The quality of nanoparticles that are obtained by spray flame synthesis depends strongly on the thermophysical properties of the precursor solutions. Solutions of iron(III)nitrate -nonahydrate (INN) in ethanol are interesting precursor solution s for the production of iron oxide nanoparticles in these processes . However, no data on thermophysical properties of solutions of INN in ethanol are available in the literature . Therefore, in the present work, the specific density, viscosity , therma l conductivity and molar isobaric heat capacity of solutions of INN in solvent mixtures of ethanol and water were measured at 101.3 kPa between 288.15 and 333.15 K , solvent compositions ranging from pure ethanol to pure water , and INN molalities up to 1.3 mol kg-1. Empirical correlations of the experimental data are provided. 1. Introduction Spray flame synthesis is an interesting process for the production of nanoparticles. In that process , the pyrolysis of aerosol droplets of a combustible precursor solution leads to the formation of nanoparticles. Different combinations of metal -containing substances and combustible solvents have been used to obtain various forms of nanoparticles1–4. For gaining insight in to the phenomena in the spray flame and for the design and optimization of the process, simulations are performed, for which information on the thermophysical properties of the precursor solutions5–7 is needed, namely the density, viscosity, thermal conductivity and isobaric heat capacity . In a recent work of our group, t hese properties were investigated for precursor solutions for the production of titanium oxide nanoparticles8. A further motivation to investigate thermophysical properties of precursor solutions is the recent suggestion of a standardized syn thesis setup by the SpraySyn initiative9, in which also benchmark precursor systems were defined. Iron(III)nitrate -nonahydrate (Fe(NO 3)3·9 H 2O, INN) is a common precursor used in spray flame synthesis processes for the production of iron oxide nanoparticles 1–3,9– 14. A popular solvent for INN is ethanol2,9,12 –15. As INN releases its nine crystal water molecule s upon dissolution in ethanol, precursor solutions of INN in ethanol always contain large am ounts of water. Recently, Stodt et al.15 investigated the chemistry of INN-based precursor -solutions for the spray flame synthesis process , such as INN + ethanol, with Fourier -transform infrared spectroscopy . As ethanol has a higher vapor pressure than water , and water has a strong affinity to the ions, ethanol will evaporate from the precursor solution droplet preferentially, leading to an increase of the water concentration in the droplet . Hence, for the simulation of the evaporation process, not only the thermophysical properties of solutions of INN in pure ethanol are required but also those of INN in ethanol with additional water . Moreover, water produced by combustion in the flame may enter the droplet by mass transfer from the gas phase13. Despite the high interest in the spray flame synthesis of nanoparticles from INN solutions, thermophysical data are only available for the pure solvents and the salt- free solvent mixture of ethanol and water , but are scarce for solutions of INN. There are only two papers in the literature that report the density of aqueous solutions of INN16,17. To the best of our knowledge, no information is available on ethanolic INN solutions. In contrast, abundant data are available in the literature for mixtures of e thanol and water (without INN) . Many authors have measured their density18–30. The molar excess volume of these mixtures is negative, which is attributed to H-bonding and the resulting structuring of the eth anol + water solutions . Also the m ixture v iscosity has been reported by several authors18–21,31 –33. The viscosity of mixture s of ethanol and water is higher than that of the pure components , which is again attributed to the H - bonding between the molecules. Several authors34–38 measured the thermal conductivity of mixtures of ethanol and water . For p ure ethanol , the thermal conductivity decreases with increasing temperature. For pure water , the trend is opposite . As a result , mixture compositions can be found for which the temperature dependence of the thermal conductivity changes its sign37. The isobaric heat capacity of mixtures of ethanol and water was measured by two groups39,40 and a positive excess was found . To summarize: the properties of mixtures of ethanol and water are well -known. In contrast, not much is known about the properties of solutions of INN in these solvents, only the specific density of aqueous INN solutions has been reported in the literature. Thus, the specific density, viscosity, thermal conductivity and molar isobaric heat capacity in solutions of INN in mixtures of ethanol and water were measured in the present work at the temperature range from 288.15 to 333.15 K and ambient pressure , with solvent compositions ranging from pure ethanol to pure water and overa ll INN molalities up to 1. 