Liquid Chromatograph Data Processing Apparatus, and Liquid Chromatograph Apparatus

Abstract

To facilitate determination of an analysis condition.SOLUTION: A liquid chromatographic data processing apparatus generates, based on data related to an analysis condition for and separation performance of a chromatograph device, display data displaying a graph indicating the correspondence relationship between these data, and the liquid chromatographic data processing apparatus generates data in a bi-axial direction of a first group related to the analysis condition, data in the bi-axial direction of a second group each determined through operations including multiplication and division of two pieces of data in the first group, and display data according to a graph representing the correspondence relationship of the data related to the separation performance. At least the axes of the first group and the second group are each represented by a logarithmic axis.SELECTED DRAWING: Figure 18

Description

Technical Field

[0001] The present invention relates to a chromatograph data processing apparatus, and more particularly to a quantitative visualization analysis apparatus for searching separation conditions of a liquid chromatograph.

Background Art

[0002] In order to understand the relationship between the analysis time and separation performance of HPLC, Patent Document 1 is first fundamental. In Patent Document 1, a variable identical to the velocity-length product Π (m 2 / s) was introduced by the expression of the flow constant Cf.

[0003]

Equation

[0004] Here, K V (m 2 ) is column permeability (column liquid permeability), and η (Pa·s) is viscosity. The pressure loss ΔP is nothing but Π with K V and η as proportional factors. In the present invention, for the sake of convenience, in order to exclude the secondary factors of K V and η, Π is treated as a more essential variable than ΔP. Π is also called pressure-driven strength. The u 0 (m / s) in (Equation 1) is the linear velocity of non-retained components, and L (m) is the column length, which is an important variable of the same rank as Π as will be described later.

[0005] Next, in Patent Document 1, the method is called the KPA (Kinetic Plot Analysis) method, and the theoretical plate number N is used as an index of separation performance, and the hold-up time t 0 (s) is used as an index of speed. t 0 is the retention time t RIt plays the role of the basic unit for formation. In the present invention, the retention coefficient k of each component is fixed for discussion. Therefore, the stationary phase (column packing material, particle size, etc.), the mobile phase (eluent composition), the solute (components of the analysis species), and the column temperature are fixed, and isocratic elution is assumed. FIGS. 1 to 3 are all based on the results measured under the same separation conditions (the stationary phase is a C18 silica fully porous packing material with a particle size of 2 μm, the mobile phase is a 60% aqueous acetonitrile solution, the column temperature is 40°C, and the sample solute is butyl benzoate). When these separation conditions change, a corresponding theoretical model will be used separately. Also, in the present invention, the KPA method is called the KPL (Kinetic Performance Limit) method as also described in Patent Document 2.

[0006] In Patent Document 1, t o -N plots were stacked in layers and it was proposed to represent them as a three-dimensional graph. The third axis at this time is ΔP, that is, an axis proportional to Π. The 3D graph N (Π, t 0 ) or N (ΔP, t 0 ) called in the present invention in Patent Document 1 was completed.

[0007] Patent Document 2 solved the problem that it is difficult to see the relationship between N (Π, t 0 ) and L and u 0 . It was graphically shown that the plane can be coordinate-transformed from (Π, t 0 ) to (u 0 , L). It was called LRT (Logarithmically Rotational Transformation) in the sense of the transformation that rotates the logarithmic coordinate system. It applies the property that the product of real numbers becomes the sum of logarithms. The base of the logarithm is 10.

[0008] Furthermore, in Patent Document 2, N (Π, t 0) A contour map using the antilogarithm axis instead of the logarithmic axis is also shown (Figure 2). There exists a KPL surface presenting a hilly terrain-like shape in three-dimensional space. Based on the slope of the hilly terrain, two types of coefficients are defined as two kinds of PAC (Pressure-Application Coefficient) and TEC (Time-Extension Coefficient). Since it is three-dimensional, a total of three types of coefficients regarding the slope can be defined. Each coefficient is normalized with the slope of the Opt. method operating at the optimal linear velocity u 0,opt as 1 of the reference. By introducing the three types of coefficients, the efficiency of each point on this KPL surface can be measured by the slope of the target performance per applied variable respectively.

Prior Art Documents

Patent Documents

[0009]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0010]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 4

[0011] So far, N has been treated as a resulting property to be imparted. For example, there has been no discussion such as the improvement of the height equivalent to a theoretical plate H by reducing the particle size of the column packing material. Also, K mentioned above is related to the particle size. The problem of the present invention is to clarify the cause and how they act when N is positioned as an effect, and to provide a display method that allows a user to easily see such an action at a glance, as well as a liquid chromatograph data processing device. In other words, there has been a limitation due to representing only N on the z-axis up to Patent Document 2, but the main purpose of the present invention can be to visualize the degree of influence from H beyond that limitation. V

[0012] ​The next task begins by first assuming, as an ideal case, that N does not decrease along the high flow velocity u0. When the C term in the so-called van Deemter's equation (Equation 8) is zero, H can be regarded as approximately constant, and the curve of N(Π, t 0 ) drawn under the condition of constant L becomes approximately the same as the contour line. However, in reality, due to the C term, N decreases to some extent. Therefore, just by looking at the van Deemter plot of H vs u0, it is not immediately possible to imagine the extent to which N decreases and the extent to which the C term affects t0. This application also shows a display method that enables the user to intuitively understand this relationship.

[0013] For example, in FIG. 2, it can be seen that the contour line of N = 10,000 plates and the N curve obtained under the condition of constant L = 70 mm deviate more as Π increases. Against this background, in order to increase Π while keeping L constant, u0 has to be increased. However, in doing so, it is affected by the aforementioned C term, H gradually increases, and as a result, N decreases. However, this relationship cannot be intuited just by looking at FIG. 2. Visualizing not only H but also the degree of influence of the C term, including the overlay method as shown in FIG. 2, can also be another problem of the present invention.

Means for Solving the Problems

[0014] To achieve the above object, the present invention is a liquid chromatograph data processing device that generates display data for displaying a graph showing the correspondence relationship of these data based on the analysis conditions of a chromatograph device and data related to separation performance, the data in the two-axis direction of the first group related to the above analysis conditions, the data in the two-axis direction of the second group obtained by an operation including multiplication and division of the two data in the first group respectively, and generates display data corresponding to the graph representing the correspondence relationship of the data related to the above separation performance, characterized in that at least each axis of the data of the first group and the second group is represented by a logarithmic axis.

[0015] This makes it easier to grasp the relationships between the respective data, and enables the easy determination of analysis conditions according to the user's intention.

Advantages of the Invention

[0016] According to the present invention, it is possible to make it easier to grasp the relationships between the respective data such as the analysis conditions of the chromatograph device, and to easily determine the analysis conditions according to the user's intention.

Brief Description of the Drawings

[0017]

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Mode for Carrying Out the Invention

[0018] First, a preliminary overview will be described.

[0019] For example, in Fig. 1, looking at the intersection of u0 = 10 mm / s and L = 10 mm, it can be read as 100 mm·mm / s on the Π axis. Since the Π axis is a logarithmic axis, it can correspond to the product of u0 and L. Also, it is characteristic that the length of the axis is shrunk by a factor of 1 / √2. When looking at the bar obliquely, it appears shorter. Using a metaphor, it corresponds to using a scale that is exactly shrunk in this way to measure the length of the bar. Similarly, when looking at the point with coordinates (u0, L) = (4, 100) from the axes of coordinates (Π, t0), the coordinate point (Π, t0) = (400, 25) can be read. It can be seen that the first component corresponds to the product of u0 and L, and the second component corresponds to the quotient of u0 and L. This is a distinct feature of the LRT that the same hilly landscape can be read by changing the meaning of the coordinate plane according to the difference in axes.

[0020] Also, in the present invention, instead of H, the number of theoretical plates per meter N / m, for which the value becomes larger for a column with better separation performance, is newly used. However, although this notation is common, N is dimensionless and is not a physical quantity having the dimension of length in the first place. Therefore, in the present invention, N / m is redefined as the number of theoretical plates per unit length n (small n). That is, it is the reciprocal of H (Equation 2).

[0021]

Equation

[0022] n is a physical quantity having the dimension of the reciprocal of length with the unit of (1 / m) or (1 / mm) and has the property of being a desirable large value. The n used in the present invention is positioned as an operation, setting, and input variable of the cause system, similar to u0 and L. On the other hand, N is an output variable of the result system, similar to Π and t0. N and t0 are variables related to separation and speed, respectively, and can be said to be the results of the performance system. However, it is unnatural to simply call Π performance. In the present invention, it is widely called a result system variable in the sense of an adverse effect. When using a constant flow rate or a constant speed u0 pump, K VLet η be a proportionality constant, which generates a pressure loss ΔP at the L part of the column, and Π is the aforementioned result proportional to the ΔP.

[0023] On the other hand, although Π is such a result, there is also an aspect that requires a driving force that can increase u0 and L, or ΔP or Π as the pressure-driven strength as described above. Therefore, Π has the nature of a kind of feedback variable that can be an input variable related to the pressure resistance of the column itself as a limiting condition and the maximum pressure performance of the (U)HPLC system, or an output variable as the reverse effect as described above.

[0024] One of the objects of the present invention is to elegantly visualize three cause system input variables and three result system output variables, and to provide a graph that can be systematically and easily understood and imaged by the user at the same time. That is, it is a display analysis device that can instantaneously grasp the influence and limitation relationship of six variables when exploring separation conditions.

[0025] In addition, in order to intuitively show the influence of the aforementioned item C, the liquid chromatograph data processing device of the present invention overlays and draws a curve with a constant L on the contour map. By this overlay drawing, it is possible to show how the curve with a constant L deviates from the curve with a constant N, that is, the contour line (Figure 2). Also, according to preference, it can be displayed as a 3D graph having three axes.

[0026] n(u0) is a function of u0 similar to H(u0). It has a maximum value n at u0,opt in (Equation 19) maxis obtained. The graph is two-dimensional, with n vs u0. An L-axis is added as a third straight axis orthogonal to the two-dimensional plane of the Cartesian coordinate system with right hand rule to form a 3D graph. Here, to align with Patent Document 2, the axis order x, y, z is re-labeled in the order of u0, L, n(u0). These three variables are newly displayed on logarithmic axes and are used as unit vectors, so-called basis vectors, that generate the 3D graph. Henceforth, using the basis vectors x, y, z, it is denoted as an xyz-type 3D graph. For example, it is denoted as uLn-type or ΠtN-type. All are abbreviated to one character, u 0 are u, t 0It is abbreviated like t. The total logarithm or the bottom plane logarithm is attached as a modifier, and it is expressed like the bottom plane logarithm uLN type contour map. Since n(u0) does not depend on L, the n vs u0 plane is the same along L, that is, the sheet-like curved surface continuously extends in a constant manner in the depth L direction (Figure 3). Hereinafter, this sheet-like curved surface is called the n membrane. In fact, the starting point of the present invention is only this image. Since L is a mathematically added axis only, it can be said that the truly necessary data is only the two-dimensional data of n(u0). However, by means of the invention related to expanding the two-dimensional data into a 3D graph, all other necessary variables can be obtained only by conversion, projection, or cross-sectional display. It will be explained hereinafter that the necessary graphs associated with such conversion etc. can also be visibly displayed. In other words, although the two-dimensional data is originally sufficient, by expanding it into a three-dimensional space using L and logarithmically displaying all of them, the interrelationships of various characteristic variables can be visualized. It is useful to logarithmically display all variables as a new matter. The display method of the present invention is characterized by coordinate system conversion or projection onto a unit vector dedicated to measurement. The aforementioned LRT is a kind of LCT (Logarithmical Coordinate Transformation), and in the present invention, LCT is used as a superordinate concept. Also, when it is desired to clearly show that it is an orthogonal projection, this method can also be called LOP (Logarithmically Orthogonal Projection). The orthogonal projection can measure the magnitude of the target vector by the inner product with a specific unit vector. Furthermore, when it is intended to express that the coordinate system rotates, it is called LRCS (Logarithmically Rotating Coordinate System), or simply abbreviated as LRC. For example, in the case of the total logarithm uLN type 3D graph, by grasping the N axis and rotating it, the bottom plane coordinate system of L - u is rotated as a whole. As a feature of the present invention, a logarithmic axis is used to facilitate the calculation of the product and quotient between the variables of each physical quantity.

[0027] Summarizing the means applicable to the present invention, (1) introduce n and make the target six variables, (2) display all variables in logarithmic form, and (3) visualize the influence relationships and constraints of the variable group by means of three-dimensional graphs including contour maps and cross-sectional displays, coordinate transformation, and orthogonal projection.

[0028] The present invention can provide a method for tracing back to three causal variables (u 0 , L, n) to be explored as separation conditions and an analysis device or the like in order to obtain a 3D graph (Π, t 0 , N) that displays the results required by the user as performance. The small n is defined as the reciprocal of H as a variable having a desired large property. The basis for realizing this effect is that, starting from the LRT coordinate transformation from the bottom plane coordinates (x, y) of (Π, t 0 ) to (u 0 , L), by also displaying N in logarithmic form, the causal variable n (u 0 ) appears as a cross-section of a logarithmic 3D graph.

