Method for measuring zeta potential and measuring device

Abstract

The present invention provides a measurement method and a measurement device for Zeta potential with reproducible high reliability and high precision by predicting equilibrium value from temporal change of streaming potential. In measuring Zeta potential on the surface of a sample using a streaming potential method, an external pressure is changed in steps to set a pressure change curve having an ascending phase or a descending phase with a time shorter than a relaxation time τ required for a streaming potential change response to occur with a change in external pressure, and a stable phase in which the pressure is kept in a stable state for a time longer than the relaxation time τ. Then, Zeta potential is calculated using a streaming potential asymptotic value estimated by regression from a transient response of streaming potential generated from the pressure change curve.

Description

Technical Field

[0001] The present invention relates to a method for measuring the zeta potential of a solid surface in contact with a medium and an apparatus for measuring the potential. Background Technology

[0002] When a solid surface comes into contact with a liquid containing water or various organic solvents, or with dissolved salts as ionic dissociative substances, ionic species adsorb onto the solid surface, thereby generating a surface potential. This distribution of ionic species can be represented using a double-layer model. A known double-layer model structure is the Stern model, which consists of a stationary layer in contact with the adsorbed ions and a diffuse layer located outside the stationary layer. The surface potential generated at the solid-liquid interface is measured as the Zeta potential on the slip surface slightly outside the Stern plane at the interface between the stationary and diffuse layers. Because changes in the Zeta potential sensitively reflect the physical and chemical properties of various solid surfaces, it plays a very useful role in analyzing these properties. In particular, it has been used as an indicator for evaluating colloidal dispersion and aggregation, interactions, and surface modification.

[0003] Electrophoresis and similar methods are mainly used to measure the zeta potential of the surface of colloidal and other dispersed particles in a relatively stable dispersed state in liquids. However, when electrophoresis cannot be used to determine the zeta potential in dense systems, coarse particles, fibrous materials, or flat samples, flow potential methods and electroosmotic methods are used.

[0004] Although both methods are used to observe the same physical phenomenon, electroosmosis measures the flow of a sample solution generated by a voltage applied to the electrodes at both ends of the sample cell. The velocity of the osmotic flow varies depending on the distance from the upper and lower surfaces inside the sample cell, thus requiring the addition of monitoring particles and the measurement of the relationship between the distance from the sample cell surface and the particle's velocity. Therefore, the measurement is complex and the accuracy may not always be sufficient.

[0005] In contrast, the flow potential method determines the zeta potential of a solid sample inside a sample cell by measuring the potential or current generated when a pressure difference is applied across the sample cell. Essentially similar to electroosmosis, it can be universally used to measure the zeta potential of solid surfaces of various shapes. As for the parameters to be determined by the flow potential method, it measures the potential difference or current value generated by the applied pressure, and these values ​​can be determined relatively easily and accurately. Non-Patent Literature 1 describes various zeta potential measurement methods, the obtained measurement results, and their relationship with the properties of the solid-liquid interface.

[0006] Traditionally, the properties of solid-liquid interfaces in various materials have been evaluated and studied primarily through knowledge obtained from Zeta potential measurements in aqueous media. Recently, however, there has been a growing demand for Zeta potential measurements in non-aqueous media across various fields. For example, Zeta potentials hold promise for assessing the dispersibility of fibrous materials such as carbon nanotubes in organic solvents, evaluating the impregnation of electrolyte solutions in battery manufacturing, and understanding the relationship between ion transport and electrode reactions. Similarly, the measurement of Zeta potentials at electrode surfaces in electrolytes is increasingly needed to assess the stability and properties of various electrode surfaces in electrolyte solutions.

[0007] Various surface analysis techniques have been used to analyze solid surfaces. However, for practical systems, it is necessary to understand the dynamic state of the electric double layer by in-situ measurement of the zeta potential at the solid-liquid interface of a solid surface placed in a medium. Therefore, measuring the zeta potential of various solid surfaces in a medium is expected to directly provide useful analysis.

[0008] On the other hand, the Helmholtz-Smoluchowski equation, described later, is widely used to calculate the Zeta potential, and the calculated value and its accuracy depend on the viscosity, conductivity, and dielectric constant of the flowing fluid. In most existing flow potential measurement devices, including commercially available ones, the solvent used is limited to water. In the case of aqueous electrolytes, these parameters are limited, and device structures are almost always optimized for these conditions. Because the physical properties of non-aqueous solvents not only vary over these parameter ranges but also because mixed solvents with water are frequently used, it is difficult to design devices capable of handling these parameter ranges. Furthermore, since the materials used in the sample cell and fluid flow area are optimized, it is difficult to limit measurement methods and numerical analyses that rely on these materials; therefore, a universal analytical method for the measured values ​​is constantly being sought.

[0009] The aforementioned Zeta potential measurements primarily focus on solid-liquid interfaces in water. However, Zeta potential measurements present various challenges not only in aqueous systems but also in non-aqueous media, hindering the analysis of the electrochemical behavior of high-concentration colloidal dispersions or porous materials used in many applications. Particularly in Zeta potential measurement methods using flow potential analysis, the resulting flow potential, when pressure is applied to the fluid within the sample cell, cannot be stabilized due to variations in potential values ​​caused by time or hysteresis effects, thus making it difficult to obtain reproducible and reliable values.

[0010] Furthermore, in Non-Patent Literature 2, R.A. Gortner, who contributed to the development of flow potential measurement methods, reported zeta potential measurements of cellulose films or alumina surfaces in various organic solvents. These zeta potential values ​​showed significant variations depending on the length of the alkyl chain in the various aliphatic alcohols, carboxylic acids, and their esters used as organic solvents. Moreover, since the zeta potential values ​​of benzene analogs depend largely on the nature of their substituents, the study suggests that the adsorption behavior between organic compound molecules and solid surfaces can be elucidated by performing zeta potential measurements.

[0011] Traditional double-layer theory is based on the static distribution of ions in a thermodynamically steady state, and the zeta potential is measured and interpreted without considering the dynamic changes at the solid-liquid interface in the fluid.

