Redetermination of low-temperature heat capacity of Cu(C5H7O2)2

J. Chem. Thermodynamics 137 (2019) 1–6

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Redetermination of low-temperature heat capacity of Cu(C5H7O2)2 M.A. Bespyatov Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia

a r t i c l e

i n f o

Article history: Received 2 April 2019 Received in revised form 9 May 2019 Accepted 18 May 2019 Available online 20 May 2019 Keywords: Adiabatic calorimetry Low-temperature heat capacity Thermodynamic functions Copper (II) beta-diketonates

a b s t r a c t The heat capacity of copper bis-acetylacetonate (Cu(C5H7O2)2) was measured over the temperature range (6.54–313.16) K by adiabatic-shield calorimetry. No anomalies associated with phase transition were found in the functional heat capacity behaviour. The Debye temperature at 0 K was calculated. The data obtained were used to calculate its thermodynamic functions (entropy, enthalpy, reduced Gibbs energy) in the range (0–313) K. They have the following values at 298.15 K: Cp° = (283.9 ± 0.5) J K
1 mol
1, D298.15 Sm° = (359.1 ± 0.8) J K
1 mol
1, D298.15 Hm° = (50.94 ± 0.09) kJ mol
1, Um° = (188.3 ± 1.1) 0 0 J K
1 mol
1. The value of the absolute entropy were used to calculate the entropy of formation of Cu (C5H7O2)2 (cr) at T = 298.15 K. The universal heat capacity behaviour of metal acetylacetonates was demonstrated in a wide temperature range. Ó 2019 Elsevier Ltd.

1. Introduction Copper bis-acetylacetonate (or bis(2,4-pentanedionate) copper, Cu(C5H7O2)2) is classified as a transition metal complex with betadiketones (Fig. 1) and crystallizes in a molecular lattice [1–3]. They have a low melting point [4] and catalytic properties [5], and can move from the condensed phase to the gas phase at moderate temperatures (above 400 K) without decomposition of molecules [6,7]. In 2018 [8], copper bis-acetylacetonate monocrystals were found to exhibit elasticity, like soft materials. Needle crystals of copper bis-acetylacetonate are so flexible that they can be bent and twisted repeatedly and reversibly without loss of crystallinity [8]. Due to its unique functional properties, copper bisacetylacetonate is a promising material for various applications [5,9–11], especially for development of flexible electronic and optical devices. In this regard, there is increased interest in investigation of various physico-chemical properties of these materials [12–14]. Improvement of existing technologies and development of new advanced ones require knowledge of material properties, such as heat capacity, entropy, enthalpy, Gibbs energy, and phase transition temperature and heat, as well as temperature dependences of these properties. For example, data on thermodynamic properties in a wide temperature range are used to optimise the synthesis of complexes, calculate equilibrium and stability parameters for a crystal-gas system, study and optimise gas-phase processes [15,16]. In addition, experimental data on the functional heat capacity behaviour are of great importance for verifying results E-mail address: [email protected] https://doi.org/10.1016/j.jct.2019.05.010 0021-9614/Ó 2019 Elsevier Ltd.

of computer simulation calculations [17–19]. Experimental methods are the major source of information on thermodynamic properties of complex materials such as metal beta-diketonates [20–22]. Adiabatic calorimetry is the most accurate experimental method to determine the heat capacity and thermodynamic properties of substances. In a study [23], the heat capacity of Cu(C5H7O2)2 was investigated in a temperature range of 4.2–450 K. Fig. 2 presents the heat capacity data for Cu(C5H7O2)2 and its isoligand analogue Pt (C5H7O2)2 [24] in Cp,mT
1 vs. T coordinates. A study [27] found that metal tris-acetylacetonates had a similar functional heat capacity behaviour in a wide temperature range (Fig. 2). We may expect that similar heat capacity behaviour will be observed for metal bis-acetylacetonates. In this case, however, we can see an obvious deviation from the universal dependence reported in the literature. As seen in Fig. 2, the heat capacity data for Cu(C5H7O2)2 reported in the literature are proportional to T2 in a temperature range of 4.2–200 K. Theoretically, this behaviour is possible only for an ideal two-dimensional object with a high boundary frequency of the phonon spectrum, which does not make any contribution to the heat capacity associated with harmonic and anharmonic vibrations of molecules and molecular fragments. It seems unlikely that a metal beta-diketonate complex with similar heat capacity behaviour may exist. The functional heat capacity behaviour of Cu(C5H7O2)2 above 200 K (Fig. 2) changes dramatically, which indicates a phase transition in this temperature range. An analysis of crystal structure studies reported in the literature [1–3,12] does not reveal phase transformations in this complex in a temperature range of 100–295 K. Therefore, a repeated exper-

