Equilibrium surface tension equivalence points

For multicomponent systems, the expression for y here employed may be shown equivalent to that involved in the cluster diagram technique (6), which is currently being employed in a variety of problems. The present derivation shows that the starting expressions satisfy the thermodynamic consistency relation embodied by the adsorption isotherm. It is, however, important to observe that any direct application of these alternative rigorous approaches, which is of necessity of an approximate nature, leads to some violation of the complete internal equilibrium conditions. Similarly, calculations of surface tension which employ the adsorption equation as a starting point invariably violate mechanical equilibrium in some order of approximation. 

Surface tension measurement. Adsorption titration, also called soap titration, (2.3) was carried out by the drop volume method at different polymer concentrations. The equivalent concentration of salt was held constant. The amount of emulsifier necessary to reach the critical micelle concentration (CMC) in the latex was determined by each titration. The total weight of emulsifier present in the latex is the weight of emulsifier in the water plus the weight of emulsifier adsorbed. The linear plot of emulsifier concentration (total amount of emulsifier corresponding to the end-point of each titration) versus polymer concentration gives the CMC as the intercept and the slope determines the amount of emulsifier adsorbed on the polymer surface in equilibrium with emulsifier in solution at the CMC (E ). 

Now consider a tapered tube, wider at the top. This represents a stable equilibrium. For a given pressure applied, the mercury is stable in only one position in the capillary. If the pressure is increased momentarily (or the surface tension is decreased, say, by a fluctuation in the applied potential), the mercury meniscus will move to a lower point, where the radius is a little smaller, to establish a new equilibrium, in accordance with Eqs. 51H-53H. The mechanical equivalent of this configuration is a sphere at the bottom of a concave surface, shown in Fig. 4H(b). Stability is attained by negative feedback. If the... 

Because of the thermodynamic imperative to attain a state of minimum free energy for the system as a whole, surface units are subjected to a net inward attraction normal to the surface. Geometrically, that can be equivalent to saying that the surface is in a state of net lateral tension defined as a force acting tangent to the surface at each point on it. It is this apparent tangential force that leads to the concept of a surface tension. The units of surface tension and of the excess surface free energy are dimensionally equivalent and, for pure liquids in equilibrium with their... 

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