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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
J Chromatogr A. Author manuscript; available in PMC 2010 August 28.
Published in final edited form as:
PMCID: PMC2769502
NIHMSID: NIHMS131565

Mathematical Model of Computer-Programmed Intermittent Dual Countercurrent Chromatography Applied to Hydrostatic and Hydrodynamic Equilibrium Systems

Abstract

Dual high-speed countercurrent chromatography (Dual CCC) literally permits countercurrent flow of two immiscible solvent phases continuously through the coiled column for separation of solutes according to their partition coefficients. Application of this technique has been successfully demonstrated by separation of analytes by gas-liquid and liquid-liquid two-phase systems. However, the method can not be directly applied to the system with a set of coiled columns connected in series, since the countercurrent process is interrupted at the junction between the columns. However, this problem can be solved by intermittent dual CCC by eluting each phase alternately through the opposite ends of the separation column. This mode of application has an advantage over the conventional dual CCC in that the method can be applied to all types of CCC systems including hydrostatic equilibrium systems such as toroidal coil CCC and centrifugal partition chromatography. Recently, the application of this method to high-speed CCC (hydrodynamic system) has been demonstrated for separation of natural products by Hewitson et al. using a set of conventional multilayer coil separation columns connected in series. Here, we have developed a mathematical model for this intermittent dual CCC system to predict retention time of the analytes, and using a simplified model system the validity of the model is justified by a series of basic studies on both hydrodynamic and hydrostatic CCC systems with a computer-programmed single sliding valve. The present method has been successfully applied to spiral tube assembly high-speed CCC (hydrodynamic system) and toroidal coil CCC (hydrostatic system) for separation of DNP-amino acid samples with two biphasic solvent systems composed of hexane-ethyl acetate-methanol-0.1 M hydrochloric acid (1:1:1:1 and 4:5:4:5, v/v).

Keywords: programmed intermittent dual countercurrent chromatography, mathematical model, spiral tube assembly, toroidal coil countercurrent chromatography, sliding valve, hydrostatic and hydrodynamic equilibrium systems

1. Introduction

High-speed countercurrent chromatography (HSCCC) has been widely used for the separation and purification of natural products [1-3]. However, closely related compounds which give similar partition coefficients in the two-phase solvent system were still difficult to separate by this method. Usually one can improve the resolution of these compounds by increasing the length of the column or using multidimensional countercurrent chromatography technique with two columns each mounted on a separate high-speed CCC centrifuge [4]. Alternatively, enhanced peak resolution can be achieved by dual CCC where mutually equilibrated two solvent phases are simultaneously eluted each in opposite directions while the sample is injected at the middle portion of the column [5]. This method permits the retention of target compounds in the column for a longer period of time by adjusting their partition coefficients hence improving the peak resolution. Since 1985, dual CCC has been successfully applied to HSCCC with a multilayer coil separation column for separation of dyes and proteins [6], antibiotics [7] and natural products [5]. Recently the dual CCC was applied for pesticide analysis from food using an HSCCC centrifuge [8]. More recently dual counter-current extraction (CCCE) has been successfully applied for liquor separation with continuous sample injection to give a throughput of 30 g/h [9].

However, the operation of continuous dual CCC described above is limited to a separation column that consists of a single multilayer coil. In order to perform this dual CCC operation in a set of multilayer coils connected in series, it is necessary to modify the system to intermittent dual CCC by alternately eluting the two phases in the opposite directions through the column at given intervals. This intermittent dual CCC method has been successfully applied to the separation using a pair of multilayer coil columns mounted on a high-speed CCC centrifuge [10-13].

In the present paper, a mathematic model on intermittent dual CCC is proposed and, using a simplified model system, the validity of the theory is justified by the separation of a set of DNP-amino acid test samples with the two-phase solvent system composed of hexane-ethyl acetate-methol-0.l M hydrochloric acid in both hydrodynamic (spiral HSCCC) and hydrostatic (toroidal coil CCC) instruments by the aid of a computer-programmed 10-port single sliding valve.

