Langmuir 1999, 15, 5023-5028
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Equilibrium and Transport Properties of Alkylpyridinium Bromides Jozˇe Sˇ kerjanc,* Ksenija Kogej, and Janez Cerar Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000 Ljubljana, Slovenia Received December 16, 1998. In Final Form: April 21, 1999 The osmotic coefficient, the apparent molar volume, and the electrical conductivity of aqueous solutions of the homologous series of decyl-, undecyl-, dodecyl-, tridecyl-, tetradecyl-, pentadecyl-, and hexadecylpyridinium bromides (CnPyBr) have been determined at 25 °C. From these data the variation of the critical micelle concentration (cmc) with the chain length of the surfactant has been obtained. Measurements were performed usually at concentrations from well below to well above the cmc. From osmotic coefficient and conductivity measurements, the degree of counterion binding to micelles, β, has been calculated. It has been found that the values of β are rather insensitive to the chain length, and as expected, the values determined from transport measurement are lower than those from the osmotic pressure measurements. From the apparent molar volumes the aggregation numbers of alkylpyridinium bromides have been estimated, following simple geometrical considerations suggested by Tartar and Tanford.
Introduction It has been generally recognized that studies of thermodynamic and transport properties of surfactants are important to understand their behavior in solutions.1 Therefore, the limited interest of scientists working in this field for direct measurement of some fundamental solution properties, such as the activity and osmotic coefficients, enthalpy and volume changes on dilution, electrical conductivity, transport numbers, etc., is somewhat surprising. These properties are indispensable to test various theories and models of surfactant solutions. Between those, the mass-action model based on a twostate approximation has been applied to the micellization process for nonionic2 and ionic3 surfactants with some success. The model for ionic surfactants is founded on the chemical equilibrium between monomeric surfactant ions, counterions, and monodisperse micelles.4 The charge of the micelles is usually substantially reduced by the bound counterions. The degree of counterion binding to micelles, β, is thus one of the key parameters which characterizes ionic micelles. It may be obtained in numerous ways, and depending on the experimental technique adopted, it may vary considerably. These variations are outside experimental errors, indicating that various methods measure different quantities. The situation is well-known from the field of charged macromolecules where the values of the degree of counterion binding to the polyion determined by transport phenomena are appreciably lower than those from equilibrium measurements.5 In some previous papers from this laboratory the interactions between oppositely charged polyelectrolyte and ionic surfactant have been studied.6-8 It became * Corresponding author. (1) Kresheck, G. C. In WatersA Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1975; Vol. 4, p 95. (2) Desnoyers, J. E.; Caron, G.; DeLisi, R.; Roberts, D.; Roux, A.; Perron, G. J. Phys. Chem. 1983, 87, 1397. (3) Burchfield, T. E.; Woolley, E. M. J. Phys. Chem. 1984, 88, 2149. (4) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1987; Vol. 1, p 564. (5) Katchalsky, A. Pure Appl. Chem. 1971, 26, 327. (6) Sˇ kerjanc, J.; Kogej, K.; Vesnaver, G. J. Phys. Chem. 1988, 92, 6382. (7) Sˇ kerjanc, J.; Kogej, K. J. Phys. Chem. 1989, 93, 7913.
