Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations

Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size is the highest, whereas an increase of the pore size and the density of hydrogen volumetric energy causes the polymer swelling up to a value slightly below the one computed from the bulk phase. Quantum confinement-inducing polymer shrinking is of great importance for realizing the potential of quantum molecular sieves.     

Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.     

Synthesis and adsorption properties of gold nanoparticles within pores of surface‐functional porous polymer microspheres

Mesoporous polymer microspheres with gold (Au) nanoparticles inside their pores were prepared considering their surface functionality and porosity. The Au/polymer composite microspheres prepared were characterized by transmission electron microscope (TEM), X‐ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) techniques. The results showed that the adsorption of Au nanoparticles could be increased by imparting the pore structure and surface‐functional groups into the supporting polymer microspheres (in this study, poly (ethylene glycol dimethacrylate‐co‐acrylonitrile) and poly (EGDMA‐co‐AN) system). Above all, from this study, it was established that the porosity of the polymer microspheres is the most important factor that determines the distribution and adsorption amount of face‐centered cubic (fcc) Au nanoparticles in the final products. Our study showed that the continuous adsorption of Au nanoparticles with the aid of the large surface area and surface interaction sites formed more favorably the Au/polymer composite microspheres. The BET measurements of Au/poly(EGDMA‐co‐AN) composite microspheres reveals that the adsorption of Au nanoparticles into the pores kept the pore structure intact and made it more porous. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5627–5635, 2004     

Ethyl acrylate copolymers as promising porogens for the synthesis of polydimethacrylates with controlled porous structures

The crosslinking radical polymerization of triethylene glycol dimethacrylate in bulk in the presence of 0–40 wt % ethyl acrylate-based copolymers of various compositions is studied, and some structuralphysical properties of the crosslinked polymers are investigated. The quantitative characteristics of their porous structures, such as the specific surface areas and the total pore volumes, are measured via the low-temperature adsorption of nitrogen. During sol-gel analysis, polymer additives are removed from network polymers with the use of benzene and pores with sizes from 4 to 500 nm occupy their places. The maximum specific surface area is approximately 17 m²/g. It is found that the specific surface area and total pore volume depend on the content of the polymer additive in the initial composition.     

Quantitative analysis of cationic poly(vinyl alcohol) diffusion into the hairy structure of cellulose fiber pores: charge density effect

The diffusion of charged polymers into the pores of cellulose fibers has not yet been fully understood due to the complexity of the interaction between polymers and fibers. In this paper, the diffusion of cationic-modified poly(vinyl alcohol) (CPVA) with tailored charge densities and a relatively high molecular weight into the pores of bleached aspen high-yield pulp (via a chemi-thermomechanical pulping process) was quantitatively investigated via an adsorption analysis, charge density analysis, and solute exclusion technique (SET). The results showed that the adsorption of the low-charged CPVA was substantially higher than that of the high-charged CPVA on fibers. The surface charge density analysis confirmed that approximately 17 mg/g of the high-charged CPVA adsorbed on the outer surface and on the macropores of fibers and the remaining (23 mg/g) diffused into the pores. The SET analysis confirmed that the pore size of fibers was more significantly reduced by applying the low-charged CPVA than the high-charged one. The influencing factors for the diffusion of CPVA into the large and small pores were related to the repulsion force developed between the adsorbed polymers and approaching polymers, entropy increase, and the polymer flexibility. The Brunauer-Emmett-Teller surface area analysis showed an increase in the surface area of fibers upon CPVA adsorption. It was proposed that the diffused CPVA prevented complete fiber pore collapse during drying, which eventually increased the surface area of fibers.     

Effect of surface grafted polymers on the adsorption of different model proteins

Adsorption of a model protein to a surface with end-grafted polymers was studied by Monte Carlo simulations. In the model the effect on protein adsorption in the presence of end-grafted polymers was evaluated by calculating the change in free energy between an end-grafted surface and a surface without polymers. The change in free energy was calculated using statistical mechanical perturbation theory. Apart from ordinary athermal polymer-polymer and protein-polymer interactions we also study a broad selection of systems by varying the interaction between proteins and polymers and effective polymer-solvent interactions. The interactions between the molecules span an interval from -0.5 to +0.5 kT. Consequently, general features of protein adsorption to end-grafted surfaces is investigated by systematically changing properties like hydrophilicity/hydrophobicity of the polymer, protein and surface as well as grafting density, degree of polymerization and protein size. Increasing grafting density as well as degree of polymerization decreases the adsorption of protein except in systems with attractive polymer-protein interactions, where adsorption increases with increasing chain length and higher grafting density. At a critical polymer-protein interaction neither chain length nor grafting density affects the free energy of adsorption. Hydrophilic polymers were found to prevent adsorption better than hydrophobic polymers. Very small particles with radii comparable to the size of a polymer segment were, however, better excluded from the surface when using hydrophobic than hydrophilic polymers. For systems with attractive polymer-protein interaction not only the volume of the protein was shown to be of importance but also the size of the exposed surface.     

