Method of determining the Complex Capacitance of an Electrochemical System and Complex Capacitance Detection System of using the same

Abstract

A method for detecting the complex capacitance of an electrochemical system and a system for detecting complex capacitance using said method are disclosed. A rheological state vector is used, a coordinate transformation is performed, and then a variable substitution operation is performed. Through the variable substitution operation, a state vector of an electrochemical signal is formed. A longitudinal normal vector for the state vector is formed, and the complex capacitance that changes instantaneously is derived.

Description

Technology Field

[0001] The present invention relates to a technique for deriving the nonlinear response of an electrochemical system by analyzing it, and more specifically, to a method for calculating instantaneous complex capacitance using geometric state vectors based on voltage-current-charge time domain data and a complex capacitance detection system. Background Technology

[0002] An electrochemical system is a system in which various elements such as resistance, capacitance, and diffusion coexist. For example, in the relationship between electrodes and electrolytes, various factors such as charge transfer resistance, double-layer capacitance, diffusion impedance, and reaction rate-governing steps act sequentially or simultaneously. Since these elements exhibit different responses depending on time, speed, and frequency, it is impossible to distinguish and interpret them solely through current-voltage measurements.

[0003] Electrochemical Impedance Spectroscopy (EIS) involves applying a sinusoidal wave with a specific frequency and amplitude to an electrochemical system under measurement and measuring the response signal. The impedance, expressed as a complex number, is derived from the response signal. Additionally, as the measurement frequency is changed, the impedance corresponding to the changed frequency is derived. Finally, various electrochemical characteristics of the electrochemical system, such as charge transport and diffusion, are derived through spectrum analysis.

[0004] The above electrochemical impedance spectroscopy is used to diagnose battery performance or to evaluate the performance of various electrochemical systems.

[0005] As mentioned above, electrochemical impedance spectroscopy is performed through impedance analysis of small signals based on linearity. However, actual electrochemical systems exhibit nonlinear response characteristics due to the intervention of various factors.

[0006] Various techniques have been proposed for the analysis of nonlinear responses. For example, Total Harmonic Distortion (THD) or Fourier-based harmonic analysis is used. However, these methods cannot track time-varying nonlinear responses in real time, and there are difficulties in physically interpreting the simultaneous nonlinear behavior of current and charge.

[0007] Meanwhile, the field of Large Amplitude Oscillatory Shear (LAOS) analyzes the nonlinear viscoelastic behavior of materials in rheology. It involves applying shear deformation of large amplitude to a material and measuring the resulting stress response. Distortion of stress waveforms is observed in the nonlinear region, through which information regarding changes in the material's internal structure is obtained.

[0008] In the field of LAOS, the analysis of nonlinear viscoelastic behavior is performed using Lissajous curves.

[0009] The above technique is used to analyze the nonlinear rheological properties of materials. In the field of LAOS, the Sequence of Physical Processes (SPP) technique is used to interpret the temporal variation patterns of nonlinear responses. SPP is a type of analytical tool that derives plane equations using shear stress, shear strain, and strain rate in linear viscoelastic and nonlinear viscoelastic regions, and plots trajectories in these regions. Through this, the storage modulus and loss modulus are derived.

[0010] The aforementioned technique is used to analyze nonlinear stress responses in rheology. In particular, while various analytical techniques provide meaningful data on nonlinear phenomena and instantaneous changes, they are currently not applicable to electrochemical analysis. The problem to be solved

[0011] The first technical problem to be achieved by the present invention is to provide a method for detecting complex capacitance that changes in real time in an electrochemical system by applying rheological techniques.

[0012] In addition, the second technical objective of the present invention is to provide a complex capacitance detection system using the detection method provided through the first technical objective. means of solving the problem

[0013] The present invention, for achieving the first technical objective described above, provides a method for detecting complex capacitance comprising: a step of obtaining an electrochemical signal having a voltage V, a current I, and a charge Q by applying a voltage to an electrochemical system; a step of deriving a state vector A(t) of the electrochemical signal based on a state vector based on shear stress σ, shear strain γ, and elastic modulus G defined in rheology; and a step of deriving a longitudinal normal vector B'(t) from the state vector A(t) and deriving the complex capacitance through a plane equation of the state vector A(t).

