Ion concentration measurement device and measurement method

Abstract

The purpose of the present invention is to provide an ion concentration measurement device and measurement method in which a method for selecting an ion-selective electrode that has a small measurement error and is not susceptible to interference by coexisting ions is defined, and the ion concentration can be determined with high accuracy by using the selected ion-selective electrode. The ion concentration measurement device is provided with two or more types of ion-selective electrodes that satisfy formula (1) and formula (2) in which the ratios of selection coefficients for a plurality of types of ions are different from each other, the two or more types of ion-selective electrodes being composed of n types of ion-selective electrodes (n is an integer of 2 or more), where n is the number of types of the plurality of types of ions. In formula (1), Bj represents a j-th ion, and Si represents a symbol of an i-th ion-selective electrode. KSi (B1, Bj) represents an ion selection coefficient for the ion Bj when the ion B1 is used as a reference of the ion-selective electrode Si. In formula (2), A is the absolute value of the matrix formula of the matrix A. And # imgabs0 # A > 0.1 (2).

Description

Technical Field

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

[0002] When measuring the ion concentration in blood during clinical examinations, an ion selective electrode is generally used. By immersing the ion selective electrode and the reference electrode in a sample solution, a potential difference corresponding to the ion concentration of the sample solution is obtained. Therefore, by knowing the relationship between the potential difference and the concentration in advance, the ion concentration in the sample solution can be known based on the potential difference. Since the ion concentration in the sample solution can be measured simply and in a short time by simply immersing the electrode in the sample solution, the ion concentration measurement using the ion selective electrode is currently widely used.

[0003] The case of measuring the concentration of one ion using an ion selective electrode S and a reference electrode is briefly described. a The potential difference E obtained when the sample solution S The ion concentration in the sample solution (C(X a The relationship between ) can be expressed by the Nernst formula (Formula (4))

[0004] [Number 1]

[0005]

[0006] Among them, E S is the potential difference between the ion selective electrode S and the reference electrode.

[0007] E 0,S is the standard potential difference generated between the ion selective electrode S and the reference electrode,

[0008] R is the gas constant,

[0009] T is the absolute temperature,

[0010] a is the valence of the ion,

[0011] F is Faraday's constant,

[0012] C(X a ) is ion X a concentration.

[0013] The ion selective electrode S can be used to measure the concentration of ions X a The calibration curve of the formula (4) is prepared by using the prepared calibration curve to measure the unknown sample solution and calculate the ion concentration from the potential difference.

[0014] However, in addition to the ions to be measured (hereinafter referred to as "measurement ions"), the sample solution may also contain ions other than the measurement ions (hereinafter referred to as "coexisting ions"). Here, when the concentration of the measurement ion B1 contained in the sample solution containing n types of ions consisting of the measurement ion B1 and the coexisting ions B2 to Bn is measured using the ion selective electrode S and the reference electrode, the relationship of the Nikolsky-Eisenman equation (Formula (5)) exists.

[0015] [Number 2]

[0016]

[0017] Among them, E S is the potential difference between the ion selective electrode S and the reference electrode.

[0018] E 0,S is the standard potential difference generated between the ion selective electrode S and the reference electrode,

[0019] R is the gas constant,

[0020] T is the absolute temperature,

[0021] a is the valence of ion B1,

[0022] F is Faraday's constant,

[0023] Bj represents the jth ion among n ions,

[0024] j is an integer from 2 to n,

[0025] C(Bj) is the concentration of ion Bj.

[0026] Here, K S (B1, Bj) is the ion selectivity coefficient of the ion selective electrode S for ion Bj based on ion B1. In other words, it is a coefficient that expresses the intensity of the influence of ion Bj on the potential difference generated between the ion selective electrode S and the reference electrode by using a ratio based on ion B1.

[0027] If the ion selectivity K for ion B2 is used based on ion B1, S The above measurement is performed on a sample solution containing ion B1 with a concentration of C(B1) but not containing coexisting ions B2 to Bn by using an ion selective electrode S (B1, B2). The following potential difference E is applied: B1 .

[0028] [Number 3]

[0029]

[0030] Furthermore, if ions B2 of concentration C(B2) are added to the sample solution (i.e., a sample solution containing ions B1 of concentration C(B1) and ions B2 of concentration C(B2) but not containing coexisting ions B3 to Bn) and the above measurement is performed, the following potential difference E is applied: B1+B2 .

[0031] [Number 4]

[0032]

[0033] Here, in the above formula (6) and formula (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) is B1 and E in the above formula (7) B1+B2 Equivalent to E in the above formula (5) S .

[0034] As shown in the above equations (6) and (7), if the ion selectivity K S If (B1, B2) is large, when measuring ion B1, interference from ion B2 will occur, which will become a major cause of error.

[0035] Therefore, in order to measure the concentration of a specific ion, it is desirable that the selectivity coefficient for other ions is infinitely small. When an ion selective membrane containing bis[(12-crown-4-methyl)-2-dodecyl-2-malonate [CAS No. 80403-59-4] is used in a sodium ion selective electrode, it is known that the selectivity coefficient K of potassium ions relative to sodium ions is S (Na + , K + ) represents 0.01, which has been actually applied (Non-Patent Document 1).

[0036] However, it is sometimes difficult to develop an electrode with a sufficiently small ion selectivity for other ions, depending on the ion being measured. In particular, there are few ion-selective membranes suitable for measuring anions, and in the measurement of anions, ion exchange membranes that do not have sufficient selectivity for the ions being measured are often used. For example, in order to measure bicarbonate ions (HCO 3 - ), the selection coefficient K needs to be satisfied S (HCO 3 - , Cl - ) is less than 0.01, but only K S (HCO 3 - , Cl -) is greater than 1. In clinical examinations, the presence of ions in the sample solution that are more responsive than the ions to be measured can lead to the fact that the electrode used for measuring bicarbonate ions (HCO 3 - ) concentration of electrodes becomes a problem.

[0037] Therefore, a method for measuring the concentrations of various ions using a plurality of ion selective electrodes that are insufficiently selective for the measured ions has been developed. For example, Patent Document 1, Patent Document 2, and Patent Document 3 can be cited. In addition, there is also an example in which an ion selective electrode for removing the influence of interfering ions is used in addition to the ion selective electrode used for measuring the ion concentration (Patent Document 4).

[0038] Prior art literature

[0039] Patent Literature

[0040] Patent Document 1: Japanese Patent Publication No. 1-502360

[0041] Patent Document 2: Japanese Patent Application Laid-Open No. 54-030094

[0042] Patent Document 3: International Publication No. 2019 / 163281

[0043] Patent Document 4: Japanese Patent Application Laid-Open No. 07-167818

[0044] Non-patent literature

[0045] Non-patent document 1: Anal. Chem., 1982, 54(7), 1224-1227 Summary of the invention

[0046] Problem that the invention aims to solve

[0047] As in Patent Document 2, the following method is known: the ion concentration of n kinds of ions present in the sample solution is calculated by solving simultaneous equations for the values ​​calculated based on n measured values ​​obtained by multiple (n) ion selective electrodes with low ion selectivity. However, there are errors in the measured values ​​in actual measurements. In addition, when the sample solution contains more than n+1 kinds of ions, the interference caused by coexisting ions cannot be ignored. Therefore, the results of the research by the inventors of the present invention are to clarify the following: when selecting ion selective electrodes, the ion concentration cannot be obtained with high accuracy due to measurement errors and interference from coexisting ions.

[0048] Therefore, an object of the present invention is to provide an ion concentration measuring device and a measuring method that clarifies a method for selecting an ion selective electrode having a small measurement error and being less susceptible to interference from coexisting ions, and by using the selected ion selective electrode, the ion concentration can be determined with high accuracy.

[0049] Solutions for solving problems

[0050] The present inventors have conducted intensive research to solve the above problems. As a result, they have discovered the following ion concentration measuring device and measuring method: a method for selecting an ion selective electrode with a small measurement error and not easily interfered by coexisting ions has been clarified, and by using the selected ion selective electrode, the ion concentration can be determined with high accuracy.

[0051] That is, according to the first present invention, there is provided an ion concentration measuring device as follows: comprising two or more ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the following formulae (1) and (2); when the number of types of the plurality of ions is set to n, the two or more ion selective electrodes are composed of n types of ion selective electrodes, where n is an integer greater than 2.

[0052] [Number 5]

[0053]

[0054] ||A||>0.1 (2)

[0055] In formula (1), each component of the matrix A represents the ion selectivity coefficient. Here,

[0056] Bj represents the jth ion among the n ions constituting the plurality of ions,

[0057] Si is a symbol representing the i-th ion selective electrode constituting the n-type ion selective electrodes,

[0058] i and j are each independently an integer from 1 to n,

[0059] 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.

[0060] In addition, in formula (2), ||A|| is the absolute value of the matrix formula of matrix A.

[0061] According to a second aspect of the present invention, there is provided a measurement method including the step of measuring the ion concentration in a sample solution using a plurality of ion selective electrodes satisfying the above-mentioned formula (1) and formula (2).

[0062] Effects of the Invention

[0063] In the present invention, the following method is clarified: even when there are more coexisting ions (n+1 or more) than the number of electrodes (n), an ion selective electrode with a small measurement error and not easily interfered by the coexisting ions is selected. By selecting an ion selective electrode with a large value of the absolute value (||A||) of the matrix formula of the matrix A, it is possible to perform an ion concentration measurement with a small relative standard deviation of the measurement result and good accuracy. According to the present invention, it is possible to provide an ion concentration measurement device and a measurement method that can determine the ion concentration with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a schematic diagram showing an ion concentration measuring device according to one embodiment of the present invention. DETAILED DESCRIPTION

[0065] Next, a mode for carrying out the present invention will be described.

