Application of Ion Mobility Spectrometry for Permeability Studies of Organic Substances through Polymeric Materials

Drift tube ion mobility spectrometers (DT IMS) allow the concentration of different organic compounds to be measured. This gives the opportunity to use these detectors in measuring the penetration of various substances through polymer membranes. Permeation measurements of two substances (2-heptanone and dimethyl methylphosphonate (DMMP)) through a cylindrical silicone rubber membrane were carried out. The membrane separated the aqueous solution from the air. The analyte was introduced into water, and then its concentration in air on the opposite side of the membrane was recorded. Based on the dynamics of detector signal changes, the diffusion coefficients for both tested substances were determined. Determination of permeability coefficients was based on precise quantitative measurements, which took into account the non-linearity of the detector characteristics and the effect of water on detection sensitivity. The analysis of measurement results was based on a mathematical description of diffusion process.


Introduction
Polymeric materials (PM) are commonly used in technology and everyday human activity. The most important PM performance parameters are durability, elasticity and other mechanical properties. For some applications, properties such as the permeability for some chemicals and their solubility are important. This is particularly crucial for polymer packaging and protective coatings. A specific type of PM applications are membranes used for controlled transport of substances between two phases. They are successfully used in industry [1][2][3], as well as in medicine [4,5] and analytical techniques [6,7].
In the separation technology, membranes are thin layers characterized by permeability and selectivity. High selectivity allows for the enrichment or depletion of a specific component of a mixture.
There are three basic types of membranes: porous, dense and liquid. Membranes belonging to these groups differ not only in the structure but also in the mechanism of substances' penetration through them. In the case of porous membranes, separation can occur due to the fact that the particle sizes are comparable with pore sizes. In this case, selective permeation of the substance through the membrane is called the 'sieve effect' and can occur according to various mechanisms. For larger pore sizes, molecular diffusion is observed, and for micropores at low pressure, Knudsen diffusion occurs. For dense membranes, the separation of components is determined by the diffusion rate and the solubility of the component in the material. Membranes are made of amorphous polymers. sensitivity (detection limits below 1 ppb), selectivity and usefulness for detection of various compounds. IMS detectors are devices characterized by fast analytical signal generation (time constant of a few seconds) and the possibility of continuous operation. Our measurements were made for a hollow cylinder silicone membrane that separated the analyte-containing water solution from the air.