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M.A. Bespyatov / J. Chem. Thermodynamics 137 (2019) 1–6

Fig. 1. Molecular structure of copper (II) acetylacetonate: red is copper, blue is oxygen, black is carbon, green is hydrogen. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

A high-precision adiabatic calorimeter was applied to measure the heat capacities of Cu(C5H7O2)2. The calorimeter was established in Nikolaev Institute of Inorganic Chemistry SB RAS (Russia). The structure and principle of the calorimeter have been described in detail in the literature [28,29]. The temperature of the calorimeter was measured by a standard platinum resistance thermometer (R0 = 100.4695 X; temperature coefficient of resistance a = 0.0039255) calibrated at FSUE ‘‘All-Russian Scientific Research Institute of Physical-Technical and Radiotechnical Measurements” (Moscow region, Russia) using the ITS-90 scale. The standard uncertainty for the temperature was u(T) = 0.01 K. Resolution of the thermometric apparatus was 0.00005 K above 50 K falling to 0.0015 K at 10 K. The adiabatic control system gave the temperature stability of the calorimeter vessel within 0.00001 Kmin
1. The reliability of the calorimetric apparatus is verified by heatcapacity measurements of the reference substance (benzoic acid) at the temperature range from 5 K to 300 K. Deviations of the measured heat capacity of benzoic acid from the reference data [30] were less than 1% in the range (5–20) K, less than 0.3% in the range (20–80) K, and less than 0.15% over the range (80–300) K. The results of calibration using the reference substance (benzoic acid) were in good agreement with the accepted reference data [30]. The sample of Cu(C5H7O2)2 of 3.054 (in vacuum) g was loaded into the calorimetric ampoule. The buoyancy correction was made on the basis of a sample density 1.59 gcm
3 [2]. After evacuation, the calorimetric ampoule with the sample was filled with helium gas (p = 1.0 kPa) to improve heat transfer. The heat capacity was measured using pulsed heating. The molar mass used in the calculation of the molar heat capacity was determined from the formula Cu(C5H7O2)2 as 261.77 gmol
1.

3. Results and discussion

Fig. 2. Heat capacity of metal acetylacetonates presented in the literature: black Cu(C5H7O2)2 [23], blue – Pt(C5H7O2)2 [24], orange – Ir(C5H7O2)3 [25], purple – Ru (C5H7O2)3 [26]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

imental study of the Cu(C5H7O2)2 heat capacity is of both practical and theoretical interest. This paper presents the results of an experimental study of the heat capacity of Cu(C5H7O2)2 over the temperature range from 6.54 K to 313.16 K by adiabatic calorimetry. The data obtained were used to calculate Cu(C5H7O2)2 thermodynamic functions (entropy, enthalpy, reduced Gibbs energy) over the range (0– 313) K

2. Experimental A sample of copper bis-acetylacetonate, Cu(C5H7O2)2, was prepared and purified by Sigma-Aldrich (lot No MKCC6371). The purity of the commercial sample was better than mole fraction 0.999 (see Table 1). No additional sample purification was used. At room temperature, the sample was a violet crystalline powder.

