Diﬀusion coeﬃcients at inﬁnite dilution are important basic data for all processes involving mass transfer. They can be obtained from studying samples in equilibrium using nuclear magnetic resonance spectroscopy with pulsed ﬁeld gradients (PFG-NMR), a technique which is widely used in chemistry but is only rarely applied in engineering studies. This advantageous technique was employed here to measure the self-diﬀusion coeﬃcients of diluted solutions of carbon dioxide and methane in the pure solvents water, ethanol, cyclohexane, toluene, methanol, and acetone at 298.15 K. For the systems (carbon dioxide + water) and (carbon dioxide + ethanol), measurements were also carried out at 308.15K,318.15Kand333.15K.Exceptfor(methane+water)and(methane+ toluene), no literature data for the methane-containing systems were previously available. At the studied solute concentrations, there is practically no diﬀerence between the self-diﬀusion coeﬃcient and the mutual diﬀusion coeﬃcient. The experimental results are compared to experimental literature data as well as to results from semi-empirical methods for the prediction of diﬀusion coeﬃcients at inﬁnite dilution. Furthermore, molecular dynamics simulations were carried out for all systems to determine the diﬀusion coeﬃcient at inﬁnite dilution based on Corresponding author Email address: hans.hasse@mv.uni-kl.de (Hans Hasse) Preprint submitted to Journal of Chemical Thermodynamics October 22, 2021 force ﬁelds that were taken from the literature, and the results are compared to the experimental data and those from the classical prediction methods. Keywords: Diﬀusion coeﬃcient, inﬁnite dilution, NMR, molecular simulation 1. Introduction Diﬀusion is an omnipresent phenomenon and is described using diﬀusion coeﬃcients. There are diﬀerent types of diﬀusion coeﬃcients: (i) mutual (or transport) diﬀusion coeﬃcients and (ii) self-diﬀusion coeﬃcients. The former are used for describing the mass transport in mixtures, which is important 5 for many processes in nature and technology, the latter describe the Brownian motion of the individual molecules in pure components and mixtures, which is an important basic material property. Two ways of describing mass transfer are well-established: the Fickian approach and that of Maxwell-Stefan, with corresponding diﬀusion coeﬃcients. At inﬁnite dilution, the diﬀerences between 10 the Fickian and the Maxwell-Stefan mutual diﬀusion coeﬃcients as well as the self-diﬀusion coeﬃcient of the solute vanish. Therefore, in this study, for the description of mutual and self-diﬀusion at inﬁnite dilution, the term ‘diﬀusion coeﬃcient at inﬁnite dilution’ is used without any further speciﬁcation. There are many technical processes in which the diﬀusing component is so 15 dilute that the diﬀusion coeﬃcient at inﬁnite dilution can be used directly for describing the mass transport. This applies, e.g., to many absorption processes. Furthermore, methods exist that enable the prediction of diﬀusion coeﬃcients at ﬁnite concentrations from those at inﬁnite dilution [1, 2, 3]. All this makes data on diﬀusion coeﬃcients at inﬁnite dilution particularly valuable. 20 Compared to their signiﬁcance, reliable data on diﬀusion coeﬃcients at inﬁ- nite dilution are still rare. One major reason for this is that measuring diﬀusion coeﬃcients in general, and diﬀusion coeﬃcients at inﬁnite dilution in particular, is tedious: most available methods require carrying out non-equilibrium mea- surements. In contrast, nuclear magnetic resonance spectroscopy using pulsed 25 ﬁeld gradients (PFG-NMR) yields information on the self-diﬀusion coeﬃcient 2 from equilibrium measurements, which greatly facilitates the study. With the PFG-NMR method, diﬀusion coeﬃcients can be measured with high accuracy [4]. While the method is well established in chemistry and physics, it is still not widely adopted in engineering. 