Liquid Viscosity and Surface Tension of - ACS Publications - American

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Liquid Viscosity and Surface Tension of n‑Dodecane, n‑Octacosane, Their Mixtures, and a Wax between 323 and 573 K by Surface Light Scattering Thomas M. Koller,*,† Tobias Klein,† Cédric Giraudet,† Jiaqi Chen,‡ Ahmad Kalantar,‡ Gerard P. van der Laan,‡ Michael H. Rausch,† and Andreas P. Fröba† †

Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, 91052 Erlangen, Germany ‡ Shell Global Solutions International B.V., Grasweg 31, 1031 HW Amsterdam, The Netherlands S Supporting Information *

ABSTRACT: The present contribution provides experimental data for the liquid viscosity and surface tension of n-alkane based model systems at temperatures up to 573 K. The fundamental advantage of the used surface light scattering (SLS) method lies in its application in thermodynamic equilibrium without calibration in a contactless way. The investigated systems comprise the pure fluids n-dodecane (nC12H26) and n-octacosane (n-C28H58), their binary mixture at a n-C12H26 mole fraction of about 0.3, and the commercially available hydrocarbon wax SX-70 representing a multicomponent mixture of n-alkanes with a broad chain length distribution. For the first time, it could be demonstrated that the SLS method can simultaneously access the liquid viscosity and surface tension of such medium- to long-chained n-alkane systems close to saturation conditions over a broad temperature range from 323 to 573 K. Typical measurement uncertainties of 2% based on a coverage factor k = 2, i.e., a level of confidence of more than 95%, were obtained. Over the entire temperature range, a simple polynomial equation for the dynamic viscosity and a modified van der Waals equation for the surface tension represent the measured data of the pure and binary systems well. The present investigations improve the data situation for hydrocarbon systems in the high-temperature range where no measurement results exist in literature.

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INTRODUCTION In the field of chemical and energy technology, the catalytic Fischer−Tropsch process used for the artificial production of high-valued petroleum products from synthesis gas has experienced strong revitalized interest in the most recent years.1,2 For product design and process modeling, reliable information on the viscosity and surface tension of representative fluid systems is required. Of the different transport properties, the viscosity is the central property as it affects heat as well as mass transfer processes and determines power requirements for mixers and pumps. The surface tension is important in connection with mass transfer rates of gas absorption at contacting gas−liquid interfaces and the wetting behavior at machineries or catalytic nanopores. Depending on the reaction conditions for, e.g., Fischer−Tropsch processes with temperatures between about 423 and 523 K as well as pressures between about 2 and 4 MPa,2 a certain product distribution of linear and branched alkanes as well as further side products of various chain length is obtained. Thus, knowledge on the thermophysical properties at elevated thermodynamic states, especially in the conditions of high temperatures above 423 K, is needed. © 2017 American Chemical Society

For the thermophysical properties of short-chained n-alkanes having carbon numbers between 1 and 12, there already exists an ensured reference database in the form of Refprop.3 Reliable data or models for medium- to long-chained n-alkanes and their mixtures in the temperature range which is of interest for the process are lacking. This issue seems to be related to the problems adherent to conventional, in most cases routine, measurement methods used to determine viscosity and surface tension of such systems at relatively large temperatures. Here, the adjustment of equilibrium conditions during the measurement close to thermodynamic equilibrium is hardly possible. This holds especially in connection with transport properties such as viscosity where conventional techniques have to apply a relatively large shear rate to obtain a measurable effect, resulting in unavoidable disturbances of equilibrium. Any macroscopic gradient subjected to the sample may falsify the results if not considered in data evaluation. The fundamental limitations of conventional experiments motivated to use and develop Received: April 18, 2017 Accepted: June 30, 2017 Published: July 18, 2017 3319

DOI: 10.1021/acs.jced.7b00363 J. Chem. Eng. Data 2017, 62, 3319−3333

Journal of Chemical & Engineering Data

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incident light in equally spaced directions around both the reflected and refracted beams. Surface fluctuations observable in the light scattering experiment typically cover a wavelength range from about 0.1 to 1000 μm. The total root-mean-square amplitude of the surface roughness integrated over all wavelengths is typically between 1 and 100 nm. In the SLS experiment, the dynamics of surface fluctuations in the form of their frequency and damping is probed for a defined wavelength. For the temporal decay of surface fluctuations, two cases can be distinguished. In the case of large viscosity and/or small surface tension, the amplitude is damped exponentially, while, in the case of small viscosity and/or large surface tension, the amplitude of surface fluctuations decays in the form of a damped oscillation. The scattering geometry used in this study is shown in Figure 1 where scattered light is observed in the forward direction near

modeling methods for the prediction of thermophysical properties in the form of computer simulation 4 and theoretical/empirical5 approaches. Nevertheless, even for small- to medium-weight n-alkane systems, such predictive methods can still often not be used for a reliable quantitative estimation of viscosity and surface tension, as will be shown later in this study, and can only be as accurate as the experimental data used to verify the calculation results. Surface light scattering (SLS) probes, as the name indicates, the dynamics of thermal fluctuations on the surface of a liquid or, in a more general formulation, at phase boundaries. Here, measurements are performed in or close to macroscopic thermodynamic equilibrium in a contactless way without the need for any calibration. All these features allow for defining the method as a quasi-primary method for the measurement of viscosity.6 During the past two decades, our research activities were devoted to developing a proper execution of SLS for a routine measurement of surface tension and liquid viscosity with high accuracy for fluids with relatively low viscosity, such as refrigerants,7−9 hydrofluoroethers,10 or toluene,11 the latter data which served as reference for the development of a lowviscosity standard.12 In a second step, our investigations could demonstrate that the SLS technique constitutes also a valuable tool for thermophysical property research of high-viscosity fluids in the form of ionic liquids13−16 or the reference substance diisodecyl phthalate.17 In the present study, the SLS method is applied, for the first time, to investigate n-alkane model systems containing ndodecane (n-C12H26), n-octacosane (n-C28H58), and their binary mixture at a n-C12H26 mole fraction of about 0.3 as well as a multicomponent system in the form of the commercially available wax SX-70 with a defined composition over a broad temperature range between 323 and 573 K close to saturation conditions. After an introduction to the SLS technique, the materials and sample preparation as well as the experimental setup are described. Thereafter, a measurement example and the data evaluation procedure are presented. The main objectives of this work are to show the capability of SLS for a simultaneous determination of liquid viscosity and surface tension of selected n-alkane systems over a broad temperature range in an accurate manner and to fill the existing gap in the database for an industrially relevant class of working fluids. Besides a critical analysis of the experimental uncertainties of the present measurements and of the available scarce literature data, simple correlations for the liquid viscosity and surface tension of the studied systems are provided.

Figure 1. Scattering geometry used for surface light scattering.

refraction. This arrangement has been chosen due to signal and stability considerations21 and differs from the more commonly employed scattering geometry where the scattered light is observed close to the direction of the reflected beam. By choice of the angle of incidence ΘE and the scattering angle ΘS, the scattering vector q ⃗ = kI⃗ ′ − k S⃗ ′ is determined and, from this, the wave vector and frequency of the observed surface vibration mode. Here, kI⃗ ′ and k S⃗ ′ denote the projections of the wave vectors of the reflected (kI⃗ ) and scattered (kS⃗ ) light to the surface plane, respectively. In the special optical arrangement illustrated in Figure 1, light scattered on the liquid−vapor interface is detected perpendicular to the surface plane. In addition, scattered light is observed within the irradiation plane and elastic scattering (i.e., kI ≅ kS) can be assumed. Based on these conditions, the modulus of the scattering vector can be deduced from Snell’s refraction law and simple trigonometric identities resulting in 2π q = |kI⃗ ′ − k S⃗ ′| ≅ sin(ΘE) λ0 (1)

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SURFACE LIGHT SCATTERING For the present investigations of a phase boundary between the corresponding liquid and vapor phases of the n-alkane systems, an exact treatment of the capillary wave problem taking into account the phase boundary is necessary to reliably determine viscosity and surface tension with high accuracy. For a detailed description of the fundamentals and methodological principles of SLS, the reader is referred to specialized literature.18,19 In this section, the main information on the SLS technique which is relevant for the present study is provided. In macroscopic thermal equilibrium, liquid surfaces exhibit surface waves that are caused by the thermal motion of molecules.20 The result of such fluctuations is a rough surface which can be represented by a superposition of surface waves with different amplitudes and wave vectors. Each Fourier component of the rough surface scatters a small fraction of an

where λ0 is the laser wavelength in vacuo. Each scattering vector chosen solely from the adjusted angle of incidence corresponds to a specific wavelength (2π/q) of surface vibration mode as it is shown in Figure 1. Based on classical hydrodynamic theory, the temporal decay of a particular surface mode of the form exp[iq ⃗ r ⃗ + St/τ0], with a wave vector q⃗ at a given point r,⃗ is obtained from the dispersion equation for surface waves at the interface between contacting liquid (′) and vapor (″) phases.22 By introducing the dimensionless parameter 3320


Journal of Chemical & Engineering Data Y=

g (ρ ′ − ρ ″ ) ⎞ ρ′ + ρ″ ⎛ ⎟ ⎜ σ + 4(η′ + η″)2 q ⎝ q2 ⎠

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data obtained from the SLS experiment for the dynamics of surface waves, i.e., the frequency ωq and damping Γ at a defined wavenumber q, have to be combined with reference data for the dynamic viscosity of the vapor phase η″ and density data for both phases ρ′ and ρ″ to get information on the liquid kinematic viscosity ν′ or liquid dynamic viscosity η′ (η′ = ν′ρ′) and surface tension σ. Details on the data evaluation are given later in the corresponding section. In SLS, scattered light emerging from the interaction between incident light and the fluctuating surface structure can be analyzed using photon correlation spectroscopy. In this type of detection, the time-dependent correlation function of the scattered light intensity is measured at a point in the far field. For heterodyne conditions, where the scattered light is superimposed with coherent reference light of much higher intensity, the normalized intensity correlation function for the analysis of surface fluctuations showing an oscillatory behavior is described by22

