Hailong
Li
^{a},
Markus
Bier
^{bcg},
Julian
Mars
^{ad},
Henning
Weiss
^{a},
Ann-Christin
Dippel
^{e},
Olof
Gutowski
^{e},
Veijo
Honkimäki
^{f} and
Markus
Mezger
*^{ad}
^{a}Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany. E-mail: mezger@mpip-mainz.mpg.de
^{b}Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany
^{c}Institute for Theoretical Physics IV, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
^{d}Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 10, 55128 Mainz, Germany
^{e}Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
^{f}ESRF-The European Synchrotron, Avenue des Martyrs 71, 38043 Grenoble Cedex 9, France
^{g}Faculty of Applied Natural Sciences and Humanities, University of Applied Sciences Würzburg-Schweinfurt, Ignaz-Schön-Straße 11, 97421 Schweinfurt, Germany
First published on 7th November 2018
The interfacial premelting in ice/clay nano composites was studied by high energy X-ray diffraction. Below the melting point of bulk water, the formation of liquid water was observed for the ice/vermiculite and ice/kaolin systems. The liquid fraction is gradually increasing with temperature. For both minerals, similar effective premelting layer thicknesses of 2–3 nm are reached 3 K below the bulk melting point. For the quantitative description of the molten water fraction in wet clay minerals we developed a continuum model for short range interactions and arbitrary pore size distributions. This model quantitatively describes the experimental data over the entire temperature range. Model parameters were obtained by fitting using a maximum entropy (MaxEnt) approach. Pronounced differences in the deviation from Antonow's rule relating interfacial free energy between ice, water, and clay are observed for the charged vermiculite and uncharged kaolin minerals. The resultant parameters are discussed in terms of their ice nucleation efficiency. Using well defined and characterized ice/clay nano composite samples, this work bridges the gap between studies on single crystalline ice/solid model interfaces and naturally occurring soils and permafrost.
As of today, different physical effects contributing to the interfacial premelting phenomenon have been identified.^{5,7} In ice composites, the most relevant ones are the intrinsic interfacial melting, impurities, confinement, and geometry effects (Fig. 1). For non-planar interfaces such as in ice nano-crystals,^{8} nano-pores,^{9} and spherical nano-powders^{10} the geometry of the ice/water phase boundary plays an important role. Here, the Gibbs–Thomson effect leads to a melting point depression proportional to the mean curvature of the phase boundary.^{7} Confinement leads to a hysteresis in the freezing and melting process.^{11,12} Most impurities such as ions have a lower solubility in ice compared to liquid water. These impurities will be expelled from the ice phase. Their concentration in the remaining liquid phase will therefore gradually lower its melting point.^{13} Finally, the intrinsic interfacial premelting and the grain boundary melting of a material are governed by the thickness dependent balance between the ice/liquid and the liquid/solid interfacial tension.^{14}
Since the first observations by Faraday, several experimental techniques have been employed to disentangle these contributions to the premelting mechanism for different ice interfaces. Well defined, planar, single crystalline ice surfaces and ice/solid interfaces were investigated by glancing angle X-ray scattering,^{15} X-ray reflectivity,^{16–18} X-ray photoemission spectroscopy,^{19} sum frequency generation spectroscopy,^{20} and molecular dynamics simulations.^{21,22} Premelting in nanosized ice/solid composites was studied by thermodynamic measurements,^{23,24} X-ray^{25} and neutron diffraction,^{26} quasi elastic neutron scattering,^{27} NMR,^{28} and time-domain reflectometry.^{29} However, the liquid layer thicknesses obtained by the different experimental techniques and computer simulations differ by almost two orders of magnitude.^{5,6} In particular, for the class of ice composites, most studies focused on the premelting in naturally occurring samples from permafrost regions with complex composition and morphology.^{30,31} In general, this precludes a quantitative discussion of the intrinsic premelting mechanisms in terms of physical models. This led to the development of semi-empirical descriptions^{24} rather than unifying theories as discovered for premelting at free surfaces.^{32} Thus, experimental results on well defined model systems are essential to advance the physical understanding of interfacial premelting at buried interfaces and inside slit pore confinement.
