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Langmuir 2002, 18, 6484-6490
Articles New Insights on the Interaction Mechanism within Oppositely Charged Polymer/Surfactant Systems C. Wang and K. C. Tam* Singapore-MIT Alliance, School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 Received January 23, 2002. In Final Form: April 29, 2002 The interactions between dodecyltrimethylammonium bromide and anionic polymers such as neutralized poly(acrylic acid) and methacrylic acid/ethyl acrylate copolymers were investigated using isothermal titration calorimetry (ITC). The ITC results suggest that in the initial stage of titration, the cationic headgroups of surfactant individually bind to the anionic carboxylate groups on the polymer chains due to electrostatic attraction. When the surfactant concentration reaches a critical value C′, the micellization of polymerbound surfactant occurs, resulting in the formation of insoluble polymer/surfactant complexes. The thermodynamic parameters derived from ITC measurements suggest that the electrostatic binding is an endothermic process driven by entropy. The positive entropy is attributed to the recovery of translational entropy of released counterions by the bound surfactant. The ITC curves for titrations performed in different salt conditions show that addition of salt screens the electrostatic repulsion between surfactant headgroups and attraction between oppositely charged polymer chains and surfactant molecules, which favors the formation of free micelles, and weakens the binding of surfactant onto the polymers.
Introduction Interactions between polymers and surfactants in aqueous solutions have attracted significant interest because of their widespread applications and relatively complex behaviors. Numerous research groups have devoted their attention to advancing the fundamental understanding of the physics governing these interactions.1-13 For oppositely charged polyelectrolyte and surfactant systems, the strong electrostatic attraction between the charged groups is clearly observable and occurs at concentrations several orders of magnitude below the critical micellization concentration (cmc). The interactions between cationic proteins and anionic surfactants were * To whom correspondence should be addressed. Fax: 65-67911859. E-mail:
[email protected]. (1) Hayakawa, K.; Kwak, J. C. T. In Cationic Surfactants; Rubingh, D. N., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; p 189. (2) Goddard, E. D. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadamananabham, K. P., Eds.; CRC Press, Boca Raton, FL, 1993; p 171. (3) Bloor, D. M.; Wan-Yunus, W. M. Z.; Wan-Badhi, W. A.; Li, Y.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 1995, 11, 3395. (4) Bloor, D. M.; Li, Y.; Wyn-Jones, E. Langmuir 1995, 11, 3778. (5) Olofsson, G.; Wang, G. Pure Appl. Chem. 1994, 66, 527. (6) Wang, G.; Olofsson, G. J. Phys. Chem. 1995, 99, 5588. (7) Fox, G. J.; Bloor, D. M.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 1998, 14, 1026. (8) Seng, W. P.; Tam, K. C.; Jenkins, R. D.; Bassett, D. R. Macromolecules 2000, 33, 1727. (9) Seng, W. P.; Tam, K. C.; Jenkins, R. D.; Bassett, D. R. Langmuir 2000, 16, 2151. (10) Persson, K.; Wang, G.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1994, 90 (23), 3555. (11) Thuresson, K.; Nystrom, B.; Wang, G.; Lindman, B. Langmuir 1995, 11, 3730. (12) Faes, H.; De Schryver, F. C.; Sein, A.; Bijma, K.; Kevelam, J.; Engberts, J. B. F. N. Macromolecules 1996, 29, 3875. (13) Wang, Y.; Han, B.; Yan, H.; Kwak, J. C. T. Langmuir 1997, 13, 3119.
