Two-dimensional Van Der Waals Equation Research Articles

Photoisomerizable Guanosine Derivative as a Probe for DNA Base-Pairing in Langmuir Monolayers.

Mixtures of azo-functionalized amphiphilic derivatives of guanosine and of amphiphilic derivatives of other DNA nucleobases were deposited at an air–water interface and repeatedly irradiated with light of 340 and 440 nm wavelengths. The consequent switching between cis and trans configurations of the azobenzene moiety caused changes in the surface pressure of the film, which were analyzed using a model based on the two-dimensional Van der Waals equation of state. For mixed films of guanosine and cytidine derivatives, the analysis revealed a significant modification of the strength of intermolecular interaction caused by the optical irradiation, while no such modifications were identified in mixed films involving other nucleobases. The difference is attributed to light-induced breaking of the hydrogen bonding that is established only between specific nucleobases. The results demonstrate that photosensitive nucleoside derivatives can be used as an efficient probe for base-pairing in Langmuir monolayers.

Surface organic monolayers control the hygroscopic growth of submicrometer particles at high relative humidity.

Although many organic molecules commonly found in the atmosphere are known to be surface-active in macroscopic aqueous solutions, the impact of surface partitioning of organic molecules to a microscopic aqueous droplet interface remains unclear. Here we measure the droplet size formed, at a relative humidity (∼99.9%) just below saturation, on submicrometer particles containing an ammonium sulfate core and an organic layer of a model compound of varying thickness. The 12 model organic compounds are a series of dicarboxylic acids (C3 to C10), cis-pinonic, oleic, lauric, and myristic acids, which represent a broad range in solubility from miscible (malonic acid) to insoluble. The variation in droplet size with increasing organic aerosol fraction cannot be explained by assuming the organic material is dissolved in the bulk droplet. Instead, the wet droplet diameters exhibit a complex and nonlinear dependence on organic aerosol volume fraction, leading to hygroscopic growth that is in some cases smaller and in others larger than that predicted by bulk solubility alone. For palmitic and stearic acid, small droplets at or below the detection limit of the instrument are observed, indicating significant kinetic limitations for water uptake, which are consistent with mass accommodation coefficients on the order of 10(-4). A model based on the two-dimensional van der Waals equation of state is used to explain the complex droplet growth with organic aerosol fraction and dry diameter. The model suggests that mono- and dicarboxylic acids with limited water solubility partition to the droplet surface and reduce surface tension only after a two-dimensional condensed monolayer is formed. Two relatively soluble compounds, malonic and glutaric acid, also appear to form surface phases, which increase hygroscopicity. There is a clear alternation in the threshold for droplet growth observed for odd and even carbon number diacids, which is explained in the model by differences in the excluded molecular areas of even (∼40 Å(2)/molecule) and odd (∼20 Å(2)/molecule) diacids. These differences are consistent with the odd diacids arranged at the droplet interface in "end-to-end" configurations with only one acid group in contact with the aqueous phase, which is in contrast to even carbon numbered diacids forming "folded" films with both acid groups in contact with the bulk phase. Organic matter produced by the ozonolysis of α-pinene forms surface films that exhibit similar behavior and become thinner with oxidation, allowing for greater water uptake. These results reveal a new and complex relationship between the composition of an organic aerosol and its hygroscopicity, suggesting that organic surface films might strongly influence cloud droplet formation as well as the multiphase chemistry of organic aerosols.

Adsorption of 2-phenylethyl alcohol on silica aerogel from saturated solution in supercritical CO2

Adsorption of 2-phenylethyl alcohol (PEA) from supercritical CO2 onto silica aerogel was investigated. A monolayer to multilayer adsorption isotherm was observed, measured at 15.0MPa and 323.2K, from the PEA-unsaturated to PEA-saturated supercritical CO2, indicating the potential utility of the solute-saturated supercritical adsorption (SSA). The amount of PEA adsorbed on the silica aerogel with SSA at different temperatures and pressures was measured, and the release of PEA from the aerogel at 303.2K was also evaluated. A theoretical model for the SSA equilibrium was developed with the assistance of the adsorption isotherms of pure CO2 onto the silica and considering a three-phase binary system, where the two-dimensional van der Waals equation of state and the three-dimensional Stryjek–Vera modification of the Peng–Robinson equation of state were used respectively to describe the adsorbed phase and the bulk phases (vapor phase and liquid phase). Results showed that the model was capable of describing the adsorption behavior of the system with an average absolute relative deviation of 3.3%.