(2)

with ρ′ and ρ″ being the densities of the liquid and vapor phases, η′ and η″ the dynamic viscosities of the liquid and vapor phases, respectively, σ the surface tension, and g the local acceleration of free-fall, as well as introducing the reduced frequency S = iατ0 ,

with τ0 =

ρ′ + ρ″ 2(η′ + η″)q2

(3)

the dispersion relation can be transformed into its reduced form22 D(S) = Y +

ρ′2 − ρ″2 + 2Rρ′ρ″ η′(M′ − 1) − η″(M″ − 1) S η′(M′ + 1) + η″(M″ + 1) (ρ′ + ρ″)2

⎧ η′(M′2 + 1) + η″[M′ − 1 + M″(M′ + 1)] ρ′ +⎨ ⎩ (ρ′ + ρ″) (M′ − 1)[η′(M′ + 1) + η″(M″ + 1)] ⎪

⎪

+

η″(M″2 + 1) + η′[M″ − 1 + M′(M″ + 1)] ⎫ 2 ρ″ ⎬S (ρ′ + ρ″) (M″ − 1)[η′(M′ + 1) + η″(M″ + 1)] ⎭

g(2)(τ ) = a + b cos(ωq τ − ϕ) exp( −τ /τC)

The experimental constants a and b in eq 8 are essentially determined by the total number of registered counts, the ratio of scattered light to reference light, and the coherence properties of the optical system. The time-dependent parts of eq 8 are proportional to the correlation function of the surface fluctuations, whose Fourier transform is, according to the Wiener−Khintchine theorem, the corresponding power spectrum of the surface fluctuations. The phase term ϕ largely accounts for the deviations of the spectrum from the Lorentzian form and was used as a variable in the data evaluation procedure. The correlation time τC and the frequency ωq are identical with the mean lifetime or the reciprocal of the damping constant Γ (=1/τC) of the surface ripplons and their frequency of propagation, respectively. The latter relate to the fluid properties through the capillary wave dispersion equation; see eq 4.

(4)

In eq 4, the dimensionless properties R, M′, and M″ are given by R=

η′ / ρ ′ − η″ / ρ ″ (η′ + η″)/(ρ′ + ρ″)

M′ =

M″ =

1+2

1+2

(5)

ρ′ + ρ″ S ρ′ + ρ″ + Rρ″

(6)

ρ′ + ρ″ S ρ′ + ρ″ − Rρ′

(7)

(8)

The reduced frequency S is related to the complex frequency α (α = ωq + iΓ) and to the characteristic viscous time τ0. Furthermore, the real part of the complex frequency α represents the frequency ωq and the imaginary part the damping Γ of the observed surface vibration mode with the corresponding wavenumber q. At relatively small surface wavelengths, as it is relevant in this work, the last term in eq 2, which arises from the force of inertia, can be neglected without significant increase in uncertainty. The solution of the dispersion relation in eq 4 shows that there exists a critical value for Y for which the temporal behavior of the surface fluctuations changes depending on the thermophysical properties of the fluid and the wavenumber selected. For Y < 1 associated with large liquid viscosities and/or low surface tensions, surface fluctuations are overdamped and do not propagate (ωq = 0). For Y > 1 associated with small liquid viscosities and/or large surface tensions, surface fluctuations propagate and show an oscillatory behavior. This case has been observed in all measurements presented in this work, where the smallest Y value was 1.6, and is only studied in the following. When Y ≫ 1 or Y ≪ 1, firstorder approximations11,18 for S can be used for an accurate description of the dynamics of surface waves. For intermediate values of Y, the dynamics of surface waves can no longer be described with sufficient certainty by the first-order approximation as it is often carried out in literature.23−25 For an accurate determination of liquid viscosity and surface tension from the light scattering experiment, the dispersion relation eq 4 must be considered in its complete form. For this,

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EXPERIMENTAL SECTION In the following experimental section, the materials and sample preparation as well as the experimental setup and procedure relevant for the present investigations are summarized. Materials and Sample Preparation. According to the specifications of the manufacturer, the linear n-alkanes ndodecane (n-C12H26, molar mass M = 170.33 g·mol−1, purchased from Merck GmbH) and n-octacosane (n-C28H58, M = 394.77 g·mol−1, purchased from Alfa Aesar GmbH & Co. KG) had both nominal purities in terms of mass fractions of w > 0.99. The wax SX-70 (XTL heavy HPS paraffins) was obtained from Shell Global Solutions B.V. and represents a mixture of heavy n-alkanes. A detailed analysis of the composition of the four different n-alkane systems investigated in our SLS measurements was obtained by gas chromatography (GC) and can be found in the Supporting Information in Tables S1 and S2. The results are based on the analysis of theoretical flame ionization detector response factors. These factors have been calculated by the effective carbon number method published by Sternberg et al.26 Besides the main components, other groups commonly found in Fischer− Tropsch related samples such as branched alkanes, aromatics, or oxygenated compounds were categorized according to the number of carbon atoms NC. The absolute uncertainty of the mass fractions w measured by the GC method can be estimated 3321



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Table 1. Specification of the Used Chemicals system

source

n-C12H26 n-C28H58 0.3n-C12H26/0.7n-C28H58

Merck GmbH Alfa Aesar GmbH & Co. KG Merck GmbH/Alfa Aesar GmbH & Co. KG Shell Global Solutions B.V. Linde AG

wax SX-70 helium

purification method

purity or composition before the measurement

purity or composition after the measurement

none filtration none/filtration

w = 0.9945a w = 0.9950a x1/x2 = 0.300/0.700b (total w > 0.99)

w = 0.9941a w = 0.9832a x1/x2 = 0.287/0.713a (total w = 0.9957a)

filtration none

see Table S2 and Figure S1 ψ = 0.99999

a

Obtained from GC analysis. The expanded uncertainties U of the mass fractions w of the pure and binary systems of interest are U(w) = 0.001 (level of confidence = 0.95). bEstimated from the GC results for the pure substances and the weighing procedure. The expanded uncertainties U of the overall mass fraction w of the binary system is U(w) = 0.002 (level of confidence = 0.95).

Figure 2. Scheme of the experimental setup.

between 373.15 and 573.15 K. Filtered n-C28H58 was liquefied in a beaker at about 340 K before an appropriate amount of nC12H26 was added. To achieve the desired composition of the n-alkane mixture, both liquid compounds were weighed before and after filling with a balance (Sartorius BP110) with an expanded uncertainty (k = 2) of 1 mg. From the weighing procedure, an initial mass fraction ratio for n-C12H26/n-C28H58 of w1/w2 = 0.156/0.844, corresponding to a mole fraction ratio of x1/x2 = 0.300/0.700, was adjusted. Here, the absolute uncertainty (k = 2) in both the mass and mole fractions based on the weighing procedure is supposed to be 0.001. Taking into consideration the uncertainty of the GC results for the pure substances of w = 0.001, the total expanded uncertainty (k = 2) of the overall mass fraction of the binary mixture is estimated to be w = 0.002. To avoid any change in the sample composition of the binary mixture and the wax SX-70 during sample preparation caused by different evaporated amounts of the components, a fast preparation procedure was necessary. The inevitable variation in the composition of the liquid binary mixture over the investigated temperature range could be estimated by mass balance calculations detailed later on. Helium (M = 4.0026 g· mol−1), which served as an inert gas for sample handling and control of the sample composition during the experiments, was

to be U(w) = 0.001 based on a confidence level of more than 95% (k = 2). According to the GC results, the initial purities of w = 0.9945 for n-C12H26 and w = 0.9950 for n-C28H58 obtained before the SLS experiments could confirm the specifications given by the supplier. Referring to the mass distribution in Figure S1 in the Supporting Information, the sample for the wax SX-70 analyzed before the measurements shows a broad, slightly asymmetric distribution of linear n-alkanes ranging between about n-icosane (n-C20H42) and n-hexacontane (n-C60H122). The compound mostly found in the wax is n-tritriacontane (n-C33H68) with w = 0.068. At ambient conditions, the n-C28H58 and wax samples are solid and start to melt at about 335 K. Due to the broader distribution of heavy alkanes in the wax sample, the melting temperature reaches up to about 373 K. Both liquefied samples showed particle-like impurities presumably resulting from the manufacturing process. To obtain ideally particle-free samples as necessary for SLS experiments, samples of n-C28H58 and the wax SX-70 were filtered with a syringe filter with 220 nm pore size at about 373 and 423 K, respectively. The binary n-alkane mixture consisting of mole fractions x of about x1 = 0.30 of n-C12H26 and x2 = 0.70 of n-C28H58 (0.3nC12H26/0.7n-C28H58) was investigated in the temperature range 3322



