Ion concentration measurement device and measurement method

Abstract

The purpose of the present invention is to provide an ion concentration measurement device and a measurement method capable of reducing measurement errors, distinguishing a method for selecting an ion-selective electrode which is less likely to be interfered by coexisting ions, and obtaining an ion concentration highly accurately by using the selected ion-selective electrode. The ion concentration measurement device includes two or more kinds of ion-selective electrodes which have mutually different selectivity coefficient ratios for multiple ions and which satisfy expression (1) and expression (2), wherein when the number of the kinds of the multiple ions is defined as n, the two or more kinds of ion-selective electrodes are formed from n kinds of ion-selective electrodes, and n is an integer equal to or greater than 2. In expression (1), Bj represents the j-th ion, and Si is a symbol representing the i-th ion-selective electrode. KSi (B1, Bj) represents the ion selectivity coefficient of the ion-selective electrode Si for the ion Bj based on an ion B1. In expression (2), ||A|| is the absolute value of the determinant of the matrix A.

Description

Ion concentration measuring device and measuring method

[0001] The present invention relates to an ion concentration measuring device and a measuring method.

[0002] Ion selective electrodes are commonly used to measure ion concentrations in blood in clinical tests. By immersing an ion selective electrode and a reference electrode in a sample solution, a potential difference corresponding to the ion concentration of the sample solution is obtained. Therefore, by understanding the relationship between the potential difference and concentration in advance, the ion concentration in the sample solution can be determined from this potential difference. Ion concentration measurements using ion selective electrodes are now widely used because the ion concentration in a sample solution can be measured simply and quickly by simply immersing the electrode in the sample solution.

[0003] A brief description will be given of the case where the concentration of one type of ion is measured using the ion selective electrode S and the reference electrode. a The potential difference E obtained when immersed in a sample solution containing S and the ion concentration in the sample solution (C(X a The relationship between these two can be expressed by the Nernst equation (Equation (4)).

[0004] However, E S is the potential difference developed between the ion-selective electrode S and the reference electrode, and E 0,S is the standard potential difference developed between the ion selective electrode S and the reference electrode, R is the gas constant, T is the absolute temperature, a is the valence of the ion, F is the Faraday constant, and C(X a ) is ion X a is the concentration.

[0005] Ion X of known concentration is detected by the ion selective electrode S. a By measuring a solution containing , a calibration curve representing formula (4) can be created. Using the created calibration curve, an unknown sample solution can be measured and the ion concentration can be calculated from the potential difference.

[0006] However, in addition to the ion to be measured (hereinafter referred to as the "measurement ion"), the sample solution may contain ions other than the measurement ion (hereinafter referred to as the "coexisting ions"). When the concentration of the measurement ion B1 contained in a sample solution containing n types of ions consisting of the measurement ion B1 and coexisting ions B2 to Bn is measured using an ion selective electrode S and a reference electrode, the relationship of the Nikolsky-Eisenman equation (Equation (5)) holds.

[0007] However, E S is the potential difference developed between the ion-selective electrode S and the reference electrode, and E 0,S is the standard potential difference generated between the ion selective electrode S and the reference electrode, R is the gas constant, T is the absolute temperature, a is the valence of ion B1, F is the Faraday constant, Bj represents the jth ion among n types of ions, j is an integer from 2 to n, and C(Bj) is the concentration of ion Bj.

[0008] Here, K S (B1, Bj) is the ion selectivity coefficient of the ion selective electrode S for the ion Bj with respect to the ion B1 at the ion selective electrode S. In other words, it is a coefficient that expresses the strength of the influence of the ion Bj on the potential difference generated between the ion selective electrode S and the reference electrode as a ratio with respect to the ion B1.

[0009] The ion selectivity coefficient for ion B2 based on ion B1 is K S When the above measurement is performed using an ion selective electrode S (B1, B2) for a sample solution containing ion B1 at a concentration C(B1) but not containing coexisting ions B2 to Bn, the following potential difference E B1 Give.

[0010] Furthermore, when ion B2 at a concentration of C(B2) is added to this sample solution (i.e., in the case of a sample solution containing ion B1 at a concentration of C(B1) and ion B2 at a concentration of C(B2) but not containing coexisting ions B3 to Bn), the following potential difference E B1+B2 Give.

[0011] Here, in the above formulas (6) and (7), E 0,S , R, T, a, and F are the same as those defined in the above formula (5), and E in the above formula (6) B1 and E in the above formula (7) B1+B2 is E in the above formula (5). S is equivalent to

[0012] As suggested by the above equations (6) and (7), the ion selectivity coefficient K S If (B1, B2) is large, when ion B1 is measured, it is interfered with by ion B2, which causes an error.

[0013] Therefore, in order to measure the concentration of a specific ion, it is desirable that the selectivity coefficient for other ions is as small as possible. When an ion-selective membrane containing Bis[(12-crown-4)methyl]2-dodecyl-2-methylmalonate [CAS No. 80403-59-4] is used for a sodium ion-selective electrode, the selectivity coefficient K for potassium ions relative to sodium ions is S (Na + , K + ) is known to exhibit a coefficient of refraction of 0.01 and has been put into practical use (Non-Patent Document 1).

[0014] However, depending on the ion to be measured, it can be difficult to develop an electrode with a sufficiently small ion selectivity coefficient for other ions. In particular, there are few ion-selective membranes suitable for measuring anions, and for measuring anions, ion-exchange membranes that are not sufficiently selective for the ion to be measured are often used. For example, bicarbonate ion (HCO3 - ) is measured by the selectivity coefficient K S (HCO3 - , Cl - ) is required to satisfy 0.01 or less, S (HCO3 - , Cl - ) is greater than 1. In clinical tests, the presence of ions in the sample solution that respond more strongly than the ions to be measured is known to be a sign of bicarbonate ions (HCO3 - This poses a problem in practical application of electrodes for measuring the concentration of ammonium nitrate.

[0015] Therefore, methods have been developed for measuring the concentrations of multiple types of ions using multiple ion selective electrodes that have insufficient selectivity for the ions to be measured, as described in Patent Documents 1, 2, and 3. Furthermore, there is also an example in which an ion selective electrode for eliminating the influence of interfering ions is used in addition to the ion selective electrode used to measure the ion concentration (Patent Document 4).

[0016] Special Publication No. Hei 1-502360 Publication JP 54-030094 Publication International Publication No. 2019 / 163281 JP 07-167818 Publication

[0017] Anal. Chem. , 1982, 54(7), 1224-1227

[0018] As disclosed in Patent Document 2, a method is known in which the concentrations of n ions present in a sample solution are calculated by solving simultaneous equations based on n measured values ​​obtained from multiple (n) ion-selective electrodes with low ion selectivity. However, actual measurements involve measurement errors. Furthermore, when a sample solution contains n+1 or more ions, interference from coexisting ions cannot be ignored. Therefore, the inventors' investigations revealed that, depending on the choice of ion-selective electrode, measurement errors and interference from coexisting ions can make it difficult to accurately determine ion concentrations.

[0019] Therefore, an object of the present invention is to clarify a method for selecting an ion selective electrode that has a small measurement error and is not susceptible to interference from coexisting ions, and to provide an ion concentration measuring device and a measuring method that can accurately determine ion concentrations by using the selected ion selective electrode.

[0020] The present inventors have conducted extensive research to solve the above problems, and as a result have clarified a method for selecting an ion selective electrode that has a small measurement error and is less susceptible to interference from coexisting ions, and have discovered an ion concentration measuring device and a measuring method that can accurately determine ion concentrations by using the selected ion selective electrode.

[0021] That is, the first aspect of the present invention provides an ion concentration measuring device including two or more types of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the following formulas (1) and (2), wherein the two or more types of ion selective electrodes consist of n types of ion selective electrodes, where n is an integer of 2 or more.

[0022] In formula (1), each element of matrix A represents an ion selectivity coefficient, where Bj represents the jth ion among the n types of ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n types of ion selective electrodes, i and j are each independently an integer from 1 to n, and K Si (B1, Bj) represents the ion selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as a reference.

[0023] In addition, in equation (2), ∥A∥ is the absolute value of the determinant of matrix A.

[0024] The second aspect of the present invention provides a measurement method including the step of measuring the ion concentration in a sample solution using a plurality of ion selective electrodes that satisfy the above formulas (1) and (2).

[0025] This invention clarifies a method for selecting an ion selective electrode that minimizes measurement error and is less susceptible to interference from coexisting ions, even when there are more types of coexisting ions (n+1 or more types) than the number of electrodes (n). By selecting an ion selective electrode with a large absolute value (||A||) of the determinant of matrix A, accurate ion concentration measurements with a small relative standard deviation of the measurement results are possible. This invention provides an ion concentration measurement device and measurement method that can accurately determine ion concentrations.

[0026] 1 is a schematic diagram showing an ion concentration measuring device according to an embodiment of the present invention;

[0027] Hereinafter, an embodiment of the present invention will be described.

