Simulation of calibration curve in size exclusion chromatography

Abstract

To simulate a calibration curve when a plurality of columns of the same grade are connected or when a plurality of columns of different grades are connected, based on calibration curve data for every column, and, to provide a simulation of how separation of an actual polymer sample changes, by using the technique.SOLUTION: A simulation method of calibration curves in size exclusion chromatography, includes: retaining calibration curve information in a storage medium, the calibration curve information consisting of logarithms of elution times and molecular weights of two or more types of size exclusion chromatography columns prepared in advance, having different separation characteristics; combining the calibration curve information of the two or more types of columns by mathematical processing; and simulating the calibration curve of when the two or more types of columns are connected in series.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for calculating the molecular weight or molecular weight distribution of a polymer sample with an unknown molecular weight in size exclusion chromatography. The method involves preparing calibration curves by analyzing two or more standard samples with a narrow molecular weight distribution and known molecular weights, storing calibration curve information consisting of the elution times and logarithms of the molecular weights of two or more size exclusion chromatography columns with different separation characteristics in a storage medium in advance, combining the calibration curve information of the two or more columns through mathematical processing, and simulating the calibration curve when the two or more columns are connected in series.

Background Art

[0002] Size exclusion chromatography (hereinafter also referred to as SEC) is a type of liquid chromatography that separates polymers by size based on elution from a column filled with a porous gel. SEC is a technique widely used for measuring the molecular weights of proteins, synthetic polymers, and natural polymers. In principle, in SEC, components with a large molecular weight elute earlier, and the elution becomes slower as the molecular weight decreases. The elution time and the logarithm of the molecular weight have a relationship as shown in Figure 2.

[0003] When actually measuring the molecular weight of an unknown polymer sample, a calibration curve is prepared using a plurality of standard samples with a narrow molecular weight distribution and clear molecular weight values, and the elution time of the unknown polymer sample is applied to the calibration curve to calculate the molecular weight. Since SEC has a relatively long measurement time, a "standard sample mixture" in which a plurality of standard samples are pre-mixed is often used. Figure 2 shows an example using three types of "standard sample mixtures".

[0004] Generally, when the calibration curve of SEC is plotted with the logarithm of the molecular weight, it can be approximated by a linear equation in a certain molecular weight range, but it has a large upward slope near the "exclusion limit" of the column and a large downward slope near the "penetration limit" of the column. Therefore, in a wide range, it is often approximated by a cubic equation or an odd polynomial for measurement.

[0005] In addition, there are multiple grades of SEC columns, such as those specialized for separation in the low molecular weight region, those specialized for separation in the middle molecular weight region, those specialized for separation in the high molecular weight region, and those with relatively good separation across all regions. Therefore, when creating a calibration curve, it is necessary to appropriately select the types of standard samples (molecular weights) for each type of SEC column.

[0006] Also, in SEC, unlike other liquid chromatographies, there are few factors that can adjust the separation of the components to be measured. In reverse phase chromatography, separation adjustment / improvement can be carried out using gel properties, eluent composition, elution method (isocratic elution or gradient elution method), column temperature, etc. However, since SEC is a method of separation based on molecular size, in principle, as long as it is dissolved in the eluent, separation is possible, and changing the composition of the eluent cannot improve the separation. When the separation of the target polymer sample is insufficient in SEC, the separation can only be improved by connecting columns of different grades in series or connecting multiple columns of the same grade in series (see Figure 1). To determine which column combination is suitable for the separation of the target polymer sample, it is important to check the profile of the calibration curve created for each column combination. However, creating a calibration curve for each column combination requires a lot of time. Also, SEC columns are about five times more expensive (200,000 - 300,000 yen per column) compared to columns for other liquid chromatographies, and it is not common to purchase them for the purpose of trial to check the calibration curve profile. Therefore, the optimal column combination is determined by relying on the user's past experience, etc., or by relying on the judgment of the manufacturer's engineers, and there is an issue of relying on personal means.

Prior Art Documents

Patent Documents

[0007] Patent Document 1: JP-A-11-51923

Summary of the Invention

Problems to be Solved by the Invention

[0008] The present invention has been made to solve the above problems, and simulates calibration curves when a plurality of columns of the same grade are connected or when a plurality of columns of different grades are connected, based on the calibration curve data for each column. Further, it simulates how the separation of an actual polymer sample changes from the above technique.

Means for Solving the Problems

[0009] As a result of intensive research in view of the above object, the present inventor has retained in a storage medium calibration curve information consisting of the elution time and the logarithm of the molecular weight of two or more size exclusion chromatography columns with different separation characteristics prepared in advance in size exclusion chromatography, combined the calibration curve information of the two or more columns by mathematical processing, and designed a method for simulating the calibration curve when the two or more columns are connected in series, thereby solving the above problems and completing the present invention. That is, the present invention can be exemplified as follows.