[0066] [Explanation of Formula (1), Formula (2), and Formula (3)]

[0067] First, the formula (1), formula (2) and formula (3) used in the present invention are described. By using the formula (1) and formula (2), an ion selective electrode with a small measurement error and a strong ability to resist interference from coexisting ions can be selected. Thus, an ion concentration measuring device that can achieve the feature of the present invention, i.e., determine the ion concentration with high accuracy, can be provided.

[0068] As a prelude to the description of the case of measurement using n types of ion selective electrodes, the case of measurement using one type of ion selective electrode will be described.

[0069] When measuring with one ion selective electrode

[0070] When using an ion selective electrode S (hereinafter, sometimes also referred to as "electrode S") and a reference electrode to measure the concentration of a specific ion (ion B1) contained in a sample solution containing n types of ions (n ​​is an integer greater than 2), there is a relationship of the Nikolsky-Eisenman equation (formula (5)). Here, (2.303RT) / aF is set as Slope. In other words, Slope is a constant. In fact, Slope does not usually represent a theoretical value due to various reasons such as resistance in the device and potential difference between liquids. In this case, it is preferred to prepare a calibration curve to obtain Slope.

[0071] [Number 6]

[0072]

[0073] Among them, E Sis the potential difference between the ion selective electrode S and the reference electrode.

[0074] E 0,S is the standard potential difference generated between the ion selective electrode S and the reference electrode,

[0075] Slope is 2.303RT / aF,

[0076] R is the gas constant,

[0077] T is the absolute temperature,

[0078] a is the valence of ion B1,

[0079] F is Faraday's constant,

[0080] Bj represents the jth ion among n ions,

[0081] j is an integer from 2 to n,

[0082] C(Bj) is the concentration of ion Bj,

[0083] K S (B1, Bj) is the selectivity coefficient of the electrode S for the ion Bj when the ion B1 is used as a reference.

[0084] The ion selective electrode S and the reference electrode can be used to measure a sample solution (calibration curve solution) with a known concentration of ion B1, and a calibration curve represented by equation (5') can be prepared. The Slope and the standard potential difference E when measured using the ion selective electrode S can be obtained from the calibration curve. 0,S .

[0085] The following formula (8) can be derived by transposing the formula (5'). This formula (8) can be used to obtain the following formula (8) according to E 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 , to calculate the ion concentration when the n ion concentrations in the sample solution are converted into the concentration of an arbitrary ion B1.

[0086] [Number 7]

[0087]

[0088] Here, when n=2, the above formula (8) can be expressed as the following formula (8A).

[0089] [Number 8]

[0090]

[0091] Furthermore, the above-mentioned formula (8A) can be further transformed into the following formula (8B) by transposing the terms.

[0092] [Number 9]

[0093]

[0094] That is, when n=2, the selectivity coefficient K of the electrode S for ion B2 based on ion B1 can be obtained using the above formula (8B): S (B1, B2).

[0095] When measuring using n types of ion selective electrodes (Explanation of formula (1))

[0096] The following case is shown: 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 greater than or equal to 2). At this time, the above equation (8) holds for each of the n types of ion selective electrodes S1 to Sn. Therefore, the simultaneous equations of equation (9) hold.

[0097] [Number 10]

[0098]

[0099] In formula (9),

[0100] Bj represents the jth ion among the n ions,

[0101] Si is a symbol representing the i-th ion selective electrode constituting the n-type ion selective electrodes,

[0102] i and j are each independently an integer from 1 to n,

[0103] K Si (B1, Bj) is the K when the ion selective electrode Si (the 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,

[0104] E Si is the potential difference generated between the ion selective electrode Si and the reference electrode,

[0105] E 0,Si It is the standard potential difference generated between the ion selective electrode Si and the reference electrode.

[0106] Slope is 2.303RT / aF,

[0107] R, T, a, and F are respectively the same as those specified in the above formula (5). Here, the right side of the formula (9) is set to the calculated value obtained by the ion selective electrode Si. This value is obtained using the potential difference E Si , Slope obtained by the calibration curve and the standard potential difference E 0,Si The calculated value.

[0108] If the simultaneous equations of the above equation (9) are set in the form of a matrix, the following equation (10) is obtained.

[0109] [Number 11]

[0110]

[0111] The matrix on the left side of equation (9) is referred to as matrix A'. Here, for each of the n types of ion selective electrodes S1, S2, ..., Sn, the selectivity coefficient K for the arbitrary ion B1 itself as the reference is S (B1, B1)(i.e., K S1 (B1, B1), K S2 (B1, B1), ···, K Sn (B1, B1)) is 1. Therefore, if 1 is rewritten as K S (B1, B1) (i.e., for n kinds of ion selective electrodes S1, S2, ..., Sn, K S1 (B1, B1), K S2 (B1, B1), ···, K Sn (B1, B1)), the matrix A' can be transformed as in equation (11). The right side of equation (11) corresponds to the matrix A (equation (1)) of the present invention.

[0112] [Number 12]

[0113]

[0114] In matrix A,

[0115] Bj represents the j-th ion (j is an integer from 1 to n) among the n ions.

[0116] Si is a symbol indicating the i-th (i is an integer from 1 to n) ion selective electrode constituting the n types of ion selective electrodes.

[0117] 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. S1(B1, B1) represents the selectivity coefficient of the ion selective electrode S1 for ion B1 when ion B1 is used as the reference, K S2 (B1, B3) represents the selectivity coefficient of the ion selective electrode S2 for the ion B3 when the ion B1 is used as a reference.

[0118] Explanation of formula (2)

[0119] In the present application, |A| represents the matrix expression of the matrix A, and ||A|| represents the absolute value of the matrix expression. Generally, the matrix expression |A| can be calculated by cofactor expansion or the like.

[0120] When three (n=3) ion selective electrodes S1, S2 and S3 are used to measure three ions in a sample solution (ions: B1, B2 and B3, ion concentrations: C(B1), C(B2) and C(B3)), the matrix A represented by the above formula (1) can be represented as a 3×3 square matrix shown below. In this case, the Saha formula in the matrix can be used, and the matrix formula |A| corresponding to the matrix A can be obtained by formula (12).

[0121] [Number 13]

[0122]

[0123] When the matrix A is an n×n matrix, the matrix expression |A| can be easily obtained by using spreadsheet software (such as Microsoft Excel) or numerical calculation software. When using spreadsheet software Excel, the matrix expression |A| can be calculated using functions such as "=MDETERM". If the matrix expression |A| can be obtained, the absolute value ||A|| of the matrix expression can be calculated.

[0124] The most important point in the present invention is that the absolute value of the matrix ||A|| satisfies equation (2).

[0125] [Number 14]

[0126] ||A||>0.1 (2)

[0127] <Meaning of Formula (2)>

[0128] Based on equation (10) and equation (11), the following equation (13) can be expressed.

[0129] [Number 15]

[0130]

[0131] When the matrix form |A| of matrix A is not 0, there exists an inverse matrix A in matrix A-1 If we multiply both sides of equation (13) by the inverse matrix A- 1 , it can be transformed into formula (14). 1 A is a unit matrix, so the cofactor matrix of the matrix A shown in equation (16) can be used to transform equation (14) into equation (15).

[0132] [Number 16]

[0133]

[0134] The cofactor matrix of A

[0135] Generally, in the measurement using a single ion selective electrode S, measurement errors and the influence of interfering ions occur. When the calculated value obtained by the ion selective electrode S contains an error, the error is set to Δs. In the present invention, when n types of ion selective electrodes (ion selective electrodes S1, S2, . . . , Sn) are used as the ion selective electrode S, the errors Δs related to these ion selective electrodes can be set to Δs, respectively. S1 , Δ S2 ,···,Δ Sn Formula (15) can be expressed as Formula (17). It can be divided into terms representing errors using the property of the sum of matrices and expressed as Formula (17').

[0136] [Number 17]

[0137]

[0138] Since the matrix formula |A| exists in the denominator of the term representing the error, the greater the absolute value ||A|| of the matrix formula |A| is, the smaller the value of the term representing the error is. Specifically, if the absolute value ||A|| of the matrix formula is greater than 0.1, the value of the term representing the error becomes smaller, and an electrode that can be measured in practical applications can be selected. Therefore, in the present invention, the absolute value ||A|| satisfies the relationship shown in the following formula (2).

[0139] [Number 18]

[0140] ||A||>0.1 (2)

[0141] The absolute value ||A|| of the matrix is ​​more preferably greater than 0.2, and further preferably greater than 0.4. The absolute value ||A|| of the matrix is ​​preferably as large as possible, and although there is no upper limit, it is usually 100 or less.

[0142] This formula (2) shows the selectivity coefficient K such that the influence of the error is reduced in the relationship between n kinds of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) used as the ion selective electrode S and n kinds 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, when two or more ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions are used as the ion selective electrode S, n ion selective electrodes satisfying formula (2) are selected as the two or more ion selective electrodes, thereby providing an ion concentration measuring device and method with little influence of error.

[0143] Explanation of formula (3)

[0144] When the n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) are used as the ion selective electrode S to measure n types of ions in a sample solution, the concentrations of the n types of ions can be expressed by Formula (3).

[0145] [Number 19]

[0146]

[0147] Here, A -1 represents the inverse matrix of the matrix A, C(Bj) represents the concentration of the ion Bj (j is an integer from 1 to n). The calculated value obtained by the electrode Si (i is an integer from 1 to n) represents the value when the potential difference measured by the ion selective electrode Si is converted according to the following formula.

[0148] [Number 20]

[0149]

[0150] In the above formula,

[0151] E Si is the potential difference generated between the ion selective electrode Si and the reference electrode,

[0152] E 0,Si It is the standard potential difference generated between the ion selective electrode Si and the reference electrode.

[0153] Slope is 2.303RT / aF,

[0154] R, T, a, and F are respectively the same as R, T, a, and F defined in the above formula (5).

