PC-OC phase transition in NPG at atmospheric pressure

At room temperature and atmospheric pressure, NPG adopts an ordered monoclinic structure (P2 1 /c) with four molecules per unit cell19 (Fig. 1a). On heating, the material undergoes a reversible structural phase transition to a cubic structure (\(Fm\bar 3m\)) with four molecules per unit cell that adopt an orientationally disordered configuration at any typical instant20 (Fig. 1a). The first-order structural phase transition yields sharp peaks in dQ/|dT| (Q is heat, T is temperature) recorded on heating and cooling (Fig. 1a), with a well-defined transition start temperature T 0 ~ 314 K on heating (Supplementary Fig. 1). By contrast, as a consequence of the nominally isothermal character of the PC-OC transition21, the temperature ramp rate influences the transition finish temperature on heating, and the transition start and finish temperatures on cooling (e.g., by up to ~5 K for 1–10 K min−1, Supplementary Fig. 1). Integration of the calorimetric peaks yields a large latent heat of |Q 0 | = 121 ± 2 kJ kg−1 on heating, and |Q 0 | = 110 ± 2 kJ kg−1 on cooling (Fig. 1a). These values of |Q 0 | are independent of the temperature ramp rate (Supplementary Fig. 1), and in good agreement with previous experimental values1,22,23 of |Q 0 | ~ 123–131 kJ kg−1.

Fig. 1 Thermally driven phase transition in NPG at atmospheric pressure. a Measurements of dQ/|dT| after baseline subtraction, on heating (red) and cooling (blue) across the first-order cubic-monoclinic phase transition, revealing a large latent heat. The insets represent simplified plan views of the globular (CH 3 ) 2 C(CH 2 OH) 2 molecules (C = dark green spheres, H = grey spheres and O = light green spheres), which are configurationally ordered in the monoclinic ordered-crystal (OC) phase (left inset), and configurationally disordered in the cubic plastic-crystal (PC) phase (right inset). We assume only one molecule per unit cell for ease of representation. b Specific heat C p either side of the transition on heating (red) and cooling (blue). c Entropy S′(T) = S(T)−S(250 \({\mathrm{K}}\)), evaluated via \({S\prime (T) = S(T) - S(250\,{\mathrm{K}}) = {\int}_{250\,{\mathrm{K}}}^{T} \left( {C_{p} + \left| {{\mathrm{d}}Q/{\mathrm{d}}T\prime } \right|} \right)/T\prime {\mathrm{d}}T\prime}\), revealing a large entropy change |ΔS 0 | for the transition. d Specific volume V(T) on heating, revealing a large volume change |ΔV 0 | for the transition. Symbols represent experimental data, lines are guides to the eye Full size image

Integration of (dQ/|dT|)/T and C p /T (Fig. 1b), permits the evaluation of entropy S′(T) = S(T)−S(250 K) over a wide temperature range (Fig. 1c), as explained in the Experimental Section (C p is specific heat at atmospheric pressure). The large entropy change at the transition (|ΔS 0 | ~ 383 J K−1 kg−1 on heating and |ΔS 0 | ~ 361 J K−1 kg−1 on cooling) is in good agreement with previous experimental values1,21,22,23 of |ΔS 0 | ~ 390–413 J K−1 kg−1. This large value of |ΔS 0 | arises due to a non-isochoric order-disorder transition in molecular configurations, such that it exceeds values of |ΔS 0 | << 100 J K−1 kg−1 for first-order structural phase transitions associated with changes of ionic position24,25,26,27 and electronic densities of states24,27,28. Consequently, the configurational degrees of freedom that are accessed via the non-isochoric order-disorder transition in our solid material yield entropy changes that compare favourably with those associated with the translational degrees of freedom accessed via solid-liquid-gas transitions in various materials29, including the hydrocarbon fluids used for commercial refrigeration18.

On heating through the transition, x-ray diffraction data confirm the expected changes in crystal structure19,20 (Supplementary Figs. 6 and 7). The resulting specific volume V undergoes a large ~4.9% increase of ΔV 0 = 0.046 ± 0.001 cm3 g−1 across the transition, for which (∂V/∂T) p=0 > 0 (Fig. 1d), presaging large conventional BC effects that may be evaluated30 by using the Maxwell relation (∂V/∂T) p = −(∂S/∂p) T to calculate the isothermal entropy change \(\Delta S\left( {p_1 \to p_2} \right) = - {\int}_{p_1}^{p_2} {\left( {\partial V/\partial T} \right)_p{\mathrm{d}}p}\) due to a change in pressure from p 1 to p 2 . Near the transition, the volumetric thermal expansion coefficients for the OC and the PC phases are both ~10−4 K−1, implying the existence of additional15 BC effects ΔS + that are large and conventional at temperatures lying on either side of the transition. These additional BC effects are evaluated here using the aforementioned Maxwell relation, for changes in pressure |p−p atm | ~ |p| where atmospheric pressure p atm ~ 0 GPa, to obtain ΔS + (p) = −[(∂V/∂T) p=0 ]p, where (∂V/∂T) p is assumed to be independent of pressure13,15,17 (Supplementary Fig. 4 shows the error in (∂V/∂T) p to be ~20% for the PC phase, which implies an error in the total entropy change ΔS of ~3%).