[0010] [1] In size exclusion chromatography for calculating the molecular weight or molecular weight distribution of a polymer sample with an unknown molecular weight, using a calibration curve prepared by analyzing two or more standard samples with a narrow molecular weight distribution and a known molecular weight, A method of retaining in a storage medium calibration curve information consisting of the elution time and the logarithm of the molecular weight of two or more size exclusion chromatography columns with different separation characteristics prepared in advance, combining the calibration curve information of the two or more columns by mathematical processing, and simulating the calibration curve when the two or more columns are connected in series, The mathematical processing is as follows: (1). For different calibration curve information for each column, taking the elution time as x and the logarithm of the molecular weight as y, and calculating the relational expression between x and y; (2) A step of interpolating calibration curve information by calculating the corresponding elution time x according to the relational expression obtained in (1) above, such that the logarithm y of the molecular weight corresponding to each of two or more arbitrarily specified columns in the calibration curve information of all columns is the same; (3) A step of obtaining the sum of x by adding the elution times obtained in (2) above, and simulating the calibration curve for the corresponding y and the combination of two or more specified columns; A method for simulating a calibration curve.

[0011] [2] In size exclusion chromatography using two or more columns with different or the same separation characteristics connected in series, -- A size exclusion chromatography device that holds calibration curve information consisting of the logarithm of the molecular weight of a previously prepared standard sample and the elution time in the column in a storage medium, performs mathematical processing on the calibration curve information to simulate the calibration curve, and calculates the molecular weight or molecular weight distribution of a target sample, The mathematical processing includes: (1) A step of calculating the relational expression between each x and y from the calibration curve information different for each column, with the elution time of the previously prepared standard sample being x and the logarithm of the molecular weight being y; (2) A step of calculating each corresponding x with y specified for the relational expression calculated above; (3) A step of adding the x values, and simulating the calibration curve for the combination of the two or more columns from the sum of x and the specified y, characterized by including this step. A size exclusion chromatography device.

[0012] [3] The relational expression between x and y in (1) above is represented by the following formula: y = ax 3 + bx 2 + cx + d The method for simulating a calibration curve according to [1].

[0013] [4] Express the relational formula between x and y in the above (1) by the following formula: y = ax 3 + bx 2 + cx + d [2] The size exclusion chromatography apparatus according to [2].

[0014] [5] Further, a step of storing the number of stages for each column, adding the number of stages for each column, and simulating the number of stages when using the combination of the specified columns is included. The method for simulating a calibration curve according to [1].

[0015] [6] Further, a step of storing the number of stages for each column, adding the number of stages for each column, and simulating the number of stages when using the combination of the specified columns is included. The size exclusion chromatography apparatus according to [2].

[0016] [7] For a polymer sample whose molecular structure is known and whose molecular weight and molecular weight distribution can be estimated, the molecular weight for each degree of polymerization of the polymer sample is applied to the "calibration curve when using the combination of the specified columns" obtained in claim 1, the elution time or elution volume of the peak apex is calculated, and from the "number of stages when using the combination of columns" obtained in [5], the peak width is calculated using the following liquid chromatography number of stages calculation formula (1) or formula (2). TIFF2025083816000002.tif33100

[0017] From these values, the peak curve for each degree of polymerization is calculated by a normal distribution function or a non-normal distribution function, and the chromatogram obtained in the combination of the specified columns is simulated by summing up the obtained peak curves for each degree of polymerization.

[0018] For a polymer sample with a known molecular structure and an estimable molecular weight and molecular weight distribution, the molecular weight for each degree of polymerization of the polymer sample is applied to the "calibration curve obtained when using the specified combination of columns" obtained in claim 2, and the elution time or elution volume at the peak apex is calculated. Also, from the "number of stages obtained when using the combination of columns" obtained in [6], the peak width is calculated using the following number-of-stages calculation formula (1) or formula (2) for liquid chromatography. TIFF2025083816000003.tif33100

[0019] A method of simulating a chromatogram obtained in a specified combination of columns by calculating peak curves for each degree of polymerization from these values using a normal distribution function or a non-normal distribution function and summing the obtained peak curves for each degree of polymerization.

[0020] Hereinafter, the present invention will be described in detail.

[0021] The present invention is mainly composed of two modes. As a first mode, In size exclusion chromatography, In a method of preparing a calibration curve in advance using two or more standard samples with a narrow molecular weight distribution and a known molecular weight and calculating the molecular weight or molecular weight distribution of a polymer sample with an unknown molecular weight, A method of holding calibration curve information consisting of the elution time and the logarithm of the molecular weight of at least two size exclusion chromatography columns with different separation characteristics in a storage medium, combining the calibration curve information of the plurality of types of columns by mathematical processing, and predicting the calibration curve when the plurality of types of columns are connected in series. The mathematical processing includes the following methods. (1) For calibration curve information different for each column, a step of calculating a relational expression between x and y, where x is the elution time and y is the logarithm of the molecular weight. (2) Interpolating the calibration curve information by calculating the corresponding elution time x according to the relational expression obtained in (1) such that the logarithm y of the molecular weight corresponding to each of any two or more arbitrarily specified columns in the calibration curve information of all columns is the same; (3) Obtaining the sum of x by adding the elution times obtained in (2), and simulating the calibration curve when using the corresponding y and the combination of two or more specified columns. y = ax 3 + bx 2 + cx + d Also, in size exclusion chromatography, "elution volume" may be used instead of elution time.

