State of Hydrogen in Idealized Carbon Slitlike Nanopores at 77 K

P. Kowalczyk, R. Hołyst, A. P. Terzyk and P. A. Gauden

Langmuir 2006, 22, 5, 1970–1972

The purpose of this letter is to clarify recent findings and answer to the question:  “What is the state of hydrogen in carbon slitlike pores at 77 K?” For this purpose, we determined the volumetric density of hydrogen in idealized carbon pores of molecular dimension at 77 K and pressure up to 1 MPa. We used quantum corrected grand canonical Monte Carlo simulation. We recognized the highest volumetric density of confined hydrogen (around 71% of hydrogen liquid at boiling point) for effective pore width 5.6 Å (H* = 3.04) in the considered pressure range. Our computational results are in agreement with the calculations performed by Wang and Johnson and Rzepka et al. In contrast, we did not observe the high volumetric density of hydrogen in slitlike carbon pores exceeding the density of hydrogen liquid at the boiling point as was reported by Jagiello and Thommes. Moreover, we obtained qualitative agreement between the simulation results and some experimental findings reported by Nijkamp.

Movement of Proteins in an Environment Crowded by Surfactant Micelles:  Anomalous versus Normal Diffusion

J. Szymański, A. Patkowski, J. Gapiński, A. Wilk and R. Hołyst

J. Phys. Chem. B 2006, 110, 14, 7367–7373

Small proteins move in crowded cell compartments by anomalous diffusion. In many of them, e.g., the endoplasmic reticulum, the proteins move between lipid membranes in the aqueous lumen. Molecular crowding in vitro offers a systematic way to study anomalous and normal diffusion in a well controlled environment not accessible in vivo. We prepared a crowded environment in vitro consisting of hexaethylene glycol monododecyl ether (C12E6) nonionic surfactant and water and observed lysozyme diffusion between elongated micelles. We have fitted the data obtained in fluorescence correlation spectroscopy using an anomalous diffusion model and a two-component normal diffusion model. For a small concentration of surfactant (below 4 wt %) the data can be fitted by single-component normal diffusion. For larger concentrations the normal diffusion fit gave two components:  one very slow and one fast. The amplitude of the slow component grows with C12E6 concentration. The ratio of diffusion coefficients (slow to fast) is on the order of 0.1 for all concentrations of surfactant in the solution. The fast diffusion is due to free proteins while the slow one is due to the protein−micelle complexes. The protein−micelle interaction is weak since even in a highly concentrated solution (35% of C12E6) the amplitude of the slow mode is only 10%, despite the fact that the average distance between the micelles is the same as the size of the protein. The anomalous diffusion model gave the anomality index (〈r2(t)〉 ∼ tα), α monotonically decreasing from α = 1 (at 4% surfactant) to α = 0.88 (at 37% surfactant). The fits for two-component normal diffusion and anomalous diffusion were of equally good quality, but the physical interpretation was only straightforward for the former.

Phase Separation in Binary Polymer/Liquid Crystal Mixtures:  Network Breaking and Domain Growth by Coalescence-induced Coalescence

I. Demyanchuk, S. A. Wieczorek and R. Hołyst

J. Phys. Chem. B 2006, 110, 20, 9869–9875

A small-angle light scattering (SALS) technique together with optical microscopy observation are used to investigate phase separation kinetics in films of low molecular weight thermotropic liquid crystal (4-cyano-4‘-n-octyl-biphenyl, 8CB) with flexible polymer (polystyrene, PS). The growth of domains is studied as a function of time, film thickness, and film composition. The light scattering results are correlated with the images obtained by optical microscopy observation. In this paper, we study the breaking of a bicontinuous network of polymer in liquid crystal into droplets and their further growth via the coalescence-induced coalescence mechanism. The appearance of droplets in the system leads to a strong scattering at small wave vectors, while the bicontinuous network gives a peak at a nonzero wave vector. Superposition of these scattering intensities leads to the appearance of a second peak in the full scattering intensity signal, when the bicontinuous network starts to break up into disjointed elongated domains. Finally, both peaks merge into a single peak, which moves quickly toward zero wave vectors, indicating a complete transformation of elongated domains into spherical droplets of variable size. We found that the separation process does not depend on the size of the system. Irrespective of the sample thickness, the network breaks into fragments always at the same time after temperature quench. On the basis of morphological analysis, we found that the average size of the droplets which formed from the network grows with time, t, as tα, α = 0.9 ± 0.1, in the isotropic phase and in the nematic phase.

