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.

Some features of soft matter systems

R. Hołyst

Soft Matter, 2005,1, 329-333

Pierre Gilles de Gennes was awarded a Nobel prize in physics “for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers”. Thanks to his works “soft matter” became a new legitimate discipline in physics. Soft matter includes a vast range of materials, which cannot be classified as simple liquids or solids. Many soft matter systems exhibit partially broken translational and/or rotational symmetry. In others we observe mesoscopic self-assembling into supramolecular structures leading to viscoelastic behavior. The partial ordering with viscoelastic properties, topological and geometrical complexity, and long relaxations associated with broken symmetries and/or supramolecular assembling are the main features of these systems. Among them we find liquid crystals, gels, biological membranes, colloidal suspensions, polymer solutions and polymer melts and blends, surfactant solutions etc. Typical models used in soft matter theory are based on statistical mechanics and classical thermodynamics, supplemented by the theory of elasticity, hydrodynamics and thermodynamics of irreversible processes and also some elements of the field theory. In this short overview I would like to discuss three theoretical issues related to soft matter systems: interactions, the role of the entropy, and finally the order parameter description.

Minimization of the Renyi entropy production in the stationary states of the Brownian process with matched death and birth rates

O. Cybulski, V. Babin and R. Hołyst

Phys. Rev. E 2004, 69, 016110

We analyze the Fleming-Viot process. The system is confined in a box, whose boundaries act as a sink of Brownian particles. The death rate at the boundaries is matched by the branching (birth) rate in the system and thus the number of particles is kept constant. We show that such a process is described by the Renyi entropy whose production is minimized in the stationary state. The entropy production in this process is a monotonically decreasing function of time irrespective of the initial conditions. The first Laplacian eigenvalue is shown to be equal to the Renyi entropy production in the stationary state. As an example we simulate the process in a two-dimensional box.

The unphysical pinning of the domain growth during the separation of homopolymer blends near the spinodal

M. Fiałkowski and R. Hołyst

J. Chem. Phys. 2004, 120, 5802

We simulate model B of mesoscopic dynamic with the Flory–Huggins free energy for the homopolymer blend. We concentrate the study on the rescaling of the spatial coordinates in the model. We show that the commonly used rescaling of the spatial coordinates, by the function vanishing at the spinodal, leads to the unphysical freezing of the domains. We study the evolution of the system in two different processes: One is the growth process induced by the temperature quench to the metastable or unstable region of the phase diagram and the second is the quench-jump process in which we first allow the system to separate below the spinodal and next heat it up below or above the spinodal. The proper rescaling avoiding the unphysical pinning of the domain growth at the spinodal is proposed.

Absorption of Mercury in Gold Films and Its Further Desorption:  Quantitative Morphological Study of the Surface Patterns

M. Fiałkowski, P. Grzeszczak, R. Nowakowski and R. Hołyst

J. Phys. Chem. B 2004, 108, 16, 5026–5030

A thin film of Au exposed to mercury vapor disrupts forming separated domains of AuHg amalgam. After evaporation of Hg at high temperature Au islands are formed and the domain pattern changes. A detailed quantitative morphological analysis and comparison of two types of surface patterns before and after the evaporation of Hg is performed. We have found that during the evaporation of Hg at high temperature the islands decrease their sizes and their shapes become more circular. The domain pattern formed by the amalgam domains is found to be characterized by one length scale. After the removal of mercury the characteristic length scale vanishes and the structure function takes the shape typical for the random droplet morphologies.

Relaxation processes in mixtures of liquid crystals and polymers near phase boundaries and during phase separation

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

J. Chem. Phys. 2004, 120, 8277

We present experimental studies of the relaxation of concentration fluctuations in a semidilute solution of polystyrene (PS) (30% by weight) in 4-cyano-44′n-octyl-biphenyl (8CB) (70% by weight) using the photon correlation spectroscopy (PCS). In the homogeneous phase there are two modes of relaxation. The slow one (typical time scale is τs=0.001 s)τs=0.001 s) is due to the diffusion of polymer chains (of molecular mass 65 000) in the LC matrix (of molecular mass 290), while the fast one has the time scale of the order of τf≈0.00001 s.τf≈0.00001 s. The amplitude of the fast mode is much weaker than the one for the slow mode. Moreover it does not depend on the scattering wave vector, q. The value of the diffusion coefficient, Dc=1/(τsq2)Dc=1/(τsq2) for the slow mode decreases with temperature according to the Arhenius law until we reach the coexistence curve. Its value close to the coexistence is Dc=4×105nm2/sDc=4×105 nm2/s and the activation energy in the homogeneous mixture is Ec=127 kJ/mol.Ec=127 kJ/mol. If we gradually undercool the mixture below the coexistence into the metastable two-phase region without inducing the phase separation we find unexpectedly that DcDc does not change with temperature even 4° below the coexistence curve. The characteristic time of the fast mode does not depend on the scattering wave vector indicating that it is related to the transient gel structure. We have shown that it is possible to measure the short time relaxation of concentration fluctuations during the phase separation in the mixture. At low temperature close to the isotropic–nematic phase transition we have observed that the relaxation is well separated in time from the typical time of the domain growth. This relaxation mode is characterized by the large diffusion coefficient D=2×108nm2/s.D=2×108 nm2/s. The mode probably comes from the coupling between the orientational dynamics of liquid crystals and the transient gel structure of polymers.

