Colossal and Reversible Barocaloric Effect in Phase Change Materials n-Alkanes

: The emergent cooling technologies based on the caloric effect provide a green alternative to the conventional vapor-compression one which brings about the serious environment problem. However, the existing caloric materials are much inferior to their traditional counterparts in cooling performance. Here we report the colossal barocaloric effect in liquid-solid-transition materials, i.e. n -alkanes. Their excellent cooling performance is superior to those for existing caloric materials and comparable to those of traditional refrigerants. Theoretical calculations suggest the liquid state n alkanes has huge configuration entropy characterized by large dispersion of bond lengths. Appling pressure significantly reduces the configuration entropy and eventually induces the liquid-solid-transition, leading to the colossal barocaloric effect. This work provides promising refrigerants for caloric cooling technology, and opens a new avenue for exploring colossal barocaloric materials.

Matters have various states (e.g., gas, liquid and solid) depending on the strength of the interaction among molecules. The stronger the intermolecular interaction, the more ordered the matter state, the lower the entropy. So, the colossal entropy change can be anticipated when a matter transforms from one state to another. It is based on the gasliquid transformation that the traditional vapor-compression technology realizes the strong cooling capacity. The reported SSC effect is mainly associated with the transformation between two "solid" states with notably different degrees of lattice, spin, polar or electron ordering [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] . Therefore, it is a big challenge for SSC materials to acquire as good refrigeration performance as conventional refrigerants. Alike the gasliquid transitions, the liquid-solid (LS) transitions also exhibit huge entropy change [22][23][24][25][26] . Moreover, the LS transition is often characterized by a large volume change since the density changes, which is thus sensitive to external pressure and could be utilized for realizing colossal BC effects [26][27][28] . As typical LS-transition materials, the n-alkanes with general chemical formula CnH2n+2 have been widely used in food, medicine, packaging, fruit preservation and other fields, indicating good environmental friendliness. Here, we evaluated the colossal BC effect associated with the LS transition in CnH2n+2 (n=14, 16,18). Under an external pressure of 100 MPa, a high adiabatic temperature change (ΔTd) ~18 K was achieved by direct method, which is doubled when the applying pressure is increased to 200 MPa. Moreover, the reversible entropy change (ΔSr) reaches ~ 700 J kg -1 K -1 under only ~50 MPa. Both the ΔTd and ΔSr of nalkanes are well exceeding those of existing SSC materials, promising for caloric cooling applications. The colossal BC effect can be understood in terms of pressureinduced drastic change of configuration entropy in the liquid state.
The temperature variation of n-alkanes as function of time, T(t)s, were measured by direct method under different pressures (Supplementary Fig. 1-3). The results of C18H38 at selected temperatures were shown in Fig. 1A-C. In the solid state (e.g., at 294 K), the sample's temperature rises when pressure is applied and decreases when pressure is released, corresponding to the exothermic and endothermic peaks in the T(t) curves, respectively. Both the endothermic and exothermic peaks are gradually enhanced with increasing the pressure up to 500 MPa. When the measurement temperature is set at 305 K which is slightly higher than the LS transition temperature (TLS ~ 301.3 K), under pressures at ≥ 100 MPa, the exothermic peak during the pressure-loading process is sharp and gets further enhanced as the pressure increases 25 . In contrast, the endothermic peak during the pressure unloading process always presents shape distortion and broadening. When the temperature is set well above TLS (e.g., at 356 K), the endothermic peak shows an abrupt enhancement at pressure 367 MPa. However, the exothermic peak is distorted into a small peak with a long tail. The above behaviors were also observed for C16H34 and C14H30 samples, as shown in Supplementary Fig. 2 and 3, respectively.
The hydrostatic pressure can significantly enhance TLS of CnH2n+2 [26][27] . Therefore, when CnH2n+2 lies in liquid state, the strong pressure could drive the mutual transformation between liquid and solid state. So, the extra enhancement of the exothermic and endothermic peaks ( Fig. 1A-C) can be attributed to the transition from liquid to solid state under pressure loading and the reverse transition as a result of pressure release, respectively. The magnitude of the pressure depends directly on the temperature. The higher the temperature is, the greater the pressure is required. So, at 305 K only 100 MPa can trigger the phase transition, but at 356 K a high pressure of 367 MPa is required. In the solid state, like at 294 K, the pressure can't drive any phase transformations, and thus the abnormal increase of sample's temperature is absent. The different behaviors of endothermic and exothermic peaks, sharp and single or broad and distorted, can be understood in terms of the cooperation and competition between pressure and temperature (Supplementary Note 1).
