2024 Volume 25 Issue 1 Pages 15-22
A method for determining the optimum temperature for the separation of two polyphenols by polystyrene divinylbenzene resin reversed phase liquid chromatography with the ethanol-water mixture mobile phase was proposed based on the iso-resolution curve concept. The distribution coefficient and the stationary phase diffusion coefficient were formulated as a function of temperature T and ethanol concentration I. From the iso-resolution curve, the productivity P* was calculated as a function of T. It was found that there is an optimum T, where the highest P* can be obtained.
逆相クロマトグラフィー分離の生産性を最大化する，最適温度の決定法を開発した．エタノール-水移動相を用いたポリマー（ポリスチレンジビニルベンゼン）粒子充填クロマトグラフィーによる2種類のポリフェノール（カテキン，エピカロカテキンガレート）分離をモデル系として選択した．15-45°Cにおける勾配溶出実験と等組成溶出実験データから，分配係数と拡散係数を温度とエタノール濃度の関数として定式化した．
既に開発した等分離度曲線決定方法を温度の影響を考慮できるように拡張した．温度が高くなると分離溶媒量が減少し分離時間が長くなり，温度が低下すると分離時間は短縮されるものの多量の溶媒が必要であることが明らかとなった．
次に分離度が一定の条件下において，カラム体積，時間，消費移動相当たりの生産性を計算したところ，生産性が最大となる温度が存在し，また温度は移動相エタノール濃度にも依存した．この方法により試料の安定性等を考慮して最適温度条件を決定することができる．簡単に液体クロマトグラフィーの最適温度を決定できる本手法は，産業上有用であると考えられる．
Although temperature is an important parameter affecting the performance of liquid chromatography (LC), it has not been considered as a tunable parameter for the process performance compared to other parameters. High temperature operation is frequently used for improving the separation performance in HPLC [1,2] although detailed theoretical studies are not sufficient. In the preparative separation process, flow rate, gradient condition, mobile phase composition, etc. are used as operating variables [3-6]. There are few cases where the conditions have been optimized accurately by controlling the temperature. Most studies are on thermodynamic analysis of the retention of solutes in reversed phase chromatography (RPC) [5-7].
In our previous paper [8], a simple method for predicting the effect of temperature on the performance of LC was presented for a model separation system, two polyphenol separations by RPC with polymer-resins. Since both the retention of solutes and the peak widths are influenced not only by temperature but also by the mobile phase composition (ethanol-water mixture), finding the optimum condition is complicated. Therefore, in our previous paper, the flow-velocity was fixed for calculating the separation performance as a function of temperature. It was found that the separation performance defined by the resolution Rs does not increase significantly with temperature mainly because the difference in retention volume of the two components decreases with temperature.
In this study, a more elaborate method for determining the optimum temperature was developed based on the iso-resolution curve concept [9,10]. The same two-component model separation system as in our previous studies [8,9,10] was used. The model samples were two polyphenols, catechin and epigallocatechin gallate (EGCG). The chromatography resin was polystyrene divinylbenzene particles and the mobile phase was ethanol-water mixture.
We have already proposed a method for calculating the iso-resolution curve based on the distribution coefficient K and the stationary phase diffusion coefficient Ds as a function of ethanol concentration, I [10]. The same resolution Rs can be obtained on the iso-resolution curve with different combinations of mobile phase velocity, u and I. This method was further extended in this study to include the effect of T. For this purpose, both K and Ds were formulated as a function of I and T. A method for calculating the iso-resolution curve as a function of T at fixed I was developed. From the iso-resolution curve, the productivity was calculated as a function of I and T. It was found that there is an optimum T, where the highest productivity can be achieved.
Two polyphenols, catechin (C15H14O6 , mol.wt. 290) from Sigma (MO, USA) and epigallocatechin gallate (C22H18O11, mol.wt. 458) abbreviated as EGCG from Wako (Osaka, Japan) were used as samples. The resin used was polystyrene divinylbenzene particles, Diaion HP20SS from Mitsubishi Chemical (Tokyo, Japan), which is used for reversed phase chromatography [i]. The particle diameter dp ＝ 65 μm was used for the calculation. Experiments were carried out using an HPLC equipment by JASCO (Tokyo, Japan) by the method described in our previous studies [7, 9, 10]. Single component experiments were carried out for determining the peak retention time and the peak width as a function of flow rate at a fixed temperature and mobile phase ethanol concentration.
