Binary Diffusion Coefficients of the Liquid Organic ... - ACS Publications

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Binary Diffusion Coefficients of the Liquid Organic Hydrogen Carrier System Dibenzyltoluene/Perhydrodibenzyltoluene Andreas Heller,† Michael H. Rausch,†,‡ Peter S. Schulz,§ Peter Wasserscheid,§,∥ and Andreas P. Fröba*,†,‡ †

Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, D-91052 Erlangen, Germany ‡ Department of Chemical and Biological Engineering, Institute of Engineering Thermodynamics (LTT), University of Erlangen-Nuremberg, Am Weichselgarten 8, D-91058 Erlangen, Germany § Department of Chemical and Biological Engineering, Institute of Chemical Reaction Engineering, University of Erlangen-Nuremberg, Egerlandstraße 3, D-91058 Erlangen, Germany ∥ Helmholtz-Institute Erlangen-Nuremberg for Renewable Energies, IEK-11, Forschungszentrum Jülich, Nägelsbachstraße 59, D-91058 Erlangen, Germany S Supporting Information *

ABSTRACT: Liquid organic hydrogen carrier (LOHC) systems constitute a very promising concept for future hydrogen storage and logistics. The concept builds on the conversion of excess renewable energy to hydrogen via electrolysis followed by reversible catalytic hydrogenation/dehydrogenation of a diesel-like organic carrier molecule. For an ideal design of the catalytic process, insight into reaction mechanisms and kinetics but also precise knowledge on mass transport properties are necessary. In the present study, binary diffusion coefficients in selected binary LOHC mixtures with five different compositions of perhydrodibenzyltoluene (H18-LOHC) and dibenzyltoluene (LOHC) were measured by dynamic light scattering (DLS). The compositions were defined by mixing appropriate amounts of LOHC and H18-LOHC to realize different hydrogenation degrees of the LOHC. Binary diffusion coefficients were investigated over a temperature range from (264 to 571) K with an absolute uncertainty of (3 to 25) %. Moreover, an empirical equation describing the binary diffusion coefficients of all five mixture compositions over the complete temperature range with a root-mean-square deviation of less than 3 % was established. It was observed that the binary diffusion coefficient is independent of the hydrogenation degree of LOHC at temperatures above 430 K. For lower temperatures, the binary diffusion coefficient increases with decreasing degree of hydrogenation.

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INTRODUCTION

A very promising idea that largely avoids new infrastructure for handling pure hydrogen and builds on existing storage facilities for liquid fuels for a future hydrogen economy is the reversible binding of hydrogen onto unsaturated organic liquids. This concept, known as Liquid Organic Hydrogen Carrier (LOHC) systems,3−5 is based on the conversion of excess renewable energy at energy-rich times to hydrogen via electrolysis followed by catalytic hydrogenation of LOHC compounds. The hydrogen-rich LOHC compound can be stored6 and transported7 in large quantities with no energy losses over time for a later release of hydrogen and energy on demand at energy-lean times or energy-lean places. The LOHC material itself can be used in many repeated hydrogenation− dehydrogenation cycles and acts like a liquid container for the stored hydrogen. Therefore, reversible binding of hydrogen to

In the context of using an increasing share of renewable, unsteady energy sources, chemical energy storage technologies have gained increasing attention from society and scientists.1,2 They are attractive to align the intermittent electricity production from wind turbines and photovoltaic to the consumption profile. Due to its high gravimetric storage density of 33.3 kWh·kg−1, hydrogen is considered as a sustainable energy carrier. Furthermore, the whole energy storage cycle based on hydrogen, which includes electrolysis using renewable electricity and energetic use in fuel cells or hydrogen combustion engines, represents a zero-emission process. The volumetric energy density of hydrogen is, however, very low (3 kWh·m−3, at ambient conditions). Even in compressed form (CGH2, 70 MPa H2 corresponds to 1.3 × 103 kWh·m−3) or in form of liquefied cryogenic hydrogen (LH2, liquid H2 at 20 K corresponds to 2.4 × 103 kWh·m−3), the volumetric storage density of elemental hydrogen is still quite limited. © XXXX American Chemical Society

