J. Phys. Chem. 1995,99, 5413-5417
5413
Low-Frequency Dielectric Effects in the Measurement of P-Cyclodextrin Interactions with Sodium Dodecyl Sulfate Duncan Q. M. Craig* and Charles McDonald? Centre for Materials Science, School of Pharmacy, University of London, 29-39 Brunswick Square, London WClN I A X , U.K., and School of Pharmacy, Curtin University of Technology, Kent Street, Perth, Westem Australia Received: March 24, 1994; In Final Form: July 15, 1994@
The dielectric response of a range of sodium dodecyl sulphate solutions (0.0035-0.035 M) has been measured Hz. The response comprised in the presence of 0.0081 M P-cyclodextrin over a frequency range of lo4 to that of the bulk solution in series with that of electrode layers, seen respectively above and below a characteristic frequency which lay between 0.5 and 10 Hz, depending on the system under examination. The presence of the electrode layers resulted in conductance effects which were observed at frequencies approaching those which may be used for measuring the conductivity of the bulk solution itself. Measurement of the dielectric behavior at low frequencies therefore allows a clear characterization of the response of these layers. Furthermore, the results indicate that it may be advisable to measure the frequency dependent behavior in order to ensure that the response at the frequency used for conductance measurements is not influenced by the presence of electrode layers.
Introduction Conductance measurements are widely used as a means of detecting the critical micelle concentration (cmc) of surfactant solutions. Most conductance measurements involve the use of an alternating field, as the application of a direct current leads to the migration of anions and cations to the corresponding electrodes, where electrodeposition will occur. Alternating signals with frequencies in the kilohertz region are generated using bridge methods, from which the conductance may be measured directly and the specific conductivity calculated, the latter taking account of the cell dimensions and geometry. In addition to the conductance, the real permittivity (equivalent to the capacitance) may be measured in this frequency region using the same apparatus, from which additional informationregarding the micellization process may be obtained.'%* It is, however, recognized that such low-frequency measurements may be complicated by electrode effects, whereby accumulation of ions or charge injection may lead to the establishment of a charge layer adjacent to the electrodes. This layer may give rise to a measurable dielectric response at frequencies in the sub-kilohertzregion. A number of techniques have been adopted in order to attempt to minimize the effects of such layers, including the coating of electrode surfaces with platinum black andor the use of four-electrode systems, whereby the electrodes which deliver the signal are physically separate from the electrodes which measure the respon~e.~ Even these techniques do not give an absolute guarantee that electrode effects have been removed. Consequently, it is important to have a fundamental understanding of the stnicture and properties of these layers in order to interpret their dielectric effects and to correct for them accordingly. To do this, it is helpful to measure the dielectric response down to very low frequencies (sub-hertz), as such effects may not usually be observed with
* Author to whom correspondence should be addressed at the University of London. ' Curtin University of Technology. Abstract published in Advance ACS Abstracts, March 15, 1995. @
0022-365419512099-5413$09.0010
any clarity over higher frequency ranges. Such measurements are comparatively rare in the literature; hence, there is a need for further exploration of dielectric effect in the sub-hertz region in order to develop the understanding of electrode layers. In order to allow interpretation of the low-frequency (subhertz) responses, a model has been proposed by Hill and Pickup4 which describes the dielectric behavior in terms of the presence of two types of responding system within the sample. These responses correspond to the bulk of the material and the electrode layers, the latter being composed of molecules which have been adsorbed from the bulk solution or added to the system from the electrodes. The electrode response therefore includes not only the charge layers considered to be responsible for electrode polarization effects but also layers of physically adsorbed molecules. Such adsorbed layers have been previously described for alginate gels5 and liposome suspensions6and may yield useful information on the behavior of the sample, providing that the systems are studied to a sufficiently low frequency in order to allow the layers to be observed in their entirety. The electrode and bulk layers are considered to be electrically in series; hence, the system may be described by a modification of the Maxwell-Wagner analysis. Due to the differences in thickness and conductance of the two systems, the electrode layer will generally be observed below approximately 1 Hz, while at higher frequencies the response of the bulk will dominate the response. This is shown schematically in Figure l a for a system which may be modeled by two parallel RC circuits in series. The data are expressed in terms of the capacitance and dielectric loss (Glw, where G is the conductance and w is the angular frequency). These two parameters are directly related to the real and imaginary (loss) permittivities but have been used here in order to clarify the relationship between the dielectric response and the conductance. Using the logarithmic scales shown in Figure la, it may be seen that if the conductance is frequency independent (as is the case for a simple conductivity process), then the frequency exponent of the dielectric loss will be - 1.
