Viscosity and Surface Tension of Branched Alkanes 2-Methylnonane

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Viscosity and Surface Tension of Branched Alkanes 2‑Methylnonane and 4‑Methylnonane Tobias Klein,† Junwei Cui,†,‡ Ahmad Kalantar,§ Jiaqi Chen,§ Michael H. Rausch,† Thomas M. Koller,*,† and Andreas P. Fröba†

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†

Institute of Advanced Optical Technologies − Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 6, 91052 Erlangen, Germany ‡ Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China § Shell Global Solutions International B.V., Grasweg 31, 1031 HW Amsterdam, The Netherlands ABSTRACT: The liquid viscosity, surface tension, and liquid density of the two branched alkanes 2-methylnonane and 4-methylnonane were studied for temperatures between 283.15 and 448.15 K. The surface tension and liquid dynamic viscosity were obtained from surface light scattering (SLS) measurements close to saturation conditions with average relative expanded uncertainties (k = 2) of 1.5 and 0.9 %. Two vibrating-tube densimeters were used for the measurement of the liquid density at atmospheric pressure with relative expanded uncertainties (k = 2) between 0.01 and 0.5 %. The measured data could be correlated mostly within their expanded uncertainties by appropriate equations. Comparison with the few available literature data shows good agreement.

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INTRODUCTION For the thermophysical properties of linear n-alkanes having carbon numbers between 1 and 12, a validated reference exists in the form of the REFPROP database.1 Here, a relatively large amount of reliable experimental data was used for data correlation. Experimental data for branched alkane systems are, however, extremely scarce, especially in connection with the viscosity as well as surface tension and at temperatures above 373 K. This can be related to the fact that often linear hydrocarbons are the desired products in many industrial processes such as the revitalized Fischer−Tropsch process,2 whereas impurities given by, for example, branched alkanes, which originate from side-reactions, are considered to degrade the quality of the products. Nevertheless, such impurities can have an impact on the corresponding thermophysical properties of process-relevant fluid systems and thus need to be determined in a reliable way. In addition, the study of branched systems allows for an analysis of structure−property relationships among a series of isomers. In the present study, two branched isomers of n-dodecane, namely, 2-methylnonane and 4-methylnonane, were chosen as model systems to study the effect of branching for alkanes with same molecular weight on selected thermophysical properties. For the investigated substances, it is the major objective to provide reliable viscosity and surface tension data over a broad temperature range between 283.15 and 448.15 K close to saturation conditions. For this, liquid density data are also © XXXX American Chemical Society

required, which were measured for the probed samples at a pressure of p = 0.1 MPa in the temperature range from 283.15 to 423.15 K. After the section about the materials studied and the sample preparation, the applied experimental methods in the form of surface light scattering for the simultaneous measurement of liquid viscosity and surface tension at macroscopic thermodynamic equilibrium as well as vibrating tube densimeters for the measurement of the liquid density are briefly explained. Thereafter, the results for the investigated properties as well as corresponding temperature-dependent correlation schemes are presented and compared with the available literature data. Furthermore, the influence of the position of branching on the studied thermophysical property data is discussed.

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EXPERIMENTAL SECTION

Materials and Sample Preparation. On the basis of the specifications of the providers, the mass fractions w of branched C10H22-based alkanes 2-methylnonane purchased from Alfa Aesar GmbH & Co.KG and 4-methylnonane purchased from Sigma-Aldrich were larger than 0.98.3,4 Both liquids showed a small amount of particle-like impurities presumably resulting from the manufacturing process. To obtain ideally particle-free Received: February 27, 2018 Accepted: May 23, 2018

A

DOI: 10.1021/acs.jced.8b00163 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Specification of the Studied Chemicals substance 2-methylnonane (CH3(CH2)6CH-(CH3)2) 4-methylnonane (CH3(CH2)4CH-(CH3)(CH2)2CH3) helium n-dodecane (n-C12H26) a