[0012] However, the properties of the solid-liquid interface change dynamically due to fluctuations in the external electric field or variations in shear stress, and transient states exist before reaching a steady state. In the electric double-layer model, a fixed layer formed by molecules or ions adsorbed on the solid surface and an external diffuse layer are assumed. However, the distribution of ion species at and near these interfaces is sensitive to changes in external pressure or potential. Conversely, it is believed that by analyzing these changing states, it is possible to study the characteristics of the solid-liquid interface in detail. For example, when ions in the electrolyte interact with various alcohol and ester solvent molecules with high dielectric constants, it is generally assumed that higher-order structures formed in the liquid by hydrogen bonds or dipole-ion-dipole interactions are formed through long-range dipole-to-dipole interactions. However, if these higher-order structures deform due to pressure fluctuations applied to the medium, electrostatic relaxation phenomena with relatively long relaxation times can be considered due to this deformation. Furthermore, in the absence of specific ion adsorption, the adsorption state of ions on the solid surface is affected by external pressure fluctuations, potentially leading to ion re-equilibrium adsorption over a longer period. Alternatively, when impregnated with electrolyte in a porous material or when flow paths within the pores are reconstructed due to the movement of a flowing liquid, the ions in the diffused double layer in the surface layer exhibit viscoelastic behavior due to their interaction with the solids in the solution, or the thickness variation of the diffused layer becomes a factor in the double layer. Therefore, the resulting Zeta potential is considered to be influenced by the dynamic relaxation phenomenon of ions in the viscoelastic medium. Furthermore, the properties of the double layer change sharply with variations in external pressure or potential caused by various factors. For example, in the measurement of flow potential, the inventors of this application discovered that the flow potential does not immediately reach equilibrium after being subjected to changes in external pressure, but rather exhibits transient behavior, reaching a steady-state value within a relaxation timeframe after reaching equilibrium. Flow potential measurement is expected to provide a highly advantageous analytical technique for fundamental research on various relaxation processes of this double layer.

[0013] Traditional methods for measuring zeta potential do not consider the transient phenomenon (relaxation process) of the diffused bilayer as described above. Therefore, the measurement results obtained using conventional methods are affected by hysteresis and suffer from reproducibility problems, making it impossible to obtain accurate zeta potential values. Furthermore, analytical results based on these values ​​are questionable, thus significantly hindering the evaluation of electrode materials or research on improvements based on them.

[0014] Non-patent document 3 discloses a method for obtaining a response potential by continuously changing the pressure when measuring the Zeta potential of a solid-liquid interface using the flow potential method. However, since the flow potential is measured when the pressure is continuously rising or falling, the flow potential does not immediately follow the pressure change and is therefore greatly affected by the hysteresis of pressure changes, resulting in an unclear meaning of the obtained apparent Zeta potential value.

[0015] In addition, in Patent Document 1, the Zeta potential is calculated using the following formula based on the rate of change of the flow potential relative to the rate of change of the pressure by continuously changing the pressure in the same manner.

[0016]

Mathematical Formula 1

[0017]

[0018] In the above formula, U str ε represents the measured value of the flow potential when the pressure changes continuously. Δp represents the amount of pressure change. rel ε₀ and ε₀ represent the relative permittivity and vacuum permittivity, respectively. L represents the length of the sample cell, and A represents the cross-sectional area of ​​the sample cell. R represents the fluid resistance.

[0019] Similarly, in this case, if the flow potential cannot instantaneously follow the rate of pressure change, it is impossible to establish a linear relationship between the rate of pressure change and the flow potential based on the above formula, and the Zeta potential value has the problem of low reliability.

[0020] [Patent Documents]

[0021] [Patent Document 1] US Patent Publication No. 2015 / 0330925

[0022] [Non-patent literature]

[0023] [Non-Patent Literature 1] Isayu Takasato, "Measurement of Potential Dynamics at Non-Aqueous Interfaces", Color Materials, 43, 1970, pp. 510-517.

[0024] [Non-patent document 2] RAGortner, "ELECTROKINETICS XXIII.ELECTROKINETICS AS ATOOL FOR THE STUDY OF THE MOLECULAR STRUCTURE OF ORGANIC COMPOUNDS", Trans.Farad.Soc., 35(1940) p63-68.

[0025] [Non-Patent Literature 3] Fumio Kitahara et al., “Comparison of Interfacial Potential Dynamics Measurement Methods for Non-Aqueous Suspensions - Barium Sulfate”, Journal of Industrial Chemistry, Vol. 70, No. 12, 1967, pp. 2222-2225. Summary of the Invention

[0026] The technical problem that the invention aims to solve

[0027] As described above, in the prior art, in the Zeta potential measurement method using the flow potential method, when pressure is applied to the fluid in the sample cell and the resulting flow potential is measured, the obtained flow potential value fluctuates with time or hysteresis, resulting in the inability to obtain highly reliable measurement results with reproducibility.

[0028] In view of this situation, the object of the present invention is to provide a method and apparatus for measuring Zeta potential with high reliability and high accuracy by predicting the equilibrium value based on the time-dependent change of the flow potential.

[0029] To address the aforementioned problems, the Zeta potential measurement method of the present invention is a method for measuring the Zeta potential of a sample surface using the flow potential method. The external pressure changes in a stepwise manner along a pressure change curve, wherein the pressure change curve has a rising phase or a falling phase, the time of which is shorter than the relaxation time τ required to respond to the change in flow potential caused by the change in external pressure, and a steady phase, wherein the pressure remains in a steady state for a longer time than the relaxation time τ. Then, the Zeta potential is calculated using the asymptotic value of the flow potential estimated by regression from the transient response of the flow potential generated from the pressure change curve.

[0030] The key feature of this invention is the artificial generation of transient flow potential changes. By applying stepped pressure, various problems associated with continuous pressure changes, such as hysteresis and issues with the reliability and reproducibility of measurements, can be resolved. Furthermore, it allows for the analysis of the electric double layer, reflecting electrostatic interactions near the solid-liquid interface, and the transient behavior of mass movement, reflecting viscoelasticity and transport properties.

[0031] Furthermore, the process (steps) of the Zeta potential measurement method of the present invention can be executed by a computer program.

[0032] Furthermore, the Zeta potential measuring device of the present invention is an apparatus for measuring the Zeta potential of a sample surface using the flow potential method. This apparatus includes: a pressure adjustment unit that changes the external pressure in a stepwise manner along a pressure change curve, wherein the pressure change curve has a rising phase or a falling phase whose time is shorter than the relaxation time τ required to respond to the change in flow potential caused by the change in external pressure; and a steady phase in which the pressure remains in a steady state for a time longer than the relaxation time τ. The apparatus also includes a Zeta potential calculation unit for calculating the Zeta potential using an asymptotic value of the flow potential estimated by regression of the transient response of the flow potential generated from the pressure change curve.

