Characterization and Classification of Pseudo-Stationary Phases in

Article pubs.acs.org/ac

Characterization and Classification of Pseudo-Stationary Phases in Micellar Electrokinetic Chromatography Using Chemometric Methods Cexiong Fu¶ and Morteza G. Khaledi* Department of Chemistry, North Carolina State University, Box 8204, Raleigh, North Carolina, 27695-8204, United States S Supporting Information *

ABSTRACT: Two types of chemometric methods, principal component analysis (PCA) and cluster analysis, are employed to characterize and classify a total of 70 pseudostationary phases (54 distinct systems and 16 decoy systems) in micellar electrokinetic chromatography (MEKC). PCA excels at removing redundant information for micellar phase characterization and retaining principal determinants for phase classification. While PCA is useful in the characterization of micelle selectivities, it is ineffective in defining the grouping of micellar phases. Hierarchical clustering yields a complete dendrogram of cluster structures but provides only limited cluster characterizations. The combination of these two chemometric methods leads to a comprehensive interpretation of the micellar phase classification. Moreover, the k-means analysis can further discern subtle differences among those closely located micellar phases. All three chemometric methods result in similar classifications with respect to the similarities and differences of the 70 micelle systems investigated. These systems are categorized into 3 major clusters: fluoro-surfactants represent cluster I, identified as strong hydrogen bond donors and dipolar but weak hydrogen bond acceptors. Cluster II includes sulfonated acrylamide/acrylate copolymers and surfactants with trimethylammonium head groups, characterized by strong hydrophobicity (v) and weak hydrogen bond acidity (b). The last cluster consists of two subclusters: clusters III and IV. Cluster III includes siloxane-based polymeric micelles, exhibiting weak hydrophobicity and medium hydrogen bond acidity and basicity (a), and the cluster IV micellar systems are characterized by their strong hydrophobicity and medium hydrogen bond acidity and basicity but rather weak dipolarity. Cluster III differs from cluster IV by its slightly weaker hydrophobicity and hydrogen bond donating capability. The classification by chemometric methods is in good agreement with the classification by the micellar selectivity triangle (MST) (Fu, C.; Khaledi, M. G. J. Chromatogr., A 2009, 1216, 1891−1900).

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to characterize the chemical selectivity of a wide range of PSPs in MEKC, including anionic, cationic, bile salts, fluorinated micelles, microemulsion, ionic polymers, polymeric micelles, solvent-modified and mixed micelles as well as vesicles and liposomes.1 The MST classification is based on the relative strength of the underlying chemical interactions that have been derived from the LSER system parameters. The elution patterns in MEKC could be readily estimated on the basis of chemical selectivity of the PSPs as characterized and classified by the MST. However, there are still questions that remain to be answered and cannot be resolved solely by the triangle scheme, for example, the minimum number of variables that are sufficient to represent the selectivity properties of micelle phases or the extent to which each variable can influence the partitioning process of the solute. In this paper, two chemometric methods, namely, principal component analysis

icellar electrokinetic chromatography (MEKC) has gained enormous attention since its inception in the 1980s.2,3 In spite of the rapid development, selection of an optimum micellar phase in a systematic manner has been a challenge and largely relies on analysts’ experience and intuition. The imminent need for a systematic characterization of pseudostationary phases (PSP) in MEKC has encouraged continued efforts.4−6 Poole et al.6 summarized the linear solvation energy relationships (LSER) parameters of a large number of surfactant phases that had been applied to MEKC in the literature. General recommendations on micellar phase selection were suggested to utilize different interactive properties of various surfactant types. Notably, LSER parameters for many micellar phases are partially correlated in this report. This is especially true for the dipolarity parameter (s) and polarizability term (e). Therefore, the redundant information in the LSER database could interfere with and camouflage the essential factors for micellar phase characterization and classification. In our previous study, a novel micellar selectivity triangle (MST) scheme was successfully developed © 2014 American Chemical Society

Received: September 18, 2013 Accepted: January 21, 2014 Published: January 21, 2014 2371

dx.doi.org/10.1021/ac403231h | Anal. Chem. 2014, 86, 2371−2379

Analytical Chemistry

Article

Figure 1. Scatter plot of system parameter distribution for MEKC micelle systems.

chromatographic parameters required for the classification of 69 reversed phase columns. The PCA results indicated that a minimum of 4 system parameters were needed to produce a fairly good classification. It shall be noted that the abovementioned investigations all involved analysis with preselected test compounds that were significantly different in structures and numbers in the test set. Consequently, conflicting results have been reported when columns were characterized with different sets of test compounds. In this study, we apply multiple chemometric methods to analyze the system parameters of PSP that are derived from the LSER models and are less dependent on the test solutes number and properties. To the best of our knowledge, this is the first report on the application of chemometric methods for characterization and classification of PSP in MEKC.