[0155] In the present invention, the ion selective electrode S is also described as electrode S, and the i-th (i is an integer from 1 to n) ion selective electrode Si among the n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) is also described as electrode Si. By using formula (3), the ion concentration of the sample solution can be obtained from the calculated values ​​obtained by each of the n types of ion selective electrodes used as electrode S.

[0156] When using standard solution

[0157] In the case of long-term measurement, the standard potential difference E 0,S The standard potential difference E may vary depending on the measurement conditions such as temperature, so it is preferable to use a standard solution to calibrate the standard potential difference E. 0，S .

[0158] Use standard solution to calibrate the standard potential difference E 0，S The method is described below. The ion selective electrode S and the reference electrode are immersed in a solution with a known ion concentration (C std ) standard solution is set as E std (Formula (18)). At this time, the standard potential difference E 0，S It is expressed as formula (19).

[0159] [Number 21]

[0160] E Std =E 0，S +Slope×log 10 C std (18)

[0161] E 0，S =E Std -Slope×log 10 C std (19)

[0162] In the above formula (18) and formula (19),

[0163] Slope is 2.303RT / aF,

[0164] R, T, a, and F are respectively the same as R, T, a, and F defined in the above formula (5).

[0165] If the standard solution is measured and the standard potential difference E is replaced 0，S Substituting into equation (19), the calculated value obtained by electrode S can be expressed by equation (20).

[0166] [Number 22]

[0167]

[0168] By using equation (20) for the calculated value obtained from the electrode S, it is possible to correct the standard potential difference E when the measurement conditions such as temperature change or when the measurement is performed for a long time. 0，S It is preferred because it measures the changes in the value of the sample while maintaining the value of the sample.

[0169] 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 the calculated values ​​obtained from these ion selective electrodes, the standard potential difference E for these ion selective electrodes can be corrected in the same manner. 0,S (i.e., E 0，S1 、E 0，S2 、···、E 0,Sn ) is measured while keeping in mind the change of the value. For example, when the above formula (20) is applied to 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), the above formula (20) can be expressed as the following formula (20').

[0170] [Number 23]

[0171]

[0172] In the above formula (20'),

[0173] E Si is the potential difference generated between the ion selective electrode Si and the reference electrode,

[0174] E 0,Si It is the standard potential difference generated between the ion selective electrode Si and the reference electrode.

[0175] E Stdi It is immersed in a known ion concentration (C std ) standard solution, the potential difference generated between the ion selective electrode Si and the reference electrode,

[0176] Slope is 2.303RT / aF,

[0177] R, T, a, and F are respectively the same as R, T, a, and F defined in the above formula (5).

[0178] [Ion concentration measuring device]

[0179] The ion concentration measuring device of the present invention includes two or more ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the above-mentioned formula (1) and formula (2). Here, when the number of types of the plurality of ions is set to n, the two or more ion selective electrodes are composed of n types of ion selective electrodes, and n is an integer greater than 2.

[0180] Furthermore, in the above formula (1),

[0181] Bj represents the jth ion among the n ions constituting the plurality of ions,

[0182] Si is a symbol representing the i-th ion selective electrode constituting the n-type ion selective electrodes,

[0183] i and j are each independently an integer from 1 to n,

[0184] 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.

[0185] In the present invention, it is preferred to calculate the ion concentration using the above-mentioned formula (3).

[0186] Here, in the present invention, ion B1 (i.e., ion with j=1 in Bj) is one type of ion appropriately selected from the n types of ions constituting the plurality of ions. This ion B1 is usually an ion that is often selected as an ion to be measured in concentration measurement by a single ion selective electrode.

[0187] On the other hand, ions other than the ion B1 among the n types of ions constituting the plurality of ions are set to ions B2, B3, ..., Bn (i.e., ions with j ≥ 2). Here, the ions B2, B3, ..., Bn may also include ions whose concentrations are difficult to directly and selectively measure using a single ion selective electrode.

[0188] In addition, for the above two or more ion selective electrodes, in the present invention, as long as the combination of ion selective electrodes selected as n ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) satisfies the above formula (2), there is no special regulation on the allocation method of the symbols S1, S2, ..., Sn, and these symbols can be appropriately allocated to these ion selective electrodes. Here, the ion concentration measuring device of the present invention may also include more than n types of ion selective electrodes, and n types of ion selective electrodes that satisfy formula (2) may be selected from these ion selective electrodes for ion concentration measurement. In addition, the ion selective electrodes constituting the ion concentration measuring device of the present invention may be respectively marked with unique identifiers arbitrarily determined separately from the symbol Si. In this case, a correspondence table between these identifiers and symbols S1, S2,..., Sn may be prepared according to the components that may be contained in the sample solution and the types of ion selective electrodes, and based on the correspondence table, ion selective electrodes to be used as 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.

[0189] The ion concentration measuring device in the present invention is not particularly limited as long as it includes two or more ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying equations (1) and (2). Figure 1 In general, the ion concentration measuring device is composed of an ion selective electrode 1, a reference electrode 2, and a potentiometer 3. Here, the ion selective electrode 1 functions as the above-mentioned ion selective electrode S, and the ion selective electrode 1 and the potentiometer 3, as well as the potentiometer 3 and the reference electrode 2, are connected via electric wires. That is, the n types of ion selective electrodes (ion selective electrodes S1, S2, ..., Sn) used as two or more ion selective electrodes are connected in Figure 1 In the above, an ion selective electrode 1 is constituted. In addition, a computing device capable of calculating the above-mentioned formula and a tank 4 for loading a solution can also be combined. Here, the computing device is connected to the potentiometer 3, and performs computing processing such as calculation of ion concentration based on the potential difference input from the potentiometer 3. The computing processing can include a process of forming the above-mentioned matrix formula |A| and a process of calculating the absolute value of the matrix formula |A|. The computing device and the potentiometer 3 can be independent devices, or they can exist in a form integrated into a single device. These are examples and are not used to limit the form of the device.

[0190] There only need to be two or more ion selective electrodes 1, and several ion selective electrodes 1 may be combined. It only needs to be adjusted to appropriately match the number of ions to be measured, but from the perspective of measurement accuracy, it is preferably more than 2 and less than 10. From the perspective of the size of the ion concentration measuring device, it is most preferably more than 2 and less than 5. If the n is used to say it another way, the n is preferably more than 2 and less than 10, and most preferably more than 2 and less than 5. Since more than two ion selective electrodes are needed, the number of ion selective electrodes 1 needs to be more than 2. There is no particular limitation as long as there are more than 2. In an exemplary embodiment of the present invention, there are three ion selective electrodes 1 (i.e., n=3), but it is not limited to this. It is also possible to combine multiple ion selective electrodes of the same type.

[0191] The reference electrode 2 is not particularly limited as long as it is one or more, but usually a smaller number than the ion selective electrode is used.

[0192] The potentiometer 3 is not limited as long as it can measure the potential difference between two or more ion selective electrodes and the reference electrode. A voltmeter can also be used as long as the potential difference can be obtained.

[0193] The tank 4 for loading the solution can be used without any particular limitation as long as it can soak the ion selective electrode and the reference electrode. A plurality of tanks may be used to match the number of types of ion selective electrodes, or a plurality of ion selective electrodes may be soaked in one tank. A tank may be used to soak each electrode in batches, or a flow path may be assembled to circulate the sample solution. In addition, the sample solution may be stirred or circulated to make the sample solution uniform.

[0194] Ion Selective Electrode

[0195] The ion selective electrode 1 functions as the ion selective electrode S. Any commonly used electrode such as a liquid-filled ion selective electrode or a solid electrode ion selective electrode can be used without particular limitation. In the present invention, n types of ion selective electrodes 1 having different ratios of selectivity coefficients for a plurality of ions are combined to serve as the ion selective electrodes S1, S2, ..., Sn.

[0196] like Figure 1 As shown, the internal liquid-filled ion selective electrode comprises 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 .

[0197] The internal electrode 5 is not particularly limited as long as it is an electrode commonly used. Generally, a silver / silver chloride electrode is used.

[0198] The internal liquid 6 generally uses an aqueous solution of an electrolyte such as KCl or NaCl.

[0199] The ion selective membrane 7 is not particularly limited, and a ligand for selecting ions is mixed with a plasticizer in a polymer base material such as polyvinyl chloride. Chlorine or the like may also be contained. Specifically, when the ion selective electrode 1 is a cation selective electrode of sodium, potassium, calcium, magnesium or the like (i.e., a cation selective electrode that selectively senses cations of sodium, potassium, calcium, magnesium or the like and generates an output corresponding to the concentration (activity) of the cation), as the ion selective membrane 7, a membrane such as that described in Pure Appl. Chem., 2000, Vol. 72, No. 10, pp. 1851-2082 can be used. In addition, when the ion selective electrode 1 is an anion selective electrode of chlorine, carbonic acid, thiocyanic acid, nitric acid, hydroxyl, phosphoric acid, sulfuric acid, iodine, etc. (i.e., an anion selective electrode that selectively senses anions of nitric acid, hydroxyl, phosphoric acid, sulfuric acid, iodine, etc. and generates an output corresponding to the concentration (activity) of the anion), as the ion selective membrane 7, a membrane as described in Pure Appl. Chem., 2002, Vol. 74, No. 6, pp. 923-994, a silver halide such as silver chloride and silver bromide, and an ion exchange membrane (Japanese Patent Laid-Open No. 10-318973, Japanese Patent Laid-Open No. 11-132991, Japanese Patent Laid-Open No. 2003-207476) can be used. The membrane as described above can be self-made and used, and a commercially available membrane can also be used. That is, the ion selective membrane 7 can 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 ASTO Corporation) and Neosepta ASE (manufactured by ASTO Corporation).

[0200] Choice of ion selective electrode

[0201] In the present invention, as the ion selective electrodes constituting the above-mentioned ion concentration measuring device, it is necessary to select two or more ion selective electrodes satisfying equations (1) and (2). Whether equations (1) and (2) are satisfied is determined by the selectivity coefficient K of each ion selective electrode. S (B1, Bj) to decide.

