Poly(oxymethylene) dimethyl ethers (OME, CH 3O(CH2O)nCH3) are new synthetic fuels that can be produced from renewable resources. An interesting application of OME fuels is using them in mixtures with hydrogenated vegetable oils (HVO), which mainlyconsistofalkanes. DataondiffusioncoefficientsofOMEcontainingmixturesare lacking in the literature, but are needed for modelling OME production processes and OME combustion. Therefore, in the present work self-diffusion coefficients of binary mixtures of OME and alkanes were measured by pulsed field gradient nuclear magnetic resonance (PFG-NMR). OME with chain lengths n=1...4 were studied; the alkanes were n-dodecane (C12) and n-hexadecane (C16). The measurements in the binary mixtures were carried out at high dilution of the diffusing components and extrapo- lated to obtain the self-diffusion coefficients at infinite dilution that are identical with the mutual diffusion coefficient. For completeness, also the self-diffusion coefficients of 1 the pure components were measured. The experiments were carried out at tempera- tures between 298.15 and 353.15 K at ambient pressure. The experimental data for the diffusion coefficients at infinite dilution were compared to results from established prediction methods (SEGWE, Wilke and Chang), revealing considerable discrepancies. Furthermore, entropy scaling (ES) was applied here for the first time for modeling dif- fusion coefficients at infinite dilution. By coupling the results from entropy scaling with the Vignes equation, mutual diffusion coefficients in mixtures of OME and alkanes can be predicted now as a function of the temperature, pressure and composition for a wide range of conditions. Introduction Blendsofpoly(oxymethylene)dimethylethers(OME)andhydrogenatedvegetableoils(HVO) are interesting new synthetic fuels that can be produced from renewable resources.1–4OME are oligomers with the chemical structure CH 3O(CH2O)nCH3with n≥2. For synthetic fuels OME with chain lengths n= 3−5are often used.5These oligomers have suitable physical properties to replace fossil diesel, but produce much less soot upon combustion be- cause they contain oxygen in their backbone.6–8HVO consist predominantly of n-alkanes, with C-numbers between 15 and 20.8For the modelling of production processes and com- bustion applications, information and models for the transport properties of OME and HVO and their mixtures are required. They are needed, e.g., for calculating the Lewis number Le, which is the ratio of the heat conductivity and the diffusion coefficient, which must be known to decide whether explosions of droplets in fuel sprays may occur.9,10 There are several types of diffusion coefficients. The self-diffusion coefficient character- izes the mobility of individual molecules, whereas the mutual diffusion coefficient describes the mobility of the collectives of molecules. Mutual diffusion coefficients are needed for the description of mass transport on a macroscopic scale. Mutual diffusion is commonly de- scribed either by the Maxwell-Stefan or the Fickian framework. The corresponding diffusion 2 coefficients are related by the thermodynamic factor.11At infinite dilution of the diffusing component in a binary mixture, the self-diffusion coefficient, the Maxwell-Stefan diffusion coefficient and the Fickian diffusion coefficient are identical. Interpolation schemes exist that enable the prediction of diffusion coefficients at finite concentrations form those at infinite dilution, the most widely used of which is that of Vignes et al.12 Pulsed field gradient nuclear magnetic resonance (PFG-NMR) is an excellent method for measuring self-diffusion coefficients and, by extrapolation, also information on the diffusion coefficients at infinite dilution can be obtained. While PFG-NMR measurements of diffusion coefficients are common in the natural sciences, they have been applied only occasionally in engineering studies.13–15Compared to other physico-chemical properties, experimental data on diffusion coefficients is relatively scarce in the literature.16Therefore, many