Determination of the Effective Charge Numbers and Ionic Mobilities of Single Isomer and Randomly Highly Sulfated Cyclodextrins by Capillary Isotachophoresis and Zone Electrophoresis

ABSTRACT

Sulfated cyclodextrins (CDs) are multiply negatively charged molecules widely used as chiral selectors in capillary electrophoresis (CE). In some of their applications, the effective charge numbers of their molecules were observed to be lower than the numbers of the attached sulfated groups due to strong binding of counterions. However, degree of reduction of the theoretical charge was not quantified. For that reason, in this study, capillary isotachophoresis (CITP) and capillary zone electrophoresis (CZE) were applied for the determination of the effective charge numbers and actual ionic mobilities of two kinds of sulfated CDs: single isomer sulfated α‐, β‐, and γ‐CDs (SI‐CDs) and randomly highly sulfated α‐, β‐, and γ‐CDs (HS‐CDs). The effective charge numbers of the SI‐CDs and HS‐CDs were determined from the length of their ITP zones, the ionic mobilities determined by CZE, and molar concentrations of their solutions applied for CITP analysis, and from the same parameters of reference compounds, formic acid for SI‐CDs and dichloroacetic acid for HS‐CDs. The determined effective charge numbers of the SI‐CDs were equal to or only slightly lower than the numbers of sulfate groups in their molecules but the effective charge numbers of randomly HS‐CDs were significantly (22.2%–27.8%) reduced as compared to the average numbers of sulfate groups in their molecules. In accordance with a lower number of sulfate groups in SI‐CDs than in HS‐CDs, the absolute values of the actual ionic mobilities of SI‐CDs (35.5–37.5) × 10⁻⁹ m² V⁻¹ s⁻¹ were lower than those of HS‐CDs (43.5–44.1) × 10⁻⁹ m² V⁻¹ s⁻¹.

Abbreviations

CD

cyclodextrin

Glu

glutamic acid

His

histidine

HPC

hydroxypropylcellulose

HS‐CDs

randomly highly sulfated CDs

HVL

Haarhoff‐Van der Linde

LE

leading electrolyte

SI‐CDs

single isomer sulfated CDs

TE

terminating electrolyte

TU

Tiselius unit (1.0 × 10⁻⁹ m² V⁻¹ s⁻¹)

1. Introduction

Sulfated cyclodextrins (CDs) belong to the most powerful and most frequently used chiral selectors in capillary electrophoresis (CE) [1, 2, 3]. As shown in several earlier published as well as recent articles, sulfated CDs are able to separate enantiomers or diastereomers of various neutral, basic, amphoteric, and even anionic chiral analytes [1, 4, 5, 6, 7, 8, 9, 10, 11, 12]. This makes them preferred chiral selectors not only among the CDs but also among the other stereoselective resolving agents applied in chiral CE. Sulfated CDs are available in two forms, either as single isomer CDs (SI‐CDs) with well‐defined number and distribution of the sulfate groups [13, 14, 15, 16, 17], see Figure 1A–C, or as randomly highly sulfated CDs (HS‐CDs) with various degrees of substitution (DS) and with various distributions of sulfate group per CD molecules [1–3, 18, 19], see Figure 1D–F.

FIGURE 1.

Structures of the single isomer 6‐sulfated‐2,3 acetylated α‐, β‐, and γ‐CDs (SI‐CDs) (A–C) and randomly highly sulfated α‐, β‐, and γ‐CDs (HS‐CDs) (D–F). The number of sulfate groups in HS‐CDs is equal to the rounded value of the average degree of substitution of their molecules, and the presented positions of sulfate groups represent one random distribution of positional isomers of HS‐CDs from a high number of other potential distributions. HS‐CDs, randomly highly sulfated cyclodextrins; SI‐CDs, single isomer sulfated cyclodextrins.

For the randomly substituted HS‐CDs, only an average DS is known but the actual isomeric heterogeneity, effective charge, and charge distribution are not exactly specified [18, 19]. However, not the average DS but the actual effective charge and the actual distribution of the differently substituted CD regioisomers are the most important parameters for the enantioselectivity of the HS‐CDs. This is due to the different effective charges, electrophoretic mobilities, and binding capabilities of the individual differently substituted HS‐CDs. When a complex mixture of HS‐CDs is used for chiral separations, the different regioisomers may exhibit both positive and negative effects on the overall separation of enantiomers. Moreover, the great proximity of sulfate groups in HS‐CDs and high proximity energies of such systems [20] cause that the effective charge of HS‐CDs is usually lower than the number of sulfate groups in the CD molecules because the total high negative charge of HS‐CDs is partially compensated by the strong noncovalent binding of the cationic counterions to the neighboring negatively charged sulfate groups. This effect is called counterion condensation [21, 22].