[0028] [Explanation of Equations (1), (2), and (3)] First, equations (1), (2), and (3) used in the present invention will be described. By using equations (1) and (2), it is possible to select an ion selective electrode that has a small measurement error and is resistant to interference from coexisting ions. This makes it possible to provide an ion concentration measuring device that can accurately determine ion concentrations, which is a feature of the present invention.

[0029] Before explaining the case where measurement is performed using n types of ion selective electrodes, the case where measurement is performed using one type of ion selective electrode will be explained.

[0030] Measurement Using One Type of Ion-Selective Electrode When measuring the concentration of a specific ion (ion B1) contained in a sample solution containing n types of ions (n ​​is an integer of 2 or more) using one type of ion-selective electrode S (hereinafter, sometimes referred to as "electrode S") and a reference electrode, the relationship expressed by the Nikolsky-Eisenman equation (Equation (5)) holds. Here, (2.303RT) / aF is taken as the slope. In other words, the slope is a constant. In practice, the slope often does not indicate a theoretical value due to various reasons, such as the electrical resistance within the device and the liquid junction potential difference. In this case, it is preferable to create a calibration curve to determine the slope.

[0031] However, E S is the potential difference developed between the ion-selective electrode S and the reference electrode, and E 0,S is the standard potential difference generated between the ion selective electrode S and the reference electrode, Slope is 2.303 RT / aF, R is the gas constant, T is the absolute temperature, a is the valence of ion B1, F is the Faraday constant, Bj represents the jth ion among n types of ions, j is an integer from 2 to n, C(Bj) is the concentration of ion Bj, and K S (B1, Bj) is the selectivity coefficient for ion Bj when ion B1 at electrode S is used as the reference.

[0032] Using the ion selective electrode S and the reference electrode, a sample solution (calibration curve solution) with a known concentration of ion B1 can be measured, and a calibration curve representing formula (5') can be created. From the calibration curve, the slope and standard potential difference E when measuring with the ion selective electrode S can be calculated. 0,S can be obtained.

[0033] By rearranging the terms in equation (5'), the following equation (8) can be derived. 0,S and the potential difference E obtained when the ion selective electrode S and the reference electrode are immersed in the sample solution. S From this, the ion concentration can be calculated when the concentrations of n types of ions in the sample solution are converted into the concentration of an arbitrary ion B1.

[0034] Here, when n=2, the above formula (8) can be expressed as the following formula (8A).

[0035] Then, by rearranging terms, the above formula (8A) can be further transformed into the following formula (8B).

[0036] That is, when n = 2, using the above formula (8B), the selectivity coefficient K for ion B2 when ion B1 at electrode S is used as the reference is S (B1, B2) can be found.

[0037] Measurement using n types of ion selective electrodes (Explanation of formula (1)) This section describes the case where n types of ions (ions: B1, B2, ..., Bj, ..., Bn, ion concentrations: C(B1), C(B2), ..., C(Bj), ..., C(Bn)) in a sample solution are measured using n types of ion selective electrodes S1 to Sn (n is an integer of 2 or more). In this case, the above formula (8) holds for each of the n types of ion selective electrodes S1 to Sn. Therefore, the simultaneous equations of formula (9) hold.

[0038] In formula (9), Bj represents the jth ion among the n types of ions, Si is a symbol representing the i-th ion selective electrode constituting the n types of ion selective electrodes, i and j are each independently an integer from 1 to n, and KSi (B1, Bj) is the K when the ion selective electrode Si (i-th ion selective electrode) is used as the ion selective electrode S. S (B1, Bj), that is, the selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as the reference, and E Si is the potential difference developed between the ion-selective electrode Si and the reference electrode, and E 0,Si is the standard potential difference generated between the ion selective electrode Si and the reference electrode, Slope is 2.303RT / aF, and R, T, a, and F are the same as R, T, a, and F defined in the above formula (5), respectively. Here, the right side of formula (9) is the calculated value obtained with the ion selective electrode Si. This value is the potential difference E Si , the slope obtained from the calibration curve and the standard potential difference E 0,Si This is the value calculated using

[0039] When the simultaneous equations of the above equation (9) are converted into a matrix form, the following equation (10) is obtained.

[0040] The matrix on the left side of equation (9) is matrix A'. Here, for each of the n types of ion selective electrodes S1, S2, ..., Sn, the selectivity coefficient K for the reference arbitrary ion B1 itself is S (B1, B1) (i.e., K S1 (B1, B1), K S2 (B1,B1),...,K Sn (B1, B1)) is 1. So, 1 is S (B1, B1) (i.e., for n types of ion selective electrodes S1, S2, ..., Sn, respectively, K S1 (B1, B1), K S2 (B1,B1),...,K Sn (B1, B1)), the matrix A' can be transformed into equation (11). The right side of equation (11) corresponds to the matrix A (equation (1)) of the present invention.

[0041] In the matrix A, Bj represents the jth ion (j is an integer from 1 to n) among the n types of ions.

[0042] Si is a symbol representing the ith (i is an integer from 1 to n) ion selective electrode constituting the n types of ion selective electrodes.

[0043] K Si (B1, Bj) is the selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as the reference. For example, K S1 (B1, B1) is the selectivity coefficient for ion B1 in the ion selective electrode S1 when ion B1 is used as the reference, K S2 (B1, B3) represents the selectivity coefficient of the ion selective electrode S2 for ion B3 when ion B1 is used as the reference.

[0044] Explanation of Equation (2) In this application, the determinant of matrix A is represented by |A|, and the absolute value of the determinant is represented by ||A||. The determinant |A| can generally be calculated by cofactor expansion or the like.

[0045] When three types of ions (ions: B1, B2, and B3, ion concentrations: C(B1), C(B2), and C(B3)) in a sample solution are measured using three types (n=3) of ion selective electrodes S1, S2, and S3, the matrix A expressed by the above formula (1) can be expressed as the following 3 × 3 square matrix. In this case, Salas' formula for matrices can be used, and the determinant |A| corresponding to the matrix A can be found by formula (12).

[0046] If matrix A is an n x n matrix, the determinant |A| can be easily found using spreadsheet software (e.g., Microsoft Excel) or numerical calculation software. When using spreadsheet software Excel, calculations can be performed using functions such as "=MDETERM." Once the determinant |A| can be found, the absolute value of the determinant, ||A||, can be calculated.

[0047] The most important point in the present invention is that the absolute value ∥A∥ of the determinant satisfies equation (2).

[0048] <Significance of Formula (2)> From formulas (10) and (11), the following formula (13) can be expressed.

[0049] When the determinant |A| of matrix A is not 0, matrix A has an inverse matrix A -1 On both sides of equation (13), the inverse matrix A -1 By multiplying this, it can be transformed into equation (14). -1 Since A is a unit matrix, Equation (14) can be transformed into Equation (15) using the cofactor matrix of matrix A shown in Equation (16).

[0050] Normally, measurements using a single ion selective electrode S are affected by measurement errors and interfering ions. When an error is included in the calculated value obtained using the ion selective electrode S, the error is defined as Δs. In the present invention, n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) are used as the ion selective electrodes S, and the error Δs for these ion selective electrodes is defined as Δ S1 , Δ S2 , ..., Δ Sn Equation (15) can be expressed as equation (17). By utilizing the property of matrix sum, it can be divided into terms indicating errors and expressed as equation (17').

[0051] Since the denominator of the term indicating the error contains the determinant |A|, the larger the absolute value ||A|| of the determinant |A|, the smaller the value of the term indicating the error. Specifically, if the absolute value of the determinant ||A|| is 0.1 or greater, the value of the term indicating the error becomes small, and an electrode capable of practical measurement can be selected. Therefore, in the present invention, this absolute value ||A|| satisfies the relationship shown in the following formula (2).

[0052] The absolute value of the determinant ∥A∥ is more preferably greater than 0.2, and even more preferably greater than 0.4. The larger the absolute value of the determinant ∥A∥, the better. Although there is no upper limit, the value is usually 100 or less.

[0053] This formula (2) is a selectivity coefficient K that reduces the influence of errors in relation to the n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) used as the ion selective electrode S and the n types of ions (ions: B1, B2, ..., Bn) in the sample solution. S (B1, Bj) (i.e., K S1 (B1, Bj), K S2 (B1,Bj),...,K Sn In the present invention, two or more types of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions are used as the ion selective electrode S. By selecting n types of ion selective electrodes that satisfy formula (2) as the two or more types of ion selective electrodes, it is possible to provide an ion concentration measuring device and method that are less affected by errors.

[0054] Explanation of Equation (3) When n types of ions in a sample solution are measured using the above-mentioned n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) as the ion selective electrode S, the concentrations of the n types of ions can be expressed by Equation (3).

