Phase transitions study of the liquid crystal DIO with a ferroelectric nematic, a nematic, and an intermediate phase and of mixtures with the ferroelectric nematic compound RM734 by adiabatic scanning calorimetry

High-resolution calorimetry has played a significant role in providing detailed information on phase transitions in liquid crystals. In particular, adiabatic scanning calorimetry (ASC), capable of providing simultaneous information on the temperature dependence of the specific enthalpy $h\left(T\right)$ and on the specific heat capacity $c_p\left(T\right)$, has proven to be an important tool to determine the order of transitions and render high-resolution information on pretransitional thermal behavior. Here we report on ASC results on the compound 2,3′,4′,5′-tetrafluoro[1,1′-biphenyl]-4-yl 2,6-difluoro-4-(5-propyl-1,3-dioxan-2-yl) benzoate (DIO) and on mixtures with 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). Both compounds exhibit a low-temperature ferroelectric nematic phase ($N_F$) and a high-temperature paraelectric nematic phase $\left(N\right)$. However, in DIO these two phases are separated by an intermediate phase ($N_x$). From the detailed data of $h\left(T\right)$ and $c_p\left(T\right)$, we found that the intermediate phase was present in all the mixtures over the complete composition range, albeit with strongly decreasing temperature width for that phase with decreasing mole fraction of DIO ($x_{\mathrm{DIO}}$). The $x_{\mathrm{DIO}}$ dependence on the transition temperatures for both transitions could be well described by a quadratic function. Both these transitions were weakly first order. The true latent heat of the $N_x\text{−}N$ transition of DIO was as low as $L=0.0075\pm 0.0005\mathrm{J}/\mathrm{g}$ and $L=0.23\pm 0.03\mathrm{J}/\mathrm{g}$ for the $N_F\text{−}{N}_x$ transition, which is about twice the previously reported value of 0.115 J/g for the $N_F\text{−}N$ transition in RM734. In the mixtures both transition latent heats decrease gradually with decreasing $x_{\mathrm{DIO}}$. At all the $N_x\text{−}N$ transitions pretransition fluctuation effects are absent and these transitions are purely but very weakly first order. As in RM734 the transition from the $N_F$ to the higher-temperature phase exhibits substantial pretransitional behavior, in particular, in the high-temperature phase. Power-law analysis of $c_p\left(T\right)$ resulted in an effective critical exponent $\alpha =0.88\pm 0.1$ for DIO and this value decreased in the mixtures with decreasing $x_{\mathrm{DIO}}$ toward $\alpha =0.50\pm 0.05$ reported for RM734. Ideal mixture analysis of the phase diagram was consistent with ideal mixture behavior provided the total transition enthalpy change was used in the analysis.

Figure 1

Chemical structure of DIO (top) and RM734 (bottom).

Figure 2

Adiabatic scanning calorimetry results above and below the melting transition temperature of neat DIO, upon heating at an average rate of 0.056 K/min. Temperature dependence of the specific enthalpy $h\left(T\right)$ in panel (a) and of effective specific heat capacity $c_p\left(T\right)$ in panel (b) of neat DIO across the first-order transition from the solid crystalline phase to the nematic phase.

Figure 3

Adiabatic scanning calorimetry results for neat DIO at an average heating rate of 0.058 K/min. Overview of the temperature dependence of the effective specific heat capacity $c_p\left(T\right)$ between 60 °C and 90 °C crossing the $N_F\text{−}{N}_x$ and the $N_x\text{−}N$ transitions. The inset gives the detailed behavior around the $N_x\text{−}N$ transition.

Figure 4

Adiabatic scanning calorimetry results for neat DIO at an average heating rate of 0.058 K/min. Temperature dependence of the specific enthalpy $h\left(T\right)$ across the transition from the ferroelectric nematic $N_F$ phase to the $N_x$ phase after subtraction (for display reasons) of a linear temperature background $1.5(T\text{−}{T}_{\mathrm{ref}}$) (J/g), with $T_{\mathrm{ref}}$ an arbitrary reference temperature.

Figure 5

Adiabatic scanning calorimetry results for neat DIO at an average heating rate of 0.058 K/min. The temperature dependence of the specific enthalpy $h\left(T\right)$ in panel (a) and the effective specific heat capacity $c_p\left(T\right)$ in panel (b) are shown across the very small first-order transition from the $N_x$ phase to the nematic phase $N$. From the data of $h\left(T\right)$ a linear temperature dependent background $1.5(T\text{−}{T}_{\mathrm{ref}}$) (J/g), with $T_{\mathrm{ref}}$ an arbitrary reference temperature, has been subtracted.

Figure 6

Adiabatic scanning calorimetry results for the $N_F\text{−}{N}_x$ transition for two different samples of neat DIO. Double logarithmic plot for the difference ($C\text{−}{c}_p$) expressed in J/(g K) as a function of the reduced temperature difference τ [see Eq (8)].The upper open green circles (sample A) and open red triangles (sample B) are for the data of $T>T_{\mathrm{tr}}$. The gray solid circles (sample A) and blue solid triangles (sample B) are for the data of $T<T_{\mathrm{tr}}$. The average slopes of the different trend lines are consistent with an effective critical exponent $\alpha \approx 0.88\pm 0.10$.

