Absorption of pressurized methane in normal and supercooled p-xylene revealed via high-resolution neutron imaging

Supercooling of liquids leads to peculiarities which are scarcely studied under high-pressure conditions. Here, we report the surface tension, solubility, diffusivity, and partial molar volume for normal and supercooled liquid solutions of methane with p-xylene. Liquid bodies of perdeuterated p-xylene (p-C8D10), and, for comparison, o-xylene (o-C8D10), were exposed to pressurized methane (CH4, up to 101 bar) at temperatures ranging 7.0–30.0 °C and observed at high spatial resolution (pixel size 20.3 μm) using a non-tactile neutron imaging method. Supercooling led to the increase of diffusivity and partial molar volume of methane. Solubility and surface tension were insensitive to supercooling, the latter substantially depended on methane pressure. Overall, neutron imaging enabled to reveal and quantify multiple phenomena occurring in supercooled liquid p-xylene solutions of methane under pressures relevant to the freeze-out in the production of liquefied natural gas.

www.nature.com/scientificreports/ Experimental data on density, solubility, speed of sound, heat capacity, surface tension and viscosity have been so far reported for several supercooled liquids, chiefly water 3,10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] . With the exception of one investigation on the speed of sound and derived quantities for supercooled water 16 , the above studies report data observed at pressures near atmospheric or do not report experimental pressure. The common high-throughput methods for studying liquids under high-pressure conditions are the vibrating tube densimetry, pendant drop method, Taylor dispersion method, the method of capillary waves, methods utilizing Raman spectroscopy and Nuclear Magnetic Resonance [30][31][32][33][34][35][36][37][38][39][40][41] . To our knowledge, no report on their use for supercooled liquids under high pressures is available. We certainly admit that these or other methods can be applied to study the properties of supercooled liquids. For instance, Raman spectroscopy and Nuclear Magnetic Resonance were used for studies on the formation of natural gas hydrate under relevant conditions 42,43 . As we show in this study, our non-tactile one-pot neutron imaging method 44 is applicable for studying systems involving supercooled liquids exposed to pressurized gases.
In this work, methane (CH 4 ) absorption in liquid perdeuterated p-xylene (p-C 8 D 10 ) and o-xylene (o-C 8 D 10 ) was studied while this choice of isotopic composition exploits the high neutronic contrast 45 between protium (H) and deuterium (D). The influence of the isotopic composition on the physical properties of chemical species has been thoroughly reported for benzene rather than for the xylenes and appears low. For instance, the molar volume (molar mass over density) of perdeuterated benzene (C 6 D 6 ) differs by less than 0.24% from that of benzene (C 6 H 6 ) under conditions relevant for this study 46 ; see Supplementary Information (SI) for more discussion. Viscosity, melting point, boiling point and surface tension of perdeuterated benzene differ from those of benzene by 5% 47 , 1.0 °C 48 , 0.8 K 49 and 2% (− 0.5 mN·m −1 ) 50 , respectively. Systematical errors caused by using deuterated xylenes instead of the protium-based (normal) ones are expected to be comparable to those for benzene.

