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Reversed-phase column selection for pharmaceutical and compendial analysis: an overview

D. Mangelings, Y. Vander Heyden

Department of Analytical Chemistry and Pharmaceutical Technology, Vrije Universiteit Brussel-VUB, Laarbeeklaan 103, B-1090 Brussels, Belgium

Corresponding author: Y. Vander Heyden

Dept. Analytical Chemistry and Pharmaceutical Technology

Laarbeeklaan 103

B-1090 Brussel

Belgium

Tel: +32 2 477 47 34, Fax: +32 2 477 47 35

Email: yvanvdh@vub.ac.be

1 Introduction

When either developing or transferring an application in liquid chromatography, and certainly in reversed-phase liquid chromatography (RPLC), analysts are confronted with the large number of commercialized RPLC columns. Already, more than 600 different types are available on the market, and their number is still increasing.

Usually, the transfer of an existing separation does not present much problems when the brand and type of column are known. However, some compendial reference works, such as the European Pharmacopoeia, describe in detail the mobile phases and analyzing conditions that should be used for a given pharmaceutical compound, but they only describe the column in general terms. Specification of the brand, on which the method was developed, is not allowed. On the other hand, one should not expect either that a lab possesses the recommended column for a given separation. Therefore, different attempts have been made to classify columns with similar selectivity, hoping to be able to distinguish groups of columns that behave similarly at given conditions, and thus can be used for the same analysis.

This manuscript is divided in two major sections. A first section will focus on a project which tries to give practical and simple guidelines to select a suitable column from the range of columns available in one’s lab. It is the intention to describe this procedure as simple as possible.

In a second section, we will focus on an overview of the approaches that were described since 1995 for column classification.

Some research groups also focused on the selection of dissimilar or orthogonal systems for method development. These systems are then to be used as a first screening step in the method development for mixtures with unknown composition, e.g. a new drug molecule and its impurities. It should be noted that the selection of such systems is not considered in this paper.

2. Simple approach to select columns for compendial analyses

In a series of papers by the group of Hoogmartens [1-6], a simple approach was derived to classify and select columns. We will briefly describe their methodology, followed by an explanation of the practical approach used to select a column.

Methodology

In a first instance [1], eight methods were chosen from the literature, which allowed the determination of 36 chromatographic test parameters, displaying different properties of a stationary phase. Efficiency, hydrophobicity, silanol activity, ion-exchange capacity, steric selectivity and presence of metal impurities were measured by the parameters.  It was evaluated which of the published parameters allowed determining the characteristics of a column in a repeatable and reproducible way on 69 commercially available columns, and their correlation was described. It was concluded that columns cannot be distinguished using one single parameter, a combination of parameters is a more suitable approach. In a next step [2], Ivanyi et al. demonstrated that columns can be differentiated by means of principal component analysis (PCA) using the chromatographic parameters as variables and the considered stationary phases as objects. The data sets applied consisted of an earlier published data set [7], where five parameters were measured on 89 RPLC columns, and a set of 47 self-tested columns, where seven parameters were determined. The columns of both sets were classified into groups using all measured parameters and it was investigated to which extent the number of parameters can be reduced, still maintaining the classification. It was concluded from this study that only three or four parameters were necessary to achieve an acceptable classification without losing much information. The information from that paper was used in [3] to reduce the number of parameters measured in [1] for classification of the 69 columns. Of the original 36 parameters, only 24 were further considered because of insufficient precision with the other 12. Using PCA on the maintained parameters, an initial classification was made. Four groups of columns could be distinguished.          Then, the correlation of the parameters responsible for the observed classification was investigated by means of the PCA loading plots, in order to reduce their number but maintaining the clustering of columns. The use of four parameters, reflecting ion exchange capacity (determined by the relative retention factor of benzylamine/phenol at pH 2.7, rk’_{benzylamine/phenol} pH 2.7), metal impurities (determined by the retention factor of 2,2’ dipyridyl, k’_{2,2’-dipyridyl}), hydrophobicity (determined by the retention factor of amylbenzene, k’_amylbenzene) and steric selectivity (determined by the relative retention factor of triphenylene/o-terphenyl, rk’_{triphenylene/o-terphenyl}), which can be measured using three mobile phases, gave a classification similar to using all 24 parameters.

The classification of [3] was used in [4] to evaluate whether columns from the same group give similar results regarding the European Pharmacopoeial (Eur. Ph.) analysis of acetylsalicylic acid and its impurities. From the 69 classified columns, only 56 were considered. Some columns were omitted because they did not meet the requirements given by the Eur. Ph. It was found that the system suitability test (SST) prescribed by the Eur. Ph. does not always displays the usefulness of a column. A better criterion was the CRF value, reflecting the overall selectivity. The CRF value is calculated as:

                                                                                   (Equation 1)

with n the total number of solutes, g the interpolated peak height (distance between baseline and the line that connects two peak tops measured at the time the valley occurs) and f the valley depth (distance between valley signal and the line that connects the two peak tops, measured at the same time).

