# Density and Dynamic Viscosity of Perfluorodecalin-Added n-Hexane Mixtures: Deciphering the Role of Fluorous Liquids

^{*}

## Abstract

**:**

^{−3}), and dynamic viscosity (η/mPa·s), of neat perfluorodecalin (PFD) and PFD-added n-hexane mixtures with select compositions are reported. Density follows a linear decrease with temperature and a quadratic increase with the mole fraction of PFD. The sensitivity or dependence of density on temperature increases with an increase in PFD mole fraction. The temperature-dependence of the dynamic viscosity of the investigated mixtures follows the Arrhenius-type expression from which the resultant activation energy of the viscous flow (E

_{a,η}) is determined. Interestingly, the composition-dependence of dynamic viscosity shows exponential growth with an increase in PFD mole fraction. Excess molar volumes (V

^{E}) and deviation in the logarithmic viscosities ∆(ln η) of the mixtures are calculated to highlight the presence of strong repulsive interactions between the two mixture components.

## 1. Introduction

## 2. Materials and Methods

_{PFD}/x

_{Hex}= 0.2/0.8; 0.5/0.5; 0.8/0.2 were used for physical property determination. Densities (ρ) of the neat components, as well as of the (PFD + n-hexane) mixtures, were measured using a Mettler Toledo, DE45 delta range density meter. The density measurement with the above-mentioned density meter was based on the electromagnetically induced oscillations of a U-shaped glass tube. The standard deviations associated with the density measurement are ±0.0001 g·cm

^{−3}. The measurements were performed in a temperature range (293 to 333 K). The dynamic viscosities (η) were measured with a Peltier-based (resolution of 0.01 K and accuracy <0.05 K) automated Anton Paar microviscometer (model AMVn) having calibrated glass capillaries of different diameters (1.6, 1.8, 3.0, and 4.0 mm). This instrument is based on the rolling-ball principle, wherein a steel ball rolls down the inside of inclined, sample-filled calibrated glass capillaries. The deviation in η was ±0.001 mPa·s.

## 3. Results and Discussion

^{−3}and 5.412 mPa·s, respectively) and neat n-hexane (0.6593 g·cm

^{−3}and 0.300 mPa·s, respectively) at 298 K are reported in the literature [17,18]. These reported values are in good agreement with our measured values (vide infra). The slight disparities in the values may be attributed to the differences in the instrumentation used, the purity of the chemicals, and the source of the compounds.

#### 3.1. Density of PFD and (PFD + n-Hexane) Mixtures

^{−3}is the density of (PFD + n-hexane) mixtures. The values of the parameters ${\rho}_{0,T}$(representing density at T = 0 K) and the slope a along with the standard deviation of the fits are listed in Table 2 (measured densities of (PFD + n-hexane) mixtures along with the fits to a linear expression are presented in Figure 2).

_{5}) × 10

^{−3}g·cm

^{3}·K

^{−1}for PFD as opposed to only −0.9 (± 0.0

_{1}) × 10

^{−3}g·cm

^{3}·K

^{−1}for n-hexane). Such a high sensitivity of density on temperature for PFD may find uses in several industrial applications and processes and also as temperature sensors based on physical property changes [19].

_{PFD}is the mole fraction of PFD in the (PFD + n-hexane) mixtures, and values of parameters $\rho $

**, b, and c are listed in Table 3, while the fits are represented with dark curves in Figure 3. Quadratic dependence of the density on PFD mole fraction of the (PFD + n-hexane) mixtures is clearly established. Excess molar volume (V**

_{0,xPFD}^{E}) was estimated using equation 3 to assess the extent of molecular-level interactions within (PFD + n-hexane) mixtures.

_{PFD}, x

_{n}

_{-hexane}, and ρ

_{PFD}, ρ

_{n}

_{-hexane}refer to the mole fractions and densities, respectively, of PFD and n-hexane at a given temperature, and ρ

_{m}is the density of the mixture. M

_{PFD}and M

_{n}

_{-hexane}are the molecular weights of PFD and n-hexane, respectively. The V

^{E}at each investigated temperature for (PFD + n-hexane) mixtures are presented as a function of x

_{PFD}in the inset of Figure 3. It is clear that, irrespective of the T, V

^{E}are mostly positive and have maxima at ca. x

_{PFD}= 0.2. The positive V

^{E}points to volume expansion on mixing PFD and n-hexane and thus hints more at the presence of repulsive interaction (s) between PFD and n-hexane or weaker interactions between them than the interactions present within neat PFD and n-hexane, respectively. It may be inferred that the incompatibility of fluorous solvents with most non-fluorous substances brings in the repulsive interaction when the two substances are mixed.

