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Densities of selected phase change materials in liquid state
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Densities of Selected Phase Change Materials in Liquid State Vladim´ır Danielik , Edita Bogarov a´ ´ PII: DOI: Reference:
S2405-8300(16)30055-6 10.1016/j.cdc.2016.11.005 CDC 31
To appear in:
Chemical Data Collections
Received date: Revised date: Accepted date:
19 August 2016 9 November 2016 16 November 2016
Please cite this article as: Vladim´ır Danielik , Edita Bogarov a´ , Densities of Selected Phase Change ´ Materials in Liquid State, Chemical Data Collections (2016), doi: 10.1016/j.cdc.2016.11.005
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Densities of Selected Phase Change Materials in Liquid State Vladimír Danielik* and Edita Bogárová Slovak University of Technology in Bratislava, Institute of Inorganic Chemistry, Technology and Materials, Radlinského 9, SK – 812 37 Bratislava, Slovakia
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Contact email: [email protected]
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Abstract Temperature dependencies of densities of ten liquid phase change materials were measured: (i) Mg(NO3)2.6H2O; (ii) Ca(NO3)2.4H2O; (iii) 50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O; (iv) 67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O; (v) 33 wt. % Ca(NO3)2.4H2O + 67 wt. % Mg(NO3)2.6H2O; (vi) Mn(NO3)2.6H2O; (vii) Zn(NO3)2.6H2O; (viii) CaCl2.6H2O; (ix) 28 wt. % Na2SO4 + 72 wt. % H2O; (x) 56 wt. % CH3COONa + 44 wt. % H2O. The two last compositions were chosen near the peritectic compositions of incongruently melting compounds Na2SO4.10H2O and CH3COONa.3H2O, respectively. Data are presented in the article.
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Keywords: phase change materials, density, density of nitrates, density of liquids Specifications Table Subject area Compounds
Data category Data acquisition format Data type Procedure
Physical Chemistry, Inorganic Chemistry Magnesium nitrate hexahydrate, calcium nitrate tetrahydrate, manganese nitrate hexahydrate, zinc nitrate hexahydrate, calcium chloride hexahydrate, sodium sulphate dekahydrate, sodium acetate trihydrate Physicochemical Density of liquid state Raw, analyzed Linear regression analysis (least square method)
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Data accessibility
Data are presented in the article
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Rationale One of the main disadvantages of renewable energy is a non-constant production. To achieve that renewable energy can be used as a primary source of energy worldwide, it is necessary to develop and implement effective methods of energy storage. Thermal solar energy can be stored as latent heat. Latent heat is the heat that is consumed in changing the physical state of the material (enthalpy of fusion). When you change state from solid or liquid to gas it causes a large volume changes. Therefore, change of state from solid to liquid is using in devices for heat storage. Systems using latent heat energy transmission are known as phase change materials (PCMs). When selecting PCM material the technical requirements for a suitable design have to be taken into account. In order to have the longest construction material life it must meet certain criteria: a change of a PCM phase change volume should be minimized, the storage material has to be chemically stable and non-toxic in the environment. In economic terms it is important a low price in order to compete the PCM materials with other means of energy storage. Easy recycling is important for environmental protection. Considering an optimal material for the PCM system all of these properties should be taken into account [1, 2]. This work focuses on the volume change on phase transformation. A temperature dependency of volume changes of liquid phase was investigated, as well. Densities of ten liquid systems were measured: (i) Mg(NO3)2.6H2O; (ii) Ca(NO3)2.4H2O; (iii) 50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O; (iv) 67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O; (v) 33 wt. % Ca(NO3)2.4H2O + 67 wt. % Mg(NO3)2.6H2O; (vi) Mn(NO3)2.6H2O; (vii) Zn(NO3)2.6H2O; (viii) CaCl2.6H2O; (ix) 28 wt. % Na2SO4 + 72 wt. % H2O; (x) 56 wt. % CH3COONa + 44 wt. % H2O. The two last compositions were chosen in order to avoid incongruent melting of Na2SO4.10H2O and CH3COONa.3H2O, respectively. Known literature data on the densities of studied systems are summarized in Table 1.
