J. Phys. Chem. 1995,99, 17628-17631
17628
Thermodynamics of Micelle Formation of Chlorhexidine Digluconate F. Sarmiento? J. M. del Ria,+ G. Prieto? D. Attwood,' M. N. Jones,B and V. Mosquera*J Departamento de Fisica Aplicada and Departamento de Fisica de la Materia Condensada, Facultad de Fifica, Universidade de Santiago de Compostela. E-15706 Santiago de Compostela, Galicia, Spain; Department of Pharmacy, University of Manchester, Manchester MI3 9PL, U.K.; and School of Biological Sciences, Division of Biochemistry and Molecular Biology, University of Manchester, Manchester MI3 9PT, U.K. Received: May 3, 1995; In Final Form: September 15, 1995@
The critical micelle concentrations (cmcs) of chlorhexidine digluconate (CG) in aqueous solution were determined over the temperature range 15-40 "C by a method based on deconvolution into Gaussians of the second derivative of the conductivity/concentration data. The mass-action model was modified in order to calculate the thermodynamic parameters (Ac",, & ,, As",) of micelle formation. To verify the theoretical predictions the enthalpy of micelle formation at 25 "C was calorimetrically determined.
1. Introduction
We have recently r e p ~ r t e d l -systematic ~ studies on the micellar behavior of both anionic and cationic surfactants in different media and at different temperatures. The influence of alkyl chain length, pH, and ionic strength in the n-alkyl sulfates and n-alkyltrimethylammonium systems was studied in detail using theoretical models and an empirical treatment of conductivity data. These two treatments were in perfect concordance. As a continuation of the above investigation, in this work we analyzed using the same methodology the micellar behavior of a more complex surfactant, chlorhexidine, which is doubly charged, unlike the surfactant previously studied. We modified the mass-action model introducing the valence of the monomer as a new parameter and considered this theory for low values of the aggregation number. Micelle formation enthalpies were experimentally determined and the results compared with the theoretical predictions. The chlorhexidine (I) is a symmetrical dicationic molecule with two charged centers at a relatively large distance apart. Evidence has been reported on the surface activity of the diacetate and digluconate salts4s5 of this compound. The chlorhexidine forms small aggregates (four monomers) in an aqueous solution6 and is interesting in comparison with other surfactants which have larger number aggregation such as the above mentioned. HN
II
NH
C-NH-C-NH
I
HN
I
.. .
I
C-NH-C-NH
II
NH
I1
NH
chlorhexidine digluconate (I)
Also, mixed systems of alkyltrimethylammonium bromides and chlorhexidine digluconate are of practical interest since these mixtures are used in commercial antiseptic solutions.'
2. Experimental Section The chlorhexidine digluconate was donated by IC1 Zeneca as an aqueous solution of concentration 20.5 wlv and was sufficiently well characterized to be used as received. Water was doubly-distilled, deionized and degased before use. The conductance was measured by using a specific conductivity meter (Kyoto Electronics type C-117) and the conductivity cell was calibrated with KC1 solutions in the appropriate concentration range. The cell constant was calculated using molar conductivity data for KC1 published by Shedlovskys and Chambers et al.9 Chlorhexidine solutions of know molal concentration were progressively added to water using an automatic pump Dosimat 665 (Metrohm). The measuring cell was immersed in a thermostat bath, keeping the temperature constant within &0.01 K. Control was achieved using a Hewlett Packard Vectra computer. The calorimetric measurements were performed at 25 "C with a Beckman 190B microcalorimeter. This is a twin differential calorimeter in which the heat produced in the reaction vessels is rapidly conducted through two surrounding thermopiles to an aluminum heat sink encasing the thermopiles. The thermopiles surrounding each reaction vessel are wired in opposition in order that the thermoelectric response is a measure of the difference in heat flux from the two vessels. The entire system is held in position by a yoke which can be rotated to mix the components in the reaction vessels, heat effects due to the rotation and friction in each vessel canceling. The calorimeter was calibrated as described by Pilcher et al.'O The experiments were made by mixing 2 cm3 of each solution of chlorhexidine with 2 cm3 of water in one side of the calorimeter and on the other side a blank of 2 cm3 of water and 2 cm3 of water; therefore only the dilution enthalpy of chlorhexidine is measured. 3. Results and Discussion
* Author to whom correspondence should be addressed. Departamento de Fisica Aplicada, Universidade de Santiago de Compostela. Department of Pharmacy, University of Manchester. 8 School of Biological Sciences, University of Manchester. Departamento de Fisica de la Materia Condensada, Universidade de Santiago de Compostela. Abstract published in Aduunce ACS Absrructs, November 15, 1995. @
Critical Micelle Concentrations. Plots of specific conductivity, K , against square root of the molality, ml'*, for aqueous solutions of chlorhexidine over the temperature range 15-40 "C are illustrated in Figure 1. The two linear segments of the plots, corresponding to the monomeric and micellar forms of the surfactant, intersect, as is illustrated in Figure 2. The cmcs
0022-365419512099-17628$09.00/0 0 1995 American Chemical Society
Micelle Formation of Chlorhexidine Digluconate
J. Phys. Chem., Vol. 99, No. 49, 1995 17629 -6.63
54-
-6.64
3-6.65
2-
Ps o' I
h
0
-6.66
5 X
0-
-
W
C
00-
-6.67
-6.88
0-
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.12
0.16 0.20
0.24
0.28
0.32
-6.69
0.36
m In (-)1n Figure 1. Specific conductance versus square root of molal concentra-
tion of CG in aqueous solution at different temperatures: (e)288.15 K, (0)293.15 K, (4) 298.15 K, (0) 303.15 K, (0)308.15 K, (0) 313.15 K. Note that the 0 is displaced by one division for each conductivity curve (from 0 to 1). The m o w s denote the cmcs. 4,O
1
-6.70 285
295
290
305
300
310
315
T (4 Figure 3. Variation of the critical micelle concentrations (expressed in mole fractions) with the temperature for CG in aqueous solution. Continuous line calculated from eq 3.