[0202] Ion selectivity K S (B1, Bj) can generally be calculated by a single solution method or a mixed solution method. In the mixed solution method, the potential difference of a mixed solution containing ions B1 of known concentration and ions Bj for which the selectivity is desired is measured, and the ion selectivity K is calculated. S (B1, Bj).

[0203] An example of such calculation is shown with specific numerical values ​​when two types of ion selective electrodes (first ion selective electrode S1 and second ion selective electrode S2) are used as ion selective electrodes S to measure a mixed solution containing ion B1 and second ion B2. It is assumed that the ion selectivity K of the ion selective electrode S1 and the ion selective electrode S2 for ion B2 when ion B1 is used as the reference is S (B1, B2) are K S1 (B1, B2) = 0.5 and K S2 (B1, B2) = 0.1, where the ion selective coefficient K of the ion selective electrode S1 and the ion selective electrode S2 for ion B1 itself when ion B1 is used as a reference S (B1, B1) can be regarded as K S1 (B1, B1) = 1 and K S2 (B1, B1) = 1. The matrix A and the matrix expression |A| can be expressed by the following equations using these selection coefficients. In this case, the matrix expression |A| = -0.4 can be calculated.

[0204] [Number 24]

[0205]

[0206] Matrix |A|=K S1 (B1,B1)K S2 (B1,B2)-K S1 (B1,B2)K S2 (B1, B1)

[0207] =K S2 (B1, B2)-K S1 (B1,B2)

[0208] =0.1-0.5=-0.4

[0209] Reference electrode

[0210] The reference electrode 2 is not particularly limited as long as it is a commonly used reference electrode. However, in a typical embodiment, the reference electrode 2 is Figure 1 As shown in the figure, it has an internal electrode 5, an internal liquid 6 and a liquid junction 8. As an example of the reference electrode 2 that can be used in the present invention, the following silver / silver chloride reference electrode can be cited: a 3M potassium chloride aqueous solution is used for the internal liquid 6, a silver / silver chloride electrode is used for the internal electrode 5, and there is a liquid junction 8 between the sample solution and the internal liquid. However, the reference electrode 2 may also be other reference electrodes, such as a saturated calomel electrode.

[0211] ion

[0212] As long as it is an ion that can prepare an ion solution and can be measured by the device, there is no particular limitation. It can be either an anion or a cation. For example, if it is an anion, chloride ions, bicarbonate ions, anions of organic acids, nitrate ions, sulfate ions, etc. can be cited. If it is a cation, potassium ions, silver ions, copper ions, etc. can be cited. When it is intended that the characteristics of this device play a role most effectively, if more preferred examples are cited, there are multiple ions contained in the blood (chloride ions, bicarbonate ions, and anions of organic acids such as lactic acid, pyruvic acid, propionic acid, fatty acids and amino acids, etc.).

[0213] Here, the "multiple ions" used in the present invention may be composed of more than two kinds of anions in anions, or may be composed of more than two kinds of cations in cations. When the "multiple ions" are anions, the "multiple ions" may also be more than two kinds of anions 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 of the preferred and illustrative modes 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 ions exemplified above, and may also be appropriately selected to match the object of measurement.

[0214] Here, in the present invention, when performing evaluation using the above-mentioned formulas (1) and (2), one of the above-mentioned ions B1 (i.e., ions with j=1 in Bj) is selected from the n types of ions constituting the above-mentioned "multiple ions", and the other n-1 types of ions are set as ions B2, B3,...Bn (i.e., ions with j≥2 in Bj).

[0215] Among them, ions B1 are ions whose concentration can be directly measured using only one ion selective electrode having an infinitely small selectivity coefficient for other ions. Examples of ions that can be ions B1 include chloride ions and sodium ions.

[0216] On the other hand, ions other than ion B1 (i.e., ions B2, B3, ..., Bn) may be ions whose concentration can be directly measured using a single ion selective electrode, or ions whose concentration is difficult to be directly measured using a single ion selective electrode. Examples of ions other than ion B1 include anions of organic acids such as bicarbonate ions and acetate ions.

[0217] According to the present invention, even ions that are difficult to obtain by electrodes with sufficiently small ion selectivity for other ions such as bicarbonate ions can be measured. Based on this, in one of the preferred and exemplary embodiments of the present invention, the ions B1 are chloride ions, and the ions other than the ions B1 include bicarbonate ions.

[0218] [Measurement method of ion concentration]

[0219] The method for measuring ion concentration of the present invention comprises the following steps: using a plurality of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the above formula (1) and formula (2) to measure the ion concentration of a sample solution. Here, when the number of types of the plurality of ions is set to n, the two or more ion selective electrodes are composed of n ion selective electrodes, and n is an integer greater than 2.

[0220] Furthermore, in the above formula (1),

[0221] Bj represents the jth ion among the n ions constituting the plurality of ions,

[0222] Si is a symbol representing the i-th ion selective electrode constituting the n-type ion selective electrodes,

[0223] i and j are each independently an integer from 1 to n,

[0224] 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.

[0225] In the present invention, it is preferred to calculate the ion concentration using the above-mentioned formula (3).

[0226] Regarding the method for measuring ion concentration of the present invention, as long as it is an ion concentration measuring method using a plurality of ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the above-mentioned formulas (1) and (2), there is no particular limitation on the instruments, devices, etc. used, but it is simple to use, for example, an ion concentration measuring device such as that shown above.

[0227] The concentration of the ion to be measured (the above-mentioned ion B1) is not particularly limited, but is preferably 0 mM to 1 M. More preferably, it is 0 mM to 300 mM.

[0228] In the case of long-term measurement, the standard potential difference E 0,S Since the value may fluctuate due to changes in measurement conditions such as temperature, it is preferable to perform calibration using a standard solution.

[0229] First, the sample solution and the standard solution are described.

[0230] Sample solution

[0231] <Sample>

[0232] The sample is not particularly limited. When it is set as a solution, any sample containing ions can be measured. In particular, the sample with good effect of the present invention is a sample containing multiple ions such as a biological sample (blood, serum, plasma, etc.). Depending on the state, concentration, and coexisting substances of the sample, the sample can also be measured directly, but it is preferred to dilute the sample with a buffer, water, an organic solvent, etc. and measure it as a sample solution to suppress pH changes and eliminate potential differences between liquids. Depending on the coexisting substances, it can also be used after pretreatment using a column, a filter, etc.

[0233] <Buffer>

[0234] If the ion concentration can be stably measured, it is not necessarily necessary to use a buffer solution, but it is preferable to use a buffer solution in order to suppress pH fluctuations and eliminate potential differences between liquids.

[0235] As long as it is a buffer that can achieve the above purpose, then well-known buffers can be used without restriction. Specifically, buffers (HEPES buffer, MES buffer, ADA buffer) and Tris buffers of the kind known as Good buffer (Good's Buffer) can be cited. For example, if it is the determination of bicarbonate ions, then the buffer with little interference with the response of the ion-selective electrode to the ions is preferably a HEPES buffer. If it is a Good buffer, the pH of the buffer is about 6.0 to 8.0. The concentration of the buffer is not particularly limited, preferably 1mM to 1M. More preferably, it is a buffer of 1mM to 500mM. More preferably, it is a buffer of 5mM to 300mM.

[0236] Standard solution

[0237] The standard solution is used to measure the standard potential difference E 0,S Ion solution with known concentration for calibration. std ) is not particularly limited. Two or more ions can be used in a mixed manner, but it is usually convenient to select one ion from the measurement ions, so it is preferred.

[0238] The solvent used in the standard solution is water, an organic solvent, etc., and there is no restriction as long as the potential can be measured. It is also possible to use two or more solvents in a mixed manner. From the perspective of pH stability, water is preferably used as a solvent. In order to suppress the change of pH and eliminate the potential difference between liquids, a buffer solution is more preferably used. As a buffer solution, a buffer solution that can be used for a sample solution as shown above can be used.

[0239] The ion concentration of the standard solution (C std ) is not particularly limited and can be appropriately determined in accordance with the purpose of the measurement. An ion concentration (C) of 0.1 mM to 10 mM is usually used. std ). The ion concentration is more preferably 0.5 mM to 3 mM.

[0240] Potential difference measurement and ion concentration calculation

[0241] The method for measuring the ion concentration is described below, but this is just an example and is not particularly limited.

[0242] Generally speaking, the potential difference E is measured S , and find E 0,S , Slope values, and based on these values, the calculated value obtained by electrode S is obtained. Then, based on the calculated value obtained by electrode S, the ion concentration is calculated.

[0243] The calculation of the ion concentration when a standard solution is used will be described, but this is one method of measuring with high accuracy and is not intended to limit the present invention.

[0244] <The potential difference E of the sample solution S Determination of>

[0245] The potential difference E is measured by immersing the ion selective electrode and the reference electrode in the sample solution and measuring the potential difference with a potentiometer. S As long as the potential difference E can be measured S That is, the measurement conditions such as the measurement temperature and the measurement time are not particularly limited. From the viewpoint of being able 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.

[0246] <Preparation of calibration curve (E 0,S 、Calculation of Slope value)>

[0247] The potential difference E of a known solution containing a certain ion B1 with an ion concentration C(B1) is S By measuring, a calibration curve can be prepared according to the Nernst formula, and E can be obtained. 0,S , Slope value.

[0248] [Number 25]

[0249] E S =E 0,S +Slope×log 10 C(B1)

[0250] In the above formula,

[0251] Slope is 2.303RT / aF,

[0252] R, T, a, and F are respectively the same as R, T, a, and F defined in the above formula (5).

[0253] The ions used for the calibration curve are usually any one of the ions to be measured, which is referred to as B1 here.