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CaCl2.6H2O
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Table 1. Density literature data of the studied systems PCM Melting temperature (°C) Mn(NO3)2.6H2O 25.5 [3, 4] 25.8 [5]
Na2SO4.10H2O
Zn(NO3)2.6H2O
Ca(NO3)2.4H2O CH3COONa.3H2O Mg(NO3)2.6H2O
29 [7, 8] 29.2 [9] 29.6 [11] 29.7 [10, 12] 30 [13] 32.4 [9, 10, 12] 32 [15] 36 [7, 8, 9] 36.4 [10, 12] 42.7 [9] 47 [13] 58 [11, 15] 58.4 [9, 16] 89 [7, 8, 11]
Density (kg m-3) 1738 (liquid, 20 °C) [6]* 1728 (liquid, 40 °C) [6] 1795 (solid, 5 °C) [6] 1562 (liquid, 32 °C) [7, 8] 1496 (liquid) [10] 1802 (solid, 24 °C) [7, 8] 1710 (solid, 25 °C) [10] 1620 [11] 1624 [14] 1485 (solid) [10] 1458 [15] 1828 (liquid, 36 °C) [7, 8] 1937 (solid, 24 °C) [7, 8] 1896 (solid, 25 °C) [18] 1450 (solid) [11] 1280 (liquid) [17] 1550 (liquid, 94 °C) [7, 8]
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90 [9, 13] 30 [10]
67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O *supercooled liquid
1636 (solid, 25 °C) [7, 8] 1670 [17]
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Procedure Following chemicals were used: magnesium nitrate hexahydrate (99+%, Acros Organics); calcium nitrate tetrahydrate (analytical grade, Fisher); sodium sulphate dekahydrate (p.a., Lachema); sodium acetate trihydrate (p.a., Mikrochem); calcium chloride hexahydrate (p.a., Lachema), manganese nitrate hexahydrate (p.a., Lachema) and zinc nitrate hexahydrate (p.a., Lachema). The method using the submersible corpuscle was used for density determination. Laboratory scales Radwag AS 60/220.X2 with the mounted “KIT 85 for determination of densities of solids and liquids” were used. The scales allow the weighing with the accuracy 0.02 mg. The amount of chemical that responded to ca 400 ml of liquid was placed in the closed flask that was placed in thermostat. The thermostat was filled in with the glycol liquid Shell EasyCare Premium Antifreeze with the boiling point 139 °C. The temperature dependence of submersible corpuscle volume was calibrated by using tabulated values of water densities [19, 20]. The calibration was made at the temperatures 20 °C; 40 °C; 60 °C and 80 °C. The experimental procedure was as follows: Submersible corpuscle was weighed in air at room temperature. Then it was placed into the flask with the melted chemical for 20 minutes which was heated to chosen temperature. The hold time was sufficient to heat the whole corpuscle. After that time the corpuscle was pulled out from the solution, the solution was poured into the measuring container; and then the submersible corpuscle was placed into that container and weighed in the solution. At the same time, the temperature of solution was recorded on the thermometer with the accuracy 0.1 °C. The density was calculated as follows: m msol t air (1) Vc ,t
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where ρ(t) is the density at the temperature t; mair, msol are weights of submersible corpuscle in air and solution, respectively; Vc,t is the volume of submersible corpuscle at the temperature t. The temperature dependence of density was treated by the well-known expression (2) a bt where t is the temperature in °C, a,b are the empirical parameters that were obtained by linear regression analysis (least square method). Reproducibility of experiments was checked out by six measurements of density of water at 21 °C. The measured density values were in the range (997.7 – 998.6) kg m-3 with the average value (997.98 ± 0.33) kg m-3. This value is in agreement with the tabulated value of 997.995 kg m-3 [19]. Based on the standard deviation of the average, the uncertainty of the measured value is 0.04 %. Experimentally measured densities are summarized in Table 2. The densities were usually measured in the range of 30 °C. The coefficients of eqn. (2) are listed in Table 3. As can be seen from the correlation coefficients presented in Table 3 eqn. (2) describes the dependence and can be used also for extrapolation purposes in reasonable range. Comparison of experimental data, calculated values and previously published data is shown in Fig. 1. Based on the data published in this work, an approximation of densities in the system Ca(NO3)2.4H2O – Mg(NO3)2.6H2O can be made. The eqn. (2) can be divided into two terms: (i) hypothetical density of liquid phase at 0°C (parameter a); (ii) the temperature dependence (parameter b) that is related with
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the coefficient of thermal volume expansion. Molar volumes of the hypothetical liquid phase at 0 °C are compared with the prediction of additivity of molar volumes (dotted line) in Fig. 2. As can be seen, the system behaves nearly ideally. Differences from ideality can be expressed in the form of excess molar volume (3) Vm xiVm0,i V E
V E x1 x2 A
(4) 0 m ,i
where : Vm is the molar volume of the mixture, V
is the molar volume of the pure component of the
mixture, V is the excess molar volume, xi is the mole fraction of the component i, A is the parameter obtained by regression analysis (2.25 ± 0.05 cm3 mol-1; r2 = 0.998). (Subscripts 1, 2 denote Mg(NO3)2.6H2O and Ca(NO3)2.4H2O, respectively.) Excess molar volumes of hypothetic liquid state at 0 °C compared with calculated ones are shown in Fig. 3a. The parameter b depends on the molar composition of the system by second order polynomial (Fig. 3b) (coefficients were determined by least square method): (5) b 0.3566x 2 0.9885x 0.9143 where x is mole fraction of Mg(NO3)2.6H2O; r2 = 0.999 A rough approximation of the density can be calculated from these dependencies at any composition and reasonable range of the temperature.