(PCA) and cluster analysis, were used as alternative and complementary approaches for characterization and classification of selected PSP in MEKC. The PCA and cluster analysis methods are powerful in processing a large quantity of multidimensional and intercorrelated data and reducing data complexity. These multivariate analysis methods have been used to characterize retention patterns and selectivity of stationary phases and mobile phases in various GC and LC techniques.7−13 Abraham et al.13 reviewed the chemometric classifications of stationary phases in gas chromatography and identified the dipole−dipole interactive strength and the hydrogen bond basicity of the stationary phases as the main factors contributing to the first principal component in PCA. Cluster analysis also clearly visualized the grouping structure in the form of hierarchical trees. Chemometric methods have also gained significant popularity in liquid chromatography. Carr and co-workers14 evaluated three types of bonded phases (alkyl, aromatic, and fluorinated phases) with a PCA method in comparison to the LSER model. It was shown that the PCA method was more accurate in predicting solute retention than the LSER model, but the principal components could not provide a clear explanation for the differences between these three stationary phases. Euerby et al.9 characterized 135 commercially available reversed-phase columns by their surface coverage, hydrogen bonding capacity, hydrophobicity, and ion exchanging capability. The PCA analysis enabled the rationalization and identification of columns with similar selectivity. Ivanyi and colleagues15 applied the PCA method to determine the minimal number of

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EXPERIMENTAL SECTION Chemometric analysis was performed on a Dell Inspiron 4100; the software platform is Matlab 6.5 release 13 (The Math Works, Inc., Natick, MA). A database composed of the LSER models for 70 MEKC micelle systems was collected from the literature and this laboratory (Table 1S, Supporting Information) as reported previously.1,16−29

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RESULTS AND DISCUSSION The distribution patterns of the mean-centered LSER system parameters are presented in Figure 1. The distribution map reveals some intriguing information about the original data set prior to any chemometric analysis. First, a center-focused 2372



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weights of individual system parameter on the principle components are shown in Table 2. Hydrogen bond acidity (b) and dipolarity (s) are the two major factors that contribute positively to the first PC. While the second PC gains contribution mainly from hydrophobic interaction and minor contribution from dipolarity (s), the third PC features considerable negative contribution from system parameters (a and s). Two system parameters (b and e) play significant roles in the fourth PC, while the fifth PC obtains positive contribution from system parameters (v, b, and a) and negative contribution from s and e. The initial PCA results confirm that the best representation of the micelle systems require all five variables. These explain the success of LSER methodology using five different molecular interactions to characterize PSP in MEKC. However, since these five types of molecular interactions do not contribute evenly to the system characterization and contain correlated and redundant information, there is an opportunity to use a reduced number of parameters to describe the chemical selectivities of the PSPs with reasonable accuracy. The plot of the first PC against the second PC in Figure 3 employs the major determinants to differentiate the micelle systems. Two clusters of micelle systems are well-separated in the plot, namely, cluster I and cluster II. For the other two clusters, III and IV, no clear boundary could be defined, indicating comparable selectivity between these two clusters in the current PC space. Cluster I is the fluorinated surfactant series, located at the top-right corner and possessing a large first PC and intermediate second PC. As discussed above, the first PC is mainly determined by the strength of the hydrogen bond acidity and dipolarity. Thus, cluster I possesses strong hydrogen bond acidity and dipolarity, which agrees well with the LSER characterization. Moreover, the micellar selectivity triangle scheme also distinguished these fluoro-surfactants as strongly hydrogen bond acidic micelles. Cluster II consists of two micelle genres: one is a cationic surfactant (38, hexadecyltrimethyl ammonium bromide); another one is a group of alkyl methacrylate-based polymeric micelles. The location of cluster II is on the top-left corner of the plot, implying a small first PC but a large second PC. This unique assignment is attributed to the modest hydrogen bond acidity and dipolarity but a strong hydrophobic type of surfactant. Again, these findings are in good agreement with the LSER results. The division of cluster III and IV cannot be defined unambiguously as the first two clusters. However, a tentative classification was made on the basis of the ranges of the first and second PCs. Cluster III is a collection of the micelle systems located in the lower-left corner. The first two PCs for cluster III are considerably smaller than other clusters. Consequently, these surfactants have the lowest hydrogen bond acidity and dipolarity and weakest hydrophobic effects. The pseudophases 40 to 47 are siloxanebased polymers composed of an allyl glycidyl ether N-methyl taurine side chain. The pseudophase 33 is an anionic triblock copolymer, poly (methyl methacrylate-ethyl acrylate-methacrylic acid, Elvacite 2669). These PSPs share a common feature that all of them are rather slightly hydrophobic as indicated by a small second PC. These types of surfactants are grouped as strong hydrogen bond accepting agents in the MST method. However, the strength of the hydrogen bond basicity of the micellar phases cannot be evaluated in the plot of the first and second PCs because neither of the two PCs is influenced substantially by the hydrogen bond basicity of the PSP. Cluster IV is a collection of various types of PSPs in the center of the