Diffusion and Viscosity in a Crowded Environment:  from Nano- to Macroscale

J. Szymański, A. Patkowski, A. Wilk, P. Garstecki and R. Holyst

J. Phys. Chem. B 2006, 110, 51, 25593–25597

Although water is the chief component of living cells, food, and personal care products, the supramolecular components make their viscosity larger than that of water by several orders of magnitude. Using fluorescence correlation spectroscopy (FCS), photon correlation spectroscopy (PCS), NMR, and rheology data, we show how the viscosity changes from the value for water at the molecular scale to the large macroviscosity. We determined the viscosity experienced by nanoprobes (of sizes from 0.28 to 190 nm) in aqueous micellar solution of hexaethylene-glycol-monododecyl-ether (in a range of concentration from 0.1% w/w to 35% w/w) and identified a clear crossover at the length scale of 17 ± 2 nm (slightly larger than persistence length of micelles) at which viscosity acquires its macroscopic value. The sharp dependence of the viscosity coefficients on the size of the probe in the nanoregime has important consequences for diffusion-limited reactions in crowded environments (e.g., living cells).

Evaporation of a thin liquid film

V. Babin and R. Hołyst

J. Chem. Phys. 2005, 122, 024713

Evaporation of a thin (submicrometer size) liquid film confined between two solid substrates is studied using diffuse interface hydrodynamic model supplemented by the van der Waals equation of state. The time and space evolution of the basic thermodynamic quantities such as temperature, density, entropy, chemical potential, and entropy production is presented. The values of numerical parameters chosen correspond to those of argon. The time and space scales studied range from picoseconds to microseconds and from nanometers to micrometers correspondingly.

Global symmetry breaking in the nonconserved order parameter system during phase ordering

M. Fiałkowski and R. Hołyst

The European Physical Journal E 2005, 6, 247–251

We study global symmetry breaking in the 2D system of scalar nonconserved order parameter following a quench to zero temperature. We show that the instant of time when the symmetry is broken and the final morphology is chosen corresponds to the saturation of the order parameter inside the domains. There are three possible final morphologies: the positive and negative order parameter final morphology, and the state of the coexisting positive and negative order parameter subsystems with a flat interface between them. We find also that each type of the final morphology constitutes about 1/3 of all cases, what agrees with the results obtained recently by Spirin et al. [Phys. Rev. E 65, 016119 (2001)]. Our results are pertinent for the two dimensional systems, but we suspect that there is also a way to apply similar arguments for the three dimensional ones.

Coalescence-Induced Coalescence and Dimensional Crossover during the Phase Separation in Ternary Surfactant/Polymer/Water Mixtures

I. Demyanchuk, K. Staniszewski and R. Hołyst

J. Phys. Chem. B 2005, 109, 10, 4419–4424

We studied the separation process in the ternary mixtures of nonionic surfactant (C12E6, hexaethylene glycol monododecyl ether), polymer (PEG = poly(ethylene glycol)), and water. The separation process of PEG/water rich domains from the surfactant rich matrix was observed by the optical microscopy. From the morphological analysis, we determined the size of the domains as a function of time. On this basis we identified a dominating mechanisms of domains growth, that is the coalescence-induced coalescence mechanism. The coalescence (collision) event of two droplets induces a flow or a change of concentration distribution around droplets which pushes other droplets together inducing further growth. We also observed the evaporation−condensation (Lifshitz−Slyozov) mechanism of growth, but it did not affect the growth of large domains appreciably. We determined two regimes of the coalescence-induced coalescence associated with the dimensionality of the system. When the domains were smaller or comparable in size to the sample thickness we observe a three-dimensional growth. When the domains became larger than the sample thickness, a two-dimensional growth was observed. In the first regime, the size of the domains, L(t), grew linearly with t, while in the second regime, L(t) ∼ t0.3. In the binary, surfactant/water system, water domains grew by the geometrical coalescence-induced coalescence as L(t) ∼ t in three dimensions.