[0055] Here, A -1 indicates the inverse matrix of matrix A, and C(Bj) indicates the concentration of the ion Bj (j is an integer from 1 to n). The calculated value obtained by electrode Si (i is an integer from 1 to n) indicates the value obtained by converting the potential difference measured by the ion selective electrode Si according to the following formula:

[0056] In the above formula, E Si is the potential difference developed between the ion-selective electrode Si and the reference electrode, and E 0,Si is the standard potential difference generated between the ion selective electrode Si and the reference electrode, Slope is 2.303RT / aF, and R, T, a, and F are the same as R, T, a, and F defined in the above formula (5), respectively.

[0057] In the present invention, the ion selective electrode S is also referred to as electrode S, and the i-th (i is an integer from 1 to n) ion selective electrode Si among n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) is also referred to as electrode Si. By using equation (3), the ion concentration of the sample solution can be calculated from the calculated values ​​obtained from each of the n types of ion selective electrodes used as electrode S.

[0058] When using a standard solution, if measurements are taken over a long period of time, the standard potential difference E 0,S Since the potential difference E may fluctuate, a standard solution is used. 0,S It is preferable to correct for

[0059] Standard potential difference E using standard solution 0,S The method for correcting the ion concentration is explained below. std The potential difference obtained when immersed in the standard solution of E std (Equation (18)) At this time, the standard potential difference E 0,S can be expressed by equation (19).

[0060] In the formulas (18) and (19), the slope is 2.303RT / aF, and R, T, a, and F are the same as R, T, a, and F defined in the formula (5), respectively.

[0061] The standard solution is measured, and the standard potential difference E 0,S By substituting equation (19) instead of equation (19), the calculated value obtained at electrode S can be expressed as equation (20).

[0062] By using the formula (20) for the calculated value obtained from the electrode S, when the measurement conditions such as temperature change or when the measurement is performed over a long period of time, the standard potential difference E 0,S This is preferable because it allows measurements to be made while correcting for fluctuations in the temperature.

[0063] In the present invention, n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) are used as the electrode S. Therefore, by applying the above formula (20) to each of the calculated values ​​obtained from these ion selective electrodes, the standard potential difference E 0,S (i.e., E 0,S1 , E 0,S2 , ..., E 0,Sn For example, when the above formula (20) is applied to the ith (i is an integer from 1 to n) ion selective electrode Si among n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn), the above formula (20) can be expressed as the following formula (20'):

[0064] In the above formula (20′), E Si is the potential difference developed between the ion-selective electrode Si and the reference electrode, and E 0,Si is the standard potential difference developed between the ion-selective electrode Si and the reference electrode, E Stdi is the ion concentration known (C std ) is the potential difference generated between the ion selective electrode Si and the reference electrode when immersed in a standard solution of 0.1 μm / μL, the slope is 2.303 RT / aF, and R, T, a, and F are the same as R, T, a, and F defined in the above formula (5), respectively.

[0065] The ion concentration measuring device of the present invention includes two or more types of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the above formulas (1) and (2), where n is the number of types of the plurality of ions, and n is an integer of 2 or more.

[0066] In the above formula (1), Bj represents the jth ion among the n types of ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n types of ion selective electrodes, i and j are each independently an integer from 1 to n, and K Si(B1, Bj) represents the ion selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as a reference.

[0067] In the present invention, it is preferable to calculate the ion concentration using the above formula (3).

[0068] In the present invention, ion B1 (i.e., the ion where j=1 among Bj) is an ion appropriately selected from the n types of ions constituting the plurality of ions. This ion B1 is generally an ion that is often selected as a measurement target ion in concentration measurement using a single ion selective electrode.

[0069] On the other hand, the ions other than the ion B1 among the n types of ions constituting the plurality of ions are ions B2, B3, ..., Bn (i.e., ions where j ≥ 2). Here, the ions B2, B3, ..., Bn may include ions whose concentrations are difficult to directly and selectively measure using a single ion selective electrode.

[0070] Furthermore, with regard to the two or more types of ion selective electrodes, in the present invention, there is no particular rule regarding how to assign the symbols S1, S2, ..., Sn, as long as the combination of ion selective electrodes selected as the n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) satisfies the above formula (2), and these symbols can be appropriately assigned to these ion selective electrodes. Here, the ion concentration measuring device of the present invention may include more than n types of ion selective electrodes, and n types of ion selective electrodes may be selected from these ion selective electrodes so as to satisfy formula (2) and used for ion concentration measurement. Furthermore, each ion selective electrode constituting the ion concentration measuring device of the present invention may be assigned an arbitrarily determined unique identifier separate from the symbol Si. In this case, a correspondence table between these identifiers and the symbols S1, S2, ..., Sn may be prepared in advance according to the components that may be contained in the sample solution and the types of ion selective electrodes, and ion selective electrodes to be used as the n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) may be selected from the ion selective electrodes constituting the ion concentration measuring device based on this correspondence table.

[0071] The ion concentration measuring device of the present invention is not particularly limited as long as it includes two or more types of ion-selective electrodes whose selectivity coefficient ratios for multiple ions are different from one another and satisfy Equations (1) and (2). A specific example is the device shown in FIG. 1 . Typically, the ion concentration measuring device comprises an ion-selective electrode 1, a reference electrode 2, and a potentiometer 3. Here, each ion-selective electrode 1 functions as the ion-selective electrode S, and the ion-selective electrode 1 and the potentiometer 3, and the potentiometer 3 and the reference electrode 2 are connected via electric wires. In other words, the n types of ion-selective electrodes (ion-selective electrodes S1, S2, ..., Sn) used as two or more types of ion-selective electrodes all constitute the ion-selective electrode 1 in FIG. 1 . It is also possible to combine a computing device capable of calculating the above-described equations and a tank 4 for holding a solution. Here, the computing device is connected to the potentiometer 3 and performs computations such as calculating the ion concentration based on the potential difference input from the potentiometer 3. The calculation process can include a step of forming the determinant |A| and a step of calculating the absolute value of the determinant |A|. The calculation device and the potentiometer 3 may be separate devices, or may be integrated into a single device. These are merely examples and do not limit the form of the device.

[0072] Any number of types of ion selective electrodes 1 may be combined, provided that they are two or more. The number can be adjusted appropriately according to the number of types of ions to be measured, but from the perspective of measurement accuracy, the number is preferably two or more and ten or less. In terms of the size of the ion concentration measurement device, two or more and five or less are most preferable. In other words, using the n, n is preferably two or more and ten or less, and most preferably two or more and five or less. The number of ion selective electrodes 1 must be two or more, since two or more types of ion selective electrodes must be used. There is no particular limit as long as there are two or more. In an exemplary embodiment of the present invention, the ion selective electrodes 1 are three types (i.e., n = 3), but this is not limited to this. It is also possible to combine multiple ion selective electrodes of the same type.

[0073] There is no particular limitation on the number of reference electrodes 2, provided that there is one or more, but usually fewer than the number of ion selective electrodes are used.

[0074] The potentiometer 3 is not limited as long as it can measure the potential difference between two or more types of ion selective electrodes and a reference electrode. If the potential difference is to be measured, a voltmeter can also be used.

[0075] The tank 4 for holding the solution can be used without any particular limitation as long as it can immerse the ion selective electrode and the reference electrode. Multiple tanks may be used according to the number of types of ion selective electrodes, or multiple ion selective electrodes may be immersed in one tank. The tank may be capable of immersing each electrode in a batch system, or a flow path may be set up to circulate the sample solution, etc. Furthermore, the sample solution may be stirred or circulated to make it homogenous.

[0076] Ion Selective Electrode The ion selective electrode 1 functions as the ion selective electrode S, and any commonly used electrode such as an internal liquid type ion selective electrode or a solid electrode type ion selective electrode can be used without any particular limitation. In the present invention, n types of ion selective electrodes 1, each having a different ratio of selectivity coefficients for a plurality of ions, are combined and used as the ion selective electrodes S1, S2, ..., Sn.

[0077] As shown in FIG. 1, the internal liquid type ion selective electrode has an internal electrode 5, an internal liquid 6, and an ion selective membrane 7, and the ion selective membrane 7 is in contact with a sample solution 9.

[0078] There are no particular limitations on the internal electrode 5 as long as it is a commonly used electrode. Typically, a silver / silver chloride electrode is used.

[0079] The internal liquid 6 is usually an aqueous solution of an electrolyte such as KCl or NaCl.