Calculation of the surface pressure and the contact energy in the adsorption of alkanes on water

In an attempt to complete the theoretical description of the complex wetting of alkanes on aqueous substrates, the surface pressure in the adsorption of pentane, hexane, and heptane on water is calculated as a function of the bulk gas pressure using a two-dimensional van der Waals equation in conjunction with Hirasaki’s expression for the Henry’s law constant. The contact energy as defined within Cahn theory is subsequently deduced using Dobbs’ modified version of this theory and employed to calculate the wetting behavior of the above-mentioned alkanes on water. The experimentally observed sequence of two changes in the wetting state, namely a first-order transition between a microscopically thin and a mesoscopically thick film, followed by a continuous divergence of the film thickness, is found within the theory as well. While the critical wetting transition is brought about by long-range forces and can be described by Dzyaloshinskii–Lifshitz–Pitaevskii theory, the first-order thin–thick transition involves the short-range interactions between substrate and adsorbate. In the absence of a complete theory for the latter, they are accounted for in an effective way in the present approach, which relies only on the macroscopic bulk properties of the different media involved and which leads to satisfactory results for the transition temperatures.

Theoretical description of the adsorption and the wetting behavior of alkanes on water

The wetting behavior of alkanes of medium chain length (e.g., pentane, hexane, and heptane) on water is more complex than the usually observed first-order wetting transition from partial to complete wetting by showing a sequence of two transitions. In this sequential-wetting scenario, a first-order transition from a microscopically thin to a mesoscopically thick layer of liquid on the substrate surface is followed by a continuous divergence of the film thickness upon increase of the temperature. This critical transition to complete wetting at T(w,c) is solely determined by long-range interactions between substrate and adsorbate, which are well-described by Dzyaloshinskii-Lifshitz-Pitaevskii [Adv. Phys. 10, 165 (1961)] theory in terms of the static dielectric constants and the refractive indices of the media involved. The first-order thin-thick transition, however, which occurs at a lower temperature T(w,1), results from an interplay of short-range and long-range forces and is notoriously more difficult to describe because a satisfactory theory of the short-range interactions between substrate and adsorbate is still missing. The approach presented in this paper attempts to account for the short-range interactions in an effective way: Within a Cahn-type [J. Chem. Phys. 66, 3667 (1977)] theory that has been augmented for long-range interactions and modified to treat the first layer of adsorbed molecules in a lattice-gas approach, the contact energy is deduced from the surface pressure, which in turn is calculated using a two-dimensional van der Waals equation of state and an expression for the Henry's law constant that was derived by Hirasaki [J. Adhes. Sci. Technol. 7, 285 (1993)]. The method uses only the dielectric properties of the isolated bulk media and simple assumptions on the size and the shape of the adsorbed alkane molecules and leads to satisfactory results for the transition temperatures T(w,1) and T(w,c).

New theory of equation of state for surface monolayer.

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.

Thermodynamic modeling of solute adsorption equilibrium from near-critical carbon dioxide

Modeling of adsorption equilibrium for supercritical fluid mixtures, with as few parameters as possible, is important in applications of the technology of supercritical fluid adsorption. In this paper, a correlative model has been developed to represent the adsorption equilibria of solutes from the near-critical CO 2 fluid. A two-dimensional van der Waals equation of state and the three-dimensional P– R equation of state were used to describe the adsorbed and bulk phases, respectively. This model contains five parameters for adsorption equilibrium isotherms at finite concentrations and two parameters for adsorption equilibrium constants at infinite dilution. All the parameters are independent of temperature and pressure. By applying the model to the experimental data from the literature, it was shown that this model is capable of describing the adsorption behavior of solutes from supercritical carbon dioxide over relatively wide temperature and pressure ranges. In addition, the adsorption behavior of supercritical fluid mixtures was investigated at finite and infinite dilution conditions.