apparent that much more information could be gained if systematic studies of surfactant used would be carried out. In this paper we report results on electrical conductivity, osmotic coefficient, and apparent molar volume measurements of seven alkylpyridinium bromides (from C10PyBr to C16PyBr) in water. From these data the variation of the critical micelle concentration (cmc) with the chain length of the surfactant, as well as the degree of counterion binding, β, was determined. It has been found that the values of β are rather insensitive to the chain length, and as expected, the values determined from transport measurements are considerably lower than those from the osmotic pressure measurements. Experimental Section Materials. N-Decyl- (C10PyBr), N-undecyl- (C11PyBr), N-tridecyl- (C13PyBr), N-tetradecyl- (C14PyBr), and Npentadecyl- (C15PyBr) pyridinium bromides monohydrates were synthesized by treating the corresponding 1-bromoalkanes (all from Aldrich, Milwaukee, WI) with pyridinium (Riedel-de Hae¨n, Seelze, Germany) by the procedure reported in the literature.9 They were thoroughly purified by repeated recrystallization from acetone and dried by lyophilization. N-Cetylpyridinium bromide monohydrate (C16PyBr‚H2O) was supplied by Merck, Darmstadt, Germany, and was also purified by recrystallization from acetone. N-Dodecylpyridinium bromide (C12PyBr) was prepared by ion exchange from N-dodecylpyridinium chloride (C12PyCl, Merck, Darmstadt, Germany), which was previously purified by the same procedure as other surfactants. Later in the text, abbreviations C10, C11, C12, C13, C14, C15, and C16 are used for these surfactants. The stock solutions of C10, C11, C13, C14, C15, and C16 were prepared by weight from dried substances using triple-distilled water. The concentration of C12 stock solution, obtained by ion exchange, was determined by potentiometric titration with a bromide ion-selective electrode using a AgNO3 standard solution. All other surfactant solutions were prepared by diluting the stock. (8) Sˇ kerjanc, J.; Kogej, K. In Macro-ion Characterization: From Dilute Solutions to Complex Fluids; Schmitz, K. S., Ed.; American Chemical Society: Washington, DC, 1994; Chapter 20, p 268. (9) Knight, A.; Schaw, B. D. J. Chem. Soc. 1938, 682.
10.1021/la981710+ CCC: $18.00 © 1999 American Chemical Society Published on Web 06/23/1999
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5024 Langmuir, Vol. 15, No. 15, 1999
Figure 2. Plots of the molar conductivity of alkylpyridinium bromides in water at 25 °C against the logarithm of the reduced concentration. Table 1. Critical Micelle Concentrations of Alkylpyridinium Bromides in Water at 25 °C
Figure 1. Concentration dependence of the specific conductivity of alkylpyridinium bromides CnPyBr (from C10PyBr to C16PyBr) in water at 25 °C.
Conductivity. The conductivity of surfactant solutions was measured using a Jones conductance bridge (Leeds & Northrup Co., North Wales, PA). All measurements were carried out in an oil-thermostated bath at 25.00 ( 0.01 °C and at a frequency of 20 kHz. The conductivity of triple-distilled water used for the preparation of solutions was below 1.2 × 10-6 Ω-1 cm-1. Osmotic Coefficients. The osmotic coefficient measurements were performed at 25 °C with a Knauer differential vapor pressure osmometer which was calibrated with standard KCl solutions. A detailed description of the osmometer and the experimental procedure has been described elsewhere.10 Density Measurements. Densities of solutions were measured with a Paar digital densimeter model DMA 60 with external measuring cell DMA 602. An ultrathermostat attached to the instrument controlled the temperature at 25.00 ( 0.002 °C. The accuracy of density measurements was within (4.5 × 10-6 g cm-3. It is well-known11 that this error in density would cause an uncertainty of about 0.5 cm3/mol in the apparent molar volume, Φv, when c ) 0.01 mol dm-3. By three or more parallel runs at c < 0.01 mol dm-3, the uncertainty in Φv was considerably reduced, so that it roughly corresponds to the size of the experimental points in Figure 7. Results and Discussion Experimental specific conductivities, κ, of aqueous solutions of alkylpyridinium bromides are presented as functions of surfactant concentration in Figure 1. A characteristic shape of the curves can be observed. Once micelles are formed, κ undergoes an abrupt change in concentration dependence. By linearly extending the (10) Burge, D. E. J. Phys. Chem. 1963, 67, 2590. (11) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions; Reinhold: New York, 1958; pp 221, 359, 396, 415.