30 In this work, diﬀusion coeﬃcients at inﬁnite dilution of the single solutes carbon dioxide (CO 2) and methane (CH 4) in the pure solvents (water, ethanol, cyclohexane, toluene, methanol, and acetone) were determined with PFG-NMR at 298.15 K. Additionally, for the systems (CO 2+ water) and (CO 2+ ethanol), further data at 308.15 K, 318.15 K and 333.15 K were measured. For these 35 systems, a strong enrichment of the solute at the vapor-liquid interface is ex- pected and accurate data on the diﬀusion coeﬃcient of the solute is needed for evaluating experimental studies on the inﬂuence of this enrichment on the mass transfer through the interface [5, 6]. Another goal of this work is to demonstrate the usefulness of PFG-NMR for 40 engineering studies. Consequently, measurements were not only carried out for systems, for which no diﬀusion coeﬃcients were previously available (all systems withthesoluteCH 4, except(CH 4+water)), butalsoforsystems, forwhichdata was available for comparisons. This is in particular the case for the two systems with the solvent water. For (CO 2+ water), abundant data for the diﬀusion 45 coeﬃcient at inﬁnite dilution are available [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]. Fewer data are available for CO 2in ethanol [35, 10, 11, 36, 37, 29, 38], cyclohexane [39], toluene [10,40,41], methanol[35,10,11,19,31,42], andacetone[10]. ForCH 4, diﬀusion coeﬃcientshavebeeninvestigatedbeforeinwater[8,43,9,44,45,46,47,48,34]. 50 Fortheremainingsolvents, onlyastudyonthesystem(CH 4+toluene)at323K [49] seems to be available. Themethodsthatwereusedintheliteratureforstudyingthediﬀusioncoeﬃ- cient can be categorized as follows: diaphragm cells [8], wetted surface absorbers [13, 17], laminar jets [20], capillary cells [29], Taylor dispersion [50, 51], and dy- 55 namic light scattering (DLS) [38]. In a diaphragm cell, two solutions of diﬀerent composition are brought into contact by a diaphragm. The cell usually has to 3 be calibrated with a mixture of known diﬀusion coeﬃcient. In the wetted sur- face absorber technique, absorption takes place in a laminar ﬁlm ﬂowing over a surface of deﬁned geometry, such as a sphere or a wall. The laminar jet method 60 is similar, but the absorption takes place in a free-ﬂowing laminar jet. The two latter methods require knowledge of the ﬂuid dynamics for the analysis. Cap- illary cells make use of the capillary eﬀect in order to restrict convection. One component is placed in the capillary and then brought into contact with the second component. For studying the diﬀusion coeﬃcient of a gas in a solvent 65 by the Taylor dispersion technique, a sample of a solution containing the gas and the solvent is injected into a stream of the pure solvent and the dispersion of the gas upon the laminar ﬂow through a capillary is monitored. Dynamic light scattering is able to obtain mutual diﬀusion coeﬃcients from equilibrated samples. This is accomplished by observing coherent (laser) light being scat- 70 tered by the sample which is inﬂuenced by local concentration ﬂuctuations (i.e. diﬀusion). PFG-NMR makes use of magnetic gradient ﬁelds which imprint phase shifts on the nuclear spins of the diﬀusing species resulting in decreasing NMR sig- nals with increasing gradient strength and increasing Brownian motion of the 75 molecules. This way, the molecular motion can be quantiﬁed and the self- diﬀusion coeﬃcient can be extracted [52]. In contrast to the aforementioned methods, the PFG-NMR method does not require any calibration or additional information on the investigated systems. The PFG-NMR data in this work are complemented by molecular simula- 80 tion studies of the diﬀusion coeﬃcients in all considered systems as well as by comparisons with results from two semi-empirical methods for the prediction of diﬀusion coeﬃcients at inﬁnite dilution, namely those of Wilke and Chang [53] and Evans et al. [54]. This paper is organized as follows: First, the PFG-NMR measurements are 85 described, then the semi-empirical methods and the molecular simulations for the prediction of the diﬀusion coeﬃcient at inﬁnite dilution. In the results section, the experimental data are presented and compared to experimental 4 literature data and the results from the predictions with semi-empirical methods and molecular simulations. 