Helmholtz interfacial energy

In the absence of specific interactions of the receptor - ligand type the change in the Helmholtz free energy (AFadj due to the process of adsorption is AFads = yps - ypi - Ysi, where Yps, YPi and ys, are the protein-solid, protein-liquid and solid-liquid interfacial tensions, respectively [5], It is apparent from this equation that the free energy of adsorption of a protein onto a surface should depend not only of the surface tension of the adhering protein molecules and the substrate material but also on the surface tension of the suspending liquid. Two different situations are possible. 

The plane of closest approach of hydrated ions, the outer Helmholtz plane (OHP), is located 0.3 to 0.5 run away from the electrode interface hence, the thickness of the interfacial compact layer across which electrons transfer is in the range of 0.3 to 0.5 nm. Electron transfer across the interfacial energy barrier occurs through a quantum tunneling mechanism at the identical electron energy level between the metal electrode and the hydrated redox particles as shown in Fig. 8-1. 

Bifacial Tension the tension of the biface. The Helmholtz free energy per unit of biface. In the absence of surface-active materials the term simply refers to twice the oil-water interfacial tension (yo/w). 

Key Concepts of Interfacial Properties in Food Chemistry Equation D3.5.12 G = U + PV - TS = yA + p,/j, i Equation D3.5.13 where H is the enthalpy, F the Helmholtz free energy, and G the Gibbs free energy. These basic equations can be used to derive explicit expressions for these quantities as they apply... 

Before turning to the surface enthalpy we would like to derive an important relationship between the surface entropy and the temperature dependence of the surface tension. The Helmholtz interfacial free energy is a state function. Therefore we can use the Maxwell relations and obtain directly an important equation for the surface entropy ... 

The SSL theory regards chemically distinct blocks to be completely immiscible. The Helmholtz energy of the molten diblock copolymer system consists of two contributions one is the interfacial energy Fint and the other the elastic energy of blocks Fst. In Semenov s SSL theory (Likhtman and Semenov, 1994 Semenov, 1985), the excess Helmholtz energy per copolymer chain is simplified and expressed as ... 

Application of DFT as a general methodology to classical systems was introduced by Ebner et al. (1976) in modeling the interfacial properties of a Lennard-Jones (LJ) fluid. The basis of all DFTs is that the Helmholtz free energy of an open system can be expressed as a unique functional of the density distribution of the constituent molecules. The equilibrium density distribution of the molecules is obtained by minimizing the appropriate free energy. 

The SCF [Eq. (39)] minimizes the free energy of the interfacial system. The Helmholtz free energy per area of segment for restricted equilibrium is... 

Tarazona and Navascues have proposed a perturbation theory based upon the division of the pair potential given in Eq. (3.5.1). In addition, they make a further division of the reference potential into attractive and repulsive contributions in the manner of the WCA theory. The resulting perturbation theory for the interfacial properties of the reference system is constructed through adaptation of a method developed by Toxvaerd in his extension of the BH perturbation theory to the vapor-liquid interface. The Tarazona-Navascues theory generates results for the Helmholtz free energy and surface tension in addition to the density profile. Chacon et al. have shown how the perturbation theories based upon Eq. (3.5.1) may be developed by a series of approximations within the context of a general density-functional treatment. 

If the monolayer and its associated double layer occupy a separate phase which lies between two homogeneous bulk phases, then for constant temperature, volume, and total number densities of species in this phase, the total differential Helmholtz free energy for a planar interfacial region is given by (20) ... 

The Helmholtz free energy F for the interfacial region is defined in the usual way ... 

As indicated in the discussion following Equation 1.29, the interfacial tension Y is equal to the smface excess Helmholtz free energy per unit area (F IA) when the reference surface is chosen to make the surface excess mass T vanish. But... 

In this section interfacial tensions will be computed using the APACT in combination with the gradient theory. For such computations the expression for the Helmholtz free energy is needed as well as for the equilibrium pressure and chemical potential, as is shown in Equation 2. Another input for the computations is the influence parameter, c. In a first approach this parameter is obtained by fitting computed interfacial tensions to experimental values at reduced temperatures, T/Tc, in the range of 0.3 to 0.8. The results have been included in Table 3. 

