#
Thermophysical Characterization of MgCl_{2}·6H_{2}O, Xylitol and Erythritol as Phase Change Materials (PCM) for Latent Heat Thermal Energy Storage (LHTES)

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Investigated PCM

#### 2.2. Heat Capacity, Melting Temperature and Latent Heat

#### 2.2.1. DSC

^{®}from Netzsch, Selb, Germany. The analysis was carried out in accordance with the procedure given by Gschwander et al. [33], but, due to the supercooling of the specimen, only the heating cycles were analysed. Three samples with masses of about 10 $\mathrm{m}\mathrm{g}$ were taken from every PCM and placed as powder in 25 $\mathsf{\mu}$L aluminium crucibles and sealed by cold welding. Each sample was exposed to three consecutive cooling and heating cycles with a heating and cooling rate of 0.5 $\mathrm{K}/\mathrm{min}$. The heating rate was determined with a heating rate test to ensure thermal equilibrium within the samples [33]. Since these small heating rates result in a bad signal-to-noise ratio within the sensible regions (pure solid and liquid state) of the PCM, additional measurements with heating rates of 10 $\mathrm{K}/\mathrm{min}$ for determining the heat capacity were performed. All measurements were conducted under nitrogen atmosphere at 20 mL/min. Temperature and heatflow calibration were realised with pure water, gallium, indium, bismuth and zinc. A sapphire reference standard was applied for the determination of the heat capacities. The accuracy of the DSC for the enthalpy and heat capacity measurements can be assumed within a range of ±5% and ±3%, respectively [34]. The melting temperature ${\vartheta}_{m}$ was determined as the extrapolated onset temperature of the melting peak and the melting enthalpy ${h}_{m}$ was calculated with a linear baseline [35].

#### 2.2.2. Three-Layer-Calorimeter

#### 2.3. Density

#### 2.4. Thermal Diffusivity and Conductivity

^{®}from Netzsch, Selb, Germany. Three different samples of each PCM with five consecutive diffusivity measurements at different temperatures in the solid and the liquid phase were investigated. A specimen holder for low viscosity liquids was used for the measurements. As sketched in Figure 3, it consists of two stainless steel platelets that are separated by a PEEK (polyether ether ketone) torus. The torus has an inner diameter of 15 $\mathrm{m}\mathrm{m}$ and the thickness of the torus and the platelets is 1.5 $\mathrm{m}\mathrm{m}$ and 0.1 $\mathrm{m}\mathrm{m}$, respectively. The three parts are held together by a bolted housing not shown in the sketch. Normally, the liquid sample is filled in the specimen holder with a syringe through two small holes in the PEEK torus. Due to the high melting point of the investigated PCM (between 90 ${}^{\circ}\mathrm{C}$ and 120 ${}^{\circ}\mathrm{C}$), this procedure is not applicable. Instead of filling in as a liquid, the specimen was adapted in at solid state. Therefore, the PCM was milled to fine powder (Figure 3a) and afterwards pressed in a cylindrical mould (Figure 3b) with a diameter of 13.8 $\mathrm{m}\mathrm{m}$ and a depth of 1.55 $\mathrm{m}\mathrm{m}$. The diameter difference between the pressed powder pellet and the PEEK torus allows for the expansion of the PCM during the phase change and the slightly greater thickness of the pellet ensures sufficient contact with the platelets. The pellet was then placed in the specimen holder (Figure 3d) and the whole assembly was inserted in the LFA. Each measurement started above the melting point of the specimen to ensure the thermal contact between the PCM and the platelets (Figure 3e). Afterwards, the sample was cooled down and the thermal diffusivity in the solid state was determined (Figure 3f). After each series of measurements, the solidified specimen was reviewed to make sure that there were no air bubbles within the sample and that there was contact of the PCM with the platelets. When the sample was fine, the thermal diffusivity had been calculated with the Proteus LFA Analysis software version 6.1.0 from Netzsch, Selb, Germany applying a three-layer-model (platelet—sample—platelet). According to Netzsch, the accuracy of the LFA measurement with this type of sample holder can be assumed within a range of ±5% (tested with water).

#### 2.5. Cycling

## 3. Results and Discussion

#### 3.1. Heat Capacity, Melting Temperature and Latent Heat

#### 3.1.1. DSC

#### 3.1.2. Three-Layer-Calorimeter

#### 3.2. Density

^{−4}$/\mathrm{K}$, followed by MCHH with 1.17 · 10

^{−4}$/\mathrm{K}$ and erythritol with 2.94 · 10

^{−5}$/\mathrm{K}$. In the liquid state, the order is xylitol, erythritol and MCHH with values of 5.02 · 10

^{−4}$/\mathrm{K}$, 3.95 · 10

^{−4}$/\mathrm{K}$ and 3.76 · 10

^{−4}$/\mathrm{K}$, respectively. For the calculation of ${\alpha}_{V}$, a linear behaviour of the change of density was assumed. This assumption results in a maximum deviation of 0.3% between measured values and the linear fit. The density change from solid to liquid is 10.1% for erythritol, followed by 8.4% for xylitol and 7.7% for MCHH. For these values, the measured results were extrapolated to the melting point of the specimen. Some key results of the measurements are summarized in Table 4.