0 1995 American Chemical Society
Craig and McDonald
5414 J. Phys. Chem., Vol. 99, No. 15, 1995
I
Log Frequency
Log Frequency Figure 1. Diagrammatic representation of the Maxwell-Wagner response observed at low frequencies in the presence of adsorbed electrode layers: (a) ideal response; (b) real response. G,, conductance of surface layer; C, capacitance of surface layer; Gb, conductance of bulk; Rb, resistance of bulk; c b , capacitance of bulk. See text for explanation of s and n.
As the frequency is lowered, there is a characteristic frequency at which the electrode layer begins to dominate the response, given by the crossover point of the capacitance and loss as indicated in Figure la. This frequency is termed WMW, the Maxwell-Wagner crossover frequency and, assuming that the circuit elements of the response are nondispersive, is given by
where z is the characteristic relaxation time of the sample, Rb is the bulk layer resistance, and C, is the electrode (surface) layer capacitance. It should be noted that, for samples with high bulk conductivities (lower Rb), the crossover frequency will occur at correspondingly higher frequencies. The lower limit of frequency at which the bulk conductivity process will be observed therefore rises. In practice, the response is often more complex than the ideal system shown in Figure la. In particular, the capacitance and loss curves may show power law behavior, whereby the logarithmic slopes of the two components are fractional, as shown in Figure lb. This behavior may be interpreted by the Dissado-Hill modification of the Maxwell-Wagner response.
The Dissado-Hill theory7 describes the susceptibility 01) at any frequency w in terms of two indices, m and n, via
where 0 5 m, n 5 1, 2F1( , ; ; ) is the Gaussian hypergeometric function, xo is the static susceptibility, and wp is the relaxation frequency. The indices m and n describe the power law behavior of the response and contain information conceming the interactions between dipoles within a material; hence, this approach has the advantage over other methods in that the two indices are nonempirical. This model may be extended to interpret low-frequency p h e n ~ m e n ahence, ;~ it is possible to model deviations from the perfect Maxwell-Wagner response in terms of power law indices which account for nondispersive behavior in the circuit elements of the response. This approach may be applied to the response shown in Figure l b by considering the slope of the low-frequency capacitance to be given by -s. The value of the exponent s reflects the structure of the barrier, with s = 0 implying a barrier which blocks the movement of charge, as was seen in the perfect
/3-Cyclodextrin Interactions with SDS
0,
0 -I
J. Phys. Chem., Vol. 99, No. 15, 1995 5415
(a1
-2-
Y
u)
0
-4
-
-6
-
-8
-
-10
4
-I
\ Q)
o c
Q c
0-
0 Q
n Q
w O !
I
I
I
:
-12
O
1
-2
-3
0
0.59Hz
I
I
I
1
I
f
-1
0
1
2
3
4
3
4
Log Frequency (Log
E Q c
Capacitance Dielectric Loss
Hz)
0 Capacitance
.-
0
Dielectric Loss
Q
n -10 5.49Hz
-2 n
-1
0
1
2
0-
LL
c3,
0
4
(Cl -2-4
-
o c
-6
-
0
-8
-
-10
-
v)
0
.A
\ Q)
.-cQ Q
n Q
m
I
O 0
0
Capacitance Dielectric Loss 6.63Hz
0
-3
-2
-1
0
1
Log Frequency (Log
2
3
4
Hz)
Figure 2. Low-frequency dielectric response of (a) 0.0081 M P-cyclodextrin, (b) 0.0035 M sodium dodecyl sulfate in the presence of 0.0081 M P-cyclodextrin, and (c) 0.021 M sodium dodecyl sulfate in the presence of 0.0081 M P-cyclodextrin.
5416 J. Phys. Chem., Vol. 99, No. 15, 1995
Craig and McDonald
-3.0 1 IC-
u, Q,
0
-3.6 -
-I
Y
VI
0 J
.-L0 w
-4.2
-
-4.8
-
0
-cucu
U
.-
0 -5.4 u 3 0 -I
n Y
c
-6.0
0 1 E l Hz 6. 0
-
t 0.000
0 I
0.010
1E2 Hz 1E3 H z 1E4 Hz
I
I
1
0.020
0.030
0.04
Concentration
(MI
Figure 3. Dielectric loss measurements of sodium dodecyl sulfate solutions in the presence of 0.0081 M P-cyclodextrin taken at a range of frequencies.
