# Review of Thermophysical Property Data of Octadecane for Phase-Change Studies

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## Abstract

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## 1. Introduction

## 2. Literature Review of Thermophysical Properties of Octadecane

#### 2.1. Melting Temperature

#### 2.2. Melting Enthalpy

#### 2.3. Density

#### 2.4. Heat Capacity

#### 2.5. Thermal Conductivity

#### 2.6. Viscosity

## 3. Preselection of Data

#### 3.1. Melting Temperature and Enthalpy

- Only temperature data which were achieved as the extrapolated onset temperature ${T}_{e}$ or the temperature ${T}_{*}$ (see Section 2.1) are considered since these temperatures seem to represent a realistic melting point of octadecane.

#### 3.2. Density

- One datapoint of Shlosinger and Bentilla [67] was neglected since it was located in the 2-phase-region.
- The whole series of solid state data from Seyer et al. [62] was removed because of the indicated solid-solid transformation.
- All data of Würflinger and Schneider [73] were excluded due to the applied inverse method for determining the solid-state density.
- The data of Müller and Lonsdale [74] were neglected since their results where achieved with X-ray measurements resulting in very high theoretical density calculations based on the distance between the molecules.
- Liquid state densities from van Hook and Silver [64] were excluded because of incomprehensible corrections in their data.
- The liquid state data point of McKinney [72] was removed since it was given at a temperature of 25 ${}^{\circ}$C which is obviously in the solid state.

#### 3.3. Thermal Conductivity

#### 3.4. Heat Capacity

- Data points near the phase change temperature were neglected since they may be affected by phase change phenomena and therefore do not describe pure sensible heating of octadecane.
- The liquid state heat capacity of Parks et al. [53] was excluded because the indicated temperature is in the solid state range.
- The data of Djordjevic and Laub [46] were removed in both phases because they were outliers on the high side of values found in the literature.

#### 3.5. Viscosity

## 4. Statistics

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | Coefficient |

B | Coefficient |

AC | Adiabatic calorimeter |

CV | Capillary viscometer |

DM | Dilatometer |

DSC | Differential scanning calorimetry |

FV | Falling-body viscometer |

g | Study/cluster number |

G | Total number of studies/clusters |

HM | Hydrometer |

HW | Hydrostatic weighing |

${H}_{0}$ | Null hypothesis |

IM | Inverse method |

N | Number of observations |

n/a | Not available |

NC | Not classified |

OR | Own research |

PM | Pycnometer |

RR | Rotational rheometer |

SC | Stationary cylinder |

SP | Stationary plate |

${t}_{\alpha /2}$ | Critical value from a student t-distribution |

T | Temperature |

TA | Transient thermal analyser |

${T}_{c}$ | Extrapolated offset temperature |

${T}_{e}$ | Extrapolated onset temperature |

${T}_{f}$ | Final peak temperature |

${T}_{i}$ | Initial peak temperature |

${T}_{p}$ | Peak maximum temperature |

TP | Transient plane source |

${T}_{*}$ | Temperature with insufficient information about its determination |

TR | Translational rheometer |

TW | Transient hot wire |

VE | Vibrating-element |

VV | Vibrating viscometer |

${\widehat{\mathbf{V}}}_{OLS}$ | Esitmated variance-covariance matrix of the ordinary least squares estimator |

${\widehat{\mathbf{V}}}_{WLS}$ | Esitmated variance-covariance matrix of the weighted least squares estimator |

