6382
J . Phys. Chem. 1988, 92, 6382-6385
Polyelectrolyte-Surfactant Interactions. Enthalpy of Binding of Dodecyl- and Cetylpyridinium Cations to Poly(styrenesu1fonate) Aniont J. Skerjanc,* K. Kogej, and G. Vesnaver Department of Chemistry, University of Ljubljana, 61 000 Ljubljana, Yugoslavia (Received: March 28, 1988)
The degree and the enthalpy of binding of dodecyl- and cetylpyridinium (DP' and CP') cations to poly(styrenesu1fonate) anion at 25 OC in aqueous solutions containing excess of NaCl are reported. The degree of binding has been determined by using a potentiometric technique based on surfactant-cation-selective membrane electrodes. The appreciable binding mol/L which is a few orders of magnitude below of both surfactants starts at the total detergent concentration about the critical micelle concentrations, cmc, and the binding of CP' cation is almost complete. Above this concentration the enthalpy of binding, calculated per mole of bound surfactant cations, is practically constant and for the DP' cation (for which the corresponding literature calorimetric data exist) approximately equal to the enthalpy of micellization of dodecylpyridinium iodide. From the solution of the Poisson-Boltzmann equation for the cell model of a polyelectrolyte solution with two kinds of monovalent counterions of different size, the distribution of counterions around the polyion is calculated. The calculations show that the local concentration of the surfactant counterions at the surface of the polyion exceeds the average concentration by a factor of about 1800, at the experimental conditions (Cp = 5 X lo4 monomol/L). On the basis of the experimental results and these calculations it is concluded that many small surfactant aggregates are formed in the polyion domain, much below the cmc. This finding agrees with the results of previous photochemical studies of polyelectrolyte-surfactant interactions.
Introduction Interactions between polyelectrolytes and surfactants have been the subject of some recent studies.'-4 These interactions are especially strong when a polyelectrolyte and an ionic surfactant are oppositely charged, with the consequence of a strong binding of the surfactant ion to the polyion often starting several orders of magnitude below the critical micelle concentration, cmc, of the surfactant. The degree of binding has usually been determined by using surfactant-ion-selective more rarely, the membrane equilibrium method.' In the paper of Kwak et aL2 it has been demonstrated that the binding constant increases with increasing surfactant chain length, so that, for example, the binding of cetylpyridinium cation to dextrane sulfate polyion is practically complete and starts already at surfactant concentrations much below the applicability of the electrode. As far as we could ascertain the calorimetric measurements with these systems are scarce for the present. In this paper we report on the measurements of the enthalpies of binding of dodecyland cetylpyridinium cations to the poly(styrenesu1fonate) anion. For this purpose the enthalpy of mixing of aqueous solutions of dodecylpyridinium and cetylpyridinium chlorides with solutions of sodium poly(styrenesu1fonate) in the presence of added NaCl was measured at 25 "C, and the corresponding enthalpies of dilution of all solutes were taken into account. Simultaneously similar potentiometric measurements as mentioned above were performed to determine the degree of binding of both surfactants to poly(styrenesu1fonate) anion, and the results of the two experimental techniques were correlated with each other. Experimental Section Materials. Solutions of sodium poly(styrenesulfonate), NaPSS, with a molecular weight of about 70000 and a degree of sulfonation I .O, supplied by Polysciences, Inc. (Warrington, PA), were exhaustively dialyzed against triple distilled water, and the concentration of the stock solutions was determined from optical density measurements at 261.5 n n 6 N-Dodecylpyridinium chloride, DPC, a gift from MerckSchuchardt, and N-cetylpyridinium chloride, CPC (Kemika, Zagreb, Yugoslavia) were thoroughly purified by repeated recrystallization from acetone. Calorimetry. Calorimetric measurements were carried out at 25 "C in an LKB 10700-2 batch microcalorimeter with golden 'Taken in part from a work presented by K. Kogej to the University of Ljubljana in partial fulfillment of the requirements for the M.Sc. Degree.
0022-3654/88/2092-6382$01.50/0
reaction cells. Into one compartment of the reaction cell 2.5 cm3 of 0.001 monomol/L NaPSS solution in water (or in 0.01 M NaCl or 0.1 M NaC1) was pipetted, and into the other an equal amount of DPC or CPC in the same solvent. The reference cell was filled with 2.5 cm3of water (or 0.01 M NaCI, or 0.1 M NaCl) and with 2.5 cm3 of the same surfactant solution. In this way the heat effect due to the dilution of surfactant was subtracted from the main effect. The enthalpy of dilution of NaPSS from 0.001 to 0.0005 monomolar solution can be neglected in the present studies. Most of the measurements were performed in the presence of an excess of simple salt (NaC1). In this way the ionic strength of the initial and final solutions was practically constant, and the heat effects measured may be considered to ensue solely from the binding of the surfactant cation to the polyion. In a few instances the flow version 10700-1 of the calorimeter was also used, and the experimental procedure corresponding to that adopted with the batch type was applied.
