Two-dimensional order-disorder transition of argon monolayer adsorbed on graphitized carbon black: kinetic Monte Carlo method

We present results of application of the kinetic Monte Carlo technique to simulate argon adsorption on a graphite surface at temperatures below and above the triple point. We show that below the triple point the densification of the adsorbed layer with loading results in the rearrangement of molecules to form a hexagonal structure, which is accompanied by the release of an additional heat, associated with this disorder-order transition. This appears as a spike in the plot of the heat of adsorption versus loading at the completion of a monolayer on the surface. To describe the details of the adsorbed phase, we analyzed thermodynamic properties and the effects of temperature on the order-disorder transition of the first layer.     

Thermodynamic analysis of ordered and disordered monolayer of argon adsorption on graphite

We presented a detailed thermodynamic analysis of argon adsorption on a graphitized carbon black with a kinetic Monte Carlo scheme. In this study, we particularly paid attention to the formation of a hexagonal two-dimensional molecular layer on a graphite surface and discuss conditions of its stability and thermodynamic properties of the adsorbed phase as a function of loading. It is found that the simulation results are substantially affected by the dimensions of the simulation box when the monolayer forms a hexagonal ordered structure. This is due to the fact that the lattice constant is constrained by the dimensions of the surface. To circumvent this, we presented a thermodynamic technique, which allows for the variation of the box size as a function of loading, to determine the "intrinsic" lattice constant (rather than apparent average value because of the fixed dimensions of the simulation box) and the thermodynamic functions for the adsorbed phase: the Helmholtz free energy, the chemical potential, and the surface tension. The tangential and normal pressures as a function of the distance from the surface are also discussed.     

Explanation of the unusual peak of calorimetric heat in the adsorption of nitrogen, argon and methane on graphitized thermal carbon black

Heats of adsorption and adsorption isotherms of argon, nitrogen and methane on a perfect graphitic surface and a defective graphitic surface are studied with a Grand Canonical Monte Carlo Simulation (GCMC). For the perfect surface, the isosteric heat versus loading shows a typical pattern of adsorption of simple fluids on graphite. Depending on adsorbate, degree of graphitization and temperature, a spike in the heat curve versus loading is observed when the first layer is mostly covered with adsorbate molecules. The heat spike is observed for argon and nitrogen at 77 K while for argon at 87.3 K it is no longer present. These simulation results are consistent with the experimental data of J. Rouquerol, S. Partyka and F. Rouquerol, J. Chem. Soc., Faraday Trans. 1, 1977, 73, 306. In the case of methane we observe heat spikes at low temperatures, 84.5, 92.5 and 104 K. The heat spike shifts to higher loading with temperature and it then disappears at high temperatures. These observations are in qualitative agreement with the experimental data of A. Inaba, Y. Koga and J. A. Morrison, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1635. In all cases where heat spikes are observed, the GCMC simulation results indicate that the heat spike is associated with the squeezing of molecules into the already dense first layer, and the rearrangement of molecules to form a highly structured fluid of this layer. While this squeezing into the first layer is happening, molecules continue to adsorb onto the relatively sparse second layer.     

Simulation study of two-dimensional phase transitions of argon on graphite surface and in slit micropores

