METHODS FOR PREPARING LIQUID MIXTURES

Abstract

A method of preparing a liquid mixture for use in a liquid chromatography system is provided. The mixture comprises one or more acids, one or more bases, one or more solvents and water, and the method comprises the steps of: calculating pH and/or solvent concentration at a particular time t from a user-determined gradient function; and, based on the values obtained, calculating percent acid, percent base, percent solvent and percent water in the liquid mixture at time t. A liquid chromatography system incorporating such method is also provided.

Claims

1. A method of preparing a liquid mixture, the mixture comprising one or more acid solutions, one or more base solutions, and one or more solvents, the method comprising the steps of : i) calculating pH and/or solvent concentration at a particular time t from a user-determined gradient function; and ii) based on the values obtained in step (i), calculating percent acid solution, percent base solution, and percent solvent in the liquid mixture at time t.

2. The method of claim 1, wherein the gradient function comprises a fraction multiplier that provides predetermined changes in pH and/or solvent concentration, each being independent of the other, over a time period of interest.

3. The method according to claim 1, wherein the gradient function is based on the following equation:
y−y.sub.s+(y.sub.n−y.sub.s)×fraction   (equation 1) where y is selected from the group consisting of pH and solvent concentration, y.sub.s is the value at time 1 and y.sub.n is the value at time 2.

4. The method according to claim 1, wherein the fraction multiplier is selected from the group consisting of: $\begin{array}{cc}\mathrm{fraction}=1.0,& 1\\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^8,& 2\\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^5,& 3\\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^3,& 4\\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^2,& 5\\ \mathrm{fraction}=\frac{t}{t_1-t_0},& 6\\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^2,& 7\\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^3,& 8\\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^5,& 9\\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^8.Math..Math.\mathrm{and}& 10\\ \mathrm{fraction}=0.Math..Math.\mathrm{if}.Math..Math.t<\left(t_1-t_0\right).Math..Math.\mathrm{and}.Math..Math.\mathrm{fraction}=1.Math..Math.\mathrm{if}.Math..Math.t=\left(t_1-t_0\right).& 11\end{array}$

5. The method according to claim 1, wherein for a particular pH or solvent concentration the % base can be calculated, using interpolation, from values provided in a pH look-up table.

6. The method according to claim 5, wherein the pH look-up table is empirically derived or is calculated from the pK.sub.a of the acid.

7. The method according to claim 6, wherein the pH look-up table provides pH values for a given acid+base percentage, ratio, or relative concentration.

8. The method according to claim 6, wherein the pH look-up table provides pH values for a given acid+base percentage, ratio, or relative concentration, and solvent concentration.

9. The method according to claim 6, wherein the pH look-up table provides pH values for a given acid+base percentage, ratio, or relative concentration, solvent concentration and temperature.

10. The method according to claim 1, wherein the proportions of acid, base, and solvent are used for controlling a liquid mixture device.

11. The method according to claim 1, wherein liquid mixtures are prepared from stock solutions of at least one acid, at least one base, and at least one solvent.

12. The method of claim 1, wherein the one or more solvents include at least one organic solvent.

13. The method of claim 12, wherein the at least one organic solvent is selected from the group consisting of acetone, acetonitrile, methanol, ethanol, n-propanol and isopropanol, and tetrahydrofuran (THF).

14. The method of claim 1, wherein the acid solution includes one or more of maleic acid, citric acid and succinic acid.

15. The method of claim 1, wherein the base solution includes one or more of 4-methyl morpholine, morpholine, ammonium hydroxide and piperidine.

16. A computer program for determining relative proportions in a liquid mixture according to claim 1, wherein the proportions are used for controlling a liquid mixture preparation device.

17. An eluent preparation device comprising i) a liquid mixture preparation device comprising a mixed liquid outlet port and a plurality of inlet ports connected to component sources of at least one of an acid, a base, a solvent, and water, and ii) a mixer control unit arranged to control the relative component proportions supplied through the inlet ports of the liquid mixture preparation device, wherein the mixer control unit i) calculates pH and solvent concentration from a gradient function; and ii) based on the values obtained in step (i), calculates percent acid, percent base, percent solvent, and percent water in the liquid mixture.

