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Crystal structures and thermodynamic properties of phase change materials (1-CnH2n+1NH3)2CdCl4(s) (n = 15 and 16)
Renewable Energy 50 (2013) 498e505
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Crystal structures and thermodynamic properties of phase change materials (1-CnH2nþ1NH3)2CdCl4(s) (n ¼ 15 and 16) D.F. Lu, Y.Y. Di*, D.H. He Shandong Provincial Key Laboratory of Chemical Energy Storage and Novel Cell Technology, College of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2012 Accepted 16 July 2012 Available online 12 August 2012
Two novel crystalline compounds (1-C15H31NH3)2CdCl4(s) and (1-C16H33NH3)2CdCl4(s), which may be used as the solidesolid phase change materials, were synthesized. X-ray crystallography was applied to characterize crystal structures of the two compounds. Both of them are monoclinic, the space group is both C2/ c, and Z ¼ 4. Lattice potential energies (UPOT) of the title compounds were calculated to be 832.31 kJ mol1 for (1-C15H31NH3)2CdCl4(s) and 814.26 kJ mol1 for (1-C16H33NH3)2CdCl4(s). Low-temperature heat capacities of the two compounds were measured by a precise automatic adiabatic calorimeter in the temperature range from 78 to 395 K. The temperatures, molar enthalpies and entropies of two phase transitions for each of the two compounds were determined. The smoothed heat capacities and thermodynamic functions of the two compounds relative to the standard reference temperature 298.15 K were calculated and tabulated at 5 K intervals based on experimental heat capacities. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: X-ray crystallography Crystal structure Adiabatic calorimetry Low-temperature heat capacity Solidesolid phase transitions Energy conversion
1. Introduction With social development, energy crisis is becoming more and more serious. Thermal energy storage is a relatively new technology with a growing interest for many thermal applications. Phase change materials (PCMs) are one of the most important thermal energy storage materials due to high latent heat storage density and almost constant temperature during phase change. Bis-alkylammonium tetrahalogenometallate (II) (1CnH2nþ1NH3)2MX4, in which M is a divalent transition metal atom, X is a halogen atom, and n varies between 8 and 18, is a kind of important solidesolid phase change material [1e5]. It is mainly composed of thick alkylammonium layer (1-CnH2nþ1NH3)þ and thin inorganic layer [MCl4]2, and each alkylammonium chain is bound to the layer [MCl4]2 by NeH.Cl hydrogen bonds [6]. Bisalkylammonium tetrachlorometallate (II) can be also called as a layered perovskite compound. Phase change materials have many applications fields, such as solar energy storage, waste heat recovery, smart air-conditioning buildings, temperature-adaptable greenhouses, electric appliances with thermostatic regulator, energy storage kitchen utensil, and insulation clothing [7]. And due to some unique properties which
* Corresponding author. College of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, PR China. Tel.: þ86 635 8230645; fax: þ86 635 8239121. E-mail addresses: [email protected], [email protected] (Y.Y. Di). 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.07.016
solidesolid phase change material owns during phase transition, such as small change in volume, no volatilization and shape plasticity, this kind of material has attracted the great attention in recent years. In this paper, crystal compounds (1-C15H31NH3)2CdCl4(s) and (1-C16H33NH3)2CdCl4 are synthesized, and their crystal structures are characterized by X-ray crystallography. Low-temperature heat capacities of the two compounds are measured by a precise automatic adiabatic calorimeter in the temperature range from (78e395) K and their thermodynamic properties of solidesolid phase transitions are determined. 2. Materials and methods 2.1. Materials Anhydrous methyl alcohol as the solvent, n-pentadecylamine (J&K Scientific Ltd. China), n-cetylamine (J&K Scientific Ltd. China), hydrochloride acid (37%) and cadmium chloride hydrate as the reactants are all of analytical grade. The reactants are accurately weighed at molar ratio of n[(1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16)]:n(hydrochloride acid):n(CdCl2∙2.5H2O) ¼ 2:2:1. Hydrochloride acid is slightly excessive and slowly dissolved in anhydrous methyl alcohol. The mixture is heated by an electric jacket, stirred under boiling, and refluxed for 4 h. The final solution is laid aside, and several days later, the colorless transparent crystals are obtained. The crystals are washed by ether three times and
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505 Table 1 Crystal data and structure refinement for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16)(s). Name of the properties
Crystallographic data and structure refinement
Empirical formula Formula weight Temperature Wavelength Crystal system Space group Unit cell dimensions
C30H68CdCl4N2 711.06 298(2) K 0.71073 Å Monoclinic C2/c a ¼ 69.062(5) Å; b ¼ 7.4588(8) Å; c ¼ 7.3299(5) Å; a ¼ 90 ; b ¼ 91.1090(10); g ¼ 90
Volume Z Calculated density Absorption coefficient F(000) Crystal size Theta range for data collection Limiting indices
3775.0(5) Å3 4 1.251 g cm3 0.881 mm1 1512 0.50 0.46 0.08 mm 1.77e25.02
C32H72CdCl4N2 739.12 298(2) K 0.71073 Å Monoclinic C2/c a ¼ 72.750(5) Å; b ¼ 7.4670(8) Å; c ¼ 7.3361(7) Å; a ¼ 90 ; b ¼ 91.5030(10) ; g ¼ 90 3983.8(6) Å3 4 1.232 g cm3 0.838 mm1 1576 0.41 0.30 0.09 mm 2.24e25.02
75 h 81, 5 k 8, 8 l 7 8816/3332 [R(int) ¼ 0.00752] 99.6%
86 h 70, 6 k 8, 8 l 8 9351/3512 [R(int) ¼ 0.0596] 99.5%
Semi-empirical from equivalents 0.9328 and 0.6670
Semi-empirical from equivalents 0.9284 and 0.7251
Full-matrix leastsquares on F2 3332/219/171
Full-matrix leastsquares on F2 3512/240/180
1.108 R1 ¼ 0.1059, wR2 ¼ 0.3228
1.157 R1 ¼ 0.1198, wR2 ¼ 0.3304 R1 ¼ 0.1377, wR2 ¼ 0.3469 2.526 and 1.791 e Å3
Reflections collected/ unique Completeness to q ¼ 25.02 Absorption correction Max. and min. transmission Refinement method Data/restraints/ parameters Goodness-of-fit on F2 Final R indices [I > 2sigma(I)] R indices (all data) Largest diff. peak and hole
R1 ¼ 0.1345, wR2 ¼ 0.3502 2.364 and 1.354 e Å3
recrystallized three times by anhydrous methyl alcohol. Finally, the sample is placed in a vacuum desiccator (at T ¼ 310 K) to dry in vacuum for 5 h, the final product is put into a weighing bottle and preserved in a desiccator. Theoretical contents of C, H, N, Cd, and Cl in the compound (1-C15H31NH3)2CdCl4(s) are calculated to be 50.67%, 9.64%, 3.94%, 15.81% and 19.94%, and for (1C16H33NH3)2CdCl4(s) they are 52.00%, 9.82%, 3.79%, 15.21% and 19.18%. Chemical and elemental analysis (model: PE-2400, Perkin Elmer, USA) show that the practical contents of C, H, N, Cd, and Cl in the compound (1-C15H31NH3)2CdCl4(s) are measured to be 50.64%, 9.65%, 3.96%, 15.80% and 19.95%, and those in the compound (1C16H33NH3)2CdCl4(s) are 51.97%, 9.81%, 3.78%, 15.23% and 19.21%. These results show that the purities of the two samples prepared are above 0.995 in mass fraction. 2.2. Methods 2.2.1. X-ray crystallography X-ray crystallography is applied to characterize crystal structures of the two compounds. A crystal is glued to a fine glass fiber and then mounted on Bruker Smart-1000 CCD diffractometer with Mo-Ka radiation, l ¼ 0.71073 Å. The intensity data are collected in the 4eu scan mode at T ¼ 298(2) K. The empirical absorption corrections are based on multi-scan. The structures are solved by direct method and different Fourier syntheses, and all non-hydrogen atoms are refined
499
Table 2 Selected bond lengths (Å) and bond angles (deg) for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s)a,b. (1-C15H31NH3)2CdCl4 Cd(1)eCl(2)#1 Cd(1)eCl(2) Cd(1)eCl(1)#2 Cd(1)eCl(1)#3 Cd(1)eCl(1)#1 Cd(1)eCl(1) Cl(1)eCd(1)#4 Cl(2)#1eCd(1)eCl(2) Cl(2)#1eCd(1)eCl(1)#2 Cl(2)eCd(1)eCl(1)#2 Cl(2)#1eCd(1)eCl(1)#3 Cl(2)eCd(1)eCl(1)#3 Cl(1)#2eCd(1)eCl(1)#3 Cl(2)#1eCd(1)eCl(1)#1
