Fast and Simultaneous Determination of Gas Diffusivities and

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Fast and Simultaneous Determination of Gas Diffusivities and Solubilities in Liquids Employing a Thin-Layer Cell Coupled to a Mass Spectrometer, Part I: Set-up and Methodology Pawel Peter Bawol, Philip Heinrich Reinsberg, and Helmut Baltruschat Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b04319 • Publication Date (Web): 09 Nov 2018 Downloaded from http://pubs.acs.org on November 10, 2018

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Analytical Chemistry

Fast and Simultaneous Determination of Gas Diffusivities and Solubilities in Liquids Employing a Thin-Layer Cell Coupled to a Mass Spectrometer, Part I: Set-up and Methodology

Pawel Peter Bawol, Philip Heinrich Reinsberg and Helmut Baltruschat* Institut für Physikalische und Theoretische Chemie, Universität Bonn, Römerstraße 164, D-53117 Bonn, German

*Corresponding author: [email protected]

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Analytical Chemistry 1 2 3 4 5 6 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 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Transport properties and solubilities of volatile species in liquid solutions are of high interest in different chemical, biological and physical systems. In this work, a new approach for determining the diffusivity and solubility simultaneously is presented. The method presented relies on the diffusion of a volatile species through a thin, liquid layer and the subsequent detection of the species using a mass spectrometer. Evaluation of the time-development of the resulting transient yields the diffusion coefficient, while the concentration of the species in the liquid layer can be calculated from the steady state value of the flux into the mass spectrometer. Apart from the geometry of the thin-layer and the calibration constant of the mass spectrometer no additional or external data are required. Experimental results of the temperature-dependent solubility and diffusivity of oxygen in DMSO are presented in our companion paper Part II and serve as a proof of concept.

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Introduction Proper knowledge of the solubility and diffusion coefficients of volatile species in liquids was rarely as important as it is today with the growing interest in non-aqueous metal– air batteries1-5. Due to the variety of electrolytes employed for research and to rapid developments related to the electrolyte’s composition, as exemplarily illustrated by different articles regarding Li–air batteries

6-13,

there is a need for a method to

determine the relevant parameters sufficiently accurate, fast and ideally with small amounts of electrolyte. The latter might be of interest if the electrolyte itself is very expensive, which is the case for most of the ionic liquids used in metal–air research1416.

Methods currently used for the determination of the oxygen solubility in the context of metal–air batteries usually rely on a combination of volumetric and gravimetric measurements

17-19,

spectroscopic techniques, either directly detecting oxygen

detecting probes for oxygen

21,

mass spectrometric methods

20, 22, 23,

20

or

pressure

measurements24-26 and electrochemical techniques, which allow for the simultaneous determination of the solubility and diffusion coefficient27-30. It is noteworthy that the mass spectrometric determination of the oxygen solubility by Khodayari et al. also allows for the determination of the diffusivity, which is achieved by the changing hydrodynamic conditions upon changing the electrolyte flow rate22. Most of these methods need a rather large electrolyte volume owing to the limited sensitivity of the actual measurement devices or the conditions under which the solubility can be determined (e.g. flow-through cells). Regarding simultaneous determination of the solubility constant KH and the diffusion coefficient D, electrochemical techniques, such as chronoamperometry29, 30 are promising. Nevertheless, electrochemical techniques can only be applied if there is a reaction, which can be electrochemically followed within the potential window of the solvent, and some basic knowledge of the reaction 3



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mechanism is available (i.e. the number of electrons transferred per molecule). The latter often is not guaranteed in organic electrolytes due to the complex role of the dissolved salts in the reaction mechanism. Although determination of D in experiments under well-defined convective conditions do not explicitly rely on knowledge of a reaction mechanism, the precision of these experiments is usually unsatisfactory 31, 32. In this article we present a new method for simultaneously determining gas solubilities and diffusion coefficients using a thin-layer cell with a low electrolyte volume (down to 20µL) coupled to a differentially pumped mass spectrometer (MS). The diffusion coefficient can be determined by fitting a signal, which is simulated according to Fick’s second law, to the time-resolved MS signal observed after a sudden change in gas pressure, while the absolute concentration of volatile species in the electrolyte can be obtained from the steady-state value of the MS signal applying Fick’s first law of diffusion. Experimental section Thin-layer cell A sketch of the cross-section of the thin-layer cell used for determination of the solubility and diffusivity data is shown in Figure 1. Thin-layer cells in combination with DEMS have been previously used in electrochemical applications