CAS number 871-83-0 17301-94-9 7440-59-7 112-40-3

source Alfa Aeasar GmbH & Co. KG Sigma-Aldrich Linde AG Merck

molar mass M/(g·mol−1)

specified purity

purification method

critical temperature TC/K

142.29

mass fraction ≥0.98a

filtration

610.70d

142.29

mass fraction ≥0.98b volume fraction ≥0.99999c mass fraction ≥0.99

filtration

606.15e

4.0026 170.34

none evacuation at 323.15 K

5.195f 658.1g

Reference 3. bReference 4. cReference 5. dReference 6. eReference 7. fReference 1. gReference 8.

into the cleaned cell via its upper window at atmospheric conditions. To avoid any contamination with air or other gases which may cause an oxygenation of the sample, the gas phase was flushed by helium several times. After that, the system was closed by fixing the upper window, adjusting an initial partial pressure of about 0.1 MPa of helium. Any effect of the helium gas on the liquid density, liquid viscosity, and surface tension of the studied systems can be neglected. The temperature of the sample cell, which was placed inside an insulated housing, was regulated through resistance heating and measured by calibrated 100 Ω platinum resistance probes with expanded uncertainties (k = 2) of 15 mK. Both branched alkanes were investigated in the temperature range from 298.15 to 448.15 K in steps of 25 K. For each temperature, six measurements at different angles of incidence ΘE = 3.0, 3.1, and 3.2° were performed, where the laser was irradiated from either side with respect to the axis of observation in order to check for a possible misalignment. The temperature stability was better than ±2 mK during each experimental run. The expanded uncertainty for all reported temperatures is estimated to be 0.05 K (k = 2). The data directly accessible by SLS for the dynamics of surface waves are their frequency ωq (average relative expanded uncertainty Ur(ωq) = 0.2%) and damping Γ (average relative expanded uncertainty Ur(Γ) = 1.1%) at a defined wave vector q⃗ (relative expanded uncertainty of the modulus of the wave vector Ur(q) = 0.2%). These data have been combined with the correlations for the density of the liquid phase ρ′ based on our experimental data (relative expanded uncertainty Ur(ρ′) between 0.01 and 0.5%) as well as reference data for the density of the vapor phase ρ″ (relative expanded uncertainty Ur(ρ″) = 10%) and for the dynamic viscosity of the vapor phase η″ (relative expanded uncertainty Ur(η″) = 10%) to determine the surface tension σ and kinematic viscosity ν′ of the studied branched alkanes by an exact numerical solution of the equation of dispersion for surface waves according to ref 12. The required vapor properties of the studied systems were determined in an ideal approach from the vapor pressure of the corresponding pure branched alkane and the partial pressure of helium used as inert gas. For helium, the gas density and viscosity data were obtained from a Helmholtz equation of state published by Ortiz-Vega14 and the pure fluid model of Arp et al.,15 respectively. Because of the lack of experimental ρ″ and η″ data for 2-methylnonane and 4-methylnonane, the corresponding values for the linear isomer n-decane16,17 were used. To model the vapor density of the binary gas mixtures at low pressures, a linear mole-based mixing rule using the pure densities was applied. For the description of the vapor viscosity η″, the corresponding-states model of Lucas18 was employed.