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supplied by Linde AG with a volume fraction purity ψ of 0.99999. All liquefied samples were transparent at the beginning of the measurements. After the measurements up to 573 K in the case of n-C12H26, n-C28H58, and 0.3n-C12H26/0.7n-C28H58, a slight yellowish coloration could be found. A further GC analysis was carried out to check if any thermal decomposition or oxygenation of n-alkanes27 occurred in the high-temperature range. The GC results obtained for the samples after the SLS measurements are also given in Table S1 in the Supporting Information and show no distinct change in the composition of the n-C12H26 (w = 0.9941) and n-C28H58 (w = 0.9832) samples. For the binary mixture of n-C12H26 and n-C28H58, the total fraction of both substances in the sample was w = 0.9957 according to the GC results. The reduction of the mole fraction ratio of n-C12H26/n-C28H58 from 0.300/0.700 to about 0.287/ 0.713 is caused by the larger volatility of n-C12H26 than nC28H58, resulting in a weak depletion of n-C12H26 relative to nC28H58 in the liquid phase during the measurements. A summary of the used chemicals is given in Table 1. Experimental Setup and Procedure. The experimental setup used for the investigation of a liquid−vapor interface of the studied n-alkane systems close to saturation conditions is the same as that used in our former studies11,16,17 and shown in Figure 2. The main information on the setup necessary for the present study is detailed below. A frequency-doubled continuous-wave Nd:YVO4-laser (Coherent, Verdi-V2) operated in a single mode with a wavelength of λ0 = 532 nm serves as a light source. The laser power was about 500 mW when working at temperatures T < 350 K and somewhat lower for higher temperatures. For the observation of light scattered by surface waves, the optical path has to be aligned in such a way that the laser beam and the direction of detection intersect on the liquid−vapor interface in the measurement cell. For large scattering intensities from the vapor−liquid interface, scattered reference light from the cell windows is not sufficient to realize heterodyne conditions. Here, an additional reference beam is added. For this, part of the incident laser light is split by a glass plate and superimposed with the scattered light behind the sample cell. The time-dependent intensity of the scattered light is detected by two photomultiplier tubes (PMTs) operated in cross-correlation in order to suppress after-pulsing effects. The signals are amplified, discriminated, and fed to a linear-tau digital correlator featuring 256 equally spaced channels operated with a sample times down to 37.5 ns. The design of the optical arrangement is based on the analysis of scattered light at variable and relatively high wave numbers of capillary waves, whereby instrumental broadening effects are negligible.11 According to eq 1, the wavenumber q can be adjusted as a function of the easily accessible angle of incidence ΘE. To measure the latter property, the laser beam is first adjusted through the detection system consisting of two apertures (diameter 1 mm) at a distance of about 4 m. Then, the laser beam is set to the desired angle. For the experiment, the angle of incidence ΘE was set between 3.0° and 3.2° and was measured with a high-precision rotation table. The error in the angle measurement was determined to be approximately 0.005° (k = 2). A sample cell consisting of stainless steel and having the same outer dimensions as that employed in our previous light scattering measurements from the bulk of fluids28−30 was used. Compared to the latter investigations, the special feature of the cell used in this study is that it provides a larger effective surface

length of 7 cm due to the larger total inner volume of about 105 mL instead of 40 mL. A length of 7 cm corresponds to the same value as that used in our former study on toluene11 and is sufficient to avoid disturbing capillary effects of the liquid at the edges of the cell on the probed region. Also due to this arrangement, line broadening effects could be suppressed completely. The four optical accesses, which are uniformly distributed around the cell and where two of them are used to guide the incident beam and collect the scattered light, were made of quartz windows (Herasil, diameter 30 mm × length 20 mm). The temperature of the sample cell was controlled by resistance heating and measured by a calibrated Pt-100 Ω resistance probe. This is integrated into the wall of the sample cell close to the heating wire and connected to an AC bridge (Anton Paar MKT 100). Given the large thermal conductivity of the cell material and the close proximity of the resistance probe to the vapor−liquid interface, it can reliably be assumed that the temperature of the resistance probe corresponds to the temperature of the fluid. The uncertainty in the absolute temperature measurement is 15 mK (k = 2). The temperature stability of the temperature probe used for temperature control and measurement was better than 5 mK during each experimental run. The reported sample temperature data stem from the average of the recorded readings of the sensor for a given temperature point. Taking also the uncertainty and position of the used resistance probe into account, the expanded uncertainty for all reported temperatures is estimated to be 0.05 K (k = 2) over the entire temperature range. Before each measurement series, a pressure test of the cell using helium at pressures of about 2 MPa was successfully performed. Thus, a tightness of the cell during the measurements could be ensured. For the filling of the sample cell, first the liquefied samples were inserted into the cell via the upper window. The gas phase was then flushed by helium several times in order to avoid any contamination of the sample with air or other gases which may enable an oxygenation of the sample. After that, the system was closed by inserting and fixing the upper window, and an initial partial pressure of about 0.1 MPa of helium could be adjusted. The pressure was not registered during the measurement in order to keep the system volume and the disturbance of the thermodynamic equilibrium small, but could be estimated to be smaller than 0.2 MPa in all cases. Given the insignificant effect of pressure on the liquid viscosity and surface tension of n-alkane systems at relatively small pressures below 0.2 MPa,3 all presented measurements can be considered to be carried out close to saturation conditions. For each temperature, six measurements at different angles of 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. Furthermore, line-broadening effects can be excluded for such a choice of incident angles. The measurement times for a single run were typically on the order of 20 min down to a couple of minutes for the highest temperatures in this study. During a measurement series for each system, the temperature was increased step by step. While for pure n-C12H26 the lowest temperature was set to 323.15 K, larger temperatures of T = 398.15 K for n-C28H58 and T = 373.15 K for 0.3n-C12H26/0.7nC28H58 were required to suppress disturbing influences from scattering due to solid agglomerates which were not yet molten below the stated temperatures. Temperature steps of 25 K were 3323



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dynamic viscosity of the almost saturated vapor phase. Since the systems investigated in this work are still relatively far away from the critical point, the liquid phase is mainly dominating the dynamics of the surface waves. For the vapor properties, uncertainties of about 20% are sufficient enough to determine the liquid properties accessible by SLS within less than 1%. In the following, the sources used for the required input values for the thermophysical properties of the studied systems are given and discussed. For n-C12H26, the densities of the liquid and vapor phases have been adopted from the equation of state of Lemmon and Huber.31 Data for the dynamic viscosity of the vapor phase are calculated from a pure fluid model according to Huber et al.32 For n-C28H58, the liquid density was employed from a correlation of Dutour et al.33 based on their experimental data measured between 353.15 and 403.15 K at atmospheric pressure with a U-tube densimeter. The uncertainty of the measurement results is not specified but can be estimated to be 0.1%. The vapor viscosity of n-C28H58 was deduced from the temperature-dependent correlation given by Yaws’ Handbook of Thermodynamic and Physical Properties of Chemical Compounds,5 a database which is freely available in the Internet. Therein, it is stated that the tabulated values are based on regression of experimental data and researched estimates. The uncertainty of the apparently purely predictive estimations for the vapor viscosity of n-C28H58 provided by Yaws’ handbook is not specified but can be estimated with a value of 20% (k = 2). Even for the largest temperature studied (T = 573.15 K), the vapor viscosity of pure n-C28H58 (η″ = 0.0051 mPa·s) is about 80 times smaller than the corresponding liquid viscosity. Similar vapor viscosities in the zero-density limit (e.g., η″ = 0.0058 mPa·s at T = 573.15 K), which applies well for the current investigations, were calculated for n-C28H58 using the recent prediction model of Riesco and Vesovic.34 For the saturated vapor of n-C28H58, no density data are available. Instead, Yaws’ handbook5 allows for estimations of the vapor pressure of n-C28H58, which is more than 100 times smaller than that of pure n-C12H26 over the entire temperature range studied. The influence of the vapor properties of n-C28H58 on the values for liquid viscosity and surface tension of pure n-C28H58 was exemplarily estimated at a temperature of 573.15 K where the effect of the vapor properties is the largest. In the two cases where the vapor properties of n-C28H58 are considered or neglected, relative deviations between the final liquid dynamic viscosities of 0.2% and surface tensions of 0.1% are obtained. These differences are about an order of magnitude smaller than the experimental uncertainties of the measured properties. Thus, due to the very small impact of the vapor properties of nC28H58, the vapor phase for the liquid systems consisting of pure n-C28H58 and of the binary mixture of 0.3n-C12H26/0.7nC28H58 can sufficiently be modeled by estimating a gas phase consisting of pure helium and a binary mixture of helium and nC12H26, respectively. The liquid density of the wax SX-70 was obtained based on volumetric measurements of a given amount of sample at temperatures between 363.15 and 423.15 K in steps of 20 K. For the density data which are provided in the Supporting Information in Table S3, the uncertainty can be specified with a value of 0.2% (k = 2). The experimental data were correlated by a linear fit with respect to temperature which was used to extrapolate to the temperature range between 473.15 and 523.15 K studied in the SLS experiments. At these conditions,

used for the pure and binary systems. For the wax SX-70, a limited temperature range between 473.15 and 523.15 K in steps of 10 K was studied in order to avoid any thermal decomposition of very long chained hydrocarbons at overly large temperatures. For all studied systems, repetition measurements were performed at least one time within the series and after the last measurement at the largest temperature of 523.15 or 573.15 K. This allowed checking of the stabilities of the investigated samples.

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MEASUREMENT EXAMPLE AND DATA EVALUATION Figure 3 shows an example correlation function obtained from scattering on the interface of liquid n-C28H58 close to saturation

Figure 3. Measurement example of a normalized correlation function (upper graph) and the residuals (lower graph) for n-C28H58 at a temperature of 498.15 K using an incident angle of 3°: □, measurement data; −, fit according to eq 8.

conditions at a temperature of 498.15 K and an incident angle ΘE = 3°. The experimental correlation function, eq 8, has to be evaluated for the central quantities, ωq and τC, which is performed by a nonlinear regression based on a Levenberg− Marquardt (LM) algorithm in which the squared sum of residuals is to be minimized. Within the entire fit range, no systematic deviations or any disturbing signals in the long-time range of the correlation function can be observed. This is illustrated in the residual plot in Figure 3 and was confirmed for all present measurements. The uncertainties (k = 2) obtained from the fit are given in brackets and are below 0.4% for ωq and 1.3% for τC. In most of the cases, uncertainties below 1% for ωq and 2% for τC could be obtained. It is obvious that the error in the determination of the frequency was generally smaller than that of the decay time, especially at larger temperatures where more and more oscillations appeared in the correlation functions. As discussed above and detailed in our former studies,11,18 a reliable determination of surface tension and viscosity is only possible by an exact numerical solution of the dispersion equation, eq 4, where the frequency ωq, the decay time τC, and the modulus of the scattering vector q are used as input values. This procedure has always been performed within the present study. Further input data for solving the dispersion relation are the density of the liquid phase as well as the density and 3324



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Table 2. Liquid Dynamic Viscosity η′ and Surface Tension σ of the Pure Substances n-C12H26 and n-C28H58 Close to Saturation Conditions Obtained by Surface Light Scattering as a Function of Temperature T Using Corresponding Literature Data for the Liquid Density ρ′, Vapor Density ρ″, and Vapor Viscosity η″a T/K

ρ′/(kg·m−3)

ρ″/(kg·m−3)