Electric charge is an important parameter of ionogenic/charged molecules. It significantly influences their structure, stability, solubility, and interactions with other molecules. The effective charge of an oligo‐ or polyelectrolyte is defined as the real charge of the molecule considering all the ionized groups of this molecule and any ionic species tightly bound to it. Effective charge of the molecule depends on several parameters, such as pH, counterion condensation, and interactions with components of the surrounding medium [23, 24]. For weak and amphoteric electrolytes, the charge may be regulated by pH and composition of the background electrolyte (BGE). The effective charge of multivalent ions depends also on the positions of charged groups relative to one another. Close positions of the charges with the same sign result in a high electrostatic potential energy in their vicinity and counterion binding to these local charges. Counterion condensation occurs especially if the distances between charges are comparable or less than the Bjerrum length (0.71 nm in water solution at 25°C) [21, 22].

The effective charge of polycationic or polyanionic species may differ significantly from the number of ionogenic groups and from the theoretically calculated charge using the acidity constants of ionogenic groups [25, 26, 27, 28]. These theoretical calculations neglect counter‐ion condensation and may significantly differ from the real values [20, 29].

Several experimental and theoretical methods have been used for determination of effective charge of various polyelectrolytes, such as electric conductivity [30] and osmotic pressure [31] measurements, light scattering techniques [27], and CE [23–25, 27, 29, 32–34]. In addition, capillary isotachophoresis (CITP) was introduced as a suitable method for determination of effective charge of nanoparticles [35] and various both cationic and anionic polyelectrolytes [36, 37] and peptides [38]. In CITP, the studied compounds are separated in a discontinuous electrolyte system constituted by the leading electrolyte (LE) and the terminating electrolyte (TE), and the determination of the effective charge of separated compounds is based on the linear dependence of their ITP zone length on their concentration and charge.

For the evaluation and characterization of the binding and enantioselective capabilities of SI‐CDs and HS‐CDs, it is important to know the effective charge and the distribution of charge in their molecules, because they significantly influence the strength and stereospecificity of the enantiomer‐selector interactions. In some of sulfated CDs applications, it was observed that the effective charge of their molecules is lower than the number of the attached sulfated groups [1, 10, 39, 40]. However, the degree of the reduction of the theoretical charge due to counterion condensation was not quantified. For that reason, the aim of this study was to apply CITP and capillary zone electrophoresis (CZE) methods for determination of the effective charge numbers and the actual ionic mobilities of single isomer α‐, β‐, and γ‐CDs (SI‐CDs) and randomly HS α‐, β‐, and γ‐CDs (HS‐CDs), that is, to estimate the range of counterion condensation in these polyanionic compounds.

2. Materials and Methods

2.1. Chemicals

All the chemicals used were of analytical‐grade purity. Hydrochloric acid (cat. no. 84415) and formic acid (cat. no. 94318) were obtained from Fluka. l‐Glutamic acid (Glu) was supplied by Merck. l‐Histidine (His, cat. no. 53319), dichloroacetic acid (Cl₂CHCOOH, cat. no. D54702), and hydroxypropylcellulose (HPC, M = 1 × 10⁵ g mol⁻¹, cat. no. 191884) were obtained from Sigma Aldrich (Steinheim, Germany). Sodium hydroxide and dimethyl sulfoxide (DMSO) were supplied by Lachema (Brno, Czechia).