18. A liquid chromatography system comprising the eluent preparation device of claim 17.

19. The liquid chromatography system of claim 17 wherein the system comprises a low-pressure mixing system.

20. The liquid chromatography system of claim 17 wherein the system comprises a high-pressure mixing system.

Description

DESCRIPTION OF THE DRAWINGS

[0008] The invention is further illustrated by the following drawings in which:

[0009] FIG. 1 is a diagram of different curves that can be used to change the pH and organic solvent concentration over the course of an elution.

[0010] FIG. 2 illustrates an exemplary relationship between mobile phase pH and proportion of base buffer component.

[0011] FIG. 3A is a chromatogram showing separation according to the invention as described in the example.

[0012] FIG. 3B is a chromatogram showing separation according to the invention as described in the example.

[0013] FIG. 3C is a chromatogram showing separation according to the invention as described in the example.

[0014] FIG. 3D is a chromatogram showing separation according to the invention as described in the example.

DETAILED DESCRIPTION OF THE INVENTION

[0015] As used herein in the specification and claims, including as used in the examples and unless otherwise expressly specified, all numbers may be read as if prefaced by the word “about”, even if the term does not expressly appear. Also, any numerical range recited herein is intended to include all sub-ranges subsumed therein.

[0016] The chromatographic system uses four stock solvents to create the desired pH-solvent gradients for an elution, the solvents comprising an acid solution, a base solution, a solvent, and water. In exemplary embodiments, the acid and base buffer solutions include volatile acids and bases that are compatible with mass spectrometry, e.g., electrospray ionization mass spectrometry. The acid and base solutions can include a combination of various components. For example, the acid solution can include maleic acid, citric acid and succinic acid. The base solution can include, for example, 4-methyl morpholine, morpholine, ammonium hydroxide and piperidine. The solvent can be any organic solvent compatible with reversed-phase LC/MS, e.g., acetone, acetonitrile, methanol, ethanol, n-propanol and isopropanol, tetrahydrofuran (THF) or any other compatible organic solvent. The water component can be distilled and/or deionized water.

[0017] These four stock solutions are metered in different relative concentrations to generate a given pH condition for the delivered mobile phase at a given point of time.

[0018] In an embodiment of the invention, four different types of data can be entered by the user into the computer program which controls operation of the chromatography system and specifically delivery of the correct solutions at the pump: 1) a pH-gradient table; 2) an empirical pH calibration table (or pK.sub.a); 3) molar concentrations of acid and base stock solutions; and 4) the desired acid+base molar concentration that will be delivered to the stationary phase.

[0019] A pH look-up table is used by the software to calculate the percentage flow from acid solution and base solution lines during the elution. The look-up table is created by the software either from a user-input pK.sub.a or from a user-input empirical calibration table. The empirical calibration table is created by the user by mixing the 2-4 solutions in known proportions and measuring the pH. The software then uses these input values to calculate the percent acid and base (described further below) at a given time point in the gradient table.

[0020] The gradient that is delivered to the stationary phase is determined in the following manner, based on the user-entered information.

[0021] A pH-solvent gradient table includes values for 1) flow rate, 2) pH, and 3) change in pH, (referred to herein as a “pH curve”). In some embodiments, the a pH gradient table can also include values for 4) organic solvent concentration and 5) change in organic solvent concentration (referred to herein as the “solvent gradient curve”), for each time t during the course of the separation. The pH-solvent gradient table can have any number of rows for any range of times. Typically, a user will prepare a table having 5 to 6 rows, for times t.sub.0 to t.sub.5 (or t.sub.6). An example of a pH-solvent gradient table is shown in Table 1:

TABLE-US-00001 TABLE 1 Solvent Time Flow pH % Gradient (min) (mL/min) pH Curve Organic Curve Init. 0.5 6.8 . . . 0 . . . 10 0.5 6.8 6 40 6 12 0.5 6.8 6 60 6 15 0.5 6.8 11  80 11 

[0022] Each time period, for example the time from t.sub.1 to t.sub.2, is referred to a “time segment”. The pH or solvent gradient curve determines how the pH or organic solvent concentration will change over that particular time segment. Examples of curves, which can be used to vary both the pH and organic solvent concentration are depicted in the FIG. 1. The change can be linear, where halfway through the time segment the percentages are halfway between the starting and the ending percentages. The change may also occur more quickly at the beginning of the time segment and more slowly at the end of the segment, a convex curve. The opposite pattern, a concave curve is also possible. The change can also be a step at either the beginning or the end of the segment. The change of pH and organic solvent concentration can be independently varied or held constant from one time segment to another, depending on the needs of the user.