surfactants
cmc (mol L-1)
decylpyridinium bromide undecylpyridinium bromide dodecylpyridinium bromide tridecylpyridinium bromide tetradecylpyridinium bromide pentadecylpyridinium bromide hexadecylpyridinium bromide
0.044 0.021 0.010 0.0053 0.0027 0.0013 0.00064
portions of the lines before and after breaks, we determined the cmc’s for each surfactant. An example of these determinations is presented for C16PyBr in Figure 1. The values of cmc’s are collected in Table 1. They can be also represented by a well-known linear relation (the coefficient of correlation, R ) -0.9998) between log cmc and the number of carbon atoms in the chain, nc:
log cmc ) 1.66 - 0.303nc
(1)
Inspection of the existing literature data1,12 shows that the values of both coefficients in eq 1 are close to those found for related homologous series of cationic surfactants, such as alkyltrimethylammonium bromides and alkylpyridinium bromides, obtained at different temperatures and by other methods. From specific conductivities calculated molar conductivities, Λ, are plotted in Figure 2 against the logarithm of the reduced concentration, c/cmc. It can be seen that above cmc the values of Λ fit almost the same curve. The molar conductivities of alkylpyridinium bromides at infinite dilution, Λ0, are plotted vs nc in Figure 3. By subtracting from Λ0 the corresponding conventional value for the bromide anion, Λ0Br- ) 78.4 Ω-1 cm2 mol-1, the values of Λ0 for surfactant cations were obtained. As expected, Λ0+ values slightly decrease with the increasing chain length and are about 3 times lower than Λ0 for the bromide anion. From Λ0 and Λ0+ values the transport numbers of alkylpyridinium cations can be calculated, t0+ ) Λ0+/Λ0. The corresponding values of t0+ range from 0.26 for C10PyBr to 0.24 for C16PyBr. They are in reasonable agreement with literature data13 for C12PyBr, t0+ ) 0.22, (12) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; Wiley: New York, 1989; p 136. (13) Hartley, G. S.; Collie, B.; Samis, C. S. Trans. Faraday Soc. 1926, 32, 795.
Properties of Alkylpyridinium Bromides
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Figure 3. Variation of the molar conductivity at infinite dilution of alkylpyridinium bromides, Λ0, and alkylpyridinium cations, Λ0+, with the chain length.
determined directly by the moving boundary method at 35 °C. Following the mass-action approach the micellization process for a cationic surfactant can be represented as4
nS+ + (n - p)C- f Mp+
(2)
where S represents the surfactant ions, C the counterions (in our case Br-), and M the aggregate of n surfactant monomers with an effective charge of p. The degree of counterion binding, β, is thus given by
β ) 1 - p/n
(3)
At this stage we shall interpret the conductivity data by using a pseudophase approach. We assume that above the cmc the concentration of surfactant ions remains constant. The molar conductivities of the surfactant ions, Λ+, and bromide counterions, Λ-, refer14 to the concentration of free counterions, i.e., to the cmc. The specific conductivity κ of the solution beyond the cmc is thus given by
κ)
∑i κi ) cmc × Λ+cmc +
(
cmc +
c - cmc
)
p Λcmc + n (c - cmc)Λm (4)
In eq 4 Λm is the molar conductivity of the micelle ion calculated per monomeric unit. Because Λcmc ) Λ+ cmc + Λcmc, the molar conductivity of a solution can be expressed as
(
Λ ) Λcmc -
p cmc p Λ - Λm + Λcmc + Λm (5) n cmc c n
)
For c > cmc a plot of Λ against reduced reciprocal concentration cmc/c should give a straight line with the intercept equal to pΛcmc/n + Λm. This type of plot is shown for alkylpyridinium bromides in Figure 4. An enlargement of the plot for values of cmc/c lower than 1 gives the value of the intercept 25 ( 2 Ω-1 cm2 mol-1, with no systematic selectivity for the chain length. Assuming that the contribution of the bulky micelle ion, with highly reduced charge, to the overall conductivity is small in comparison (14) Mukerjee, P.; Mysels, K.; Kapauan, P. J. Phys. Chem. 1967, 71, 4166.