#### 3.2. Dynamic Viscosity of PFD and (PFD + n-Hexane) Mixtures

_{η}is a parameter, and E

_{a,η}is the activation energy of the viscous flow.

_{η}and E

_{a,η}along with goodness-of-fit are presented in Table 5. As expected, E

_{a,η}increases monotonically as the concentration of the component with higher η PFD is increased in the mixture; neat PFD has the highest E

_{a,η}. It is established that fluorous liquid, PFD, possesses relatively high activation energy of viscous flow compared to the organic solvent n-hexane.

_{0}, d, and f, along with the goodness-of-the-fit in terms of R

^{2}, are given in Table 6. In order to assess the interactions within (PFD + n-hexane) mixtures, deviation in logarithmic viscosities, ∆(ln η), are estimated from the equation [21],

_{m}is the dynamic viscosity of the (PFD + n-hexane) mixture, and x

_{PFD}, x

_{n}

_{-hexane}, and η

_{PFD}, η

_{n}

_{-hexane}refer to the mole fractions and dynamic viscosities, respectively, of PFD and n-hexane at a given temperature. Plots of ∆(ln η) versus for (PFD + n-hexane) mixtures in a temperature range (293 to 333 K) are presented in the inset of Figure 5. A careful examination of Figure 5 reveals that, irrespective of the T, ∆(ln η) are negative and that no clear trend exists with variation in T. The negative ∆(ln η) further emphasizes the lack of attractive interaction within the (PFD + n-hexane) mixture; it rather indicates that repulsive interactions are present between PFD and n-hexane within the mixture, leading to lower viscosities than expected ideally. In this context, the negative ∆(ln η) corroborates and compliments the positive V

^{E}.

## 4. Conclusions

^{E}and ∆(ln η) hint at the repulsive interactions between PFD and n-hexane. The stark differences in the molecular architecture and the size of the two components might be responsible for such interactions. The work suggests that fluorous liquids may be used to effectively modulate the physical properties of common organic solvents. The data presented in this work is the beginning of physicochemical data on fluorous solvents as these solvents may afford a link between the interactions present in the gas phase and in the condensed phase.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Variation in densities of the investigated mixtures with temperature at different mole fraction ratios and at pressure p = 0.1 MPa. The solid line represents fit to the equation $\rho $/(g·cm

^{−3}) = $\rho $

_{0,T}/(g·cm

^{−3}) + $a$(T/K). Parameters $\rho $

_{0,T}and $a$, along with R

^{2}are provided in Table 2.

**Figure 3.**Variation in densities of the investigated mixtures with varying mole ratios of the constituents at different temperatures (T = 293 to 333 K) and at pressure p = 0.1 MPa. The solid line represents fit to the equation $\rho $/(g·cm

^{−3}) = $\rho $

_{0,xPFD}/(g·cm

^{−3}) + $b$(x

_{PFD}) + c(x

_{PFD}

^{2}). Parameters $\rho $

_{0,xPFD}, $b$, and $c$, along with R

^{2}, are provided in Table 3.

**Figure 4.**Variation in ln η of the investigated mixtures with T

^{−1}at different mole fraction ratios and at pressure p = 0.1 MPa. The solid curves represent the best fit to the Arrhenius model: $\mathrm{ln}(\eta /\mathrm{mPa}\xb7\mathrm{s})=\mathrm{ln}({A}_{\eta})+\frac{Ea,\eta}{RT}$. Parameters ln (A

_{η}), and E

_{α,η}, along with R

^{2}are reported in Table 5.

**Figure 5.**Variation in dynamic viscosities of the investigated mixtures with varying mole ratios of the constituents at different temperatures (T = 293 to 333 K) and at pressure p = 0.1 MPa. The solid line represents fit to the equation $\eta $/(mPa·s) = $\eta $

_{0}/(mPa·s) + $d\xb7$ e

^{f(xPFD)}. Parameters $\eta $

_{0}, $d,$ and $f$, along with R

^{2}, are provided in Table 6.

**Table 1.**Densities

^{a}($\rho $/g·cm

^{−3}) of the investigated mixtures of PFD and n-hexane at different mole fraction ratios at pressure p

^{b}= (0.1 MPa) and temperature T

^{c}= (293 K to 333 K).

