Method and System for Liquid Choromatography Separations

This invention relates to liquid chromatography and more particularly to an automated system for performing isocratic interactive high performance liquid chromatographic separations and finding the optimum mobile phase strength and selectivity for use in such separations.

Liquid chromatography (LC) is a technique capable of separating a sample mixture into its components. The sample is transported through a separating column, using a mobile phase carrier, which resolves or separates the sample components such that they elute from the column in seriatim. A detector provides an electrical signal in response to each component, which signal appears graphically as a peak.

Chromatographic resolution of the components or peaks is dependent on many factors. Three primary factors that contribute to resolution (R.sub.s) are relative retention (K'), separation selectivity (.alpha.), and column efficiency (N). The factors are related to resolution by the equation ##EQU1## The mobile phase composition has a dominant influence on retention and selectivity. Changes in the mobile phase strength primarily affect the retention. Changes in the ingredients used in the mobile phase affects the specific chemical interactions in the resultant separation and therefore the selectivity. In the past, mobile phase strength and especially selectivity were adjusted empirically with an open-ended approach.

Chemical data is now available which classifies mobile phase solvents used in reverse phase and bonded phase LC according to the several selectivity interactions; proton acceptor, proton donor and dipole interaction. Similar data is available for the selectivity interactions or localization effects that affect separations in liquid-solid chromatography. These effects include a nonlocalizing solvent, a basic localizing solvent, and a nonbasic localizing solvent. These interactions are summarized in a so-called "selectivity triangle" with each apex representing one of the interactions. Mobile phase solvents are located within the triangle according to the relative contributions of these three interactions to the total solvent strength. Conversely, the location of each solvent is indicative of its selectivity effect.

This "selectivity triangle" has been used as the basis for rational solvent selectivity determinations. Recently, Glajch, Kirkland, Squire and Minor showed, in their article Optimization of Solvent Strength and Selectivity for Reversed-Phase Liquid Chromatography (J. Chromatogr. 199, 57 (1980)), an efficient and systematic technique for optimization of the mobile phase selectivity .alpha. for reversed phase LC separations. This technique uses four solvents, one from each apex of the selectivity triangle and a diluent, in various blends, which exhibit different selectivity but maintain constant retention K', to perform seven experiments. The computerized mapping technique used to facilitate finding the optimum solvent blend for the mobile phase is based on Snee (Experimenting with Mixtures, Chemtech, 9 (Nov.), 702 (1979)).

Even with these prior art techniques, it was difficult and time consuming to select the proper solvent strength (composition) for a particular retention. And since this selection had to be made for each of the three selectivity solvents, it became a slow and inefficient manual operation. In addition, for each of the seven experiments, the total number of sample injections required is one plus the number of components in the sample mixture. This also increased the time required. As a result, most chromatographers did not adopt these techniques and many separations were effected under less than desirable conditions. In those cases where proper conditions were attained, many more experiments than necessary were usually performed to determine such conditions.

Accordingly, it is an object of this invention to improve this traditional approach. The methods development procedure has been reduced to a series of logic steps to rapidly and systematically scout first mobile phase strength and second selectivity with a closed end approach. Third, this procedure has been automated which further increases its speed. And, fourth, the data from the scouting experiments is automatically evaluated to find the optimum mobile phase conditions and run the separation using such conditions.

The invention is a method and system for improving isocratic LC separations using improved logic and equations, a plurality of selectivity adjusting solvents, and system automation. Physically, the system is comprised of: a pump module; a source of supply for the solvents connected to the input of the pump module; a separating column connected to the output of the pump module; and automatic sampler module coupled to introduce samples to the input of the column; a detector connected to the output of the column, and a controller module coupled to the pump module, the automatic sampler and to the detector. The controller also contains methods development and automation software for determining the optimum mobile phase composition and precisely controlling the operation of the system using such composition.