[0029] Also, since the LRT transformation is logarithmic and is based on the orthogonal projection onto a specific unit vector again, it can be widely called the LOP method. Once regarded as the LOP method, it can also be applied to operations for measuring other variables. With such a mathematical basis, while showing various 3D graph display methods including contour maps as examples, the present invention exhibits the effect of visualization.

[0030] [Orthogonal Projection from uLn Type to N] An embodiment of the present invention is shown. In order to obtain N from the causal / input system three-dimensional graph, first, after converting all variables of u0, L, and n(u0) from real numbers to logarithms, first display the three-dimensional coordinate system (log u0, log L, log n) by their respective basis vectors. For example, when fixing u0 = u0,opt, attention can be paid to the two-dimensional coordinates (log L, log n) that are the cross-section thereof.

[0031]

Number

[0032] From this equation (Equation 3), it can be seen that log N is a mixture of the components of log L and log n with certain weights. The sum of the squares of the weights is normalized to 1. The respective basis vectors e of log L and log n 1 =(1, 0), e 2 =(0, 1) are arranged orthogonally. Then, the unit vector of (log N) / √2 is rotated 45° from log L in the direction of log n, that is, e 3 =(1 / √2, 1 / √2) (Figure 4a). This is a dedicated unit vector that can measure (log N) / √2. In other words, by dividing the length of the scale log N by √2 and making the scale finer, the magnitude of the vector in the log n-log L coordinate system is normalized to 1. Including the scaling factor of the axis, it is the same as the relationship of the log Π axis to the log L-log u0 bottom plane coordinates in Figure 1.

[0033] Note that in Figure 4, it is also depicted that since H is the reciprocal of n, log H is represented in the negative direction of log n.

[0034] If u0 = u0,opt, then whether L is L1 or L2, n is always n max constant. Focusing on L1, at that time n is also max so, when projected onto the unit vector of (log N) / √2, it exactly corresponds to the product of L1 and n max Similarly, for L2, the orthogonal projection means that the product of L2 and n max corresponds to the inner product with the unit vector of (log N) / √2 (Figure 4b).

[0035] When generating a three-dimensional graph of the cause system, this two-dimensional graph plane of u0 = u0,opt can be stacked not only along the u0,opt plane but also along other u0 planes along the u0 axis. Extend the logarithmic u0 axis of the straight line orthogonally to the origin of the two-dimensional plane in Fig. 4 and forward. Using the function n(u0), stack while gradually changing the n value little by little from the back to the front direction in Fig. 4. Stack in the back direction in the same way. Then, a 3D graph in logarithmic coordinates (log u0, log L, log n) is formed. This is the logarithmic representation of each axis in Fig. 3. In this logarithmic coordinate system (log u0, log L, log n), by convention, all three axes are orthogonal to each other. The curve function n(u0) forms a sheet-like n film by stretching along the L axis while remaining the same curve. This means that no matter where it is cut along L, the cross-section (log u0, log n) is the same upwardly convex curve n(u0), but when viewed in three-dimensional space, it becomes a continuous upwardly convex n(u0) film.

[0036] With the n(u0) film existing in this 3D graph, form a unit vector dedicated to log N that is inclined at 45° in the (log L, log n) plane. The scale factor multiplying log N is 1 / √2 as described above. However, note that since this unit vector does not serve as a basis vector indicating coordinates, it does not form an oblique coordinate system. The purpose of the inclination is to obtain the product of L and n and to mix the components L and n in the plane with a certain weighting. As a measurement method, simply project orthogonally onto the unit vector of the scale of (log N) / √2. After all, the three-dimensional space uses the original cause system coordinates (log u0, log L, log n). With the three-dimensional space and the n(u0) film remaining as they are, only the inclined unit vector of (log N) / √2 is placed and orthogonally projected, so that log N can be read from the original coordinate system (log u0, log L, log n).

[0037] [Orthogonal projection from the uLN type to n] Similarly, by using the reverse projection relationship, the unit vector n can also be found from the orthogonal coordinate system of (u0, L, N).

[0038]

Number

[0039] By this transformation in the log N-log L plane, the unit vector (log n) / √2 can be found to have rotated 45° counterclockwise from the log N axis, i.e., in the direction opposite to the log L axis, when viewed from the front side (Fig. 5). This is exactly the same as the relationship in Fig. 1 where the log t0 axis with respect to the log L-log u0 base plane coordinates is the logarithm of the quotient of L and u0.

[0040] This makes it possible to display using orthogonal projection in both the coordinate systems (u0, L, n) and (u0, L, N). Therefore, the same n(u0) film can be displayed in different coordinate systems. The coordinates (u0, L, n) are the cause input system, and the z-axis of the latter has only N as the variable of the result output system. As described in Patent Document 2, since the coordinate system (u0, L, z) can be logarithmically coordinate-transformed to the coordinate system (Π, t0, z) by LRT, by using the log N<->log n orthogonal projection method of the present invention (hereinafter referred to as nN projection: small n large N projection method) together, the cause input system coordinates (u0, L, n) can be easily shifted to the result output system coordinates (Π, t0, N). As described above, this shifting method is an extended LRT from the cause input system two-variable function n(u0, L) to the result output system two-variable function N(Π, t0). When emphasizing that it is an extended version of LRT, it is called expanded LRT, or eLRT.

[0041] Based on adding log L to log n, the reason for projecting onto the log N axis corresponding to their product, which is nN, will be explained. It's not that these cannot be represented on the real number axis instead of the logarithmic axis. A two-dimensional orthogonal plane graph with N on the vertical axis and L on the horizontal axis can be drawn, and N can be displayed as a proportional linear function of L. This straight line passes through the origin. In this case, n corresponds to the slope of the straight line. This slope is the first derivative coefficient and is represented graphically as a rate of change or ratio. However, it's difficult to project as a scale while keeping it as a ratio. Therefore, by displaying on the logarithmic axis, n can be measured as a numerical value rather than a ratio.

[0042] There is another reason. This application generally displays graphs on the logarithmic axis. Since L is already displayed as log L on the graph, it is more unified to display the related variable group in logarithmic form as well.

[0043] [Transition from the cause input system coordinates (u0, L, n) to the result output system coordinates (Π, t0, N)] The diagram of the transition from the cause input system coordinates (u0, L, n) to the result output system coordinates (Π, t0, N) is shown in FIG. 6. First, the unit vector (log N) / √2 is generated in the plane including the log n axis and the log L axis. Next, the (log Π) / √2 axis and the (log t0) / √2 axis are generated by logarithmic coordinate transformation in the base plane including the log u0 axis and the log L axis. As a result, the three logarithmic variables that are the components of the result output system coordinates (Π, t0, N) can be read from the cause input system 3D graph (FIG. 6).

[0044] [n in the all-logarithmic uLN type 3D graph] Figure 7 is a 3D graph when the vertical z-axis is the logarithmic N-axis of the result type. This is the case when the so-called base vectors are made logarithmic N. By drawing in this state, it will correspond to a contour map having a result type logarithmic axis for all three components as shown in Figure 1. The bottom plane can be bidirectionally coordinate-transformed from logarithmic coordinates (u0, L) to logarithmic coordinates (Π, t0) due to the relationship of LRT. When the vertical z-axis is the result type, it should be the logarithmic N-axis. In that case, the unit vector of (log n) / √2 can be arranged in the same space by the nN projection method and is inclined at 45° in the plane including log L and log N. The cause will be found in that n. Since u0 is constant in the log L - log N plane, log n is fixed. When log L is 0, that is, L = 1 m, n(u0) is drawn on the u0 axis. It can be seen that n(u0) is the intercept at log L = 0. Incidentally, it is also possible to change the unit of the length of L from m to mm and set log L = 0.

[0045] The advantage of making the vertical z-axis logarithmic N is that log n appears as an intercept. That is, the variable n can be displayed in the result type 3D graph. Since N is proportional to L, that is, it is a power exponent of 1, if it is displayed on both logarithmic axes of log N and log L, it will simply have a slope of 1. Incidentally, if it is the second power, it is a power exponent with a slope of 2. The goodness or badness of n can be expressed as the height of the cliff of the upwardly convex cross-sectional function log n(u0) at the intercept of the log N axis obtained at log L = 0.

[0046] In the cause-based 3D coordinates (log u0, log L, log n), log N was found as a unit vector inclined at 45° by the nN projection method, but here it can be seen that a new coordinate axis system (log u0, log L, log N) with log N as one of the base vectors is very convenient, just like standing the mast of a sailboat vertically. This is because (1) log n(u0) can be seen as an intercept function on the cross-section of log L = 0, and (2) it is possible to easily shift the eyes to the result-based 3D coordinates (log Π, log t0, log N) by the LRT transformation. The coordinate system of the new axis is called the all-logarithmic uLN type 3D graph.

[0047] The reason for taking the logarithm of log N on the z-axis is, first of all, that log n(u0) is regarded as a sectional function with log L = 0. (1) Specifying the n membrane is the starting point of the present invention. (2) By displaying in the uLN type 3D coordinates (log u0, log L, log N), the n membrane becomes a slope of log N that climbs the log L axis with a power exponent of 1. (3) By the LRT transformation, the slope can be viewed on the log Π axis and the log t0 axis. (4) When exploring the separation conditions, t0 is understood as the normal time. (5) Considering the limiting condition ΔP, log Π is added and subtracted with log K V and log η.

[0048] As described above, starting from the n membrane, log N on the z-axis climbs the log L axis with a power exponent of 1. In this visualized image, since the characteristics of the column packing agent are only reflected in the function of log n, each packing agent simply presents a 45° slope along the log L axis (Figure 12). On the other hand, regarding the log Π axis, since the slope climbs in the reverse direction along the descending moving line, the power exponent is at most 1 / 2. This is due to the combined effect of the scale factor 1 / √2 of the log Π axis and the power exponent contribution of log Π to log N when climbing in a descending-sloping manner being at most 1 / √2 times, resulting in a power exponent of at most 1 / 2. The reason why the power exponent of the log L axis is exactly 1 while the power exponent of log Π is at most 1 / 2 is that the hilly terrain of log N is not a flat plate but a surface generated from the function n(u0) of u0. Similarly, the power exponent of log t0 with respect to log N is also at most 1 / 2.

[0049] Here, once again, let's take an overview of the relationship between physical entities and mathematical expressions. First, represent three-dimensional space in a coordinate system of three basis vectors (log u0, log L, log N) (Figure 12). For simplicity, orthogonal linear coordinates are used. The three axes are independent unit vectors. Since the physical entity n can be expressed as a function of u0, n(u0), n and u0 are in a dependent relationship. Therefore, it exists with two degrees of freedom within three-dimensional space and is called the n membrane. In fact, the n membrane slopes with a slope of 1 along the log L axis within this space. It is thus represented as a log N surface inclined in the three-dimensional space (log u0, log L, log N). The surface N is inclined at 45° within the (log N, log L) plane for any log u0.

[0050] The LRT shown in Patent Document 2 is the origin of the invention. The two-dimensional bottom plane orthogonal to u0 and L can be coordinate-transformed by the LRT into the two-dimensional bottom plane Π and t0, which are also orthogonal. However, it is characterized by being a logarithmic axis and having a scale factor of 1 / √2.

[0051] Fortunately, in the LRT, since the two-dimensional orthogonal plane of u0 and L could be transformed into the two-dimensional orthogonal plane of Π and t0, the coordinate system rotation of the bottom plane was simple by changing the axes. There is no need to unreasonably use log n as one axis and basis vector to span three-dimensional space. It is sufficient if log n can be displayed as a cliff section in its graph with the basis vector log N as the axis.

[0052] [Application of the Logarithmic Orthogonal Projection Method LOP] When wanting to display using the result-type three-dimensional space (log Π, log t0, log N), after first displaying it in the uLN-type three-dimensional space (log u0, log L, log N) of the new axis, only the bottom plane needs to be LRT-transformed. log n(u0) appears as a section function with L = 0 in this uLN-type 3D graph. In any three-dimensional space, the n(u0) membrane appears horizontally or inclined as a physical entity. Also, the desired physical quantity can be measured by placing a specific unit vector within the three-dimensional space.

[0053] Once this physical image, i.e., the mathematical structure, is noticed, various visualizations using 3D graphs become possible. It can also be seen that any product and quotient operations can be replaced by the arrangement of logarithmic measurement unit vectors. Power operations are also available. If the relationship of the two-dimensional curved surface film in this three-dimensional space is understood, the plate time t P and the impedance time t E can also be measured by orthogonally projecting the n(u0) film by the dedicated unit vector arrangement.

[0054]

Number

[0055] That is, as shown in FIG. 8, from (Equation 5a), log tP can be regarded as a rotational transformation in the plane spanned by log N and log t0. The scale factor in this case is 1 / (√2).

[0056] Similarly, as shown in FIG. 9, from (Equation 5b), log tE can also be regarded as a rotational transformation in the plane spanned by log N and log t0. The scale factor in this case is 1 / (√5).