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Data, value and validation The density of Mn(NO3)2.6H2O is in agreement with the published data [6] (Fig. 1a). In the case of liquid CaCl2.6H2O the density value published in [7, 8] (at 32 °C) is higher about 5% than that observed in this work; while the data published in [10] is in agreement with this work (Fig. 1b). Also for other studied systems there is an agreement among the published and measured data (Zn(NO3)2.6H2O; Mg(NO3)2.6H2O) (Figs. 1d and 1g, respectively). Published density data of the mixture 67 wt.% Ca(NO3)2.4H2O + 33 wt.% Mg(NO3)2.6H2O [17] is in agreement with the data of this work (Fig. 1h). However, it should be noted that the melting temperature presented in [17] is 30 °C and it is stated as eutectic. It is in contradiction with phase diagram of the system Ca(NO3)2 – Mg(NO3)2 – H2O [21]. Based on the published phase diagram we have made indicative attempt to obtain the temperature of primary crystallization of the three mixtures: 67 wt.% Ca(NO3)2.4H2O + 33 wt.% Mg(NO3)2.6H2O; 50 wt.% Ca(NO3)2.4H2O + 50 wt.% Mg(NO3)2.6H2O and 33 wt.% Ca(NO3)2.4H2O + 67 wt.% Mg(NO3)2.6H2O. The results (44.6 °C; 63.3 °C and 73.8 °C, respectively) are in agreement with published phase diagram [21]. It follows that the published density value measured at 30 °C [17] corresponds to the liquid phase that is in equilibrium with the solid state at 30 °C or to the supercooled liquid. Based on the agreement with the density data of this work, it seems that the density presented in [17] corresponds to the supercooled liquid.
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Table 2. Experimentally observed densities of liquid phase Temperature (°C) Density (kg m-3)
29.3 1735.1
31.6 1733.2
33.4 1732.4
Mn(NO3)2.6H2O 36.9 39.8 1731.3 1729.1
44.1 1726.8
49.5 1724.2
53.2 1721.8
CaCl2.6H2O 47.5 55.0 1480.5 1476.0
66.5 1469.2
35.5 1488.3
36.7 1489.0
47.0 1480.9
55.0 1476.5
66.5 1469.1
Temperature (°C) Density (kg m-3)
38.0 1259.4
38.0 1260.3
28 wt. % Na2SO4 + 72 wt. % H2O 47.0 47.8 57.4 57.4 1255.1 1255.2 1248.8 1249.1
64.0 1248.3
65.4 1245.8
54.8 1801.3
58.1 1796.1
60.6 1791.4
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Temperature (°C) Density (kg m-3)
38.7 1824.1
40.5 1820.9
45.1 1814.0
Temperature (°C) Density (kg m-3)
42.6 1732.9
43.8 1729.5
49.4 1723.6
Ca(NO3)2.4H2O 51.0 57.8 1722.1 1716.4
59.0 1714.7
74.8 1701.5
77.4 1699.6
83.2 1236.8
84.6 1236.5
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Temperature (°C) Density (kg m-3)
Zn(NO3)2.6H2O 47.3 52.0 1809.6 1804.7
Temperature (°C) Density (kg m-3)
58.2 1254.8
60.4 1252.4
56 wt. % CH3COONa + 44 wt. % H2O 64.8 65.8 74.8 75.0 1249.9 1249.0 1243.7 1243.3
Temperature (°C) Density (kg m-3)
91.0 1550.6
91.5 1550.5
92.5 1550.0
75.8 1616.7
79.1 1592.1
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38.1 1664.4
67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O 42.7 45.7 48.2 50.6 53.1 55.5 1661.5 1660.2 1658 1656.4 1655.6 1653.5
50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O 77.2 81.8 82.0 84.2 88.1 91.8 1613.7 1613.5 1613.8 1611.8 1609.3 1608.1
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Temperature (°C) Density (kg m-3)
Mg(NO3)2.6H2O 94.0 1549.8
33 wt. % Ca(NO3)2.4H2O + 67 wt. % Mg(NO3)2.6H2O 82.3 86.7 88.2 91.6 91.8 93.8 1590.7 1588.6 1588 1586.6 1587.1 1586.1
59.4 1651.5 94.6 1606.6 79.1 1592.1
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Corr. coeff. r2 0.995 0.995 0.974 0.995 0.992 0.996 0.926 0.995
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Table 3. The empirical parameters of the density eqn. (2). Densities are in kg m-3. PCM Parameter a Parameter b Mn(NO3)2.6H2O 1750.6 ± 0.6 0.538 ± 0.015 CaCl2.6H2O 1511.3 ± 1.0 0.636 ± 0.019 28 wt. % Na2SO4 + 72 wt. % H2O 1278.7 ± 1.8 0.500 ± 0.034 Zn(NO3)2.6H2O 1879.0 ± 2.0 1.434 ± 0.04 Ca(NO3)2.4H2O 1769.7 ± 2.0 0.916 ± 0.034 56 wt. % CH3COONa + 44 wt. % H2O 1294.1 ± 1.3 0.682 ± 0.018 Mg(NO3)2.6H2O 1576.1 ± 5.2 0.281 ± 0.057 67 wt. % Ca(NO3)2.4H2O + 1687.7 ± 0.9 0.612 ± 0.018 33 wt. % Mg(NO3)2.6H2O 50 wt. % Ca(NO3)2.4H2O + 1653.7 ± 4.2 0.498 ± 0.049 50 wt. % Mg(NO3)2.6H2O 33 wt. % Ca(NO3)2.4H2O + 1624.3 ± 1.8 0.409 ± 0.020 67 wt. % Mg(NO3)2.6H2O
0.946 0.988
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(i) (j) Fig. 1. Comparison of experimentally observed densities, calculated values and previously published data. (a): Mn(NO3)2.6H2O; (b): CaCl2.6H2O; (c): 28 wt. % Na2SO4 + 72 wt. % H2O; (d): Zn(NO3)2.6H2O; (e): Ca(NO3)2.4H2O; (f): 56 wt. % CH3COONa + 44 wt. % H2O; (g): Mg(NO3)2.6H2O; (h): 67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O; (i): 50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O.