η″/(μPa·s)

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15

727.2 708.6 689.9 670.7 651.0 630.4 608.8 585.8 560.9 533.4 502.4

0.14 0.15 0.15 0.16 0.20 0.41 1.03 2.44 5.20 10.08 18.07

19.7 20.4 21.4 22.7 23.5 23.2 21.7 19.1 16.5 14.6 13.8

398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15

738.5 721.3 704.0 686.7 669.6 653.0 637.0 622.0

0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

24.2 25.3 26.3 27.3 28.3 29.3 30.2 31.2

η′/(mPa·s)

100Ur(η′)

σ/(mN·m−1)

100Ur(σ)

0.9225 0.6763 0.5070 0.4003 0.3223 0.2595 0.2156 0.1821 0.1532 0.1277 0.1051

2.3 1.8 1.4 1.5 1.8 1.7 1.5 1.5 2.1 1.4 2.2

21.64 19.91 18.19 16.22 14.33 12.38 10.67 8.95 7.25 5.64 4.14

1.0 1.5 1.7 0.8 1.8 1.9 0.7 1.8 1.0 1.2 1.6

1.8142 1.3609 1.0252 0.8318 0.6847 0.5675 0.4753 0.3995

4.3 2.8 1.8 1.7 2.1 2.2 2.4 1.5

21.33 19.53 17.78 16.57 15.38 14.18 12.86 11.51

3.1 2.5 1.5 2.8 1.7 1.6 1.1 1.3

n-C12H26

n-C28H58

a

The expanded uncertainties U are U(T) = 0.05 K, while the relative expanded uncertainties Ur(η′) and Ur(σ) are given in the table (level of confidence = 0.95).

mated with the term surface tension referring to a liquid or liquid mixture in equilibrium solely with their own vapor phase. While for the liquid n-C28H58 and wax SX-70 samples, a pure helium gas phase can be considered, binary gas mixtures of helium and n-C12H26 are modeled for the liquid systems containing pure n-C12H26 and the binary mixture of n-C12H26 and n-C28H58. For the latter system, the vapor phase composition was calculated in an ideal approach in which the partial pressures related to helium and n-C12H26 were added. Here, the partial pressure related to n-C12H26 is calculated from the product of the vapor pressure of pure n-C12H26 and its corresponding mole fraction in the liquid phase. For the binary liquid mixture 0.3n-C12H26/0.7n-C28H58, it is assumed that only those two substances are present in the liquid phase. Furthermore, the mole fraction ratio of 0.300/ 0.700 is only valid for the initial temperature of 373.15 K studied in the experiment. Due to the strongly increasing vapor pressure of n-C12H26 with increasing temperature, more and more n-C12H26 transfers from the liquid into the vapor phase, while the amount of liquid n-C28H58 can be approximated as constant at the various T states. To calculate the mole fractions of n-C12H26 and n-C28H58 in the liquid phase, mass balance calculations considering the volumes and densities of the two phases were carried out. Based on this scheme, the mass fraction w of n-C12H26 in the liquid phase varies between 0.156 ± 0.002 at T = 373.15 K and 0.148 ± 0.002 at 573.15 K. The latter value corresponds to the value obtained by the GC analysis performed after SLS measurements up to 573.15 K. The detailed values for the composition in the liquid phase of the binary mixture are tabulated in the next section. Based on the procedure given above, the corresponding liquid density for the binary mixture 0.3n-C12H26/0.7n-C28H58 was modeled according to a mixing rule developed by Assael et al.39 for linear liquid n-alkanes. This model requires only information on

an uncertainty of 1% for the liquid density of the wax can be estimated. According to the composition of the wax SX-70 analyzed before the measurements (see Table S2 and Figure S1 in the Supporting Information), predominantly heavy n-alkanes with chain lengths of more than 20 carbon atoms can be found. The mass fraction of alkanes having NC values smaller than 20 is about 0.03%. According to estimations based on Yaws’ handbook,5 the vapor pressure of n-alkanes decreases strongly with increasing chain length and becomes negligible for NC > 20 within the temperature range investigated in this study. Due to the strong presence of barely volatile long-chained alkanes in the liquid mixture, a very low total vapor pressure originating from the liquid wax sample can be expected. Thus, the vapor phase for the wax system can be modeled solely by pure helium. The vapor phase properties were determined from the vapor pressures of the corresponding saturated liquids present in the samples and the partial pressure from the helium used as inert gas in all cases. These data could be used to estimate the composition of the partially saturated vapor phase for all studied systems. For helium, the gas density and viscosity data were obtained from the Helmholtz equation of state for helium published by Ortiz-Vega35 and the pure fluid model of Arp et al.,36 respectively. The solubility of the inert gas helium in ndodecane can be estimated to be below x = 0.001, i.e., below w = 0.00002 for low pressures of about 0.1 MPa and temperatures up to 573 K, and it rather decreases with increasing alkyl chain length.37,38 Thus, the effect of the helium gas on the liquid properties density, viscosity, and surface tension of the systems studied can reliably be neglected. In this context, thestrictly speakingcorrect property measured for the n-alkane systems close to saturation conditions by SLS, the interfacial tension between the liquid−vapor interface, may reliably be approxi3325



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Table 3. Liquid Dynamic Viscosity η′ and Surface Tension σ of the Binary Mixture 0.3n-C12H26/0.7n-C28H58 Close to Saturation Conditions Obtained by Surface Light Scattering as a Function of Temperature T Using Corresponding Literature Data for the Liquid Density ρ′, Vapor Density ρ″, and Vapor Viscosity η″ as Well as Estimated Mass Fractions w of n-C12H26 in the Liquid Phasea T/K

w/%

ρ′/(kg·m−3)

ρ″/(kg·m−3)

η″/(μPa·s)

η′/(mPa·s)

100Ur(η′)

σ/(mN·m−1)

100Ur(σ)

373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15

15.6 15.6 15.6 15.5 15.5 15.4 15.2 15.0 14.8

744.3 727.0 709.4 691.5 673.4 655.2 637.0 618.9 600.9

0.15 0.15 0.17 0.25 0.51 1.20 2.78 5.94 11.74

22.4 23.4 24.5 25.0 24.4 22.9 20.9 19.0 17.5

1.9440 1.4119 1.0885 0.8604 0.6912 0.5671 0.4787 0.4075 0.3445

3.0 2.7 2.1 2.0 1.4 1.9 1.9 2.1 1.4

21.71 19.80 18.50 17.07 15.59 14.15 12.84 11.56 10.30

2.5 2.4 1.1 1.2 1.1 1.1 1.6 1.2 1.7

a


Table 4. Liquid Dynamic Viscosity η′ and Surface Tension σ of the Wax SX-70 Close to Saturation Conditions Obtained by Surface Light Scattering as a Function of Temperature T Using Corresponding Literature Data for the Liquid Density ρ′, Vapor Density ρ″, and Vapor Viscosity η″a T/K

ρ′/(kg·m−3)

ρ″/(kg·m−3)

η″/(μPa·s)

η′/(mPa·s)

100Ur(η′)

σ/(mN·m−1)

100Ur(σ)

473.15 483.15 493.15 503.15 513.15 523.15

732.2 727.2 722.3 717.3 712.3 707.3

0.15 0.15 0.15 0.15 0.15 0.15

27.3 27.7 28.1 28.5 28.9 29.3

1.230 1.083 1.000 0.921 0.872 0.791

4.6 3.6 4.0 4.4 4.5 3.6

16.80 16.09 15.27 14.08 13.45 13.31

3.0 3.6 3.9 4.3 4.5 5.2

a


Summary of Dynamic Viscosity and Surface Tension Data. The results for the liquid dynamic viscosity η′ and surface tension σ of the four hydrocarbon systems n-C12H26, nC28H58, 0.3n-C12H26/0.7n-C28H58, and the wax SX-70 between 323.15 and 573.15 K obtained from SLS close to saturation conditions are summarized in Tables 2−4. The listed data are average values of at least six independent measurements with different angles of incidence ΘE. Furthermore, the used input data for the liquid density ρ′, vapor density ρ″, and vapor viscosity η″ required for data evaluation as described in the previous section are tabulated. Uncertainty Analysis. From the typical variation of liquid viscosity and surface tension of the studied systems with temperature, the uncertainty in the temperature measurement of 0.05 K leads to maximum relative uncertainties below 0.07% and 0.02% in the measured liquid dynamic viscosities and surface tensions, respectively, over the entire temperature range. Estimated uncertainties in the liquid mass fraction of up to 0.002 are adherent to uncertainties in the liquid density of up to 1%. The latter uncertainties are taken into account in the following error analysis considering the uncertainties induced by the primary measured variables and input data. Although the approximate solution for the dynamics of surface waves given in ref 11 never allows for the determination of viscosity and surface tension with high accuracy (for doing this, the exact solution of the dispersion relation, eq 4, has always been used in this work), yet it can be applied to get a good estimate for the total uncertainty of our SLS results in an analytical manner. The direct quantity related to the liquid kinematic viscosity ν̃ is determined by both vapor and liquid properties, i.e., ν̃ = (η′ + η″)/(ρ′ + ρ″).11 Thus, the estimate for

the mass composition and the saturated densities of the pure liquids as a function of temperature. Such a mixing rule works sufficiently well for binary combinations of linear n-alkanes having carbon numbers NC between 6 and 24 with relative deviations between modeled and experimental data of less than 0.5% for various temperatures.39 To model the vapor density of the binary mixtures, a linear mole-based mixing rule using the densities of helium gas and nC12H26 vapor according to the corresponding data from the Refprop database3 was applied. Such a simple prediction scheme can represent the density of gas mixtures at low pressures well within ±5%.3 To model the vapor viscosity, a more sophisticated model in the form of the Lucas method40 was applied since the vapor viscosity has a stronger impact on the properties of interest than the vapor density. The corresponding-states model of Lucas40 requires information on the mole composition, critical data of the pure compounds, and corrections for polarity and quantum effects, the latter data which were considered for helium. Using this model, the viscosity of gas mixtures at low pressures can typically be represented within ±10% compared to experimental data.41