Maxwell-Wagner response. If 0 c: s < 1, then the capacitance in the barrier region is dispersive; i.e., its value varies with the frequency of the applied electrical field, with the value indicating the ‘leakiness’ of the layer. The exponent n - 1 describes the slope of the loss curve, with a value of 0 indicating a simple conductivity process. The slope of the high-frequency capacitance is given by -(2 - s - 2n), demonstrating that, according to this model, the structure of the barrier layer (and hence the value of s) may affect the response in the higher frequency region. In particular, the increase in capacitance seen in the kilohertz region may be explained in terms of this model. It should also be noted that, in the case of a bulk dc conductivity ( n = 0), the slope of the high-frequency capacitances will equal 1-(2 - s) and that of the low-frequency capacitance will be -s; hence, the sum of the two slopes will equal -2. The implications of this approach are that electrode layers must be considered as part of the overall dielectric response, irrespective of whether they arise from charge accumulation or molecular adsorption processes. It is therefore of interest to use the analysis outlined above to examine the consequences of the establishment of such layers in the characterization of surfactant solutions. In particular, we have studied the formation of micelles composed of sodium dodecyl sulfate in the presence of P-cyclodextrin. The cyclodextrins are a family of cyclic oligosaccharides, whose torus shape allows the formation of inclusion complexes with a variety of molecules. These systems have been widely studied as a means of improving the solubility and stability of drugs; hence, there is considerable interest in characterizing their solution properties. A number of studies have described the interactions between surface active agents and cycl~dextrins.*-’~ In particular, conductivity measurements have been used to detect the cmc value, particularly examining the effects of cyclodextrins on the conductivity of surfactant solution^.'^ These systems therefore represent a topical model with which the importance of characterizing low-frequency effects may be demonstrated. In this study, these systems are examined with a view to assessing the information that may be gained by performing low-frequency sweeps, both in terms of understanding the nature of the electrode layers and also in terms of considering the implications of the presence of such layers for the use of conductivity measurements.
Experimental Section P-Cyclodextrin (Chinoin Ltd., Hungary), sodium dodecyl sulfate (SDS), and water (all Analar grade, BDH) were used as received. Dielectric measurements were performed using a lowfrequency bridge system (Dielectric Instrumentation Ltd.) over a frequency range of lo4 to Hz. A stainless steel cell (Texas Instrumentation) was used throughout, one electrode of which consisted of a cylinder and the other of a tubular insert. Measurements was performed at 298 K and are expressed in terms of the real capacitance and dielectric loss (G/w, where w is the angular frequency). A voltage of 0.1 V root mean square was used throughout. Solutions containing SDS in the molar concentration range 0.0035-0.035 M (0.1 - 1.0% w/v) were tested in aqueous solutions containing 0.0081 M P-cyclodextrin, this concentration being equivalent to the molar cmc of SDS in water at 298 K.
