DOI 10.1140/epje/i2005-10036-4 Eur. Phys. J. E 18, 149–158 (2005) THE EUROPEAN PHYSICAL JOURNAL E NMR relaxation study of molecular dynamics in columnar and smectic phases of a PAMAM liquid-crystalline co-dendrimer A. Van-Quynh 1, a , D. Filip 1,4 , C. Cruz 1,2 , P.J. Sebasti˜ ao 1,2 , A.C. Ribeiro 1,2 , J.-M. Rueff 3 , M. Marcos 3 , and J.L. Serrano 3 1 Centro de F´ısica da Mat´eria Condensada, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal 2 IST-UL, Av. Rovisco Pais, 1049-001, Lisboa, Portugal 3 Departamento de Quimica Org´ anica, Nuevos Materiales Org´ anicos, Universidad de Zaragoza-CSIC, E-50009 Zaragoza, Spain 4 “Petru Poni” Institute of Macromolecular Chemistry, Aleea Gr. Ghica Voda 41 A, 700487 Iasi, Romania Received 21 June 2005 / Published online: 21 October 2005 – c  EDP Sciences / Societ` a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present the first results obtained by proton ( 1 H) nuclear magnetic relaxation studies of molecular dynamics in a supermolecular liquid-crystal dendrimer exhibiting columnar rectangular and smectic-A phases. The 1 H spin-lattice relaxation time (T1) dispersions are interpreted using two relaxation mechanisms associated with collective motions and local molecular reorientations of the dendritic segments in the low- and high-frequency ranges, respectively. The T1 values show a drop around 2.3 MHz that is attributed to a contribution coming from cross-relaxation between 1 H and nitrogen nuclear spins. In the high-frequency range the motions appear to be of similar nature in both mesophases and are ascribed to reorientations of dendritic segments (belonging to the core and/or to the mesogenic units) characterized by two correlation times. Notable differences in the dynamics between the columnar and layered phases are observed in the low-frequency range. Depending on the mesophase they are discussed in terms of elastic deformations of the columns and layer undulations. In this study we find that the dendritic core influences the dynamics of the mesogenic units both for local and collective motions. These results can be understood in terms of spatial constraints imposed by the dendritic architecture and by the supermolecular arrangement in the mesophases. PACS. 61.30.-v Liquid crystals – 61.18.Fs Magnetic resonance techniques; M¨ ossbauer spectroscopy 1 Introduction Recent advances in chemistry include the design and the control of the synthesis of molecular entities in the nano- to micrometer scale exhibiting self-organization proper- ties [1]. Liquid crystals (LCs) appear to be ideal sys- tems for nanoscale modelling materials due to their self- organizing properties and in the last decades research in liquids has expanded towards complex LCs [2], molecular superstructures of dendritic molecules [3], and biomem- branes [4]. Dendrimers are a class of molecules with a highly branched structure that emanates from a central (focal) point. The branches of the molecules are formed by branch cells and organize in a series of concentric lay- ers around the focal point. The number of layers determine the dendrimer generation and for a dendrimer of a given generation G the grafting at the extremity of each branch of one branch cell leads to a dendrimer of generation G + 1 [3, 5]. Dendrimers are remarkable with respect to a e-mail: aquynh@cii.fc.ul.pt other high molecular weight (M w ) molecules in that they can be synthesized with an index of polydispersity lower than 1.05. Their molecular dimensions are at the nanome- ter scale and exhibit a three-dimensional fractal structure at the terminal part of which functional groups can be at- tached, leading thus to highly functional compounds with potential medical an pharmaceutical applications [6–8]. Pure dendritic molecules (i.e. without functional groups attached at the periphery of the molecule) tend to adopt a very regular structure, the so-called starbust shape [9, 10] in which the branches of the supermolecule radiate isotropically from the focal point. As mesogenic or promesogenic units are attached at the extremities of the arms, two opposite tendencies compete within the same molecule: the dendritic architecture tends to adopt a pseudospherical morphology, while the terminal aniso- metric units tend to arrange anisotropically by interacting with each other to form parallel aggregation. The type of mesophases observed in this kind of compounds will de- pend on the balance between entropy and enthalpy that will lead to micro-segregation where the dendritic core and