■

RESULTS AND DISCUSSION

First, the temperature-dependent values for dynamic viscosity and surface tension data of the investigated n-alkane systems are presented. Then, an uncertainty analysis of the measurement results and a data correlation including an interpretation of the data from a molecular point of view is performed. Finally, the experimental results are compared with available literature data. 3326



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the uncertainty of the liquid dynamic viscosity values Δη′ (k = 2) results in Δη′ ≈ [[(ρ′ + ρ″)Sν̃]2 + (νΔ ̃ ρ′)2 + (νΔ ̃ ρ″)2 + (Δη″)2 ]1/2 (9)

based on the double standard deviation Sν̃ of the measurement values for the kinematic viscosity and on the uncertainty of the reference data needed for the determination of the liquid kinematic viscosity from the directly observable ν̃. Similarly, the quantity directly accessible by the numerical solution of the approximate solution, where only data obtained from the light scattering experiment are used as input parameters, is the ratio σ̃ = σ/(ρ′ + ρ″) of the surface tension to the sum of the densities of the liquid and vapor phases.11 In an analogous way, the uncertainty for the surface tension can be estimated according to Δσ ≈ [[(ρ′ + ρ″)Sσ̃]2 + (σ ̃Δρ′)2 + (σ ̃Δρ″)2 ]1/2

(10)

For the relative uncertainties of the vapor properties viscosity Δη″/η″ and density Δρ″/ρ″ of all studied systems, values of 10% (k = 2) have been estimated. The relative uncertainty of the liquid density Δρ′/ρ′ was assumed to be 0.5% for n-C12H26 and 1% for the other three systems. As observed in many DLS applications,11,42 the standard deviation of individual measurements may be considered as a reasonable measure for the experimental uncertainty. The value for Sν̃ is mainly determined by the uncertainty of the angle measurement and the uncertainty associated with the determination of the decay time from the correlation function. The relative expanded measurement uncertainties (k = 2) with respect to the liquid dynamic viscosity, Ur(η′), and the surface tension, Ur(σ), of our values for n-C12H26 as estimated by eqs 9 and 10 are displayed in Figure 4a,b, respectively. Here, the individual contributions are shown relative to the values of η′ and σ. As can be seen from Figure 4a, for the temperature range investigated in this study, the uncertainties in the reference data and correlations used have comparatively small influence on the final results for liquid viscosities. Only at larger temperatures, the influence of the increasing vapor properties becomes more important, especially for the systems containing the relatively strongly volatile n-C12H26. The main factor determining the overall uncertainty of the liquid viscosity is given by Sν̃ which is typically between 1 and 2%. For n-C12H26, a total measurement uncertainty (k = 2) of between 1.4 and 2.3% in the temperature range between 323.15 and 573.15 K can be deduced. Following the calculation procedure, total measurement uncertainties Δη′/η′ (k = 2) of between 1.5 and 2.4% at T between 448.15 and 573.15 K for n-C28H58 and between 1.4 and 2.1% at T between 423.15 and 573.15 K for 0.3n-C12H26/0.7n-C28H58 were achieved. Only at lower temperatures, the uncertainties increase to 4.3% at T = 398.15 K for n-C28H58 and 3.0% at T = 373.15 K for 0.3n-C12H26/0.7n-C28H58. The larger uncertainties at lower temperatures are related to the weaker scattering signals and the less pronounced oscillatory signal, causing larger uncertainties in τC and thus in Sν̃. The same reasons are also responsible for the total uncertainties Δη′/η′ (k = 2) for the wax SX-70 ranging between 3.6 and 4.6% for the temperatures between 473.15 and 523.15 K. As visible in Figure 4b, the double standard deviation Sσ̃ of the individual measurements for n-C12H26 was relatively constant around 1% over the entire temperature range. In combination with the uncertainties introduced by the available

Figure 4. Estimated relative total measurement uncertainties (k = 2) for the liquid dynamic viscosity Δη′/η′ (a) and the surface tension Δσ/σ (b) of n-C12H26 and individual contributions to those values. The lines in both graphs indicate the upper limit for the estimated total uncertainties and should serve as guides for the eye. (a) Δx: □, Δη′; + , (ρ′+ρ″)Sṽ; ○, ṽΔρ′; ◊, ṽΔρ′; △, Δη″. (b) Δx: □, Δσ; + , (ρ′+ρ″)Sσ̃; ○, σ̃Δρ′; ◊, σ̃Δρ″.

density data which are in most cases smaller than those related to Sσ̃, the value for Δσ/σ of between 0.7 and 1.9% can be regarded as a reliable estimate for the total uncertainty (k = 2) of the surface tension of n-C12H26 over the entire temperature range. For the systems n-C28H58 and 0.3n-C12H26/0.7n-C28H58, uncertainties (k = 2) of between 1.1 and 2.8% in the temperature range between 423.15 and 573.15 K can be estimated. Due to the experimental complexity in connection with weak oscillatory signals, the uncertainties Δσ/σ increase to 3.1% for n-C28H58 and 2.5% for 0.3n-C12H26/0.7n-C28H58 at low temperatures and amount to between 3.0 and 5.2% for the wax SX-70. The relative expanded uncertainties (k = 2) for the desired properties liquid dynamic viscosity, Ur(η′), and surface tension, Ur(σ), deduced from the procedure given above are provided in Tables 2−4. In order to check our present data and also the stability of the systems, about two to three independent repetition measurements were performed at a specific temperature in the lower temperature range after having investigated state points at larger temperatures. Especially for repeated measurements after the study of the largest temperature of 523.15 or 573.15 K, slightly lower viscosity and surface tension data were found which may indicate a slight sample decomposition at high temperatures. Nevertheless, all results from the repetition measurements agreed with the presented data within combined uncertainties. Data Correlation. The temperature-dependent experimental results for the liquid viscosity and the surface tension of the four studied n-alkane systems are shown in Figures 5 and 6, respectively. For all systems except for the wax SX-70 where only a limited temperature range was investigated by SLS, both properties were correlated as a function of temperature. To represent the dynamic viscosity of liquids at the saturation line, usually a Vogel-type or Andrade-type equation can be used within a limited temperature range.41 Such 3327



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temperature range covered. Instead, an inverse polynomial series of third order was used in the form η′calc = η′0 + η′1T −1 + η′2 T −2 + η′3 T −3

(11)

in order to represent our experimental dynamic viscosity data η′ for the systems n-C12H26, n-C28H58, and 0.3n-C12H26/0.7nC28H58. In eq 11, T is the temperature in Kelvin and η′0, η′1, η′2, and η′3 are fit coefficients given in Table 5. For the correlation, each data point of a system was considered with the same statistical weight. In Table 5, also the root-mean-square deviation (rms) of our data relative to those calculated by eq 11 is reported and between 0.50 and 0.67%. It should be noted that the residuals of the experimental data from the fit are always smaller than the experimental uncertainties of the individual data points; see the lower part in Figure 5. As expected, the liquid viscosity of n-alkanes increases with increasing alkyl chain length.3 Due to the stronger van der Waals interactions and entanglement of long alkyl chains, a larger density of n-C28H58 compared to n-C12H26 is found. This is in accordance with an increased momentum transport and thus a larger viscosity for n-C28H58. For the binary system 0.3nC12H26/0.7n-C28H58, the viscosities are between the data for the pure components and closer to the values for n-C28H58. The larger η′ values of the wax SX-70 compared to those of nC28H58 may be due to fact that on average longer-chained nalkanes than n-C28H58 are found in the wax. In literature,41 many mixing rules for the viscosity of liquids were developed. Within the scope of this study, only simple estimation methods were considered in connection with the binary mixture of n-C12H26 and n-C28H58 investigated in this study. The method of Grunberg and Nissan43 expresses the natural logarithm of the mixture liquid viscosity in terms of the sum of the natural logarithms of the viscosities of the pure components weighted by the corresponding mole fraction, and a residual part which includes a binary interaction parameter G12. Based on the viscosity data correlated according to eq 11 between 398.15 and 573.15 K for the pure and binary systems, the calculated G12 data vary strongly with temperature between 1.29 at T = 398.15 K and 0.34 at T = 573.15 K. Since usually G12 should only vary weakly with temperature for nonassociating compounds such as n-alkanes, it seems that the broad temperature range studied in this work does not allow for a use of the method of Grunberg and Nissan.43 Instead, the same form of mixing rule was employed using a mass fraction weighted scheme and neglecting a binary interaction parameter according to

Figure 5. Liquid dynamic viscosity of investigated n-alkane systems close to saturation conditions from surface light scattering. □, nC12H26; ◊, n-C28H58; ○, 0.3n-C12H26/0.7n-C28H58; △, wax SX-70; −, eq 11; --, eq 12.