$\mathbf{W}$ | Weighting matrix |

$\mathbf{x}$ | Explanantory variable vector |

$\mathbf{X}$ | Explanantory variable matrix |

y | Measured values |

$\mathbf{y}$ | Vector of measured values |

$\widehat{y}$ | Estimated value |

$\alpha $ | Significance level |

$\beta $ | Parameter |

$\mathit{\beta}$ | Parameter vector |

$\widehat{\mathit{\beta}}$ | Estimated parameter vector |

${\widehat{\mathit{\beta}}}_{OLS}$ | Ordinary least squares estimator |

${\widehat{\mathit{\beta}}}_{WLS}$ | Weighted least squares estimator |

$\epsilon $ | Random error term |

$\tilde{\mathit{\epsilon}}$ | Vector of residuals |

$\eta $ | Viscosity |

$\sigma $ | Uncertainty of observation |

## Appendix A

#### Appendix A.1. Estimated Fit Functions and Confidence Intervals

#### Appendix A.1.1. Melting Temperature

#### Appendix A.1.2. Melting Enthalpy

#### Appendix A.1.3. Density

#### Appendix A.1.4. Heat Capacity

#### Appendix A.1.5. Thermal Conductivity

#### Appendix A.1.6. Viscosity

#### Appendix A.2. Comparison of Estimated Fit Functions with Functions from Literature

**Figure A1.**Comparison of the estimated fit functions with functions from literature. The black lines are the estimated fit functions from Table 6 (solid line) and the corresponding confidence intervals of 95 % (dashed line) and 99 % (dotted line) from Appendix A.1. The red and blue lines represent the functions from the VDI heat atlas [101] and from Yaws [104], respectively.

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**Figure 1.**Summary of melting temperature (

**a**) and enthalpy (

**b**) data from the literature. The melting temperature (

**a**) is arranged according to the given temperature definition. The blue bars represent the mean value of the data at each temperature definition. The melting enthalpy data (

**b**) are presented in the histogram according to their frequency.

**Figure 2.**Summary of density data from the literature in the solid (

**a**) and liquid (

**b**) state. The error bars are the specified uncertainty of the data. The values named OR are results from our own research. (

**a**) ∘ [62] □ [64] ⋄ [66] Δ [67] ∇ [73] ◊ [74] ⬠ OR; (

**b**) ∘ [6] □ [27] ⋄ [27] Δ [28] ∇ [61] ◊ [62] ⬠ [63] ∘ [64] □ [65] ⋄ [67] Δ [68] ∇ [69] ◊ [70] ⬠ [71] ∘ [72] □ [73] ⋄ [75] Δ OR.

**Figure 3.**Summary of heat capacity data from the literature in the solid (

**a**) and liquid (

**b**) state. The error bars are the specified uncertainty of the data. The displayed data of Vélez et al. [27] and of our own research (OR) are reduced to every tenth and fourth point of the available results, respectively. (

**a**) ∘ [27] □ [46] ⋄ [47] Δ [53] ∇ [54] ◊ OR; (

**b**) ∘ [27] □ [45] ⋄ [46] Δ [53] ∇ [54] ◊ [67] ⬠ [76]∘ [77] □ [78] ⋄ OR.

**Figure 4.**Summary of thermal conductivity data from the literature in the solid (

**a**) and liquid (

**b**) state. The error bars are the specified uncertainty of the data. (

**a**) ∘ [27] □ [32] ⋄ [38] Δ [39] ∇ [80] ◊ [80] ⬠ [80] ∘ [81] □ [82] ⋄ [83] Δ [85] ∇ [86] ◊ [88] ⬠ [90] ∘ [91] □ [94]; (

**b**) ∘ [27]□ [28] ⋄ [80] Δ [81] ∇ [82] ◊ [83] ⬠ [84] ∘ [85] □ [86] ⋄ [87] Δ [88] ∇ [89] ◊ [92] ⬠ [93] ∘ [94].

**Figure 6.**Summary of the estimated fit functions for the temperature-dependent thermophysical properties of octadecane. The displayed points indicate the preselected data applied for the calculation and the color scale corresponds to the associated uncertainty. The grey shaded areas between the dashed lines describe the confidence interval of 95% and the dotted lines a confidence of 99%.