Using the method and/or system of this invention the user can automatically obtain the isocratic mobile phase composition required for optimum separation of all of the components in a complex sample mixture given a set of starting conditions. They may be used for either reversed phase or normal phase chromatography and are based upon the use of four solvents and results in an optimization of solvent strength and selectivity. This results in significantly increased speed of methods development and provides faster, more accurate analyses, all on an automatic basis without the direct intervention of a human operator. In one aspect of the invention, the controller determines mobile phase composition to provide a chosen value of retention for each of the three binary mixtures. Alternatively, or as a later step in the procedure the controller automatically scouts mobile phase compositions to find the optimum selectivity. The controller automatically adjusts the mobile phase solvent composition to provide a chosen value of retention and with such retention to provide optimum solvent selectivity or optimum resolution in a sample separation. Also, the controller identifies elution orders of the sample components in the seven liquid chromatographic experiments.

FIG. 1 is a block diagram of the chromatographic system of the invention.

FIG. 2 is a schematic diagram of the solvent system of this invention.

FIGS. 3-3N are flow diagrams of the various programs used to operate a preferred embodiment of this invention.

FIG. 4 is a solvent selectivity triangle for solvents used in reverse phase and normal bonded phase chromatography.

FIG. 5 is a solvent optimization triangle showing seven experiments needed to optimize LC resolution.

There is attached hereto Appendix I which is a program listing Basic of a program used to implement the method and system of this invention as described in the flow diagram of FIGS. 3-3N. "AUTOST" provides the user imputs described in this application as part of the SAMPLE section. In addition "DOWNLD" and 4100 contained basic calculations required throughout all the sections. "EQUIL2" is a subroutine which is taught any time the column is to be equilibrated. The SCOUT, SEARCH and SOLVE programs correspond directly with the SCOUT, SEARCH and SOLVE sections described in this application. The SEPARATE section is a combination of the programs labeled %B, C, D and SORT.

Referring to FIG. 1, there is seen an LC system that may be used in performing the method of this invention. The system includes as its main elements a controller module 1, a pump module 2, a column module, an automatic sampler 3 and a conventional LC detector 5 such as an absorbance detector. The controller 1 is a microprocessor-based instrument which provides timing signals for solenoid valves and drive signals for a stepper drive motor for the pump in the pump module 2 via cable 9. Communications between controller 1, column compartment 4 and detector 5 are accomplished using a general purpose interface bus 11. The controller 1 provides sample injection pulses and timing control to the autosampler 3 via cable 8. Communications between controller 1 and data system 6 is accomplished via cable 10 using a standard current loop configuration. The data system 6 receives an analog signal from the detector 5 via cable 12 whose signal level (a peak) represents the absorbance or concentration of a sample component entrained in the mobile phase passing through the detector cell. It converts the analog signal into digital form and stores it until needed by the controller. All of the components are of conventional design and are available commercially from various vendors. The controller 1 provides visual information to the operator via the graphics display module 7. Displayed information is sent over cable 13.

As noted above, it is possible to obtain selected retention times and to optimize either the selectivity or the resolution of LC separations by adjusting the makeup and strength of the mobile phase. The adjustments and their relation to the LC system may be better understood with reference to FIGS. 2, 3, 4 and 5. In these figures, the quaternary solvents used to make up the mobile phase are derived each of four separate solvent reservoirs designated in FIG. 2 by the letters A, B, C, and D respectively. It is known from equation (1) that the resolution R.sub.s, which is a quantitative measure of the relative separation of the peaks, is a function of column efficiency N, retention k', and selectivity .alpha.. The retention k' is a function of mobile phase solvent strength whereas the selectivity factor .alpha. is a measure of chemical difference between the solvent components of the mobile phase. It is these two factors which are automatically varied by the system and method of this invention to achieve the desired retentions and optimizations.

L. R. Snyder in his article in J. Chromatographic Science, volume 16, page 223 (1978) developed a selectivity classification triangle which positions solvents within the triangle according to the solvent's contribution to the three factors at the apices of the triangle to the total solvent strength. The apices of the triangle are determined in the case of reverse and bonded phase LC by proton acceptor, proton donor and dipole interaction as may be seen in FIG. 4. For the liquid-solid LC selectivity triangle (not shown), the apices represent the selectivity factors nonlocalizing solvent (methylene chloride-CH.sub.2 Cl.sub.2), a basic localizing solvent (methytert-butyl ether-MTBE) and a nonbasic localizing solvent (acetonitrile-ACN). Hexane may be used as the fourth or strength-adjusting solvent.