2.2. Single Isomer and Randomly HS‐CDs

The list of analyzed single isomer 6‐sulfated‐2,3‐diacetylated α‐, β‐, and γ‐CDs (SI‐CDs) and randomly HS α‐, β‐, and γ‐CDs (HS‐CDs), their abbreviations, relative molecular masses of their sodium salts, M _r, and the DS by sulfated groups are presented in Table 1, and their molecular structures are shown in Figure 1. They were obtained from the following suppliers: The SI‐CDs, hexakis‐(2,3‐diacetyl‐6‐sulfato)‐α‐CD sodium salt (SI‐α‐CD), heptakis‐(2,3‐diacetyl‐6‐sulfato)‐β‐CD sodium salt (SI‐β‐CD), and octakis‐(2,3‐diacetyl‐6‐sulfato)‐γ‐CD sodium salt (SI‐γ‐CD) were from TM Chemicals LP (Deer Park, TX, USA). The randomly HS α‐CD sodium salt hydrate (HS‐α‐CD) and randomly HS β‐CD sodium salt (HS‐β‐CD) were from Sigma Aldrich (Steinheim, Germany). Randomly HS γ‐CD sodium salt (HS‐γ‐CD) was delivered by Ara Chemie GmbH (Wiehl, Germany).

TABLE 1.

Known and calculated physicochemical parameters of analyzed single isomer sulfated cyclodextrin (SI‐CDs), randomly highly sulfated cyclodextrins (HS‐CDs), and reference compounds, HCOOH and Cl₂CHCOOH.

Analyte	M r	z eff,theor (DS)	μ ± SD (10−9 m2 V−1 s−1]	Δt ± SD (s)	z eff,exp ± SD	z eff,exp/z eff,theor	R (%)	(z eff,exp/M r) × 1000
SI‐α‐CD	2089.6	−6.0	37.53 ± 0.07	50.9 ± 0.42	−6.10 ± 0.18	1.017	−1.7	2.92
SI‐β‐CD	2437.8	−7.0	36.54 ± 0.27	52.1 ± 0.22	−6.58 ± 0.24	0.940	6.0	2.70
SI‐γ‐CD	2786.1	−8.0	35.52 ± 0.10	53.6 ± 0.17	−7.54 ± 0.30	0.943	5.7	2.71
HCOOH	46.03	−1.0	52.40 ± 0.03	22.5 ± 0.23	−1.0 ± 0.0	1.0	0.0	21.72
HS‐α‐CD	2024.5 a	−10.2 a	44.06 ± 0.07	49.9 ± 0.19	−7.37 ± 0.10	0.722	27.8	3.64
HS‐β‐CD	2462.3 a	−13.0 a	43.76 ± 0.02	49.7 ± 0.23	−9.70 ± 0.22	0.746	25.4	3.94
HS‐γ‐CD	2726.5 a	−14.5 a	43.45 ± 0.11	51.8 ± 0.10	−11.30 ± 0.05	0.778	22.2	4.14
Cl2CHCOOH	128.94	−1.0	30.07 ± 0.02	24.6 ± 0.00	−1.0 ± 0.0	1.0	0.0	7.76

Note: M _r, molecular mass of sodium salts; z _eff,theor, theoretical effective charge number (equal to the degree of substitution [DS]); μ, actual ionic mobility at 25°C and 10 mM ionic strength; Δt, length of the ITP zone; z _eff,exp, experimentally determined effective charge number; R, reduction of the theoretical charge number.

^a Average values.

2.3. Capillary Isotachophoresis

CITP analyses were performed in Agilent 7100 CE system (Agilent Technologies, Waldbronn, Germany) with built‐in UV–vis spectrophotometric diode array detector and additionally equipped with TraceDec contactless conductivity detector (Innovative Sensor Technologies GmbH, Strasshof an der Nordbahn, Austria). Total length of the 50 µm id/375 µm od fused silica capillary with polyimide outer coating (Polymicro Technologies, Phoenix, AZ, USA) was 424 mm. Effective length to the conductivity detector was 279 mm and to the UV–vis detector 339 mm. The inner capillary wall was permanently coated with HPC as described elsewhere [41, 42]. Prior to analysis and between the CITP runs, the capillary was rinsed with the LE at 2 bar for 2 min. The samples containing a mixture of the SI‐CDs and reference compound (formic acid) or the mixture of HS‐CDs and reference compound (dichloroacetic acid) were introduced into the capillary hydrodynamically (30–40 mbar × 25–35 s). The separation capillary inside the cartridge was thermostated at 25°C. UV detector wavelength was set at 210 nm. Parameters of the contactless conductivity detector were adjusted in order to have a signal between 0 and 300 mV for all CITP runs. For the composition of the LE and TE of the selected anionic ITP electrolyte system, see Section 4.1.