Molecular simulation has been increasingly used in the analysis and modeling of gas adsorption on open surfaces and in porous materials because greater insight could be gained from such a study. In case of homogeneous surfaces or pore walls the adsorption behavior is often complicated by the order–disorder transition. It is shown in our previous publications (Ustinov and Do, Langmuir 28:9543–9553, 2012a; Ustinov and Do, Adsorption 19:291–304, 2013) that once an ordered molecular layer has been formed on the surface, the lattice constant depends on the simulation box size, which requires adjusting the box dimensions parallel to the surface for each value of loading. It was shown that this can be accomplished with the Gibbs–Duhem equation, which results in decreasing lattice constant with an increase of the amount adsorbed. The same feature is expected to be valid for gas adsorption in narrow pores, but this has not been analyzed in the literature. This study aims at an extension of our approach to adsorption in slit graphitic pores using kinetic Monte Carlo method (Ustinov and Do, J Colloid Interface Sci 366:216–223, 2012b). The emphasis rests on the thermodynamic analysis of the two-dimensional (2D) ordering transition and state of the ordered phase; if the ordered phase exists in narrow slit pores, simulation with constant volume box always leads to erroneous results, for example, seemingly incompressible adsorbed phase. We proposed a new approach that allows for modeling thermodynamically consistent adsorption isotherms, which can be used as a basis for further refinement of the pore size distribution analysis of nanoporous materials.     

On the anatomy of the adsorption heat versus loading as a function of temperature and adsorbate for a graphitic surface

In this paper we review and classify the various patterns of isosteric heat versus loading for adsorption of gases on graphitised thermal carbon black at temperatures ranging from below the 3D triple point to temperatures above it, but less than the 3D critical point. We have identified the features of heat curve and highlighted the microscopic origin of these features. The patterns vary with temperature and with the relative strength of the fluid-fluid interaction and solid-fluid interaction. For simple adsorptives (by simple we meant there is no strong association between fluid particles), the heat curve is typified by fluid-fluid attraction and layering phenomena. For adsorptives showing strong association such as water, ammonia and methanol, the heat curve essentially begins below the condensation heat and then approaches it as loading is increased. This is mainly due to the strong hydrogen bonding in these fluids. A third group includes adsorptives such as benzene, where the heat curve is constant in the sub-monolayer coverage region (but is higher than the condensation heat) and then drops off to the condensation heat when higher layers are formed. The constant heat in the sub-monolayer region is due to the balance between the energy factor (from fluid-fluid interaction) and entropy factor (due to re-orientation of adsorbed molecules). Our proposed classification is supported by detailed GCMC simulations of various gases that have been reported in the literature, and we supplement these with new results for the adsorption of xenon on graphite to investigate in more detail the change in heat pattern with temperature. Xenon is chosen because of its high fluid-fluid interaction, allowing us to study the 2D-phase transition in the first as well as higher layers.     

On the Henry constant and isosteric heat at zero loading in gas phase adsorption

The Henry constant and the isosteric heat of adsorption at zero loading are commonly used as indicators of the strength of the affinity of an adsorbate for a solid adsorbent. It is assumed that (i) they are observable in practice, (ii) the Van Hoff's plot of the logarithm of the Henry constant versus the inverse of temperature is always linear and the slope is equal to the heat of adsorption, and (iii) the isosteric heat of adsorption at zero loading is either constant or weakly dependent on temperature. We show in this paper that none of these three points is necessarily correct, first because these variables might not be observable since they are outside the range of measurability; second that the linearity of the Van Hoff plot breaks down at very high temperature, and third that the isosteric heat versus loading is a strong function of temperature. We demonstrate these points using Monte Carlo integration and Monte Carlo simulation of adsorption of various gases on a graphite surface. Another issue concerning the Henry constant is related to the way the adsorption excess is defined. The most commonly used equation is the one that assumes that the void volume is the volume extended all the way to a boundary passing through the centres of the outermost solid atoms. With this definition the Henry constant can become negative at high temperatures. Although adsorption at these temperatures may not be practical because of the very low value of the Henry constant, it is more useful to define the Henry constant in such a way that it is always positive at all temperatures. Here we propose the use of the accessible volume; the volume probed by the adsorbate when it is in nonpositive regions of the potential, to calculate the Henry constant.     