[0057] Furthermore, the particle diameter d can be introduced as a fourth orthogonal axis. P However, since it becomes a four-dimensional space, graph display becomes more difficult. d P is one variable of a two-variable function such as n(u0, d P ), and is also related to the column permeability K V as a function K V (d P ). The framework of the particle diameter does not apply to the monolithic column, but if a five-dimensional space is generated with a new axis of K V , the monolithic column can also be handled by fixing d P to a fixed value. Alternatively, d P can be replaced by some index corresponding to the d P peculiar to the monolithic column.

[0058] When increasing the dimension of space, what should be noted is the presence or absence of the subordinate relationship. d P Add it as the fourth axis, and when generating the cause system four-dimensional space (log u0, log L, log n, log d P ), since there is a function of n (u0, d P ), a three-dimensional solid constrained by d P and u0 will float in the four-dimensional space.

[0059] If K V is added to the fifth-dimensional axis, even though the function K V (d P ) constrains K V by d P , in the fifth-dimensional space (log u0, log L, log n, log d P , log K V ), the independent unit vectors, that is, the independent axes, are the three of (log u0, log L, log d P ). Therefore, a 3D object still floats.

[0060] Developing this argument, since the pressure loss ΔP is the product or quotient of K V , Π, and the viscosity η (Equation 1), a new three-dimensional space (log Π, log K V , log η) can be generated with these three variables as independent orthogonal logarithmic axes. ΔP can be measured by arranging specific unit vectors and mixing the variables K V , Π, and η with a certain mixing angle, that is, weights.

[0061]

Equation

[0062] As shown in Figure 10, the base vectors (log Π, log K V, Place the unit vector of log ΔP in the three-dimensional space spanned by (log η). As before, multiply by the scale factor 1 / √3 to normalize the magnitude of the unit vector to 1. As a result, the change in Π can be projected onto the unit vector of the logarithmic ΔP. The 3D graph can be positioned as a kind of scale tool for the two-way representation of Π <-> ΔP. It could also be called the ΠΔP projection method.

[0063] Also, other variables t0 and n can be added as independent orthogonal logarithmic axes, and it is also possible to generate a five-dimensional space with a higher number of dimensions.

[0064] Similarly, the separation impedance E is also placed as a specific unit vector in the three-dimensional space with n, u0, and K V as the three orthogonal axes and is measurable.

[0065]

Number

[0066] Here, n is the reciprocal of H. As shown in Figure 11, for example, the change in H can be orthogonally projected onto the logarithmic unit vector E.

[0067] Of course, if necessary, like expressing ΔP as a function of Π, the retention time t R can be expressed as a function of the retention coefficient k or (k + 1) with t0. The resolution R S can also be expressed as a function of √N with the separation coefficient α and k by adding axes or explicitly stating the binding function (Equation 23).

[0068] [LRT Transformation of the All-Logarithmic uLN-Type 3D Graph] The desirable embodiments of the present invention are shown. This embodiment starts with a uLN-type logarithmic axis 3D graph and stays with the LRT conversion without explicitly using the LOP method. In a separation analysis method using any column packing material having the characteristic n of column efficiency, a chromatography analysis device is provided for visualizing both the separation performance N and the analysis speed t0 in order to optimize the column length L and the flow rate u0. This visualization technique uses the product of speed and length Π proportional to pressure as the driving force. On the premise, the mobile phase and the stationary phase are fixed, and isocratic elution conditions are set. Since the temperature is also fixed, the viscosity η of the mobile phase is also fixed. The pressure loss ΔP has some upper limit ΔP max and has. Also, since the column packing material is fixed, the column permeability K V which is its inherent characteristic can also be treated as a constant.

[0069] In visualizing the relationship between the optimization variables and the performance, there is data that must be input in advance to the analysis and display device. The n(u0) function and K V are. In addition, η and ΔP max are available as needed. The parameters of van Deemter's equation can also be used for the n(u0) function which is the reciprocal of H.

[0070]

Equation

[0071] Here, the coefficients A, B, and C are constants specific to the column packing material. In the case of van Deemter's equation, u0,opt is obtained by the following mathematical formula.

[0072]

Equation

[0073] First, all 3D graphs display the logarithmic axis uLN type. The n(u0) function can be seen in the cliff-like cross-section with the intercept log L = 0. Figure 12 shows the intercept at L = 1 mm. In fact, since n has the physical dimension of the reciprocal of length, whether the unit is 1 (1 / mm) or 1 (1 / m), it does not affect the product N of n and L.

[0074] By the LRT coordinate transformation, a ΠtN type 3D graph spanned by the log Π axis and the log t0 axis can also be displayed. Also, ΔP max -based Π max limiting conditions can also be displayed. The relationship between the required performance from the ΠtN type 3D graph and log u0 and log L can be intuited immediately. Also, the limiting condition Π max obtained by adding log K V to log ΔP max can be used to determine how much u0 and L can be increased (Figure 13). Note that the LRT coordinate transformation called in Patent Document 2 is preferably called the LCT logarithmic coordinate transformation because it is not only a rotation when explicitly stating that 1 / √2 is a significant scale factor.

[0075] In other words, as shown in Figure 3, the film formation process of stretching the n(u0) function by L is the starting point of the present invention. Standing at this starting point, by normalizing this z-axis to N, up to the so-called Weber's Figure 14 can be easily displayed (Non-Patent Document 2). Next, considering logarithmizing all these axes, as shown in Figure 12, it can be seen again that log N forms a slope with a slope of exactly 1 along the log L axis. The reason is that N is proportional to L, that is, it is a linear function passing through the origin. It is important that the slope becomes 1 by logarithmizing.

[0076] Next, it is noticed that the function of log n(u0) still remains as a trace on the cross-section of the cliff where the slice log L = 0. It can be said that all the characteristics of the column packing agent are aggregated in this log n(u0) function. This is because the hilly terrain in Fig. 12 is simply a slope that slopes along the n-axis with a slope of 1 on the log L-axis. Interestingly, the only characteristic that characterizes this hilly terrain is the characteristic of n, and there is no other feature. In the subsequent process, the LRT transformation is utilized. By rotating the LRT by 45°, the log Π-axis and the log t0-axis can be found. It should be noted again that attention must be paid to the axis scale of 1 / √2. Here, all six variables of the present invention are shown in Fig. 13. When the log n(u0) function is difficult to see in the contour map of Fig. 13, the cross-section of n can be clearly seen when it is displayed as a 3D graph as in Fig. 12.

[0077] The log L-axis in Fig. 13 is orthogonal to the origin where log u0 = 0, but there can also be a convention to make it orthogonal to the optimal flow rate where log u0 = log u0,opt. In Fig. 12, the line of u0,opt is seen as the ridge line of the hilly terrain. Also, on the right side of this ridge line, the coefficient C of the van Deemter equation is dominant, and on the left side, the coefficient B is dominant. Furthermore, it is necessary for the coefficient A not to be zero to ensure the monotonic increase in the following discussion, and each of the coefficients A, B, and C has an important role.

[0078] When each t0 is fixed, the N-Π cross-section can be seen for each t0. In Fig. 13, it is the cross-section in the direction of 45° to the right and is almost monotonically increasing. N has the characteristic of increasing approximately in proportion to the square root of Π. Similarly, when each Π is fixed, the N-t0 cross-section can also be seen respectively. As seen in Fig. 13, this is also almost monotonically increasing, and in the cross-section in the direction of 45° to the left, N increases approximately in proportion to the square root of t0. Under logarithmic representation, it climbs with a slanting slope and a contribution of at most 1 / √2 times, but combined with the axis scale of 1 / √2 in the example, ultimately it climbs at most to the power of 1 / 2, that is, it is proportional to the square root, and this logic is extremely interesting. The expression "at most" is because the coefficients B and C are not zero. This logic will be described in detail later.

[0079] Finally, as the particle size d P changes, K V also changes. But where in Fig. 13 would this phenomenon be reflected? This affects the limiting condition ΔP. That is, when expressing the log Π axis in terms of the log ΔP axis, the constant log K V is added. The larger K V is, that is, the higher the liquid permeability, the more the limit naturally extends (Fig. 15). K V increases in the order of 2, 3, and 5 μm, with the monolithic column being the largest.

[0080] Explain Fig. 15. Each straight line is the Opt. line of the optimum flow rate u0,opt. Π and t0 are correlated. For example, the Opt. line for a particle size of 2 μm has u0,opt at a relatively high flow rate, so the slope is shallow in this graph. And despite the maximum pressure being as high as 60 MPa, the upper limit of Π is not very high. This is because the liquid permeability K V is small (see Equation 6). This interpretation seems suitable for high-speed analysis because of the shallow slope. However, since the characteristics of n cannot be seen in this graph, the information is not sufficient. Also, as the particle size decreases, the liquid permeability deteriorates, and Π does not increase as expected. On the other hand, in the case of the Opt. line for a particle size of 5 μm, although the slope is large, since K V is relatively large, Π extends even when the pressure ΔP max is as low as 20 MPa. Although n is not shown and nothing can be said for sure, since Π can be effectively utilized over time, it may be advantageous for high-resolution analysis methods. It can be seen that a particle size of 3 μm has intermediate characteristics between 2 μm and 5 μm. Furthermore, it can be seen that the monolithic column is comparable to the slope of a particle size of 2 μm suitable for high speed and effectively extends Π at a low pressure. By looking at this graph in a full logarithmic uLN type 3D graph (Figs. 12, 13), each n can be seen on the cliff section with the intercept log L = 0, and the information on the z-axis is added compared to Fig. 15.

[0081] [Proof of Monotonic Increase] Assume that the coefficient A in the van Deemter equation (Equation 8) is a positive number, and the coefficients B and C are zero or positive numbers. Π = u 0Since it is L, N can be expressed by the function N(Π, t0) from (Equation 10).

[0082]

Equation

[0083]

Equation

[0084] Here, Π and t0 are treated as variables. The variable u0 can be synthesized from Π and t0. It should be noted that (Equation 11) has the symmetry that Bt0 and CΠ are commutative.

[0085]

Equation

[0086] The variable ranges of Π, t0, and u0 are all positive only. (Equation 12) is obtained from (Equation 13).

[0087]

Equation

[0088] First, fix Π in (Equation 11) and handle the one-variable function N(t0). Differentiate N(t0) with respect to t0 to examine whether N(t0) is monotonically increasing.

[0089]

Equation

[0090] Since A and Π are positive, and B and C are non-negative, (Equation 14) is always positive. Therefore, it is proved that N(t0) is a monotonically increasing function in the positive variable range of t0.

[0091] For example, in the case of a filler with a particle diameter of 2 μm, A = 5.1 x 10 -6m, B = 3.3 x 10 -9 m 2 s -1 , and C = 2.7 x 10 -4 s.

[0092] Next, fix t0 in (Equation 11) and handle the single-variable function N(Π).

[0093] [Equation]

[0094] Differentiate N(Π) with respect to Π to examine that N(Π) also increases monotonically in the same way.

[0095] [Equation]

[0096] Since A and t0 are positive and B and C are non-negative, (Equation 16) is always positive. Therefore, it is proven that N(Π) is a monotonically increasing function in the positive domain of Π.

[0097] [Relationship between N and Π] If the coefficients B and C in (Equation 11) are set to zero, it can be seen that N is proportional to √Π. Let's derive this relationship (Equation 17) from the uLN-type logarithmic contour map (Figure 13).

[0098] [Equation]

[0099] First, as shown in Figure 17(a), the log Π axis can be found in the 45° upward-right diagonal direction on the bottom plane pasted with the log u0 axis and the log L axis. However, when reading the unit vector e 4 in that direction and rewriting it as log Π, the value read out must be multiplied by √2 times. This is the meaning of the scale factor 1 / √2 of the log Π axis. By means of projection, etc., e 4When reading the magnitude of an arbitrary vector in a direction as the value of log Π, it must always be multiplied by √2. This is because when rotating a unit vector by a rotation matrix, the magnitude of any unit vector is preserved. That is, the logarithmic operation of finding log Π from the sum of log u0 and log L is not actually simply a rotation (see Patent Document 2). In this sense, it is desirable to call LRT (logarithmic rotation transformation) LCT (logarithmic coordinate transformation).

[0100] Next, use the characteristic that log N is a function that increases with a slope of 1 with respect to log L. Try replacing the hilly terrain in Fig. 12 with an ideal rectangular flat plate inclined at 45° with respect to the log L axis. Although the hilly terrain is inclined to the left and right by coefficients B and C respectively, when both B and C are zero, the inclination disappears and it becomes a simple flat plate. The front side is a section function when log u0 = 0, and in this case, the so-called cliff section becomes a horizontal straight line. This flat plate is inclined such that log N increases with a slope of 1 with respect to log L, but when climbing back in the direction of the log Π axis along a 45° skiing line, only 1 / √2 times the log N can be climbed for each unit vector e 4 climb. The ratio is exactly tan θ = 1 / √2, so θ is about 35.3° (Fig. 17(a)).

[0101] Ultimately, even for an ideal flat plate where coefficients B and C correspond to zero, if log Π does not increase by √2, e 4 does not increase by 1, and even if e 4 increases by 1, only 1 / √2 times the log N increases. Therefore, as shown by the number (S8), log Π can increase horizontally by 2 up to point B, and only then can log N increase by 1 (Fig. 17b).

