的溶液电阻。一般将双电层电容Cd 与法拉第阻抗的并联称为界面阻抗Z 。 实际测量中，电极本身的内阻很小，且辅助电极与工作电极之间的距离较大，故电容Cab 一般远远小于双电层电容Cd 。如果辅助电极上不发生电化学反映，即Zf ’特别大，又使辅助电极的面积远大于研究电极的面积（例如用大的铂黑电极），则Cd ’很大，其容抗Xcd ’比串联电路中的其他元件小得多，因此 辅助电极的界面阻抗可忽略，于是图1可简化成图2，这也是比较常见的等效电路。 图2. 用大面积惰性电极为辅助电极时电解池的简化电路 2. 阻抗谱中的特殊元件 以上所讲的等效电路仅仅为基本电路，实际上，由于电极表面的弥散效应的存在，所测得的双电层 电容不是一个常数，而是随交流信号的频率和幅值而发生改变的，一般来讲，弥散效应主要与电极表面电流分布有关，在腐蚀电位附近，电极表面上阴、阳极电流并存，当介质中存在缓蚀剂时，电极表面就会为缓蚀剂层所覆盖，此时，铁离子只能在局部区域穿透缓蚀剂层形成阳极电流，这样就导致电流分布 极度不均匀，弥散效应系数较低。表现为容抗弧变“瘪”，如图3所示。另外电极表面的粗糙度也能影响弥散效应系数变化，一般电极表面越粗糙，弥散效应系数越低。 2.1 常相位角元件（Constant Phase Angle Element ，CPE ） 在表征弥散效应时,近来提出了一种新的电化学元件CPE,CPE 的等效电路解析式为： p j T Z )(1ω?=，CPE 的阻抗由两个参数来定义，即CPE-T ，CPE-P ，我们知道， )2sin()2cos(ππp j p j p +=，因此CPE 元件的阻抗Z 可以表示为
电化学阻抗谱的应用分析 交流阻抗法是电化学测试技术中一类十分重要的方法，是研究电极过程动力学和表面现象的 重要手段。特别是近年来，由于频率响应分析仪的快速发展，交流阻抗的测试精度越来越高， 超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步，对阻抗谱解析的自动化 程度越来越高，这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的诱 发、发展、终止以及活性物质的吸脱附过程。 阻抗谱中的基本元件 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R,纯电容C,阻抗值为1/j 3 C,纯电感L,其阻抗值为j 3 L。实际测量中，将某一频率为3的微扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应所引 起的阻力均视为电阻，则等效电路如图1所示。 Element Freedom Value Error Error % 图中A、B分剁谡示电解池唯e(尊极和辅1200极两端，N/A Ra、Rb分N/表示电极材料本身的电阻，Cab表郴跳电极与辅助豳极立间的电容--7 Cd与N Cd'表示研究翩A和辅助电极的双电 层电容，Zf与C Zf '表示研究电核肉XI助电极的交流阻抗。顺称为电解阻NA法拉第阻抗，其数值决定于电皱动力学参数族苗密令号的频% Rl源A辅助电极与WA作电极之间的溶液Rt Fixed(X) 0 N/A N/A 电阻。一般将双Cd层电容C 电化学阻抗谱的应用分析 交流阻抗法是电化学测试技术中一类十分重要的方法，是研究电极过程动力学和表面现象的重要手段。特别是近年来，由于频率响应分析仪的快速发展,交流阻抗的测试精度越来越高，超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步，对阻抗谱解析的自动化程度越来越高，这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的诱发、发展、终止以及活性物质的吸脱附过程。 