On the meaning of parameters of the two state model in the case of photochemical reactions under restricted geometry conditions Eva Bernal, Francisco Sánchez, María Marchena ⇑ Departamento de Química Física, Facultad de Química, Universidad de Sevilla, C/ Profesor García González S/N, 41012 Sevilla, Spain article info Article history: Received 18 November 2010 In final form 2 February 2011 Available online 21 February 2011 abstract The classical Pseudophase Model (a two state model) describes well the reactivity in the presence of receptors. This model assumes that the exchange between free and bound reactants is at equilibrium in spite of the reaction, a condition that usually cannot be maintained if the reactants are excited. How- ever, the equation of the Pseudophase Model holds, at least formally, in this case. The formalism devel- oped to clarify this question indicates that the parameters acquire a somewhat different meaning in the case of photochemical reactions. The experiments carried out in the presence of DNA and b-cyclodextrin support the formalism developed. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction When a molecule or ion, R (the ligand), binds to a receptor, M, there is a decrease in the number of degrees of freedom in the system. This situation is normally described by indicating that the ligand is under restricted geometry conditions (r.g.c.). The ef- fects of r.g.c. on chemical and physical properties of ligands have been one of the most frequently studied topics in the field of solu- tion physical chemistry in the last half century. This interest arises from the involvement these effects have in several fields related to experimental, theoretical and applied research. Thus, the fields of catalysis [1], the development of systems for drug delivery [2], molecular machines [3], molecular electronic devices [4], gene delivery [5], etc. are within the scope of the effects of r.g.c. We are currently interested in the study of the effects of r.g.c. on the reactivity of ligands. In this field, generally speaking, the changes in reactivity caused by r.g.c. have been explained by taking as a basis the Pseudophase Model of Menger and Portnoy [6] and related models [7]. A formulation based on the Brönsted equation has also been developed [8], as well as some extensions of the ori- ginal formulation [9]. These formulations, except the one based on the Brönsted equation, are two state models; that is, models which consider that the reactant, R, in the presence of the receptor, M, is present in two states, free and bound: R f þ M ¡ K R b ð1Þ These states are considered to be at equilibrium and it is as- sumed that this equilibrium still holds if R takes part in a reaction. In other words: the reaction does not perturb the equilibrium in Eq. (1). This, of course, implies that the rate of the reaction in which R participates is slow in relation to the forward and reverse pro- cesses in Eq. (1). As matter of fact, the equation resulting from the Pseudophase Model (see Eq. (3)) describes well the data in cases of rapid photochemical reactions, when the equilibrium con- dition does not hold [10–13]. This introduces the following ques- tion: What is the meaning of parameters obtained by fitting the experimental data to the equation of the Pseudophase Model, in the case of photochemical reactions? In a previous Letter [14] we considered, from a theoretical point of view, a model that can explain the above mentioned facts and gives the meaning of the parameters. Now, we have performed experiments in order to check this model. These experiments corre- spond to the study of the quenching of the excited state of 1-pyrene- carboxaldehyde in the presence of DNA and b-cyclodextrin (b-CD), two receptors of different characteristics. As will be seen later, our model, in spite of its simplicity, describes fairly well the experimen- tal results. 2. Experimental 2.1. Materials Pyren-1-carboxyaldehyde (PyCHO), tert-butanol (t-BuOH) and quinine sulphate (QUI) meeting USP testing specifications, were from Sigma–Aldrich. Ethanol (EtOH), KI and NaCl were from Merck and H 2 SO 4 (95% w/w) was from Prolabo. b-CD is a commercial product from Fluka. CT-DNA was purchased from Pharmacia. An agarose gel electrophoresis test using ethidium bromide indicated that the average number of base pairs per DNA molecule is above 10,000 bp. Polynucleotide concentrations were determined spec- trophotometrically from the molar absorptivity (6600 M 1 cm 1 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.02.010 ⇑ Corresponding author. Fax: +34 95 455 71 74. E-mail address: marijose@us.es (M. Marchena). Chemical Physics Letters 504 (2011) 165–169 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett