Mixtures of 2-ethylhexanoic acid (EHA) and ethanol are common solvents for pre- cursor solutions in spray flame synthesis for the production of nanoparticles, however, no thermophysical data are available in the literature for these mixtures. Therefore, in this work, the density, viscosity, thermal conductivity, isobaric heat capacity, and self-diffusion coefficients of mixtures of EHA and ethanol were measured at atmospheric pressure and temperatures between 293.15 and 333.15 K. Additionally, isobaric vapor- liquid equilibria of the system were measured at pressures between 20 and 80 kPa. Empirical models were parametrized and are provided for all measured properties for convenient use in spray flame synthesis process simulations and related applications. 1 Introduction Sprayflamesynthesisisaversatileaerosolprocessfortheproductionoffunctionalnanomate- rials1,2for applications in several fields, including gas sensors,3–5energy,6–8biomedicine,9,10 and catalysis.11–13In spray flame synthesis, a mixture of a combustible solvent and a metal- containing precursor – the so-called precursor solution – is sprayed into a flame. Mixtures of 2-ethylhexanoic acid (EHA) and ethanol are common solvents, especially in combination with metal nitrates as low-cost metal-containing precursors.10,14–19 The quality of the obtained nanomaterials depends strongly on the properties of the pre- cursor solution. Thus, the thermophysical properties are necessary for gaining an improved process understanding and for the investigation by numerical techniques.20–22Property data are widely available for pure ethanol. For pure EHA, only some measurements of the vapor pressure,23–31enthalpy of vaporization,29,32,33and density at atmospheric pressure32as well as along the saturation line29have been reported. The viscosity was measured at 298.15, 313.15 and 373.15 K.34Furthermore, data on critical properties29,35,36as well as on the en- thalpy of formation32and two-phase heat capacities29of EHA are available. For mixtures of EHA and ethanol, to the best of our knowledge, there are no data. Therefore, in this work, the density, viscosity, thermal conductivity, and isobaric heat capacity of pure EHA and ethanol and of mixtures of EHA and ethanol were measured at atmospheric pressure and temperatures between 293.15 and 333.15 K. Additionally, self-diffusion coefficient mea- surements at atmospheric pressure and temperatures between 298.15 and 333.15 K were performed. Isobaric vapor-liquid equilibria (VLE) were measured at pressures between 20 and 80 kPa. Empirical models were established and fit to the experimental data of all properties. 2 Experimental Section Chemicals and Sample Preparation The CAS registry numbers, suppliers, and purities of the chemicals used for sample prepa- ration are given in Table 1. 1,4-Dioxane was used as an internal standard for gas chro- matography (GC). Certified viscosity and density standards S6 and N.8 were purchased from Sigma-Aldrich. All chemicals were used without further purification. The samples were prepared gravimetrically using a Mettler-Toledo AG204 laboratory balance (specified standard uncertainty u(m) = 0 .0001g of the mass m) for sample masses smaller than 50 g and a Mettler-Toledo PR2003 Comparator laboratory balance (specified standard uncer- tainty u(m) = 0 .001g) for larger samples. A sample amount of approximately 10 ml is needed for the density and viscosity measurements at each temperature. Comparatively large samples are also necessary for the thermal conductivity and isobaric heat capacity measurements because the measurement cell has a volume of approximately 40 ml. The combined expanded uncertainty of the mole fraction of gravimetrically prepared samples is U(xEtOH) = 0 .001 mol mol−1(k= 2). [Table 1 about here.] Measurements All measurement methods are as in our previous work.37–40Only the sample composition analysis for the VLE measurements was methodically different as explained below. In the supporting information, a comparison of the experimental results for the density and the viscosity of pure EHA from this work and the literature is presented in Figures S1 and S2. Figures S3 – S11 show a comparison of the experimental results for the pure component properties of ethanol from this work and the literature. As in our previous work,39good agreement is obtained in all cases. Furthermore, Figure S12 shows additional data for the self-diffusion coefficient of pure EHA as a function of temperature at temperatures between 3 298.15 and 353.15 K, for which no data for comparison are available in the literature. All measurements except for the VLE measurements were conducted at an atmospheric pressure ofp= 101 .3kPa. The standard uncertainty of the pressure is u(p) = 3 kPa . Density and Viscosity A combined densimeter and viscosimeter from Anton Paar (SVM 3000) was used for density andviscositymeasurements. Theaccuracyofitsmeasurementresultsintheexpecteddensity and viscosity range was checked using density and viscosity standards S6 and N.8. The