[0102] [Regarding the particle diameter d P Non-Patent Document 3 lists the relational expression (Equation 18) between H and d P .

[0103]

Equation

[0104] Here, a, b, and c are coefficients. First, u0,opt is obtained as (Equation 19), and when u0 is fixed to u0,opt, H becomes (Equation 20).

[0105]

Equation

[0106]

Equation

[0107] When u0 = u0,opt, H is proportional to d P and a proportional relationship is obtained. On the other hand, K V is proportional to the square of d P E can be regarded as a proportionality constant that arises when explaining the relationship where N is proportional to √Π through d P That is, under the ideal condition of u0 = u0,opt, when d P changes, the responses of Π and N 2 are each proportional to the square of d P and E is a dimensionless variable related to H and K V defined based on that relationship. This will be described in detail again later ([When the particle size is refined]).

[0108] Also, a 3D graph can be displayed where log L is fixed in the full logarithmic uLN type 3D graph and the log d P axis is added.

[0109] [Visualize the influence of item C] From the ΠtN type contour map all displayed on the real number axis, N obtained with L = constant can be seen. In Figure 2, it can be seen that as Π increases, the curve with L = constant gradually moves away from the contour line of N = 10,000. This can also be intuited from the ΠtN type 3D graph (Figure 16).

[0110] [Function allocation of the arithmetic processing unit] The liquid chromatography data processing apparatus of the present invention has the configuration shown in FIG. 18. An input unit 2 such as a keyboard and a mouse and a display unit 3 such as a display and a printer are connected to the data processing apparatus 1. The internal configuration of the data processing apparatus 1 includes a data storage unit 4, an arithmetic processing unit 5, and a graph processing unit 10. The data storage unit 4 stores data generated in the intermediate processing steps from the basic characteristic data of the column packing material to the data for final graph display, including the data group generated in the intermediate processing steps. The basic characteristic data includes the theoretical number of plates per unit length n(u0) corresponding to the cliff cross-section function and the column permeability K V and the like. If necessary, η and the upper limit of pressure loss ΔP max can also be stored. The coefficients A, B, C, a, b, c, or d P of the van Deemter equations (Equations 8 and 18) can also be stored.

[0111] The arithmetic processing unit 5 includes a logarithmic processing unit 8, a coordinate conversion unit 6, an orthogonal projection unit 7, and a general arithmetic unit 9. The coordinate conversion unit 6 can also execute rotation conversion processing. The graph processing unit 10 can display both logarithms and true numbers. It consists of a 3D graph unit 11, a contour map unit 12, a 2D cross-sectional view unit 13, and an overlay drawing unit 14. As display examples, the 3D graph is shown in FIG. 12, the contour map is shown in FIG. 13, the 2D cross-sectional view unit is shown in FIG. 19, and the overlay drawing is shown in FIG. 16.

[0112] The functions of each part of the data processing apparatus are shown using [LRT conversion of the all-logarithmic uLN-type 3D graph] as an example. First, data of n(u0) is input from the input unit. This is temporarily stored in the data storage unit. Next, the arithmetic processing unit expands the data n(u0) into three-dimensional space by adding the L axis using the general arithmetic unit. For example, the nN projection method is executed using the orthogonal projection unit to generate a true three-dimensional space of the uLN type. Further, the logarithmic processing unit performs a logarithmic operation on the true numbers of the three axes. As the arithmetic processing unit, finally, the coordinate conversion unit is activated to generate the log Π axis and the log t0 axis with a scale factor by LRT conversion.

[0113] When the user of the data processing device activates the graph processing unit and selects, for example, the 3D graph unit, a full logarithmic uLN type 3D graph as shown in FIG. 12 is displayed on the display unit. If the user uses the contour line part, a full logarithmic type contour map as shown in FIG. 13 can be displayed. Further, if the user uses the 2D cross-sectional view, log n-log u0 as a slicing function can be observed as a cliff cross-section. Using the overlay drawing part, a graph with a constant L as shown in FIG. 16 can also be formed.

[0114] [When granulating the particle size] Here, the property that the product of the mantissas such as multiples becomes the sum of the logarithms is also utilized. d P What will happen if d becomes 1 / 2 times? H also becomes 1 / 2 times, and n is the reciprocal. Using the full logarithmic uLN type 3D graph, log n becomes -log 2, and the cliff cross-section rises by about +0.30 (FIG. 20). Even if log N rises by +0.30 as a whole, it does not affect log u0, log L, and thus log Π. The coefficients B and C have a slope of 45° because an ideal flat plate model with zero is used.

[0115] d P If d becomes 1 / 2 times, then next K V is proportional to the square and becomes 1 / 4 times. That is, the logarithm log K V becomes about -0.60 with -log 4. As shown in FIG. 21(a), the straight line of the pressure upper limit ΔP max intersects the log Π axis perpendicularly. Since ΔP max is constant, using (Equation 6), d P due to 1 / 2 times of d, K V changes, and log Π loses -0.60. The division by 1 / 4 becomes the subtraction of the logarithm. When the liquid permeability K V becomes 1 / 4 times worse, the effective velocity-length product Π also decreases by 1 / 4 times, and the logarithm also becomes a subtraction of -0.60.

[0116] Incidentally, when the unit vector e4 spanning the log Π axis has a magnitude of 1, log Π is scaled by a factor of 1 / √2. Since it is displayed in the all-logarithmic uLN type 3D space, this scaling factor also applies to the lost log Π of -0.60. The loss on the (log Π) / √2 axis is about -0.43, which is 1 / √2 times -0.60.

[0117] Looking at Fig. 21(b), from the original point C where ΔP max is, although it rises by +0.30 in log n, it loses -0.43 along the (log Π) / √2 axis due to the action of K V . Along the flow line of the oblique sliding with θ = approximately 35.3°, log N decreases. Since tan θ is 1 / √2, the horizontal movement of -0.43 of the triangle results in a decrease of -0.30 in log N. Eventually, the level of log N at point D is equal to that of the original point C, and it returns to the starting point. The K V at point D is 1 / 4 times, and Π is also 1 / 4 times.

[0118] Let's illustrate with specific numerical values. Suppose the particle size of 2 μm is refined to 1 μm. H becomes 1 / 2 times, but K V 7×10 -15 m 2 becomes 1 / 4 times, which is 1.75×10 -15 m 2 . Therefore, if ΔP max remains at 60 MPa, the driving force Π decreases from 400 mm·mm / s to 100 mm·mm / s. Then, even if we manage to double the reciprocal n of H, there is no gain as the upper limit of Π becomes 1 / 4 times.

[0119] In reality, since it is not an ideal flat plate, it falls below the original level N due to the influence of term C. Therefore, when refining d P , we must always raise ΔP max simultaneously. The scaling factor of (-log4) / √2 for the horizontal movement along the (log Π) / √2 axis is exactly applicable, but the flow line of the oblique sliding is curved due to the influence of term C, and tan θ is only approximately in a relationship of 1 / √2.

[0120] From the perspective of E, H is proportional to d P but K V is proportional to the square of d. Also, N is approximately proportional to the square root of Π. Conversely, Π is approximately proportional to the square of N. H is proportional to N, and when ΔP P is fixed, since K max is proportional to Π, K V is approximately proportional to the square of H. Therefore, the definition formula of E shown in (Equation 7) is considered reasonable. Looking back once again, the fact that d V acts on n and d P acts on K P goes through completely different logics as shown in FIGS. 20 and 21, but ultimately results in the E in (Equation 7). V

[0121] [Display operation example] A display example of this data processing device will be described. Based on data such as n(u 0 ) input from the input unit, the arithmetic processing unit stores 3D data with all starting L axes added in the data storage unit. The display unit can display not only a true number uLn type 3D graph like FIG. 3 but also various graphs.

[0122] From here on, the order is arbitrary, but without using the nN projection method by user specification, a true number uLN type 3D graph (FIG. 14) can be displayed by the general arithmetic unit based on (Equation 2). If the logarithmic processing unit displays a contour map (FIG. 1) of both logarithmic axes only on the bottom plane, in addition to the bottom plane logarithmic uLN type contour map, using the LRT rotation of the coordinate conversion unit, FIG. 1 can be viewed as a bottom plane logarithmic ΠtN type contour map. If the logarithmic processing unit is used for inverse calculation, a true number tN type contour map (FIG. 2) can also be displayed. To show the influence of item C, a curve with a constant L can also be overdrawn in FIG. 2 by an overdrawn part.

[0123] ​Using FIG. 14, a hilly terrain can be displayed on the all-logarithmic uLN type 3D graph (FIG. 12) newly shown in the present invention. It is an important feature of the all-logarithmic display that the section function log n can be seen on the cliff section where log L = 0. The contour map part can also display the all-logarithmic uLN type contour map (FIG. 13). The coordinate conversion part can also find the all-logarithmic ΠtN type contour map in FIG. 13 by LRT coordinate conversion with a scale factor. In FIG. 13, the undulation of the section function log n can be seen on the cross-section of the log u 0 axis. Also, the all-logarithmic uLN type 3D graph is convenient for graphically understanding the relationship between the square of N and Π as shown in FIG. 17. Furthermore, FIG. 21 from the all-logarithmic uLN type 3D graph shows that the P granulation of d contributes to the performance improvement of n, but has an adverse effect on K V and ultimately cancels out, which is geometrically proven. As a related concept, it can also be understood that E, which is the reciprocal of the product of the square of n and K V , is related (Equation 7).

[0124] Using FIG. 2, the 3D graph part can also display a true-real ΠtN type 3D graph like FIG. 19. The 2D cross-section part can display the t0-N type 2D cross-section shown in the lower right of FIG. 19. As proven in Equation 14, it can be clearly seen at a glance that it is indeed monotonically increasing.

[0125] The orthographic projection part can also measure the magnitude of ΔP by the LOP orthographic projection method using the unit vector ΔP after showing the all-logarithmic ΠKη type 3D graph of Π, K V and η as shown in FIG. 10 (Equation 6).

[0126] Now, regarding FIGS. 12 and 13, the subject is the same hilly terrain, but the display methods are different only. This is because logarithmic Π-axis and logarithmic t0-axis can also be shown together in FIG. 12. If it is difficult to view on the axis, it is also possible to display a vertical plane on each of the corresponding axes and, in addition, display the curve where the hilly terrain intersects with the vertical plane. On the other hand, although it may be difficult to view in FIG. 13, it can be regarded that a cutting plane perpendicular to the slice function n(u0) is displayed as a contour map on the logarithmic u0-axis. The user may select the display method according to the purpose. Also, for example, using virtual reality techniques, a 3D model of a sheet-like hilly terrain with an axis frame for a measuring stick can be floated in space. These will become new display tools that can be conveniently used when finding the separation conditions of HPLC.

[0127] It can be said that Patent Document 2 disclosed up to the framework of the display method. There, only five variables of u0, L, N, Π, and t0 were handled, and it only showed the LRT rotation of the bottom plane coordinate system. At this stage, N was still a two-variable function that was automatically given as long as the bottom plane coordinates were specified. For the first time in the present invention, six variables could be simultaneously displayed in a form including the characteristic function n(u0) of the column packing agent as the cause for generating N.

[0128] As can be seen in FIG. 12, once the cliff section of n(u0) is determined, the surface of the hill N has no other characteristics, and it just climbs strictly along the L logarithmic axis with a gradient of 1.

[0129] Looking at FIG. 13, the user can only select the flow rate u0, the length L of the column, and the packing agent with n(u0) as the three variables of the operating system. However, what the user really wants is the theoretical plate number N indicating separation and the basic unit t0 of the analysis time which is a measure of high speed. And since there must always be a pressure upper limit as a limiting condition, the user needs to know the three variables of the result system including the velocity-length product Π proportional to the pressure.

[0130] Figure 13 is a contour map when using a filler with a particle size of 2 μm. As described above, it is a hilly terrain based only on the n(u0) function of the filler characteristics. For example, the black circle Π can be read as 400 mm·mm / s. The product Π of velocity and length is a variable proportional to the pressure loss ΔP, and 400 mm·mm / s corresponds to approximately 60 MPa. Column permeability K V and viscosity η can be easily calculated with a proportionality constant, and it is convenient to also write down the scale of ΔP beside the logarithmic axis of Π for reading purposes.

[0131] Suppose the user optimizes the separation conditions to aim for the maximum N with the pressure upper limit of the device system and the column being 60 MPa or less. At this time, with Π of 400 mm·mm / s as the upper limit, exploration will be carried out. As explained in the text, when Π is fixed and constant, N is a monotonically increasing function with respect to t0. That is, the longer the time, the higher the N obtained. This constant-pressure method was called the KPL method. For example, if the black circle in Figure 13 is selected, it can be read that N of 14,000 plates is obtained at t0 of 25 s. Furthermore, from this contour map, the operating conditions in that case, u0 of 4 mm / s and L of 100 mm, can be read out simultaneously.