Ordering in Surfactant Mixtures Induced by Polymers

R. Holyst, K. Staniszewski, and I. Demyanchuk

J. Phys. Chem. B 2005, 109, 11, 4881–4886

We studied ternary mixtures of nonionic surfactant (C12E6n-dodecyl hexaoxyethylene glycol monoether), polymer (PEG, polyethylene glycol), and water. A small amount of PEG induces demixing into the polymer-rich and surfactant-rich phases in the ternary PEG/C12E6/water mixture. Above a certain concentration and/or molecular weight of PEG, the surfactant-rich phase orders, even in a solution consisting of a few percent of surfactant. The phase boundary acts as a semipermeable membrane, and the equilibrium is determined by the chemical potential of water in two phases. The explicit expression for the amount of PEG needed to order C12E6 water solution is given and verified experimentally. The analysis of the coexistence conditions leads to the conjecture that only two oxygen atoms in the outward part of the hydrophilic surfactant head strongly affect the chemical potential of water. Our methodology is generic, i.e., on the same basis one can design a similar experiment for any surfactant/polymer/water system and find the right proportions of polymer that induce order in a surfactant-rich phase.

Minimization of the Renyi entropy production in the space-partitioning process

O. Cybulski, V. Babin and R. Hołyst

Phys. Rev. E 2005, 71, 046130

The spontaneous division of space in Fleming-Viot processes is studied in terms of nonextensive thermodynamics. We analyze a system of n different types of Brownian particles confined in a box. Particles of different types annihilate each other when they come into close contact. Each process of annihilation is accompanied by a simultaneous nucleation of a particle of the same type, so that the number of particles of each component remains constant. The system eventually reaches a stationary state, in which the available space is divided into n separate subregions, each occupied by particles of one type. Within each subregion, the particle density distribution minimizes the Renyi entropy production. We show that the sum of these entropy productions in the stationary state is also minimized, i.e., the resulting boundaries between different components adopt a configuration which minimizes the total entropy production. The evolution of the system leads to decreasing of the total entropy production monotonically in time, irrespective of the initial conditions. In some circumstances, the stationary state is not unique—the entropy production may have several local minima for different configurations. In the case of a rectangular box, the existence and stability of different stationary states are studied as a function of the aspect ratio of the rectangle.

Pattern formation in nonextensive thermodynamics: Selection criterion based on the Renyi entropy production

O. Cybulski, D. Matysiak, V. Babin and R. Hołyst

J. Chem. Phys. 2005, 122, 174105

We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.

Hidden Minima of the Gibbs Free Energy Revealed in a Phase Separation in Polymer/Surfactant/Water Mixture

R. Hołyst, K. Staniszewski, A. Patkowski, and J. Gapiński

J. Phys. Chem. B 2005, 109, 18, 8533–8537

We observed a very unusual kinetic pathway in a separating C12E6/PEG/H2O ternary mixture. We let the mixture separate above the spinodal temperature (cloud point temperature) for some time and next cool it into a metastable region of a phase diagram, characterized by two minima of the Gibbs potential, one corresponding to the homogeneous mixture and one to the fully separated PEG-rich and C12E6-rich phases. Despite the fact that in the metastable region the thermodynamic equilibrium corresponds to the separated phases (global minimum of the Gibbs free energy), we observe perfect mixing of the initially separated phase. The homogeneous state, obtained in this way, does not separate, if left undisturbed. However, many cooling−heating cycles or full separation with visible meniscus above the cloud point temperature induce the phase separation in the metastable region. The metastable region can exist tens of degrees below the cloud point temperature. This effect is not observed in the binary mixture of C12E6/H2O.