[0254] From the perspective of increasing the accuracy of the calibration curve, the solution with a known concentration used to prepare the calibration curve is preferably a solution with a composition close to that of the sample solution to be measured, so the sample solution and the solution used for the calibration curve preferably have the same solvent. The ion concentration C (B1) may be appropriately determined to match the sample solution to be measured. The calibration curve can be prepared by measuring the ion concentration at two different points, but from the perspective of improving the accuracy, the ion concentration C (B1) at three or more points is measured to prepare the calibration curve.

[0255] <Calculation Values ​​Obtained by Electrode S and Calculation of Ion Concentration>

[0256] The potential difference E between the ion selective electrode and the reference electrode obtained by immersing the electrode in the sample solution can be used. S and E obtained using the calibration curve as described above 0,S , Slope values, and calculate the calculated value obtained by electrode S according to the following formula.

[0257] [Number 26]

[0258]

[0259] The “calculated values ​​obtained by the electrode S” are obtained for each of the n types of ion selective electrodes S1 to Sn used as the electrode S, and are respectively set as “calculated values ​​obtained by the electrode S1”, “calculated values ​​obtained by the electrode S2”, ..., “calculated values ​​obtained by the electrode Sn”, and the inverse matrix A of the matrix A composed of these calculated values ​​and the selectivity coefficients of the ion selective electrodes used is used. -1 , the concentration of each ion (C(B1), C(B2),..., C(Bn)) can be calculated for each of n types of ions (ions: B1, B2,..., Bn).

[0260] [Number 27]

[0261]

[0262] <Calculation of ion concentration when using a standard solution>

[0263] 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 , and calibrate the standard potential difference E 0,S If the potential difference E can be measured std The apparatus and device used are not particularly limited, but it is convenient to use the same apparatus as that used to measure the sample solution.

[0264] In the measurement of the standard solution, the measurement temperature is preferably 20° C. to 45° C., and the measurement time is preferably 2 seconds to 15 minutes, from the viewpoint of being able to measure a stable potential difference.

[0265] As long as the potential difference E of the standard solution is measured once std However, in order to obtain the calculated value obtained by the electrode S with higher accuracy, it is preferable to repeat the measurement between the measurements of the sample solution. The potential difference E of the standard solution for repeated measurements is appropriately determined. std In the case of repeated measurements, no matter which time point the potential difference E is used, std You can also use the potential difference E at several points to calibrate std From the perspective of accuracy, it is preferred to use the potential difference E in the target sample solution for measurement. S The potential difference E measured from 2 seconds to 1 hour ago std .

[0266] The potential difference E obtained when immersed in the standard solution can be used std and the ion concentration of the standard solution (C std ), and calculate the calculated value obtained by electrode S according to formula (20).

[0267] [Number 28]

[0268]

[0269] The “calculated values ​​obtained by the electrode S” are obtained for each of the n types of ion selective electrodes S1 to Sn used as the electrode S, and are respectively set as “calculated values ​​obtained by the electrode S1”, “calculated values ​​obtained by the electrode S2”, ..., “calculated values ​​obtained by the electrode Sn”, and the inverse matrix A of the matrix A composed of these calculated values ​​and the selectivity coefficients of the ion selective electrodes used is used. -1 , the concentration of each ion (C(B1), C(B2), ..., C(Bn)) can be calculated for each of n types of ions (ions: B1, B2, ..., Bn).

[0270] Example

[0271] The present invention will be described in more detail below by way of examples, but the present invention is not limited to these examples.

[0272] [Structure of ion concentration measuring device]

[0273] 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 containing a solution, and a calculation device.

[0274] The ion selective electrode and the potentiometer, and the potentiometer and the reference electrode are connected via electric wires, respectively. In addition, the potentiometer is connected to a computing device. When measuring the ion concentration, the liquid to be measured (for example, the sample solution, standard solution or calibration curve solution described later) is introduced into the "tank for loading the solution", and the ion concentration is measured in a state where the part of the ion selective electrode having the ion selective electrode and the part of the reference electrode having the liquid interface are immersed in the "liquid to be measured".

[0275] In the following examples and comparative examples, as reference electrodes, potentiometers, tanks for containing solutions, and computing devices, the reference electrodes, potentiometers, tanks, and computing devices shown below were used unless otherwise specified. In addition, the ion selective electrodes used in the following examples and comparative examples will be described later through the following examples and comparative examples.

[0276] (reference electrode)

[0277] As a reference electrode, a commercially available silver / silver chloride reference electrode (218087) manufactured by A&T Corporation was used.

[0278] (Potentiometer, calculation device, tank for solution)

[0279] As the potentiometer, the computing device, and the tank for storing the solution, the potentiometer, the computing device, and the tank which are attached to the electrolyte analyzer ELA08 manufactured by A&T Corporation were used.

[0280] [Preparation of ion selective electrode]

[0281] As the ion selective electrode, a commercially available chloride ion electrode (manufactured by A&T Corporation) was modified by replacing the ion selective membrane.

[0282] The ion selective membrane was prepared by changing the ratio of amine to halide and the reaction time as shown in Table 1 based on the method described in Example 1 of Japanese Patent Application Laid-Open No. 2018-004633. At this time, trimethylamine was used as anhydrous phosphoric acid. The reaction time was appropriately adjusted between 12 hours and 24 hours to obtain 7 ion selective membranes with different ion selectivity.

[0283] Ion selective electrodes (respectively referred to as electrode symbols EL1 to EL7) obtained by using these seven types of ion selective membranes were used in the ion concentration measurement of the following examples and comparative examples. Here, in the following description, the ion selective electrodes with electrode symbols EL1 to EL7 are sometimes referred to as electrodes EL1 to EL7, respectively. In addition, the electrode symbols EL1 to EL7 shown below correspond to unique identifiers determined separately from the symbols S1 to Sn of the ion selective electrodes for the matrix A.

[0284] [Table 1]

[0285] Electrode symbol Amine:halide ratio Response time (hours) EL1 1：9 12 EL2 1：1 24 EL3 2：1 15 EL4 1：2 12 EL5 1：1 20 EL6 2：1 24 EL7 1：2 24

[0286] [Example 1]

[0287] 1-1 Structure of ion concentration measuring device

[0288] In this embodiment, as the ion concentration measuring device, a device having the structure described in the above-mentioned "Structure of ion concentration measuring device" was used.

[0289] (Ion Selective Electrode)

[0290] As the ion selective electrodes, 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" were used.

[0291] (reference electrode, potentiometer, calculation device, tank for solution)

[0292] As the reference electrode, the potentiometer, the computing device, and the tank for containing the solution, the reference electrode, the potentiometer, the computing device, and the tank described in the above-mentioned "Structure of the ion concentration measuring device" were used.

[0293] In the apparatus used in the embodiment, the potential difference E of a plurality of ion selective electrodes can be measured simultaneously in parallel with respect to the solution introduced into the tank for containing the solution. STherefore, in the examples, the potential differences of multiple ion selective electrodes with respect to the solution are measured simultaneously, but this does not limit the present invention. As long as the method is used to obtain the potential differences of multiple ion selective electrodes with respect to the same solution, it can be used without special restrictions, and the potential differences obtained by the ion selective electrodes can be measured simultaneously or in different orders.

[0294] 1-2 Sample solution

[0295] The order of anions in blood from most to least is Cl - >HCO 3 - > Organic acid (lactic acid, pyruvic acid, propionic acid, fatty acids, amino acids, etc.) ions (here acetate ions (AcO - ) was used as the sample solution. Since the blood also contained impurity ions, a solution to which phosphate ions, bromide ions, and thiocyanate ions were added was used as the sample solution. The chlorine containing the ions to be measured and impurity ions shown in Table 2 was dissolved in a HEPES buffer solution (100 mM, pH 8.0) to prepare a sample solution X.

[0296] [Table 2]

[0297]

[0298] The solvent was HEPES buffer (100 mM, pH 8.0)

[0299] 1-3 standard solution

[0300] 0.58 g of sodium chloride (NaCl) was dissolved in 1 L of HEPES buffer (100 mM, pH 8.0) to prepare 1 mM (=C std ) sodium chloride (NaCl) / HEPES buffer.

[0301] 1-4 Calibration curve solution

[0302] Sodium chloride (NaCl) was dissolved in HEPES buffer (100 mM, pH 8.0) to prepare 80 mM, 100 mM, and 120 mM sodium chloride (NaCl) / HEPES buffers, which were used as calibration curve solutions.

[0303] 1-5 Preparation of calibration curve (E std , Slope value calculation)

[0304] The calibration curve was prepared as follows.

[0305] 2 ml of the calibration curve solution was placed in a vial, set in an electrolyte analyzer ELA08 manufactured by A&T Co., Ltd., and measured at room temperature. The measurement was performed by the following operation: using the ion selective electrode (the electrode EL1, the electrode EL2, or the electrode EL3) and the reference electrode connected to each other via the potentiometer, the potential difference E of the standard solution prepared in 1-3 above was first measured for each calibration curve solution. std Then, the potential difference E of the solution used for the calibration curve is measured. S The above series of operations were performed for the three calibration curve solutions. The following structure is used: if the standard solution is set in a predetermined location, the standard solution will automatically circulate and the potential E of the standard solution will be measured at any time. std .

[0306] Table 3 shows the potential difference E when the calibration curve solutions of 80 mM, 100 mM, and 120 mM (=C(Cl-)) prepared in 1-4 above were measured using electrodes EL1, EL2, and EL3. S and the potential difference E of the standard solution std .

[0307] The value of Slope is calculated as follows.

[0308] The following equation (X1) is obtained from equation (18') and equation (19). Substituting the above values ​​into equation (X1) to calculate the potential difference (E S -E std ) and (log 10 C(Cl - )-log 10 C std ), a calibration curve was prepared, and the Slope was calculated. Table 3 shows the Slope of each electrode.