Received: August 3, 2015 Accepted: November 5, 2015

A

DOI: 10.1021/acs.jced.5b00671 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

liquid organic molecules is ideally suited for decentralized energy storage scenarios.8 Among the known LOHC systems, the system dibenzyltoluene/perhydrodibenzyltoluene is particularly attractive.9 It is based on a commercial heat transfer oil consisting of dibenzyltoluene isomers, which is marketed for this purpose, e.g., under the trade name Marlotherm SH. This brings along many practical advantages such as known toxicology, high thermal stability, and well-known and very favorable physicochemical properties. In addition, the hydrogen capacity of the LOHC system dibenzyltoluene/perhydrodibenzyltoluene is 6.2 wt %, which corresponds to a maximum energy content of perhydrodibenzyltoluene of 2.05 kWh·kg−1. Full conversion from a thermodynamic point of view can be achieved at moderate hydrogen loading and release conditions. The boiling points of all components of the LOHC system are high (bp(dibenzyltoluene) = 663 K)10 and thus enable the production of very pure hydrogen in the hydrogen release process by simple condensation of evaporated LOHC from the product gas stream. Flammability and other safety-relevant data are, e.g., more favorable than for diesel fuel.8 The price of dibenzyltoluene at industrial scales is below 5 €·kg−1, and its availability in even larger amounts than produced today is guaranteed by its synthetic origin from toluene. Precise knowledge on transport properties is the key for an optimized design of catalyst materials and the hydrogenation or dehydrogenation processes for LOHC systems. Physicochemical properties for dibenzyltoluene, however, had been collected in the past with a clear focus on the application as industrial heating oil. Due to the resulting lack of mass transport property data for this and other LOHC systems, important processes such as the hydrogen uptake reaction could not be fully described as either diffusion or reaction limited so far.11−13 In the present study, dynamic light scattering (DLS) is used to measure molecular binary diffusion coefficients D12 of binary mixtures consisting of dibenzyltoluene (LOHC) and perhydrodibenzyltoluene (H18-LOHC) over a temperature range from (264 to 571) K. These data should allow for a better insight into the dynamics of the hydrogenation and dehydrogenation processes of this LOHC system.

G(2)(τ ) = (ILO + It + Ic)2  background + 2ILOIt exp( −τ /τC,t) + 2ILOIc exp( −τ /τC,c)  heterodyne term + It2 exp( −2τ /τC,t) + Ic2 exp(− 2τ /τC,c)  homodyne term + 2ItIc exp( −τ /τC,t − τ /τC,c)  (1)

cross term

Here, ILO is the intensity of reference light or a so-called local oscillator. The heterodyne term in eq 1 will only be observed in case the reference light is coherently superimposed with the scattered light. It and Ic denote the scattered light intensities caused by temperature and concentration fluctuations. The homodyne and the cross term result from the scattered light of the sample. The heterodyne and the homodyne term are characterized by decay times of fluctuations in temperature and concentration, τC,t and τC,c. For a multitude of binary fluid mixtures, thermal diffusivities and binary diffusion coefficients differ by 2 to 3 orders of magnitude. Thus, the corresponding DLS signals in time-dependent CFs appear on different time scales. In this case, both transport properties can be separated by choosing an appropriate scattering geometry. The decay time τC,c , which is equivalent to the mean lifetime of the concentration fluctuations observed, is related to the binary diffusion coefficient D12 by

D12 =

1 τC,cq2

(2)

In eq 2, q is the modulus of the scattering vector, 4πn q = |k ⃗i − k S⃗ | ≅ 2ki sin(ΘS/2) = sin(ΘS/2) λ0

