Effect of hockey-stick-shaped molecules on the critical behavior at the nematic to isotropic and smectic-$A$ to nematic phase transitions in octylcyanobiphenyl

In the field of soft matter research, the characteristic behavior of both nematic–isotropic ($N-I$) and smectic-$A\mathrm{nematic}(\mathrm{Sm}\text{−}AN)$ phase transitions has gained considerable attention due to their several attractive features. In this work, a high-resolution measurement of optical birefringence $\left(\Delta n\right)$ has been performed to probe the critical behavior at the $N-I$ and $\mathrm{Sm}\text{−}AN$ phase transitions in a binary system comprising the rodlike octylcyanobiphenyl and a laterally methyl substituted hockey-stick-shaped mesogen, 4-(3-$n$-decyloxy-2-methyl-phenyliminomethyl)phenyl 4-$n$-dodecyloxycinnamate. For the investigated mixtures, the critical exponent $\beta$ related to the limiting behavior of the nematic order parameter close to the $N-I$ phase transition has come out to be in good conformity with the tricritical hypothesis. Moreover, the yielded effective critical exponents (${\alpha }^{\prime }$, ${\beta }^{\prime }$, ${\gamma }^{\prime }$) characterizing the critical fluctuation near the $\mathrm{Sm}\text{−}AN$ phase transition have appeared to be nonuniversal in nature. With increasing hockey-stick-shaped dopant concentration, the $\mathrm{Sm}\text{−}AN$ phase transition demonstrates a strong tendency to be driven towards a first-order nature. Such a behavior has been accounted for by considering a modification of the effective intermolecular interactions and hence the related coupling between the nematic and smectic order parameters, caused by the introduction of the angular mesogenic molecules.

Figure 1

The chemical structure and phase behavior of (a) the hockey-stick-shaped compound (H-22.5) and (b) the rodlike compound (8CB).

Figure 2

Partial phase diagram of the binary system comprising H-22.5 and 8CB. $x_{\mathrm{H}-22.5}$ denotes the mole fraction of H-22.5. I: isotropic phase; N: nematic phase; $\text{Sm-}{A}_d$: smectic-$A_d$ phase. Open circles: nematic to isotropic transition temperature; filled squares: smectic-$A_d$ to nematic transition temperature. Inset shows concentration dependence of the nematic range for the present system. Dashed and solid lines are drawn for guidance to eye.

Figure 3

Experimental values of birefringence $(\Delta n=n_e-n_o)$ for 8CB as a function of temperature. The solid line presents a fit to Eq. (5), extrapolated to the $\mathrm{Sm}\text{−}A$ phase. Inset shows comparison of the temperature dependence of birefringence close to the Sm-A–N phase transition for the same compound. Blue circles: first run; red circles: second run. Dashed vertical arrow denotes the $\mathrm{Sm}\text{−}AN$ phase transition temperature $\left(T_{SN}\right)$.

Figure 4

Experimental values of birefringence $(\Delta n=n_e-n_o)$ as a function of temperature for different mixtures. (a) $x_{\mathrm{H}-22.5}=0.021$; (b) $x_{\mathrm{H}-22.5}=0.035$. Solid lines present fit to Eq. (5), extrapolated to the $\mathrm{Sm}\text{−}A$ phase. Dashed vertical arrow denotes the $\mathrm{Sm}\text{−}AN$ phase transition temperature $\left(T_{SN}\right)$.

Figure 5

Temperature-dependent variation of $Q\left(T\right)$ for pure 8CB. Inset shows temperature dependence of $-d\left(\Delta n\right)/dT$ for the same compound.

Figure 6

Temperature-dependent variation of the quotient $Q\left(T\right)$ in the vicinity of smectic-$A\mathrm{nematic}$ phase transition at different mole fractions $x$ of H-22.5 in the mixtures of H-22.5 and 8CB. Data are arranged in sequence of increasing mole fraction $x$ of H-22.5 from left to right with 1: 8CB; 2: $x_{\mathrm{H}-22.5}=0.021$; 3: $x_{\mathrm{H}-22.5}=0.035$; 4: $x_{\mathrm{H}-22.5}=0.052$; 5: $x_{\mathrm{H}-22.5}=0.06$; 6: $x_{\mathrm{H}-22.5}=0.07$; 7: $x_{\mathrm{H}-22.5}=0.08$. The solid lines are fit to Eq. (9).

Figure 7

Concentration dependence of the critical exponent $\left({\alpha }^{\prime }\right)$ obtained by fitting $Q\left(T\right)$ to Eq. (9). The vertical dashed line corresponds to the tricritical point (TCP). The solid line is a second-order polynomial fit to the data.

Figure 8

Variation of the critical exponent $\left({\alpha }^{\prime }\right)$ with McMillan ratio $(T_{SN}/T_{NI})$. The vertical dashed line corresponds to the tricritical point (TCP). The solid line is a second-order polynomial fit to the data.

Figure 9

Plot of birefringence $(\Delta n=n_e-n_o)$ as a function of reduced temperature $|{\tau }^{\prime }|=|\left(1-T/T_{SN}\right)|$ for different mixtures. The solid lines are fit to Eq. (10).

Figure 10

Variation of order parameter critical exponent $\left({\beta }^{\prime }\right)$ with McMillan ratio $(T_{SN}/T_{NI})$. The solid line is a second-order polynomial fit to the data. Inset shows variation of susceptibility critical exponent $\left({\gamma }^{\prime }\right)$ with McMillan ratio $(T_{SN}/T_{NI})$.