Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels N.Le´on 1 , J.-P. Korb 2, ∗ , I. Bonalde 1 and P. Levitz 2 1 Centro de F´ ısica, Instituto Venezolano de Investigaciones Cient´ ıficas, Apartado 21874, Caracas 1020-A, Venezuela. 2 Laboratoire de Physique de la Mati` ere Condens´ ee, UMR 7643 du CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France (Dated: March 17, 2004) We show how the low frequency dependence of the proton spin-lattice relaxation time T1(ν ) of 8CB liquid crystals confined in high density silica gels evidences a long range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(ν ) ∝ ν 2/3 , is interpreted within a relaxation model due to director fluctuations in nematic LCs confined to mass fractal porous media. The model provides a relation T1(ν ) ∝ ν 2−d/2 , giving a reliable value of the structural fractal dimension d f =2.67 for all the host silica gels. PACS numbers: 61.43.Hv, 61.30.Pq, 76.60.Es In recent years confined liquid crystals (LCs) have re- ceived considerable attention due to the apparent disap- pearance of the nematic phase when they are strongly confined [1–6]. A number of theoretical works have con- cluded that the inherent disorder of host porous media makes the long-range orientational order (LRO) charac- teristic of the nematic phase to be replaced by a ”glassy” state [7–9]. But this seems to happen only under cer- tain conditions [9–11]. To get a direct evidence for the existence or not of the LRO nematic phase under strong confinement in disordered porous media, we probed a dy- namic process which at large length scales is unique to the ordered phases of LCs: the orientational order direc- tor fluctuations (ODF). Director fluctuations involve collective motions of a macroscopic number of molecules, and such motions have a relatively long correlation times. The ODF are known to be the main cause of NMR relaxation at quite low frequencies, and the frequency dependence of the spin- lattice relaxation T 1 (ν ) in the range below about 1 MHz is used normally to get information on bulk ordered phases [12]. Pincus [13, 14] proposed that in bulk LCs, T 1 (ν ) ∝ ν 1/2 , law that is supported by a large number of experimental results [12].There is no indication of how Pincus law would be modified in an aerogel-LC system. Silica gel is of interest in the study of confined LC, due to its quenched disorder and mass fractal structure. We report here on measurements of the proton-NMR spin-lattice relaxation frequency profiles between 0.01 to 10 MHz of the thermotropic 4-octyl-4’-cyanobiphenyl (8CB) liquid crystal both bulk and strongly confined in a series of silica gels of different densities. These mea- surements were performed over the temperature range of 25 to 50 ◦ C, which spans the liquid crystalline and ∗ Corresponding author. Tel.:+33 1 69 33 47 39;fax:+33 1 69 33 30 04. e-mail address:jean-pierre.korb@polytechnique.fr isotropic phases. We develop also a model for the NMR relaxation originated by the ODF in a nematic LC con- fined to a structurally fractal porous matrix. All silica gel samples were prepared by hydrolysis and polycon- densation of TEOS (tetraethoxysilane) in ethanol under slightly acidic conditions of pH. Three kinds of gels were synthesized: a xerogel (X), a xeroaerogel (XA), and two xerogel composites (XC) [15]. The parameters charac- terizing each gel are given in Table I. In the case of xerogel composites some silica fumed particles (aerosil) were added during the hydrolysis step, namely 5% and 45% in wt% for the 10 and 16 nm pore size samples, re- spectively. These composite samples have larger density and are more homogeneous. The silica surfaces have - OH and -OR groups in the xerogel and xeroaerogel and only -OH groups in the composites, due to a special ther- mal treatment. Dried gel samples were vacuum baked at 120 ◦ C for more than 12 hours. The filling process of 8CB was then performed by capillary action for more than 24 hours at 60 ◦ C, to ensure that 8CB was in the isotropic phase. Finally, the embedded gel samples were dried to eliminate any residual LC in the surface. Measurements of the T 1 frequency profiles were made using a fast-field- cycling NMR spectrometer from Stelar Company. The profiles were obtained from monoexponential time de- cays of longitudinal magnetizations, verifying that there were no fast components coming from cross-relaxation with protons at the surface of the pores. The experimen- tal error of the T 1 measurements was less than 5 %, but increased slightly for short relaxation times of the order of the field switching time (1 ms). Figure 1 shows T 1 as a function of the Larmor frequency in the liquid crystalline and isotropic phases of bulk 8CB. All the expected behav- iors are seen from this figure [12]. There is a crossover at ν c = 1 MHz from fast individual to slow collective molec- ular motions. In the high-temperature isotropic phase at 43 ◦ C a leveling off of the T 1 dispersion curve is observed below ν c , caused by the averaging of the fast isotropic