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METHODS The principles of DLS for the determination of transport and other thermophysical properties are described in detail elsewhere.14−16 Here, only the essential features relevant for the present study are presented. DLS analyses the temporal behavior of scattered light intensity originating from bulk fluids. The underlying scattering process is governed by microscopic fluctuations in temperature, in pressure, and in species concentration in the case of mixtures. The decay of the hydrodynamic modes present in binary fluid mixtures follows the same laws which are valid for macroscopic systems. Thus, the relaxation of temperature fluctuations is related to the thermal diffusivity a. In the case of binary fluid mixtures, the decay of concentration fluctuations reflects the binary diffusion coefficient D12. Whether it is possible to determine signals from concentration fluctuations mainly depends on the difference between the refractive indices of the pure mixture components and their concentration. The mean decay times of the two hydrodynamic modes are calculated from the time-dependent correlation function (CF) of the intensity of scattered light. The most general form of the intensity CF G(2)(τ) is

(3)

which is defined by the difference of the wave vectors of incident and scattered light, ki⃗ and kS⃗ . Assuming elastic scattering (ki ≅ kS), the modulus of the scattering vector is given in terms of the fluid refractive index n, the laser wavelength in vacuo λ0, and the scattering angle ΘS. Due to the large number of parameters in eq 1, it is very difficult to obtain the decay time τC,c. The problem is simplified if heterodyne conditions can be arranged experimentally, i.e., It ≪ ILO and Ic ≪ ILO. Furthermore, by a good choice of the scattering angle and thus the scattering vector, the term related to thermal fluctuations in eq 1 will not be resolved by the detection scheme. Thus, the normalized CF as observed in the experiment is reduced to one exponentially decaying function reflecting the mean lifetime of concentration fluctuations according to g(2)(τ ) = b0 + b1 exp( −τ /τC,c)

(4)

The experimental constants b0 and b1 include both the corresponding terms from eq 1 and effects caused by the imperfect signal collection due to incoherent background and the finite detector area. B



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Article

EXPERIMENTAL SECTION

Materials and Sample Preparation. Marlotherm SH (LOHC) is a mixture of isomers of dibenzyltoluene and was purchased from Sasol Germany GmbH and used as received. The LOHC was hydrogenated for 16 h at 423 K and a H2pressure of 3 MPa using cylindrical catalyst pellets consisting of 0.5 wt % Ru/Al2O3. The hydrogenation degree of perhydrodibenzyltoluene (H18-LOHC) was found to be > 99 %, which was confirmed by 1H NMR spectroscopy without solvent and elementary analysis; see Figure S1 in the Supporting Information. For NMR spectroscopy, the areas of the signals at low field (aromatic area) were compared with those at high field (aliphatic area). Results of elementary analyses of H18LOHC were 86.72 % C and 13.28 % H (calc. 86.82 % C; 13.18 % H). The uncertainty in the determined hydrogenation degree can be estimated to be 0.5 % on a 95 % confidence level. Samples with different hydrogenation degree were obtained by mixing appropriate amounts of LOHC and H18-LOHC. Five different mixture compositions consisting of LOHC and H18LOHC were investigated over a temperature range from (263 to 573) K. All DLS experiments were performed at atmospheric pressure. The mixture composition is assumed to be constant over the whole temperature range, because the vapor pressure of pure LOHC is less than 20 kPa at 573 K.17 The different compositions were realized by weighing the pure components with a balance (Sartorius, BP110S) with a precision of 0.1 × 10−6 kg and an estimated expanded uncertainty (k = 2) of 1 × 10−6 kg. Table 1 summarizes the investigated samples including the masses of the pure components.

Figure 1. Applied optical setup.

