Barocaloric response of plastic crystal 2-methyl-2-nitro-1-propanol across and far from the solid-solid phase transition

Plastic crystals have emerged as benchmark barocaloric (BC) materials for potential solid-state cooling and heating applications due to huge isothermal entropy changes and adiabatic temperature changes driven by pressure. In this work we investigate the BC response of the neopentane derivative 2-methyl-2-nitro-1-propanol (NO2C(CH3)2CH2OH) in a wide temperature range using x-ray diffraction, dilatometry and pressure-dependent differential thermal analysis. Near the ordered-to-plastic transition, we find colossal BC effects of ≃ 400 J K−1 kg−1 and ≃ 5 K upon pressure changes of 100 MPa. Although reversible effects at the transition are obtained only from higher pressure changes due to hysteretic effects, we do obtain fully reversible BC effects from any pressure change in individual phases, that become giant at moderate pressures due to very large thermal expansion, especially in the plastic phase. From our measurements, we also determine the crystal structure of the low-temperature phase and estimate the contribution of the configurational disorder and the volume change to the total transition entropy change.


Introduction
Plastic crystals feature phase transitions with a very large latent heat among solid-solid phase transitions, which are typically associated with the emergence of orientational disorder in the plastic phase [1].While these phase change materials have traditionally attracted interest for passive thermal energy management [2], recent studies have reported in these materials unrivaled isothermal entropy changes and large adiabatic temperature changes driven by pressure changes thanks to the significant sensitivity of the phase transition to pressure.These barocaloric (BC) effects could be functionalized in more sustainable coolers and heat pumps [3][4][5], as a potential solution to the environmental thread posed by billions of current appliances that use potent greenhouse hydrofluorocarbon fluids.Similarly, BC effects in plastic crystals have also been proposed for thermal energy management actively controlled by pressure [6,7].Furthermore, plastic crystals are, overall, of null or low toxicity, cheap and readily available.In addition, as any other BC material, their use in form of powder makes the drawback of fatigue disappear.
Based on phase transition equilibrium properties at atmospheric pressure available in the literature [1], molecular plastic crystals can be preselected as potentially among the best BC materials.However, some of them are actually limited or not suited for BC cooling and heating due to irreversibility issues and a deeper analysis including high-pressure and out-of-equilibrium data is needed to determine the actual BC performance of any compound.To date, the BC performance of different molecular plastic crystal families has been investigated: organic compounds as neopentane derivatives [3][4][5]8] and adamantane derivatives [6,9], and inorganic compounds as carboranes [10].Neopentane derivatives have shown by far the largest BC effects, but some of the adamantane derivatives and carboranes exhibit a better reversible BC performance at lower pressures due to relatively low transition hysteresis.Here it must be pointed out that many plastic crystals, and in particular neopentane derivatives, typically show a very large volumetric thermal expansion α ∼ 10 −4 K −1 in individual phases [11], which exceeds one order of magnitude or more the typical values achieved by other BC materials, and that is comparable with that of polymers [12] and spin-crossover compounds [13].This anticipates significant BC effects also in individual phases which, interestingly, are fully reversible upon any pressure change because they do not involve hysteresis associated with first-order phase transitions.However, this contribution has often been overlooked, thus underrating the overall BC response of these materials.In this work we investigate the BC response of the neopentane derivative 2-methyl-2-nitro-1-propanol (MNP, with chemical formula NO 2 C(CH 3 ) 2 CH 2 OH) both across the ordered-to-plastic phase transition and in each individual phase.For this purpose we use single crystal and powder x-ray diffraction, high-pressure dilatometry, modulated calorimetry and differential thermal analysis at high pressures.