combined expanded uncertainty of the density measurements is U(ρ) = 1 kg m−3(k= 2). The combined expanded uncertainty of the viscosity measurements is between U(η) = 0.009 mPa s ( k= 2)andU(η) = 0 .146 mPa s ( k= 2)in the investigated viscosity range and is reported for each measurement result. The standard uncertainty of the temperature measurement specified by the manufacturer is u(T) = 0 .05K. Before the samples were introduced to the instrument, they were degassed in an ultrasonic bath for at least ten minutes. Thermal Conductivity and Isobaric Heat Capacity Thermal conductivity and isobaric heat capacity were measured with the hot-wire method. Theinstrument(LAMBDA,fluconfluidcontrolGmbH)providesmeasurementresultsforthe thermal conductivity λand the thermal diffusivity a. From this, the isobaric heat capacity cpcan be calculated from eq. (1) if the sample density ρis known: cp=λ a ρ(1) The samples were thermostatted in a double-walled vessel. The instrument’s temperature sensor was calibrated with a certified reference thermometer. The standard uncertainty of the temperature measurement in the measurement cell is estimated to be u(T) = 0 .1K. 4 The combined expanded relative uncertainties of the thermal conductivity and isobaric heat capacity measurements are Urel(λ) = 0 .04 (k= 2)andUrel(cp) = 0 .06 (k= 2)respectively. Self-Diffusion Coefficients The self-diffusion coefficients of EHA and ethanol were determined by1H-NMR spectroscopy with pulsed field gradients following the procedures described in more detail by Bellaire et al..41,42The NMR spectrometer was equipped with an Ascend 400 magnet and an Avance III HD 400 console (both by Bruker) and provided a magnetic field strength of 9.4 T. The spectrometer’stemperaturesensorwascalibratedusingaPt100resistancethermometer. The standard uncertainty of the temperature measurement is estimated to be u(T) = 0 .1K. The self-diffusion coefficients were measured by a stimulated spin-echo technique with bipolar pulsed gradients using the pulse sequence stebpgp1s . The self-diffusion coefficients were calculated from the Stejskal-Tanner43equation: lnI I0 =−Diϱ2δ2g2 ∆−1 3δ−1 2τ (2) Here, Iis the signal intensity, I0is the signal intensity without a gradient, Diis the self- diffusion coefficient of component i,ϱis the gyromagnetic ratio, δis the duration of the application of the field gradient, gis the field gradient strength, ∆is the so-called diffusion time, and τis a correction constant due to the use of bipolar gradients. The value of Di was obtained from a fit of the natural logarithm of the relative intensityI I0as a function of the squared field gradient g2. For details see Refs. 41 and 42. The combined expanded uncertainty of the self-diffusion coefficient U(Di)from the fit to the experimental NMR data using eq. (2) depends strongly on the sample composition and the temperature and is specified here together with the measurement results. 5 Vapor-Liquid Equilibrium Isobaric VLE of binary mixtures of ethanol and EHA were measured in a recirculating still glass apparatus, which is described in more detail in Ref. 44. The apparatus is an improved version of that designed by Rafflenbeul and Hartmann.45Measurements were performed at 20, 40, 60, and 80 kPa and temperatures up to 400 K. It is not possible to measure VLE at temperatures above 400 K with that setup. The pressure in the measurement cell was mea- suredwithaWIKAP-30pressuresensorwithastandarduncertaintyof u(p) = 0 .05 kPa. The equilibrium temperature was measured with a Pt100 resistance thermometer that was cali- brated against a certified reference thermometer. While the calibrated thermometer provides a standard uncertainty better than 0.1 K, the uncertainty of the equilibrium temperature u(T)is higher due to fluctuations during the measurement and is specified here together with the measurement results. The compositions of the liquid phase and the condensed gas phase were determined from an analysis of corresponding samples by gas chromatography (GC) using an Agilent 7890A GC system equipped with a flame ionization detector (FID) and a Zebron Phenomenex ZB-FFAP (30 m ×0.32 mm ×0.5µm) column. In the GC measurements, 1,4-dioxane was used as an internal standard. The standard uncertainty of the ethanol mole fraction determined by GC is u(x) = 0 .01 mol mol−1. 