Here, we present a high energy X-ray diffraction (XRD) study of the interfacial melting in ice/vermiculite and ice/kaolin composites. Vermiculite and kaolin are phyllosilicate clay minerals, forming planar platelets with a large aspect ratio and a large specific surface area (Fig. 2). The paper is structured as follows: In Section 2 we introduce a premelting model for water and ice inside slit pores with specified size distributions. In Section 3 we report the preparation and characterization of the nano composite materials. Well defined vermiculite samples of high purity were obtained by chemical processing of the natural mineral. This suppresses geometry and impurity driven effects. The high energy X-ray diffraction experiments and data processing are described in Sections 3.2 and 4.1. The growth law of the effective premelting layer thickness vs. temperature, (T), is calculated from the scattering data and clay powder properties. The quantitative analysis of the experimentally obtained growth law using the maximum entropy (MaxEnt) approach is described in Section 4.2. In Section 5 we discuss the parameters extracted from the experimental data. From comparison between the results obtained for charged vermiculite and uncharged kaolin clays we extract information on the relevant molecular interactions governing the intrinsic interfacial melting mechanism.
γ(d) = γ_{i−s} + φ(d)Δγ, | (1) |
φ(d) = 1 − e^{−d/λ}. | (2) |
(3a) |
(3b) |
At surfaces and buried interfaces, as is expressed by the Yvon equation,^{40} these correlations drive an interfacial profile that decays with exp(−r/ξ).^{41} Hence, the decay length λ in the growth given by eqn (3) is linked to the bulk correlation length ξ of the liquid.
Information on ξ is contained in the liquid structure factor. It can be determined from MD simulations, or from X-ray or neutron scattering. From high precision scattering data^{42–45} we extract λ = ξ = 2.42 Å for the bulk correlation length introduced in eqn (2) (Section A, ESI†). Temperature changes lead to slight variation in the X-ray scattering patterns,^{46} mainly affecting the periodicity.
(4) |
Two different premelting configurations are conceivable. Firstly, the slit pore can be partially molten. In this case, layers of liquid water of thickness d ∈ [0, 1/2D) cover each solid substrate (Fig. 3a). The free energy of the liquid layers F(d) per substrate area A is obtained from eqn (1) and (2):
(5) |
Fig. 3 Partially (a) and completely (b) molten case of liquid water (l) and ice (i) confined in a slit pore made of two solids (s) spaced by a distance D. |
The first term on the right-hand side of eqn (5) accounts for the free energy of the liquid/solid and the ice/liquid interfaces. The second term describes the free energy increase due to the premelting layers of bulk metastable liquid water being formed instead of bulk stable ice.
In the second case, the slit pore is completely molten i.e. d = 1/2D. Here, liquid water fills the entire pore such that no ice/liquid interfaces are present (Fig. 3b). Then the free energy per interfacial area is given by
(6) |
For reduced temperatures τ < 0, the equilibrium layer thickness
(7) |
(8) |
In the case of partial premelting, an equilibrium water layer thickness
(9) |
In analogy to eqn (3b), the reduced onset temperature
(10) |
(11) |
To include interface coupling via long-range van der Waals forces,^{47–50}eqn (2) is modified. However, the procedure described here for interactions dominated by exponentially decaying effective short-range forces can be followed in an analog way.
Let P(D) denote the probability density of a surface element of the substrate walls to belong to a pore of width D. Using eqn (7), the effective layer thickness (T) at temperature T can be expressed as
(12) |
In Section 4.2 this relation is inverted to obtain the pore size distribution P(D) from expermimetally determined effective water layer thicknesses (T) by a MaxEnt approach.
BL | Vermiculite | Kaolin | |
---|---|---|---|
ρ | 2.63 g cm^{−3} | 2.70 g cm^{−3} | |
s | 36.4 m^{2} g^{−1} | 10.9 m^{2}g^{−1} | |
L | 20.9 nm | 68.0 nm | |
w _{m} | ID31 | 27 wt% | 20 wt% |
P07 | — | 12 wt% | |
_{sa} | ID31 | 20.3 nm | 45.9 nm |
P07 | — | 25.0 nm | |
c _{s} | ID31 | 0.40 μmol m^{−2} | 0.35 μmol m^{−2} |
P07 | — | 0.04 μmol m^{−2} |
After azimuthal integration, high temperature scattering patterns of the molten samples were subtracted from each temperature set (Fig. 4, Section G, ESI†). This procedure efficiently eliminates most of the scattering signal from the clay minerals, CeO_{2} reference, and sample container. Thermal expansion leads to S-shaped curves in the difference patterns in the region around the kaolin (002) and (111), vermiculite (021), and CeO_{2} (111) Bragg reflections.
Fig. 4 Azimuthally integrated XRD difference patterns between partially frozen samples at −60 °C < T − T_{m} < 0 °C and the molten samples above T_{m}; (a) vermiculite, (b) kaolin (ID31, ESRF). |
Integrated Bragg intensities of ice Ih were determined from simultaneously fitting three Gaussian peaks for the ice (100), (002), and (101) Bragg reflections to the corrected azimuthally integrated XRD difference patterns (Tables S3–S5, ESI†). The positions of the Bragg reflections agree well with literature values for the ice lattice spacings and thermal expansion.^{54} The peaks’ FWHM are limited by the angular resolution of the experimental setup using large pellet samples of 6 mm diameter. Therefore, details in the line shape of the Bragg reflections are concealed.