Experimental
MNP (NO 2 C(CH 3 ) 2 CH 2 OH) was purchased in powder form from Sigma-Aldrich with a purity of 99% and used as received.A single crystal of MNP in the ordered phase was obtained by sublimation.
Crystallographic data of MNP samples were collected at 153 K with a R-Axis Rapid Rigaku MSC diffractometer with monochromatic Cu-Kα radiation (λ = 1.541 87 Å) and a curved image plate detector.The unit cell determination and data reduction were performed using the Crystal Clear program suite [14] on the full set of data.The structure was solved by direct methods and refined using Shelx 97 suite of programs [15] in the integrated WinGX system [16].The H coordinates of the hydroxyl group were refined.The positions of all the other H atoms were deduced from coordinates of the non-H atoms and confirmed by Fourier synthesis [17].These H atoms were included for structure factor calculations but not refined, as usual.The non-H atoms were refined with anisotropic temperature parameters.
High-resolution x-ray powder diffraction (XRPD) was performed at atmospheric pressure and as a function of temperature using Cu-Kα 1 = 1.540 56 Å radiation in an INEL diffractometer with a curved-quartz monochromator, a cylindrical position-sensitive detector (CPS-120) and the Debye-Scherrer geometry.Powder MNP was introduced into a 0.5 mm diameter Lindemann capillary, and a 600 series Oxford Cryostream Cooler was used to control temperature.The Materials Studio software [18] was used to determine the lattice parameters for the high-temperature cubic (C) and low-temperature monoclinic (M) phases by the Pawley method and the crystal structure at 100 K by Rietveld refinement, respectively.
High-pressure dilatometry measurements were performed using custom-built pVT apparatus (uncertainty of ca. 10 −4 g cm −3 ) from the high-pressure laboratory of Prof. Dr A Würflinger (Ruhr-Universität, Bochum, Germany).Around 2 g of MNP were sealed in liquid form to remove air bubbles, in stainless-steel cells.Relative volume changes caused the movement of a Bridgman piston placed inside a coil, which could be determined due to electromagnetic induction [19].Absolute volume was calculated using data obtained from x-ray diffraction at normal pressure.Further details of the experimental system and the procedure have been reported elsewhere [20].
Differential scanning calorimetry at atmospheric pressure was carried out using a DSC Q100 and DSC250 (TA Instruments), with ∼5 mg of powder MNP encapsulated in aluminum pans.Temperature ramps were performed at 2-10 K min −1 .Heat capacity experiments were performed in a DSC250 (TA Instruments) by means of modulated calorimetry with a modulation period of 120 s, a modulation amplitude of 2 K and a temperature rate of 2 K min −1 .
High-pressure differential thermal analysis (HP-DTA) was performed using two bespoke Cu-Be high-pressure calorimeters.One can achieve pressures up to ∼0.3 GPa and operates with Bridgman pistons with K-type thermocouples and the other is a MV1-30 pressure cell (Unipress, Poland) that can achieve pressures up to ∼0.6 GPa and uses Peltier modules as thermal sensors.In both calorimeters, temperature is controlled by means of an external thermal jacket connected to a Lauda Proline RP 1920 refrigerating circulator, within a temperature range from 205 K to 393 K. Temperature rates were ∼2 K min −1 .A few hundreds of mg of MNP were sealed in Sn capsules in liquid form to remove air.The pressure-transmitting fluid was DW-Therm M90.200.02(Huber).

Results and discussion
Chemically, neopentane molecule C(CH 3 ) 4 consists of a carbon linked to four methyl groups and displays achiral tetrahedral symmetry [21] and its derivatives are obtained by substitution of some of the methyl groups.Physically, neopentane and its derivatives undergo an endothermic first-order phase transition from an ordered phase to a cubic plastic phase, whose transition properties such as temperature, latent heat and volume change depend significantly on each particular derivative [22].MNP is a neopentane derivative obtained by the substitution of two methyl groups by one nitro group and one hydroxyl group.At room temperature and at atmospheric pressure, MNP molecules arrange in a monoclinic symmetry [23] (phase M for short, space group P2 1 /c, Z = 12).Upon heating, at 310 K MNP transforms to a face centered cubic (fcc, C for short) phase through a first-order phase transition with a very large enthalpy change determined to be within the range ≃15.0-17.2kJ mol −1 [11,[24][25][26].This is much higher than the enthalpy change at the melting at 364 K (3.4-3.7 kJ mol −1 ), as typically occurs in plastic crystals.