2.564(3) 2.564(3) 2.646(3) 2.646(3) 2.650(3) 2.650(3) 2.646(3) 180.00(2) 90.58(11) 89.42(11) 89.42(11) 90.58(11) 180.00(15) 88.45(11)
Cl(2)eCd(1)eCl(1)#1 Cl(1)#2eCd(1)eCl(1)#1 Cl(1)#3eCd(1)eCl(1)#1 Cl(2)#1eCd(1)eCl(1) Cl(2)eCd(1)eCl(1) Cl(1)#2eCd(1)eCl(1) Cl(1)#3eCd(1)eCl(1) Cl(1)#1eCd(1)eCl(1) Cd(1)#4eCl(1)eCd(1) Cl(1)#2eCd(1)eCl(1)#3 Cl(2)#1eCd(1)eCl(1)#1 Cl(2)eCd(1)eCl(1)#1 Cl(1)#2eCd(1)eCl(1)#1 Cl(1)#3eCd(1)eCl(1)#1
91.55(11) 88.11(2) 91.89(2) 91.55(11) 88.45(11) 91.89(2) 88.11(2) 180.00(18) 161.77(15) 180.00(15) 88.45(11) 91.55(11) 88.11(2) 91.89(2)
(1-C16H33NH3)2CdCl4 Cd(1)eCl(1)#1 Cd(1)eCl(1) Cd(1)eCl(2)#1 Cd(1)eCl(2) Cd(1)eCl(2)#2 Cd(1)eCl(2)#3 Cl(2)eCd(1)#4 Cl(1)#1eCd(1)eCl(1) Cl(1)#1eCd(1)eCl(2)#1 Cl(1)eCd(1)eCl(2)#1 Cl(1)#1eCd(1)eCl(2) Cl(1)eCd(1)eCl(2)
2.553(4) 2.553(4) 2.638(4) 2.638(4) 2.641(4) 2.641(4) 2.641(4) 180.00(3) 89.05(12) 90.95(12) 90.95(12) 89.05(12)
Cl(1)eCd(1)eCl(2)#2 Cl(2)#1eCd(1)eCl(2)#2 Cl(2)eCd(1)eCl(2)#2 Cl(1)#1eCd(1)eCl(2)#3 Cl(1)eCd(1)eCl(2)#3 Cl(2)#1eCd(1)eCl(2)#3 Cl(2)eCd(1)eCl(2)#3 Cl(2)#2eCd(1)eCl(2)#3 Cd(1)eCl(2)eCd(1)#4 Cl(2)#1eCd(1)eCl(2) Cl(1)#1eCd(1)eCl(2)#2
91.07(12) 88.04(2) 91.96(2) 91.07(12) 88.93(12) 91.96(2) 88.04(2) 180.00(18) 165.01(18) 180.00(18) 88.93(12)
a Symmetry codes: #1 [x þ 1/2, y þ 1/2, z]; #2 [x þ 1/2, y1/2, z þ 1/2]; #3 [x, y þ 1, z1/2]; #4[ex þ 1/2, y þ 1/2, ez þ 1/2]. b Symmetry codes: #1 [x þ 1/2, y þ 1/2, z þ 1]; #2 [x þ 1/2, y1/2, z þ 3/ 2]; #3 [x, y þ 1, z1/2]; #4 [x þ 1/2, y þ 1/2, z þ 3/2].
anisotropically on F2 by full-matrix least square method. All calculations are performed with the program package SHELXTL [8]. The crystal data and details of data collection and refinements for these compounds are summarized in Table 1. The selected bond lengths and angles for these compounds are listed in Table 2. The hydrogen bond lengths and angles of the compounds are presented in Table 3. We have applied for two CCDC numbers 787884 for (1C15H31NH3)2CdCl4 and 804713 for (1-C16H33NH3)2CdCl4. 2.2.2. Adiabatic calorimetry A precise automatic adiabatic calorimeter is used to measure molar heat capacities of the two compounds in the temperature range from 78 to 395 K. The calorimeter is established in Thermochemistry Laboratory of College of Chemistry and Chemical Engineering, Liaocheng University, China. The principle and performance of the adiabatic calorimeter and the procedure of heat Table 3 Hydrogen bond lengths (Å) and bond angles (deg) for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s)a,b. DeH.A
d (DeH)
d (H.A)
d (D.A)
<(DHA)
(1-C15H31NH3)2CdCl4 N(1)–H(1A)#1.Cl(2) N(1)–H(1B)#2.Cl(1) N(1)–H(1B)#3.Cl(1) N(1)–H(1C)#4.Cl(2) C(1)–H(1E)#2.Cl(2)
0.89 0.89 0.89 0.89 0.97
2.56 2.63 2.75 2.56 2.82
3.375(15) 3.289(14) 3.484(14) 3.187(13) 3.74(2)
153 131 141 128 159
(1-C16H33NH3)2CdCl4 N(1)-H(1A).Cl(1)#1 N(1)-H(1B).Cl(2)#2 N(1)-H(1B).Cl(2) N(1)-H(1C).Cl(1)#3
0.89 0.89 0.89 0.89
2.81 2.61 2.64 2.93
3.234(18) 3.297(19) 3.338(19) 3.67(2)
110.8 135.1 135.7 140.9
a Symmetry codes: #1 [x, y þ 1, z þ 1/2]; #2 [x, y, z þ 1]; #3 [x, y þ 1, z þ 1/2]; #4 [x, y þ 1, z þ 1]. b Symmetry codes: #1 [x, y þ 1, z]; #2 [x, y þ 1, z1/2]; #3 [x, y þ 1, z þ 1/2].
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D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
Fig. 1. Molecular structures. (a) (1-C15H31NH3)2CdCl4; (b) (1-C16H33NH3)2CdCl4.
capacity measurement are described in detail elsewhere [9,10]. Heat capacity measurement is continuously and automatically carried out by the standard method of intermittently heating the sample and alternately measuring the temperature. The liquid nitrogen is used as the refrigerating medium. The heating rate and temperature increment during heat capacity measurement are generally controlled at 0.1e0.4 K min1 and 1e3 K. The heating duration is 10 min, and the temperature drift rate of the sample cell measured in an equilibrium period is always kept within 104 K min1 during the acquisition of all heat capacity data. The data of heat capacity and corresponding equilibrium temperature [10] are corrected according to heat exchange of the sample cell with its surroundings. The reliability of the performance of the calorimeter is confirmed by measuring heat capacities of the reference standard material (a-Al2O3) in the temperature range from 78 to 400 K. Deviations of experimental results from the
smoothed curve lie within 0.20%, while the uncertainty is 0.30%, as compared with the data given by the former National Bureau of Standards [11] in the whole temperature range. The sample masses used for calorimetric measurement is 1.93755 g for (1-C15H31NH3)2CdCl4(s), and 1.81725 g for (1C16H33NH3)2CdCl4(s), which is equivalent to 2.725 103 mol and 2.459 103 mol on the basis of their molar masses M[(1C15H31NH3)2CdCl4, s] ¼ 711.06 g mol1 and M[(1-C16H33NH3)2CdCl4, s] ¼ 739.12 g mol1. 3. Results 3.1. Crystal structures of (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) It is found from Table 1 that crystal structures of the two compounds are both monoclinic and their space groups are
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
both C2/c, and Z ¼ 4. Their unit cell dimensions are also very close. The molecular structures of (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) in crystallographic independent units are plotted in Fig. 1, which shows that both of them have one type of nonequivalent alkylammonium chains. It can be seen from Fig. 1 and Table 2 that the central ion (Cd2þ) in the two compounds adopts the sixcoordinated configuration, an octahedral geometry is produced, and an infinite net is formed from ½CdCl4 2n n . The packing structures of the unit cells of the two complexes are shown in Fig. 2. It can found from Fig. 2 that the space structures of (1-C15H31NH3)2CdCl4 and (1-C16H33NH3)2CdCl4 are very alike when viewing along c-axis or b-axis, and the monomeric ½CdCl4 2n n moieties bind with the monomeric [1-CnH2nþ1NH3]þ (n ¼ 15 and 16) through several hydrogen bonds (see Table 3). The compound (1C15H31NH3)2CdCl4(s) not only includes classical NeH.Cl hydrogen bonds, but also has non-classical C(1).H(1E).Cl(2) hydrogen bonds. The bond length of C(1).Cl(2) equals 3.74(2) Å and the bond angle of C(3)eH(3A).Cl(2) is 159 , and the symmetry code is [x, y, and zþ1]. For both of the two compounds, the symmetric units are stacked, a sandwich construction is formed, the units ½CdCl4 2n n reside in the “sandwich floor”, an infinite two-dimensional plane is
501
formed along the bc-plane, and on account of binding action of the hydrogen bonds the molecule unit extends to a space supermolecule, which helps to establish a two-dimensional perovskite structure. The results indicate that the hydrogen bonds play an important role in the stabilization of the whole structures of the two compounds. The steric configurations of the two compounds are similar to other compounds (1-CnH2nþ1NH3)2MCl4(s). 3.2. Lattice potential energy The title compounds (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s) can be regarded as a simple salt of the type M2X (charger ratio 1:2), and the lattice potential energy of the compound can be obtained from the formula [12],
UPOT ¼ g
r Mm
1=
3
þd:
(1)
in which the constants g ¼ 8375.6 kJ mol1 cm and d ¼ 178.8 kJ mol1 for the salt with a formula M2X (charge ratio 1:2). From crystal structure information of Table 1, for the crystal (1C15H31NH3)2CdCl4, r ¼ 1.251 g cm3 and Mm ¼ 711.06 g mol1, and
Fig. 2. Packing of structure. (A) viewing along b-axis; (B) viewing along c-axis. (a) (1-C15H31NH3)2CdCl4; (b) (1-C16H33NH3)2CdCl4 (Dashed lines represent the hydrogen bonds. Hydrogen atoms are omitted for clarity).