3 mol kg-1. Empirical correlations of the data were established, which facilitate the application of the new information on the thermophysical properties in numerical simulations. For the sake of brevity, we write “density” for “specific density” and “isobaric heat capacity” fo r “molar isobaric heat capacity”. The specified standard uncertainties for all measurements include statis tical and method uncertainties. 2. Experimental 2.1 Chemicals and sample prep aration INN and ethanol were purchased from Sigma- Aldrich and used without furt her purification. Information on the CAS registry number and purity are listed in Table 1 . [Table 1 about here.] Water from a Milli- Q System (Millipore) with a specific electrical resistance greater than 18.2 MΩcm was used for preparing the aqueous solutions . INN was handled in a nitrogen atmosphere in an inert gas glove box (GS Glovebox Technik), with a water content below 2∙10-6 g g-1 and an oxygen content below 1.2∙10-6 g g-1. Samples were prepared using a laboratory bal ance (Mettler -Toledo AG204 ) with a standard uncertainty of u(m) = 0.0001 g . 2.2 Measurements All measurements of solutions of INN in ethanol , INN in water , or INN in mixtures of ethanol and water were performed at p = 101.3 kPa , with a standard uncertainty of u(p) = 3 kPa. Throughout this article, the mixtures are considered as ternary system s comprising the components INN (Fe(NO 3)3·9 H 2O), ethanol and water , i.e. the overall composition of the solution is reported. Salt-free properties are denoted by a circumflex (^). The composition of the ternary mixtures is specified by the overall molality of INN b INN and the mole fraction of ethanol (E) in the salt -free solvent mixture x ̂E, which are defined as follows. T he overall molality b INN is INN INN Solvˆnb m= . (1) Here, nINN is the number of moles of INN and m̂Solv is the mass of the INN-free solvent mixture Solv E E W Wˆm nM n M=⋅+⋅ , (2) where nE and nW denote the mole numbers of the solvent s ethanol and water (W), respectively . The mole fraction of ethanol in the salt-free solvent mixture x ̂E is given by E E EWˆnxnn=+ . (3) In the experiments carried out in the present work, the overall INN molality varied between 0 ≤ bINN ≤ 1.3 mol kg-1, and the solvent composition varied between 0 ≤ x̂E ≤ 1 mol mol-1. From an error propagation of the steps in the gravimetrical sample preparation , the standard uncertainty of b INN is estimated to be u(bINN) = 0.005 mol kg-1 and the standard uncertainty of x̂E is estimated to be u(x̂E) = 0.0005 mol mol-1 . All samples were hermetically sealed in 40 mL glass vials and measurements were performed within 1 h after sample preparation. 2.2.1 Density and shear viscosity The measurements of the liquid density and viscosity were carried out using an instrument of Anton Paar (SVM 3000) at 293.15 to 333.15 K. The density measurements were conducted with the vibrating tube technique according to the ASTM method D4052, with a relative standard uncertainty ur(ρ) = 0.002, and the viscosity measurements were conducted with a Stabinger viscosimeter according to the ASTM method D7042 with a relative standard uncertainty ranging from ur(η) = 0.02 (for pure ethanol as the solvent) to ur(η) = 0.07 (for pure water as the solvent). The increase of the relative standard uncertainty in the viscosity for mixtures with high water content s results from an incomplete wetting of the Stabinger viscosimeter by the samples . After each set of measurements , the apparatus was cleaned twice with water and ethanol and flushed with dry air. The temperature was measured with a built -in thermometer, for which the manufacturer claims a standard uncertainty of u( T) = 0.05 K. The apparatus was calibrated with calibration standard s provide d by the manufacturer. For validation, the density and viscosity of ethanol + water were measured and compared to literature values of several authors. Additionally , the density data of solutions of INN in water at 298.15 K of Arrad et al.16 were compared to the data of this work. The results of these comparisons are presented in the Supporting Information. Heydweiller17 also reports data for the density of such solutions, however, the employed measure of concentration is not defined clearly in his work, so that a comparis on with the present data is not possible. The relative deviations dr between the reported density data and the own measurements are dr(ρ) ≤ 0.0016. Relative deviations between the reported viscosity data are dr(η) ≤ 0.02 for pure ethanol and dr(η) ≤ 0.05 for mixtures of ethanol and water . 2.2.2 Thermal conductivity and isobaric heat capacity The measurements of the thermal conductivity and the isobaric heat capacity were carried out with an instrument of flucon fluid control GmbH (LAMBDA) at 288.15, 298.15 and 308.15 K. In the instrument, the transient hot wire method according to the ASTM method D7896 was applied to determine the thermal conductivity λ and the thermal diffusivity a. The molar isobaric heat capacity cp was then calculated by the relationship pλMcaρ⋅=⋅ , (4) where the specific density ρ of the liquid was determined as explained in the previous section. T he reported values of λ and cp are the average over 10 measurements . The relative standard uncertainty of the thermal conductivity measurement is estimated to be ur(λ) = 0.03, and the relative standard uncertainty of the isobaric heat capacity measurement is estimated to be u r(cp) = 0.05 for INN in the pure