6 Modeling Density, Viscosity, Thermal Conductivity, and Isobaric Heat Capac- ity Instead of modeling the results for the density ρdirectly, a correlation for the molar volume vis presented, where v=¯M ρ. (3) ¯Mis the average molar mass ¯M=xEtOHMEtOH+xEHAMEHA, (4) where xEtOHandxEHAare the mole fractions of ethanol and EHA and MEtOHandMEHA are the molar masses of ethanol and EHA, respectively. The same modeling approach was used for the molar volume v, the viscosity η, the thermal conductivity λ, as well as for the molar isobaric heat capacity cp. It is hence illustrated here using the symbol zfor the studied property and [z]for its unit, where [v] = m3mol−1,[η] = mPa s ,[λ] = W m−1K−1, [cp] = J mol−1K−1. The property zis described by the sum of an ideal mixture term and an excess term zE(eq. (5)). z/[z] =xEtOHzpure EtOH+xEHAzpure EHA+zE(5) Therein, the pure component properties zpure iandzEare functions of the temperature T, since we only study properties at ambient pressure. The temperature dependence of the pure component properties zpure iis described by a polynomial (eq. (6)). zpure i/[z] =ai+biT/K +ci(T/K)2(6) 7 Asanexception, anexponentialtemperaturedependence(seeeq. (7))ofthepurecomponent viscosities ηpure iis used: ηpure i/mPa s = aiexpbi T/K +ci (7) In both cases, ai,bi, and ciare adjustable parameters. The excess term is modeled by a Redlich-Kister-type correlation (see eq. (8)) with the adjustable parameters E,F, and G. zE/[z] = (E+F T/ K +G x EtOHxEHA)xEtOHxEHA (8) Self-Diffusion Coefficients The self-diffusion coefficients were modeled using an empirical polynomial equation (eq. (9)) based on the approach of our previous work.37However, for describing the experimental data of the present work, a cubic term with respect to the mole fraction of ethanol xEtOHwas found to give better results than the quadratic term used in Ref. 37. Furthermore, a better description of the data is obtained if the mole fraction of ethanol xEtOHis used instead of the mole fraction of the diffusing component xi. Di/(10−9m2s−1) =ai+biT/K + ( ci+diT/K)xEtOH+ (ei+fiT/K)x3 EtOH (9) Vapor-Liquid Equilibrium The VLE of binary mixtures of ethanol and EHA were modeled based on the extended Raoult’s law ps ixiγi=p yi, (10) where ps iis the vapor pressure of component i,xiis the liquid phase mole fraction of com- ponent i,γiis the activity coefficient of component i,pis the total pressure, and yiis the gas phase mole fraction of component i. The vapor pressures ps iwere calculated from an Antoine-type equation with the empirical parameters A,B, and Cwhich were obtained 8 from a fit to literature data. ln(ps i/kPa) = Ai+Bi T/K +Ci(11) The NRTL model (eq. (12)) was used for modeling the activity coefficients, which were assumed to be temperature-independent. lnγi=x2 j" τjiGji xi+xjGji2 +τijGij (xj+xiGij)2# (12) Therein, Gijis defined as Gij= exp ( −ατij). (13) The adjustable parameters of the model are the two dimensionless interaction parameters τij. The non-randomness parameter αwas set to 0.3. Fitting Procedure Twodifferent pythonsolverswereemployedinthiswork. numpy.polyfit wasusedtofitparam- etersofpolynomials. Parametersforotherequationtypeswereobtainedwith scipy.optimize.curve_fit . For each property z, allNcorresponding measured data points were considered simultane- ously in the fit. The objective function was the sum of squared deviations between the measured and the calculated values for this property, as shown in eq. (14). OFz=NX j=1 zexp j−zcal j2(14) The objective function for the fit of the NRTL parameters was the sum of the squared deviations between measured and calculated pressures pj. The results for the composition of the gas phase were not used as it contains predominantly the low-boiling component ethanol in the pressure range where experiments were possible. 9 Results and Discussion The parameters ai,bi, and cifor the correlations for the pure component properties (eqs. (6) and (7)) are given in Table 2. Table 3 lists the values of the parameters E,F, and Gof the excess property correlations (eq. (8)). Table 4 lists the parameters for the empirical cor- relation (eq. (9)) for the self-diffusion coefficients. The parameters of the Antoine equation (11) for the pure component vapor pressures as obtained from a fit to literature data are given in Table 5. The NRTL parameters, which were determined from a fit of the present experimental data to the VLE model (eqs. (10), (12), and (13)), are given in Table 6. [Table 2 about here.] [Table 3 about here.] [Table 4 about here.] [Table 5 about here.] [Table 6 about here.] Density The experimental results for the density of mixtures of EHA and ethanol are shown in Table 7 and are depicted in Figure 1 together with the model results. Pure EHA has a higher density than pure ethanol and thus, the mixture density decreases with increasing ethanolmolefraction xEtOH. Asexpected, thedensitydecreaseswithincreasingtemperature. The molar volume decreases almost linearly with increasing ethanol mole fraction and the molar excess volume is small compared to the overall molar volume. Thus, binary mixtures of ethanol and EHA behave approximately ideally with respect to the molar volume. [Table 7 about here.] [Figure 1 about here.] 10 Viscosity Table 8 contains the experimental results for the mixture viscosities at different tempera- tures. Figure 2 depicts the measured and modeled viscosities as a function of the mixture composition at different temperatures. As expected, the viscosity decreases with increasing temperature. PureEHAhasasignificantlyhigherviscositythanpureethanol. Consequently, the viscosity of the mixtures of EHA and ethanol decreases with increasing ethanol content. The roughly linear relationship between viscosities at different