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for the crystal (1-C16H33NH3)2CdCl4, r ¼ 1.232 g cm3 and Mm ¼ 739.16 g mol1, lattice potential energies of the two compounds are calculated as UPOT [(1-C15H31NH3)2CdCl4, s] ¼ 832.31 kJ mol1 and UPOT [(1-C16H33NH3)2CdCl4, s] ¼ 814.26 kJ mol1. 3.3. Low-temperature heat capacities The experimental results of low-temperature heat capacities are plotted in Fig. 3. It can be seen from Fig. 3(a) for (1C15H31NH3)2CdCl4(s) that two continuous endothermic peaks appear in the temperature ranges from 337 to 352 K and from 352 to 363 K. The experimental heat capacities in the temperature ranges from 78 to 337 K and from 363 to 395 K are fitted by least square method, and two polynomial equations of experimental molar heat capacities (Cp,m) vs. reduced temperature (X), X ¼ f (T), are obtained as follows: Before phase transition from 78 to 337 K, Fig. 4. Comparison for curves of experimental molar heat capacities for (1C15H31NH3)2CdCl4 and (1-C16H33NH3)2CdCl4.
Cp;m ¼ 805:497 þ 497:519X 3:122X 2 59:849X 3 199:497X 4 þ 167:811X 5 þ 239:519X 6 :
(2)
After phase transition from 363 to 395 K,
Cp;m ¼ 1382:009 þ 90:047X þ 5:512X 2 þ 24:912X 3 þ 15:659 X 4 15:351X 5 19:198X 6 :
(3)
X represents the reduced temperature, X ¼ [T(TmaxTmin)/2]/ [(Tmax þ Tmin)/2], T represents the experimental temperature, Tmax and Tmin represent the upper and lower limits in the temperature regions. The correlation coefficient of the fitting R2 ¼ 0.99996 and 0.99976 corresponding to Eqs. (2) and (3). Similarly, it is also seen from Fig. 3(b) for (1-C16H33NH3)2CdCl4 that two continuous endothermic peaks appear in the temperature ranges from 343 to 354 K and from 354 to 365 K. The experimental heat capacities in the temperature ranges from 78 to 343 K and from 365 to 390 K are fitted by least square method as follows: Before phase transition from 78 to 343 K,
Cp;m ¼ 458:518 þ 200:564X 13:938X 2 68:033X 3 188:460X 4 þ 102:685X 5 þ 167:550 X 6 :
(4)
After phase transition from 365 to 390 K,
Cp;m ¼ 692:565 þ 16:375X 1:135X 2 þ 0:860X 3 þ 0:241X 4 :
(5)
2
The correlation coefficients of the fitting R ¼ 0.99933 and 0.99929 corresponding to Eqs. (4) and (5). 3.4. Molar enthalpy and entropy of solidesolid phase transition Three series of repeated heat capacity experiments during the whole phase transitions are carried out after the sample is treated Table 4 Results of the two phase transitions obtained from three series of repeated experiments of (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s). Thermodynamic properties (1-C15H31NH3)2CdCl4 Ttrs,1/K DtrsHm,1/(kJ mol1) DtrsSm,1/(J K1 mol1) Ttrs,2/K DtrsHm,2/(kJ mol1) DtrsSm,2/(J K1 mol1) (1-C16H33NH3)2CdCl4 Ttrs,1/K DtrsHm,1/(kJ mol1) DtrsSm,1/(J K1 mol1) Ttrs,2/K DtrsHm,2/(kJ mol1) DtrsSm,2/(J K1 mol1) a
Fig. 3. Curves of experimental molar heat capacities. (a) (1-C15H31NH3)2CdCl4; (b) (1C16H33NH3)2CdCl4.
Series 1 xi
Series 2 xi
Series 3 xi
Mean value (x sa)a
347.99 50.68 145.63 356.85 42.64 119.49
346.28 49.07 141.71 356.45 40.98 114.95
346.93 49.44 142.50 355.62 41.52 116.76
(347.07 (49.73 (143.28 (356.31 (41.71 (117.07
0.50) 0.49) 1.20) 0.36) 0.49) 1.32)
350.22 24.71 70.55 361.11 22.95 63.54
350.06 24.07 68.77 360.91 23.67 65.59
349.40 24.76 70.87 359.89 22.80 63.37
(349.89 (24.51 (70.06 (360.64 (23.14 (64.17
0.25) 0.22) 0.65) 0.38) 0.27) 0.71)
x qX is the mean value of a set of measurement results; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ðx xÞ2= , n is the experimental number; xi, a single value in i¼1 nðn 1Þ a set of measurements.
sa ¼
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
503
Table 5 Smoothed molar heat capacities and thermodynamic functions for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s). T K
Cp;m
HT H298:15 K
ST S298:15 K
Cp;m
HT H298:15 K
ST S298:15 K
J K mol1
kJ mol1
J K mol1
J K mol1
kJ mol1
J K mol1
157.27 155.99 154.59 153.08 151.43 149.66 147.75 145.72 143.56 141.28 138.88 136.36 133.73 130.99 128.14 125.19 122.13 118.97 115.72 112.36 108.91 105.37 101.72 97.984 94.149 90.217 86.190 82.066 77.847 73.532 69.122 64.619 60.022 55.332 50.553 45.683 40.726 35.682 30.551 25.334 20.030 14.637 9.1525 3.5702 0 2.1171 7.9199 13.852 19.931 26.181 32.628 39.308 46.262
822.98 807.49 791.49 775.00 758.06 740.72 723.01 704.97 686.64 668.07 649.28 630.32 611.21 591.99 572.68 553.31 533.89 514.43 494.96 475.49 456.01 436.55 417.09 397.65 378.22 358.80 339.40 320.01 300.63 281.27 261.91 242.57 223.24 203.93 184.63 165.36 146.10 126.88 107.68 88.514 69.374 50.257 31.153 12.047 0 7.0820 26.266 45.546 64.977 84.628 104.59 124.96 145.87
145.03 151.61 158.34 165.20 172.22 179.39 186.75
426.64 444.54 462.60 480.79 499.12 517.65 536.37
(1-C15H31NH3)2CdCl4 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 298.15 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395
245.216 267.507 291.454 316.471 342.079 367.894 393.617 419.023 443.950 468.295 491.996 515.034 537.421 559.192 580.400 601.112 621.401 641.344 661.016 680.488 699.823 719.074 738.283 757.480 776.682 795.892 815.100 834.287 853.422 872.467 891.382 910.123 928.650 946.931 964.948 982.698 1000.21 1017.53 1034.75 1052.03 1069.56 1087.59 1106.47 1126.61 1140.19 1148.55 1172.89 1200.38 1231.90 1268.47 1311.27 1361.64 1421.14 Phase change Phase change Phase change Phase change Phase change 1299.19 1330.49 1359.52 1387.67 1418.01 1453.73 1483.59
(1-C16H33NH3)2CdCl4
with different cooling rates so that the reversibility and repeatability of the phase transitions of the sample are verified. The cooling rate of the series 1 is about 15 K min1 (liquid nitrogen used as the cooling agent), that of the series 2 is about 2.5 K min1 (ice-
192.89 204.88 217.76 231.17 244.81 258.41 271.81 284.85 297.44 309.51 321.03 332.00 342.42 352.34 361.80 370.84 379.53 387.92 396.07 404.04 411.87 419.61 427.29 434.94 442.56 450.17 457.76 465.31 472.80 480.19 487.44 494.51 501.34 507.90 514.14 520.01 525.49 530.55 535.20 539.45 543.37 547.02 550.52 554.04 556.36 557.79 562.03 567.10 573.39 581.40 591.69 604.91 621.84 643.36 Phase change Phase change Phase change Phase change Phase change 682.18 689.24 695.80 702.20 708.91
89.76 88.76 87.71 86.59 85.40 84.14 82.81 81.42 79.97 78.45 76.87 75.24 73.55 71.82 70.03 68.20 66.32 64.40 62.44 60.44 58.40 56.32 54.21 52.05 49.86 47.63 45.36 43.05 40.70 38.32 35.90 33.45 30.96 28.43 25.88 23.29 20.68 18.04 15.37 12.69 9.980 7.254 4.510 1.749 0 1.031 3.830 6.653 9.504 12.39 15.32 18.31 21.38 24.54
488.31 476.29 464.19 452.01 439.77 427.47 415.14 402.78 390.41 378.06 365.72 353.43 341.19 329.01 316.91 304.90 292.98 281.15 269.43 257.81 246.29 234.88 223.57 212.36 201.24 190.22 179.28 168.43 157.66 146.97 136.36 125.82 115.36 104.97 94.656 84.424 74.275 64.213 54.242 44.368 34.595 24.925 15.362 5.9049 0 3.4495 12.708 21.883 30.993 40.065 49.132 58.242 67.453 76.837
77.54 80.97 84.43 87.93 91.45
225.91 235.11 244.29 253.43 262.53
water cooling), and that of the series 3 is about 0.5 K min1 (natural cooling). The results of three series of repeated experiments are plotted in the inset of Fig. 3. It can be seen from the inset that there are some slight differences in heights and widths of peaks
504
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
