Extracting the equation of state of lattice gases from Random Sequential Adsorption simulations by means of the Gibbs adsorption isotherm

A novel approach for deriving the equation of state for a 2D lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from Random Sequential Adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure

Adsorption Kinetics and Phase Behavior of Particles Adsorbed at an Interface

The ability to predict the adsorption dynamic, phase behavior, and surface pressure of a monolayer of adsorbed particles in two-dimensional systems are key aspects of many current research areas. Examples include phase transitions in amphiphilic monolayers, emulsion stability due to particle adsorption at interfaces, and melting at an interface. In this thesis, a new approach for deriving the equation of state for a two-dimensional lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. This work aims to predict the adsorption kinetics and phase behavior of a system composed of many hard-core particles based on kinetic arguments and the Gibbs adsorption isotherm. To that purpose, the random sequential adsorption with a surface diffusion model is used to samples the configuration of the system at different coverage. This configuration is used to calculate the thermodynamic properties of the system where many interesting collective phenomena are observed. The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite-size effects and by access to the appropriate thermodynamic regime. We address these issues using our new model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage. The next part of this work concentrates on reversible adsorption by introducing a desorption process into our model and varying the equilibrium rate constant as a control parameter. We find that an exact prediction of the temporal evolution of fractional surface coverage and the surface pressure dynamics of reversible adsorption can be achieved by the use of the blocking function of a system with irreversible adsorption of highly mobile particles. For systems out of equilibrium, we observe several features of glassy dynamics, such as slow relaxation dynamics, the memory effect, and aging. In particular, the analysis of our system in the limit of small desorption probability shows simple aging behavior with a power-law decay. A detailed discussion of Gibbs adsorption isotherm for non-equilibrium adsorption is given, which exhibits a hysteresis between this system and its equilibrium counterpart. The next chapter focus on the adsorption kinetics and the thermodynamic properties of a binary mixture on a square lattice are studied using the random sequential adsorption with surface diffusion (RSAD). We compare the adsorption of binary species with different equilibrium rate constants and effective rates of adsorption to a surface and find that the temporal evolution of surface coverages of both species can be obtained through the use of the blocking function of a system with irreversible adsorption of highly diffusive particles. Binary mixtures, when one of the components follows the random sequential adsorption (RSA) without surface diffusion and the other follows the RSAD model, display competitive adsorption in addition to cooperative phenomena. Specifically, (i) species replacement occurs over a long period of time, while the total coverage remains unchanged after a short time, (ii) the presence of the RSAD component shifts the jamming coverage to the higher values, and (iii) the maximum jamming coverage is obtained when the effective adsorption of the RSA type components is lower than the other adsorbing particles. Then our new approach is used to analyze the interfacial behavior of asphaltenes at the water/oil interface. RSAD method reveals the phase transition of asphaltenes at the interface from disordered to ordered phase at high coverage due to the steric hindrance effect. This ordered phase is consistent with the observation of birefringence within asphaltenes laden interfaces upon contracting the aged droplet. Corresponding surface pressure obtained from this model is equal to the surface pressure that a droplet containing asphaltenes solution loses its Laplacian shape over the contraction experiment. Another outcome of this model is the observation of dynamic frustration within the dense interfacial layers due to the fast increase of surface coverage in comparison with interfacial diffusion either during spontaneous adsorption or during interfacial area reduction. As a result, the interfacial layer could enter into a metastable glass state that would slowly relax towards a crystalline state with time. Finally, we investigated the phase behavior of particles adsorbed at the liquid/vapor interface using molecular dynamic simulations (MD). The results obtained from these simulations provide complementary insight about the orientation of particles at the interface and the formation of micelles in a real experiment such as pendant drop and Langmuir trough

Liquid-Hextic-Solid Phase Transition of a Hard-Core Lattice Gas with Third Neighbor Exclusion

The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by use of the random sequential adsorption with surface diffusion (RSAD) model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage

Mixture Effect on the Dilatation Rheology of Asphaltenes-Laden Interfaces

Asphaltenes are a solubility class of crude oils comprising polyaromatic and heterocyclic molecules with different interfacial activities. The previously neglected effects of compositional mixture on dilatational rheology are discussed in the light of diffusional relaxation models. It is demonstrated that the reported deviations from the Lucassen–van den Tempel model for a single-component solution could largely originate from a distribution in adsorption coefficients within the asphaltenes class. This particularly applies to the peculiar gel point rheology previously ascribed to asphaltenes cross-linking at the interface. Furthermore, an extensive bibliographical review shows that asphaltenes dilatational rheology data always verify the main features of diffusional relaxation, including a decrease in modulus at high bulk concentrations and phase shift values always lower than 45°. Using diffusional relaxation concepts, the reanalysis of the most extensive dataset so far confirmed recently published studies, showing that asphaltenes exhibit a unique equation of state (EOS) irrespective of adsorption conditions. This EOS proves to be very similar for bitumen and petroleum asphaltenes. Finally, a numerical application of a binary diffusional model proved efficient to capture both dynamic interfacial tension and dilatational rheology, with the same parameters. It appears that a minority of asphaltenes (less than 10%) have a much stronger interfacial activity than the bulk of them, as previously demonstrated by fractionation. These results open up the need for a reinterpretation of the physical mechanisms of asphaltenes adsorption in terms of classical amphiphilic behavior, with a potential impact on emulsion breaking and enhanced oil recovery strategies