33-35.The

upper cell

holder, which is connected to an oxygen containing chamber, and the lower cell holder, which is connected to the vacuum chamber of a mass spectrometer, are made of stainless steel, while the cell body itself is made from brass. Each cell holder contains a porous steel frit, which mechanically stabilizes the PTFE-membranes M1 and M2 and allows the gas transport from the gas reservoir into the liquid layer and from the liquid layer into the vacuum of the mass spectrometer. The porous PTFE-membranes (Goretex®, porosity of 50%, pore diameter 20 nm) separate the liquid phase in the cell body from the vacuum below and the gas phase above the solution. Water perfused 4


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tubes made from copper are attached to the holders to enable temperature control of the whole measurement set-up via a thermostat, with the temperature directly measured in a cavity within the cell body using a previously calibrated type K thermos element.

The cell body itself is constructed in a way that there is a small cavity of known height h (h = 700 µm) and radius r (r = 3 mm) between the upper membrane M1 and the lower membrane M2. The height of this cavity defines the thickness of the thin-layer. The two small capillaries (diameter 1 mm) are used as in- and outlet for the electrolyte.

Figure 1: Cross-section of the measurement cell. The upper cell holder is connected to an oxygen bottle, while the lower cell holder connects the cell body to the vacuum of a mass spectrometer. Two PTFE-

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membranes separate the liquid from the vacuum and the gas-phase and prevent leakage. Both membranes are mechanically stabilized by porous steel-frits flush-mounted into the cell holders. Copper tubes attached to the steel holders ensure proper temperature control of the whole set-up.

Set-up and Experimental Procedure The complete set-up consisting of the thin-layer cell, a differentially-pumped mass spectrometer (see MS in Figure 2, QMA 430, Pfeiffer Vacuum) and the gas cylinder including the connecting valves as well the pressure sensor (see P in Figure 2, TPG202, Pfeiffer Vacuum) is shown in Figure 2. The experiment proceeds as follows: First, the solution is introduced into the cell via the capillaries. Immediately after that, the volume below and above the cell is evacuated by opening V2 as well as V5 and V3. By this approach, the thin-layer of solution can be degassed (usually for 30 min) and additional contaminations from the ambient air are avoided. After that V2 is closed and V1 is opened to establish a connection between the high vacuum of the mass spectrometer and the cell.

Figure 2: Measurement Set-up. After introducing the solution into the measurement cell, it can be evacuated from below via valve V2 and from above via V5 and V3. The connection to the mass

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spectrometer (MS) is established via V1, while V4 and V5 connect the cell to a gas cylinder. By opening V4 with V3 and V5 closed, the vacuum tubes are filled with gas. After having closed V4, the abrupt opening of V5 leads to a slight decrease in pressure (as monitored by the pressure sensor P) and the gas can saturate the solution in the cell. The time-resolved detection of gaseous species in the MS is directly proportional to flow of gaseous species through the solution.

In the next step valves V5 and V3 are closed and the throttle valve V4 is opened, flushing the vacuum tube with oxygen from the gas cylinder. After closing valve V4 oxygen is then removed again via V3 and the procedure is repeated for at least three times to reduce possible contaminations arising from residual amounts of gas in the vacuum tube. After that, a certain oxygen pressure (usually 900 mbar) is adjusted via the help of pressure sensor P with closed valve V4. To start the measurement, V5 is abruptly opened and the flux of volatile species through the liquid layer into the mass spectrometer is measured with a time resolution of 20 ms. Due to the finite volume of the stainless steel holder connecting the cell and the valve V5, an almost instantaneous drop in pressure can be observed when V5 is opened, which gives us the starting point (t0) of the measurement. After approximately 150 s the steady state value of the ionic current is achieved, indicating the end of the measurement. As a first proof of concept, a transient of the oxygen signal in pure water is shown in Figure 3. With a theoretical thickness of 700 µm and the calibration constant of the mass spectrometer as determined via the electrochemical oxygen reduction reaction in a 0.5 M tetrabutylammonium perchlorate containing dimethyl sulfoxide

36

(K* = 25 x 10-6), the

diffusivity and solubility can be evaluated. The electrochemical cell we are using for the determination of K* is described in

35.

