Adsorbing Wall Research Articles

Transmission conductance of a cylindrical tube with wall pumping

The concept of transmission conductance is required to describe phenomena occurring in a tube with wall pumping. This is because the gas flow is not constant along the length of the tube but decreases, which implies that the geometric conductance determined by dimensional parameters of the tube cannot be further used. In one of the previous studies, the transmission conductance of a cylindrical tube was analytically derived using the particle balance equation based on the continuity principle. However, the calculated results well agreed with those of the test particle Monte Carlo (TPMC) simulation only when the sticking coefficient was less than 0.1. This is due to the intrinsic limitation of the analytical method, in which the constant conductance of a tube of unit length with uniform wall pumping was used. In this study, we introduced another analytical method based on the cosine law and finite element analysis using the conductance of the tube of unit length as a function of the position in the tube, considering the beaming effect. Using both methods, the relative difference in transmission conductance with TPMC considerably decreased compared to the previous study when the sticking coefficient was greater than 0.1. The results can be used in the design of a non-evaporable getter coated tube or a cryogenic water pump using an adsorbing wall to determine characteristic dimensions. Furthermore, this can be employed in a windowless vacuum coupling or a distributed pumping system for various light source systems.

Effects of inclusions and the presence of an adsorbing surface on lateral and flip-flop phase transitions in fluid membranes

In this paper, we first investigate the effects of inclusions on the critical behavior of a fluid bilayer biomembrane made of two incompatible amphiphiles A and B. Upon variation of certain appropriate parameters (temperature, lateral pressure, etc.), these lipid molecules can undergo a lateral or transverse phase separation into macro-phase domains. Such transitions are of ordered liquid-disordered liquid type, and the free energy allowing the description of the physical system is a two-order parameters field theory. We show that the presence of a random distribution of inclusions (proteins, enzymes, etc.) may generate a high order coupling interaction term Ωφ2ψ2, which tends to favor flip-flop transition. We evaluate in particular the effect, close to the consolute point, of inclusions on the behavior of the composition fluctuations, φ and ψ, as well as that of the partial and the overall compressibilities in terms of temperature T and chemical potential difference Δμ. Moreover, we show that the presence of inclusions (such as translocases) leaves the values of the critical exponents unchanged, but that the amplitudes are shifted to their high values. We have also established clear links with some experimental work, which concerns a vesicle membrane, proving in particular the existence of a critical temperature Tc in the medium coupling regime. In the second part of this work, we investigate how the critical behavior of the system is affected near an adsorbing wall. We assume that one or both amphiphiles are strongly adsorbed on the surface. We assist therefore to a quenched composition on the wall. The segregation is assumed to occur at low temperature. The influence, on the critical properties of the fluid membrane, of the quenched surface fluctuations is discussed, in all cases, and the composition profile determined.

Density of Obstacles Affects Diffusion in Adsorbed Polymer Layers.

The translational diffusion of molecules dispersed into polymer matrices slows down tremendously when approaching a nonrepulsive interface. To unravel the origin of this phenomenon, we investigated the diffusion of molecular probes in the direction normal to an adsorbing wall. Using adsorbed polymer layers as matrices, wewere able todecouple interfacial and finite size effects and determined the relation between the diffusion time and the area available at the polymer/solid interface. Based on the results of our investigation, we present a physical picture, suggesting that the reduction indiffusion rate is correlated to the degree of chain adsorption onto the substrate, that is, the density of surface obstacles encountered by tracer molecules.