[0022] Also, as a second aspect, For a polymer sample with a known molecular structure and whose molecular weight and molecular weight distribution can be estimated to a certain extent, the molecular weight for each degree of polymerization of the polymer sample is applied to the "calibration curve when using the specified combination of columns" obtained in the first aspect to calculate the elution time or elution volume at the peak apex, and from the "number of stages when using the combination of columns" obtained in the first aspect, the peak width is calculated using the following liquid chromatography number of stages calculation formula (1) or (2). TIFF2025083816000004.tif33100

[0023] A method characterized by calculating a peak curve for each degree of polymerization using a normal distribution function or a non - normal distribution function from these values, summing the peak curves for each degree of polymerization, and synthesizing the expected chromatogram.

[0024] First, the first aspect will be described in detail. First, the characteristics of the column used in size exclusion chromatography are stored in a storage medium. The characteristics of the column include calibration curve information created with a plurality of standard samples having a narrow molecular weight distribution and known molecular weights, and the flow rate during measurement. In addition to these, it is better to include conditions such as the eluent and column temperature at the time of creating the calibration curve. The calibration curve information is composed of a combination of the elution time of the standard sample and the logarithm of the molecular weight. In SEC, when the elution time or elution volume is taken on the horizontal axis (X-axis) and the logarithm of the molecular weight is taken on the vertical axis (Y-axis), the molecular weight can be approximated by a linear equation in a certain region, but it rises sharply near the "exclusion limit" of the column and falls sharply near the "penetration limit" of the column, resulting in a profile. Therefore, in a wide range, an odd-order polynomial, especially a cubic equation, is often used for approximation and used as a calibration curve.

[0025] Also, there are multiple grades of SEC columns, such as those with improved separation in the low molecular weight region, those with improved separation in the middle molecular weight region, those with improved separation in the high molecular weight region, and those with relatively good separation in the entire region (see Figure 3). Therefore, it is necessary to use different types of standard samples (molecular weights) depending on the SEC column type when creating the calibration curve.

[0026] When using two columns of the same type connected in series, theoretically, the calibration curve can be predicted by doubling the elution time of the standard sample when using a single column. However, when using columns of different separation characteristics connected in series, the elution times of the standard samples cannot simply be added together. This is because the separation characteristics are different for each column, and the calibration points often vary. For example, in a column with good separation in the low molecular weight region, there may be many calibration points in the low molecular weight region and few in the high molecular weight region. Conversely, in a column with good separation in the high molecular weight region, there may be many calibration points in the high molecular weight region and few in the low molecular weight region. Figure 4a is a diagram simulating the calibration curves of four types of columns with different separation characteristics. In the figure, the legend ▲ represents the calibration points of column A, the legend ■ represents column B, the legend □ represents column C, and the legend ◆ represents column D. Table 1 shows the presence or absence of calibration points for each column, Table 2 shows the molecular weights of the calibration points for each column, and Table 3 shows the elution times of the calibration points for each column. When connecting columns with the same calibration points in series, the elution times can simply be added. However, when connecting columns with different calibration points as described above, since there may be a column without calibration points, the calibration curve cannot be simply estimated by addition (Tables 3 and 4). Table 5 shows the corrected calibration curve data (elution times of the correction points), and Table 6 shows the addition in the corrected calibration curve data. Therefore, in the present invention, correction of the calibration points is performed so that calibration points exist in all columns. Figures 6 and 7 are diagrams showing the flow of calibration curve simulation when connecting multiple types of columns from the correction of the calibration curve.

[0027] Raw calibration curve data (presence or absence of calibration points)

Table 1

[0028] Raw calibration curve data (molecular weights of calibration points)

Table 2

[0029] Raw calibration curve data (elution times of calibration points) [Table 3]

[0030] Addition results with raw calibration data [Table 4]

[0031] Corrected calibration curve data (elution times of correction points) [Table 5]

[0032] Addition result of correction standard curve data [Table 6]

[0033] First, the logarithm of the elution time and molecular weight of the standard sample for each column is approximated by a polynomial, and the coefficients of the above-mentioned function are calculated. Normally, odd-order polynomials are used in SEC, but the most commonly used cubic polynomial is used as an example. The coefficients (a, b, c, d) of the approximation formula are determined for all columns using the cubic polynomial. y=ax 3 +bx 2 +cx+d y:Log(molecular weight), x:elution time In order to align the calibration points of each column, x is calculated backwards from y so that the y value is the same. The y value may be determined arbitrarily, and may be set to cover all the molecular weights of the standard samples to be used, or may be specified at regular intervals. Here, we will explain the case where the y value is specified to cover all the molecular weights of the standard samples to be used. In other words, the process is performed to fill in the blanks in Tables 1 to 3 (see Figure 4b).

[0034] This calculation is the inverse calculation using polynomials (calculating x from y), and the calculation is complex. However, by performing the calculation in advance for each column and storing it in a storage medium as a corrected calibration curve database, subsequent processing can be simplified. Next, using the above-mentioned corrected calibration curve data, the calibration curves when combining columns of the same type and columns of different types are simulated. Since the corrected calibration curve data has the same value (LogMW) for all columns, the calibration points can be obtained by simply adding the x-values (elution times) of the columns to be combined. By approximating this group of calibration points with an odd-degree polynomial, the calibration curve when columns are combined can be predicted (see Figure 5). Also, the flow rate when the original calibration curve data was obtained and the flow rate during the calibration curve simulation by combining columns do not necessarily have to be the same. When the flow rate during calibration curve creation is Fa and the flow rate during simulation is Fx, the approximation formula can be calculated by multiplying the ratio (Fa / Fx) by the time term of the corrected calibration curve data. Also, by connecting multiple columns, the elution is delayed for a certain period due to the connecting pipes between the columns and other factors. By reflecting this delay time in this method, a more accurate simulation can be performed (see Figure 7).