known in the 1930s, well before the first study of synthetic polymer/surfactant systems.14 Anionic surfactants such as sodium dodecyl sulfate (SDS) were found to bind to positive charge sites on proteins in stoichiometric proportions, and this alters the conformation of the protein molecules from a random structure to a folded helix, which is surrounded by surfactant micelles.15 White and coworkers examined the binding of cationic surfactant to anionic cellulosic polymers and concluded that the initial binding of surfactant cations was due to ion exchange, which was followed by clustering of surfactant and counterions on those binding sites.14 In sodium hyaluronate and a cationic surfactant of the alkyl trimethylammonium system, it was reported that the polymer/ surfactant attraction is purely electrostatic and the surfactant micelles are separated from the oppositely charged polyelectrolyte by a layer of water molecules.16 Fundin et al. reported from light scattering studies that micelles of cetyltrimethylammonium bromide (C16Tab) bind onto poly(acrylic acid) chains due to both the electrostatic attraction and hydrophobic interaction.17 A strong electrostatic attractive force was also found in the interactions between SDS and cationic polymers, such as dendrimers and methylvinylimidazole/vinylpyrrolidone/ vinyl acrylic acid copolymers, which were reported by Ghoreishi et al. based on microcalorimetry and electromotive force (emf) measurements.18,19 The interaction (14) Rodenhiser, A. P.; Kwak, J. C. T. In Polymer-Surfactant System; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; p 1. (15) Shirahama, K. In Polymer-Surfactant System; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; p 143. (16) Linse, P.; Piculell, L.; Hansson, P. In Polymer-Surfactant System; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; p 193. (17) Fundin, J.; Hansson, P.; Brown, W.; Lidegran, I. Macromolecules 1997, 30, 1118. (18) Ghoreishi, S. M.; Fox, G. A.; Bloor, D. M.; Holzwarth, J. F.; WynJones, E. Langmuir 1999, 15, 5474.
10.1021/la025573z CCC: $22.00 © 2002 American Chemical Society Published on Web 07/27/2002
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is generally accepted as an ion-exchange process where the electrostatic forces of interaction are reinforced by aggregation of alkyl chains of the bound surfactant molecules. Heat effects in micellar and polymer/surfactant solutions are relatively small. However, modern calorimetric methods, such as the microcalorimetric technique, are sensitive enough to monitor such small heat changes. Isothermal titration calorimetry can be used to extract thermodynamic parameters such as enthalpy (∆H), entropy (∆S), Gibbs energy (∆G), and heat capacity (Cp), which are critical to the understanding of polymer/ surfactant interactions.3-6,9,11,13,20 Microcalorimetry also allows the characterization of a polymer/surfactant system in terms of critical concentrations, such as critical aggregation concentration (cac) corresponding to the occurrence of onset of binding, saturation concentration (C2) corresponding to the full saturation of polymer chains with bound surfactant, and the second critical concentration (Cm) corresponding to the formation of free micelles in polymer solutions.3-6,20 The current understanding on the interaction between a fully ionized polyelectrolyte such as poly(acrylic acid) and a cationic surfactant is that the polymer chains induce the formation of micelles on the polymer chains. However, our recent experimental studies seem to suggest that surfactant unimers are attracted to the charged sites of the polymer backbone prior to the formation of micelles caused by the polymer-induced micellization process. We have devised a series of experiments on a well-studied polyelectrolyte system (i.e., poly(acrylic acid)) to confirm our hypothesis. In this paper, we report an experimental investigation on the interactions between a cationic surfactant (DoTab) and anionic polyelectrolytes, for example, poly(acrylic acid) (PAA) and methacrylic acid/ethyl acrylate copolymers (MAA/EA copolymers). We also examine the effects of the hydrophobic moiety of the cationic surfactant on the nature of the observed interactions. The critical concentrations and thermodynamic parameters were determined by analyzing the isothermal calorimetric titration data. We hope that our present results can advance our understanding on the binding mechanism in oppositely charged polymer/surfactant systems. Experimental Details Materials. Poly(acrylic acid) with MW ) 450 000 Da was obtained from Aldrich Chemical Co. The MAA/EA copolymers were synthesized by Dow Chemicals (formerly Union Carbide) at a concentration of 10 vol % using conventional semicontinuous emulsion polymerization. They have an average molecular weight of approximately 200 000-250 000 Da, determined by static light scattering measurements.21,22 These polymers are designated as HASEx-y, where x and y correspond to the molar percentages of the MAA and EA groups, respectively. The polymer latex at low pH (ca. 3-4) was dialyzed in distilled-deionized water using a regenerated cellulose tubular membrane. The dialysis process was carried out over a 1 month period during which the water was replaced every week. This cleaning process removes all the impurities and unreacted chemicals. PAA solutions containing 5 mM carboxylate groups and 0.05 wt % of HASE polymer solutions which were neutralized to pH ) 9 (using 1 M standard NaOH solution from Merck) were prepared for microcalorimetric titration studies. (19) Li, Y.; Ghoreishi, S. M.; Warr, J.; Bloor, D. M.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 1999, 15, 6326. (20) Wang, G. Ph.D. Thesis, Lund University, Lund, Sweden, 1997. (21) Islam, M. F.; Jenkins, R. D.; Ou-Yang, H. D.; Bassett, D. R. Macromolecules 2000, 33, 2480. (22) Dai, S.; Tam, K. C.; Jenkins, R. D. Eur. Polym. J. 2000, 36, 2671.