Figure 7

Temperature dependence of the specific heat capacity ${\mathrm{c}}_p$ from well into the ferroelectric nematic phase $N_F$ to well into the nematic phase $N$, crossing the $N_F\text{−}{N}_x$ and the $N_x\text{−}N$ transitions for DIO and five mixtures with weight fractions $w_{\mathrm{D}}$ of 0.741 (red), 0.549 (orange), 0.409 (green), 0.252 (dark green), and 0.118 (blue), respectively. The arrows point to the very weak signals of the $N_x\text{−}N$ transitions.

Figure 8

Phase diagram for several mixtures of RM734+DIO. The red solid circles are present ASC values for the $N_x\text{−}N$ transition temperatures. The solid blue rhombs are the ASC results for the $N_F\text{−}{N}_x$ transition temperatures for DIO and the mixtures plus the data point at $w_D=0$ for RM734 from Ref. [32]. The dashed red and blue curves represent quadratic trend lines through the data. The green open triangle and open black square symbols represent values derived from Fig. 2 in Ref. [31]. The triangles are, according to Ref. [31], for the $N_x\text{−}N$ transitions and the squares are for the $N_F\text{−}{N}_x$ transition for $w_{\mathrm{D}}>0.4$ and for the $N_F\text{−}N$ transition for $w_{\mathrm{D}}<0.4$.

Figure 9

Overview of the observed widths of the two-phase regions for neat DIO and RM734 and for the eight mixtures investigated. The upper blue (open circles) data points denote the $N_F\text{−}{N}_x$ transition. The blue data point at $w_D=0$ is the value reported in Ref. [32] for the $N_F\text{−}N$ transition for RM734. The blue dashed line corresponds to a fit with a cubic equation. The lower red (solid circles) data points denote the $N_x\text{−}N$ transition and the red dashed line is from a quadratic fit. At $w_D=0$ no red data point is plotted because no $N_x\text{−}N$ transition was reported in Ref. [32].

Figure 10

True latent heat values $L_{N_F\text{−}{N}_x}$ and $L_{N_x\text{−}N}$ for the $N_F\text{−}{N}_x$ transition (upper open blue data points) and for the $N_x\text{−}N$ transition (lower solid red data points). Note that the right and left vertical axes use different scales. Thus the latent heats for the $N_x\text{−}N$ transitions are about a factor of 20 smaller than the ones for the $N_F\text{−}{N}_x$ transitions. The dashed lines are quadratic trend lines. The blue data point at $w_D=0$ is the value reported in Ref. [32] for the $N_F\text{−}N$ transition of RM734. At $w_D=0$ no red data point is plotted because no $N_x\text{−}N$ transition was reported in Ref. [32].

Figure 11

Double logarithmic plot for the difference ($C\text{−}{c}_p$), expressed in J/(g K) as a function of the reduced temperature difference τ [see Eq. (8)]. The upper panel (a) shows data above the transition temperature $T_{\mathrm{tr}}$. The lower panel (b) shows data below $T_{\mathrm{tr}}$. Red data points are for neat DIO and the black ones for neat RM734. The intermediate curves are for mixtures of DIO and RM734 with weight fraction $w_D=0.741$ (orange), $w_D=0.549$ (blue), $w_D=0.409$ (violet), $w_D=0.252$ (green), and $w_D=0.118$ (gray). Some of the data sets have been shifted upward for display reasons. The slopes of the curves correspond to the effective critical exponent α of Eq. (8).

Figure 12

Comparisons, as a function of the weight fraction of DIO, between the effective critical exponent α values [see Eq. (4)] at the $N_F\text{−}{N}_x$ transition for neat RM734 (to the left) and neat DIO (to the right) and for eight different mixtures of these compounds. The open (red) squares are from $c_p\left(T\right)$ data above the transitions and the open (blue) triangles below the transition. The solid (black) circles are average values and the dashed line shows a linear fit through these data.

Figure 13

Transition temperatures as a function of the mole fraction of DIO. The red open circles are data of the $N_x\text{−}N$ transition temperatures, and the solid blue circles are the results for the $N_F\text{−}{N}_x$ transition temperatures of DIO and of the mixtures and for the $N_F\text{−}N$ transition temperature of RM734 (at $x=0$), reported in Ref. [32]. The dashed red and blue curves represent quadratic trend lines through the corresponding data points.

Figure 14

Total specific enthalpy change $\mathrm{\Delta }{h}_{\mathrm{tr}}$ associated with the transitions from the $N_F\text{−}{N}_x$ transitions as a function of the weight fraction $w_{\mathrm{D}}$ of DIO [see Eq. (3)]. The point at $w_D=0$ is for the $N_F\text{−}N$ transition of RM734 [32].