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Fig. 2. Molar volume of the hypothetical liquid phase at 0 °C. (full line): calculated; (dotted line): ideal behavior (additivity of molar volumes).
(a) (b) Fig. 3. Composition dependence of density in the system Ca(NO3)2.4H2O + Mg(NO3)2.6H2O. (a): Excess molar volume of the hypothetical liquid phase at 0 °C. (full line): calculated; (b): Composition dependence of the parameter b of eqn. (2). (full line): eqn. (5).
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Acknowledgment This work was supported by courtesy of the Slovak Grant Agency (VEGA 1/0101/14)
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References [1] H. Mehling, L.F. Cabeza, Heat and cold storage with PCM an up to date introduction into basics and applications, Springer, Berlin, 2008. ISBN 978-3-540-68557-9 [2] Z. Khan, Z. Khan, A, Ghafoor, A review of performance enhancement of PCM based latent heat storage system within the context of materials, thermal stability and compatibility, Energy Convers Manage 15 (2016) 132–158. doi:10.1016/j.enconman.2016.02.045 [3] V.V. Tyagi, D. Buddhi, PCM thermal storage in buildings: A state of art, Renewable and Sustainable Energy Reviews 11 (2007) 1146–1166. http://dx.doi.org/10.1016/j.rser.2005.10.002 [4] A. Sharma, V.V. Tyagi, C.R. Chen, D. Buddhi, Review on thermal energy storage with phase change materials and applications, Renewable and Sustainable Energy Reviews 13 (2009) 318–345. doi:10.1016/j.rser.2007.10.005 [5] B. Zalba, J.M. Marín, L.F. Cabeza, H. Mehling, Review on thermal energy storage with phase change: materials, heat transfer analysis and applications, Applied Thermal Engineering 23 (2003) 251– 283. http://dx.doi.org/10.1016/S1359-4311(02)00192-8 [6] K. Nagano, T. Mochida, K. Iwata, J. Hiroyoshi, R. Domanski, Thermal performance of Mn(NO3)2.6H2O as a new PCM for cooling system, 5th Workshop of the IEA ECES IA Annex 10, Tsu (Japan), 2000. [7] I. Dincer, M.A. Rosen, Thermal energy storage, Systems and Applications, John Wiley & Sons, Chichester (England), 2002. ISBN 0-471-49573-5 [8] G.A. Lane, J. Int, Low temperature heat storage with phase change materials, Ambient Energy 1 (1980) 155–168. http://dx.doi.org/10.1080/01430750.1980.9675731 [9] R. Naumann, H.H. Emons, J. Results of thermal analysis for investigation of salt hydrates as latent heat-storage materials, Thermal Analysis 35 (1989) 1009–1031. doi: 10.1007/BF02057256 [10] A. Abhat, Low temperature latent heat thermal energy storage: heat storage materials, Solar Energy 30 (1983) 313–332, cited by [5]. [11] J. Heckenkamp, H. Baumann, Latentwärmespeicher, Sonderdruck aus Nachrichten 11 (1997) 1075–1081, cited by [5]. [12] D. W. Hawes, D. Feldman, D. Banu, Latent heat storage in building materials, Energy Buildings 20 (1993) 77–86. http://dx.doi.org/10.1016/0378-7788(93)90040-2 [13] G. Belton, F. Ajami, Thermochemistry of salt hydrates, Report No. NSF/RANN/SE/GI27976/TR/73/4, Philadelphia (Pennsylvania, USA), 1973. [14] M. Telkes, Thermal storage for solar heating and cooling, Proceedings of the Workshop on Solar Energy Storage Subsystems for the Heating and Cooling of Buildings, Charlottesville (Virginia, USA), 1975, cited by [5]. [15] F. Lindner, Wärmespeicherung mit Salzen und Salzhydraten, Ki Luft- und Kältetechnik 10 (1996) 462–467, cited by [5]. [16] T. Wada, F. Kimura, Y. Matsuo, Studies on salt hydrate for latent heat storage. IV. Crystallization in the binary system CH3CO2Na-H2O, Bul. Chem. Soc. Jpn. 56 (1983) 3827–3829. http://dx.doi.org/10.1246/bcsj.56.3827
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[17] L.F. Cabeza, A. Castell, C. Barreneche, A. de Gracia, A.I. Fernández, Materials used as PCM in thermal energy storage in buildings: A review, Renewable and Sustainable Energy Reviews 15 (2011) 1675–1695. http://dx.doi.org/10.1016/j.rser.2010.11.018 [18] https://en.wikipedia.org/wiki/Calcium_nitrate (date:07.07.16) [19] http://antoine.frostburg.edu/chem/senese/javascript/water-density.html (date:07.07.16) [20] https://en.wikipedia.org/wiki/Density (date:07.07.16) [21] Xia Yin, Dongdong Li, Yuqi Tan, Xiaoya Wu, Xiuli Yu and Dewen Zeng, Solubility Phase Diagram of the Ca(NO3)2–Mg(NO3)2−H2O System, J. Chem. Eng. Data 59(12) (2014) 4026–4030. doi:10.1021/je500629s
