Three-dimensional space partition based on the first Laplacian eigenvalues in cells

O. Cybulski and R. Hołyst

Phys. Rev. E 2008, 77, 056101

We determine a partition of three-dimensional space into cells by minimization of the sum of the first Laplacian eigenvalues over the cells. This partitioning scheme emerges as a stationary state of a reaction-diffusion process taking place in a system of n different species which mutually annihilate, and simultaneously are duplicated in an autocatalytic reaction, so that the number of particles is kept constant and equal for each species. The system is considered in the limit of strong reactivity, so that the species separate each other into cells with well-defined, sharp boundaries. For a given n and fixed sizes of a periodic simulation box, this partition minimizes the aforementioned sum of eigenvalues. Further minimization is done by changing n and the side ratio of the periodic box. The global minimum is obtained for the structure with A15 symmetry, similar to the Weaire-Phelan foam. Depending on n and the side ratio, there are also many local minima, in particular: hcp (hexagonal close packed), fcc (face centered cubic), the Kelvin structure, and Frank-Kasper sigma phase.

Late Stage of the Phase-Separation Process: Coalescence-Induced Coalescence, Gravitational Sedimentation, and Collective Evaporation Mechanisms

T. Kalwarczyk, N. Ziebacz, M. Fiałkowski and R. Hołyst

Langmuir 2008, 24, 13, 6433–6440

We study the separation in the binary and ternary mixtures of the water/surfactant C12E5/polymer PEG system. The phase separation in the mixtures at late stages is governed by two distinct mechanisms: the coalescence-induced coalescence and the droplet evaporation mechanism. We show that when the coalescence-induced coalescence process is globally terminated in the sample consisting of a dense system of domains, another mechanism, which we call the collective droplet evaporation, starts to dominate. It manifests itself as a front of “evaporating” domains, which propagates at constant speed in the system. We show that the collective evaporation is induced by the gravitational drift of large droplets.

Dynamics of Phase Separation in Polymer Blends Revisited: Morphology, Spinodal, Noise, and Nucleation

M. Fiałkowski and R. Hołyst

Macromolecular Theory and Simulations, 2008, 17, 6, 263-273

The properties of the model B of mesoscopic dynamic with the Flory–Huggins free energy for the homopolymer blend are discussed. We focus on the rescaling of the spatial coordinates in the model and demonstrate that the commonly used rescaling of the spatial coordinates by the function vanishing at the spinodal leads to the unphysical pinning of the domains. The proper rescaling function for the spatial variables which avoids the unphysical pinning of the domain growth at the spinodal is proposed. We discuss in detail the evolution of morphological measures during separation in homopolymer blends and the problem of nucleation close to the spinodal.

Collective Rotations of Ferroelectric Liquid Crystals at the Air/Water Interface

P. Milczarczyk-Piwowarczyk, A. Żywociński, K. Noworyta and R. Hołyst

Langmuir 2008, 24, 21, 12354–12363

We study the Langmuir monolayers of four different ferroelectric liquid crystals on water surface. Two of them are attached to water surface by their polar groups, and the chiral groups, at the opposite ends of the elongated molecules, remain well above the interface. The other two ferroelectrics have both groups (polar and chiral) at close proximity, and therefore the chiral group is also attached to the surface or even submerged in water. We demonstrate that only when the chiral group of the ferroelectric liquid crystal in Langmuir monolayer is not attached to the interface and stays in the air does the system exhibit the collective rotations induced by evaporation of water (described for the first time by: Tabe, Y.; Yokoyama, H. Nat. Mater20032, 806). The isotherms of surface pressure and surface potential versus molecular area of four compounds were measured with simultaneous observations using Brewster angle microscopy. Experimental data of the compression isotherms are described with a van der Waals model with very good accuracy, and the fitted parameters were used for calculations of compressibility coefficients for different phases found in the compounds under investigations. The ability of the two compounds for rotation and the disability of the two others is discussed in a context of thermodynamic properties of the monolayers.

Hydrogen storage in nanoporous carbon materials: myth and facts

P. Kowalczyk, R. Hołyst, M. Terrones and H. Terrones

Phys. Chem. Chem. Phys., 2007,9, 1786-1792

We used Grand canonical Monte Carlo simulation to model the hydrogen storage in the primitive, gyroid, diamond, and quasi-periodic icosahedral nanoporous carbon materials and in carbon nanotubes. We found that none of the investigated nanoporous carbon materials satisfy the US Department of Energy goal of volumetric density and mass storage for automotive application (6 wt% and 45 kg H2 m−3) at considered storage condition. Our calculations indicate that quasi-periodic icosahedral nanoporous carbon material can reach the 6 wt% at 3.8 MPa and 77 K, but the volumetric density does not exceed 24 kg H2 m−3. The bundle of single-walled carbon nanotubes can store only up to 4.5 wt%, but with high volumetric density of 42 kg H2 m−3. All investigated nanoporous carbon materials are not effective against compression above 20 MPa at 77 K because the adsorbed density approaches the density of the bulk fluid. It follows from this work that geometry of carbon surfaces can enhance the storage capacity only to a limited extent. Only a combination of the most effective structure with appropriate additives (metals) can provide an efficient storage medium for hydrogen in the quest for a source of “clean” energy.

