Solid-liquid interface theoretical models

Contact angle — The contact angle is the angle of contact between a droplet of liquid and a flat rigid solid, measured within the liquid and perpendicular to the contact line where three phases (liquid, solid, vapor) meet. The simplest theoretical model of contact angle assumes thermodynamic equilibrium between three pure phases at constant temperature and pressure [i, ii]. Also, the droplet is assumed to be so small that the force of gravity does not distort its shape. If we denote the - interfacial tension of the solid-vapor interface as ysv. the interfacial tension of the solid-liquid interface as ySL and the interfacial tension of the liquid-vapor interface as yLV, then by a horizontal balance of mechanical forces (9 < 90°)... 

The observation of natural icicles showed the weak increase of ripple wavelength with icicle diameter. The wavelength also increased slowly with increasing water supply rate per width, which was calculated from the present theoretical model that takes account of the effect of the restoring forces due to gravity and surface tension on the liquid-air surface in the icicle growth under a thin shear flow. The two models for the destabilization and/or stabilization of the solid-liquid interface under a thin shear flow were compared and discussed in some detail. It was concluded that different boundary conditions in the two models lead to the completely different final results. 

Abstract In this chapter we discuss the results of theoretical and experimental studies of the structure and dynamics at solid-liquid interfaces employing the quartz crystal microbalance (QCM). Various models for the mechanical contact between the oscillating quartz crystal and the liquid are described, and theoretical predictions are compared with the experimental results. Special attention is paid to consideration of the influence of slippage and surface roughness on the QCM response at the solid-liquid interface. The main question, which we would like to answer in this chapter, is what information on... 

Some theoretical models based on the thermodynamics of surfactant self-assembly have also been recently used to predict the critical surface aggregation concentration (the bulk concentration at which surfactants start to self-assemble at the solid-liquid interface), and the self-assembled surfactant structure at the solid-liquid interface (11). These models, although providing useful insight into the surfactant self-assembly process, require an estimate of the interaction energies, which are difficult to determine experimentally. Variations in the estimated interaction energies can lead to different self-assembled surfactant structures, depending on the values used for the calculations. 

Neither the surface charge density nor the surface potential at the solid/liquid interface can be measured directly. They are to be retrieved from pH potentiometric or electrokinetic data on the basis of certain theoretical concepts and models. 

Y. Y. Tong, C. Rice, E. Oldfield et al. in Theoretical Modeling of the Solid/Liquid Interface Electronic Perspective and Comparison with Experiment (Ed. W. Halley), American Chemical Society, Washington, DC, 2001. 

Even though some progress has been made towards understanding electrocatalytic process and screening electrocatalysts from DFT, the method has difficulty in providing quantitative numbers for detailed reaction steps. On one hand, methodological improvements are required to describe the electron transfer at solid-liquid interface, the band structure, and the excited states effectively, which is currently limitation of DFT. On another hand, the model systems in DFT studies are somewhat too simplified to model the real catalysts effectively. For instance, the real catalysts are powders, which may behave differently with size. Recently, efforts have been made to model the nanoparticles with the size of the real catalysts (<5 nm), showing indeed different behaviors from the extended surfaces even in term of trend (Fig. 3), a common model used in DFT studies [24, 25]. Thus, theoretical... 

Zeta potential is a fundamental parameter for modelling and characterizing electrokinetic flows in a variety of microfluidics and Lab-on-a-Chip devices. Because the zeta potential depends on so many factors (pH, concentration, liquid, surface etc.) more measurements are required for a variety of surface-liquid combinations particularly, biological and biochemical fluids. Since measurements can vary greatly between methods and experiments, multiple tests should be employed to accurately determine the zeta potential. In addition, measurements performed using multiple techniques can be corroborated which will reduce errors between results. The ultimate goal is to develop an accurate database of zeta potential measurements for various solid-liquid interfaces, however this will most likely require the development of new theoretical models and experimental methods to increase the accuracy and throughput of current devices. 

Adsorption at the solid-liquid interface is generally similar to the adsorption at the solid phase-gaseous phase interface. Theoretical modelling of the adsorption process is more difficult because, in addition to adsorbing dissolved substances, solvent is present (e.g. water), the molecules of which can also adsorb, and interactions of adsorbed molecules with molecules of the solvent may occur. Molecular adsorptions, when molecules of a substance are adsorbed, and ion adsorptions, in which ions of a substance are adsorbed, can similarly take place. Solid phase-liquid phase interfaces are usually described by empirical equations and theoretically derived equations of the Freundlich and Langmuir type. 