Chirality-Biased Point Defects Dynamics on a Disclination Line in a Nematic Liquid Crystal

A. Żywociński, K. Pawlak, R. Hołyst and P. Oswald

J. Phys. Chem. B 2005, 109, 19, 9712–9718

Chiral additives in the nematic liquid crystal can alter the dynamics of point defects moving on a disclination line. They exert a constant force on defects, leading to the bimodal distribution of distances between them at long times. The evolution of the system of defects in the presence of chiral additives provides a very direct proof of the existence of repulsive forces between the defects at large distances. We find that addition of a sufficient amount of chiral compound removes all point defects from the system. The process is studied in the system of 8CB (4-n-octyl-4‘-cyanobiphenyl) doped with the chiral compound S811 (from Merck Co.) and in the computer simulations.

Evaporation of a Sub-Micrometer Droplet

V. Babin and R. Holyst

J. Phys. Chem. B 2005, 109, 22, 11367–11372

Evaporation of a spherically symmetric sub-micrometer size liquid droplet is studied using a diffuse interface hydrodynamic model supplemented by the van der Waals equation of state with parameters characteristic for argon. The droplet, surrounded by saturated vapor, is held in a container with the temperature of the walls kept fixed. The evaporation is triggered by a sudden rise of the temperature of the walls. Time and space evolution of the basic thermodynamic quantities is presented. The time and space scales studied range from picoseconds to microseconds and from nanometers to micrometers, respectively. We find that the temperature and chemical potential are both continuous at the interface on the scale larger than the interfacial width. We find that at long times the radius R of the droplet changes with time t as R2(t) = R2(0) − 2tκv(Tw − Tl)/𝓁nl, where κv is the heat conductivity of the vapor, nl and Tl are the density and the temperature of liquid inside the droplet, respectively, 𝓁 is the latent heat of transition per molecule, and Tw is the temperature of the ambient vapor.

Modeling of the Hysteresis Phenomena in Finite-Sized Slitlike Nanopores. Revision of the Recent Results by Rigorous Numerical Analysis

P. Kowalczyk, K. Kaneko, L. Solarz, A. P. Terzyk, H. Tanaka and R. Hołyst

Langmuir 2005, 21, 14, 6613–6627

The systematic investigation of the hysteresis phenomena in finite-sized slitlike nanopores via the Aranovich−Donohue (AD) lattice density functional theory (LDFT) is presented. The new reliable quantitative modeling of the adsorption and desorption branch of the hysteresis loop, through the formation and movement of the curved meniscus, is formulated. As a result, we find that our proposal, which closely mimics the experimental findings, can reproduce a rounded shape of the desorption branch of the hysteresis loop. On the basis of the exhausted commutations, we proved that the hysteresis loop obtained in the considered finite-sized slitlike geometry is of the H1 type of the IUPAC classification. This fundamental result and the other most important results do not confirm the results of the recent studies of Sangwichien et al., whereas they fully agree with the recent lattice studies due to Monson et al. We recognize that the nature of the hysteresis loops (i.e. position, width, shape, and the multiple steps) mainly depends on the value of the energy of both the adsorbate−adsorbate and adsorbate−adsorbent interactions; however, the first one is critical for the appearance of hysteresis. Thus, for relatively small adsorbate−adsorbate interactions, the adsorption−desorption process is fully reversible in the whole region of the bulk density. We show that the strong adsorbate−adsorbent interactions produce (also observed experimentally) multiple steps within hysteresis loops. Contrary to the other studies of the hysteresis phenomena in confined geometry via the LDFT formalism, we constructed both ascending and descending scanning curves, which are known from the experimental observations. Additionally, we consider the problem of the stability of both the obtained adsorption and desorption branches of the computed hysteresis loop in finite-sized slitlike nanopores.

Infinite networks of surfaces

R. Hołyst

Nature Materials 2005, 4, 510–511

An effective route to investigate complex periodic motifs in liquid crystals reveals that molecular packing alone can result in a tricontinuous network of channels separated by two periodic surfaces.

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