90 2. Experiments Table 1 lists the chemicals that were used in this work, their suppliers, and their purities. Table 1: Overview of chemicals that were used with the respective suppliers and purities. The chemicals were used as provided by the suppliers without further puriﬁcation. Structure Molar mass Supplier Purity gmol1molmol1 13C-Carbon dioxide 45.01 Sigma-Aldrich 0.99 Methane CH4 16.04 Air Liquide S.A. 0.99 Water OH2 18.01 This worky Ethanol OH 46.07 Merck KGaA 0.999 Cyclohexane 84.16 Merck KGaA 0.999 Methanol OH 32.04 Merck KGaA 0.999 Acetone O 58.08 Merck KGaA 0.999 Toluene 92.14 AppliChem GmbH 0.999 yElix Essential 5 Puriﬁcation System (Merck KGaA), TOC < 30 ppb, resistivity > 5 M cm. 1H and13C PFG-NMR spectra were recorded with a Bruker Biospin NMR spectrometer with a magnetic ﬁeld strength of 9.4 T, corresponding to a proton 95 Larmor frequency of 400.40 MHz, which was equipped with a probe with cryo- genically cooled electronics (magnet: Ascend 400; console: Avance III HD 400; probe: CryoProbe Prodigy). The spectrometer’s temperature control unit was calibrated with a platinum resistance thermometer (Pt-100) that was, in turn, 5 calibrated using a standard, certiﬁed by PTB, Braunschweig. The standard un- 100 certainty of the temperature measurement is estimated to be u(T) = 0:1K. All samplesweremeasuredinpressure-tightNMRtubeswithvalves(5mmExtreme Series Level 3, Norell). For the measurements involving CO 2, isotope-enriched 13CO2was used, which facilitated the measurement signiﬁcantly. Due to its slightly higher mass,13CO2diﬀuses slower and the experimental self-diﬀusion 105 coeﬃcients were corrected by Eq. (1) in order to apply the data to12CO2[55]. D12CO2=D13CO2s M13CO2 M12CO2(1) All reported CO 2diﬀusion coeﬃcients were corrected by Eq. (1) and refer to12CO2. In the rest of the paper, the superscript 12 is omitted, as it is customary. The solvents were ﬁlled into the pressure tubes in which they were degassed by applying vacuum.13CO2or CH 4was then added and the tube was 110 thermostattedatthetargettemperature. Theamountofthegaswasadjustedso that the desired total pressure in the thermostatted sample was reached. These conditions were maintained until the dissolution process was ﬁnished, which was checked by NMR measurements. The NMR measurements were carried out using a stimulated spin-echo pulse 115 sequence with bipolar pulsed gradients as implemented in the spectrometer’s software (pulse sequence: stebpgp1s ) [56]. The experimental data was eval- uated using the Stejskal-Tanner equation [52]. This equation was modiﬁed to compensate for gradient non-linearity as well as the application of bipolar gra- dient pulses, resulting in Eq. (2); details are reported elsewhere [4]. 120 lnI I0 =2X n=1cn Di 22  3 2 g2n (2) Iis the signal intensity, I0is the signal intensity without gradient, is the gyromagnetic ratio of the measured nucleus, is the duration of the gradient pulse, is the diﬀusion time, is a correction constant that is applied when bipolar gradient pulses are used, and gis the gradient strength. cn(in this case c1andc2) are probe-speciﬁc ﬁt coeﬃcients correcting for gradient non-linearity 125 6 which have been determined through calibration measurements on samples with well-known self-diﬀusion coeﬃcients. The number for the diﬀusion coeﬃcient Diis determined from a ﬁt of Eq. (2) to experimental data for IandI0. Theexperimentalparameterswerechosenasfollows:  = 50ms, = 0:2ms. The gradient strength gwas incremented from 2.5 to 48.5 G cm1in 8 steps 130 with 32 scans for1H and 16 scans for13C measurements, respectively. The pre-scan delay and gradient pulse duration were adjusted to the respective sample in order to facilitate suﬃcient sample relaxation and diﬀusion encod- ing, respectively. With the described parameters, the measurement time per sample ranged between one and four hours, which depended on the respective 135 sample’s relaxation time. Lower experimental time spans are possible with a slight decrease in accuracy. It should be noted that the described experiments were carried out on equilibrated samples. This study aims at determining the diﬀusion coeﬃcient at inﬁnite dilution. Therefore, measurements were carried out at low solute concentrations. The 140 mole fraction of dissolved gas in the solvent was determined by direct integra- tionoftherespectivepeaksintherecorded1DNMRspectra. Phaseandbaseline correction were applied using the processing tool developed by Sawall et al. [57]. Three measurements at diﬀerent low solute mole fractions were carried out for each mixture in order to be able to detect any