For a more detailed description of the

calibration procedure, see chapter “Calibration of the System for Determination of the Solubility” in the methods section. The resulting diffusivity of 20.1x10-6 cm²/s and solubility of oxygen 1.42 mM at a temperature of 20 °C are in close agreement with values reported in the literature (c =1.39 mM37, 38, D(O2) =  19.6x10-6 cm²/s 39, D(O2) =  20.1x10-6 cm²/s 40).

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900 880 120

n(O2) / pmol/s

100

.

80 60

experiment (H2O, T=20 °C)

40

simulation -6 2 (D=20.1·10 cm /s, 1.42 mM, d=700 µm)

20 0 0

25

50

75

100

125

150

time / s

Figure 3: A typical example of a measurement obtained in ultrapure water (18.2 MΩ cm) at 20 °C. The upper part of the figure shows the oxygen pressure within the tubes over membrane M1. The starting point of the measurement can be set through the sudden oxygen pressure drop. The lower part shows the measured flux transient of mass 32 together with a simulated transient.

Results and discussion Evaluation of the Solubility and Diffusivity For determination of the diffusivity of the gaseous species, analysis of the timedependent development of the concentration gradients (Figure 4 a) or the transients of

time

0

distance within the cell

(b)

into the MS

vacuum of the MS

(a)

flux of the investigated species

the ionic currents is necessary (Figure 4 b).

gas

1 2 3 4 5 6 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 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

p(O2) / mbar


h

time

Figure 4: Concentration gradients within the thin-layer and the resulting current transient.(a) Concentration gradients for different times t. The concentration at x = 0 always equals the equilirbium concentration c0, while the one at x = h remains 0. (b) Resulting current transient of the flux of the investigated species into the vacuum of the MS. The arrows indicate the points in the transients resulting out of the concentration profiles in (a).

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Mathematical treatment of this planar diffusion problem was carried out by Aiba based on the work of Carslaw and Jaeger 41, 42. The most important boundary conditions are as follows: The concentration at the boundary between gas and liquid (x = 0, Figure 4 a) equals the equilibrium concentration; the concentration at the boundary between liquid and vacuum (x = h, Figure 4 a) is 0 (and thus, the partial pressure of the gas in the vacuum is sufficiently close to 0 on a linear scale, even though the exact partial pressure of the gas has to be non-zero in order to be able to measure a signal in the MS). This implies both, absorption and desorption are arbitrarily fast compared to diffusion of the gas in the liquid and the partial pressure of the gas at the vacuum side is close to zero. Furthermore, the pressure at x = 0 is assumed to be constant, which is true due to the large amount of gas contained in the tubing (50 mmol) as compared to the low flow rates (in the range of 10-10 mol/s). It is noteworthy that the diffusion problem differs significantly from semi-infinite diffusion problem invoked in the derivation of the well-known Cottrell equation, where the initial concentration at the electrode’s surface equals the bulk concentration and thus, a current signal is observed immediately after a change in potential (which is the analogy to the change in pressure). Applying the different boundary conditions and treating the problem in terms of a 1D planar diffusion problem a series expansion is obtained describing the transient of the flux (eq. (1))43: 



n 1



 (t )  1  2 (1) n exp  ( n) 2

t   6tc 

(1)

With  (t ) as the normalized flux, n as a natural number, t as time measured in the experiment and tc is defined as:

h2 6tc  D 9


(2)


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In eq. (2) h is the thickness of the layer and D represents the diffusion coefficient. To obtain the diffusion coefficient D, current transients with different values for D were simulated (n = 25) and fitted to the experimental current transients via the least square method. The thus calculated diffusion coefficient can be used to evaluate the solubility or rather Henry’s constant by applying Fick’s first law of diffusion (3), which correlates the flux of volatile species (J) to the diffusion coefficient D, the opening for the gas at the site of the MS with a cross section area of A and the concentration gradient at x = h:

 c  J  D  A   x  x  h

(3)

Although the theoretical steady-state maximum of the flux is never achieved, the current after 110 s equals already 99 % of the maximum flux and can be interpreted as a steady-state value, for which the concentration gradient is approximately linear between x = 0 and x = h (see red pictured gradient in Figure 4 (a)). Therefore, eq. (3) can be simplified, directly yielding a relation between gas solubility c and the steadystate ionic current (Imax): c

h  I max D  A K o

(4)