A CRF of 1.00 means that all compounds are baseline separated, a CRF of 0.00 means that two or more peak pairs co-eluted.

The four groups of columns, resulting from the classification of [3] appeared to be overall well-defined. It was observed that two groups were suited for the analysis of acetylsalicylic acid impurities. It must be noted however that, although the Eur. Ph. allows differences up to 70 % in specified column length only those columns from the suitable groups that had the specified column length, were found adequate. Because there were exceptions to the statement that overall the groups of columns defined by PCA showed similar behavior and because it is not evident for a given analyst to situate one’s column within the PCA score plot, it was tried in [5] to make the column classification system simpler. After autoscaling the parameters (to ensure the same weighing of each parameter) according to Eq. 2, for each given column an F-value was calculated (Eq. 3) that incorporated the four previously selected parameters, relative to the parameters of a reference column.

                                                                                                  (Equation 2)

with X_ij the value of parameter j on column i, the mean of parameter j on all considered columns and  the standard deviation on the X_ij values.

F = (k’_{amylbenzene, ref} - k’_{amylbenzene, i})² + (rk’_{benzylamine/phenolpH2.7,ref} - rk’_{benzylamine/phenolpH2.7, i})² + (k’_{2,2’-dipyridyl, ref} - k’_{2,2’-dipyridyl, i})² + (rk’_{triphenylene/o-terphenyl, ref} - rk’_{triphenylene/o-terphenyl, i})²                                                                                                                                (Equation 3)

The analysis of acetylsalicylic acid and its impurities was reconsidered. The reference column is the column recommended for a given analysis, or the one selected as appropriate by the lab. It was seen that columns with F-values < 2 were suited for the aimed analysis. Not all suitable columns had low F-values, but when they did have low F-values (F<2), they were suitable, which demonstrates the practical applicability of the system. Again, it must be noted that only those columns that have the specified column length, i.e. the length of the reference column, were found adequate when F<2. Thus, it is possible that a shorter column, displaying an F value < 2, is unable to give a baseline separation of all compounds. However, it was also seen that increasing the length of such column resulted in a situation suited for the analysis. The selection of a good reference column is very important. This can be the column on which the method has been developed, or a suitable column mentioned in the literature. The above approach indeed allows a good ranking of columns according to similar selectivity relative to the reference column. However, it is not always known which column was originally used for the analysis, and this can present a drawback. However, the approach allows specifying suitable columns for a given separation without mentioning the brand and type names. The test parameters of a suitable column or of the column where the method was developed on can be specifid, e.g. in the monograph of a Pharmacopoeia. Any user can then evaluate from the F-value relative to the literature reference which of one’s available columns are suitable for the considered separation.

The column classification system also was incorporated in a database which is freely accessible on a website (see further). Over 80 column types are included at this moment, i.e. the parameter values of these columns have been measured.

The applicability of the F-value introduced in [5] was further evaluated in [6] where the Eur. Ph. analyses of seven mixtures were considered. It was demonstrated that for 6 of the 7 separations, columns with an F < 2 were all able to baseline separate the compound mixture when the prescribed column length was used. Of course, the selection of the reference column is evidently very important: when an unsuitable column is taken as reference, low F-values will not represent suitable columns anymore, only columns behaving similarly as the reference.

The F-value can also be useful when one wants to find a column behaving differently from the reference column, for example, to obtain different selectivity for a given separation. Then, one searches for a column with a large F-value relative to the reference column.

Practical guidelines to select an appropriate column for compendial analysis

Figure 1 gives an overview of the different steps an analyst should take to find the appropriate column(s) for ones analysis.

Figure 1: Flow chart for column selection

* http://pharm.kuleuven.be/pharmchem/columnclassification

First, a reference column for the analysis is searched for in the literature. For the Eur. Ph. analyses of newer compounds, this column can sometimes be found in the journal Pharmeuropa. When the column is available in the lab, it can be used for the aimed analysis. If the reference column is not available, an option is to purchase it. Another option is to see whether the column is incorporated in the database http://pharm.kuleuven.be/pharmchem/columnclassification), and if so execute the ranking procedure for the columns available in the lab. Then, one can see which columns will probably give most similar results compared to the reference column. When a column with an F-value < 2 is available in the lab, the analysis can be performed on this column. It must be noted that when only columns with F-value > 2 are available, the success rate will be lower and it might be suggested to purchase the reference column.

