Confined water - From the perspective of supercooled water and relaxation processes

13 Jul 2024

Water, the elixir of life, might seem simple on the surface. But delve a little deeper, and things get fascinating, especially when it’s confined within tight spaces. Here I will discuss the intriguing world of confined water, where its properties take surprising twists and turns. Here, we’ll see how confining water in different geometries unlocks secrets relevant to biology, geology, and beyond.

One key reason for exploring confined water is its ability to defy nature’s usual script. In its bulk form, water readily crystallizes into ice at very low temperatures. But when confined, it can exist in a supercooled liquid state, far below its freezing point! This opens a window to studying water’s behaviour in a whole new regime.

Scientists have discovered that water trapped in tight spaces can defy freezing altogether! This magic trick works as long as the confinement is strong enough to stop water molecules from organizing into the ice crystal structure (think of it like a specific puzzle they need to form). There are three main ways to achieve this confinement:

Squeezing water into tiny pores of special materials like sponges.
Mixing water with a partner, like salt or another liquid, that disrupts the water molecule party.
Sticking water to surfaces or larger molecules, like biological ones, where the water molecules can’t arrange themselves freely.

The exact recipe for preventing ice formation is a bit tricky, though. While there’s no single size limit for non-crystallizing water clusters, studies on water trapped within cylindrical pores offer some clues. It depends on a bunch of factors, like how water interacts with its confinement, the shape of the tiny water pockets, and how spread out the water molecules are in a solution.

Therefore, we have several methods to trap water and prevent it from freezing normally in the ‘no man’s land region’. A special region of water phase diagram where it is difficult to conduct any experiment because water nucleates rapidly.

The question is whether the structural and dynamical properties of such supercooled water are of relevance for supercooled bulk water. Here I will discuss about relaxation processes that are of primary importance.

How can we relate relaxation data for confined supercooled water to supercooled bulk water?

Let’s begin with experiments… The experiments with which we can probe into viscosity and glass-transition-related structural relaxation process (α-relaxation) are:

nuclear magnetic resonance (NMR)
dielectric spectroscopy (BDS)
quasielastic neutron scattering (QENS)

A common observation across these techniques is the presence of a dynamic crossover in the temperature dependence of relaxation data for confined supercooled water.

The dynamic cross-over tells us two things:

how confined supercooled water behaves
what the most likely relaxation scenario is for supercooled bulk water. (The relaxation scenario for bulk water is currently under debate due to the possibility of a fragile-to-strong (FS) crossover and uncertainty in glass transition temperature) Fragility: refers to the temperature dependence of the viscosity ($\eta$) or related α-relaxation time ($\tau_{\alpha}$) of a supercooled liquid. A fragile glass-forming liquid, exhibits a highly non-Arrhenius temperature dependence, such as ionic and van der Waals systems. Strong supercooled liquid: shows a temperature dependence close to the Arrhenius law, typical for materials with strong (commonly covalent) bonds forming a network structure.

Water is known to be one of the most fragile liquids, meaning its viscosity and relaxation time change dramatically with temperature as it cools (above 233 K). Existing studies suggest this change follows a power law that diverges around 228 K. To get a glass transition temperature (Tg, typically defined as the temperature where relaxation time reaches 100 seconds), we need strong like behaviour, i.e. Arrhenius-like dependence slightly below 233 K. This possible shift from fragile to strong has led to the proposal of a fragile-to-strong (FS) transition around 228 K, potentially caused by a limit in forming a hydrogen-bonded, tetrahedral network structure.

Importance of Technique Choice:
- The results from studying confined water depend heavily on the specific confinement and the interaction between the measuring tool (probe) and the water itself.
- Different techniques probe different aspects of water dynamics, offering a more complete picture when combined.
BDS - Electric Dipole Interaction:
- Measures the interaction between an electric field and water molecules’ electric dipoles.
- Provides information about relaxation processes (α and β) and their temperature dependence.
- Doesn’t offer details on the location or movement of water molecules within the confinement.
QENS - Probing Motion:
- Analyses how neutrons scatter off water molecules, revealing their movement on various scales.
- Shows how relaxation times change with the distance traveled by the water molecules (momentum transfer).
- Limited frequency range compared to BDS.
NMR - Rotational and Translational Motion:
- Uses magnetic fields to study both water molecule rotation and movement within the confinement.
- Offers insights into the shape and speed of water molecule reorientation (rotational correlation).
- Can measure translational diffusion coefficient (Ds) to understand how far water molecules move.
Combining Techniques & Challenges:
- Combining BDS, NMR, and QENS provides a more comprehensive view of confined water dynamics.
- However, different techniques might yield slightly different results for similar parameters due to their varied approaches.
- The “rototranslation paradox” suggests a potential decoupling of rotational and translational motion near the glass transition, further complicating interpretation.

