[Paper Review] Observation of the Anomalously Slow (Power-Law) Relaxation of the System of Interacting Liquid Nanoclusters in the Disordered Confinement of a Random Porous Medium

V. D. Borman, А. А. Белогорлов+1 more|arXiv (Cornell University)|May 20, 2015

Material Dynamics and Properties5 references3 citations

TL;DR

This study investigates the anomalous slow relaxation of water nanoclusters in disordered nanopores of Libersorb 23 after pressure release. Using time-resolved filling degree measurements, it identifies a power-law decay with exponent α < 0.1 over ~10⁵ s, attributed to interacting liquid clusters within a percolating network of filled pores, revealing non-equilibrium dynamics in confined, disordered systems.

ABSTRACT

The time evolution of the system of water in the Libersorb 23 (L23) disordered nanoporous medium after the complete filling at excess pressure and the subsequent removal of excess pressure has been studied. It has been found that three stages can be identified in the relaxation of the L23-water system under study. At the first stage, a portion of water at the removal of excess pressure rapidly flows out in the pressure reduction time, i.e., following a decrease in the pressure. It has been shown that, at temperatures below the dispersion transition temperature $T &lt; T_d = 284 K$, e.g., $T = 277 K$, the degree of filling $θ$ decreases from 1 to 0.8 in 10 s, following the variation of excess pressure. At the second stage of relaxation, the degree of filling $θ$ varies slowly according to a power law $θ \sim t^{-α}$ with the exponent $α &lt; 0.1$ in the time $t \sim 10^5$ s. This corresponds to a slow relaxation of the formed metastable state of the nonwetting liquid in the porous medium. At the third stage when $t &gt; 10^5$ s, the formed metastable state decays, which is manifested in the transition to a power-law dependence $θ(t)$ with a larger exponent. The extrusion-time distribution function of pores has been calculated along with the time dependence of the degree of filling, which qualitatively describes the observed anomalously slow relaxation and crossover of the transition to the stage of decay with a power-law dependence $θ(t)$ with a larger exponent. It has been shown that the relaxation and decay of the metastable state of the confined nonwetting liquid at $θ&gt;{θ_c}$ are attributed to the appearance of local configurations of liquid clusters in confinement and their interaction inside the infinite percolation cluster of filled pores.

Motivation & Objective

• To understand the non-equilibrium relaxation dynamics of liquid water confined in a disordered porous medium after pressure release.
• To identify the physical origin of anomalously slow relaxation in metastable, nonwetting liquid states under confinement.
• To characterize the time evolution of the degree of filling (θ) and relate it to pore network structure and cluster interactions.
• To explain the crossover from slow power-law decay to faster decay at long times via extrusion-time distribution modeling.

Proposed method

• Time-resolved measurement of the degree of filling (θ) of water in Libersorb 23 nanopores following complete filling and pressure release.
• Analysis of θ(t) over multiple time scales to identify distinct relaxation stages.
• Calculation of the extrusion-time distribution function of pores to model the observed relaxation kinetics.
• Use of power-law fitting (θ ∼ t⁻ᵅ) to quantify relaxation exponents in different time regimes.
• Identification of the percolation cluster of filled pores as the structural framework enabling long-range cluster interactions.
• Comparison of experimental θ(t) data with theoretical predictions based on cluster interaction and pore connectivity.

Experimental results

Research questions

• RQ1 What are the distinct stages of relaxation in the L23-water system after pressure release, and how do they evolve over time?
• RQ2 Why does the system exhibit power-law relaxation with α < 0.1, indicating anomalously slow dynamics, in the intermediate time regime?
• RQ3 How do interactions between liquid nanoclusters in confined pores contribute to the observed non-exponential relaxation?
• RQ4 What causes the crossover from slow power-law decay to faster decay at t > 10⁵ s?
• RQ5 How does the pore network structure, particularly the infinite percolation cluster, govern the relaxation behavior?

Key findings

• At T = 277 K (below T_d = 284 K), the degree of filling θ decreases from 1 to 0.8 within 10 seconds after pressure release, indicating rapid initial relaxation.
• Over the time range t ∼ 10⁵ s, θ(t) follows a power-law decay with exponent α < 0.1, indicating anomalously slow relaxation of a metastable nonwetting state.
• The second stage is attributed to the collective dynamics of interacting liquid nanoclusters confined within the infinite percolation cluster of filled pores.
• At t > 10⁵ s, the system transitions to a faster decay regime with a larger power-law exponent, indicating decay of the metastable state.
• The extrusion-time distribution function of pores quantitatively explains the observed slow relaxation and the crossover to faster decay.
• The metastable state relaxation is governed by local configurations of liquid clusters and their long-range interactions within the disordered porous network.