Entropic surface tension

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Lindahl, E. and Edholm, O. (2000). Spatial and energetic-entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations, J. Chem. Phys., 113, 3882-3893. 

Hydrophobic binding. The hydrophobic effect can have both enthalpic and entropic components, although the classical hydrophobic effect is entropic in origin (Section 1.9.1). Studies on the associations between planar aromatic molecules show an approximately linear relationship between the interaction energy and their mutual contact surface area with slope 64 dyn cm-1, very close to the macroscopic surface tension of water (72 dyn cm-1). Hence, in the absence of specific host or guest interactions with the solvent the hydrophobic effect can be calculated solely from the energy required to create a free surface of 1 A2 which amounts to 7.2 X 10 12 J or 0.43 kjA 2 mol. ... 

One way to improve the Adam-Gibbs model is to include details of the structure of the interface between the various aperiodic minima [39]. Near the Kauzmann temperature, the interface broadens, and correct scaling laws are obtained by wetting the droplet surface [39]. In this case, the surface tension of the entropic droplet is a function of its radius and can be obtained by renormalization group arguments. Analysis reveals that the activation barrier to configuration rearrangement is [39]... 

Fig. 8 Monomer chemical potential in a droplet comprising monomer and hydrophobe as a function of the monomer volume fraction (top) and droplet radius (bottom). The global potential (as given by Ugelstad s equation) is given, as well as the entropic term due to mixing and the Laplace term due to surface tension. Parameters m Y=l Vm,h=0 y=25 mN/m Vjn=l-1 10 m mol T=298.15 K (p =0,96 r =100 nm...

In Fig. 9c, the effects of different surface tension values on the equilibrium are examined. By decreasing the interfacial tension, the Laplace term becomes less significant than the contribution given by the entropy of mixing, and therefore ripening is decreased and stability is enhanced. Theoretically, in a system with zero surface tension at the oil/water interface, the total monomer chemical potential is given solely by the entropic terms, and it is always stable. 

Using [2.2.9] the surface tension of a pure liquid can be split into its entropic and energetic contribution. For a pure liquid, where the Gibbs dividing plane is determined by setting n°= 0, introducing U° =U°/A and S° =S°/A as the interfacial excess energy and entropy p>er unit area, respectively, we have... 

Fowkes own expression does not contciin the entropic contribution but has a term accounting for the surface pressure of the SG interface (we do not need that because our y is the surface tension of the solid in the presence of vajx)ur). 

Figure 5 shows the temperature dependence of the surface tension. The differences between calculated values and the experimental ones do not exceed ca. 1 mN m-1. An adjustable parameter is not used by assuming that the k does not vary with the temperature and is fixed at 0.5, a theoretical value for both PS and PVME. This indicates that the simulated equation-of-state parameters for the component polymers are reasonable. It has been known that the LCST behaviors are originated from the specific interactions between components and/or the finite compressibility of mixture and that the phase separation is entropically... 

Here 6, = FitOi is the monolayer coverage, Fi is the adsorption, n = yo - y is the surface pressure, yo is the surface tension of solvent, n, = coj/too, and coo are the partial molar surface areas of the surfactant and solvent, respectively, bi is the adsorption constant, Cj is the surfactants concentration in the solution bulk. The Frumkin parameters ai and a2 represent the interactions of components 1 and 2 with the solvent, while the parameter ai2 accounts for interactions between the two surfactants 1 and 2 in the ternary regular mixture (see Eq. 2.32) a,=HJ,/RT aj=HJ2/RT a,2=(Ho,+Ho2-HJj)/2RT, where Hy=A,jRT. Choosing the dividing surface after Lucassen-Reynders (cf. Chapter 2), one can eliminate the contributions from the entropic non-ideality of the solvent, thus reducing Eq. (3.27) to a much simpler form... 

Minnikanti, V.S., Archer, L.A. Entropic attraction of polymers toward surfaces and its relationship to surface tension. Macromolecules 39, 7718—7728 (2006)... 

As discussed in section 2.2.1, surface tensions are measured under conditions of constant temperature and pressure - in this case the work done against the surface tension is equal to the increase in the Gibbs free energy. Thus for isothermal changes at finite temperature the surface tension is strictly a surface free energyf The fact that the surface tension at finite temperature has a substantial entropic component is very important, as we shall see. 

Frisch and Frisch speculated that the minimum in surface tension might be due to a large entropic contribution to the reversible work of wetting. This, in turn, may have been caused by an elastic straining of the immediate surface layers near a critical point of inversion. One of the network components may have been leaving the interface, and the other migrating there at the minimum. 

Here a is the statistical segment length that for simplicity reasons we assume to be equal for both components. The surface tension y is defined as the excess free energy in the interface per unit surface. It contains an entropic part, the chain conformations have to adapt to the concentration profile, and an interaction part. As always, in equilibrium, both contributions are of the same order, which makes it simple to derive an approximate expression for y by only focusing on the interaction part ylW=n lS, where Mab is the number of AB interactions in the interface with surface S. Since tiabSSAIv, it follows from eqn [38] that... 

---