Energy versus Entropy in Cooperative Electrostatic Interactions: Comparative Study of Binding of Sodium Poly(Styrenesulfonate), Dodecylbenzenesulfonate, and Methylbenzenesulfonate to Polycations J. Kr ˇ ı ´z ˇ ,* J. Dybal, and D. Kurkova ´ Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, HeyroVsky Square 2, 162 06 Prague 6, Czech Republic ReceiVed: July 27, 2001; In Final Form: December 2, 2001 Electrostatic coupling of sodium 4-dodecylbenzenesulfonate (DDBS), sodium 4-methylbenzene-sulfonate (MBS), and sodium poly(styrenesulfonate) (PSS) with the homopolymers of N-diallyldimethylammonium chloride (DADMAC) and chloride of 2-N-trimethylammonioethylmethacrylate (TMAEMA) or their copolymers with neutral hydrophilic groups were studied using 1 H and 35 Cl (single- and double-quantum) NMR, relaxations, and pulsed field-gradient (PFG) diffusivity measurements. Both DDBS and PSS were found to react cooperatively with the polycations, in contrast to MBS. However, PSS binds more strongly to the polycations and is thus able to substitute DDBS in its complex with an appropriate polycation. The binding isotherms of DDBS and MBS with DADMAC polymer agree well with the theoretical model suggested by Kuhn, Levin, and Barbosa, providing that the hydrophobic energy parameter  has the value -3.5k B T for DDBS and 0.0 for MBS. Energy stabilization by hydrophobic interactions is thus suggested to be the determining factor in the cooperative binding of DDBS. This conclusion is supported by clusters of bound DDBS with a mean length of about 30 molecules in its complex with DADMAC polymer, which were indirectly found using 35 Cl T 2 3 relaxation. In conclusion, the interaction of DDBS with polycations is suggested to be an example of cooperative electrostatic binding with unfavorable entropy but strong energy stabilization by, e.g., hydrophobic interactions. Entropy change due to liberation of bound counterions into a disordered state, found by us earlier 1-3 to be operative in the couplings of complementary polyions, is thus not the only possible driving force of cooperative electrostatic interactions. Introduction In our systematic study of cooperative electrostatic couplings, 1-3 we explored the interaction of poly(sodium styrenesulfonate) (PSS) and polyphosphates (PP) with homo- or copolymers of chloride of 2-(N-trimethylammonioethylmethacrylate) (TMAE- MA) or N-diallyldimethylammonium chloride (DADMAC), the latter having already been studied by other authors. 4-8 Among factors influencing the effectiveness of binding, the most important appeared 2 to be (i) entropy gain due to liberation of small counterions, (ii) energy stabilization due to long-range Coulomb forces, (iii) lateral correlation of the binding groups, and (iv) hydrophobic interaction. Among them, i depends on the polyelectrolyte effect (nonstatistical distribution of counte- rions in the parent polyions). All three factors i-iii are ascertained by the polymeric (or, to a lower degree, aggregate, e.g., micellar) structure of the reactants. Contrary to i, factor iv is probably anti-entropic and points to energy (or rather enthalpy) stabilization as the driving force of the process. It is quite difficult, both experimentally and theoretically, to establish the quantitative weights of the factors i-iv (or others). Some insight into the matter can be gained by comparing the binding of a polyion with that of analogous low-molecular- weight compounds, which either do or do not possess the ability to gain additional stabilization by hydrophobic interactions in the electrostatic complex. Considering PSS as coupling partner to a polycation, two different low-molecular-weight compounds have a very similar structure in the vicinity of the same sulfonate anionic group: sodium 4-methylbenzenesulfonate (MBS) and sodium 4-dodecylbenzenesulfonate (DDBS). MBS in water solution can be shown to remain in a monomeric form in the concentration range 2-30 mM/L, its hydrophobic interactions thus being too weak to overcome electrostatic repulsions and entropy demands of aggregation. In contrast to it, DDBS was shown 9 to form various aggregates in this concentration range and was found by us to bind effectively to polycations even at very low concentrations below 2.0 mM/L. Interactions of surfactants with polyions were extensively explored. 10-19 The binding of surfactant molecules (SM) to an oppositely charged polyelectrolyte (PE) usually occurs at surfactant concentrations much lower than the critical micellar concentration (CMC) and leads to electrostatic complexes, sometimes thought (but not evidenced) to contain micelle-like domains. Its cooperativity clearly can be viewed from two complementary perspectives: 12 (i) the ionic binding of SM to PE is cooperative, being supported by the hydrophobic interac- tions of SM in the resulting complex; (ii) the hydrophobic self- assembly of SM micelles (unstable but possible below CMC) is cooperative, being facilitated by the neutralization of micellar charges by the bound PE. The first alternative can be further divided into two ways of binding, namely, (ia) gradual binding of individual SM, with a probability low for the first several SM but fast increasing as the collection of neighboring bound SM approximates a stable aggregate and (ib) almost-simulta- neous binding of a micelle (or a smaller SM aggregate), which itself has to be assumed to be formed (and disintegrated again) even below CMC. If all the elementary steps are reversible and * Corresponding author. E-mail: kriz@imc.cas.cz. Fax: 420-2-35357981. 2175 J. Phys. Chem. B 2002, 106, 2175-2185 10.1021/jp012916d CCC: $22.00 © 2002 American Chemical Society Published on Web 02/12/2002