2. Theory

Mathematical analysis of intermittent dual countercurrent chromatography has been proposed as follows:

2.1. General Model

Retention time of the solute peak for intermittent dual CCC is mathematically analyzed. The method elutes each phase alternately through the opposite ends of the separation column at a given interval and flow rate while the sample solution is charged at the middle portion of the column as shown in Fig. 1A. At the hydrodynamic equilibrium state established in each elution mode, the separation channel with a cross sectional area Ac is divided into the area occupied by the lower phase, AL, and the upper phase, AU. Here we assume that the two phases are uniformly distributed at a given volume ratio throughout the channel. As indicated in the figure, the lower phase is introduced from the left terminal at a flow rate of FL ml/min and the upper phase from the right terminal at a flow rate of FU ml/min intermittently at given intervals, ti, L and ti, U, respectively. Then, the analysis of the solute peak motion in the channel is divided into two parts, i.e., for the forward (from left to right) elution and the backward (right to left) elution as follows:

Fig 1
Schematic diagram for mathematical model of intermittent countercurrent chromatography. A) general model; B) present model.

For lower phase elution, the lower mobile phase is introduced from the left side of the channel at FLml/min flows through the channel at a linear velocity of μL cm/min,

μL=(FL/AC)(AU,L+AL,L)/AL,L=(FL/AC)(βL+1)
(1)

where βL = AU,L/AL,L (volume ratio of two phases when lower phase mobile). Then the solute in the lower phase moves forward through the channel at a rate of μX,L cm/min according to its partition coefficient, K, and the volume ratio of the two phases in the channel,

μX,L=(FL/AC)(βL+1)/(1+KβL)
(2)

where K = concentration of solute in the upper phase divided by that in the lower phase.

Similarly in the backward elution, the upper mobile phase introduced from the right end of the channel at FU ml/min flows through the channel at a linear velocity of μU cm/min,

μU=(FU/AC)(AU,U+AL,U)/AU,U=(FU/AC)(1+1/βU)
(3)

where βU = AU,U/AL,U (volume ratio of two phases when upper phase mobile) and the solute in the mobile upper phase moves backward through the channel at a rate of μX,U cm/min according to K (concentration of solute in the upper phase divided by that in the lower phase) and the two-phase volume ratio in the channel, or

μX,U=(FU/AC)(1+1/βU)[KβU/(1+KβU)]=(FU/AC)K(1+βU)/(1+KβU)]
(4).

Then, from Eq (2) and (4) the average linear velocity (μX,i) of the solute peak is given by

μX,i=(μX,Lti,LμX,Uti,U)/(ti,L+ti,U)=[(FL/A)ti,L(βL+1)/(1+KβL)(FU/A)ti,UK(1+βU)/(1+KβU)]/(ti,L+ti,U)
(5)

where ti, L and ti, U indicate the unit programmed time for forward and backward elution, respectively.

Therefore, the retention time (tR) of solute at the end of the unit programmed dual elution is computed from the following equation,

tR=L/|μX,i|=0.5Vc(ti,L+ti,U)/|FLti,L(1+βL)/(1+KβL)FUti,UK(1+βU)/(1+KβU)|
(6)

where L is a half length of the channel and Vc, the total capacity of the channel where Vc = 2LAc. When μX,LX,U or μX,i>0, the solute peak moves forward and is eluted from the right terminal of the channel, and when μX,LX,U or μX,i<0, it moves backward and is eluted from the left terminal of the channel. If μX,LX,U or μX,i = 0, tR becomes infinite and the solute peak will be permanently retained within the channel.

In a simplified case of ti, U = 0, Eq (6) is reduced to a familiar form,

FLtR=RS=VL+KVU
(7)

where RS is the retention volume, and VL and VU are volume of the lower mobile phase and upper stationary phase in the column, respectively. Similarly, if ti, L = 0, Eq (6) becomes

FUtR=RS=VU+VL/K
(8)

and the solute peak would be eluted from the left outlet of the channel.

2.2. Simplified Model

In the simplified study, only the right half of the above separation channel is used and the sample was injected at the left terminal with the lower mobile phase as shown in Fig. 1B for both hydrostatic and hydrodynamic systems. In order to avoid the elution of the test sample through the left terminal with the upper mobile phase, the partition coefficient was chosen to satisfy the formula

FLti,L(1+βL)/(1+KβL)>FUti,UK(1+βU)/(1+KβU)
(9).

As discussed later, there are some considerations required for application of the above formula to each CCC system.