In order to optimize solvent selectivity, these solvents are selected from groups near the respective apices of the triangle in order to obtain large differences in the selectivities of the solvents. The solvents are blended to obtain intermediate selectivities. The three selectivity adjusting solvents for normal phase chromatography are ether-MTBE, methylene chloride-CH.sub.2 Cl.sub.2, and chloroform-CHCl.sub.3. The fourth or strength adjusting solvent is hexane. These are shown interconnected by dashed lines. The three solvents typically used for reverse phase chromatography, methanol-MeOH, tetrahydrofuran-THF, and acetonitrile-ACN, are shown in FIG. 4 connected by the dash dot lines. In this instance the strength adjusting solvent is water.

These respective groupings of four solvents thus make up the several inputs A, B, C, D of FIG. 2. By convention, for reverse phase chromatography, the strength adjusting solvent is solvent A, solvent B is the strongest proton acceptor solvent, solvent C is the strongest proton donor, and solvent D is the strongest dipple interactor. Thus for reverse phase separations, water is A, MeOH is B, ACN is C, and THF is D. A similar convention is used for other types of chromatography. These solvents are introduced on a timed basis by solenoid valves 9 and mixed. The resulting composition is dictated by the relative open time of each valve and is brought to high pressure by the pump 2a. The solvent stream passes through connecting tubing 10 to the injection valve 4a in column compartment 4. A liquid sample from the autosampler 3 is introduced into the liquid stream from the pump 2a via line 3a and injection valve 4a. When the valve is actuated, the sample passes through the separating column 4b. If the components of the sample each have different affinities for the packing material contained in the column 4b, the output of the column is a band of each component, each having a particular retention on the column.

The output of the column is passed through tubing 14 to the detector 5. In the preferred embodiment, this includes an ultraviolet lamp 5a , a photodiode assembly 5b and an aperture 5c positioned between the lamp and the photodiode assembly. Using this detector, the output of the column is irradiated by the ultraviolet lamp 5a whose output is filtered in a band centered at 254 nanometers. The photodiode assembly 5b measures the amount of ultraviolet light passing through the aperture 5c. As each sample component passes through the detector, the resulting ultraviolet level at the photodiode assembly 5b changes. The photodiode assembly output is converted to an analog voltage representing the peak or sample component. The sample is then passed through tubing 16 to a waste container 17.

The method and system of this invention perform what may be grouped into five different modes of operation. The first mode, designated SAMPLE, provides automatic injection and automatic sampling as required during the following four steps. Also during this mode, the operator introduces into the system, through the microprocessor, the desired column and solvent equilibration times, analysis times and data acquisition functions that he desires.

The next operational mode, designated SCOUT, effects a standard gradient run using one of the solvents depicted in FIG. 4 for the selected type of chromatography. Based on this gradient run, the peak retentions obtained are examined and translated to corresponding isocratic conditions. The desired retention range of the sample is inputted to the microprocessor in the controller in terms of the retention factor of the last sample peak. The controller uses a novel routine to predict the isocratic solvent composition required for the desired retention factor. The particular relationship used in making this conversion will be discussed in the following sections in an example using reverse phase chromatography.

The next operational mode, designated SEARCH, sets up the experimental conditions established during the SCOUT routine and chromtographs the sample with the initial solvent pair selected and compares the data obtained with the desired value of the retention factor. If the actual retention factor K' is not within the desired range, the system used the data from the first separation to recalculate and establish the next solvent composition to produce the desired k'. When an acceptable retention factor k' is obtained for the first solvent, the equivalent solvent strength for the remaining two solvents is then calculated using the equation S.sub.t =.SIGMA.S.sub.i .phi..sub.i where S.sub.t is the total solvent strength, S.sub.i are the solvent strength weighting factors for each component and .phi..sub.i are the volume fractions of each component. The %B is equal to 100 times .phi..sub.B. Experiments are performed to verify the predictions and recalculate as above.