Theory
Penetration of the substance through dense polymeric materials occurs according to the aforementioned dissolution mechanism. The diffusion process determines the time-dependent distribution of the penetrating substance concentration in the polymeric material. In the simplest case, for homogeneous flat layers made of a dense polymer, the mass flow of the penetrant can be described by the first Fick diffusion law: where F is the penetrant flux density, defined as the amount of substance flowing through the surface unit in the time of 1 second, D is the diffusion coefficient, and C is the concentration of the penetrant in the membrane. In general, the concentration C and the flux density F are time dependent values. In steady state, for a membrane with a thickness of l, the flux density F ST of the substance penetrating through the membrane is described by the formula: where C 0 and C l are the penetrant concentrations in the membrane material on both sides of it. They are linearly dependent on the concentrations of C 0,ext and C l,ext in the environments separated by the membrane, with the proportionality constant, which is the solubility S, being the measure of the ability of the polymer for penetrant absorption: The permeability P of a given membrane material for given penetrant is defined as the amount of substance penetrating per area unit of the membrane with a unit thickness in 1 second, related to the difference in concentration in the media separated by the membrane: It follows from formulas (2), (3) and (4) that the permeability is a product of diffusion coefficient D and solubility S: Determination of the permeability coefficient based on the formula (4) can be performed for the equilibrium state. In this case, it is necessary to know the dimensions of the membrane, the value of the diffusion flux and the concentration values on both sides of the membrane. Determination of the diffusion coefficient can be made only on the base of the results obtained from dynamic measurements.
The most commonly used for considerations of the diffusion process is the assumption that the polymeric material is isotropic. Diffusion in such material occurs equally in all directions. Theoretical determination of concentration distribution is possible by solving the equation describing the second diffusion law: Solutions of this equation for different geometries can be found in many publications [39][40][41]. Sketches illustrating the process of penetration through a flat and hollow cylindrical membrane are presented in Figure 1a,b. Both cases are one-dimensional. The drawings also include formulas describing concentration distributions for zero initial condition and boundary conditions corresponding to constant concentration values on the edges. Shapes of the concentration distribution for flat and cylindrical membranes are different (Figure 1c). In order to determine the diffusion coefficient in flow experiments, the dependence of the diffusing substance mass flux on time is used. Values of flux at x = 0 for a flat membrane and r = a for a hollow cylindrical membrane were calculated by numerical differentiation of concentration distributions. The dependence of the diffusion flux shape on time for flat and hollow cylindrical membranes are shown in Figure 1d. These shapes are almost identical in both cases. This means that the flow experiment results obtained experimentally for a hollow cylindrical membrane can be carried out based on the formulas resulting from the mathematical model for a flat membrane. Solutions of this equation for different geometries can be found in many publications [39][40][41]. Sketches illustrating the process of penetration through a flat and hollow cylindrical membrane are presented in Figures 1a and 1b. Both cases are one-dimensional. The drawings also include formulas describing concentration distributions for zero initial condition and boundary conditions corresponding to constant concentration values on the edges. Shapes of the concentration distribution for flat and cylindrical membranes are different (Figure 1c). In order to determine the diffusion coefficient in flow experiments, the dependence of the diffusing substance mass flux on time is used. Values of flux at x = 0 for a flat membrane and r = a for a hollow cylindrical membrane were calculated by numerical differentiation of concentration distributions. The dependence of the diffusion flux shape on time for flat and hollow cylindrical membranes are shown in Figure 1d. These shapes are almost identical in both cases. This means that the flow experiment results obtained experimentally for a hollow cylindrical membrane can be carried out based on the formulas resulting from the mathematical model for a flat membrane. The analysis of the mass flux dependency of the penetrant through the membrane is often made using the so-called short-time approximation method. It is based on the solution of the diffusion equation (6) with the use of Laplace transform [39][40][41][42]. For short times it is possible to present the solution for mass flux density in the form: The analysis of the mass flux dependency of the penetrant through the membrane is often made using the so-called short-time approximation method. It is based on the solution of the diffusion Equation (6) with the use of Laplace transform [39][40][41][42]. For short times it is possible to present the solution for mass flux density in the form: Molecules 2020, 25, 2983

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The application of formula (7) to data obtained from the measurement of the mass flux allows the determination of the diffusion coefficient. It is crucial for determination of maximum value of the flux. Using formula (4) and knowing the maximum value of the flux F ST in steady state, one can determine the value of permeability.

Chemicals
Permeability tests were performed for a commercially available silicone tube-SILASTIC ® Laboratory Tubing (Dow Corning, Midland, MI, USA)-made of translucent, platinum hardened, tear resistant silicone. This type of tube is used in laboratory systems requiring flexible and temperature resistant connections, as well as where high purity of fluids flowing through the tubes is of great importance. Tubes with an outer diameter of 0.318 cm, an inner diameter of 0.198 cm and a length of 32 cm were used in this study.
Measurements of permeability and diffusion coefficient were made for two organic compounds: 2-heptanone (Sigma-Aldrich, Saint Louis, MO, USA, 99% purity) and dimethyl methylphosphonate (DMMP) (Alpha Aesar, GmbH, Germany, 97% purity). Water solubilities of these compounds are about 0.4 g/100 ml and about 10 g/100 ml, respectively. Water used in the tests was purified in the Hydrolab HLP5UV filter system (Wenk Labtec, Germany). The gas flowing inside the tube was air purified in a filter of 2000 cm 3 volume filled with molecular sieves with 1.0 nm pores diameter (Merck, Germany).