[0023] The pH-solvent gradient table is prepared by the user based on experimentation and prior experience with particular solvents and analytes of interest, and is within the ability of one skilled in the art of chromatography systems.

[0024] The user enters the pK.sub.a from which the look-up table is calculated, or they may enter an empirical calibration from which the pH look-ups are calculated, into the computer program. Optionally, the system can include pre-generated look-up tables for common buffer systems that can be selected by the user. The look-up table can be a one-variable, two-variable or three-variable table; in each, the pH is calculated or measured based on the values of the other variables. A three-variable table will have values for temperature, organic solvent concentration and base percent (%); a two-variable look-up table will have values for solvent concentration (molar) and base percent (%), and a one-variable look-up table has values for base percent. The one-variable table can either be directly entered by the user or calculated by the software based on an input value for the pK.sub.a of the acid used. Typically, a two-variable look-up table may have between 30-60 rows, and a one-variable look-up table will have fewer rows. The two- and three-variable look-up tables are constructed by manually preparing specific mixtures of acid and base buffers, organic solvent and water, and for the three-variable table, temperature. The pH of each mixture at the given conditions is measured and entered into the table.

[0025] The user also enters the molar concentrations for each of the acid and base stock solutions that will be combined at the pump in the system. The user can also enter the percentages of solvent and water that will be combined at the pump in the system.

[0026] A final component of the user-entered information is the delivered acid+base concentration. It has been found from experience that a convenient ratio of acid+base percent and solvent percent is about 20% acid+base, and about 80% solvent. However, these numbers are not required, and can be adjusted according to the needs of the user and the analytes being separated.

[0027] At a point in time, the pump in the chromatography systems is delivering the specified total flow rate of liquid to the separation column. The software calculates the pH and solvent concentration at a particular time t, using the information provided in the gradient table and the look-up table, and a fraction multiplier calculated using the particular pH curve and/or solvent curve in the gradient table. Then, for this particular pH and salt concentration, the % base, % acid, and % solvent can be calculated, using interpolation, from values provided in the pH look-up table. These values are sent to the chromatographic system to generate the specific mobile phase conditions for time t.

[0028] The method of the invention is further illustrated by way of the following example.

TABLE-US-00002 TABLE 2 pH-Solvent Gradient Table (provided by the user) Solvent flow Gradient time (min) (ml/min) pH pH curve % Organic Curve T.sub.0 = 0 1.0 (f.sub.0) 5 (pH.sub.0) — 0 — T.sub.1 = 10 1.0 (f.sub.1) 6 (pH.sub.1)  6 (pHC.sub.1) 20  6 (sCC.sub.1) T.sub.2 = 15 1.0 (f.sub.2) 5 (pH.sub.2)  6 (pHC.sub.2) 40  6 (sCC.sub.2) T.sub.3 = 16 0 (f.sub.3) 5 11 60 11

TABLE-US-00003 TABLE 3.1 One Variable - pH Look-Up Table (empirical calibration table) base % pH  0 4.0  5 (bP.sub.0) 5.0 (pHL.sub.0) 10 (bP.sub.1) 5.5 (pHL.sub.1) 20 6.0

TABLE-US-00004 TABLE 3.2 Two Variables - pH Look-Up Table (empirical calibration table) % Organic Solvent Base % pH 20 (sPL.sub.0)  5 (bP.sub.0) 5.0 (pHL.sub.0) 20 (sPL.sub.0) 10 (bP.sub.1) 5.5 (pHL.sub.1) 40 (sPL.sub.1)  5 (bP.sub.0) 5.2 (pHL.sub.2) 40 (sPL.sub.1) 10 (bP.sub.1) 5.7 (pHL.sub.3) . . . . . . . . .