#### 3.3. Thermal Diffusivity and Conductivity

#### 3.4. Cycling

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

3LC | 3-layer-calorimeter | |

DSC | Differential scanning calorimeter | |

FEP | Fluorinated ethylene propylene | |

LFA | Light flash apparatus | |

LHTES | Latent heat thermal energy storage | |

M | Measurement | |

MCHH | Magnesiumchloride hexahydrate | |

PEEK | Polyether ether ketone | |

PCM | Phase change material | |

ss | Stainless steel | |

S | Sample | |

a | $\mathrm{m}{\mathrm{m}}^{2}/\mathrm{s}$ | Thermal diffusivity |

${c}_{p}$ | $\mathrm{J}/(\mathrm{g}\text{}\mathrm{K})$ | Heat capacity |

${d}_{1}$, ${d}_{2}$ | Factors for linear equations | |

${e}_{1}$, ${e}_{2}$ | Factors for linear equations | |

h | $\mathrm{J}/\mathrm{g}$ | Enthalpy |

k | Coverage factor | |

W | $\mathrm{g}$ | Weighing value |

${\alpha}_{V}$ | $1/\mathrm{K}$ | Volumetric coefficient of thermal expansion |

$\Delta {\varrho}_{sl}$ | % | Change of density from solid to liquid state |

$\vartheta $ | ${}^{\circ}\mathrm{C}$ | Temperature |

$\Delta {\vartheta}_{sup}$ | $\mathrm{K}$ | Supercooling |

$\lambda $ | $\mathrm{W}/\left(\mathrm{m}\mathrm{K}\right)$ | Thermal conductivity |

$\varrho $ | $\mathrm{g}/{\mathrm{cm}}^{3}$ | Density |

${\square}_{0}$ | Reference state | |

${\square}_{l}$ | Liquid (state) | |

${\square}_{m}$ | Melting | |

${\square}_{s}$ | Solid (state) |

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**Figure 3.**Sketch of the LFA sample holder (

**left**) and steps of the sample preparation for the LFA measurements (

**right**).

**Figure 4.**Heat capacity of erythritol at different melting cycles. The sample has two different melting points depending on the present crystal structure within the solid phase.

**Figure 5.**Enthalpy h and heat capacity ${c}_{p}$ as a function of the temperature $\vartheta $ for MCHH. The upper graph presents the mean value of three samples. The grey areas are determined with the c${}_{p}$-comparative method and the melting peak with a sensitivity calibration. The dashed lines represent the standard deviation.

**Figure 6.**Enthalpy h as a function of the temperature $\vartheta $ for MCHH. The solid line is the result of the DSC measurement (Figure 5) and the dashed lines connect the resulting measuring points from the 3LC. The arrows indicate the direction of temperature change within the measurements.

**Figure 7.**Density $\varrho $ as a function of the temperature $\vartheta $ of the investigated PCM. The dashed line represents the linear fit of the measured points.

**Figure 8.**Thermal diffusivity a of the investigated PCM. The error bars are the standard deviation from three different samples and five shots at each temperature. The dashed line represents the linear fit of the points, used to calculate the temperature dependency of a, and extrapolated to the melting point of the PCM.

**Figure 9.**Results of the cycling test with MCHH. The enthalpies and temperatures of each cycle are related to the value of the first cycle.

Property | Erythritol | Source | Xylitol | Source | MCHH | Source |
---|---|---|---|---|---|---|

${\vartheta}_{m}$ in ${}^{\circ}\mathrm{C}$ | 117–120 | [5,7,9,10,28,29] | 92–94 | [5,7,19,28,29,30] | 110.8–117.5 | [5,20,21,24,25,26] |

${h}_{m}$ in $\mathrm{J}/\mathrm{g}$ | 315–379.57 | [5,7,9,10,12,28,29] | 232–280 | [5,7,19,28,29,30] | 133.9–200 | [5,12,20,21,24,25,26] |

${c}_{p,s}$ in $\mathrm{J}/(\mathrm{g}\text{}\mathrm{K})$ | 1.38 (20 ${}^{\circ}\mathrm{C}$) | [31] | 1.33 | [30] | 2.25 (100 ${}^{\circ}\mathrm{C}$) | [20] |

