Free energy of adhesion

Oxidation of polyethylene by sulphuric acid and potassium chlorate [9,10] improves its adhesiveness. The free energy of adhesion of the polymer is found to increase linearly with the surface density of the hydrophyl-lic sites created by oxidation. 

E(hg) is negative for adhesive systems and —E(he) is traditionally known as the free energy of adhesion. 

In adhesional wetting, a liquid which is not originally in contact with the solid substrate makes contact and adheres to it. In contrast to spreading wetting, the area of liquid-gas interface decreases. The work (free energy) of adhesion is given by the Dupr6 equation (see equation (4.29) in the form... 

Interfacial Energy of Adhesion. When the polyelectrolyte-grafted nylon surface, in equilibrium with 50% relative humidity, is brought into contact with water or a salt solution, various interactions will occur together they comprise the reversible work of adhesion or free energy of adhesion at the interface of these two phases. This free energy of adhesion should be composed of the following contributions ... 

Of the above contributions, 1, 3, and 4 will tend to lower the free energy of adhesion and favor wetting (lower 6) 2 will raise the free energy and oppose wetting (higher 6) the effects of 5 and 6 may go in either direction. 

All these types of interactions could affect significantly the free energy of adhesion at the interface. It is impossible at this time to estimate these contributions to the free energy of adhesion, and they are omitted from the following discussion. 

Thus, the total contribution estimated for the loosely bound Cl ions is — 3900 — 170 -f- 26 or about —4000 ergs/cm.2, while that for the tightly bound C1 ions may vary between about —90 and —900 ergs/cm.2 (i.e., if all the bound CT ions were site-bound ion pairs, their contribution to the free energy of adhesion would be (0.6 X 1014) X ( —1500 X 10"14) or about —900 ergs/cm.2. If all these Cl" ions were covalently bonded, this figure would be about —90 ergs/cm.2). 

In any case, it is clear that when even half the counterions are tightly bound to the surface, the contribution of the loosely bound ions to the free energy of adhesion is greater. (This is still true even if a value of 3 A. is taken as the average separation in the van der Waals calculations). The comparison is perhaps clearer when made on the basis of one ion or ion pair (Table V). 

Thus, in general for any counterion species the free energy of adhesion will probably always be higher and the contact angle lower when more counterions are able to escape the local fields of the individual charges on the polyelectrolyte. Figure 8 depicts schematically this behavior for the different counterions. Therefore, for grafted polyquaternary cations on a nylon surface, the counterions F", CT, and I03 are... 

SchrOder (1979) was able to improve this approach by using a refined expression of the Gibbs free energy of adhesion as a function of the various intermolecular attraction energies between the liquid and the solid. In this way, by using up to 10 different immersion liquids with known parameters, he has calculated the apparent dipole moment and polarizability characterizing the immersion behaviour of various pigment surfaces (e.g. rutile, iron oxide and several phtalocyanines). 

It has been shown that the free energy of adhesion can be positive, negative, or zero, implying that van der Waals interactions can be attractive as well as repulsive [130,133,134]. While Eq. (14) can, strictly speaking, be expected to hold only for systems that interact by means of dispersion forces only, there are no restrictions on Eq. (15). Since this equation describes very well the fundamental patterns of the behavior of particles, including macromolecules, independent of the type of molecular interactions present, it was found to be convenient to define an "effective Hamaker coefficient that reflects the free energy of adhesion [130],... 

In 1969, based on the Fowkes equation, Owens and Wendt proposed a new expression by dividing the surface tension into two components, dispersive, yf, and polar, y , using a geometric mean approach to combine their contributions. They assumed that the free energy of adhesion of a polymer in contact with a liquid can be represented by the equation... 

Later, by combining Equations (699), (703) and (707), one obtains the total interfacial free energy of adhesion as ... 

H hysteresis of the polymer-water free energy of adhesion... 

The hysteresis of the polymer-water free energy of adhesion was calculated from H = y , (cos0r — cos 0 ). where ywll is the water-air interfacial tension and 0r the receding contact angle. 

The free energy of adhesion, r, glass solution [26], has been related to the surface density of transfer red molecules by using the usual definition of the free energy of adhesion, r = yg - Vsa [2>16] and... 

The free energy of adhesion or adhesion tension for the system silica-LNBr aqueous solutions has been measured. The model, which explains the above-mentioned peculiarities of the isotherm of chemisorption at the surface of the solids, is confirmed by the results of adhesion tension measurements. 

The above discussion assiimes naively that protein molecules act as small particles having a distinct surface tension. It should be noted, however, that agreement between thermodynamic model predictions and experimental results does not stipulate that the individual macromolecules have a surface tension. The fact is that, since there is a close correlation between the thermodynamic free energy of adhesion and van der Waals interactions (M 17), the results can be understood as manifestations of the latter. 

The initial state is an idealized one in which the polymer material, and the block of substrate, have been detached from the surrounding matter, so that we can examine stages 3 and 4 of the scenario. If AG is the free energy of adhesion (i.e., "anchoring" the column base or foot to the solid) and Oy is the yield strength of the polymer, then the condition for drawing a fibril by extension, at constant mass, vs. that for interfacial peeling, is ... 

Small values of the free energy of adhesion, AG, for the polymer on the solid, and low levels of roughness, will be conducive to low wear and high wear will be the consequence of large values of AG and of p. 

Third, numerical calculations based on the inequalities that we have proposed lead to qualitative predictions of the transfer of matter, and of general strength in adhering systems, that are in agreement with observations. The trends of these practical properties, with variation in fundamental properties such as polymer yield strength and free energy of adhesion, are in excellent agreement with observed results. 

Figure 2. Thermodynamics of the engulfment of a bacterium B by Phase 2 from Phase 1. Step 1, AG, approximates the free energy of adhesion. The net free energy change is ixGnet = yis — yta-...

In the first part of this section, wetting criteria as well as surface and interface free energies are defined quantitatively. The estimation of a reversible work of adhesion W from the surface properties of materials in contact is therefore considered. Next, various models relating the measured adhesion strength G to the free energy of adhesion W are examined. 

Using Eq. [4] for the free energy of adhesion between phases i and j gives ... 

Good introduced an interaction parameter <1> [33], which is the raho of the free energy of adhesion and the geometric mean of the free energies of cohesion ... 

Finally, this new model clearly shows that both approaches studied (i) on the one hand, the estimation of the free energy of adhesion, -thermodynamic quantity-. 

The free energies of adhesion, wetting and spreading are expressed in terms of the free energies of each interface, y, such that... 

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