[0014] The present invention, for achieving the second technical objective described above, provides a complex capacitance detection system comprising: a data measuring unit that applies a voltage V to an electrochemical system and measures a current I and a charge Q to obtain an electrochemical signal composed of the voltage V, the current I, and the charge Q; a state vector forming unit that receives the electrochemical signal from the data measuring unit and derives a state vector A(t) of the electrochemical signal based on a state vector based on shear stress σ, shear strain γ, and elastic modulus G defined in rheology; and a complex capacitance calculation unit that receives the state vector A(t), derives a longitudinal normal vector B'(t) from the state vector A(t), and derives a complex capacitance through a plane equation of the state vector A(t). Effects of the invention

[0015] According to the present invention described above, the complex capacitance, which changes instantaneously through the measured voltage and current, can be tracked in real time. In particular, the complex capacitance is derived through the operation of a plane equation that considers coordinate transformation, variable substitution, and behavior in a nonlinear region, and this has a tendency consistent with the actual measured data. Through this, the complex capacitance of an electrochemical system can be derived in real time. Brief explanation of the drawing

[0016] FIG. 1 is a block diagram illustrating a detection system for deriving the complex capacitance of an electrochemical system according to a preferred embodiment of the present invention. Figure 2 shows graphs illustrating the impedance in the linear region of an electrochemical system according to a measurement example of the present invention. Figure 3 is a graph showing a Lisza curve to confirm the nonlinear characteristics of an electrochemical system according to a measurement example of the present invention. Figure 4 is a graph showing the complex capacitance component obtained through calculations using the voltage and current obtained according to the measurement example of the present invention, through coordinate axis transformation, variable substitution, and derivation of complex capacitance according to the present embodiment. Specific details for implementing the invention

[0017] The present invention is susceptible to various modifications and may take various forms; therefore, specific embodiments are illustrated in the drawings and described in detail in the text. However, this is not intended to limit the invention to the specific disclosed forms, and it should be understood that the invention includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention. Similar reference numerals have been used for similar components in the description of each drawing.

[0018] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as generally understood by those skilled in the art to which the present invention pertains. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology, and should not be interpreted in an ideal or overly formal sense unless explicitly defined in this application.

[0019] Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the attached drawings.

[0021] Examples

[0022] FIG. 1 is a block diagram illustrating a detection system for deriving the complex capacitance of an electrochemical system according to a preferred embodiment of the present invention.

[0023] Referring to FIG. 1, the detection system has a data measurement unit (100), a state vector forming unit (200), and a complex capacitance calculation unit (300).

[0024] The above data measuring unit (100) applies a voltage to the electrochemical system (10) and measures the applied voltage. In addition, an operation to measure the current flowing through the electrochemical system (10) is performed.

[0025] The voltage applied from the data measuring unit (100) takes the form of a sinusoidal wave with a constant amplitude. Additionally, the current is determined by the impedance of the electrochemical system (10). When the flow of current is integrated over time, the amount of charge is determined. Therefore, the voltage V, current I, and amount of charge Q are determined through the data measuring unit (100). These constitute an electrochemical signal that changes over time.

[0026] The electrochemical signals obtained from the above data measurement unit (100) are input to the state vector forming unit (200).

[0027] The state vector forming unit (200) has plane equations for linear viscoelastic regions and nonlinear viscoelastic regions through shear stress σ, shear strain γ, storage modulus G' and loss modulus G" in the rheological SPP.

[0028] The plane equation is It follows the state vector of the axis. In the state vector forming unit (200), through coordinate axis transformation Forming a coordinate system, Through variable substitution for the coordinate system Forms a state vector within the coordinate axes. In the above coordinate system refers to dγ / dt, and refers to dσ / dt. Also, refers to dV / dt. Formed through the above variable substitution The coordinate system It can also be used as a coordinate system. This is because the current I is attributed to dQ / dt. As described below The coordinate system It is explained as a concept that also includes coordinate systems. In addition, the explained state vector Is It can be expanded to.

[0029] Hereinafter, in the process of deriving the instantaneous complex capacitance using the state vector A(t) in the present invention, the charge quantity Q can be substituted with the current I, and the formula explained based on the charge quantity Q needs to be interpreted as including the current I.

[0030] formed state vector The values ​​of the real and imaginary parts of the complex capacitance are derived through the complex capacitance calculation unit (200).

[0031] Below, the method for detecting complex capacitance is explained in a time-series manner.

[0032] In the state vector generation section, through coordinate axis transformation and variable substitution operations Derive the state vector A(t) of the coordinate system.

[0033] The above state vector is a vector representing the response of the electrochemical system, and ε is the time rate of change of the voltage response, and when divided by the angular velocity w, it becomes a dimensionless and standardized value. Additionally, Q(t) represents the amount of electric charge as another state variable of the electrochemical system.

[0034] This is the normalized current state variable V(t) and the time rate of change of the state variable dV(t) / dt, and Q(t) represents an additional state.