solvents and ur(cp) = 0.1 for INN in mixtures of ethanol and water . After each set of measurements, the apparatus was cleaned with water and ethanol and flushed with dry air. T he sensor and sample are thermostatted by a double jacket vessel , in which preheated water is circulating . The temperature wa s measured with a built -in Pt100 resistance thermometer. The standard uncertainty of the temperature measurement is u( T) = 0.2 K. For the measurement of the thermal conductivity, the appa ratus was calibrated to the thermal conductivit ies of pure ethanol and pure water at 293.15 K . For the measurement of the isobaric heat capacity, the apparatus was calibrated to the isobaric heat cap acities of pure ethanol and pure water at 293.15 K . For validation, the thermal conductivity and isobaric heat capacity of mixtures of ethanol and water were measured and compared to literature values of several authors. The results are presented in the Su pporting Information. The r elative deviations between the reported thermal conductivity data and our own measurements are dr(λ) ≤ 0.025 for pure ethanol , dr(λ) ≤ 0.02 for pure water , and d r(λ) ≤ 0.03 for mixtures of ethanol and water . The r elative d eviations between the reported isobaric heat capacity data are d r(cp) ≤ 0.03 for pure ethanol and dr(cp) ≤ 0.005 for pure water . 3. Modeling For correlating the specific density ρ, the values are converted to molar volumes v , Mvρ= . (5) where M̅ is the mean molar mass of the mixture consisting of solvent ethanol, solvent water and INN (the INN crystal water does not add on to the solvent water ). The molar volume of a mixture is represented as a sum of two terms: Solv vv ξ= + (6) The first term, Solvv, is the molar volume of the INN -free solvent mixture. The second term, ξ , accounts for the influence of IN N on the molar volume . Both terms are correlated here by simple polynomials in composition and temperature. The molar volume of the INN -free solvent mixture vSolv is described by pure pure E Solv E E W W Solv ˆˆ v xv x v v=++ . (7) Here, pure Ev and pure Wv are the temperature- dependent pure component molar volumes of ethanol and water , pure 3 -1 2/ cm mol ( / K) ( / K) v abT cT=+⋅ +⋅ , (8) where a, b and c are adjustable parameters. The excess molar volume E Solvv of the solvent mixture is correlated using a Redlich-Kister polynomial , E Solv EW 3 -1 EW E W 2 EW E Wˆˆ cm mol ˆˆ ˆ ˆ () ˆˆ ˆ ˆ ()vAxx Bxx x x C xx x x= ⋅ +⋅ ⋅ - +⋅ ⋅ - , (9) where A, B and C are temperature- dependent adjustable parameter s, which are correlated with 2( / K) ( / K) A d eT f T=+⋅ +⋅ . (10) The term ξ, which describes the influence of INN on the molar volume , is given by ( ) ( )3 -1 2 3 INN E E E 2 23 INN E E Eˆˆˆ / cm mol ˆˆ ˆξ x D Ex Fx Gx x H Ix Jx Kx= ⋅+⋅+⋅+⋅ + ⋅ + ⋅+ ⋅+⋅. (11) Here, xINN is the mole fraction of IN N in the mixture , and D , E, F, G, H, I, J and K are temperature- dependent adjustable parameters , which are correlated with ( / K) D g hT=+⋅ . (12) The mole fraction of INN in the mixture x INN is defined as INN INN INN E Wnxn nn=++, (13) where nINN, nE and nW are the mole numbers of INN, ethanol and water, respectively . Inserting Eq. (13) in Eq. (1) and rearrang ing leads to the conversion of bINN to xINN as follows INN INN INN Solv1bx bM= + . (14) Here, SolvM is the mean molar mass of the salt -free solvent mi xture. The viscosity η (in units mPa s ), thermal conductivity λ (in units mW m-1K-1) and isobaric heat capacity cp (in units J mol-1K-1) are correlated in the same way as the molar volume, i.e. using Eqs. (6) - (14). In most cases, not all of the polynomial coefficients in Eq s. (8) - (12) are needed. Only those terms required for obtaini ng a satisfactory fit of the data were included to reduce the risk of overfitting and to allow meaningful extrapolations of the correlations to some extent. Also other approaches to correlating the data were tested, e.g. using the INN molality b INN instead of the INN mole fraction x INN, but necessitated the use of more adjustable parameters. In order to obtain an adequate fit of the experimental data, parameters were adjusted using a least squares minimization p erformed by the MATLAB ®41 solver “lsqnonlin”, using the objective function 2exp cal p exp 1OFN ii iizz z =-= ∑ , (15) where z is either of the properties considered in this work and N p is the number of experimental points. The superscripts “exp” and “cal” denote experimental and calculated results. 4. Results and discussion In the following section s, results for the differen t properties of mixtures of INN, ethanol and water are shown as functions of the mole fraction of ethanol in the INN - free solvent mixture x ̂E, the overall molality bINN and temperature T. The experimental data are reported in Tables 2 – 5 and repeated for convenience in the Supporting Information as a function of the true mole fractions in the mixture . The correlation parameters, cf. Eq s. (8) - (12), are provided in Tables 6 - 8. Results for the thermal diffusivity a are shown in the Support ing Information. 