TABLE-US-00005 TABLE 3.3 Three Variables - pH Look-Up Table (empirical calibration table) % Organic Temp. ° C. Solvent Base % pH 20° C. (Temp.sub.0) 20 (sPL.sub.0)  5 (bP.sub.0)  5.0 (pHL.sub.0) 20° C. (Temp.sub.0) 20 (sPL.sub.0) 10 (bP.sub.1)  5.5 (pHL.sub.1) 20° C. (Temp.sub.0) 40 (sPL.sub.1)  5 (bP.sub.0)  5.2 (pHL.sub.2) 20° C. (Temp.sub.0) 40 (sPL.sub.1) 10 (bP.sub.1)  5.7 (pHL.sub.3) 30° C. (Temp.sub.1) 20 (sPL.sub.0)  5 (bP.sub.0) 5.05 (pHL.sub.4) 30° C. (Temp.sub.1) 20 (sPL.sub.0) 10 (bP.sub.1) 5.56 (pHL.sub.5) 30° C. (Temp.sub.1) 40 (sPL.sub.1)  5 (bP.sub.0) 5.24 (pHL.sub.6) 30° C. (Temp.sub.1) 40 (sPL.sub.1) 10 (bP.sub.1) 5.77 (pHL.sub.7)

Molar Concentrations (Provided by the User):

[0029] acid concentration: acU=100 mM

[0030] base concentration: bcU=100 mM

[0031] organic solvent concentration: scU=1000 mM

[0032] acid and base concentration (bufferConcentrationU)=20 mM

[0033] (bufferConcentrationU≦min (acU, bcU)

Gradient Function

[0034] The gradient function is defined by the following set of equations:

y=y.sub.s+(y.sub.n−y.sub.s)×fraction   equation 1

[0035] where y is pH and salt concentration (or solvent, if an organic solvent is used), and “fraction” is defined as follows (where values for t.sub.1 and t.sub.0 are obtained from the pH—salt gradient table, and t is the time of interest,

t.sub.0≦t≦t.sub.1):

[00001]$\begin{array}{cc}\mathrm{Curve}.Math..Math..Math.1.Math.\text{:}.Math..Math..Math.\mathrm{fraction}=1.0& \mathrm{equation}.Math..Math.2\\ \mathrm{Curve}.Math..Math..Math.2.Math.\text{:}& \\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^8& \\ \mathrm{Curve}.Math..Math..Math.3.Math.\text{:}& \\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^5& \\ \mathrm{Curve}.Math..Math..Math.4.Math.\text{:}& \\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^3& \\ \mathrm{Curve}.Math..Math..Math.5.Math.\text{:}& \\ \mathrm{fraction}=1-{\left(1-\frac{t}{t_1-t_0}\right)}^2& \\ \mathrm{Curve}.Math..Math..Math.6.Math.\text{:}& \\ \mathrm{fraction}=\frac{t}{t_1-t_0}& \\ \mathrm{Curve}.Math..Math..Math.7.Math.\text{:}& \\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^2& \\ \mathrm{Curve}.Math..Math..Math.8.Math.\text{:}& \\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^3& \\ \mathrm{Curve}.Math..Math..Math.9:& \\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^5& \\ \mathrm{Curve}.Math..Math..Math.10.Math.\text{:}& \\ \mathrm{fraction}={\left(\frac{t}{t_1-t_0}\right)}^8& \\ \mathrm{Curve}.Math..Math..Math.11.Math.\text{:}& \\ \mathrm{fraction}=0.Math..Math.\mathrm{if}.Math..Math.t<\left(t_1-t_0\right).Math..Math.\mathrm{and}.Math.\text{.Math.}.Math.\mathrm{fraction}=1.Math..Math.\mathrm{if}.Math..Math.t=\left(t_1-t_0\right).Math.& \end{array}$

pH and Solvent Concentration at Any Gradient Time t

[0036] At any gradient time t, the pH value can be calculated from the gradient function, Equation 1 above, as follows:

[0037] From Table 2, the pH—Solvent Gradient Table, y=pH, y.sub.s=pH.sub.0, and y.sub.n=pH.sub.1, for all values of t where t.sub.0≦t≦t.sub.1.

[0038] Using curve 6 as an example, the fraction is

[00002]$\frac{t}{t_1-t_0}.$

[0039] At time t,

[00003]$\begin{array}{cc}\mathrm{pH}\left(t\right)={\mathrm{pH}}_0+\left({\mathrm{pH}}_1-{\mathrm{pH}}_0\right)\times \frac{t}{t_1-t_0}.& \mathrm{equation}.Math..Math.3\end{array}$

[0040] Similarly, at time t, and using curve 6 as an example, the salt concentration is calculated as:

[00004]$\begin{array}{cc}\mathrm{sC}\left(t\right)={\mathrm{sC}}_0+\left({\mathrm{sC}}_1-{\mathrm{sC}}_0\right)\times \frac{t}{t_1-t_0}.& \mathrm{equation}.Math..Math.4\end{array}$