Densities of Selected Phase Change Materials in Liquid State Vladim´ır Danielik , Edita Bogarov a´ ´ PII: DOI: Reference:
S2405-8300(16)30055-6 10.1016/j.cdc.2016.11.005 CDC 31
To appear in:
Chemical Data Collections
Received date: Revised date: Accepted date:
19 August 2016 9 November 2016 16 November 2016
Please cite this article as: Vladim´ır Danielik , Edita Bogarov a´ , Densities of Selected Phase Change ´ Materials in Liquid State, Chemical Data Collections (2016), doi: 10.1016/j.cdc.2016.11.005
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Densities of Selected Phase Change Materials in Liquid State Vladimír Danielik* and Edita Bogárová Slovak University of Technology in Bratislava, Institute of Inorganic Chemistry, Technology and Materials, Radlinského 9, SK – 812 37 Bratislava, Slovakia
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Contact email: [email protected]
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Abstract Temperature dependencies of densities of ten liquid phase change materials were measured: (i) Mg(NO3)2.6H2O; (ii) Ca(NO3)2.4H2O; (iii) 50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O; (iv) 67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O; (v) 33 wt. % Ca(NO3)2.4H2O + 67 wt. % Mg(NO3)2.6H2O; (vi) Mn(NO3)2.6H2O; (vii) Zn(NO3)2.6H2O; (viii) CaCl2.6H2O; (ix) 28 wt. % Na2SO4 + 72 wt. % H2O; (x) 56 wt. % CH3COONa + 44 wt. % H2O. The two last compositions were chosen near the peritectic compositions of incongruently melting compounds Na2SO4.10H2O and CH3COONa.3H2O, respectively. Data are presented in the article.
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Keywords: phase change materials, density, density of nitrates, density of liquids Specifications Table Subject area Compounds
Data category Data acquisition format Data type Procedure
Physical Chemistry, Inorganic Chemistry Magnesium nitrate hexahydrate, calcium nitrate tetrahydrate, manganese nitrate hexahydrate, zinc nitrate hexahydrate, calcium chloride hexahydrate, sodium sulphate dekahydrate, sodium acetate trihydrate Physicochemical Density of liquid state Raw, analyzed Linear regression analysis (least square method)
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Data accessibility
Data are presented in the article
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Rationale One of the main disadvantages of renewable energy is a non-constant production. To achieve that renewable energy can be used as a primary source of energy worldwide, it is necessary to develop and implement effective methods of energy storage. Thermal solar energy can be stored as latent heat. Latent heat is the heat that is consumed in changing the physical state of the material (enthalpy of fusion). When you change state from solid or liquid to gas it causes a large volume changes. Therefore, change of state from solid to liquid is using in devices for heat storage. Systems using latent heat energy transmission are known as phase change materials (PCMs). When selecting PCM material the technical requirements for a suitable design have to be taken into account. In order to have the longest construction material life it must meet certain criteria: a change of a PCM phase change volume should be minimized, the storage material has to be chemically stable and non-toxic in the environment. In economic terms it is important a low price in order to compete the PCM materials with other means of energy storage. Easy recycling is important for environmental protection. Considering an optimal material for the PCM system all of these properties should be taken into account [1, 2]. This work focuses on the volume change on phase transformation. A temperature dependency of volume changes of liquid phase was investigated, as well. Densities of ten liquid systems were measured: (i) Mg(NO3)2.6H2O; (ii) Ca(NO3)2.4H2O; (iii) 50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O; (iv) 67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O; (v) 33 wt. % Ca(NO3)2.4H2O + 67 wt. % Mg(NO3)2.6H2O; (vi) Mn(NO3)2.6H2O; (vii) Zn(NO3)2.6H2O; (viii) CaCl2.6H2O; (ix) 28 wt. % Na2SO4 + 72 wt. % H2O; (x) 56 wt. % CH3COONa + 44 wt. % H2O. The two last compositions were chosen in order to avoid incongruent melting of Na2SO4.10H2O and CH3COONa.3H2O, respectively. Known literature data on the densities of studied systems are summarized in Table 1.