阻抗谱中的基本元件 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R ，纯电容C ，阻抗值为1/j ωC ，纯电感L ，其阻抗值为j ωL 。实际测量中，将某一频率为ω的微扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应所引起的阻力均视为电阻，则等效电路如图1所示。 图1. 用大面积惰性电极为辅助电极时电解池的等效电路 图中A 、B 分别表示电解池的研究电极和辅助电极两端，Ra 、Rb 分别表示电极材料本身的电阻，Cab 表示研究电极与辅助电极之间的电容，Cd 与Cd ’表示研究电极和辅助电极的双电层电容，Zf 与Zf ’表示研究电极与辅助电极的交流阻抗。通常称为电解阻抗或法拉第阻抗，其数值决定于电极动力学参数及测量信号的频率，Rl 表示辅助电极与工作电极之间的溶液 电阻。一般将双电层电容Cd 与法拉第阻抗的并联称为界面阻抗Z 。 实际测量中，电极本身的内阻很小，且辅助电极与工作电极之间的距离较大，故电容Cab 一般远远小于双电层电容Cd 。如果辅助电极上不发生电化学反映，即Zf ’特别大，又使辅助 电极的面积远大于研究电极的面积（例如用大的铂黑电极），则Cd ’很大，其容抗Xcd ’比串 联电路中的其他元件小得多，因此辅助电极的界面阻抗可忽略，于是图1可简化成图2，这也是比较常见的等效电路。 图2. 用大面积惰性电极为辅助电极时电解池的简化电路 Element Freedom Value Error Error %Rs Free(+)2000N/A N/A Cab Free(+)1E-7N/A N/A Cd Fixed(X)0N/A N/A Zf Fixed(X)0N/A N/A Rt Fixed(X)0N/A N/A Cd'Fixed(X)0N/A N/A Zf'Fixed(X)0N/A N/A Rb Free(+)10000N/A N/A Data File: Circuit Model File:C:\Sai_Demo\ZModels\12861 Dummy Cell.mdl Mode: Run Fitting / All Data Points (1 - 1) Element Freedom Value Error Error %Rs Fixed(X )1500N/A N/A Zf Fixed(X )5000N/A N/A Cd Fixed(X ) 1E-6 N/A N/A Data File: Circuit Model File:C:\Sai_Demo\ZModels\Tutor3 R-C.mdl Mode: Run Simulation / Freq. Range (0.01 - 10000Maximum Iterations: 100 B 电化学交流阻抗谱（可编辑） Work report 万逸电化学交流阻抗谱注意事项: 1. Rp近似Rct+Zw，但不是完全的相等 2. 极化阻抗通过计划曲线也可以得到 (腐蚀电位出切线的斜率) . 等效电路元件下一步计划: 2. 动电位极化曲线简介极化的分类极化曲线获取信息腐蚀电位 Ecorr ，腐蚀电流(icorr) 获得Tafel参数(阴极极化斜率ba，阳极极化斜率bk) 研究防腐蚀机理，可以知道是阳极机制剂、阴极抑制剂或者是混合型抑制剂。通过腐蚀电流可以计算腐蚀抑制效率(IE% 1-i1.corr/i2.corr) 极化曲线在腐蚀与防护中应用线性极化简介活化控制的腐蚀体系线性极化法铝合金在含有氯离子的乙二醇-硼酸溶液中的腐蚀行为研究氨基苯唑在3.5% NaCl中铜镍合金的防腐蚀的研究缓蚀剂的存在改变了阳极钝化过程，使铜镍合金更加容易钝化，增加抗腐蚀的性能。 * 1. 电化学交流阻抗谱简介 1.1 交流阻抗谱方法是一种以小振幅的正弦波电位为扰动信号的电测量方法。