filters (PF) and one interference filter (IF). With the setup, a scattering angle ΘS of 90° is realized. The scattering angle ΘS is adjusted employing the back-reflection originating from the walls of the used cuvette. The precision of the adjusted scattering angle is estimated to be ± 0.2° on a confidence level of 95 %. Two stops (P1, P2) with a distance of about 0.5 m are installed behind the cuvette defining the detection direction. The resulting signal is detected by two photomultiplier tubes (PMTs). During the experiment, the pseudocross CF is calculated by a digital single-tau correlator (ALV GmbH) featuring equally spaced correlation channels. About 3 cm3 of the sample were transferred into square cuvettes made of quartz glass with a cross section of 1 cm2 and a volume of 3.5 cm3. In the low temperature regime from (263 to 350) K, the cuvette was inserted into a thermostated cuvette holder which is described in detail in a former study.18 This low temperature cuvette holder was temperature-controlled by a lab thermostat (Julabo CF41). At elevated temperatures above 350 K, a cuvette holder was utilized which exhibits the same geometry as the low temperature cuvette holder but was completely made of stainless steel. The high temperature cuvette holder is temperature-controlled by a high temperature lab thermostat (Julabo HT30) which is operated with a thermal oil stable up to 623 K. A Pt 100 Ω resistance probe (Heinz Messwiderstände GmbH) calibrated over a temperature range from (373 to 573) K with an absolute uncertainty of 0.04 K is used to measure the sample temperature. It is directly inserted into the sample through a bore in the top cover of the cuvette holders. The high temperature cuvette holder was initially insulated by a ceramic material. During the investigations, the porous ceramic insulation broke and was replaced by several layers of glass wool and aluminum foil. Both insulations provided a temperature stability of the sample of better than ± 0.1 K at about (530 and 570) K. In the lower temperature regime from about (373 to 498) K, the temperature stability was better than ± 0.05 K. The temperature stability in the temperature regime from about (264 to 353) K, where the low temperature cuvette holder was utilized, was better than ± 0.01 K. At temperatures below 284 K, the lab thermostat (Julabo CF41) was operated with ethanol. The refractive index nD at the sodium line (λD = 589.3 nm) and the refractive index difference nF − nC for the Fraunhofer lines F (λF = 486.1 nm) and C (λC = 656.3 nm) of the samples

Table 1. Specification of the Studied Mixtures Consisting of LOHC (MLOHC = 272.38 g·mol−1) and H18-LOHC (MH18‑LOHC = 290.53 g·mol−1)a LOHC

H18-LOHC

mole fraction

m/g

m/g

xLOHC/mol·mol−1

1.4961 11.8933 24.1909 36.8606 15.0057

14.3509 38.0801 25.8044 13.1120 1.7802

0.1001 0.2499 0.5000 0.7499 0.8999

(± (± (± (± (±

0.00006) 0.00002) 0.00002) 0.00002) 0.00007)

a

The combined expanded uncertainties Uc are Uc(m) = 0.001 g (level of confidence = 0.95).

Experimental Setup. A scheme of the optical setup used in this study is shown in Figure 1. A diode pumped solid state laser (Cobolt Samba) operated at 532.1 nm and 1000 mW output power is focused into a cuvette by mirrors (M) and a lens (L) with a focal length of f = 0.5 m. The path of the main beam is indicated by the solid line. Depending on the sample temperature, the intensity of the main beam was adjusted by a combination of a half-wave plate (λ/2 retardation) and a polarization beam splitter (PBS). At sample temperatures between (264 and 313) K, the laser power of the main beam was reduced to approximately 500 mW. The increasing density at lower temperatures causes an increase in the scattered light intensity. To fulfill experimentally heterodyne conditions here, the intensity of the main beam and thus the scattered light intensity originating from the fluid mixture was reduced. The reference beam which is superimposed with the scattered light originating from the sample is indicated by the dashed line. The intensity of the local oscillator is adjusted by two polarization C



Article

Figure 2. (a) Experimental CF for xLOHC = 0.5 at 273.9 K. (b) Experimental CF for the same mixture at 570.3 K.