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Table 1. Density literature data of the studied systems PCM Melting temperature (°C) Mn(NO3)2.6H2O 25.5 [3, 4] 25.8 [5]
Na2SO4.10H2O
Zn(NO3)2.6H2O
Ca(NO3)2.4H2O CH3COONa.3H2O Mg(NO3)2.6H2O
29 [7, 8] 29.2 [9] 29.6 [11] 29.7 [10, 12] 30 [13] 32.4 [9, 10, 12] 32 [15] 36 [7, 8, 9] 36.4 [10, 12] 42.7 [9] 47 [13] 58 [11, 15] 58.4 [9, 16] 89 [7, 8, 11]
Density (kg m-3) 1738 (liquid, 20 °C) [6]* 1728 (liquid, 40 °C) [6] 1795 (solid, 5 °C) [6] 1562 (liquid, 32 °C) [7, 8] 1496 (liquid) [10] 1802 (solid, 24 °C) [7, 8] 1710 (solid, 25 °C) [10] 1620 [11] 1624 [14] 1485 (solid) [10] 1458 [15] 1828 (liquid, 36 °C) [7, 8] 1937 (solid, 24 °C) [7, 8] 1896 (solid, 25 °C) [18] 1450 (solid) [11] 1280 (liquid) [17] 1550 (liquid, 94 °C) [7, 8]
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90 [9, 13] 30 [10]
67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O *supercooled liquid
1636 (solid, 25 °C) [7, 8] 1670 [17]
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Procedure Following chemicals were used: magnesium nitrate hexahydrate (99+%, Acros Organics); calcium nitrate tetrahydrate (analytical grade, Fisher); sodium sulphate dekahydrate (p.a., Lachema); sodium acetate trihydrate (p.a., Mikrochem); calcium chloride hexahydrate (p.a., Lachema), manganese nitrate hexahydrate (p.a., Lachema) and zinc nitrate hexahydrate (p.a., Lachema). The method using the submersible corpuscle was used for density determination. Laboratory scales Radwag AS 60/220.X2 with the mounted “KIT 85 for determination of densities of solids and liquids” were used. The scales allow the weighing with the accuracy 0.02 mg. The amount of chemical that responded to ca 400 ml of liquid was placed in the closed flask that was placed in thermostat. The thermostat was filled in with the glycol liquid Shell EasyCare Premium Antifreeze with the boiling point 139 °C. The temperature dependence of submersible corpuscle volume was calibrated by using tabulated values of water densities [19, 20]. The calibration was made at the temperatures 20 °C; 40 °C; 60 °C and 80 °C. The experimental procedure was as follows: Submersible corpuscle was weighed in air at room temperature. Then it was placed into the flask with the melted chemical for 20 minutes which was heated to chosen temperature. The hold time was sufficient to heat the whole corpuscle. After that time the corpuscle was pulled out from the solution, the solution was poured into the measuring container; and then the submersible corpuscle was placed into that container and weighed in the solution. At the same time, the temperature of solution was recorded on the thermometer with the accuracy 0.1 °C. The density was calculated as follows: m msol t air (1) Vc ,t
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where ρ(t) is the density at the temperature t; mair, msol are weights of submersible corpuscle in air and solution, respectively; Vc,t is the volume of submersible corpuscle at the temperature t. The temperature dependence of density was treated by the well-known expression (2) a bt where t is the temperature in °C, a,b are the empirical parameters that were obtained by linear regression analysis (least square method). Reproducibility of experiments was checked out by six measurements of density of water at 21 °C. The measured density values were in the range (997.7 – 998.6) kg m-3 with the average value (997.98 ± 0.33) kg m-3. This value is in agreement with the tabulated value of 997.995 kg m-3 [19]. Based on the standard deviation of the average, the uncertainty of the measured value is 0.04 %. Experimentally measured densities are summarized in Table 2. The densities were usually measured in the range of 30 °C. The coefficients of eqn. (2) are listed in Table 3. As can be seen from the correlation coefficients presented in Table 3 eqn. (2) describes the dependence and can be used also for extrapolation purposes in reasonable range. Comparison of experimental data, calculated values and previously published data is shown in Fig. 1. Based on the data published in this work, an approximation of densities in the system Ca(NO3)2.4H2O – Mg(NO3)2.6H2O can be made. The eqn. (2) can be divided into two terms: (i) hypothetical density of liquid phase at 0°C (parameter a); (ii) the temperature dependence (parameter b) that is related with
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the coefficient of thermal volume expansion. Molar volumes of the hypothetical liquid phase at 0 °C are compared with the prediction of additivity of molar volumes (dotted line) in Fig. 2. As can be seen, the system behaves nearly ideally. Differences from ideality can be expressed in the form of excess molar volume (3) Vm xiVm0,i V E
V E x1 x2 A
(4) 0 m ,i
where : Vm is the molar volume of the mixture, V
is the molar volume of the pure component of the
mixture, V is the excess molar volume, xi is the mole fraction of the component i, A is the parameter obtained by regression analysis (2.25 ± 0.05 cm3 mol-1; r2 = 0.998). (Subscripts 1, 2 denote Mg(NO3)2.6H2O and Ca(NO3)2.4H2O, respectively.) Excess molar volumes of hypothetic liquid state at 0 °C compared with calculated ones are shown in Fig. 3a. The parameter b depends on the molar composition of the system by second order polynomial (Fig. 3b) (coefficients were determined by least square method): (5) b 0.3566x 2 0.9885x 0.9143 where x is mole fraction of Mg(NO3)2.6H2O; r2 = 0.999 A rough approximation of the density can be calculated from these dependencies at any composition and reasonable range of the temperature.
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Data, value and validation The density of Mn(NO3)2.6H2O is in agreement with the published data [6] (Fig. 1a). In the case of liquid CaCl2.6H2O the density value published in [7, 8] (at 32 °C) is higher about 5% than that observed in this work; while the data published in [10] is in agreement with this work (Fig. 1b). Also for other studied systems there is an agreement among the published and measured data (Zn(NO3)2.6H2O; Mg(NO3)2.6H2O) (Figs. 1d and 1g, respectively). Published density data of the mixture 67 wt.% Ca(NO3)2.4H2O + 33 wt.% Mg(NO3)2.6H2O [17] is in agreement with the data of this work (Fig. 1h). However, it should be noted that the melting temperature presented in [17] is 30 °C and it is stated as eutectic. It is in contradiction with phase diagram of the system Ca(NO3)2 – Mg(NO3)2 – H2O [21]. Based on the published phase diagram we have made indicative attempt to obtain the temperature of primary crystallization of the three mixtures: 67 wt.% Ca(NO3)2.4H2O + 33 wt.% Mg(NO3)2.6H2O; 50 wt.% Ca(NO3)2.4H2O + 50 wt.% Mg(NO3)2.6H2O and 33 wt.% Ca(NO3)2.4H2O + 67 wt.% Mg(NO3)2.6H2O. The results (44.6 °C; 63.3 °C and 73.8 °C, respectively) are in agreement with published phase diagram [21]. It follows that the published density value measured at 30 °C [17] corresponds to the liquid phase that is in equilibrium with the solid state at 30 °C or to the supercooled liquid. Based on the agreement with the density data of this work, it seems that the density presented in [17] corresponds to the supercooled liquid.