A theoretical model can be developed to express the function constants that appear in Eq. (19) in terms of selected molecular, solution, and surface properties. As indicated with reference to Eq. (19), the Langmuir-type model is the most popular model used in the hterature to describe adsorption equilibrium isotherms at solid-liquid interfaces. The Langmuir-type isotherm is characterized by an initial (usually steep) slope at low concentration followed by plateau attainment at high concentration. A mathematical expression of this statement can be developed as follows ... 

The CFD model deals with three-phase flow (liquid-gas-solid) while the theoretical models deal with quasi-two-phase flow (hquid-solid). The theoretical models consider that the particle is totally immersed in the liquid if the particle sinks below the hquid surface. In contrast, the cavity formed behind the particle can be well described by the CFD model. The cavity dynamics can influence the final penetration outcomes. For example, the experimental observation in Verezub et al. [48] indicates that the cavity can drag the particle back to the surface at low impact velocities, and finally the particle stabilizes at the liquid-gas interface, not able to penetrate into the bulk liquid Akers and Belmonte (2006) pointed out that if the penetrating particle stops before the formed air cavity has closed, the energy stored in the liquid can be partially released, which can result in the particle rebounding before completely submerging into the liquid. 

The availability of thermodynamically reliable quantities at liquid interfaces is advantageous as a reference in examining data obtained by other surface specific techniques. The model-independent solid information about thermodynamics of adsorption can be used as a norm in microscopic interpretation and understanding of currently available surface specific experimental techniques and theoretical approaches such as molecular dynamics simulations. This chapter will focus on the adsorption at the polarized liquid-liquid interfaces, which enable us to externally control the phase-boundary potential, providing an additional degree of freedom in studying the adsorption of electrified interfaces. A main emphasis will be on some aspects that have not been fully dealt with in previous reviews and monographs [8-21]. 

Johans et al. derived a model for diffusion-controlled electrodeposition at liquid-liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173-175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid-liquid interface. Other nucleation work at the liquid-liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. 

For the remainder of this chapter, we discuss results for various studies of interfacial solvation dynamics. We first discuss studies at liquid liquid interfaces at planar interfaces and in microheterogeneous media in Section II. In Section III, we discuss solvation dynamics at liquid solid interfaces. In Section IV, we review theoretical models and simulations of solvation dynamics at liquid interfaces. Finally, we conclude with a discussion of future studies. 

Catalysis and Electrocatalysis at Nanoparticle Surfaces reflects many of the new developments of catalysis, surface science, and electrochemistry. The first three chapters indicate the sophistication of the theory in simulating catalytic processes that occur at the solid-liquid and solid-gas interface in the presence of external potential. The first chapter, by Koper and colleagues, discusses the theory of modeling of catalytic and electrocatalytic reactions. This is followed by studies of simulations of reaction kinetics on nanometer-sized supported catalytic particles by Zhdanov and Kasemo. The final theoretical chapter, by Pacchioni and Illas, deals with the electronic structure and chemisorption properties of supported metal clusters. 

This name covers all polymer chains (diblocks and others) attached by one end (or end-block) at ( external ) solid/liquid, liquid/air or ( internal ) liquid/liq-uid interfaces [226-228]. Usually this is achieved by the modified chain end, which adsorbs to the surface or is chemically bound to it. Double brushes may be also formed, e.g., by the copolymers A-N, when the joints of two blocks are located at a liquid/liquid interface and each of the blocks is immersed in different liquid. A number of theoretical models have dealt specifically with the case of brush layers immersed in polymer melts (and in solutions of homopolymers). These models include scaling approaches [229, 230], simple Flory-type mean field models [230-233], theories solving self-consistent mean field (SCMF) equations analytically [234,235] or numerically [236-238]. Also first computer simulations have recently been reported for brushes immersed in a melt [239]. 

The protein adsorption studies described were all at the liquid - solid or solid - air interface. Lateral scanning elllpsometry was made to evaluate the surfaces with a wettability gradient. Experiments were most often made on (modified) silicon surfaces. The experimental results are also discussed in relation to the proposed theoretical models for protein adsorption. 

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