Figure 4. Variation of Λ for CnPyBr with the reciprocal reduced concentration.
with the bromide ion, in the first approximation Λm can be neglected. From the intercept we can thus calculate the values of the ratio p/n or β. The necessary values of Λcmc were calculated from experimental data for Λcmc and transport numbers of alkylpyridinium ions reported above (t0- ) 1 - t0+) assuming11 t0- ≈ tcmc. The resulting values of p/n are 0.38 ((0.03) for C10PyBr, 0.36 for C11PyBr, 0.34 for C12 and C13PyBr, and 0.31 ((0.03) for C14PyBr, C15PyBr, and C16PyBr. It has to be mentioned that these values of p/n lie on the upper limit. For example, with the values of Λm ranging from 12 Ω-1 cm2 mol-1 (C10PyBr) to 9 Ω-1 cm2 mol-1 (C16PyBr), we get the same values of p/n as from osmotic coefficient measurements (see below). The experimental osmotic coefficients, φ, are plotted against the reduced concentration cmc/c in Figure 5. Included are the values (the smaller symbols) obtained from recent mean activity coefficient, γ(, measurements from this laboratory.15 The relation between φ and γ( is11
φ)1+
1 m
∫0m m d ln γ(
(6)
where m is the molality of the surfactant. The osmotic coefficient has been defined11 as the ratio of the real to the ideal osmotic pressure
φ)
π πid
)
∑i cifree 2c
(7)
For the process 2 we have assumed above that beyond the cmc the concentration of the free surfactant ions remains constant, cmc × φcmc, and so the concentrations of the free counterions and micelles are cmc × φcmc + p(c - cmc)/n and (c - cmc)/n, respectively. Thus, we get
(
φ ) φcmc -
1 + p cmc 1 + p + 2n c 2n
)
(8)
A plot of φ against cmc/c is presented in Figure 6. Equation 8 predicts a linear dependence of φ on cmc/c with an intercept (1 + p)/2n. Taking into account the aggregation numbers estimated from the apparent molar measurements (see Figure 8), the observed intercept 0.1 (15) Bezˇan, M.; Malavasˇicˇ, M.; Vesnaver, G. J. Chem. Soc., Faraday Trans. 1993, 89, 2445.
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5026 Langmuir, Vol. 15, No. 15, 1999
Figure 5. Plots of the osmotic coefficient of alkylpyridinium bromides in water at 25 °C against the logarithm of the reduced concentration. The values calculated from the literature data15 for activity coefficients are marked with the smaller symbols.
Figure 7. Variation of the relative apparent molar volumes for alkylpyridinium bromide series with the square root of concentration.
(R ) 0.9993) of Φv0 (in cm3mol-1!) on the number of carbon atoms in the chain, nC, can be represented by the expression
Φv0 ) 107.2 + 15.24nC
(10)
By subtracting from Φv0 the corresponding conventional 0 3 -1 , we get value for bromide ion,18 ΦBr - ) 24.71 cm mol 0 0 ΦCnPy+, the conventional value of Φv for alkylpyridinium cations. Considering also the existing literature data19 of Φv0 for C8PyCl, C10PyCl, and C12PyCl, the following 0+ on nC is obtained (R ) 0.9995): dependence of ΦCnPy
ΦC0 nPy+ ) 80.2 + 15.41nC
Figure 6. Variation of the osmotic coefficient for CnPyBr with the reciprocal reduced concentration.