[0033] In the Zeta potential measurement method and device of the present invention, the pressure change curve can have at least two step sizes relative to the relaxation time τ, satisfying 0 < t1 < τ and τ < t2 < 10τ, where t1 is the time of the rising or falling phase, and t2 is the time of the stable phase. Furthermore, the pressure change amplitude in the stable phase can be controlled within ±5% of the center value. Moreover, the transient response of the flow potential can be approximated by using the least squares method of an exponential function, and the Zeta potential can be calculated using an estimate of the flow potential over an infinite time.

[0034] Invention Effects

[0035] According to the present invention, the zeta potential measurement method using the flow potential method can effectively obtain measurement results, and is fast, simple, reproducible and highly reliable. Attached Figure Description

[0036]

【 Figure 1 [This is a step-like pressure change curve applied to a fluid to measure its flow potential, showing the relaxation time τ of the flow potential due to the applied pressure, the rise time t1 of the applied pressure, and the holding time t2.]

[0037] Diagram illustrating the relationship

[0038]

【 Figure 2 [This is a step-like pressure change curve showing the pressure reduction of a fluid used for flow potential measurement under pressurized conditions. It is an explanatory graph showing the relationship between the relaxation time τ of the flow potential caused by depressurization, the pressure drop time t1, and the holding time t2.]

[0039]

【 Figure 3 Schematic diagram of the flow potential measuring device

[0040]

【 Figure 4 The flowchart of the flow potential measurement process of the present invention.

[0041]

【 Figure 5 The symbol represents the pressurization and depressurization process and the evolution of the flow potential in Example 1 from the start of the experiment.

[0042] The diagram of the shift

[0043]

Figure 6

[0044]

Figure 7

[0045]

【 Figure 8 The graph shows the linear relationship between the flow potential and the steady-state value obtained under various pressures in Example 1 (the Zeta potential is calculated based on the slope of the straight line).

[0046]

【 Figure 9 [Image showing a schematic diagram illustrating the pH dependence of the zeta potential of the lithium cobalt oxide film determined in Examples 1-3]

[0047]

【 Figure 10 The diagram shows the change in flow potential during the Zeta potential measurement of the lithium cobalt oxide film surface in a non-aqueous medium in Example 4.

[0048]

【 Figure 11 [Image showing the relationship between pressure and flow potential obtained in Example 4]

[0049]

【 Figure 12 The image shows a view of the Maxwell model (left) and the Voigt model (right), which are viscoelastic models.

[0050]

【 Figure 13 The mechanical equivalent model (left) and relaxation process (right) used to represent the phenomenon of flow potential relaxation.

[0051]

【 Figure 14 The generalized Maxwell model used to analyze the relaxation phenomenon of flow potential.

[0052]

【 Figure 15 The graph shows the normalized potential difference in LiClO4-PC / solution (1 mol / L) at 700 MPa as a function of time.

[0053]

【 Figure 16 The graph represents the relationship between the zeta potential of the lithium cobalt oxide powder surface under different concentrations of lithium perchlorate salt in a non-aqueous medium in Example 5.

[0054]

【 Figure 17The graph represents the dependence of the zeta potential on the surface of the lithium cobalt oxide film in a non-aqueous medium under different concentrations of lithium perchlorate salt in Example 6. Detailed Implementation

[0055] Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the accompanying drawings. Furthermore, the scope of the present invention is not limited to the following embodiments or examples, and many more modifications and variations are possible.

[0056] The present invention is characterized in that, in the measurement of flow potential, the pressure of the sample liquid applied to the sample cell varies in a stepwise manner, and the pressure remains stable for a certain period of time. The flow potential change occurring under these conditions causes the measured sample to converge to a steady-state value within its inherent relaxation time. By analyzing the measured values ​​of the flow cell thus measured using an exponential function approximation, a highly reliable and accurate method for measuring zeta potential with reproducibility can be provided.

[0057] Here, the relaxation time, as generally defined, is obtained by dividing the difference between the physical property value at equilibrium and the physical property value at any point before reaching equilibrium by the rate of change of any physical property value over time from a non-equilibrium state to an equilibrium state. In this invention, the rate of change of the flow potential relative to time is considered the relaxation process, and as shown in the embodiments described later, since the rate of change of the flow potential relative to time is proportional to the difference in equilibrium, the relaxation time relative to the measured change in flow potential is a constant value. In this case, the difference between the flow potential and the equilibrium value at any given time changes exponentially, and the relaxation time τ is defined as the time required for the difference between the flow potential and the equilibrium value to decrease by a ratio of 1 / e (i.e., approximately 37%).

[0058] Figure 1 The step pressure variation curves applied to the fluid used for flow potential measurement are shown, as well as the relationship between the relaxation time τ of the flow potential generated by the applied pressure and the rise time t1 and hold time t2 of the applied pressure.

[0059] Figure 2 The figure shows a step-like pressure change curve for depressurizing a fluid used for measuring flow potential under pressurized conditions, based on the relationship between the relaxation time τ of the flow potential generated by the pressure depressurization, the drop time t1 of the depressurization pressure, and the holding time t2.

[0060] In any of the above cases, for the relaxation time τ, it is preferable that t1 is shorter than τ and t2 is longer than τ. If t1 exceeds τ, the measured flow potential may not converge to a steady-state value. If t2 is equal to or less than τ, a similar steady-state value of the flow potential may not be observed. Although any time exceeding τ can be set as t2, it is best to minimize the time required for measurement as much as possible. Therefore, the upper limit of t2 is preferably less than 10 times τ, i.e., 10τ, and more preferably less than 5τ.

[0061] As illustrated in the embodiments described later, in the flow potential measurement of the present invention, the relaxation time to reach approximately 37% of the difference between the initial and equilibrium values ​​of the flow potential is actually several seconds to several minutes or longer. On the other hand, since the time required to pressurize the fluid in the sample cell by opening the pressure valve to reach the set pressure is less than 1 second, the condition τ>>t1 is maintained.

[0062] In this invention, as described above Figure 1 and Figure 2 As shown, it is preferable to set two or more pressure change steps for flow potential measurement. Using the flow potential values ​​measured at multiple steps, the Zeta potential of the sample surface can be calculated from the Helmholtz-Smoluchowski equation, described later, based on the flow potential value for each pressure.

[0063] Figure 3 Examples of schematic diagrams showing measuring devices that can be used to implement the present invention.