[0035] First, for coordinate axis transformation In the linear viscoelastic region based on the axis, the plane equation of Equation 1 below is used.

[0036] [Formula 1]

[0037]

[0038] In the above formula 1 is the time rate of change of shear strain and is equal to dγ / dt.

[0039] In the linear region, the Lissajous curve forms a static plane. However, in the non-linear region, the position modulus is added to the above formula. This position modulus serves as an indicator reflecting yielding or residual deformation, moving away from the viscoelastic region.

[0040] When expressed as a Lissajous curve, a symmetric ellipse is formed in the linear region depending on the phase difference. However, depending on the phase difference between the input and output, the symmetric ellipse appears close to a straight line.

[0041] On the other hand, in the nonlinear region, the ellipse is distorted, and effects depending on amplitude, phase difference, and frequency appear.

[0042] In addition, the above equation is Forms an axis-based plane.

[0043] Next, the above Through coordinate axis transformation with respect to the axis A coordinate system is formed. The above coordinate axis transformation is achieved through the introduction of a coordinate transformation matrix.

[0044] Next Variable substitution operations are performed in the coordinate system.

[0045] The substitution of the above variables is based on replacing the input shear stress σ with voltage V and the shear strain γ with charge Q. dQ / dt is the current I, and this is dγ / dt(= It is replaced with ).

[0046] In large-amplitude vibratory shear, if the input is defined as a shear strain γ with amplitude γ0 and angular velocity w, the response shear stress is expressed as Equation 2.

[0047] [Equation 2]

[0048]

[0049] In the above formula 2 It is defined as the positional modulus, an indicator that reflects yield or residual deformation.

[0050] In addition, considering the above variable substitution, the elastic modulus G can be substituted with 1 / C. Therefore, in large-amplitude oscillating shear, the variables of SPP and the variables in the electrochemical system have the following correspondence and substitution relationships, which are summarized in Table 1 below.

[0051] Large-amplitude vibration variation electrochemical systems Shear stress σ Voltage V Shear strain γ Electric charge Q Time rate of change of shear strain Current I Elastic modulus G Reciprocal of capacitance 1 / C

[0052] Through the above coordinate axis transformation and variable substitution operations, the rheological plane equation Equation 1 below can be expressed as the plane equation of the electrochemical system Equation 3 below.

[0053] [Equation 3]

[0054]

[0055] In Equation 3 above, C' represents the real part of the complex capacitance of the electrochemical system and indicates the charge storage capacity. Also, C" represents the imaginary part of the complex capacitance and indicates the degree of charge loss. Furthermore, since Equation 1 above represents the linear region, Equation 3 above also indicates that the behavior of the electrochemical system occurs in the linear region.

[0056] The plane equation of the transformed electrochemical system is a state vector It is expressed as, The state vector within the coordinate axes is expressed as in Equation 4.

[0057] [Equation 4]

[0058]

[0059] In the above Equation 4 and represents the magnitude of the state vector on the V-axis that changes instantaneously at a specific time t with the same value, and Is At t with the same value as Represents the magnitude of the state vector on the axis, and Represents the magnitude of the state vector on the Q-axis at t with the same value as .

[0060] The above state vector A(t) is input to the complex capacitance calculation unit. The complex capacitance calculation unit receives the state vector A(t), which is formed based on the electrochemical signal measured in the electrochemical system, derives the longitudinal normal vector, and then calculates the instantaneous charge Q in the nonlinear region. Additionally, through calculation, it derives the real and imaginary parts of the complex capacitance based on the instantaneous charge.

[0061] First, a binormal vector B'(t) is derived based on the received state vector A(t). The binormal vector B'(t) is derived from the cross product of the unit normal vector and the principal unit normal vector from the spatial trajectory of the state variable A(t).

[0062] The unit binormal vector B'(t) is equal to Equation 5 below.

[0063] [Formula 5]

[0064]

[0065] In the above Equation 5 represents dA(t) / dt, and the trajectory formed by the state vector at a specific time t represents the tangential direction, and is d 2 A(t) / dt 2 It represents the direction of curvature of the trajectory. The binormal vector B'(t) represents the direction of the normal to the plane instantaneously formed by the trajectory. Since this indicates a different direction as time t elapses, In the coordinate system, component values ​​change over time.

[0066] This It is expressed.

[0067] Using the above-mentioned binormal vector, the plane equation in the form of a point-normal at a specific instantaneous state A of the plane is given by Equation 6 below.

[0068] [Equation 6]

[0069]

[0070] In the plane equation of Equation 6 above, the component intersecting the Q-axis is V and It can be obtained by setting the component to 0. Therefore, the Q-axis intersection component Q I It is displayed as in Formula 7.