( 0.01 gives for p/n the mean value 0.18 ( 0.02, which differs approximately by a factor of 2 from the p/n values obtained with the conductance measurements. As discussed already in the Introduction, the phenomenon that transport properties give appreciably higher values for the fraction of free counterions than the equilibrium ones has been observed before not only for micellar14,17 but also for polyelectrolyte solutions.5 The apparent molar volumes, Φv, for the alkylpyridinium bromide series were obtained from measured densities of solutions and solvent, F and F0, respectively, by using eq 9
Φv ) M/F0 + 1000(F0 - F)/cF0
(9)
where M is the molar mass of the surfactant monomer. The plots of Φv as functions of concentration are shown in Figure 7. To compress the ordinate, the relative value Φv - Φv0 is plotted, where Φv0 is the apparent molar volume of surfactants at infinite dilution. The linear dependence (16) Fowler, R.; Guggenheim, E. A. Statistical Thermodynamics; University Press: Cambridge, U.K., 1949; p 381. (17) Ingram, T.; Jones, M. N. Trans. Faraday Soc. 1969, 65, 297.
(11)
The limiting value 80.2 cm3 mol-1 for the hypothetical zero chain length (nC ) 0) can be compared to the value 0 3 -1 . for the pyridinium cation,20 ΦPy + ) 72.7 cm mol It is well-known that in ternary mixtures the additivity principle14
cΦv )
∑i ciΦi
(12)
may be expected to be fulfilled very closely at high dilution and to be a reasonable approximation at moderate concentrations. By applying eq 12 to the ionic species resulting in the process 2, we obtain
cΦv ) cmc × Φcmc + + [cmc + (c - cmc) p/n]Φ- + (c cmc)Φm (13) where Φm is the apparent molar volume of the monomer and Φcmc ) Φcmc + in the micelle. Because Φ- ≈ Φcmc v + cmc Φ- ,we get
(
Φv ) Φcmc v
p cmc cmc p cmc Φ - Φm + Φ - + Φm (14) n c n
)
The plots of the experimental Φv from Figure 7 against cmc/c yielded straight lines for cmc/c values lower than (18) Millero, F. J. Chem. Rev. 1971, 71, 147. (19) Causi, S.; De Lisi, R.; Milioto, S. J. Solution Chem. 1991, 20, 1031. (20) Hamann, S. D.; Lim, S. C. Aust. J. Chem. 1954, 7, 329.
Properties of Alkylpyridinium Bromides
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1. The difference between various alkylpyridinium salts was demonstrated by different slopes of the lines and different intercepts. From the intercepts, pΦcmc - /n + Φm, we calculated Φm, taking into account the p/n value from the osmotic coefficient measurements and the apparent cmc molar volume of the bromide ion at the cmc,11,18 ΦBr - . The resulting values of Φm are 260.7, 276.6, 292.5, 309.3, 325.6, 343.6, and 358.1 cm3 mol-1 for C10-, C11-, C12-, C13-, C14-, C15-, and C16PyBr, respectively. These data can also be expressed as (R ) 0.9998)
Φm/(cm3 mol-1) ) 96.2 + 16.40nC
(15)
Light-scattering studies21 on aqueous solutions of dodecylpyridinium bromide have proved that micelles of C12PyBr are spherical or globular even in the presence of excess NaBr. Following the idea of Tartar22 and Tanford,23 we can estimate the aggregation numbers, n, of micelles from geometric consideration alone. The calculation is based on the assumption that micelles contain a hydrophobic core consisting entirely of portions of the hydrocarbon chains. The hydrophilic headgroups, as well as one or more methylene groups near the headgroup, are excluded from the core. To obtain the volume of the hydrophobic part of a micelle, Vh, we shall use the experimental values of Φm’s, subtracting from them the contributions of the hydrophilic pyridinium headgroup and bound bromide ions. At the concentration at which the distances between ions correspond to the distances of headgroups on the micelle surface (c = 2.2-2.4 mol dm-3), the apparent molar volume of ions exceed their conven0 3 tional values18,20 at infinite dilution, ΦPy + ) 72.7 cm 0 -1 3 -1 11,18 mol and ΦBr- ) 24.7 cm mol , for about 1.4 cm3 mol-1. This gives the following Φv values at this concentration: ΦPy+ ) 74.1 cm3 mol-1 and ΦBr- ) 26.1 cm3 mol-1. Considering for the degree of counterion binding the value β ) 0.8, determined from the osmotic coefficient measurements, eq 15 yields the mean volume of the hydrophobic portion of the monomer within a micelle (Vh ) Φm - ΦPy+ - βΦBr-):