Computational comparison of the efficiency of nanoporous zeolite frameworks for separation of phenol from water

Abstract The adsorption through zeolite is an efficient way of phenol removal from water. The adsorption performance of all-silica zeolites including BEA (Beta), FAU (Faujasite), MFI (silicalite-1), and MOR (Mordenite) to adsorb phenol from phenol/water vapor mixture was predicted and compared through Grand Canonical Monte Carlo (GCMC) simulation. The results show that the adsorption of phenol on zeolites is a function of diameter of largest included sphere and largest free sphere dimensions at high loading (FAU > BEA > MFI > MOR). At low pressure, the phenol adsorption is a function of Framework Density, FDSi, as: MFI > MOR ∼ BEA > FAU due to dominant adsorbate–wall attractions compared to other interactions. The preferential siting of zeolite is suggested by both GCMC simulation and quantum mechanics approaches. Hydrogen bonding and dispersion can improve the formation of clusters of organic compounds in the intersection and middle channel of zeolite. In distribution function versus energy curve, FAU shows a clear peak at about −20 kcal mol−1 since it possesses supercages with one tetrahedral center. Our results show that both the difference between structures of the zeolites and the interactions can be taken into account to determine the adsorption capacity.

FORCE-INDUCED DESORPTION OF SEMI-FLEXIBLE POLYMERS IN NON-HOMOGENEOUS MEDIA

Force-induced desorption of semi-flexible linear polymers in good solvents and non-homogeneous media is studied. We apply the model of self-avoiding walk with bending rigidity on 3-simplex fractal lattice. One boundary of the lattice represents an adsorbing wall, while an external force (perpendicular to the wall) pulls the polymer from the wall. Due to the hierarchical structure of the lattice under study, the phase diagram of polymer critical behavior can be exactly studied by real-space renormalization group method. Temperature dependence of the critical force, at which desorption occurs, is obtained and discussed for various values of the bending rigidity. Influence of the force and the polymer rigidity on the nature of desorption phase transition is also analyzed. All obtained results are compared with the related previous ones.

Gas flow towards an adsorbing planar wall subject to partial gas-surface thermal accommodation

The steady half-space single gas flow driven by an adsorbing planar wall is investigated based on the solution of the BGK kinetic model. The mass and heat transfer between the gas and the plate are characterized by the sticking and thermal accommodation coefficients, the surface temperature and the far upstream velocity and temperature. The work is focused on the influence of partial thermal gas-surface interaction on all flow quantities including the sticking coefficient. It has been found that as the gas thermal accommodation on the surface is reduced, for prescribed adsorbing flux and temperature difference, the sticking coefficient must be increased to sustain the prescribed flux or otherwise for the same sticking coefficient the adsorbing flux is reduced. This behavior is enhanced as the difference, between the surface and the far upstream temperatures, is increased. Overall, the effect of the thermal accommodation coefficient is significant in all flow quantities and must be accordingly taken into consideration. The present theoretical/computational investigation of partial thermal accommodation effect may provide a more clear interpretation of measurements of sticking coefficients, and conversely, improve performance calculations for cryopumps.

Conformation and dynamics of a diluted chain in the presence of an adsorbing wall: A simulation with the bond fluctuation model

The bond fluctuation model has been used to simulate the adsorption process of a single long polymer chain on an adsorbing surface. Simulations start at high temperature with the chain in an equilibrium coil structure. The inter- and intra chain energy potential were selected in such a way that on cooling the polymer chain vitrifies without any indication of chain ordering or chain folding. The structure attained on cooling is analysed for a range of values of the interaction potential between the surface and the polymer segments. Adsorption is measured by the fraction of polymer segments situated on the adsorbing wall whilst crystalline ordering is characterized by the pair correlation function g(r), the bond order parameter P2(r) and the bond correlation function M(j). Isothermal adsorption is followed as well as a function of temperature. The work shows that adsorbing surface nucleates crystalline order by suppressing one dimension in the segmental mobility of the polymer chain, along with factors as thermal treatment and inter and intra-potentials.