优点: 体系干扰小提供多角度的界面状态与过程的信息，便于分析腐蚀缓蚀作用机理数据分析过程相对简单，结果可靠缺点: 复杂的阻抗谱的解释 1.2 物理参数和等效电路元件物理参数溶液电阻 (Rs) 双电层电容 (Cdl) 极化阻抗 (Rp) 电荷转移电阻 (Rct) 扩散电阻 (Zw) 界面电容 (C)和常相角元件(CPE) 电感 (L) 对电极和工作电极之间电解质之间阻抗工作电极与电解质之间电容当电位远离开路电位时时，导致电极表面电流产生，电流受到反应动力学和反应物扩散的控制。电化学反应动力学控制反应物从溶液本体扩散到电极反应界面的阻抗通常每一个界面之间都会存在一个电容。溶液电阻 (Rs) B. 极化阻抗 (Rp) C. 电荷转移电阻 (Rct) D. 扩散电阻(Zw) E. 界面电容 (C) 和常相角元件(CPE) R 阻抗 C 电容 L 电感 W 无限扩散阻抗 O 有限扩散阻抗 Q 常相角元件阻抗导纳 1.3 等效电路 (A)一个时间常数 Nyquist图相位图 电化学阻抗谱的应用及其解析方法 交流阻抗发式电化学测试技术中一类十分重要的方法，是研究电极过程动力学和表面现象的重要手段。特别是近年来，由于频率响应分析仪的快速发展,交流阻抗的测试精度越来越高，超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步，对阻抗谱解析的自动化程度越来越高，这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的诱发、发展、终止以及活性物质的吸脱附过程。 1.阻抗谱中的基本元件 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R，纯电容C，阻抗值为1/jωC，纯电感L，其阻抗值为jωL。实际测量中，将某一频率为ω的微扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应所引起的阻力均视为电阻，则等效电路如图1所示。 图1. 用大面积惰性电极为辅助电极时电解池的等效电路 图中A、B 分别表示电解池的研究电极和辅助电极两端，Ra、Rb分别表示电极材料本身的电阻，Cab表示研究电极与辅助电极之间的电容，Cd与Cd’表示研究电极和辅助电极的双电层电容，Zf与Zf’表示研究电极与辅助电极的交流阻抗。通常称为电解阻抗或法拉第阻抗，其数值决定于电极动力学参数及测量信号的频率，Rl表示辅助电极与工作电极之间的溶液电阻。一般将双电层电容Cd与法拉第阻抗的并联称为界面阻抗Z。 实际测量中，电极本身的内阻很小，且辅助电极与工作电极之间的距离较大，故电容Cab一般远远小于双电层电容Cd。如果辅助电极上不发生电化学反映，即Zf’特别大，又使辅助电极的面积远大于研究电极的面积（例如用大的铂黑电极），则Cd’很大，其容抗Xcd’比串联电路中的其他元件小得多，因此辅助电极的界面阻抗可忽略，于是图1可简化成图2，这也是比较常见的等效电路。 图2. 用大面积惰性电极为辅助电极时电解池的简化电路 2.阻抗谱中的特殊元件 以上所讲的等效电路仅仅为基本电路，实际上，由于电极表面的弥散效应的存在，所测得的双电层电容不是一个常数，而是随交流信号的频率和幅值而发生改变的，一般来讲，弥散效应主要与电极表面电流分布有关，在腐蚀电位附近，电极表面上阴、阳极电流并存，当介质中存在缓蚀剂时，电极表面就会为缓蚀剂层所覆盖，此时，铁离子只能在局部区域穿透缓蚀剂层形成阳极电流，这样就导致电流分布极度不均匀，弥散效应系数较低。表现为容抗弧变“瘪”，如图3所示。另外电极表面的粗糙度也能影响弥散效应系数变化，一般电极表面越粗糙，弥散效应系数越低。 2.1常相位角元件（Constant Phase Angle Element，CPE） 在表征弥散效应时,近来提出了一种新的电化学元件CPE,CPE的等效电路解析式为：，CPE的阻抗由两个参数 锂离子电池的电化学阻抗谱分析 1. 锂离子电池的特点 锂离子电池充电时，正极中的锂离子从基体脱出，嵌入负极；而放电时，锂离子会从负极中脱出，嵌入正极。