The heat capacity of Cu(C5H7O2)2 was measured by the adiabatic method over the range of (6.54–313.16) K. Two series of heat capacity measurements are presented in the chronological order in Table 2. An analysis of the functional heat capacity Cp,m(T) behaviour (Fig. 3) did not reveal any thermal anomalies. At a temperature of 313 K, the heat capacity of Cu(C5H7O2)2 reaches only  40% of the limiting Dulong and Petit value [31], with a tendency for further growth. This indicates a high boundary frequency and a significant mode density in the high-frequency phonon region. Fig. 3 presents the heat capacity data for Cu(C5H7O2)2 obtained in this study and the data presented in [23]. These data are very different. Relative deviations of the heat capacity values obtained in this study from the values presented in [23] reach 1100% (at 30 K). The study [23] did not present parameters of the sample and a description of the experiment itself, so we were not able to analyse the found data discrepancies. Crystalline copper bis-acetylacetonate is a dielectric and paramagnetic in the studied temperature range [12]. Therefore, the main contribution to the heat capacity is made by the phonon component. The Debye temperature is the most important parameter characterising the phonon component of the heat capacity. The characteristic Debye temperature HD(T) was calculated over the range of (6.54–313.16) K based on experimental heat capacity data using a procedure described in [32].

Table 1 Sample characteristics. Chemical Name

Source

Initial Mole Fraction Purity

Purification Method

Final Mole Fraction Purity

Analysis Method

Bis(2,4-pentanedionato) copper(II), CAS Number: 13395-16-9

SigmaAldrich

0.999

none

–

–

3

M.A. Bespyatov / J. Chem. Thermodynamics 137 (2019) 1–6 Table 2 Experimental values of heat capacitya for crystalline Cu(C5H7O2)2 (molar mass: 261.77 gmol
1) at pressure p = 0.1 MPa (u(p) = 0.05p). T/K Cp,m/JK
1mol
1

T/K Cp,m/JK
1mol
1

Series 1 80.07 85.04 89.68 94.05 98.21 102.43 106.73 110.87 115.52 120.66 125.63 130.45 135.15 139.73 144.22 148.61 152.93 157.17 161.35 165.97 171.03 176.00 180.90 185.74 190.50 195.21

127.4 132.9 137.8 142.1 146.0 149.8 153.5 157.3 160.9 165.0 169.0 172.4 176.0 179.1 182.5 185.6 188.8 191.5 194.4 197.3 200.5 203.5 206.9 210.1 213.3 216.6

199.87 204.46 209.01 213.51 217.97 222.38 226.74 231.06 235.35 239.58 243.77 248.11 252.68 257.27 261.90 266.49 271.04 275.54 280.45 285.75 291.00 296.16 300.51 304.76 308.97 313.16

T/K Cp,m/JK
1mol
1 219.6 222.6 225.1 228.2 231.3 234.3 236.8 239.5 242.2 245.1 247.8 250.8 253.8 256.6 259.8 262.7 266.1 268.5 272.3 275.1 279.0 282.5 285.7 288.6 291.5 294.6

Series 2 6.54 9.03 11.38 13.66 16.64 20.00 22.84 25.85 29.17 32.85 36.85 40.60 44.11 48.18 52.32 56.30 60.23 64.13 68.13 72.30 76.49 80.38

1.427 3.433 6.016 9.127 13.96 20.52 26.59 33.31 40.64 49.04 57.90 65.62 72.98 80.84 88.52 95.12 101.6 107.0 112.6 118.2 123.2 128.0

a Standard uncertainty for temperature u(T) = 0.01 K; relative combined standard uncertainty for the heat capacities uc,r(Cp,m): 0.013 at T/K < 20, 0.003 at 20  T/K < 80, 0.0016 at T/K  80.

Fig. 3. Experimental heat capacity Cu(C5H7O2)2: black – data from this work; red – literary data [23]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The Debye temperature HD(T) over the range (6.54–313.16) K increases from 222 K to 1468 K. This Debye temperature behaviour is typical of metal beta-diketonates. As seen in Fig. 4, the experimental data still do not reach the Debye limit [33]. An analysis of the experimental heat capacity of solids, which was made in [34], demonstrates that the Debye law for complex isotropic solids is valid below the temperature T0 = HD(0)/100. According to the Born-von Karman theory, which is valid for many solids [35], the Debye temperature behaviour near zero can be described as follows:





HD ðT Þ ¼ HD ð0Þ 1
aT 2 ; T << HD ð0Þ;