${\mathit{x}}_{\mathbf{P}\mathbf{F}\mathbf{D}}^{}$^{d} | T/K | |||||
---|---|---|---|---|---|---|

293 | 298 | 303 | 313 | 323 | 333 | |

0.0 | 0.6596 | 0.6553 | 0.6515 | 0.6413 | 0.6320 | 0.6219 |

0.2 | 1.0433 | 1.0355 | 1.0298 | 1.0134 | 0.9983 | 0.9835 |

0.5 | 1.4735 | 1.4633 | 1.4553 | 1.4332 | 1.4127 | 1.3943 |

0.8 | 1.7855 | 1.7750 | 1.7661 | 1.7420 | 1.7199 | 1.7015 |

1.0 | 1.9412 | 1.9303 | 1.9212 | 1.8961 | 1.8733 | 1.8468 |

^{a}Standard uncertainty: u($\rho $ ) = ±0.0001 g·cm

^{−3};

^{b}Standard uncertainty: u(p) = ±0.005 MPa;

^{c}Standard uncertainty: u(T) = ±0.05 K;

^{d}Standard uncertainty: u(x) = ±0.01.

**Table 2.**Result of the regression analysis of density ($\rho $/g·cm

^{−3}) versus temperature (T/K) data according to equation: $\rho $/(g·cm

^{−3}) = $\rho $

_{0,T}/(g·cm

^{−3}) + $a$(T/K) for the investigated mixtures at different mole ratios over the temperature range 293 K to 333 K.

^{a}

${\mathit{x}}_{\mathbf{P}\mathbf{F}\mathbf{D}}^{}$^{b} | $\mathit{\rho}$_{0,T} (g·cm^{−3})
| $\mathit{a}$ 10^{−3} (g·cm^{−3}·K^{−1})
| R^{2} |
---|---|---|---|

0.0 | 0.9379 ± 0.0048 | −0.9 ± 0.0_{1} | 0.9990 |

0.2 | 1.4839 ± 0.0064 | −1.5 ± 0.0_{2} | 0.9993 |

0.5 | 2.0610 ± 0.0094 | −2.0 ± 0.0_{3} | 0.9991 |

0.8 | 2.4134 ± 0.0134 | −2.1 ± 0.0_{4} | 0.9984 |

1.0 | 2.6338 ± 0.0154 | −2.4 ± 0.0_{5} | 0.9982 |

^{a}Standard uncertainties u are, u(T) = ±0.05 K, u($\rho $) = ±0.0001 g·cm

^{−3};

^{b}Standard uncertainty: u(x) = ±0.01; Standard deviations are given with ± sign.

**Table 3.**Result of the regression analysis of density ($\rho $/g·cm

^{−3}) versus mole fraction of PFD (x

_{PFD}) data according to equation: $\rho $/(g·cm

^{−3}) = $\rho $

_{0,xPFD}/(g·cm

^{−3}) + $b$(x

_{PFD}) + c(x

_{PFD}

^{2}) for the investigated mixtures over the temperature range 293 K to 333 K.

^{a}

T/K | $\mathit{\rho}$_{0,xPFD} (g·cm^{−3})
| $\mathit{b}$ | $\mathit{c}$ | R^{2} |
---|---|---|---|---|

293 | 0.6661 ± 0.0107 | 1.9682 ± 0.0548 | −0.6984 ± 0.0529 | 0.9998 |

298 | 0.6616 ± 0.0102 | 1.9521 ± 0.0526 | −0.6883 ± 0.0508 | 0.9998 |

303 | 0.6578 ± 0.0103 | 1.9409 ± 0.0527 | −0.6824 ± 0.0509 | 0.9998 |

313 | 0.6474 ± 0.0099 | 1.9091 ± 0.0507 | −0.6650 ± 0.0489 | 0.9998 |

323 | 0.6378 ± 0.0095 | 1.8789 ± 0.0487 | −0.6478 ± 0.0471 | 0.9998 |

333 | 0.6267 ± 0.0076 | 1.8682 ± 0.0392 | −0.6507 ± 0.0379 | 0.9999 |

^{a}Standard uncertainties u are, u(T) = ±0.05 K, u($\rho $) = ±0.0001 g·cm

^{−3}, u(x) = ±0.01. Standard deviations are given with ± sign.

**Table 4.**Dynamic viscosity

^{a}($\eta $ /mPa·s) of the investigated mixtures of PFD and n-hexane at different mole fraction ratios at pressure p

^{b}= (0.1 MPa) and temperature T

^{c}= (293 K to 333 K).