[0071] [Equation 7]

[0072]

[0073] In addition, the Q-axis intersection component Q in Equation 7 above I is the charge at the intersection point of the Lissajous curve, corresponding to the difference between the Q value in the non-linear region and the Q value in the linear region.

[0074] The plane equation in a linear domain In this case, considering the nonlinear characteristics due to instantaneous changes in voltage and charge, the intersection component Q of the Q-axis I ... must be reflected, and this is expressed as shown in Formula 8 below.

[0075] [Equation 8]

[0076]

[0077] In, the Q-axis value Q(t) of the state vector and A Q Since (t) is mutually identical, the following equation is obtained.

[0078] This is summarized and expressed as Equation 9.

[0079] [Formula 9]

[0080]

[0081] Therefore, the real component of the instantaneous capacitance in Equation 9 above It becomes, and the imaginary component of the instantaneous capacitance This becomes.

[0082] Complex capacitance C reflecting the derived real and imaginary components * (t) is expressed as follows.

[0083]

[0084] The real component of capacitance in the above formula An increase indicates that the charge storage capacity of the electrochemical system increases in real time, and If it has a negative value, it indicates that the inductor component is dominant.

[0085] also, As increases, it indicates that the loss of charge increases in real time, and If it has a negative value, it indicates that energy loss is minimal and an ideal cycle is achieved.

[0086] Through the above-described operation, a complex capacitance that fluctuates in real time in an electrochemical system can be derived.

[0088] Measurement example

[0089] Distilled water is used as the electrolyte in the electrochemical system, and rod-type platinum electrodes are used. The spacing between the platinum electrodes is 1 cm. An AC voltage in the form of an amplitude sine wave is applied through the platinum electrodes, and the impedance is measured using the measuring instrument Zive SP1 while varying the frequency. Through this, the change in impedance in the linear region is investigated.

[0090] Figure 2 shows graphs illustrating the impedance in the linear region of an electrochemical system according to a measurement example of the present invention.

[0091] Referring to FIG. 2(a), the x-axis represents the real part of the complex impedance, and the y-axis represents the imaginary part. It is observed that the change in impedance appears linearly with increasing frequency. The supplied input voltage V has an amplitude of 10 mV.

[0092] Referring to Figure 2(b), under the condition of an amplitude of 10 mV, the frequency is varied from 0.1 Hz to 1,000 Hz. From 10 Hz to 1,000 Hz, the magnitude of the impedance is constant, and the phase also has a constant value. That is, almost no change in the capacitance of the electrolyte is observed with respect to the change in frequency, and pure resistance characteristics are exhibited. However, around 0.1 Hz, a decrease in impedance occurs with increasing frequency, which is attributed to the influence of capacitance expressed as 1 / wC.

[0093] In other words, it is expected that nonlinear behavior will appear at low frequencies in electrochemical systems using water.

[0094] To verify the nonlinear behavior of the electrochemical system, a signal with an amplitude of 500 mV is used, and frequencies of 0.1 Hz, 1 Hz, 10 Hz, and 100 Hz are employed. Current is measured according to the applied voltage, and 10 measurement cycles are applied for each frequency.

[0095] Figure 3 is a graph showing a Lisza curve to confirm the nonlinear characteristics of an electrochemical system according to a measurement example of the present invention.

[0096] Referring to Fig. 3, at a frequency of 0.1 Hz, the frequency remains constant, but the Lissajous curve has an elliptical shape. This is attributed to the phase difference between the voltage and current caused by the capacitance component, as explained in Fig. 2 above. As the frequency increases, the change in the phase difference decreases, and at 100 Hz, the Lissajous curve forms a linear straight line. In other words, no phase difference occurs between the voltage and current, and only the pure resistive component appears.

[0097] Figure 4 is a graph showing the complex capacitance component obtained through calculations using the voltage and current obtained according to the measurement example of the present invention, through coordinate axis transformation, variable substitution, and derivation of complex capacitance according to the present embodiment.

[0098] Referring to Fig. 4, under conditions where four types of frequencies are supplied with an amplitude of 500 mV, each frequency is applied in 10 cycles. In addition, to ensure the stability of the measurement, the complex capacitance is calculated based on the voltage and current of the 10th applied signal.

[0099] Under a frequency condition of 0.1 Hz, the instantaneous change in capacitance appears as a graph, and a change in complex capacitance in the shape of a triangle, which is a typical nonlinear characteristic, is derived. However, as the frequency increases, the change in capacitance appears as a dotted line from the triangular shape, and at 100 Hz, the capacitance component appears close to zero. This demonstrates that the calculation of complex capacitance according to the present invention tends to match the physically measured Lizeau curve.