Structural and thermodynamic characterization
The crystal structure of the M phase (see figure 1) was determined from single crystal x-ray diffraction at 153 K (cif number: CCDC 2253858, see figure 2(a)).The asymmetric unit contains three independent molecules that differ little from each other (see table 1).The crystalline cohesion is ensured by the two types of hydrogen bonds (see table 2).The first type corresponds to hydrogen bonds of type O-H• • • O between the hydroxyl groups of the three independent molecules.They are organized in helices in a single direction, parallel to the Ox crystallographic axis, with coordinates close to x; 1/4; 1/4 and their symmetrical.The other  ) allowed to determine the temperature dependence of lattice parameters (see figure 2(c)), and hence volume (see figure 2(d)).The obtained discontinuity indicates the occurrence of the first-order phase transition with a volume change at the endothermic transition of ∆V t ≃ 0.32 × 10 −4 m 3 kg −1 , which corresponds to a very large relative change of ∆Vt V ≃ 3.8%.Using a second-order polynomial and a linear fit for V(T) in phase M and C, respectively, the thermal expansion coefficient α was determined (see figure 2(e)).
Volume was measured isothermally at 321.0 K and 325.8K on decompression across the phase transition (see figure 3(a)).From the sharp increase in volume associated with the phase transition, two points of the coexistence line T(p) of the phase diagram (see empty triangles in figure 4(b)) and the associated transition volume changes (see empty triangles in figure 4(c)) were determined.By fitting V(p) data in each phase, the isothermal compressibility χ T was calculated (see figure 3(b)).Heat capacity was measured at atmospheric pressure as a function of temperature (see figure 3(c)), yielding values in agreement with literature values within uncertainty [25].
Heat flow at atmospheric pressure (not shown) yielded an endothermic peak with onset transition temperatures at ≃310 K associated with the latent heat of the equilibrium first-order phase transition.Peak integration after baseline subtraction yielded a latent heat ∆H t ≃ 121 J g −1 whereas integration of the peak in Q T after baseline subtraction yielded the transition entropy change ∆S t ≃ 391 J K −1 kg −1 , in good agreement with literature values [25,26].In this family of materials, this quantity is typically expected to be mainly contributed by changes in the number of configurations (both orientational and conformational) and in the transition volume change.In phase C, MNP has ten possible orientations, each of which has nine different conformations derived from the fact that both nitro and hydroxyl groups have each three different conformations.This yields a total number of configurations of N C = 90 for phase C whereas N M = 1 for the fully ordered phase M, which leads to a configurational entropy change ∆S c = RM −1 ln NC NM = 314 J K −1 kg −1 (R is the universal gas constant and M the molar mass).In turn, the volumetric entropy change can be estimated using [27,28] ∆S V = ⟨α⟩ ⟨χT⟩ ∆V t where ⟨α⟩ and ⟨χ T ⟩ are averaged over the two phases close to the transition.In particular, from figure 2(e) we calculate ⟨α⟩ ≃ 4.3 × 10 −4 K −1 and from figure 3(b), ⟨χ T ⟩ ≃ 0.22 GPa −1 , which yields ∆S V ≃ 62 J K −1 kg −1 .As expected, we obtain ∆S c + ∆S V ≃ ∆S t and confirm that the major contribution to the total entropy change at the transition is due to the emergence of the molecular orientational and conformational disorder.
Heat flow in temperature dQ d|T| = Q |T| recorded by means of HP-DTA at different constant pressures is shown in figure 4(a).Notice that the peaks obtained on cooling are narrower, hence more abrupt, than those on heating, consistently with the out-of-equilibrium nature of hysteretic exothermic transitions.The in-and out-of-equilibrium T(p) phase diagram (see figure 4(b)) was constructed using peak temperatures in HP-DTA (circles for the peak onset, filled triangles for the peak maximum), and, as mentioned previously, data from x-ray diffraction from figure 2(d) (black square) and dilatometry from figure 3(a) (empty triangles).Values of dT dp ≃ 67 K GPa −1 and dT dp ≃ 58 K GPa −1 were obtained for the endothermic and exothermic transitions, respectively.From the phase diagram, the minimum pressure to achieve reversible effects (p rev ) can be determined as the pressure at which the exothermic transition temperature equals the endothermic transition temperature at atmospheric pressure.As discussed elsewhere [8] and applied here later on, by using the onset transition temperature we obtain p rev ≃ 100 MPa (see continuous black lines) for reversible isothermal entropy changes whereas by using the peak maximum we obtain p rev ≃ 200 MPa (see dashed black lines) for reversible adiabatic temperature changes.
Entropy change at the transition as a function of pressure (see figure 4(c)) was found to decrease with pressure at a rate of d|∆St| dp ≃ −0.24 J K −1 kg −1 MPa −1 .The feature d|∆St| dp < 0 is usually observed in this family of materials and in other organic plastic crystals [3,6,8,9].Volume change at the transition as a function of pressure (see figure 4(d)) was determined from x-ray diffraction (figure 2(d)), dilatometry (figure 3(a)) and the Clausius-Clapeyron equation ∆V t = dT dp ∆S t from figures 4(b) and (c).While overall there is a good agreement between data from different experiments, the point derived from dilatometry at 321.0 K (see green symbols in figure 3(a)) is somewhat out of trend.This can be ascribed to the appearance of pretransitional effects.