Extended Veytsman statistics for the solid–fluid transition in the framework of lattice fluid

Lattice fluid can describe a vapor–liquid transition but not a solid–fluid transition. In this work, we propose a simple and analytic term which yields a solid–fluid transition when coupled with a lattice based equation of state (EOS). The proposed term is derived based on the two assumptions that (1) solid can be considered as highly associated phase affected by strong attractive force and (2) this force is distinct from the conventional attractive forces yielding a vapor–liquid transition. To formulate these assumptions, we extend Veytsman statistics by modifying its density dependency. The derived term was combined with a quasi-chemical nonrandom lattice fluid theory (QLF) developed by the authors. The combined model was found to require only two parameters besides 3 QLF parameters for physical properties calculation of three phases. When tested against equilibrium properties of 8 components, the combined model was found to closely reproduce melting pressure, sublimation pressure, and vapor pressure, but underestimate solid density as well as heat of melting at the triple point temperature. It was found that the present approach can yield a solid–liquid transition at all temperatures.     

Modeling of adsorption on nongraphitized carbon surface: GCMC simulation studies and comparison with experimental data

We model nongraphitized carbon black surfaces and investigate adsorption of argon on these surfaces by using the grand canonical Monte Carlo simulation. In this model, the nongraphitized surface is modeled as a stack of graphene layers with some carbon atoms of the top graphene layer being randomly removed. The percentage of the surface carbon atoms being removed and the effective size of the defect (created by the removal) are the key parameters to characterize the nongraphitized surface. The patterns of adsorption isotherm and isosteric heat are particularly studied, as a function of these surface parameters as well as pressure and temperature. It is shown that the adsorption isotherm shows a steplike behavior on a perfect graphite surface and becomes smoother on nongraphitized surfaces. Regarding the isosteric heat versus loading, we observe for the case of graphitized thermal carbon black the increase of heat in the submonolayer coverage and then a sharp decline in the heat when the second layer is starting to form, beyond which it increases slightly. On the other hand, the isosteric heat versus loading for a highly nongraphitized surface shows a general decline with respect to loading, which is due to the energetic heterogeneity of the surface. It is only when the fluid-fluid interaction is greater than the surface energetic factor that we see a minimum-maximum in the isosteric heat versus loading. These simulation results of isosteric heat agree well with the experimental results of graphitization of Spheron 6 (Polley, M. H.; Schaeffer, W. D.; Smith, W. R. J. Phys. Chem. 1953, 57, 469; Beebe, R. A.; Young, D. M. J. Phys. Chem. 1954, 58, 93). Adsorption isotherms and isosteric heat in pores whose walls have defects are also studied from the simulation, and the pattern of isotherm and isosteric heat could be used to identify the fingerprint of the surface.     

Comparative features of ar adsorption on smooth and amorphous surfaces examined by density functional theory

We analyze argon adsorption isotherms and isosteric heat of adsorption on graphitized and nongraphitized carbon black and silica surfaces by means of nonlocal density functional theory (NLDFT). It is shown that in the case of graphitized carbon black the behavior of the adsorbed phase is nearly identical to that in the bulk phase at a distance larger than about 3-4 molecular diameters from the surface. At a smaller distance argon forms solid-like molecular layers at a temperature at least 3.5 K above the triple point, with the interlayer distance being markedly smaller than the argon collision diameter. In the case of defected or amorphous surfaces adsorbed argon is liquid-like below its triple point. Our extension of the Tarazona NLDFT to amorphous solids (NLDFT-AS) and the Kierlik and Rosinberg version of NLDFT excellently fit argon adsorption isotherms and properly predict the isosteric heat of adsorption. We showed that the surface roughness affects the calculated heat of adsorption, which allowed us to adjust the width of the diffuse zone of the nongraphitized carbon black and the silica surface.     