corresponding to each series of heat capacity measurements during phase transitions of the sample. However, the phase transitions basically exhibit good reversibility and repeatability, and different cooling rates do not almost affect the experimental results. A closed agreement in Cp,m values of each series of repeated experiment is obtained. The molar enthalpy of the phase transition (DtrsHm) in Cp,meT curve is obtained from Eq. (6). The molar entropy DtrsSm of the phase transition is calculated from the following thermodynamic Eq. (7): [13] (Fig. 4)
"
Dtrs Hm ¼ Q n,
ZTtrs
ZTf CPðiÞ dT n,
Ti 1
kJ mol
Dtrs Sm ¼ Dtrs Hm=T
CPðf Þ dT Ttrs
H0 dT Ti
# .
n (6)
(7)
where Ti in Eq. (6) represents the temperature when the phase transition starts, Tf represents the temperature when the phase transition finishes, CP(i) represents the heat capacity at the temperature Ti, CP(f) represents the heat capacity at the temperature Tf, Q represents the total heat quantity introduced to the calorimeter from temperature Ti to Tf, Ttrs represents the peak temperature of the phase transition of the sample, n represents the mole number of the sample, and H0 represents the heat capacity of the empty sample cell. The data of Q and H0 are calculated with the program stored in the computer linking with the adiabatic calorimetric system, and printed out along with experimental results of heat capacities. The results of Ttrs(K), DtrsHm(kJ mol1), and DtrsSm(J K1 mol1) obtained from every series of repeated experiment are listed in Table 4. For the two compounds, two continuous solidesolid phase transitions are found, which are similar to many other compounds (1-CnH2nþ1NH3)2MX4, so the mechanism [14e18] of the phase transition may be also similar. With the increase of temperature, the hydrogen bonds become weakened, which makes constraints become weakened. The between [1-CnH2nþ1NH3]þ and ½CdCl4 2n n disorder of partial alkylammonium chains occurs together with the reversal of polar NH3 groups, thus the structure of the molecule is transformed, and another kind of free and partly disordered solid phase is formed, which leads to a dynamic orderedisorder transition of rigid alkyl chains in the first phase transition. In the second phase transition, further conformational change of the hydrocarbon part is dominant, complete disorder of the conformation is assumed to be similar to a “molten” state. When the second phase transition is over, the whole solid phase is in complete disorder. After that, the solidesolid phase change has finished, and the compound maintains the stable structure of new solid phase until solideliquid phase change occurs. 3.5. Smoothed heat capacities and thermodynamic functions of the compounds The smoothed molar heat capacities and thermodynamic functions are calculated based on the fitted polynomial equations of heat capacities as a function of the reduced temperature (X) according to the following thermodynamic equations,
ZT ðHT H298:15 Þ ¼
Cp;m dT:
(8)
298:15
ZT ðST S298:15 Þ ¼ 298:15
Cp;m ,T 1 dT:
ZT Cp;m dT T$
298:15
Cp;m ,T 1 dT:
(10)
298:15
The polynomial fitted data of molar heat capacities and fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K are tabulated in Table 5 at an interval of 5 K. 4. Discussion
: ðJ=K molÞ:
m
ZTf
ZT ðGT G298:15 Þ ¼
4.1. The comparison of crystal structures and thermodynamic properties of the two compounds By comparison, some laws on crystal structures and thermodynamic properties of the two compounds is found as follows: (1) The crystal data and structure refinement for (1CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) show that they have similar unit cell parameters and similar two-dimensional perovskite structures. (2) UPOT [(1-C15H31NH3)2CdCl4] >UPOT [(1-C16H33NH3)2CdCl4], which shows that the larger electrostatic attraction exists in the (1between [1-C15H31NH3]þ and ½CdCl4 2n n C15H31NH3)2CdCl4 rather than between [1-C16H33NH3]þ and in the (1-C16H33NH3)2CdCl4. The values of lattice ½CdCl4 2n n potential energies (LPE) demonstrate that (1-C15H31NH3)2CdCl4 is structurally more stable than (1-C16H33NH3)2CdCl4. In addition, Cp,m[(1-C15H31NH3)2CdCl4] > Cp,m[(1-C16H33NH3)2CdCl4], which reveals that the intermolecular acting force in (1is greater than that in (1C15H31NH3)2CdCl4 C16H33NH3)2CdCl4, which agrees with the results of lattice potential energies. It shows that the former needs to absorb more energy when the same temperature is increased and the equilibrium state within the molecule is attained. (3) Twice phase change temperatures of (1-C15H31NH3)2CdCl4 are smaller than those of (1-C16H33NH3)2CdCl4, but molar enthalpies of the phase transitions of (1-C15H31NH3)2CdCl4 are higher than those of (1-C16H33NH3)2CdCl4, which may be caused by the more CH2 group added in the cation, the steric hindrance is strengthened, this leads to a decrease of enthalpy and entropy in the solidesolid phase transition of (1-C16H33NH3)2CdCl4. It is indicated that (1-C15H31NH3)2CdCl4 is more appropriate for practical applications in storage and effective utilization of solar energy and industrial waste heat recovery based on its lower phase change temperature and higher molar enthalpy of phase transition. 5. Conclusions This paper mainly reports crystal structures, lattice potential energies, and low-temperature heat capacities of the crystal compounds (1-C15H31NH3)2CdCl4(s) and (1-C16H33NH3)2CdCl4(s) in the temperature range from 78 to 395 K. Two solid to solid phase transitions are found in Cp,meT curves for the two compounds. The temperatures, molar enthalpies and molar entropies of two solidesolid phase changes for each of the two compounds are obtained according to relevant thermodynamic equations. The thermodynamic functions of the crystal compounds (1CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16)(s) are derived. Acknowledgments
(9)
This work is financially supported by the National Natural Science Foundations of China under the contract NSFC No. 20673050 and 20973089.
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
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[10] Tan ZC, Liu BP, Yan JB, Sun LX. A fully automated adiabatic calorimeter workable between 80 and 400 K. J Comput Appl Chem 2003;20:264e8. [11] Archer DG. Thermodynamic properties of synthetic sapphire (a-Al2O3), standard reference material 720 and the effect of temperature-scale differences on thermodynamic properties. J Phys Chem Ref Data 1993;22:1441e54. [12] Jenkins HDB, Tudela D, Glasser L. Lattice potential energy estimation for complex ionic salts from density measurements. Inorg Chem 2002;41: 2364e7. [13] Di YY, Tan ZC, Wu XM, Meng SH, Qu SS. Heat capacity and thermochemical study of trifluoroacetamide (C2H2F3NO). Thermochim Acta 2000;356:143e51. [14] Guo N, Wang W. Infrared spectroscopic study of mechanism of phase transition in dodecylammonium tetrachlorozincate. Chin J Appl Chem 1994;11: 25e30 [in Chinese]. [15] Lee CH, Lee KW, Lee CE. Quasi-two-dimensional magnetism in (CnH2nþ1NH3)2CuCl4 studied by electron paramagnetic resonance. Curr Appl Phys 2003;3:477e9. [16] Guo N, Wang W, Zeng GF, Xi SQ. Infrared spectroscopic study of mechanism of phase transition in dodecylammonium tetrachlorozincate. Acta Chimica Sinica 1994;52:705e10 [in Chinese]. [17] Kind R, Plesko S, Arend H. Dynamics of the n-decylammonium chains in the perovskite-type layer structure compound (C10H21NH3)2CdCl4. J Chem Phys 1979;71(5):2118e30. [18] Zuo P, Wu KZ, Cui WZ, Liu XD. Synthesis characterization of bis (n-decylammonium) tetrachlorometallates(U). J Hebei Norm Univ (Nat Sci Edition) 2002;26:53e5 [in Chinese].