However, when one does not want to purchase the reference column, the same situation occurs as when no reference column is available or it is not included in the database. One then goes back to the old trial-and-error approach used before. Columns available in the lab then sequentially are tested on their performance, using the system suitability test (SST) prescribed in the compendium or the monograph. Preferably, a CRF value (Eq. 1) for the aimed separation is also calculated, reflecting the baseline separation ability of the column. When a column of the lab displays a CRF of 1 and fulfills the SST requirements, this column can be used for the analysis. Such a column can become a reference column; it can be characterized by measuring the test parameters using the test solutes and mobile phases of table 1, and including them in the Open data base. When no available column gives acceptable results, the only option here is either to stop or to purchase other columns.

Table 1: Test procedure to characterize a column according to Hoogmartens’ approach, to be executed in this order.

Other chromatographic conditions: temperature: 40°C; flow rate: 1 ml/min; injection volume: 20 µl; detection at 254 nm; equilibration: 90 minutes; three injections per sample.

3. Column classification approaches

In the following section, the different column classification approaches that have been described from 1995 on will be discussed more in detail. Their practical applicability will also be evaluated.

In a number of studies PCA score plots were drawn to distinguish several groups of similar columns. In a first, seventeen commercially available octadecylsilyl bonded-phase silica columns were classified [8]. Using test mixtures, the trace metal activity, silanol interactions and shape selectivity of the considered stationary phases were determined. Based on the results of these analyses, PCA and two clustering algorithms (average linkage and Ward’s minimum variance [9]) were used to obtain a column classification. Four groups of columns were distinguished. The stationary phases based on the same silica, treated or untreated for basic compounds, usually clustered. Also those resulting in broad and narrow peaks for basic compounds were split into separate groups. Columns with intermediate properties are situated in between. The column classification was confirmed by executing some separations of two tricyclic antidepressants, a mixture of dirithromycin, epi-dirithromycin and erythromycylamine, and of three b-lactam antibiotics, respectively. Columns from a given group generally behaved similarly, indicating that they can be good alternatives for each other. Columns from different groups behaved differently, and can possibly be used during method development to obtain different selectivities, better retentions or better peak shapes.

Neue et al. [10] conducted various experiments on more than 50 columns in order to determine the most relevant parameters for column characterization. They selected the retention factor of acenaphtene (hydrophobicity), the relative retention between butylparabene and dipropylphtalate (to differentiate between classical and polar-embedded packings), the relative retention between propanolol and toluamide at pH 3, and the relative retention between amitriptyline and acenaphtene at pH 7 (both for silanol activity) as most important test parameters. Using cluster analysis, four groups could be distinguished. The first group contains packings with an incorporated polar functional group, the second are stationary phases based on C8, the third includes C18 packings based on high purity silica and the last group consists of packings that exhibit different behavior than the first three groups. The results showed that cluster analysis of the proper parameters is able to make a clear distinction between different groups and can serve as a guide for similarity or dissimilarity of columns.

Column classification using a practical separation is described in [11]. Here, a better method was developed for the separation of vancomycin and its related compounds compared with the rather inappropriate methods prescribed in official monographs such as the United States Pharmacopoeia [12] and the Eur. Ph. [13]. Fourty-one different columns were tested for their applicability for this separation. First, the existing method was optimized on the initial column by changing the type of buffer salt, investigating the use of other modifiers and decreasing the analyzing pH. The adapted method was used for analysis on the different stationary phases. Different critical parameters were measured such as the selectivity of given peak pairs and the efficiency. These data were used to classify all columns with PCA. Then, an appropriate column was chosen, taking into account its pH stability because it was seen during the experiments that a better separation of some related compounds could be achieved at high pH. In [11], the practical utility of a PCA-based column classification was demonstrated. Because the initially chosen column was not appropriate in terms of pH stability (i.e. it was not stable at high pH values), another reference column had to be selected, and here the PCA plot provided useful information. The finally selected best column was close to the initial one on the PCA plot. Further optimization of the separation conditions was performed using an experimental design approach, and the final method was validated in terms of repeatability, linearity and sensitivity.

In [14], Quantitative Structure-Retention Relationships (QSRR) were developed for a series of 15 test analytes. These equations describe the retention of analytes on 9 tested stationary phases in terms of the structure of the analytes. Two models were used; one based on the clogP value, i.e. the calculated logarithm of the octanol-water partition coefficient, and a model based on structural descriptors obtained from molecular modeling. The used descriptors were the total dipole moment, the electron excess charge of the most negatively charged atom and the water-accessible molecular surface area. The PCA clustering of the columns using the regression coefficients of both QSRR models was compared with the PCA clustering using the regression coefficients of the hydrophobic subtraction model proposed by Snyder et al. in [15] (equation 6, see further). According to the authors, similar classifications were obtained using the two approaches [14].