[0309] [Number 29]

[0310] E S =E 0，S +Slope×log 10 C(Cl - ) (18')

[0311] E 0，S =E Std -Slope×log 10 C std (19)

[0312] E S -E Std =Slope×(log 10 C(Cl - )-log10 C std ) (X1)

[0313] [Table 3]

[0314] Table 3 Potential and Slope values ​​obtained by measuring the solution for the calibration curve using electrode EL1, EL2 or EL3 as electrode S

[0315]

[0316] 1-6 Calculation of the selectivity coefficient related to ion selective electrodes and preparation of matrix A

[0317] (Calculation of selection coefficient)

[0318] The selectivity coefficients for the ions to be measured are calculated for the electrodes EL1 to EL3 (electrodes EL1 to EL3) with respect to the ions to be measured. - ) is used as an example of the case where the ion to be measured is used.

[0319] The selectivity coefficient was calculated as follows.

[0320] (1) Bicarbonate ion (HCO 3 - ) Calculation of selection coefficient

[0321] First, bicarbonate ions (HCO 3 - ) selectivity coefficient calculation solution, the bicarbonate ion (HCO 3 - ) The solution for calculating the selectivity coefficient contains the ions (ion to be measured) used as the reference for preparing the calibration curve (chloride ion (Cl - )) and the ion for which the selectivity is to be calculated (bicarbonate ion (HCO 3 - )).

[0322] Sodium bicarbonate (NaHCO 3 ) and sodium chloride (NaCl) were dissolved in HEPES buffer (100 mM, pH 8.0) to prepare 10 mM sodium bicarbonate (NaHCO 3 ), 100 mM sodium chloride (NaCl) / HEPES buffer, and bicarbonate ion (HCO 3 - )Select the solution for coefficient calculation.

[0323] 2 ml of bicarbonate ions (HCO 3 -) The solution for calculating the selectivity coefficient was placed in a vial, set in an electrolyte analyzer ELA08 manufactured by A&T Co., Ltd., and measured at room temperature. The measurement was performed by the following operation: using the ion selective electrode (the electrode EL1, EL2 or EL3) and the reference electrode connected to each other via the potentiometer, for each solution for calculating the selectivity coefficient, firstly, the potential difference E of the standard solution was measured. std Then, the potential difference E of the solution used for the selectivity calculation is measured. S .

[0324] Here, the potential difference E when the standard solution is measured std , the Slope value recorded in the above Table 3 obtained in the above "Preparation of 1-5 Calibration Curve" and the ion concentration C of the standard solution std Substitute into the following formula (19) to obtain the standard potential difference E 0，S , and the standard potential difference E 0，S , the above potential difference E S , the Slope value and the bicarbonate ion (HCO 3 - ) The selectivity coefficient is calculated by the ion concentration in the solution (chloride ions (Cl - ) concentration is C(B1), and the bicarbonate ion (HCO 3 - ) is denoted as C(B2). ) is substituted into the following formula (8B), thereby obtaining the chloride ion (Cl - ) as the target ion for measurement: 3 - ) selectivity coefficient (Ks(Cl - , HCO 3 - )).

[0325] [Number 30]

[0326] E 0，S =E Std -Slope×log 10 C std (19)

[0327] [Number 31]

[0328]

[0329] Table 4 shows the above bicarbonate ion (HCO 3 - ) The potential difference E when the selectivity coefficient is calculated using the solution S , the potential difference of the standard solution Estd And the selectivity coefficient (Ks(Cl - , HCO 3 - )).

[0330] [Table 4]

[0331] Table 4 Potential difference E when electrode EL1, EL2 or EL3 is set as electrode S S The potential difference E between the std The measured values ​​of bicarbonate ions (HCO 3 - )Selection coefficient

[0332]

[0333] (2) Calculation of acetate ion (AcO-) selectivity

[0334] A solution for calculating the selectivity coefficient of acetate ion (AcO-) was prepared in the same manner as in the above (1).

[0335] 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, which was used as a solution for calculating the selectivity coefficient of acetate ion (AcO-).

[0336] 2 ml of the acetate ion (AcO-) selectivity calculation solution was placed in a vial, and the solution was placed in an electrolyte analyzer ELA08 manufactured by A&T Co., Ltd. and measured at room temperature. The measurement was performed by the following operation: using the ion selective electrode (the electrode 1, 2, or 3) and the reference electrode connected to each other via the potentiometer, the potential difference E of the standard solution was first measured for each calibration curve solution. std Then, the potential difference E of the solution used for the calibration curve is measured. S .

[0337] Here, in addition to the potential difference E S Used as potential difference E S , acetate ion (AcO - )Selectivity calculation uses chloride ions (Cl - ) and acetate ions (AcO - ) concentrations are used as C(B1) and C(B2), respectively, and in addition to the above “(1) bicarbonate ion (HCO 3 -) selectivity coefficient is calculated by substituting various parameters into the above formula (19) and formula (8B) to obtain the chloride ion (Cl - ) as the target ion for determination (Ks(Cl - ,AcO - )).

[0338] Table 5 shows the acetate ion (AcO - ) The potential difference E when the selectivity coefficient is calculated using the solution S , the potential difference of the standard solution E std And the selectivity coefficient (Ks(Cl - ,AcO - )).

[0339] [Table 5]

[0340] Table 5 Potential difference E when electrodes EL1, EL2 and EL3 are set as electrode S S The potential difference E between the std The measured values ​​of acetate ion (AcO - )Selection coefficient

[0341]

[0342] (Creation of Matrix A)

[0343] The matrix A is created based on the values ​​of the selectivity coefficients obtained in the above-mentioned “calculation of selectivity coefficients” for the above-mentioned electrodes EL1 , EL2 , and EL3 .

[0344] The selectivity coefficients obtained in the above-mentioned "Calculation of Selectivity Coefficient" are summarized in Table 6 below. - )) The selectivity coefficient (Ks(Cl - , Cl - )) is set to 1.

[0345] [Table 6]

[0346] Table 6 Selectivity coefficient of each ion selective electrode for the ion to be measured

[0347]

[0348] The matrix A corresponding to the selectivity coefficients shown in Table 6 can be expressed as follows. Here, whenever the following matrix A is obtained, the electrodes EL1, EL2, and EL3 are respectively set as the first type ion selective electrode (ion selective electrode S1), the second type ion selective electrode (ion selective electrode S2), and the third type ion selective electrode (ion selective electrode S3). In the following matrix A, the selectivity coefficient K associated with the i-th type (i is 1 or more and 3 or less) ion selective electrode among the three types of ion selective electrodes is expressed as follows: S (Cl - , Cl - ), K S (Cl - , HCO 3 - ) and K S (Cl - ,AcO - ) are respectively represented as K Si (Cl - , Cl - ), K Si (Cl - , HCO 3 - ) and K Si (Cl - ,AcO - ).

[0349] [Number 32]

[0350]

[0351] When the matrix A is input into a cell (A1:C3) of spreadsheet software Excel and the "=MDETERM(A1:C3)" function is used to find the absolute value of the matrix expression ||A||, the result is 0.42.

[0352] Here, specifically, the absolute value ||A|| in Excel can be calculated in the following manner. First, input 1 into cell A1, input 1 into cell A2, input 1 into cell A3, input 0.10 into cell B1, input 0.56 into cell B2, input 0.87 into cell B3, input 0.07 into cell C1, input 0.76 into cell C2, and input 0.32 into cell C3. Next, if "=MDETERM(A1:C3)" is input into any cell other than these cells, the calculated value of "=MDETERM(A1:C3)" can be obtained as the value of the matrix formula || (in this case, -0.42). Moreover, by applying the ABS function to the value of the matrix formula ||, the absolute value of the matrix formula || can be obtained, and this value can be used as the absolute value ||A||.

[0353] Here, in the above Tables 4 to 6 and the above Matrix A, K S (Cl - , HCO 3 - ) and K S (Cl - ,AcO - ) is rounded to the third decimal place for the sake of documentation. However, in the following "1-8 Calculation of ion concentration of sample solution", the inverse matrix A described later is calculated. -1 When calculating the concentration of each ion, these values ​​are not rounded off at the third decimal place, but are used in a form taking into account the third decimal place and beyond.

[0354] 1-7 Potential difference E of sample solution S Determination of

[0355] 2 ml of the sample solution X was placed in a vial, set in an electrolyte analyzer ELA08 manufactured by A&T Co., Ltd., and measured at room temperature. The measurement was performed by the following operation: first, the potential difference E of the standard solution was measured using the ion selective electrode (the electrode EL1, EL2, or EL3) and the reference electrode connected to each other via the potentiometer. std Then, the potential difference E of the sample solution X is measured. S Table 7 shows the measured values ​​and the calculated values ​​obtained from the measured values ​​(calculated values ​​obtained by electrode S). std , Slope value calculation)" and use the Slope value of Table 4 to calculate the Slope value of Table 7 std Correction was made.

[0356] [Table 7]

[0357] Table 7 Potential difference E when electrode EL1, EL2 or EL3 is set as electrode S S The potential difference E between the std The measured value and the calculated value obtained by electrode S

[0358] Electrode symbol Es / mV Estd / mV Calculated value obtained by electrode S EL1 45.68 146.21 108.72 EL2 42.37 144.49 125.10 EL3 39.85 144.26 130.24

[0359] [Number 33]

[0360]

[0361] 1-8 Calculation of ion concentration of sample solution

[0362] The ion concentration of the sample solution (sample solution X) is calculated as follows.

[0363] First, the inverse matrix A of the matrix A obtained in the above "1-6 Calculation of the selectivity coefficient related to the ion selective electrode and creation of the matrix A" is calculated. -1 The matrix A is obtained by setting the electrodes EL1, EL2 and EL3 as ion selective electrodes S1, ion selective electrodes S2 and ion selective electrodes S3, respectively. Input the matrix A into the cell (A1:C3) of the spreadsheet software Excel, and use the function "=MINVERSE(A1:C3)" to find the inverse matrix A. -1 .