因此锂离子电池正负极材料的充放电容量、循环稳定性能和充放电倍率等重要特性均与锂离子在嵌合物电极材料中的脱出和嵌入过程密切相关。这些过程可以很好地从电化学阻抗谱（EIS ）的测量与解析中体现出来。 2. 电化学阻抗谱的解析 2.1. 高频谱解析 嵌合物电极的EIS 谱的高频区域是与锂离子通过活性材料颗粒表面SEI 膜的扩散迁移相关的半圆（高频区域半圆），可用一个并联电路R SEI /C SEI 表示。 R SEI 和C SEI 是表征锂离子活性材料颗粒表面SEI 膜扩散迁移过程的基本参数，如何理解R SEI 和C SEI 与SEI 膜的厚度、时间、温度的关系，是应用EIS 研究锂离子通过活性材料颗粒表面SEI 膜扩散过程的基础。 2.1.1. 高频谱解析R SEI 和C SEI 与SEI 膜厚度的关系 SEI 膜的电阻R SEI 和电容C SEI 与SEI 膜的电导率、介电常数 的关系可用简单的金属导线的电阻公式和平行板电容器的电容公式表达出来 S l R SEI ρ= (1) l S C SEI ε= (2) 以上两式中S 为电极的表面积，l 为SEI 膜的厚度。倘若锂离子在嵌合物电极的 嵌入和脱出过程中、和S 变化较小，那么R SEI 的增大和C SEI 的减小就意味着SEI 厚度的增加。由此根据R SEI 和C SEI 的变化，可以预测SEI 膜的形成和增长情况（这是理解高频容抗弧的关键）。 2.1.2. SEI 膜的生长规律（R SEI 与时间的关系） 嵌合物电极的SEI 膜的生长规律源于对金属锂表面SEI 膜的生长规律的分析而获得。对金属锂电极而言，SEI 膜的生长过程可分为两种极端情况：（A ）锂电极表面的SEI 膜不是完全均匀的，即锂电极表面存在着锂离子溶解的阳极区域和电子穿过SEI 膜导致的溶剂还原的阴极区域；（B ）锂电极表面的SEI 膜是完全均匀的，其表面不存在阴极区域，电子通过SEI 膜扩散至电解液一侧为速控步骤。这对于低电位极化下的炭负极和过渡金属氧化物负极以及过渡金属磷酸盐正极同样具有参考价值。下面分别讨论这两种情况。 （A ）锂电极的SEI 膜不完全均匀 电极过程的推动力源自金属锂与电解液组分之间的电位差 V M-S 。假设：（1）腐蚀电流服从欧姆定律；（2）SEI 膜的电子导电率（ e ）随时间变化保持不变，此时腐蚀电流密度可表示为： l V i e S M corr ρ/-?= (3) 式中导电率e 的量纲为 m ，SEI 膜的厚度l 的量纲为m 。通过比较（3）式两端的量纲，可以判断公式成立。 进一步假设腐蚀反应的全部产物都沉积到锂电极上，形成一个较为均匀的薄膜，那么 corr Ki dt dl = (4) K 为常数，其量纲为m 3A -1s -1。 电化学阻抗谱的应用及其解析方法 董泽华 华中科技大学 交流阻抗发式电化学测试技术中一类十分重要的方法,是研究电极过程动力学和表面现象的重要手段。特别是近年来,由于频率响应分析仪的快速发展,交流阻抗的测试精度越来越高,超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步,对阻抗谱解析的自动化程度越来越高,这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的诱发、发展、终止以及活性物质的吸脱附过程。 1. 阻抗谱中的基本元件 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R ，纯电容C ，阻抗值为1/j ωC ，纯电感L ，其阻抗值为j ωL 。实际测量中，将某一频率为ω的微扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应所引起的阻力均视为电阻，则等效电路如图1所示。 