Investigation of the percolation transition in a nonwetting liquid-nanoporous medium system

The flows of liquid into and out of a nanoporous medium are studied as processes leading to the fluctuation formation and the growth of fractal clusters of filled and empty pores, respectively. The conditions for stable growth of such fluctuations are analyzed as a function of the interfacial energy between the liquid and the porous medium and the surface energy of the liquid. Expressions are obtained for the pressure at which the barrier for fluctuation filling and emptying of the pores vanishes. In general, it is shown for porous media with a pore-size distribution that these processes can be interpreted as a percolation phase transition. The volume and susceptibility of a liquid-porous medium system near the transition points with inflow and outflow of the liquid are calculated. The phenomenon of nonoutflow of a nonwetting liquid from a porous medium and hysteresis of the flow of liquid into and out of a porous medium are explained on the basis of the mechanism considered. The results of an experimental investigation of these processes in the system liquid Wood’s alloy-silochrome 80 and silochrome 120 are presented. The experimental data obtained can be described on the basis of the proposed mechanism.     

Multiplicity of metastable nonergodic states of a dispersed nonwetting liquid in a disordered nanoporous medium

Three different metastable nonergodic states of a dispersed nonwetting liquid (water) in the Fluka 100 C8 and Fluka 100 C18 disordered porous media, as well as transitions between these states under variation of the temperature and the degree of filling, have been qualitatively described. It has been shown that the appearance of such states is due to spatial variations of the number of the nearest neighbors because of the broadening of the pore size distribution function f(R), fluctuations of various local configurations of neighbors in the system of pores, and fluctuations of a configuration of a pore and its environment consisting of filled and empty pores on a percolation cluster. These states and transitions are caused by the competition between the effective repulsion of the nonwetting liquid from the wall of the pore, which is responsible for the “extrusion” of the liquid from the pore, and the effective collective multiparticle attraction of the liquid cluster in the pore to clusters in the neighboring connected pores. The theoretical dependences obtained make it possible to qualitatively describe experimental data.     

Anomalously slow relaxation of a nonwetting liquid in the disordered confinement of a nanoporous medium

The time evolution of the water–disordered nanoporous medium Libersorb 23 (L23) system has been studied after complete filling at elevated pressure followed by full release of overpressure. It is established that relaxation of the L23 rapidly flows out during the overpressure relief time, following the variation in pressure. At a temperature below that of the dispersion transition (T < T _d = 284 K), e.g., at T = 277 K, the degree of filling θ decreases from 1 to 0.8 within 10 s. The degree of filling varies with time according to the power law θ ~ t ^–α with the exponent α < 0.1 over a period of t ~ 10⁵ s. This process corresponds to slow relaxation of a metastable state of a nonwetting liquid in a porous medium. At times t > 10⁵ s, the metastable state exhibits decay, manifested as the transition to a power dependence of θ(t) with a larger exponent. The relaxation of the metastable state of nonwetting liquid in a disordered porous medium is described in the mean field approximation as a continuous sequence of metastable states with a barrier decreasing upon a decrease in the degree of filling. Using this approach, it is possible to qualitatively explain the observed relaxation process and crossover transition to the stage described by θ(t) with a larger exponent.     

Correlation effects during liquid infiltration into hydrophobic nanoporous media

To explain the thermal effects observed during the infiltration of a nonwetting liquid into a disordered nanoporous medium, we have constructed a model that includes correlation effects in a disordered medium. It is based on analytical methods of the percolation theory. The infiltration of a porous medium is considered as the infiltration of pores in an infinite cluster of interconnected pores. Using the model of randomly situated spheres (RSS), we have been able to take into account the correlation effect of the spatial arrangement and connectivity of pores in the medium. The other correlation effect of the mutual arrangement of filled and empty pores on the shell of an infinite percolation cluster of filled pores determines the infiltration fluctuation probability. This probability has been calculated analytically. Allowance for these correlation effects during infiltration and defiltration makes it possible to suggest a physical mechanism of the contact angle hysteresis and to calculate the dependences of the contact angles on the degree of infiltration, porosity of the medium, and temperature. Based on the suggested model, we have managed to describe the temperature dependences of the infiltration and defiltration pressures and the thermal effects that accompany the absorption of energy by disordered porous medium-nonwetting liquid systems with various porosities in a unified way.     

Fluctuations of the number of neighboring pores and appearance of multiple nonergodic states of a nonwetting liquid confined in a disordered nanoporous medium

Multiple nonergodic states have been observed for nonwetting liquid in the Fluka100 C18 and Fluka100 C8 porous media with broad pore size distributions having different widths. The dispersion transition where the volume of confined liquid depends critically on the degree of filling of the porous medium and temperature is observed in the temperature range 293–343 K under study for the Fluka100 C18 porous medium and is not observed for the Fluka100 C8 porous medium. A mechanism of the appearance of multiple nonergodic states has been proposed. It has been shown that fluctuations of the number of the nearest neighbors in the disordered system are mainly responsible for the features of confinement of nonwetting liquid and nonergodic states of nonwetting liquid in the nanoporous media under investigation with wide pore size distributions.     