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Table 2. Experimentally observed densities of liquid phase Temperature (°C) Density (kg m-3)
29.3 1735.1
31.6 1733.2
33.4 1732.4
Mn(NO3)2.6H2O 36.9 39.8 1731.3 1729.1
44.1 1726.8
49.5 1724.2
53.2 1721.8
CaCl2.6H2O 47.5 55.0 1480.5 1476.0
66.5 1469.2
35.5 1488.3
36.7 1489.0
47.0 1480.9
55.0 1476.5
66.5 1469.1
Temperature (°C) Density (kg m-3)
38.0 1259.4
38.0 1260.3
28 wt. % Na2SO4 + 72 wt. % H2O 47.0 47.8 57.4 57.4 1255.1 1255.2 1248.8 1249.1
64.0 1248.3
65.4 1245.8
54.8 1801.3
58.1 1796.1
60.6 1791.4
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Temperature (°C) Density (kg m-3)
38.7 1824.1
40.5 1820.9
45.1 1814.0
Temperature (°C) Density (kg m-3)
42.6 1732.9
43.8 1729.5
49.4 1723.6
Ca(NO3)2.4H2O 51.0 57.8 1722.1 1716.4
59.0 1714.7
74.8 1701.5
77.4 1699.6
83.2 1236.8
84.6 1236.5
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Zn(NO3)2.6H2O 47.3 52.0 1809.6 1804.7
Temperature (°C) Density (kg m-3)
58.2 1254.8
60.4 1252.4
56 wt. % CH3COONa + 44 wt. % H2O 64.8 65.8 74.8 75.0 1249.9 1249.0 1243.7 1243.3
Temperature (°C) Density (kg m-3)
91.0 1550.6
91.5 1550.5
92.5 1550.0
75.8 1616.7
79.1 1592.1
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38.1 1664.4
67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O 42.7 45.7 48.2 50.6 53.1 55.5 1661.5 1660.2 1658 1656.4 1655.6 1653.5
50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O 77.2 81.8 82.0 84.2 88.1 91.8 1613.7 1613.5 1613.8 1611.8 1609.3 1608.1
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Temperature (°C) Density (kg m-3)
Mg(NO3)2.6H2O 94.0 1549.8
33 wt. % Ca(NO3)2.4H2O + 67 wt. % Mg(NO3)2.6H2O 82.3 86.7 88.2 91.6 91.8 93.8 1590.7 1588.6 1588 1586.6 1587.1 1586.1
59.4 1651.5 94.6 1606.6 79.1 1592.1
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Corr. coeff. r2 0.995 0.995 0.974 0.995 0.992 0.996 0.926 0.995
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Table 3. The empirical parameters of the density eqn. (2). Densities are in kg m-3. PCM Parameter a Parameter b Mn(NO3)2.6H2O 1750.6 ± 0.6 0.538 ± 0.015 CaCl2.6H2O 1511.3 ± 1.0 0.636 ± 0.019 28 wt. % Na2SO4 + 72 wt. % H2O 1278.7 ± 1.8 0.500 ± 0.034 Zn(NO3)2.6H2O 1879.0 ± 2.0 1.434 ± 0.04 Ca(NO3)2.4H2O 1769.7 ± 2.0 0.916 ± 0.034 56 wt. % CH3COONa + 44 wt. % H2O 1294.1 ± 1.3 0.682 ± 0.018 Mg(NO3)2.6H2O 1576.1 ± 5.2 0.281 ± 0.057 67 wt. % Ca(NO3)2.4H2O + 1687.7 ± 0.9 0.612 ± 0.018 33 wt. % Mg(NO3)2.6H2O 50 wt. % Ca(NO3)2.4H2O + 1653.7 ± 4.2 0.498 ± 0.049 50 wt. % Mg(NO3)2.6H2O 33 wt. % Ca(NO3)2.4H2O + 1624.3 ± 1.8 0.409 ± 0.020 67 wt. % Mg(NO3)2.6H2O
0.946 0.988
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(i) (j) Fig. 1. Comparison of experimentally observed densities, calculated values and previously published data. (a): Mn(NO3)2.6H2O; (b): CaCl2.6H2O; (c): 28 wt. % Na2SO4 + 72 wt. % H2O; (d): Zn(NO3)2.6H2O; (e): Ca(NO3)2.4H2O; (f): 56 wt. % CH3COONa + 44 wt. % H2O; (g): Mg(NO3)2.6H2O; (h): 67 wt. % Ca(NO3)2.4H2O + 33 wt. % Mg(NO3)2.6H2O; (i): 50 wt. % Ca(NO3)2.4H2O + 50 wt. % Mg(NO3)2.6H2O.