2.4. Capillary Zone Electrophoresis

CZE was carried out in the same apparatus (Agilent 7100 CE system with UV–vis and contactless conductivity detectors) and using the same HPC‐coated fused silica capillary of the same dimensions as those used for the CITP analyses. CZE determination of the ionic mobilities of SI‐CDs, HS‐CDs, and the reference compounds, formic acid and dichloroacetic acid, respectively, was performed in the BGE of the same composition as that of the LE used in CITP (10 mM HCl, 20 mM His, pH 6.1) and at the same temperature of 25°C. Between runs, the capillary was rinsed with the BGE (1 bar × 2 min). Solutions of SI‐CDs and HS‐CDs and reference compounds were injected hydrodynamically (10 mbar × 5 s). Separation voltage was set at −11.0 kV (cathode at the injection capillary end), and the detection wavelength of the UV–vis detector was 200 nm.

3. Theoretical Background

3.1. Determination of Actual Ionic Mobilities

The actual ionic mobility, µ, of the SI‐CDs and HS‐CDs and of the reference compounds, formic acid, and dichloroacetic acid, that is, the mobility of the fully charged ionic species at the 10 mM ionic strength of the BGE and at 25°C, was calculated as a difference between their apparent ionic mobility, µ _a, and the electroosmotic flow (EOF) mobility of the BGE, µ _eof:

$$\mu ={\mu }_{\mathrm{a}}-{\mu }_{\mathrm{eof}}$$ (1)

The apparent ionic mobility, µ _a, was obtained from the following equation:

$${\mu }_{\mathrm{a}}=\frac{L_{\mathrm{tot}}{L}_{\mathrm{eff}}}{U_{\mathrm{sep}}{t}_{\mathrm{mig}}}$$ (2)

where L _tot is the total capillary length, L _eff is the effective (to the detection point) capillary length, t _mig is the migration time of the analyte, and U _sep is the applied separation voltage.

The EOF mobilities (0.5–1.5 Tiselius unit (TU = 1 × 10⁻⁹ m² V⁻¹ s⁻¹)) in HPC‐coated fused silica capillaries were determined from the migration times of the uncharged species (DMSO) using the method developed by Williams and Vigh [43].

3.2. Determination of the Effective Charge

In our previous works [36, 37], the following equation was derived for calculation of the effective charge number, z_{i ,eff}, of the ith charged species from the data obtained by its CITP and CZE analyses:

$$\frac{z_{i,\mathrm{eff}}}{z_{\mathrm{ref}}}=\frac{\mathrm{\Delta }{t}_i{c}_{\mathrm{ref}}{V}_{\mathrm{ref}}}{\mathrm{\Delta }{t}_{\mathrm{ref}}{c}_i{V}_i}\frac{{\mu }_{i,z}({\mu }_{\mathrm{ref},z}+{\mu }_{c,z})}{{\mu }_{\mathrm{ref},z}({\mu }_{i,z}+{\mu }_{c,z})}$$ (3)

In this equation, the subscripts i, ref, and c refer to the species of interest, reference compound, and counterion of the applied ITP electrolyte system, respectively. The Δt is the ITP zone length in time units (s), V is the injected sample volume (nL), c is the molar concentration (mol L⁻¹), and µ is the actual ionic mobility (TU), that is, mobility of the fully charged ion at the actual ionic strength and temperature of the BGE. If the analyte and reference compound are injected in the mixed sample of the same volume, the parameters of the injected volumes, V _ref and V_i , can be avoided in Equation (3).