The group of Euerby and co-workers also dedicated extensive research on column classification. In [16], they performed a column characterization approach on 30 commercially available RP-columns, based on the methodology of Tanaka. Using three mobile phases, six test parameters were determined according to the Tanaka approach: the retention factor of amylbenzene (reflecting the length of alkyl chains), the retention factor ratio of amylbenzene and butylbenzene (hydrophobicity), the retention factor ratio of triphenylene and o-terphenyl (reflecting steric selectivity), the retention factor ratio of caffeine and phenol (hydrogen bonding capacity) and the retention factor ratio of benzylamine and phenol, determined at pH 2.7 and 7.6, which reflects the ion-exchange capacity at low and high pH. Additionally to these parameters, two efficiency parameters were also taken into account. Using a fourth mobile phase, the relative base peak efficiency of 2,7-dihydroxynapthalene over the one of 2,3- dihydroxynapthalene was calculated. Further, the column efficiency at 50 % peak height of amylbenzene was calculated from the experiment to determine the length of alkyl chains. When performing PCA on all data, they found that this technique was able to make a distinction between columns that are considerably different from each other, for example, between classical and electrostatic shielded columns. PCA analysis also showed that the chosen parameters provided valuable information regarding the variability between the studied columns. Cluster analysis performed on the parameters, excluding efficiency, could cluster columns which were highly similar. Finally, radar plots were used to compare the columns and were found very useful in representing seven-dimensional data. In a radar plot, all seven parameters are first normalized to obtain a value between 0 and 1, and then displayed in a graphical manner, as illustrated in Fig 2. When the resulting plots are similar, such as in Fig 2a and 2b, the columns will exhibit similar separation abilities. When they are different (Fig 2a and 2c), the columns will also differ from each other. However, this approach is partly based on the visual expression of an analyst and did not allow a clear classification.

Figure 2: Examples of radar plots

In a next paper [7], 85 columns were characterized by the properties ligand density (retention factor of pentylbenzene), efficiency (plates per meter of pentylbenzene), hydrophobicity (retention factor ratio of pentylbenzene and butylbenzene), steric selectivity (retention factor ratio of triphenylene and o-terphenyl), hydrogen bonding capacity (retention factor ratio of caffeine and phenol) and the ion-exchange capacity at pH 2.7 and at pH 7.6, determined by calculating the retention factor ratios of benzylamine and phenol at the respective pH. Then, a chemometrical evaluation was performed using PCA. Three groups of columns could be distinguished. One group contained non-endcapped columns with poor surface coverage, based on acidic silica (type A), a second included polar-embedded C8 and C18 columns, and the largest group contained columns with different degrees of endcapping and differing silicas. When the first two groups were excluded, PCA analysis revealed another three clearly differentiated groups, and one somewhat more embedded group. The first three groups contained C8 columns, C18 columns with type A silica and/or with poor surface coverage and modern C18 columns with type B silica, respectively. The embedded group was situated within the group of C18 columns with type B silica, and contained the relatively hydrophobic C18 columns. It was demonstrated that PCA offers some possibilities to distinguish between columns, although it is not ideal. The authors recommend for rational method development where different selectivities are desired the use of columns from different groups, and of columns close to each other in the PCA score plot when column equivalence is searched for.

Ten perfluorophenyl and perfluoroalkyl phases have been evaluated in [17] by determining the properties ligand density, hydrophobicity, steric selectivity, hydrogen bonding capacity and the ion-exchange capacity at pH 2.7 and at pH 7.6-, in analogy with [7,16], followed by PCA analysis of the results. These phases could be further divided into three sub-groups: the perfluorophenyl phases, the perfluorohexyl and –octyl phases and the perfluorohexyl non-endcapped and propyl phases. The authors also demonstrated that the main difference between the perfluorophases and conventional alkyl and phenyl phases is their high discriminating power towards shape selectivity. The orthogonality of the perfluoro phases towards the alkyl phases was seen for both hydrophilic and lipophilic bases. A high retention of basic compounds was observed, compared with neutral analytes, and appeared to be controlled by a hydrophilic interaction mechanism in a high organic modifier content/low buffer concentration mobile phase. Further, the applicability of these phases for the analysis of a mixture containing hydrophilic and lipophilic compounds using LC/MS was demonstrated.

A more extended database of 135 columns, containing alkyl, cyano, phenyl, perfluorinated, polar embedded enhanced polar selectivity, aqua type and some novel stationary phases, was also analyzed as in [7,16,17] by determining the  chromatographic properties surface coverage (ligand density), hydrophobicity, shape selectivity, hydrogen bonding capacity and the ion-exchange capacity at low and high pH [18]. These properties were measured by determining the same parameters as in [7]. PCA provided a graphical comparison of the phases. For example, when the non-silica and amino phases were excluded, the first and second PC allowed dividing the silica-based stationary phases into three groups: 1) mostly non-C18 and type A C18 phases, 2) mostly type B C18 phases, and 3) polar-embedded phases. The PC1 and PC 3 score plot of the same subset allowed to define five groups: non C18 phases, acidic phases, perfluorophenyl phases, highly hydrophobic phases and cyano phases. Different subsets of the database were subjected to a further PCA analysis, and mostly groups of similar columns could be distinguished. Finally, an approach was proposed in Excel format that was able to perform a column ranking towards a reference column, rather similar to the database of Hoogmartens et al [5,6]. However, here the distances between the columns are obtained by calculating the Euclidean distances after autoscaling the six parameters.