[0132] If you want to further increase the speed, for example, set t0 to 10 s, which is 1 / 2.5 of the original value, and view the contour map. It is at the midpoint from the 100 s coordinate point on the logarithmic axis of t0 towards the origin. Starting from there and climbing the hilly terrain parallel to the logarithmic axis of Π, you will reach a point where you approximately touch the N contour line of about 10,000 steps. This means that when t0 is 10 s and Π is raised to 400 mm·mm / s, N = 10,000 can be obtained. Since N is a monotonically increasing function even when t0 is fixed, if the pressure is increased further, a higher N can be obtained. The u0 and L at this coordinate point are approximately 6 mm / s and about 70 mm respectively. As u0, a flow rate slightly higher than the optimal linear velocity will be set. In fact, when using a commercially available column with a length L = 50 mm and raising Π to 400 mm·mm / s, u0 reaches 8 mm / s, and it can also be seen that N becomes much lower than 10,000 steps. This is because the decrease in N due to shortening L and the contribution of the decrease in the n(u0) function due to increasing u0 simultaneously act doubly.

[0133] From the perspective of maximizing the utilization of the characteristics of the n(u0) function, one can also understand the psychology of trying to use it around the optimal u0, that is, around the ridgeline of about 4 mm / s. This method was called the Opt. method. The effect of the present invention is that it enables instant consideration of coordinate points located at intermediate conditions between the two optimization methods, such as the KPL method and the Opt. method, without being biased towards any one of the optimization methods. The means is, for example, to simultaneously visualize six variables on a 3D graph.

[0134] Furthermore, as described above, since the function n(u0) represents the characteristics of the filler, similar contour maps with particle diameters of 3 μm and 5 μm can also be displayed using it as an input function. By comparing each contour map, the user can consider the separation conditions. In that case, it is a more desirable embodiment to also record the scale of the logarithmic axis of ΔP parallel to the logarithmic axis of Π. It should be noted that the proportional constant connecting ΔP to Π varies depending on the particle diameter of the filler.

[0135] [Method of tracing back from the result-based 3D graph to the cause-based] Using FIG. 22, a method of geometrically finding the cause-based three variables u0, L, and n from the result-based ΠtN type three-dimensional graph is shown. First, the inverse transformation of Patent Document 2 is derived (Equation 21). By this LRT coordinate transformation, a uLN type 3D graph is obtained. Rotate counterclockwise, that is, rotate the -45° Π-t0 bottom plane. The generated u0-L bottom plane is multiplied by a scaling factor of √2 for each axis. Since the unit vectors are enlarged rather than scaled, it is called a scaling factor in a broad sense.

[0136]

Equation

[0137] Next, the method of finding n is to use the nN projection method. (Equation 22) is derived from the defining equation of (Equation 2). As shown in FIG. 22, a vertical plane is formed with log L multiplied by the scaling factor √2 as one unit vector and the log N axis as the other unit vector. In that plane, the unit vector log n is located in the direction away from log L, that is, rotated counterclockwise by the mixing angle φ = about 35.3°. A scaling factor of (√6) / 3 is multiplied by log n. Since it is the nN projection method, the magnitude of the inner product is obtained by orthogonally projecting the points on the hilly terrain onto this unit vector e 5 and is measured as (√6) / 3 × log n. Going around, on the plane formed by log n and log u 0 in FIG. 22, the n (u 0 ) function is drawn as a curve, and returning to the image where the n (u 0 ) function is continuously formed as an n film in the direction orthogonal to that plane.

[0138]

Equation

[0139] Even without using the nN projection method, the cliff section with log L = 0 can be utilized. First, starting from the result system's all-logarithmic ΠtN-type 3D graph, when coordinate transformation is performed by LRT, the axes of the u0-L bottom plane in both logarithms can be represented. Next, if the cliff section with log L = 0 is displayed, the n(u 0 ) function, which is a two-dimensional log N - log u0 fault plane as a section function, appears. Exactly, it can be observed as the log n(log u 0 ) function. The 2D sectional view part 13 generates discrete log u 0 to be swept. Since log L = 0 is fixed, the corresponding log Π and log t 0 are uniquely determined (Equation 21). Since the starting point is the all-logarithmic ΠtN-type 3D graph, the two-variable function log N(log Π, log t 0 ) can also be easily obtained. Eventually, it becomes log N with log L = 0, that is, log n.

[0140] This method can be similarly applied to the bottom plane logarithmic ΠtN-type contour map. The z-axis obtains the true number N(log u 0 ), and by looking at the vertical section N - log u 0 on the log u 0 axis, it becomes the true number n(log u 0 ), which is the theoretical number of plates per unit length.

[0141] [Application of Scaling Factor and Offset] In the present invention, various offsets can be utilized. On the logarithmic axis, the addition and subtraction of offsets correspond to the multiplication and division of the true numbers. Since the flow rate F is the product of the linear velocity u 0 and the effective cross-sectional area S eff of the column, by adding the offset log S 0 to the scale of the log u eff axis, u 0 can be read as the flow rate.

[0142] Similarly, log ΔP can be read from the log Π axis using (Equation 6). The positive offset on the log Π axis is log η, and the negative offset is log KV In addition, because of the reciprocal relationship as shown in (Equation 2), log H can be easily read out by multiplying the log n axis by minus 1 as a kind of scaling factor. Retention time t R Log t 0 It can be read out by adding an offset log(k+1) to the axis, where k is the retention factor.

[0143] Separation degree R S As shown in (23), the offset on the right hand side can be added to the log N axis and then multiplied by the scaling factor 1 / 2 to read it out. This is the same as the relationship when log Π is read out from a full logarithmic uLN type 3D graph by multiplying it by the scaling factor 1 / √2. In other words, if the magnitude is 1 on the log N graph after shifting the offset mentioned above, then log R S The magnitude of is read as 1 / 2. S The factor 2 in front of α exerts this effect, where α is the separation factor.

[0144]

number

[0145] Π, t visualized on a fully logarithmic uLN 3D graph 0 The six variables, including n, are calculated by using a scaling factor and offset to obtain the flow rate F and resolution R. S , pressure drop ΔP, holding time t R , which can be read out as the height equivalent to a theoretical plate, H. The necessary constants here are S eff , K V , η, k, α.

[0146] [van Deemter Plot and Hold-up Time Measurement Apparatus] H(u 0 ) or its reciprocal n(u 0) has been described as the starting point of the present invention, but a liquid chromatograph (Fig. 23) that automatically measures the van Deemter Plot can also be used. Subsequently, a system for measuring the hold-up time t 0 is also shown.

[0147] For example, set the analysis method on the sample table so that u 0 changes from 0.5 mm / s to 5.0 mm / s in steps of 0.5 mm / s, and measure each N. The flow rate setting of the pump (liquid delivery section) is converted by multiplying the previous S eff . If the column length L = 50 mm, n can be obtained from (Equation 2). The analysis conditions are, for example, as described in the background art. Using butyl benzoate as the analysis sample solute, aspirate 10 μL from the sample vial on the autosampler (sample injection section) and inject it. In the column thermostat, keep the column at a constant temperature of 40 °C, and in the ultraviolet absorption photometric detector (detection section), set the wavelength to 270 nm. If it is predicted that the pressure will reach the upper limit pressure of the column, 60 MPa, stop increasing the flow rate before that. N is calculated by a data processing device that also serves as a control unit for processing the detection results, identifying the peaks of the analysis species, and using the method of the Japanese Pharmacopoeia or the United States Pharmacopoeia.

[0148] As shown in (Equation 2), H is the reciprocal of n, and as shown in (Equation 8), that H can be regressed to the coefficients A, B, and C. Here, there is a little technique. The method of regressing the product u 0 H as a quadratic function of u 0 is simple. That is, C is the coefficient of the next term of u 0 , A is the coefficient of the first-order term, and B is the constant term for regression. Using these coefficient groups, the graphs of the present invention can be displayed.

[0149] Also, it is necessary to obtain the hold-up time t0 by a data processing device or the like. It is common to use uracil for this analysis species. It is convenient to add and mix it to the previous butyl benzoate sample. The non-retained time of uracil can be set as t 0 for each injection. u 0 is L divided by t 0Since it is a physical quantity to be excluded by [specific method], each t can be measured without using the set flow rate. 0 By measuring, each u for each injection can be obtained. 0 Therefore, once u is obtained, the effective cross-sectional area Seff of the column is also determined as the proportionality constant with the set flow rate F. 0 As six variables, for the column length L of the column thermostat, the specification value at the time of purchase is used, and it is sufficient for the data processing device to measure the t of butyl benzoate and uracil.

[0150] As six variables, for the column length L of the column thermostat, the specification value at the time of purchase is used, and it is sufficient for the data processing device to measure the t of butyl benzoate and uracil. 0 For the other three variables u 0 , Π, n, all can be obtained by calculation. L = u 0 t 0 , Π = u 0 L, (t 0 Π = L 2 ), and N = nL.

[0151] [Plot the measurement results directly on a 3D graph] In the above method, the value of butyl benzoate was used as N, but the N of uracil can also be adopted. Anyway. Among the six variables, if there are three variables of L of the column dimension value and t 0 and N directly measured by the data processing device, without performing the arithmetic processing of variable conversion, a plurality of sets (L, t 0 , N) as they are can be directly plotted on a 3D graph. For example, it can be plotted on a log-log uLN type 3D graph as shown in Fig. 12. Each measured value (t 0 , N) measured by changing the flow rate is measured from the same column, so L is constant. It should be noted that this measured value (t 0 , N) is different from the t 0 -N graph used in the KPL method. In the KPL method, L changes uniquely in synchronization with t 0 so that ΔP is constant in the background of the t 0 -N graph. On the other hand, in the case of the measured value (t 0 , N) of this example, since L is constant, ΔP changes inversely proportional to t 0 in the background. That is, ΔP is inversely proportional to t 0It is uniquely linked to

[0152] Figure 13 is a contour diagram of Figure 12. The log L axis and (log t 0 ) / √2 axis is seen. These two axes function as an oblique coordinate system that forms an angle of 45°, and any coordinate position on the bottom plane can be specified. However, in this example, each measured value (t 0 , N) will be plotted. 0 When placing the value of t 0 It is important to note that the logarithmic axis scaling factor must be multiplied before plotting. When plotting the log N values ​​on the z-axis, the log t 0 The coordinate position of the bottom plane of t 0 The plot point is placed at the height of log N corresponding to the value of t 0 , N) are plotted. As a result, the actual measured values ​​(t 0 , N) are lined up.

[0153] So far, we have only plotted each plot point (t 0 , N), but these measured points must be expanded in a three-dimensional graph space as shown in Figure 12. Here, we apply the characteristics of an N-surface, which is a hilly terrain. That is, a log N surface is a surface with a slope of 1 along the log L axis. Each plot point (t 0 , N) is extended along the log L axis with a slope of 1 in the direction of large expansion of L and the direction of small contraction of L. As a result, the surface N shown in Figure 12 is formed.

[0154] Of the other three variables, u 0 and Π can be found using the LRT transformation relationship. 0 The base plane of the 3D graph is drawn using an oblique coordinate system with the log u axis as shown in Figure 13. 0The axes of the shaft and (log Π) / √2 can be found. Since the bottom plane is two-dimensional, if two variables out of the four variables are selected, the remaining two variables are subordinate to them.

[0155] The last sixth variable n is the sectional function log n(u 0 ) observed as the cliff section of the curved surface N at log L = 0. Eventually, by directly plotting all six variables L, the two variables t 0 and N measured by the data processing device on a 3D graph, all six variables can be displayed.

[0156] Figure 24 is a graph showing the output variable N on the vertical axis when the column length is 100 mm using (Equation 18). The input variables are the two-variable function N(dp, u0) of dp and u0. The Opt. curve drawn from u0,opt for each dp is drawn as a ridge line. It can be seen that the larger dp is, the slower u0,opt becomes. This is why a relatively large N can be obtained by reducing u0 for larger fillers of dp and separating over time. Although Π and pressure are not explicitly shown, it can be inferred from Figure 24 that fillers with a large dp are positioned relatively more emphasis on separation than time.

[0157] Note that as described above, as a method for displaying graphs of planes and lines for data of three dimensions or more, it is not limited to a so-called 3D graph such as a perspective view, but as a generalized 3D graph display, a graph display may be performed such that contour lines are displayed according to the values of the coordinate axes perpendicular to the paper surface.

[0158] Also, logarithmic display includes not only cases where the scale of the coordinate axes is displayed logarithmically, but also cases where the interval of the contour lines is displayed according to the logarithmic scale.

[0159] [Display Regarding the Number of Theoretical Plates N] Next, the display regarding the number of theoretical plates N in liquid chromatography will be described.

[0160] In order to understand the relationship between the analysis time and separation performance of HPLC, Patent Document 1 is first the basis. In Patent Document 1, the flow constant C f introduces the same variable as the velocity-length product Π (m 2 / s) by the expression of.

[0161]

Equation

[0162] Here, K V (m 2 ) is the column permeability (column liquid permeability), and η (Pa·s) is the viscosity. The pressure loss ΔP is nothing but Π with K V and η as proportional factors. Since the secondary factors of K V and η can be excluded, in the present invention, Π is considered a more convenient variable than ΔP. Π is also called pressure-driven strength. The u 0 (m / s) in (Equation 24) is the linear velocity of the non-retained component, L (m) is the column length, and Π is their simple product.