[0064] In this invention, the pressure is changed in a stepwise manner. It does not involve continuous pressure changes caused by piston movement within the syringe as in conventional methods. For example, in this invention, the pressure is preferably adjusted by applying the pressure of a pressurized gas to the liquid used for measurement. In this case, a pressure regulating mechanism is preferably provided for digital, real-time adjustment of the gas pressure. The rate of pressure change is adjusted to a time shorter than the relaxation time τ of the flow potential, which will be described later. Alternatively, various liquid delivery pumps can be used to deliver the liquid while pressurizing it.

[0065] To minimize the delay in response speed caused by friction or weight, pressure regulating mechanisms are preferably mechanisms that are operated immediately by electrical signals, such as solenoid valves.

[0066] The flow rate of the delivered liquid can be arbitrarily adjusted by pressurization. However, by adjusting the volume of delivered liquid supplied to the sample cell per unit time, the flow of the fluid inside the sample cell can be set to laminar or turbulent flow. In this invention, the shape of the sample cell can be various, such as cylindrical, right-angled, or flat, depending on the sample to be tested.

[0067] Regarding the material of the sample cell, various plastics, ceramics, and metals can be used. However, to avoid surface charging, a substrate with a physicochemically inert and stable surface can be used to construct the sample cell.

[0068] It is also preferable to construct the flow potential measurement sample cell of the present invention using organic polymer materials instead of inorganic materials typically used in aqueous solution systems. In this case, the organic polymer materials that can be used are preferably sample cells composed of various resin materials such as acrylic resins, styrene resins, polyester resins, polycarbonate resins, polyurea resins, polyether resins, polyethylene resins, and polypropylene resins. Furthermore, more preferably, to confirm the state within the sample cell, a sample cell that is transparent, resistant to various acids or alkalis, and exhibits good solvent resistance to various organic solvents is preferred. Preferred resins generally suitable for the above purposes include polypropylene resins. However, since the solubility in various solvents should be appropriately selected, the suitability of the material should be determined based on its solvent solubility; the present invention does not limit the materials used.

[0069] One feature of this invention is that the pressure is maintained at an arbitrary set value for a certain period of time. In this case, to maintain pressure stability, the aforementioned gas pressure is continuously applied to the liquid. It is preferable to use a pressure regulator or the like to suppress pressure fluctuations within ±5%, more preferably within 1%, and more preferably within ±0.1%. When the liquid used for measurement is delivered via various fluid pumps, pulsating flow can be prevented, and the pressure fluctuation range during the stable phase is maintained within ±5% of the center value. This results in a more accurate flow potential value. If the pressure fluctuation exceeds ±5% during measurement, the measured flow potential may be unstable, and an accurate value cannot be obtained. Furthermore, considering that transient response is taken into account for accuracy requirements when calculating the Zeta potential in the processing flow described in the next section, the pressure also needs to be of the same level of accuracy. Therefore, to maintain a range of ±0.1% relative to the center value, it is preferable to use a pressure regulator that avoids the influence of pressure loss upstream of the sample cell and measures the pressure portion of the fluid or the pressure inside the fluid.

[0070] Figure 4 A flowchart illustrating the process from the start of measurement to the determination of the Zeta potential in the measurement method for implementing the present invention is shown.

[0071] Wait until the charge between the electrodes converges to a constant potential when the electrometer is connected (step S101), apply a pressure difference (step S102), measure the flow potential (step S103), and confirm the transient response of the flow potential (step S104). Select an approximate function for the transient response curve (step S105). Determine if there is a change in the flow potential indicating a relaxation process (step S106). If a change in the flow potential indicates a relaxation process, confirm the time constant during the longest relaxation process (step S107). Calculate the estimated value of the flow potential using the nonlinear approximation of the Gauss-Newton method (step S108). Preferably, the estimation is performed using a time period τ = 5 times the relaxation time and with an estimated value of 3 significant figures. Compare this potential with the previously measured potential (step S109). If they are consistent, determine the values ​​of the time constant and the flow potential (step S110). Then, calculate the Zeta potential based on the linear approximation of the Helmholtz-Smoluchowski method (step S111). To improve measurement accuracy, the value is compared with the previously measured calculated Zeta potential (step S112). If four or more measurement points are consistent, the measured Zeta potential is determined and the measurement ends. Preferably, six or more measurement points are consistent. If fewer than four measurement points are consistent with the previously measured calculated Zeta potential, the process returns to before applying the differential pressure (step S102). Alternatively, if the comparison result is inconsistent with the previously measured calculated Zeta potential, the process returns to before measuring the flow potential (step S103).

[0072] The measurement method for implementing the present invention will be described in detail using the following embodiments, but the present invention is not limited to the constituent elements shown in the following embodiments.

[0073]

Example 1

[0074] <Example of Zeta potential measurement on the surface of a lithium cobalt oxide film in water (pH = 5.86)>

[0075] A dispersion of lithium cobalt oxide (LiCoO2) was prepared using polyvinylidene fluoride (PVDF) as a binder in NMP (N-methylpyrrolidone), coated onto a support surface, and dried to obtain a LiCoO2 membrane. The sample cell was constructed by placing parallel polypropylene sheets (20 mm long and 10 mm wide) with gaps between them. LiCoO2 membranes were adhered to the upper and lower surfaces of the sample cell, with the distance between the membranes adjusted to 50 μm. A 10 mmol / L aqueous solution of lithium perchlorate was used as the electrolyte solution. The pH of the aqueous solution was adjusted to 5.86.

[0076] A schematic diagram of the measuring device is shown below. Figure 3 As shown.

[0077] exist Figure 3 In this process, the gas pressure from the dry nitrogen cylinder 13, equipped with a pressure gauge 12 and a pressure reducing valve 11, pushes the aqueous solution supplied to the storage container 17 upwards into the flow channel and introduces it into the sample cell 19 through the three-way stopcock valve 14. The aqueous solution in the sample cell 19 is then conveyed to the recovery container via the three-way stopcock valve 14. The flow rate of the aqueous solution in the sample cell 19 varies with the gas pressure. The applied pressure is a parameter used to change the output voltage and affects its accuracy. Therefore, the pressure is regulated to 0.1 MPa by a pressure regulator connected to the upstream gas cylinder 13, and pressure fluctuations are suppressed to ±0.1% or lower using a pressure regulator (Cofflock Pressure Regulator 6600A) with reproducibility within ±1%, regardless of upstream pressure fluctuations. The same measurements were also performed in non-aqueous media, as described later.