defined the cmc as the concentration at which the gradient slope of a physical property of solution, 4, against concentration, C , shows the most rapid change:
d3$/d? = 0; C = cmc
(1)
This definition can be easily applied to any system as long the measured physical property is a linear function of the concentration of all the species that take part in the micellization process. In this work, this condition was applied to the specific conductivity of chlorhexidine, K , assuming that this can be defined approximately as follows: K 0,lS
0,20
030
0,25
O M
0 3
= a[S]
+ b[M]
(2)
a and b are proportionality constants, and [SI and [MI are the
m'" (mmolkg)'"
Figure 2. Plot of specific conductivity versus square root of molal concentration of CG in aqueous solution at 288.15 K. The small plot inserted shows the determination of the cmc according to eq 1.
TABLE 1: Critical Micelle Concentration of CG in Aqueous Solutions at Different Temperatures temp (K)
cmc (mmol/kg)
temp (K)
cmc (mmolkg)
288.15 293.15 298.15
70.5 69.5 69.2
303.15 308.15 313.15
69.4 70.4 72.0
are given in Table 1. We chose this plot, as recommended by Mukerjee and Mysels," because it is about 3% more exact than that obtained by plotting conductance versus concentration. Comparison with previous cmc values shows that discrepancies exist between different authors. Heard and Ashworth5 give a value for the cmc at 25 "C of 6.6 x M determined by conductivity and surface tension methods; Pemn and WitzheI2 give a value of 4.4 x M at 25 "C from conductivity data; Attwood et aL6 report a cmc at 25 "C of 51 x mol kg-' obtained by light scattering, which is closer to our results. The discrepancies between different researchers could be due to chlorhexidine having a very low aggregation number and therefore it is difficult to determine the cmc. Because of these discrepancies and in order to be able to calculate reliable results we employed the definition of the cmc by P h i l l i p ~ 'which ~ is in widespread use14and seems to be the best method. Phillips
concentration of the monomeric surfactant and micelle, respectively. Figure 2 shows with a continuous line a schematic illustration of cmc determined according to the definition of Phillips. The results obtained for,both methods coincide. The variation of the cmc of chlorhexidine with temperature is shown in Figure 3 and passes through a minimum of 298.9 K. This plot was fitted to the equation
with the cmc in mole fraction units. The values of the fitting constants were a = O.OO0 187 f 1 x b = -0.1118 f 7 x and c = 10.0 f 0.1. Figure 3 shows this fit, which was the best obtainable. Mass-Action Model of Micelle Formation. The mass-action approach has been widely used to investigate the micellization process. This approach was extended by M ~ k e r j e e . ' ~ .Hall '~ and Pethica" have also refined this model through small-system thermodynamics. In the present treatment a modification was applied by introducing the valence of monomer which form the micelle. For our dicationic surfactant, the equilibrium between the ions and the micelles is represented by eq 4,where G-,
nSUf
+ (nu - p)G-
-
Mp+
(4)
Sv+, and MP+ represent the counterion, surfactant ion, and micelles of aggregation number n and net charge p . The
17630 J. Phys. Chem., Vol. 99, No. 49, 1995
S d e n t o et al.
micellization constant is written as
In order to calculate K , it is necesssary to know, in addition to n and p , the concentration of both the single ions and the micelles at any one total surfactant ion concentration. However, due to the large exponential term involved in the equilibrium constant this is virtually impossible to determine experimentally. Nevertheless, this difficulty may be overcome by making use of the Phillips method explained above. The mass balances for surfactant ions (ct) and counterions (c,) respectively are expressed as
+ n[MP+] cg = v[S"+]+ p[Mp+] ct = [S"']
(6)
1 = nu""-P[n(v+ 1) - p][2n(v+ 1) - 2p - 11 X n(v
I
+ 1) -p - 2
+ 1) -p][2n(v + 1) - 2p - 13 [n(v+ 1 ) - p - 1][2n(v+ 1) - 2p + 21 [n(v
581
58.0
I
I 290 0
Cmc}n(i+ll-p-
I
(8) To apply this equation, plvn, the degree of ionization of the micelles must be calculated. This calculation is possible from the gradient, ,S, of plots of K against m above the cmc as proposed by Evans.Is Assuming that the micelles do not contribute significantly to the conductivity, S, may be approximated byL9
I
I
300.0
I 310 0
T (K)
(7)
and simultaneously solving eqs 1,2,5,6, and 7, with the Phillips assumption that p[MP+]