sample at low temperatures promotes this kind of distortions of the CFs. It should be mentioned that, in experimental CFs, the signal originating from concentration fluctuations associated with D12 is superimposed with, but not changed by additional disturbing signals due to particles, incoherent external stray light, or convection in the sample. When a nonlinear regression is performed to find the experimental constants and decay times related to molecular diffusion, the theoretical model has to take these disturbances into account. In general, the disturbances can be expressed by a polynomial up to the third order. In the present study, where no particles or corresponding signals were observed visually or in the experimental CF, a linear term or a polynomial of second order was sufficient to be added to the theoretical CF, eq 4. A good description of each experimental CF by the selected fit model could be qualified by performing a multifit procedure introduced in an earlier study.19 In the CFs shown in Figure 2, the disturbances were already eliminated to get a good impression of the signals related to molecular diffusion of the mixture components. According to theory, DLS signals originating from thermal fluctuations are also present in the recorded CFs. Thus, the thermal diffusivity of LOHC was calculated based on density, heat capacity, and thermal conductivity data provided by the commercial producer Sasol.17 The calculated thermal diffusivities range from (85 to 43) × 10−9 m2·s−1 at temperatures from (273.15 to 633.15) K. At the applied scattering angle of 90°, corresponding thermal fluctuations would exhibit relaxation times between (75 and 170) ns at temperatures from (264 to 571) K. Relaxation times related to concentration fluctuations range from (0.5 to 1500) μs in this temperature regime. Thus, the two hydrodynamic modes related to the thermal diffusivity and the binary diffusion coefficient cannot be resolved simultaneously by the applied detection scheme.

were measured with an Abbe refractometer (Leo Kuebler, R 6000 G). The temperature of the samples was controlled with a lab thermostat within ± 0.02 K and measured by a mercury thermometer with an expanded uncertainty (k = 2) of 0.5 K. The refractometer was calibrated with water. Its expanded uncertainties (k = 2) in the measurement of the refractive index and the refractive index difference are estimated to be less than 0.0005 and 0.001. Data Evaluation and Experimental Procedure. As soon as a stable sample temperature was reached, two to five consecutive experimental runs were performed. Measurement durations varied from (5 to 60) min depending on mixture composition and temperature. Here, the mixture composition plays a minor role, because the refractive index difference between the pure components constituting the binary mixtures is sufficiently large to give rise to well-measurable light scattering intensities for all mixture compositions at a given temperature. Figures 2a and b exemplarily illustrate recorded CFs for the mixture composition xLOHC = 0.5 at (273.9 and 570.3) K. The uncertainty of the determined relaxation time τC deduced from a nonlinear regression applied to the experimental CFs strongly depends on the measurement duration. In the low temperature regime, measurement durations of (5 to 10) min were sufficient to achieve a low noise level in the CFs, whereas (40 to 60) min were necessary in the high temperature regime to achieve similar statistics. At temperatures of about (530 and 570) K, rapid sample coloration made long measurement durations impossible. This lead to worse signal statistics, see Figure 2b, and thus to higher uncertainties in the calculated relaxation time τC. In contrast, measurement durations of 5 min were sufficient at temperatures of (264 to 284) K, but vibrations induced by the lab thermostat influenced the recorded CFs. At these low temperatures, the time range in which the relaxation of concentration fluctuations is observed extends to 12 ms where also vibrations of the thermostat’s circulation pump are present. In this case, systematic oscillatory deviations in the residuals calculated from the nonlinear regression are visible, see the lower part of Figure 2(a). The increasing viscosity of the

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RESULTS AND DISCUSSION To access the binary diffusion coefficient, the scattering vector which is a function of the refractive index of the sample must be known; see eq 2 and 3. Thus, refractive index data nD and the D



Article

refractive index difference Δn = nF − nC of the investigated samples were measured in the temperature range from (293 to 347) K at atmospheric pressure. These data are summarized in Table S1 in the Supporting Information. The refractive index n can be described as a function of temperature T and the refractive index difference Δn by the linear equation ncalc = n0 + n1T +

Δn (λ − λD) Δλ

strong coloration of the sample was avoided, see Figure 3c. The D12 data obtained from the two experimental runs differ by less than 3 %, which is within the estimated combined measurement uncertainty (k = 2) of the individual measurements. Furthermore, the hydrogenation degree of the used sample as shown in Figure 3b was determined using NMR spectroscopy, see Figure S2 in the Supporting Information, and compared with results obtained for the untreated sample. The determined hydrogenation degrees of both samples differed by less than 0.5 %, which is within the combined measurement uncertainty. Significant influence of the minor oxidation process on the measured D12 data and the mixture composition can thus be excluded on the time-scale of our experiments. The tabulated D12 data for the xLOHC = 0.5 mixture represent the average values including the results from all experimental runs. Figure 4 shows that in the investigated temperature range, the D12 data of all mixtures strongly increase with increasing temperature and, according to Table 3, vary by 4 orders of magnitude. Such behavior is reasonable because the viscosity of LOHC varies from (321 to 0.41) × 10−6 m2·s−1 in the same temperature range. The binary diffusion coefficient can be represented well by the empirical equation