ð1Þ

where HD(0) is the Debye temperature at 0 K, expressed in K; a is the constant associated with the phonon state density, expressed

Fig. 4. The Debye temperature HD(T) for Cu(C5H7O2)2. The dots represent HD(T) values derived from experimental heat capacity data, the line represents HD(T) values obtained from calculations by Eq. (1), HD(0) = 214 ± 2 K is the Debye temperature at 0 K.

in K
2. Unknown constants in equation can be found by fitting

HD(T) to a linear equation in HD(T)T
2 vs. T
2 coordinates (Fig. 5). As seen in Fig. 5, Eq. (1) describes well the experimental HD(T) values within the range (6–20) K. The standard deviations of experimental HD(T) values from those calculated by Eq. (1) are 0.5%, which does not exceed experimental heat capacity uncertainties in this temperature range. The characteristic Debye temperature at 0 K that is obtained by fitting experimental HD(T) values to Eq. (1) is equal to HD(0) = (214 ± 2) K. Eq. (1) was used to calculate HD(T) below 6.54 K (Fig. 4). To calculate the thermodynamic functions (entropy, enthalpy, and reduced Gibbs energy), the experimental heat capacity was smoothed using the Rumshiskiy procedure [36,37]. This method

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M.A. Bespyatov / J. Chem. Thermodynamics 137 (2019) 1–6

=
(1020.5 ± 1.1) JK
1mol
1. This value corresponds to the following reaction:

CuðcrÞ þ 10CðgrÞ þ 7H2 ðgÞ þ 2O2 ðgÞ ! CuðC5 H7 O2 Þ2 ðcrÞ; ð2Þ

Fig. 5. Fitting of the experimental Debye temperature data to Eq. (1).

approximates the experimental curve by spline functions. Each spline function of the third, fourth or a higher order approximates a pre-selected number of points k (k = 5, 6, 7 or more) depending on the degree of curvature of the function to be smoothed. In so doing, spline functions with matching at the connection point of the first derivatives for the i-th and (i + 1)-th spline functions can be used. Graphical smoothing was used at the ends of the temperature ranges. Deviation of the experimental values from the smoothed curve is shown in Fig. 6. The standard deviation of the experimental points from the smoothed curve is equal to: 0.8% (6.54–20) K, 0.16% (20–80) K, 0.06% (80–313.16) K. The values of entropy D0TSm°, enthalpy D0THm° and reduced Gibbs’ energy Um° were obtained by numerical integration of the smoothed dependence Cs(T) in the range of (0–313) K. The heat capacity data below 6.54 K were derived from the Debye temperature data near zero calculated by Eq. (1). The smoothed values of the heat capacity and the thermodynamic functions are listed in Table 3. Using the value of the absolute entropy of copper bisacetylacetonate (data of this work) and copper [38], carbon [39], hydrogen [38] and oxygen [38], the entropy of formation at T = 298.15 K was calculated to be DfS(298.15, Cu(C5H7O2)2, cr)