[0078] In this embodiment, firstly, the valve of the dry nitrogen cylinder 13 is opened to apply pressure to the aqueous solution in the storage container 17, increasing the pressure on the sample cell side to 700 hPa. Then, the stopcock is opened, and the flow rate in the sample cell is set to 90 mL / min. Since the cross-sectional area of ​​the electrolyte storage container 17 is 144 cm²... 2 Therefore, the linear velocity of the gas is only (90 / 144)×(1713 / 1013)=1.06sccm, with almost no pressure loss in the flow path of the pressurized gas. Furthermore, almost no fluctuation is visible in the pressure monitor (minimum display pressure 1hPa) connected to the pressure regulator, and the pressure fluctuation during the measurement process is less than ±0.1%. Platinum wires 15 are placed at both ends of the sample cell 19, and the potential difference between the two ends is measured using an electrometer 21 (Advantest TR8652). Analog data output from the electrometer 21 is collected as digital data at 5-second sampling intervals using a data logger (not shown). The voltage change from the start of the measurement is as follows: Figure 5 As shown.

[0079] After pressurization begins, maintain the pressure for approximately 30 minutes to ensure continuous flow of the aqueous solution. Then, reduce the pressure in a stepwise manner. Figure 5 The stepped pattern shown at the top of the graph represents the pressure change curve after the fluid inside the sample cell is pressurized. For example... Figure 3As shown, a pressure sensor 20, directly mounted above the upstream side of the sample cell, measures the pressure applied to the sample cell. The time t1 required to reach the set pressure in each step is less than 1 second, and the measured values ​​during the measurement time t2 after reaching the set point remain within ±0.1% of the set value under all conditions. Pressure is reduced at 100 hPa intervals starting from 700 hPa, and maintained for two and a half minutes in each step, while measuring the flow potential as the pressure is gradually reduced. Upon reaching 0 hPa, pressure is increased, again maintaining the pressure for two and a half minutes in 100 hPa increments until reaching 700 hPa.

[0080] Next, the pressure was repeatedly increased and decreased in a cycle of 700→0→700→0, and the flow potential was measured each time. In subsequent cycles, the changes in flow potential observed between 120 and 160 minutes after the start of the measurement were repeated, and no hysteresis was observed after 160 minutes of the experiment. Therefore, reproducibility was confirmed, indicating that the state inside the sample cell had stabilized.

[0081] In each pressure change cycle, the pressure change (rise and fall) between each step is completed within a few seconds. Figure 6 The changes in flow potential are shown as a result of the decompression step, which begins with pressurization to 700 hPa, approximately 275 minutes after the start of the measurement.

[0082] exist Figure 6 In the figure, the values ​​of the flow potential for each pressure step are approximated by an exponential function and displayed together as an approximate curve.

[0083] exist Figure 6 From the approximate curves showing the changes in flow potential during each step shown, calculate the numerical value (equilibrium value) V at the equilibrium state of each step. ∞ For the numerical value (V(t) - V) standardized based on the difference from the initial value V0, ∞ ) / (V0-V ∞) The Gauss-Newton approximation method is used, which approximates the value using the exponential function exp(-t / τ). Figure 7 The results show the logarithm of the measured values ​​and the approximate values ​​of the resulting approximate equations plotted against time.

[0084] from Figure 7 It can be confirmed that the changes in flow potential measured at various pressures are in excellent agreement with the approximation derived through the exponential approximation. The relaxation time τ is approximately 70 seconds. Since the appropriateness of the exponential approximation has been confirmed, the equilibrium value V at each pressure is used. ∞The Zeta potential is obtained by a linear approximation of the Helmholtz-Smoluchowski equation based on the following mathematical formula 2. Where V represents the flow potential, P represents the pressure, η is the viscosity of the solution, λ is the conductivity of the solution, ε is the relative medium constant, and ε0 represents the vacuum medium constant (8.854 × 10⁻⁶). -12 ).

[0085]

Mathematical Formula 2

[0086]

[0087] Figure 8 The graph shows the relationship between pressure and flow potential after four repeated pressure steps from 700 to 0 hPa. A good linear relationship was obtained in all cases, and the resulting Zeta potential was -20.5 mV.

[0088]

Example 2

[0089] <Example of Zeta potential measurement on the surface of a lithium cobalt oxide thin film in water (pH = 11.41)>

[0090] The flow potential was measured in the same manner as in Example 1, except that lithium hydroxide was added to the aqueous lithium perchlorate solution to adjust the pH of the solution to 11.41. As a result, a Zeta potential of -45.2 mV was obtained.

[0091]

Example 3

[0092] <Example of Zeta potential measurement on the surface of a lithium cobalt oxide thin film in water (pH = 2.06)>

[0093] The flow potential was measured in the same manner as in Example 1, except that an aqueous solution of perchloric acid was added to the lithium perchlorate solution to adjust the pH of the solution to 2.06. As a result, a Zeta potential of 7.1 mV was obtained. Figure 9 The results of Examples 1-3 are summarized. As can be seen from the figure, the Zeta potential value on the surface of the LiCoO2 film in the lithium perchlorate aqueous solution changes linearly from positive to negative with increasing pH value, and shows an isoelectric point at a pH value of approximately 3.

[0094]

Example 4

[0095] <Example of Zeta potential measurement on the surface of lithium cobalt oxide film in non-aqueous medium>

[0096] Using the LiCoO2 membrane prepared in Example 1, experiments were conducted by changing the solvent used to dissolve lithium perchlorate from water to propylene carbonate (PC) and setting the concentration of lithium perchlorate to 1.0 mol / L. The PC solution had a conductivity of 611 mS / m and a viscosity of 7.85 × 10⁻⁶ mS / m.-2 Pa / s, relative permittivity is 64.92.

[0097] Figure 10 The displacement of the electrometer output value is shown from the start of the experiment to the measurement of the flow potential. When the electrometer was connected to the two ends of the platinum wire positioned at both ends of the sample cell, and the pressure was increased to 700 hPa while the solution was passed through the sample cell, a slow potential change was generated over approximately 60 minutes due to the charging between the electrodes caused by the load of the electrometer. After about 60 minutes, the potential stabilized, and from this point onward, the pressure change cycle repeated in a stepwise manner between 700→0 hPa and 0→700 hPa in 100 hPa steps. Each step was maintained at the pressure for approximately 4 minutes. The pressure change between each step was completed within a few seconds. By changing the pressure between the initial 700→0 hPa and 0→700 hPa, the surface state of the sample placed in the sample cell was stabilized, and the flow potential observed during subsequent pressure changes showed a highly reproducible relationship between flow potential and pressure. In this case, the flow potential was measured starting at a time point of approximately 110 minutes from the start of the experiment to determine the Zeta potential.