Two contributions to |ΔS 0 | may be identified as follows. One is the configurational entropy31,32 given by M−1Rln Ω, where M = 104.148 g mol−1 is molar mass, R is the universal gas constant, and Ω is the ratio between the number of configurations in the PC and the OC phases. The other is the volumetric entropy31,32 \((\bar \alpha /\bar \kappa )\) ΔV 0, where the coefficient of isobaric thermal expansion \(\bar \alpha\) (Supplementary Fig. 4), and the isothermal compressibility \(\bar \kappa\) (Supplementary Fig. 5), have both been averaged across the PC-OC transition. Molecules of (CH 3 ) 2 C(CH 2 OH) 2 display achiral tetrahedral symmetry33 (point group T d , subgroup C 3v ), yielding one configuration in the OC phase and 60 configurations in the PC phase (10 molecular orientations that each possesses six possible hydroxymethyl conformations). Therefore the configurational entropy is M−1Rln 60 ~ 330 J K−1 kg−1, and the volumetric entropy is ~60 J K−1 kg−1 (data from Fig. 1d and Supplementary Fig. 3a). The resulting prediction of |ΔS 0 | ~ 390 J K−1 kg−1 agrees well with the experimental values reported above, and the previously measured experimental values1,21,22,23 reported above.

PC-OC phase transition in NPG under applied pressure

Measurements of dQ/|dT| under applied pressure (Fig. 2a, b) reveal that the observed transition temperatures vary strongly with pressure (Fig. 2c), with dT/dp = 113 ± 5 K GPa−1 for the start temperature on heating, and dT/dp = 93 ± 18 K GPa−1 for the start temperature on cooling, for pressures p < 0.1 GPa (black lines, Fig. 2c). These values of dT/dp are amongst the largest observed for BC materials (Supplementary Table 1), and indicate that the first-order PC-OC transition of width ~10 K (Fig. 2a, b) could be fully driven in either direction using |Δp| ~ |p| ~ 0.1 GPa. At higher pressures, values of dT/dp fall slightly, but remain large (Fig. 2c).

Fig. 2 Pressure-driven phase transition in NPG. a, b Measurements of dQ/|dT| on heating and cooling across the first-order PC-OC transition for different values of increasing pressure p, after baseline subtraction. c, d Transition temperature and entropy change |ΔS 0 (p)| on heating (red symbols) and cooling (blue symbols), derived from the calorimetric data of a, b and equivalent data at other pressures (shown in Supplementary Fig. 2). Black lines in c are linear fits. Red and blue lines in c, d are guides to the eye. e Volume change for the transition |ΔV 0 (p)|: solid symbols obtained from the dilatometric data (DD) in Supplementary Fig. 3a; open circle obtained from the x-ray diffraction data in Fig. 1c, open square obtained from the x-ray diffraction data in Supplementary Fig. 3b; orange line obtained from c, d via the Clausius–Clapeyron (CC) equation Full size image

Integration of (dQ/|dT|)/T at finite pressure reveals that the entropy change |ΔS 0 | decreases slightly with increasing pressure (Fig. 2d). This decrease arises because the additional entropy change ΔS + (p) increases in magnitude on increasing temperature in the PC phase [(∂V/∂T) p=0 at 370 K is ~240% larger than (∂V/∂T) p=0 at 320 K, Fig. 1d], whereas it is nominally independent of temperature in the OC phase near the transition. The fall seen in both dT/dp and |ΔS 0 | implies via the Clausius–Clapeyron equation dT/dp = ΔV 0 /ΔS 0 that there is a reduction in |ΔV 0 | at finite pressure (Fig. 2e), as confirmed using pressure-dependent dilatometry (Supplementary Fig. 3a) and pressure-dependent x-ray diffraction (Supplementary Fig. 3b).