pattern was observed for the system parameters. This is especially true for the hydrophobic parameter v. Most of the distributions are packed in a narrow range at the center. For system parameters b, a, and s, a much wider spread of normal distribution was observed; however, one still cannot recognize any pattern for grouping. A distinct trend is found for the distribution with system parameter e, where a “tadpole” shape distribution is observed because of the negative polarizability e of fluorinated surfactants, owing to their weak interaction with the n and π electrons of solutes. Another piece of useful information is that the highly centered distribution indicates an intercorrelated relationship between these system parameters, which cannot be differentiated without careful data processing. Thus, it is essential to employ chemometric methods to recognize classification information from these redundant and correlated data. Principal Component Analysis. LSER system parameters of the 70 MEKC pseudostationary phases were analyzed by a PCA method. The eigenvectors and eigenvalues are listed in Tables 1 and 2. The first principle component (PC) accounts Table 1. Contributions of LSER System Parameters to Principal Components v b a s e

PC1

PC2

PC3

PC4

PC5

−0.25 0.51 −0.42 0.47 −0.53

0.83 −0.30 −0.36 0.20 −0.23

−0.07 0.12 −0.73 −0.65 0.15

0.40 0.69 0.05 0.15 0.58

0.29 0.39 0.40 −0.54 −0.56

Table 2. Eigenvalues for Principal Components eigenvalue cumulated variance (%)

PC1

PC2

PC3

PC4

PC5

2.84 56.78

1.10 78.84

0.62 91.30

0.26 96.46

0.18 100.00

for the largest variance, 56.8%. The combination of the first and second PC describes 78.8% of the total variance. With the incorporation of the third and fourth PC, 96.5% of the total variances can be accounted for. The cumulative variance by the number of principal components is shown in Figure 2. Clearly, to obtain a satisfactory classification of the MEKC PSP systems, at least 4 parameters shall be taken into account. The respective

Figure 2. PCA analysis of LSER models in EKC. Eigenvalues explained by each principal component. 2373



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Figure 3. PCA analysis of LSER models in EKC: plot of the first principal component vs the second principal component.

Figure 4. PCA analysis of LSER models in EKC: 3D Plot of the distribution of micelle systems in three principal components space.

plot, indicating most of these systems have similar selectivity patterns and could be categorized as a group with intermediate strength in hydrogen bond acidity and dipolarity, as well as hydrophobicity. These surfactants were clustered in a similar manner in the classification of the MST. It is notable that various SDS micelle systems (1−6, 8−14, 66 and 70) from different laboratories and under various buffer solutions, which are used as decoy systems, are located closely in the cluster IV.

In MEKC, micelle concentration influences retention but should not have an effect on selectivity patterns of a PSP. Thus, clustering of a PSP at different concentrations into a small region is indicative of the validity of a classification method. To illustrate the effect of PCA analysis, three representative phases were selected: PSP 14 (SDS, with LSER parameters v, b, a, s, and e, as 2.56, −1.56, −0.33, −0.66, and 0.57), PSP 15 (0.04 M SDS+0.4 M PeOH: 2.85, −2.4, −0.03, −0.89, and 2374



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Figure 5. Hierarchical clustering for classification of MEKC micelle systems. Note: The leaf node numbers are the same as the micelle system identities in Table 1S, Supporting Information.