Results and Discussion The responses of 0.0081 M P-cyclodextrin and two concentrations of SDS in the presence of P-cyclodextrin are shown in Figure 2. These responses may be interpreted in terms of the model proposed by Hill and Pickup4 as follows. The response of 0.0081 M P-cyclodextrin shows a high-frequency conductance (indicated by the loss slope of - 1.01) with a surface layer being seen below 1 Hz. The sum of the slopes of the low- and high-frequency capacitances is -1.96, which is close to the theoretical value of -2; hence, these data support the model used here. Figure 2b shows the response of 0.0035 M SDS in the presence of P-cyclodextrin. In this case, not only is the highfrequency conductance increased (as may be expected on the addition of an electrolyte) but the nature of the electrode layer has also altered. In this c?.se, the value of s is 0.21, which indicates an electrode layer which is considerably less permeable to charge; Le., it is a more effective blocking layer. It is reasonable to propose that the layer now contains adsorbed surface active agent molecules. On increasing the concentration of SDS to 0.021 M, which is above the cmc, the high-frequency conductance is again increased, while the low-frequency capacitance slope (s) remains effectively unchanged (s = 0.22),
J. Phys. Chem., Vol. 99, No. 15, 1995 5417
P-Cyclodextrin Interactions with SDS indicating that the electrode layer has not altered. It should also be noted that the crossover point rises as the conductance is increased, as predicted by the theory outlined earlier. This means that the electrode barrier layer will contribute increasingly to the response in the kilohertz region as the concentration of surfactant is raised. Clearly, therefore, the conductance values of the system are frequency dependent as a result of the response of these layers. Consequently, it is of interest to consider the dependence of the relationship between conductance and surfactant concentration on the frequency at which these conductance values are taken. Figure 3 shows the values for the dielectric loss (G/w) for the various solutions taken at a range of frequencies between lo4 and 10 Hz. The loss rather than conductance has been plotted in order to separate the various curves on the one axis. Figure 3 indicates that the discontinuity associated with the formation of micelles occurs at 0,0114 and 0.0115 M when measured at 104 and lo3 Hz, respectively;hence, these measurements are in good agreement. The observed cmc values are higher than that obtained for SDS in water due to inclusion complex formation with P-cy~lodextrin.'~However, on measuring the conductance at lower frequencies, the discontinuity disappears as the electrode layer dominates the response.
Conclusions The study has demonstrated that, by measuring the response of liquids down to subhertz frequencies, the nature of the electrode layers may be more thoroughly understood. Furthermore, the dependence of the high-frequency (kilohertz) capacitance on that corresponding to the electrode layer (seen in the sub-kilohertz range) has been outlined. This dependence may at least partially explain the dramatic rise in real permittivity on lowering the frequency that has often been observed for liquid systems. The study has also highlighted the importance of the surface layers in the measurement of conductivity. The presence of these layers may have a profound effect on the measured
conductance and may lead to errors in measuring the specific conductivity using standard bridge methods. Electrode effects were well-known to influence such measurements if too low a frequency is used, although this study indicates that the frequency up to which these effects may influence the response varies according to the system used. The investigationtherefore suggests that frequency sweeps may be a useful supplement to single frequency determinations, as by measuring the response over a range of frequencies it is possible not only to gain information on the nature of the electrode layers but also to establish whether the measured conductance is a simple reflection of the bulk properties of the solution or whether the presence of the electrode layers is influencing the response.
References and Notes (1) Hanai, T.; Koizumi, N.; Gotoh, R. Kolloid-Z. 1959, 167, 41-47. (2) Sjoblom, J.; Jonsson, B.; Nylander, C.; Lundstrom, I. J . Colloid Inter$ace Sci. 1983, 96, 504-516. (3) Myers, D. F.; Saville, D. A. J. Colloid Interface Sci. 1989, 131, 448-460. (4) Hill, R. M.; Pickup, C. J . Mater. Sci. 1985, 20, 4431-4444. (5) Binns, J.; Craig, D. Q. M.; Hill, R. M.; Davies, M.; Melia, C.; Newton, J. M. J . Mater. Chem. 1992, 2, 545-549. (6) Barker, S . A,; Craig, D. Q.M.; Hill, R. M.; Taylor, K. M. G. J. Colloid Interface Sci., in press. (7) Dissado, L. A,; Hill, R. M. Nuture (London) 1979,279,685-689. (8) Hersey, A.; Robinson, B. H.; Kelly, H. C. J . Chem. SOC.,Faraday Trans. 1 1986, 82, 1271-1287. (9) Georges, J.; Desmettre, S. J. Colloid Interface Sci. 1987,118, 192200. (10) Jobe, D. J.; Verrall, R. E.; Palepu, R.; Reinsborough, V. C. J. Phys. Chem. 1988, 92, 3582-3586. (1 1) Nakanishi, K.; Masada, M.; Nadai, T.; Miyajima, K. Chem. Phurm. Bull. 1989, 37, 211-214. (12) Park, J. W.; Song, H. J. J. Phys. Chem. 1989, 93, 6454-6456. (13) Aman, E. S.; Serve, D. J . Colloid Interface Sci. 1990, 138, 365375. (14) Tan, X.; Lindenbaum, S. Int. J. Pharm. 1991, 74, 127-135. ( 1 5 ) Wan Yunus, W. M. Z.; Taylor, J.; Bloor, D. M.; Hall, D. G.; WynJones, E. J . Phys. Chem. 1992, 96, 8979-8982. JP940756I