[0364] Here, for the cells A1 to C3 entered in the above “1-6 Calculation of selectivity coefficients related to ion selective electrodes and creation of matrix A”, “=MINVERSE(A1:C3)” is entered in any cell away from these cells, thereby performing the inverse matrix A in Excel. -1 The calculation of the inverse matrix A can be performed by using a set of calculated values ​​displayed in the cell with the input "=MINVERSE(A1:C3)" and the cells located near it. -1 .

[0365] [Number 34]

[0366]

[0367] The potential difference E of the sample solution in the above "1-7" S The "calculated value obtained by electrode S" recorded in the above Table 7 obtained in the "measurement of" is applied to the above inverse matrix A -1 , to find the chloride ion (Cl - ) concentration C(Cl - ), bicarbonate ion (HCO 3 - ) concentration C(HCO 3 - ) and acetate ions (AcO - ) concentration C(AcO - ). Here, the "calculated value obtained by electrode S" related to the above-mentioned electrode EL1 is set to the "calculated value obtained by electrode S1", the "calculated value obtained by electrode S" related to the above-mentioned electrode EL2 is set to the "calculated value obtained by electrode S2", and the "calculated value obtained by electrode S" related to the above-mentioned electrode EL3 is set to the "calculated value obtained by electrode S3". As a result, C(Cl - )=105.7mM、C(HCO 3- )=26.0mM、C(AcO - )=6.09mM.

[0368] [Number 35]

[0369]

[0370] Here, as the inverse matrix A -1 , the K related to each ion selective electrode obtained in the above "1-6 Calculation of the selectivity coefficient related to the ion selective electrode and preparation of the matrix A" S (Cl - , HCO 3 - ) and K S (Cl - ,AcO - ) value, and the potential difference E of the sample solution in the above "1-7 S For the convenience of documentation, the values ​​of "calculated values ​​obtained by electrode S" obtained in "measurement of" are shown as values ​​rounded off to the third decimal place. However, when calculating the concentration of each ion, these values ​​are not used as values ​​rounded off to the third decimal place, but are used in a form that also takes into account the third decimal place. Moreover, in the middle of calculating the concentration of each ion, rounding processing (Rounding) based on the rounded value is not performed, and only rounding processing (Rounding) based on the rounded value is performed on the final concentration value.

[0371] Furthermore, the same processing was performed when calculating the concentration of each ion in Example 2 and Comparative Example 1 described below.

[0372] In addition, due to the error caused by such rounding of numerical values, the calculation results of the concentrations of each ion obtained in this embodiment and the following embodiment 2 and comparative example 1 may deviate to some extent from the concentration values ​​obtained by using the value obtained by rounding off at the third decimal place as the value of the "calculated value obtained by the electrode S", and using the inverse matrix composed of the values ​​obtained by rounding off at the third decimal place of each element as the inverse matrix A. -1 , simply combine them to find .

[0373] The potential difference E of the sample solution in the above-mentioned "1-7" S The operations of "Determination of ion concentration" and "Calculation of ion concentration of sample solution 1-8" were repeated 6 times to determine the relative standard deviation (the percentage of the value obtained by dividing the standard deviation by the average value) (%) for chloride ions, bicarbonate ions and acetate ions, respectively.

[0374] The results are shown in Table 18.

[0375] [Example 2]

[0376] 2-1 Structure of ion concentration measuring device

[0377] As the ion concentration measuring device, a device having the structure described in the above “Structure of the ion concentration measuring device” was used in the same manner as in Example 1. Here, as the ion selective electrode, reference electrode, potentiometer, tank for containing the solution, and computing device, the ion selective electrode, reference electrode, potentiometer, tank, and computing device shown below were used.

[0378] (Ion Selective Electrode)

[0379] As the ion selective electrodes, 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" were used.

[0380] (reference electrode, potentiometer, calculation device, tank for solution)

[0381] Reference electrode, potentiometer, calculation device, and tank for containing solution As in Example 1, the reference electrode, potentiometer, calculation device, and tank described in the above “Structure of ion concentration measuring device” were used.

[0382] 2-2 Sample solution

[0383] As the sample solution, the same sample solution as the sample solution X used in Example 1 was used.

[0384] 2-3 Standard solution

[0385] The same standard solution as in Example 1 was used as the standard solution.

[0386] 2-4 Solution for calibration curve

[0387] The same calibration curve solution as in Example 1 was used as the calibration curve solution.

[0388] 2-5 Preparation of calibration curve (E std , Slope value calculation)

[0389] The preparation of the calibration curve and the calculation of the Slope value were 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. Table 8 shows the obtained Slope values.

[0390] [Table 8]

[0391] Table 8 Potential and Slope values ​​obtained by measuring the solution for the calibration curve using electrode EL1, EL2 or EL4 as electrode S

[0392]

[0393] 2-6 Calculation of the selectivity coefficient related to ion selective electrodes and preparation of matrix A

[0394] (Calculation of selection coefficient)

[0395] The selectivity coefficients for the ions to be measured were calculated for 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. Tables 9 and 10 show the measured values ​​and the calculated selectivity coefficients.

[0396] [Table 9]

[0397] Table 9 Potential difference E when electrode EL1, EL2 or EL4 is set as electrode S S The potential difference E between the std The measured value of the bicarbonate ion (HCO 3 - )Selection coefficient

[0398]

[0399] [Table 10]

[0400] Table 10 Potential difference E when electrode EL1, EL2 or EL4 is set as electrode S S The potential difference E between the std The measured value of the acetate ion (AcO - )Selection coefficient

[0401]

[0402] (Creation of Matrix A)

[0403] The matrix A is created based on the values ​​of the selectivity coefficients obtained in the above-mentioned “calculation of selectivity coefficients” for the above-mentioned electrodes EL1 , EL2 , and EL4 .

[0404] The selectivity coefficients obtained in the above-mentioned "Calculation of Selectivity Coefficient" are summarized in Table 11 below. - )) The selectivity coefficient (Ks(Cl - , Cl - )) is set to 1.

[0405] [Table 11]

[0406] Table 11 Selectivity coefficient of each ion selective electrode for the ion to be measured

[0407]

[0408] The matrix A corresponding to the selectivity coefficients shown in Table 11 can be expressed as follows. Here, whenever the following matrix A is obtained, the electrodes EL1, EL2, and EL4 are respectively set as the first type of ion selective electrode (ion selective electrode S1), the second type of ion selective electrode (ion selective electrode S2), and the third type of ion selective electrode (ion selective electrode S3). In the following matrix A, the selectivity coefficient K associated with the i-th type (i is 1 or more and 3 or less) of the ion selective electrodes among the three types of ion selective electrodes is expressed as follows: S (Cl - , Cl - ), K S (Cl - , HCO 3 - ) and K S (Cl - ,AcO - ) are respectively represented as K Si (Cl - , Cl - ), K Si (Cl - , HCO 3 - ) and K Si (Cl - ,AcO - ).

[0409] [Number 36]

[0410]

[0411] When the matrix A is input into a cell (A1:C3) of spreadsheet software Excel and the "=MDETERM(A1:C3)" function is used to find the absolute value of the matrix expression ||A||, the result is 0.20.

[0412] 2-7 Potential difference E of sample solution S Determination of

[0413] The potential difference E of the sample solution SThe measurement of , except that the electrode EL1, the electrode EL2 or the electrode EL4 is used as the ion selective electrode, is performed in the same manner as in Example 1. The measured values ​​and the calculated values ​​obtained from the measured values ​​(the calculated values ​​obtained by the electrode S) are shown in Table 12. The Slope value of Table 8 obtained in the same manner as in Example 1 is used, and the E value of Table 12 is used. std Correction was made.

[0414] [Table 12]

[0415] Table 12 Potential difference E when electrode EL1, EL2 or EL4 is set as electrode S S The potential difference E between the std The measured value and the calculated value obtained by electrode S

[0416] Electrode symbol Es / mV Estd / mV Calculated value obtained by electrode S EL1 44.54 145.14 109.02 EL2 41.35 143.49 125.01 EL4 26.57 143.22 118.51

[0417] 2-8 Calculation of ion concentration of sample solution

[0418] The ion concentration of the sample solution was calculated in the same manner as in Example 1.

[0419] First, the inverse matrix A of the matrix A obtained in the above-mentioned "2-6 Calculation of selectivity coefficients related to ion selective electrodes and creation of matrix A" is obtained in the same manner as in Example 1. -1 The matrix A is obtained by setting the electrodes EL1, EL2 and EL4 as ion selective electrodes S1, ion selective electrodes S2 and ion selective electrodes S3, respectively. Input the matrix A into the cell (A1:C3) of the spreadsheet software Excel, and use the function "=MINVERSE(A1:C3)" to find the inverse matrix A. -1 .

[0420] [Number 37]

[0421]

[0422] The potential difference E of the sample solution in the above "2-7" S The "calculated value obtained by electrode S" recorded in the above Table 12 obtained in the "measurement of" is applied to the above inverse matrix A -1 , to find the chloride ion (Cl - ) concentration C(C1-), bicarbonate ion (HCO 3 - ) concentration C(HCO 3 -) and the concentration C(AcO-) of acetate ions (AcO-). Here, the "calculated value obtained by electrode S" related to the above-mentioned electrode EL1 is set to the "calculated value obtained by electrode S1", the "calculated value obtained by electrode S" related to the above-mentioned electrode EL2 is set to the "calculated value obtained by electrode S2", and the "calculated value obtained by electrode S" related to the above-mentioned electrode EL4 is set to the "calculated value obtained by electrode S3". As a result, C(Cl - )=105.7mM、C(HCO 3 - )=27.6mM、C(AcO - )=5.21mM.

[0423] [Number 38]

[0424]

[0425] The potential difference E of the above "2-7 sample solution S The operations of "Determination of 2-8" and "Calculation of ion concentration of sample solution 2-8" were repeated 6 times to determine the relative standard deviation (%) in the same manner as in Example 1. The results are shown in Table 18.