[0098] The displacement of the flow potential at each pressure during repeated pressure step changes was calculated using a first-order exponential function, based on an algorithm that considered the approximate function of the transient response curve. Since this change exhibits a stable exponential function variation during measurement, the Gauss-Newton approximation method was used, as in Example 1, to approximate the flow potential at each pressure and determine its stable value. Figure 11 The relationship between the steady-state flow potential and pressure is shown by plotting the results of repeating the measurement process four times.

[0099] The results of the four measurements were consistent, and the average value of the Zeta potential was calculated to be 108 mV. Furthermore, the relaxation time τ was approximated using an exponential function and found to be approximately 6 minutes. This value is approximately five times longer than the approximately 70 seconds relaxation time in the aqueous solution case of Example 1.

[0100] The characteristics of the measured system and the relaxation phenomenon are key to interpreting the results. As previously shown, the response of the measured flow potential to rapid pressure changes at each pressure can be expressed by the following equation.

[0101]

Mathematical Expression 3

[0102]

[0103] In mathematical formula 3, t represents the time when the measurement begins, and V0 represents the initial value of the flow potential at the start of the measurement. ∞ This represents the steady-state value of the flow potential when the pressure remains constant and time is infinitely long during each step change in pressure.

[0104] The relaxation phenomenon in the above formula may be caused by the following three reasons.

[0105] First, the phenomenon is derived from the time constant of the response time of the device system; second, it is a macroscopic characterization when the sample cell is regarded as an RC series circuit consisting of a capacitor c and a resistor r; third, it is a relaxation response derived from the adsorption and diffusion of ions on the surface of the LiCoO2 film inside the sample cell, or a stress relaxation phenomenon caused by the strain of the double layer.

[0106] Since the fluid velocity is lower than the speed of sound, the time constant of the entire system is sufficiently small, the response time of the pressure change is much shorter than the measurement time, and the electrometer has a very fast response speed, thus ruling out the first possibility. Next, considering the measuring device as an RC series circuit, if the application of pressure is replaced by a transient process of applying a voltage to the RC series circuit, the relaxation time τ in this case can be expressed by the following equation.

[0107]

Mathematical Expression 4

[0108] τ=R×C

[0109] Here, the conductivity of the lithium perchlorate PC solution measured in 1.0 M was 611.4 mS / m, based on a sample cell length of 50 mm = 5 × 10⁻⁶ mS / m. -2 m, cross-sectional area is 10mm × 0.05mm = 5 × 10 -7 m 2 Calculate R = 1.636 × 10 5 Ω.

[0110] On the other hand, based on a relative permittivity of 64.92, the area of ​​the parallel plates is 5 × 10⁻⁶. -4 m 2 The electrode plate distance is 0.05 × 10⁻⁶. -3 The capacitance of the capacitor is calculated to be C = 5.75 × 10 m. -9 F, from which the relaxation time (time constant) τ is derived to be 9.40 × 10 -4 Seconds. The relaxation time, estimated to be at most about 1 millisecond due to the electrochemical nature of the measuring device, is difficult to attribute to the minute-level relaxation time observed in this embodiment and the like.

[0111] Regarding the explanation of the third type of mechanical relaxation phenomenon, the sample in this embodiment is in the form of a thin film material facing each other. Since the fluid flows through its gaps, an explanation method related to viscous flow is illustrated.

[0112] First, calculate the Reynolds number Re of the fluid flowing in the sample cell according to the following formula.

[0113]

Mathematical Expression 5

[0114]

[0115] In this formula, ρ represents the fluid density, U represents the flow velocity, L represents the length, and η represents the fluid viscosity coefficient. Assume the density of a 1M lithium perchlorate (PC) solution is 1.31 × 10⁻⁶. 3 kg / m 3 (Data from LiPF6), and the volume inside the sample cell is 2.5 × 10⁻⁶. -8 m 3 To achieve a maximum flow rate of 90 mL / min = 1.5 x 10⁻⁶, -6 m 3 / sec through the sample cell volume, assuming an average flow rate U = 0.05 m x 1.5 x 10 -6 m 3 / sec / 2.5x10 -8 m 3 = 3m / sec, representing a length L of 2 × 5 × 10 -7 / (10.05×10 -3 ) = 10 -2 The viscosity coefficient is 7.85 × 10⁻⁶. -3 From Pa·sec, Re = 516 can be calculated. Since this value is much smaller than the standard range of 2000–4000 for transitioning from laminar to turbulent flow, the fluid in the sample cell in this embodiment can be considered to be laminar. In this case, the estimated flow profile inside the sample cell exhibits a parabolic velocity distribution, with zero velocity near the wall and maximum velocity near the center of the sample cell cross-section.

[0116] Fluid flows into the sample cell under a maximum pressure of 700 hPa from a nitrogen cylinder. When the difference between the inner diameter of the pipe and the inner diameter of the sample cell is large, a considerably high pressure is applied to the LiCoO2 film mounted on the inner wall surface of the sample cell as normal stress. Therefore, the stress applied to the surface of the LiCoO2 film is considered to be normal stress and shear stress. 700 hPa = 0.7 kg / cm² 2 This means that a considerable stress of 700g or more per square centimeter was applied.

[0117] Although fluids are incompressible, in non-aqueous media with high dielectric constants, such as those used in lithium-ion batteries, or when polymers are dissolved in the medium, the adsorption or diffusion of ions can take a relatively long time. Furthermore, in cases where higher-order structures are formed due to dipole interactions or in polymer solutions, the viscosity of the solvent is known to increase significantly near the solid phase, and it exhibits relaxation behavior in response to applied compressive or shear stress.

[0118] For example, in the reference "M. Mizukami et al., "Hydrogen-Bonded MacroclusterFormation of Ethanol on Silica Surfaces in Cyclohexane", J.AM.CHEM.SOC.124, (2002)12889-12897", it has been elucidated that ethanol molecules in an ethanol / cyclohexane mixed solvent are selectively adsorbed onto the surface of quartz glass via hydrogen bonds, forming an adsorption layer of several nanometers to tens of nanometers. Studies have shown that in this case, the adsorption layer forms a cluster structure through hydrogen bonds, with ethanol molecules linked together by hydrogen bonds, essentially existing in a polymeric form.

[0119] Figure 12 The Maxwell and Voigt models shown are general models representing various relaxation processes. The Maxwell model represents the stress relaxation process, and the Voigt model represents the creep process.