[0080] The ion-selective membrane 7 is not particularly limited, but may be a polymer substrate such as polyvinyl chloride mixed with a plasticizer and a ligand that selects ions. It may also contain salts. Specifically, when the ion-selective electrode 1 is a cation-selective electrode for sodium, potassium, calcium, magnesium, or the like (i.e., a cation-selective electrode that selectively responds to cations such as sodium, potassium, calcium, and magnesium to generate an output corresponding to the concentration (activity) of the cation), a membrane such as that described in Pure Appl. Chem., 2000, Vol. 72, No. 10, pp. 1851-2082 can be used as the ion-selective membrane 7. Furthermore, when the ion selective electrode 1 is an anion selective electrode for chloride, carbonate, thiocyanate, nitric acid, hydroxide, phosphoric acid, sulfuric acid, iodine, or the like (i.e., an anion selective electrode that selectively responds to anions such as nitric acid, hydroxide, phosphoric acid, sulfuric acid, and iodine to generate an output corresponding to the concentration (activity) of the anion), the ion selective membrane 7 can be a membrane such as that described in Pure Appl. Chem., 2002, Vol. 74, No. 6, pp. 923-994, or a silver halide membrane such as silver chloride or silver bromide, or an ion exchange membrane (see JP-A-10-318973, JP-A-11-132991, and JP-A-2003-207476). Such membranes can be self-prepared and used, or commercially available membranes can be used. That is, the ion selective membrane 7 may be a self-made membrane or a commercially available membrane as long as it is a membrane as described above. Examples of commercially available membranes include Neosepta (registered trademark) CSE (registered trademark) (manufactured by Astom Co., Ltd.) and Neosepta ASE (manufactured by Astom Co., Ltd.).

[0081] In the present invention, two or more types of ion selective electrodes that satisfy the formulas (1) and (2) must be selected as the ion selective electrodes that constitute the ion concentration measuring device. Whether or not the formulas (1) and (2) are satisfied is determined by the selectivity coefficient K of each ion selective electrode. S It is determined by (B1, Bj).

[0082] Ion selectivity coefficient K S(B1, Bj) can generally be calculated by the single solution method or the mixed solution method. In the mixed solution method, the potential difference of a mixed solution containing an ion B1 of known concentration and an ion Bj of which the selectivity coefficient is to be calculated is measured, and the ion selectivity coefficient K S Calculate (B1, Bj).

[0083] An example of such calculation is shown below with specific numerical values ​​for a case where two types of ion selective electrodes (a first ion selective electrode S1 and a second ion selective electrode S2) are used as the ion selective electrode S and a mixed solution containing ion B1 and a second ion B2 is measured. The ion selectivity coefficient K for ion B2 when ion B1 is used as the reference for the ion selective electrode S1 and the ion selective electrode S2 is S (B1, B2) are K S1 (B1, B2) = 0.5, and K S2 Assume that (B1, B2) = 0.1. Here, the ion selectivity coefficient K for the ion B1 itself when the ion B1 is used as the reference for the ion selective electrodes S1 and S2 is S (B1, B1) are K S1 (B1, B1) = 1 and K S2 It can be considered that (B1, B1) = 1. The matrix A and the determinant |A| can be expressed by the following equation using these selection coefficients. In this case, the determinant |A| can be calculated as -0.4.

[0084]

[0085] Reference Electrode The reference electrode 2 is not particularly limited as long as it is a commonly used electrode. However, in a typical embodiment, the reference electrode 2 has an internal electrode 5, an internal solution 6, and a liquid junction 8, as shown in FIG. 1. An example of a reference electrode 2 that can be used in the present invention is a silver-silver chloride reference electrode, which uses a 3 M potassium chloride aqueous solution as the internal solution 6, a silver-silver chloride electrode as the internal electrode 5, and has a liquid junction 8 between the sample solution and the internal solution. However, the reference electrode 2 may also be another reference electrode, such as a saturated calomel electrode.

[0086] Ions are not particularly limited as long as an ion solution can be prepared and the ion can be measured using the device. Anions can be either anions or cations. Examples of anions include chloride ions, bicarbonate ions, anions of organic acids, nitrate ions, and sulfate ions, while examples of cations include potassium ions, silver ions, and copper ions. More preferred examples, which make the most of the features of the device, include the multiple ions contained in blood (chloride ions, bicarbonate ions, and anions of organic acids such as lactate, pyruvate, propionic acid, fatty acids, and amino acids).

[0087] Here, the "multiple ions" used in the present invention may consist of two or more anions, or may consist of two or more cations. When the "multiple ions" are anions, the "multiple ions" may be two or more selected from the anions exemplified above, for example, chloride ions and bicarbonate ions, preferably chloride ions, bicarbonate ions, and anions of organic acids. In one preferred and exemplary embodiment of the present invention, the "multiple ions" are chloride ions, bicarbonate ions, and acetate ions. However, the "multiple ions" used in the present invention are not limited to the above examples and may be selected appropriately depending on the object to be measured.

[0088] Here, in the present invention, when evaluation is performed using the above formulas (1) and (2), one ion B1 (i.e., an ion in Bj where j=1) is selected from the n types of ions constituting the "plural ions," and the other n-1 types of ions are designated as ions B2, B3, ... Bn (i.e., ions in Bj where j≧2).

[0089] Among these, ion B1 is an ion whose concentration can be directly measured using a single ion selective electrode having an extremely small selectivity coefficient for other ions. Examples of ions that can be ion B1 include chloride ions and sodium ions.

[0090] On the other hand, the ions other than ion B1 (i.e., ions B2, B3, ... Bn) may be ions whose concentrations can be directly measured using a single ion selective electrode, or may be ions whose concentrations are difficult to measure directly using a single ion selective electrode. Examples of ions that can be ions other than ion B1 include bicarbonate ions and anions of organic acids such as acetate ions.

[0091] According to the present invention, it is possible to measure the concentration of an ion such as bicarbonate ion, for which it is difficult to obtain an electrode with a sufficiently small ion selectivity coefficient relative to other ions. Based on this, in one preferred exemplary aspect of the present invention, the ion B1 is a chloride ion, and the ions other than the ion B1 include bicarbonate ion.

[0092] The method for measuring ion concentration of the present invention includes a step of measuring the ion concentration of a sample solution using a plurality of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the above formulas (1) and (2), where n is the number of types of ions, and the two or more types of ion selective electrodes are composed of n types of ion selective electrodes, where n is an integer of 2 or more.

[0093] In the above formula (1), Bj represents the jth ion among the n types of ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n types of ion selective electrodes, i and j are each independently an integer from 1 to n, and K Si (B1, Bj) represents the ion selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as a reference.

[0094] In the present invention, it is preferable to calculate the ion concentration using the above formula (3).

[0095] The ion concentration measuring method of the present invention is not particularly limited to the instruments or devices to be used, as long as it is a method of measuring ion concentrations using a plurality of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the above formulas (1) and (2). However, it is convenient to use, for example, the ion concentration measuring device shown above.

[0096] The concentration of the ion to be measured (the ion B1) is not particularly limited, but is preferably 0 mM to 1 M. More preferably, it is 0 mM to 300 mM.

[0097] When measuring over a long period of time, the standard potential difference E 0,S Since the value may fluctuate, it is preferable to perform correction using a standard solution.

[0098] First, the sample solution and the standard solution will be explained.

[0099] Sample Solution <Sample> There are no particular limitations on the sample, and any sample that contains ions when made into a solution can be measured. The present invention is particularly effective for samples that contain multiple types of ions, such as biological samples (blood, serum, plasma, etc.). Depending on the state and concentration of the sample and the coexisting substances, the sample may be measured as is. However, preferably, the sample is diluted with a buffer solution, water, an organic solvent, etc., and measured as a sample solution to suppress pH fluctuations and eliminate liquid junction potential differences. Depending on the coexisting substances, the sample may be used after pretreatment using a column, filter, etc.

[0100] <Buffer Solution> If ion concentrations can be measured stably, it is not always necessary to use a buffer solution, but it is preferable to use one because it suppresses pH fluctuations and eliminates liquid junction potential differences.

[0101] Any commonly known buffer solution can be used without limitation as long as it achieves the above-mentioned purpose. Specific examples include buffer solutions known as Good's buffers (HEPES buffer, MES buffer, ADA buffer) and Tris buffer. For example, when measuring bicarbonate ions, HEPES buffer is preferred because it minimizes the inhibition of the response of the ion-selective electrode to the ions. The pH of the buffer solution is approximately 6.0 to 8.0 for Good's buffer. The concentration of the buffer solution is not particularly limited, but is preferably 1 mM to 1 M. A buffer solution of 1 mM to 500 mM is more preferred. A buffer solution of 5 mM to 300 mM is even more preferred.

[0102] Standard solution The standard solution has a standard potential difference E 0,S It is an ionic solution with a known concentration that is used to correct the potential (E std There are no particular limitations on the ion species as long as they can be measured. Two or more ions can be used in combination, but it is usually preferable to select one ion species from the ions to be measured, as this is simple and convenient.

[0103] The solvent used for the standard solution is not limited to water, organic solvents, etc., as long as the potential can be measured. Two or more solvents can also be mixed. From the viewpoint of pH stability, water is preferably used as the solvent. To suppress pH fluctuations and eliminate liquid junction potential differences, it is more preferable to use a buffer solution. As the buffer solution, those that can be used for the sample solution as described above can be used.

[0104] Ion concentration of the standard solution (C std ) is not particularly limited and may be determined appropriately depending on the purpose of measurement. std ) is used at 0.1 to 10 mM. More preferably, the ionic concentration is 0.5 to 3 mM.