Remarks. Close inspection of the nonequilibrium model outputs reveals that assumption of nonequilibrium capillary pressure in the studied range of experimental conditions was not necessary and static equilibrium described by PcxPg-Pe was sufficient to account for the interfacial forces [54], However, recourse to empirical capillary relationships, such as the Leverett /-function, is unnecessary as the nonequilibrium two-phase flow model enables access to capillary pressure via entropy-consistent constitutive expressions for the macroscopic Helmholtz free energies. Also, the role of mass exchange between bulk fluid phase holdups and gas-liquid interfacial area was shown to play a nonnegligible role in the dynamics of trickle-bed reactor [ 54]. By accounting for the production/destruction of interfacial area, they prompted much briefer response times for the system to attain steady state compared to the case without inclusion of these mass exchange rates. 

Considering a colloidal system at constant temperature, volume, and composition, the change of Helmholtz free energy (dF) for any process undergoing the expansion of the oil-water interfacial area (dA > 0) can be expressed as... 

On the other hand, if there is no exchange of matter, whatsoever, between the interfacial system and the adjacent bulk phases, the appropriate free energy to invoke is the Helmholtz free energy F. In such a case, the appropriate system variables are, of course, T, V, and all A,. 

For partially open interfacial systems, the correct function of state to invoke is a mixed Q potential/Helmholtz free energy (H), where the Q potential part refers to the k soluble, and the Helmholtz free energy part refers to the r—k insoluble components, that is. 

Let us consider a multicomponent two-phase system with a plane interface of area A in complete equilibrium, and let us focus on the inhomogeneous interfacial region. Our approach is a point-thermodynamic approach [92-96], and our key assumption is that in an inhomogeneous system, it is possible to define, at least consistently, local values of the thermodynamic fields of pressure P, temperature T, chemical potential p, number density p, and Helmholtz free-energy density xg. At planar fluid-fluid interfaces, which are the interfaces of our interest here, the aforementioned fields and densities are functions only of the height z across the interface. 

From the definition of y and Equation (1.32) at constant T and V, the change in Helmholtz free energy for the creation of an increment of planar interfacial area dA for a unary two-phase system will be equal to the work done on the system,... 

In this section we shall consider some elementary thermodynamics relations involving interfaces [4]. Since molecules at an interface are in a different environment from molecules in the bulk, their energies and entropies are different. Molecules at a liquid-air interface, for example, have larger Helmholtz free energy than those in the Bulk. At constant V and T, since every system minimizes its Helmholtz free energy, the interfacial area shrinks to its minimum possible value, thus increasing the pressure in the liquid (Fig. 5.4). 

Figure 5.4 To minimize the interfacial Helmholtz free energy a liquid drop shrinks its surface area to the least possible value. As a result, the pressure p" inside the drop is larger than the external pressure p. The excess pressure (p" -p )=27/r.

Combining Eqs. (10.7) to (10.12) gives the Helmholtz free energy of the complete emulsion. The free energy is minimised with respect to a change in the interfacial area A. This involves transfer of adsorbed components to or from the interface, thereby changing the bulk concentration and thus y the result is. 

In the emerging theory of interfacial thermodynamics, the properties of the thermodynamic functions (PVT or free energy quantities) at densities corresponding to thermodynamically unstable states play a crucial role. For example, the Interfacial tension is computed from a formula calling for Helmholtz free energy data at every density (composition) between the compositions of the bulk phases in equilibrium. A particular implication of the theory is that Method (a) of Professor Prausnltz s classification is useful for interfacial calculations of vapor-liquid systems, but Method (b) is not. For those interested in the interfacial theory to which I refer, the following papers and references therein may be useful ... 

Let us now consider the interfacial tension of a plane interface from the thermodynamic point of view. On the basis of the concept of Guggenheim, the Helmholtz free energy A of the entire system (phases a and j3 plus the interfacial layer) is expressed by the following equation ... 

Equation (62) is rigorous (assuming Gibbs and Helmholtz free energies are the same for ions in a solid—solution interfacial system) but requires explicit electrostatic potential equations in order to obtain an explicit activity coefficient equation. Since rigorous, explicit electrostatic potential equations for solute and surface site ions have yet to be derived, the approximate electrostatic potential equations, which are solutions to the linearized Poisson—Boltzmann equation, were used here and by Debye—Hiickel to give... 

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