[0035] Next, the second mode will be described in detail. For a polymer sample whose molecular structure is known to a certain extent and whose molecular weight and molecular weight distribution can be estimated to a certain extent, the molecular weight for each degree of polymerization of the polymer sample is applied to the "calibration curve when using the specified combination of columns" obtained in the first mode, and the elution time or elution volume at the peak apex is calculated. Also, from the above-mentioned "number of stages when using the combination of columns", the peak width is calculated using the number-of-stages calculation formula (Equation 1) or (Equation 2) of liquid chromatography. From these values, the peak curve for each degree of polymerization is calculated, and the expected chromatogram can be synthesized by summing the obtained peak curves. Here, it is assumed that the peak curve is a "normal distribution symmetric about the y-axis", and the "probability density function of the normal distribution" (Equation 3) is used. TIFF2025083816000011.tif2690

[0036] The procedure will be described in detail.

[0037] First, specify the peak shape of the entire polymer sample. Functionalize the molecular weight and distribution of the entire polymer sample. The peak shape may be a "normal distribution symmetric about the left and right", or a "function asymmetric about the left and right" may be used. An example of a usable peak function is shown in Fig. 13. Since these become complex function expressions, considering the computational load, it is preferable to use the Bigaussian peak function. TIFF2025083816000012.tif30113

[0038] When using the Bigaussian peak function (Fig. 11a), Xc is the time at the peak top. Obtain the elution time at which the assumed molecular weight value can be obtained by inverse calculation from the equation of the calibration curve simulated above. Next, specify the coefficient regarding the distribution. In the case of this equation, specify the width (w1) of the first half of the peak and the width (w2) of the second half of the peak. This value can be determined arbitrarily. When w1 and w2 are increased, the distribution becomes a wide shape, and when w1 and w2 are decreased, the distribution becomes a narrow shape. When w1 > w2, it is a leading peak shape, and when w1 < w2, it is a tailing peak shape. When w1 and w2 have the same value, it is a symmetric peak shape about the left and right.

[0039] Obtain the output (y value, H) of the "peak function of the entire polymer sample" corresponding to the peak time of the peak function for each degree of polymerization obtained above, and multiply the peak function for each degree of polymerization by the (y value) to reflect the distribution. When simply adding the peak functions for each degree of polymerization, as shown in Fig. 14, a chromatogram having a distribution is not obtained (Fig. a is for each degree of polymerization, and Fig. b is the curve obtained by summing all).

[0040] Next, calculate the molecular weight for each degree of polymerization. Inversely calculate the elution time (x) from the logarithm (y) of the molecular weight for each degree of polymerization and the coefficients (a, b, c, d) of the approximate equation obtained above.

[0041] Next, substitute the elution time and estimated number of stages obtained above into the number-of-stages calculation formula (Formula 1 or Formula 2) of liquid chromatography to calculate the peak half-width (W1 / 2) by back-calculation, and calculate the standard deviation (σ) therefrom (W1 / 2 corresponds to 2.354 times the standard deviation σ). Since the number of stages is theoretically a value for one column used, when multiple columns are connected in series, it is the sum of the individual numbers of stages.

[0042] Calculate the peak function for each degree of polymerization from the above parameters. FIG. 10 is a diagram showing the process. From the molecular weight for each degree of polymerization, the elution time, half-width, and standard deviation are obtained, and the intensity (H) for the elution time is calculated from the "peak function of the entire polymer sample" shown in FIG. 11, and the peak function is calculated using the normal distribution function (Formula 3).

[0043] FIG. 10a illustrates up to a degree of polymerization of 1, FIG. 10b illustrates up to a degree of polymerization of 2, and FIG. 10c illustrates up to a degree of polymerization of 3. FIG. 12 shows the separation simulation results (predicted chromatogram) obtained by summing up to a degree of polymerization of 1 to 20. Thus, when the molecular structure can be estimated to some extent and the overall molecular weight and molecular weight distribution can be estimated, according to the present invention, the separation pattern can be predicted without actually performing measurement.

Advantages of the Invention

[0044] In the present invention, by giving the molecular weight and distribution of the entire polymer sample as a functional formula, the intensity of the peak function for each degree of polymerization can be obtained, and a simulation chromatogram close to the actual chromatogram can be obtained. FIG. 14 shows the result of simulation without including intensity information in the peak function for each degree of polymerization. As can be seen from this figure, without intensity information, a profile (chromatogram) having a distribution cannot be obtained.

Brief Description of the Drawings

[0045]

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Figure 14

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Example

[0046] To verify the effects of the present invention, it was carried out by the following method.