Instrumental
The detector used for measuring the flux of the substance permeating through the membrane was a drift tube ion mobility spectrometer (DT IMS). The operation principle of this detector is illustrated in Figure 2a. The detector consists of two parts: an ionization region in which ions are formed and a drift section where separation of ions occurs. Both parts are separated by a shutter grid that allows the narrow portion of ions to be introduced into the drift section. Two gas streams are introduced into the detector: carrier gas, which contains the sample, and drift gas. In most cases, purified air is used as the carrier gas and drift gas. The output signal from the DT IMS collector electrode (Figure 2b The scheme of the system used for the measurement of the flux of substance permeating through a hollow cylinder membrane is shown in Figure 3. The design of this system is similar to that presented in the work by Du [33]. The basic element of the system was a reaction kettle filled with water, inside which the tested tube was placed. The water temperature in the kettle was kept at 25 °C. By means of mass flow controller (mfc), 0.7 Ln/min of gas was introduced into the tube. The polymer membrane (silicone tubing) was submerged in water, into which the analyzed substance The DT IMS used in the study was designed and manufactured at the Institute of Chemistry, Military University of Technology in Warsaw. The detector is equipped with 63-Ni ionization source with an activity of approximately 15 MBq, which is placed in ionization region. Its length is 5.7 cm. The ionization region is separated from the drift section by a Bradbury-Nielsen shutter grid opened for a time of 0.150 ms with a repetition period of 25 ms. The drift section is 6.1 cm long, and the electric field in this section is equal to about 250 Vcm −1 . The inner diameter of the detector is equal to 3.6 cm. Laboratory air dried with molecular sieves with a pore diameter of 1 nm (Merck) was used as the carrier and drift gases.
The scheme of the system used for the measurement of the flux of substance permeating through a hollow cylinder membrane is shown in Figure 3. The design of this system is similar to that presented in the work by Du [33]. The basic element of the system was a reaction kettle filled with water, inside which the tested tube was placed. The water temperature in the kettle was kept at 25 • C. By means of mass flow controller (mfc), 0.7 Ln/min of gas was introduced into the tube. The polymer membrane (silicone tubing) was submerged in water, into which the analyzed substance was injected and mixed with a magnetic stirrer. The air passing through the tube was directed to the IMS detector via the DPT-21 humidity sensor (Czaki Thermo-Product). The analytical signal obtained from IMS detectors is strongly related to the water vapor content in analyzed gas. It significantly affects the ionization process. This involves the formation of hydrated cluster ions with a higher number of water molecules, which leads to the reduction of ionization efficiency. It has been proven [43,44] that with the increase of humidity there is a simultaneous decrease in peaks amplitude and a shift towards higher drift times. Due to these phenomena, it is necessary to control the water vapor concentration in the carrier gas. The scheme of the system used for the measurement of the flux of substance permeating through a hollow cylinder membrane is shown in Figure 3. The design of this system is similar to that presented in the work by Du [33]. The basic element of the system was a reaction kettle filled with water, inside which the tested tube was placed. The water temperature in the kettle was kept at 25 °C. By means of mass flow controller (mfc), 0.7 Ln/min of gas was introduced into the tube. The polymer membrane (silicone tubing) was submerged in water, into which the analyzed substance was injected and mixed with a magnetic stirrer. The air passing through the tube was directed to the IMS detector via the DPT-21 humidity sensor (Czaki Thermo-Product). The analytical signal obtained from IMS detectors is strongly related to the water vapor content in analyzed gas. It significantly affects the ionization process. This involves the formation of hydrated cluster ions with a higher number of water molecules, which leads to the reduction of ionization efficiency. It has been proven [43,44] that with the increase of humidity there is a simultaneous decrease in peaks amplitude and a shift towards higher drift times. Due to these phenomena, it is necessary to control the water vapor concentration in the carrier gas.
The measurement of the diffusion flux began when the analyte had been injected into the water filling the reaction kettle. From this moment, drift time spectra were recorded at 4 minutes intervals.
The tests were quantitative, and therefore, it was necessary to perform calibration measurements of the detector first. A gas mixtures generator was used in calibration studies. The generator system enabled the introduction of the analyte with a concentration of 0-20 ppb for 2-heptanone or 0-12 ppb for DMMP into the carrier gas. The mixture produced in the generator was moisturized in order to obtain the same water vapor content as during permeability tests.  The measurement of the diffusion flux began when the analyte had been injected into the water filling the reaction kettle. From this moment, drift time spectra were recorded at 4 min intervals.
The tests were quantitative, and therefore, it was necessary to perform calibration measurements of the detector first. A gas mixtures generator was used in calibration studies. The generator system enabled the introduction of the analyte with a concentration of 0-20 ppb for 2-heptanone or 0-12 ppb for DMMP into the carrier gas. The mixture produced in the generator was moisturized in order to obtain the same water vapor content as during permeability tests.