(5)

Here, T represents the temperature in K, λ the wavelength in m, and λD (= 589.3 × 10−9 m) the wavelength of the sodium vapor line. The coefficients n0 and n1 are calculated from a linear fit applied to the experimental data as a function of temperature. The fit coefficients and the mean dispersion (Δn·Δλ−1) for all mixtures are summarized in Table 2. Table 2. Coefficients of eq 5 and Mean Dispersion xLOHC 0.00 0.10 0.25 0.50 0.75 0.90 1.00

n0 1.6029 1.6220 1.6412 1.6658 1.6919 1.7121 1.7253

n1/K−1 −3.518 −3.869 −4.066 −4.056 −4.057 −4.098 −4.093

× × × × × × ×

Δn·Δλ−1/m−1 −4

10 10−4 10−4 10−4 10−4 10−4 10−4

−59663 −64095 −73092 −89308 −110744 −118350 −128161

⎛a a 2T ⎞ D12(T ) = a0 exp⎜ 1 + ⎟ 1 − a3T ⎠ ⎝T

(6)

To find the fit coefficients a0, a1, a2, and a3, the natural logarithm of the D12 data is fitted as a function of the inverse temperature. In the fit, the natural logarithm of each experimental datum was weighted according to its inverse expanded uncertainty. The first part in eq 6, which includes the fit parameters a0 and a1, represents the Arrhenius equation. The last part takes a convergence of the experimental data at lower temperatures into account. This term was adopted from a fit equation which was formerly used to describe thermal diffusivity data of refrigerants as a function of temperature.20 The resulting fit parameters as well as the root-mean-square (rms) deviation of the experimental data from eq 6 are summarized in Table 4. The lower part of Figure 4 shows that the relative deviations of the experimental data from the fits on the basis of eq 6 are clearly smaller than the expanded uncertainty. For all compositions, the rms deviation from the fit model is smaller than 3 %. A comparison between the different mixtures is given as a deviation plot; see Figure 5. Here, the D12 data of the mixture with xLOHC = 0.5 serves as a basis to which all other data of the mixtures with various compositions are compared. In the temperature regime from (430 to 571) K, the D12 data of all investigated compositions are within their combined measurement uncertainties. This observation shows that the diffusion process at temperatures above 430 K does not depend significantly on the hydrogenation degree. At temperatures below 430 K, the diffusion process accelerates with increasing concentration of non-hydrogenated LOHC. At about 293 K, for example, D12 in the mixture with xLOHC = 0.9 is nearly three times larger than in the mixture with xLOHC = 0.1. Thus, increasing binary diffusion coefficients with decreasing hydrogenation degree can be observed at lower temperatures. Such behavior of the binary diffusion coefficient as a function of temperature and mixture composition can only be compared with the viscosity of the pure components. While the viscosity of LOHC is well described as a function of