Since the present testing apparatus cannot be fully insulated, the precision of adiabatic temperature change (|ΔTd|, i.e. the magnitude of temperature jump in the T(t) curves) will be strongly affected by the exothermic and endothermic time. By analyzing the original data (Supplementary Note 1), the reliable |ΔTd| for C18H38, C16H34 and C14H30, are shown in Fig. 1D, Fig. 1E and Supplementary Fig. 3D, respectively. For all samples, |ΔTd| increases almost linearly with pressure when the pressure is too small to drive the LS phase transition. When the pressure is larger than the critical value, the extra contribution from the LS phase transition comes in and results in an abrupt increase of |ΔTd|. In this case, a large |ΔTd| can be accepted under the low pressure as soon as setting the temperature slightly above TLS. When the pressure is increased to a high value, a much larger |ΔTd| was obtained. For example, |ΔTd| reaches ~ 45 K under 300 MP and ~ 57 K under 400 MPa for present samples. But in the solid state, a high pressure of 500 MPa can only induce a small |ΔTd| (~10 K).
Based on the DSC results at ambient pressure ( Supplementary Fig. 4) and DTA signals recorded at different pressures ( Supplementary Fig. 5), the temperature dependent entropy change solely due to the LS phase transition (denoted as ΔSLS) for C18H18 and C16H34 can be obtained ( Supplementary Fig. 6). In combination with the specific heat results reported 25 , the temperature dependent total entropy, ΔSt(T), was constructed at different pressures ( Supplementary Fig. 7). Finally, the pressure driven entropy changes, ΔSir(T) (the irreversible one), were derived and plotted in Supplementary Fig. 8. The derived reversible entropy changes, ΔSr(T)s, were shown in Fig. 1F and Fig. 1G for C18H18 and C16H34, respectively. A small pressure of about 40 MPa and 58MPa can nearly activate the total ΔSr(T) of 698 J K -1 kg -1 and 759 J kg -1 K -1 for C18H38 and C16H36, respectively. With further increasing pressure, ΔSr(T) is increased slightly to 779 J kg -1 K -1 at 232 MPa for C18H38, and 808 J kg -1 K -1 at 152 MPa for C16H34. Furthermore, the temperature window of the colossal and reversible ΔSr(T), i.e., the "platform" in the ΔSr(T) curve, expands with increasing pressure. For C18H38, it reaches ~38 K at 232 MPa, while for C16H34 it reaches ~22 K at 152 MPa. Such a temperature window for reversible BC effect is much wider than that reported in other colossal BC materials, such as NPA (less than 10 K at 330 MPa) 10 . The wide temperature window is a premise for designing cooling devices with a broad operating temperature range. Additionally, we note that ΔSr(T) in Supplementary Fig. 9 is underestimated because the calculated St(T) curves are based on the specific heat at ambient condition (Supplementary Note 2) since the pressure-dependent specific heat is not available.
The maximum |ΔTd| and |ΔSr| values as a function of pressure were summarized and shown in Fig. 2A and Fig. 2B for CnH2n+2 (n=14, 16 and 18) along with those reported for existing BC materials 10,[13][14][15][16][17]20,21,[29][30][31][32][33][34][35][36][37][38][39] . Here, the isothermal entropy change in references is mainly obtained by indirect method or quasi-direct method 6 . According to different treatment methods, reversible entropy change (|ΔSr|) and non-reversible entropy change (|ΔSir|) can be obtained. In literatures, the adiabatic temperature changes were measured either by direct measurement (|ΔTd|), or by quasi-direct method (reversible adiabatic temperature changes |ΔTr| and non-reversible adiabatic temperature changes |ΔTir|) 6 . In general, |ΔSir| and |ΔTir|, which ignore the inherent thermal hysteresis effect, are easily overestimated compared with |ΔSr| and |ΔTr|, while |ΔTd| is often less than the real value as it is hard to get a fully adiabatic environment.  10 . Overall, compared with the other BC materials, CnH2n+2 shows more excellent BC performance under the pressure window tested, especially in the low-pressure range. The |ΔSr| of CnH2n+2 under 50 MPa reaches ~700 J kg -1 K -1 , which already lies in the scope of entropy change for commercial Freon-based refrigerants and is even larger than that for the widely used R134a (~520 J kg -1 K -1 ) 8 . The excellent low-pressure BC performance can ensure a strong cooling ability for the massive loading, which is beneficial to their practical applications as caloric refrigerants.