Figure 6. Surface tension of investigated n-alkane systems close to saturation conditions from surface light scattering. □, n-C12H26; ◊, nC28H58; ○, 0.3n-C12H26/0.7n-C28H58; △, wax SX-70; −, eq 13; --, eq 14.

ln η′ = w1 ln η′calc,1 + w2 ln η′calc,2

(12)

where the indices 1 and 2 refer to the substances n-C12H26 and n-C28H58, respectively. The prediction according to eq 12 represents the correlation for the mixture viscosity obtained

equations cannot describe the experimental viscosity data for the three pure and binary systems sufficiently over the broad

Table 5. Liquid Dynamic Viscosity Data from the Correlation for the Studied Pure and Binary n-Alkane Systems η′0/(mPa·s) η′1/(mPa·s·K) η′2/(mPa·s·K2) η′3/(mPa·s·K3) rmsa/% T range/K a

n-C12H26

n-C28H58

0.3n-C12H26/0.7n-C28H58

−1.439199 2059.310 −1.00160 × 106 1.88305 × 108 0.50 323−573

−9.896327 15616.33 −8.31603 × 106 1.57478 × 109 0.67 398−573

−6.734002 10504.53 −5.53216 × 106 1.05233 × 109 0.64 373−573

Standard percentage deviation of η′ to the fit. 3328



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from the experimental data based on eq 11 within ±5% over the temperature range between 398.15 and 573.15 K. The correlation according to eq 12 is also shown in Figure 5 as a dashed line. The experimental data for the surface tension of the three investigated pure and binary systems can be represented by a modified van der Waals equation, which is suitable for extrapolations up to the critical point,44 according to

smaller surface tension enriches at the surface in terms of surface energy minimization. This causes the mixture surface tension to be less than the mole fraction average of the surface tension of the pure compounds.40 Using the surface tensions measured for the pure systems n-C12H26 and n-C28H58, a mole fraction based mixing rule for the system 0.3n-C12H26/0.7nC28H58 would result in between −2 and −8% lower surface tensions than the data correlated by eq 13 over the temperature range between 398.15 and 573.15 K, with a different temperature-dependent trend. Thus, the surface region seems to be enriched by n-C28H58 having a larger surface tension than n-C12H26. According to that, a mixing rule based on the mass fraction of the two components in the form of σ = w1σcalc,1 + w2σcalc,2 (14)

σcalc = σ0(1 − TR )1.26 [1 + σ1(1 − TR )0.5 + σ2(1 − TR )] (13)

where TR (=T/TC) denotes the reduced temperature. In eq 13, σ0, σ1, and σ2 represent fit parameters and are given in Table 6. Table 6. Coefficients of Equation 13 and Root-Mean-Square (rms) Deviation of the Experimental Surface Tension Data from the Correlation for the Studied Pure and Binary nAlkane Systems σ0/(mN·m−1) σ1 σ2 TC / K rmsa/% T range/K

n-C12H26

n-C28H58

0.3n-C12H26/0.7n-C28H58

48.5580 0.466141 −0.559672 658.65b 0.77 323−573

114.8963 −1.659485 1.185501 828.3b 0.88 398−573

104.6797 −1.482824 1.023485 788.59c 0.43 373−573

was applied. As illustrated in Figure 6 as a dashed line, the mixing rule based on eq 14 represents the measured surface tension data within 2% over the entire temperature range between 398.15 and 573.15 K, which is within most of the uncertainties of the experimental data for the binary mixture. Comparison with Literature. A data comparison with experimental literature data for the systems studied in this work can only be performed for the pure substances n-C12H26 and nC28H58. No experimental data are available for the systems 0.3nC12H26/0.7n-C28H58 and the wax SX-70. In Figure 7, our values for the dynamic viscosity of n-C12H26 measured close to saturation conditions are shown in

Standard percentage deviation of σ to the fit. bEmployed from ref 45. Calculated according to ref 46, using the data from ref 45.

a c

In this table, also the critical temperatures TC are listed which were directly used from literature45 for the systems n-C12H26 and n-C28H58. For the critical temperature of the binary mixture 0.3n-C12H26/0.7n-C28H58, the mixing rule according to Lee and Kesler46 was employed taking into consideration the TC values of the pure substances and assuming a constant mole fraction ratio of 0.3/0.7 over the entire temperature range. The present correlation which assumes the same statistical weight of each data point of the temperature-dependent measurement sets represents the experimental values of the surface tension with a rms deviation of between 0.43 and 0.88%. Except for two single data points, the relative deviation of the experimental data from the data correlated by eq 13 is smaller than their uncertainties. The surface tensions of the n-alkanes n-C12H26 and n-C28H58 show the expected trend of increasing values with increasing carbon number.3 The larger density of longer-chained n-alkanes also allows for forming more dispersive interactions at the liquid surface, causing a larger surface energy and thus surface tension. In a manner similar to that observed for the liquid viscosity, the surface tensions of the binary mixture are closer to the values for the pure n-C28H58. Interestingly, the surface tension data for the wax SX-70 are between the data for the pure n-C28H58 and for the binary mixture 0.3n-C12H26/0.7nC28H58. It seems that the liquid surface of the wax is rather enriched by short-chained n-alkanes with a carbon number below 30, which results in a minimization of the surface energy. This may also explain the relatively large liquid viscosity of the wax in comparison with n-C28H58. A correlation for the surface tension of a binary liquid mixture is usually not a simple function of the composition because the composition in the bulk can be different from that at the surface. This issue could already be observed from the aforementioned behavior of the viscosity and surface tension data for the wax SX-70. Typically, the component with the

Figure 7. Data comparison for dynamic viscosity of liquid dodecane. ■, this work; −, eq 11; --, Huber et al.;32 △, Dymond and Young;47 ◊, Knapstad et al.;48 ▽, Knapstad et al.;49 ○, Caudwell et al.50

comparison with literature data. Deviations between our results from SLS and the literature values are plotted using our correlation, eq 11, as a basis. For the reference fluid n-C12H26, the Refprop database3 refers to the pure fluid model from Huber et al.,32 which represents the dynamic viscosity as the sum of a dilute gas contribution and a residual part containing higher order density terms. For this model representing the considered experimental data in the temperature range between 262 and 473 K with an absolute average deviation of 0.95%, the estimated uncertainty in viscosity along the saturated liquid line is specified to be 0.5%.32 As shown in Figure 7, agreement between our experimental data and the correlation of Huber et al.32 within ±2% and thus within the experimental uncertainty of our data can be found for the temperature range between 323 and 523 K. At larger temperatures up to 573 K, the correlation gives slightly lower values compared to our values outside combined uncertainties. This seems to be related to the limited temperature range of the data used to develop the correlation which takes the character of an extrapolation at higher temperatures. 3329



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correlation based on eq 11 to lower temperatures, relative deviations between the data of Mazee58 and our correlated data ranging from +16.0 to +26.4% can be found. These deviations are outside the combined uncertainties considering the uncertainty of the experimental data of Mazee58 of 0.2% and the uncertainty intervals of the extrapolated correlated data based on a confidence level of more than 95% (k = 2). One possible reason for the discrepancies may be the limited applicability of the correlation to lower temperatures close to the melting point where typically a strong increase in the liquid viscosity is observed. An estimation of the liquid viscosity of n-C28H58 can be carried out using the database in Yaws’ handbook.5 The correlation based on the regression of unstated experimental data and researched estimates provides viscosity values which are distinctly lower than our measured data. The relative deviation increases with increasing temperature and covers a range between −6.5% at 398.15 K and −56.3% at 573.15 K. Hence, the reliability of viscosity estimations or extrapolations as those used in the database of Yaws’ handbook5 is highly questionable, especially for weakly characterized substances such as n-C28H58. The surface tensions of n-C12H26 obtained from SLS are plotted in Figure 8 together with available experimental

The experimental data sources used for the development of the correlation of Huber et al.32 are discussed below and only considered here. The data of Dymond and Young47 were measured with a suspended level viscometer at saturation pressure between 283 and 393 K using a sample with mole fraction purity of more than 0.99. Knapstad et al.48 determined the viscosity of a sample with a purity w > 0.9966 using an oscillating cylinder viscometer at atmospheric pressure for temperatures between 293 and 425 K. Both aforementioned sets have an estimated uncertainty of 0.5%. Knapstad et al.49 later reported further measurements on n-C12H26 of the same sample purity (w > 0.9966) at atmospheric pressure from 289 to 343 K, stating estimated uncertainties of between 0.4 and 0.6%. Caudwell et al.50 performed the most recent viscosity measurements, which were made with a vibrating-wire instrument operated between 298 and 473 K in the compressed liquid phase at a pressures of 0.1 MPa with a reported uncertainty of 2%. The data obtained by Lyusternik and Zhdanov51 in the gaseous region between 503 and 681 K as well as by Giller and Drickamer52 near the freezing point of about 262 K up to 293 K cannot be used for data comparison here. More recent experimental viscosity data for n-C12H26 at or close to saturation conditions are generally determined only around ambient temperature below 323 K53,54 or agree with our present results within combined uncertainties.55 Further recently published experimental data from Yang et al.56 were obtained over an extended temperature range from 303 to 673 K in the compressed liquid phase at 5 MPa. For temperatures between 323 and 573 K studied in our measurements, the relative deviations between the data of Yang et al.56 measured by a thermal expansion method and the correlation according to eq 11 increase from +4.2% at 323.2 K to +16.4% at 573.2 K. The larger viscosities for the data of Yang et al.56 compared to our data are reasonable due to the larger pressure in their measurements, and are in agreement with the correlation of Huber et al.32 within combined uncertainties. In Figure 7, only those literature data points which fit to the temperature range and conditions at or close to saturation as studied in this work are shown. All experimental data points described above agree with our present data within combined uncertainties, with relative deviations of the data sets below ±2.5%. The aforementioned discrepancy between our data and the correlation of Huber et al.32 at temperatures above 523 K may be related in that the latter correlation is strongly influenced by the temperature-dependent trend of the experimental data of Caudwell et al.50 For the liquid viscosity of n-C28H58, only two data sources providing experimental results could be found. In 1951, Doolittle and Peterson57 performed measurements at atmospheric pressure for a temperature range between 263 and 573 K employing a Ubbelohde capillary viscometer with a claimed uncertainty of between 1.2 and 1.5%. No information on the purity of the sample is given. Compared to our correlation in the temperature range developed from our measurements, the liquid viscosity data of Doolittle and Peterson57 show larger values outside combined uncertainties with deviations between +8.2% at 373.15 K and +4.4% at 548.15 K. Such deviations might be related to the different sample purities, which is likely to be possible for long-chained alkane systems. The other data set measured by Mazee58 with an Ostwald-type viscometer reports viscosity values in a temperature range between 343.15 and 363.15 K, which is outside the temperature range investigated in the present study. By extrapolating our