3. Experimental

3.1. Apparatus

The following two different types of centrifugal CCC instruments were employed in the simplified studies: one is the hydrostatic equilibrium system (toroidal coil CCC) [14] and the other, the hydrodynamic equilibrium system (type-J high-speed CCC) [15].

The apparatus of the hydrostatic system is a rotary-seal-free centrifuge fabricated by Pharma-Tech Research Corporation, Baltimore, Maryland, USA. It holds an aluminum rotary plate measuring about 34 cm in diameter to mount a toroidal coil separation column. The column is made by winding ca 1 mm ID PTFE (polytetrafluoroethylene) tubing (SW No. 18, Zeus Industrial Products, Orangeburg, SC, USA) onto a 2.4 m long, 4 mm O.D. nylon pipe making ca 1200 helical turns with a total capacity of about 15 ml. It is mounted around the periphery of the rotary plate at a distance of about 15 cm from the central axis of the centrifuge. Each terminal of this toroidal column is connected to a flow tube with a tubing connector (Upchurch Scientific, Palm Spring, CA, USA). These flow tubes are put together and passed through the center of the central shaft downward and the hollow horizontal shaft of a miter gear, then led upward into the vertical hollow tube support, and finally exit the centrifuge from the center of the upper plate where they are tightly held with a pair of clamps. The rotational speed of the separation column was regulated with a speed controller at 1000 rpm.

The apparatus of the hydrodynamic equilibrium system is a J-type coil planet centrifuge manufactured by P.C. Inc., Potomac, MD, USA. It holds a separation column on one side and a counterweight on the other side of the rotor symmetrically at 10 cm from the central axis of the apparatus. The spiral tube assembly for HSCCC was designed in our laboratory and fabricated in the National Institutes of Health Machine Instrumentation Facility. This original spiral tube assembly was made from an aluminum disk with channels, 5 cm deep and 3 mm in width forming the four interwoven spirals. The β values of each spiral are circa 0.25 at the inner terminal and 0.75 at the outer terminal. The sharp turn at each end of the radial grooves was rounded to prevent kinking of the tubing. The column is made by inserting a single piece of fluorinated plastic cross-pressed tubing of 1.6 mm I.D. (PTFE SW No. 14, Zeus Industrial Products, Orangeburg, SC, USA) into the grooves making four spirals in each layer. Therefore, the present design of the spiral tube assembly requires placing a set of four transfer tubes in radial grooves between the neighboring spiral tube layers, taking up the column space, thus limiting the column capacity. In order to increase the column capacity, the tubing in the four radial grooves was pressed down with a metal or hard plastic tool that fits into two or all four of the grooves. The spiral tube assembly consists of 13 spiral layers with a total capacity of 130 ml12. The rotational rate of the apparatus is regulated up to 800 rpm with a speed controller (Bodine Electric, Chicago, IL, USA).

In both instruments two metering pumps (Shimadzu LC-10ADVP, Columbia, MD, USA) were used for pumping the solvents, and the effluent was continuously monitored with a UV detector (LKB Instruments, Stockholm, Sweden).

Switching between normal and reverse phases was carried out at regular intervals by a 10-port sliding valve (MX Series II, Idex Health and Science Group, Oak Harbor, WA, USA) controlled by a Rheodyne TitanMX control software (Idex Health and Science Group, Oak Harbor, WA, USA) as described later (Fig. 2).

Fig 2
Schematic diagram of a single sliding valve for computer-programmed intermittent dual countercurrent chromatography A) valve position I; B) valve position II.

Dimensions of the separation columns used in the simplified studies are listed in Table 1

Table 1
Dimensions of the separation columns and experimental conditions in DNP-amino acids separation.

3.2. Reagents

Hexane, ethyl acetate and methanol were purchased from Fisher Scientific, Fair Lawn, NJ, USA and hydrochloric acid was purchased from Mallinckrodt Chemicals, Phillipsburg, NJ, USA. N-2, 4-dinitrophenyl-L-serine (DNP-ser), N-2,4-dinitrophenyl-L-aspartic acid (DNP-asp), N-2,4-dinitrophenyl-β-alanine (DNP-β-ala), N-2,4-dinitrophenyl-DL-Glutamic acid (DNP-glu) were obtained from Sigma Chemicals, St. Louis, MO, USA.