[0105] Measurement of Potential Difference and Calculation of Ion Concentration A method for measuring ion concentration will be described below, but this is merely an example and is not particularly limited.

[0106] Generally, the potential difference E S Measure E 0,S, Slope are calculated, and from these values, the calculated value obtained at electrode S is calculated. Then, the ion concentration is calculated from the calculated value obtained at electrode S.

[0107] Calculation of ion concentration when a standard solution is used will also be described, but this is one means for measuring with high accuracy and does not limit the present invention.

[0108] <Potential difference E of sample solution S Measurement of potential difference E S The measurement is carried out by immersing an ion selective electrode and a reference electrode in the sample solution and measuring the potential difference with a potentiometer. The measurement conditions, such as the measurement temperature and measurement time, are S In order to measure a stable potential difference, the measurement temperature is preferably 20° C. to 45° C. and the measurement time is preferably 2 seconds to 15 minutes.

[0109] <Creating a calibration curve (E 0,S Calculation of the value of Slope)> The potential difference E of a known solution containing a certain ion B1 at an ion concentration C(B1) S By measuring the value, a calibration curve was created using the Nernst equation. 0,S , Slope can be calculated.

[0110] In the above formula, Slope is 2.303RT / aF, and R, T, a, and F are the same as R, T, a, and F defined in the above formula (5), respectively.

[0111] The ion used for the calibration curve is usually one of the ions to be measured, which is designated as B1 here.

[0112] In order to increase the accuracy of the calibration curve, it is preferable that the solution with known concentration used to create the calibration curve has a composition similar to that of the sample solution to be measured, and therefore it is preferable that the solvent of the sample solution and the solution used for the calibration curve be the same. The ion concentration C (B1) can be determined appropriately according to the sample solution to be measured. Although the calibration curve can be created by measuring the ion concentration at two different points, in order to increase accuracy, the ion concentration C (B1) is measured at three or more points to create the calibration curve.

[0113] <Calculation of the calculated value obtained with electrode S and the ion concentration> The potential difference E between the ion selective electrode and the reference electrode obtained by immersing the sample solution S and E obtained using the calibration curve as described above. 0,S , Slope, the calculated value obtained at electrode S can be calculated using the following formula:

[0114] For each of the n types of ion selective electrodes S1 to Sn used as the electrode S, the "calculated value obtained at electrode S" is calculated, and these are respectively designated as "calculated value obtained at electrode S1," "calculated value obtained at electrode S2," ..., "calculated value obtained at electrode Sn." The inverse matrix A of the matrix A consisting of these calculated values ​​and the selectivity coefficients of the ion selective electrodes used is calculated. -1 By using the above formula, it is possible to obtain the respective ion concentrations (C(B1), C(B2), ..., C(Bn)) of n types of ions (ions: B1, B2, ..., Bn).

[0115]

[0116] <Calculation of ion concentration when using a standard solution> When using a standard solution, immerse the ion selective electrode and the reference electrode in the standard solution and calculate the potential difference E std Calculate the standard potential difference E 0,S Correct the potential difference E std There are no particular limitations on the instruments, devices, etc. that can be used as long as the above can be measured, but it is convenient to use the same device as that used to measure the sample solution.

[0117] In order to measure the standard solution in a stable manner, the measurement temperature is preferably 20° C. to 45° C. and the measurement time is preferably 2 seconds to 15 minutes.

[0118] Potential difference E of standard solution std Although correction can be made by measuring once, it is preferable to measure repeatedly between measurements of the sample solution in order to obtain a calculated value obtained by the electrode S with higher accuracy. std The interval at which the potential difference E is repeatedly measured may be determined appropriately. std It is also possible to correct the potential difference Estd From the viewpoint of accuracy, the potential difference E of the target sample solution may be averaged and used for correction. S The potential difference E measured 2 seconds to 1 hour before measuring std It is preferable to adopt

[0119] The potential difference E obtained when immersed in the standard solution std and the ion concentration of the standard solution (C std ) can be used to calculate the calculated value obtained at electrode S from equation (20).

[0120] For each of the n types of ion selective electrodes S1 to Sn used as the electrode S, the "calculated value obtained at electrode S" is calculated, and these are respectively designated as "calculated value obtained at electrode S1," "calculated value obtained at electrode S2," ..., "calculated value obtained at electrode Sn." The inverse matrix A of the matrix A consisting of these calculated values ​​and the selectivity coefficients of the ion selective electrodes used is calculated. -1 By using the above formula, it is possible to obtain the respective ion concentrations (C(B1), C(B2), ..., C(Bn)) of n types of ions (ions: B1, B2, ..., Bn).

[0121] The present invention will be described in more detail below with reference to examples, but the present invention is not limited to these examples in any way.

[0122] [Configuration of Ion Concentration Measuring Device] The ion concentration measuring device used in the following examples and comparative examples includes an ion selective electrode, a reference electrode, a potentiometer, a tank for holding a solution, and a computing device.

[0123] The ion-selective electrode and the potentiometer are connected via electric wires, and the potentiometer and the reference electrode are connected via electric wires. The potentiometer is also connected to a computing device. When measuring ion concentrations, a liquid to be measured (e.g., a sample solution, a standard solution, or a calibration curve solution, as described below) is introduced into the "solution tank," and the ion concentration measurement is performed with the portion of the ion-selective electrode having the ion-selective electrode and the portion of the reference electrode having the liquid junction immersed in the "liquid to be measured."

[0124] In the following Examples and Comparative Examples, the following reference electrodes, potentiometers, solution tanks, and computing devices were used unless otherwise specified. The ion-selective electrodes used in the following Examples and Comparative Examples will be described later in the following Examples and Comparative Examples.

[0125] (Reference Electrode) A commercially available silver-silver chloride reference electrode (218087) manufactured by A&T Corporation was used as the reference electrode.

[0126] (Potentiometer, Calculating Device, and Tank for Holding Solution) The potentiometer, calculating device, and tank for holding the solution were those attached to an electrolyte analyzer ELA08 manufactured by A&T Corporation.

[0127] [Preparation of Ion-Selective Electrode] As the ion-selective electrode, an electrode obtained by modifying a commercially available chloride ion electrode (manufactured by A&T Corporation) by replacing the ion-selective membrane was used.

[0128] The ion-selective membranes were prepared based on the method described in Example 1 of JP 2018-004633 A, by varying the compounding ratio of amine to halide and the reaction time as shown in Table 1. Trimethylamine was used as the tertiary amine. The reaction time was adjusted appropriately between 12 and 24 hours, and seven types of ion-selective membranes with different ion selectivities were obtained.

[0129] Ion-selective electrodes (respectively designated by electrode symbols EL1 to EL7) obtained using these seven types of ion-selective membranes were used to measure ion concentrations in the following examples and comparative examples. In the following description, the ion-selective electrodes designated by electrode symbols EL1 to EL7 may be referred to as electrodes EL1 to EL7, respectively. The electrode symbols EL1 to EL7 shown below are unique identifiers defined separately from the symbols S1 to Sn of the ion-selective electrodes in matrix A.

[0130]

[0131] Example 1 1-1 Configuration of Ion Concentration Measuring Device In this example, an ion concentration measuring device having the configuration described above in "Configuration of Ion Concentration Measuring Device" was used.

[0132] (Ion-selective electrodes) The ion-selective electrodes used were the ion-selective electrode with electrode symbol EL1 ("electrode EL1"), the ion-selective electrode with electrode symbol EL2 ("electrode EL2"), and the ion-selective electrode with electrode symbol EL3 ("electrode EL3") obtained in the above "Preparation of ion-selective electrodes."

[0133] (Reference electrode, potentiometer, computing device, and tank for holding solution) The reference electrode, potentiometer, computing device, and tank for holding solution were those described in the above "Configuration of ion concentration measuring device."

[0134] In the device used in the examples, the potential difference E between the solution introduced into the tank and the multiple ion selective electrodes is S can be measured in parallel at the same time. Therefore, in the examples, the potential differences of multiple ion selective electrodes with respect to the solution were measured simultaneously, but this does not limit the present invention. Any method can be used without particular limitations as long as it can obtain the potential differences of multiple ion selective electrodes with respect to the same solution, and the potential differences obtained by the ion selective electrodes may be measured simultaneously or in any order.

[0135] 1-2 Sample solution The anions in blood are Cl, in descending order of abundance. - >HCO3 - > Ions of organic acids (lactic acid, pyruvic acid, propionic acid, fatty acids, amino acids, etc.) (here, acetate ions (AcO - ) are used as substitutes), so these three were used as the ions to be measured. In addition, blood contains impurity ions, so phosphate ions, bromide ions, and thiocyanate ions were added to prepare the sample solution. Sample solution X was prepared by dissolving the salts containing the target ions and impurity ions shown in Table 2 in HEPES buffer (100 mM, pH 8.0).

[0136] The solvent was HEPES buffer (100 mM, pH 8.0).