[0047] The SEC device used data obtained by the high-speed GPC devices HLC-8320GPC or HLC-8420GPC manufactured by Tosoh Corporation. The basic configuration of the device is as shown in Fig. 1, and it is equipped with a reference flow type differential refractometer as a detector. All calibration curve data was created from the signals of the differential refractometer.

[0048] The separation columns used were also the TSKgel SuperHZ and SuperMultipore series manufactured by Tosoh Corporation (see Table 7 for the target columns). The standard samples for creating the calibration curve also used TSKgel standard polystyrene manufactured by Tosoh Corporation. Table 8 shows the molecular weights of the individual standard samples. Table 9 shows the composition of the "kit" in which a plurality of standard samples were pre-mixed. As the standard sample, either an individually adjusted sample or a standard sample kit was used.

[0049] Column specifications (TSKgel series)

Table 7

[0050] Molecular weight standard sample (individual)

Table 8

[0051] Molecular weight standard sample (kit)

Table 9

Example 1

[0052] In this example, “calibration curve simulation of multiple columns”, which is one of the aspects of the present invention, was verified.

[0053] Table 10 shows the calibration curve data for one column of SuperHZ2500 in the left column ※1 and SuperHZ3000 in the right column ※1, and Table 11 shows the calibration curve data for one column of SuperMultiporeHZ-N in the left column ※1 and SuperMultiporeHZ-M in the right column ※1. Here, the values presented by the column supply manufacturer are used. As can be seen from this, the calibration points (molecular weights of the standard samples) vary depending on the column type. In this state, it is difficult to estimate the calibration curve when connecting different types of columns. Therefore, a process of adjusting the calibration points (molecular weights of the standard samples) is performed.

[0054] Taking SuperHZ2500 as an example for explanation. First, a third-order polynomial approximation is performed at the calibration points when creating the calibration curve to obtain the coefficients of the polynomial. y = ax 3 + bx 2 + cx + d y: log[MW] x: Elution time (min) a: -0.53013 b: 6.45839 c: -26.82755 d: 40.97019 Next, the elution time (x value) is calculated by inverse calculation of the third-order polynomial obtained above so that log[MW] (y value) is at equal intervals from 8.0 to 1.5 at intervals of 0.5. Table 10 shows the calibration points obtained by the above process in the left column ※2. While there are 12 calibration points during measurement, log[MW] (y value) becomes 26 points at equal intervals by this process. The coefficients of the third-order polynomial after the correction process are a: -0.53013 b: 6.458391 c: -26.8275 d: 40.97019 This is almost the same as the coefficient of the calibration curve during measurement. Therefore, it can be seen that there is no change in the profile of the calibration curve even after correction.

[0055] The same applies to SuperHZ3000. First, perform a cubic equation approximation at the calibration points when creating the calibration curve to obtain the coefficients of the polynomial. y = ax 3 + bx 2 + cx + d y: log[MW] x: Elution time (min) a: -0.27183 b: 3.44410 c: -15.18977 d: 26.62235 Next, calculate the elution time (x value) by inverse calculation of the cubic equation obtained above so that log[MW] (y value) is at equal intervals of 0.5 from 8.0 to 1.5. The calibration points obtained by the above process are shown in the right column of Table 10 ※2. While there are 12 calibration points during measurement, log[MW] (y value) becomes 26 points at equal intervals by this process. The coefficients of the cubic equation after the correction process are a: -0.27183 b: 3.444099 c: -15.1898 d: 26.62235 This is almost the same as the coefficient of the calibration curve during measurement.

[0056] Also, in the case of SuperMultiporeHZ - N, it is the left column of Table 11, and in the case of SuperMultiporeHZ - M, it is the right column of Table 11. In all cases, the coefficients of the approximation formula at the time of creating the calibration curve and the coefficients of the cubic equation after the correction process are almost the same.

[0057] Calibration curve and corrected calibration curve during measurement

Table 10

[0058] Calibration curve and corrected calibration curve during measurement

Table 11

Table 12

Table 13

[0059] In an actual SEC, by increasing the number of columns, the elution time is delayed by the capacity of the column connection piping. Although the "delay time" is not considered here, considering the "delay time" can obtain a more accurate simulated calibration curve. When considering the "delay time", it can be calculated by adding the "delay time" to the elution time and then approximating with a cubic equation.

[0060] Table 14 also shows the calibration curves simulated for combinations of one SuperMultipore HZ-N column (Pattern 1), two SuperMultipore HZ-N columns (Pattern 2), three SuperMultipore HZ-N columns (Pattern 3), connecting SuperMultipore HZ-N and SuperMultipore HZ-M (Pattern 4), connecting SuperHZ2500 and SuperHZ3000 (Pattern 5), and two SuperHZ2500 (Pattern 6).

[0061]

Table 14

[0062] The present invention is roughly divided into a step of correcting the calibration curve obtained by actual measurement and a step of performing a simulation by combining columns using the corrected calibration curve obtained above to obtain a calibration curve.

[0063] When specifying the column combination, there are "a method of correcting the calibration curve obtained by actual measurement" and "a method of correcting the calibration curve obtained by prior measurement, creating a database, storing it in a storage medium, and reading and using it when performing a simulation". The "method of correcting the calibration curve obtained by actual measurement" performs inverse calculation of a polynomial and has a large computational load, so it is more desirable to perform the correction process in advance and create a database. As described above, according to the present invention, it is possible to obtain a calibration curve based on the combination of column types by simulation without actually measuring a standard sample.