Different Types of Confinements

Hard Confinement Systems When water is confined in porous materials (hard confinements) to study its liquid behaviour below the homogeneous nucleation temperature.

Scientists categorize rigid porous materials based on three key factors:

Network Structure: This refers to how ordered or disordered the network of pores is within the material.
Pore Size: Pores are classified as:
- Micropores: smaller than 2 nanometres (nm)
- Mesopores: between 2 nm and 50 nm
- Macropores: larger than 50 nm
Wettability: This describes how well the material interacts with water. It can be hydrophilic (water-loving) or hydrophobic (water-repelling).

Examples of disordered porous materials: silica hydrogels, Vycor glasses, molecular sieves, mineral clays, graphite oxide, and cement-like materials. All these materials exhibit interconnected pore structure and broad pore size distribution. Because the pores aren’t completely filled, water molecules interact more strongly with the pore surfaces. These interactions, which vary depending on the specific system, then alter how the confined water molecules move and behave.

Soft Confinement Systems This “soft confinement” works by surrounding the water molecules with these additives such as sugars, salts, polymers, biomaterials (proteins, DNA), etc. The solution itself acts as a barrier once it falls below its glass transition temperature, a point where the solute molecules become sluggish due to water’s influence. This approach is highly relevant in various fields, from biology to solving technological challenges. The structure, interactions, and even the movements of the dissolved substances (solutes) can significantly influence water’s properties. For example, the dynamics of bulk water at room temperature is typically faster than that of water in solutions, as interactions with solute molecules tend to slow down the water dynamics.

Studying water movement (dynamics) in solutions is tricky. Two main challenges exist: 1) Solute molecules and water molecules can’t help but interact, and 2) the size and shape of these interactions are hard to pin down.

Despite these difficulties, there are some interesting trends when solutions contain pools of liquid water. Here’s what has been observed:

As the solution reaches its glass transition temperature, water dynamics shift to a simpler behaviour (low-temperature Arrhenius dependence).
Surprisingly, the water molecules in the solution actually move faster (up to 4 times!) at lower temperatures. This speed increase, along with a lower activation energy, happens with more water in the solution.

Confined Water Dynamics: Hard vs. Soft This section compares water dynamics in different confinement scenarios: hard confinement (like tiny pores), soft confinement (like solutions), and microemulsions.

High Temperatures: Not interesting. General Stokes–Einstein relationship (SER) is valid at high temperatures; that is, the rotational and translational diffusions exhibit the same temperature dependence.
Low Temperatures: Here, water dynamics become more similar across different confinements.
- In some specific hard confinements and highly concentrated solutions (dominated by water-water interactions), water relaxation is remarkably similar with a consistent activation energy (around 0.5 eV). This suggests a “universal” water relaxation behaviour.
- Most solutions exhibit slower water dynamics compared to this “universal” behavior, likely due to interactions with solutes. Conversely, water dynamics in some disordered hard confinements are faster.
- In the case of fragile supercooled liquids approaching $T_g$, it is common that the inverse rotational diffusion constant 1/$D_r$ (or the corresponding relaxation time τr) has the same temperature behaviour as viscosity ($\eta$), whereas translational diffusion $D_s$ declines more slowly than $D_r$ with decreasing temperature. Such a breakdown of the SER at low temperatures has also been observed for confined water.
Bulk Water vs. Confined Water: The “universal” water relaxation observed in some confinements might be relevant for understanding bulk water at low temperatures. However, current data suggests significant differences in relaxation times and activation energy between confined and bulk water. This raises questions about the type of relaxation process being probed in bulk water studies.
Finite Size Effects: Properties of confined water can be influenced by the size and surface chemistry of the confining environment. This makes it challenging to directly translate confined water behaviour to bulk water.