0.51), and PSP 18 (0.04 M SDS+0.4 M HFIP: 2.72, −1.38, −0.63, −0.38, and 0.2). It is difficult to differentiate the phases with various degrees of differences among the 5 descriptors. However, after PCA processing, only one PC (the first PC, 0.15, −1.25, and 1.75 for PSP 14, 15, and 18, respectively) is needed to separate these three systems. One interesting finding is that micelle system 34 (mixed micelle of LiDS and LiPFOS) is located midway between the SDS micelles and the LiPFOS micelles indicating the opportunity for constructing hybrid PSP with tunable selectivity with these mixed micelles. A similar trend was observed in the MST method. For a better view and representation of PSP properties, we incorporate the third PC together with the first two PCs to construct a 3-D score plot (Figure 4) of the 70 PSPs. Clearly, the addition of another dimension enhances the separation of the original condensed clustering. Thus, it enables one to further scrutinize the subtle selectivity differences among the micelle phases. This will be the most beneficial for PSP in cluster IV, which can be better separated in a 3-PC space than a 2-PC space. It is worthwhile to mention that the addition of a new PC dimension does not alter the previous 2D classification. Cluster Analysis. The hierarchical clustering method constructed a dendrogram structure for the classification of the 70 PSPs (Figure 5). A cophenetic correlation test was used

to assess the validity of the classification. A cophenetic correlation coefficient is often used to evaluate a hierarchical clustering model by comparing the fusion level of sublevel elements and their intrinsic distances. A cophenetic correlation coefficient close to unity indicates a synergetic correlation between the fusion level and the object distance within the subcluster. In our test, the cophenetic correlation test was performed on three different linkage algorithms: single linkage, average linkage, and complete linkage. The ranking of the cophenetic correlation coefficients is as follows: average linkage (0.88) > single linkage (0.81) > complete linkage (0.71). The relative high cophenetic correlation coefficient values of all three linkages indicate a satisfactory classification of PSPs without distorting the intrinsic structure. The complete linkage has the lowest cophenetic correlation coefficient probably because the complete linkage has a preference for a spherical shape clustering, which is not an ideal description of the current data. An “upper tail rule” test was used to determine the optimal number of clusters to define the data structure. The underlying mechanism of the method is that, at an optimal number of clusters, a further increase in the number of clusters will not significantly reduce the fusion level. This transition point on the plot of the fusion level vs the cluster number (Figure 6) will appear as a plateau or a shallower slope. It can be seen that the 2375



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Figure 6. Upper-tail rule for determining the number of clusters. (The steepness of the slope indicates the degree of the clusters separation.)

first transition occurs at 3 clusters and there is another transition at 5 clusters indicating some clusters could be further divided into subclusters. The complete classification of the 70 PSPs using the hierarchical clustering method is shown in Figure 5. Overall, it shows three clusters of micellar phases and one of the clusters can be further divided into two subclusters. For cluster I, these fluoro-surfactants (in blue) again are markedly distinguished from other micellar phases. The next cluster on the hierarchical clustering map is the cluster III in the PCA method with only addition of the micelle system (15). The hierarchical clustering method merged cluster II together with some PSPs in cluster IV. Examination of these reclassified PSPs reveals that these micelle phases reside on the left side of cluster IV in the PCA method. This group of PSPs can be either assigned to an independent subcluster or merged with cluster II. Apparently, the algorithm of the hierarchical clustering fused these pseudophases together with cluster II. The advantage of hierarchical clustering is the presentation of a visually and structurally clear classification of PSP selectivity. However, the pitfall is the lack of chemical characterization of each cluster. Consequently, one would not have knowledge about the characteristics of each cluster. On the contrary, the PCA method provides details on the properties of the micellar phases but cannot have a clear boundary to separate the cluster. Now with the combination of these two complementary chemometric methods, the analyst can make the classification with confidence. K-means clustering is another clustering method investigated in this study. As with other clustering methods, the optimum number of clusters shall be defined first. Here, a silhouette plot