Results and discussion
Composition revealed using neutron imaging. Liquids were maintained at a constant temperature and exposed to a methane pressure step at the zero time in cylindrical cells 44 . Since the cells were axially symmetric (inner diameter 9.0 ± 0.1 mm), the onion-peeling algorithm 51 was used to provide the tomographic reconstructions at the central plane of the sample. The overall linear attenuation coefficient of the liquid (Σ) was contributed by the two components, A (CH 4 ) and B (p-or o-C 8 D 10 ). The Beer-Lambert law thus has the form Cross-sections (σ) of the pure components were evaluated based on the tomographic reconstruction observed just after the release of pressurized methane to the vessel with sample liquid by assuming negligible evaporation of the liquid and diffusion of methane to the bottom part of the liquid body (Fig. 1). Symbols I, N 0 and d are intensity, Avogadro number and length, respectively. The mole concentration (c) and density ( ρ ) of pure methane in the gas and supercritical fluid phase were calculated using the Peng-Robinson equation of state 52 . Evaporation of the xylenes was neglected 53,54 ; see SI for the assessment of the combined systematic uncertainty. For the liquid perdeuterated xylenes, mole concentration and density were calculated from the known equations www.nature.com/scientificreports/ of state for the pure p-and o-xylene (p-and o-C 8 H 10 ) liquids 46 by assuming that the molar volume of the deuterated and protium-based chemicals are equal (see SI for uncertainty estimation). Cross-sections and densities for the pure components at the studied conditions are listed in Table S1 in SI. In the case of supercooled p-xylene, density was calculated by extrapolating from the region of (normal) liquid. Since the cross-section of p-xylene held constant over all the inspected conditions, such extrapolation provided a meaningful approximation and supercooled p-xylene did not solidify as the solidification of p-xylene is accompanied with the change of density by about 20% 12 . The level of supercooling was assessed as the difference between the melting temperature and the actual temperature using the available literature data for the melting point of the protium-based p-xylene (p-C 8 H 10 ) under relevant conditions, see SI and Materials and Methods. It is substantial to note that the liquid swelled during methane absorption, which did not enable for the simplistic use of Beer-Lambert law, Eq. (1).
Phase interface, swelling, diffusion. The shape of the mobile axially symmetric phase interface in gravity (red curves in Fig. 1) was parameterized by solving the Young-Laplace equation in form 55,56 The boundary value problem, z'(r = 0) = 0 and z'(r = R) = cot(θ), was solved using the midrich method as in the Maple 2021 software package, r ∈ (0, R). Optimum values of the surface tension (γ) and contact angle at the wall of the cell (θ), and their uncertainty due to random errors (u r , cover factor 2) were calculated using Gauss-Newton and Bonferroni methods 57,58 , combined systematic uncertainty of surface tension was calculated using the law of uncertainty propagation (see SI). The density difference at the phase interface, ∆ρ, was calculated as follows.
The volume of the liquid (V) was calculated by computing the volume of the solid of revolution (see insert in Fig. 1), which is a generalization of an earlier method utilizing projections (photography in visible light) of phase interfaces in glass tubes without using the reconstruction of the central plane 59 . The partial molar volume of methane ( V A = ∂V /∂n A ) and its uncertainty due to random errors (u r , cover factor 2) were calculated based on the mole amount of absorbed methane ( n A ) in the entire liquid body and its volume at fixed T, p, and mole amount of the perdeuterated xylene ( n B ), see Fig. 2A and Table S4 in SI. The molar volume ( V m ) of the liquid and its density ( ρ ) depend on the mole fractions [