where cr – crystalline, gr – graphite, g – gas. We compared the heat capacity values obtained for Cu (C5H7O2)2 with the low-temperature heat capacity data for other metal acetylacetonates studied earlier in [24–26,40–43]. Data on heat capacity Cp,m(T) at low temperatures for Pt(C5H7O2)2 [24], Ir (C5H7O2)3 [25], Ru(C5H7O2)3 [26], Fe(C5H7O2)3 [40], Cr(C5H7O2)3 [41], Al(C5H7O2)3 [42] were obtained by the adiabatic method. The uncertainty of heat capacity measurements below 20 K makes up 1%, above 20 K: about 0.2%. The heat capacity data for Mn (C5H7O2)3 were obtained in [43] by the relaxation method on the PPMS-calorimeter. The uncertainty of these data on the heat capacity over the range (10–280) K is within (1–2)% [44,45]. Fig. 7 shows the heat capacity of Cu(C5H7O2)2, Pt(C5H7O2)2, Mn(C5H7O2)3, Al (C5H7O2)3, Cr(C5H7O2)3, Fe(C5H7O2)3, Ru(C5H7O2)3, Ir(C5H7O2)3 in the coordinates of Cp,m(T)/(nT) (where n is the number of atoms in the molecule). This corresponds to the representation of the heat capacity of these compounds in the same number of degrees of freedom. As seen in Fig. 7, the heat capacity data for all metal acetylacetonates almost coincide (relative deviations of about 3%) above 130 K. Below 130 K, there is a significant difference in the heat capacity behaviour. Metal acetylacetonates are molecular crystals; therefore, their vibrational spectrum can be divided into intermolecular and intramolecular components. Therefore, the heat capacity of these compounds may be represented as a sum of these two components. In [46,47], spectra of intermolecular and intramolecular vibrations for metal acetylacetonates were calculated based on lattice dynamics modelling. According to these data, we may conclude that all intermolecular vibration modes are excited at 0 K to 130 K; therefore, at higher temperatures (above 130 K), their contribution to the heat capacity is constant. However, intermolecular vibration spectra of these compounds differ significantly, and their contribution to the heat capacity at low temperatures (below 130 K) is different. This is illustrated by a significant divergence of heat capacities of the studied compounds below 130 K, as shown in Fig. 7. The contribution of the intramolecular component to the heat capacity is approximately the same as that of acetylacetonates up to 300 K. Metal acetylacetonates have the same ligand structure. The mentioned structural features in the isoligand series ensure that high-frequency regions of their spectrum are similar, and determine the observed heat capacity behaviour of these compounds (Fig. 7). The proximity of heat capacity curves in the specified coordinates for metal bis- and tris-acetylacetonates enables prediction of thermodynamic parameters for other metal acetylacetonates for which no experimental data are available. This result is consistent with the previously found regularities in the behaviour of thermodynamic properties for metal tris-beta-diketonates [25,27,42] and allows these regularities to be generalised for any isoligand groups, regardless of the number of ligands.

4. Conclusions

Fig. 6. Relative deviation (DC = Cp,m(T) – Cs(T)) of the experimental values of heat capacity Cp,m(T) from the smoothed curve Cs(T) for Cu(C5H7O2)2.

We experimentally studied the heat capacity of copper bisacetylacetonate over the temperature range 6.54–313.16 K and presented the findings in this paper. The data obtained were used to calculate the Debye characteristic temperature, entropy, enthalpy, and reduced Gibbs energy over the temperature range 0–313 K as well as formation entropy at 298.15 K. We compared

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Table 3 Molar thermodynamic functionsa (heat capacity C°p,m, entropy D0TS°m, enthalpy D0TH°m, reduced Gibbs energy Um° = D0TSm°
D0THm°/T) of Cu(C5H7O2)2 at pressure p = 0.1 MPa (u(p) = 0.05p); molar mass: 261.77 gmol
1.

a

T/K

C°p,m/JK
1mol
1

D0TS°m/JK
1mol
1

D0TH°m/Jmol
1

U°m/JK
1mol
1

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300 310 313

0 0.667 ± 0.009 4.40 ± 0.06 11.23 ± 0.15 20.50 ± 0.06 31.33 ± 0.09 42.65 ± 0.13 53.76 ± 0.16 64.51 ± 0.19 74.72 ± 0.22 84.29 ± 0.25 93.10 ± 0.28 101.0 ± 0.3 108.3 ± 0.3 115.1 ± 0.3 127.4 ± 0.3 138.1 ± 0.3 147.6 ± 0.3 156.4 ± 0.3 164.5 ± 0.3 172.1 ± 0.3 179.4 ± 0.3 186.6 ± 0.3 193.5 ± 0.3 199.8 ± 0.3 206.2 ± 0.3 213.0 ± 0.3 219.6 ± 0.4 225.9 ± 0.4 232.5 ± 0.4 238.9 ± 0.4 245.4 ± 0.4 252.0 ± 0.4 258.5 ± 0.4 265.2 ± 0.4 271.7 ± 0.4 278.3 ± 0.4 283.9 ± 0.5 285.2 ± 0.5 292.4 ± 0.5 294.5 ± 0.5