empirical methods have been developed for their prediction. They generally refer to the state of infinite dilution. For an overview, see e.g. Poling et al.17In the present study, we use the fairly recent model of Evans et al.18(SEGWE) as well as the well-established method of Wilke and Chang (WC)19for comparisons with the new data presented here. Transport properties can also be modeled based on entropy scaling (ES). The basic idea behind this approach is that the considered transport property can be transformed in a way so that it becomes a univariate function of the configurational entropy.20,21The entropy can be calculated as a function of state variables such as temperature and pressure, e.g. from equations of state (EOS).22,23Entropy scaling has been applied multiple times in the literature for modeling the thermal conductivity, the shear viscosity as well as self-diffusion coefficients in pure components.24–27Entropy scaling has also been applied for modeling the viscosity and thermal conductivity of mixtures. Furthermore, diffusion coefficients at infinite dilution have been predicted indirectly based on the Stokes-Einstein theory that was corrected using results from entropy scaling.28Yet, to the best of our knowledge, entropy scaling has not yet been applied directly to describe diffusion coefficients in mixtures, i.e. for scaling mixture diffusion coefficients. 3 In this work, diffusion coefficients at infinite dilution in binary mixtures of OME nand alkanes were determined from data obtained by PFG-NMR spectroscopy at temperatures between 298.15 K and 353.15 K at ambient pressure. The results were compared to those from the models of Evans et al.18(SEGWE) and Wilke and Chang19(WC). An entropy scaling method for predicting diffusion coefficients at infinite dilution was developed and applied to the new data, enabling extrapolations over a wide range of conditions. Experimental Section Chemicals and Sample Preparation. Table 1 gives an overview of the chemicals that were used in the present work, their structural formula and their purity. Alkanes and OME 1 were purchased from Sigma Aldrich, OME 2-4were supplied by BASF SE. The alkanes were used as received, the OME nwere dried with molecular sieve (3Å) before use. The samples were prepared gravimetrically using a laboratory balance (Mettler-Toledo XSR225DU) with an uncertainty of 10-5g. A PTFE syringe filter from Captiva (pore size 0.45 µm) was used to weigh in OME nin order to trap any debris of the molecular sieve. The total mass of each sample was approximately 5g, from which the amount needed to fill the NMR tube (about 0.1g) was taken. The uncertainty of the mole fraction is estimated to be 0.0001molmol-1 for all components. The concentrations of the diluted component xiin the studied binary mixtures were approximately 0.005,0.010,0.025molmol-1. Measurement of self-diffusion coefficients. The measurements were carried out as in our previous works.14,15 1H PFG-NMR measurements were carried out with a NMR spec- trometer with a magnetic field strength of 9.4T corresponding to a proton Larmor frequency of 400.25MHz that was equipped with a double resonance broad band probe (magnet As- cend 400, console Avance III HD 400, probe BBFO, Bruker Biospin). The spectrometer’s temperature sensor was calibrated with a platinum resistance thermometer (Pt-100) that was, in turn, calibrated in our laboratory using a certified standard. The uncertainty of the 4 Table 1: Overview of chemicals that were used and their purities. Structure Molar mass Purity / gmol-1/ gg-1 OME1 H3CO OCH3 76.09 0.985 OME2 H3CO O OCH3 106.12 0.985 OME3 H3CO O O OCH3 136.15 0.985 OME4 H3CO O O O OCH3 166.17 0.985 n-dodecane H3CCH3170.33 0.990 n-hexadecane H3CCH3226.41 0.990 temperature measurement is 0.1K. Special sample tubes with an outer diameter of 2.5mm (Deutero) were used in order to minimize sample convection.29The pulse sequence contained bipolar pulsed gradients and was applied as implemented in the NMR spectrometer’s soft- ware (pulse sequence: stebpgp1s). The self-diffusion coefficient Diof species iwas obtained