Open Questions:

Is the “universal” water relaxation in confinements truly representative of bulk water behaviour?

How much do finite size effects and surface chemistry impact confined water properties?

Does confinement affect the existence of a liquid-liquid phase transition in water?

Dynamic Crossover under Confinements

It is evident that a dynamic crossover occurs in supercooled water in hard confinements. However, since it is widely debated exactly how experimental data should be analysed. Therefore, we there are 3 different relaxation scenarios, which are the main scenarios presented in the literature. These 2 main relaxation scenarios for confined water also suggest different relaxation scenarios for supercooled bulk water.

Scenario 1: This is based on QENS and NMR data. At this point I will assume we are both familiar with the ‘Widom line’ in the phase diagram of supercooled water. Essentially, this is a liquid-liquid coexistence line in the no-man’s land that separates LDL and HDL phase of water. For reference I add the relevant phase diagram from here. ‘Widom line’ is the grey line in the no-man’s land.

If we take a very small region of the end of this Widom line, at very low pressure, we will get LDL-HDL transition by varying the temperature. Now, in the first scenario, although we believe the presence of this line by extrapolation from other parts of the phase diagram, this region of no man’s land is very hard to probe in experiment. But for confined water at ambient pressure inside MCM-41, experiments have shown LDL-like to HDL-like continuous structural transition that occurs upon crossing the Widom line at 255 K. This could mean that if the hypothesised LLCP exists, according to the convergence of supercritical phenomena in the vicinity of the critical point, one should be able to trace the LLCP as the terminal point of the dynamic crossover, located in the supercooled region at $P_C$ = 1600 ± 400 bar and $T_C$= 200 ± 10 K. (i) Water molecules move differently: The way water molecules move around (translation) becomes less connected to how they rotate. (ii) Water becomes more resilient: It changes from a “fragile” liquid (whose properties change rapidly with temperature) to a “strong” one (whose properties change more gradually). (iii) Standard ways of measuring movement break down: Existing methods to describe how water molecules move no longer work perfectly, and a new approach involving fractions is needed. (iv) Extra stiffness leads to new vibrations: When water gets very cold (below the Widom temperature), the stiffer structure of the water molecules allows for a new type of vibration.

While experiments hint at the existence of a Liquid-Liquid Critical Point (LLCP) in supercooled water, there’s debate about the exact location of the boundary separating the two liquid phases (LDL and HDL). This could be because the experimental setups themselves might be influencing the results by confining the water.

That’s where computer simulations come in. They allow scientists to zoom in and observe the microscopic processes happening in this fascinating region of the water phase diagram.

Here’s what simulations have shown:
- Confining water in tiny spaces (slits) affects the LLCP. As the space gets smaller, the LLCP moves to lower temperatures and higher pressures.
- Importantly, under extreme confinement, the LLCP might even disappear completely. This suggests that very strong confinement can “blur” the sharp transition between the two liquid phases.
- Even though direct evidence of a clear-cut structural change during the transition might be missing in strongly confined water, it doesn’t necessarily mean there’s no LLPT altogether.
- In fact, simulations have observed a Liquid-Liquid Phase Transition in confined water models (like ST2 water), but the transition temperature depends on the type of confinement (hydrophilic or hydrophobic pores).
Scenario 2: This study utilizes Broadband Dielectric Spectroscopy (BDS) – a powerful technique – to delve deeper into how water molecules behave when trapped within a specific material. The chosen material, modeled as MCM-41 (C10), has tiny pores with a diameter of 21 Å. BDS allows us to observe the water molecules at much slower timescales (up to seconds) and colder temperatures compared to other methods like QENS and NMR. This lets us explore the dynamics of water at a different level of detail.