Based on the previous paper [18], the software ACD/Column Selector (Advanced Chemistry Development) was developed. Here, after autoscaling of the parameters according to Eq. 2, a CDF value is calculated according to Eq. 4.

CDF = {(xn_t1–xn₁)²+ (xn_t2–xn₂)² + (xn_t3–xn₃)²+ (xn_t4–xn₄)²+ (xn_t5–xn₅)²+

(xn_t6–xn₆)²}^1/2                                                                         (Equation 4)

The CDF value represents the Euclidean distance between a test column with parameters xn_ti and a reference column with parameters xn_i. The lower the CDF value, the more similar the columns are. A high CDF value can be used to find dissimilar columns when one wants to obtain a different selectivity for a separation. In the software, it is also possible to give different weighing to the parameters. When one wants to find a column which is equivalent on the level of a given parameter, then the highest weighing is given to this parameter.

When the approaches defined by the groups of Euerby and Hoogmartens are compared, much analogy between their column ranking methodologies can be seen. Three mobile phases are used in the Hoogmartens’ approach to determine the column properties considered, in the one of Euerby, four mobile phases must be used. In the approach of Euerby, six properties are measured using 8 substances, i.e. surface coverage (ligand density), hydrophobicity, shape selectivity, hydrogen bonding capacity and the ion-exchange capacity at low and high pH, whereas in the one of Hoogmartens, only four, i.e. ion exchange capacity, presence of metal impurities, hydrofobicity and steric selectivity, are estimated using 7 substances. The column properties are determined in an easy way, i.e. only retention factors and relative retention factors of the test solutes are needed. Both groups have defined a column ranking methodology by defining a criterion (CDF value and F value, respectively) to calculate the differences between a test column and a reference column, which allows the user to find columns that are expected to behave similarly. Which approach performs best cannot be expressed at the moment, but it can be mentioned that the test parameters that are used in common by both groups (rk’_{benzylamine/phenol} pH 2.7, k’_amylbenzene and rk’_{triphenylene/o-terphenyl}) show high correlation [19], even though measured with different mobile phases.

After these studies, Euerby and Petersson also published a paper concerning classification of polar-embedded phases [20] by means of PCA. On eighteen polar embedded phases with a diverse range of polar functionality/alkyl chain length, 13 corresponding alkyl phases and 4 polar endcapped phases, four modified column characterization protocols were used. The protocols were based on the ones of Tanaka [18,21], Neue [22], Layne [23]. It was shown that these protocols, combined with PCA, were able make a distinction between the three types of phases included in this study. The chromatographic differences that are displayed in the PCA plots for polar embedded phases could be explained by the way they were fabricated, e.g. one- or two stage synthesized. The loading plots for the correlation of the column characterization protocols demonstrated that many measured parameters are correlated, meaning that the number of tests on a column can be reduced significantly to characterize the column completely. One of the proposed methods is that the Tanaka protocol is extended with the following tests: an anion exchange parameter a_BSA/Tl, measured by the retention factor ratio between benzene sulfonic acid and toluene; a phenolic selectivity parameter a_P/BA, measured by the retention factor ratio of phenol and benzylalcohol; and possibly an extra shape/steric term a_BN/S, measured by the retention factor ratio of benzoic acid and sorbic acid.

Dolan, Snyder and co-workers have also dedicated much research in the context of column selectivity. In [24], they have proposed an equation (Eq. 5) based on the solvation relationship introduced by the group of Abraham [25,26]. This equation should be applicable in RPLC to predict the retention of a given solute and includes both solute parameters (η’, σ’, b’, a’ and κ’) and column parameters (H, S, A, B and C). The applicability of this equation was evaluated by means of 67 test solutes, from which the retention was measured on 10 different C18 columns, and an additional 86 solutes on five C8 or C18 columns from a previous study [27]. The proposed equation enabled quite accurate predictions for both test sets considered, thus for a wide range of solute structures, but it was only evaluated in this study using measurements on similar monomeric C8 and C18 columns without a polar-embedded group.

In [28], the influence of changes in experimental conditions such as gradient time, temperature and solvent type was investigated by means of 67 test solutes on three C18 columns. It was seen that when changes in the log k of a solute, as a result of changes in experimental conditions, are the same on different columns, column selectivity and the relative values of H, S, A, B and C will not change. The authors demonstrated that changes in experimental conditions result in similar changes in log k for solutes measured on the three columns, thus the column parameters did not vary when changes in experimental conditions were induced. This means that the values of H, S, A, B and C in Eq. 5 can be determined once on a given column using one set of experimental conditions, and remain valid when other experimental conditions are applied. The only exception mentioned is when differences in mobile phase pH occur, which can have an effect on the value of C, a measure of the silanol ionisation.