3.3. Partition Coefficient Measurement

Partition coefficient (KUP/LP) of each sample in the two-phase solvent system was determined using the conventional test tube method with a UV spectrophotometer (Genesis 10 UV, Thermo Spectronic, Rochester, NY, USA) at 280 nm as described elsewhere [16] From 17 DNP-amino acids, two sets of suitable test sample were selected on the bases of their partition coefficient. DNP-glu and DNP-β-ala are used for the solvent system composed of hexane-ethyl acetate-methanol-0.1 M HCl at a volume ratio of 1:1:1:1 (solvent system 1) in the hydrostatic CCC system and DNP-ser and DNP-asp for hexane-ethyl acetate-methanol-0.1 M HCl at a volume ratio of 4:5:4:5 (solvent system 2) in the hydrodynamic CCC system as listed in Table 2.

Table 2
Partition coefficient (K) and separation factors (α) of test samples in the two-phase solvent system

3.4. Two-phase Solvent Systems and Sample Solutions

As mentioned above, two typical two-phase solvent systems including hexane-ethyl acetate-methanol-0.1 M HCl (1:1:1:1, v/v) (solvent system 1) and hexane-ethyl acetate-methanol-0.1 M HCl (4:5:4:5, v/v) (solvent system 2) were each used to separate a set of DNP-amino acid test samples. Each solvent mixture was thoroughly equilibrated in a separatory funnel by vigorous shaking and degassing several times, and the phases separated shortly before use. The sample solution for solvent system 1 was prepared by dissolving 10 mg of DNP-β-ala and 10 mg of DNP-glu in 20 ml of the upper phase of hexane-ethyl acetate-methanol-0.1 M HCl. A 50 μl amount of each sample solution was charged in each run; and for solvent system 2 by dissolving 10 mg of DNP-ser and 10 mg of DNP-asp in 20 ml of the upper phase of hexane-ethyl acetate-methanol-0.1 M HCl. A 400 μl amount of each sample solution was charged in each run.

3.5. HSCCC Procedure

In each separation, the separation column was first entirely filled with the stationary phase, either upper or lower phase, followed by sample injection, and the column was rotated at 800 rpm while the mobile phase was pumped into the coiled column at a given flow rate. The effluent from the outlet of the coiled column was continuously monitored with a Uvicord IIS (LKB, Stockholm, Sweden) at 280 nm and the elution curve was traced using a stripped-chart recorder (Pharmacia, Stockholm, Sweden). After the desired peaks were eluted, the run was stopped and the column contents were collected into a graduated cylinder by pressured air to determine the volume of the stationary phase retained in the column. The retention of the stationary phase was computed by dividing the volume of the retained stationary phase with the total column volume.

3.6. Procedure for Programmed Intermittent Dual CCC

Fig. 2 shows the operation scheme of the 10-port sliding valve (Upchurch Scientific, Oak Harvor, WA, USA) that was used to program the intermittent CCC process through the HSCCC column. As shown in the diagram, the valve has 10 ports including 5 inlets and 5 outlets (among those 8 ports were used as shown in the figure) and it allows the flow to be repeatedly switched back and forth to retain the two similar analytes until the two peaks are resolved. At position I, the first pump (pump A) pumps the lower phase through the column head to the tail while effluent from the outlet of the column is monitored and collected into a fraction collector through the valve, and in the meantime the second pump (pump B) is recycling the upper phase from the reservoir back to the same reservoir continuously through the valve waiting for its turn (Fig. 2A). At position II, the second pump (pump B) pumps the upper phase through the column from the tail toward the head while effluent from the outlet of the column is monitored and collected into a fraction collector through the valve, and in the meantime pump A can recycle the solvent from the reservoir back to the same reservoir through the valve to avoid wasting solvent (Fig. 1B). The sliding valve can be controlled to intermittently switch to position I or II by the programmed workstation. The above process is successfully applied to resolve the two peaks which are not separable in the single passage through the column.

The system was initially run in the reverse phase with the lower phase mobile. Switching between normal and reverse phase was carried out at predetermined regular intervals with the sliding valve controlled by the computer software. Thus, the sliding valve allows the flow back and forth to retain the two analytes until the two peaks are separated. The time intervals of back and forth were programmed according to the results obtained from the initial isocratic run. And the run time was based on the results of calculation from Eqs. (6) and (9).

