Cohesion-tension theory

The tensile properties of liquid water are not just a curiosity of the physical chemist. Indeed, the long standing cohesion tension theory of transpiration mo tion of water from the root to the leaves of plants states that the flow of water in the capillaries is driven by a reduction of pressure in the leaves and that this pressure frequently drops below zero (e.g., in trees of greater than 10 m in height) [5 8]. Experimental measurements indicate that water in certain plants can reach pres sures down to approximately —10 MPa [9]. The suckers on the tentacles of octopi... 

On the above theory the osmotic pressure of an ideal solution depends upon the fact that there is a difference between the values of the solvent piessure in the pure solvent and in the solution respectively Let us denote the solvent pressure m the pure solvent by ir and its value m the solution by ir We have been considering an ideal solution as defined by Tinker (It will be shown later that in non-ideal solutions, e those m which the molecular volume of the solvent is altered as a result of addition of solute, the resulting osmotic pressure is a more complex phenomenon, involving the intrinsic or cohesion tension of the solvent as well as its liquid thermal pressure For the present we are dealing with the ideal case, however )... 

The relations between the intrinsic pressure and other physical constants developed in the foregoing paragraphs have been found from theoretical considerations based on Laplace s theory, that is, on the assumption of cohesive forces acting over very small distances. They are of interest to us inasmuch as there is a necessary connection between intrinsic pressure and surface tension. While no numerical expression has so far been found for this, it is obvious that high intrinsic pressures must be accompanied by high surface tensions, since the surface tension is a manifestation of the same cohesive force as causes intrinsic pressure. (See, however, equation 3, p. 27, for an empirical relation between the two.)... 

The attempt to show that surface tension phenomena were the cause of osmotic pressure was first made by Jager, and his theories were vigorously supported and developed by Traube, whose conclusions we shall state and examine briefly. He finds that the more a dissolved substance reduces the surface tension of water the greater is the velocity of osmosis of the solution. Hence he concludes that it is the difference in the surface tensions of solvent and solution which determines the direction and velocity of osmosis. The direction of flow Traube obtains by the following consideration let M (Fig. 7) be a membrane separating two liquids A and B. The molecules of each liquid are then drawn into its interior by the cohesion or intrinsic pressure. If the intrinsic... 

In the preceding pages we have availed ourselves of only one of the theories of surface tension, that of Laplace. It has led us directly to recognise an important property of liquids—their cohesion or intrinsic pressure—and has enabled us to establish... 

A nonpolar neutral species in a polar medium such as water experiences interfacial tension. Solvophobic theory is a general statement of hydrophobic theory, which has been developed to explain the tendency of neutral organic species to flee the water phase. It has been reported that the solution of nonelectrolytes in water is attended by a net decrease in entropy [65,158]. This has been attributed to an increased structuring of water molecules in the vicinity of the solute. The process may be conceptually rationalized by considering that a solute must occupy space in a cohesive medium. The solute must create a cavity in the water milieu and then occupy that cavity [19,65,158]. The very high cohesive density of water creates considerable interfacial tension in the... 

Edser3 has worked out a theory of the internal cohesion and surface tension of liquids, based on the assumption that the molecules may be regarded as occupying a space spherical in shape (not because the molecules themselves are spherical, but because they will probably sweep out a space more or less spherical during any considerable period of time), and concludes that about 94 per cent, of the free energy of the surface resides... 

This equation has been known for over a century it was given by Young2 (without proof ) and by Dupre 3 it can be deduced also from Laplace s theory of Capillarity, or indeed from any theory of the cohesive forces, since it can be obtained from consideration of energies only. Until recent years it has been little noticed, which is unfortunate, as the meaning of the contact angles is much clarified when the work of adhesion is introduced, and the surface tensions of the solid surfaces, which are not measurable, are eliminated. Most authors are now, however, expressing their results in terms of the work of adhesion or of closely related expressions. 

Solvophobic theory provides a theoretical framework to evaluate hydrophobic effects. To place a polypeptide or protein into a solvent, a cavity of the same molecular dimensions must first be created. The amount of energy or work required to create this cavity is related to the cohesive energy density or the surface tension of the solvent. The fusion of cavities reduces the total surface area in the combined cavity, and thus the free energy of the... 

In Bakker s theory of capillarity the internal forces in a liquid are regarded ais the cohesion (molecular attraction) Rnd the opposing thermal pressure, and the surface tension then appears as the difference between pressures normal... 

There are many theories [1] and empirical correlations [1,3,5] to calculate y. The intermolecular interactions which play a role in determining y and the cohesive energy density ecoh arc Quite similar. The surface tension at room temperature (where ecoh has been best quantified) can therefore be estimated by Equation 7.1 [3] ... 

It needs to be noted here that since the surface tension fundamentally originated from the intermolecular forces and can be related to the thermodynamic work of adhesion and cohesion, the slip length can be estimated by appealing to the pertinent molecular theories as [8]... 

Let us now return to the question of whether we can calculate the surface energies of polymers from first principles. The rough estimates in section 2.1 tell us correctly the order of magnitude of surface tensions and correctly draw attention to the intimate connection between surface energies and the cohesive forces in liquids, but they have a number of drawbacks. Firstly, temperature makes no appearance in these theories, despite the experimental fact that surface tensions depend quite strongly on temperature. Secondly, we have assumed that the density of the liquid near the surface is the same as the bulk density. These shortcomings are seen at their most extreme if we consider a liquid near the liquid-vapour critical point. Here the distinction between liquid and vapour vanishes completely the surface tension of the liquid approaches zero and the system becomes in effect all interface. An improved theory of surface tension must be able to accoxmt for these phenomena, at least qualitatively. 

The superscript d indicates that only the contribution of the dispCTsion potential to the interfacial tension and work of cohesion has been included. If the molecules are nonpolar, Waa = Wm andyA= Ya. Padday(1969) examined the above relation after adjustments were made for the improvement of the intermolecular potentials, improved liquid theories, etc. He found the agreement with measured values of liquid-vapor interfadal tensions to be exceUmt. 

Fowler [8] used the above intermolecular theory to calculate the energy required to break a column of liquid of unit cross section and remove the two halves to infinite separation. Using statistical thermodynamics he calculated the work of cohesion and found it to be equal to twice the surface tension. 

Approximate theories exist to calculate the interfacial tension from a knowledge of the cohesive energy of the two pure phases. The specific free energy of cohesion of a pure phase is given by... 

---