from a fit of the natural logarithm of the relative NMR signal integral as a function of the squared gradient strength using the Stejskal-Tanner30equation: lnI I0 =−Diγ2δ2g2 ∆−δ 3−τ 2 (1) whereIis the signal integral, I0is the signal integral without gradient, γis the gyromagnetic ratio, δis the duration of the gradient pulse, gis the gradient strength, ∆is the diffusion time, and τis the correction constant due to the usage of bipolar gradients. Each diffusion experiment consisted of 16 gradient steps with 16 scans each for the pure solvents and 32 scans each for the binary mixtures, respectively, with a prescan delay that was chosen long enough to ensure complete relaxation, resulting in numbers between 10 and 45 s. The gradient pulse duration δwas adjusted to the respective sample between 0.5 and 1.9ms. The gradient strength gwas incremented following a square root relationship from 2.3 to 43.1Gcm-1and the diffusion time ∆was chosen as 50ms for all measurements. The time 5 constant τwaschosenas0.2ms, correspondingtothetimedelaybetweenthebipolargradient lobes. Baseline and phase correction of the spectra were performed manually. All peaks were integrated manually. Mutual diffusion coefficients at infinite dilution D∞ ijwere obtained by linear extrapolation of self-diffusion coefficients to infinite dilution of the diffusing component i. In most cases, theresultsfromthethreedilutedsamplesagreedwithintheexperimentaluncertainty, sothat taking the average value would have been sufficient. The relative standard uncertainty for the determination of Difrom the fit to the experimental NMR data using the Stejskal Tanner Eq.(1) was0.01 ·10-9m2s-1. The statistical relative standard uncertainty estimated from the results of three repeated measurements also was0.01 ·10-9m2s-1. We therefore estimate the uncertainty of the diffusion coefficient data measured in the present work to be0.02 ·10-9 m2s-1. Models Established methods for predicting diffusion coefficients. The SEGWE model of Evans et al.18for predicting the diffusion coefficient of solute "1" at infinite dilution in a solvent "2" D∞ 12is given by D∞,SEGWE 12 /m2s−1= kB/J K−1 (T/ K)3α 2+1 1+α 6π(η2/Pa·s)3r 3(M1/g mol−1) 4π(ρeff/g m−3)(NA/mol−1) α=3s M2/g mol−1  M1/g mol−1(2) where kBis Boltzmann’s constant, Tis the temperature, η2is the dynamic viscosity of the solvent "2", M1is the molar mass of the solute "1", M2is the molar mass of the solvent "2",ρeff= 619kg m−3is an "effective density", the number of which was fitted to literature data by the authors18andNAis Avogadro’s constant. 6 The model of Wilke and Chang (WC)19is given by D∞,WC 12 /m2s−1= 7.4·10−12q Φ2 M2/g mol−1 (T/ K) (η2/cP) v1/cm3mol−10.6(3) where Φ2is the association factor of the solvent "2" which was set to 1 here in all cases, andv1is the liquid molar volume of the pure solute "1" at their normal boiling point.19 Data for the dynamic viscosity η2of alkanes31,32and of OME33,34were taken from the literature. Data for the liquid molar volume of the solutes at their normal boiling point v1 were computed from correlations from DIPPR35and Burger et al.1and are listed in Table S.5 in the Supporting Information. Entropy Scaling. In this work, entropy scaling was used to model the self-diffusion coefficients of the pure components as well as diffusion coefficients at infinite dilution in binary systems. The latter has, to the best of our knowledge, not been done before. The approach we use here is based on the entropy scaling framework from Schmitt et al.36and was used in combination with the PC-SAFT37equation of state (EOS). The EOS parameters to model all pure components were taken from the literature, for the alkanes from Gross and Sadowski37and for the OME nfrom Schappals et al.38The self-diffusion coefficients of the pure components were scaled according to Schmitt et al.36For applying this framework to the diffusion coefficients at infinite dilution, some modifications were necessary, which are introduced in the following. The Rosenfeld-scaled diffusion coefficient of solute "1" at infinite dilution in solvent "2" D∞,+ 12is D∞,+ 12=D∞ 12ρ1/3 Np RT/M 2−sconf R2/3 (4) where Ristheuniversalgasconstant, M2isthemolarmassofthesolvent"2", ρNthenumber density of the solvent at the given state point, and sconfthe molar configurational entropy of the solvent at the given state point and describes the part of the entropy originating from the interactions of the molecules. 