High pressure effect in nanoporous carbon materials: Effects of pore geometry

Abundant experimental evidence suggests that adsorbates confined in nanoporous materials exhibit high pressures, such as high pressure crystal structures, high pressure chemical reactions, and the deformation of pore walls due to the adsorbate. We report molecular simulation studies of the pressure tensor for simple adsorbates (e.g. argon) in carbon nanopores of slit, cylindrical and spherical geometries. We find that for modest bulk phase pressures of 1bar or less, the pressures parallel to the pore walls (tangential pressure) is of the order 104–105bar, while the pressure normal to the wall is of the order of 103bar, and can be positive or negative depending on the pore size. Moreover, we find that the pore geometry has a large effect on the structure of the adsorbate and thus on the in-pore pressure because of the curvature that determines the strength of the adsorbate–wall interaction. For the same pore size, temperature and bulk pressure, the in-pore tangential pressure is the largest in spherical pores, followed by that in cylindrical pores and slit pores. We also study the normal pressure of carbon tetrachloride and water confined in activated carbon fibers by molecular simulations and experiments. The pressure acting on the pore wall is found to be of the order of several thousand bar by both methods. Experiments also find that the pore can be expanded or contracted, depending on pore width, as we predict by molecular simulation.

Force-induced desorption of self-avoiding walks on Sierpinski gasket fractals

In this work we investigate force-induced desorption of linear polymers in good solvents in non-homogeneous environment, by applying the model of self-avoiding walk on two- and three-dimensional fractal lattices, obtained as generalization of the Sierpinski gasket fractal. For each of these lattices one of its boundaries represents an adsorbing wall, whereas along one of the fractal edges, not lying in the adsorbing wall, an external force acts on the self-avoiding walk. The hierarchical nature of the lattices under study enables an exact real-space renormalization group treatment, which yields the phase diagram of polymer critical behavior. We show that for this model there is no low-temperature reentrance in the cases of two-dimensional lattices, whereas in all studied three-dimensional cases the force-temperature dependance is reentrant. We also find that in all cases the force-induced desorption transition is of first order.

A free-space density functional theory for polymer adsorption: Influence of packing effect on conformations of polymer

We propose a free-space density functional theory for polymer adsorption. The derivation within the framework of density functional theory leads to the splitting of the intrinsic free energy into an ideal-gas term and a residual term responsible for the intrinsic energy and the nonbonded interactions between monomers, respectively. A more reasonable treatment is adopted for the residual free energy to count for the monomer-monomer correlation underestimated by the local density approximation. An approach using propagators is proposed to calculate the single-chain partition function and the segment-density distributions, the three adsorption conformations as trains, loops, and tails are further described by propagators. Dirac's bra-ket notation used makes the derivation simpler and provides clearer physical meanings. The theoretical calculations for the adsorption of hard-sphere chains onto a nonadsorbing and an adsorbing hard wall show that the structure of the adsorption layer is strongly affected by the packing effect which has been underestimated by the previous lattice adsorption theory.

Effect of stiffness on the pulling of an adsorbing polymer from a wall: an exact solution of a partially directed walk model

Recently the effect of stiffness, or semi-flexibility, on the adsorption and also the collapse phase transitions of isolated polymers has been explored via the exact solutions of partially directed walk models. Here we consider its effect on the stretching transition mediated by the application of a force to one end of the polymer when the other end is attached to an adsorbing wall.

Exact solution for semi-flexible partially directed walks at an adsorbing wall

Recently it was shown that the introduction of stiffness into the model of self-interactingpartially directed walks modifies the polymer collapse transition seen from a second-orderto a first-order one. Here we consider the effect of stiffness on the adsorption transition. Weprovide the exact generating function for non-interacting semi-flexible partiallydirected walks and analyse the solution in detail. We demonstrate that stiffness doesnot change the order of the adsorption transition, in contrast to its effect oncollapse.