Calorimetric studies of poly(ethylene terephthalate) stretching over a wide temperature range

Heat effects and structural transformations in amorphous crystallizable poly(ethylene terephthalate) (PET) during uniaxial stretching accompanied by neck formation, have been investigated by calorimetric and x-ray methods over a wide range of temperatures and deformation rates. At small deformation (not exceeding 1–2%) and at temperatures below the glass transition temperature of the polymer, PET behaves as an elastic body. Upon stretching at a constant rate, constant heat power is absorbed, heat effects during loading and unloading coincide completely, and no hysteresis is observed. At large deformations (of the order of 50%), cold drawing develops in this temperature range. The internal energy change in cold drawing is zero within experimental error. A periodic heat release during the self-oscillation regime of drawing PET corresponds to periodic changes in stress, in the rate of the neck formation, and in the appearance of the sample. The temperature limits of the region where crystallization resulting from an uniaxial drawing of the polymer is possible, have been determined, and the heat effect of this phase transition has been measured. Orientation crystallization develops only from 70 to 94°C. These limits are insensitive to changes in deformation rate within one decimal order. The structure of PET in this temperature range has been investigated. The heat of phase transition of orientation crystallization of PET has been determined from the relationship between the measured values of the internal energy change during this process and the limiting degree of crystallinity for the stretched samples. This heat proves to be 5.5 ± 0.1 cal/g.     

Modeling of monolayer adsorption of hydrogen on ZSM‐5 zeolite by lattice density functional theory

The adsorption isotherms of hydrogen on microporous zeolite ZSM‐5, at supercritical conditions, have been modeled using the monolayer lattice density functional theory (LDFT) models, where the simple cubic lattice, face‐centered cubic lattice, body‐centered cubic lattice and tetragonal lattice structures are assumed for the arrangements of the adsorption sites inside pores based on the size and shape of the zeolite. The results indicate that the monolayer LDFT models appear to be effective in describing hydrogen adsorption on zeolite ZSM‐5 at supercritical conditions, and the calculated adsorption isotherms agree well with the experimental isotherms measured previously. The layer density of adsorbed phase is presented versus the bulk density and temperature. It is found that the densities of adsorbed phase on adsorbent surface are much higher than the bulk density for temperature range under study. However, in the core region, the layer densities are close to the bulk density. The monolayer adsorption is suitable for hydrogen on ZSM‐5 zeolite. Copyright © 2013 John Wiley & Sons, Ltd.     

氢在沸石上的吸附行为

应用基于Ono-Kondo格子理论得到的通用吸附等温方程, 通过分析氢在不同温度下, 在沸石NaX、CaA、NaA和ZSM-5上的吸附数据, 确定了氢的最大单层吸附容量. 并引入维里吸附方程, 由第二维里吸附系数和圆柱孔的Lennard-Jones(12-6)势模型计算了氢与沸石微孔壁面的作用势. 结果表明, 通用吸附等温方程可较好地描述氢在沸石上的超临界吸附行为, 拟合所得的氢在沸石上的最大单层吸附容量与吸附剂相关, 而与吸附温度无关. 圆柱孔作用势模型计算所得的氢分子在沸石上的吸附作用势与吸附热相近. 氢分子间的作用力表现为吸引力.     

Adsorption of gases on layered silicates at high pressures

Equilibrium adsorption of nitrogen, carbon dioxide, and argon was examined on the sodium and pyridinium forms of montmorillonite and on the hydrogen form of bentonite. The measurements were carried out at 303, 343, 373, and 400 K over pressure ranges of 0.1–90 MPa (Ar and N₂) and 0.1–6 MPa (CO₂). The amount of nitrogen vapor adsorbed was determined at 77 K and pressures from 0 to 0.1 MPa. The porous structure parameters of the studied samples were determined using adsorption isotherms of nitrogen, argon, and carbon dioxide vapors. At elevated temperatures and pressures >10 MPa, Ar and N₂ adsorption processes on the Na-form of montmorillonite and Ar adsorption on bentonite are activated, since the amounts of the gases adsorbed and adsorption volumes increase with temperature. No activated adsorption is observed for carbon dioxide adsorption on these adsorbents. A comparison of the excess adsorption isotherms of gases on the Py-form of montmorillonite and H-form of bentonite shows that adsorption in micropores predominates for the Py-form of montmorillonite, whereas for the Na-form of bentonite and H-form of bentonite adsorption occurs mainly in meso- and macropores.     