Calculation of Base Percent 1) Using the one-variable pH Look-up table (Table 3.1), the base percent can be calculated, using interpolation, as follows:

[00005]$\begin{array}{cc}\mathrm{BasePercent}={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_1-{\mathrm{pHL}}_0}\times \left(\mathrm{pH}-{\mathrm{pHL}}_0\right)& \mathrm{equation}.Math..Math.5.1\end{array}$

[0041] 2) For a given organic solvent percent (sP) and pH, where

[0042] sPL.sub.0<sP<sPL.sub.1, pHL.sub.0<pH<pHL.sub.1, and pHL.sub.2<pH<pHL.sub.3,

[0043] the base percent (%) can be calculated from the values provided by the user in the two-variable pH Look-up table (Table 3.2), using interpolation:

[00006]$\begin{array}{cc}{\mathrm{bPI}}_0={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_1-{\mathrm{pHL}}_0}\times \left(\mathrm{pH}-{\mathrm{pHL}}_0\right).Math..Math.{\mathrm{bPI}}_1={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_3-{\mathrm{pHL}}_2}\times \left(\mathrm{pH}-{\mathrm{pHL}}_2\right).Math..Math.\mathrm{then}.Math..Math.\mathrm{basePercent}={\mathrm{bPI}}_0+\frac{{\mathrm{bPI}}_1-{\mathrm{bPI}}_0}{{\mathrm{sPL}}_1-{\mathrm{sPL}}_0}\times \left(\mathrm{sP}-{\mathrm{sPL}}_0\right)& \mathrm{equation}.Math..Math.5.2\end{array}$

[0044] 3) For a given temperature (Temp), solvent percent (sP) and pH, where

Temp.sub.0<Temp<Temp.sub.1,

sPL.sub.0<sP<sPL.sub.1,

pHL.sub.0<pH<pHL.sub.1,

pHL.sub.2<pH<pHL.sub.3,

pHL.sub.4<pH<pHL.sub.5,

pHL.sub.6<pH<pHL.sub.7,

[0045] the base percent (%) can be calculated from the values provided by the user in the three-variable pH Look-up table (Table 3.3), using interpolation:

[00007]$\begin{array}{cc}.Math.{\mathrm{bPI}}_0={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_1-{\mathrm{pHL}}_0}\times \left(\mathrm{pH}-{\mathrm{pHL}}_0\right).Math..Math..Math.{\mathrm{bPI}}_1={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_3-{\mathrm{pHL}}_2}\times \left(\mathrm{pH}-{\mathrm{pHL}}_2\right).Math..Math..Math.{\mathrm{bPI}}_2={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_5-{\mathrm{pHL}}_4}\times \left(\mathrm{pH}-{\mathrm{pHL}}_4\right).Math..Math..Math.{\mathrm{bPI}}_3={\mathrm{bP}}_0+\frac{{\mathrm{bP}}_1-{\mathrm{bP}}_0}{{\mathrm{pHL}}_7-{\mathrm{pHL}}_6}\times \left(\mathrm{pH}-{\mathrm{pHL}}_6\right).Math..Math..Math.{\mathrm{bPI}}_4={\mathrm{bPI}}_0+\frac{{\mathrm{bPI}}_1-{\mathrm{bPI}}_0}{{\mathrm{sPL}}_1-{\mathrm{sPL}}_0}\times \left(\mathrm{sP}-{\mathrm{sPL}}_0\right).Math..Math..Math.{\mathrm{bPI}}_5={\mathrm{bPI}}_2+\frac{{\mathrm{bPI}}_3-{\mathrm{bPI}}_2}{{\mathrm{sPL}}_1-{\mathrm{sPL}}_0}\times \left(\mathrm{sP}-{\mathrm{sPL}}_0\right).Math..Math..Math.\mathrm{and}.Math..Math..Math.\mathrm{basePercent}={\mathrm{bPI}}_4+\frac{{\mathrm{bPI}}_5-{\mathrm{bPI}}_4}{{\mathrm{Temp}}_1-{\mathrm{Temp}}_0}\times \left(\mathrm{Temp}-{\mathrm{Temp}}_0\right)& \mathrm{equation}.Math..Math.5.3\end{array}$

Calculation of % A, % B, % C and % D in the Total Mixture (Sent to Gradient Proportioning Valve by Software)