Concentration of Surfactant Cations Close to the Polyion Due to the large electrostatic potentials that exist in the vicinity of polyions the concentration of the counterions in these regions is very high.'-'] In the following we shall calculate the distribution of surfactant cations around a charged cylinder representing a polyelectrolyte molecule in solution in the presence of another cationic species. We presume that the main forces that direct counterions in the vicinity of the polyion are essentially of electrostatic nature and that any nonelectrostatic interactions appearing later are the consequence of the accumulation of counterions in these regions. ( I ) Satake, I.; Yang, J. T. Biopolymers 1976, 15, 2263.
(2) Malovikova, A,; Hayakawa, K.; Kwak, J. C . T. J . Phys. Chem. 1984, 88, 1930 and references cited therein.
(3) Abuin, E. B.; Scaiano, J. C. J . A m . Chem. Sac. 1984, 106, 6274. (4) Methemitis, C.; Morcellet, M.; Sabbadin, J.; Francois, J. Eur. Polym. J . 1986, 22, 619. ( 5 ) Jones, M. N. Presented at the 30th International Congress of Pure And Applied Chemistry; Manchester, 1985. (6) Skerjanc, J.; Pavlin, M. J . Phys. Chem. 1977, 81, 1166. (7) Katchalsky, A,; Alexandrowitz, 2 . ; Kedem, 0. In Chemical Physics of Ionic Solutions; Conway, B. E.; Barradas, R. S . , Eds.; Wiley: New York, 1966; p 295. (8) Armstrong, R. W.; Strauss, U. P. In Encyclopedia of Polymer Science and Technology; Interscience: New York, 1968; Vol IO, p 781. (9) Manning, G.S. J . Chem. Phys. 1969, 51, 924, 3249. (10) Le Bret, M.; Zimm, B. H. Biopolymers 1984, 23, 271, 287. ( I 1) Anderson, C. F.; Record, Jr., M. T. Annu. Reu. Phys. Chem. 1982, 33, 191.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6383
Polyelectrolyte-Surfactant Interactions The system examined is the cell modelI2 of Fuoss, Katchalsky, and Lifson and Alfrey, Berg, and Morawetz which has been extended to two kinds of equally charged counterions differing in size.I3J4 A cylindrical polyion A of radius a and length h with v negative charges uniformly smeared over its surface is centered in a larger cylinder of radius R that contains a neutralizing number of monovalent counterions B and C. The exclusion radii from the polyion axis to the center of the smaller and larger counterions are b and c, respectively. The detailed description and the basic equations of this extended cell model have been given previously.13J4 We shall calculate the concentration of counterions i at the radial distance r from the axis of the cylindrical polyion, Ci, relative to their average or analytical concentration, Ci ni - = - = rR2hn: exp(-zieoJ./kT)/Ni (1) iii
I = 2.03 y
=
x,-
4.4
0
ci
ci
where the local number density of counterions has been expressed by the familiar Boltzmann’s equation. In eq 1 zi is the valency of counterions, n? is their number density at the boundary of the cell where J., the electrostatic potential, is 0, eo is the protonic charge, Ni is the total number of counterions i, and k and T have their usual significance. Using for J. the equations of ref 13 and 14 we get for the relative concentration of the smaller counterions B in the interval between b and c (inaccessible to the larger counterions C): CB _
CB
-- p 1 2 e Z ( ~ - f ) / 2cos2 ~ B h(Pit - C,)
C 9
l b
L
I; I
I
10
20
I
I
I
30
40
50
60
r/nm
(2)
Figure 1. Variation of the local concentrations,CBand CC,of a mixture of two monovalent counterions B and C with the radial distance, r, from the axis of the cylindrical polyion of radius a = 0.8 nm. The radii of the counterions B and C are 0.2 and 0.3 nm, respectively, and and I?C are their average concentrations. Polymer concentration: C, = 5 X lo4 monomol/L.