samples as necessary for light scattering experiments, the branched alkane samples were filtered with a syringe filter with 220 nm pore size at about 293 K and then used for the individual measurements detailed in the next sections. Helium, which served as an inert gas for sample handling and control of the sample composition during the experiments, was supplied by Linde AG with a volume fraction purity of 0.99999.5 For the calibration of a used densimeter, n-dodecane (n-C12H26, purchased from Merck) with a specified mass fraction w = 0.99 was used. More volatile impurities were reduced by applying vacuum at 50 Pa and 323.15 K for about 3 h. A summary of the chemicals studied and their properties is given in Table 1. Surface Light Scattering: Liquid Viscosity and Surface Tension. For the simultaneous determination of liquid viscosity and surface tension of the two branched substances close to saturation conditions, surface light scattering (SLS) was applied. Using this contactless technique, the dynamics of microscopic fluctuations on liquid surfaces or, in a more general formulation, at phase boundaries are probed at macroscopic thermodynamic equilibrium. In SLS, these dynamics of the microscopic surface fluctuations are analyzed by recording the intensity of scattered light emerging from the interaction between the incident light and the fluctuating surface structure on a temporal basis by using photon correlation spectroscopy. For the studied branched alkanes associated with relatively small liquid viscosities and/or large surface tensions, surface fluctuations propagate and show an oscillatory behavior. In this case, which has been observed in all present measurements, the frequency ωq and damping Γ of surface fluctuations at the vapor−liquid interface are governed by the surface tension σ and the liquid kinematic viscosity ν′, respectively, in a first order approximation. For an accurate determination of ν′ and σ by SLS, the exact numerical solution of the dispersion relation for hydrodynamic surface fluctuations at the interface between contacting liquid (′) and vapor (″) phases was considered in its complete form.9 For this, measured data for the dynamics of surface waves, that is, the frequency ωq and damping Γ at a defined wavenumber q, are combined with data for the dynamic viscosity of the vapor phase η″ and density data for both phases, ρ′ and ρ″. For a more detailed description of the fundamentals and methodological principles of SLS and its comparison with other methods for the measurement of viscosity and surface tension, the reader is referred to specialized literature.10−12 The SLS setup and the sample cell used in the present study are the same as those employed in our former investigations of alkane-based systems.12,13 In the following, only the experimental conditions relevant for the present investigations of the branched alkanes are summarized. The sample was inserted B



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water where the deviation from the reference data of Wagner and Pruss20 was less than 0.08%. For both investigated methylnonane isomers, the deviation of the density measured at 298.15 K after the temperature scan from that at the beginning was less than 0.05%. Taking this as well as the calibration procedure and the uncertainties of the used reference data into account, the expanded uncertainty (k = 2) of the reported density data obtained with the DMA 4200 M is estimated to be 0.3%.

The required critical pressures of the two pure branched compounds, which are not available, were approximated with that of pure n-decane1 due to its similar molecular structure. Also owing to the small impact of the critical pressure on the calculated η″ data, the applied calculation procedure is sufficiently accurate to estimate the viscosity of the vapor phase with an expanded uncertainty of 10%. For the properties of interest liquid kinematic viscosity ν′ and surface tension σ, the total measurement uncertainties (relative expanded uncertainties Ur(ν′) between 1.0% and 2.0% as well as Ur(σ) between 0.3% and 1.7%) were calculated by error propagation schemes12 considering the uncertainties induced by the primary measured variables and by the adopted reference data. In this connection, the very weak effect of slightly different pressures present during the SLS and density measurements on the liquid density has no significant influence on the uncertainties of the ν′ and σ values obtained by SLS. Vibrating-Tube Method: Density. The liquid density ρ′ required for evaluation of the SLS experiments was measured at atmospheric pressure of 0.1 MPa with two instruments from Anton Paar based on the vibrating-tube method. The DMA 5000 M is specified with measurement uncertainties of 5 × 10−6 g·cm−3 as well as 0.01 K and was successfully checked with deionized water and air before and after each experimental run. The liquid density of the investigated substances was measured from 283.15 to 363.15 K in steps of 5 K, where check measurements at 293.15 K were additionally performed before and after the temperature scan. For 4-methylnonane, the three available measurement data for 293.15 K deviated less than 0.002% from each other. On this basis, an expanded uncertainty (k = 2) of 0.01% is estimated for the corresponding density data. For 2-methylnonane, the result of the check measurement after the temperature scan was by 0.06% larger than that of the initial check measurement, indicating changes within the probed sample inside the U-tube. These changes within the probed 2-methylnonane sample may be caused by the degassing of impurities with larger volatilities which seem to be present in 4-methylnonane to a smaller extent. Thus, an additional temperature scan from 363.15 to 283.15 K was performed for a fresh 2-methylnonane sample. Here, the check measurement at 293.15 K after the temperature scan showed again an increase of the measured density of 0.08% compared to the initial one. All densities determined for a given temperature during these procedures were averaged and showed a mean deviation of 0.05% from each other. Thus, the expanded uncertainty (k = 2) of the density data reported for 2-methylnonane measured by the DMA 5000 M is estimated to be 0.1%. The DMA 4200 M gives access to density data for temperatures up to 473.15 K with a specified uncertainty of 0.03 K and to pressures up to 50 MPa where calibration is required at the probed conditions. In the present investigation, the instrument was used at atmospheric pressure of 0.1 MPa and temperatures from 298.15 to 423.15 K in steps of 25 K and a check measurement at 298.15 K after the temperature scan. For the calibration, air relying on the reference data from Lemmon et al.19 with an expanded uncertainty (k = 2) of 0.1% as well as n-dodecane were used. For n-dodecane, reference data from Lemmon and Huber8 with an expanded uncertainty (k = 2) of 0.2% were employed. Check measurements of the ndodecane sample studied with the DMA 5000 M from 283.15 to 363.15 K showed deviations of less than 0.11% from the reference data. The calibration was checked with deionized

