Introduction

Cyclodextrins (CDs), naturally occurring cyclic oligosaccharides, mostly consist of six, seven and eight d-glucose units for α-CD, β-CD and γ-CD, respectively [1]. Instead of cylinders, truncated cones provide a better approximation to the shape of CDs. CDs play important roles in including organic molecules owing to their hydrophobic cavities in aqueous solution [2, 3, 4]. Furthermore, because they are nontoxic and are very cheap and easy to get, they are applied widely in medicine, food, perfumes, environmental protection and industry [5, 6, 7, 8, 9, 10]. Surfactants are a kind of suitable guest molecule and their many physical and chemical properties, such as surface tension [11, 12], electrochemical properties [13, 14] and spectra behavior [15, 16], can be changed with the addition of CDs. Compared with α-CD and γ-CD, β-CD is studied more widely because its interior diameter (7–8 nm) fits many more guest molecules, such as the hydrocarbon chains of surfactants. However, research on the interaction of β-CD with surfactants was only limited to the inclusion constant and the corresponding molecular ratio of host molecule to guest molecule with the concentration of surfactant lower than the first critical micellar concentration (cmc1, the concentration forming spherical micelles). Few studies [17] have been carried out where the surfactant concentration is higher than cmc1.

Considering the important possible applications of the β-CD/micelle mixed system, in the present work we studied the structures and properties of β-CD/cetyltrimethylammonium bromide (CTAB) mixed micelles by the determination of the diffusion coefficient of the CTAB/β-CD inclusion complex and the effect of β-CD on the diffusion coefficient and the micellar aggregation number of the CTAB system.

Experimental

Materials

β-CD (Shanghai Biochemicals), pyrene (Aldrich, 99%), CTAB (Sigma, 99+%) and cetylpyridine chloride (CPC, Fluka, 98%) were used as received. The water used was deionized and distilled twice.

Determination of the partial phase diagram for the CTAB/H2O/β-CD system

The partial phase diagram was measured by addition of β-CD to CTAB–water solutions with different weight ratios. The change point of the samples from clear to cloudy was carefully observed in order to determine the boundaries of the isotropic area.

Determination of the diffusion coefficient of CTAB micelles

The CTAB micellar diffusion coefficient was determined by a cyclic voltammetric method without any probe [18]. Electrochemical experiments were conducted by using an electrochemical analyzer system with a bipotentiosat (model SHD-1, Yanbian Electrochemical Apparatus Co., Jilin, China) and a 3036 X–Y recorder (Sichuan Fourth Meters Co., China). The electrochemical cell was a standard three-electrode configuration. The working electrode (Shanghai Rex Instruments Factory, China; model 213) was a platinum plate (area 0.24 cm2). A saturated calomel electrode (Jiangsu Electroanalytical Instrument Factory, China; model 232C) was used as the reference electrode and a platinum plate was used as the auxiliary electrode.

Determination of the aggregation number

Pyrene (1.2×10−7 mol/l) was used as the fluorescence probe and CPC as the quencher. The steady-state fluorescence spectra of pyrene were recorded with a Shimadzu RF-5301 fluorescence spectrophotometer with an increasing amount of CPC. Pyrene was excited at 338 nm.

The micellar aggregation number, N, can be obtained according to the following equation [19]:

$$ N = {{\left[ {c - {\rm cmc}} \right]} \mathord{\left/ {\vphantom {{\left[ {c - {\rm cmc}} \right]} {\left[ {S_{{\rm assoc}} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {S_{{\rm assoc}} } \right]}} = {{c_{\rm m} } \mathord{\left/ {\vphantom {{c_{\rm m} } {\left[ {S_{{\rm assoc}} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {S_{{\rm assoc}} } \right]}} $$
(1)

where c is the total concentration of CTAB, c m is the concentration of CTAB-forming micelles, and [S assoc] is the micellar concentration. [S assoc] can be calculated according to Eq. (2) by the fluorescence intensity of pyrene at 372.2 nm:

$$ {{\ln I} \mathord{\left/ {\vphantom {{\ln I} {I_0 }}} \right. \kern-\nulldelimiterspace} {I_0 }} = {{\left[ {\rm Q} \right]} \mathord{\left/ {\vphantom {{\left[ {\rm Q} \right]} {\left[ {S_{{\rm assoc}} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {S_{{\rm assoc}} } \right]}} $$
(2)

Here [Q] is the concentration of the quencher. I and I 0 are the fluorescence intensities of pyrene with and without quencher, respectively. Thus,

$$ {{\ln I} \mathord{\left/ {\vphantom {{\ln I} {I_0 }}} \right. \kern-\nulldelimiterspace} {I_0 }} = {{N\left[ {\rm Q} \right]} \mathord{\left/ {\vphantom {{N\left[ {\rm Q} \right]} {\left( {c - {\rm cmc}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {c - {\rm cmc}} \right)}} $$
(3)

Then, N can be calculated from the slope of the straight line of lnI/I 0 versus [Q].