Langmuir, Vol. 18, No. 17, 2002 6485 The cationic surfactants used in the studies of polymer/ surfactant interactions are dodecyl trimethylammonium bromide (DoTab from Fluka, g98%, C15H34BrN), tetradecyl trimethylammonium bromide (TTab, from Tokyo Kasei, g99%, C17H34BrN), and cetyl trimethylammonium bromide (CTab, from Merck, g99%). Isothermal Titration Calorimetry (ITC). The calorimetric data were obtained using the Microcal isothermal titration calorimeter. This power compensation, differential instrument was previously described in detail by Wiseman et al.23,24 It has a reference cell and a sample cell of approximately 1.35 mL, and the cells are both insulated by an adiabatic shield. The titration was carried out at 25.0 ( 0.02 °C, by injecting 0.1 M surfactant solution from a 250 µL injection syringe into the sample cell filled with polymer solution. The syringe is tailor-made such that the tip acts as a blade-type stirrer to ensure an optimum mixing efficiency at 400 rpm. An injection schedule was automatically carried out using interactive software after setting up the number of injections, volume of each injection, and time between each injection. Electromotive Force and Light Scattering Measurements. Electromotive force and light scattering measurements were conducted to support the binding isotherms obtained from ITC. The Metrohm Na+ glass membrane electrode was used in conjunction with the Metrohm Ag/AgCl double junction reference electrode. The Brookhaven BI-MAS light scattering system was used to determine the scattered light intensity of the polymer/ surfactant complex at different degrees of binding.
Results and Discussion The isothermal titration experiments were conducted by step-by-step injections of concentrated DoTab into a cell containing an aqueous solution of neutralized poly(acrylic acid) (poly(acrylate), i.e., PA). The thermogram for the titration of 0.1 M DoTab into the PA solution containing 5 mM carboxylate groups is shown in Figure 1a. Integration of the area under the raw signal curve at each injection gives the differential enthalpy curves as shown in Figure 1b. The enthalpy measured in the ITC experiment is a sum of heat from several different contributing factors, such as the dissociation of surfactant micelles to monomers, the dilution effect, and the binding of surfactant onto polymers. However, the enthalpy from the dilution effect is small compared to that from the micellization and the binding of surfactant onto polymers. The enthalpy curve shown in Figure 1b indicates that DoTab interacts with PA in two stages, which are characterized by the pronounced endothermic peak (denoted as peak A) and a less evident shoulder peak (denoted as peak B). The pronounced endothermic peak A is believed to correspond to the binding of the cationic headgroups of DoTab molecules to the negatively charged carboxylate sites along the PA chains, which is similar to the binding of anionic SDS to positive charges on protein molecules. The peak occurs at the first injection of surfactant and increases rapidly with further addition of DoTab, indicating that the binding is highly cooperative and starts at a very low concentration. The enthalpy curve levels off at [DoTab]/[∼COO-] ) ∼1, where an equal amount of opposite charges is present, suggesting that DoTab binds to positive charge sites on PA in stoichiometric proportion. The shoulder peak B may correspond to the micellization of DoTab molecules bound on the polymer chains. The bulk concentration of DoTab at this degree of binding is 3.34 mM, which is far below the cmc of DoTab in an aqueous medium (∼15 mM). However, the local concen(23) Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L. Anal. Biochem. 1989, 28, 131. (24) Jelesarov, I.; Bosshard, H. R. J. Mol. Recognit. 1999, 12, 3.
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Figure 3. Binding isotherms obtained from titrating 0.1 M DoTab in 5 mM PA in 0.1 M ([), 0.5 M (2), and 1 M (b) NaCl solutions, plotted together with the dilution curves in 0.1 M (]), 0.5 M (4), and 1 M (O) NaCl solutions.
Figure 1. Calorimetric titration of 0.1 M DoTab into PA solution (5 mM carboxylate groups) at 298 K: (top panel) thermogram showing cell feedback (CFB) versus time; (bottom panel) differential enthalpic curves versus the concentration of DoTab.