[0163] In the present invention, for simplicity, the van Deemter equation is adopted as the model showing the flow rate dependence of the number of theoretical plates N. That is, the height equivalent to a theoretical plate H (m) is represented by the function H (u 0 ) of u 0 .

[0164]

Equation

[0165] Here, the coefficients A (m), B (m 2 / s), and C (s) are constants specific to the column packing material and also depend on the mobile phase, column temperature, analysis species, etc. The number of theoretical plates N is a dimensionless index obtained by (Equation 26) using H and L. As can be seen from (Equation 26), N also has a flow rate dependence.

[0166] [Number]

[0167] There is an optimal flow rate u for this related matter. 0,opt In the case of the van Deemter equation, u 0,opt is obtained by the following mathematical formula (Equation 27).

[0168] [Number]

[0169] Furthermore, (Equation 25) depicts a downward convex curve and takes a minimum value H 0,opt at the time of u min (Equation 28).

[0170] [Number]

[0171] The maximum value N of N max is obtained by dividing L by H min (Equation 29).

[0172] [Number]

[0173] As an index of high-speed performance, the hold-up time t 0 (s) is used. In reversed-phase chromatography, for example, the appearance time of generally non-retained uracil is generally adopted. Actually, the previously mentioned u 0 can also be positioned as a variable calculated from the measured variable t 0 using L if viewed from a different perspective.

[0174] [Number]

[0175] The Π, u that have appeared so far 0, L, H, N, and t 0 The six variables of and their relational expressions are the preparation for the model calculation of the present invention. And the constants A, B, and C in (Equation 25) play important roles.

[0176] (Overview) (Problem) In Patent Document 2, a three-dimensional graph was shown. This is a display of the two-variable function N(Π, t 0 ), and the Coefficient of Pressure-Application (CPA) and the Coefficient of Time-Extension (CTE) have been proposed. For N, CPA is a kind of effectiveness index indicating how much N can be increased as the pressure loss increases. t 0 There is also a CPA for t, which becomes an index indicating how effectively the pressure increase works for speeding up. CTE is an index for N, indicating how effectively N can be enhanced by extending the analysis time, that is, t 0 .

[0177] Although the effectiveness of pressure and time can be shown by these indexes, it was not possible to mention up to how much N can be improved. The separation conditions of the present invention are limited to the optimization of only u 0 and L. That is, without using the gradient elution method and without increasing the column temperature. The retention factor k of each component is fixed and the discussion proceeds. Therefore, the stationary phase (column packing material, particle size, etc.), the mobile phase (eluent composition), the solute (components of the analysis species), and the column temperature are fixed, and isocratic elution is assumed. As an example, it is based on the results measured under all the same separation conditions (the stationary phase is a C18 silica fully porous packing material with a particle size of 2 μm, the mobile phase is a 60% aqueous acetonitrile solution, the column temperature is 40°C, and the sample solute is butyl benzoate).

[0178] The problem is, first, in the optimization of the separation conditions of only u 0 and L, N(Π, t 0It is to see how the constants A, B, and C of the van Deemter equation affect the behavior of [[ID=]]. As a result, the user will prioritize and control the factors with a high degree of influence.

[0179] The user also wants to examine the N that can be reached by optimization. Is there an upper limit? If so, what is it? That upper limit may be related to the variable Π and t 0 and may also have some relationship with them.

[0180] (Means) To achieve the above object, the present invention is a liquid chromatograph data processing device that can calculate the behavior of N (Π, t 0 ) from the flow rate characteristics of N or H and display the result. It is also possible to display the upper limit value of N and the ratio of the currently realized N to that upper limit value.

[0181] (Effect) According to the present invention, it is possible to make it easier to grasp the relationship between each data such as the separation conditions of the chromatograph device, and to easily obtain the separation conditions according to the intention of the user.

[0182] (Specific example) [Upper limit number of theoretical plates] In Patent Document 2, a three-dimensional graph was shown. This is a two-variable function N(Π, t 0 ) and can be clearly described by Equation 31.

[0183] [Equation]

[0184] Here, Π and t 0 are treated as two variables. The variable u 0 can be synthesized from Π and t 0 (Equation 32).

[0185] [Equation]

[0186] Π, t 0 , u 0 The variable ranges of all are positive. (Equation 32) is obtained from (Equation 33) derived from (Equation 24) and (Equation 30).

[0187]

Equation

[0188] Also, since (Equation 31) can be expressed by (Equation 34), it should be noted that for N, Π / B and t 0 / C have the symmetry that can be interchanged.

[0189]

Equation

[0190] By the way, since (Equation 31) was clearly expressed as described above, the condition for it to be a monotonically increasing function can also be shown. First, fix Π with (Equation 31) and treat it as a univariate function N(t 0 ). To examine that N(t 0 ) is monotonically increasing, differentiate N(t 0 ) with respect to t 0 .

[0191]

Equation

[0192] For this derivative coefficient to be positive, looking at the numerator of the fraction, it can be seen that the condition is that A is not zero or C is not zero. Originally, the constants A, B, and C are assumed to be non-negative. Therefore, this is the necessary and sufficient condition for N(t 0 ) to be a monotonically increasing function. For example, in the case of a filler with a particle diameter of 2 μm, A = 5.1 x 10 -6 (m), B = 3.3 x 10 -9 (m 2 s -1), and C = 2.7 x 10 -4 (s) and is a monotonically increasing function.

[0193] Next, fix t in (Equation 31) 0 and handle the single-variable function N(Π).

[0194]

Equation

[0195] Differentiate N(Π) with respect to Π to examine whether N(Π) also monotonically increases in the same way.

[0196]

Equation

[0197] Looking at the numerator as in (Equation 35), it can be seen that the condition is that A is not zero or B is not zero, that is, the necessary and sufficient condition for N(Π) to be a monotonically increasing function has been found. Here too, the constants A, B, and C are non-negative.

[0198] N(t 0 ) and the respective conditions for N(Π) to be a monotonically increasing function are known, but will N(Π, t 0 ) diverge to infinity? First, set t 0 to infinity in (Equation 31). As shown in (Equation 38), it can be seen that there exists an asymptotic upper limit value N sup (Π) corresponding to Π. Similarly, although Π does not actually become infinite in reality, if we hypothetically set Π to infinity, N 0 corresponding to t sup (t 0 ) can be obtained (Equation 38).

[0199]

Equation

[0200] Each N supWhen projected onto the vertical wall plane of the three-dimensional graph, it becomes as shown in Fig. 25. For example, N(Π) at t 0 = 20 s exhibits a square-root-shaped cross-section on the vertical wall N - Π plane, while interestingly, the projected N sup (Π) is a straight line proportional to Π.

[0201] Similarly, under the maximum pressure loss, ΔP max = 60 MPa, N(t 0 ) exhibits a square-root-shaped cross-section on the vertical wall N - t 0 plane, while the virtually projected N sup (t 0 ) is also a straight line proportional to t 0 . The data processing device can display the projection straight lines of N sup on the three-dimensional graph as the reach limit values for separation condition optimization.

[0202] Also, for example, the display data corresponding to the limit value of the theoretical plate number as the separation performance may be data corresponding to the display line for displaying the limit value in the two-dimensional graph as shown in Fig. 26. Also, as shown in conjunction with the same figure, it may be data corresponding to the display line for displaying the value of a predetermined ratio of the above limit value, or the scale of the coordinate axis. Also, for example, data for displaying the ratio value of the limit value at the theoretical plate number of one or more predetermined plots in the graph showing the correspondence between the flow velocity u0 and the theoretical plate number N, etc., may be used.

[0203] Regarding the display of the limit values as described above, coefficients A to C in (Equation 25), etc., may be obtained based on, for example, automatic measurement, etc., or may be input by a user, etc.

[0204] Summarizing the liquid chromatograph data processing device enabling the above display, it can be configured, for example, as follows.

[0205] The first liquid chromatograph data processing device A liquid chromatograph data processing apparatus that generates display data for displaying a graph showing the correspondence relationship of these data based on the analysis conditions of a chromatograph apparatus and data related to separation performance. Generates display data showing the correspondence relationship between data corresponding to the analysis time and data related to separation performance, and further, a liquid chromatograph data processing apparatus characterized in that it is configured to generate display data according to the limit value of the separation performance.

[0206] A second liquid chromatograph data processing apparatus is a first liquid chromatograph data processing apparatus, wherein the display data according to the limit value of the separation performance is data according to a display line for displaying the limit value, and a liquid chromatograph data processing apparatus is characterized in that.

[0207] A third liquid chromatograph data processing apparatus is a first liquid chromatograph data processing apparatus, wherein the display data according to the limit value of the separation performance is data according to a display line for displaying the limit value and a value of a predetermined ratio of the limit value, or a scale of a coordinate axis, and a liquid chromatograph data processing apparatus is characterized in that.

[0208] A fourth liquid chromatograph data processing apparatus is a first liquid chromatograph data processing apparatus, wherein the display data according to the limit value of the separation performance is data showing a ratio value of the limit value of the value related to the separation performance in the plot corresponding to a predetermined plot of the graph, and a liquid chromatograph data processing apparatus is characterized in that.

[0209] Furthermore, in a special case of u 0 = u 0,opt u becomes the square root of the value obtained by dividing B by C as in (Equation 27), and a relationship as in (Equation 39a) is obtained. That is, interestingly, u 0,opt becomes the square root of the value obtained by dividing B by C as in (Equation 27), and a relationship as in (Equation 39a) is obtained. That is, interestingly, u 0= u 0,opt On the straight line of t 0 Making N infinite sup (Π) and the virtual N with Π made infinite sup (t 0 ) will have the same value.

[0210]

Mathematics

[0211] u 0 = u 0,opt The straight line of ΔP max , that is, Π max The boundary condition of intersects. In particular, this intersection point is called the vertex of the delta region meaningful for optimization. Since the N of the vertex is obtained from Π max , including the meaning on the u 0,opt line, it is expressed as N ver (Π max ) (Figure 40).

[0212]

Mathematics

[0213] Generally, for any two-variable function N(Π, t 0 ), there exist asymptotic upper limit values N sup (Π) and N sup (t 0 ), respectively. Therefore, the ratio of N(Π, t 0 ) in each upper limit value can be calculated. As a special case, the ratio of N ver (Π max ) in N sup is obtained (Figure 41). Since it is on the u 0,opt line, as described above, N sup (t 0,ver ) = N sup (Π max ).

[0214]

Mathematics

[0215] Here, (Equation 40) was divided by (Equation 38). As a result, since the variation range of A / (√BC) is from zero to infinity, the N at the vertex is N sup The ratio in N is 50% at the upper limit.

[0216] The data processing device can output various results of this kind.

[0217] [Consideration Regarding Particle Size] Non-Patent Document 3 shows the relational expression (Equation 42) between H and the particle size d P (μm).

[0218] [Equation]

[0219] Here, a, b, and c are coefficients. As can be seen by comparing with the coefficients of (Equation 25), A = a d P , B = b , C = c d P 2 are in the relationship of. First, the optimal flow velocity u 0,opt is obtained as (Equation 43), and when u 0 = u 0,opt is fixed, H becomes (Equation 44).

[0220] [Equation]

[0221] [Equation]

[0222] That is, the minimum value H 0 = u 0,opt at u min is proportional to d P and the relational expression (Equation 44) was obtained.

[0223] When the coefficients B and C in the aforementioned (Equation 38) are reinterpreted as the coefficients in (Equation 42), interestingly, B = b Therefore, N sup (Π) is found to be independent of the particle size. That is, if d P is 2 μm or 5 μm and the same Π is obtained, the same N sup (Π) can be obtained. However, when converting Π to ΔP, it is necessary to divide by K V (Equation 24). According to Non-Patent Document 5, by the Kozeny-Carman equation, K V is proportional to the square of d P (Equation 45).

[0224]

Equation

[0225] Here, the flow resistance φ P is a proportionality constant and is empirically a number larger than 1, such as several hundred.

[0226] K V is proportional to the square of d P Therefore, a larger d P makes it relatively easier to achieve the same Π with a smaller ΔP. Conversely, from the perspective of obtaining the same N sup (Π), for smaller particle sizes, d P 2 must be increased in inverse proportion to ΔP. Expressing this in a mathematical formula, (Equation 46) can be obtained from (Equation 38) and (Equation 24).

[0227]

Equation

[0228] Therefore, the upper limit theoretical plate number N sup (ΔP) can be newly defined (Equation 46). Its interpretation is a bit of a technical expression. For example, if we want to obtain an arbitrary same N sup (Π), such as 100,000 plates, then ΔP must be adjusted with respect to dP 2 must be pulled up in inverse proportion.

[0229] On the other hand, N in (Equation 38) sup (t 0 ) migrates to (Equation 47).

