Self-Diffusion in Confined Water: A Comparison between the Dynamics of Supercooled Water in Hydrophobic Carbon Nanotubes and Hydrophilic Porous Silica

Abstract

Confined liquids are model systems for the study of the metastable supercooled state, especially for bulk water, in which the onset of crystallization below 230 K hinders the application of experimental techniques. Nevertheless, in addition to suppressing crystallization, confinement at the nanoscale drastically alters the properties of water. Evidently, the behavior of confined water depends critically on the nature of the confining environment and the interactions of confined water molecules with the confining matrix. A comparative study of the dynamics of water under hydrophobic and hydrophilic confinement could therefore help to clarify the underlying interactions. As we demonstrate in this work using a few representative results from the relevant literature, the accurate assessment of the translational mobility of water molecules, especially in the supercooled state, can unmistakably distinguish between the hydrophilic and hydrophobic nature of the confining environments. Among the numerous experimental methods currently available, we selected nuclear magnetic resonance (NMR) in a field gradient, which directly measures the macroscopic translational self-diffusion coefficient, and quasi-elastic neutron scattering (QENS), which can determine the microscopic translational dynamics of the water molecules. Dielectric relaxation, which probes the re-orientational degrees of freedom, are also discussed.

Keywords: MCM-41; NMR; QENS; carbon nanotubes; molecule dynamics; supercooled water.

Figure 2

Temperature dependence of correlation times $\tau$ in bulk supercooled H₂O. Open squares (□) are rotational correlation times ${\tau }_R$ derived from ¹⁷O NMR data (Qvist et al. [67]), inverted triangles (▽) are translational residence times τ₀ obtained from quasi-elastic incoherent neutron-scattering data (QENS) (Teixeira et al. [61]), and the filled green squares (◼) along with the dashed line are the calculated translational correlation times ${\tau }_c$ using Equation (1) (see text). Upright triangles (∆) are the structural relaxation data of pulsed heated water films monitored using reflection-absorption IR spectroscopy (Kringle et al. [59]). The filled circles (●) and filled diamonds (◆) are MD simulations for the correlation times ${\tau }_c^{short}$ and ${\tau }_c^{long}$, respectively, according to Gallo et al. [47] and as presented by Lokotosh et al. [60]. Open circles (◯) are the dielectric (DS) relaxation times ${\tau }_D$ of supercooled water Bertolini et al. [64].

Figure 1

Temperature dependence of the inverse self-diffusion coefficient $1/D$ in supercooled bulk H₂O. Squares (□) (Holz et al. [44]) and circles (◯) (Price et al. [45]) represent the self-diffusion coefficient (D) obtained from pulsed field gradient NMR experiments. The solid line is the singular Speedy and Angell [1] power law fit to the experimental data. The dashed line is the continuation of the fit below 238 K to show the singularity of the power law. Inverted triangles (▽) are self-diffusion coefficients derived from growth rates of crystalline ice experiments (Xu et al. [46]). Diamonds (◊) (Gallo et al. [47]) and upright triangles (△) (Dueby et al. [48]) are self-diffusion coefficients derived from molecular dynamics simulations. The inset is an expanded temperature region around 238 K.

Figure 3

Temperature dependence of the inverse self-diffusion coefficient in supercooled confined H₂O. The orange line represents a guide to the eye for the available experimental data for bulk H₂O presented in Section 2.1 (filled inverted triangles (▼)). Filled circles (●) and filled diamonds (◆) represent the self-diffusion coefficient (D) obtained from QENS experiments of H₂O confined in single- and double-walled carbon nanotubes, respectively (Mamontov et al. [73]). Filled hexagons (), dark grey triangles (), and stars (★) are the D values of H₂O confined in SW 1.1 nm, MW 3.0 nm, and DW 3.5 nm, respectively, acquired via 2D D-T2 static field gradient NMR experiments (Gkoura et al. [74]). Inverted open triangles (▽) are the self-diffusion coefficients obtained from the pulsed field gradient NMR experiments of water confined in MCM-41 (Chen et al. [75]). Open circles (◯), open squares (□), and open upright triangles (△) are the self-diffusion coefficients obtained from static field gradient NMR experiments on water in open 2.8 nm, capped 2.8 nm, and capped 2.1 nm MCM-41 samples, respectively (Weigler et al. [76]).

Figure 4

Temperature dependence of the translational correlation times (residence times in QENS experiments) in supercooled confined H₂O. Filled circles (●) and filled diamonds (◆) represent the residence times ${\tau }_0$ obtained from QENS experiments of H₂O confined in single-walled (1.4 nm) and double-walled (1.6 nm) carbon nanotubes, respectively (Mamontov et al. [73]). Filled squares (◼) represent the residence times ${\tau }_0$ obtained from QENS experiments of H₂O confined in 1.6 nm double-walled carbon nanotubes Chu et al. [93]. Inverted filled triangles (▼) are the residence times obtained from QENS experiments of H₂O confined in MCM-41-S samples with a 1.8 nm pore diameter (Chen et al. [75]). Orange open squares (□) represent the residence times ${\tau }_0$ obtained from QENS experiments of bulk H₂O (Teixeira et al. [61]). The blue solid line is a guide to the eye for the calculated correlation times obtained from the NMR experiments by Holz et al. [44] and Price et al. [45] and for the growth rate from pulsed heating experiments by Xu et al. [46]. Upright triangles (∆) are the structural relaxation data of pulsed heated water monitored via reflection–absorption IR spectroscopy (Kringle et al. [59]).

Figure 5

Temperature dependence of rotational correlation times ${\tau }_R$ in bulk and confined water H₂O. Open squares (□) are the rotational correlation times ${\tau }_R$ of bulk H₂O obtained from ¹⁷O NMR experiments (Qvist et al. [67]). Open circles (◯) are the corresponding ${\tau }_D$ values reported from the dielectric measurements of Bertolini et al. [64]; open upright triangles (△) are the ${\tau }_R$ values in bulk H₂O obtained from the QENS experiments of Teixeira et al. [61]. Filled diamonds (◆) are the correlation times ${\tau }_R$ for supercooled H₂O within MCM-41 pores with a diameter of around 2.1 nm obtained from the broadband dielectric spectroscopy (BDS) measurements of Sjöström et al. [94]. Filled circles (●) are the corresponding ${\tau }_R$ values for supercooled H₂O confined in MCM-41 pores with a 2.5 nm diameter reported by Lederle et al. [92].

Figure 6

Temperature dependence of the rotational correlation times ${\tau }_R$ in bulk and confined heavy water D₂O. Inverted triangles (▼) are the rotational correlation times ${\tau }_R$ of bulk D₂O obtained from ²H NMR experiments (Qvist et al. [67]). Filled circles (●) are the correlation times for D₂O within 1.4 nm SW carbon nanotubes obtained from ²H T₁ NMR data (Kyakuno et al. [95]). Filled squares (◼) are the rotational correlation times for D₂O confined in MCM-41 with pores in the range of 2.1–2.8 nm obtained from ²H T₁ and stimulated-echo experiments (Weigler et al. [96]).