and molar masses (M) such that
where the partial molar volume of each perdeuterated liquid xylene was set to its molar volume.
The simultaneous measurement of the neutron attenuation and the shape of the liquid (and thus volume) enabled to derive the concentration distributions of both species (Fig. 3A) using Eqs. (1) and (3), constant mole amount of the xylene in the liquid was assumed. This, in turn, enabled to extrapolate the methane concentration in the xylene phase at the phase interface and thus to derive the respective density (Figs. 2B, 3A) needed for the Young-Laplace equation, Eq. (2). Moreover, the z coordinate (depicted in Fig. 1B) was transformed to the B-fixed coordinate ξ (Fig. 3B) along which mole concentration of the perdeuterated xylene ( c B ) is fixed.
Diffusion of methane in the axially symmetric liquid body ( Fig. 1) was modelled using Fick's second law in cylindrical B-fixed coordinates in form 60 www.nature.com/scientificreports/ where D is diffusivity in the B-fixed reference frame and ξ ranges from zero to the initial liquid level at a given radius. Concentration at the phase interface (Fig. 2B) and its shape (Fig. 1) were used for the construction of the Dirichlet boundary condition; impermeable walls of the cell were represented by Neumann boundary conditions. We have solved Eq. (4) using an explicit differentiation scheme 58 , and calculated optimum value and uncertainty due to random errors (u r , cover factor 2) of diffusivity (D) using Gauss-Newton and Bonferroni methods 57,58 . Fick's second law, Eq. (4), provided a good approximation of the experimental data (Fig. 3B).
Surface tension and solubility. The surface tension of the binary methane solutions with perdeuterated p-xylene (p-C 8 D 10 ) and o-xylene (o-C 8 D 10 ) showed a mild dependence on temperature and a strong dependence on (methane) pressure that followed one master trend irrespective of the supercooling and of the actual xylene isomer (Fig. 4, Table S3 in SI). Surface tension measured for the studied perdeuterated xylenes saturated with methane at 1.0 bar followed the correlations from the database for the pure protium-based xylenes 12 . Interestingly, no influence of the ongoing methane diffusion through the phase interface (Fig. 5A) on the surface tension   Table S3 in SI. Curves represent guides for the eye (A) and correlations for protium-based xylenes taken from the database 12 ; the blue part of the curve is the extrapolation for the supercooled liquid at 1.0 bar (B). www.nature.com/scientificreports/ was detected within the experimental uncertainty. Neither the liquid supercooling nor the actual isomer form of xylene (o-and p-) thus measurably influenced the methane adsorption on the phase interface, which appears insensitive to the concentration gradient in the liquid. Thus, the measurement of interfacial tension among liquid and gas (or supercritical fluid) does not apparently necessitate reaching the phase equilibrium. Methane solubility in the xylene phase at the interface was expressed using Henry's law in which H is the Henry's law constant; see 61 for more discussion. The Henry's constant for methane and p-xylene showed mild dependences on pressure and temperature, no influence of the liquid supercooling was observed to within the experimental uncertainty (Fig. 5B, Table S4 in SI, rel. u c (H ) ≈ 15%). Our data differed by about 4% from the only available literature datum 14  Diffusivity and partial molar volume of methane. Diffusivity and partial molar volume of methane both showed positive deviations from the master trends due to the supercooling of p-xylene, while no such deviations were found for control experiments with o-xylene that becomes supercooled at much lower temperatures (Fig. 6, Table S4 in SI). The higher deviations of both quantities were observed at the lowest explored pressure and temperature (average 44.8 bar, 7.0 °C). This suggests that i) supercooling of liquid p-xylene presumably leads to the molecular-level heterogeneity that facilitates diffusion of methane and reduces the free volume accessible to the methane molecules, ii) the dissolved methane disrupts this heterogeneity.

Conclusions
The supercooling of liquid mixtures of p-xylene (p-C 8 D 10 ) and methane (CH 4 ) led to the peculiar increase of the methane partial molar volume and diffusivity under pressures relevant to the p-xylene freeze-out in the production of liquefied natural gas (7.0-30.0 °C, 1.0-101.1 bar). Thus, methane diffused more readily in the supercooled solutions, which also showed higher swelling than the normal ones. Systems involving o-xylene (o-C 8 D 10 ) and not showing supercooling were studied for reference. Surface tension was influenced by temperature and pressure and was sensitive neither to the liquid supercooling nor to the isomerism of xylene (ortho, para), no impact of supercooling on the methane solubility was discerned. Our inherently non-tactile neutron imaging method enabled to observe the supercooled liquid bodies and to derive information on their composition and shape at a high spatial resolution (pixel size 20.3 μm). The provision of experimental data at conditions inherently relevant to applications can be fruitful for the community studying supercooled liquids on the molecular level. www.nature.com/scientificreports/