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RESULTS AND DISCUSSION The liquid densities ρ′ of the investigated branched alkanes 2methylnonane and 4-methylnonane needed for the evaluation of the SLS experiments and measured with two different U-tube densimeters at atmospheric pressure of 0.1 MPa are summarized in Table 2. All data obtained for each isomer are Table 2. Density ρ′(T) of the Studied Branched Alkanes at Temperature T and 0.1 MPaa T/K

ρ′/(kg·m−3)

ρ′/(kg·m−3)

100·Ur(ρ′)

2-methylnonane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

735.134 731.326 727.469 723.632 719.960 716.109 712.275 708.490 704.628 700.722 696.794 692.852 688.883 684.896 680.890 676.827 672.811

298.15 323.15 348.15 373.15 398.15 423.15

723.54 704.14 684.45 664.34 643.46 621.59

100·Ur(ρ′)

4-methylnonane

DMA 5000 M 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 DMA 4200 M 0.30 0.30 0.30 0.30 0.30 0.30

739.362 735.555 731.743 727.929 724.098 720.253 716.396 712.527 708.634 704.729 700.808 696.873 692.918 688.940 684.943 680.922 676.877

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

728.35 708.82 689.00 668.81 647.86 626.00

0.30 0.30 0.30 0.30 0.30 0.30

a

The expanded uncertainties U are U(p) = 3 kPa as well as U(T) = 0.01 K for the DMA 5000 M and U(T) = 0.03 K for the DMA 4200 M, while the relative expanded uncertainties Ur(ρ′) are given in the table (level of confidence = 0.95).

represented well as a function of temperature by a polynomial of second order with respect to the temperature T ρ′calc (T ) = ρ′0 + ρ′1T + ρ′2 T 2

(1)

where the experimental data were weighted with their inverse relative uncertainties. The corresponding fit parameters ρ′0, ρ′1, and ρ′2 as well as the standard percentage deviations (rms) of the measured ρ′ data from the correlation according to eq 1, which are 0.023 for 2-methylnonane and 0.030 for 4methylnonane, are given in Table 3. C



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Table 3. Coefficients of Equation 1 for the Liquid Density ρ′calc(T) of 2-Methylnonane and 4-Methylnonane sample 2-methylnonane 4-methylnonane a

ρ0/(kg·m−3)

ρ1/(kg·m−3·K−1)