In the next operational mode, SEPARATE, the retention time of each component contained in the sample mixture is determined for each of the seven mobile phase blends described in the method development triangle depicted in FIG. 5 as taught by Glajch et al. The compositions of the mobile phase, as represented by the apices of the triangle, are calculated from the results of the prior SEARCH mode of operation. Experiments 4, 5 and 6 use ternary mobile phases which are calculated from the three predetermined binary mobile phases taken two at a time. For example, in FIG. 5, the series of three members refer to the relative contribution of the three selectivity solvents B, C and D to the total selectivity, i.e., the ternary mobile phase at point 6 is made up of half of mobile phases Nos. 1 and 3. The condition used in experiment 7 is a quaternary mobile phase whose composition is also calculated from the three binary mobile phases. The separations obtained from experiments 4 through 7 together with those from 1 through 3 provide a sufficient data base to generate a closed-ended optimization of the separation. The retention data obtained during the SEPARATE mode is used to identify the retention position of each compound in each experiment. SOLVE, the last operation, then uses this data to provide an overlapping resolution map (ORM) using conventional statistical computer routines for all peak pairs. These computerized mapping techiques are discussed by Snee in his article referred to above. Based upon this ORM map an optimum solvent composition for obtaining the optimum resolution for the overall separation can be predicted. The data generated during the four operational modes results in an automatically obtained analysis (SOLVE) of the sample under evaluation using optimum resolution conditions according to the desire of the operator.

In an alternative embodiment of the invention, using this same ORM map, a separation based on optimum solvent selectivity may be effected. This is accomplished by taking the data from the seven experiments and from this data calculating the retention behavior of each composition with any mobile phase composition described by the triangle. With this complete description of retention, either selectivity or resolution can be calculated. The optimization procedure searches for the maximum value of either resolution or selectivity. The predicted compositions may be different because the selectivity optimization ignores the effect of K' on resolution. Resolution is proportional to K'/k'+1.

To better understand the particular mechanisms of these five operational modes, they will be explained in detail with respect to a reverse phase separation utilizing the solvents, methanol (MeOH), acetonitrile (CH.sub.3 CN) and tetrahydrofuran (THF) with water as the strength adjusting solvent.

FIGS. 3 through 3N contain the flow chart of a preferred controller program for automatically performing separations at optimum resolution. Also, Appendix I contains a listing of a computer program used to implement this flow chart. Turning to FIG. 3, the operator interface is shown. The controller program is divided into five distinct sections: SAMPLE, SCOUT, SEARCH, SEPARATE and SOLVE. Any individual program section or sequential combination is allowed to be run.

The operator's first action is to select the first and last modes or sections to be run. This is accomplished typically by positioning arrows on a graphics display module via the controller keyboard. Depending on the programs selected, the operator is prompted to provide the necessary inputs. Typical inputs during the SAMPLE mode include void volume of the column, desired k', number of standards to be run, initial % methanol (MeOH), initial % acetonitrile (CH.sub.3 CN), and initial % tetrahydrofuran (THF). Water is used as the strength adjusting solvent. The program then branches to FIG. 3A if SCOUT is the first section to run, to FIG. 3C if SEARCH is the first section to run, to FIG. 3H if SEPARATE is the first section to run, or to FIG. 3M if SOLVE is the first section to run. Further discussion is based on assumption that the entire program SCOUT through SOLVE will be run.

Referring to FIG. 3A, if SCOUT is to be run, the controller first sets up a standard gradient LC run consisting of a flow rate of 3 ml/min, oven temperature of 50.degree. C. and linear gradient profile of 100% water to 100% methanol (one of the solvents of the solvent triangle) in 20 minutes and holding at 100% methanol for 10 minutes. These values are suitable for a majority of samples. In this illustrative example, it is assumed the sample contains the steroids Prednisone, Cortisone, Hydrocortisone, Dexamethasome, Corticosterone, and Cortexolone. The user is instructed that a Zorbax.RTM. C-8 packed column (0.46.times.15 cm) is to be used for this step. The pump is started and an equilibration clock in the controller 1 begins runnings. When the equilibration clock reaches the preset time of a sample of the steriod mixture from the first vial is injected. The user has been instructed that the first sample vial must contain the sample mixture while the next six vials contain standard solutions of each of the steroids. The controller 1 starts measuring time since the injection was made. When 30 minutes has elapsed, the controller commands the data system to send the retention times, peak areas and baseline correction codes, derived from the gradient run and stored in the data system 6, to the controller 1.