Isocratic elution experiments were carried out at 15～45 °C. Typical elution curves are shown in Fig. 1. As is clear from Fig. 1 A and B, the elution curve became sharper and the retention volume VR decreased with temperature, T. An increase in ethanol concentration I [vol %] from 20% (Fig. 1C) to 27% (Fig. 1D) decreased VR. Increasing T also decreased VR (Fig. 1E).
Typical elution curves.
A and B: dc＝1.1 cm, Z≈5 cm, ε＝ 0.38, Fv ＝ 1 mL/min, C: dc ＝1.1 cm, Z ＝ 15.5 cm, ε＝ 0.44, Fv ＝ 3.25 mL/min, D: dc ＝ 1.1 cm, Z ＝ 17.5 cm, ε＝ 0.41, Fv ＝ 0.29 mL/min, E: dc ＝1.1 cm, Z ＝ 15.5 cm, ε＝ 0.38, Fv ＝ 0.7 mL/min (dc : column diameter, Fv : volumetric flow-rate).
Fig. 1A, 1B, 1C, 1D and 1E were modified from our previous papers [7, 10]. Single component catechin and EGCG curves are plotted on the same graph (superposed curves). Bold curves in Fig. 1C, 1D and 1E are calculated curves by Eq. (1) with the VR values determined by Eqs. (3) and (9), and the σv values determined by Eqs. (2), (4), (8) and (9).
The peak retention time tR and the peak width (standard deviation σt) values were measured by fitting the experimental elution curves with a modified Gaussian curve (Cmax is the maximum peak concentration).
 | (1) |
HETP, a measure of column efficiency, was calculated according to following equation.
 | (2) |
Here Z is the column length, σv ＝ Fvσt is the σ value in volume. Fv is the volumetric flow rate. W ＝ 4σt is the baseline peak width.
The retention volume VR＝FvtR is related to the distribution coefficient K as
 | (3) |
where Vo ＝ void volume, Vt ＝ bed volume and H ＝ (Vt – Vo)/Vo ＝ (1 – ε)/ε is the volumetric phase ratio. The column void fraction ε ＝ Vo/Vt was determined from the peak retention volume of a non-retained and completely excluded solute (Dextran mol.wt. 2,000,000, Fluka). From VR of retained solutes (catechin and EGCG), K was determined. For the detection of catechin and EGCG, UV at 280 nm was used whereas dextran was monitored at 210 nm.
The stationary phase diffusion coefficient Ds can be determined based on the following van Deemter-type equation [3, 4, 9, 10].
 | (4) |
Here N is the plate number, u ＝ Fv/(Acε) is the mobile phase velocity, DL is the axial dispersion coefficient, Ao ＝ 2(DL/u) and Co ＝ HKdp2/[30Ds(1+HK)2]. DL/u is usually constant and approximately equal to 0.5dp ~ 5dp [3]. DL/u ＝ 0.0225 cm was used in this study [9, 10].
In previous studies, K values at 25°C [9, 10] were determined experimentally, and molecular diffusion coefficient Dm at 25°C were calculated by the Wilke-Change equation (Appendix). They were formulated as a function of I.
 | (5) |
 | (6) |
Here, I is the ethanol concentration in volume %.
The values for the parameters A, B and KC for catechin and EGCG are summarized in Table 1.
| A | B | KC | a1 | a2 | a3 | ΔH | ED | |
|---|---|---|---|---|---|---|---|---|
| (%)B | − | − | m2∙s-1∙ (%)-2 | m2∙s-1∙(%)-1 | m2∙s-1 | kJ∙mol-1 | kJ∙mol-1 | |
| Catechin | 5.34 × 104 | 3.1 | 0.69 | 1.62×10-13 | -1.51×10-11 | 6.33×10-10 | -22.9 | 51.6 |
| EGCG | 8.62 × 106 | 4.5 | 0.69 | 1.26×10-13 | -1.17×10-11 | 4.91×10-10 | -37.1 | 73.9 |
The a1, a2 and a3 values for Dm,catechin and Dm,EGCG are shown in Table 1.