3.7. Evaluation of Partition Efficiency

The partition efficiency of separation column in each run was evaluated by computing theoretical plate number (N) for each peak and peak resolution (Rs) between the peaks using the following conventional equations:

N=(4R/W)2
(10)
RS=2(R2R1)/(W1+W2)
(11)

where R and W indicate the retention time and the peak width in Eq 10 and those for the specified peaks in Eq 11, respectively.

4. Results and discussion

4.1 Some Considerations on the Application of the Mathematical Model for the Intermittent Dual CCC System

In order to predict the retention time of solute peaks in the intermittent dual CCC operation, a general mathematical model was introduced and its validity justified for both hydrostatic and hydrodynamic CCC systems, using the simplified model. As mentioned earlier, it is necessary to consider some adjustment of the formula for each CCC system as follows:

The separation column used for the hydrostatic system consists of multiple helical turns of ca 1 mm I.D. tubing arranged at the periphery of the rotary plate. Stable radially acting centrifugal force field retains the stationary phase, either lighter or heavier phase, at each helical turn. In this column arrangement, a half of each turn is completely occupied by the mobile phase while partition process takes place in the other half of each turn. This uneven hydrostatic distribution of two phases through the column should be adjusted to the average volume ratio and used as SU/SL in the model equation where we assumed that the distribution of each phase is uniform throughout the column.

The hydrodynamic system used in the simplified study is a spiral tube assembly which contains only a few percentage of dead space in the radial transfer tubing in each spiral segment compared with 50 % in the toroidal coil system. On the other hand this hydrodynamic system produces fluctuating centrifugal force vectors constantly changing its amplitude and direction, the pattern of which varies at the location on the column holder according to its β values. Consequently, hydrodynamic equilibrium pattern of the two-phase solvent systems in the column varies with this β value in the ordinary multilayer coil separation column, and some solvent systems change their hydrodynamic trend at β values around 0.25 [17]. (Here, β is defined by r/R where r is the distance from the spiral channel to the center of the column holder, and R, the distance between the center of the column holder and the central axis of the centrifuge.) However, in the spiral tube configuration used in the simplified studies, the above hydrodynamic trends induced by the Archimedean screw effect is offset by the centrifugal force gradient acting along the radius of the spiral, sending the upper phase toward the center and the lower phase toward the periphery of the spiral channel. It is very important to note that this centrifugal force gradient effect is increased by the spiral pitch per length of the coil segment that is greatest in the inner portion of the spiral with low β values. Consequently, due to this spiral pitch effect, all two-phase solvent systems send the lower phase toward the periphery of the spiral channel regardless of the β values. In the spiral tube assembly used in the simplified studies has a spiral pitch of 1.6 cm compared with 0.4 cm in the spiral tube assembly with single spiral layers. Of course the two phase distribution through the spiral channel is not considered to be uniform and here again the average volume ratio of two phases in the hydrodynamic equilibrium state, that is obtained by stationary phase retention given by the single straight elution of each phase, should be used for AU/AL in the model equation.

4.2. Experimental Data on CCC Separation of DNP-Amino Acids

As mentioned earlier, the retention of stationary phase in the hydrostatic equilibrium system is always less than 50 % which is much lower than that in the hydrodynamic equilibrium system. Therefore, DNP-glu and DNP-β-ala with a large separation factor (α=2.68) were used for separation in the hydrostatic equilibrium system while in the hydrodynamic equilibrium system which can yield higher retention of stationary phase over 50 %, DNP-ser and DNP-asp with a much smaller separation factor (α=1.12) was used as test samples.