The constant Ko is a calibration constant of the mass spectrometer containing the ionization probability of the investigated species and can be determined in different ways. From the concentration c and the partial pressure p the Henry constant KH can be calculated according to:

KH 

c p

(5)

Calibration of the System for Determination of the Diffusivity Although it is not required theoretically, for practical purposes proper determination of the thickness of the layer h is useful to increase accuracy of the diffusion coefficients. 10


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Therefore, the following procedure was used for calibration: Ultrapure water (18.2 MΩ cm) was introduced in the cell and a pressure step experiment as described above was performed. From the time-dependent current transients and the diffusion coefficient of oxygen in water at 20 °C (D = 20.1*10-6 cm2s−1)40 the thickness of the cell can be evaluated. The thus obtained thickness h equals h = (693 ± 13) µm, where the uncertainty reflects the t-distributed standard error of mean of a series of 7 independent experiments. This value is in excellent agreement with the approximately 700 µm thickness obtained by a simple length measurement. Calibration of the System for Determination of the Solubility According to eq. (4) for the determination of the solubility c the knowledge of the calibration constant of the mass spectrometry system K0 as well as the cross sectional area A is needed. While A and h can be manufactured with relatively high precision, Ko has to be determined in an external experiment. The calibration constant Ko can either be evaluated from the correlation of the ionic current and the known flux of the specific gas under investigation through a throttle valve in terms of a calibration leak experiment44, by using a solvent in which the equilibrium concentration as well as diffusivity of the gas is known or by performing an electrochemical reaction of known stoichiometry 45. The latter approach only yields the calibration constant K*, which has to be multiplied with Faraday’s constant to yield Ko 44. The calibration leak experiment directly gives Ko, but does not yield information about A and h. In this study, Ko has initially been determined by using the electrochemical oxygen reduction in 0.5 M TBAClO4 in DMSO with an experimental setup described in 35. It is known, that in this electrolyte system the electrochemical reduction of oxygen quantitatively yields superoxide36:

O 2  e  O 2

11


(6)


Therefore out of a correlation of the faradaic current measured for reaction (6) to the leak of the oxygen signal detected via mass spectrometry, the value of K

*

was

determined with 2.38 C mol−1.. To account for changes in the calibration constant due to aging of the filament, the oxygen solubility in pure DMSO at 19 °C was determined before every measurement and was used as an internal reference. This allowed us to see changes in Ko and correct our determination of the solubilities. Furthermore, these measurements in pure DMSO showed that the shape of the transients did not change even after 130 days (see Figure 5). This is an indication of the reproducibility and the quality of the performed experiments.

1.0

normalized flux of O2

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0.8 0.6 0.4

reference 130 days after reference

0.2 0.0

0

50

t/s

100

150

Figure 5: Typical transients obtained in pure DMSO at 19 °C. The curve in red was obtained 130 days after the black curve. Most of the experiments have been carried out within this time-frame.

Conclusions A new thin-layer cell for determination of temperature-dependent diffusivities and solubilities of volatile species in liquid phase coupled to a mass spectrometer is presented. A major advantage of this cell as compared to e.g. electrochemical measurements is that the diffusivity and solubility can be measured simultaneous without any external knowledge. Moreover, the duration of a single run is below five minutes enabling the cell for high throughputs. 12


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The measurement contains the following steps: Initially, the thin-layer is evacuated from both sides to remove any residual, volatile species. The diffusivity is subsequently determined by applying an abrupt change in the pressure of the (gaseous) analyte and evaluating the transient signal in the mass spectrometer. Finally, from the steady state value of the transient and the calibration constant of the mass spectrometer the solubility can be calculated. Acknowledgements The authors gratefully acknowledge financial support by the German Federal Ministry of Education in the framework of the LiBaLu-project (grant number: 03XP0029A), which is part of the “Vom Material zur Innovation”-initiative and the MeLuBatt-project (grant number: 03XP0110D). P.H.R. wishes to thank the National German Merit Foundation. Notes German patent applied for the measurement cell (DE 10 2017 128 269.6).

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Fast and Simultaneous Determination of Gas Diffusivities and

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