4. Results and Discussion

4.1. Selection of Experimental Conditions

For the selection of suitable CITP separation conditions, the most important factors are the compositions of the LE and TE. The LE must contain the leading ion with the highest ionic mobility in the system and the counterion ensuring the buffering capacity of the system at the selected pH. TE has to be composed of the terminating ion with the lowest effective mobility in the system and of a counterion ensuring electroneutrality of TE. Especially the composition and pH of the LE are relevant because they determine the concentration and charge of the analytes in the ITP steady state. The LE and TE operational systems have to ensure a complete separation of the analytes and stability of their sharply separated neighboring steady state zones. The analytes should be maximally charged (dissociated or protonated), if CITP is applied for the determination of their effective charge. Sulfated CDs are strong electrolytes with highly acidic sulfated groups fully dissociated at pH > 2. For that reason, a weakly acidic anionic ITP electrolyte system within the “safe” pH range (4–10) was selected for determination of effective charge of sulfated CDs. This pH range is “safe” for the ITP separation principle (because the influence of highly mobile hydrogen cations and hydroxide anions on the ITP electrolyte system can be neglected thanks to their much lower concentrations than those of the leading ion and counterion of the LE and terminating ion of the TE) as well as for the analyzed sulfated CDs (because the sulfate groups are fully dissociated). On the basis of our previous experience with the selection of the ITP electrolyte systems [44, 45], the LE was composed of 10 mM HCl, 20 mM His, pH 6.1, that is, with fast chloride ion with high actual ionic mobility (−74.80 TU) as the leading anion and His cation with effective mobility (12.75 TU) as pH buffering counterion at selected pH of the LE (pK _a,2 of His = 6.1). The TE consisted of 20 mM Glu, 20 mM NaOH, pH 7.1; partially dissociated Glu anion with effective mobility −23.79 TU served as terminating ion, and sodium cation was the TE counterion. The above mobilities were calculated by the freeware program PeakMaster [46] (available at http://web.natur.cuni.cz/gas/peakmaster.html). Formic and dichloroacetic acids were selected as reference compounds for the effective charge determination as under the applied experimental conditions (pH 6.1), both of them are fully dissociated and negatively charged (z _ref = −1) and could be well separated from SI‐CDs (formic acid) and HS‐CDs (dichloroacetic acid) by both CITP and CZE.

CITP experiments were carried out at the constant electric current mode with a low current intensity of 4.0 µA and with a low input power (product of the current and the separation voltage), maximum 95.1 mW per meter of capillary length, to prevent the increase of 25°C temperature inside the capillary. During the CITP experiments, the voltage was increasing from the initial 2.0 kV up to 10.1 kV due to the increasing electric resistance inside the capillary because of decreasing length of the high‐conductive LE zone and increasing length of the low‐conductive TE zone.

4.2. Determination of Ionic Mobilities

The actual ionic mobilities of SI‐CDs and HS‐CDs and reference compounds (formic and dichloroacetic acids) were determined by CZE in the BGE of the same composition as that of the LE of CITP (10 mM HCl, 20 mM His, pH 6.1) and under the experimental conditions described in Section 2.4. Representative CZE separations of the SI‐CDs and formic acid as a reference compound in fused silica capillaries coated with HPC preventing sorption of analytes to the inner capillary wall are shown in Figure 2A–C and CZE separations of the HS‐CDs and dichloroacetic acid as a reference compound in Figure 2D–F. In Figure 2D–F, an additional peak of different height and area (very small in Figure 2D,E, and relatively high in Figure 2F) has appeared. This peak was identified as sulfate anion as shown in Figure S1. Probably, it comes from the sulfatation procedure of CDs during preparation of HS‐CDs. Due to the electromigration dispersion of some SI‐CDs, HS‐CDs, and reference compounds zones and triangular shape of their peaks (see Figure 2A–F), Haarhoff‐Van der Linde (HVL) function [47] was employed for the determination of their correct migration times. Peaks were fitted with the CEval software [48]. The average actual ionic mobilities, μ, of the all analyzed CDs determined using Equations (1) and (2) are presented in Table 1. With respect to the high charge/size (charge/mass) ratio of both SI‐CDs and HS‐CDs, their ionic mobilities are relatively high, in the range −35.5 to −44.0 TU. The ionic mobilities of the SI‐CDs were slightly decreasing, ca. by 1 TU, with the increasing size of their molecules. On the other hand, the ionic mobilities of the three HS‐CDs were almost the same (−43.5 to −44.1 TU).

FIGURE 2.

CZE separations of SI‐CDs and reference compound HCOOH (A–C) and of HS‐CDs and reference compound Cl₂CHCOOH (D–F). Experimental conditions: HPC‐coated fused silica capillary, 50/375 µm id/od, 424/279 mm total/effective length; BGE: 10 mM HCl, 20 mM His, pH 6.1; separation voltage −11.0 kV; current 4.8 µA; temperature 25°C; sample concentration: 1.0 mM SI‐CDs, 1.0 mM HCOOH, 1.0 mM HS‐CDs, 1.0 mM Cl₂CHCOOH; hydrodynamic injection: 10 mbar × 10 s (3.5 nL); SO₄ ²⁻, sulfate admixture of HS‐CDs. BGE, background electrolyte; CZE, capillary zone electrophoresis; HS‐CDs, randomly highly sulfated cyclodextrins; SI‐CDs, single isomer sulfated cyclodextrins.