1) Calculation of Solvent Percent Max

[0046]
acidPercent×aCU+basePercent×bCU=100%×bufferConcentrationU   eq. 5.4.1

acidPercent+basePercent+solventPercent+aqueousPercent=100%   eq. 5.4.2

[0047] From equations 5.4.1 and 5.4.2 the following can be derived:

[00008]$\begin{array}{cc}.Math.\mathrm{acidPercent}.Math.\mathrm{Max}=100.Math.\%\times \frac{\mathrm{bufferConcentrationU}}{\mathrm{aCU}}& \mathrm{eq}..Math.5.4.Math.\mathrm{.3}\\ .Math.\mathrm{basePercen}.Math.t.Math.\mathrm{Max}=100.Math.\%\times \frac{\mathrm{bufferConcentrationU}}{\mathrm{bCU}}.Math..Math..Math.\mathrm{and}& \mathrm{eq}..Math.5.4.Math.\mathrm{.4}\\ \mathrm{solventPercent}.Math.\mathrm{Max}=100.Math.\%-\left(\max .Math..Math.\mathrm{of}.Math..Math.\mathrm{acidPercentMax}.Math..Math.\mathrm{and}.Math..Math.\mathrm{basePercen}.Math.t.Math.\mathrm{Max}\right)& \mathrm{eq}..Math.5.4.Math.\mathrm{.5}\end{array}$

2) Calculation Of Solvent Percentages Sent To Pump:

[0048] From equations 5.1, 5.2 or 5.3 basePercent is obtained. From this value, the following can be calculated:

[00009]$\begin{array}{cc}\mathrm{acidPercent}=\frac{100.Math.\%\times \mathrm{bufferConcentrationU}-\mathrm{basePercen}.Math.t\times \mathrm{bCU}}{\mathrm{aCU}}.Math..Math..Math.\mathrm{From}.Math..Math.\mathrm{Equation}.Math..Math.4,\mathrm{solventPercent}.Math..Math.\mathrm{is}.Math..Math.\mathrm{calculated}.Math..Math.\mathrm{as}.Math.\text{:}& \mathrm{eq}..Math.6.1\\ .Math.\mathrm{solventPercent}=\frac{\mathrm{sC}}{\mathrm{sCU}}\times 100.Math.\%.Math.& \mathrm{eq}..Math.6.2\end{array}$

[0049] if (solventPercent>solventPercentMax) then solventPercent=solventPercentMax

aqueousPercent=100%−acidPercent−basePercent−solventPercent   eq. 6.3

[0050] The values for acidPercent, basePercent, solventPercent and aqueousPercent can be assigned to solvent A, B, C and D in the pumps.

Calculations for a One-Variable Look−Up Table from pK.sub.a

[0051] For a given pK.sub.a value

pH.sub.min=pK.sub.a−1

pH.sub.max=pK.sub.a+1

numPH=40

[0052] for arrayIndex=0 to arrayIndex=39,

[00010]$\begin{array}{cc}\mathrm{pH}\left[\mathrm{arrayIndex}\right]={\mathrm{pH}}_{\min }+\left({\mathrm{pH}}_{\max }-{\mathrm{pH}}_{\min }\right)\times \frac{\mathrm{arrayIndex}}{\mathrm{numPH}-1}& \mathrm{equation}.Math..Math.8\\ \mathrm{basePercen}.Math.t\left[\mathrm{arrayIndex}\right]=\frac{{10}^{-{\mathrm{pK}}_a}}{{10}^{-{\mathrm{pK}}_a}+{10}^{-\mathrm{pH}\left[\mathrm{arrayIndex}\right]}}\times 100.Math.\%& \mathrm{equation}.Math..Math.9\end{array}$

[0053] So, for example, for a pK.sub.a=6.8, pH.sub.min=5.8, pH.sub.max=6.5 and numPH=40,

[0054] a one-variable pH look-up table can be obtained from equations 8 and 9:

TABLE-US-00006 TABLE 4 one-variable pH look-up Base % pH 9.09% 5.8 . . . . . .   50% 6.8 . . . . . . 90.9% 7.8

[0055] The acid and base components can theoretically be any acid and base. In exemplary embodiments, the acid and base components each include combinations or mixtures of components to provide a combined mobile phase that is compatible with mass spectrometry, e.g., electrospray ionization mass spectrometry. For example, the acid solution can include maleic acid, citric acid and succinic acid. The base solution can include, for example, 4-methyl morpholine, morpholine, ammonium hydroxide and piperidine. Any suitable molar concentrations of the acid and base solution components can be selected. An exemplary acid solution can include or consist of 50 mM Maleic Acid, 25 mM Citric Acid, and 25 mM Succinic Acid. A corresponding exemplary base solution can include or consist of 50 mM 4-methyl Morpholine, 50 mM Morpholine, 50 mM Ammonium Hydroxide+50 mM Piperidine.