We have also shown that KDs ＝ constant in this separation system [10]
Therefore, Ds,ref (＝Ds at 25°C) can be calculated by the following relationship.
 | (7) |
Kref is the K value at 25°C calculated by Eq. (5), and α＝ 0.07 [10].
Ds can be described as a function of T by the Arrhenius equation with the activation energy ED as shown in Eq. (8).
 | (8) |
where T is the absolute temperature, RG is the gas constant in J/(mol・K), ED is the activation energy in J/mol, and Tref ＝ 273.15 + 25 [K].
Ds values were obtained from HETP - u curves measured at different temperatures by Eq.(4)
Then, by plotting ln Ds against 1/T, ED, catechin ＝ 51.6 kJ/mol and ED,EGCG ＝ 73.9 kJ/mol were obtained with the coefficient of determination > 0.98 (data not shown).
Effect of T on K can be described by the van’t Hoff equation, Eq. (9) with the enthalpy of adsorption, ΔH.
 | (9) |
By plotting ln K against 1/T, ΔHcatechin ＝ – 22.9 kJ/mol and ΔHEGCG ＝ – 37.1 kJ/mol were obtained with the coefficient of determination > 0.98 (data not shown).
K is now calculated as a function of both I and T by Eqs.(5) and (9)with parameters shown in Table 1. Similarly, Ds(I, T) is calculated with parameters shown in Table 1 as follows. Dm(I) at 25 °C is first calculated by Eq.(6). Then, Ds,ref(I) calculated by Eq.(7) is used for calculating Ds(I, T) by Eq.(8).
3.2 Iso-resolution curve and ProductivityWe have proposed a method for predicting the separation conditions based on the iso-resolution curve [8, 9]. For example, at a given I, there is a u value that can achieve the required Rs of two components defined by the following equation (Fig. 2).
 | (10) |
Subscript 1 and 2 indicate the first and the second peak, respectively.
Two component separations.
When Rs＝1.0, the baseline separation of two components is attained if the peak is approximated as a triangle as shown in Fig. 2. For the Gaussian curves Rs >1.2 is needed for the complete baseline separation.
By substituting Eqs. (2) and (3) into Eq. (10), Rs can be described as Eq. (11).
 | (11) |
Note that Ao is assumed to be the same for the two components as it only depends on the particle diameter and the bed packing quality [3 - 5]. K1 (I, T) and K2 (I, T) can be calculated by Eq.(9) where as Ds1(I, T) and Ds2 (I, T) by Eq. (8)
The separation time tSEP and separation volume VSEP are defined by Eq. (12) and (13), respectively.
 | (12) |
 | (13) |
V1a needed for calculating Vc can be described by Eq. (14).
 | (14) |
Finally, for the repeated cyclic operation [10], the cycle volume VC and the cycle time tC can be described by Eq. (15) and (16), respectively as shown in Fig.2.
 | (15) |
 | (16) |
The name “iso-resolution curve” is based on the concept that the same Rs can be obtained by choosing any point on this curve, which is a combination of I and u. This concept has already been applied to study the optimal solvent composition [10]. It is possible to calculate the iso-resolution curve by Eq. (11) at a fixed I in order to understand the effect of T.
Rs ＝ 1.0 was chosen as an assigned value as it is easy to confirm the calculated results by triangle approximations. The Goal-Seek function of Microsoft Excel was used to find u to achieve Rs ＝ 1.0 as a function of T at a fixed I by Eq. (11). A typical calculated iso-resolution curve is shown in Fig. 3 for I ＝ 20%. Considering practical operational conditions, the calculation was performed in the range of K > 1 and u < 15 cm/min.
Iso-resolution curve (separation time vs. separation volume curve) for I = 20%.
Inset shows the calculated elution curves (triangle approximation) to confirm the assigned Rs value (= 1.0).
Increasing T results in smaller separation volume and longer separation time whereas larger separation volume is needed for a short time separation at low T.
Although the iso-resolution curve provides important information, additional evaluation index is needed to determine the optimum conditions.
The productivity P is usually defined as Eq. (17).
 | (17) |
Here C0 is the sample concentration and VF is the sample volume.