[0137] 1-3 Standard solution Dissolve 0.58 g of sodium chloride (NaCl) in 1 L of HEPES buffer (100 mM, pH 8.0) to obtain a 1 mM (= C Std ) sodium chloride (NaCl) / HEPES buffer solution was prepared.

[0138] 1-4 Solutions for Calibration Curve Sodium chloride (NaCl) was dissolved in HEPES buffer (100 mM, pH 8.0) to prepare 80, 100, and 120 mM sodium chloride (NaCl) / HEPES buffer solutions, which were used as solutions for calibration curves.

[0139] 1-5 Preparation of calibration curve (E std (Calculation of Slope Value) The calibration curve was prepared as follows.

[0140] 2 ml of the calibration curve solution was placed in a vial and set in an electrolyte analyzer ELA08 manufactured by A&T Corporation, and measurements were carried out at room temperature. The measurements were carried out using the ion selective electrode (electrode EL1, electrode EL2, or electrode EL3) and the reference electrode connected to each other via the potentiometer, and the potential difference E Std Then, the potential difference E S This series of operations was carried out for each of the three types of calibration curve solutions. Here, if the standard solution is set in a predetermined location, it will automatically circulate and the potential E of the standard solution can be measured at any time. std is a system that can be measured.

[0141] 80, 100, 120 mM (=C(Cl)) prepared in 1-4 above - )) the potential difference E when the calibration curve solution was measured with electrodes EL1, EL2, and EL3 S and the potential difference E of the standard solution Std is shown in Table 3.

[0142] The value of Slope was calculated as follows.

[0143] From the formula (18') and the formula (19), the following formula (X1) is obtained. By substituting the above values ​​into this formula (X1), the potential difference (E S -E Std ) and (log 10 C(Cl - )-log 10 C std The slope of each electrode is shown in Table 3.

[0144]

[0145]

[0146] 1-6 Calculation of selectivity coefficient for ion selective electrode and creation of matrix A (Calculation of selectivity coefficient) The selectivity coefficient for the ion to be measured was calculated for each of the electrodes with the electrode symbols EL1 to EL3 (electrodes EL1 to EL3). Here, the ion to be measured was chloride ion (Cl - ) is used as an example.

[0147] The selectivity coefficient was calculated as follows.

[0148] (1) Bicarbonate ion (HCO - Calculation of the selectivity coefficient First, the reference ion (measurement target ion) (chloride ion (Cl)) used to create the calibration curve was - )) and the ion for which you want to calculate the selectivity coefficient (bicarbonate ion (HCO3 - )), including bicarbonate ions (HCO - ) A solution for calculating the selectivity coefficient was prepared.

[0149] Sodium bicarbonate (NaHCO3) and sodium chloride (NaCl) were dissolved in HEPES buffer (100 mM, pH 8.0) to prepare 10 mM sodium bicarbonate (NaHCO3) and 100 mM sodium chloride (NaCl) / HEPES buffer. - ) was used as a solution for calculating the selectivity coefficient.

[0150] Bicarbonate ion (HCO3 - ) 2 ml of the solution for calculating the selectivity coefficient was placed in a vial, which was then set in an electrolyte analyzer ELA08 manufactured by A&T Corporation, and measurements were carried out at room temperature. The measurements were carried out using the ion selective electrode (electrode EL1, EL2 or EL3) and the reference electrode connected to each other via the potentiometer, and for each solution for calculating the selectivity coefficient, the potential difference E Std Then, the potential difference E S This was done by measuring

[0151] Here, the following formula (19)

[0152] The potential difference E when measuring the standard solution Std , the slope value shown in Table 3 obtained in "1-5 Preparation of calibration curve" above, and the ion concentration C of the standard solution Std Substituting the standard potential difference E 0,S and further calculate the following formula (8B):

[0153] The standard potential difference E 0,S , the potential difference E S , the Slope value, and bicarbonate ion (HCO - ) Ion concentration in the solution for calculating the selectivity coefficient (chloride ion (Cl - ) is defined as C(B1), and the concentration of bicarbonate ions (HCO3 - ) is C(B2). By substituting ), we can obtain the chloride ion (Cl - ) is the target ion to be measured. - ) to the selectivity coefficient (Ks(Cl - , HCO3 - )) is obtained.

[0154] The bicarbonate ion (HCO - ) The potential difference E when the solution for calculating the selectivity coefficient is measured with the electrodes EL1, EL2, and EL3 S and the potential difference E of the standard solution Std and the selectivity coefficient (Ks(Cl - , HCO3 - )) are shown in Table 4.

[0155]

[0156] (2) Acetate ion (AcO - Calculation of the selectivity coefficient: As in (1) above, acetate ion (AcO - ) A solution for calculating the selectivity coefficient was prepared.

[0157] Sodium acetate (NaOAc) and sodium chloride (NaCl) were dissolved in HEPES buffer (100 mM, pH 8.0) to prepare 10 mM sodium acetate (NaOAc) and 100 mM sodium chloride (NaCl) / HEPES buffer. - ) was used as a solution for calculating the selectivity coefficient.

[0158] Acetate ion (AcO - ) 2 ml of the solution for calculating the selectivity coefficient was placed in a vial and set in an electrolyte analyzer ELA08 manufactured by A&T Corporation, and measurements were carried out at room temperature. The measurements were carried out using the ion selective electrode (electrode 1, 2 or 3) and the reference electrode connected to each other via the potentiometer, and for each calibration curve solution, the potential difference E Std Then, the potential difference E S This was done by measuring

[0159] Here, the potential difference E S As the potential difference E S As C(B1) and C(B2), acetate ions (AcO - ) Chloride ions (Cl) in the solution for calculating the selectivity coefficient - ) and acetate ions (AcO - ) are used in the same manner as above except that the concentrations of bicarbonate ions (HCO - As in "Calculation of the selectivity coefficient," various parameters are substituted into the above formulas (19) and (8B) to obtain the chloride ion (Cl - ) as the measurement target ion, acetate ion (AcO - ) to the selectivity coefficient (Ks(Cl - , AcO - )) is obtained.

[0160] The acetate ion (AcO - ) The potential difference E when the solution for calculating the selectivity coefficient is measured with the electrodes EL1, EL2, and EL3 S and the potential difference E of the standard solution Std and the selectivity coefficient (Ks(Cl - , AcO - )) are shown in Table 5.

[0161]

[0162] (Creation of Matrix A) Matrix A was created from the values ​​of the selectivity coefficients obtained in the above "Calculation of Selectivity Coefficients" for the electrodes EL1, EL2, and EL3.

[0163] The selectivity coefficients obtained in the above "Calculation of Selectivity Coefficients" are summarized in Table 6 below. - )) selectivity coefficient (Ks(Cl - , Cl - )) is set to 1.

[0164] The matrix A corresponding to the selectivity coefficients shown in Table 6 above can be expressed as follows. In determining the matrix A below, the electrodes EL1, EL2, and EL3 are the first ion selective electrode (ion selective electrode S1), the second ion selective electrode (ion selective electrode S2), and the third ion selective electrode (ion selective electrode S3), respectively. In the matrix A below, the selectivity coefficient K for the ith ion selective electrode (i is 1 to 3) of these three ion selective electrodes is S (Cl - , Cl - ), K S (Cl - , HCO3 - ), and K S (Cl - , AcO - ) respectively as K Si (Cl - , Cl - ), K Si (Cl - , HCO3 - ), and K Si (Cl - , AcO - ) is shown.

[0165] This matrix A was entered into cells (A1:C3) of the spreadsheet software Excel, and the absolute value of the determinant ||A|| was calculated using the function "=MDETERM(A1:C3)", which was 0.42.

[0166] Specifically, the absolute value ||A|| in Excel can be calculated as follows. First, enter 1 into cell A1, 1 into cell A2, 1 into cell A3, 0.10 into cell B1, 0.56 into cell B2, 0.87 into cell B3, 0.07 into cell C1, 0.76 into cell C2, and 0.32 into cell C3. Next, enter "=MDETERM(A1:C3)" into any cell other than these cells. The calculated value of "=MDETERM(A1:C3)" can be obtained as the value of the determinant |A| (in this case, -0.42). Then, apply the ABS function to the value of the determinant |A| to obtain the absolute value of the determinant |A|, which can be used as the absolute value ||A||.

[0167] Here, in Tables 4 to 6 and the determinant A, the K S (Cl - , HCO3 - ) and K S (Cl - , AcO - For convenience of documentation, the value of ) is rounded to three decimal places. However, the inverse matrix A described below in "1-8 Calculation of ion concentration of sample solution" is -1 In calculating the concentration of each ion, the values ​​were not rounded off to the third decimal place, but were used in a way that took into account the third decimal place and beyond.