Below the bulk melting point T_{m}, the intensities I(T) of the (100), (002), and (101) ice Ih Bragg reflections rapidly increase (Fig. 4). This corresponds to a decreasing liquid water fraction (Fig. S8, ESI†) that is related to the effective premelting layer thickness (Section G, ESI†). Fig. 5 shows vs. temperature below melting, T_{m} − T. Upon cooling, a rapid decrease of is observed for all samples.
Fig. 5 Effective premelting layer thickness vs. temperature below melting, T_{m} − T, for vermiculite (blue) and kaolin (ID31: red; P07: orange) composite samples extracted from the intensity of the ice (100), (002), (101) Bragg reflections (dots). Solid curves are calculated by eqn (2) with pore size distributions P(D) obtained from a MaxEnt analysis (Section 4.2 and Fig. 6). |
The functional form of the pore size distribution P(D) is constrained by the normalization condition
(13) |
(14) |
Note that (D,τ) in eqn (7) additionally depends on the a priori unknown reduced onset temperature τ_{0}.
The MaxEnt method yields the least biased distribution P(D) compatible with the boundary conditions eqn (13) and (14) by constrained maximization of a certain entropy functional H[] on the set of all distributions (D).^{55,56} For the present case of linear constraints, the relevant functional is given by^{57}
(15) |
(16) |
The entropy functional H[] was maximized under the constraints eqn (13) and (14) with respect to (D) and τ_{0} using the method of Lagrange multipliers. For all samples, the effective premelting layer thicknesses (T) (Fig. 5, solid lines) calculated from the resultant pore size distributions P(D) (Fig. 6) reproduce the experimentally observed values (Fig. 5, symbols). The value of Δγ for each individual sample is calculated from τ_{0}viaeqn (10). Parameters for the reduced onset temperature τ_{0}, the deviation from Antonow's rule Δγ, and the average pore size _{psd} are summarized in Table 2.
Sample | τ _{0} | Δγ (mJ m^{−2}) | _{psd} (nm) | D _{max} (nm) |
---|---|---|---|---|
Vermiculite | −0.158 | −12.8 | 15.8 | 134 |
Kaolin (ID31) | −0.675 | −54.5 | 26.2 | 123 |
Kaolin (P07) | −0.534 | −43.1 | 21.6 | 87 |
However, for a quantitative analysis and interpretation the interactions with the solid substrate governing Δγ and the pore size distribution P(D) have to be taken into account. A slit pore premelting model (Section 2) in conjunction with a MaxEnt method (Section 4.2) allows for a full quantitative analysis of experimentally determined growth laws (T). Fig. 5 demonstrates that this continuum model adequately describes the experimental premelting data over the entire measured temperature range.
The pore size distribution P(D), extracted by the MaxEnt analysis (Fig. 6), is an important parameter of the model. Its functional dependency exhibits a fast decay for larger D values. For all clay nano composite samples, the average slit pore widths _{psd} calculated from P(D) (Table 2) are consistent with the _{sa} values determined from the gas adsorption isotherms (Table 1). The systematically smaller values obtained for the dry powders (_{sa}) compared to the pressed clay/water pellets (_{psd}) are explained by their different preparation states.
For the effective coupling between the solid/liquid and liquid/ice interface we assume effective short-range forces, generating an exponentially decaying interfacial free energy γ(d) in eqn (2). Their decay length λ equals the bulk correlation length ξ in the liquid phase.^{37} From bulk X-ray scattering data of liquid water, we extract λ = ξ = 2.42 Å. Indeed, our experimental premelting data is perfectly reproduced using this bulk value for all samples independent of the contained clay mineral. Thus, our results are in agreement with the standard theory of interface phase transitions. Likewise, Smit et al. found that the characteristic spectroscopic response from the ice premelting layer and supercooled bulk water is indistinguishable by sum-frequency generation spectroscopy.^{59} However, changes in the water structure have been observed for water confined in nano-pores.^{60} Scattering experiments indicate that confined water exhibits a higher order compared to bulk.^{61–64} Likewise, the increase in premelting liquid layer density adjacent to hydrophilic SiO_{2} by 20% compared to bulk water^{16} and surface spectroscopy experiments^{20,65} indicate different properties. Such huge density changes would require structural changes that are much larger compared to the temperature variations observed for supercooled water.^{46} The interpolation of the interfacial free energy γ(d) between d = 0 and d → ∞ given in eqn (1) and (2) obeys the thermodynamically correct exponential asymptotic decay on the scale of the bulk correlation length λ = ξ. However, from the results discussed above it is expected that the structural properties of confined water lead to deviations from this simple form. Hence, deviations from eqn (9) may occur for small water layer thicknesses d_{p} at low temperatures. The present work highlights the importance of the pore size distribution P(D) for the premelting behavior in nano composite materials such as sheet silicates. In consequence, the specific small-thickness features of the interfacial free energy γ(d) are expected to become relevant only for samples with a large fraction of very small pores.