Surface characterization of poly(methyl methacrylate-co-n-butyl acrylate-co-cyclopentylstyryl-polyhedral oligomeric silsesquioxane) by inverse gas chromatography

The surface properties of poly(methyl methacrylate-co-n-butyl acrylate-co-cyclopentylstyryl polyhedral oligomeric silsesquioxane) (poly(MMA-co-BA-co-styryl-POSS)) were studied by means of inverse gas chromatography (IGC) using 10 non-polar and polar solvents as the probes. Thermodynamic parameters of adsorption, e.g., specific retention volume, the dispersive component of the surface free energy, the specific interaction contribution to the free energy of adsorption and the acid/base constants were obtained to investigate the interactions between the surfaces of the copolymers and different solvents. It was found that incorporation of styryl-POSS into polymer resulted in increasing interactions between polymers and solvents, dispersive component of surface free energy of polymer and acidity of the surfaces of the polymers. The more the styryl-POSS were embedded, the stronger the interaction between the polymer surface and solvent, the dispersive component of the surface free energy and the acidity of the polymer surface were.     

Confinement in nanopores at the oxide/water interface: modification of alumina adsorption properties

There is limited knowledge on the influence of the pore size on surface phenomena (adsorption, dissolution, precipitation, etc.) at the oxide/water interface and a better understanding of the space confinement in nanoscale pores should have practical implications in different areas, such as transport of contaminants in the environment or heterogeneous catalyst preparation, to name a few. To investigate the modifications of the oxide adsorption properties at the oxide/water interface in a confined environment, the surface acidobasic and ion adsorption properties of six different aluminas (5 porous commercial aluminas with pore diameters ranging from 25 to 200 A and 1 non-porous alumina) were determined by means of acid-base titration and Ni(II) adsorption. It is shown that the confinement has a moderate impact on the alumina adsorption capacity because all materials have similar surface charging behaviours and ion saturation coverages. However, a confined geometry has a much larger impact on the ion adsorption constants, which decrease drastically when the average pore diameter decreases below 200 A. These results are discussed in terms of nanoscale pore space confinement.     

Effect of pore size on adsorption of a polyelectrolyte to porous glass

The adsorption of quaternized poly(vinylpyridine) (QPVP) on controlled pore glass (CPG) size, over the ionic strength range 0.001-0.5 M was found to display nonmonotonic behavior as a function of pore size. Both adsorption kinetics and ionic strength effects deviated dramatically from behavior typical of adsorption on flat surfaces when the ratio of the pore radius Rp to the polymer hydrodynamic radius Rh became smaller than ca. 2. Ionic strength enhancement of adsorption for small pore sizes was observed at much higher salt concentrations than is typical for polycation adsorption on flat surfaces. The amount of polymer adsorbed per unit surface area of glass GammaA, in 0.5 M NaCl, exhibited a shallow maximum at Rp/Rh approximately 5. Since the value of GammaA for small pore size CPG is strongly depressed by the large surface area, an alternative and more interesting observation is that the amount of polymer adsorbed per gram of CPG, Gammaw, displays a strong maximum when Rp is equal to or slightly smaller than Rh. The efficiency with which QPVP binds anionic micelles to (negatively charged) CPG (grams of surfactant/grams of QPVP) increases strongly with diminishing pore size, indicating that the configuration of polycation bound to small pores favors micelle binding. Since the micelles are larger than small pores, the results indicate that when Rp < Rh, adsorbed polycation molecules reside only partially within the pore. The results of this study are supported by simulations of polyelectrolytes within cylindrical cavities.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Structure and thermodynamics of protein-polymer solutions: effects of spatially distributed hydrophobic surface residues

Protein-polymer association in solution driven by a short-range attraction has been investigated using a simple coarse-grain model solved by Monte Carlo simulations. The effect of the spatial distribution of the hydrophobic surface residues of the protein on the adsorption of weakly hydrophobic polymers at variable polymer concentration, polymer length, and polymer stiffness has been considered. Structural data on the adsorbed polymer layer and thermodynamic properties, such as the free energy, energy, and entropy, related to the protein-polymer interaction were calculated. It was found that a more heterogeneous distribution of the surface residues promotes adsorption and that this also applies for different polymer concentrations, polymer chain lengths, and polymer flexibilities. Furthermore, the polymer adsorption onto proteins with more homogeneous surface distributions displayed larger sensitivity to polymer properties such as chain length and flexibility. Finally, a simple relation between the adsorption probability and the change in the free energy was found and rationalized by a simple two-state adsorption model.     