[0168] 1-7 Potential difference E of sample solution S 2 ml of sample solution X was placed in a vial and set in an electrolyte analyzer ELA08 manufactured by A&T Corporation, and measurements were carried out at room temperature. The measurement was carried out using the ion selective electrode (electrode EL1, EL2 or EL3) and the reference electrode connected to each other via the potentiometer, and first, the potential difference E Std Then, the potential difference E of the sample solution X is measured. S The measured values ​​and the calculated values ​​obtained from the measured values ​​(calculated values ​​obtained with electrode S) are shown in Table 7. std Using the Slope values ​​in Table 4 obtained in the "Calculation of Slope Values" procedure,std was corrected with.

[0169]

[0170]

[0171] 1-8 Calculation of Ion Concentration of Sample Solution The ion concentration of the above sample solution (sample solution X) was calculated as follows.

[0172] First, the inverse matrix A of the matrix A obtained in the above "1-6 Calculation of the selectivity coefficient for the ion selective electrode and creation of matrix A" is calculated. -1 This matrix A is obtained by treating the electrodes EL1, EL2, and EL3 as the ion selective electrodes S1, S2, and S3, respectively. -1 was calculated by inputting matrix A into cells (A1:C3) of the spreadsheet software Excel and using the function "=MINVERSE(A1:C3)."

[0173] Here, the inverse matrix A in Excel -1 The calculation of the inverse matrix A can be performed by inputting "=MINVERSE(A1:C3)" into any cell away from the cells A1 to C3 input in "1-6 Calculation of selectivity coefficients for ion selective electrodes and creation of matrix A" above. The group of calculated values ​​displayed in the cell into which "=MINVERSE(A1:C3)" has been input and in the cells nearby can be used to generate the inverse matrix A. -1 It can be adopted as.

[0174] The above "1-7 Potential difference E of sample solution S The "calculated value obtained at electrode S" shown in Table 7 above was obtained by "measurement of -1 Applying chloride ions (Cl - ) concentration C(Cl - ), bicarbonate ion (HCO3 - ) concentration C(HCO - ), and acetate ions (AcO - ) concentration C(AcO -) was calculated. Here, the "calculated value obtained at electrode S" for electrode EL1 was defined as the "calculated value obtained at electrode S1", the "calculated value obtained at electrode S" for electrode EL2 was defined as the "calculated value obtained at electrode S2", and the "calculated value obtained at electrode S" for electrode EL3 was defined as the "calculated value obtained at electrode S3". As a result, C(Cl - ) = 105.7mM, C(HCO3 - )=26.0mM, C(AcO - ) = 6.09 mM.

[0175] Here, the inverse matrix A -1 , the K for each ion selective electrode calculated in the above "1-6 Calculation of the selectivity coefficient for the ion selective electrode and creation of matrix A" S (Cl - , HCO3 - ) and K S (Cl - , AcO - ) value, and the above "1-7 Potential difference E of sample solution S For the sake of documentation, the "calculated values ​​obtained with electrode S" obtained in the "measurement of ion concentration" are rounded to two decimal places. However, when calculating the concentration of each ion, these values ​​were not rounded to two decimal places, but were used in a way that took into account the decimal places after the third decimal place. Rounding was not performed during the calculation of the concentration of each ion, but was only performed on the final concentration values.

[0176] The same procedure was followed when calculating the concentration of each ion in Example 2 and Comparative Example 1 below.

[0177] In addition, due to errors caused by such rounding of values, the calculation results for the concentration of each ion obtained in this example and the following Example 2 and Comparative Example 1 were calculated by rounding to three decimal places as the "calculated value obtained at electrode S" and calculating the inverse matrix A -1An inverse matrix is ​​used, in which the values ​​of each element are rounded to two decimal places, and the concentration value obtained by simply combining these may differ slightly.

[0178] The above "1-7 Potential difference E of sample solution S The procedures in "Measurement of ion concentration in sample solution" and "1-8 Calculation of ion concentration in sample solution" were repeated six times, and the relative standard deviation (standard deviation divided by the average value) (%) was calculated for each of chloride ion, bicarbonate ion, and acetate ion. The results are shown in Table 18.

[0179] [Example 2] 2-1 Configuration of Ion Concentration Measuring Device An ion concentration measuring device having the configuration described above in "Configuration of Ion Concentration Measuring Device" was used, similarly to Example 1. Here, the ion selective electrode, reference electrode, potentiometer, solution tank, and computing device used were as follows.

[0180] (Ion-selective electrodes) The ion-selective electrodes used were the ion-selective electrode with electrode symbol EL1 ("electrode EL1"), the ion-selective electrode with electrode symbol EL2 ("electrode EL2"), and the ion-selective electrode with electrode symbol EL4 ("electrode EL4") obtained in the above "Preparation of ion-selective electrodes."

[0181] (Reference electrode, potentiometer, computing device, and solution tank) As in Example 1, the reference electrode, potentiometer, computing device, and solution tank described above in "Configuration of ion concentration measuring device" were used.

[0182] 2-2 Sample Solution The sample solution used was the same as sample solution X used in Example 1.

[0183] 2-3 Standard Solution The same standard solution as in Example 1 was used.

[0184] 2-4 Solution for Calibration Curve The same solution for calibration curve as in Example 1 was used.

[0185] 2-5 Preparation of calibration curve (E std(Calculation of Slope Value) The calibration curve was prepared and the slope value was calculated in the same manner as in Example 1, except that the electrode EL1, the electrode EL2, or the electrode EL4 was used as the ion selective electrode. The obtained slope values ​​are shown in Table 8.

[0186]

[0187] 2-6 Calculation of selectivity coefficients for ion selective electrodes and creation of matrix A (Calculation of selectivity coefficients) The selectivity coefficients for the ions to be measured were calculated for each of the electrodes with the electrode symbols EL1, EL2, and EL4 (electrodes EL1, EL2, and EL4). The selectivity coefficients were calculated in the same manner as in Example 1. The measured values ​​and the calculated selectivity coefficients are shown in Tables 9 and 10.

[0188]

[0189]

[0190] (Creation of Matrix A) Matrix A was created from the values ​​of the selectivity coefficients obtained in the above "Calculation of Selectivity Coefficients" for the electrodes EL1, EL2 and EL4.

[0191] The selectivity coefficients obtained in the above "Calculation of Selectivity Coefficients" are summarized in Table 11 below. Here, the measurement target ions (chloride ions (Cl - )) selectivity coefficient (Ks(Cl - , Cl - )) is set to 1.

[0192] The matrix A corresponding to the selectivity coefficients shown in Table 11 above can be expressed as follows. In determining the matrix A below, the electrodes EL1, EL2, and EL4 were respectively the first ion selective electrode (ion selective electrode S1), the second ion selective electrode (ion selective electrode S2), and the third ion selective electrode (ion selective electrode S3). In the matrix A below, the selectivity coefficient K for the ith ion selective electrode (i is 1 to 3) of these three ion selective electrodes is S (Cl - , Cl - ), K S (Cl -, HCO3 - ), and K S (Cl - , AcO - ) respectively as K Si (Cl - , Cl - ), K Si (Cl - , HCO3 - ), and K Si (Cl - , AcO - ) is shown.

[0193] This matrix A was entered into cells (A1:C3) of the spreadsheet software Excel, and the absolute value of the determinant, ∥A∥, was calculated using the function "=MDETERM(A1:C3)", which was 0.20.

[0194] 2-7 Potential difference E of sample solution S Measurement of the potential difference E of the sample solution S The measurement was carried out in the same manner as in Example 1, except that the electrode EL1, the electrode EL2, or the electrode EL4 was used as the ion selective electrode. The measured values ​​and the calculated values ​​obtained from the measured values ​​(calculated values ​​obtained with electrode S) are shown in Table 12. The Slope values ​​in Table 8 obtained in the same manner as in Example 1 were used to calculate the E std was corrected with.

[0195]

[0196] 2-8 Calculation of Ion Concentration of Sample Solution The ion concentration of the above sample solution was calculated in the same manner as in Example 1.

[0197] First, the inverse matrix A of the matrix A obtained in the above "2-6 Calculation of the selectivity coefficient for the ion selective electrode and creation of matrix A" is calculated. -1 is calculated in the same manner as in Example 1. This matrix A is obtained by treating the electrodes EL1, EL2, and EL4 as the ion selective electrodes S1, S2, and S3, respectively. -1 was calculated by inputting matrix A into cells (A1:C3) of the spreadsheet software Excel and using the function "=MINVERSE(A1:C3)".

[0198] The above "2-7 Potential difference E of sample solution S The inverse matrix A is calculated using the "calculated value obtained at electrode S" shown in Table 12 above, which is obtained by the "measurement of -1 Applying chloride ions (Cl - ) concentration C(Cl - ), bicarbonate ion (HCO3 - ) concentration C(HCO - ), and acetate ions (AcO - ) concentration C(AcO - ) was calculated. Here, the "calculated value obtained at electrode S" for electrode EL1 was defined as the "calculated value obtained at electrode S1", the "calculated value obtained at electrode S" for electrode EL2 was defined as the "calculated value obtained at electrode S2", and the "calculated value obtained at electrode S" for electrode EL4 was defined as the "calculated value obtained at electrode S3". As a result, C(Cl - ) = 105.7mM, C(HCO3 - )=27.6mM, C(AcO - ) = 5.21 mM.