Turning to FIG. 3B, the flow chart indicates the controller finds the largest peak retention time t.sub.R that occurred during the gradient runs. When this is done, the controller checks the baseline correction code for that retention time. This is done to eliminate the possibility of baseline shifts or other effects from being counted as a peak. If the baseline correction code is greater than 10, which could occur for example if the largest retention time is caused by refractive index effects, the peak with the second largest retention time is selected for use in computations.

The next two calculations are carried out to define the linear dependence of the logarithm of isocratic retention (k') on % methanol in the mobile phase. First, the Y-axis intercept (L.sub.1) of the log k' vs % MEOH plot is calculated using the formula:

where

A=0.00233 B=-0.06118

C=0.63021

D=0.57685 and x=largest retention time.

The slope (D.sub.2) of the log k' vs % MeOH (or %B) plot (the line defining relationship between the retention and solvent strength) is now computed based on L.sub.1 calculated from equation (1) as follows:

Next, knowing the slope and the Y-axis intercept of the line defining this relationship, the isocratic % of methanol (E.sub.1) necessary to obtain the desired k' is predicted using the equation:

Note that all percentages calculated in this and other sections are adjustable to match the the instrument (e.g. 66.66666% is truncated to 66% for an instrument with a 1% minimum increment).

The predicted value of E.sub.1 is first checked to see if it is more than 100%. If so the predicted value is set at 100%. Next, the predicted E.sub.1 is checked to see if the % methanol in water predicted is less than zero. If so, a value of 20% methanol is used. % B is now determined.

The operator's selection of programs is examined. If SCOUT was to be the only program run, the controller prints its predicted % B, then stops. If not, the controller moves into the SEARCH section or mode.

Referring to FIG. 3C, the first SEARCH operation performed is to check whether this is the first section run. If yes, the operator-supplied value for initial % methanol is used. If not, the predicted isocratic % methanol from SCOUT is used.

The controller now sets the % methanol and % water (100-% methanol) into the current conditions memory location and starts an equilibration timer. When the equilibration timer reaches a predetermined value, a sample is injected, again from the first sample vial and a run time clock begins.

Turning to FIG. 3D, when the run time clock reaches its predetermined value, indicating completion of the run, the controller sends for the peak areas, retention times and baseline correction codes from the data system. The controller now computes the retention factor k' for the peak with the largest retention time using the formula: ##EQU2##

The k' (result) is now compared to k' (desired). If k' (result) is greater than 90% of k' (desired) Flag 1 is set to 1. If k' (result) is less than 110% of k' (desired) Flag 2 is set to 1.

Referring to FIG. 3E, the status of Flags 1 and 2 is checked. If both are 1, then the k' result) is considered to have satisfied k' (desired). Under these circumstances, the program jumps to FIG. 3G. The first step is to identify which solvent conditions have been satisfied and to store the conditions. If the last k' (result) was obtained under methanol/water conditions, the next combination to be run is solvent C from the solventtriangle, i.e., acetonitrile/water. If the last k' (result) was obtained from acetonitrile/water, then the next combination is the third solvent D from the solvent triangle, i.e., tetrahydrofuran/water. When another solvent is to be tested, the initial percent is calculated from the relative strength values, using the equation S.sub.T =.SIGMA.S.sub.i .phi..sub.i described previously. The program then returns to FIG. 3F. In the preferred embodiment, S.sub.A =0; S.sub.B =2.67; S.sub.C =3.14; and S.sub.D =4.40. This equation, when solved for the particular solvents of this exemplary program, is: ##EQU3## If the last run was tetrahydrofuran/water, then the SEARCH section ends since this is always the last combination to be run. Each value of the solvent composition which gives the desired k' is stored as soon as it is verified.

Referring back to FIG. 3E, if the k' (result) does not satisfy the requirements of k' (desired) in the initial SEARCH run using methanol/water, a new value for the mobile phase strength must be determined. This is accomplished by redetermining the log k'-solvent strength linear relationship using the actual value of log k' obtained. Specifically, the slope of the new line is computed by assuming that the relationship between log k' and % B is linear and that equation (2) holds. Then the slope may be ascertained in terms of the log k' (result). If the k' (result) is the first k' obtained for the particular combination of mobile phases, this new slope is computed using the formula: ##EQU4##

If more than one result for a given mobile phase has been obtained, then the formula is: ##EQU5##

The next step is to predict a new value for the % methanol. First, we compute the new Y-axis intercept using the new slope using the formula: ##EQU6##

The new solvent composition is computed using the following formula: ##EQU7## The % solvent (new) is tested to ensure that a value of less than 0 hasn't been computed. If it has, the % solvent used in the previous run is divided by 3 and used as the new % solvent.