Comparative study of normal and branched alkane monolayer films adsorbed on a solid surface. I. Structure

The structure of a monolayer film of the branched alkane squalane (C30H62) adsorbed on graphite has been studied by neutron diffraction and molecular dynamics (MD) simulations and compared with a similar study of the n-alkane tetracosane (n-C24H52). Both molecules have 24 carbon atoms along their backbone and squalane has, in addition, six methyl side groups. Upon adsorption, there are significant differences as well as similarities in the behavior of these molecular films. Both molecules form ordered structures at low temperatures; however, while the melting point of the two-dimensional (2D) tetracosane film is roughly the same as the bulk melting point, the surface strongly stabilizes the 2D squalane film such that its melting point is 91 K above its value in bulk. Therefore, squalane, like tetracosane, will be a poor lubricant in those nanoscale devices that require a fluid lubricant at room temperature. The neutron diffraction data show that the translational order in the squalane monolayer is significantly less than in the tetracosane monolayer. The authors' MD simulations suggest that this is caused by a distortion of the squalane molecules upon adsorption on the graphite surface. When the molecules are allowed to relax on the surface, they distort such that all six methyl groups point away from the surface. This results in a reduction in the monolayer's translational order characterized by a decrease in its coherence length and hence a broadening of the diffraction peaks. The MD simulations also show that the melting mechanism in the squalane monolayer is the same footprint reduction mechanism found in the tetracosane monolayer, where a chain melting drives the lattice melting.     

On the heat capacity of adsorbed phases using molecular simulation

The heat capacities of argon, ammonia, and methanol on carbon black at 87.3, 240, and 300 K, respectively, have been investigated. The carbon black surface has been modeled with and without carbonyl groups. Part of this investigation is a decomposition of the heat capacity into its contributions from the different interaction potentials of an adsorption system. All systems show a spectrum of heat capacity versus loading, and this behavior depends on the carbonyl configuration present on the surface. For methanol and ammonia the variation of the heat capacity between the two for the same carbonyl configurations is greater than the variation in the heat of adsorption. Heat capacities of methanol and ammonia are generally dominated by fluid-fluid interactions due to the strong association of fluid particles through hydrogen bonding. The difference in the heat capacity behavior of the two fluids is an indicator of their different clustering behaviors on the carbon black surface. The presence of carbonyl groups reduces the fluid-fluid contributions to the heat capacity. This is due to the compensation of fluid-fluid interactions with fluid-functional group interactions. At 87.3 K a first layer transition to a solidlike state is present for argon and results in a large peak in the heat capacity on a bare surface. The presence of functional groups greatly reduces this peak in the heat capacity by disrupting the packing of argon on the surface and preventing a transition to a solidlike state.     

The effect of lattice compressibility on the thermodynamics of gas sorption in polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration-dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory-Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.     

Effect of thickness and monolayer location on thermostability of metal stearate LB films studied by FT-IR reflection—absorption spectroscopy

LB films of Cd and Ca stearates with 1, 3, 9, and 21 monolayers were fabricated on silver-coated glass slides. 9-Monolayer LB films of Cd and Ca salts of deuterated stearic acid, in which the 1st, 5th, or 9th layer was replaced by 1 monolayer of undeuterated analogues, were also prepared on the above substrates. Temperature dependences of Fourier transform infrared (FT-IR) reflection—absorption (RA) spectra were examined for these LB films in the range 31–140°C. At room temperature, the hydrocarbon chains in these LB films were in a well-ordered state with a high degree of perpendicular orientation to the substrate. However, they became disordered at elevated temperatures. These order-disorder phase transition temperatures were dependent on the film thickness, to a small degree in the Cd stearate LB film (102–108°C), but to a large degree in the Ca stearate LB film (103–129°C). In the latter LB film, the effect of dehydration was inferred. The degree of disorder at high temperatures was dependent on the film thickness and the location of monolayer in the 9-monolayer LB films. This result is discussed in terms of the internal pressure within the LB film.     