0 0.229 ± 0.003 1.632 ± 0.021 4.62 ± 0.06 9.07 ± 0.12 14.79 ± 0.13 21.50 ± 0.15 28.92 ± 0.18 36.80 ± 0.20 44.99 ± 0.22 53.37 ± 0.25 61.8 ± 0.3 70.3 ± 0.3 78.6 ± 0.3 86.9 ± 0.4 103.1 ± 0.4 118.8 ± 0.4 133.8 ± 0.4 148.3 ± 0.5 162.3 ± 0.5 175.7 ± 0.5 188.8 ± 0.5 201.4 ± 0.6 213.6 ± 0.6 225.6 ± 0.6 237.2 ± 0.6 248.5 ± 0.6 259.6 ± 0.6 270.5 ± 0.7 281.1 ± 0.7 291.6 ± 0.7 301.9 ± 0.7 312.1 ± 0.7 322.1 ± 0.7 331.9 ± 0.8 341.7 ± 0.8 351.4 ± 0.8 359.1 ± 0.8 360.9 ± 0.8 370.4 ± 0.8 373.2 ± 0.8

0 0.860 ± 0.011 12.07 ± 0.16 50.1 ± 0.7 128.5 ± 1.7 257.7 ± 2.0 442.6 ± 2.6 684 ± 3 980 ± 5 1328 ± 5 1726 ± 6 2170 ± 8 2655 ± 9 3179 ± 11 3738 ± 12 4952 ± 16 6281 ± 18 7710 ± 20 9231 ± 23 10840 ± 30 12520 ± 30 14280 ± 30 16110 ± 30 18010 ± 40 19970 ± 40 22000 ± 40 24100 ± 50 26260 ± 50 28490 ± 50 30780 ± 60 33140 ± 60 35560 ± 70 38050 ± 70 40600 ± 70 43220 ± 80 45900 ± 80 48650 ± 90 50940 ± 90 51470 ± 90 54360 ± 100 55240 ± 100

0 0.057 ± 0.005 0.42 ± 0.04 1.28 ± 0.10 2.64 ± 0.20 4.48 ± 0.22 6.75 ± 0.24 9.38 ± 0.27 12.3 ± 0.3 15.5 ± 0.3 18.9 ± 0.4 22.4 ± 0.4 26.0 ± 0.5 29.7 ± 0.5 33.5 ± 0.5 41.2 ± 0.6 49.0 ± 0.6 56.7 ± 0.7 64.4 ± 0.7 72.0 ± 0.7 79.4 ± 0.7 86.8 ± 0.8 94.0 ± 0.8 101.1 ± 0.8 108.1 ± 0.8 114.9 ± 0.9 121.6 ± 0.9 128.3 ± 0.9 134.8 ± 0.9 141.2 ± 0.9 147.5 ± 1.0 153.7 ± 1.0 159.9 ± 1.0 165.9 ± 1.0 171.9 ± 1.1 177.8 ± 1.1 183.6 ± 1.1 188.3 ± 1.1 189.3 ± 1.1 195.0 ± 1.1 196.7 ± 1.1

Where the number following the symbol ‘‘±” is the numerical value of a combined standard uncertainty.

It has been shown that the heat capacity behaviour of metal bisand tris-acetylacetonates is universal over a wide temperature range. Our findings may be used to generalise the previously discovered regularities in the behaviour of thermodynamic properties in isoligand groups of metal beta-diketonates as well as to predict thermodynamic characteristics of metal acetylacetonates that have not been explored yet. Acknowledgement The research was supported by the Ministry of Science and Education of the Russian Federation References

Fig. 7. Heat capacity for metal acetylacetonates: black – our data for Cu(C5H7O2)2, blue – Pt(C5H7O2)2 [24], gray – Mn(C5H7O2)3 [43], olive – Fe(C5H7O2)3 [40], red – Cr (C5H7O2)3 [41], green – Ru(C5H7O2)3 [26], wine – Al(C5H7O2)3 [42], orange – Ir (C5H7O2)3 [25]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the heat capacity values for Cu(C5H7O2)2 with the known literature data on heat capacity for other metal acetylacetonates.

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JCT 2019-276