Determination of the BC effects
From our V(T) (figure 2(d)) and heat capacity C p (figure 3(c)) at atmospheric pressure, and pressure-and temperature-dependent heat flow data associated with the transition dQ dT (figure 4(a)), we calculated the entropy as a function of temperature and pressure S(T, p) with respect to a reference value at temperature T 0 = 250 K and at atmospheric pressure S(T 0 , p atm ) using the following equation: Given that at T > T 0 , the volume of each phase is nearly linear with temperature (see figure 2(d)), the thermodynamic equation ∂T 2 ) p establishes that C p is approximately independent of pressure in that regime.On the other hand, to account for the pressure dependence of the transition temperature on C p , for each phase C p was extrapolated to high temperatures an incremented range dT dp ∆p, where ∆p = p − p atm ≃ p.As for the last term in equation ( 1), we assumed that at T 0 and in the pressure range under analysis, ) T0;patm ≃ 2.27 × 10 −4 cm 3 g −1 K −1 was calculated at T 0 (i.e. in phase M).This assumption is reasonable given the available data for other compounds of the same family [11] and consistent with the rough trends that can be estimated from V(p) data at two different temperatures in figure 3 T;patm ≃ 5.0 × 10 −4 cm 3 g −1 K −1 calculated in phase C (see the corresponding linear fit in figure 2(d)).
Since MNP exhibits dT dp > 0, isothermal subtraction of entropies obtained on heating and on cooling, independently, yields isothermal entropy changes on first decompression and on first compression, respectively (see figure 5(c)).Adiabatic subtraction of inverted T(S, p) functions, obtained from entropy on heating and on cooling, independently, yields adiabatic temperature changes on first decompression and on first compression, respectively (see figure 5(d)).For cooling and heating applications operating in cycles [29], the need for the refrigerant to transform forth and back in each cycle is hindered by the transition hysteresis.To take into account this feature, the so-called reversible BC effects must be determined.Following the standard procedure [8], reversible isothermal entropy changes ∆S rev (see figure 5(e)) are calculated from the overlapping between ∆S on compression and decompression as determined in figure 5(c), and confirm a minimum pressure p rev ≃ 100 MPa to obtain non-null ∆S rev .In turn, adiabatic temperature changes ∆T rev (see figure 5(f)) are calculated as differences between the isobaric entropy function on heating at atmospheric pressure and isobaric entropy functions on cooling at pressure p, which confirm a minimum pressure p rev ≃ 200 MPa to obtain non-null ∆T rev .As a summary, maximum values for isothermal entropy changes, adiabatic temperature changes and refrigerant capacity RC [30] associated with the first-order phase transition are displayed as a function of pressure in figure 6 for first compressions (blue symbols), first decompressions (red symbols) and reversible processes (green symbols).
A comparison of representative irreversible and reversible values for ∆S and ∆T with other colossal BC materials can be found in table 3.For potential applications related to BC thermal management such as  pressure-driven waste heat recovery [6,7,31,32], ∆S is the relevant quantity.Upon a moderate pressure decrease from ∆p ≃ 100 MPa to atmospheric pressure (+86 MPa upon compression), MNP displays |∆S| ≃ 400 J K −1 kg −1 , which exceeds most of the values reported previously.For cooling and heating cycles, relevant quantities are ∆S rev and ∆T rev .In this case the required pressure changes for reversible BC effects  a This value has been estimated from V(T) data.
are larger than for other materials, but still the obtained magnitudes for the BC effects outperform most of other materials.Despite caloric effects are usually investigated near phase transitions, it may be also interesting to pay special attention to the caloric effects in single phases away from the transition because these are reversible from the first field change as they do not involve hysteretic effects [38] and thus may widen the temperature span useful for applications.In single phases, isothermal entropy changes correspond to those arising due to the last term in equation ( 1): p dp.While these effects are small for many solid materials, plastic crystals in general may display very large isothermal entropy changes due to the large thermal expansion, although they have been typically looked down in previous works.In particular, in MNP, ∆S rev obtained by isothermal subtractions of S(T, p) in single phases (see orange and black lines for phases C and M, respectively in figure 6(a)) are very large, reaching in phase C |∆S + | ≃ 50 J K −1 kg −1 upon pressure changes of ≃180 MPa, and colossal values (|∆S + | > 100 J K −1 kg −1 ) for pressure changes ≳240 MPa.In table 4 we show a comparison of reversible isothermal entropy changes in individual phases ∆S + obtained in different materials, which reflects that neopentane and adamantane derivatives show indeed very large values.In fact, MNP and NPG exhibit a very similar BC performance, both across and outside the transition, and in similar temperature ranges.Having such a catalog of similar colossal BC materials may be useful because other important features for applications like cost and availability, or methods to tune the transition temperature and hysteresis [39,40], or thermal conductivity [41,42] may yield different results in both materials.
In turn, ∆T rev in single phases, which is generally lacking in the literature, has been obtained by two methods: (i) adiabatic subtraction of inverted T(S, p) in single phases (see continuous black and orange lines in figure 6(b) for the M and C phase, respectively) and (ii) calculated via [43] |∆T rev | ≃ Tt Cp |∆S rev | (see dashed black and orange lines in figure 6(b) for the M and C phase, respectively).It must be mentioned here that adiabatic temperature changes in single phases are affected by large uncertainties because they may strongly depend on C p and on the approximation ) patm used to estimate the entropy functions S(T, p).Nevertheless, the good agreement between the two methods provides confidence in the obtained ∆T rev which, surprisingly, is larger than those obtained across the first-order phase transition (green symbols in figure 6