In the next paper [29], the possible origin of the five terms of Eq. 5 in the context of physicochemical interactions that determine RPLC retention and selectivity were further explored. The finally resulting equation from the above studies [24,28,29], with denomination of all its components is:

log (k/k_ref) = log a = η’H + σ’S + b’A + a’B + κ’C                                    (Equation 5)

with k the retention factor of any solute, k_ref the value of the reference solute ethylbenzene; η’ the solute hydrophobicity, σ’ the steric resistance of the solute, b’ the solute hydrogen bond basicity, a’ the solute hydrogen bond acidity, and κ’ the relative charge on solute molecules. These are all properties that are related and dependent on the solute. The column/stationary phase properties that are included in this equation are the column hydrophobicity (H), the steric resistance to insertion of bulky solute molecules into the stationary phase (S), the column hydrogen-bond acidity (A), the column hydrogen-bond basicity (B), and the cation exchange activity due to ionized silanols (C). For the procedure to estimate the solute and stationary phase properties we refer to [24].

The equation was further explored for 92 Type B alkyl-silica columns with varying ligand length [30]. From this point on, the authors used only 18 test solutes instead of 67, as was initially the case. It was seen that H and S increase with increasing ligand length and –concentration, and decrease for large pore diameters, that A and C decrease for end-capped columns, and that B is not significantly affected by end-capping.

Further, an F_s value was defined to enable the comparison between different columns. It determines the distance between 2 columns in a 5-dimensional space.

F_s = {[f_ch(H₂–H₁)]² + [f_cs(S₂–S₁)]² + [f_ca(A₂–A₁)]² + [f_cb(B₂–B₁)]² + [f_cc(C₂ – C₁)]²}^½

(Equation 6)

The individual weighing factors f_i are calculated by taking 1/Δ(allowed) with Δ(allowed) the allowed variation in each column parameter for a  1% or  3% change in selectivity. Table 2 displays the Δ(allowed) values of each column parameter that were reported in [30].

Table 2: Weighing factors for F_s, reported in [30].

Note  that the values for a change of 1 % are used in the  following papers by the same group.

It was demonstrated that two columns with F_s ≤ 3 can be considered equivalent by plotting the Fs values against the standard deviation, i.e. columns with an F_s value below 3 display an acceptable standard deviation on the log k value. When columns with different selectivities are wanted, the F_s value is preferably as large as possible.

However, equation 6 assumes that the sample analyzed is sufficiently diverse so that all column properties are significantly important, although this is mostly not the case. Therefore, the authors suggest using adapted equations depending on the sample. When no bases are present, the C-term must be omitted; when no acids are present, the B term, and when neither acids nor bases are present, both B and C terms are deleted. Because these adapted F_s values will be smaller than those calculated originally, more equivalent columns will be found for samples free of acids and/or bases.

In a next study [31], 38 higher metal content (Type A) alkyl silica columns and three bonded-zirconia columns were investigated. For the Type A columns, a reduced accuracy of the revised equation 5, equation 7, was seen.

log (k/k_ref) = log a = η’H - σ’S* + b’A + a’B + κ’C                                  (Equation 7)

Equation 7 is the same as equation 5, only the term + σ’S was replaced by -σ’S* where S* = -S, because this term is repulsive in nature while the others are attractive. The decrease in accuracy with the columns in [31] can arise from a changed steric hindrance in the RPLC interactions of different solutes with Type A columns. When equivalent columns were sought using equation 6, it was seen that the F_s value was above 3 for the 41 investigated columns, meaning that the probability in finding similar Type A columns is low. When an equivalent Type B column was searched for a given Type A column, only one Type A column appeared equivalent (Fs ≤ 3) with a Type B column. When terms were omitted from equation 6 as a function of the sample properties, in analogy with [30], more F_s values were found smaller than 3 when the samples did not contain either acids or bases. The percentage of equivalent Type B columns increased from 70 to 94 %, and for the Type A columns from 0 to 90 % when the samples were free of acids and bases.

The procedure that has been used to determine the parameters H, S*, B, A and C of alkyl silica columns by means of the 18 selected test solutes in the previous papers [30,31] was evaluated for reproducibility in four different labs in [32]. It was found that the reproducibility of the proposed method was adequate for its purpose.

Similarly to [30,31], 21 columns with embedded or end-capping polar groups were investigated in [33]. It was investigated whether equation 7 was still applicable to describe selectivity on these columns. Although agreement with the measured retention data on these columns with equation 7 was not spectacularly good, the authors concluded that it could be used also for these columns without any changes. This means that the equation was already applicable on a set of 154 (92+41+21) columns. When equation 6 was used to compare the 21 embedded polar group columns with each other, and with 87 Type-B columns or 43 type A columns, only one column displayed an F_s value smaller than 3. This indicates that there is a great diversity between the embedded polar group columns, making it less likely to find an equivalent replacement column. Another possibility is that F_s ≤ 3 is defined too strict to represent similarly behaving columns. Occasionally, a more representative critical F_s value could be defined from a number of relevant separations, e.g. from compendial analyses, as was done by Hoogmartens’ group [5,6,34,35]. Now the authors only consider a limited test set of compounds, no separations are taken into account.