All the experiments were conducted at 25±0.1 °C

Results and discussion

The effect of β-CD on the cmc1 and the cmc2 of CTAB

When β-CD is added into CTAB aqueous solution (7.1×10−4 mol/l), the peak current of the CTAB cyclic voltammetric curve decreases (Fig. 1) because CTAB is included into the β-CD cavity. According to the relation between the peak current i p (amps) and the potential sweep rate v (volts per second), the diffusion coefficient D (centimeters per second) can be obtained according to Eq. (4) [18]:

$$ i_{\rm p} = 2.69 \times 10^5 n^{3/2} cDAv^{1/2} $$
(4)
Fig. 1.
figure 1

The cyclic voltammogram of cetyltrimethylammonium bromide (CTAB) (7.1×10−4 mol/l) in water with sweep rate 120 mV/s. 1 β-cyclodextrin (β-CD) concentration 0. 2 β-CD concentration 1.9×10−3 mol/l

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Here, n is the electron number per molecule oxidized or reduced and can be calculated from the peak potential, E p, and the half-peak potential, E p/2. For the electrochemical reaction of CTAB on a Pt electrode, n≈1 [20]. c is the surfactant concentration (moles per liter) and A the electrode area (centimeters squared).

For the CTAB micellar system, D decreases with the increase of the CTAB concentration (Fig. 2a). According to the cyclic voltammetric method [21] for determining the cmc, the two change points in Fig. 2a represent cmc1 (elucidates the formation of spherical micelles from CTAB monomer) and cmc2 (demonstrates the change of the spherical micelle to the rodlike micelle) [20]. Figure 2b shows the effect of β-CD on D, from which the effect of β-CD on cmc1 and cmc2 can be determined. Figure 3 shows that both cmc1 and cmc2 increase linearly with the increase in the concentration of β-CD. Because CTAB can be included into the β-CD cavity, the CTAB monomer content in the water continuous phase will decrease with the addition of β-CD; therefore, the CTAB concentration needed to form micelles (i.e. cmc1) becomes larger. Similarly, cmc2 also increases (for detailed discussion see the following section). The relations between cmc1 and cmc2 with the concentration of β-CD can be described as follows:

$$ {\rm cmc}_1 = k_1 \left[ {\beta - CD} \right] + {\rm cmc}_{\rm 1}^{\rm 0} $$
(5)
$$ {\rm cmc}_2 = k_1 \left[ {\beta - CD} \right] + k_2 \left[ {\beta - CD} \right] + {\rm cmc}_{\rm 2}^{\rm 0} = k\left[ {\beta - CD} \right] + {\rm cmc}_{\rm 2}^{\rm 0} $$
(6)
Fig. 2.
figure 2

CTAB micellar diffusion coefficient, D, a with no β-CD and b with β-CD (1.6×10−3 mol/l)

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Fig. 3a,b.
figure 3

The effect of β-CD on cmc1 and cmc2 for CTAB

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Here, \( {\rm CMC}_{\rm 1}^{\rm 0} \) and \( {\rm CMC}_{\rm 2}^{\rm 0} \) represent the first and second cmcs of CTAB without β-CD, respectively, and k1 and k2 the molecular ratios of CTAB/β-CD in the CTAB–β-CD inclusion complex with a CTAB concentration lower than cmc1 and between cmc1 and cmc2, respectively. Thus, from the slope of Fig. 3, the molecular ratio of host/guest can be obtained. The slope (k1) of Fig. 3a is 1.2; thus, when the concentration of CTAB is lower than cmc1, the molecular ratio of β-CD to CTAB is 1.2/1 (equal to 1/k1), which shows that β-CD molecules include equal numbers of CTAB molecules. The slope (k) of Fig. 3b is 10; thus, when the CTAB concentration is between cmc1 and cmc2, the molecular ratio of β-CD to CTAB is about 1/9 [equal to 1/(k−k1)], which may elucidate that β-CD and CTAB can form mixed spherical micelles with the molecular ratio of β-CD to CTAB being about 1:9.

The effect of β-CD on CTAB micellar properties

The effect of β-CD on the diffusion coefficient of CTAB monomers and aggregates is illustrated in Fig. 4. It can be concluded from this figure that when the CTAB content is lower than cmc1 (curve 1 in Fig. 4), CTAB exists in the form of monomers or premicelles and its hydrocarbon chain can be included into the β-CD cavity with the molar ratio of β-CD to CTAB being 1.2:1 as discussed earlier. Thus, the apparent volume of the CTAB monomer is increased and the diffusion coefficient of the CTAB monomer is decreased. After this inclusion reaches equilibrium, the diffusion coefficient of CTAB remains unchanged. When the CTAB content is higher than cmc1, β-CD can include both CTAB monomers and CTAB molecules in micelles, i.e., the inclusion of β-CD with CTAB can exist in both the water continuous phase and mixed micelles. On the one hand, the β-CD/CTAB inclusion complex in the water continuous phase may decrease the apparent diffusion coefficient, D, of CTAB monomers and aggregates as discussed earlier. On the other hand, the β-CD/CTAB inclusion complex in micelles can make the micellar aggregation number decrease and thus the diffusion coefficient of CTAB may increase. Curves 2–4 in Fig. 4 show that the diffusion coefficient increases at first with β-CD content, and then remains almost unchanged. Curve 1 in Fig. 5 elucidates that the micellar aggregation number decreases initially with β-CD content, and then remains almost unchanged. Thus, the latter effect is more important when the β-CD concentration is low for the β-CD/CTAB/H2O system and the former effect gradually becomes obvious with the increase in β-CD cotent. In other words, β-CD prefers to locate in spherical micelles than in the water continuous phase. When the CTAB concentration is higher than cmc2, the changes of both the diffusion coefficient of CTAB (Fig. 4, curves 5, 6) and micellar aggregation number (Fig. 5, curves 2, 3) are very small with increasing β-CD content, which shows that the inclusion of β-CD with CTAB in rodlike micelles is very hard.