Contents lists available at SciVerse ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Crystal structures and thermodynamic properties of phase change materials (1-CnH2nþ1NH3)2CdCl4(s) (n ¼ 15 and 16) D.F. Lu, Y.Y. Di*, D.H. He Shandong Provincial Key Laboratory of Chemical Energy Storage and Novel Cell Technology, College of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2012 Accepted 16 July 2012 Available online 12 August 2012
Two novel crystalline compounds (1-C15H31NH3)2CdCl4(s) and (1-C16H33NH3)2CdCl4(s), which may be used as the solidesolid phase change materials, were synthesized. X-ray crystallography was applied to characterize crystal structures of the two compounds. Both of them are monoclinic, the space group is both C2/ c, and Z ¼ 4. Lattice potential energies (UPOT) of the title compounds were calculated to be 832.31 kJ mol1 for (1-C15H31NH3)2CdCl4(s) and 814.26 kJ mol1 for (1-C16H33NH3)2CdCl4(s). Low-temperature heat capacities of the two compounds were measured by a precise automatic adiabatic calorimeter in the temperature range from 78 to 395 K. The temperatures, molar enthalpies and entropies of two phase transitions for each of the two compounds were determined. The smoothed heat capacities and thermodynamic functions of the two compounds relative to the standard reference temperature 298.15 K were calculated and tabulated at 5 K intervals based on experimental heat capacities. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: X-ray crystallography Crystal structure Adiabatic calorimetry Low-temperature heat capacity Solidesolid phase transitions Energy conversion
1. Introduction With social development, energy crisis is becoming more and more serious. Thermal energy storage is a relatively new technology with a growing interest for many thermal applications. Phase change materials (PCMs) are one of the most important thermal energy storage materials due to high latent heat storage density and almost constant temperature during phase change. Bis-alkylammonium tetrahalogenometallate (II) (1CnH2nþ1NH3)2MX4, in which M is a divalent transition metal atom, X is a halogen atom, and n varies between 8 and 18, is a kind of important solidesolid phase change material [1e5]. It is mainly composed of thick alkylammonium layer (1-CnH2nþ1NH3)þ and thin inorganic layer [MCl4]2, and each alkylammonium chain is bound to the layer [MCl4]2 by NeH.Cl hydrogen bonds [6]. Bisalkylammonium tetrachlorometallate (II) can be also called as a layered perovskite compound. Phase change materials have many applications fields, such as solar energy storage, waste heat recovery, smart air-conditioning buildings, temperature-adaptable greenhouses, electric appliances with thermostatic regulator, energy storage kitchen utensil, and insulation clothing [7]. And due to some unique properties which
* Corresponding author. College of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, PR China. Tel.: þ86 635 8230645; fax: þ86 635 8239121. E-mail addresses: [email protected], [email protected] (Y.Y. Di). 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.07.016
solidesolid phase change material owns during phase transition, such as small change in volume, no volatilization and shape plasticity, this kind of material has attracted the great attention in recent years. In this paper, crystal compounds (1-C15H31NH3)2CdCl4(s) and (1-C16H33NH3)2CdCl4 are synthesized, and their crystal structures are characterized by X-ray crystallography. Low-temperature heat capacities of the two compounds are measured by a precise automatic adiabatic calorimeter in the temperature range from (78e395) K and their thermodynamic properties of solidesolid phase transitions are determined. 2. Materials and methods 2.1. Materials Anhydrous methyl alcohol as the solvent, n-pentadecylamine (J&K Scientific Ltd. China), n-cetylamine (J&K Scientific Ltd. China), hydrochloride acid (37%) and cadmium chloride hydrate as the reactants are all of analytical grade. The reactants are accurately weighed at molar ratio of n[(1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16)]:n(hydrochloride acid):n(CdCl2∙2.5H2O) ¼ 2:2:1. Hydrochloride acid is slightly excessive and slowly dissolved in anhydrous methyl alcohol. The mixture is heated by an electric jacket, stirred under boiling, and refluxed for 4 h. The final solution is laid aside, and several days later, the colorless transparent crystals are obtained. The crystals are washed by ether three times and
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505 Table 1 Crystal data and structure refinement for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16)(s). Name of the properties
Crystallographic data and structure refinement
Empirical formula Formula weight Temperature Wavelength Crystal system Space group Unit cell dimensions
C30H68CdCl4N2 711.06 298(2) K 0.71073 Å Monoclinic C2/c a ¼ 69.062(5) Å; b ¼ 7.4588(8) Å; c ¼ 7.3299(5) Å; a ¼ 90 ; b ¼ 91.1090(10); g ¼ 90
Volume Z Calculated density Absorption coefficient F(000) Crystal size Theta range for data collection Limiting indices
3775.0(5) Å3 4 1.251 g cm3 0.881 mm1 1512 0.50 0.46 0.08 mm 1.77e25.02
C32H72CdCl4N2 739.12 298(2) K 0.71073 Å Monoclinic C2/c a ¼ 72.750(5) Å; b ¼ 7.4670(8) Å; c ¼ 7.3361(7) Å; a ¼ 90 ; b ¼ 91.5030(10) ; g ¼ 90 3983.8(6) Å3 4 1.232 g cm3 0.838 mm1 1576 0.41 0.30 0.09 mm 2.24e25.02
75 h 81, 5 k 8, 8 l 7 8816/3332 [R(int) ¼ 0.00752] 99.6%
86 h 70, 6 k 8, 8 l 8 9351/3512 [R(int) ¼ 0.0596] 99.5%
Semi-empirical from equivalents 0.9328 and 0.6670
Semi-empirical from equivalents 0.9284 and 0.7251