2.1 (25 ${}^{\circ}\mathrm{C}$) | [32] | |||||

${c}_{p,l}$ in $\mathrm{J}/(\mathrm{g}\text{}\mathrm{K})$ | 2.76 (140 ${}^{\circ}\mathrm{C}$) | [31] | 2.36 | [30] | 2.61 (120 ${}^{\circ}\mathrm{C}$) | [20] |

${\lambda}_{s}$ in $\mathrm{W}/\left(\mathrm{m}\mathrm{K}\right)$ | 0.733 (20 ${}^{\circ}\mathrm{C}$) | [5] | - | - | 0.704 (110 ${}^{\circ}\mathrm{C}$) | [5,20] |

${\lambda}_{l}$ in $\mathrm{W}/\left(\mathrm{m}\mathrm{K}\right)$ | 0.326 (140 ${}^{\circ}\mathrm{C}$) | [5] | - | - | 0.570 (120 ${}^{\circ}\mathrm{C}$) | [5,20] |

${\varrho}_{s}$ in $\mathrm{g}/{\mathrm{cm}}^{3}$ | 1.480 (20 ${}^{\circ}\mathrm{C}$) | [5] | 1.500 (20 ${}^{\circ}\mathrm{C}$) | [5] | 1.569 (20 ${}^{\circ}\mathrm{C}$) | [5,20] |

${\varrho}_{l}$ in $\mathrm{g}/{\mathrm{cm}}^{3}$ | 1.300 (140 ${}^{\circ}\mathrm{C}$) | [5] | - | - | 1.450 (120 ${}^{\circ}\mathrm{C}$) | [5,20] |

1.422 (128 ${}^{\circ}\mathrm{C}$) | [32] |

**Table 2.**Factors for the linear equation ${c}_{p}\left(\vartheta \right)={d}_{1}$$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$$\vartheta +{d}_{2}$ to describe the temperature dependency of the heat capacity of MCHH.

Range | ${\mathit{d}}_{1}$ | ${\mathit{d}}_{2}$ |
---|---|---|

solid (80–110 ${}^{\circ}\mathrm{C}$) | $7.00\times {10}^{-3}$ | 1.155 |

liquid (120–150 ${}^{\circ}\mathrm{C}$) | $5.145\times {10}^{-3}$ | 1.945 |

**Table 3.**Factors for the linear equation $a\left(\vartheta \right)={e}_{1}$$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$$\vartheta +{e}_{2}$ to describe the temperature dependency of the thermal diffusivity.

Range | ${\mathit{e}}_{1}$ | ${\mathit{e}}_{2}$ |
---|---|---|

Erythritol | ||

s. (20–118 ${}^{\circ}\mathrm{C}$) | $-1.099\times {10}^{-3}$ | $4.813\times {10}^{-1}$ |

l. (118–150 ${}^{\circ}\mathrm{C}$) | $3.338\times {10}^{-5}$ | $8.390\times {10}^{-2}$ |

Xylitol | ||

s. (20–90 ${}^{\circ}\mathrm{C}$) | $-7.351\times {10}^{-4}$ | $2.865\times {10}^{-1}$ |

l. (90–140 ${}^{\circ}\mathrm{C}$) | $-2.666\times {10}^{-5}$ | $1.035\times {10}^{-1}$ |

MgCl${}_{2}$$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$6H${}_{2}$O | ||

s. (20–115 ${}^{\circ}\mathrm{C}$) | $-1.437\times {10}^{-4}$ | $2.471\times {10}^{-1}$ |

l. (115–150 ${}^{\circ}\mathrm{C}$) | $-5.794\times {10}^{-4}$ | $2.377\times {10}^{-1}$ |

**Table 4.**Results of the three investigated PCMs including the standard deviation of the measurements. The results for the thermal conductivity are calculated from the measured thermal diffusivities a, densities $\varrho $ and heat capacities ${c}_{p}$ and the deviation is the combined uncertainty of the applied measurement devices.

Property | Erythritol | Xylitol | MCHH |
---|---|---|---|

${\vartheta}_{m,DSC}$ in ${}^{\circ}\mathrm{C}$ | 105.1 ± 0.1 | 90 ± 1 | 115.1 ± 0.1 |

118.1 ± 0.6 | |||

${\vartheta}_{m,3LC}$ in ${}^{\circ}\mathrm{C}$ | 118.2 | - | 115.8 |

$\Delta {\vartheta}_{sup,DSC}$ in $\mathrm{K}$ | 60 | >90 | 30 |

$\Delta {\vartheta}_{sup,3LC}$ in $\mathrm{K}$ | 47 | - | 2.8 |

${h}_{m,DSC}$ in $\mathrm{J}/\mathrm{g}$ | 316 ± 1 (90–135 ${}^{\circ}\mathrm{C}$) | 237.6 ± 1.3 (70–116 ${}^{\circ}\mathrm{C}$) | 166.9 ± 1.2 (114–118 ${}^{\circ}\mathrm{C}$) |