[0120] In flow potential measurements, when pressure is applied in a stepped manner, the electric double layer on the LiCoO2 surface reaches equilibrium over time. For simplicity, the relaxation phenomenon will be described below as stress relaxation when strain is applied to a mechanically equivalent model. When stress relaxation under constant strain is used... Figure 13 The modified Maxwell model is used to represent the parallel spring combination shown. Figure 13 In the diagram, the left side shows a deformed Maxwell model consisting of a spring and a damper, while the right side shows the stress relaxation over time.

[0121] exist Figure 13 In the figure, the external force corresponding to stress is the pressure applied to the fluid in the sample cell. When the liquid inside the double layer is deformed by a rapid pressure change, the spring components represented by Ge and Gi in the figure will initially be stretched by ε, and the stress will increase by an amount equivalent to (Ge+Gi). The damper component gradually relaxes as it expands. The stress G(t) is shown in the following formula.

[0122]

Mathematical Expression 6

[0123] G(t) = Ge + G i exp(-t / τ)

[0124] Here, the relaxation time τ is expressed by the following formula.

[0125]

Mathematical Expression 7

[0126] τ=η / G i

[0127] Here, η is the viscosity, and Gi is the elastic modulus of the spring component connected in series with the damper. As shown above, in the measurement of flow potential, since the elastic modulus is equivalent to the flow potential V(t), the following mathematical formula can be obtained.

[0128]

Mathematical Expression 8

[0129]

[0130] In this mechanical equivalent model, the relaxation time τ is considered to vary exponentially with various relaxation times specific to the sample under different conditions, such as in electrolyte solutions with structural viscous behavior or electrode materials with surface polymer layers, where the relaxation time ranges from short to relatively long.

[0131] Therefore, the relaxation phenomenon of the flow potential in this invention provides a method for directly observing the strain and relaxation of the double-layer model, which was previously unknown.

[0132] Preferably, the Gauss-Newton approximation method described in Example 1 above is used to perform an exponential function approximation on the measured value of V(t). In the above measurement algorithm, V is preferably used. ∞ Measurements were performed, where V ∞ It is estimated inductively from measurements taken during the transient response using a predetermined algorithm. In practice, this method estimates V using a measurement time approximately five times the relaxation time τ. ∞ As described above, in the flow potential measurement method of the present invention, the measured flow potential change can be accurately described using a nonlinear least squares approximation of a single exponential function. For more complex measurement systems, in addition to using the single exponential function approximation, it is preferable to use a nonlinear least squares approximation of multiple exponential functions connected by connecting multiple exponential functions to describe the flow potential change. Specifically, for a data sequence (V0, t) sampled at equal intervals using the difference method... 0) 、(V1,t1),……、(V n ,t n The following formula can be used to approximate this. This is equivalent to... Figure 14 The mechanical model.

[0133]

Mathematical Expression 9

[0134] V(t)=V ∞ +∑ i C i exp(a i t)

[0135] To illustrate the calculation method, we first use only (V0, t0), (V1, t1), ..., (V n , t nThe least squares approximation is performed on one exponential function term of V. That is, if V i =Aexp(ai), (i = 0, 1, 2, 3, ..., N), then the relation V1 = exp(a)V0, V2 = exp(a)V1, ..., V n =exp(a)V n-1 To find the value that makes Q = Σ(V) i -eaV i-1 ) 2 Minimizing the mean square error of 'a' yields the following mathematical formula.

[0136]

Mathematical Formula 10

[0137]

[0138] Therefore, we obtain Equation 1 below, and thus Equation 2 below. The least squares error of coefficient A is obtained by Equation 3 below. Therefore, V is obtained using Equation 4 below. i =The least squares approximation formula for Aexp(ai).

[0139]

Mathematical Expression 11

[0140]

[0141]

[0142]

[0143]

[0144] Next, repeat the above method according to Equation 5 below to obtain Equations 6 and 7 below. By repeating the above method, the least squares approximation formula V(t)=ΣC can be obtained. i exp(a i t) is the sum of exponential functions. At this point, it corresponds to V. ∞ The terms are automatically calculated as terms that are as close to zero as possible to ai.

[0145]

Mathematical Expression 12

[0146] Z i =V i -Aexp(ai)=Bexp(bi)…(Equation 5)

[0147]

[0148]

[0149] Besides the thin film material of this embodiment, samples measured by the flow potential method are typically measured by flowing through the pores of porous materials such as powders and fibers. In this case, the pore size is known to exhibit a variety of distributions ranging from nanometer to millimeter scale. Furthermore, in the distribution of electrolytes, the gas-liquid interface shape may change due to the interface with the gas components remaining within the pores, and a three-phase interface may exist between the solid, liquid, and gas phases. Therefore, potential changes caused solely by viscoelasticity are not necessarily the only factor leading to relaxation phenomena, and unexpected transient responses may be observed. This invention is applicable not only to relaxations having a single relaxation time expressed as an exponential function, but also to transient responses expressed by formulas, such as multiple exponential function terms according to the concept of this embodiment, where the relaxation time in each term can be empirically attributed to factors of the assumed corresponding relaxation phenomenon.

[0150] (Comparative Examples)

[0151] Here, a comparative example of measuring the Zeta potential on the surface of a lithium cobalt oxide film in a non-aqueous medium is illustrated. Figure 15 The display shows the transient potential response in a 1 mol / L LiClO4 PC solution.

[0152] In the normal measurement process of flow potential, the usual method is to set the pressure of the electrolyte solution flowing through the sample cell, wait for the potential to stabilize, and then continuously take values ​​until the potential can be confirmed to be constant. The average of these values ​​is then used. That is, if... Figure 15 As shown, after confirming that the potential changes exponentially with time and is almost constant around 4τ, measurements are continued up to 6τ to confirm that the value remains constant and to obtain the average value of the potential obtained during this time.

[0153] In the Zeta potential measurement example of the lithium cobalt oxide film surface in a non-aqueous medium shown in Example 4, the Zeta potential was calculated from the potential at each predetermined pressure using the value up to the relaxation time. On the other hand, in the comparative example, instead of using a regression curve represented by an exponential function, the average value of the Zeta potential was calculated starting from the point where the Zeta potential became constant over time. This method of obtaining data is completely different from that of this patent. In this case, it takes 5τ, approximately 30 minutes, to reach the steady-state value, indicating that these values ​​have actually converged to the values ​​calculated by the measurement up to τ. The results, showing the E / P after stabilization and its correlation coefficient R, are shown in Table 1 below, compared with the results of the regression calculation performed in Example 4. Figure 11 Compare them.