Turning to FIG. 3F, the % solvent (new) is tested for any value greater than 100%. If the value is greater than 100, then the % solvent (new) is computed by: ##EQU8##

The next step is to find the 100's complement to the % solvent (new). When this is done, the computed conditions are loaded into current conditions memory and the equilibration timer started.

When the equilibration timer determines the end of the delay time (FIG. 3C), a sample is injected from the first sample vial and the entire process repeats.

After all % solvents have been determined, the program shifts to FIG. 3G. A summary table is printed and the operator's inputs on FIG. 3 are examined. If the operator specified to run the SEPARATE section, the controller automatically proceeds to it (FIG. 3H), otherwise the program stops.

Referring to FIG. 3H, the SEPARATE section or mode of the software is shown. The first test is to determine if SEPARATE is the first section run. If it is, the operator-supplied values for % methanol, % acetonitrile and % tetrahydrofuran are used; otherwise the values determined in SEARCH are used.

The solvent compositions for all seven experiments are now computed and stored in the controller memory. The values of X, Y and Z are taken either from the operator's input or from SEARCH and ratioed according to the solvent triangle described in connection with FIG. 5. In the case at hand, these values would be:

The water content in each experiment is the 100's complement of the sum of the % solvent used. The first experiment is loaded into current conditions memory, the pump started and an equilibration timer starts.

When the equilibration timer completes its timeout, a sample is injected (FIG. 3I) from the first sample vial and the run timer starts. This is the first sample vial position, in which the user has inserted the sample mixture. When the run timer is finished, the controller sends for the retention times, peak area and baseline correction codes from the data system and stores this information for later use.

For SEPARATE, unlike SCOUT or SEARCH, more than one vial is required in the autosampler. The first sample vial must contain the sample mixture, and subsequent sample vials must contain standard solutions of compounds found in the sample mixture. Flush vials, used to eliminate cross-contamination, can be present anywhere in the sequence.

The autosampler now moves to the next sample vial and makes an injection. The run timer reinitiates and runs until it times out. Upon timeout, the controller sends for the information from the data system. Since this is not the first vial, it must contain one component of the sample mixture and that component is assumed to be the major peak of the chromatogram.

Turning to FIG. 3J, the routine used to identify the major peak is shown. The simplest identification is to use the peak with the largest area. However, in order to eliminate the requirement for pure standards, a secondary selection process is also used. All peak areas received from the data system are examined to see if any have an area greater than 75% of the largest. If not, then the largest area is used. If another peak has an area which qualitifies, the baseline codes are examined. Priority is assigned to a baseline code of 01 which indicates a baseline resolved peak. The second highest priority is assigned to the peak with a code 03, which is the last of a fused group.

Referring to FIG. 3K, if a peak doesn't qualify under one of the above priorities, then the peak with the largest area is used. In either case, the program now discards all information concerning peaks other than the selected peak from the standard vial under test.

This process repeats for each successive standard vial until the total number of standard vials run equals the number of standards the operator said were to be run. At this point, the retention factors k' are computed for all peaks remaining in memory using formula (4) shown above.

Turning to FIG. 3L, the first operation is to sort the results obtained from the sample vial chromatograph run against the results obtained from the chromatograph runs of the standard vials. To allow for variances in the retention factor k', a sliding scale is used. For k' less than 1, a 15% tolerance is allowed; for k' equal to or greater than 1 but less than 10, 10% is allowed; and for k' greater than or equal to 10, a 5% tolerance is allowed. This routine assigns a mixture peak number to each standards vial.

After the first experiment run on the first or sample vial, a map array is constructed. This array creates a correspondence between the peak elution order in the first experiment and the vial codes. For convention, the vial code is X for the sample vial, which is vial #1 in the autosampler. The following vials, numbered 2 and up, which each contain a single standard solution, each corresponding to one of the different sample components, are coded alphabetically A, B, C, etc. The map array consist of a series of 2 entries, a vial code, and the first experiment elution order number. All further data presentations utilize the first experiment elution number.