For the calculation of D12, the refractive index according to eq 5 is extrapolated to higher temperatures. To take the extrapolation up to 571 K into account, the relative uncertainty in the refractive index used for estimating the uncertainty in D12 is expanded from (0.03 to 0.3) %. The measured binary diffusion coefficients for all mixture compositions at the studied temperatures and atmospheric pressure are summarized in Table 3. The tabulated D12 data represent the mean values of the individual measurements for each temperature. The listed uncertainties correspond to the averaged expanded uncertainties (k = 2) calculated for each individual measurement by an error propagation analysis. Here, the maximum error (k = 2) is determined on the basis of the already specified estimated uncertainties in the scattering angle ΘS and in the refractive index n, as well as on the uncertainty in the decay time τC. The latter results from the nonlinear regression applied to the experimental CFs. Because the probing volume was not evacuated, all experiments were performed in the presence of air. Thus, a slight oxidation process started at temperatures higher than 450 K. It should be noted that in all LOHC applications oxygen is strictly excluded from the hot LOHC materials for stability and safety reasons. In our experiments, the oxidation process led to a coloration of the sample in contact with air and thus a worse DLS signal formation. According to the vendor, dibenzyltoluene is thermally stable up to 573 K, where at higher temperatures decomposition products can be formed. The stated technical applicability ranges up to 613 K.17 To study a possible influence of the coloration of the sample on the D12 data, the initially colorless sample, see Figure 3a, with xLOHC = 0.5 was investigated several times at elevated temperatures. First, experiments were performed from (352 to 493) K, where at the end of the experimental run the sample was strongly colored, see Figure 3b. Then, experiments were performed on a new sample of same composition from (493 to 352) K. The experimental durations were reduced to a minimum, such that a E



Article

Table 3. Binary Diffusion Coefficient D12 of Different Mixtures Consisting of LOHC and H18-LOHC Obtained by DLS as a Function of Temperature T at 0.1 MPaa T K

ΔD12b

D12 −12

10

2 −1

m ·s

−12

10

T

2 −1

m ·s

K

xLOHC = 0.1

293.30 312.83 332.36 351.90 372.4

5.83 25.6 68.4 138.1 243

0.2 0.7 2.3 5.5 20

412.0

562

51

451.6 490.7 531.2

1.06 × 103 1.78 × 103 2.9 × 103

115 170 930

264.46 273.92 283.35 293.19 312.81 332.43 352.36 372.3 392.0 411.9 431.6 452.3 473.2 492.6 530.8 570.3 293.24 312.87 332.41 351.94 372.4 412.1 451.9 491.8 531.8 570.5

xLOHC = 0.5 0.2054 0.917 2.848 6.90 25.48 63.5 124.8 215.1 339 491 662 904 1200 1.55 × 103 2.20 × 103 3.16 × 103 xLOHC = 0.9 15.14 44.30 95.28 170.9 280 583 1020 1.62 × 103 2.44 × 103 3.2 × 103

273.89 283.34 293.19 312.81 332.42 352.02 372.5 392.2 412.0 431.9 451.4 490.8 530.4 570.0

0.007 0.02 0.06 0.14 0.6 1.6 3.4 6.4 11 19 27 27 69 100 230 550

264.58 274.04 283.39 293.19 312.74 332.29 351.81 373.0 392.3 412.0 431.8 451.5 471.3 491.2 530.9 570.2

ΔD12b

D12 −12

10

2 −1

−12

m ·s

10

xLOHC = 0.25 0.564 2.211 6.26 24.38 63.8 129.1 228.4 360 525 733 968.1 1.68 × 103 2.39 × 103 3.5 × 103 xLOHC = 0.75 0.3552 1.484 4.122 9.30 31.35 73.3 138.8 241.3 362 512 707 912 1182 1448 2.29 × 103 2.91 × 103

m2·s−1

0.03 0.07 0.1 0.5 1.8 3.2 7.1 12 18 39 55 131 320 1200 0.01 0.03 0.08 0.2 0.7 1.6 3 7.3 11 16 24 34 62 56 290 250

0.4 1.1 2.7 6.1 10 21 58 120 310 1100

a

The combined expanded uncertainties Uc are Uc(T) = 0.01 K for T = (264 to 353) K, Uc(T) = 0.05 K for T = (372 to 571) K, and Uc(p) = 3 kPa (level of confidence = 0.95). bThe level of confidence of the combined expanded uncertainties Uc(D12) = ΔD12 is 0.95.

viscosities of both components constituting the binary mixture differ significantly, the diffusion process was found to slow down with increasing amount of the compound exhibiting the higher viscosity.