Net charge and electrophoretic mobility of lysozyme charge ladders in solutions of nonionic surfactant

J. Szymański, E. Poboży, M. Trojanowicz, A. Wilk, P. Garstecki and R. Hołyst

J. Phys. Chem. B 2007, 111, 19, 5503–5510

We report on the electrophoretic mobility and on the thermal diffusion of lysozyme proteins dissolved in aqueous solutions of a nonionic surfactant (C12E6) at a wide range of concentrations of the surfactant (0−20% by weight). We want to estimate the influence of a dense network of elongated micelles of C12E6 on the effective charge of the proteins as observed in the capillary electrophoresis experiments. The possible mechanism leading to the change in the effective charge of protein could involve the deformation of the cloud of counterions around the protein when it squeezes through the narrow (of the order of a protein diameter) aqueous channels formed in the solution of elongated micelles. The combination of independent measurements of the electrophoretic mobility of a family of modified proteins (lysozyme charge ladder [Colton et al. J. Am. Chem. Soc1997119, 12701]), of the microviscosity of the solutions of surfactant (obtained via fluorescence correlation spectroscopy), and of the hydrodynamic radius of the proteins (photon correlation spectroscopy) allow us to conclude that the effective charge of the proteins is not affected by the presence of surfactant, even at high concentrations.

Influence of poly(ethylene glycol) molecular mass on separation and in solutions of CiEj nonionic surfactants: Depletion interactions and steric effects

S. Makulska, E. Chudy, K. Urbaniak, S. A. Wieczorek, A. Zywocinski and R. Holyst

J. Phys. Chem. B 2007, 111, 28, 7948–7953

We study ternary mixtures of nonionic surfactants CiEj (i = 12; j = 5, 6, 8) and poly(ethylene glycol) (PEG) in water. For sufficiently large molecular mass of PEG (M >Msep ∼ 600), we observe a lowering of phase separation temperature with an increase in polymer concentration. The value of Msep is consistent with the analysis based on depletion interactions between micelles induced by polymer chains. We also demonstrate that there is another critical molecular mass of PEG (M = M* ∼ 2000) necessary to induce ordering in the surfactant-rich phase. This critical molecular mass follows from two requirements:  (a) PEG has to reduce the separation temperature below a temperature of hexagonal−isotropic phase transition in a binary surfactant−water mixture and (b) the PEG radius of gyration has to be larger than the size of the water channels in the hexagonal phase.

Brownian motion with inert drift, but without flux: A model

K. Burdzy, R. Hołyst and Ł. Pruski

Physica A: Statistical Mechanics and its Applications 2007, 384, 2, 278-284

We study the motion of a Brownian particle which interacts with a stationary obstacle in two dimensions. The Brownian particle acquires drift proportionally to the time spent on the boundary of the obstacle. The system approaches equilibrium, and the equilibrium distribution for the location and drift magnitude has the product form. The distribution for the location is uniform, while the drift distribution depends on the shape of the obstacle, resembling a gamma function for the circular or elliptic obstacle.

Kinetics and dynamics of dissolution/mixing of a high-viscosity liquid phase in a low-viscosity solvent phase

T. Kalwarczyk, N. Ziebacz, S. A. Wieczorek and R. Holyst

J. Phys. Chem. B 2007, 111, 41, 11907–11914

We studied mixing in the initially separated binary mixture of polystyrene/5CB liquid crystal and ternary mixtures of water/surfactant C12E5/polymer PEG system. In both systems the domains of one phase were characterized by a much higher viscosity than the solvent matrix. We demonstrated experimentally that during mixing these domains decrease their size linearly with time without a visible change of the optical contrast (i.e., without a rapid change of their compositions). Computer simulations and a theoretical model explain quantitatively our experimental observations.

Kinetic Trapping of Large Amount of Long Polymers in Nanopores

A. Żywociński, A. Korda, J. Gosk, S. A. Wieczorek, A. Wilk and R. Hołyst

J. Am. Chem. Soc. 2007, 129, 44, 13398–13399

It is well-established that when polymer size exceeds the size of a confining space, the equilibrium partition of polymer between the confined space and the bulk solution is zero. Surprisingly, we found that the long water-soluble polymers with a small hydrophobic group can be efficiently trapped inside the water channels (nanopores) of the hexagonal phase of non-ionic surfactant.

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.

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