4.2.1. Separation of DNP-amino acids with hydrostatic CCC system

Fig 3A shows that the separation of the DNP-glu and DNP-β-ala in the hydrostatic equilibrium system with a single straight run using a two-phase solvent system composed of hexane-ethyl acetate-methanol-0.1M HCl (1:1:1:1) (solvent system 1). The peak resolution is 1.07. Under otherwise the same experimental condition, peak resolution was improved at 1.35 by the intermittent dual CCC (Fig. 3B). After the sample solution was loaded in the CCC system, the system was initially eluted with the lower mobile phase at a flow rate of 0.3 ml/min with the valve position I (see Fig. 2). After 4 minutes, the valve was switched to position II with the upper mobile phase at the same flow rate of 0.3 ml/min. Then, after 3 minutes, the valve was again returned to position I with the lower mobile phase at the same flow rate. This valve switching between upper and lower phases was continued at the programmed time interval until the samples were eluted. In the second run, the interval time was doubled and returned to lower mobile phase in 8 minutes, followed by the upper mobile phase in 6 minutes. The result indicated that the peak resolution at 1.34 and retention time were similar with those obtained by the first experiment with the interval time at lower mobile phase in 4 minutes and upper mobile phase 3 minutes (Fig 3C).

Fig 3
Intermittent dual CCC chromatograms of DNP-β-ala and DNP-glu separation in the hydrostatic equilibrium system. Column capacity: 15 ml; Solvent system: hexane-ethyl acetate-methanol-0.1 M HCl (1:1:1:1, v/v); Detection: 280 nm. Revolution: 1000 ...

Usually in the hydrostatic CCC system, the peak resolution can be improved by reducing the flow rate of the mobile phase. So a series of protocols at different flow rates were investigated. The results showed that as expected application of the lower flow rate improved the peak resolution substantially as shown in Fig 4A. When the flow rate was 0.1 ml/min, the single isocratic run produced a separation time almost equal to the total separation time with the dual CCC run at the interval times of lower mobile phase for 4 minutes and upper mobile phase for 3 minutes. However, the resolution of the single isocratic run yielded a peak resolution of 1.46 which is higher than that of the dual CCC (Rs = 1.35) (Fig 3D). The results clearly show that the resolution using the dual CCC method failed to improve the results obtained by the regular CCC method with the conventional hydrostatic toroidal coil column obtained in about the same retention time (Fig. 3D) using a flow rate of 0.1 ml/min.

Fig 4
Relationship between flow rate and peak resolution in the single isocratic CCC separation. A) hydrostatic equilibrium system; B) hydrodynamic equilibrium system.

This problem may be explained by visualizing the two phase motion through the coiled column at the critical switching period between the forward and backward elution modes as illustrated in Fig. 5 where upper and lower phases intermittently counterflow through a series of coiled column segments. At the critical time period between the lower phase elution and upper phase elution, the two phases must reestablish their hydrostatic equilibrium as shown in Fig. 5 C and D. At the moment of switching the sliding value, the heavy phases will settle at the bottom of the loops as shown in Fig. 5B, where two phases occupy each coiled turn according to their volume ratio which is 65 % for the lower mobile phase (LP) and 35 % for the upper stationary phase (UP). Then the upper phase starts to penetrate the first coiled turn as shown in Fig. 5C. Because of the difference in volume between the two phases, percolated upper phase must push the excess amount of the lower phase into the second coil which locally produces an effect adverse to peak resolution. This process continues through each turn of the coil until all excess stationary phase is displaced backward through the column. A similar two-phase motion will take place when the upper mobile phase is switched to the stationary phase. The above speculation proposes two ways to improve the intermittent dual CCC operation for the hydrostatic CCC system: The first method is to increase both forward and backward elution periods to minimize the number of switching times for a given retention time of the analytes, and the second strategy is to use a slow flow rate and/or a different column design such as triangular core [18] to retain the stationary phase near 50% of the total column volume. If such optimization is achieved, intermittent dual CCC operation on the hydrostatic CCC system would yield higher peak resolution compared to that obtained by the single straight run in a given separation time.

Fig 5
Diagrammatical presentation of two-phase motion at the critical switching point of flow direction in intermittent dual CCC operation in the hydrostatic CCC system.

