Universal Behavior of Linear Alkanes in a Confined Medium: Toward a Calibrationless Use of Thermoporometry
Résumé
A general law has been derived for predicting the transition temperature of linear alkanes confined in nanoporous materials from the simple knowledge of the free solvent transition temperature. This law is in very good agreement with the one previously determined for substituted benzenes, attesting a possible universal behavior of confined solvents. The lowering of the transition temperature of liquids confined in porous materials was first observed a very long time ago. By the end of the 19th century, the theoretical thermodynamical description of this phenomenon was given. 1 In particular, the transition temperature shift, ∆T, is related to the size of the pore in which the solvent is confined. In the late 1970s, it was proposed to use this observation as a tool to study the texture of divided materials. 2 In principle, the recording of the differential scanning calorimetry (DSC) curve of a given solvent confined in a porous material would allow one to determine its pore size distribution. The main limitation in applying this technique known as thermoporometry is the lack of knowledge of the R p (1/∆T) law for a given solvent. Another required law is the evolution of the apparent energy of crystallization, W a , as a function of ∆T. Several authors have been using ther-moporometry to study the texture of porous materials of polymers, but in fact, until very recently, the studies were mainly limited to a few solvents including water and benzene. 3-7 Thanks to the use of porous materials of known texture (measured by gas sorption, for instance), calibrations have been proposed for various solvents including cyclohexane, 8 acetoni-trile, 9 carbon tetrachloride, 10 and substituted benzenes. 11 At this step, thermoporometry can be used as a substitution tool for gas sorption measurements 12 as can the related NMR cry-oporometry. 13 We have shown recently 14,15 that thermoporom-etry can also be used very efficiently to characterize soft matter like polymers or gels. In the case of polymers, an analogy is proposed between the meshes constituting the polymer network and the pores of a solid material. When the polymer is swollen in a solvent, the latter experiences a shift of its transition temperature, as observed in porous media. The application of thermoporometry can give access to the size distribution of the meshes and thus a direct image of the reticulation of the network. This is very crucial information in particular if one wants to study the photoaging behavior of the polymer. Of course, in this case, the choice of the solvent is very important, and this motivated our systematic search for calibration procedures. The aim of this paper is to report original results concerning the possibility to extrapolate calibration curves for any solvent belonging to a specific family. Results concerning substituted benzenes have been published recently, 11 and this paper will focus on linear alkanes. We will show that it is possible to derive a general law that relates T p , the crystallization temperature of a given alkane confined in a pore of radius R p , to the normal transition temperature of the solvent, T 0. Nanoporous silica gels A-E were used as standard materials for calibration. They were prepared by controlled hydrolysis/ condensation of tetraethoxysilane (Si(OC 2 H 5) 4) following procedures described elsewhere. 16 The materials used in this study are the same as those reported in previous work. 8,11,14,17 Textural data of the reference samples are displayed in Table 1. Linear alkane C n H 2n+2 (n) 6, 7, 10, 12, and 18) solvents of HPLC grade were used without further purification. The first four solvents were calibrated following the procedure described in ref 11, and the last one (n) 18) was used as a control solvent. As an illustration, thermograms recorded for n-hexane confined in the reference porous silica gels are displayed in Figure 1a. The endothermic peak corresponds to the melting of the free solvent and has been used for the determination of T 0. Calibration curves are displayed in parts b and c of Figure 1 for the R p (1/∆T) and W a (∆T) curves, respectively. As already performed in our previous work, fitting equations of the following form were considered: where R p is the pore radius, ∆T) T p-T 0 is the freezing point depression, with T 0 corresponding to the onset of the endotherm of the melting of the pure solvent (see Figure 1), T p is the