Element Freedom Value Error Error %Rs Free(+)2000N/A N/A Cab Free(+)1E-7N/A N/A Cd Fixed(X)0N/A N/A Zf Fixed(X)0N/A N/A Rt Fixed(X)0N/A N/A Cd'Fixed(X)0N/A N/A Zf'Fixed(X)0N/A N/A Rb Free(+)10000N/A N/A Data File: Circuit Model File:C:\Sai_Demo\ZModels\12861 Dummy Cell.mdl Mode: Type of Weighting: Data-Modulus 图1.用大面积惰性电极为辅助电极时电解池的等效电路 图中AB 分别表示电解池的研究电极和辅助电极两端，Ra,Rb 分别表示电极材料本身的电阻,Cab 表示研究电极与辅助电极之间的电容,Cd 与Cd ’表示研究电极和辅助电极的双电层电容,Zf 与Zf ’表示研究电极与辅助电极的交流阻抗。通常称为电解阻抗或法拉第阻抗，其数值决定于电极动力学参数及测量信号的频率，Rl 表示辅助电极与工作电极之间的溶液电阻。一般将双电层电容Cd 与法拉第阻抗的并联称为界 面阻抗Z 。 实际测量中，电极本身的内阻很小，且辅助电极与工作电极之间的距离较大，故电容Cab 一般远远小于双电层电容Cd 。如果辅助电极上不发生电化学反映，即Zf ’特别大，又使辅助电极的面积远大于研 究电极的面积（例如用大的铂黑电极），则Cd ’很大，其容抗Xcd ’比串联电路中的其他元件小得多,因此辅 助电极的界面阻抗可忽略,于是图1可简化成图2，这也是比较常见的等效电路。 Element Freedom Value Error Error % Rs Fixed(X )1500N/A N/A Zf Fixed(X )5000N/A N/A Cd Fixed(X )1E-6N/A N/A Data File:Circuit Model File:C:\Sai_Demo\ZModels\Tutor3 R-C.mdl Mode: Run Simulation / Freq. Range (0.01 - 100Maximum Iterations: 100Optimization Iterations: Type of Fitting: Complex 图2.用大面积惰性电极为辅助电极时电解池的简化电路 2. 阻抗谱中的特殊元件 以上所讲的等效电路仅仅为基本电路，实际上，由于电极表面的弥散效应的存在，所测得的双电层电容不是一个常数，而是随交流信号的频率和幅值而发生改变的，一般来讲，弥散效应主要与电极表面电流分布有关，在腐蚀电位附近，电极表面上阴、阳极电流并存，当介质中存在缓蚀剂时，电极表面就会为缓蚀剂层所覆盖，此时，铁离子只能在局部区域穿透缓蚀剂层形成阳极电流，这样就导致电流分布 极度不均匀，弥散效应系数较低。表现为容抗弧变“瘪”，如图3所示。另外电极表面的粗糙度也能影响弥散效应系数变化，一般电极表面越粗糙，弥散效应系数越低。 2.1 常相位角元件（Constant Phase Angle Element ，CPE ） 电化学曲线极化曲线阻抗谱分析 1 / 4 电化学曲线极化曲线阻抗谱分析 一、极化曲线 1.绘制原理 铁在酸溶液中，将不断被溶解，同时产生H2，即：Fe + 2H+ = Fe2+ + H2 (a) 当电极不与外电路接通时，其净电流I 总为零。在稳定状态下，铁溶解的阳极电流I(Fe)和H ＋还原出H2的阴极电流I(H)，它们在数值上相等但符号相反，即： (1) I(Fe)的大小反映Fe 在H+中的溶解速率，而维持I(Fe)，I(H)相等时的电势称为Fe ／H+体系的自腐蚀电势εcor 。 图1是Fe 在H+中的阳极极化和阴极极化曲线图。 图2 铜合金在海水中典型极化曲线 当对电极进行阳极极化(即加更大正电势)时，反应(c)被抑制，反应(b)加快。此时，电化学过程以Fe 的溶解为主要倾向。通过测定对应的极化电势和极化电流，就可得到Fe ／H+体系的阳极极化曲线rba 。 