[0101] According to the present invention described above, the complex capacitance, which changes instantaneously through the measured voltage and current, can be tracked in real time. In particular, the complex capacitance is derived through the operation of a plane equation that considers coordinate transformation, variable substitution, and behavior in a nonlinear region, and this has a tendency consistent with the actual measured data. Through this, the complex capacitance of an electrochemical system can be derived in real time. Explanation of the symbols

[0102] 100: Data measurement unit 200: State vector forming unit 300 : Complex capacitance calculation unit

Claims

Claim 1 A method for detecting complex capacitance, comprising: a step of obtaining an electrochemical signal having a voltage V, a current I, and a charge Q by applying a voltage to an electrochemical system; a step of deriving a state vector A(t) of the electrochemical signal based on a state vector based on shear stress σ, shear strain γ, and elastic modulus G defined in rheology; and a step of deriving a longitudinal normal vector B'(t) from the state vector A(t) and deriving the complex capacitance through a plane equation of the state vector A(t). Claim 2 In claim 1, the step of deriving the state vector A(t) of the electrochemical signal is Coordinate system is dγ / dt, where w is angular velocity) Coordinate system is a step of performing a coordinate axis transformation with dσ / dt); and the above Through variable substitution for the coordinate system Coordinate system Converted to dV / dt) the above state vector A method for detecting complex capacitance characterized by including a step of deriving Claim 3 A method for detecting complex capacitance according to paragraph 2, characterized in that the elastic modulus has a substitution relationship of the reciprocal of the complex capacitance. Claim 4 In paragraph 2, the step of deriving the complex capacitance comprises: the step of deriving the longitudinal normal vector B'(t) of the state vector A(t); and using the longitudinal normal vector, the Q of the intersection component of the Q-axis in the coordinate system I A step of deriving; and the intersection component Q of the Q-axis in the plane equation of the state vector A(t); I A method for detecting complex capacitance characterized by including a step of deriving the complex capacitance by applying the above. Claim 5 In paragraph 4, the above-mentioned longitudinal normal vector B'(t) When expressed as, the above Q-axis intersection component Q I A method for detecting complex capacitance characterized by following the following Equation 7. [Equation 7] In the above Equation 7 The above The component of the V-axis vector in the coordinate system, Is The vector component of the axis normal and represents the Q-axis binormal vector component, and Av is the V-axis component of state vector A, is of state vector A Axial components and represents the Q-axis component. Claim 6 In paragraph 5, the above complex capacitance When expressed as, the real part of the above complex capacitance Is With the value of, the imaginary part Is A method for detecting complex capacitance characterized by having a value. Claim 7 A complex capacitance detection system comprising: a data measuring unit that applies a voltage V to an electrochemical system and measures a current I and a charge Q to obtain an electrochemical signal composed of the voltage V, the current I, and the charge Q; a state vector forming unit that receives the electrochemical signal from the data measuring unit and derives a state vector A(t) of the electrochemical signal based on a state vector based on shear stress σ, shear strain γ, and elastic modulus G defined in rheology; and a complex capacitance calculation unit that receives the state vector A(t), derives a longitudinal normal vector B'(t) from the state vector A(t), and derives a complex capacitance through a plane equation of the state vector A(t). Claim 8 In claim 7, the state vector forming part Coordinate system is dγ / dt, where w is angular velocity) Coordinate system ) performs coordinate axis transformation with dσ / dt, and the above Through variable substitution for the coordinate system Coordinate system Converted to dV / dt) the above state vector A complex capacitance detection system characterized by deriving Claim 9 In claim 8, the complex capacitance calculation unit derives the longitudinal normal vector B'(t) of the state vector A(t), and uses the longitudinal normal vector to the Q of the intersection component of the Q-axis in the coordinate system I By deriving the intersection component Q of the Q-axis in the plane equation of the state vector A(t), I A complex capacitance detection system characterized by deriving the complex capacitance by applying the above. Claim 10 In claim 9, the above-mentioned binormal vector B'(t) When expressed as, the above Q-axis intersection component Q I A complex capacitance detection system characterized by following the following Equation 7.[Equation 8] In the above formula 8 The above The component of the V-axis vector in the coordinate system, Is The vector component of the axis normal and represents the Q-axis binormal vector component, and Av is the V-axis component of state vector A, is of state vector A Axial components and represents the Q-axis component. Claim 11 In item 10, the above complex capacitance When expressed as, the real part of the above complex capacitance Is With the value of, the imaginary part Is A complex capacitance detection system characterized by having a value of

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