Example 2

[0064] In this example, the "simulation of chromatogram", which is the second aspect of the present invention, was verified.

[0065] Synthetic polymers are generally materials composed of small repeating units as shown in Fig. 8, and their molecular weight is the value obtained by adding the molecular weight of the end groups to the product of the molecular weight of the repeating unit and the degree of polymerization. Therefore, when the molecular structure is known and the approximate molecular weight distribution is estimated, it is possible to predict the chromatogram. Thus, the molecular weight can be calculated for each degree of polymerization, and the elution time can be calculated inversely from the given calibration curve equation. Also, the number of columns in theory is the sum of the numbers of columns of each individual column. The peak width can be calculated from the number-of-stages equation of liquid chromatography. Based on this information, a peak curve with the degree of polymerization can be drawn using a peak function. Finally, the separation pattern (chromatogram) can be simulated by summing the peak curves for each degree of polymerization.

[0066] In this example, the probability density function of the normal distribution was used as the peak function (see Equation 3). Naturally, the peak function is not limited to the normal distribution function, and a non-normal distribution function with left-right asymmetry may be used and is not limited. TIFF2025083816000021.tif2897

[0067] In this example, the structure of Epicoat 1001, which is an epoxy resin (manufactured by Mitsubishi Chemical, hereinafter also referred to as E1001), was used for verification. Epicoat 1001 has a structure as shown in Fig. 17, with a molecular weight of the repeating group of 212 and a molecular weight of the end group of 268. That is, the individual molecular weight is 268 + 212 × degree of polymerization (n). An example of connecting three Multipore HZ-N in series is shown to make the separation simulation process easier to understand.

[0068] As shown in Example 1, the calibrated calibration curve for one MultiporeHZ-N column is as shown in Table 15. In Example 1, the delay time when multiple columns are connected was not considered, but in this example, the "delay time" (0.15 minutes) was taken into account to obtain a result closer to the actual chromatogram. After adding the "delay time" to the time term of the calibrated calibration curve data obtained in Example 1, approximation was performed with a cubic equation to obtain the calibration curve. y = ax 3+ bx 2 + cx + d y: Log (molecular weight), x: elution time a: -0.006195 b: 0.251259 c: -3.658538 d: 21.940626

[0069] Calibration curve during chromatogram simulation

Table 15

[0070] If the molecular weight is known, the elution time can be calculated by inverse calculation from the calibration curve (cubic equation).

[0071] Also, the number of columns of the column theoretically becomes the sum of the number of columns of each individual column. The peak width can be calculated by inverse calculation from the stage formula of liquid chromatography.

[0072] Based on this information, by using the probability density function of the normal distribution, a peak curve for each degree of polymerization can be drawn. Finally, the separation pattern (chromatogram) can be simulated by summing up the peak curves for each degree of polymerization.

[0073] Table 16 shows each parameter for each degree of polymerization. In the case of a degree of polymerization of 1, the molecular weight is the sum of the molecular weight of the end group 268 and the molecular weight of the repeating group 212, which is 480. When applied to the approximation formula, it becomes the following formula, and x (elution time) is calculated by inverse calculation from here. Several methods for obtaining the solution of the polynomial are shown, but as long as the solution can be obtained, there is no limitation on the method. Log(480) = -0.006195x 3+ 0.251259x 2 -3.658538x + 21.940626 In this case, X (time) can be calculated as → 15.0 minutes.

[0074] The number of stages of the column may be actually measured and obtained, or the value of the "Inspection Certificate (Inspection Data)" presented by the column supplier may be used. The latter "Inspection Certificate (Inspection Data)" is the data per column. When multiple columns are connected, due to the spread outside the column, the performance may slightly decrease compared to the theoretical value. Considering this decrease enables more accurate simulation.

[0075] The number of stages in the "Inspection Certificate (Inspection Data)" of the column used here is 20,000 per column. In the case of connecting 3 columns, theoretically it would be 20,000 × 3 = 60,000, but considering a 10% decrease due to the spread, it was used as 54,000 in the calculation.

[0076] The relationship between the elution time and the number of stages obtained above is 54,000 = 5.54 × (15.0 / W1 / 2)^2. From this, by calculating the half-width (W1 / 2) inversely, it becomes 0.152 minutes, and the standard deviation σ can be calculated as 0.064. Up to this point, the elution time and peak width of the peak for each degree of polymerization have been calculated.

[0077] Next, specify the characteristics of the polymer sample to be simulated. Since the polymer sample has a molecular weight distribution, it is necessary to specify a rough molecular weight distribution. Since the rough molecular weight distribution requires the horizontal axis to be time and the vertical axis to be the shape of the detector output, it is important that it can be represented by a function formula. The distribution of an actual polymer sample rarely becomes a symmetric normal distribution, and often takes a profile close to an asymmetric normal distribution. Therefore, in this example, "Bigaussian" which can handle both symmetric and asymmetric cases was used (Equation 4, Figure 19). Here, it was assumed that the molecular weight of the high molecular weight sample was about 680, the peak width (w1) of the first half was 0.3, and the peak width (w1) of the first half was 0.3. The profile based on this is as shown in Fig. 19. TIFF2025083816000023.tif2594

[0078] So far, the intensity of the profile with respect to the elution time of the peak for each degree of polymerization has been taken as the peak height, the peak shape has been fitted to the normal distribution probability function of Equation 3, and the peak profile has been calculated.