To give an insight into the mechanism of the colossal BC effect in n-alkanes, we performed the theoretical calculation for C18H38 by combining the classical molecular dynamics (MD) simulation [40][41][42][43] and first-principles calculation based on density functional theory (DFT) 44,45 . The coexisting solid-liquid phases was used to simulate the melting temperature of C18H38, since the two-phase MD method is more accurate for the melting simulation 42,43 . To acquire the exact thermodynamic data of C18H38, onephase MD method was employed and the related temperature ( S MD T ) is larger than the real temperature due to the superheating problem. Figure 3A shows that the evolutions of TLS and ΔSLS (calculated from the enthalpy change shown in Supplementary Fig. 10) with pressure present a high consistency with the experiment results 26,27 This indicates the rationality of the relevant models and parameters adopted in the present MD simulation. The previous studies definitely indicate that DFT is highly reliable in estimating the lattice vibration entropy (Svib) of crystalline materials 46 . Therefore, the Svib of C18H38 in solid state was estimated by this mean and compared with the total entropy (St) obtained by experiments. The results indicate the Svib always contributes dominantly to St for solid C18H38, while its proportion decreases as the temperature is raised (Fig. 3B). At 100 K, Svib accounts for about 94.6% of St. When the temperature is close to TLS, i.e., 290 K, the value drops to 92.3%, indicating the involvement of other contributions than the lattice vibrations.
The n-alkanes have a simple chain structure in solid state (Fig. 3C). As shown in Supplementary Fig. 11, the spatial distribution of the bond lengths (C-C and C-H) is enhanced upon heating. Accordingly, when heating towards TLS, the long-range structure is gradually collapsed (Fig. 3D) and the configurational entropy increases, which is in accordance with the DFT results. After entering the liquid state, the irregular vibrations of the C and H atoms are significantly enhanced (Supplementary Video 1). The long-range structural order is completely lost (Fig. 3E) and bond lengths are highly dispersed, corresponding to an extremely high configuration entropy. It is the remarkable structural difference between solid and liquid states that results in the different pressure-response behaviors, which will be discussed in the following paragraph. is increased to 400 K, which is close to TLS, the molecular chains show a weak twisting, but each molecule is relatively independent and does not twine with the others (Fig. 3D). The RDF peaks are broadened relative to those at S MD T = 300 K ( Supplementary Fig. 11). At S MD T = 400 K, applying 200 MPa makes the structure more ordered than that at 0 MPa (Fig. 3D). Accordingly, RDF shows visible response to this pressure (Fig. 3G). When S MD T was further increased to 500 K, C18H38 is completely in liquid state. Due to the strong atomic irregular vibration (Supplementary Video 1), the molecular chains are severely twisted and entangled with each other (Fig. 3E), and the RDF peaks are highly collapsed and broadened ( Supplementary Fig. 11). At 200 MPa, the winding of molecular chains is weakened and all RDF peaks are significantly narrowed (Fig. 3H), which should be correlated with the suppressed atomic irregular vibrations. Accordingly, the configuration entropy is greatly suppressed even though a LS phase transition is not yet triggered at this pressure. This explains the considerably large incipient BC effect in the liquid state that we observed under pressures less than the critical value (e.g., Fig. 1D and E). When the pressure reaches the critical value, the n-alkanes undergo the LS transition, the configurational entropy will be greatly suppressed as the structure becomes long-range ordered. The LS transition brings upon a huge thermal response in addition to the incipient one. As a result, the colossal BC effect occurs in n-alkanes.
For the most solid-state BC materials (such as AgI, ANMn3, Ni1-xFexS and etc) 12,15,16,20 , the thermal response to the external pressure is solely due to the first-order phase transition. However, as shown in Fig. 1D and E for CnH2n+2, the incipient contribution can be close to the half of the total |ΔTd|. For instance, at 342 K for C16H34, |ΔTd| is about 20 K at 293 MPa. At 367 MPa, the pressure-induced LS transition happens and |ΔTd| jumps to 47 K. The incipient BC effect could be inherent to liquids that are much more compressible than solids, which favors a colossal BC effect based on LS transition.