The specific focus here is on the relaxation time of the confined water, which essentially tells us how long it takes for the water molecules to return to equilibrium after a disturbance. In the temperature region of 180 K, we observe a change in the dynamics from liquidlike behaviour [Vogel–Fulcher–Tammann (VFT)] toward localized (Arrhenius activated) motions with decreasing temperature. The change of dynamics is produced at lower temperatures and longer time scales. The low-temperature activation energy in BDS is substantially higher than that in QENS. The characteristics of high-temperature water relaxation are quite similar to those exhibited by the well-known α-relaxation, which is observed in supercooled systems above the glass-transition temperature ($T_g$). The low-temperature water relaxation exhibits all the characteristics typical for β-relaxations. Therefore, this low-temperature process is not related to the viscosity of the water molecules, which further implies that the dynamic crossover is likely due to a crossover from a α-like relaxation above the crossover temperature to a β-like process below the crossover.

The question is whether this behaviour is general for water under confinement, or it is a feature of this particular system. The answer can be found in studies of water dynamics in other types of confinements such as water solutions or even imperfect porous solids (for instance, molecular sieves). However, when temperature dependence of the relaxation time of water in these diverse materials is considered, the same scenario as that proposed earlier is found, even if the nature of the confinement is different. When the temperature approaches $T_g$, upon decreasing temperature, the global dynamics becomes frozen but water molecules still have enough mobility to be detected by dielectric spectroscopy. Below $T_g$, water molecules are trapped in the frozen matrix and their motions are restricted and similar to those corresponding to a secondary β-relaxation in a simple glass. As a consequence, temperature dependence of relaxation times is Arrhenius-like. This restricted dynamic is called α-confined.

Overall, the following common features of water dynamics under confinements can be identified:
- low-temperature relaxation is symmetrically broadened and Arrhenius-like,
- activation energy is 0.50 ± 0.03 eV,
- the time scale of this Arrhenius relaxation differs by less than 1 order of magnitude for all systems, and
- high-temperature relaxation depends on the host system since surface or solute interactions dominate.
Therefore, the change of temperature dependence for water in MCM-41 is not an exceptional result, since it shares the most common features for supercooled water in other types of confinement. As a conclusion, the low-temperature relaxation can be regarded as the universal β-relaxation of water. This type of relaxation involves all atoms in the water molecule in a local (noncooperative) and anisotropic motion, and it is coupled to translational motions. These last characteristics of water under confinement were probed by means of NMR studies of water in MCM-41.

Why Does This Happen?

To understand why confined water behaves this way, scientists compared it to other liquids like ethylene glycol or poly(ethylene oxide) trapped in tiny cages. These studies revealed that severe confinement (being squeezed into very small spaces) can actually eliminate a specific type of water movement called α-relaxation.

In the case of supercooled water trapped within pores, this suggests the observed dynamic crossover (change in movement) might be caused by the limited space. We know that confinement can significantly alter how a liquid behaves, both in terms of structure and movement.

Here’s the idea: imagine there’s a “typical distance” water molecules move during α-relaxation. In a confined space, this distance can’t be larger than the size of the pore itself. So, there’s a critical temperature where this typical distance becomes equal to the pore size. This essentially stops the distance from increasing any further. As a result, the way water moves changes from a liquid-like behaviour (VFT dependence) at higher temperatures to a more localized, jerky motion (Arrhenius dependence) at lower temperatures.

Reminding ourselves of our quest again: whether there’s a special point (Liquid-Liquid Critical Point or LLCP) where supercooled water can exist in two distinct liquid forms (LDL and HDL). One way to test for this is by looking for a change in a key property like water density (order parameter) as temperature and pressure change. This change should be “reversible” – meaning water should return to its original state when conditions change back. Zhang and colleagues looked for this “reversal” (hysteresis) in the density of heavy water confined within a material called MCM-41. They observed some changes at low pressures, but these were weak and might be due to temperature differences during the experiment, not a true phase transition. However, Limmer and Chandler challenged this conclusion. Using computer simulations, they argued that the observed changes were actually due to a different transition – water turning into a solid (liquid-solid transition or LST) within the confined space. The key difference here is that the LLCP scenario predicts a specific pressure point where the liquid-liquid transition disappears. In the LST scenario, the water can always turn solid under pressure, no matter the temperature.

So, although there is a great volume of proxy studies that hint towards the theory of LLCP the hunt for the same in real bulk water continues!

Contents of this article was adopted from many different sources, and the references are given bellow:

References

Jeet Majumdar

jeet.Log

Confined water - From the perspective of supercooled water and relaxation processes

Different Types of Confinements

Dynamic Crossover under Confinements