7 For the zero-density limit, the Chapman-Enskog theory is used, which yields the term given in Eq. (5) for the binary diffusion coefficient17in the gas phase and is thus independent of the mole fraction. D∞ CE,12=3 8r RT πM 121 ρNσ2 12ΩD(5) Herein, M12is a reduced molar mass calculated as M12= 2/(1/M1+ 1/M2)from the molar masses of both components M1andM2,σ12is the mean particle size calculated as σ12= (σ1+σ2)/2with σ1andσ2being parameters describing the particle size of both components "1" and "2", ΩDis the reduced collision integral for diffusion. The collision integral is a function of the reduced temperature T / ε 12k−1 B, i.e. ΩD= Ω D(T / ε 12k−1 B). The parameter ε12isanenergyparameterofthemixturewhichiscalculatedfromthepure-componentenergy parameters ε1andε2asε12=√ε1ε2. The calculation of the pure component parameters σ1, σ2,ε1andε2as well as the collision integral ΩDis based on the Lennard-Jones model39,40 and is described in Schmitt et al.36 The final ’CE-scaled’ value of the diffusion coefficient at infinite dilution bD+ 12is given as bD+ 12=D+ 12 D+ CE,12W+D+ 12 min(D+ CE,12)(W−1) (6) where Wis a function that realizes the transition from the low-density scaling D+ 12/D+ CE,12 to the high-density scaling D+ 12/min(D+ CE,12)(see Schmitt et al.36for details). These scaled diffusion coefficients are expressed as function of the dimensionless configu- rational entropy ˜s=−sconf/(R m)where mis the chain length parameter of the PC-SAFT equation of state. The function bD+(˜s)is given by ln bD+ 12(˜s) =α(D) 2,12˜s2+α(D) 3,12˜s3 1 +g(D) 1ln(˜s+ 1) + g(D) 2˜s(7) where α(D) 2,12andα(D) 3,12are component-specific parameters fitted to experimental data and g(D) 1andg(D) 2are global parameters that were fitted to Lennard-Jones simulation data.36 8 The global and component-specific parameters are given in the Supporting Information. Vignes equation. The Vignes equation12for predicting mutual diffusion coefficients in a binary mixture 1 +2 from the diffusion coefficients at infinite dilution D∞ 12andD∞ 21(where the first index indicates the diluted component) is: D12= D∞ 12x2 D∞ 21x1(8) Results and discussion In the following, first the experimental results for the self-diffusion coefficients of the pure components are presented and compared to literature data, wherever this is possible. Then, the results from the entropy scaling model of the self-diffusion coefficients of the pure compo- nents are discussed. After this, the experimental results of the self-diffusion coefficients for the binary mixtures are presented, together with their extrapolation to infinite dilution. The results for the diffusion coefficients at infinite dilution are then compared to the SEGWE and the WC model and the application of entropy scaling to the data is discussed. Pure components. The experimental data of the self-diffusion coefficients of pure alkanes measured in this work are compared to literature data41–43in Figure 1 (left). Good agreement is observed. The experimental data for the studied pure OME nare shown in Figure 1 (right). Due to the low boiling temperature of OME 1(Ts OME1= 315 .15K),7the self-diffusion coefficient was measured only at 298.15K. No literature data of pure OME n are available for comparison. The data presented in Figure 1 show the expected trends regarding the influence of temperature and molar mass of the components. The numerical experimental data for the pure components measured in this work are given in Table 2. Figure 1 also shows the results form the modeling of the experimental data by entropy scaling. Good agreement is observed. This is not astonishing as two parameters were fitted to the data for each studied component and the data were measured only in a quite narrow 9 temperature