4.2.2. Separation of DNP-amino acids with hydrodynamic CCC system

As earlier hydrodynamic CCC system yields much higher peak resolution for DNP-glu and DNP-β-ala with the solvent system 1 mainly due to higher column capacity (130 ml) and better retention of the stationary phase. The method produced excellent peak resolution (Rs=4.44) of these test samples as shown in Fig 6A. In order to critically examine the capability of the dual CCC separation in this hydrodynamic equilibrium system, two test samples of DNP-ser and DNP-asp with a much smaller separation factor (α=1.12) were selected among 17 different DNP-amino acids using the second two-phase solvent system composed of hexane-ethyl acetate-methanol-0.1M HCl (4:5:4:5)(solvent system 2). The chromatogram of these DNP-amino acids obtained from the single isocratic with solvent system 2 is shown in Fig. 6B. In this separation the peak resolution was only 0.74 due to the small separation factor. Using the intermittent dual CCC operation, however, the resolutions was remarkably improved to Rs = 1.37 under otherwise the same experimental conditions as shown in Fig. 6C. This intermittent dual CCC operation was programmed by switching the sliding value at every 5 minutes forward with lower mobile phase and 4.5 minutes backward with upper mobile phase. When this programming was changed to 10 minutes forward with lower mobile phase and 9 minutes backward with upper mobile phase, the peak resolution was reduced to 1.31 with a similar retention time (Fig. 6D).

Fig 6
Intermittent dual CCC chromatograms of DNP-amino acid separation in the hydrodynamic equilibrium system. Column capacity: 130 ml; Solvent system (Fig.6A): hexane-ethyl acetate-methanol-0.1 M HCl (1:1:1:1, v/v); Solvent system (Fig. 6B-F): hexane-ethyl ...

A series of experiments for the isocratic elution in the hydrodynamic system were performed using different flow rates of the mobile phase, the results of which are shown in Fig 4B. It was found that the results were quite different with those in the hydrostatic equilibrium system (Fig. 4A). At a lower flow rate of 0.1 ml/min, the peak resolution is lowest at 0.72 which sharply increases to the maximum value reaching 0.94 at the flow rate of 0.35 ml/min followed by a gradual decrease as the flow rate is further increased to 2 ml/min. The peak retention time (t) obtained at the best resolution of 0.94 at a flow rate 0.35 ml/min (Fig. 6E) in this isocratic run is very similar to that of the dual CCC operation at 2 ml/min (Fig. 6D) but with much lower peak resolution. When the flow rate is decreased to 0.105 ml/min, peak resolution becomes lowered at 0.72 (Fig. 6F) apparently due to longitudinal solute band broadening by violent mixing of the two phases in the column produced by the fluctuating centrifugal force field by the planetary motion. These findings indicate that the intermittent dual CCC method applied to the hydrodynamic system improves the peak resolution at a given elution time in contrast with the hydrostatic CCC system described earlier.

4.2.3. Optimization of intermittent dual CCC operation

In order to optimize the intermittent dual CCC operation, the effects of dual cycle times (reversed and normal phase flow cycle) and flow rate for each elution period on peak resolution (Rs) were investigated in both hydrostatic and hydrodynamic CCC systems. Fig. 7 shows the relationship between dual CCC cycle times and peak resolution which indicates that in both CCC systems the resolution increases with the frequency of intermittent dual CCC operation under a given flow rate of the mobile phase apparently due to the increased elution time. In the hydrostatic CCC system, the plot was obtained at the 0.3 ml/min of flow rate using solvent system 1. Rs increased with the increased elution frequency (Fig. 7A). In the hydrodynamic system, the plot was obtained at the 2 ml/min of flow rate using solvent system 2. Rs also increased with the increased elution frequency (Fig. 7B).

Fig 7
Relationship between forward and backward elution times and peak resolution using programmed intermittent dual CCC under otherwise the same conditions. Detection: 280 nm. A) Hydrostatic equilibrium system; Sample: DNP-β-ala, DNP-glu; Solvent system: ...

In the second series of experiments, the effects of backward elution time interval was investigated at a fixed forward elution time interval. In the hydrostatic CCC system, the plot was obtained at the 0.3 ml/min of flow rate using solvent system 1 (Fig. 8A). In the hydrodynamic system, the plot was obtained at the 2 ml/min of flow rate using solvent system 2 (Fig. 8B). As shown in Fig. 8 the peak resolution is improved in both CCC systems as the backward elution time interval is increased. As for backward flow rate, increasing the flow rate is also beneficial to the separation of test samples under the fixed forward flow rate (Fig. 9).