The TLS of n-alkanes CnH2n+2 is strongly dependent on the n value and can range from ~247 K to ~356 K when n increases from 11 to 40, which supplies a large temperature window for BC applications 23,25,26 . Besides, the n-alkanes have the advantages of self-nucleation to avoid supercooling, non-corrosiveness, long-term chemical stability without segregation, and commercial availability at reasonable costs 22 . Nowadays, n-alkanes, as the main component of paraffin, have been widely used for the storage of solar thermal energy in buildings, heat pumps, and spacecraft [22][23][24] . Practically, paraffin wax can be sealed into capsules with variable shapes to improve the heat transfer rate and avoid liquid leakage, and metal particles or flakes were often added in paraffin to improve its thermal conductivity 22,23 . As a caloric refrigerant, nalkanes may also need to be sealed in elastic containers (plastic tubes in our measurement) so that external pressure can penetrate through. Therefore, many technical solutions for thermal energy storage based on paraffin can be readily invoked for the applications of n-alkanes as refrigerants of caloric cooling in future.
In summary, we reported the colossal BC effect near room temperature in n-alkanes CnH2n+2 (n=14, 16 and 18). The n-alkanes exhibit extremely huge thermal responses to pressure near room temperature, which outperforms those ever reported in any types of caloric materials. The theoretical calculations based on DFT and MD methods indicate a significant reduction of configuration entropy at low pressures, which causes an incipient BC effect. When the external pressure is strong enough to induce the LS transition, the long-range structure is formed and thus the configuration entropy is fully suppressed. Both mechanisms work together, leading to the colossal BC effect. The excellent BC performance, tunable operating temperatures, lost-cost raw materials, good environmental friendliness and well-known thermal properties suggest n-alkanes are promising refrigerants for caloric cooling. This work also indicates that more excellent BC materials could be obtained based on the LS transition materials in the near future.

Methods
DTA measurement. The Pressure-DTA equipment was constructed for calorimetry measurement under different hydrostatic pressures. One end of K-type thermocouple along with C n H 2n+2 was sealed in a separate plastic capsule, and the other end along with the reference compound (i.e. C n H 2n+2 with different n) was sealed in another capsule. Then they all were put into the DTA cell made of Teflon, using Daphne oil 7373 as the pressure medium. The Teflon cell was inserted in a Be-Cu based pressure cylinder. The hydrostatic pressure was applied by the hydraulic machine. The annular heating sheet is adhered to the outer surface of the cylinder, which is used for the temperature control in liquid nitrogen dewar. During the experiment, the heating and cooling rate was set at 1 K/min. The entropy change at the first order phase transition under ambient pressure was evaluated by the differential scanning calorimeter (DSC). Based on the DSC and DTA results, the entropy change of first-order phase transition under different pressures can be calculated.
Finally, the applied pressure will be corrected according to the measured phase transition temperature and the reported transition temperature-pressure phase diagram 26,27 .
Adiabatic temperature change measurement. When it comes to the direct measurement of the adiabatic temperature change, the same pressure apparatus used in DTA measurement was employed. Due to the high liquidity in liquid and extreme low modulus, the C n H 2n+2 itself can serve as the pressure medium. So, one end of K-type thermocouple along with C n H 2n+2 was sealed in the DTA cell made of Teflon, and the other end was embedded in the Be-Cu based pressure cylinder. The measurements were carried out at the desired temperatures in cooling process and the data was collected in both pressure loading and unloading processes. Pressure was applied quickly to target values by manual means and maintained stably throughout the heat release cycle. Then the pressure relief value was opened and the pressure was released. The present hydraulic machine using the single-acting cylinder can realize the instant release of pressure, which is much faster than the pressure loading process.

Theoretical calculation methods.