903.687 921.346

−0.453846 −0.535632

ρ2/(kg·m−3·K−2) −4

−5.01948 × 10 −3.79097 × 10−4

rmsa 0.023 0.030

Standard percentage deviation of measured ρ′ data to the fit.

region of the alkane as given in 2-methylnonane tends to disturb the packing of the chains, resulting in lower densities compared to the linear n-decane. All experimental density data used for the following data comparison have been measured at atmospheric pressure, that is, at a pressure of about 0.1 MPa. The data for 2-methylnonane reported by Luning Prak et al.21 were obtained using two devices from Anton Paar in the form of a SVM 3000 Stabinger viscometer between 283.15 and 373.15 K as well as a DSA 5000 density and sound analyzer between 283.15 and 323.15 K. Taking into account the uncertainty of 0.3 kg·m−3 for the SVM 3000 device and 0.2 kg·m−3 for the DSA 5000 device, that is, relative uncertainties between 0.027 and 0.045%, good agreement between their concordant data sets and our correlation within combined uncertainties is found. Regarding all other available literature data for ρ′ discussed below, no experimental uncertainties are specified. For 2-methylnonane and 4-methylnonane, data are given by Calingaert and Soroos22 for 293.15 K and by Geist and Cannon23 for temperatures from 273.15 to 313.15 K, without mentioning the used method in both references. Relative absolute deviations of less than 0.09% for the results of Calingaert and Soroos22 as well as below 0.07% for the results of Geist and Cannon23 indicate good agreement with our data. A pycnometer was employed by Mears et al.24 for the investigation of 2-methylnonane at 293.15 and 298.15 K and by Trew25 for the investigation of 4methylnonane at 293.15 K. A comparison with our correlations according to eq 1 yields relative deviations of −0.16 and −0.17% for the data of Mears et al.24 and +0.06% for the data of Trew.25 In Table 4, the input data for ρ′, ρ″, and η″, which were combined with the directly measured values for frequency and damping of surface waves at defined wave vectors, are summarized together with the values for the liquid kinematic viscosity ν′ and the surface tension σ of the studied branched alkanes obtained by SLS close to saturation conditions between 298.15 and 448.15 K. The employed ρ′ data were obtained from eq 1, whereas ρ″ and η″ were estimated on a theoretical basis.1,18 For the representation of the experimentally deduced data for the liquid dynamic viscosity η′ (= ν′ρ′), which are also listed in Table 1, a modified Andrade equation according to

The measured liquid density data, the correlations according to eq 1, and available literature data are illustrated in the upper part of Figure 1. In the lower part of the figure, the deviation of

Figure 1. Liquid densities ρ′ of 2-methylnonane and 4-methylnonane (upper panel) and their relative deviations from calculated values ρ′calc based on eq 1 (lower panel) at ambient pressure as a function of temperature T in comparison with literature data: ○, 2-methylnonane, DMA 5000 M, this work; ●, 2-methylnonane, DMA 4200 M, this work; ◒, 2-methylnonane, SVM 3000, Luning Prak et al.;21 ◐, 2methylnonane, DSA 5000, Luning Prak et al.;21 ◓, 2-methylnonane, Calingaert and Soroos;22 ◑, 2-methylnonane, Geist and Cannon;23 ⊗, 2-methylnonane, pycnometer, Mears et al.;24 ◇, 4-methylnonane, DMA 5000 M, this work; ⧫, 4-methylnonane, DMA 4200 M, this work; diamond top solid, 4-methylnonane, Calingaert and Soroos;22 diamond right solid, 4-methylnonane, Geist and Cannon;23 diamond bottom solid, 4-methylnonane, pycnometer, Trew;25 , eq 1 using coefficients from Table 2.