range at ambient pressure. Furthermore, as only the temperature was varied, the entropy scaling brings no immediate advantages for correlating the data set. The advan- tage of entropy scaling is that based on the limited amount of data that is provided here, self-diffusion coefficients can be predicted for a much wider range of conditions (tempera- tures, pressures) for all studied components. That such extrapolation yield good results has been demonstrated in extensive studies with model fluids.26 /s51/s48/s48 /s51/s49/s48 /s51/s50/s48 /s51/s51/s48 /s51/s52/s48 /s51/s53/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53 /s51/s48/s48 /s51/s49/s48 /s51/s50/s48 /s51/s51/s48 /s51/s52/s48 /s51/s53/s48/s48/s46/s48/s49/s46/s48/s50/s46/s48/s51/s46/s48/s52/s46/s48/s53/s46/s48 /s84/s104/s105/s115/s32/s119/s111/s114/s107/s32/s32/s76/s105/s116/s101/s114/s97/s116/s117/s114/s101 /s32/s32/s32/s32 /s32/s32/s32/s32/s32/s32/s32/s32/s32 /s32/s32/s32/s32/s32/s32/s32/s67/s49/s50 /s32/s32/s32/s32 /s32/s32/s32/s32/s32/s32/s32/s32/s32 /s32/s32/s32/s32/s32/s32/s32/s67/s49/s54/s49/s48/s57/s46 /s68 /s49/s32/s47/s32/s109/s50 /s32/s115/s45/s49 /s84 /s32/s47/s32/s75/s32/s79/s77/s69 /s49 /s32/s79/s77/s69 /s50 /s32/s79/s77/s69 /s51 /s32/s79/s77/s69 /s52 /s84 /s32/s47/s32/s75 Figure 1: Self-diffusion coefficients of n-dodecane (C12) and n-hexadecane (C16) (left) and OME n(right) as a function of temperature. Symbols: experimental results from this work obtained with PFG-NMR spectroscopy (open) and literature data41–43(filled). Solid lines: results from entropy scaling. Error bars are within symbol size. Table 2: Experimental data from PFG-NMR spectroscopy for the self-diffusion coefficients ofn-dodecane (C12), n-hexadecane (C16), and OME nat ambient pressure. Relative un- certainty of self-diffusion coefficient: ∆D1=0.02 ·10-9m2s-1. Uncertainty of temperature: ∆T=0.1K. C12 C16 OME 1OME2OME3OME4 T/ K 109·D1/ m2s-1 298.15 0.856 0.376 4.031 2.002 1.113 0.656 303.15 0.942 0.424 2.162 1.212 0.729 313.15 1.128 0.531 2.504 1.431 0.886 323.15 1.334 0.651 2.873 1.678 1.058 333.15 1.557 0.784 3.272 1.937 1.246 343.15 1.848 0.957 3.836 2.278 1.494 353.15 2.122 1.125 4.389 2.553 1.733 10 Binary mixtures. As an example, Figure 2 shows the experimental data obtained in the present work for the self-diffusion coefficient of OME 1in binary mixtures with either n-dodecane (C12) or n-hexadecane (C16) at 298.15K. The results at high concentrations of OME1were obtained in measurements to determine the diffusion coefficient of the alkanes in OME 1and are only shown for completeness. As expected, the self diffusion coefficient of OME1is close to that in pure OME 1in that region. The addition of the alkane lowers the self-diffusion coefficient of OME 1and the effect is more important for n-hexadecane than for n-dodecane. In the region of very low OME 1 concentrations that was studied here, the dependency of the OME 1diffusion coefficient on the OME 1concentration is almost linear, so that the extrapolation to infinite dilution poses no problem. The numerical experimental data for the self-diffusion coefficients in binary mixtures measured in this work are given in the Supporting Information. The numerical data for the extrapolated diffusion coefficients at infinite dilution are given in Tables 3 and 4. 11 /s48/s46/s48/s48 /s48/s46/s48/s50 /s48/s46/s48/s52 /s48/s46/s57/s54 /s48/s46/s57/s56 /s49/s46/s48/s48/s48/s46/s48/s49/s46/s48/s50/s46/s48/s51/s46/s48/s52/s46/s48/s53/s46/s48 /s32/s79/s77/s69 /s49/s32/s43/s32/s67/s49/s50 /s32/s79/s77/s69 /s49/s32/s43/s32/s67/s49/s54/s49/s48/s57/s46 /s68 /s79/s77/s69 /s49/s32/s47/s32/s109/s50 /s32/s115/s45/s49 /s120 /s79/s77/s69 /s49/s32/s47/s32/s109/s111/s108/s32/s109/s111/s108/s45/s49Figure 2: Self-diffusion coefficients of OME 1as a function of composition in n-dodecane (C12) and n-hexadecane (C16) at 298.15 K. Open symbols: experimental results. Filled symbols: extrapolated results. Solid lines: extrapolation. Error bars are within symbol size. Figure 3 shows the results for the diffusion coefficients at infinite dilution in binary mixtures of OME