Materials and methods
The neutron imaging experiments were conducted at the NEUTRA beamline 65 66,67 . For the evaluation of the data from the first two respective series, ten data points were provided as an average of 10 images having the respective time stamp of the average time of the respective 10 images; for the latter series, the entire 50 images were averaged into a single data point having the time stamp of the average of the 50 images. The experimental setup was described in our previous study 44 and consisted of a pair of equivalent axially symmetric titanium measuring cells from which one was used for this study were placed in a duralumin block maintained at a constant temperature to within ± 0.2 °C using a Julabo F12-MA water circulator, the temperature was measured using a platinum resistance thermometer (Greissinger GMH 3710), the setup was placed in a duralumin box purged with nitrogen to avoid moisture condensation on the outer parts of the measuring setup. The cells were rinsed with acetone, vacuumed (< 0.01 Pa, Leybold D4B), and twice washed with the fresh sample liquid prior to the filling. One cell contained p-xylene (p-C 8 D 10 ), the other o-xylene (o-C 8 D 10 ) or a heterogeneous system consisting of water (the bottom phase) and p-xylene (p-C 8 D 10 ); data for the latter system will be published elsewhere. Chemicals and gases were used as obtained and are listed in Table 1. The interior of the apparatus was then purged, and the liquids were separately bubbled first with nitrogen and second with methane . Typical uncertainties of diffusivity and partial molar volume due to random error (u r , cover factor 2) are 0.3·10 -9 m 2 s −1 and 7 cm 3 mol −1 , respectively. Curves in (A) represent the Wilke-Chang model 61,63 with parameters from the database 12 (viscosity was temperature-extrapolated in the case of p-xylene supercooled at 1.0 bar) and with the association factors adjusted to 1.5. Green line in (B) shows mean over all non-supercooled systems (this work), literature data for the partial molar volume of methane in n-hexane at infinite dilution are shown 64 . Experimental data are listed in Table S4 in SI, sc abbreviates supercooled. Table 1. Used gases and chemicals, initial purity as in the certificate of analysis by the supplier unless indicated otherwise. # Chemical purity was not declared by the supplier and was determined using a GC-MS (Clarus 500, Perkin Elmer) with a capillary column containing Elite WAX ETR stationary phase (Perkin Elmer), value represents purity with respect to other C 8 aromatic hydrocarbons. www.nature.com/scientificreports/ at atmospheric pressure. Experiments included the steep change of methane pressure from atmospheric to a fixed value, which was maintained constant using a pressure reducer RSD 1 (Siad) to within 0.2 bar and sensed using a PXM409-175BAV (Omega) with a DP41-B control unit (Omega). Experiments were terminated by bubbling the liquid with methane at atmospheric pressure, which was done at 15.0 °C in the case of experiments below the normal melting point of p-xylene. The steep change of methane pressure in the cell inherently causes a shift of the melting temperature of the initially pure liquid p-xylene (p-C 8 D 10 ), which then changes as methane diffuses into the liquid. The degree of supercooling thus changes as methane diffuses through the liquid ( Fig. 1 and Table S3 in SI). The melting temperature of perdeuterated p-xylene (p-C 8 D 10 ) and p-xylene (p-C 8 H 10 ) were measured by immersing two ampules with the solidified compounds at atmospheric pressure (rest was air) into the water bath of the Julabo F12-MA water circulator, the temperature was measured using a platinum resistance thermometer (Greissinger GMH 3710). The normal (at 1.0 bar) melting temperature of perdeuterated p-xylene (p-C 8 D 10 ) was 14.1 ± 0.2 °C and that of p-xylene (p-C 8 H 10 ) was 13.3 ± 0.2 °C; the latter agrees with the value from the literature for p-xylene (p-C 8 H 10 ), 13.25 °C 12 . Hence, the melting temperatures of perdeuterated p-xylene (p-C 8 D 10 ) were considered to be by higher 0.8 °C than those for p-xylene (p-C 8 H 10 ) 14 also in the case of the solutions with methane. The pressure dependence of the melting point of pure p-xylene (p-C 8 H 10 ) was taken from the literature 68 , see Table S3 in SI for details.

Data availability
Experimental data are listed in Supplementary Information.