4.1 Density The experimental data of the density of solutions of INN in mixtures of ethanol and water obtained in the present work are shown in Figure 1 together with the correlation . [Figure 1 about here.] The density increases with increasing molality of INN and with decreasing temperature. For bINN = 0.74 mol kg-1 and T = 333.15 K in pure ethanol the precipitation of a solid was observed after sample preparation , which is the reason for the missing data point . Astonishingly, no prec ipitation was observed for higher or lower overall molalities of INN or lower temperatures . Studying t he solid precipitation in mixtures of INN and ethanol is beyond the scope of the present work. The correlation describes the experimental data within the experimental standard uncertainty. 4.2 Viscosity The experimental data of the viscosity of solutions of INN in mixtures of ethanol and water obtained in the present work are shown in Figure 2 together with the correlation . [Figure 2 about here.] The viscosity of mixtures of INN and ethanol increases with increasing molality of INN and with decreasing temperature. The same holds for aqueous solutions and mixed solvents. As for the density, no experimental data for b INN = 0.74 mol kg-1 and T = 333.15 K in pure ethanol can be reported here due to the formation of a solid precipitate. Due to the incomplete wetting of the Stabinger viscosimeter mentioned above, data on the viscosity of pure water used for establishing the correlation were taken from the literature42–45. The correlation describes the experimental data within the experimental standard uncertainty, except for high INN molalities and low temperatures, where the slope of the viscosity is steep. 4.3 Thermal conductivity The experimental data of the therm al conductivity of solutions of INN in mixtures of ethanol and water obtained in the present work are shown in Figure 3 together with the correlation. As we have only considered one composition of the salt -free solvent mixture, additional data of the thermal conductivity of mixtures of ethanol and water were taken from the literature34–37 for establishing the correlation. [Figure 3 about here.] The dependence of the thermal co nductivity of mixtures of INN, ethanol and water on the variables T , x̂E, and b INN is more complex than for the other properties studied here. There are several interesting features: Firstly, for pure ethanol as the solvent an invariant point is observed, in which all isotherms λ (bINN) intersect at bINN = 0.12 mol kg-1. This is due to the fact that the temperature dependence of λ is different for pure water, for which λ increases with T, and pure ethanol, for which the opposite trend is observed. Thus, the invariant point observed for pure ethanol as the solvent arises from the fact that adding INN also means adding water. A similar invariant point is also observed for the salt- free solvent mixture37. Secondly , depending on the composition of the solvent, the curves λ (bINN) show maxima or minima. For pure water as the solvent minima are observed at all temperatures, for pure ethanol as the solvent maxima are observed instead . For the intermediate x̂E = 0.28 mol mol-1 the curves λ (bINN) are flat for all studied temperatures. We have explored plotting the results for λ as a func tion of the true mole fractions but have not found simpler tre nds. The correlation describes the experimental data within the experimental standard uncertainty. 4.4 Isobaric heat capacity The experimental data of the isobaric heat capacity of solutions of INN in mixtures of ethanol and water obtained in the present work are shown in Figure 4 together with the correlation . Due to the high deviation to the literature data39,40 of the heat capacity measurements of the mixtures of ethanol and water, experimental data for the excess heat capacity for the salt -free solvent mixture E p,Solvc were taken from the literature39,40 for establishing the correlation. [Figure 4 about here.] The isobaric heat capacity of mixtures of INN, ethanol and water decreases with increasing molality of INN and with increasing temperature. The correlation describes the experimental data within the exp erimental standard uncertainty. 5. Conclusions In the p resent work, thermophys ical properties of mixtures of iron(III)nitrate- nonahydrate (INN), ethanol and water, which are used in spray flame synthesis processes for the production of iron oxide nanoparticles, were measured . The presented data include the densit y, viscosit y, thermal conductivit y and isobaric heat capacit y. From this comprehensive set of data, only the density of the binary system INN + water was available previously . Empirical correlations to the the rmophysical data are provided . The data presented here establish a basis for the simulation of spray flame synthesis processes for the production of iron oxide nanoparticles and can thereby contribute to a better understanding of the droplet atomization and evaporation process of the precursor s olution. 6. Acknowledgements This work was supported by the German Research Foundation (DFG) within the priority program SPP 1980 SPRAYSYN under grant HA 1993/18- 1. 7. Associated content Supporting Information Available: Comparison of experimental data for pure ethanol, pure water, mixtures of ethanol and water , and densities of aqueous solutions of INN to literature data ; results for the thermal diffusivity, experimental results as functions of the true mole fract ions.