In [36], it was seen that equation 7 was also applicable for 11 cyanopropyl columns, thus for a total of 163 RPLC columns. Although the agreement of the retention data of these columns with Eq. 7 was found worse than for Type B columns, it was better than for Type A columns and those with an incorporated polar group. When three columns were compared with the Discovery CN column by calculation of the F_s value using equation 6, it was seen that similar separations can be observed also on a column that exhibits an Fs value of 5, thus the maximum value of 3 is somewhat liberalized for these columns. Comparison of cyanopropyl columns with C18 column types was not found practical, because these columns usually require a less strong mobile phase (reduced solvent strength), changing the selectivity. Thus, a replacement of a C8 or C18 column with an “equivalent” cyanopropyl column is usually not possible.

A next study [37] involved 11 phenyl and 5 fluoro-substituted columns. Again, the applicability of equation 7 was investigated. For this type of columns, additional column-solute interactions contribute to retention and selectivity. Therefore, H, S*, A, B and C values for fluoro-substituted columns are found less reliable to compare the selectivities. Phenyl columns on the other hand can be compared by means of their column parameters, because any additional contribution to selectivity seems similar in magnitude for the different phenyl columns. Regarding finding equivalent columns, both types must also be considered separately. For phenyl columns, which are made from type B silica, column replacement within the phenyl group is often possible. They exhibit all relatively similar selectivities, as the cyanopropyl columns do [36]. However, for the fluoro-substituted columns, replacement of one fluoro-substituted column by another is often not possible. Here again, the probability in finding an equivalent column increases when samples do not contain bases or acids, when a larger number of columns is available and/or for separations with a large resolution.

In the most recent paper of the Dolan, Snyder et al. series [38], a general approach was presented to select an equivalent replacement column for RPLC assays. In this paper, an adapted F^*_s value was defined which takes into account the sample compositions:

F*_s = {[12.5(H₂–H₁)]² + [100(S*₂–S*₁)]² + [30(A₂–A₁)]² + [143 x_B (B₂–B₁)]² + [83x_C(C₂ – C₁)]²}^½                                                                                                        

(Equation 8)

The values 12.5; 100; 30; 143 and 83 in this equation are valid for an “average” sample and are the 1/Δ (allowed) (see table 2) values for a 1% change in selectivity. For specific samples, an adjustment of the weighing factors can be beneficial, and it is incorporated in the equation by introducing the terms x_B and x_C., which have a value between 0 and 1. When no bases are present in the sample, x_C = 0, because the C term (cation exchange activity due to ionized silanols) is mostly affected by the retention of ionized basic solutes. Similarly, x_B = 0 when no acids are present in the sample. Values of x_C can also vary with mobile phase pH, because when the basic solutes are only partly ionized, x_C around 0.1 is to be used.

Also, another criterium Q was defined, i.e. the maximum allowable value of F^*_s as:

Q = 3/2 Rs                                                                                                 (Equation 9)

with Rs the critical resolution, i.e. the smallest resolution between two peaks from the sample.

For equivalent columns:

F*_s ≤ Q                                                                                                     (Equation 10)

With equivalent columns, the authors mean columns where i) the critical resolution does not decrease by more than 25 %, ii) major changes in resolution of other peaks were not observed, and iii) no peak reversals are present.

The authors evaluated the applicability of equations 8 and 10 by means of examples of separations of different mixtures on columns of which the F*_s value was calculated. It was seen that two columns are probably interchangeable when equation 10 is fulfilled. However, it was also found that when F*_s ~ Q, the prediction of column similarity is less certain.

Below we give the six steps for the convenient use of equation 8, as described by the authors [38]:

1. Collect values of H, S*, A, B, C(pH 2.8) and C(pH 7.0) for column 1 (original column) and 2 (potential replacement column); data for more than 300 columns are listed in [15] and included as part of the software package Column Match (Rheodyne LLC, Rohnert Park, CA).

When the values of these column parameters are unknown, they can be determined by application of the proposed test methods, i.e. by measuring the retention of 18 solutes using 2 mobile phases (acetonitrile/buffer (50/50, v/v) composition using a 60 mM phosphate buffer with either pH 2.8 or 7.00). However, the determination of the parameters themselves is a rather complex matter. They are determined from Eq. 5 (or Eq. 7) by multiple regression of log a as a function of the solute parameters, which are listed in [30]. For more details about the determination of the parameters H, S*, A, B, C(pH 2.8) and C(pH 7.0), we refer to [24].