If the condition
cB
is satisfied (cf. eq 21 of ref 13) eq 2 has the form
_ cB - fl12e2(7-r)/2~BX sinhZ (pit - C,)
(2a)
where all symbols have been defined13 previously; y = In (R/a, r = In ( r i a ) , tl = In (bla),t2 = In ( c i a ) , xBis the mole fraction of counterions B, 6 is the dielectric constant of the solvent, and PI, C,, P2, and C2are the integration constants. The charge-density parameter X has been definedIza by X = vzeoz/tkTh
(4)
For the radial distance c Ir IR, accessible to both counterions
on the pyridinium cation can approach the polyion axis.15 The curves are calculated for the limiting value of the mole fraction xc = 0, e.g., for the trace concentrations of the surfactant ion. It has to be mentioned that the value of xc does not influence much the general character of the logarithmic diagram presented in Figure 1. For example, for xc = 0 and xc = 1, respectively, the ratio Cc/cc is 1844 and 2277 at the distance r = c = 1.1 nm; it is 1.000 and 0.915 at r = 17.0 nm, and it is 0.259 and 0.234 at r = R = 65.2 nm, e.g., at the cell boundary. The latter two values represent also the fraction of free counterions C,fc, defined by
B and C, we have
fc = ncO/fic= CcQ/Cc
_ -- klP22eZ(Y-f)/2k2~BX cos2 (PZt - c2) CB CB
(5)
and for the larger counterions C CC _ - (k2 - kl)P22e2(Y-f)/2k2~CX cos2 (P2t - C2)
cc
(6)
where k, and k2 are constants determinedL3by nBo and nco. Values of CB/cBand Cc/cc computed from eq 2-6 are presented in Figure 1 as functions of the radial distance r. For the charge-density parameter the structural value7,* for poly(styrenesulfonates) in water was used (A = 2.83 at 298.15 K). The value of the concentration parameter y = 4.4 corresponds moto the experimental polymer concentration (C, = 5 X nomol/L) and to the polyion radius a = 0.8 nm. For the radii of closest approach b and c the values 1.O and 1.1 nm were taken, respectively, corresponding roughly to the ionic radius of the sodium ion and to the closest distance to which the positive charge (12) (a) Fuoss, R. M.; Katchalsky, A,; Lifson, S. Proc. N a f l .Acad. Sci. U.S.A. 1951, 37, 579. (b) Alfrey, T. Jr.; Berg, P. W.; Morawetz, H. J. Polym. Sci. 1951, 7 , 543. (13) Dolar, D.; Skerjanc, J. J . Polym. Sci., Polym. Phys. Ed. 1976, 14, 1005. (14) 1355.
Skerjanc, J.; Dolar, D. J . Polym. Sci., Polym. Phys. Ed.
(7)
Figure 1 demonstrates the well-known phenomenon of a striking accumulation of counterions in layers close to the surface of the polyion. For example, the local concentration of the larger counterions C exceeds the average concentration by a factor of about 1800 at the polyion surface, and by a factor of 100 at a radial distance r = 2.5 nm, e.g., at the distance from the polymer surface which is comparable to the length of DPC or CPC hydrocarbon chain. One may thus conclude that due to pure electrostatic interactions between the polyion and detergent counterions there is also an extensive accumulation of nonpolar parts of the surfactant molecules in the vicinity of the polymer. As a consequence, the aggregation process takes place in these regions even at a total surfactant concentration that is a few orders of magnitude below the cmc. The resulting small aggregates behave as multivalent “minimicelles” and become “trapped” in the regions of high electrostatic potential close to the macroion. A similar model for binding of detergent (dodecyltrimethylammonium bromide) to polyelectrolyte (sodium poly(styrenesulfonate)) has been recently proposed by Abuin and S ~ a i a n o . ~ On the basis of laser flash and luminescence measurements they have estimated the aggregation number of these small aggregates ~~~~~
~
~
~
(1 5) The latter value has been estimated from apparent molar volumes’“ 1982, 20,
of CPC and DPC and the known structural data for the pyridinium cation by using the semiempirical method of Conway et al.”