Fig. 4.
figure 4

The effect of β-CD on CTAB the micellar diffusion coefficient, D, with the CTAB concentration being 1 8.3×10−4 mol/l, 2 4.0×10−3 mol/l, 3 9.0×10−3 mol/l, 4 1.5×10−2 mol/l, 5 3.0×10−2 mol/l, 6 6.0×10−2 mol/l

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Fig. 5.
figure 5

The effect of β-CD on the CTAB micellar aggregation number, N. CTAB concentration: 1 1.0×10−2mol/l; 2 3.0×10−2 mol/l; 3 6.0×10−2 mol/l (3)

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Moreover, the aggregation number decreases rapidly (more than 10) in the spherical micelles with the addition of a small amount of β-CD (Fig. 5, curve 1). Since the aggregation number for the rodlike micelles is much larger than that for the spherical micelles (Fig. 5, curves 2, 3), more CTAB is needed to form the rodlike micelles, i.e., cmc2 is increased markedly, which is further elucidated by the conclusion in the previous section.

The combination of β-CD with CTAB micelle

In Fig. 6, L 1 represents the micellar area for the CTAB/β-CD/H2O system. With the increase of CTAB content, the CTAB micellar number is increased and more β-CD can be solubilized. When the content of CTAB is 1.9 wt% (about 0.06 mol/l), the solubilized β-CD reaches a maximum of 5.4 wt% (about 0.051 mol/l). Figure 7 shows that the diffusion coefficient of the β-CD/CTAB mixed micelle increases slowly at first and then sharply with increasing water content. With the addition of water, the aggregation number of the CTAB micelles decreases and as a result, the micellar volume is decreased. Thus, the diffusion coefficient of the CTAB micelles increases with increasing water content. Furthermore, since the migration rate for rodlike micelle is slower than that for spherical micelles, the change points in the four curves in Fig. 7 indicate the change of micellar structure. At the fixing weight ratio of β-CD to CTAB, when the water content is lower than that at the change point, the micelle has a rodlike structure. Otherwise, the micelle has a spherical structure. The change points are symbolized by dots in Fig. 6; it can be clearly seen that there are two micellar structures in the L 1 area—spherical and rodlike as shown by S and R, respectively. Furthermore, the intersection of the line connecting the dots with the H2O–CTAB boundary of the phase diagram represents cmc2 for CTAB in water, which is coincident with Fig. 3b.

figure 6
Fig. 7.
figure 7

The diffusion coefficient for the β-CD/CTAB system with different water content

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The phase line of the L 1 area in Fig. 6 indicates the solubility of β-CD in CTAB micelles. Figure 8 illustrates that the molecular ratio of β-CD to CTAB along this phase line decreases although the solubility of β-CD is initially increases and then decreases with increasing CTAB content. Moreover, the ratio of β-CD/CTAB decreases abruptly before the solubility of β-CD reaches the maximum and then decreases slowly. From Fig. 6, it can be seen that the micelles have a spherical structure before the solubility of β-CD reaches the maximum and β-CD can be solubilized in the spherical micelle by the formation of the mixed micelle. However, since nine CTAB molecules can only lead to one β-CD molecule being solubilized in the micelle as discussed earlier, the ratio of β-CD to CTAB decreases fast although the solubility of β-CD increases with CTAB content. After the solubility of β-CD reaches the maximum, the micelles have a rodlike structure (Fig. 6), which makes it very difficult for β-CD to be solubilized. So, β-CD is solubilized through inclusion with CTAB monomer (about 1:1) in the aqueous phase, which explains that the molecular ratio of β-CD to CTAB decreases slowly, and is even unchanged when the solubility of β-CD is higher than the maximum (Fig. 8).

Fig. 8.
figure 8

The variation of the molecular ratio of β-CD to CTAB (n β-CD/n CTAB) and the solubility of β-CD (c β-CD) with different CTAB concentration (c CTAB)

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Conclusions

β-CD makes both cmc1 and cmc2 of CTAB increase. The inclusion complex of β-CD with CTAB is formed with the molecular ratio being about 1:1 when the CTAB content is lower than cmc1. And a mixed spherical micelle can be formed with the molecular ratio of β-CD to CTAB being 1:9 when the CTAB content is higher than cmc1. With the addition of β-CD, the diffusion coefficient of the spherical micelle increases and the micellar aggregation number decreases, while those of the rodlike micelles are almost unchanged because β-CD cannot be solubilized in the rodlike micelles.