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.

Distribution of Carbon Nanotube Sizes from Adsorption Measurements and Computer Simulation

P. Kowalczyk, R. Hołyst, H.Tanaka and K. Kaneko

J. Phys. Chem. B 2005, 109, 30, 14659–14666

The method for the evaluation of the distribution of carbon nanotube sizes from the static adsorption measurements and computer simulation of nitrogen at 77 K is developed. We obtain the condensation/evaporation pressure as a function of pore size of a cylindrical carbon tube using Gauge Cell Monte Carlo Simulation (Gauge Cell MC). To obtain the analytical form of the relationships mentioned above we use Derjaguin−Broekhoff−deBoer theory. Finally, the pore size distribution (PSD) of the single-walled carbon nanohorns (SWNHs) is determined from a single nitrogen adsorption isotherm measured at 77 K. We neglect the conical part of an isolated SWNH tube and assume a structureless wall of a carbon nanotube. We find that the distribution of SWNH sizes is broad (internal pore radii varied in the range 1.0−3.6 nm with the maximum at 1.3 nm). Our method can be used for the determination of the pore size distribution of the other tubular carbon materials, like, for example, multiwalled or double-walled carbon nanotubes. Besides the applicable aspect of the current work the deep insight into the problem of capillary condensation/evaporation in confined carbon cylindrical geometry is presented. As a result, the critical pore radius in structureless single-walled carbon tubes is determined as being equal to three nitrogen collision diameters. Below that size the adsorption−desorption isotherm is reversible (i.e., supercritical in nature). We show that the classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena is a powerful method that can be applied for the determination of the distribution of nanotube sizes.

Tiling a Plane in a Dynamical Process and its Applications to Arrays of Quantum Dots, Drums, and Heat Transfer

O. Cybulski and R. Hołyst

Phys. Rev. Lett. 2005, 95, 088304

We present a reaction-diffusion system consisting of N components. The evolution of the system leads to the partition of the plane into cells, each occupied by only one component. For large N, the stationary state becomes a periodic array of hexagonal cells. We present a functional of the densities of the components, which decreases monotonically during the evolution and attains its minimal value in the stationary state. This value is equal to the sum of the first Laplacian eigenvalues for all cells. Thus, the resulting partition of the plane is determined by minimization of the sum of the eigenvalues, and not by the minimization of the total perimeter of the cells as in the famous honeycomb problem.

Relaxation Processes in Semidilute Solutions of Polymers in Liquid Crystal Solvents

S. A. Wieczorek, E. Freyssingeas and R. Hołyst

J. Phys. Chem. B 2005, 109, 34, 16252–16262

We investigate the relaxation phenomena in a polymer (polystyrene)/liquid crystal (4-cyano-4‘-n-octyl-biphenyl) system, in its homogeneous isotropic phase near the isotropic−isotropic, isotropic−nematic, and isotropic−smectic coexistence curve, using both polarized and depolarized photon correlation spectroscopy (PCS). We study this system for different polystyrene molecular weights (4750, 12 500, and 65 000 g/mol), different compositions (50, 40, 30, and 10% polystyrene (PS) by weight), and different temperatures close to phase boundaries. First of all, we determine the phase diagrams of this system for the different molecular weights. The shape of the phase diagrams strongly depends on the molecular weight. However, in all cases, at low temperatures, these systems separate into an almost pure liquid crystalline (LC) phase and polystyrene-rich phase. PCS measurements show that the relaxation processes in the homogeneous phase are not affected by the proximity of the nematic, or smectic, boundaries (even at a temperature of 0.1 °C above the phase separation in two phases). In polarized PCS experiments, we always see three relaxation processes well separated in time:  one, very fast, with a relaxation time of the order of 10-5 s; a second one with a relaxation time within the range 10-2−10-3 s; and a last one, very slow, with a relaxation time of the order of 1 s. Both the fast and slow modes are independent of the wave vector magnitude, while the intermediate relaxation process is diffusive. In depolarized PCS experiments, the intermediate mode disappears and only the fast and slow relaxation processes remain, and they are independent of the magnitude of the wave vector. The diffusive mode is the classical diffusive mode, which is associated with the diffusion of polymer chains in all polymer solutions. The fast mode is due to the rotational diffusion of 4-cyano-4‘-n-octyl-biphenyl (8CB) molecules close to polystyrene chains (transient network). Finally, we assign the slowest mode to reorientational processes of small aggregates of PS chains that are not dissolved in 8CB.

Condensation of a vapor bubble in submicrometer container

V. Babin, and R. Holyst

J. Chem. Phys. 2005, 123, 104705

Condensation of a spherically symmetric submicrometer size vapor bubble is studied using diffuse interface hydrodynamic model supplemented by the van der Waals equation of state with parameters characteristic for argon. The bubble, surrounded by liquid, is held in a container of constant volume with temperature of the wall kept fixed. The condensation is triggered by a sudden rise of the wall temperature. We find that in the same container and subjected to a similar increase of the wall temperature the condensation process is totally different from the opposite process of droplet evaporation. In particular, the rapid change of the wall temperature excites the wave, which hits the interface and compresses the bubble, leading to a considerable increase of the temperature inside. The condensation of the submicrometer size bubble takes tens of nanoseconds, whereas evaporation of the same size droplet lasts roughly 50 times longer. In contrast to evaporation the condensation process is hardly quasistationary.

Storage of hydrogen at 303 K in graphite slitlike pores from grand canonical Monte Carlo simulation

P. Kowalczyk, H. Tanaka, R. Hołyst, K. Kaneko, T. Ohmori and J. Miyamoto

J. Phys. Chem. B 2005, 109, 36, 17174–17183

Grand canonical Monte Carlo (GCMC) simulations were used for the modeling of the hydrogen adsorption in idealized graphite slitlike pores. In all simulations, quantum effects were included through the Feynman and Hibbs second-order effective potential. The simulated surface excess isotherms of hydrogen were used for the determination of the total hydrogen storage, density of hydrogen in graphite slitlike pores, distribution of pore sizes and volumes, enthalpy of adsorption per mole, total surface area, total pore volume, and average pore size of pitch-based activated carbon fibers. Combining experimental results with simulations reveals that the density of hydrogen in graphite slitlike pores at 303 K does not exceed 0.014 g/cm3, that is, 21% of the liquid-hydrogen density at the triple point. The optimal pore size for the storage of hydrogen at 303 K in the considered pore geometry depends on the pressure of storage. For lower storage pressures, p < 30MPa, the optimal pore width is equal to a 2.2 collision diameter of hydrogen (i.e., 0.65 nm), whereas, for p ≅ 50MPa, the pore width is equal to an approximately 7.2 collision diameter of hydrogen (i.e., 2.13 nm). For the wider pores, that is, the pore width exceeds a 7.2 collision diameter of hydrogen, the surface excess of hydrogen adsorption is constant. The importance of quantum effects is recognized in narrow graphite slitlike pores in the whole range of the hydrogen pressure as well as in wider ones at high pressures of bulk hydrogen. The enthalpies of adsorption per mole for the considered carbonaceous materials are practically constant with hydrogen loading and vary within the narrow range qst ≅ 7.28−7.85 kJ/mol. Our systematic study of hydrogen adsorption at 303 K in graphite slitlike pores gives deep insight into the timely problem of hydrogen storage as the most promising source of clean energy. The calculated maximum storage of hydrogen is equal to ≈1.4 wt %, which is far from the United States Department of Energy (DOE) target (i.e., 6.5 wt %), thus concluding that the total storage amount of hydrogen obtained at 303 K in graphite slitlike pores of carbon fibers is not sufficient yet.

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