Translational diffusion in a smectic-A phase by electron spin resonance imaging: The free-volume model

Abstract

The method of dynamic imaging of diffusion (DID)‐ESR (electron spin resonance) has been utilized to study the anisotropy of translational diffusion of spin probes in the smectic A phase of a eutectic liquid crystal, S2. In particular, the nearly spherical perdeuterated‐TEMPONE (PDT) and the rigid and elongated cholestane spin label (CSL) molecules were studied. Whereas D_⊥ (the coefficient of diffusion perpendicular to the nematic director) showed simple Arrhenius dependence for both probes, diffusion parallel to the director displayed two different temperature regimes with a changeover of D_∥ at t*≊26–27 °C. The regime above (below) t* is characterized by weak (strong) translational ordering. For CSL the ratio D_⊥/D_∥t* which indicates nematiclike behavior, but below t* the behavior is more smecticlike, i.e., D_⊥/D_∥≳1; for PDT D_⊥/D_∥≳1 over the whole temperature range. A free volume model is developed to interpret the activation energies associated with D_⊥ and D_∥ (i.e., E_⊥ and E_∥) in terms of the orientational and translational order parameters for the smectic phase and those for the spin probes. Also included are the variation of the compressibility across the smectic layer and the length of the probe relative to that of the thickness of the smectic layer. The fact that above t* E_∥/E_⊥ is unity for CSL but a little greater that unity for PDT is interpreted as due to the weaker coupling of the larger CSL molecule to the weak translational ordering and compressibility variation. Below t*, E_∥/E_⊥ becomes 1.52 and 1.80 for CSL and PDT, respectively, which may be interpreted in terms of enhancement of these smectic features. The free volume model may be used to analyze E_∥ and E_⊥ for self‐diffusion and for a wide range of spin probes, including such very small probes like methane, as a function of the key parameters.