4.3. Determination of the Effective Charge

For calculation of the effective charge of SI‐CDs and HS‐CDs using Equation (3), first, all the parameters of this equation were determined. The zone lengths, Δt_i and Δt _ref, of the ith analyte (SI‐CDs or HS‐CDs) and the reference compounds (HCOOH or Cl₂CHCOOH), respectively, were obtained from their CITP separations performed under the conditions described in Sections 2.3 and 4.1. Representative CITP separations of the SI‐CDs and HCOOH are shown in Figure 3A–C and of the HS‐CDs and Cl₂CHCOOH in Figure 3D–F. Sharply separated ITP zones were obtained both for the SI‐CDs, HS‐CDs, and the above reference compounds; see the traces a in Figure 3A–F. Electrophoretic homogeneity of all SI‐CDs and HS‐α‐CD was confirmed by the constant signal of conductivity detector corresponding to their ITP zones. On the other hand, in the ITP‐gram of HS‐β‐CD, not quite constant height of the HS‐β‐CD step was observed, probably due to higher polydispersity of their molecules. In the CITP analysis of HS‐γ‐CD, the zone of sulfates has been identified on the basis of CZE experiments shown in Figure 2F and Figure S1.

FIGURE 3.

CITP separations of SI‐CDs and reference compound HCOOH (A–C) and of HS‐CDs and reference compound Cl₂CHCOOH (D–F). Displayed ITP‐grams show the conductivity detector signal (trace a) and its first derivative (trace b). Experimental conditions: HPC‐coated fused silica capillary, 50/375 µm id/od, 424/279 mm total/effective length; LE: 10 mM HCl, 20 mM His, pH 6.1; TE: 20 mM Glu, 20 mM NaOH, pH 7.1; constant current 4.0 µA; voltage 2.0–10.1 kV; temperature 25°C; sample concentration: 2.5 mM SI‐CDs, 7.5 mM HCOOH, 2.5 mM HS‐CDs, 7.5 mM Cl₂CHCOOH, hydrodynamic injection: 30 mbar × 30 s (32 nL); SO₄ ²⁻, sulfate admixture of HS‐γ‐CD. CITP, capillary isotachophoresis; Glu, glutamic acid; HS‐CDs, randomly highly sulfated cyclodextrins; LE, leading electrolyte; SI‐CDs, single isomer sulfated cyclodextrins, TE, terminating electrolyte.

Exact lengths of the ITP zones were obtained as the distances between the maxima of the first derivation of the conductivity detector signal (traces b in Figure 3A–F). The first derivation was calculated using OriginPro 8.5 software package (OriginLab, Northampton, MA, USA) and the original conductivity detector signal data. Injected volumes of the analyzed SI‐CDs and HS‐CDs and the reference compounds were identical (they were injected together as a mixed sample zone); therefore, the parameters V_i and V _ref were omitted in Equation (3). Ionic mobilities of SI‐CDs and HS‐CDs and reference compounds, HCOOH and Cl₂COOH, were obtained by CZE as described in Section 4.2. Ionic mobility of the counterion (His), μ_c,z , in the used ITP electrolyte system was found to be equal to 25.50 TU using the freeware program PeakMaster [46] available at above website.

Substituting the above parameters into Equation (3), the effective charge numbers, z_{i ,eff}, of the SI‐CDs and HS‐CDs were calculated; see Table 1. For the SI‐CDs, the lowest charge number was found for SI‐α‐CD and the highest charge number for SI‐γ‐CD. This corresponds to the increasing number of sulfate groups in their molecules. The effective charge number of the SI‐α‐CD (6.10) is approximately equal to the number of six sulfated groups in this CD. The effective charge numbers of the SI‐β‐CD and SI‐γ‐CD are a little bit lower than the numbers of sulfate groups in their molecules, 6.58 for SI‐β‐CD containing seven sulfated groups, and 7.54 for SI‐γ‐CD comprising eight sulfated groups.