当对电极进行阴极极化，即加更负的电势时，反应(b)被抑制，电化学过程以反应(c)为主要倾向。同理，可获得阴极极化曲线rdc 。 2.图形分析 （1）斜率 斜率越小，反应阻力越小，腐蚀速率越大，越易腐蚀。 斜率越大，反应阻力越大，腐蚀速率越小，越耐腐蚀。 （2）同一曲线上各各段形状变化 如图2，在section2中，电流随电位升高的升高反而减小。这是因为此次发生了钝化现象，产生了致密的氧化膜，阻碍了离子的扩散，导致腐蚀电流下降。 （3）曲线随时间的变动 以 7天和0天两曲线为例，对于Y 轴，七天后曲线下移（负移），自腐蚀电位降低，说明更容易腐蚀。对于X 轴，七天后曲线正移，腐蚀电流增大，亦说明更容易腐蚀。 二、阻抗谱 1.测量原理 它是基于测量对体系施加小幅度微扰时的电化学响应，在每个测量的频率点的原始数据中，都包含了施加信号电压（或电流）对测得的信号电流（或电压）的相位移及阻抗的幅模值。从这些数据中可以计算出电化学响应的实部和虚部。阻抗中涉及的参数有阻抗 电化学阻抗谱的应用及其解析方法 1 2 交流阻抗发式电化学测试技术中一类十分重要的方法,是研究电极过程动力学和表面现 3 象的重要手段。特别是近年来,由于频率响应分析仪的快速发展,交流阻抗的测试精度越来越 4 高,超低频信号阻抗谱也具有良好的重现性，再加上计算机技术的进步,对阻抗谱解析的自动 5 化程度越来越高,这就使我们能更好的理解电极表面双电层结构，活化钝化膜转换，孔蚀的 6 诱发、发展、终止以及活性物质的吸脱附过程。 7 1. 阻抗谱中的基本元件 8 交流阻抗谱的解析一般是通过等效电路来进行的，其中基本的元件包括：纯电阻R ，纯9 电容C ，阻抗值为1/j ωC ，纯电感L ，其阻抗值为j ωL 。实际测量中，将某一频率为ω的微10 扰正弦波信号施加到电解池，这是可把双电层看成一个电容，把电极本身、溶液及电极反应11 所引起的阻力均视为电阻，则等效电路如图1所示。 12 Element Freedom Value Error Error % Rs Free(+)2000N/A N/A Cab Free(+)1E-7N/A N/A Cd Fixed(X)0N/A N/A Zf Fixed(X)0N/A N/A Rt Fixed(X)0N/A N/A Cd'Fixed(X)0N/A N/A Zf'Fixed(X)0N/A N/A Rb Free(+)10000N/A N/A Data File: Circuit Model File:C:\Sai_Demo\ZModels\12861 Dummy Cell.mdl Mode: Run Fitting / All Data Points (1 - 1)Maximum Iterations:100Optimization Iterations:0Type of Fitting: Complex Type of Weighting: Data-Modulus 13 图1.用大面积惰性电极为辅助电极时电解池的等效电路 14 15 图中AB 分别表示电解池的研究电极和辅助电极两端，Ra,Rb 分别表示电极材料本身的16 电阻,Cab 表示研究电极与辅助电极之间的电容,Cd 与Cd ’表示研究电极和辅助电极的双电17 层电容,Zf 与Zf ’表示研究电极与辅助电极的交流阻抗。通常称为电解阻抗或法拉第阻抗， 18 其数值决定于电极动力学参数及测量信号的频率，Rl 表示辅助电极与工作电极之间的溶液19 电阻。一般将双电层电容Cd 与法拉第阻抗的并联称为界面阻抗Z 。 20 实际测量中，电极本身的内阻很小，且辅助电极与工作电极之间的距离较大，故电容 21电化学阻抗谱的应用分析
电化学交流阻抗谱(可编辑)
电化学阻抗谱的应用及其解析方法
内容(十三)锂离子电池的电化学阻抗谱分析报告
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