2. Determine the value of C for the pH of the mobile phase:

C=C(2.8) + ([pH] − 2.8/[7.0 − 2.8])(C[7.0] − C[2.8])

If pH < 2.8, assume C=C(2.8); if pH > 7.0, assume C=C(7.0).

3. Determine values of the correction factors x_B and x_C: If the sample contains strong bases (pKa in water >9; e.g., molecules substituted by aminoalkyl groups), then

x_C = 1.0 when pH < 6; 0.1 when 6 < pH< 10, and 0.0 when pH ≥10. If the sample contains only weak bases (anilines, pyridines), then x_C = 0.1 when pH < 5, and 0.0 when pH > 5. If the sample contains neither strong nor weak bases, x_C =0.

If the sample contains carboxylic acids, x_B = 1.0; if not, x_B =0.

The values of x_B and x_C estimated above are necessarily quite approximate, but are the best available at the present time. More precise values of x_B and x_C would require a knowledge of solute pKa values and their dependence on separation conditions (i.e., organic solvent type and concentration, buffer concentration, temperature, etc.), and of the quantitative dependence of values of κ’ on the relative ionization of the solute.

4. Calculate a value of F^*_s from equation 8, using the above values of H, S*, A, B, C and values of x_B and x_C.

5. Determine the critical resolution Rs of the original chromatogram; calculate a maximum value of F^*_s = Q from equation 9.

6. Compare the above values of F^*_s and Q; if F^*_s ≤ Q, then the two columns are likely to be equivalent. Two columns may be equivalent for F^*_s larger than Q.

When comparing the approach of column ranking according to the group of Dolan and Snyder with those defined by the groups of Euerby and Hoogmartens, it can be stated that only two mobile phases must be used to determine the column parameters compared with three and four mobile phases in the approaches of Euerby and Hoogmartens, respectively, to measure the required parameters. However, the number of test solutes is large, i.e. 18 test solutes are considered to determine five column parameters compared with 8 substances for six parameters and 7 compounds to estimate four parameters with Euerby and Hoogmartens, respectively. The calculations that are involved to determine the values of the column parameters, seem however relatively complex, but the parameters for more than 300 columns are available through their developed software.

In the approach of Dolan and Snyder, a criterion for column ranking in terms of selectivity is also defined, as in the other two, and includes a weighing of the parameters, depending on the sample characteristics. Summarized, this approach is more complex to understand and to use.

Which of the three approaches is best still should be examined. A comparison between the approaches of Hoogmartens and Euerby was made [39]. It was concluded that both systems allowed a similar classification of columns and can be useful in the selection of a suitable column. From a practical point of view, preference was given to the system of Hoogmartens, as the experiments are less time-consuming.

Conclusion

Although the stated problem of column selection in case of compendial analysis is very well known, only few groups really performed investigation in finding an appropriate column as an alternative for the recommended, i.e. selecting a column with similar selectivity. Amongst the chemometric approaches to cluster columns based on various parameters, we can find Principal Component Analysis as the most frequently used. Although some clear classifications are obtained in the stated works, it is often difficult to determine the groups of similar columns when there is no prior knowledge of the column properties (C18, C8, polar-embedded, etc.).

More practical approaches to characterize and rank columns have undoubtedly been proposed by the respective groups of Dolan and Snyder, Euerby and Hoogmartens. Column similarity was defined by comparing test parameters of a tested column with those of a reference column. All approaches can also be used to find dissimilar columns, for example when different selectivities are sought.

Deciding which approach is better and why needs further research, but we can mention the advantages and drawbacks. The approaches of Hoogmartens and Euerby can be considered similar in the labor that is required in the determination of the column parameters (three and four mobile phases using 7 and 8 test solutes, respectively). The parameters used in the equation to compare columns are simply derived from the measured retention of the test compounds. The approach of Snyder requires the use of 2 mobile phases and a set of 18 test solutes. The determination of the column parameters from the measured retention factors is more tedious and requires a multiple regression. Further, we can mention that weighing of the parameters is (possibly) considered for the approaches of Snyder and Euerby, for the one of Hoogmartens it was not. For the three approaches, software was developed. For the one of Dolan/Snyder’s group only a free evaluation version is available; for the one of Euerby, a license is needed, while the software of Hoogmartens is freely accessible on the internet. Regarding the software content, 80 columns were characterized in the one of Hoogmartens, more than 300 were included by Dolan/Snyder, while the number of incorporated columns in the software of Euerby is unknown.

From the above, we can therefore conclude preference can be given to the less complex approaches to start with, i.e. the approaches of Euerby or Hoogmartens. Since the latter offers free software for columns ranking on the internet, one might start with this approach when searching for columns with equivalent selectivity.

Acknowledgements

D. Mangelings is a Postdoctoral Fellow of the Research Foundation-Flanders (FWO)

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