Influence of clustering on a two-dimensional state equation

A general master equation accounting for the concentration dependence of the excluded area is presented, whose particular results are the two-dimensional van der Waals equation of state as the first approximation and a new much more precise state equation as the second approximation.

Modified van der Waals Equation for the Prediction of Multicomponent Isotherms

A modified two-dimensional van der Waals equation model was proposed for the prediction of multicomponent gas–solid adsorption isotherms from corresponding single-component adsorption equilibrium data. The model was used to predict adsorption isotherms of CO–CO2mixtures and CO2–N2mixtures on Cu(I)–NaY zeolite. Experimental adsorption equilibrium data of the two systems were compared with results calculated from the model and three other models in the literature: the ideal adsorbed solution model, the vacancy solution theory of adsorption using the Flory–Huggins activity coefficient equation, and the two-dimensional van der Waals equation. The results indicated that the modified van der Waals equation predicted the experimental results better than the three other models for the two systems studied, especially for the CO–CO2system, which involved chemical reaction during adsorption and exhibited azeotropic behavior.

Surface Equation of State for Insoluble Surfactant Monolayers at the Air/Water Interface

A surface equation of state is derived and used to interpret the liquid-expanded (LE)−liquid-condensed (LC) phase transition. The monolayer is treated as a two-dimensional mixture consisting of LC domains, disordered molecules in the LE state, and free sites. The free sites are assumed to have two-dimensional size only and to be located at the internal surface between the headgroups and the tails of the surfactant. They are introduced to account for the translational freedom of the domains and of the disordered molecules on the surface. The model can explain the nonhorizontal LE/LC phase transition and its dependence on temperature. In addition, the equilibrium radius and equilibrium area fraction of the domains are calculated as a function of the average molecular surface area (A). In the absence of domains, the surface equation of state reduces to a modified two-dimensional van der Waals equation. The dependence of the surface cohesion pressure on the molecular surface area A is calculated by including three contributions: the dipole−dipole interactions, the chain van der Waals interactions, and the chain conformation. The theoretical model is compared with the experimental π−A isotherms for six phospholipid surfactants, and good agreement is obtained.

A Simple Surface Equation of State for the Phase Transition in Phospholipid Monolayers

Phospholipid monolayers at an oil/water interface are treated as two-dimensional regular solutions made up of three components, namely, singly dispersed phospholipid molecules, clusters of phospholipid molecules, and “empty” sites occupied by water and oil molecules. A simple surface equation of state is derived and used to explain the phase transition that occurs in the monolayer. The equation contains two terms: one is due to the two-dimensional mixing entropy and the other one arises from intermolecular interactions calculated in the nearest-neighbor approximation. The equation reduces to the two-dimensional van der Waals equation of state when no clustering occurs. The temperature-dependent interaction parameter is obtained by fitting the experimental data for 1,2-dimyristoyl phosphatidylcholine at relatively large surface areas per molecule. Good agreement with experiment is obtained for 1,2-dimyristoyl (C14), 1,2-dipalmitoyl (C16), 1,2-distearoyl (C18), 1,2-diarachidoyl (C20), and 1,2-dibehenoyl (C22) phosphatidylcholines (lecithins) over the entire range of surface areas and temperatures.

Study of the interaction between adsorbed hydrocarbon molecules on graphitized carbon using the chromatographic step-and-pulse method

The chromatographic step-and-pulse method has been applied to a study of the adsorption of pure gases and gas mixtures on graphitized carbon black. It is shown how the retention time of a small pulse of a vapour B on a step of preadsorbed vapour A is related to the parameters of an equation of state (two-dimensional van der Waals equation) for the adsorbed gas mixture. The method is used to study the adsorption of isomeric C6-alkanes, cyclohexane and benzene at 343.2 K. The adsorption isotherms derived for the pure vapours are compared with results obtained by static (gravimetric) measurements. The retention results of B on preadsorbed A are analysed and the bestfit values of the interaction parameter αAB are derived. These values are found to be smaller than the geometric mean of αA and αB for the pure gases.