The percolation transition in filling a nanoporous body by a nonwetting liquid

The paper presents the results of an experimental study of the percolation transition in filling by nonwetting liquids of nanoporous bodies of various natures with different specific surface areas and mean pore and granule sizes. The liquid that we used was an aqueous solution of ethylene glycol. The hysteresis and non-outflow phenomena observed in this transition at various (known) surface energies of liquids were studied by varying the concentration of ethylene glycol. This helped us explain the mechanism of the percolation transition in filling nanoporous bodies with nonwetting liquids. It was shown that, to quantitatively describe the observed dependences in terms of percolation theory taking into account energy barriers to filling, we must use a non-scaling distribution function of clusters of accessible and filled pores that admits the formation of pore clusters of arbitrary dimensions.     

Observation of a dispersion transition and the stability of a liquid in a nanoporous medium

It has been found that the removal of overpressure is accompanied by a transition of some nonwetting-liquid nanoclusters to the stable state in narrow ranges of the filling factor and temperature. This means that the nonwetting liquid becomes ??wetting.??     

Investigation of the dynamics of a percolation transition under rapid compression of a nanoporous body-nonwetting liquid system

The dynamics of infiltration of a nanoporous body with a nonwetting liquid under rapid compression is studied experimentally and theoretically. Experiments are carried out on systems formed by a hydrophobic nanoporous body Libersorb 23, water, and an aqueous solution of CaCl₂ at a compression rate of \(\dot p\) ≥ 10⁴ atm/s. It is found that the infiltration begins and occurs at a new constant pressure independent of the compression energy and viscosity of the liquid. The time of infiltration and the filled volume increase with the compression energy. A model of infiltration of a nanoporous body with a nonwetting liquid is constructed; using this model, infiltration is described as a spatially nonuniform process with the help of distribution functions for clusters formed by pores accessible to infiltration and filled ones. On the basis of the proposed system of kinetic equations for these distribution functions, it is shown that under rapid compression, the infiltration process must occur at a constant pressure p _c whose value is controlled by a new infiltration threshold θ _c = 0.28 for the fraction of accessible pores, which is higher than percolation threshold θ _c0 = 0.18. Quantity θ _c is a universal characteristic of porous bodies. In the range θ _c0 < θ < θ _c , infiltration of the porous body should not be observed. It is shown that the solution to the system of kinetic equations leads to a nonlinear response by the medium to an external action (rapid compression), which means the compensation of this action by percolation of the liquid from clusters of filled pores of finite size to an infinitely large cluster of accessible but unfilled pores. As a result of such compensation, infiltration is independent of the viscosity of the liquid. It is found that all experimental results can be described quantitatively in the proposed model.     

Analysis of permeability and percolation properties of systems of solid rectangular particles by computer simulation method

A 2D porous medium containing solid rectangular particles has been investigated using the computer simulation method. We have used the model of nonintersecting rectangles on a square lattice. An analysis of the effect of area, linear sizes, and degree of orientation of rectangles on the percolation of pores and particles of the system has been carried out for different methods of lattice filling. The resulting dependences have been compared and an explanation of the observed effects has been proposed.     

Percolation transition in carbon composite on the basis of fullerenes and exfoliated graphite

The electrical conductivity of a carbon composite on the basis of C₆₀ fullerenes and exfoliated graphite is investigated in the range of relative contents of components from 0 to 100%. The samples are obtained by the thermal treatment of the initial dispersed mixtures in vacuum in the diffusion–adsorption process and their further cold pressing. The resistivity of the samples gradually increases with an increase in the fraction of fullerenes, and a sharp transition from the conductive state to the dielectric one is observed after achieving certain concentrations of C₆₀. The interpretation of the results within the percolation theory makes it possible to evaluate the percolation threshold (expressed as a relative content of graphite) as equal to 4.45 wt % and the critical conductivity index as equal to 1.85 (which is typical for three-dimensional twocomponent disordered media including those having pores).

     

Effective permittivity of liquid crystal nanodispersions and composites with different pore structure

The volume filling fraction dependence of the effective permittivity of the nematic liquid crystal 4-n-pentyl-4’-cyanobiphenyl embedded in different porous membranes and dispersed with aerosil nanoparticles was determined using broadband dielectric spectroscopy in the frequency range from 10⁶ to 10⁹ Hz. The experimental data were analyzed and compared with some existing theories based on the effective medium approximation and their modifications. The obtained effective permittivities as a function of the volume filling fraction lie between the lower limits of the Wiener and Hashin–Shtrikman bounds. The observed shift of the experimental points reflects the changes in the structure of the investigated composites.     

Optical percolation in ceramics assisted by porous clusters

We investigated optical transparency in ceramics assisted by disordered porous clusters. The structure and statistical properties of three-dimensional (3D) well porous ceramics is studied. Theoretical model based on the percolation theory and numerical simulations are applied to interpret the observed phase transition from an optically opaque state to a transparent state. The porous ceramic samples were fabricated by the technique of slurry casting. The transmission of optical radiation (optical percolation) over the entire porous samples is observed since the critical concentration of porosity was exceeded. We explain this effect by the rising of the spanning cluster inside of the porous structure that produces a network of porous voids. Our experimental results are in good agreement with the numerical simulations.     