Figure 8. Data comparison for surface tension of dodecane. ■, this work; −, eq 13; --, Mulero et al.;59 △, Jasper;61 ◊, Körösi and Kováts;62 ○, Cumicheo et al.63

literature data covering the temperature range investigated in this work. Our correlation according to eq 13 serves as a reference. The Refprop database3 recommends the use of the surface tension model of Mulero et al.59 The correlation represents the 60 experimental data points measured in a temperature range between 273.15 and 473.15 K and used for the development of the model with an absolute average deviation of 0.49%. Both the data sources considered and the uncertainty of the model are not defined. According to Figure 8, the model of Mulero et al.59 yields between 2.4 and 4.6% larger values than our correlation over the entire temperature range between 323 and 573 K. Assuming an uncertainty of 2% for the correlation of Mulero et al.,59 both data sets would be within combined uncertainties in most cases, even for the extrapolated data at temperatures above 473 K. Most experimental σ data for n-C12H26 are generally determined only around ambient temperature below 323 K53,55,60 and are thus not used for data comparison here. In total, three data sources providing surface tension data of nC12H28 above 323 K were found and are discussed below. Jasper61 applied the capillary rise method for measuring the surface tension under isobaric conditions with an atmosphere 3330



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other long-chained alkane systems, theoretical estimations in literature for n-octacosane show distinct discrepancies from our measurements, especially for the liquid viscosity with deviations of more than 50%. In this connection, the experimental data obtained in this work can improve the data situation for viscosity and surface tension of medium- to long-chained nalkane systems in the high-temperature regime. Furthermore, they can be used to develop modeling approaches by serving as reference values for theoretical and empirical models as well as molecular simulations.

consisting of nitrogen and dodecane vapor at temperatures between 283.15 and 393.15 K. A low uncertainty of 0.01 mN· m−1, i.e., smaller than 0.1%, is claimed by the authors. The capillary rise method was also used by Körösi and Kováts62 for temperatures of 293.15 and 353.15 K, without specifying the ambient conditions. The uncertainty of their surface tension data is below 0.3%. Cumicheo et al.63 determined the surface tension at ambient pressure and a single temperature of 344.15 K with the help of the pendant drop method with an uncertainty of 0.01 mN m−1. Except for Jasper,61 who provides no purity specification, the mass fraction purity of the samples was specified to be better than w = 0.999. Figure 8 shows that all literature data are comparable to each other and by trend larger than our data. Furthermore, the temperature-dependent data of Jasper61 converge with the present measurement results at larger T values. Discrepancies in published surface tension values are not uncommon because the determination of this property may be affected by two factors which may not be easily controlled experimentally. First, values for surface tension are strongly influenced by contamination and/or impurities. Second, if surface tension is measured for liquid−air systems, as in most cases cited above, the surface temperature may be somewhat below the temperature in the bulk of the fluid, a fact which may rather increase the surface tension. An influence of this error can be excluded for the present investigation, which has been carried out inside a closed sample cell close to saturation conditions in thermodynamic equilibrium. Since no experimental surface tension data are available for nC28H58, estimated data were derived from Yaws’ handbook.5 The calculated results, which are based on a simple van der Waals equation, deviate between +2.4 and +6.1% from our data correlated via eq 13 within the temperature range between 398.15 and 573.15 K. The source of the parameters used in the model and the reliability of the model itself, which is applied for a broad temperature range here but theoretically only valid close to the critical region, is debatable.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00363. Composition analysis of the systems investigated by SLS and liquid density data of the wax SX-70 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49-9131-85-23279. Fax: +49-9131-85-25851. E-mail: [email protected]. ORCID

Thomas M. Koller: 0000-0003-4917-3079 Cédric Giraudet: 0000-0003-2051-7042 Jiaqi Chen: 0000-0002-2591-0073 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.

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Notes

CONCLUSIONS The present investigations on a horizontal liquid−vapor interface of four different n-alkane systems containing pure ndodecane and n-octacosane, their binary mixtures at a mole fraction for n-dodecane of about 0.3, and a commercially available hydrocarbon wax have shown that surface light scattering can be used to reliably determine the liquid viscosity and surface tension over a broad temperature range between 323 and 573 K close to saturation conditions. Based on the recorded light scattering signals as well as literature data and correlations for the liquid densities, vapor densities, and vapor dynamic viscosities, an expanded measurement uncertainty (k = 2) of less than 2% for the liquid dynamic viscosity and less than 1.5% for the surface tension could typically be achieved. Over the entire temperature range, a simple polynomial equation for the liquid viscosity and a modified van der Waals equation for the surface tension can represent the measured data of the pure and binary systems mostly within experimental uncertainties. For the reference fluid n-dodecane, agreement between our and the current reference data exists for the liquid viscosity in the low-temperature region, but deviations are found at higher temperatures where extrapolations are used in the case of the reference data. Our measured surface tensions are in general lower than the available sources of reference data within relative deviations below 5%. Due to a lack of experimental data for the

The authors declare no competing financial interest.

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REFERENCES

(1) de Klerk, A.; Li, Y. W.; Zennaro, R. Greener Fischer−Tropsch Processes for Fuels and Feedstocks; Wiley-VCH: Weinheim, Germany, 2013. (2) Pöhlmann, F.; Jess, A. Interplay of reaction and pore diffusion during cobalt-catalyzed Fischer−Tropsch synthesis with CO2-rich syngas. Catal. Today 2016, 275, 172−182. (3) Lemmon, E. W.; Huber, M. L.; McLinden, M. O.; REFPROP, Standard Reference Data Program; National Institute of Standards and Technology: Gaithersburg, MD, USA, 2013. (4) Martin, M. G.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 1. United-Atom Description of n-Alkanes. J. Phys. Chem. B 1998, 102, 2569−2577. (5) Yaws, C. L. Yaws’ Handbook of Thermophysical and Physical Properties of Chemical Compounds; Knovel, 2003; online version available at http://app.knovel.com/hotlink/toc/id:kpYHTPPCC4/ yaws-handbook-thermodynamic/yaws-handbook-thermodynamic. (6) Wakeham, W. A.; Nagashima, A.; Sengers, J. V. Measurement of the Transport Properties of Fluids: Experimental Thermodynamics, Vol. 3; Blackwell Scientific: Oxford, U.K., 1991. (7) Fröba, A. P.; Botero, C.; Leipertz, A. Thermal Diffusivity, Sound Speed, Viscosity, and Surface Tension of R227ea (1,1,1,2,3,3,3Heptafluoropropane). Int. J. Thermophys. 2006, 27, 1609−1625. (8) Fröba, A. P.; Kremer, H.; Leipertz, A.; Flohr, F.; Meurer, C. Thermophysical Properties of a Refrigerant Mixture of R365mfc 3331



Article

(1,1,1,3,3-Pentafluorobutane) and Galden® HT 55 (Perfluoropolyether). Int. J. Thermophys. 2007, 28, 449−480. (9) Fröba, A. P.; Leipertz, A. Thermophysical Properties of the Refrigerant Mixtures R410A and R407C from Dynamic Light Scattering (DLS). Int. J. Thermophys. 2003, 24, 1185−1206. (10) Rausch, M. H.; Kretschmer, L.; Will, S.; Leipertz, A.; Fröba, A. P. Density, Surface Tension, and Kinematic Viscosity of Hydrofluoroethers HFE-7000, HFE-7100, HFE-7200, HFE-7300, and HFE7500. J. Chem. Eng. Data 2015, 60, 3759−3765. (11) Fröba, A. P.; Leipertz, A. Accurate Determination of Liquid Viscosity and Surface Tension Using Surface Light Scattering (SLS): Toluene under Saturation Conditions between 260 and 380 K. Int. J. Thermophys. 2003, 24, 895−921. (12) Santos, F. J. V.; Nieto de Castro, C. A.; Dymond, J. H.; Dalaouti, N. K.; Assael, M. J.; Nagashima, A. Standard Reference Data for the Viscosity of Toluene. J. Phys. Chem. Ref. Data 2006, 35, 1−8. (13) Fröba, A. P.; Kremer, H.; Leipertz, A. Density, Refractive Index, Interfacial Tension, and Viscosity of Ionic Liquids [EMIM][EtSO4], [EMIM][NTf2],[EMIM][N(CN)2], and [OMA][NTf2] in Dependence on Temperature at Atmospheric Pressure. J. Phys. Chem. B 2008, 112, 12420−12430. (14) Hasse, B.; Lehmann, J.; Assenbaum, D.; Wasserscheid, P.; Leipertz, A.; Fröba, A. P. Viscosity, Interfacial Tension, Density, and Refractive Index of Ionic Liquids [EMIM][MeSO3], [EMIM][MeOHPO2], [EMIM][OcSO4], and [BBIM][NTf2] in Dependence on Temperature at Atmospheric Pressure. J. Chem. Eng. Data 2009, 54, 2576−2583. (15) Koller, T. M.; Rausch, M. H.; Ramos, J.; Schulz, P. S.; Wasserscheid, P.; Economou, I. G.; Fröba, A. P. Thermophysical Properties of the Ionic Liquids [EMIM][B(CN)4] and [HMIM][B(CN)4]. J. Phys. Chem. B 2013, 117, 8512−8523. (16) Koller, T. M.; Rausch, M. H.; Schulz, P. S.; Berger, M.; Wasserscheid, P.; Economou, I. G.; Leipertz, A.; Fröba, A. P. Viscosity, Interfacial Tension, Self-Diffusion Coefficient, Density, and Refractive Index of Ionic Liquid 1-Ethyl-3-methylimidazolium Tetracyanoborate as a Function of Temperature at Atmospheric Pressure. J. Chem. Eng. Data 2012, 57, 828−835. (17) Fröba, A. P.; Leipertz, A. Viscosity of Diisodecyl Phthalate by Surface Light Scattering (SLS). J. Chem. Eng. Data 2007, 52, 1803− 1810. (18) Fröba, A. P. Simultane Bestimmung von Viskosität und Oberflächenspannung transparenter Fluide mittels Oberflächenlichtstreuung, Dr.-Ing. Thesis, Friedrich-Alexander-University ErlangenNuremberg, 2002. (19) Fröba, A. P.; Will, S. Light Scattering by Surface Waves − Surface Light Scattering. In Experimental Thermodynamics, Vol. IX: Advances in Transport Properties of Fluids; Assael, M. J., Goodwin, A. R. H., Vesovic, V., Wakeham, W. A., Eds.; Royal Society of Chemistry: Cambridge, U.K., 2014; pp 22−35. (20) Brouwer, W.; Pathria, R. K. On the Surface Tension of Liquid Helium II. Phys. Rev. 1967, 163, 200−205. (21) Sakai, K.; Choi, P. K.; Tanaka, H.; Takagi, K. A new light scattering technique for a wide-band ripplon spectroscopy at the MHz region. Rev. Sci. Instrum. 1991, 62, 1192−1195. (22) Langewin, D. Light Scattering by Liquid Surfaces and Complementary Techniques; Marcel Dekker: New York, 1992. (23) Nishimura, Y.; Hasegawa, A.; Nagasaka, Y. High-precision instrument for measuring the surface tension, viscosity and surface viscoelasticity of liquids using ripplon surface laser-light scattering with tunable wavelength selection. Rev. Sci. Instrum. 2014, 85, 044904. (24) Nishio, T.; Nagasaka, Y. Simultaneous Measurement of Surface Tension and Kinematic Viscosity Using Thermal Fluctuations. Int. J. Thermophys. 1995, 16, 1087−1097. (25) Tin, P.; Adin Mann, J.; Meyer, W. V.; Taylor, T. W. Fiber-optics surface-light-scattering spectrometer. Appl. Opt. 1997, 36, 7601−7604. (26) Sternberg, J. C.; Gallaway, W. S.; Jones, D. T. L. The mechanism of response of flame ionization detectors. In Gas Chromatography, Third International Symposium; Brenner, N., Callen, J. E., Weiss, M. D., Eds.; Academic Press: New York, 1962; pp 231−267.