Conclusions
In this work, the BC response of a plastic crystal derived from neopentane, 2-methyl-2-nitro-1-propanol, was investigated via the quasi-direct method using x-ray diffraction, pressure-dependent calorimetry and dilatometry.The structure of the monoclinic phase was determined by single crystal x-ray diffraction and the thermal expansion, the isothermal compressibility and the endothermic and exothermic transition properties were characterized.It was found that the huge transition entropy change emerges mainly due to the orientational and conformational disorder in the plastic phase.As for the BC effects, under a pressure change of 0.1 GPa, we obtained isothermal entropy changes of 400 J K −1 kg −1 and adiabatic temperature changes of 5 K, thus surpassing most of previously reported plastic crystals and that could be used for potential thermal management applications such as waste heat recovery.Instead, to drive reversibly BC effects associated with the transition that could be used in cooling or heating devices working in cycles, we found a relatively large transition hysteresis that imposes a minimum pressure of ≃0.2 GPa.Therefore, our work confirms that the characterization of the reversible response is key for a proper BC material selection for cooling and heat pumping and that controlling hysteresis is still a major scientific and technological challenge.Notwithstanding, very large and fully reversible BC effects under low pressure changes were found in the individual phases thanks to a large thermal expansion, in particular in the plastic phase.These findings should encourage investigating BC effects also away from phase transitions in this type of materials.

