Free volume in the smectic-$E$ phase of 4-hexyl-4′ isothiocyanatobiphenyl studied by positron annihilation spectroscopy

Positron annihilation lifetime spectroscopy has been used to study 4-hexyl-4′-isothiocyanatobiphenyl. Changes of the orthopositronium lifetime parameters with temperature have been observed for the supercooled smectic-$E$ phase. The measurements confirm that positronium is created and annihilates in a layer of a lower electron density containing alkyl chains of molecules. The two-state bond-lattice model of glass transition explains the thermal activation of the centers where orthopositronium is created and annihilates when the glass of the smectic-$E$ phase softens. However, the subsequent cold crystallization of the softened regions also influences the orthopositronium lifetime and intensity, which complicates the picture seen by positrons. The measurements during isothermal crystallization suggest that it progresses in two stages. The first stage can be described by the Avrami equation with the Avrami exponent close to unity, which indicates low-dimensional crystallization. Similarly to liquid $n$ alkanes, the application of pressure is equivalent to temperature lowering with the similar equivalence relationship between pressure and temperature, which seems to confirm the structure of the smectic-$E$ phase with sublayers containing alkyl chains in a molten state. The dependence of the orthopositronium lifetime on pressure for the smectic-$E$ phase may be described by the bubble model where the positronium bubble is approximated with a finite square potential well with the depth of $U=1.45\mathrm{eV}$.

Figure 1

Positron lifetime spectra for the Sm-$E$ phase of 6TCB at 95 K (red) and 315 K (black). The hatched area shows the time range between 2.2 and 8.2 ns, where the main contribution to the spectrum comes from the o-Ps annihilation.

Figure 2

Temperature dependencies of (a) ${\tau }_3$ and (b) $I_3$ for four different measurement procedures. The right vertical axis shows the values of the free volume radius $R$ calculated from Eq. (1).

Figure 3

Temperature dependencies of (a) ${\tau }_3$ and (b) $I_3$ for the sample after fast cooling from the Sm-$E$ phase. The triplets of points were obtained from the three spectra registered for 1 h each without changing the sample temperature.

Figure 4

Temperature dependencies of $I_3$ for 6TCB and 4TCB. The dependence for 4TCB is taken from Ref. [14]. The solid line was fitted to the experimental points using Eq. (2). The dashed line is obtained by rescaling the solid line for 4TCB by the ratio of the melting temperatures to the Sm-$E$ phase $T_m^{6\mathrm{TCB}}/\phantom{T_m^{6\mathrm{TCB}}{T}_m^{4\mathrm{TCB}}}{T}_m^{4\mathrm{TCB}}$ and the ratio of the o-Ps component intensity $I_3^{6\mathrm{TCB}}/\phantom{I_3^{6\mathrm{TCB}}{I}_3^{4\mathrm{TCB}}}{I}_3^{4\mathrm{TCB}}$ for the Sm-$E$ phase above the melting temperature. The dotted line is a fit of Eq. (2) to the experimental points for 6TCB for temperatures up to 215 K and then above the transition temperature to the Sm-$E$ phase.

Figure 5

The normalized number of counts between 2.2 and 8.2 ns calculated from the spectra registered in 3 min intervals as a function of time for the measurement on heating of the sample after fast cooling with longer annealing stages between 245 and 275 K. The dependencies of ${\tau }_3$ and $I_3$ for this measurement is depicted in Fig. 2 (triangles up). The temperature is shown on the right axis.

Figure 6

The normalized number of counts between 2.2 and 8.2 ns calculated from the spectra registered in 3 min intervals as a function of time for the measurement on cooling of the sample with a more extended annealing stage at 255 K. The dependencies of ${\tau }_3$ and $I_3$ for this measurement are depicted in Fig. 2 (triangles down). The temperature is shown on the right axis.

Figure 7

Temperature dependencies of (a) ${\tau }_3$ and (b) $I_3$ from the spectra registered for 1 h when the sample was kept at 255 K. The normalized number of counts for this measurement is shown in Fig. 6. The inset shows log-log plot obtained from $I_3$ dependence on time and the fitted Avrami equation.

Figure 8

Schematic illustration of (a) the antiparallel pair of 6TCB molecules and molecular arrangement in the Sm-$E$ phase proposed in Ref. [25]: for (b) 6TCB and (c) 4TCB. The core chain layer contains biphenyl moieties, which fully overlap each other in the antiparallel pairs of molecules. Its thickness is equal to the average distance between C1 and C1′ in the adjacent antiparallel molecules. The chain layer contains the ends of the disordered alkyl chains, which conformations change dynamically. The pure chain layer together with two layers containing isothiocyanate groups $\left(-\mathrm{N}=\mathrm{C}=\mathrm{S}\right)$ and parts of the alkyl chain adjacent to the biphenyl moieties form the chain layer. The estimated thickness of the core and chain layers and the size of the Ps bubble are shown.

Figure 9

The dependencies of (a) ${\tau }_3$ and (b) $I_3$ on pressure plotted against the upper axis and dependencies of (a) ${\tau }_3$ and (b) $I_3$ on the temperature measured on cooling of the sample, taken from Fig. 2. The solid line was obtained by calculating the Ps energy approximating the bubble with a finite square potential well of a spherical geometry with the depth $U=1.46\mathrm{eV}$.