Spherical Tensor Characterization of Multi-Spin-Order Quasi-invariants in Liquid Crystals: an Analytical-Experimental Study

BONIN C. J., GONZÁLEZ C. E., SEGNORILELE H. H.Y ZAMAR R. C.

Alta Gracia, Cordoba

Congreso; Magnetic Resonance in a Cordubensis Perspective VI: New Developments in NMR; 2011

Facultad de Matematica, Astronomia y Fisica

Proton spins of liquid crystal (LC) molecules are small clusters of strongly interacting spins (dipole-dipole), magnetically isolated in the average from spins at other molecules, while mechanically coupled with an orientationally ordered molecular environment. Previous work1 showed that quasi-equilibrium states (quasi-invariants (QI)) associated with constants of motion of the residual dipolar Hamiltonian Hd, can be prepared in LC through the Jeener-Broekaert (JB) experiment2. An efficient application of the QI in many fields, from the basic physics of open quantum systems and quantum information processing, to the study of cooperative molecular dynamics, demands a complete analytical description of the constants of motion. We report the first complete characterization of a multi-spin-order QI in spherical tensor operator, in a 4-spin-1/2 model, as a first approach for a typical LC (e.g. PAAd6). Describing the spin dynamics over a large time scale generally requires a number of constants of motion compatible with the cluster symmetry, however, we show that for short preparation times t1 in the JB sequence, the experiment can be described with a similar strategy of truncation of Hd as in hydrated salts3. That is, that the initial Zeeman order can alternately be transferred to only two QI, called strong (HS, dipolar) and weak (HW, multi-spin-order). We found the following analytical expansion of HW in spherical tensor operators TLM 5 (numbers in parenthesis indicate the spins) . Consistently with multiple-quantum-coherence encoding experiments in orthogonal basis4, our expresion for HW has only zero coherence order in the z-basis and even coherences in the x-basis. Fig.1 shows the close agreement between the experimental and calculated dipolar signals on PAAd6 with HW expressed as above. In Fig. 1(right) we plot the time at which the maximum of the dipolar signals occurs, vs. t1. Notice that the linear behavior for t1>0.3ms cannot be explained by assuming only two QI, which points out that the description of the long time dynamics in PAAd6 demands considering additional QI´s, of more complex tensor structure.