Analysis of Adsorbate–Adsorbate and Adsorbate–Adsorbent Interactions to Decode Isosteric Heats of Gas Adsorption

A qualitative interpretation is proposed to interpret isosteric heats of adsorption by considering contributions from three general classes of interaction energy: fluid–fluid heat, fluid–solid heat, and fluid—high‐energy site (HES) heat. Multiple temperature adsorption isotherms are defined for nitrogen, T=(75, 77, 79) K, argon at T=(85, 87, 89) K, and for water and methanol at T=(278, 288, 298) K on a well‐characterized polymer‐based, activated carbon. Nitrogen and argon are subjected to isosteric heat analyses; their zero filling isosteric heats of adsorption are consistent with slit‐pore, adsorption energy enhancement modelling. Water adsorbs entirely via specific interactions, offering decreasing isosteric heat at low pore filling followed by a constant heat slightly in excess of water condensation enthalpy, demonstrating the effects of micropores. Methanol offers both specific adsorption via the alcohol group and non‐specific interactions via its methyl group; the isosteric heat increases at low pore filling, indicating the predominance of non‐specific interactions.     

Ellipsometric and neutron diffraction study of pentane physisorbed on graphite

High-resolution ellipsometry and neutron diffraction measurements have been used to investigate the structure, growth, and wetting behavior of fluid pentane (n-C(5)H(12)) films adsorbed on graphite substrates. We present isotherms of the thickness of pentane films adsorbed on the basal-plane surfaces of a pyrolytic graphite substrate as a function of the vapor pressure. These isotherms are measured ellipsometrically for temperatures between 130 and 190 K. We also describe neutron diffraction measurements in the temperature range 11-140 K on a deuterated pentane (n-C(5)D(12)) monolayer adsorbed on an exfoliated graphite substrate. Below a temperature of 99 K, the diffraction patterns are consistent with a rectangular centered structure. Above the pentane triple point at 143.5 K, the ellipsometric measurements indicate layer-by-layer adsorption of at least seven fluid pentane layers, each having the same optical thickness. Analysis of the neutron diffraction pattern of a pentane monolayer at a temperature of 130 K is consistent with small clusters having a rectangular-centered structure and an area per molecule of approximately 37 A(2) in coexistence with a fluid monolayer phase. Assuming values of the polarizability tensor from the literature and that the monolayer fluid has the same areal density as that inferred for the coexisting clusters, we calculate an optical thickness of the fluid pentane layers in reasonable agreement with that measured by ellipsometry. We discuss how these results support the previously proposed "footprint reduction" mechanism of alkane monolayer melting. In the hypercritical regime, we show that the layering behavior is consistent with the two-dimensional Ising model and determine the critical temperatures for layers n = 2-5.     

Adsorption of CF4 on graphite preplated with a monolayer of CF3Cl

We report a study of the adsorption of CF(4) on graphite preplated with a monolayer of CF(3)Cl, using infrared reflection absorption spectroscopy combined with ellipsometry. The saturated vapor pressure of CF(3)Cl is nearly 3 orders of magnitude smaller than that of CF(4) at the same temperature, so the main control variables are the temperature and the pressure (or chemical potential) of CF(4), together with the initial coverage of CF(3)Cl. The temperature range covered is 60-105 K. We find that, if the initial monolayer of CF(3)Cl is liquid, CF(4) continuously displaces CF(3)Cl by substitution in the monolayer. If the initial monolayer of CF(3)Cl is solid, due to either lower temperature or compression, CF(4) condenses as a second layer on the top of the CF(3)Cl layer, with only slight mixing with the original layer. This behavior persists to multiple layers of CF(4).