Full-matrix leastsquares on F2 3332/219/171
Full-matrix leastsquares on F2 3512/240/180
1.108 R1 ¼ 0.1059, wR2 ¼ 0.3228
1.157 R1 ¼ 0.1198, wR2 ¼ 0.3304 R1 ¼ 0.1377, wR2 ¼ 0.3469 2.526 and 1.791 e Å3
Reflections collected/ unique Completeness to q ¼ 25.02 Absorption correction Max. and min. transmission Refinement method Data/restraints/ parameters Goodness-of-fit on F2 Final R indices [I > 2sigma(I)] R indices (all data) Largest diff. peak and hole
R1 ¼ 0.1345, wR2 ¼ 0.3502 2.364 and 1.354 e Å3
recrystallized three times by anhydrous methyl alcohol. Finally, the sample is placed in a vacuum desiccator (at T ¼ 310 K) to dry in vacuum for 5 h, the final product is put into a weighing bottle and preserved in a desiccator. Theoretical contents of C, H, N, Cd, and Cl in the compound (1-C15H31NH3)2CdCl4(s) are calculated to be 50.67%, 9.64%, 3.94%, 15.81% and 19.94%, and for (1C16H33NH3)2CdCl4(s) they are 52.00%, 9.82%, 3.79%, 15.21% and 19.18%. Chemical and elemental analysis (model: PE-2400, Perkin Elmer, USA) show that the practical contents of C, H, N, Cd, and Cl in the compound (1-C15H31NH3)2CdCl4(s) are measured to be 50.64%, 9.65%, 3.96%, 15.80% and 19.95%, and those in the compound (1C16H33NH3)2CdCl4(s) are 51.97%, 9.81%, 3.78%, 15.23% and 19.21%. These results show that the purities of the two samples prepared are above 0.995 in mass fraction. 2.2. Methods 2.2.1. X-ray crystallography X-ray crystallography is applied to characterize crystal structures of the two compounds. A crystal is glued to a fine glass fiber and then mounted on Bruker Smart-1000 CCD diffractometer with Mo-Ka radiation, l ¼ 0.71073 Å. The intensity data are collected in the 4eu scan mode at T ¼ 298(2) K. The empirical absorption corrections are based on multi-scan. The structures are solved by direct method and different Fourier syntheses, and all non-hydrogen atoms are refined
499
Table 2 Selected bond lengths (Å) and bond angles (deg) for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s)a,b. (1-C15H31NH3)2CdCl4 Cd(1)eCl(2)#1 Cd(1)eCl(2) Cd(1)eCl(1)#2 Cd(1)eCl(1)#3 Cd(1)eCl(1)#1 Cd(1)eCl(1) Cl(1)eCd(1)#4 Cl(2)#1eCd(1)eCl(2) Cl(2)#1eCd(1)eCl(1)#2 Cl(2)eCd(1)eCl(1)#2 Cl(2)#1eCd(1)eCl(1)#3 Cl(2)eCd(1)eCl(1)#3 Cl(1)#2eCd(1)eCl(1)#3 Cl(2)#1eCd(1)eCl(1)#1
2.564(3) 2.564(3) 2.646(3) 2.646(3) 2.650(3) 2.650(3) 2.646(3) 180.00(2) 90.58(11) 89.42(11) 89.42(11) 90.58(11) 180.00(15) 88.45(11)
Cl(2)eCd(1)eCl(1)#1 Cl(1)#2eCd(1)eCl(1)#1 Cl(1)#3eCd(1)eCl(1)#1 Cl(2)#1eCd(1)eCl(1) Cl(2)eCd(1)eCl(1) Cl(1)#2eCd(1)eCl(1) Cl(1)#3eCd(1)eCl(1) Cl(1)#1eCd(1)eCl(1) Cd(1)#4eCl(1)eCd(1) Cl(1)#2eCd(1)eCl(1)#3 Cl(2)#1eCd(1)eCl(1)#1 Cl(2)eCd(1)eCl(1)#1 Cl(1)#2eCd(1)eCl(1)#1 Cl(1)#3eCd(1)eCl(1)#1
91.55(11) 88.11(2) 91.89(2) 91.55(11) 88.45(11) 91.89(2) 88.11(2) 180.00(18) 161.77(15) 180.00(15) 88.45(11) 91.55(11) 88.11(2) 91.89(2)
(1-C16H33NH3)2CdCl4 Cd(1)eCl(1)#1 Cd(1)eCl(1) Cd(1)eCl(2)#1 Cd(1)eCl(2) Cd(1)eCl(2)#2 Cd(1)eCl(2)#3 Cl(2)eCd(1)#4 Cl(1)#1eCd(1)eCl(1) Cl(1)#1eCd(1)eCl(2)#1 Cl(1)eCd(1)eCl(2)#1 Cl(1)#1eCd(1)eCl(2) Cl(1)eCd(1)eCl(2)
2.553(4) 2.553(4) 2.638(4) 2.638(4) 2.641(4) 2.641(4) 2.641(4) 180.00(3) 89.05(12) 90.95(12) 90.95(12) 89.05(12)
Cl(1)eCd(1)eCl(2)#2 Cl(2)#1eCd(1)eCl(2)#2 Cl(2)eCd(1)eCl(2)#2 Cl(1)#1eCd(1)eCl(2)#3 Cl(1)eCd(1)eCl(2)#3 Cl(2)#1eCd(1)eCl(2)#3 Cl(2)eCd(1)eCl(2)#3 Cl(2)#2eCd(1)eCl(2)#3 Cd(1)eCl(2)eCd(1)#4 Cl(2)#1eCd(1)eCl(2) Cl(1)#1eCd(1)eCl(2)#2
91.07(12) 88.04(2) 91.96(2) 91.07(12) 88.93(12) 91.96(2) 88.04(2) 180.00(18) 165.01(18) 180.00(18) 88.93(12)
a Symmetry codes: #1 [x þ 1/2, y þ 1/2, z]; #2 [x þ 1/2, y1/2, z þ 1/2]; #3 [x, y þ 1, z1/2]; #4[ex þ 1/2, y þ 1/2, ez þ 1/2]. b Symmetry codes: #1 [x þ 1/2, y þ 1/2, z þ 1]; #2 [x þ 1/2, y1/2, z þ 3/ 2]; #3 [x, y þ 1, z1/2]; #4 [x þ 1/2, y þ 1/2, z þ 3/2].
anisotropically on F2 by full-matrix least square method. All calculations are performed with the program package SHELXTL [8]. The crystal data and details of data collection and refinements for these compounds are summarized in Table 1. The selected bond lengths and angles for these compounds are listed in Table 2. The hydrogen bond lengths and angles of the compounds are presented in Table 3. We have applied for two CCDC numbers 787884 for (1C15H31NH3)2CdCl4 and 804713 for (1-C16H33NH3)2CdCl4. 2.2.2. Adiabatic calorimetry A precise automatic adiabatic calorimeter is used to measure molar heat capacities of the two compounds in the temperature range from 78 to 395 K. The calorimeter is established in Thermochemistry Laboratory of College of Chemistry and Chemical Engineering, Liaocheng University, China. The principle and performance of the adiabatic calorimeter and the procedure of heat Table 3 Hydrogen bond lengths (Å) and bond angles (deg) for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s)a,b. DeH.A
d (DeH)
d (H.A)
d (D.A)
<(DHA)
(1-C15H31NH3)2CdCl4 N(1)–H(1A)#1.Cl(2) N(1)–H(1B)#2.Cl(1) N(1)–H(1B)#3.Cl(1) N(1)–H(1C)#4.Cl(2) C(1)–H(1E)#2.Cl(2)
0.89 0.89 0.89 0.89 0.97
2.56 2.63 2.75 2.56 2.82
3.375(15) 3.289(14) 3.484(14) 3.187(13) 3.74(2)
153 131 141 128 159
(1-C16H33NH3)2CdCl4 N(1)-H(1A).Cl(1)#1 N(1)-H(1B).Cl(2)#2 N(1)-H(1B).Cl(2) N(1)-H(1C).Cl(1)#3
0.89 0.89 0.89 0.89
2.81 2.61 2.64 2.93
3.234(18) 3.297(19) 3.338(19) 3.67(2)
110.8 135.1 135.7 140.9
a Symmetry codes: #1 [x, y þ 1, z þ 1/2]; #2 [x, y, z þ 1]; #3 [x, y þ 1, z þ 1/2]; #4 [x, y þ 1, z þ 1]. b Symmetry codes: #1 [x, y þ 1, z]; #2 [x, y þ 1, z1/2]; #3 [x, y þ 1, z þ 1/2].
500
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
Fig. 1. Molecular structures. (a) (1-C15H31NH3)2CdCl4; (b) (1-C16H33NH3)2CdCl4.