(Figure 7) was employed for this purpose. For a two-cluster division, the silhouette plot yields one huge cluster with a silhouette value lower than 0.5, indicating poor separation between the clusters. In the three-cluster test, two small clusters yield high silhouette values and are well-separated. Meanwhile, significant improvement of the silhouette values is obtained for the components in the major cluster. We also attempted a fourcluster classification, in which the first two clusters yield high silhouette values indicating complete separation. However, clusters 3 and 4 result in decreasing silhouette values reflecting an overfitting of the classification. By using the silhouette plot, the classification of these PSPs with a 3-cluster scheme gave a better representation of the data. The classification by the k-means method is shown in Figure 8 with three factors (v, b, and a). The division of three clusters is similar to the classification of the hierarchical clustering. Fluoro-surfactant series (in pink diamond) are characterized as strong hydrogen bond donating agents but weak hydrogen bond acceptors. In contrast, the systems in the red triangle represent the PSPs originally included in cluster III by PCA. These PSPs show drastically different characteristics compared with the fluoro-surfactants. They are more hydrogen bond basic but less hydrogen bond acidic. The remaining micelle systems are all grouped into one cluster, located near the center of the 3-D plot, and show moderate hydrogen bond acidity and basicity. One of the advantages of k-means clustering is that the detailed analysis of the influence of all chemical interactions on the clustering can be seen in one distribution plot (Figure 9). In comparison to the distribution plot prior to any chemometric data processing (Figure 1), k-means clustering resolved those subtle differences of micelle phases, which benefit the 2376



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Figure 7. Silhouette plot to determine the number of clusters for k-means clustering. From top to bottom are silhouette plots for 2, 3, and 4 clusters, respectively.

recognition of the patterns and characterization of the micelle phases. The three clusters are well-resolved in the distribution map, especially for the hydrophobic interaction parameter (v) dimension. In the first column of the map, the three clusters

exhibit significant separation in various plots. For instance, fluoro-surfactants could be assigned as strong hydrogen bond donating (b) and dipolar (s) micelles and medium hydrophobicity (v) but very weak hydrogen bond basicity (a) and 2377



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Figure 8. K-means clustering for classification of MEKC micelle systems. Note: the circles with a cross inside indicate the centroids of the clusters. The axes are the LSER system parameters after k-means clustering.

Figure 9. Scatter plot of the distribution of LSER coefficients after k-means clustering.

hydrophobicity (v). The last cluster is represented by the SDS type of hydrocarbon surfactants, possessing strong hydrophobicity (v) but rather moderate characteristics for the other four types of molecular interactions. A subcluster is observed in the green group. These trends are obvious in the distribution

polarizability (e). The cluster in blue represents the siloxanebased polymeric micelles. These micelle systems also have unique selectivity characteristics, which are identified as strong hydrogen bond acceptors, polarizable, and moderate hydrogen bond donating ability and dipolarity but with significantly lower 2378



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plots between v and b, but merged in plots involving a, s, and e. This subcluster consists mainly of the PSPs from cluster II of the PCA classification. This evidence casts new light on the chemical properties of the clusters: cluster II has a similar strength in a, s, and e parameters with cluster IV but differs primarily in hydrophobicity and hydrogen bond donating capability.

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CONCLUSIONS We systematically investigated the applications of the chemometric methods for the classification of the 70 pseudophases in MEKC. The PCA method is shown to be best at filtering redundant information and reducing the dimensionality of the data. Hydrogen bond basicity and dipolarity are the two main factors contributing to the first PC while hydrophobicity is the leading factor to influence the second PC. It is also concluded that, to obtain the best representation of the chemical selectivities of the PSPs, all five LSER parameters are required for a complete and accurate description of the PSP interactive properties. Meanwhile, it is recognized that the first four PCs can account for over 96% of the total variances and represent a satisfactory classification of the PSPs. All chemometric methods are assessed with the corresponding test methods to ensure the validity of the classifications. The classifications of three chemometric methods result in good agreement. Slight differences between the PCA method and cluster analysis exist, mainly because the PCA method does not define the boundary for each cluster. In contrast, the dendrogram of hierarchical clustering presents a visually clear classification of the micelle systems but lacks the chemical characterization of each cluster. The combination of the PCA and hierarchical clustering yielded a satisfactory classification of the 70 PSPs into three clusters. Furthermore, the k-means clustering revealed more subtle differences than PCA and hierarchical clustering in the distribution map. With the kmeans clustering, we can resolve the details of the contributions of various types of interactions contributing to chemical selectivity in the classification and characterize each cluster. For future classification of micelle systems, one should employ at least the PCA method and one clustering method in order to obtain a well-resolved and accurate classification.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ¶

C.F.: Hospira, Inc., H3-3N, 275 N. Field Drive, Lake Forest, IL 60045.

Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Fu, C.; Khaledi, M. G. J. Chromatogr., A 2009, 1216, 1891−1900. (2) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834−841. (3) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchiya, A.; Ando, T. Anal. Chem. 1984, 56, 111−113. (4) Muijselaar, P. G.; Otsuka, K.; Terabe, S. J. Chromatogr., A 1997, 780, 41−61. 2379


Characterization and Classification of Pseudo-Stationary Phases in

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