Simulation of Phase Transitions of Single Polymer Chains: Recent Advances

AbstractSummary:The behaviour of a flexible polymer chain in solvents of variable quality in dilute solution is discussed both in the bulk and in the presence of an adsorbing wall. Monte Carlo simulations of coarse‐grained bead‐spring models and of the bond fluctuation model are presented and interpreted in terms of phenomenological theories and scaling concepts. Particular attention is paid to the behaviour of the polymer chain when the temperature of the polymer solution gets lower than the Theta temperature. It is argued that the adsorption transition line at the Theta temperature splits into lines of wetting and drying transitions of polymer globules attached to the wall. In addition, it is shown that the coil‐globule transition is followed by a second transition, which in the bond fluctuation model is a crystallization into a regular lattice structure. Performing a finite size scaling analysis on the two transitions it is shown that (for the chosen model) both transitions coincide in the thermodynamic limit, corresponding to a direct collapse of the random coil into the crystal without intermediate coil‐globule transition. The implications of this result for the standard mean field or tricritical theory of the coil‐globule transition based on a truncated virial expansion are discussed.

Surface excess in dilute polymer solutions and the adsorption transition versus wetting phenomena

The adsorption of long flexible chains from dilute solution is studied by Monte Carlo simulation of a coarse-grained bead-spring model, and the results are interpreted in terms of phenomenological theories, using both mean field approaches and scaling concepts. It is shown that the surface excess, i.e., the integral of the local density difference of the monomers close to the surface relative to the bulk changes its sign very close to the adsorption transition (that is a sharp transition in the limit where the chain length diverges to infinity) for long chains, and it can be described in terms of the standard scaling description that has previously been tested for polymers with one end anchored on the surface (“polymer mushrooms”). Attention is also paid to the question on how this description changes when the temperature T of the polymer solution approaches the theta temperature Θ. Since the theta point can also be considered as an end point of a line of critical points, where the polymer solution phase separates into a dilute solution of collapsed chains and a more concentrated solution in the bulk, the adsorbing wall for T<Θ causes the existence of wetting layers. Conjectures about relations between wetting transitions for T near Θ and the adsorption transition are also presented.

Nonlinear effects of physisorption on static friction

The effects of a physisorbed film on the force of static friction in a model contact (monatomic adsorbate confined between plane-parallel walls) were investigated by Monte Carlo simulation. At fixed coverage the friction curve (shear yield stress vs normal stress) exhibits a marked nonlinearity, which results from a competition between adsorbate–wall interactions that predominate at low loads and wall–wall interactions that set in beyond a threshold load, which increases with coverage. Previous proximal-probe and computer experiments, carried out at high coverages, see only the initial (low-load) linear portion of the friction curve.

Desorption transition at charged interfaces: theoretical approach and experimental evidence

A field theory is used to describe an ionic solution in contact with a charged and adsorbing wall. The Hamiltonian, a functional of the ionic density fields, contains the entropy, the electrostatic energy, a nonlocal Van der Waals type contribution preventing sharp density variations, and an adsorption potential. The mean-field equations are solved numerically. However, they can be recasted so as to put in evidence a one parameter Lie group structure, which is a generalization of the charge-translation symmetry present in the Gouy-Chapman theory. There is a region in the charge-adsorption parameter space where this symmetry is broken, which corresponds to a desorption transition for the ionic species. The properties of this transition are investigated. Finally, this desorption phenomenon provides a simple explanation for a general feature in the properties of metal-electrolyte interfaces: the branching pattern observed in the experimental capacitance curves for a series of electrolytes. The part of the capacitance curves which is independent of the nature of the ions is related to the absence of interaction of the ionic species with the wall once the desorption takes place.

Adsorption of Associating Fluids on Solid Surfaces: Wetting Transition from Density Functional Theory

Adsorption of associating hard spheres and particles interacting via the Lennard-Jones potential at a Lennard-Jones adsorbing wall is studied using the density functional theory. A model of association with one site per particle is considered. To test the theory we have also performed Monte Carlo simulation in the canonical ensemble for a Lennard-Jones associating fluid at high temperatures and for hard associating spheres. Next, the influence of association on the wetting behavior of the fluid−solid interface is investigated. It is shown that the prewetting transition in associating systems is considerably influenced by the association processes.