As the solvent consumption is another important factor for the separation process, the following definition P1 considering the mobile phase consumption has been proposed in our previous paper [10].
 | (18) |
P1 is the productivity per column volume, mobile phase consumption, and cycle time, having the unit [(kg-product)(m3-bed)-1(m3-solvent)-1s-1] where (m3-bed) is the column void volume. As the isotherm is linear, P* ＝ P/C0 can be used. Namely, P is proportional to C0.
 | (19) |
The iso-resolution curves and the relationship between P or P* and T for I ＝ 20 are shown in Fig. 4.
Calculated iso-resolution curves (tSEP or tC vs. reduced separation volume), and P or P* at I = 20 as a function of temperature. The arrows indicate the temperature at the minimum tC, tSEP and the maximum P, P*.
It was revealed that tSEP and tC became minimum at 41 and 43°C, respectively, while P and P* were maximum at 45 and 50°C, respectively. A sharp decrease in P* or P after the maximum value is due to lower flow velocities in order to obtain the same Rs.
Similar calculations for P* as a function of T were performed for different I values. As shown in Fig. 5, the temperature at the maximum P* increased with a decrease in I. This is mainly because K decreases with I. It is interesting to notice that (K2 － K1) at the maximum P* ranges between 1.4 and 1.7, and decreases slightly with increasing T.
P* or (K2 － K1) as a function of temperature TC. Open symbols are for (K2 － K1) vs. TC whereas closed symbols are for P* vs. TC. The arrows indicate the temperature at the maximum P*.
We have examined the effect of temperature on the separation performance of reversed phase chromatography of two polyphenol components by using an extended method for calculating the iso-resolution curve. It was found that there is a temperature TM at which the maximum productivity can be obtained, and TM increases with decreasing I. This is advantageous as reducing the ethanol concentration is more economical and environmentally friendly. However, at the same time it should be noticed that some polyphenols are not stable at high temperatures [11].
Other important parameters to be examined for the process scale separations are column dimensions and sample loadings. The column dimensions such as the column length and the column diameter can be easily examined with the model employed in this study. The volume overloading is rather easy to be considered in the calculation when the isotherm is linear. The molecular and stationary phase diffusion coefficients of two components do not change under the linear isotherm condition. However, the concentration overloading results in non-linear isotherms, which are difficult to predict with the linear isotherm information only [12]. Nevertheless, it is thought to be a general procedure that the parameters for the linear isotherm such as A and B are first determined, and then the non-linear terms are measured by additional experiments [13].
A method for determining A and B by linear gradient elution experiments implicitly assumes that the mobile phase modulator (ethanol) diffuses in and out to the stationary phase much more quickly than retained solutes do. Considering the diffusion coefficients of ethanol (mol.wt. 46) and catechins (mol.wt. 290 and 458), this assumption is still valid. However, the model (method) may not work in the case of a larger modulator molecule for a very fast and steep gradient.
A flow-sheet for the method developed in this study is shown in Fig. 6.
Flow-sheet for the calculation by the method developed in this study.
A method for predicting the temperature for the maximum productivity was developed for the separation of two polyphenols by polystyrene divinylbenzene resin reversed phase chromatography with the ethanol/water mobile phase. The distribution coefficient and the stationary phase diffusion coefficient were formulated as a function of ethanol concentration, I, and temperature, T. Based on the iso-resolution curve, the mobile phase velocity u was determined for a given T and I. Then, the productivity was calculated as a function of I and T. It was found that there is a temperature, where the highest productivity considering minimum mobile phase consumption can be achieved.
This research was partially supported by AMED under Grant Number JP21ae0121016.
The molecular diffusion coefficient of small molecules Dm in cm2/s can be well-estimated by Wilke-Chang equation [14-16].
 | (A1) |
Here,
ϕ for the ethanol-water mixture was calculated as a function of ethanol mole fraction X by the following equation.
 | (A2) |
Similarly, MB was calculated as a function of X with the molecular weight of ethanol MEtOH and that of water, MWater.
 | (A3) |
μΒ was formulated by the polynomial equation as a function of I based on the literature data.
Dm values at 25°C were calculated by the above equations.
Since KDs ＝ constant ＝ αDm is assumed, Ds can be estimated from Dm.
The experimentally obtained α value was 0.07.
(Note that some symbols in the appendix are not included in the list of symbols).
