Polyelectrolytic Amphiphilic Model Networks in Water: A Molecular Thermodynamic Theory for Their Microphase Separation † Maria Vamvakaki and Costas S. Patrickios* Department of Chemistry, UniVersity of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus ReceiVed: September 16, 2000; In Final Form: January 12, 2001 The aqueous aggregation behavior of networks comprising hydrophilic ionic blocks and hydrophobic nonionic blocks was studied by formulating a molecular thermodynamic theory, which considers the Gibbs free energies of the two possible states of the networks: the micelle-like state and the unimer-like state. The appropriate expressions for the elastic, mixing, and electrostatic components of the Gibbs free energy were developed for each of the two cases. For the micelle-like state, the interfacial free energy for the contact of the micellar core with the aqueous solvent was also included. For each of the two states, the total Gibbs free energy was minimized with respect to the polymer volume fraction. The lower from the two minimum Gibbs free energies corresponds to that of the more stable state. The effects of the length and degree of ionization of the hydrophilic block, the effect of the length of the hydrophobic block, the effect of the value of the Flory-Huggins interaction parameter between the hydrophobic block and water, the effect of the initial polymer volume fraction, and the effect of the number of arms per cross link were investigated. Under certain conditions, a unimer-to- micelle transition was observed, accompanied by a discontinuous change in the degree of swelling of the networks. Introduction Ionic hydrogels are cross-linked polyelectrolytes possessing some unique properties, 1,2 which make them promising materials for various practical applications. 3 One relatively new type of ionic hydrogels is that of ionic amphiphilic hydrogels, also containing hydrophobic units in addition to the hydrophilic ionic ones. 4-9 The presence of hydrophobic units can lead to microphase separation, which induces order formation and can impart new properties to the networks, ultimately resulting in new applications. The way the hydrophobic units are introduced in the network, belonging either to the side chains 4-6 or to the main chain, 7-9 may further affect the hydrogel structure and properties. Despite the extensive experimental work on ionic amphiphilic hydrogels, there have been no efforts to model their behavior. However, there is modeling work on a relevant system, that of noncovalent, physically associating polymer networks. 10,11 Most of the modeling work has focused on nonionic associating polymer networks 12-14 rather than on ionic associating net- works. 15,16 The aim of this study is to extend theories on the behavior of simple ionic networks 17-19 to cover ionic am- phiphilic networks. Our approach is also relevant to existing theories on the micellization of linear (not cross-linked) ionic amphiphilic block copolymers. 20-22 Our main finding from this work is the observation of a unimer-to-micelle transition for block copolymer-based ionic amphiphilic networks under certain conditions. Moreover, we reproduce the volume phase transition already known (both experimentally and theoretically 17-19 ) for statistical copolymer-based ionic amphiphilic networks. Geometry and Forces We consider an amphiphilic model (precise chain lengths between cross-links and constant functionality of the cross- link 23 ) network, based on ABA triblock copolymers 24,25 com- prising nonionic hydrophobic end-blocks and an ionic hydro- philic mid-block. The system can exist in one of two possible states. First, a unimer-like state in which no microphase separation takes place. And, second, a micelle-like state in which the hydrophobic blocks aggregate to form spherical hydrophobic microdomains. Figure 1 illustrates these two states, with the hydrophobic blocks drawn in black and the hydrophilic blocks shown in white. The main aim of this work was to determine, under a variety of conditions and network composition, the state, micelle-like or unimer-like, in which the amphiphilic networks exist. Aggregation into the micelle-like state would be driven by the reduction of the hydrophobic area, which would lead to the decrease of the unfavorable water-hydrophobe contact. At the same time, this aggregation would influence the values of the other energy components in the system. The preferred structure of the network will be determined by the relative magnitude of all participating forces. It must be recognized that it is also possible that a higher order of aggregation takes place in which two or more hydrophobic cores are combined, resulting in structures such as cylinders and lamellae. 26 Such an assembly would be favored by the hydrophobic force because it would further reduce the interfacial area per chain (depending on composition), but it would be opposed by the elastic force because it would create local stretching and compression of the network. The exact balance of the various forces would again dictate whether this intercore assembly would take place or not. This issue will be addressed in the future. However, we feel that, for our own experimental system, 9 containing many (typically 20) hydro- † This work is dedicated to the memory of Professor Toyoichi Tanaka, formerly of the Physics Department of the Massachusetts Institute of Technology (MIT), who introduced one of the authors (C.S.P.) to the science of hydrogels. * To whom correspondence should be addressed. 4979 J. Phys. Chem. B 2001, 105, 4979-4986 10.1021/jp003307t CCC: $20.00 © 2001 American Chemical Society Published on Web 05/03/2001