The effective charge determined from the CITP and CZE experiments was compared with the theoretical effective charge, z _eff,theor, which was set equal to the number of sulfated groups in the SI‐CDs and to the average DS in the HS‐CDs. The z _eff,theor values as well as the ratio of the experimentally determined and theoretical effective charges, z _eff,exp/z _eff,theor, are also presented in Table 1. The ratio z _eff,exp/z _eff,theor shows the relative decrease of the theoretical charge (number of sulfated groups). From this ratio, the percentage reduction R of the theoretical charge was obtained using the following equation and is presented in Table 1:

$$R=\left(1-\frac{z_{\mathrm{eff},\exp }}{z_{\mathrm{eff},\mathrm{theor}}}\right)\times 100$$ (4)

The R values represent the degree of the charge reduction due to the tight binding of the His cationic counterions to the sulfate groups; that is, they show the degree of counterion condensation. The charge reduction does not occur at SI‐α‐CD and is relatively small for SI‐β‐CD (6.0%) and SI‐γ‐CDs (5.7%) but achieves significant values of 22.2%–27.8% for HS‐CDs. These results suggest that the distances between the sulfated groups in SI‐CDs on the C6 carbon of the glucose units are sufficiently long (longer than the Bjerrum length of 0.71 nm), and the repulsion of their negative charges needs not be compensated by a tight counterion binding; that is, only a weak counterion condensation occurs at SI‐CDs. On the other hand, the higher numbers of sulfate groups in HS‐CDs and the shorter distances between them with sulfate groups present not only on the C6 but also on the closely neighboring C2 and C3 carbon atoms of glucose units result in a significant reduction of their theoretical charge due to the counterion condensation. Nevertheless, it is worth to mention that due to the missing information about the exact composition of HS‐CDs mixtures and using their average DS, the obtained effective charge numbers represent averaged approximate characteristics of HS‐CDs under given experimental conditions.

In addition to the effective charge, the so‐called specific effective charge, that is, the ratio of the effective charge and the relative molecular mass, z _eff,exp /M _r, was calculated and is presented in Table 1. This parameter is usually used as an estimation of the analyte charge/size (charge/hydrodynamic radius) ratio that governs the analyte mobility. In agreement with the theory, due to the higher number of sulfate groups in HS‐CDs than in SI‐CDs, this ratio was higher for HS‐CDs (3.64–4.14) than for SI‐CDs (2.70–2.92). It was also reflected by the higher negative ionic mobilities of the HS‐CDs (−43.5 to −44.1 TU) than those of SI‐CDs (−35.5 to −37.5 TU). Slightly decreasing value of this ratio with decreasing ionic mobilities was observed for SI‐CDs but the ionic mobilities of the HS‐CDs were almost the same not reflecting the increasing z _eff,exp /M _r, ratio with the increasing effective charge and size of their molecules.

As follows from the data in Table 1, the experimentally determined effective charges and ionic mobilities of SI‐CDs and HS‐CDs were obtained with a good precision; the RSDs were mostly less than 5% for the effective charges and always less than 2% for the ionic mobilities. These values are in a good agreement with the general estimation of 5%–10% uncertainty of the effective charges determined by CITP for analytes with mobilities in the 20–50 TU range [37] and with a common 2% RSD of mobilities determined by CZE.

5. Concluding Remarks

CITP and CZE proved to be suitable methods for determination of the effective charges and the actual ionic mobilities of multiply negatively charged single isomer sulfated CDs and randomly HS‐CD. The effective charge numbers of the SI‐CDs were found to be equal to or only slightly lower than their theoretical charge numbers (numbers of sulfate groups in their molecules); that is, relatively small reduction, maximum by 6% of the theoretical charge numbers, occurred under the given experimental conditions at SI‐CDs. It suggests that the distances between the negative charges of the sulfate groups in their molecules were mostly sufficiently long to prevent the counterion condensation. On the other hand, significantly lower charge numbers (by 22.2%–27.8%) than the average numbers of the sulfate groups were determined at HS‐CDs. Apparently, some distances of the negative charges of the sulfate groups in the HS‐CDs molecules were already too short, and a partial counterion condensation has already occurred in their molecules.

In accordance with the theory, the absolute values of the actual ionic mobilities of the HS‐CDs with higher numbers of sulfated groups (43.5–44.1 TU) were higher than the absolute values of the actual ionic mobilities of SI‐CDs containing less numbers of sulfated groups (35.5–37.5 TU). This was in agreement with a higher ratio of the effective charge and relative molecular mass of HS‐CDs than that of SI‐CDs. The obtained results will be utilized in further studies of the mechanism and strength of the interactions between sulfated CDs and chiral analytes.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting Information

Data Availability Statement

Data are available on request from the authors.