Figure 2. Differential enthalpy curves for titration of 0.1 M DoTab in 5 mM PA in 0 M (9), 0.1 M ([), 0.5 M (2), and 1 M (b) NaCl solutions.
tration of DoTab in the vicinity of PA chains is sufficiently high to induce micellization because of the strong Coulombic attraction between the oppositely charged polymer and surfactant. The differential enthalpy curves for titrating 0.1 M DoTab into PA solutions containing 5 mM carboxylate groups in the presence of 0, 0.1, 0.5, and 1 M NaCl are plotted in Figure 2. The height of the endothermic peak A is inversely proportional to the NaCl concentrations, indicating that the binding is weakened by the addition of salt, which suppresses the electrostatic attraction between DoTab and PA. The enthalpic binding curves obtained from titrating 0.1 M DoTab into 5 mM PA solutions containing 0.1, 0.5, and 1 M NaCl (given by closed symbols) are plotted in Figure 3, together with the dilution curves of DoTab into water containing identical amounts
of NaCl (given by open symbols). The distinct endothermic peak detected in the dilution curves characterizes the cmc of DoTab at different salt conditions. It is found that cmc decreases from 9.26 to 1.96 mM when the NaCl concentration increases from 0.1 to 1 M, since micellization is favored by the additional salt that screens the electrostatic repulsion between the surfactant headgroups. In the presence of 0.1 M NaCl, the binding isotherm exhibits a third stage (represented by the endothermic peak C) at CDoTab ) ∼13 mM besides the two stages corresponding to the electrostatic binding (peak A) and micellization of bound surfactant molecules (peak B). The third stage has an identical profile as the peak observed in the dilution curves and is believed to be due to the formation of free DoTab micelles in PA solution. When NaCl concentration is increased to 0.5 M, the profile of the binding isotherms is greatly altered. The deviation of the binding curve (shown by filled circles) from the dilution curve (shown by open circles) at CDoTab ) ∼1.28 mM represents the onset of binding. Thereafter, the enthalpy curve generally follows a similar trend as the dilution curve and exhibits an endothermic peak at CDoTab ) ∼3.57 mM, which is also identical to the peak detected in the dilution curve. This peak represents not the micellization of polymer-bound surfactant molecules but the formation of free micelles. With further addition of NaCl to 1 M, the binding curve and the dilution curve are almost identical, where the slight deviation occurring at CDoTab ) ∼1.06 mM characterizes the weak binding of DoTab molecules to PA charged sites. In excess of salt, where the Coulombic attractive force between polymer and surfactant is considerably screened, the electrostatic binding is significantly weakened and consequently the polymer-induced micellization cannot occur since negligible amounts of surfactant are electrostatically bound to the polymer backbone. On the other hand, the Coulombic repulsion between the surfactant headgroups is also shielded by the addition of salt, which favors the formation of free micelles. The binding isotherm characterized in terms of critical concentrations is depicted in Figure 4. The enthalpy curve shown in Figure 4 was obtained from the titration conducted in 0.1 M NaCl, where the electrostatic interaction is weakened but not fully screened. The binding curve deviates from the dilution curve at CDoTab ) 0.83 mM, which is considered as the concentration where the onset of electrostatic binding commences, namely, C1. However, in the salt-free PA/DoTab system, the surfactant binds on the polymer immediately due to strong electrostatic force,
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Figure 4. Classification of binding regimes and schematic binding mechanism of the PA/DoTab system: ([) binding isotherm in 0.1 M NaCl solution; (]) dilution curve in 0.1 M NaCl solution.
Figure 5. Differential enthalpy and emf of sodium ions for titrating 0.1 M DoTab into 5 mM PA in aqueous solution. Pictures of the samples at different DoTab concentrations with the scattered intensity are included.