the experimental and literature data from eq 1 is shown. For both systems, our density data obtained by the two densimeters at the same studied temperatures of 298.15, 323.15, and 348.15 K agree within their uncertainties. Furthermore, the relative deviations of all our experimental data points from the fits are within the measurement uncertainty. The measured temperature-dependent densities for 2-methylnonane are on average 0.60% smaller than those for 4-methylnonane, which is outside the combined uncertainties in most cases. The literature values for the linear isomer n-decane1 are in between the measured data of the two branched alkanes and closer to the values for 4methylnonane with an absolute average deviation of 0.20% considering the experimentally studied temperature points. It seems that a branching closer to the center of the molecule as found for 4-methylnonane allows for a denser packing of the molecules in the liquid phase, apparently due to the increasing molecular symmetry. On the contrary, a branching at the outer

η′calc = η′0 exp(η′1T −1 + η′2 T )

(2)

was used where all experimental data have the same statistical weight. The corresponding fit parameters η′0, η′1, and η′2 as well as the standard percentage deviations (rms) of the measured η′ data from the correlation according to eq 2, which are 0.46% for 2-methylnonane and 0.40% for 4-methylnonane, are given in Table 5. In the upper part of Figure 2, the experimental η′ data, the fits according to eq 2, and available literature data are shown, whereas the lower part of the figure illustrates the deviation of the experimental and literature data from eq 2. For both systems, the relative deviations of all our single experimental data points from the fits are smaller than 1.0% and within the measurement uncertainties. In addition, all relative deviations D



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Table 4. Kinematic Viscosity ν′, Dynamic Viscosity η′, and Surface Tension σ of the Studied Branched Alkanes Close to Saturation Conditions Obtained by Surface Light Scattering as a Function of Temperature T Using Corresponding Experimental Data for the Liquid Density ρ′ as Well as Literature Data for the Vapor Density ρ″ and Vapor Dynamic Viscosity η″a T/K

ρ′/kg·m−3

100·Ur(ρ′)

ρ″/kg·m−3

η″/μPa·s

298.15 323.15 348.15 373.15 398.15 423.15 448.15

723.75 704.61 684.84 664.44 643.42 621.77 599.49

0.10 0.10 0.10 0.30 0.30 0.30 0.50b

0.17 0.21 0.32 0.61 1.21 2.38 4.40

19.15 20.38 21.74 22.14 21.13 18.88 16.19

298.15 323.15 348.15 373.15 398.15 423.15 448.15

727.95 708.67 688.92 668.69 647.99 626.81 605.17

0.01 0.01 0.01 0.30 0.30 0.30 0.50b

0.17 0.21 0.32 0.61 1.21 2.38 4.40

19.15 20.38 21.74 22.14 21.13 18.88 16.19

ν′/mm2·s−1 2-Methylnonane 1.1423 0.8565 0.6759 0.5453 0.4502 0.3804 0.3318 4-Methylnonane 1.0493 0.7808 0.6040 0.4904 0.4081 0.3459 0.2976

100·Ur(ν′)

η′/mPa·s

100·Ur(η′)

σ/mN·m−1

100·Ur(σ)

1.2 1.7 1.6 1.2 1.6 1.6 1.6

0.8268 0.6035 0.4629 0.3623 0.2897 0.2365 0.1989

1.2 1.7 1.6 1.3 1.6 1.7 1.7

21.45 19.65 17.76 15.75 13.64 11.72 9.90

1.0 0.4 0.3 0.7 1.0 1.5 1.4

1.4 1.1 1.0 1.1 2.0 1.4 1.4

0.7638 0.5533 0.4161 0.3279 0.2644 0.2168 0.1801

1.4 1.1 1.0 1.1 2.0 1.5 1.5

21.67 20.06 17.93 15.92 13.77 11.89 9.95

0.8 0.8 0.4 0.8 1.7 0.5 1.0

Directly measured values for frequency and damping at a defined wave vector of surface waves were combined with calculated data for ρ′, ρ″, and η″ according to eq 1, ref 1, and refs 1 and 18, respectively, to derive ν′, η′, and σ by an exact numerical solution of the dispersion relation. The expanded uncertainties for the employed vapor properties are 10% for the vapor density and 10% for the vapor dynamic viscosity, while the expanded uncertainties for the employed liquid density Ur(ρ′) are given in the table (level of confidence = 0.95). The expanded uncertainties U are U(T) = 0.05 K, while the relative expanded uncertainties Ur(ν′), Ur(η′), and Ur(σ) are given in the table (level of confidence = 0.95). bIncludes the additional extrapolation uncertainty (level of confidence of 95%) outside the temperature range where experimental data contribute to eq 1. a