The third parameter affecting premelting in slit pore confinement is the deviation from Antonow's rule Δγ. This quantity, related to the spreading coefficient S = −Δγ of liquid water on the solid compared to ice, depends on the balance of the interactions between the three components. Both clays studied in this work form planar hydrophilic sheets (Fig. S4 and S5, ESI†). While vermiculite surfaces are charged by 1.2–1.8 unit charges per unit cell, polar kaolin surfaces are neutral.^{66} Therefore, different Δγ values are expected to result in different premelting curves for vermiculite and kaolin based ice/clay composites. Indeed, about four times larger negative Δγ values were extracted for kaolin compared to vermiculite by MaxEnt analysis (Table 2).
For vermiculite, we find Δγ = −12.8 mJ m^{−2}. For comparison, for single crystal ice/SiO_{2} interfaces Δγ = −5.03 mJ m^{−2} is obtained from T_{m} − T_{0} = 17 K reported by Engemann et al.^{16} A common property of vermiculite and SiO_{2} surfaces is their negative charge.
For the two kaolin samples, Δγ values agree well, despite their different preparation protocols leading to different ion and water concentrations. This confirms the robustness of the MaxEnt analysis method. It also indicates that the differences in the observed growth law for kaolin and vermiculite are primarily related to the surface properties and the pore size distribution of the clay minerals rather than impurities. Bare kaolin surfaces have a surface tension of 171 mN m^{−1} with a ratio of 40% dispersive and 60% nondispersive interactions.^{67} The positive spreading coefficient S = 76 mN m^{−1} of liquid water vs. its vapor, calculated by the Fowkes method,^{68} reflects the strong hydrophilic nature of the bare kaolin surface. With about 50 mJ m^{−2} the spreading coefficient of liquid water vs. ice found in this work is on the same order of magnitude.
For the free ice surface, an even larger negative Δγ value of −384 mJ m^{−2} is reported in the literature.^{58} Consistently, a large dangling hydrogen bond density was detected at the free ice surface by SFG spectroscopy.^{20,69} In contrast to ice, in liquid water the hydrogen bonding network adjacent to interfaces can rearrange. Therefore, the formation of a liquid premelting layer at ice surfaces is energetically favorable. This is reflected in a large negative Δγ value.
Generally, larger negative Δγ values indicate that the ice structure at an interface is less compatible with the opposing medium. Therefore, these media tend to be less efficient ice nucleators and vice versa. Murray et al. studied heterogeneous ice nucleation by kaolin particles in suspensions.^{70} Compared to other minerals, kaolin is a rather inefficient ice nucleator.^{71} Accordingly, we observe large premelting layer thicknesses caused by Δγ values around −50 mJ m^{−2}. On the other hand, at quartz with a smaller absolute Δγ = −5.03 mJ m^{−2}, ice nucleates with a significantly higher activity.^{71} Likewise, ice/vermiculite interfaces with Δγ = −12.8 mJ m^{−2}, exhibit thinner premelting layer thicknesses.
Premelting layer formation at ice/solid interfaces has important implications in atmospheric physics^{72} and geophysics.^{2} Our experiments on well defined ice/clay nano composite samples bridge the gap between studies on single crystalline ice/solid model interfaces^{16} and naturally occurring soils.^{30,31} Compared to naturally occurring soils, the ion concentration in the sample was reduced to investigate the influence of the surface properties of the adjacent solid. For ice/clay nano composites, in addition to the deviation from Antonow's rule the pore size distribution is a decisive parameter determining the liquid water fraction vs. temperature. The experimental premelting data is quantitatively reproduced over the entire temperature range by a theoretical continuum model including effective short-range interactions. Thorough material characterization allows for the comparison of parameters extracted by a MaxEnt analysis with independent experimental observations.
Future theoretical and experimental work focusing on the dynamics of the water molecules in the premelting layer of ice/clay nano composites might provide complementary information on the nature of the interfacial premelting layer.
Footnote |
† Electronic supplementary information (ESI) available: Sample characterization, experimental details and data processing. See DOI: 10.1039/c8cp05604h |
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