[0079] This operation is performed for each degree of polymerization, and finally, by adding all the peak profiles, separation simulation on the specified column can be carried out.

[0080] Fig. 18a is a figure in which the peak profiles for each degree of polymerization are superimposed. n in the figure is the degree of polymerization. Also, Fig. 18b is a figure in which all the peak profiles (up to n = 43) are added, which is the result of the separation simulation.

[0081] Peak information during chromatogram simulation

Table 16

[0082] Similarly, simulations with other column combinations were carried out.

[0083] Here, for any combination, it was assumed that the molecular weight of the high molecular weight sample was about 1900, the peak width (w1) of the first half was 0.3, and the peak width (w2) of the first half was 0.22.

[0084] Figure 20a shows the simulated chromatogram when two SuperHZ2500 columns are used. Figure 20b shows the simulated chromatogram when SuperHZ2500 and SuperHZ3000 are connected in series. Figure 20c shows the simulated chromatogram when one SuperMultiporeHZ-N column is used. Figure 21a shows the simulated chromatogram when two SuperMultiporeHZ-N columns are used. Figure 21b shows the simulated chromatogram when three SuperMultiporeHZ-N columns are used. Figure 21c shows the simulated chromatogram when SuperMultiporeHZ-N and TSKgel SuperMultiporeHZ-M are connected in series. Thus, it can be seen that almost no separation can be achieved with a single column. When two columns are used, peak tops can be seen in the low molecular weight region (oligomer region). Among them, it can be seen that the combination of SuperHZ2500 and SuperHZ3000 in Figure 20b provides the best separation. Furthermore, when three SuperMultiporeHZ-N columns are connected, better separation is obtained (Figure 21b).

[0085] From these results, it is considered that a separation system combining three SuperMultiporeHZ-N columns is optimal when emphasizing separation, and a separation system combining two SuperHZ2500 and SuperHZ3000 columns is optimal when emphasizing measurement time. Thus, as long as there is calibration curve information for the original column, the separation pattern can be simulated without actual measurement. The calibration curve information for each original column can be obtained by the user through actual measurement or from the column supplier.

[0086] In this embodiment, the horizontal axis of the chromatogram is "elution time", but the same effect can be obtained even if the horizontal axis is "elution volume". Here, the flow rate at the time of creating the original calibration curve and the flow rate at the time of simulation were calculated to be the same. However, even if the flow rate at the time of creating the calibration curve and the flow rate at the time of simulation are different, simulation is possible by this method. In that case, let the flow rate at the time of creating the calibration curve be Fa and the flow rate at the time of simulation be Fx, multiply the ratio (Fa / Fx) by the time term of the corrected calibration curve data, and then calculate the approximate formula. In addition, by connecting a plurality of columns, elution is delayed for a certain time due to the connecting pipe between the columns and the like, but by reflecting this delay time in this method, more accurate simulation can be performed. In addition, although there is no direct influence on the elution time, simulation of the number of column stages is also possible. In theory, the number of stages of each column may be added, but in practice, due to the connecting pipe between the columns and the like, the peak spreads and the number of stages slightly decreases, so this decrease in the number of stages may be considered.

Example 3

[0087] Regarding the simulation of the chromatogram which is the second form of the present invention, the difference from the actually measured chromatogram was verified.

[0088] The SEC device used was the HLC-8320GPC, a high-speed GPC device manufactured by Tosoh Corporation. The structure of this device is shown in FIG. 22. This device is equipped with two types of detectors, and the components eluted from the column are installed so as to flow in the order of an ultraviolet-visible detector (FIG. 22.15) and a differential refractometer (FIG. 22.11). The separation column was also used by connecting two TSKgel SuperMultipore HZ-N manufactured by Tosoh Corporation in series. The standard sample at the time of creating the calibration curve also used the TSKgel standard polystyrene kit PStQuickMP-N (F-4, A-5000, A-500) manufactured by Tosoh Corporation. Incidentally, the calibration curve and the like were evaluated based on the signal of the differential refractometer (FIG. 22.11).

[0089] In this example, since the components eluted from the column flow in the order of the ultraviolet-visible detector (Fig. 22.15) and the differential refractometer (Fig. 22.11), it is considered that the delay in the elution time will increase. Therefore, the "delay time" during simulation was calculated as 0.3 minutes.

[0090] The distribution of the entire polymer sample was specified by a Bigaussian function in the same manner as in Example 2, and separation simulation was performed. The coefficients of the Bigaussian function were such that the molecular weight was about 1993 (xc: 8.7), the peak width of the first half (w1) was 0.65, and the peak width of the second half (w2) was 0.8.

[0091] Fig. 23 shows the actual measurement results. Fig. a is the chromatogram of the molecular weight standard sample, and Fig. b is the chromatogram of the epoxy resin. Fig. c shows the chromatogram obtained from the simulation of this example.