Electro-deposition of polymer chains on an adsorbing wall: Density profiles and wall coverage

Growth of polymer density in an electro-deposition model of polymer chains on an impenetrable wall is studied on a two dimensional discrete lattice using a Monte Carlo simulation. Polymer-polymer repulsion and polymer-wall attraction for the adsorbing wall (along with the neutral and repulsive interactions) are considered in an external field. Effects of the field strength (B), temperature (T), and chain length (Lc) on the density profile of the polymer chains and wall coverage are investigated. The spatial density profile shows onset of oscillation near the wall at a characteristic field (Bc) which depends on chain length and temperature. In low field, adsorption-to-desorption transition at the wall appear on increasing the temperature (unlike neutral and repulsive walls). In high field regime, on the other hand, a non-monotonic dependence of coverage on temperature is observed with a maximum at a temperature (Tm) which increases on increasing B. The equilibrium value of the polymer density (pd) shows a power-law decay with the chain length, pd∼Lc−α, at the wall and in the bulk with corresponding values of the exponent αW and αB; these exponents differ substantially and depend on B, T, and Lc. The coverage decays monotonically with the chain length at a constant temperature and field.

Adsorption of Polymer Solutions onto a Flat Surface

We present a theoretical description of polymer adsorption from solution which is based on a mean field approximation but which goes beyond the standard ground state dominance approximation. The properties of the adsorbed polymer chains are described by two coupled order parameters. This allows a description of the chains in terms of tails and loops. When the bulk solution is dilute, the adsorbed polymer layer has a double layer structure with an inner layer dominated by loops and an outer layer dominated by tails. Explicit asymptotic forms are found for the monomer concentration profile and for the crossover distance between the loops and tail regions. The precise concentration profile is obtained by a numerical solution of two coupled differential equations. One of the surprising results is that the total polymer adsorbed amount has a nonmonotonic variation with molecular weight and decreases for large values of the molecular weight. The concentration profiles are also determined when the bulk solution is semidilute or concentrated. At any bulk concentration, the monomer concentration has a nonmonotonic variation with the distance to the adsorbing wall and shows a minimum at a finite distance. This depletion effect can be significant in the vicinity of the crossover between dilute and semidilute solutions. All the results are in agreement with the existing numerical solutions of the complete mean field theory of polymer adsorption. Excluded volume correlations are taken into account by constructing scaling laws for polymers in a good solvent both in dilute and in semidilute solutions.

Pillared layered structures vs. zeolites as sorbents and catalysts. Part 1.—Hydrocarbon separations on two alumina-pillared clays and an α-tin phosphate analogue

The dynamic sorption of a series of hydrocarbons in an alumina-pillared montmorillonite (AZA), its mixed Fe3+–alumina-pillared analogue, (FAZA) and an alumina-pillared a-tin phosphate analogue (AI-PILP) has been investigated. Separations between binary mixtures of cyclic non-aromatic/aromatic, linear chain/cyclic non-aromatic hydrocarbons, among others, have been performed in the temperature range 200–350 °C. Aromatic chlorohydrocarbons can also be separated from one another and from their ternary mixtures with hydrocarbons. Although they are the most efficient in these separations (requiring lower temperatures), the AI-PILP samples show enhanced acid-catalysis characteristics at higher temperatures. In addition, naphthalene and biphenyl are sorbed by the montmorillonite-based PILCs, but separated by the AI-PILP, confirming that shape-selection behaviour is involved. The anomalous sorption of cyclohexane by the AI-PILP demonstrates that lateral oxide-pillar ordering differs between pillared smectite clays and phosphates.Catalytic cracking phenomena observed for n-heptane differ between AZA and FAZA, indicating that in-pillar Fe in FAZA is involved, and this is confirmed via cracking of 3-methylhexane. That adsorbate–wall (i.e. pillar) interactions are important, and differ from adsorbate interactions in medium-sized zeolites, is supported by the fact that AZA and FAZA act as weak Lewis-acid reaction ‘vessels’ in the isomerisation of p-xylene.