Table 5. Coefficients of Equation 2 for the Liquid Dynamic Viscosity η′calc(T) of 2-Methylnonane and 4-Methylnonane Close to Saturation Conditions

a

sample

η′0 (mPa·s)

η′1 (K)

η′2 (K−1)

rmsa

2-methylnonane 4-methylnonane

0.069119 0.029181

953.945 1097.717

−0.002414 −0.001403

0.46 0.40

Standard percentage deviation of measured η′ data to the fit.

are within the average value of the expanded uncertainty of all experimental data of 1.47% given by the dashed lines. For the studied temperature range, the dynamic viscosities of 2methylnonane are between 8.2 and 11.2% larger than those of 4-methylnonane. The larger viscosities for the less dense 2methylnonane compared to 4-methylnonane may be related to stronger entanglement of 2-methylnonane molecules, whereas the more compact 4-methylnonane molecules provide less contact points with interacting neighbors for momentum transport. In comparison, the linear alkane isomer n-decane shows the largest dynamic viscosities1 within the set of isomers, which are on average 1.2% larger than the values for 2methylnonane. For the two branched methylnonanes studied in the present work, three experimental data sets for the liquid viscosity are available, which were obtained at a pressure of about 0.1 MPa and are limited to a maximum temperature of 373.15 K. For the data for 2-methylnonane measured by Luning Prak et al.21 with a SVM 3000 Stabinger viscometer between 283.15 and 373.15 K and an uncertainty of about 1%, the relative deviations from our fitted experimental data are between −4.4 and +2.3%. Except for two data points, all these deviations are within combined experimental uncertainties. In addition, Geist and Cannon23 determined the kinematic viscosity of 2-methylnonane and 4-methylnonane with an uncertainty of 0.5% using an Ubbelohde viscometer at T = 273.15, 293.15, and 313.15 K.

Figure 2. Liquid dynamic viscosities η′ of 2-methylnonane and 4methylnonane (upper panel) and their relative deviations from calculated values η′calc based on eq 2 (lower panel) close to saturation conditions from surface light scattering as a function of temperature T in comparison with literature data: ○, 2-methylnonane, this work; ◒, 2-methylnonane, SVM 3000, Luning Prak et al.;21 ◑, 2-methylnonane, Ubbelohde viscometer, Geist and Cannon;23 ◊, 4-methylnonane, this work; □, 4-methylnonane, Ubbelohde viscometer, Geist and Cannon;23 , eq 2 using coefficients from Table 5.

Most of the corresponding dynamic viscosity values, which were deduced from their own density measurements and are estimated with the same uncertainty as the ν′ data, do not agree with our results with relative deviations from +3.8% at 273.15 K E



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to −3.5% at 313.15 K in the case of 2-methylnonane and from +1.0% at 273.15 K to −2.3% at 313.15 K in the case of 4methylnonane. The experimental data for the surface tension of the two investigated systems can be represented by a modified van der Waals equation σcalc = σ0(1 − TR )1.26 [1 + σ1(1 − TR )0.5 ]

within combined uncertainties in most cases. Relative deviations of the experimental σ-values for 2-methylnonane from those for 4-methylnonane are between −0.5 and −2.0%. Apparently, the position of the branched methyl group has no significant influence on the surface tensions for the studied C10H22-based systems. On the contrary, the linear isomer ndecane shows distinctly larger surface tension values1 than the two branched systems. The relative deviations of the σ data for n-decane from our data for 2-methylnonane decrease gradually from +8.2% at 298.15 K to +3.8% at 448.15 K. The differences may originate from similarly reduced dispersive interactions between the branched, more bulky methylnonanes at the vapor−liquid interface compared to the linear n-decane. To the best of our knowledge, no further surface tension data for the branched alkanes studied in this work are available.