[0230] [Number]

[0231] N sup (t 0 ) is inversely proportional to d P 2 Interpreted this way, at the same t 0 , the smaller the particle size, the larger the N P 2 is obtained in a form inversely proportional to d sup . Combining (Equation 46) and (Equation 47), the act of reducing the particle size has the drawback that, for example, if trying to obtain an arbitrary same upper limit number of theoretical plates N sup such as 100,000 plates, ΔP must be pulled up in inverse proportion to d P 2 , but as a result, t 0 can be increased at a speed proportional to d P 2 . This can be mentioned because N sup (t 0 ) and N sup (ΔP) have the characteristics that they can be expressed as functions simply proportional to t 0 and ΔP respectively.

[0232] Upper limit value N sup Instead, we return to the discussion of the ordinary number of theoretical plates N. Introduce the three-variable function N(ΔP, t 0 , d P ) having the variables ΔP, t 0 , d P ), and handle the range of u 0 for which H min can be approximated as being almost constant even when u 0 is changed. Fix the bottom plane coordinates (ΔP, t 0 ) and dP is changed only. Using (Equation 26), (Equation 44), and (Equation 39b), N(ΔP, t 0 , d P ) is represented by (Equation 48).

[0233] [Equation]

[0234] Here, (Equation 24) and (Equation 45) are also used.

[0235] In (Equation 48), d is canceled out in the numerator and denominator. Therefore, when the bottom plane coordinates (ΔP, t P ) are fixed and the others are all constants, N is constant even if d 0 changes. P

[0236] This interpretation is based on the approximation that H is almost constant with respect to the change in u 0 . However, for example, even if d min is refined from 3 μm to 2 μm, the effect of making H P small and good and the adverse effect of making d P increase K min cancel each other out. Eventually, for example, from the coordinates (ΔP, t P ) fixed with ΔP = 20 MPa and t V = 10 s, N does not increase or decrease even if d 0 changes. 0 P

[0237] Regarding the influence of refinement, even if described in the image of a three-dimensional log graph, ultimately the landscape of N(u 0 , L) is overall raised by the action of H or n, and the deterioration shift of K V when converting ΔP to Π (the contribution to decreasing Π) cancel each other out.

[0238] Actually, no matter how d P is changed, N(ΔP, t 0 , d P ​​​) ΔP and t that do not change 0 relationship, that is, (ΔP, t 0 ) has a locus on the coordinates. First, using the coefficients of (Equation 31) and (Equation 42), N(Π, t 0 , d P ) is obtained (Equation 49).

[0239]

Equation

[0240] Here, Π is a two-variable function Π(ΔP, d P ) from (Equation 24) and (Equation 46) (Equation 50).

[0241]

Equation

[0242] By substituting (Equation 50) into three places in (Equation 49), all Π are replaced with ΔP, and N(ΔP, t 0 , d P ) can be expressed explicitly. Calculate the partial derivative coefficient (Equation 51), and the condition for the partial derivative coefficient to be zero is that d P even if it changes, N(ΔP, t 0 , d P ) does not change at the coordinates (ΔP, t 0 ).

[0243]

Equation

[0244] The condition for (Equation 51) to be zero is that the expression inside the parentheses in the numerator is zero (Equation 52).

[0245]

Equation

[0246] This condition can be transformed into (Equation 53) by replacing the coefficients and variables with equivalent ones.

[0247] [Number]

[0248] This means that in the model calculation of the present invention, when Π and t 0 are on the Opt. line, the partial differential coefficient becomes zero. That is, only when the relationship between ΔP and t 0 is the relationship when operating at the optimal flow velocity u 0,opt is it a necessary and sufficient condition that N(ΔP, t P , d 0 , d P ) does not change when d min is changed. The approximate calculation (Equation 48) using the aforementioned H

[0249] [Procedure for drawing a log-log 3D graph] As described in Patent Document 3, the landscape N(u 0 , L) grows with a slope of 1 from the cliff section curve n(u 0 ). Here, four procedures will be described by tracing back to the valley curve H(u 0 ) of the valley curve. First, as Procedure 0 before entering each procedure, a coordinate system for the log-log 3D graph is set up in advance. In the right-handed Cartesian system, the x, y, and z axes are assigned to log u 0 , log L, and log N, respectively.

[0250] Procedure 1 generates the valley-type curve of H(u 0 ). This is the so-called van Deemter curve (Equation 25). As shown in Fig. 27, plot the H(u 0 ) curve on the vertical plane of N - u 0 where log L = 0, that is, L = 1 (mm).

[0251] In Procedure 2, draw the cliff section curve n(u 0 ) that is in a mirror image relationship with the valley-type H(u 0 ) curve above the valley.

[0252] In Step 3, grow it on the landscape of N(u 0 , L) with a slope of 1. This is because since N is proportional to L, when expressed logarithmically, log N increases with a slope of 1 with respect to log L.

[0253] For the final Step 4, utilize the LRC (Logarithmically Rotating Coordinate system) transformation. Set the log Π / √2 axis at a point rotated 45° counterclockwise from the log u 0 axis. This √2 is a scaling factor. Similarly, set the log t 0 / √2 axis at a point rotated 45° counterclockwise from the log L axis.

[0254] The above is the procedure for generating a log-log 3D graph. Each variable regarding the landscape N(u 0 , L) can be quantitatively measured using each axis as a measure.

[0255] [Curve Fitting Procedure of van Deemter's Equation] In Patent Document 3, as also explained in the above [van Deemter Plot and Apparatus for Measuring Hold-up Time] section, a method of multiplying both the right side and the left side of (Equation 8) by u 0 and performing curve fitting as a quadratic function was mentioned. Here, a method for obtaining the coefficients based on the characteristics of van Deemter's equation is shown.

[0256] First, as Step 1, obtain the C term in a sufficiently large flow rate range of u 0 . Since there is no influence of the B term here, the slope of the straight line directly becomes the coefficient C. In practice, it is desirable to perform linear regression in a flow rate range of about twice or more of u 0,opt .

[0257] In Step 2, find the horizontal axis point u 0,opt of the minimum value of the van Deemter plot. In practice, local quadratic curve fitting is easy to use. As shown in (Equation 27), u 0,opt 2Since it is the quotient of B and C, substituting C obtained in Step 1 allows the constant B to be calculated.

[0258] Furthermore, in Step 3, based on the algebraic calculation of (Equation 28) from the vertical axis point H of the minimum value min and the constants B and C, the coefficient A can also be obtained.

[0259] [Service by Server Computer] The device system owned by the user outputs a three-dimensional graph or performs optimization calculations for separation conditions. However, by connecting the user's computer to the service provider's server computer via a network line, similar input / output results can be obtained.

[0260] For example, time-series data for a van Deemter plot is sent to the server, and after regression analysis, the coefficients A, B, and C output are received. Next, a full logarithmic three-dimensional graph can also be received using these A, B, and C. By uploading the relationship data between the flow rate and the pressure loss, as the analysis result of the server, K V is also output. By synthesizing these analysis results, graphing of N(ΔP, t 0 ) in a true real number three-dimensional graph or a contour map is also executed. If it is a server computer, it is also possible to display the output result of overwriting considering that the column length is discrete. Furthermore, by considering the upper limit number of theoretical plates and performing optimization of the separation method, a service that advises the user is also provided. It is possible to realize a unified function from the collection of raw data to numerical analysis such as mathematical statistics and the optimization of the analysis method.

[0261] Generally, the van Deemter equation is (Equation 25) or (Equation 42), but there are also various other notations as follows (Equations 54, 55). As a service by a server computer, it has the characteristic of being easy to apply various functional forms.

[0262]

Equation

[0263] There is (Equation 55) in Non-Patent Document 3.

[0264]

Number

[0265] Here, D m is the diffusion coefficient (m 2 / s) of the analysis species in the mobile phase, k d is the desorption rate constant (s -1 ), and D is a certain constant coefficient.

[0266] [Expansion of 3D Graph Using Simulation] The x-, y-, and z-axes of the 3D graph are, for example, Π, t 0 , N, but it is also possible to select variables from the upper concepts of these, such as pressure, time, and separation performance, and use them. Also, not limited to isocratic elution, expansion to gradient elution or stepwise elution is possible. In that case, it is convenient to use the resolution R or an index indicating separation performance equivalent thereto as the z-axis. R can also be defined in a local time region near the retention times of the two components. Although gradient elution can use a rather complex time program, even if the complexity is fully utilized, if time or pressure is fixed, a specific upper limit resolution R sup should not be exceeded. This can be said from the analogy of N sup .

[0267] Regarding time, even in gradient elution, the retention time t 2 of the second component among the two components can be adopted as the variable of the y-axis. When the flow rate changes, the retention volume V 2 of the second component can also be used, but the theory becomes quite complicated.

[0268] The pressure on the x-axis can simply adopt ΔP, but it is conceivable that ΔP is not constant during gradient elution. In that case, for convenience, ΔP maxTo display such a three-dimensional graph, it is no longer possible to write it using simple mathematical expressions. Therefore, 0 , L, H will be used as inputs, and it will be necessary to consolidate multiple simulation results into maximum and minimum values ​​and display them in three dimensions. Even if L is fixed, u 0 In particular, when H changes, u 0 The function H (u 0 ), so it is advisable to run a simulation.

[0269] When the analyte is changed, or the composition and concentration of the mobile phase, or the column temperature, etc. are changed, H (u 0 ) profile, retention factor k, or K V , η also change, so these must be taken into consideration in the simulation.

[0270] [Preparation of UHPLC definition] Particle diameter d P With respect to the change in the optimal flow rate u 0,opt If we focus on (Equation 19), each variable is uniquely determined (Non-Patent Document 6). This discussion is limited to the category of the so-called Opt. method. First, when a specific pressure loss ΔP is specified, the column length L is inevitably determined by the Kozeny-Carman equation (Equation 1 and Equation 20) (Equation 56).

[0271]

number

[0272] L is ΔP and d P Two-variable function L (ΔP, d P ) The minimum H min is (20), and N is also a two-variable function N (ΔP, d P ) (Number 57).

[0273]

number

[0274] For any ΔP from (Equation 57), there is a theoretical plate number N r required, and it can be seen that there exists a specific particle diameter d P,opt . That is, apart from the view that N is a two-variable function N(ΔP, d P ) as in (Equation 57), it can be interpreted that d P,opt has the form of a two-variable function d r of ΔP and N P,opt (ΔP, N r ) (Non-Patent Document 7).

[0275]

Equation

[0276] On the other hand, under the optimal flow rate Opt. method, the hold-up time t 0 is also found to have the form of a two-variable function t 0 (ΔP, d P ) (Equation 59).

[0277]

Equation

[0278] Looking at (Equation 56), (Equation 57), and (Equation 59) all together, it is found that L, N, and t 0 are respectively proportional to the cube, square, and fourth power of d P , and all are proportional to ΔP.

[0279] By the way, the coefficients a, b, c up to here were defined by the van Deemter equation that explicitly represents the particle diameter d P of (Equation 18). Incidentally, b and c determine the functional shape of the van Deemter equation, while a is a kind of offset. Hereafter, for generalization, constants h P regarding d min , U min (m 2 / s), π P (1 / s) are introduced to make it easier to view.

[0280] [Number]

[0281] [Number]

[0282] [Number]

[0283] Note that in Non-Patent Document 7, a dimensionless ν as in (Equation 63) is used, but since the diffusion coefficient D min must also be introduced simultaneously, in the present invention, we limit ourselves to the use of U m (m 2 / s). min (m 2 / s).

[0284] [Number]

[0285] Using these constants, N, L, and t 0 can be rewritten as follows (Equations 64) to (Equation 66) from (Equation 57), (Equation 56), and (Equation 59).

[0286] [Number]

[0287] [Number]

[0288] [Number]

[0289] Similarly, (Equation 58) or (Equation 64) can also be used to obtain (Equation 67).

[0290]

Number

[0291] [Definition of UHPLC] N, L, t 0 are all two-variable functions f(ΔP, d P ) defined from the bottom plane (ΔP, d P ). If d P is fixed, they are all simple functions that increase monotonically in proportion to ΔP. On the other hand, if ΔP is fixed, graphs proportional to the power of the horizontal axis d P can be drawn, such as squared, cubed, and to the fourth power.

[0292] If two equations are selected from the three equations of (Equation 64) to (Equation 66) and ΔP is eliminated, a relational expression such as N and L can be obtained, and that relational expression is also represented by the power of the horizontal axis d P . Moreover, that relational expression is an identity regarding ΔP and can theoretically hold at any ΔP, whether it is 20 MPa or 100 MPa. The identity regarding ΔP will be described later.

[0293] Similarly, if d P can be eliminated from those three equations, an identity regarding the horizontal axis ΔP that theoretically holds whether it is 5 μm or 2 μm can be obtained. For example, an identity of t P / N 0 is obtained from (Equation 64) and (Equation 66) (Equation 68). It was found that (Equation 68) that can be found from the argument of this identity is exactly the impedance time t 2 (s) (original application for priority claim). E

[0294]

Number

[0295] t Eis an index indicating how many seconds are required to obtain, for example, 10,000 plates. Squaring N is a device for eliminating d P By adopting t E t becomes a one-variable function t E that is inversely proportional to ΔP E represented by (ΔP), and a new graph with pressure loss on the horizontal axis can be drawn as shown in Fig. 28. The separation conditions are as described above, using butyl benzoate as the analyte, a 60% aqueous acetonitrile solution as the mobile phase, and setting the column temperature at 40°C.