To investigate the vibrational properties of C 18 H 38 in the solid phase, we calculate the force constants using the finite displacement method implemented in the Vienna Ab initio Simulation Package (VASP) 44 and the PHONOPY code 45 . The 2×2×2 supercell of fully-relaxed C 18 H 38 structure containing 448 atoms is constructed. The Brillouin zone (BZ) was sampled with an 8×8×2 k-point mesh for the structural relaxation of unit-cell and a 5×5×1 k-point mesh for the supercell calculations. The exchange-correlation interaction was treated by generalized gradient approximation (GGA), which is parameterized by Perdew-Burke-Ernzerhof (PBE) 47 . We use the Grimme DFT-D3 method to describe the long-range van der Waals (VDW) interactions 48 . The cut-off energy of 500 eV was used for the plane-wave basis expansion. The lattice constants and ion positions are optimized using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm with the force convergence criterion less than 10 −3 eV/Å. The vibrational entropy is calculated using vib = Here we should point out that we calculated the phonon and vibrational entropy with ignoring the thermal expansion effect, since the calculations incorporating the thermal expansion effect would require the third-order force constants, which is quite time-consuming for the C 18 H 38 supercell. To some extent, we may underestimate the vibrational entropy at high temperatures.
To get insight into the micro-process of solid-liquid phase change and the thermodynamic parameters, we perform the classic molecular dynamics (MD) simulations using the LAMMPS package with periodic boundary condition 40 . The adaptive intermolecular reactive empirical bond order (AIREBO) potential for a system of C-H atoms was used in our MD simulations 41 . The Newton equation of motion was integrated by the velocity Verlet algorithm and the time-step is 0.5 fs. We used the coexisting solid-liquid phases to simulate the melting temperature of C 18 H 38 , since the two-phase method is more accurate for the melting simulation 42,43 . To construct the coexisting solid-liquid phases, we first performed the MD simulation started with the 7×7×3 supercell (8232 atoms) in the NPT ensemble at 200 K to obtain the solid phase (1,000,000 time steps), and then heated the solid phase to 550 K (far beyond the melting point) to obtain the liquid phase (1,000,000 time steps). The obtained solid and liquid phases were constructed into the coexisting phase include solid-liquid interface. We performed the MD simulation for the coexisting solid-liquid phases in the NVE ensemble (1,000,000 time steps) to obtain the melting temperature. However, the two-phase method cannot obtain the useful thermodynamic data of C 18 H 38 from the solid to liquid phase during heating. We have to use the normal one-phase method, although it usually overestimates the melting temperature due to the superheating problem. Here we performed the MD simulations by directly heating the solid phase of the 7×7×3 supercell from 50 K to 550 K in the NPT ensemble for 15 ns (30,000,000 time steps). We evaluated the entropy change ∆ from the enthalpy change ∆ of solid-liquid phases by using ∆ = ∆ / m . Since the obtained temperature range of phase change is not narrow, the theoretically estimated entropy change may be inaccurate to a certain extent. However, it would not hinder us to analysis the law of the phase change under pressure comparing with the experimental data. The radial distribution function (RDF) and the bond-angle statistics are using RINGS code from the MD results 49 .

Data availability
All relevant data are presented via this publication and Supplementary Information.  Fig. 2. The comparision of BC performance between C n H 2n+2 and existing BC materials. Maximum adiabatic temperature change (A) and isothermal entropy change (B) as a function of pressure for C18H38, C16H34 and C14H30, are shown along with the reported BC materials. Here, the isothermal entropy change in references is mainly obtained by indirect or quasi-direct methods. According to different methods, reversible (|ΔSr|) and non-reversible entropy changes (|ΔSir|) can be obtained in literatures. For the adiabatic temperature changes, some were measured by direct measurement (|ΔTd|). Others were estimated by quasi-direct method, corresponding to either reversible (|ΔTr|) or irreversible values (|ΔTir|).   The comparision of BC performance between CnH2n+2 and existing BC materials. Maximum adiabatic temperature change (A) and isothermal entropy change (B) as a function of pressure for C18H38, C16H34 and C14H30, are shown along with the reported BC materials. Here, the isothermal entropy change in references is mainly obtained by indirect or quasi-direct methods. According to different methods, reversible (|ΔSr|) and non-reversible entropy changes (|ΔSir|) can be obtained in literatures. For the adiabatic temperature changes, some were measured by direct measurement (|ΔTd|). Others were estimated by quasi-direct method, corresponding to either reversible (|ΔTr|) or irreversible values (|ΔTir|).

Supplementary Files
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