Results
The mass flux of the substance permeating through the membrane was measured for two organic substances: 2-heptanone and dimethyl methylphosphonate (DMMP). Figure 4a  in which the silicone tube was placed. The subsequent spectra show the appearance of analyte ion peaks and change in their amplitudes. The intensity of the reactant ions peaks also changes (decreases). The relationship between the peak areas and time is shown in Figure 4b. The numerically determined peak area of the reactant ions peaks was taken as a measure of the IMS detector signal and used for the calculation of the parameters characterizing the permeation through the membrane. The calibration curve measured with the gas mixtures generator is shown in Figure 4c. Measurements were made at the same water vapor content as during permeability tests. The mass flux dependence on time shown in Figure 4d was calculated on the basis of changes in the detector signal in time and the calibration curve. In this calculation, the value of the gas flow through the tube was taken into account.

Results
The mass flux of the substance permeating through the membrane was measured for two organic substances: 2-heptanone and dimethyl methylphosphonate (DMMP). Figure 4a presents drift time spectra recorded for 2-heptanone at different times from the introduction of the sample into the water in which the silicone tube was placed. The subsequent spectra show the appearance of analyte ion peaks and change in their amplitudes. The intensity of the reactant ions peaks also changes (decreases). The relationship between the peak areas and time is shown in Figure 4b. The numerically determined peak area of the reactant ions peaks was taken as a measure of the IMS detector signal and used for the calculation of the parameters characterizing the permeation through the membrane. The calibration curve measured with the gas mixtures generator is shown in Figure 4c. Measurements were made at the same water vapor content as during permeability tests. The mass flux dependence on time shown in Figure 4d was calculated on the basis of changes in the detector signal in time and the calibration curve. In this calculation, the value of the gas flow through the tube was taken into account. Determination of the diffusion coefficient for 2-heptanone was carried out using the short time method. Figure 5a is a graph of the dependence between ln(Ft 1/2 ) and 1/t calculated on the basis of mass flow measurement results. For times from 2000 to 5000 seconds, this dependence is linear. Based Determination of the diffusion coefficient for 2-heptanone was carried out using the short time method. Figure 5a is a graph of the dependence between ln(Ft 1/2 ) and 1/t calculated on the basis of mass flow measurement results. For times from 2000 to 5000 seconds, this dependence is linear. Based on formula (7), the diffusion coefficient was determined using the slope of the linear part of this dependence. For 2-heptanone it was 6.2 × 10 −8 cm 2 s −1 . The determined D value allows to calculate the theoretical mass flow (Figure 5b) and estimate its value for equilibrium state F ST . Basing on this value and using the formula (4), it is possible to calculate permeability P. Its value for 2-heptanone is 2.0 × 10 −7 cm 2 s −1 . The results for the second analyte (DMMP) were analyzed analogously. concentration equal to half of the steady state value was achieved after approximately 400 s. Based on theoretical considerations, it can be easily demonstrated that this corresponds to a Dt/l 2 value of 0.15, which, with the known time and membrane thickness, gives a diffusion coefficient value of 1.4•10 −6 cm 2 s −1 . It can be assumed that this value is underestimated due to the quite significant time constant of the humidity sensor. All values of diffusion and permeability coefficients determined on the basis of the measurements carried out are summarized in Table 1.  The accuracy of determining the diffusion coefficient is related to the precision of reproducing the shape (but not the amplitude) of the permeation curve. We estimate that the relative uncertainty of the calculated diffusion coefficient is no more than 20%. The uncertainty of determining the permeability coefficient is mainly determined by the accuracy of measuring the concentration of the analyte in the gas flowing inside the tube. The value of this uncertainty seems not to be greater than 10%.