compositions is rather un- usual. The systems studied in our previous work37–40show a strong non-ideality of the mixture viscosity and a more complex model was necessary to describe the data. [Table 8 about here.] [Figure 2 about here.] Thermal Conductivity The results of the thermal conductivity measurements are given in Table 9 and are depicted in Figure 3 together with the model results. The thermal conductivities of both pure com- ponents and of all mixtures decrease with increasing temperature. Pure EHA has a lower thermal conductivity than pure ethanol. Thus, the mixture thermal conductivity increases with increasing ethanol mole fraction. A similar behavior is found, for example, for mixtures of ethanol with ethyl acetate46and with cyclohexane.47 [Table 9 about here.] [Figure 3 about here.] Isobaric Heat Capacity The results of the isobaric heat capacity measurements are given in Table 10 and are depicted in Figure 4 together with the model results. Pure EHA has a significantly higher isobaric 11 heat capacity than pure ethanol. The isobaric heat capacity of mixtures of EHA and ethanol decreasesalmostlinearlywiththeethanolcontentandincreaseswithincreasingtemperature. Hence, as for many mixtures investigated in our previous work,37–40the excess heat capacity is small. [Table 10 about here.] [Figure 4 about here.] Self-Diffusion Coefficients The results for the self-diffusion coefficients of pure ethanol and pure EHA as well as of ethanol and EHA in mixtures of ethanol and EHA are given in Tables 11 and 12, respectively. The experimental results together with those of the empirical correlation are depicted in Figure 5. As expected, since EHA is a larger molecule and has a higher viscosity than ethanol, its self-diffusion coefficient is generally lower than that of ethanol. Consequently, the self-diffusion coefficients of EHA and ethanol increase with increasing temperature and increasing ethanol content in the mixture. The strongly non-linear behavior with respect to the composition is in agreement with experimental and simulation results for other binary systems.41,48 [Table 11 about here.] [Table 12 about here.] [Figure 5 about here.] Vapor-Liquid Equilibrium The results of the VLE measurements are given in Table 13. Figure 6 depicts the experi- mental as well as the model results for the vapor-liquid equilibria of mixtures of ethanol and 12 EHA at the four different pressures considered in the present work. Due to the temperature limitation of 400 K of the experimental setup, it was not possible to obtain VLE data over the entire liquid phase composition range for p >40 kPa. The system (EHA + ethanol) shows a zeotropic behavior with ethanol as the low-boiling and EHA as the high-boiling component. Due to the large difference in pure component boiling temperatures at all pres- sures, ethanol is the main component in the vapor phase over a wide concentration range. Thus, during the evaporation of an (EHA + ethanol) droplet in a hot atmosphere, as found in processes such as spray flame synthesis, ethanol will evaporate from the droplet surface preferentially. Significant amounts of EHA will only be found in the gas phase around an evaporating droplet once the ethanol mole fraction xEtOHat the droplet surface is less than approximately 0.25 mol mol−1, where the mixture boiling temperature increases steeply with decreasing ethanol content. Consequently, further evaporation of ethanol leads to a strong increase of the droplet temperature. If the liquid phase mass transfer is slow compared to the heat transfer, superheating in some parts of the droplet could occur and cause droplet micro-explosions. [Table 13 about here.] [Figure 6 about here.] 13 Conclusions In the present work, thermophyiscal properties of mixtures of ethanol and EHA were mea- sured: density, viscosity, thermal conductivity, isobaric heat capacity, self-diffusion coeffi- cients of ethanol and EHA, and vapor-liquid equilibria. While the mixtures of EHA and ethanol behave almost ideally in terms of the molar volume and the isobaric heat capacity, for the viscosity, thermal conductivity, and self-diffusion coefficients important excess con- tributions were found. The VLE was found to be zeotropic with a wide-boiling behavior. Parameters for empirical correlations for all data were determined and are provided in this work. With the results of the present work, the integration of reliable property models for mixtures of EHA and ethanol in simulations of the spray flame synthesis process is made possible, which in turn enables detailed investigations to deepen process understanding and improve process designs. 14 Acknowledgement This work was supported by the German Research Foundation (DFG) within the priority program SPP 1980 SPRAYSYN under the grants HA 1993/18-2 and KO 5844/2-2. Supporting Information Available The following files are available free of charge. •SI_Thermophysical_Properties_EHA_Ethanol.pdf: Comparison of this work’s re- sults to literature data, additional self-diffusion coefficient data.