[0092] Fig. 24 is a figure in which the actual measurement results and the simulation results of this example are superimposed.

[0093] Since this sample is a "low molecular weight oligomer" with a relatively low molecular weight, peaks for each degree of polymerization can be confirmed in the low molecular weight region.

[0094] However, since a small peak can be confirmed around about 10 minutes, although the basic structure of the epoxy resin used as the sample is shown in Fig. 17, it can be estimated that actually a small amount of another structure generated by side reactions or the like is also included. Therefore, although there are some differences from the chromatogram obtained by simulation, it can be seen that the actual separation pattern is well reproduced overall.

[0095] Peak information during chromatogram simulation

Table 17

[0096] Calibration curve data during actual measurement

Table 18

[0097] Calibration curve during chromatogram simulation

Table 19

Explanation of symbols

[0098] 1. Eluent 2. Degassing device 3. Sample side liquid delivery pump 4. Reference side liquid delivery pump 5. Sample injection mechanism 6. Column thermostat 7. Reference column 8. Analytical column A 9. Analytical column B 10. Analytical column C 11. Differential refractive index detector 12. Analytical column 13. System thermostat 14. Column thermostat 15. Ultraviolet-visible detection

Claims

1. In size exclusion chromatography for calculating the molecular weight or molecular weight distribution of a polymer sample with an unknown molecular weight, using a calibration curve prepared by analyzing two or more standard samples with a narrow molecular weight distribution and a known molecular weight----, A method of simulating a calibration curve when two or more columns of size exclusion chromatography with different separation characteristics prepared in advance are connected in series, by holding calibration curve information consisting of the elution time and the logarithm of the molecular weight of the columns in a storage medium, and combining the calibration curve information of the two or more columns by mathematical processing, comprising: The mathematical processing is as follows: (1). For calibration curve information different for each column, with its elution time as x and the logarithm of the molecular weight as y, calculating the relational expression between x and y; (2). Interpolating the calibration curve information by calculating the corresponding elution time x according to the relational expression obtained in (1) so that the logarithm of the molecular weight y corresponding to any two or more columns arbitrarily specified in the calibration curve information of all columns becomes the same; (3). Obtaining the sum of x by adding the elution times obtained in (2), and simulating the calibration curve when using the corresponding y and the combination of two or more specified columns. A method for simulating a calibration curve, comprising the above steps.

2. In size exclusion chromatography in which two or more columns with different or the same separation characteristics are connected in series and used, A size exclusion chromatography apparatus that holds calibration curve information consisting of the logarithm of the molecular weight of a standard sample prepared in advance and the elution time in the column in a storage medium, simulates the calibration curve through mathematical processing of the calibration curve information, and calculates the molecular weight or molecular weight distribution of a sample target sample, comprising: The mathematical processing is as follows: (1). For the standard sample prepared in advance, with its elution time as x and the logarithm of the molecular weight as y, Calculating the relational expression between each x and y from calibration curve information different for each column; (2). For the calculated relational expression, calculating the corresponding x when y is specified; (3). Adding the x and simulating the calibration curve of the combination of the two or more columns from the sum of x and the specified y. The size exclusion chromatography apparatus is characterized by including the above steps.

3. The relational expression between x and y in (1) is represented by the following formula: 【Number 1】 A method for simulating the calibration curve according to claim 1.

4. The relational expression between x and y in (1) is represented by the following formula: 【Number 2】 The size exclusion chromatography apparatus according to claim 2.

5. The method further includes: a step of storing the number of stages for each column, adding the number of stages for each column, and simulating the number of stages when using the combination of the specified columns. A method for simulating the calibration curve according to claim 1.

6. The method further includes: a step of storing the number of stages for each column, adding the number of stages for each column, and simulating the number of stages when using the combination of the specified columns. The size exclusion chromatography apparatus according to claim 2.

7. For a polymer sample with a known molecular structure and whose molecular weight and molecular weight distribution can be estimated, the molecular weight for each degree of polymerization of the polymer sample is applied to the "calibration curve when using the combination of the specified columns" obtained in claim 1, the elution time or elution volume at the peak apex is calculated, and from the "number of stages when using the combination of columns" obtained in claim 5, the following number-of-stages calculation formula (1) or formula (2) of liquid chromatography [Number 3] is used to calculate the peak width, from these values, the peak curve for each degree of polymerization is calculated by a normal distribution function or a non-normal distribution function, and the chromatogram obtained in the combination of the specified columns is simulated by summing the obtained peak curves for each degree of polymerization.

8. For a polymer sample with a known molecular structure and whose molecular weight and molecular weight distribution can be estimated, the molecular weight for each degree of polymerization of the polymer sample is applied to the "calibration curve when using the combination of the specified columns" obtained in claim 2, the elution time or elution volume at the peak apex is calculated, and from the "number of stages when using the combination of columns" obtained in claim 6, the following number-of-stages calculation formula (1) or formula (2) of liquid chromatography [Number 4] is used to calculate the peak width, from these values, the peak curve for each degree of polymerization is calculated by a normal distribution function or a non-normal distribution function, and the chromatogram obtained in the combination of the specified columns is simulated by summing the obtained peak curves for each degree of polymerization.

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