[0154] Table 1

[0155]

[0156] The results showed that, Figure 15 The approximations in the logarithmic graph differ at each pressure, and all results indicate that the data collected in Example 4 exhibits a high degree of correlation before the relaxation time is measured, with excellent correlation. Therefore, not only is the measurement time for potential measurements at each pressure reduced from 5τ to τ, but the reproducibility of the R value in Comparative Example 1 is improved from less than 0.98 or one significant figure to greater than 0.999 or three significant figures as shown in Example 4.

[0157] This is because, although the values ​​are convergent, they still exhibit some fluctuations, and the dispersion of values ​​due to noise in the measurements can be observed over time. In other words, this indicates that the Zeta potential values ​​calculated using values ​​up to τ are shorter and relatively more accurate than those obtained using conventional methods.

[0158]

Example 5

[0159] <Example of Zeta potential measurement on the surface of lithium cobalt oxide powder under different concentrations of lithium perchlorate salt in non-aqueous medium>

[0160] Lithium cobalt oxide (LiCoO2) powder was dispersed in polycarbonate (PC), and the flow potential was measured using a system that varied the concentration of lithium perchlorate in the PC solution to investigate the effect of changing the salt concentration on the zeta potential. Figure 16 In the process of measuring the flow potential at various salt concentrations, the pressure was changed from 600 hPa to 700 hPa and then the displacement was kept constant. The relaxation time τ, which was approximately calculated by an exponential function, was about 4 minutes and gradually increased with the increase of salt concentration.

[0161]

Example 6

[0162] <Example of Zeta potential measurement on the surface of lithium cobalt oxide film under different concentrations of lithium perchlorate salt in non-aqueous medium>

[0163] In Example 4, the concentration of lithium perchlorate dissolved in PC was varied in the range of 0.1 mol / L to 3.0 mol / L to measure the flow potential. The results of investigating the effect of each salt concentration on the surface zeta potential are shown below. Figure 17 .

[0164] The potential on the LiCoO2 film in aprotic solvents depends on the adsorption amount of Li or ClO4 ions. However, since neither ion exhibits specific adsorption, the increase in potential within the concentration range of 1 mol / L indicates preferential adsorption of Li ions. In this concentration range, Li ions exhibit a solvation structure in PC solvent, but their interaction with the solid phase is also relatively strong, consistent with Raman measurements. However, above 1 mol / L, the interaction between Li ions and the solid weakens due to excessive coordination of ClO4 ions with Li, resulting in partial ion pair formation. This phenomenon is thought to be related to the sharp decrease in conductivity starting around 1.2 M. The large negative Zeta potential at high salt concentrations (~1.5 M) is likely due to the inherent properties of the LiCoO2 particles.

[0165] Industrial application

[0166] This invention can be applied to various solid surfaces because it can accurately measure the zeta potential in various electrolyte solutions, including aqueous and non-aqueous solutions, showing a wide range of values ​​for dielectric constant, conductivity, viscosity, and other properties, and significantly reducing the time required compared to conventional methods. It can also be used to analyze the viscoelasticity of solid-liquid interfaces.

[0167] Explanation of symbols in the diagram

[0168] 1 Zeta potential measuring device

[0169] 10 Pressure Regulator

[0170] 11 Pressure reducing valve

[0171] 12 pressure gauges

[0172] 13 Dry nitrogen storage cylinders

[0173] 14 Three-way plug valve

[0174] 15 Platinum Wire

[0175] 16 gaskets

[0176] 17,18 Liquid storage container

[0177] 19 Sample Cells

[0178] 20 Pressure Sensors

[0179] 21 Electrometer

Claims

1. A method for measuring zeta potential, characterized in that, The zeta potential of a sample surface is measured using the flow potential method, which includes: Change the external pressure in a stepwise manner; A pressure change curve is set, wherein the pressure change curve has a rising phase or a falling phase, the time of which is shorter than the relaxation time τ required to respond to the change in flow potential caused by the change in external pressure, and a steady phase, wherein the pressure is kept in a steady state for a longer time than the relaxation time τ. The Zeta potential is calculated using the asymptotic value of the flow potential estimated by regression of the transient response of the flow potential generated from the pressure change curve.

2. The zeta potential measurement method according to claim 1, characterized in that, The pressure change curve has at least two step sizes. The relaxation time τ satisfies 0 < t1 < τ and τ < t2 < 10τ. Where t1 is the time of the rising or falling phase, and t2 is the time of maintaining the stable phase.

3. The method for measuring Zeta potential according to claim 1 or 2, characterized in that, The pressure change during the stabilization phase is suppressed to within ±5% of the center value.

4. The method for measuring Zeta potential according to any one of claims 1 to 3, characterized in that, The transient response of the flow potential is approximated by using the least squares method of an exponential function, and the Zeta potential is calculated using an estimate of the flow potential over infinite time.

5. A zeta potential measuring device, characterized in that, The device for measuring the Zeta potential of a sample surface using the relationship between external pressure and flow potential includes: The pressure regulating section changes the external pressure in a stepped manner; and The Zeta potential calculation unit includes a pressure change curve, in which... The pressure change curve has an ascending or descending phase, the duration of which is shorter than the relaxation time τ required to respond to the change in flow potential caused by the change in external pressure. And a stabilization phase, wherein the pressure remains in a stable state for a longer period than the relaxation time τ; The Zeta potential is calculated using the asymptotic value of the flow potential estimated by regression of the transient response of the flow potential generated from the pressure change curve.

6. The Zeta potential measuring device according to claim 5, characterized in that, The pressure change curve has at least two step sizes. The relaxation time τ satisfies 0 < t1 < τ and τ < t2 < 10τ. Where t1 is the time of the rising or falling phase, and t2 is the time of maintaining the stable phase.

7. The Zeta potential measuring device according to claim 5 or 6, characterized in that, The pressure adjustment unit adjusts the time required for the external pressure applied to the fluid inside the sample cell to rise or fall using a time constant less than the relaxation time τ.

8. The zeta potential measuring device according to any one of claims 5 to 7, characterized in that, The pressure adjustment unit adjusts the pressure variation range during the stable phase, which maintains the pressure in a stable state, to within ±5% of the center value, for a period longer than the relaxation time τ.

9. The zeta potential measuring device according to any one of claims 5 to 8, characterized in that, The transient response of the flow potential is approximated by using the least squares method of an exponential function, and the device calculates the Zeta potential using an estimate of the flow potential over an infinite time period.

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