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Fig. 2. Molar volume of the hypothetical liquid phase at 0 °C. (full line): calculated; (dotted line): ideal behavior (additivity of molar volumes).
(a) (b) Fig. 3. Composition dependence of density in the system Ca(NO3)2.4H2O + Mg(NO3)2.6H2O. (a): Excess molar volume of the hypothetical liquid phase at 0 °C. (full line): calculated; (b): Composition dependence of the parameter b of eqn. (2). (full line): eqn. (5).
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Acknowledgment This work was supported by courtesy of the Slovak Grant Agency (VEGA 1/0101/14)
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References [1] H. Mehling, L.F. Cabeza, Heat and cold storage with PCM an up to date introduction into basics and applications, Springer, Berlin, 2008. ISBN 978-3-540-68557-9 [2] Z. Khan, Z. Khan, A, Ghafoor, A review of performance enhancement of PCM based latent heat storage system within the context of materials, thermal stability and compatibility, Energy Convers Manage 15 (2016) 132–158. doi:10.1016/j.enconman.2016.02.045 [3] V.V. Tyagi, D. Buddhi, PCM thermal storage in buildings: A state of art, Renewable and Sustainable Energy Reviews 11 (2007) 1146–1166. http://dx.doi.org/10.1016/j.rser.2005.10.002 [4] A. Sharma, V.V. Tyagi, C.R. Chen, D. Buddhi, Review on thermal energy storage with phase change materials and applications, Renewable and Sustainable Energy Reviews 13 (2009) 318–345. doi:10.1016/j.rser.2007.10.005 [5] B. Zalba, J.M. Marín, L.F. Cabeza, H. Mehling, Review on thermal energy storage with phase change: materials, heat transfer analysis and applications, Applied Thermal Engineering 23 (2003) 251– 283. http://dx.doi.org/10.1016/S1359-4311(02)00192-8 [6] K. Nagano, T. Mochida, K. Iwata, J. Hiroyoshi, R. Domanski, Thermal performance of Mn(NO3)2.6H2O as a new PCM for cooling system, 5th Workshop of the IEA ECES IA Annex 10, Tsu (Japan), 2000. [7] I. Dincer, M.A. Rosen, Thermal energy storage, Systems and Applications, John Wiley & Sons, Chichester (England), 2002. ISBN 0-471-49573-5 [8] G.A. Lane, J. Int, Low temperature heat storage with phase change materials, Ambient Energy 1 (1980) 155–168. http://dx.doi.org/10.1080/01430750.1980.9675731 [9] R. Naumann, H.H. Emons, J. Results of thermal analysis for investigation of salt hydrates as latent heat-storage materials, Thermal Analysis 35 (1989) 1009–1031. doi: 10.1007/BF02057256 [10] A. Abhat, Low temperature latent heat thermal energy storage: heat storage materials, Solar Energy 30 (1983) 313–332, cited by [5]. [11] J. Heckenkamp, H. Baumann, Latentwärmespeicher, Sonderdruck aus Nachrichten 11 (1997) 1075–1081, cited by [5]. [12] D. W. Hawes, D. Feldman, D. Banu, Latent heat storage in building materials, Energy Buildings 20 (1993) 77–86. http://dx.doi.org/10.1016/0378-7788(93)90040-2 [13] G. Belton, F. Ajami, Thermochemistry of salt hydrates, Report No. NSF/RANN/SE/GI27976/TR/73/4, Philadelphia (Pennsylvania, USA), 1973. [14] M. Telkes, Thermal storage for solar heating and cooling, Proceedings of the Workshop on Solar Energy Storage Subsystems for the Heating and Cooling of Buildings, Charlottesville (Virginia, USA), 1975, cited by [5]. [15] F. Lindner, Wärmespeicherung mit Salzen und Salzhydraten, Ki Luft- und Kältetechnik 10 (1996) 462–467, cited by [5]. [16] T. Wada, F. Kimura, Y. Matsuo, Studies on salt hydrate for latent heat storage. IV. Crystallization in the binary system CH3CO2Na-H2O, Bul. Chem. Soc. Jpn. 56 (1983) 3827–3829. http://dx.doi.org/10.1246/bcsj.56.3827
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[17] L.F. Cabeza, A. Castell, C. Barreneche, A. de Gracia, A.I. Fernández, Materials used as PCM in thermal energy storage in buildings: A review, Renewable and Sustainable Energy Reviews 15 (2011) 1675–1695. http://dx.doi.org/10.1016/j.rser.2010.11.018 [18] https://en.wikipedia.org/wiki/Calcium_nitrate (date:07.07.16) [19] http://antoine.frostburg.edu/chem/senese/javascript/water-density.html (date:07.07.16) [20] https://en.wikipedia.org/wiki/Density (date:07.07.16) [21] Xia Yin, Dongdong Li, Yuqi Tan, Xiaoya Wu, Xiuli Yu and Dewen Zeng, Solubility Phase Diagram of the Ca(NO3)2–Mg(NO3)2−H2O System, J. Chem. Eng. Data 59(12) (2014) 4026–4030. doi:10.1021/je500629s