In order to plot ΔS(T,p), we obtained finite-pressure plots of S′(T,p) = S(T,p)−S(250 K,0) (Fig. 3a, b) by integrating the data in Fig. 2a, b and Fig. 1b, and displacing each corresponding plot by ΔS + (p) at 250 K, as explained in the Experimental Section. (Note that ΔS + (p) was evaluated below T 0 (p = 0) to avoid the forbidden possibility of T 0 (p) rising to the temperature at which ΔS + (p) was evaluated at high pressure.) From Fig. 3a, b, we see that the entropy change associated with the transition ΔS 0 (p) combines with the smaller same-sign additional entropy change ΔS + (p) away from the transition, yielding total entropy change ΔS(p).

Fig. 3 Colossal barocaloric effects in NPG near room temperature. a, b Entropy S’(T,p) with respect to the absolute entropy at 250 K and p ~ 0, on a heating and b cooling through the first-order PC-OC phase transition. c Isothermal entropy change ΔS for 0 → p deduced from b, and for p → 0 deduced from a. d Adiabatic temperature change ΔT versus starting temperature T s , for 0 → p deduced from b. e Adiabatic temperature change ΔT versus finishing temperature T f for p → 0 deduced from a Full size image

BC performance

By following isothermal trajectories in our plots of S′(T,p) obtained on cooling (Fig. 3b), we were able to evaluate ΔS(T,p) on applying pressure (Fig. 3c), as cooling and high pressure both tend to favour the low-temperature low-volume OC phase. Similarly, by following isothermal trajectories in our plots of S′(T,p) obtained on heating (Fig. 3a), we were able to evaluate ΔS(T,p) on decreasing pressure (Fig. 4c), as heating and low pressure both tend to favour the high-temperature high-volume PC phase.

Fig. 4 Barocaloric performance near room temperature. a For NPG, we show the peak isothermal entropy change |ΔS peak | for pressure changes of magnitude |p|, on applying pressure (blue symbols) and removing pressure (red symbols). For comparison, the green envelope represents state-of-the-art barocaloric materials (Table 1) that operate near room temperature, and the orange symbol represents the standard commercial fluid refrigerant18 R134a for which operating pressures are ~0.001 GPa. For NPG alone, we show the variation with |p| of b refrigerant capacity RC = |ΔS peak | × [FWHM of ΔS(T)] and c peak values of the adiabatic temperature change |ΔT peak |, on applying pressure (blue symbols) and removing pressure (red symbols) near room temperature Full size image

Discrepancies in the magnitude of ΔS(T,p) on applying and removing pressure (Fig. 3c) are absent in the range ~314-342 K, evidencing reversibility. Our largest reversible isothermal entropy change |ΔS| ~ 510 J K−1 kg−1 arises at ~330 K for |p| ~ 0.57 GPa, and substantially exceeds the BC effects of |ΔS| ≤ 70 J K−1 kg−1 that were achieved using similar values of |p| in a range of materials near room temperature (Fig. 4a), namely magnetic alloys7,8,9,10,11,12,34, ferroelectric13,35,36 and ferrielectric15 materials, fluorides and oxifluorides14,37,38,39,40, hybrid perovskites16, and superionic conductors17,41,42. Moreover, our largest value of |ΔS| substantially exceeds the values recorded for magnetocaloric30,43,44,45,46, electrocaloric30,47,48, and elastocaloric30,49 materials, and is comparable to the values observed in the standard commercial hydrofluorocarbon refrigerant fluid R134a18, for which |ΔS| = 520 J K−1 kg−1 at ~310 K for much smaller operating pressures of ~0.001 GPa (Fig. 4a). We can also confirm that NPG compares favourably with other BC solids7,8,9,10,11,12,31 when normalizing the peak entropy change by volume30 to yield |ΔS| ~ 0.54 J K−1 cm−3 (the NPG density is 1064 kg m−3 at ~320 K). (While finalizing our manuscript, which is based on our 2016 patent, we learned about the pre-print of ref. 50, which lists literature values of thermally driven entropy changes for PC-OC transitions in NPG and other plastic crystals at atmospheric pressure, and suggests they could be used in barocalorics.)

The large variation of transition temperature with pressure (Fig. 2c) permits large entropy changes of |ΔS| ~ 445 J K−1 kg−1 to be driven with relatively moderate pressure changes of |p| ~ 0.25 GPa (Fig. 3c), yielding giant BC strengths30 of \(\left| {\Delta S} \right|/\left| p \right|\) ~ 1780 J K−1 kg−1 GPa−1. Larger pressures extend the reversible BC effects to higher temperatures (Fig. 3c), causing the large refrigerant capacity RC to increase (Fig. 4b) despite the slight reduction in |ΔS 0 (p)| (Fig. 2d). The BC effects in NPG are so large (Fig. 4a) that unpractical changes of pressure would be required to achieve comparable RC values in other BC materials.