[0426] [Comparative Example 1]

[0427] C1-1 Structure of ion concentration measuring device

[0428] As the ion concentration measuring device, a device having the structure described in the above “Structure of the ion concentration measuring device” was used in the same manner as in Example 1. Here, as the ion selective electrode, reference electrode, potentiometer, tank for containing the solution, and computing device, the ion selective electrode, reference electrode, potentiometer, tank, and computing device shown below were used.

[0429] (Ion Selective Electrode)

[0430] As the ion selective electrodes, 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-mentioned "Preparation of ion selective electrodes" were used.

[0431] (reference electrode, potentiometer, calculation device, tank for solution)

[0432] Reference electrode, potentiometer, calculation device, and tank for containing solution As in Example 1, the reference electrode, potentiometer, calculation device, and tank described in the above “Structure of ion concentration measuring device” were used.

[0433] C1-2 Sample solution

[0434] As the sample solution, the same sample solution as the sample solution X used in Example 1 was used.

[0435] C1-3 standard solution

[0436] The same standard solution as in Example 1 was used.

[0437] C1-4 calibration curve solution

[0438] The same standard solution as in Example 1 was used as the standard solution.

[0439] Preparation of C1-5 calibration curve (E std , Slope value calculation)

[0440] The preparation of the calibration curve and the calculation of the Slope value were 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. Table 13 shows the obtained Slope values.

[0441] [Table 13]

[0442] Table 13 Potential and Slope values ​​obtained by measuring the solution for the calibration curve using electrode EL5, EL6 or EL7 as electrode S

[0443]

[0444] C1-6 Calculation of selectivity coefficients related to ion selective electrodes and preparation of matrix A

[0445] (Calculation of selection coefficient)

[0446] The selectivity coefficients for the ions to be measured were calculated for 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.

[0447] [Table 14]

[0448] Table 14 Potential difference E when electrode EL5, EL6 or EL7 is set as electrode S S The potential difference E between the std The measured value of the bicarbonate ion (HCO 3 - )Selection coefficient

[0449]

[0450] [Table 15]

[0451] Table 15 Potential difference E when electrode EL5, EL6 or EL7 is set as electrode S S The potential difference E between the std The measured value of the acetate ion (AcO - )Selection coefficient

[0452]

[0453] (Creation of Matrix A)

[0454] The matrix A is created based on the values ​​of the selectivity coefficients obtained in the above-mentioned “calculation of selectivity coefficients” for the above-mentioned electrodes EL5 , EL6 , and EL7 .

[0455] The selectivity coefficients obtained in the above-mentioned "Calculation of Selectivity Coefficient" are summarized in Table 16 below. - )) The selectivity coefficient (Ks(Cl - , Cl - )) is set to 1.

[0456] [Table 16]

[0457] Table 16 Selectivity coefficient of each ion selective electrode for the ion to be measured

[0458]

[0459] The matrix A corresponding to the selection coefficients shown in the above Table 16 can be expressed as follows.

[0460] Here, whenever the following matrix A is obtained, the electrodes EL5, EL6 and EL7 are respectively set as the first type ion selective electrode (ion selective electrode S1), the second type ion selective electrode (ion selective electrode S2) and the third type ion selective electrode (ion selective electrode S3). In the following matrix A, the selectivity coefficient K associated with the i-th type (i is 1 or more and 3 or less) ion selective electrode among the three types of ion selective electrodes is S (Cl - , Cl - ), K S (Cl - , HCO 3 - ) and K S (Cl - ,AcO - ) are respectively represented as K Si (Cl - , Cl - ), K Si (Cl- , HCO 3 - ) and K Si (Cl - ,AcO - ).

[0461] [Number 39]

[0462]

[0463] When the matrix A is input into a cell (A1:C3) of spreadsheet software Excel and the "=MDETERM(A1:C3)" function is used to find the absolute value of the matrix expression ||A||, the result is 0.02.

[0464] Potential difference E of C1-7 sample solution S Determination of

[0465] The potential difference E of the sample solution S The measurement of EL5, EL6 or EL7 was performed in the same manner as in Example 1 except that the electrode EL5, EL6 or EL7 was used as the ion selective electrode. The measured values ​​and the calculated values ​​obtained from the measured values ​​(the calculated values ​​obtained by the electrode S) are shown in Table 17. The Slope value of Table 13 obtained in the same manner as in Example 1 was used, and the E value of Table 17 was used. std Correction was made.

[0466] [Table 17]

[0467] Table 17 Potential difference E when electrode EL5, EL6 or EL7 is set as electrode S S The potential difference E between the std The measured value and the calculated value obtained by electrode S

[0468] Electrode symbol Es / mV Estd / mV Calculated value obtained by electrode s EL5 62.93 144.36 120.82 EL6 60.63 141.75 134.44 EL7 62.26 141.96 120.61

[0469] Calculation of ion concentration of C1-8 sample solution

[0470] The ion concentration of the sample solution was calculated in the same manner as in Example 1.

[0471] First, the inverse matrix A of the matrix A obtained in the above-mentioned "Calculation of the selectivity coefficient related to C1-6 and the ion selective electrode and preparation of the matrix A" is obtained in the same manner as in Example 1. -1 The matrix A is obtained by setting the electrodes EL5, EL6 and EL7 as ion selective electrodes S1, ion selective electrodes S2 and ion selective electrodes S3, respectively. Input the matrix A into the cell (A1:C3) of the spreadsheet software Excel, and use the function "=MINVERSE(A1:C3)" to find the inverse matrix A.-1 .

[0472] [Number 40]

[0473]

[0474] The potential difference E of the sample solution C1-7 is S The "calculated value obtained by electrode S" recorded in the above Table 17 obtained in the "measurement of" is applied to the above inverse matrix A -1 , to find the chloride ion (Cl - ) concentration C(Cl - ), bicarbonate ion (HCO 3 - ) concentration C(HCO 3 - ) and acetate ion (AcO - ) concentration C(AcO - ). Here, the "calculated value obtained by electrode S" related to the above-mentioned electrode EL5 is set to the "calculated value obtained by electrode S1", the "calculated value obtained by electrode S" related to the above-mentioned electrode EL6 is set to the "calculated value obtained by electrode S2", and the "calculated value obtained by electrode S" related to the above-mentioned electrode EL7 is set to the "calculated value obtained by electrode S3". As a result, C(Cl - )=102.3mM、C(HCO 3 - )=43.2mM、C(AcO - )=-3.46mM.

[0475] [Number 41]

[0476]

[0477] The potential difference E of the above "C1-7 sample solution S The operations of "Determination of ion concentration of C1-8 sample solution" and "Calculation of ion concentration of C1-8 sample solution" were repeated 6 times to determine the relative standard deviation (%) in the same manner as in Example 1. The results are shown in Table 18.

[0478] [Table 18]

[0479] Table 18 Summary of results

[0480]

[0481] Description of Reference Numerals

[0482] 1: ion selective electrode; 2: reference electrode; 3: potentiometer; 4: tank for loading solution; 5: internal electrode; 6: internal liquid; 7: ion selective membrane; 8: liquid junction; 9: sample solution.

Claims

1. An ion concentration measuring device, comprising two or more ion selective electrodes having different ratios of selectivity coefficients for a plurality of ions and satisfying the following formulas (1) and (2), When the number of the plurality of ion types is n, the two or more ion selective electrodes are composed of n types of ion selective electrodes. n is an integer greater than or equal to 2, [Number 1] ||A||＞0.1 (2) In formula (1), each component of the matrix A represents the ion selectivity coefficient, where: Bj represents the jth ion among the n ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n-type ion selective electrodes, i and j are each independently an integer from 1 to n, 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 formula (2), ||A|| is the absolute value of the matrix formula of matrix A.

2. The ion concentration measuring device according to claim 1, wherein: The ion concentration is calculated using the following formula (3): [Number 2] Here, A -1 represents the inverse matrix of the matrix A, C(Bj) represents the concentration of the ion Bj, and the calculated value obtained by the electrode Si represents the value when the potential difference measured by the ion selective electrode Si is converted according to the following formula: Wherein, j is an integer from 1 to n, i is an integer from 1 to n, [Number 3] In the above formula, E Si is the potential difference generated between the ion selective electrode Si and the reference electrode, E 0,Si It is the standard potential difference generated between the ion selective electrode Si and the reference electrode. Slope is 2.303RT / aF, R is the gas constant, T is the absolute temperature, a is the valence of ion B1, F is Faraday's constant.

3. A method for determining ion concentration, comprising the following steps: The ion concentration in the sample solution is measured using two or more ion selective electrodes having different ratios of selectivity coefficients for the plurality of ions and satisfying the following equations (1) and (2), When the number of types of the plurality of ions is n, the two or more ion selective electrodes are composed of n types of ion selective electrodes, where n is an integer greater than or equal to 2. [Number 4] ||A||>0.1 (2) In formula (1), each component of the matrix A represents the ion selectivity coefficient, where: Bj represents the jth ion among the n ions constituting the plurality of ions, Si is a symbol representing the i-th ion selective electrode constituting the n-type ion selective electrodes, i and j are each independently an integer from 1 to n, 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 formula (2), ||A|| is the absolute value of the matrix formula 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): [Number 5] Here, A- 1 represents the inverse matrix of the matrix A, C(Bj) represents the concentration of the ion Bj, and the calculated value obtained by the electrode Si represents the value when the potential difference measured by the ion selective electrode Si is converted according to the following formula: Wherein, j is an integer from 1 to n, i is an integer from 1 to n, [Number 6] In the above formula, E Si is the potential difference generated between the ion selective electrode Si and the reference electrode, E 0,Si It is the standard potential difference between the ion selective electrode Si and the reference electrode. The Slope is 2.303RT / aF. R is the gas constant, T is the absolute temperature, a is the valence of ion B1, F is Faraday's constant.

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