Reference | Purity in % | Year | Method | Temperature in K | Uncert. in K | Enthalpy in J/g | Uncert. in % |
---|---|---|---|---|---|---|---|

Rossini [6] | n/a | 1952 | NC | ${T}_{*}$ = 301.34 | 0.02 | 243.6 | 0.3 |

Qiu et al. [19] | 99 | 2012 | DSC, 5 K/min | ${T}_{i}$ = 298.65 | n/a | 223.1 | n/a |

${T}_{p}$ = 301.55 | n/a | ||||||

${T}_{f}$ = 303.65 | n/a | ||||||

Li et al. [20] | 99 | 2011 | DSC, 10 K/min | ${T}_{i}$ = 298.36 | n/a | 235.9 | n/a |

${T}_{p}$ = 302.97 | n/a | ||||||

Tang et al. [21] | 97 | 2017 | DSC, 5 K/min | ${T}_{e}$ = 301.68 ${}^{a}$ | 0.2 | 239.32 | 5 |

Bayramoglu [22] | 100 | 2011 | DSC, 10 K/min | ${T}_{e}$ = 301.11 ${}^{a}$ | n/a | 239.89 | n/a |

Jeong et al. [23] | n/a | 2013 | DSC, 5 K/min | ${T}_{e}$ = 303.55 | n/a | 247.6 ${}^{b}$ | n/a |

Zhang et al. [24] | n/a | 2013 | DSC, 5 K/min | ${T}_{e}$ = 299.99 ${}^{a}$ | n/a | 207.2 | n/a |

Sun et al. [25] | n/a | 2013 | DSC, 10 K/min | ${T}_{e}$ = 301.04 | n/a | 218.8 | n/a |

Wang and Lu [26] | 99 | 2013 | DSC, 0.5-1.5 K/min | ${T}_{e}$ = 301.55 | n/a | 230.5 | n/a |

Vélez et al. [27] | 99 | 2015 | DSC, 2 K/min | ${T}_{e}$ = 300.22 ${}^{a}$ | 0.095 | 243.68 | 0.04 |

Ho and Gao [28] | 99.9 | 2009 | DSC, 2 K/min | ${T}_{e}$ = 299.65 ${}^{a}$ | n/a | 243.1 | n/a |

Li et al. [29] | 97 | 2010 | DSC, 5 K/min | ${T}_{e}$ = 301.85 ${}^{a}$ | 0.2 | 232.49 | 5 |

${T}_{p}$ = 303.47 | 0.2 | ||||||

Döğüşcü et al. [30] | n/a | 2018 | DSC, 3 K/min | ${T}_{e}$ = 300.95 | n/a | 226.2 | n/a |

Qiu et al. [31] | 99 | 2015 | DSC, 5 K/min | ${T}_{e}$ = 298.65 | n/a | 227.1 | n/a |

${T}_{p}$ = 301.55 | n/a | ||||||

Jeon et al. [32] | n/a | 2012 | DSC, 5 K/min | ${T}_{p}$ = 302.06 ${}^{a}$ | n/a | 241.97 | n/a |

Zhang et al. [33] | 99.9 | 2012 | DSC, 0.2 K/min | ${T}_{p}$ = 303.25 ${}^{a}$ | n/a | 220.4 | n/a |

Shan et al. [34] | 95 | 2009 | DSC, 10 K/min | ${T}_{p}$ = 304.15 ${}^{a}$ | n/a | 222 | n/a |

Chaiyasat et al. [35] | 99.5 | 2012 | DSC, 5 K/min | ${T}_{p}$ = 303.15 ${}^{a}$ | n/a | 241.7 | n/a |

Chung et al. [36] | n/a | 2015 | DSC, 10 K/min | ${T}_{p}$ = 301.85 ${}^{a}$ | n/a | 226 | n/a |

He et al. [37] | 90 | 2014 | DSC, 10 K/min | ${T}_{p}$ = 301.89 ${}^{a}$ | n/a | 209.1 | n/a |

Yu et al. [38] | 98.5 | 2014 | DSC, 10 K/min | ${T}_{p}$ = 301.89 ${}^{a}$ | n/a | 209.1 | n/a |

Zhang et al. [39] | 90 | 2012 | DSC, 10 K/min | ${T}_{p}$ = 301.25 ${}^{a}$ | n/a | 212.6 | n/a |

Babich et al. [40] | n/a | 1992 | DSC, 2 K/min | ${T}_{p}$ = 301.6 | n/a | 200 | n/a |

Zhu et al. [41] | 90 | 2016 | DSC, 10 K/min | ${T}_{p}$ = 301.7 ${}^{a}$ | n/a | 204.4 | 6 |