concentration-dependence of the 145 self-diﬀusion coeﬃcient. The mixtures were produced by applying 0.1, 0.2 and 0.4 MPa of solute gas pressure to the solvent. The pressure was maintained throughout the equilibration and measurement process. The mole fractions of thediﬀusingcomponentwerebelow0.01mol mol1forCH 4and0.04molmol1 for CO 2, except for (CO 2+ acetone), where the highest CO 2mole fraction was 150 0.07 mol/mol. As an example, the self-diﬀusion coeﬃcients of CO 2and CH 4in toluene at 298.15 K are shown in Fig. 1. Within the limits given by the exper- imental uncertainty of the diﬀusion coeﬃcients, no concentration dependence of the measured self-diﬀusion coeﬃcients can be discerned. The experimental uncertainty is dominated by the uncertainty of the ﬁt by Eq. 2. Similar results 155 were obtained for all other mixtures except (CO 2+ acetone) where a slight con- 7 centration dependence was observed. Therefore, the data for (CO 2+ acetone) were extrapolated linearly towards inﬁnite dilution and the resulting intercept is reported as the diﬀusion coeﬃcient at inﬁnite dilution D1;exp iwithiindicat- ing the solute. For all other mixtures investigated in this work, the arithmetic 160 mean of the three measurements at low solute mole fractions is reported. For the system (CO 2+ water), where the solute and the solvent only exhibit either proton or carbon atoms (oxygen was not measured), no direct determination of the solute mole fraction from the NMR spectrum is possible. Therefore, the solute pressure was used instead of the mole fraction to check the concentration- 165 dependence as well as to determine the diﬀusion coeﬃcient at inﬁnite dilution. The expanded, relative uncertainty is estimated as Ur(D1;exp i ) = 0:05 (k= 2) withkbeing a coverage factor. For the system (CO 2+ water), the expanded, relative uncertainty is estimated as Ur(D1;exp i ) = 0:1 (k= 2)based on a liter- ature comparison. 170 4.04.24.44.64.85.05.25.45.65.86.0 0 0.01 0.02 0.03 0.04 xCO2/ mol mol1109DCO2/ m2s1 4.04.24.44.64.85.05.25.45.65.86.0 0 0.002 0.004 0.006 xCH4/ mol mol1109DCH4/ m2s1 Figure 1: Self-diﬀusion coeﬃcients Diof CO 2(left) and CH 4(right) in toluene at 298.15 K at three diﬀerent mole fractions, respectively. The line indicates the arithmetic average number. 3. Semi-empirical methods for predicting the diﬀusion coeﬃcient at inﬁnite dilution Several methods for the prediction of diﬀusion coeﬃcients at inﬁnite dilution have been reported in the literature, many of which are based on the Stokes- Einstein equation [58, 59, 60, 61]. One of the most frequently used methods is 175 8 that of Wilke and Chang (WC) [53], which is given by Eq. (3). (D1;WC i=m2s1) =7:41012q solvent (Msolvent=gmol1) (T=K) (solvent=cP)(vi=cm3mol1)0:6(3) Here,D1;WC iisthepredicteddiﬀusioncoeﬃcientatinﬁnitedilution, Msolvent is the molar mass of the solvent, Tis the temperature, solventis the dynamic viscosity,viis the liquid molar volume of solute iat its normal boiling point and solventis the so-called association factor of the solvent. 180 More recently, Evans et al. have proposed a method that is given by Eq. (4) [54]. It is abbreviated as SEGWE (Stokes-Einstein-Gierer-Wirtz Estimation) by the authors which hints at the two equations from which it was derived, namely the Stokes-Einstein equation and an equation by Gierer and Wirtz [62]. (D1;SEGWE i=m2s1) =(kB=JK1)(T=K)h3 2+1 1+ i 6(solvent=Pas)3r 3(Mi=gmol1) 4(eff=gm3)(NA=mol1) =3s (Msolvent=gmol1) (Mi=gmol1) (4) Miis the molar mass of solute i,kBis Boltzmann’s constant and NAis 185 Avogadro’s constant. e = 619kgm3is an eﬀective density whose value was ﬁtted to literature data by the method’s authors. Data for the dynamic viscositysolventwere taken from DIPPR [63]. From the same database, data for the liquid molar volume of the solutes viat their normal boiling point were obtained, which are needed in the Wilke-Chang method. Furthermore, Wilke- 190 Chang requires data for the association factor of the solvent solvent. In this work, this parameter was obtained from a ﬁt to all available data on diﬀusion coeﬃcients at inﬁnite dilution in the Dortmund Data Bank [64]. CO 2has no normal boiling point, due to its high triple point pressure. Therefore, the liquid 9 molar volume of CO 2at the triple point was used instead. The numerical values 195 forviand solventusedinthisworkaresummarizedinTableA.1intheappendix. 