A Morphological Study of the Formation of PdHx on Thin Palladium Films

M. Fiałkowski, R. Nowakowski and R. Hołyst

J. Phys. Chem. B 2004, 108, 22, 7373–7376

We propose a mechanism for the creation of the two-dimensional ridge pattern morphology during the formation of palladium hydride on the surface of thin palladium films at 298 K. Expressions for the distribution of domain areas and circumferences, derived from the maximum entropy principle, are in very good agreement with experiment.

Liquids with internal surfaces at and out of equilibrium: the homogeneity index

M. Fiałkowski, P. Garstecki and R. Hołyst

Journal of Molecular Liquids 2004,112, 1–2, 29-35

In this article, we discuss the application of the homogeneity index to the study of the morphology of the binary mixtures (two homopolymers) undergoing phase separation below the convolute (critical) point. The homogeneity index is a measure of how homogeneous, in terms of the local curvatures, is the interface, which is formed inside the system in the process of phase separation. In this article, we will compare the value of the homogeneity index for the phase separating binary mixture with the one for magnetic systems undergoing phase ordering and also to the homogeneity index known for various bicontinuous phases observed at equilibrium in the mixtures of surfactant-water systems. We will show that the homogeneity index is probably the best tool (most sensitive) for the study of the dynamic scaling in the ordering or phase separating systems.

Percolation-to-droplets transition during spinodal decomposition in polymer blends, morphology analysis

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

J. Chem. Phys. 2004, 121, 1141

Phase separation kinetics of the off-critical mixture of polystyrene and poly(methylphenylsiloxane) is studied by the time-resolved light scattering and optical microscopy. The results from the light scattering experiments are correlated with the images obtained by the optical microscopic observation in order to find characteristic features of the scattering intensity during the percolation-to-droplets morphology transition. At the beginning of the spinodal decomposition process only a bicontinuous network is present in the system and the light scattering intensity has only one peak. The network coarsens and at the same time small droplets appear in the system resulting in a growth of the scattering intensity at very small wave vectors. When the large network starts to break up into disjoint elongated domains a second peak in the scattering intensity appears. Finally, both peaks merge into a single peak at zero wave vector, indicating a complete transformation of elongated domains into spherical droplets of variable sizes. The comparison of the direct microscopic observations with the light scattering spectra shows that the process of breaking up of the bicontinuous network starts when the growth of the first peak, corresponding to the bicontinuous pattern, becomes very slow (essentially pinned down).

Photonic properties of an inverted face centered cubic opal under stretch and shear

V. Babin, P. Garstecki and R. Hołyst

Appl. Phys. Lett. 2003, 82, 1553

We present the results of numerical calculations of the dispersion relations for an inverted fcc opal structure subjected to a stretch and shear. We find that shearing of the crystal only lowers the gap width and slightly changes the midgap frequency. Interestingly, that in a large range of stretch amplitudes (up to 10%) the gap width is preserved and even slightly enhanced. The midgap frequency depends almost linearly on the stretch amplitude allowing for tuning an inverted fcc opal structure to a desired operational frequency. This last property may be important for the manufacturing process.

Polymer Domain Growth in Ordered Liquid Crystalline Matrices

M. Graca, S. A. Wieczorek and R. Hołyst

Phys. Rev. Lett. 2003, 90, 115504

The growth of polymer domains in the isotropic, nematic, and smectic matrices is studied by the light scattering. In the smectic and isotropic matrices the growth is diffusive, and in the nematic matrix it is influenced by the elastic forces. The scaling is obeyed. A crossover to the wetting fast-mode hydrodynamic regime is also observed at long times. In order to perform these measurements we had to eliminate the multiple scattering of light.

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