Adsorption of block copolymers in nanoporous alumina

We have studied the adsorption of end-attaching block copolymer chains inside the cylindrical pores of nanoporous alumina. Highly asymmetric PS-PEO block copolymers, with a small PEO anchoring block and a long PS dangling block, were allowed to adsorb onto porous alumina substrates with an average pore diameter of ∼200 nm from toluene solution. The adsorption process was monitored using FTIR spectroscopy, whereas depth profile analysis was performed by means of XPS and Ar⁺ ion sputtering. It is found that the PS-PEO adsorption kinetics in porous alumina are ∼4 orders of magnitude slower than the corresponding case of a flat alumina substrate. It appears that chains adsorbed near the pore entrance early on tend to form a barrier for chains entering the pore at later times, thereby slowing down the adsorption process significantly. This effect is much more pronounced for large chains whose dimensions are comparable with the pore diameter. The equilibrium adsorbance value is also affected by chain size due to the additional entropic penalty associated with chain confinement, the adsorbance falling substantially when the chain dimensions become comparable with the pore diameter. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1676–1682, 2010     

Interfacial activity of particles at PI/PDMS and PI/PIB interfaces: analysis based on Girifalco–Good theory

Particles that are partially wetted by oil and water are known to adsorb at oil/water interfaces. By the same mechanism, particles that are partially wetted by two immiscible polymers should adsorb at the interface between those two polymers. However, since chemical differences between immiscible polymers are relatively modest, particle adsorption at polymer/polymer interfaces may be expected to be relatively uncommon. We have conducted experiments with several particle types added to two pairs of model polymers, polyisoprene/polydimethylsiloxane and polyisoprene/polyisobutylene. Contrary to our expectation, in every case, particles readily adsorbed at the polymer/polymer interfaces. We evaluated the Girifalco–Good theory as a means to predict the interfacial activity of the particles. The solid surface energy required by the Girifalco–Good theory was assumed to be equal to the critical surface tension, which was then found by float/sink tests. Our results suggest that this approach is not able to predict the observed interfacial activity of particles at polymer/polymer interfaces.     

Comparison of three cross‐linking agents for imprinting diethylstilbestrol in solid‐phase extraction

Molecularly imprinted polymer (MIP) has been heavily studied for years. However, most efforts focused on functional monomer and particular study of cross‐linking agents on imprinting effect and pore structure is rare. In this paper, diethylstilbestrol (DES) imprinted polymers cross‐linked by three types of agents and their imprinting effects in solid‐phase extraction (SPE) were discussed. Evolution of UV spectral and simulation of cross‐linking agents or monomer mixed with DES revealed that there was a particular interaction between divinylbenzene and DES. Clear imprinting effects towards DES showed for divinylbenzene made imprinted polymer (DM), with imprinting factors up to 16.02 (STD = 2.20), while the other two imprinted polymers showed limited effects with imprinting factors of 4.95 (STD = 0.45) and 1.63 (STD = 0.54). Specific surface areas, pore volumes, and pore size distributions of the particles also confirmed that DM showed distinguished structure, and the average pore size of it was just fit the size of DES and bisphenol A (BPA), while no pore was found in divinylbenzene made blank polymer. Other imprinted and non‐imprinted polymers showed no pore or big pores relatively. These results show that the cross‐linking monomer is not merely an inert component for the MIPs, it could play a positive role in promoting interactions with the template to afford molecular recognition in imprinting DES. Copyright © 2011 John Wiley & Sons, Ltd.     

Water in extremely narrow planar pores with crystalline walls. 2. Thermodynamics

The free energy, entropy, and work of water vapor adsorption in planar pores with widths of 0.62 and 1.25 nm located in a silver iodide crystal parallel to its basal face have been computed at the molecular level. In contrast to adsorption on a free surface, the adsorption in the pores proceeds in three stages, i.e., the formation of molecular films on the walls, coalescence of the films, and densification of the fluid in the pore volume. At the second stage, the equilibrium between the fluid in the pore and the vapor over the pore at temperatures corresponding to normal conditions is thermodynamically unstable and accompanied by the development of a free energy barrier and the existence of metastable states. As temperature is elevated, the instability is gradually evened out; however, its signs remain preserved even at the boiling temperature of water. Extremely narrow pores with widths smaller than 1 nm are always filled with water under conditions of even a rather dry natural atmosphere. The filling of pores several nanometers wide in strongly unsaturated water vapors overcomes the free-energy barrier; however, the fluid that has filled the pore remains stable with respect to evaporation in vapors with densities lower than the density of saturated vapor by several orders of magnitude. The existence of the free-energy barrier and metastable states in nanosized breaks in crystals creates conditions for hysteresis of adsorption-desorption cycles.     