4. Molecular Simulation Molecular dynamics (MD) simulations were performed using molecular mod- els of the studied components that were taken from the literature. All models belong to the class of rigid multi-center Lennard-Jones (LJ) models with super- 200 imposed electrostatic interaction sites: CH 4[65], CO 2[66], water [67], ethanol [68], cyclohexane[69], toluene[70], methanol[71]andacetone[72]. Mostofthese models stem from previous works of our group. The water model is known as TIP4P-water and one of the most widely used water models. There are many more molecular models for the substances that were considered here, but as our 205 main focus was on the PFG-NMR experiments, it was out of the scope of the present work to make a more comprehensive study of these molecular models. The unlike interaction parameters were calculated using the Lorentz-Berthelot combining rules, given in Eqs. (5) and (6) [73]: ij=i+j 2(5) ij=pij (6) whereijandijare the length and energy parameters describing the inter- 210 actionsbetweenunlikeLJsites iandjandi,j,iandjarethecorresponding parameters of the interactions between sites of the same type. The parameter can be adjusted to binary data but was set to = 1throughout the present work, except for the system (CO 2+ ethanol), as explained in more detail in the results section. All simulations were carried out using the simulation package 215 ms2 (version 3.0.0) [74]. The pure component input ﬁles were taken from the MolMod model data base [75]. In a ﬁrst step, the density was calculated in the isobaric-isothermal ensemble (NpT) for 298.15 K and 0.1 MPa. This was accomplished using 1.2 x 105 10 equilibration steps and 5 x 105production steps. The obtained density was 220 then used in a canonical ensemble ( NVT) simulation at the same temperature and composition. Here, 3 x 105equilibration steps and 106production steps were utilized in order to sample the velocity autocorrelation function. The self- diﬀusion coeﬃcients of all components in the mixture were calculated with the Green-Kubo formalism [76, 77, 78, 79, 80]: 225 Di=1 3NiZ1 0*NiX k=1vi;k(0)vi;k(t)+ dt (7) whereNiis the number of molecules of species iand the bracketed term is the ensemble average of the velocity autocorrelation function with vi;k(t)as the velocity vector of molecule kat a timet. The equations of motion were integrated with a ﬁfth-order Gear predictor- corrector numerical integrator. Velocity scaling and Anderson’s barostat were 230 used to maintain constant temperature and pressure. The integration time step was 2.92 fs and the sampling length of the autocorrelation functions, which are used to calculate the self-diﬀusion coeﬃcient, was 58.5 ps. The system size was 4000 molecules. The cutoﬀ radius for the explicit calculation of intermolecular interactions was 17.5 Å. For corrections to the LJ interactions at long ranges, 235 angle-averaging by Lustig [81] was applied. Electrostatic long-range interactions were accounted for by the reaction ﬁeld method with conducting boundary con- ditions. Statistical uncertainties were estimated with a block averaging method [82]. In order to obtain a reliable value for the diﬀusion coeﬃcient at inﬁnite dilu- 240 tion, the solute mole fraction was set to xi= 0:001molmol1. It is known from previous studies that this is suﬃcient to determine numbers for the diﬀusion coeﬃcient at inﬁnite dilution without the need for an extrapolation. 5. Results and Discussion Fig. 2 gives an overview of the results for the diﬀusion coeﬃcients at inﬁnite 245 dilution of CO 2and CH 4dissolved in water, ethanol, cyclohexane, toluene, 11 methanol, and acetone at 298.15 K that were obtained in the present work by experiments and molecular simulations. The results are compared to results from the two semi-empirical methods for the prediction of diﬀusion coeﬃcients at inﬁnite dilution described above, which are labeled here simply as Wilke- 250 Chang (Eq. (3)) and SEGWE (Eq. (4)). The corresponding numerical results are presented in Table 2. 