Wei et al. [42] | 99 | 2014 | DSC, 1 K/min | ${T}_{*}$ = 300.95 | 0.2 | 242.24 | 1 |

Chang et al. [43] | 97 | 1983 | DSC, 5 K/min | ${T}_{*}$ = 301.1 | n/a | 233.4 | n/a |

Kolesnikov and Syunyaev [44] | n/a | 1985 | DSC, 8 and 1 K/min | ${T}_{*}$ = 301.00 | n/a | 238.7 | n/a |

Huang et al. [45] | 99 | 2005 | DSC | ${T}_{*}$ = 300.83 | n/a | 232.3 | n/a |

Djordjevic and Laub [46] | n/a | 1986 | DSC | ${T}_{*}$ = 301.6 | n/a | ||

Fonseca et al. [47] | 99.5 | 2014 | DSC, 0.48 K/min | ${T}_{*}$ = 301.46 | 0.1 | 241.02 | 1 |

Boudouh et al. [48] | 99 | 2016 | DSC, 0.8 K/min | ${T}_{*}$ = 300.3 | 0.1 | 256.7 | 0.5 |

Mondieig et al. [49] | 99 | 2004 | DSC, 2 K/min | ${T}_{*}$ = 301.1 | n/a | 236.1 | n/a |

Robles et al. [50] | 99.4 | 1996 | DSC, 2 K/min | ${T}_{*}$ = 301.1 | 0.6 | 235.0 | 7 |

Wei et al. [51] | 99.5 | 2013 | DSC, 1 K/min | ${T}_{*}$ = 300.9 | 0.2 | 242.2 | 1 |

Schaerer et al. [52] | 99.9 | 1955 | AC | ${T}_{*}$ = 301.35 | n/a | 241.3 | n/a |

Parks et al. [53] | 96 | 1949 | AC | ${T}_{*}$ = 301.3 | n/a | 237.8 | n/a |

Messerly et al. [54] | 99.98 | 1967 | AC | ${T}_{*}$ = 301.33 | n/a | 242.5 | n/a |

Meyer and Meyer [55] | 99.9 | 1983 | AC | ${T}_{*}$ = 301.27 | n/a | 236.5 | n/a |

Ksiazczak [56] | 99.7 | 1989 | NC | ${T}_{*}$ = 301.27 | 0.02 | ||

Carey and Smith [57] | 97 | 1933 | NC | ${T}_{*}$ = 300.85 | n/a | ||

Domańska et al. [58] | n/a | 1999 | NC | ${T}_{*}$ = 301.65 | n/a | ||

Levene et al. [59] | n/a | 1915 | NC | ${T}_{*}$ = 301.15 | n/a | ||

Parks et al. [60] | 95 | 1946 | NC | ${T}_{*}$ = 300.85 | n/a | ||

Krafft [61] | n/a | 1882 | NC | ${T}_{*}$ = 301.15 | n/a | ||

Seyer et al. [62] | n/a | 1944 | NC | ${T}_{*}$ = 301.25 | n/a |

Reference | Purity in % | Year | Method | Uncertainty in % | Observations | |
---|---|---|---|---|---|---|