n+n-dodecane (C12) and Figure 4 of OME n+n-hexadecane (C16) at different temperatures. As expected, the diffusion coefficients of OME ninn-dodecane are higherthanin n-hexadecaneandthediffusioncoefficientsof n-dodecaneinagivenOME nare higher than those of n-hexadecane in the same OME nand the diffusion coefficients increase with increasing temperature. The correlation of the data for the diffusion coefficients at infinite dilution with entropy scaling was successful for all studied systems. For each pair solute +solvent, two parameters were fitted to the data, so that the success of the correlation is not astonishing, but it should be kept in mind that the method enables extrapolations beyond the range that was studied here. The predictions with the SEGWE and the WC model yield only poor results. No clear ranking of the models is possible; sometimes SEGWE is better, sometimes WC. 12 /s51/s48/s48 /s51/s49/s48 /s51/s50/s48 /s51/s51/s48 /s51/s52/s48 /s51/s53/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53/s51/s46/s48/s51/s46/s53/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53/s51/s46/s48/s51/s46/s53 /s32/s69/s120/s112/s46/s32/s68/s97/s116/s97 /s32/s69/s83 /s32/s83/s69/s71/s87 /s69 /s32/s87 /s67/s49/s48/s57/s46 /s68 /s67/s49/s50/s44/s32/s79/s77/s69 /s110/s32/s47/s32/s109/s50 /s32/s115/s45/s49 /s84 /s32/s47/s32/s75/s32/s69/s120/s112/s46/s32/s68/s97/s116/s97 /s32/s69/s83 /s32/s83/s69/s71/s87 /s69 /s32/s87 /s67/s49/s48/s57/s46 /s68 /s79/s77/s69 /s110/s44/s32/s67/s49/s50/s32/s47/s32/s109/s50 /s32/s115/s45/s49/s32/s32/s32 /s79/s77/s69 /s50/s32/s79/s77/s69 /s51/s32 /s79/s77/s69 /s52/s32/s32/s32Figure 3: Diffusion coefficients at infinite dilution in binary mixtures of OME n+n-dodecane (C12) as a function of temperature. Symbols: experimental results from PFG-NMR spec- troscopy. Lines: entropy scaling model (solid) and predictions with SEGWE (dashed) and WC (dotted). 13 /s51/s48/s48 /s51/s49/s48 /s51/s50/s48 /s51/s51/s48 /s51/s52/s48 /s51/s53/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53/s51/s46/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53/s51/s46/s48 /s32/s69/s120/s112/s46/s32/s68/s97/s116/s97 /s32/s69/s83 /s32/s83/s69/s71/s87 /s69 /s32/s87 /s67/s49/s48/s57/s46 /s68 /s67/s49/s54/s44/s32/s79/s77/s69 /s110/s32/s47/s32/s109/s50 /s32/s115/s45/s49 /s84 /s32/s47/s32/s75/s32/s69/s120/s112/s46/s32/s68/s97/s116/s97 /s32/s69/s83 /s32/s83/s69/s71/s87 /s69 /s32/s87 /s67/s49/s48/s57/s46 /s68 /s79/s77/s69 /s110/s44/s32/s67/s49/s54/s32/s47/s32/s109/s50 /s32/s115/s45/s49/s32/s32/s32 /s79/s77/s69 /s50/s32/s79/s77/s69 /s51/s32 /s79/s77/s69 /s52/s32/s32/s32Figure 4: Diffusion coefficients at infinite dilution in binary mixtures of OME n+n- hexadecane (C16) as a function of temperature. Symbols: experimental results from PFG- NMR spectroscopy. Lines: entropy scaling model (solid) and predictions with SEGWE (dashed) and WC (dotted). 14 Table 3: Diffusion coefficients of OME nat infinite dilution in binary mixtures with n- dodecane (C12) and n-hexadecane (C16) at ambient pressure. Relative uncertainty of diffu- sion coefficient: ∆D1=0.02 ·10-9m2s-1. Uncertainty of temperature ∆T= 0.1K. Solute OME1OME2OME3OME4OME1OME2OME3OME4 Solvent n-dodecane (C12) n-hexadecane (C16) T/ K 109·D∞ OME n,C12/ m2s-1109·D∞ OME n,C16/ m2s-1 298.15 1.759 1.410 1.180 1.104 1.094 0.849 0.690 0.640 303.15 1.579 1.289 1.220 1.036 0.780 0.717 313.15 1.860 1.534 1.415 1.211 0.995 0.885 323.15 2.214 1.796 1.666 1.446 1.151 1.081 333.15 2.673 2.090 1.952 1.890 1.393 1.287 343.15 2.945 2.463 2.230 2.296 1.652 1.555 353.15 3.348 2.807 2.560 2.585 1.885 1.802 Table 4: Diffusion coefficients of n-dodecane (C12) and n-hexadecane (C16) at infinite dilu- tion in binary mixtures with OME nat ambient pressure. Relative uncertainty of diffusion coefficient: ∆D1=0.02 ·10-9m2s-1. Uncertainty of temperature: ∆T= 0.1K. Solute n-dodecane (C12) n-hexadecane (C16) Solvent OME1OME2OME3OME4OME1OME2OME3OME4 T/ K 109·D∞ C12,OME n/ m2s-1109·D∞ C16,OME n/ m2s-1 298.15 2.482 1.433 0.929 0.620 2.051 1.181 0.747 0.503 303.15 1.544 1.015 0.691 1.279 0.821 0.559 313.15 1.810 1.196 0.834 1.461 