and hence it is not possible to detect the exact value of C1. The pronounced endothermic “plateau” peak following C1 characterizes the binding of positively charged DoTab monomers to the anionic carboxylate groups along the PA chains. Subsequently, another well-separated endothermic peak appears at CDoTab ) 4.28 mM (designated as C′), denoting the critical concentration where the polymerinduced micellization of electrostatic-bound surfactant monomers occurs. The enthalpy curve then levels off and crosses the dilution curve at CDoTab ) 7.36 mM (designated as C2), which represents the concentration where the polymer is saturated and the micellization of bound surfactant is complete. The enthalpy curve rises again to exhibit another endothermic peak at CDoTab ) 12.78 mM, which is designated as Cm corresponding to the formation of free DoTab micelles in the polymer solution. Thereafter, the enthalpic binding and dilution curves merge. According to these critical concentrations, the binding isotherm can be classified into four regimes. Region 1 (between C1 and C′) corresponds to the electrostatic binding of surfactant onto the polymer chains. Region 2 (between C′ and C2) represents the micellization of polymer-bound surfactants. In region 3 (between C2 and Cm) where the enthalpy curve levels off and intersects with the dilution curve, the polymer chains become saturated and polymer/surfactant interaction ceases. When the surfactant concentration reaches Cm, the binding curve merges with the dilution curve and becomes region 4, where free surfactant micelles begin to form. From the above, we conclude that the initial binding force is the Coulombic attraction and the micellization of the surfactants is induced by the “electrostatically” bound surfactant molecules. The addition of salt screens the Coulombic attractive forces between the cationic surfactant and the anionic carboxylate groups, which diminishes the binding and delays the occurrence of the micellization of polymer-bound surfactants. Thus, from Figure 2, C′ increases from 3.1 mM in salt-free polymer solution to 4.3 mM in polymer solution containing 0.1 M NaCl. The schematic binding mechanism is also depicted in Figure 4. Initially, the interaction between PA and DoTab is purely electrostatic, where the polymer/ surfactant complexation in such a system can be considered as a surfactant micellization perturbed by the presence of the polymer. A complete understanding of the interaction between PA and DoTab is essential for the examination and interpretation of the binding behaviors in other oppositely charged polymer/surfactant systems. The binding model depicted in Figure 4 is supported by the results obtained from emf and light scattering measurements. Figure 5 shows the binding isotherms
obtained from ITC and emf measurements in salt-free aqueous solution, together with the pictorial description of PA solutions at different DoTab concentrations. As shown in Figure 5, the two binding isotherms obtained from ITC and emf concur with each other. The critical concentrations determined from the onset of the endothermic peaks of enthalpy curves are identical with those determined from the inflection points representing the slope change on the emf curve (indicated by arrows in Figure 5). As suggested by the ITC curves, DoTab molecules electrostatically bind to carboxylate sites in region 1 and the binding is an endothermic process driven by a positive entropy gain resulting from the release of condensed counterions. In polyelectrolyte solution such as PA, the counterions, that is, Na+ ions, are condensed on the oppositely charged polymer chains, thereby losing their translational entropy.14 When DoTab is added, the binding of cations to the carboxylate groups can be considered as an ion-exchange interaction, where the condensed sodium ions are released, regaining their translational entropy, which is the essential driving force for the binding to proceed. This hypothesis is confirmed by the binding isotherm obtained from emf measurements using a sodium ion selective electrode (Figure 5). The emf, corresponding to sodium ion release, increases linearly with DoTab concentration at CDoTab < 1 mM, which is direct evidence of electrostatic binding of DoTab to the PA chains resulting in the release of condensed sodium ions. The sample is transparent with a low scattering intensity of 0.8 kcps. A slope change occurs at CDoTab ∼ 1 mM (marked by “I”), which is related to the phase change of the polymer solution as revealed by the translucent sample with a scattered intensity of 253.1 kcps. The emf continues to increase until CDoTab ∼ 3.2 mM, characterizing the continuous release of condensed sodium ions caused by the electrostatic binding of DoTab monomers to PA chains. At CDoTab ∼ 3 mM, the second endothermic peak on the ITC curve appears, and the emf curve levels off. The scattered intensity increases to 330.8 kcps and the solution becomes opaque, indicating the micellization of polymer-bound surfactant molecules. When the DoTab concentration reaches ∼4.8 mM, the enthalpy curve merges with the dilution curve and the emf value remains essentially constant, suggesting that the electrostatic binding and release of condensed sodium ions have ceased. At this point, the scattered intensity is 494.8 kcps and precipitates of PA/DoTab complexes are observed. The thermodynamics of electrostatic binding can be treated by applying Manning’s theory of counterion