Fig 8
Relationship between backward interval time and peak resolution using programmed intermittent dual CCC at the same other condition. Detection: 280 nm. A) Hydrostatic equilibrium system; Sample: DNP-β-ala, DNP-glu; Solvent system: hexane-ethyl ...
Fig 9
Relationship between backward flow rate and peak resolution using the backward and forward elution method under the identical experimental conditions. Detection: 280 nm. A) Hydrostatic equilibrium system; Sample: DNP-β-ala, DNP-glu; Solvent system: ...

4.2.4. Comparison of retention time between the experimental data and the theoretical values

Finally a series of protocols including dual CCC and isocratic CCC were carried out to justify the accuracy of the mathematical model. As summarized in table 3, the deviation of the theoretical value from the experimental data ranged from -4.53 % to +6.39 % in the hydrostatic equilibrium system, and from -6.39 % to +6.26 % in hydrodynamic equilibrium system. Deviation of calculated retention time from the actual retention time may be due to a number factors including K value, the volume ratio between the two phases in the column, column temperature and column capacity. The K value is considered to be the most sensitive factor because a minute change of K value will lead to a great change of the calculated retention time and dual CCC elution time as shown in Fig 10A. There are two important elements that would alter the K values used in the equation. One is a little deviation of measured K values from the actual values at room temperature. And another source is derived from the raised column temperature during the separation. Using a spectrophotometer, the K value of DNP-ser was measured at temperature ranging from 21 °C (room temperature) to 50 °C and their values are plotted in Fig. 10B. If the temperature had increased to 25 °C (+ 4 °C) in the separation column, K value of DNP-ser was changed from 0.77 to 0.71. If these two K values are used to calculate the retention time of DNP-ser from the Eq. (6), the calculated retention time is changed from 325.3 min to 263.7 min with a difference as large as 20% caused by the temperature change of only 4 °C. In spite of many commercial CCC instruments equipped with temperature control, temperature fluctuation of 1 or 2 °C is inevitable during the separation. In our experimental course, we tried to control the column temperature by improving ventilation to minimize the error caused by the elevated column temperature. On the other hand the volume ratio between the two phases and the variation of column capacity will cause the deviation of the theoretical value from the actual value in retention time.

Fig 10
A) Relationship of K value of DNP-ser and retention time, cycle times; B) Relationship between temperature and K value of DNP-ser.
Table 3
Comparison of calculated retention time and practical retention time in both hydrostatic and hydrodynamic equilibrium systems.

5. Conclusions

Considering the number of factors affecting the retention times of test samples, deviation of several percent around the measured values will be acceptable to justify the mathematical model proposed in this paper. Overall results of our studies demonstrate that the intermittent dual CCC technique improves the peak resolution in the hydrodynamic CCC system under the optimized experimental conditions, but it is not good for the hydrostatic system.

Glossary

AC
Cross-sectional area of the channel
AL
Cross-sectional area of the channel occupied by the lower phase
AL,L
Cross-sectional area of the channel occupied by the lower phase when the lower phase is mobile
AL,L
Cross-sectional area of the channel occupied by the lower phase when the upper phase is mobile
AU
Cross-sectional area of the channel occupied by the upper phase
AU,U
Cross-sectional area of the channel occupied by the upper phase when the lower phase is mobile
AU,U
Cross-sectional area of the channel occupied by the upper phase when the upper phase is mobile
β
Volume ratio of upper phase to the lower phase in the channel or AU/AL
βL
β for lower phase mobile or AU1/AU1
βU
β for upper phase mobile or AU2/AU2
FL
Volumetric velocity of the lower phase (ml/min)
FU
Volumetric velocity of the upper phase (ml/mi)
K
Partition coefficient of solute expressed by solute concentration in the upper phase divided by that of the lower phase
L
Half length of the channel
μL
Linear velocity of the lower phase (cm/min)
μU
Linear velocity of the upper phase (cm/min)
μX,L
Solute velocity (cm/min) through the channel with the lower phase is mobile
μX,U
Solute velocity (cm/min) through the channel with the upper phase is mobile
μX,i
Average velocity (cm/min) of solute through the channel
RS
Retention volume of solute
ti,L
Unit programmed time for lower phase mobile
ti,U
Unit programmed time for upper phase mobile
tR
Retention time of solute
VC
Total column volume
VL
Volume of the lower phase in the column (0.5 VC)
VU
Volume of the upper phase in the column (0.5 VC)

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