Effects of confinement on the molar enthalpy of argon adsorption in graphitic cylindrical pores: a grand canonical Monte Carlo (GCMC) simulation study

Using a grand canonical Monte Carlo simulation, we study argon adsorption in graphitic cylindrical pores to investigate the differences between the isosteric heat and the integral molar enthalpy under subcritical and supercritical conditions and compare these results against those for a flat graphite surface to investigate the role of confinement on the enthalpy change of adsorption. The isosteric heat curve is finite under subcritical conditions, but for supercritical adsorption, it becomes infinite at the pressure where the excess concentration versus pressure is maximum. This can be circumvented using the integral molar enthalpy, which is a better variable to describe the energy change for supercritical adsorption. Finally, the effects of pore geometry (radius and length) on argon adsorption under subcritical and supercritical conditions are discussed.     

Tuning the adsorption and fluorescence properties of aminal‐linked porous organic polymers through N‐heterocyclic group decoration

Aiming at tuning the adsorption and fluorescence properties of targeted porous organic polymer, four new aminal‐linked porous organic polymers (NAPOPs) were synthesized through the reaction of 1,4‐Bis(4,6‐diamino‐s‐triazin‐2‐yl) benzene (BATB) with four kinds of aldehydes substituted with different N‐heterocyclic groups. Among the polymers, NAPOP‐3 decorated with 5‐phenyl‐tetrazole group shows the largest CO₂ adsorption capacity (2.52 mmol g^?1 at 273 K and 100 kPa) because of its relative large surface area, while NAPOP‐1 decorated with piperazine groups shows relative large CO₂/N₂ adsorption selectivity (77 at 273 K and 100 kPa), attributable to its large CO₂ adsorption heats and cabined pore (<4 Å). Meanwhile, NAPOP‐1 and ?3 exhibit high adsorption rate toward iodine with a high capacity (>240 wt %). In addition, different luminescence emissions were also observed for NAPOPs, indicating different intramolecular charger transfer occurred inside polymer networks. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1724–1730     

Properties of Water Confined in Periodic Mesoporous Organosilicas: Nanoimprinting the Local Structure

The properties of materials confined in porous media are important in scientific and technological aspects. Topology, size, and surface polarity of the pores play a critical role in the confinement effects, however, knowledge regarding the guest–pore interface structure is still lacking. Herein, we show that the molecular mobility of water confined in periodic mesoporous organosilicas (PMOs) is influenced by the polarity of the organic moiety. Multidimensional solid‐state NMR spectroscopy directly probes the spatial arrangement of water inside the pores, showing that water interacts either with only the silicate layer or with both silicate and organic layers depending on the alternating surface polarity. A modulated and a uniform pore filling mode are proposed for different types of PMOs.     

How Does a Polymer Brush Repel Proteins？

The captioned question has been addressed by the steric effect; namely, the adsorption of proteins on a surface grafted with linear polymer chains decreases monotonically as the grafting density increases. However, there is no quantitative and satisfactory explanation why the adsorption starts to increase when the grafting density is sufficiently high and why polyethylene glycol（PEG） still remains as one of the best polymers to repel proteins. After considering each grafted chain as a molecular spring confined inside a ＂tube＂ made of its surrounding grafted chains, we estimated how its free energy depends on the grafting density and chain length, and calculated its thermal energy-agitated chain conformation fluctuation, enabling us to predict an adsorption minimum at a proper grafting density, which agrees well with previous experimental results. We propose that it is such a chain fluctuation that slows down the adsorption kinetically.     

Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions

We study the driven translocation of polymers under time-dependent driving forces using N-particle Langevin dynamics simulations. We consider the force to be either sinusoidally oscillating in time or dichotomic noise with exponential correlation time, to mimic both plausible experimental setups and naturally occurring biological conditions. In addition, we consider both the case of purely repulsive polymer-pore interactions and the case with additional attractive polymer-pore interactions, typically occurring inside biological pores. We find that the nature of the interaction fundamentally affects the translocation dynamics. For the non-attractive pore, the translocation time crosses over to a fast translocation regime as the frequency of the driving force decreases. In the attractive pore case, because of a free energy well induced inside the pore, the translocation time can be a minimum at the optimal frequency of the force, the so-called resonant activation. In the latter case, we examine the effect of various physical parameters on the resonant activation, and explain our observations using simple theoretical arguments.