[0296] By using the concept of Fig. 28, UHPLC can be defined not from the maximum pressure of the system but from the performance aspect of the separation method. That is, ΔP is a variable that is easily affected by factors such as column temperature, viscosity of the mobile phase, and column permeability and is not stable. Therefore, it is a well-known fact that ΔP is not necessarily the separation performance itself. Therefore, in order to define UHPLC, an index indicating separation performance was necessary. t in (Equation 68) E is one of the comprehensive performance indices defined from both the high-speed and high-separation aspects. Repeating, from the perspective of the Opt. method, under the condition of constant ΔP, t 0 has the characteristic of being proportional to N 2 Interestingly, for example, under a specific ΔP such as 60 MPa, for each d P such as 5 μm or 2 μm, N and t 0 show different performances respectively, but when paying attention to the ratio of t 0 / N 2 t E is constant. At this time, the background L is uniquely determined for any d P because ΔP is specified. For the same ΔP, since the column permeability of 5 μm is higher, L becomes longer and t 0 increases accordingly, but N or N 2 also increases. The good relationship between t E and ΔP is a characteristic obtained from the Opt. method of the optimal flow rate.

[0297] For example, among the performance obtained using an HPLC system, if we temporarily call the performance obtained under pressure conditions of 100 MPa or higher UHPLC-class performance. As described above, since the pressure varies due to various factors, the definition based on pressure is not suitable as a method for defining separation performance. For example, in FIG. 28, when t E is 10×10 -8 s or less, it can be defined as UHPLC (Ultra High Performance Liquid Chromatography). This corresponds to 10,000 plates in 10 s or less (10 seconds or less at 10,000 plates). Although this is the separation condition, this generally corresponds to 100 MPa or higher. The nice round number is just a coincidence, but it generally seems to match the concept considered for the maximum pressure of a general UHPLC system. Since the vertical axis of the graph shows the overall performance of separability and high speed, t E so instead of 100 MPa, the UHPLC boundary criterion of 10×10 -8 s or less can be proposed. This corresponds to 10,000 plates in 10 s or less, and is equivalent to taking 4 times as long, 40 s, for 20,000 plates. To be precise, point A in FIG. 28 corresponds to 10,000 plates in 10 s, but it cannot be said to be 10,000 plates in 10 s itself. Point A reaches N = 10,000 plates only when d P = 1.5 μm from (Equation 42) or (Equation 57), and t 0 = 10 s. Here, in the calculation, the coefficients a, b, c use the experimental values for particle diameter d P = 5 μm, and when d P = 2.1 μm, N = 20,000 plates in 40 s. Point A is a point representing the 10,000 plates in 10 s class including all arbitrary particle diameters d P . This is the intention of the definition method by t E .

[0298] The UHPLC defined from the performance can be called the UHPLC field. Although it enters from the HPLC field to the UHPLC field, the UHPLC field is a subset belonging to the HPLC field. The boundary is the reference value t E= 10×10 -8 It can be proposed as s.

[0299] Adopting the specified method from the performance means that it is possible to reach the UHPLC region even when using a system with a maximum pressure of 60 MPa. When using a monolithic column or a core-shell column, since it is possible to enter the UHPLC region at a relatively low analysis pressure, it may be called a column for UHPLC. Even in the case of a fully porous silica column, if the pressure resistance of a column with a particle size of 3 μm is increased, it may exceed the threshold of 40,000 plates in 160 s by using a relatively long column. This is t E Since it is specified, it can be understood that it is equivalent to the boundary value of UHPLC of 10×10 -8 s. Also, as usual, using acetonitrile rather than methanol as the mobile phase is easier to reach the UHPLC region because of its lower viscosity. The same is true for the method of raising the column temperature.

[0300] The curve in Fig. 28 indicates the reachable limit of the impedance time in the sense that it cannot reach below this curve. Under this separation condition, no matter what particle size d P of the same type of packing material is used, and no matter how the column length L is adjusted, it is the reachable limit. This is because at a specific pressure loss ΔP shown on the horizontal axis, it is the Knox and Saleem limit that can be reached by making the best use of d P and L (Non-Patent Document 6). Also, the impedance time t E is examined in detail in Non-Patent Document 8. The novelty of the present application lies in presenting a graph with the vertical axis t E and the horizontal axis ΔP. Note that when the reciprocal N E of t 2 / t 0 (1 / s) is adopted on the vertical axis, the boundary of the UHPLC region is similarly shown.

[0301] Similarly, when fixing a specific pressure ΔP and considering the optimal d P , there are two remaining relational expressions obtained by selecting two out of the three expressions of (Equation 64) to (Equation 66). The cube of N is proportional to the square of L (Equation 69), and the fourth power of L is t0 is proportional to the cube of (Equation 70).

[0302]

Mathematics

[0303]

Mathematics

[0304] Also, t E repeats, but when fixed at a specific pressure, an equation in which t 0 is proportional to the square of N can also be obtained. When this is plotted as t 0 -N, the locus is described by a quadratic function passing through the origin.

[0305] [Relationship equation between N and П] Another important equation (Equation 71) can be derived by the Opt. method.

[0306]

Mathematics

[0307] Here, П = u 0,opt L and L = H min Eliminating the intermediate variable L from N and using (Equation 60) and (Equation 61), d P is canceled out. In this equation, t 0 does not appear explicitly, and П is proportional to N. Therefore, it can be understood again that for any d P and the associated ΔP and H, П serves as a direct intensive variable with respect to N. In a series of this fully porous silica filler, for example, the product Π determines N and can be regarded as an index that is not affected by d P instead of ΔP. On the other hand, t 0 is given by П = u 0,opt 2 t 0 is obtained from, so from (Equation 63), d PIt can also be seen that it depends on.

[0308] [Plate time] From the three equations of (Equation 64) to (Equation 66), for a specific particle diameter d P By linking it to the corresponding pressure loss ΔP, three new relational expressions can be found. That is, by eliminating ΔP and making d P Positive, there are three identities of (Equation 72), (Equation 73), and (Equation 74).

[0309] [Number]

[0310] [Number]

[0311] [Number]

[0312] (Equation 72) and (Equation 74) are also equal to each other.

[0313] By the way, from (Equation 72), the plate time t P (Equation 75) is derived. (Patent Document 3).

[0314] [Number]

[0315] t P As shown in (Equation 75), it becomes a one-variable function of the particle diameter d P In this context, ΔP can freely increase or decrease in proportion to L, and the ratio of t 0 / N, t P alone is conserved. However, d P is a variable to be specified.

[0316] Impedance time t E is a function of ΔP, d P is symmetric with that when it was free. t E is because ΔP is constant in that context, d P for, L is L ∝ d P 2 is constrained as, and under that constraint condition, t 0 / N 2 the ratio of t E alone was conserved. t P is d P is output when input, t E is as shown in Fig. 280, when inputting ΔP on the horizontal axis, t E is output. t P is also t E is also the overall performance regarding time and theoretical plate number, but to define the UHPLC imaged at high pressure, t E is more suitable.

[0317] t E is related to the separation impedance E in Non-Patent Document 8. Shown by the notation of the present invention (Equation 76).

[0318]

Equation

[0319] From after this section [Preparation for UHPLC Definition], it is limited to the Opt. method, and N, L, t 0 are respectively considered from the viewpoint that they are functions of two variables, ΔP and d P (Equations 64 to 66), but in (Equation 76), d P does not explicitly appear. t regarding impedance E and E are functions of only ΔP. t E and E P can be understood to result from the relational expression obtained by eliminating d. t E A two-dimensional graph with t and ΔP as two axes was important.

[0320] On the other hand, plate time t PSimilarly, ΔP does not explicitly appear. It is the background where ΔP and L are interlocked that supports (Equation 75). t E In this case, in the background, d P and L are interlocked. Mathematically, starting from the point of dealing with five variables N, L, t 0 , ΔP, d P , we positioned the bottom plane where ΔP and d P are independently variable (ΔP, d P ). By fixing either ΔP or d P and combining the variables N and t 0 that can be the z-axis, we found the relational expressions and extracted the mutually symmetric t E and t P as can be seen from an overview (Equation 68)(Equation 75). Also, since it is limited to the Opt. method, H and u 0 are fixed to H min and u 0,opt respectively. Eventually, since UHPLC has an image leading the industry that higher pressure ΔP is desirable, by drawing a graph associating t E and ΔP as shown in Figure 28, it is possible to define UHPLC based on the comprehensive performance t E of high speed and high separation that replaces ΔP. If the image that a smaller particle size d P is more desirable takes precedence, UHPLC should be defined based on t P regardless of ΔP, but in reality, it is not the case.

Explanation of Symbols

[0321] 1 Data processing device 2 Input section 3 Display section 4 Data storage section 5 Arithmetic processing section 6 Coordinate conversion section 7 Orthogonal projection section 8 Logarithmic processing section 9 General arithmetic section 10 Graph processing section 11 3D graph section 12 Contour map section 13 2D cross-sectional view section 14 Overlay portion

Claims

1. A liquid chromatography data processing device that generates display data for displaying a graph showing the correspondence of these data based on data related to the analysis conditions and separation performance of a chromatograph device, the first group of two-axis data related to the analysis conditions, the second group of two-axis data obtained by an operation including multiplication and division of the two data of the first group, respectively, and generates display data corresponding to one graph representing the correspondence of the data related to the separation performance, and at least, the display data is characterized in that each axis of the data of the first group and the second group is display data corresponding to a graph represented by a logarithmic axis. A liquid chromatography data processing device.

2. The liquid chromatography data processing device according to Claim 1, wherein the data of the first group and the second group include data corresponding to at least any one of an index corresponding to the flow rate of the mobile phase, the column length, an index corresponding to the pressure loss of the column, and an index corresponding to the analysis time. A liquid chromatography data processing device.

3. The liquid chromatography data processing device according to any one of Claims 1 to 2, wherein the data related to the separation performance includes data corresponding to at least any one of the number of theoretical plates, the height equivalent to a theoretical plate, the number of theoretical plates per unit length of the column, and the resolution. A liquid chromatography data processing device.

4. The liquid chromatography data processing device according to Claim 3, wherein the display data is characterized in that the data related to the separation performance is display data corresponding to a graph represented by a logarithmic axis. A liquid chromatography data processing device.

5. The liquid chromatography data processing device according to Claim 4, wherein the data related to the separation performance includes first separation performance data corresponding to at least any one of the number of theoretical plates, the height equivalent to a theoretical plate, the number of theoretical plates per unit length of the column, and the resolution, and the first separation performance data and the first group And second separation performance data obtained by an operation including multiplication and division of at least any one of the data of the second group, or an operation including the reciprocal of the first separation performance data. A liquid chromatography data processing device.

6. The liquid chromatography data processing device according to Claim 5, The above first separation performance data is the number of theoretical plates, the above second separation performance data is the number of theoretical plates per unit length of the column, the data of the above first group or second group includes the column length, and a liquid chromatograph data processing apparatus characterized by generating display data representing a cross-sectional shape of a plane in a three-dimensional graph where the column length is the unit length.

7. A liquid chromatograph data processing apparatus according to any one of Claims 1 to 6, wherein the display data can be display data corresponding to a graph represented by a true number, with at least a part of each axis of the data of the first group and the second group, and the axis of the data regarding the separation performance, according to a given instruction.

8. A liquid chromatograph data processing apparatus according to any one of Claims 1 to 7, further characterized by being able to generate display data for displaying a cross-section obtained by cutting the graph with a predetermined plane.

9. A liquid chromatograph data processing apparatus according to any one of Claims 1 to 8, further characterized by generating display data for displaying a curve when any of the data of the first group and the second group is set to a predetermined fixed value.

10. A liquid chromatograph data processing apparatus according to any one of Claims 1 to 9, wherein the data of the first group and the second group includes the particle diameter of the column.

11. A liquid chromatograph data processing apparatus that generates display data for displaying a graph showing the correspondence relationship of these data based on the analysis conditions of the chromatograph apparatus and the data regarding the separation performance, generating display data corresponding to a graph representing the correspondence relationship between the data in two axial directions including the column length regarding the analysis conditions, and the data in one axial direction which is the number of theoretical plates regarding the separation performance, and the axes in two axial directions including the column length and the axis in one axial direction which is the number of theoretical plates are each represented by a logarithmic axis, a liquid chromatograph data processing apparatus characterized by generating display data representing a cross-sectional shape of a plane in a three-dimensional graph where the column length is the unit length.

12. A liquid chromatograph data processing apparatus according to any one of Claims 1 to 11, a liquid feed unit that feeds a mobile phase, a sample injection unit that injects a sample into the mobile phase flow path that has been fed, a column that separates the injected sample, a detection unit that detects the separated component to be analyzed, a control unit that processes the detected results, and a data processing unit that examines and sets the operations and measurement conditions of the liquid feed unit, the column, and the detection unit. A liquid chromatograph apparatus having the above components.

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