Immersion heat relationships for homogeneous surfaces

The thermodynamic relations between quantities obtained from an immersional heat curve and the heats derived from adsorption isotherms are examined from the point of view of the Gibbsian formalism. The usual interpretation of the immersional heat decrement as an integrated isosteric heat (taking the liquid phase as a reference state) is verified. It is found that, contrary to some treatments in the literature, the immersional heat decrement is not related to the film pressure and its temperature derivative by means of an equation of the Gibbs-Helmholtz type. With the use of the two-dimensional van der Waals equation as a model for monolayer adsorption on homogeneous surfaces, the contributions of lateral interactions to the integral energy and equilibrium heat curves are discussed. The model predicts that the equilibrium heat versus coverage curve will exhibit a maximum prior to the completion of the first layer. It is also pointed out that in the critical region pronounced deviations from the behavior predicted by the model can be expected to occur. In order to assess the role of lateral interactions in determining the character of immersional heat curves, a relationship between the gas-phase adsorption energy of a single molecule and the immersion heat at zero coverage is developed. This relationship is based on a quasi-continuum model, which is restricted to adsorbate-adsorbent systems for which the interaction forces are nonpolar. It is found that when the value of the zero coverage immersion heat is sufficiently low, the effect of increasing coverage is first to increase the immersion heat. This effect, coupled with that of lateral interactions, may produce a maximum in the immersion heat curve.

On physical adsorption XVII. Experimental verification of the two-dimensional van der Waals equation of state above and below the critical temperature

Adsorption isotherms of carbon tetrachloride, chloroform and fiuorotrichloromethane on a substrate of graphitized carbon are reported at temperatures between 200 and 300 °K. Evidence is presented that at these temperatures the residual heterogeneity of the substrate is not observed: under these conditions the true equation of state of the adsorbed film can be deduced directly from the measured adsorption isotherms. All the data reported are described by the adsorption isotherm equation corresponding to a two-dimensional van der Waals gas; this description continues to apply at temperatures where the isotherms show discontinuities characteristic of first-order phase changes. The two-dimensional critical temperature of each of the adsorbed films is rather less than the value predicted by the two dimensional van der Waals equation; this is taken as evidence for the polarization of the adsorbate molecules by an electric field present at the graphite surface. The results obtained with the isotropic carbon tetrachloride molecule indicate a surface field of 1 x 10 5 e. s. u./cm 2 ; we deduce that the anisotropic adsorbates should be oriented at the interface, with the axis of the permanent dipole alined with the surface field.

The two-dimensional van der Waals constants of molecules adsorbed on charcoal and graphite

Entropy data indicate that physically adsorbed molecules of many gases on charcoal or on graphite are mobile and freely rotating. This picture is in accordance with other data and it induced us to apply a two-dimensional van der Waals equation to the adsorption data. It is then found that the adsorbed molecules repel each other. Explaining this repulsion by the repulsion of dipoles, induced in the adsorbed molecules by the surface, we obtain dipole moments which are in accordance with data, found by Mignolet in similar cases. The picture of induced dipoles leads to an appreciable contribution towards the heat of adsorption. (auth)

On physical adsorption: VIII. Monolayer adsorption of argon and nitrogen on graphitized carbon

Low-pressure adsorption isotherms of argon and nitrogen at 77.8°K. and 90.1°K. on graphitized carbon black, P-33, are reported. It is found that the adsorbed monolayer behaves like a two-dimensional ideal gas at the lowest pressures measured; and that its behavior at slightly higher pressures can be described by a two-dimensional van der Waals equation. The critical temperature of the adsorbed monolayer is estimated from the van der Waals constants. Above about 50% coverage the adsorption isotherm has the form of the Langmuir equation; which is interpreted as the adsorption of a mobile film on localized sites, where the sites are superposed on the low-energy solid substrate by the packing of the adsorbate. The isosteric heats of adsorption are calculated as a function of the fraction of the surface covered, and are found to follow the same general pattern as that reported by Amberg, Spencer, and Beebe (4) for krypton adsorbed on an identical substrate.