Vh/(cm3 mol-1) ) 1.2 + 16.4nC
(16)
or in cubic angstroms per alkyl chain
Vh/Å3 ) 2.0 + 27.2nC
(17)
Equating eq 17 with Tanford’s23 equation for the volume of the core
Vcore/Å3 ) 27.4 + 26.9ncore
(18)
which has been obtained by the assumption that the volume of the alkyl chain within the hydrocarbon core is identical with the volume of the corresponding liquid hydrocarbon,24 we find
ncore ) 1.01nC - 0.94 = nC - 1
(19)
Equation 19 indicates that in the case of alkylpyridinium salts practically one methylene group must be considered to be excluded from the core, when applying eq 18, in accordance with the above Tanford’s suggestion. (21) Fujio, K.; Ikeda, S. Langmuir 1991, 7, 2899. (22) Tartar, H. V. J. Phys. Chem. 1955, 59, 1195. (23) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (24) Reiss-Husson, F.; Luzzati, V. J. Phys. Chem. 1964, 68, 3505.
Figure 8. Variation of the aggregation number of alkylpyridinium bromides and chlorides with the chain length. The curves give predictions for the spherical micelles (see text!); larger symbols are literature experimental data.21,25
The volume of the core 4πl3/3 is thus equal to the product nVcore, where n is the number of surfactant monomers that can pack in a spherical micelle with the radius of the core equal to the length of the alkyl chain embedded in the core, l, or
n ) 4πl3/3Vcore
(20)
In calculations of the aggregation number n from eq 20, we used Tanford’s formula23 for the length of the fully extended alkyl chain:
l/Å ) 1.5 + 1.265ncore
(21)
Comparison of the experimental and calculated values is presented in Figure 8. We see that the experimental aggregation number21 for C12PyBr in pure water is in reasonable agreement with the n values predicted by eqs 18-21. Included are the literature data25 for alkylpyridinium chlorides. In an estimation of aggregation numbers for chlorides, the same procedure as above has been applied. The necessary data of Φv and β for C10PyCl and C12PyCl were taken from the literature.19 It can be seen that the observed higher n values for chlorides are correctly predicted by the model and that also in this case the experimental n values lie close to the calculated curve. Conclusions We have carried out the systematic studies of some fundamental equilibrium and transport properties of aqueous solutions of alkylpyridinium bromides. The variation of the cmc with chain length for the CnPyBr series, determined from conductivity measurements, can be represented by the well-known logarithmic expression. The values of the constants in this expression are close to those observed with related homologous series. Ionic conductivities and transport numbers of alkylpyridinium cations, determined from molar conductivities of alkylpyridinium bromides at infinite dilution, slightly decrease with the increasing chain length. From diagrams in which the experimental molar conductivities were plotted against (25) McGinnis, T.; Woolley, M. E. J. Chem. Thermodyn. 1997, 29, 401.
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reduced reciprocal concentration cmc/c, we determined the degree of counterion binding to the micelle, β. The β values are rather insensitive to the chain length and range from about 0.6 to 0.7 for C10PyBr to C16PyBr, respectively. From similar plots of the osmotic coefficient, determined β values are about 0.82. On the basis of the apparent molar volume measurements, we estimated the aggregation numbers of alkylpyridinium bromides, n. The values
of n are proportional to the square of nC, the number of carbon atoms in the chain: n ) 0.34nC2. Acknowledgment. This work was supported by the Ministry of Science and Technology of the Republic of Slovenia. LA981710+