capacity measurement are described in detail elsewhere [9,10]. Heat capacity measurement is continuously and automatically carried out by the standard method of intermittently heating the sample and alternately measuring the temperature. The liquid nitrogen is used as the refrigerating medium. The heating rate and temperature increment during heat capacity measurement are generally controlled at 0.1e0.4 K min1 and 1e3 K. The heating duration is 10 min, and the temperature drift rate of the sample cell measured in an equilibrium period is always kept within 104 K min1 during the acquisition of all heat capacity data. The data of heat capacity and corresponding equilibrium temperature [10] are corrected according to heat exchange of the sample cell with its surroundings. The reliability of the performance of the calorimeter is confirmed by measuring heat capacities of the reference standard material (a-Al2O3) in the temperature range from 78 to 400 K. Deviations of experimental results from the
smoothed curve lie within 0.20%, while the uncertainty is 0.30%, as compared with the data given by the former National Bureau of Standards [11] in the whole temperature range. The sample masses used for calorimetric measurement is 1.93755 g for (1-C15H31NH3)2CdCl4(s), and 1.81725 g for (1C16H33NH3)2CdCl4(s), which is equivalent to 2.725 103 mol and 2.459 103 mol on the basis of their molar masses M[(1C15H31NH3)2CdCl4, s] ¼ 711.06 g mol1 and M[(1-C16H33NH3)2CdCl4, s] ¼ 739.12 g mol1. 3. Results 3.1. Crystal structures of (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) It is found from Table 1 that crystal structures of the two compounds are both monoclinic and their space groups are
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
both C2/c, and Z ¼ 4. Their unit cell dimensions are also very close. The molecular structures of (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) in crystallographic independent units are plotted in Fig. 1, which shows that both of them have one type of nonequivalent alkylammonium chains. It can be seen from Fig. 1 and Table 2 that the central ion (Cd2þ) in the two compounds adopts the sixcoordinated configuration, an octahedral geometry is produced, and an infinite net is formed from ½CdCl4 2n n . The packing structures of the unit cells of the two complexes are shown in Fig. 2. It can found from Fig. 2 that the space structures of (1-C15H31NH3)2CdCl4 and (1-C16H33NH3)2CdCl4 are very alike when viewing along c-axis or b-axis, and the monomeric ½CdCl4 2n n moieties bind with the monomeric [1-CnH2nþ1NH3]þ (n ¼ 15 and 16) through several hydrogen bonds (see Table 3). The compound (1C15H31NH3)2CdCl4(s) not only includes classical NeH.Cl hydrogen bonds, but also has non-classical C(1).H(1E).Cl(2) hydrogen bonds. The bond length of C(1).Cl(2) equals 3.74(2) Å and the bond angle of C(3)eH(3A).Cl(2) is 159 , and the symmetry code is [x, y, and zþ1]. For both of the two compounds, the symmetric units are stacked, a sandwich construction is formed, the units ½CdCl4 2n n reside in the “sandwich floor”, an infinite two-dimensional plane is
501
formed along the bc-plane, and on account of binding action of the hydrogen bonds the molecule unit extends to a space supermolecule, which helps to establish a two-dimensional perovskite structure. The results indicate that the hydrogen bonds play an important role in the stabilization of the whole structures of the two compounds. The steric configurations of the two compounds are similar to other compounds (1-CnH2nþ1NH3)2MCl4(s). 3.2. Lattice potential energy The title compounds (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s) can be regarded as a simple salt of the type M2X (charger ratio 1:2), and the lattice potential energy of the compound can be obtained from the formula [12],
UPOT ¼ g
r Mm
1=
3
þd:
(1)
in which the constants g ¼ 8375.6 kJ mol1 cm and d ¼ 178.8 kJ mol1 for the salt with a formula M2X (charge ratio 1:2). From crystal structure information of Table 1, for the crystal (1C15H31NH3)2CdCl4, r ¼ 1.251 g cm3 and Mm ¼ 711.06 g mol1, and
Fig. 2. Packing of structure. (A) viewing along b-axis; (B) viewing along c-axis. (a) (1-C15H31NH3)2CdCl4; (b) (1-C16H33NH3)2CdCl4 (Dashed lines represent the hydrogen bonds. Hydrogen atoms are omitted for clarity).
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D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
for the crystal (1-C16H33NH3)2CdCl4, r ¼ 1.232 g cm3 and Mm ¼ 739.16 g mol1, lattice potential energies of the two compounds are calculated as UPOT [(1-C15H31NH3)2CdCl4, s] ¼ 832.31 kJ mol1 and UPOT [(1-C16H33NH3)2CdCl4, s] ¼ 814.26 kJ mol1. 3.3. Low-temperature heat capacities The experimental results of low-temperature heat capacities are plotted in Fig. 3. It can be seen from Fig. 3(a) for (1C15H31NH3)2CdCl4(s) that two continuous endothermic peaks appear in the temperature ranges from 337 to 352 K and from 352 to 363 K. The experimental heat capacities in the temperature ranges from 78 to 337 K and from 363 to 395 K are fitted by least square method, and two polynomial equations of experimental molar heat capacities (Cp,m) vs. reduced temperature (X), X ¼ f (T), are obtained as follows: Before phase transition from 78 to 337 K, Fig. 4. Comparison for curves of experimental molar heat capacities for (1C15H31NH3)2CdCl4 and (1-C16H33NH3)2CdCl4.
Cp;m ¼ 805:497 þ 497:519X 3:122X 2 59:849X 3 199:497X 4 þ 167:811X 5 þ 239:519X 6 :
(2)
After phase transition from 363 to 395 K,
Cp;m ¼ 1382:009 þ 90:047X þ 5:512X 2 þ 24:912X 3 þ 15:659 X 4 15:351X 5 19:198X 6 :
(3)
X represents the reduced temperature, X ¼ [T(TmaxTmin)/2]/ [(Tmax þ Tmin)/2], T represents the experimental temperature, Tmax and Tmin represent the upper and lower limits in the temperature regions. The correlation coefficient of the fitting R2 ¼ 0.99996 and 0.99976 corresponding to Eqs. (2) and (3). Similarly, it is also seen from Fig. 3(b) for (1-C16H33NH3)2CdCl4 that two continuous endothermic peaks appear in the temperature ranges from 343 to 354 K and from 354 to 365 K. The experimental heat capacities in the temperature ranges from 78 to 343 K and from 365 to 390 K are fitted by least square method as follows: Before phase transition from 78 to 343 K,
Cp;m ¼ 458:518 þ 200:564X 13:938X 2 68:033X 3 188:460X 4 þ 102:685X 5 þ 167:550 X 6 :
(4)
After phase transition from 365 to 390 K,
Cp;m ¼ 692:565 þ 16:375X 1:135X 2 þ 0:860X 3 þ 0:241X 4 :
(5)
2
The correlation coefficients of the fitting R ¼ 0.99933 and 0.99929 corresponding to Eqs. (4) and (5). 3.4. Molar enthalpy and entropy of solidesolid phase transition Three series of repeated heat capacity experiments during the whole phase transitions are carried out after the sample is treated Table 4 Results of the two phase transitions obtained from three series of repeated experiments of (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s). Thermodynamic properties (1-C15H31NH3)2CdCl4 Ttrs,1/K DtrsHm,1/(kJ mol1) DtrsSm,1/(J K1 mol1) Ttrs,2/K DtrsHm,2/(kJ mol1) DtrsSm,2/(J K1 mol1) (1-C16H33NH3)2CdCl4 Ttrs,1/K DtrsHm,1/(kJ mol1) DtrsSm,1/(J K1 mol1) Ttrs,2/K DtrsHm,2/(kJ mol1) DtrsSm,2/(J K1 mol1) a
Fig. 3. Curves of experimental molar heat capacities. (a) (1-C15H31NH3)2CdCl4; (b) (1C16H33NH3)2CdCl4.
Series 1 xi
Series 2 xi
Series 3 xi
Mean value (x sa)a
347.99 50.68 145.63 356.85 42.64 119.49
346.28 49.07 141.71 356.45 40.98 114.95
346.93 49.44 142.50 355.62 41.52 116.76
(347.07 (49.73 (143.28 (356.31 (41.71 (117.07
0.50) 0.49) 1.20) 0.36) 0.49) 1.32)
350.22 24.71 70.55 361.11 22.95 63.54
350.06 24.07 68.77 360.91 23.67 65.59
349.40 24.76 70.87 359.89 22.80 63.37
(349.89 (24.51 (70.06 (360.64 (23.14 (64.17
0.25) 0.22) 0.65) 0.38) 0.27) 0.71)
x qX is the mean value of a set of measurement results; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ðx xÞ2= , n is the experimental number; xi, a single value in i¼1 nðn 1Þ a set of measurements.