(3)

where all experimental data have the same statistical weight. In eq 3, TR = T/TC denotes the reduced temperature, where the TC data given in Table 1 were employed. In Table 6, the fit parameters σ0 and σ1 as well as the standard percentage deviations (rms) of the measured σ data from the fit based on eq 3 are given.

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Table 6. Coefficients of Equation 3 for the Surface Tension σcalc(T) of 2-Methylnonane and 4-Methylnonane Close to Saturation Conditions

a

sample

σ0/(mN·m−1)

σ1

rmsa

2-methylnonane 4-methylnonane

59.160 62.447

−0.2106 −0.2487

0.65 0.73

CONCLUSIONS The present study provides accurate experimental data for the liquid dynamic viscosity, surface tension, and liquid density of the two branched alkanes 2-methylnonane and 4-methylnonane obtained with SLS and the vibrating-tube method over a broad temperature range. Correlations in the form of a modified Andrade equation for the liquid dynamic viscosity, a modified van der Waals equation for the surface tension, and a simple polynomial for the liquid density represent the experimental data mostly within experimental uncertainties. Effects of the position of branching in the isomers on the studied properties were investigated. The present investigations improve the data situation for the studied branched hydrocarbons, especially with respect to viscosity and surface tension.

Standard percentage deviation of measured σ data to the fit.

Figure 3 illustrates the experimental σ data, the corresponding fit lines according to eq 3, and the relative deviation of the

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AUTHOR INFORMATION

Corresponding Author

*Tel. +49-9131-85-23279. Fax +49-9131-85-25878. E-mail [email protected]. ORCID

Jiaqi Chen: 0000-0002-2591-0073 Thomas M. Koller: 0000-0003-4917-3079 Andreas P. Fröba: 0000-0002-9616-3888 Funding

This work was financially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative. Financial support from Shell Global Solutions International B.V. through a contracted research agreement is gratefully acknowledged.

Figure 3. Surface tensions σ of 2-methylnonane and 4-methylnonane (upper panel) and their relative deviations from calculated values σ′calc based on eq 3 (lower panel) close to saturation conditions from surface light scattering as a function of temperature T: ○, 2methylnonane, this work; ◊, 4-methylnonane, this work; , eq 3 using coefficients from Table 6.

Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. REFPROP: Reference Fluid Thermodynamic and Transport Properties, NIST Standard Reference Database 23, Version 9.1; National Institute of Standards and Technology: Gaithersburg, MD, 2013. (2) de Klerk, A.; Li, Y. W.; Zennaro, R. Greener Fischer−Tropsch Processes for Fuels and Feedstocks; Wiley-VCH: Weinheim, Germany, 2013. (3) 2-Methylnonane Datasheet. https://www.alfa.com/de/catalog/ B20849/ (accessed January 11, 2018). (4) 4-Methylnonane Datasheet. https://www.sigmaaldrich.com/ catalog/product/aldrich/68090?lang=de®ion=DE (accessed January 11, 2018).

measured data from the fit. In most cases, the deviation of our experimental data from the fit is smaller than the relative expanded measurement uncertainty (k = 2). The standard percentage deviations of 0.65 for 2-methylnonane and 0.73 for 4-methylnonane are smaller than the average value of the expanded uncertainties of all experimental data of 0.89% indicated by the dashed lines. For all studied temperatures, the surface tensions of the two branched alkanes 2-methylnonane and 4-methynonane match F



Article

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Viscosity and Surface Tension of Branched Alkanes 2-Methylnonane

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