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Table 1. Thermodynamic Parameters for the Binding and Micellization of DoTab in PA Solution at Different Salt Conditions salt concn (M)
∆Gel (kJ/mol)
∆Hel (kJ/mol)
∆Sel (J/mol K)
C′ (mM)
∆G′ (kJ/mol)
∆H′ (kJ/mol)
0 0.1 0.5 1
-10.76 -4.68 -1.41 0
12.17 4.59 2.08 1.15
76.94 31.11 11.71 3.86
3.11 4.28 N/A N/A
-25.32 -23.92 N/A N/A
9.24 6.94 N/A N/A
condensation.25 Consider the binding interaction between DoTab (represented by D+) and PA (∼COO-Na+m):
∼COO-Na+m + D+ h ∼COO-D+ + mNa+ The thermodynamic equilibrium constant KT can be expressed as
KT )
[∼COO-D+][Na+]m
(1)
[∼COO-Na+m][D+]
where [∼COO-Na+m] is the concentration of carboxylate groups with condensed sodium ions, [∼COO-D+] is the concentration of PA/DoTab complex formed due to electrostatic attractive force, [D+] is the concentration of unbound DoTab molecules, [Na+] is the concentration of free sodium ions, and the stoichiometric coefficient m represent the fraction of sodium ions that are thermodynamically condensed on the PA chains. The electrostatic binding component of the thermodynamic equilibrium constant can be expressed as
Kb )
[∼COO-D+] [∼COO-Na+m][D+]
)
KT [Na+]m
(2)
Equation 2 gives the equilibrium constant of electrostatic binding (Kb), through which the Gibbs energy corresponding to counterion condensation can be achieved. According to the theory of counterion condensation, Kb is a function of the concentration of the counterion (Na+ in our case), the valence of the counterion (+1 for our case and thus this factor is neglected), and a coefficient m representing the charge density (inverse proportion of linear charge spacing) of the polymer chains. If the linear charge spacing is higher than a critical value, that is, Bjerrum length, the charge density of the polymer is too low to condense counterions. The thermodynamic equilibrium is reached when the binding of surfactant and release of counterions is at equilibrium, when KT ) 1 and Kb ) 1/[Na+]m. According to Manning’s theory, m is a function of the reduced linear charge density of the polyelectrolyte, ξ:
m)1-
1 2ξ
(3)
where ξ is related to the Bjerrum length, lB, and the distance b between two charged sites on the polymer:
ξ)
lB b
(4)
The Bjerrum length is defined as
lB )
e2 kBT
(25) Manning, G. S. J. Chem. Phys. 1969, 51, 924.
(5)
∆S′ (J/mol K) 115.97 103.58 N/A N/A
where e is the electron charge, is the dielectric constant of water, kB is the Boltzmann constant, and T is the temperature. For PA polymer chains in aqueous solution, lB is 7.1 Å and the value of b from the literature is 2.53 Å;15 thus ξ is calculated to be 2.8 and m is 0.82. Hence, the electrostatic Gibbs energy change of the binding can be expressed as
1 ∆Gel ) -RT ln Kb ) -RT ln ) mRT ln[Na+] [Na+]m (6) For the PA solution containing 5 mM carboxylate groups without further addition of salt, the concentration of sodium ions is also 5 mM. Thus the ∆Gel was computed and possessed a value of -10.76 kJ/mol. The enthalpy for electrostatic binding, ∆Hel, is given by the amplitude of the binding isotherm corrected for the heat effect of dilution, and ∆Sel can also be obtained from the equation
∆S )
∆H - ∆G T
(7)
The thermodynamic parameters at different salt conditions for the electrostatic binding are summarized in Table 1. Addition of salt decreases the values of -∆Gel and ∆Sel, suggesting that (i) binding is unfavorable with increase of salt concentration due to the charge shielding effect and (ii) counterions cannot be fully released because of weaker binding and relatively stronger condensation in a high-salt condition. According to the binding model described above, it can be predicted that 1 M NaCl is the threshold beyond which the value of ∆Gel becomes positive and the binding is fully screened. The electrostatic binding model provides a robust method for characterizing the ITC binding isotherms. It should however be emphasized that the model has its limitations since it was derived from the theory of counterion condensation with assumptions and conditions. First, the linear charge spacing b in eq 4 is treated as a straight line, which is not true for most polymer chains. Second, the electrostatic force is the only binding force, and other effects such as hydration or dehydration, hydrogen bonding, and conformational change of polymer chains are neglected. The second and the third peaks corresponding to the formation of polymer-bound micelles and free micelles, respectively, can be analyzed in terms of the critical concentrations determined from the ITC curves, namely, C′ and Cm. By the application of a semiquantitative approach based on the pseudo-phase separation model, the thermodynamic parameters can be extracted from the cmc.16 The Gibbs energy of micellization, ∆Gmic, derived from the pseudo-phase separation model is expressed as
∆Gmic ) (1 + K)RT ln[cmc]
(8)
where K is the effective micellar charge fraction with a value of 0.77 for DoTab.13,16 The enthalpy of micellization
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Table 2. Thermodynamic Parameters for the Binding and Micellization of DoTab in MA/EA Solution polymer
∆Gel (kJ/mol)
∆Hel (kJ/mol)
∆Sel (J/mol K)
C′ (mM)
∆G′ (kJ/mol)
∆H′ (kJ/mol)
∆S′ (J/mol K)
HASE70-30 HASE40-60
-9.85 -7.21
13.82 14.47
79.43 72.75
3.10 2.18
-25.33 -26.88
8.78 4.01
114.46 103.66
Figure 6. Differential enthalpy curves of titrating 0.1 M DoTab into 0.05 wt % HASE70-30 ([) and HASE40-60 (9) solutions, together with the titration curve of DoTab into un-neutralized HASE70-30 (O) solution.