Solid | Liquid | |||||

Rossini [6] | n/a | 1944 | NC | 2.5 | 0 | 52 |

Vélez et al. [27] | 99 | 2015 | HM/VE | 1/0.01 | 0 | 10/2 |

Ho and Gao [28] | 99.9 | 2009 | HM | 0.07 | 0 | 10 |

Krafft [61] | n/a | 1882 | NC | 2 ${}^{a}$ | 0 | 1 |

Seyer et al. [62] | n/a | 1944 | DM | 2 ${}^{a}$ | 16 | 8 |

Dover and Hensley [63] | n/a | 1934 | PM | 0.02 ${}^{b}$ | 0 | 2 |

van Hook and Silver [64] | 99 | 1942 | DM | 2 ${}^{a}$ | 1 | 1 |

Cutler et al. [65] | high purity | 1958 | DM | 0.1 | 0 | 5 |

Nelson et al. [66] | n/a | 1960 | DM | 2 ${}^{a}$ | 1 | 0 |

Shlosinger and Bentilla [67] | n/a | 1965 | PM | 2.5 (s)/0.26 (l) | 8 | 6 |

Findenegg [68] | 99 | 1970 | PM | 0.02 | 0 | 6 |

Espeau and Céolin [69] | n/a | 2006 | PM and DM | 1.5 | 0 | 99 |

Caudwell et al. [70] | 99 | 2004 | VE | 0.20 | 0 | 7 |

Graaf et al. [71] | n/a | 1992 | HW | 0.5 | 0 | 10 |

McKinney [72] | n/a | 1923 | NC | 2 ${}^{a}$ | 0 | 1 |

Würflinger and Schneider [73] | 99 | 1973 | NC | 2 ${}^{a}$ | 1 | 1 |

Müller and Lonsdale [74] | n/a | 1948 | NC | 2 ${}^{a}$ | 1 | 0 |

Dutour et al. [75] | 99 | 2000 | VE | 2 ${}^{a}$ | 0 | 8 |

Own research (OR) | 97 | 2018 | HW | 0.1 | 3 | 3 |

**Table 3.**Summary of heat capacity data from the literature. The number behind the abbreviation DSC describes either the heating rate (K/min) or the step size (K) of the applied measurement method.

Reference | Purity in % | Year | Method | Uncertainty in % | Observations | |
---|---|---|---|---|---|---|

Solid | Liquid | |||||

Vélez et al. [27] | 99 | 2015 | DSC, 5 K/min | 2 ${}^{a}$ | 166 | 198 |

Huang et al. [45] | 99 | 2005 | DSC, 1 K | 1 | 0 | 25 |

Djordjevic and Laub [46] | n/a | 1983 | DSC, 5 K/min | 3 ${}^{a}$ | 1 | 1 |

Fonseca et al. [47] | 99.5 | 2014 | DSC, 0.48 K/min | 1 | 5 | 0 |

Parks et al. [53] | 96 | 1949 | AC | 0.7 | 21 | 1 |

Messerly et al. [54] | 99.98 (mol) | 1967 | AC | 0.2 | 77 | 11 |

Shlosinger and Bentilla [67] | n/a | 1965 | NC | 5 ${}^{b}$ | 0 | 5 |

Höhne [76] | very pure | 1981 | DSC, 10 K/min | 5 | 0 | 3 |

Durupt et al. [77] | 99 | 1996 | DSC | 3 ${}^{a}$ | 0 | 9 |

van Miltenburg [78] | 99.8 | 1999 | AC | 0.2 | 0 | 38 |

Own research (OR) | 97 | 2018 | DSC, 1 K/min | 3 | 41 | 57 |

Reference | Purity in % | Year | Method | Uncertainty in % | Observations | |
---|---|---|---|---|---|---|