The data is now placed in a cumulative array which forms the basis of a printed report. As each experiment is completed, the results are put into the array and the entire contents printed out.

The program now determines if the last experiment run was Experiment 7. If not, the controller places the conditions for the next experiment into the current conditions memory, starts the equilibration timer and repeats all the injections. If the last experiment was number 7, the program ascertains if SOLVE is to be executed. If not the system stops.

If "SOLVE" is to be run, the values of the selectivity solvents methanol, acetonitrile and tetrahydrofuran (in percent) that were used for the first three experiments and the number of standards are read from memory. Next, the retention factor k' for each standard for all experiments is read from memory. Using these data, an ORM map is used to predict and then execute a sample separation using optimum resolution or separating conditions. To accomplish this, as taught by Snee; seven coefficients .beta. are calculated for each standard according to the following formulae: ##EQU9## These coefficients describe the k' behavior of the standard at any blend of the three mobile phases from experiments 1, 2 and 3. The composition of such a blend is defined by three mixture coordinates X.sub.1, X.sub.2 and X.sub.3. The sum of X.sub.1 +X.sub.2 +X.sub.3 is always one. In this system X.sub.1 =0.5, X.sub.2 =0.3, X.sub.3 =0.2 means the blend consists of 50% Experiment 1 mobile phase, 30% Experiment 2 mobile phase, and 20% Experiment 3 mobile phase. The k' of each standard with any specific blend can be determined from the following equation: ##EQU10## The SOLVE program generates a comprehensive set of mixture coordinates, and for each set of coordinates predicts the k's of all standards. Using this data the separation factor between any two peaks can be calculated as shown below:

The separation factor is equal to the resolution divided by one half the square root of the efficiency. The lowest value of the separation factor limits the quality of the chomatography. This value is called the critical resolution factor. For each set of coordinates the critical resolution factor is stored.

The program then evaluates all mixture coordinates to determine the specific coordinates which give the maximum and minimum critical resolution factor. The maximum and minimum values are used to establish a critical resolution range. From this data the computer assigns symbols which correspond to certain fractions of the critical resolution range. A symbol in then assigned to each set of mixture coordinates based on its critical resolution. Then, the "solve" program plots the symbols in an overlapping resolution map and prints the composition required to give the best separation (maximum critical resolution factor) based on the previously stored coordinate and the original percentages of methanol, acetonitrile and tetrahydrofuran. Finally this optimum composition is loaded into the current memory and after equilibration an injection from the first vial is made and the separation completed. The program now stops.

While the method and system example and equation (2), 2(a) in the SCOUT program are based on specific conditions, these equations have relatively broad applicability. Successful extension of the equations used in SCOUT is predicted by theoretical gradient equations such as: ##EQU11## This equation states that the experimental results will be exactly the same if the ratio of gradient time (.DELTA.t) to composition change (.DELTA..phi.) is held constant and/or if the ratio of column volume (Vm) to flow (F) is constant. This means that there is an infinite number of chromatographic conditions defined by the above restrictions for which the SCOUT equation is strictly applicable.

These equations have been applied on other reversed phase columns, at other temperatures and with acetonitrile instead of methanol as the B solvent. The system has also been used sucessfully where a variety of modifiers have been used in the water reservoir, e.g., acetic acid buffers. In these cases, the program provided very useful predictions. Each of these conditions also implies an infinite set of variations as described by the above equation.

Beyond reversed phase, the equations are untested. It is believed that for normal bonded phase chromatography, there is a reasonable chance of success. In adsorption chromatography, the chances are less due to the differing separation mechanism. However, it probably would be possible to adapt the gradient program to provide a similar change in gradient shape and steepness (change in solvent strength per time) to make the equation equally applicable.

While the SCOUT program has the above noted limitations, the remaining sections not so limited. They may be applied to other temperatures, flow rates, with other columns, different solvents, and even in different modes.

In the event that it is desired to optimize selectivity instead of resolution, the program listing of Appendix I is slightly modified. Specifically, in the SOLVE program, to change from resolution optimization to selectivity optimization, the program is slightly modified. Line 940 is changed to R=A2 and line 950 is changed from IF R<O then R=-R . . . to IF R<1 then R=1/R. ##SPC1## ##SPC2##