was directly determined from the amplitude of the peak observed in the ITC curves. It should be emphasized that the enthalpy obtained from ITC measurement is an apparent value, which includes other contributions such as disintegration and dilution of surfactant micelles, but they are small compared to the enthalpy of micellization. Hence, the ∆Happ is not the standard value and is suitable only for semiquantitative evaluations. When the values of both ∆H and ∆G have been determined, the entropy can be calculated using eq 7. In this study, ∆G′, ∆H′, and ∆S′ are designated as the free energy, enthalpy, and entropy for the micellization of polymer-bound surfactant. The values of these thermodynamic parameters are summarized in Table 1. It is shown clearly that the formation of polymer-bound micelles is also an endothermic process driven by entropy gain. The positive entropy is attributed to the expelled water molecules from disrupted solvent cages due to micellization. The addition of 0.1 M NaCl shifts C′ from 3.11 to 4.28 mM and reduces the values of -∆G′ and ∆S′. Similar to PA, neutralized MAA/EA copolymer is also a polyelectrolyte with negatively charged sites distributed along the polymer backbone, and hence it may exhibit similar characteristics as compared to the DoTab/PA system. PA is hydrophilic and exists as single polymer chains in aqueous solution, whereas MAA/EA copolymer contains hydrophobic domains of EA associated clusters containing several polymer chains in aqueous solution.22,27 Such differences in polymer structure and conformation may considerably alter the binding behaviors and the structure of the polymer/surfactant complex. The differential enthalpy curves versus the DoTab concentration from the gradual injections of 0.1 M DoTab solution into aqueous solutions containing 0.05 wt % HASE70-30 and HASE40-60 at 298 K are plotted in Figure 6, together with the titration curve of DoTab into un-neutralized HASE70-30 (pH ∼ 4) solution. The enthalpy curves resemble that obtained from the titration (26) Lindman, B.; Thalberg, K. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadamananabham, K. P., Eds; CRC Press: Boca Raton, FL, 1993; p 203. (27) Wang, C.; Tam, K. C.; Jenkins, R. D.; Bassett, D. R. Phys. Chem. Chem. Phys. 2000, 2, 1967.
Figure 7. Differential enthalpy curves of titrating 0.1 M DoTab (2), TTab ([), and CTab (9) into 0.05 wt % HASE70-30 in 0.1 M NaCl solution.