Solid | Liquid | |||||

Vélez et al. [27] | 99 | 2015 | TW | 2 | 20 | 10 |

Ho and Gao [28] | 99.9 | 2009 | TA | 5 | 0 | 7 |

Jeon et al. [32] ${}^{a}$ | n/a | 2012 | TP | 5 ${}^{b}$ | 1 | 0 |

Yu et al. [38] ${}^{a}$ | 98.5 | 2014 | TP | 5 ${}^{c}$ | 1 | 0 |

Zhang et al. [39] ${}^{a}$ | 90 | 2012 | TP | 5 ${}^{d}$ | 1 | 0 |

Irby et al. [80] | n/a | 1988 | TW/IM | 1.5-3 | 15/3 | 13 |

Harish et al. [81] ^{e} | n/a | 2015 | TW | 3 | 2 | 7 |

Wu et al. [82] | 99 | 2015 | TW | 2 | 3 | 3 |

Khadiran et al. [83] | n/a | 2015 | TW | 5 ${}^{f}$ | 1 | 1 |

Águila V et al. [84] | 99 | 2018 | TW | 5 | 0 | 4 |

Motahar et al. [85] | 99 | 2014 | TP | 1 | 5 | 6 |

Motahar et al. [86] | 99 | 2016 | TP | 2 | 5 | 6 |

Sakiadis and Coates [87] | 95 | 1957 | SP | 1 | 0 | 17 |

Powell et al. [88] | n/a | 1961 | SP | 2 ${}^{g}$ | 6 | 6 |

Ziebland and Patient [89] | n/a | 1962 | SC | 2 | 0 | 8 |

Griggs and Yarbrough [90] | 99 | 1978 | SC | 30 | 4 | 0 |

Yarbrough and Kuan [91] | n/a | 1981 | SC | 10-14 | 5 | 0 |

Mustafaev [92] | n/a | 1973 | NC | 2 | 0 | 4 |

Rastorguev and Bogatov [93] | n/a | 1972 | NC | 1.3 ${}^{h}$ | 0 | 4 |

Holmen et al. [94] | 99 | 2002 | NC | 20 | 1 | 1 |

^{e}Octadecane has been applied for calibration purpose; ${}^{f}$ Taken from Águila V et al. [84]; ${}^{g}$ Taken from Czichos et al. [79]; ${}^{h}$ Taken from Rastorguev et al. [97];

Reference | Purity in % | Year | Method | Uncertainty in % | Observations Liquid |
---|---|---|---|---|---|

Rossini [6] | n/a | 1952 | NC | 0.7 | 58 |

Ho and Gao [28] | 99.9 | 2009 | RR | 1 | 11 |

Dover and Hensley [63] | n/a | 1934 | CV | 1 ${}^{a}$ | 2 |

Caudwell et al. [70] | 99 | 2004 | VV | 2 | 7 |

Águila V et al. [84] | 99 | 2018 | RR | 1 | 6 |

Motahar et al. [85] | 99 | 2014 | RR | 4 | 6 |

Delgado et al. [98] ${}^{b}$ | 97 | 2018 | TR/RR/RR | 1.38/7.74/2.27 | 103/110 ${}^{c}$/148 ${}^{c}$ |

Hogenboom et al. [99] | high purity | 1967 | FV | 5 | 3 |

Ducoulombier et al. [100] | purum | 1986 | FV | 1 ${}^{d}$ | 4 |

**Table 6.**Estimated fit functions for the temperature-dependent thermophysical properties of octadecane and its mean melting temperature and enthalpy.

Property | Solid State | Liquid State | |
---|---|---|---|

(261.13 K–301.13 K) | (301.13 K–341.13 K) | ||

Density in kg/m${}^{3}$ | $867.914$ | $979.826-0.674\xb7T$ | |

Heat capacity in J/(g K) | $-1.029+9.797\xb7{10}^{-3}\xb7T$ | $3.247-8.861\xb7{10}^{-3}\xb7T+1.821\xb7{10}^{-5}\xb7{T}^{2}$ | |

Thermal conductivity in W/(m K) | $0.334$ | $0.246-3.121\xb7{10}^{-4}\xb7T$ | |

Viscosity in mPa s | - | $exp\left(-5.353+2026.013/T\right)$ | |

Melting temperature in K | - | 301.13 | - |

Melting enthalpy in J/g | - | 236.98 | - |

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**MDPI and ACS Style**

Faden, M.; Höhlein, S.; Wanner, J.; König-Haagen, A.; Brüggemann, D. Review of Thermophysical Property Data of Octadecane for Phase-Change Studies. *Materials* **2019**, *12*, 2974.
https://doi.org/10.3390/ma12182974

**AMA Style**

Faden M, Höhlein S, Wanner J, König-Haagen A, Brüggemann D. Review of Thermophysical Property Data of Octadecane for Phase-Change Studies. *Materials*. 2019; 12(18):2974.
https://doi.org/10.3390/ma12182974

**Chicago/Turabian Style**

Faden, Moritz, Stephan Höhlein, Joschka Wanner, Andreas König-Haagen, and Dieter Brüggemann. 2019. "Review of Thermophysical Property Data of Octadecane for Phase-Change Studies" *Materials* 12, no. 18: 2974.
https://doi.org/10.3390/ma12182974