sa ¼
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
503
Table 5 Smoothed molar heat capacities and thermodynamic functions for (1-CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) (s). T K
Cp;m
HT H298:15 K
ST S298:15 K
Cp;m
HT H298:15 K
ST S298:15 K
J K mol1
kJ mol1
J K mol1
J K mol1
kJ mol1
J K mol1
157.27 155.99 154.59 153.08 151.43 149.66 147.75 145.72 143.56 141.28 138.88 136.36 133.73 130.99 128.14 125.19 122.13 118.97 115.72 112.36 108.91 105.37 101.72 97.984 94.149 90.217 86.190 82.066 77.847 73.532 69.122 64.619 60.022 55.332 50.553 45.683 40.726 35.682 30.551 25.334 20.030 14.637 9.1525 3.5702 0 2.1171 7.9199 13.852 19.931 26.181 32.628 39.308 46.262
822.98 807.49 791.49 775.00 758.06 740.72 723.01 704.97 686.64 668.07 649.28 630.32 611.21 591.99 572.68 553.31 533.89 514.43 494.96 475.49 456.01 436.55 417.09 397.65 378.22 358.80 339.40 320.01 300.63 281.27 261.91 242.57 223.24 203.93 184.63 165.36 146.10 126.88 107.68 88.514 69.374 50.257 31.153 12.047 0 7.0820 26.266 45.546 64.977 84.628 104.59 124.96 145.87
145.03 151.61 158.34 165.20 172.22 179.39 186.75
426.64 444.54 462.60 480.79 499.12 517.65 536.37
(1-C15H31NH3)2CdCl4 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 298.15 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395
245.216 267.507 291.454 316.471 342.079 367.894 393.617 419.023 443.950 468.295 491.996 515.034 537.421 559.192 580.400 601.112 621.401 641.344 661.016 680.488 699.823 719.074 738.283 757.480 776.682 795.892 815.100 834.287 853.422 872.467 891.382 910.123 928.650 946.931 964.948 982.698 1000.21 1017.53 1034.75 1052.03 1069.56 1087.59 1106.47 1126.61 1140.19 1148.55 1172.89 1200.38 1231.90 1268.47 1311.27 1361.64 1421.14 Phase change Phase change Phase change Phase change Phase change 1299.19 1330.49 1359.52 1387.67 1418.01 1453.73 1483.59
(1-C16H33NH3)2CdCl4
with different cooling rates so that the reversibility and repeatability of the phase transitions of the sample are verified. The cooling rate of the series 1 is about 15 K min1 (liquid nitrogen used as the cooling agent), that of the series 2 is about 2.5 K min1 (ice-
192.89 204.88 217.76 231.17 244.81 258.41 271.81 284.85 297.44 309.51 321.03 332.00 342.42 352.34 361.80 370.84 379.53 387.92 396.07 404.04 411.87 419.61 427.29 434.94 442.56 450.17 457.76 465.31 472.80 480.19 487.44 494.51 501.34 507.90 514.14 520.01 525.49 530.55 535.20 539.45 543.37 547.02 550.52 554.04 556.36 557.79 562.03 567.10 573.39 581.40 591.69 604.91 621.84 643.36 Phase change Phase change Phase change Phase change Phase change 682.18 689.24 695.80 702.20 708.91
89.76 88.76 87.71 86.59 85.40 84.14 82.81 81.42 79.97 78.45 76.87 75.24 73.55 71.82 70.03 68.20 66.32 64.40 62.44 60.44 58.40 56.32 54.21 52.05 49.86 47.63 45.36 43.05 40.70 38.32 35.90 33.45 30.96 28.43 25.88 23.29 20.68 18.04 15.37 12.69 9.980 7.254 4.510 1.749 0 1.031 3.830 6.653 9.504 12.39 15.32 18.31 21.38 24.54
488.31 476.29 464.19 452.01 439.77 427.47 415.14 402.78 390.41 378.06 365.72 353.43 341.19 329.01 316.91 304.90 292.98 281.15 269.43 257.81 246.29 234.88 223.57 212.36 201.24 190.22 179.28 168.43 157.66 146.97 136.36 125.82 115.36 104.97 94.656 84.424 74.275 64.213 54.242 44.368 34.595 24.925 15.362 5.9049 0 3.4495 12.708 21.883 30.993 40.065 49.132 58.242 67.453 76.837
77.54 80.97 84.43 87.93 91.45
225.91 235.11 244.29 253.43 262.53
water cooling), and that of the series 3 is about 0.5 K min1 (natural cooling). The results of three series of repeated experiments are plotted in the inset of Fig. 3. It can be seen from the inset that there are some slight differences in heights and widths of peaks
504
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
corresponding to each series of heat capacity measurements during phase transitions of the sample. However, the phase transitions basically exhibit good reversibility and repeatability, and different cooling rates do not almost affect the experimental results. A closed agreement in Cp,m values of each series of repeated experiment is obtained. The molar enthalpy of the phase transition (DtrsHm) in Cp,meT curve is obtained from Eq. (6). The molar entropy DtrsSm of the phase transition is calculated from the following thermodynamic Eq. (7): [13] (Fig. 4)
"
Dtrs Hm ¼ Q n,
ZTtrs
ZTf CPðiÞ dT n,
Ti 1
kJ mol
Dtrs Sm ¼ Dtrs Hm=T
CPðf Þ dT Ttrs
H0 dT Ti
# .
n (6)
(7)
where Ti in Eq. (6) represents the temperature when the phase transition starts, Tf represents the temperature when the phase transition finishes, CP(i) represents the heat capacity at the temperature Ti, CP(f) represents the heat capacity at the temperature Tf, Q represents the total heat quantity introduced to the calorimeter from temperature Ti to Tf, Ttrs represents the peak temperature of the phase transition of the sample, n represents the mole number of the sample, and H0 represents the heat capacity of the empty sample cell. The data of Q and H0 are calculated with the program stored in the computer linking with the adiabatic calorimetric system, and printed out along with experimental results of heat capacities. The results of Ttrs(K), DtrsHm(kJ mol1), and DtrsSm(J K1 mol1) obtained from every series of repeated experiment are listed in Table 4. For the two compounds, two continuous solidesolid phase transitions are found, which are similar to many other compounds (1-CnH2nþ1NH3)2MX4, so the mechanism [14e18] of the phase transition may be also similar. With the increase of temperature, the hydrogen bonds become weakened, which makes constraints become weakened. The between [1-CnH2nþ1NH3]þ and ½CdCl4 2n n disorder of partial alkylammonium chains occurs together with the reversal of polar NH3 groups, thus the structure of the molecule is transformed, and another kind of free and partly disordered solid phase is formed, which leads to a dynamic orderedisorder transition of rigid alkyl chains in the first phase transition. In the second phase transition, further conformational change of the hydrocarbon part is dominant, complete disorder of the conformation is assumed to be similar to a “molten” state. When the second phase transition is over, the whole solid phase is in complete disorder. After that, the solidesolid phase change has finished, and the compound maintains the stable structure of new solid phase until solideliquid phase change occurs. 3.5. Smoothed heat capacities and thermodynamic functions of the compounds The smoothed molar heat capacities and thermodynamic functions are calculated based on the fitted polynomial equations of heat capacities as a function of the reduced temperature (X) according to the following thermodynamic equations,
ZT ðHT H298:15 Þ ¼
Cp;m dT:
(8)
298:15
ZT ðST S298:15 Þ ¼ 298:15
Cp;m ,T 1 dT:
ZT Cp;m dT T$
298:15
Cp;m ,T 1 dT:
(10)
298:15
The polynomial fitted data of molar heat capacities and fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K are tabulated in Table 5 at an interval of 5 K. 4. Discussion
: ðJ=K molÞ:
m
ZTf
ZT ðGT G298:15 Þ ¼
4.1. The comparison of crystal structures and thermodynamic properties of the two compounds By comparison, some laws on crystal structures and thermodynamic properties of the two compounds is found as follows: (1) The crystal data and structure refinement for (1CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16) show that they have similar unit cell parameters and similar two-dimensional perovskite structures. (2) UPOT [(1-C15H31NH3)2CdCl4] >UPOT [(1-C16H33NH3)2CdCl4], which shows that the larger electrostatic attraction exists in the (1between [1-C15H31NH3]þ and ½CdCl4 2n n C15H31NH3)2CdCl4 rather than between [1-C16H33NH3]þ and in the (1-C16H33NH3)2CdCl4. The values of lattice ½CdCl4 2n n potential energies (LPE) demonstrate that (1-C15H31NH3)2CdCl4 is structurally more stable than (1-C16H33NH3)2CdCl4. In addition, Cp,m[(1-C15H31NH3)2CdCl4] > Cp,m[(1-C16H33NH3)2CdCl4], which reveals that the intermolecular acting force in (1is greater than that in (1C15H31NH3)2CdCl4 C16H33NH3)2CdCl4, which agrees with the results of lattice potential energies. It shows that the former needs to absorb more energy when the same temperature is increased and the equilibrium state within the molecule is attained. (3) Twice phase change temperatures of (1-C15H31NH3)2CdCl4 are smaller than those of (1-C16H33NH3)2CdCl4, but molar enthalpies of the phase transitions of (1-C15H31NH3)2CdCl4 are higher than those of (1-C16H33NH3)2CdCl4, which may be caused by the more CH2 group added in the cation, the steric hindrance is strengthened, this leads to a decrease of enthalpy and entropy in the solidesolid phase transition of (1-C16H33NH3)2CdCl4. It is indicated that (1-C15H31NH3)2CdCl4 is more appropriate for practical applications in storage and effective utilization of solar energy and industrial waste heat recovery based on its lower phase change temperature and higher molar enthalpy of phase transition. 5. Conclusions This paper mainly reports crystal structures, lattice potential energies, and low-temperature heat capacities of the crystal compounds (1-C15H31NH3)2CdCl4(s) and (1-C16H33NH3)2CdCl4(s) in the temperature range from 78 to 395 K. Two solid to solid phase transitions are found in Cp,meT curves for the two compounds. The temperatures, molar enthalpies and molar entropies of two solidesolid phase changes for each of the two compounds are obtained according to relevant thermodynamic equations. The thermodynamic functions of the crystal compounds (1CnH2nþ1NH3)2CdCl4 (n ¼ 15 and 16)(s) are derived. Acknowledgments
(9)
This work is financially supported by the National Natural Science Foundations of China under the contract NSFC No. 20673050 and 20973089.
D.F. Lu et al. / Renewable Energy 50 (2013) 498e505
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