of DoTab into PA solution as shown in Figure 2. The polymer-induced micellization occurs at 3.10 and 2.18 mM for HASE70-30 and HASE40-60, respectively. Peak B is believed to characterize the micellization of polymerbound DoTab molecules at the EA domains since they are sufficiently hydrophobic to induce association with DoTab molecules. To further check our hypothesis, we performed titration of HASE polymer with a series of cationic surfactants consisting of different alkyl chains. The differential enthalpy curves for the titration of 0.1 M DoTab (Ncarbon ) 12), TTab (Ncarbon ) 14), and CTab (Ncarbon ) 16) solutions into 0.05 wt % HASE70-30 polymer in 0.1 M NaCl solution are shown in Figure 7. C1 and the position of the peak marked “A” are not influenced by the hydrophobicity of the surfactant, which furthermore confirmed that the endothermic peak A is purely attributed to the electrostatic interactions between the polymer and surfactant. The enthalpy (amplitude of the peak) varies depending on the alkyl chain length, which may be attributed to the different energies required to remove the surfactant molecules from the liquid/air interface to the charged sites on the polymer chains. On the other hand, C′ denoted by the onset of peak B decreases from ∼7.36 to 4.04 mM when the carbon number of the hydrophobic tail increases from 12 to 16, indicating that higher hydrophobicity of surfactant favors the hydrophobic interaction between DoTab micelles and EA segments of polymer chains. The decreasing trend of C′ with increasing hydrophobicity of the surfactant confirms that the second peak is due to the micellization of polymer-bound surfactant. The enthalpy profile of DoTab/un-neutralized HASE7030 does not reveal any pronounced heat, which confirms that the primary binding force is Coulombic attraction, and the polymer/surfactant complexation is the result of polymer-induced micellization of the electrostatically bound surfactant molecules. HASE polymer is a weak polyacid, and only small amounts of MAA groups dissociate spontaneously at low pH. Under this circumstance, the majority of MAA groups are not ionized and there are no charged sites for the cationic surfactant to bind. The DoTab/un-neutralized HASE system is actually very similar to the cationic surfactant/neutral polymer system, which does not produce a considerable heat signal in the
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ITC measurement.18 The binding isotherms plotted in Figure 6 are characterized thermodynamically by applying the electrostatic binding model and pseudo-phase separation model described previously, and the values of the thermodynamic parameters are summarized in Table 2. The stoichiometric coefficient m in eq 6 is calculated to be 0.75 and 0.55 for HASE70-30 and HASE40-60, respectively, where the linear charge spacings for HASE70-30 and HASE40-60 are assumed to be 1.43 and 2.50 times that of PA. The concentration of sodium ions in the polymer solutions was calculated to be approximately 5 mM based on the amount of NaOH needed to achieve full ionization. As suggested by the values listed in Table 2, the electrostatic binding mechanism in HASE polymer solution resembles that of PA solution, which is an endothermic process (enthalpically opposed) driven by the regain of translational entropy from the released counterions. It is observed that the electrostatic binding over a longer range of surfactant concentration due to higher MA content (higher charge density) delays the formation of polymerbound micelles. The DoTab concentration corresponding to the micellization is 3.10 and 2.18 mM where the stoichiometric parameter [DoTab]/[∼COO-] is 0.88 and 1.03 for HASE70-30 and HASE40-60, respectively, suggesting that the micellization occurs when the charge sites on the polymer chains are fully (or nearly fully) neutralized by negatively charged surfactant. Conclusion Two peaks can be detected in the enthalpy curves obtained from the ITC measurements in the DoTab/PA system. The first peak characterizes the electrostatic binding of cationic surfactant headgroups to the anionic sites on the polymer chains; the second peak corresponds to the micellization of polymer-bound surfactant molecules
Wang and Tam
when the surfactant concentration reaches a critical value, namely, C′. Thermodynamic parameters were extracted from the ITC curves by applying Manning’s theory of counterion condensation and the pseudo-phase separation model. The thermodynamic parameters suggest that both the electrostatic binding and micellization are enthalpy opposed and driven by entropy. The positive entropy for the electrostatic binding is attributed to the recovery of translational entropy of released counterions by the bound surfactant, whereas the entropy gain for micellization is attributed to the disruption of water structure. The study on the salt effect reveals that the addition of salt shields the electrostatic attraction between the oppositely charged polymer and surfactant, making it unfavorable for the polymer-induced micellization of the surfactant to occur. The interactions between MAA/EA copolymers (HASE polymer) and DoTab were also examined using ITC. The features of the enthalpy curves and the thermodynamic characteristics resemble those observed in the DoTab/PA system. This suggests that the DoTab/HASE system also undergoes a two-stage interaction where the surfactant binds to the polyelectrolyte due to electrostatic attraction; thereafter the micellization of polymer-bound surfactant molecules occurs at the EA domains when the carboxylate groups are fully saturated by the surfactant. Extensive studies on the effect of salt and polymer concentration on the binding and micellization behaviors and the microstructure of the DoTab/HASE complex are currently in progress. Acknowledgment. We wish to thank Dr. Richard Jenkins and Mr. C. B. Tan of Dow Chemicals for providing the HASE samples. We are also grateful for the financial support provided by SMA. LA025573Z