0.971 0.694 323.15 2.207 1.402 0.996 1.694 1.140 0.822 333.15 2.352 1.626 1.180 1.935 1.321 0.979 343.15 2.849 1.893 1.397 2.228 1.571 1.199 353.15 3.037 2.155 1.600 2.472 1.767 1.376 An example for the application of the entropy scaling model based on the new data on diffusion coefficients at infinite dilution from the present work is presented in Figure 5, where the mutual diffusion coefficients in the system OME 2+n-dodecane (C12) are shown for a wide range of temperatures using the Vignes equation. Therein, the numbers of the diffusion coefficients at infinite dilution outside the temperature range that was studied by experiments here, were obtained from the entropy scaling model. The interpolation by the Vignes equation is almost linear in all cases. The results should be interpreted as predic- tions of the binary Maxwell-Stefan diffusion coefficient. For calculating Fickian diffusion coefficients, the thermodynamic factor should be considered, which can be calculated for the 15 systems studied here either based on the PC-SAFT equation of state or based on the model of the Gibbs excess energy described in Breitkreuz et al.8 /s48/s46/s48 /s48/s46/s50 /s48/s46/s52 /s48/s46/s54 /s48/s46/s56 /s49/s46/s48/s48/s46/s48/s49/s46/s48/s50/s46/s48/s51/s46/s48/s52/s46/s48/s53/s46/s48 /s32/s69/s83/s32/s100/s97/s116/s97 /s32/s78/s77/s82/s32/s100/s97/s116/s97 /s32/s86/s105/s103/s110/s101/s115 /s32/s51/s55/s51/s46/s49/s53/s32/s75 /s32/s51/s54/s51/s46/s49/s53/s32/s75 /s32/s51/s51/s51/s46/s49/s53/s32/s75 /s32/s51/s49/s51/s46/s49/s53/s32/s75 /s32/s50/s56/s51/s46/s49/s53/s32/s75/s49/s48/s57/s46 /s68 /s79/s77/s69 /s50/s44/s32/s67/s49/s50/s32/s47/s32/s109/s50 /s32/s115/s45/s49 /s120 /s79/s77/s69 /s50/s32/s47/s32/s109/s111/s108/s32/s109/s111/s108/s45/s49 Figure 5: Diffusion coefficients of OME 2+n-dodecane (C12) as a function of composition andtemperaturefromNMRdata,entropyscalingandVignes. Symbols: NMRdata(squares) and entropy scaling data (circles). Solid lines: Vignes correlation. Conclusions The self-diffusion coefficients of the pure components n-dodecane, n-hexadecane and OME n (n= 1. . .4) as well as self-diffusion coefficients in binary mixtures of an OME nwith (n- dodecane or n-hexadecane) were measured at temperatures between 298.15 and 353.15K with PFG-NMR. From the binary data, the diffusion coefficients at infinite dilution in the studied systems were determined. The comparison with literature data for the pure alkanes confirmed the reliability of the experimental method. It was found that two well established methods for predicting diffusion coefficients from the literature (SEGWE, Wilke and Chang) 16 yield only poor predictions for the studied systems. The new data were used to train models based on entropy scaling in connection with the PC-SAFT equation of state. This method was applied here for the first time to diffusion coefficients at infinite dilution. The entropy scaling models describe the experimental data very well and are expected to yield reliable predictions also far outside the range in which they were fitted. The information on the diffusioncoefficientsatinfinitedilutioncanbecombinedwiththeVignesmodelforpredicting mutual diffusion coefficients in binary mixtures as a function of the temperature, pressure and composition. Also methods for extending this approach to multicomponent mixtures exist.44The new results enable modeling of phenomena such as droplet explosions9during the combustion of mixtures of OME and HVO, which are interesting renewable synthetic fuels. Supporting Information Available The Supporting Information is available free of charge at Link. Numerical experimental data on self-diffusion coefficients in binary mixtures; details on entropy scaling; numerical data of the liquid molar volume; and mutual diffusion coefficients correlated with Vignes (PDF) Acknowledgement The authors gratefully acknowledge funding by the German Federal Ministry of Economic Affairs and Energy within the project “E2Fuels” under Grant 19I18008F. The authors thank Madeline Farr, Enid-Joy Michel and Marvin Vu for carrying out experiments.