6384
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
Skerjanc et al.
t
a b c 1
1
I
2
l
3
I
4
I
5
I
6
l
7
1
8
9
I
1
0
r/n rn
Figure 2. Comparison of the results obtained from the solution of the Poisson-Boltzmann equation (lines) with the Monte Carlo calculationsI0 (points) for a solution of DNA of concentration 0.0314 monomol/L (y = 2.30), containing a mixture of an equal number of two monovalent counterions ( X C = 0.5). The polyion radius is a = 1.0 nm, and the radii of small (B) and bulky (C) counterions are 0.2 and 1.0 nm, respectively. Charge-density parameter X = 4.2.
to be between 7 and 10 which is much smaller than ordinary micellar aggregation number. It should be mentioned that recent Monte Carlo studies of the distribution of small ions around a charged cylinder representing a polyelectrolyte molecule by Le Bret and Zimmlo have shown that the solution of the Poisson-Boltzmann equation gives good agreement with the Monte Carlo results when the radius of counterions is small compared to the polyion radius. Our calculations have shown1*that there is a reasonable agreement between the two methods also for the case examined above, e.g., for mixtures of counterions of the same charge. A comparison of the Poisson-Boltzmann and Monte Carlo treatments for DNA, with X = 4 . 2 , a = 1.0 nm, b = 1.2 nm, c = 2.0 nm, and xc = 0.5, is presented in Figure 2 as an example. We can see that the cell model extended to the mixtures of two monovalent counterions differing in size13*14 gives a satisfactory agreement with the Monte Carlo simulation, although as stated above, the case presented is not favorable for the Poisson-Boltzmann treatment, since the radii of the bulky counterion and the polyion are equal to each other.
Results and Discussion The enthalpies of binding of surfactant cations to the polyion, AHb,were obtained in experiments in which a solution of NaPSS was mixed with a solution of dodecyl- or cetylpyridinium chloride and the corresponding enthalpies of dilution of surfactants and NaPSS were accounted for. To keep the ionic strength of the initial and final solutions constant, in most cases both solutions contained an excess of the simple salt (NaC1). In order to give the observed calorimetric data more general significance we performed also some binding studies with the same systems utilizing the potentiometric method based on surfactant-ion-se(16) Kogej, K.; Skerjanc, J., unpublished results.
(17) Conway, B. E.; Desnoyes, G. E.; Smith, A. C. Philos. Trans. R. SOC. (London) 1964, 256, 389. ( I 8) Skerjanc, J., unpublished results.
Figure 3. Binding isotherms of CP+ and DP+ cations by poly(styrenesulfonate)anion at 25 O C in the presence of 0.01 M NaCl (0,O) and 0.1 M NaCl (e,.).
"
O
)j
CP-
P
d
i g
OO
1
cD
.:O"/mdm 3
-3
4
5
Figure 4. The amount of binding, p, as function of the total detergent concentration, C,, at 25 O C . Symbols as in Figure 3.
lective solid-state electrodes. As observedlg already before for the system sodium dextran sulfate-CPC-NaCl, in the case of the NaPSS-CPC-NaCl system also the binding of surfactant starts at such low free surfactant concentrations (about lo-* M) that only approximate binding isotherms can be constructed. The methods used to obtain from the potentiometric emf vs log CD curves binding isotherms, Le., plots of the amount of binding p against log CDf,where
0 = (CD - c D f ) / c P
(8)
and CDand Cor are the total and free detergent concentrations, respectively, have been described in detail.'^'^ From Figure 3 we can see that the binding of CPC starts at about 2 orders of magnitude lower free surfactant concentrations than the binding of DPC. In the context of our further discussion on the enthalpy (19) Hayakawa, K. Kwak, J. C. T. J . Phys. Chem. 1982, 86, 3866
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6385
Polyelectrolyte-Surfactant Interactions
20
c
/’
*-e-----&--
--ab-
1
‘. 4 01 5.5
-
I
I
I
I5.0
0 water 0 0.01MNaCl 0 0.1 MNaCI
ii
AA
1
I 4.0
4.5 -log
I
3.5
3.0
CD
Figure 5. The enthalpy of binding of CP+ cations to PSS- anion at 25 OC in water, 0.01 M NaC1, and 0.1 M NaCI. The values of AH, are calculated per mole of bound detergent cations. Cloudy final solutions: 0.
