Confined Polymer Chains in a Θ Solvent: A Model with Polymer-Solvent Interactions Peter Cifra* ,† and Iwao Teraoka* ,‡ Polymer Institute, Slovak Academy of Sciences, Du ´ bravska ´ cesta 9, 842 36 Bratislava, Slovak Republic, and Herman F. Mark Polymer Research Institute, Polytechnic University, 333 Jay Street, Brooklyn, New York 11201 Received May 19, 2003; Revised Manuscript Received October 13, 2003 ABSTRACT: Thermodynamics of polymer chains in the Θ condition confined to a space between two parallel walls was studied by using lattice Monte Carlo simulations. The Θ state was realized by allocating positive interaction to nearest-neighbor pairs of a polymer segment and a solvent molecule that is now explicitly included, rather than giving attractive interaction between polymer segments with no explicit solvent molecules present. The two models can be equivalent when used to specify the Θ state in unconfined solutions, but missing segment-solvent contacts at the wall make the two models different for confined solutions. The effectively attractive wall facilitates entry of polymer chains into narrow slits in the corrected model and lifts the segment density at sites adjacent to the walls. The dependence of the segment density near the wall on the distance from the wall follows a power law different from the one that holds for the conventional model of the Θ state. In particular, when the wall has explicit interaction with the polymer segments, our model makes the profile highly sensitive to the solvent quality. The corrected model explains enhanced adsorption in a poorer solvent reported in experiments. 1. Introduction Computer simulations, both lattice and off-lattice systems, are widely being used to examine thermody- namic and other statistical properties of polymer in solution. 1 In most simulation systems, solvent molecules are not explicitly included. Each system has only one interaction parameter ǫ pp that accounts for the interac- tion between nonbonded segment pairs in the polymer chains suspended in a vacuum. In athermal solutions, ǫ pp ) 0. To represent a solution with a solvent worse to the polymer, ǫ pp is turned negative. This practice has been employed broadly in the past to study the Θ state in lattice simulations 2-5 and in off-lattice simulations. 6,7 Theories for solutions in the Θ state have been using the same practice. 8-11 Computer simulations and theoretical methods have been the primary tools to study the effect of geometrical confinement such as the one given by a slit and a channelonpolymersolutionsinvarioussolventconditions. 12-16 They include a Θ solvent and solvents that have a quality between athermal and Θ. As in unconfined solutions, the solution system in the confining geom- etries consists only of polymer chains. The solvent quality is adjusted by changing ǫ pp . The pore wall remains repulsive to the polymer throughout the change, thus precluding adsorption onto the walls of the confin- ing geometries even in the Θ condition. In real polymer solution systems, however, the change in the solvent quality is accomplished by adjusting the polymer-solvent interaction, not ǫ pp . The change is made possible through a change in the temperature or the mixing ratio of a good solvent and a poor solvent or a nonsolvent. When the polymer solution is in contact with a porous medium, poorer solvents promote adsorp- tion of the polymer onto the pore walls. It is well-known in size exclusion chromatography that the mobile phase needs to be sufficiently good to the analyte polymer. Otherwise, the injected polymer may be retained by the stationary phase, indicating adsorption of polymer onto the pore wall. 17 Obviously, the shortcoming of the existing theories and simulation methods arises from transplanting the convention employed in the bulk systems into the confined systems. In the present report, we explicitly include solvent molecules by regarding the unoccupied sites as being occupied by solvent molecules in lattice Monte Carlo simulations for confined polymer solutions. We change the solvent-polymer interaction, not the polymer-polymer interaction, to bring the solution to the Θ condition. Incidentally, the wall becomes attrac- tive to the polymer since the segments prefer the walls to the solvent. We demonstrate that the partitioning and other statistical properties of the confined polymer chains are greatly different in this modified Θ condition from those in the conventional Θ condition. The same precaution will be needed whenever simulations and theories deal with polymer solutions that are in contact with any third components. 2. Lattice Model for Confined Chains in a Θ Solvent In many models for polymer solutions in discrete and continuous spaces, polymer chains are suspended in a vacuum; solvent molecules are not explicitly included in the system. 2-15 As a result, interactions other than chain connectivity are present only between a non- bonded pair of polymer segments (P-P contact). In lattice chain models, for instance, there is a well-defined interaction ǫ pp between nearest-neighbor nonbonded pair of segments, as indicated by dashed lines in part a of Figure 1, where the solid line represents the chain. We call this model a PP model. To realize the Θ condition in the PP model, net repulsion between polymer segments due to the ex- cluded volume is compensated by attractive interaction. † Slovak Academy of Sciences. ‡ Polytechnic University. * Corresponding author. 9638 Macromolecules 2003, 36, 9638-9646 10.1021/ma034656z CCC: $25.00 © 2003 American Chemical Society Published on Web 11/20/2003