${\mathit{x}}_{\mathbf{P}\mathbf{F}\mathbf{D}}^{}$^{d} | T/K | |||||
---|---|---|---|---|---|---|

293 | 298 | 303 | 313 | 323 | 333 | |

0.0 | 0.349 | 0.322 | 0.317 | 0.291 | 0.271 | 0.255 |

0.2 | 0.572 | 0.536 | 0.509 | 0.458 | 0.420 | 0.387 |

0.5 | 1.271 | 1.173 | 1.060 | 0.892 | 0.768 | 0.669 |

0.8 | 3.179 | 2.816 | 2.524 | 2.050 | 1.703 | 1.435 |

1.0 | 6.535 | 5.647 | 4.925 | 3.815 | 3.152 | 2.446 |

^{a}Standard uncertainty: u($\eta $) = ±0.001 mPa·s.

^{b}Standard uncertainty: u(p) = ±0.005 MPa.

^{c}Standard uncertainty: u(T) = ±0.05 K.

^{d}Standard uncertainty: u(x) = ±0.01.

**Table 5.**Summary of parameters associated with dynamic viscosity of the investigated mixtures according to the Arrhenius model using the equation: $\mathrm{ln}\eta =\mathrm{ln}{A}_{\eta}+Ea/RT$.

x_{PFD} | $\mathbf{l}\mathbf{n}{\mathit{A}}_{\mathit{\eta}}$ | $\mathit{E}\mathit{a},\mathit{\eta}$/kJ·mol^{−1} | R^{2} |
---|---|---|---|

0.0 | −3.589 ± 0.130 | 6.14 ± 0.33 | 0.9883 |

0.2 | −3.794 ± 0.062 | 7.87 ± 0.16 | 0.9983 |

0.5 | −5.275 ± 0.055 | 13.45 ± 0.14 | 0.9996 |

0.8 | −5.465 ± 0.065 | 16.12 ± 0.17 | 0.9999 |

1.0 | −6.303 ± 0.066 | 19.92 ± 0.17 | 0.9999 |

**Table 6.**Result of the regression analysis of dynamic viscosity ($\eta $/mPa·s) versus mole fraction of PFD (x

_{PFD}) data according to equation: $\eta $/(mPa·s) = $\eta $

_{0}/(mPa·s) + $d\xb7$ e

^{f(xPFD)}for the investigated mixtures over the temperature range 293 K to 333 K.

^{a}

T/K | $\mathit{\eta}$_{0} (mPa·s)
| $\mathit{d}$ | f | R^{2} |
---|---|---|---|---|

293 | 0.238 ± 0.060 | 0.151 ± 0.020 | 3.726 ± 0.130 | 0.9997 |

298 | 0.212 ± 0.063 | 0.151 ± 0.023 | 3.583 ± 0.149 | 0.9996 |

303 | 0.201 ± 0.041 | 0.145 ± 0.016 | 3.482 ± 0.107 | 0.9998 |

313 | 0.174 ± 0.028 | 0.137 ± 0.012 | 3.275 ± 0.084 | 0.9999 |

323 | 0.156 ± 0.024 | 0.130 ± 0.012 | 3.093 ± 0.085 | 0.9999 |

333 | 0.142 ± 0.031 | 0.124 ± 0.016 | 2.924 ± 0.121 | 0.9997 |

^{a}Standard uncertainties u are u(T) = ±0.05 K, u($\eta $) = ±0.001 mPa·s, u(x) = ± 0.01; Standard deviations are given with ± sign.

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**MDPI and ACS Style**

Deepika; Pandey, S.
Density and Dynamic Viscosity of Perfluorodecalin-Added *n*-Hexane Mixtures: Deciphering the Role of Fluorous Liquids. *Liquids* **2023**, *3*, 48-56.
https://doi.org/10.3390/liquids3010005

**AMA Style**

Deepika, Pandey S.
Density and Dynamic Viscosity of Perfluorodecalin-Added *n*-Hexane Mixtures: Deciphering the Role of Fluorous Liquids. *Liquids*. 2023; 3(1):48-56.
https://doi.org/10.3390/liquids3010005

**Chicago/Turabian Style**

Deepika, and Siddharth Pandey.
2023. "Density and Dynamic Viscosity of Perfluorodecalin-Added *n*-Hexane Mixtures: Deciphering the Role of Fluorous Liquids" *Liquids* 3, no. 1: 48-56.
https://doi.org/10.3390/liquids3010005