[0056] The solvent component can be any polar organic solvent compatible with reversed-phase LC/MS, e.g., acetone, acetonitrile, methanol, ethanol, n-propanol and isopropanol, tetrahydrofuran (THF) or any other compatible organic solvent.

[0057] Table 4 below illustrates an exemplary relationship between mobile phase pH and proportion of buffer solutions. Standard mixtures of the acid and base components were pipette and the pH was measured with a meter. Each sample was 80% water. The composition is expressed as % B (percent base) where % A (percent acid) is 20%-% B. The empirical table derived from these 21 points can be used by the data program to calculate the percentages of acid and base components required to deliver the programmed pH. As shown in Table 4, a broad pH range can be provided by mixtures of the acid and base components disclosed herein.

TABLE-US-00007 TABLE 4 % B pH 0 2.22 1 2.32 2 2.45 3 2.63 4 2.88 5 3.26 6 3.79 7 4.38 8 4.97 9 5.57 10 6.14 11 6.99 12 7.78 13 8.41 14 8.89 15 9.32 16 9.85 17 10.4 18 10.9 19 11.3 20 11.5

[0058] In a preferred embodiment, e.g. in a liquid chromatographic system, the calculations are carried out by a data program, implemented from the equations given herein above, governing directly a metering device, such as a pump and valve system, or any other equivalent means of delivering the components to the chromatography device. The program preferably includes the ability to correct for separations carried out at different temperatures, by including temperature in the empirically-derived look-up table (as in Table 3.3). As will be understood by one skilled in the art, the invention is not limited to any particular flow rate, any particular mixing system, or any particular method of generating a flow through a chromatographic device. For example, the method of the invention can be used in both low pressure liquid chromatography (where mixing occurs prior to pumping), and high pressure liquid chromatography, where pumping occurs prior to mixing.

EXAMPLE

Analysis of Metoclopramide Mixture

[0059] Instrument: [0060] ACQUITY UPLC H-Class System [0061] ACQUITY UPLC Photodiode Array Detector [0062] ACQUITY UPLC QDa Mass Detector [0063] ACQUITY Isocratic Solvent Manager with Restrictor [0064] Empower 3 Software

[0065] Column: CSH C18, 2.1—50 mm

[0066] Mobile Phase: [0067] Acid: 50 mM Maleic Acid; 25 mM Citric Acid; 25 mM Succinic Acid [0068] Base: 50 mM 4-methyl Morpholine; 50 mM Morpholine; 50 mM Ammonium Hydroxide; [0069] 50 mM Piperidine [0070] Water [0071] Methanol

[0072] Conditions: [0073] Gradient from 0-60% Methanol over 5 min at 0.6 mL/min at 40° C. Separations conducted at different pH conditions as discussed below.

[0074] Samples: [0075] MS Start-Up Solution, (Waters P/N 700002741) [0076] Metoclopramide and impurities 0.06 mg/mL of the API and each of the 8 impurities [0077] (Impurity A, B, C, D, F, G, H and 9)

[0078] The described invention was used to provide different separation buffers to adjust resolution in the separation.

[0079] The metoclopramide mixture was analyzed at different points across the range of pH controlled with the system disclosed herein. The separation was monitored with both UV detection and electrospray ionization mass spectrometry (ESI-MS). For example, each peak in the UV chromatogram is labeled with the mass identified by ESI-MS. All chromatographic runs employed the same gradient of increasing methanol (0-60% Methanol over 5 min at 0.6 mL/min at 40° C.). As shown in FIGS. 3A and 3B, the peak with m/z 316.1 is the last peak at pH 2.45 (FIG. 3A), but has moved to elute second at pH 6.45 (FIG. 3B). As shown in FIGS. 3C and 3D, the last two peaks move to later retention as pH is increased. At pH 8.45 (FIG. 3C), a small peak of m/z 182.0 becomes apparent as a coelution with m/z 300.1. At pH 10.45 (FIG. 3D), all 5 peaks are completely resolved.