(27) Heller, A.; Fleys, M. S. H.; Chen, J.; van der Laan, G. P.; Rausch, M. H.; Fröba, A. P. Thermal and Mutual Diffusivity of Binary Mixtures of n-Dodecane and n-Tetracontane with Carbon Monoxide, Hydrogen, and Water from Dynamic Light Scattering (DLS). J. Chem. Eng. Data 2016, 61, 1333−1340. (28) Heller, A.; Koller, T. M.; Rausch, M. H.; Fleys, M. S. H.; Bos, A. N. R.; van der Laan, G. P.; Makrodimitri, Z. A.; Economou, I. G.; Fröba, A. P. Simultaneous Determination of Thermal and Mutual Diffusivity of Binary Mixtures of n-Octacosane with Carbon Monoxide, Hydrogen, and Water by Dynamic Light Scattering. J. Phys. Chem. B 2014, 118, 3981−3990. (29) Koller, T. M.; Heller, A.; Rausch, M. H.; Wasserscheid, P.; Economou, I. G.; Froba, A. P. Mutual and Self-Diffusivities in Binary Mixtures of [EMIM][B(CN)4] with Dissolved Gases by Using Dynamic Light Scattering and Molecular Dynamics Simulations. J. Phys. Chem. B 2015, 119, 8583−8592. (30) Rausch, M. H.; Heller, A.; Herbst, J.; Koller, T. M.; Bahlmann, M.; Schulz, P. S.; Wasserscheid, P.; Fröba, A. P. Mutual and Thermal Diffusivity of Binary Mixtures of the Ionic Liquids [BMIM][C(CN)3] and [BMIM][B(CN)4] with Dissolved CO2 by Dynamic Light Scattering. J. Phys. Chem. B 2014, 118, 4636−4646. (31) Lemmon, E. W.; Huber, M. L. Thermodynamic Properties of nDodecane. Energy Fuels 2004, 18, 960−967. (32) Huber, M. L.; Laesecke, A.; Perkins, R. Transport Properties of n-Dodecane. Energy Fuels 2004, 18, 968−975. (33) Dutour, S.; Lagourette, B.; Daridon, J. L. High-pressure speed of sound, density and compressibility of heavy normal paraffins: C28H58 and C36H74. J. Chem. Thermodyn. 2002, 34, 475−484. (34) Riesco, R.; Vesovic, V. Extended hard-sphere model for predicting the viscosity of long-chain n-alkanes. Fluid Phase Equilib. 2016, 425, 385−392. (35) Ortiz-Vega, D. O. A New Wide Range Equation of State for Helium-4. Ph.D. Thesis, Texas A&M University, College Station, TX, USA, 2013. (36) Arp, V. D.; McCarty, R. D.; Friend, D. G. Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa, Technical Note 1334 (revised); National Institute of Standards and Technology: Boulder, CO, USA, 1998. (37) Mizerovskii, L. N.; Smirnova, K. P. Solubility of noble gases and nitrogen in n-alkanes at 298.15 K and atmospheric pressure. Correlation analysis. Russ. Chem. Bull. 2009, 58, 1547−1561. (38) Clever, H. L.; Battino, R.; Saylor, J. H.; Gross, P. M. The solubility of Helium, Neon, Argon, and Krypton in Some Hydrocarbon Solvents. J. Phys. Chem. 1957, 61, 1078−1082. (39) Assael, M. J.; Dymond, J. H.; Exadaktilou, D. An Improved Representation for n-Alkane Liquid Densities. Int. J. Thermophys. 1994, 15, 155−164. (40) Lucas, K.; Luckas, M. Berechnungsmethoden für Stoffeigenschaften. VDI-Wärmeatlas, Abschnitt DA; Verein Deutscher Ingenieure: Düsseldorf, Germany, 1984. (41) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001. (42) Kraft, K.; Matos Lopes, M.; Leipertz, A. Thermal Diffusivity and Thermal Conductivity of Toluene by Photon Correlation Spectroscopy: A Test of the Accuracy of the Method. Int. J. Thermophys. 1995, 16, 423−432. (43) Grunberg, L.; Nissan, A. H. Mixture Law for Viscosity. Nature 1949, 164, 799−800. (44) Miqueu, C.; Broseta, D.; Satherley, J.; Mendiboure, B.; Lachaise, J.; Graciaa, A. An extended scaled equation for the temperature dependence of the surface tension of pure compounds inferred from an analysis of experimental data. Fluid Phase Equilib. 2000, 172, 169− 182. (45) Bychinsky, V. A.; Tupitsyn, A. A.; Chudnenko, K. V.; Mukhetdinova, A. V. Methods for Calculating the Critical Constants of Hydrocarbons (Using the n-Alkane Series as an Example). J. Chem. Eng. Data 2013, 58, 3102−3109. 3332



Article

(46) Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States. AIChE J. 1975, 21, 510−527. (47) Dymond, J. H.; Young, K. J. Transport Properties of Nonelectrolyte Liquid Mixtures-I. Viscosity Coefficients for n-Alkane Mixtures at Saturation Pressure from 283 to 378 K. Int. J. Thermophys. 1980, 1, 331−343. (48) Knapstad, B.; SkjØlsvik, P. A.; Øye, H. A. Viscosity of Pure Hydrocarbons. J. Chem. Eng. Data 1989, 34, 37−43. (49) Knapstad, B.; SkjØlsvik, P. A.; Øye, H. A. Viscosity of Three Binary Hydrocarbon Mixtures. J. Chem. Eng. Data 1991, 36, 84−88. (50) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. The Viscosity and Density of n-Dodecane and n-Octadecane at Pressures up to 200 MPa and Temperatures up to 473 K. Int. J. Thermophys. 2004, 25, 1339−1352. (51) Lyusternik, V. E.; Zhdanov, A. G. Teplofiz. Svoistva Veshchestv Mater.. 1973; Vol. 7. (52) Giller, E. B.; Drickamer, H. G. Viscosity of Normal Paraffins near the Freezing Point. Ind. Eng. Chem. 1949, 41, 2067−2069. (53) Zhang, L.; Guo, Y.; Xiao, J.; Gong, X.; Fang, W. Density, Refractive Index, Viscosity, and Surface Tension of Binary Mixtures of exo-Tetrahydrodicyclopentadiene with Some n-Alkanes from (293.15 to 313.15) K. J. Chem. Eng. Data 2011, 56, 4268−4273. (54) Mahajan, A. R.; Mirgane, S. R. Thermodynamic Properties of Binary Liquid Mixtures of n-Dodecane with an Alkan-1-ol or an Alkan2-ol at 298.15 K: A Comparative Study. J. Solution Chem. 2013, 42, 1146−1168. (55) Luning Prak, D. J.; Alexandre, S. M.; Cowart, J. S.; Trulove, P. C. Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of n-Dodecane with 2,2,4,6,6Pentamethylheptane or 2,2,4,4,6,8,8-Heptamethylnonane. J. Chem. Eng. Data 2014, 59, 1334−1346. (56) Yang, Z.; Bi, Q.; Feng, S. Viscosity Measurement of Endothermic Fuels at Temperatures from 303 to 673 K and Pressures up to 5.00 MPa. J. Chem. Eng. Data 2016, 61, 3472−3480. (57) Doolittle, A. K.; Peterson, R. H. Preparation and Physical Properties of a Series of n-Alkanes. J. Am. Chem. Soc. 1951, 73, 2145− 2151. (58) Mazee, W. M. Some properties of hydrocarbons having more than twenty carbon atoms. Recl. Trav. Chim. Pays-Bas 1948, 67, 197− 213. (59) Mulero, A.; Cachadiñ a, I.; Parra, M. I. Recommended Correlations for the Surface Tension of Common Fluids. J. Phys. Chem. Ref. Data 2012, 41, 043105. (60) Mejía, A.; Cartes, M.; Segura, H. Interfacial tensions of binary mixtures of ethanol with octane, decane, dodecane, and tetradecane. J. Chem. Thermodyn. 2011, 43, 1395−1400. (61) Jasper, J. J. The Surface Tension of Pure Liquid Compounds. J. Phys. Chem. Ref. Data 1972, 1, 841−1010. (62) Körösi, G.; Kováts, E. s. Density and Surface Tension of 83 Organic Liquids. J. Chem. Eng. Data 1981, 26, 323−332. (63) Cumicheo, C.; Cartes, M.; Segura, H.; Müller, E. A.; Mejía, A. High-pressure densities and interfacial tensions of binary systems containing carbon dioxide + n-alkanes: (n-Dodecane, n-tridecane, ntetradecane). Fluid Phase Equilib. 2014, 380, 82−92.

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