Figure 1 .
Figure 1.Crystal structure of the unit cell of the monoclinic phase for MNP (a) along c, (b) along b and (c) along a crystallographic axes.Blue, red, grey and white atoms stand for N, O, C and H. Cyan dashed lines stand for hydrogen bonds.

Figure 2 .
Figure 2. XRPD measurements.(a) Refined powder diffraction pattern in the monoclinic phase at 100 K.The inset shows a high-angle interval enlarged 6 times.Red symbols are experimental data, blue lines are refined profiles, green segments indicate Bragg peak positions and black lines are differences between calculated and experimental data.(b) XRPD patterns at different temperatures across the phase transition.(c) Lattice parameters as a function of temperature.Monoclinic parameters are a, b, c (left axis) and β (right axis) and the cubic parameter is ac (left axis).(d) Temperature-dependent volume per formula unit (left axis) and per unit of mass (right axis).(e) Thermal expansion as a function of temperature.

Figure 3 .
Figure 3. (a) Volume and (b) isothermal compressibility as a function of pressure at two different temperatures.(c) Heat capacity at atmospheric pressure as a function of temperature.

Figure 4 .
Figure 4. Characterization at high pressure.(a) Isobaric HP-DTA as a function of temperature at different pressures on heating (positive) and on cooling (negative) across the transition.(b) Temperature-pressure phase diagram for the endothermic (red) and for the exothermic transitions (blue).Circles and triangles stand for the onset and maximum of the peaks, respectively.Continuous and dashed lines are fits to peak onsets and maximums.Data from XRPD and dilatometry are also included.(c) Entropy change at endothermic (red) and exothermic (blue) transitions as a function of pressure.(d) Volume change at the endothermic transition obtained via: (i) XRPD at atmospheric pressure as derived from figure 2(d) (square); (ii) dilatometry as derived from figure 3(a) (triangles) and (iii) the Clausius-Clapeyron (CC) equation at different pressures (circles).
(a).The resulting entropy functions S(T, p) − S(T 0 , p atm ) are shown in figures 5(a) and (b) for different pressures and as a function of temperature on heating and on cooling, respectively.Interestingly, the isothermal difference of these curves in phase C is consistent within error with the value obtained via ´p patm (

Figure 5 .
Figure 5. (a) and (b) Entropy S(T, p) with respect to a reference entropy S(T0, patm) (a) on heating and (b) on cooling.(c) Isothermal entropy changes and (d) adiabatic temperature changes obtained on first compression and on first decompression.Fully reversible (e) isothermal entropy changes and (f) adiabatic temperature changes.In panels (c)-(f), continuous lines correspond to the BC effects involving the first-order phase transition whereas dashed lines correspond to those changes obtained in single phases away from the transition.

Figure 6 .
Figure 6.Maximum absolute values of (a) isothermal entropy changes, (b) adabatic temperature changes and (c) RefrigerantCapacity for first compression (blue symbols), first (red symbols) and reversible processes (green symbols) involving the first-order phase transition (FOPT).Orange and black continuous lines refer to (reversible) BC effects obtained away from the transition within the cubic and the monoclinic phases, respectively, from the subtraction of entropy curves.For ∆T, dashed lines are obtained using the equation |∆T| ≃ Tt Cp |∆S|.

Table 1 .
Overlay of molecules identified by their hydroxyl label.

Table 2 .
H bonds with distances and angle details.O1, O11, O21 belong to hydroxyl groups whereas O6, O15 and O25 belong to nitro groups.

Table 3 .
Comparison of the irreversible and reversible barocaloric response in plastic crystals and other colossal barocaloric materials.Data for ∆Trev in round brackets are calculated through the approximation ∆Trev = |∆Srev|Tt/Cp.Data in curly brackets are obtained from modelling, without taking into account the hysteresis.The acronyms used here have been taken from the corresponding references.

Table 4 .
Estimated isothermal entropy changes ∆S + upon a pressure change of 0.1 GPa in individual phases for plastic crystals and other colossal BC materials.Here, II and I stand for the ordered or semiordered and disordered phases, respectively.