352.9 ± 0.7 (110–145 ${}^{\circ}\mathrm{C}$) | |||

${h}_{m,3LC}$ in $\mathrm{J}/\mathrm{g}$ | 337 (110–125 ${}^{\circ}\mathrm{C}$) | - | 143.4 (114–118 ${}^{\circ}\mathrm{C}$) |

${c}_{p,s}$ in $\mathrm{J}/\left(\mathrm{g}\mathrm{K}\right)$ | 1.34 ± 0.09 (20 ${}^{\circ}\mathrm{C}$) | 1.27 ± 0.05 (20 ${}^{\circ}\mathrm{C}$) | 1.83 ± 0.06 (100 ${}^{\circ}\mathrm{C}$) |

${c}_{p,l}$ in $\mathrm{J}/\left(\mathrm{g}\mathrm{K}\right)$ | 2.87 ± 0.03 (150 ${}^{\circ}\mathrm{C}$) | 2.73 ± 0.08 (120 ${}^{\circ}\mathrm{C}$) | 2.57 ± 0.06 (120 ${}^{\circ}\mathrm{C}$) |

${a}_{s,20\text{}{}^{\circ}\mathrm{C}}$ in $\mathrm{m}{\mathrm{m}}^{2}/\mathrm{s}$ | 0.456 ± 0.018 | 0.270 ± 0.002 | 0.244 ± 0.011 |

${a}_{l,120\text{}{}^{\circ}\mathrm{C}}$ in $\mathrm{m}{\mathrm{m}}^{2}/\mathrm{s}$ | 0.088 ± 0.001 | 0.100 ± 0.001 | 0.173 ± 0.008 |

${\varrho}_{s,20\text{}{}^{\circ}\mathrm{C}}$ in $\mathrm{g}/{\mathrm{cm}}^{3}$ | 1.4404 ± 0.0005 | 1.5050 ± 0.0004 | 1.5955 ± 0.0002 |

${\alpha}_{V,s(20\text{}{}^{\circ}\mathrm{C}\cdots {\vartheta}_{m})}$ in $1/\mathrm{K}$ | 2.94 · 10^{−5} | 1.64 · 10^{−4} | 1.17 · 10^{−4} |

${\varrho}_{l,120\text{}{}^{\circ}\mathrm{C}}$ in $\mathrm{g}/{\mathrm{cm}}^{3}$ | 1.2891 ± 0.0008 | 1.3446 ± 0.0003 | 1.4557 ± 0.0004 |

${\alpha}_{V,l({\vartheta}_{m}\cdots 150\text{}{}^{\circ}\mathrm{C})}$ in $1/\mathrm{K}$ | 3.95 · 10^{−4} | 5.02 · 10^{−4} | 3.76 · 10^{−4} |

$\Delta {\varrho}_{sl}$ in % | 10.1 | 8.4 | 7.7 |

${\lambda}_{s}$ in $\mathrm{W}/(\mathrm{m}\text{}\mathrm{K})$ | 0.89 ± 0.06 (20 ${}^{\circ}\mathrm{C}$) | 0.52 ± 0.04 (20 ${}^{\circ}\mathrm{C}$) | 0.70 ± 0.05 (110 ${}^{\circ}\mathrm{C}$) |

${\lambda}_{l}$ in $\mathrm{W}/(\mathrm{m}\text{}\mathrm{K})$ | 0.33 ± 0.02 (140 ${}^{\circ}\mathrm{C}$) | 0.36 ± 0.03 (140 ${}^{\circ}\mathrm{C}$) | 0.63 ± 0.04 (120 ${}^{\circ}\mathrm{C}$) |

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**MDPI and ACS Style**

Höhlein, S.; König-Haagen, A.; Brüggemann, D.
Thermophysical Characterization of MgCl_{2}·6H_{2}O, Xylitol and Erythritol as Phase Change Materials (PCM) for Latent Heat Thermal Energy Storage (LHTES). *Materials* **2017**, *10*, 444.
https://doi.org/10.3390/ma10040444

**AMA Style**

Höhlein S, König-Haagen A, Brüggemann D.
Thermophysical Characterization of MgCl_{2}·6H_{2}O, Xylitol and Erythritol as Phase Change Materials (PCM) for Latent Heat Thermal Energy Storage (LHTES). *Materials*. 2017; 10(4):444.
https://doi.org/10.3390/ma10040444

**Chicago/Turabian Style**

Höhlein, Stephan, Andreas König-Haagen, and Dieter Brüggemann.
2017. "Thermophysical Characterization of MgCl_{2}·6H_{2}O, Xylitol and Erythritol as Phase Change Materials (PCM) for Latent Heat Thermal Energy Storage (LHTES)" *Materials* 10, no. 4: 444.
https://doi.org/10.3390/ma10040444