Estimation of permeability and diffusion coefficient were also carried out for water. The water flux was measured using a capacitive humidity sensor. Measurement of water concentration in the air flowing through the tube allowed the permeability to be determined. Its value was equal to 4.3 × 10 −9 cm 2 s −1 . The diffusion coefficient for water was estimated based on the results of dynamic measurements. They involved the observation of changes in the water concentration in the air flowing through the tube after water was introduced into the reaction kettle. The shape of the dependence of water vapor concentration on time was similar to the curve shown in Figure 5b. Maximum value of water vapor concentration was equal to 230 ppm. This value was constant for times longer than 2000 s after introducing the water to the kettle. The value of water vapor concentration equal to half of the steady state value was achieved after approximately 400 s. Based on theoretical considerations, it can be easily demonstrated that this corresponds to a Dt/l 2 value of 0.15, which, with the known time and membrane thickness, gives a diffusion coefficient value of 1.4 × 10 −6 cm 2 s −1 . It can be assumed that this value is underestimated due to the quite significant time constant of the humidity sensor. All values of diffusion and permeability coefficients determined on the basis of the measurements carried out are summarized in Table 1.

Conclusions
Drift tube ion mobility spectrometer give the opportunity to measure the concentration of many organic compounds. This feature can be used in studies of the organic compounds' permeation through polymer materials.
The aim of the presented work was to test a new measurement system for studying the permeation of organic substances through polymer membranes. Until now, similar systems have been used only for analytical purposes, i.e., for checking if such membranes can be used for extracting the analyte from water. [43,44]. In our work, parameters describing the transport of chemicals in polymers, i.e., diffusion coefficients and permeability, have been determined. One should realize that in our studies the membrane separated the liquid phase from the gas. This has a significant impact on mass transport conditions. The obtained values of organic substances diffusion coefficients are relatively small. This may be due to the surface interaction of the penetrant with the polymer layer or to the fact that the polymer material is saturated with water. Relating the obtained results to literature data is difficult because the types of silicone rubber and research conditions are very different. The diffusion coefficient of methyl ethyl ketone (butanone) in the silicon membrane determined by Thiyagarajan et al. was 7.6 × 10 −6 cm 2 s −1 (at 40 • C) [45]. This is over 100 times more than the value determined based on our research. However, it should be noted that our measurements were made at a lower temperature, heptanone particles are much larger than butanone and that the structure (fillers, degree of cross-linking) of the polymer material was different. Water permeability is much lower than for organic substances. This is advantageous for membranes separating the DT IMS reaction area from the environment, as it limits the water concentration in the carrier gas. This allows the ionization efficiency of many analytes to be increased.
The concentration of organic substances in the aqueous solution was low (about 10 µg/g); however, with the use of a polymer membrane, effective detection was possible. This confirms the usefulness of silicone membranes in analytical applications, since they can be used to separate the reaction area of the detector from the environment.