-1
15c
CPC we also notice that, close to the detergent concentration (5 X M) at which 1:l complex is formed, AHbdrops again. It is rather remarkable that the steep initial rise of AHb happens for both surfactants almost at the same total concentration, e.g., around M, a finding which is in complete agreement with the potentiometric observations. It has been also shown before that at this analytical concentration the local concentrations around the polyion in the layers lying between the polyion and the radial distance which is comparable to the length of the surfactants to M. These hydrocarbon chains range from about 2 X concentrations are comparable to, or higher than, the cmc of the two surfactants studied (cmc for DPC, 1.52 X M in water, M in 0.01 M NaC1, and 0.45 X M in 0.1 M 1.24 X NaC1; cmc for CPC, 6.3 X lo4 M in water, 1.6 X lo4 M in 0.01 M NaC1, and 0.38 X in 0.1 M NaC1; determined by potentiometry at 25 “C). With the discussion of the previous section as background, the observed overall enthalpy of binding may be considered to contain the following contributions: (1) The enthalpy change due to the atmospheric binding of detergent cations after mixing surfactant and polyelectrolyte solutions, AHa;(2) The heat effect accompanying the aggregation of the bound detergent molecules into , from minimicelles, AH,,,; (3) The enthalpy change, M iensuing the interaction of the minimicelles with the polyion, which could be accompanied by the eventual coiling of the polymer chain: = AHa
-10g
I
\ X P
0 0.01MNlCl 0 0 . 1 MNaCl
5-
0 n5.5
I
I
I
I
5.0
4.5
4.0
3.5
-log
3.0
CD
Figure 6. The enthalpy of binding of DP+ cations to PSS- anion at 25 “C. Text as in Figure 5 .
of binding, it has to be stated, however, that the corresponding total surfactant concentrations at which an appreciable binding of CP+ and DP+ cations starts are approximately the same (about M). Figure 4 in which ,8 is plotted against the total detergent concentration (cf. eq 8, note that Cp = 5 X lo4 M) shows clearly that the cetylpyridinium cation is almost quantitatively associated with the poly(styrenesu1fonate) anion in the whole concentration range studied (more than 99%), whereas the degree of binding of the dodecylpyridinium cation is weaker and depends upon the surfactant and NaCl concentrations. The calorimetric results are presented in Figures 5 and 6, where AHb is plotted against the logarithm of the total detergent concentration. The enthalpy of binding, M b , is calculated per mole of bound surfactant cations, e.g., the experimental AH is divided by b = ,8Cp/CD, the degree of binding. As stated already b = 1 for the CP+ cation, whereas for the DP+ cation its values lie in the range from 0.70 to 0.99 depending on the surfactant and NaCl concentrations. Various aspects of the experimental results presented in Figure 5 and 6 are noticeable. First, the enthalpy of binding decreases with increasing concentration of the simple salt. This experimental observation is additionally demonstrated with experiments performed with CPC in pure water and presented in Figure 5 as the uppermost curve. Note that in this case each experimental point corresponds to a different final concentration of NaCl, equal to the detergent concentration, C,. The second and more significant aspect is the sharp increase of at a given critical surfactant concentration. Below this concentration the heat effects are undetectable or zero, and then they are more or less constant. For
+ AH,,, + AHi
(9)
The process 1 and partly also the process 3 should be governed predominantly by electrostatic forces, and the corresponding enthalpy contributions AHH,and AHi may be assumed to be small compared to the enthalpy change of the second process, AH,,,. Results of the apparent molar volume studies16of the CPC-PSS complex excluded the possibility of the binding of minimicelles to the specific sites on the polyion, which could make the enthalpy more significant. The measured enthalpy change contribution M i may be thus considered to reflect largely the heat effects ensuing from the formation of the small aggregates in regions close to the polyion which are governed mostly by the hydrophobic interactions. Support for this consideration is the scarce experimental data of the enthalpy of micellization obtained with the conventional micelles. The enthalpy of micellization of N-dodecylpyridinium iodide at cmc and 25 ‘C, obtained by direct calorimetric measurements,” was found to be AH,,, = -( 13.5 f 3) kJ/mol in water 2.5) kJ/mol in 0.01 M KI. These values and A H , = -(13.0 agree well with the experimental results obtained for N-dodecylpyridinium chloride in these studies. Finally, it can be noticed that also the decrease of AHm with the increasing concentration of the simple salt is consistent with the results of our measurements. In conclusion it has to be recalled that, although there exists the possibility of partial association of nonpolar parts of the surfactant molecules with the hydrophobic backbone of the polyion, the results of the present calorimetric studies indicate that the majority of the surfactant molecules close to the polyion are associated with each other well below their cmc, forming many small aggregates which become “trapped” in the polyion domain, a conclusion that is in agreement with the surfactant-polyelectrolyte interaction model proposed recently3 on the basis of photochemical measurements.
*
Acknowledgment. This material is based on work supported by the US-Yugoslav Joint Fund for Scientific and Technological Cooperation, in cooperation with the N S F under Grant 850 9373-JFP 521, and by the Research Community of Slovenia. Registry No. DPC, 104-74-5; CPC, 123-03-5; NaPSS, 9080-79-9; NaCI, 7647-14-5. (20) Jones, M. N.; Agg, G.; Pilcher, G.J . G e m . Thermodyn. 1971, 3, 801.
