Modeling of Stimulated Hydrogel Volume Changes in Photonic Crystal Pb 2+ Sensing Materials Alexander V. Goponenko and Sanford A. Asher* Contribution from the Department of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260 Received March 7, 2005; E-mail: asher@pitt.edu Abstract: We modeled the stimulated hydrogel volume transitions of a material which binds Pb 2+ and is used as a photonic crystal chemical sensing material. This material consists of a polymerized crystalline colloidal array (PCCA) hydrogel which contains a crown ether molecular recognition group. The PCCA is a polyacrylamide hydrogel which embeds a crystalline colloidal array (CCA) of monodisperse polystyrene spheres of ∼100 nm. The array spacing is set to diffract light in the visible spectral region. Changes in the hydrogel volume induced by Pb 2+ binding alter the array spacing and shift the diffracted wavelength. This system allows us to sensitively follow the hydrogel swelling behavior which results from the immobilization of the Pb 2+ by the crown ether chelating groups. Binding of the Pb 2+ immobilizes its counterions. This results in a Donnan potential, which results in an osmotic pressure which swells the hydrogel. We continue here our development of a predictive model for hydrogel swelling based on Flory’s theory of gel swelling. We are qualitatively able to model the PCCA swelling but cannot correctly model the large responsivity observed at the lowest Pb 2+ concentrations which give rise to the experimentally observed low detection limits for Pb 2+ . These PCCA materials enable stimulated hydrogel volume transitions to be studied. Introduction Our laboratory has been developing a series of photonic crystal chemical sensing materials which can be used to optically determine analytes. 1-5 The photonic crystal material is called a polymerized crystalline colloidal array (PCCA) and consists of a hydrogel which embeds a crystalline colloidal array (CCA) of particles that diffract light in the visible spectral region. 6,7 The array of particles self-assemble into an fcc lattice. Diffrac- tion from the 111 plane of the CCA lattice is designed to report on the volume of the hydrogel. 8 A molecular recognition agent is attached to the hydrogel or to the particles. The molecular recognition agent actuates a hydrogel volume change in response to analyte interactions. This changes the lattice spacing, which shifts the diffracted wavelength. We demonstrated a number of different motifs for sensing analytes. For example, we demonstrated a motif that changes the free energy of mixing of the hydrogel, 9 motifs that change the hydrogel cross-link density, 4,10 and motifs that change the number of bound ions. 1-3,11,12 In addition, for each motif we attempted to model the response in the context of the theory of hydrogel swelling. The earlier stage of this modeling examined the hydrogel volume changes which occur for PCCA with attached carboxyl groups in response to pH changes. 11 This work was followed by the development of glucose sensors which responded to changing the covalently attached charge on the hydrogel. 12 We considered in detail all three components of the model: the free energy of mixing, the free energy of the elastic network, and the free energy of Donnan-type equilibrium. We experi- mentally determined the hydrogel cross-link density, the hy- drogel Flory-Huggins interaction parameter, and the affinity constant and concentration of the molecular recognition groups. These PCCA chemical sensors enable a more careful exami- nation of hydrogel volume changes since they directly and accurately report the volume as the chemical environment is altered. We can then model these volume changes in the context (1) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829-832. (2) Holtz, J. H.; Holtz, J. S. W.; Munro, C. H.; Asher, S. A. Anal. Chem. 1998, 70, 780-791. (3) Reese, C. E.; Baltusavich, M. E.; Keim, J. P.; Asher, S. A. Anal. Chem. 2001, 73, 5038-5042. Reese, C. E.; Asher, S. A. Anal. Chem. 2003, 75, 3915-3918. (4) Asher, S. A.; Sharma, A. C.; Goponenko, A. V.; Ward, M. M. Anal. Chem. 2003, 75, 1676-1683. (5) Asher, S. A.; Holtz, J. H. U.S. Patent 5,854,078, 1998. Asher, S. A.; Holtz, J. H. U.S. Patent 5,898,004, 1999. (6) Asher, S. A.; Jagannathan, S. U.S. Patent 5,281,370, 1994. Rundquist, P. A.; Photinos, P.; Jagannathan, S.; Asher, S. A. J. Chem. Phys. 1989, 91, 4932 4941. Asher, S. A.; Weissman, J. M.; Tikhonov, A.; Coalson, R. D.; Kesavamoorthy, R. 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K.; Wilcox, C. S.; Finegold, D. N. J. Am. Chem. Soc. 2003, 125, 3322- 3329. Published on Web 07/12/2005 10.1021/ja051456p CCC: $30.25 © 2005 American Chemical Society J. AM. CHEM. SOC. 2005, 127, 10753-10759 9 10753