[0199] The above "2-7 Potential difference E of sample solution S The procedures in "Measurement of ion concentration" and "2-8 Calculation of ion concentration of sample solution" were repeated six times, and the relative standard deviation (%) was calculated in the same manner as in Example 1. The results are shown in Table 18.

[0200] Comparative Example 1 C1-1 Configuration of Ion Concentration Measuring Device An ion concentration measuring device having the configuration described above in "Configuration of Ion Concentration Measuring Device" was used, similarly to Example 1. Here, the ion selective electrode, reference electrode, potentiometer, solution tank, and computing device used were as follows:

[0201] (Ion-selective electrodes) The ion-selective electrodes used were the ion-selective electrode with electrode symbol EL5 ("electrode EL5"), the ion-selective electrode with electrode symbol EL6 ("electrode EL6"), and the ion-selective electrode with electrode symbol EL7 ("electrode EL7") obtained in the above "Preparation of ion-selective electrodes."

[0202] (Reference electrode, potentiometer, computing device, and solution tank) As in Example 1, the reference electrode, potentiometer, computing device, and solution tank described above in "Configuration of ion concentration measuring device" were used.

[0203] C1-2 Sample Solution The sample solution used was the same as sample solution X used in Example 1.

[0204] C1-3 Standard solution The same as in Example 1 was used.

[0205] C1-4 Solution for Calibration Curve The standard solution used was the same as in Example 1.

[0206] C1-5 Preparation of calibration curve (E std (Calculation of Slope Value) The calibration curve was prepared and the slope value was calculated in the same manner as in Example 1, except that the electrode EL5, the electrode EL6, or the electrode EL7 was used as the ion selective electrode. The obtained slope values ​​are shown in Table 13.

[0207]

[0208] C1-6 Calculation of selectivity coefficients for ion-selective electrodes and creation of matrix A (Calculation of selectivity coefficients) The selectivity coefficients for the ions to be measured were calculated for each of the electrodes with the electrode symbols EL5, EL6, and EL7 (electrodes EL5, EL6, and EL7). The selectivity coefficients were calculated in the same manner as in Example 1. The measured values ​​and the calculated selectivity coefficients are shown in Tables 14 and 15.

[0209]

[0210]

[0211] (Creation of Matrix A) Matrix A was created from the values ​​of the selectivity coefficients obtained in the above "Calculation of Selectivity Coefficients" for the electrodes EL5, EL6, and EL7.

[0212] The selectivity coefficients obtained in the above "Calculation of Selectivity Coefficients" are summarized in Table 16 below. Here, the target ions to be measured (chloride ions (Cl - )) selectivity coefficient (Ks(Cl - , Cl - )) is set to 1.

[0213] The matrix A corresponding to the selectivity coefficients shown in Table 16 above can be expressed as follows. In determining the matrix A below, the electrodes EL5, EL6, and EL7 were respectively the first ion selective electrode (ion selective electrode S1), the second ion selective electrode (ion selective electrode S2), and the third ion selective electrode (ion selective electrode S3). In the matrix A below, the selectivity coefficient K for the ith ion selective electrode (i is 1 to 3) of these three ion selective electrodes is S (Cl - , Cl - ), K S (Cl - , HCO3 - ), and K S (Cl - , AcO - ) respectively as K Si (Cl - , Cl - ), K Si (Cl - , HCO3 - ), and K Si (Cl - , AcO - ) is shown.

[0214] This matrix A was entered into cells (A1:C3) of the spreadsheet software Excel, and the absolute value of the determinant, ∥A∥, was calculated using the function "=MDETERM(A1:C3)", which was 0.02.

[0215] C1-7 Potential difference E of sample solution S Measurement of the potential difference E of the sample solution S The measurement was carried out in the same manner as in Example 1, except that the electrode EL5, the electrode EL6, or the electrode EL7 was used as the ion selective electrode. The measured values ​​and the calculated values ​​obtained from the measured values ​​(calculated values ​​obtained with electrode S) are shown in Table 17. The Slope values ​​in Table 13 obtained in the same manner as in Example 1 were used to calculate the E in Table 17. std was corrected with.

[0216]

[0217] C1-8 Calculation of Ion Concentration of Sample Solution The ion concentration of the above sample solution was calculated in the same manner as in Example 1.

[0218] First, the inverse matrix A of the matrix A obtained in the above "C1-6 Calculation of the selectivity coefficient for the ion selective electrode and creation of matrix A" is calculated. -1 is calculated in the same manner as in Example 1. This matrix A is obtained by treating the electrodes EL5, EL6, and EL7 as the ion selective electrodes S1, S2, and S3, respectively. -1 was calculated by inputting matrix A into cells (A1:C3) of the spreadsheet software Excel and using the function "=MINVERSE(A1:C3)".

[0219] The above "C1-7 Potential difference E of sample solution S The "calculated value obtained at electrode S" shown in Table 17 above, obtained by "measurement of -1 Applying chloride ions (Cl - ) concentration C(Cl - ), bicarbonate ion (HCO3 - ) concentration C(HCO - ), and acetate ions (AcO - ) concentration C(AcO - ) was calculated. Here, the "calculated value obtained at electrode S" for electrode EL5 was set to the "calculated value obtained at electrode S1", the "calculated value obtained at electrode S" for electrode EL6 was set to the "calculated value obtained at electrode S2", and the "calculated value obtained at electrode S" for electrode EL7 was set to the "calculated value obtained at electrode S3". As a result, C(Cl - )=102.3mM, C(HCO3 - )=43.2mM, C(AcO - ) = -3.46 mM.

[0220] The above "C1-7 Potential difference E of sample solution S The procedures of "Measurement of ion concentration" and "C1-8 Calculation of ion concentration of sample solution" were repeated six times, and the relative standard deviation (%) was calculated in the same manner as in Example 1. The results are shown in Table 18.

[0221]

[0222] 1: ion selective electrode, 2: reference electrode, 3: potentiometer, 4: tank for holding solution, 5: internal electrode, 6: internal solution, 7: ion selective membrane, 8: liquid junction, 9: sample solution

Claims

1. An ion concentration measuring device comprising two or more types of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions, satisfying the following formulas (1) and (2), wherein the two or more types of ion selective electrodes consist of n types of ion selective electrodes, where n is an integer of 2 or greater. In formula (1), each element of matrix A represents an ion selectivity coefficient, where Bj represents the jth ion among the n types of ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n types of ion selective electrodes, i and j are each independently an integer from 1 to n, and K Si (B1, Bj) represents the ion selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as a reference. In addition, in equation (2), ||A|| is the absolute value of the determinant of matrix A.

2. The ion concentration measuring device according to claim 1, which calculates the ion concentration using the following formula (3): Here, A -1 indicates the inverse matrix of matrix A, and C(Bj) indicates the concentration of the ion Bj (j is an integer from 1 to n). The calculated value obtained by electrode Si (i is an integer from 1 to n) indicates the value obtained by converting the potential difference measured by the ion selective electrode Si according to the following formula: In the above formula, E Si is the potential difference developed between the ion-selective electrode Si and the reference electrode, and E 0,Si is the standard potential difference developed between the ion selective electrode Si and the reference electrode, Slope is 2.303 RT / aF, R is the gas constant, T is the absolute temperature, a is the valence of the ion B1, and F is the Faraday constant.

3. A method for measuring ion concentrations, comprising the step of measuring the ion concentrations in a sample solution using two or more types of ion selective electrodes that have different ratios of selectivity coefficients for a plurality of ions and satisfy the following formulas (1) and (2), wherein the two or more types of ion selective electrodes consist of n types of ion selective electrodes, where n is an integer of 2 or greater. In formula (1), each element of matrix A represents an ion selectivity coefficient, where Bj represents the jth ion among the n types of ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n types of ion selective electrodes, i and j are each independently an integer from 1 to n, and K Si (B1, Bj) represents the ion selectivity coefficient of the ion selective electrode Si for the ion Bj when the ion B1 is used as a reference. In addition, in equation (2), ||A|| is the absolute value of the determinant of matrix A.

4. The method for measuring ion concentration according to claim 3, wherein the ion concentration is calculated using the following formula (3): Here, A -1 indicates the inverse matrix of matrix A, and C(Bj) indicates the concentration of the ion Bj (j is an integer from 1 to n). The calculated value obtained by electrode Si (i is an integer from 1 to n) indicates the value obtained by converting the potential difference measured by the ion selective electrode Si according to the following formula: In the above formula, E Si is the potential difference developed between the ion-selective electrode Si and the reference electrode, and E 0,Si is the standard potential difference developed between the ion selective electrode Si and the reference electrode, Slope is 2.303 RT / aF, R is the gas constant, T is the absolute temperature, a is the valence of the ion B1, and F is the Faraday constant.

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