temperature, viscosity data of the hydrogenated form are very rare in literature. For hydrogenated dibenzyltoluene, only viscosity data measured by a rotation viscometer at two temperatures could be found.21 The viscosity of hydrogenated dibenzyltoluene at 313 K is four times larger compared to the viscosity of the non-hydrogenated form. At 373 K, however, the viscosity of the hydrogenated form is less than two times larger than the viscosity of the non-hydrogenated form. At temperatures where the viscosities of both hydrogenated and nonhydrogenated dibenzytoluene are comparable, it can be assumed that the binary diffusion coefficient is independent of the mixture composition. At temperatures where the

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CONCLUSION Binary diffusion coefficients of five different binary mixtures consisting of hydrogenated and non-hydrogenated dibenzyltoluene were investigated by DLS. For these systems, the DLS measurement technique proved to be a suitable tool for providing reliable binary diffusion coefficient data covering 4 orders of magnitude with an expanded uncertainty of (3 to 25) F



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Figure 3. (a) Sample with xLOHC = 0.5 before heating in presence of air. (b) Sample after investigations performed from (352 to 493) K. (c) New sample after investigations performed from 493 to 352 K with reduced measurement times. Figure 5. Deviation of experimental D12 data from the correlation (eq 6) for the mixture with xLOHC = 0.5: ●, xLOHC = 0.1; ■, xLOHC = 0.25; ⧫, xLOHC = 0.5; □, xLOHC = 0.75; ○, xLOHC = 0.9.

hydrogenation degree at temperatures above 430 K. At lower temperatures, the diffusion process accelerates with increasing concentration of non-hydrogenated LOHC. The reported data can contribute to an optimization of hydrogenation and dehydrogenation processes of the studied LOHC system. In a next step, DLS can be applied to study the molecular diffusion process of hydrogen in LOHCs for a deeper understanding and control of reaction kinetics in such systems.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00671. Refractive index data for the investigated mixtures. 1H nuclear magnetic resonance (NMR) spectra for H18LOHC directly after hydrogenation and for the mixture with xLOHC = 0.5 after measurements performed in a temperature range from (352 to 493) K (PDF)

Figure 4. Binary diffusion coefficient D12 of the studied mixtures consisting of LOHC and H18-LOHC as a function of temperature T at 0.1 MPa and relative deviation of the measured D12 from D12,calc data calculated according to eq 7: ●, xLOHC = 0.1; ■, xLOHC = 0.25; ⧫, xLOHC = 0.5; □, xLOHC = 0.75; ○, xLOHC = 0.9. Exemplary error bars for the experimental data in the lower part are calculated from an error propagation analysis.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +49-9131-85-29789. Funding

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative.

% (k = 2) for temperatures from (264 up to 571) K. An empirical equation was found to describe the D12 data of all mixtures over the complete temperature range with a rootmean-square deviation of less than 3 %. From the comparison between the D12 data obtained for the different mixture compositions, D12 turned out to be independent of the

Notes

The authors declare no competing financial interest.

Table 4. Coefficients of eq 6 and Root-Mean-Square (rms) Deviation of the Experimental Binary Diffusion Coefficient Data from the Correlation for the Studied Mixtures a0 xLOHC 0.10 0.25 0.50 0.75 0.90 a

10−12 m2·s−1 4.9180 4.4994 4.5005 3.3636 2.7517

× × × × ×

5

10 105 105 105 105

a1

a2

K

K−1

−2151.2 −1860.8 −1509.5 −1530.0 −1960.4

2.4449 4.0541 6.5759 5.6993 2.4789

× × × × ×

rmsa

a3 K−1 −3

10 10−3 10−3 10−3 10−3

4.0190 4.2473 4.5194 4.4936 4.2035

× × × × ×

% −3

10 10−3 10−3 10−3 10−3

2.3 1.7 2.5 2.2 1.2

Standard percentage deviation of D12 to the fit. G



■

Article

R417B from Dynamic Light Scattering (DLS). Int. J. Thermophys. 2012, 33, 396−411. (21) Horita, Y.; Fujimoto, K.; Hoshino, M.; Takito, T.; Muraki, M. Composition Suitable for Mechanical Power Transmission and Process for Operating Traction Drives. U.S. Patent 4,371,726, February 1, 1983.

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