Small-angle x-ray scattering in a carbon-sulfur nanocomposite produced from bulk nanoporous carbon

A new nanocomposite material containing approximately 50 vol % S is prepared by filling pores of bulk nanoporous carbon samples with sulfur. The initial nanoporous carbon samples are synthesized from polycrystalline α-SiC through the chemical reaction. A comparative investigation of small-angle x-ray scattering (SAXS) is performed for the prepared nanocomposite and the initial material. The possible changes in the scattering power of the initial material upon filling of its pores with sulfur are considered in the framework of a simple model. The regularities revealed are used to interpret the experimentally observed changes in the scattering power. The size distribution functions of incorporated sulfur nanoclusters in the nanocomposite (or filled nanopores in the initial material) are determined within the Guinier approximation. It is demonstrated that the smallest sized pores (8–16 Å) remain unfilled, whereas the filling factor for larger sized pores can reach several ten percent by volume. The conditions favorable for small-angle x-ray scattering upon filling of the nanopores are analyzed.     

Transition to spatiotemporal chaos in a two-dimensional hydrodynamic system

We study the transition to spatiotemporal chaos in a two-dimensional hydrodynamic experiment where liquid columns take place in the gravity induced instability of a liquid film. The film is formed below a plane grid which is used as a porous media and is continuously supplied with a controlled flow rate. This system can be either ordered (on a hexagonal structure) or disordered depending on the flow rate. We observe, for the first time in an initially structured state, a subcritical transition to spatiotemporal disorder which arises through spatiotemporal intermittency. Statistics of numbers, creations, and fusions of columns are investigated. We exhibit a critical behavior close to the directed percolation one.     

Electret processes in disordered systems based on liquid dispersion media

Electret-thermal analysis (ETA) of disordered systems based on dispersed media is carried out. It is shown that the method of thermally stimulated currents makes it possible to estimate the structural changes occurring in a liquid dispersion medium. It is found that liquid water in a free state exhibits the electret properties. The observed multiple peaks on the thermally stimulated current curve are the evidence of the multicomponent nature of the ??free water?? system. The mechanisms of processes leading to the formation of the electret state in such systems are considered.     

Investigation of the dependence of the photoluminescence properties of silicon nanoclusters on their volume fraction in a silicon oxide matrix

The photoluminescence (PL) spectra and kinetics of amorphous and crystalline silicon nanoclusters are investigated. The given nanoclusters are formed by thermal annealing of thin suboxide silicon films with different volume fractions of silicon. It is demonstrated that the PL intensity and lifetime of the ensembles of silicon nanocrystals have a steplike dependence on the silicon volume fraction in the film. The influence of the percolation effect on the photoluminescence properties of the structures under study is discussed.     

NMR study of the vapor phase contribution to diffusion in partially filled silica glasses with nanometer and micrometer pores

The contribution of the vapor phase to molecular diffusion in porous silica glasses with nanometer (Vycor) and micrometer (VitraPor#5) pores partially filled with water (polar) or cyclohexane (nonpolar) was investigated with the aid of field-gradient NMR diffusometry. Due to the vapor phase, the effective diffusion coefficient of cyclohexane filling micrometer pores (VitraPor#5) increased up to 10 times relative to the value in bulk liquid upon reduction of the pore space filling factor. On the other hand, the effective diffusion coefficient of water first decreases and then increases when the liquid content is reduced. The dependence of the effective diffusion coefficient on the pore filling factor is strongly related to the pore dimension. A general two-phase exchange model is presented that is well accounting for all experimental diffusion features.     

DEM simulation of small particles clogging in the packing of large beads

The percolation of small particles through a periodic random loose packing of large beads is studied numerically with the Distinct Element Method. The representativity of periodic mono-sized sphere packing of varying system size was first studied by comparing their pore size distributions and tortuosities with those of a larger system, considered as an infinite medium. The results show that a periodic packing of size as low as 4-grain diameters gives a reasonable representation of the porous medium and allows reducing considerably the number of particles that has to be used in the simulations. The flow and clogging of small particles of varying concentrations and friction coefficients flowing through the former packing are then studied numerically. Results show that a steady state is rapidly reached where the mean velocity and mean vertical velocity of small particles are both constant. These mean velocities decrease with an increase in friction coefficient and in small particle concentration. The influence of the friction coefficient μ is much less marked for values of μ larger than or equal to 0.5. The distribution of small particles throughout the crossed packing becomes rapidly heterogeneous. Small particles concentrate in some pores where their velocity vanishes and where the density can reach values larger than the density of the random loose packing. The proportion of particles blocked in these pores varies linearly with concentration. Finally, the narrow throats of the porous medium responsible for blocking are identified and characterized for different values of the friction coefficient.