0123456789 W EtOH CYC TOL MeOH ACE 109D1 CO2/ m2s1 0123456789 W EtOH CYC TOL MeOH ACE 109D1 CH4/ m2s1 Figure 2: Comparison of diﬀusion coeﬃcients at inﬁnite dilution D1 iof CO 2(left) and CH 4 (right) dissolved in water (W), ethanol (EtOH), cyclohexane (CYC), toluene (TOL), methanol (MeOH) and acetone (ACE) at 298.15 K. Data from the present work from experiments (blue) and molecular simulations (yellow) are compared to predictions from semi-empirical methods: Wilke-Chang (red) and SEGWE (green). The diﬀusion coeﬃcients of CO 2at inﬁnite dilution in the diﬀerent studied solvents increase in the order: water, ethanol, cyclohexane, toluene, methanol, acetone. That order is basically the same for the solute CH 4, except for the 255 fact that ethanol and cyclohexane are interchanged. Moreover, the diﬀusion coeﬃcients at inﬁnite dilution of the two solutes in the same solvent do not diﬀer much. This illustrates the predominant role of the solvent for the diﬀusion of light-boiling solutes. The similarities are quite astonishing considering the fact that the solutes diﬀer considerably in size, mass, and electrostatic properties 260 (CH 4is non-polar while CO 2has a strong quadrupole moment). The low values of the diﬀusion coeﬃcient at inﬁnite dilution that are found for water are a consequenceofthestronghydrogen-bondingnetworkofwater. Whencomparing the diﬀusion coeﬃcients in methanol and ethanol, two opposing eﬀects on the 12 Table 2: Diﬀusion coeﬃcients at inﬁnite dilution (no distinction between mutual and self- diﬀusion, cf. text) for CO 2and CH 4dissolved in water, ethanol, cyclohexane, toluene, methanol and acetone from experiments ( D1;exp i, exp. rel. uncertainty Ur(D1;exp i) = 0:05 (k= 2), for (CO 2+ water):Ur(D1;exp i) = 0:1 (k= 2)), molecular simulation ( D1;sim i, last digit uncertainty in parentheses), as well as from two semi-empircial methods: Wilke- Chang, cf. Eq. (3) ( D1;WC i) and SEGWE, cf. Eq (4) ( D1;SEGWE i). Temperature standard uncertainty: u(T) = 0:1 K. T D1;exp i D1;sim i D1;WC i D1;SEGWE i Solvent K 109m2s1 CO2 Water 298.15 2.00 1.6(2) 2.17 1.33 308.15 2.70 1.2(2) 2.77 1.69 318.15 3.49 2.3(2) 3.46 2.11 333.15 4.02 2.8(3) 4.67 2.85 Ethanol 298.15 4.16 1.7(4) 1.78 1.34 308.15 5.23 1.2(5) 2.22 1.67 318.15 5.88 3.5(6) 2.74 2.06 333.15 7.24 2.9(5) 3.68 2.77 Cyclohexane 298.15 4.35 2.9(6) 3.24 1.85 Toluene 298.15 5.30 5.7(7) 4.96 3.05 Methanol 298.15 5.62 3.5(4) 3.98 2.50 Acetone 298.15 6.75 6.9(9) 4.64 4.97 CH4 Water 298.15 1.73 1.7(3) 2.15 2.26 Ethanol 298.15 4.65 3.8(9) 1.76 2.37 Cyclohexane 298.15 4.07 3.4(12) 3.21 3.34 Toluene 298.15 5.32 6.1(13) 4.91 5.52 Methanol 298.15 5.94 6.0(6) 3.93 4.35 Acetone 298.15 8.23 8.4(14) 4.58 8.84 13 solute mobility must be considered: the hydrogen-bonding strength on the one 265 side and the size and mass of the solvent on the other, where the latter prevails. Comparing the results for the solvents cyclohexane and toluene, which have a similar size and mass, one ﬁnds higher diﬀusion coeﬃcients in toluene, probably due to the fact that the voids created by the rigidity of toluene facilitate the diﬀusion of the small solutes. The highest diﬀusion coeﬃcients are found in the 270 solvent acetone, which is comparatively small, not self-associating, and has only a moderately strong dipole. Figs. 3 and 4 give an overview of the available literature data for the stud- ied systems. For the systems with CH 4, a comparison with literature data is only possible for (CH 4+ water) and for (CH 4+ toluene) (cf. Supplementary 275 Material), for all other systems, no data on the diﬀusion coeﬃcient at inﬁnite dilution could be found in the literature. Abundant literature data are available for the systems (CO 2+ water) and (CH 4+ water). Also, for the systems (CO 2+ methanol), (CO 2+ ethanol) and (CO 2+ toluene) literature data from several sources are available. The 280 literature data often scatter considerably. The width of the band in which data for a given system and temperature are found is typically of the order of109m2s1, which is far above the uncertainty that is reported for the individual data sets. The range of the reported uncertainties varies considerably for some of the methods. The uncertainties are on average about ur= 0:03 285 which is comparable to the uncertainty of the PFG-NMR measurements in this work. Average uncertainties of ur= 0:03are reported for studies employing wetted surface absorbers (range over all