^{1}, Sindee L. Simon

^{1,a)}and Gregory B. McKenna

^{1,b)}

### Abstract

The specific heat capacity was measured with step-scan differential scanning calorimetry for linear alkanes from pentane to nonadecane , for several cyclic alkanes, for linear and cyclic polyethylenes, and for a linear and a cyclic polystyrene. For the linear alkanes, the specific heat capacity in the equilibrium liquid state decreases as chain length increases; above a carbon number of 10 (decane) the specific heat asymptotes to a constant value. For the cyclic alkanes, the heat capacity in the equilibrium liquid state is lower than that of the corresponding linear chains and increases with increasing chain length. At high enough molecular weights, the heat capacities of cyclic and linear molecules are expected to be equal, and this is found to be the case for the polyethylenes and polystyrenes studied. In addition, the thermal properties of the solid-liquid and the solid-solidtransitions are examined for the linear and cyclic alkanes; solid-solidtransitions are observed only in the odd-numbered alkanes. The thermal expansion coefficients and the specific volumes of the linear and cyclic alkanes are also calculated from literature data and compared with the trends in the specific heats.

The support of the National Science Foundation Grant No. DMR-0304640 is gratefully acknowledged.

I. INTRODUCTION

II. EXPERIMENT

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Heat capacity
- 48.0
- Carbon
- 30.0
- Solid solid phase transitions
- 25.0
- Solid liquid phase transitions
- 21.0
- Entropy
- 17.0

## Figures

Dependence of the absolute specific heat capacity in the liquid state on temperature for linear alkanes, with data for both cyclic and linear alkanes shown in the inset. Symbols are as follows: 엯 ; ● ; ◻ ; ∎ ; ▵ ; ▴ ; ▿ ; ▾ ; ◇ ; ◆ ; + ; ☉ ; ⧅ ; ⊞ ; ⊠ ; ▶ ; ▷ ; ◢ . The upper four curves are labeled for clarity in the figure and the cyclic alkanes are labeled in the inset.

Dependence of the absolute specific heat capacity in the liquid state on temperature for linear alkanes, with data for both cyclic and linear alkanes shown in the inset. Symbols are as follows: 엯 ; ● ; ◻ ; ∎ ; ▵ ; ▴ ; ▿ ; ▾ ; ◇ ; ◆ ; + ; ☉ ; ⧅ ; ⊞ ; ⊠ ; ▶ ; ▷ ; ◢ . The upper four curves are labeled for clarity in the figure and the cyclic alkanes are labeled in the inset.

Chain length dependence of the absolute heat capacity in the liquid state at for both of linear and cyclic alkanes, where is the number of carbons in the chain. Our data are shown as squares (-alkanes) and circles (-alkanes), with open symbols indicating that the value was extrapolated from the liquid state to . Data at the highest values are for linear and cyclic polyethylenes extrapolated from the liquid values shown in Fig. 3. Data for -pentane (Ref. 11) and -octane (Ref. 12) are also shown. Error bars for our measurements are . Lines are not a fit of the data and are provided only to guide the eye.

Chain length dependence of the absolute heat capacity in the liquid state at for both of linear and cyclic alkanes, where is the number of carbons in the chain. Our data are shown as squares (-alkanes) and circles (-alkanes), with open symbols indicating that the value was extrapolated from the liquid state to . Data at the highest values are for linear and cyclic polyethylenes extrapolated from the liquid values shown in Fig. 3. Data for -pentane (Ref. 11) and -octane (Ref. 12) are also shown. Error bars for our measurements are . Lines are not a fit of the data and are provided only to guide the eye.

Liquid heat capacities of cyclic (-PE10 and -PE1) and linear (HDPE) polyethylenes as a function of temperature. The reference values recommended by Guar and Wunderlich (Ref. 13) are also shown, along with the error bars of 3.5% that they recommend.

Liquid heat capacities of cyclic (-PE10 and -PE1) and linear (HDPE) polyethylenes as a function of temperature. The reference values recommended by Guar and Wunderlich (Ref. 13) are also shown, along with the error bars of 3.5% that they recommend.

Heat capacities of a cyclic and linear polystyrene as a function of temperature above and below ; the materials have nominal molecular weights of 4000 and , respectively.

Heat capacities of a cyclic and linear polystyrene as a function of temperature above and below ; the materials have nominal molecular weights of 4000 and , respectively.

Change in entropy for the solid-solid and solid-liquid transitions for the linear alkanes as the function of the number of carbon atoms in the molecule; note that only the odd-numbered alkanes show a solid-solid transition(s). The total change in entropy from the low-temperature solid to the liquid is also shown and is the sum of solid-solid and solid-liquid transitions.

Change in entropy for the solid-solid and solid-liquid transitions for the linear alkanes as the function of the number of carbon atoms in the molecule; note that only the odd-numbered alkanes show a solid-solid transition(s). The total change in entropy from the low-temperature solid to the liquid is also shown and is the sum of solid-solid and solid-liquid transitions.

Chain length dependence of the thermal expansion coefficient for both linear and cyclic alkanes at , where is the number of carbons in the chain. Both values predicted from the modified Rackett equation (Ref. 25) and values from fits of experimental data in the literature (Refs. 26–28) are shown. Values from the Rackett equation and values extrapolated outside of the experimental temperature range are shown as open points; closed symbols indicate values obtained from experimental fits to data covering the temperature of interest. Lines are not a fit of the data and are provided only to guide the eye.

Chain length dependence of the thermal expansion coefficient for both linear and cyclic alkanes at , where is the number of carbons in the chain. Both values predicted from the modified Rackett equation (Ref. 25) and values from fits of experimental data in the literature (Refs. 26–28) are shown. Values from the Rackett equation and values extrapolated outside of the experimental temperature range are shown as open points; closed symbols indicate values obtained from experimental fits to data covering the temperature of interest. Lines are not a fit of the data and are provided only to guide the eye.

Chain length dependence of the specific volume for both linear and cyclic alkanes at , where is the number of carbons in the chain. Shown are values predicted from the modified Rackett equation (Ref. 25), values from fits of experimental data in the literature (Refs. 26–28), and values reported in the literature (Ref. 29). Values from the Rackett equation and values extrapolated outside of the experimental temperature range are shown as open points; closed symbols indicate values obtained from experimental fits to data covering the temperature of interest or for values reported in the literature. Lines are not a fit of the data and are provided only to guide the eye.

Chain length dependence of the specific volume for both linear and cyclic alkanes at , where is the number of carbons in the chain. Shown are values predicted from the modified Rackett equation (Ref. 25), values from fits of experimental data in the literature (Refs. 26–28), and values reported in the literature (Ref. 29). Values from the Rackett equation and values extrapolated outside of the experimental temperature range are shown as open points; closed symbols indicate values obtained from experimental fits to data covering the temperature of interest or for values reported in the literature. Lines are not a fit of the data and are provided only to guide the eye.

## Tables

Specific heat capacities in liquid state, with in °C.

Specific heat capacities in liquid state, with in °C.

Solid-solid and solid-liquid transitions for linear and cyclic alkanes.

Solid-solid and solid-liquid transitions for linear and cyclic alkanes.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content