Lifshitz-van der Waals

Good, van Oss, and Caudhury [208-210] generalized this approach to include three different surface tension components from Lifshitz-van der Waals (dispersion) and electron-donor/electron-acceptor polar interactions. They have tested this model on several materials to find these surface tension components [29, 138, 211, 212]. These approaches have recently been disputed on thermodynamic grounds [213] and based on experimental measurements [214, 215]. 

There are numerous techniques which provide information related to the surface energy of solids. A large array of high-vacuum, destructive and non-destructive techniques is available, and most of them yield information on the atomic and chemical composition of the surface and layers just beneath it. These are reviewed elsewhere [83,84] and are beyond the scope of the present chapter. From the standpoint of their effect on wettability and adhesion, the property of greatest importance appears to be the Lifshitz-van der Waals ( dispersion) surface energy, ys. This may be measured by the simple but elegant technique of... 

These equations result from assuming that the total surface energy can be split into the sum of components associated with different types of bonding, for example dispersion plus polar yP (Eqs. 14 and 15), or Lifshitz-van der Waals... 

VlSSER, J, Adv. Colloid Interface Sci. 3 (1972) 331. On Hamaker constants a comparison between Hamaker constants and Lifshitz-van der Waals constants. 

The coarse carrier particles blended with micronized drug form an ordered or interactive mixture (Fig. 8.11) (Hersey 1975) stabilized by adhesive Lifshitz—van der Waals and electrostatic forces (Podczeck 1998 Hickey et al. 1994). The shear forces exerted in the airflow of a DPI device must be greater than the adhesive forces in order to provide sufficient deaggregation and dispersion of the drug particles. Unfortunately, however, this process is more or less incomplete and disperses only a proportion of the agglomerated drug particles depending on the inhalation airflow (Zanen et al. 1992). 

The Lifshitz-van der Waals constant for the interaction between two bodies of materials 1 and 2 separated by a medium 3 is given by... 

Solving Eq. (3.91) for the Lifshitz-van der Waals constant or Hamaker s constant usually is not trivial. Many approximations for its calculation have been proposed for various cases [Landau and Lifshitz, 1960 Hough and White, 1980 Visser, 1989 Israelachvili, 1992]. For materials 1 and 2 interacting through material 3, Hamaker s constant becomes... 

Lifshitz-van der Waals surface free energies of the surface, foulant and fluid (e.g. water), respectively (N m-1) S — A2 sin 1// (Equation (26))... 

Chemical compound added to a base oil to improve oil quality as any substance that aids in the lubrication process at the rubbing interface by functionality other than viscosity. Intermolecular energy of attraction between the separate molecules making up a homogeneous liquid or solid. The energy consists of contribution from Lifshitz-van der Waals components in all cases. 

The original derivation is given in B. W. Ninham and V. A. Parsegian, "Van der Waals interactions in multilayer systems" J. Chem. Phys. 53, 3398 02 (1970). The details of a modified derivation are given in R. Podgornik, P. L. Hansen, and V. A. Parsegian, "On a reformulation of the theory of Lifshitz-van der Waals-interactions in multilayered systems, J. Chem. Phys, 119, 1070-77 (2003). 

Alternatively, the Hamaker constant can be calculated in the Lifshitz quantum electrodynamic continuum approach [7], which incorporates all three types of van der Waals interactions for condensed systems (Lifshitz-van der Waals interactions) through surface tension determinations with apolar liquids (e.g. diiodomethane, a-bromonaphthalene)... 

According to this equation, the solubility of the polymer molecules in a liquid will increase with increasing positive values of AC n. as the polymer molecules will increasingly repel each other and thereby tend to disperse. If AG n < 0. solubility decreases due to molecular attraction. In most pharmaceutical systems, molecular contributions to AG2T2 will be from apolar Lifshitz-van der Waals (AG212) forces and from Lewis acid/base (AGm) forces. Hence, AG2T2 is represented by... 

From wetting experiments on apolar surfaces = y ) the Lifshitz-van der Waals portions of... 

The data in Table 2 show that for methylated liquids the surface tension ( K/v) (interface liquid/vapour) increases from di- to tetrasiloxanes (7 9—>10). This is mainly due to an increase of the Lifshitz-van der Waals portion (yjf ). Surprisingly, we did not find a polarity increase for the change from the trisiloxane (two oxygen atoms) to the tetrasiloxane (three oxygen atoms). At the interface solid/liquid these molecules behave slightly differently. Intensive interactions of the Lifshitz-van der Waals type with the condensed perfluorinated matter yield a dramatic reduction of this interfacial tension portion (yf) ). On the other hand, this strictly apolar surface cannot compensate donor-acceptor portions These values are practically identical to those of. ... 

The change from methyl-to ethyl-substituted siloxanes (9->ll) yields a considerable surface tension increase. Again, this behavior is mainly due to an increase of the Lifshitz-van der Waals portion Considering the data for the interfacial tension solid/liquid and its portions the energy difference between methyl and ethyl groups at interfaces becomes even more transparent. For the methylated liquid 9 the donor-acceptor portion not accompanied by a significant portion. Ethyl groups make siloxanes less flexible [12] and cause a considerable portion. 

Lifshitz-van der Waals portion (/jf). Straight-chain structures improve the chances for intermolecular interactions of the Lifshitz-van der Waals type [13], On the other hand we assume that only one of the two oxygen atoms of the straight-chain trisiloxanyl moiety is sufficiently close to the water surface to influence the donor-acceptor portion. As to expect from the results for pure liquids only donor-acceptor portions fj/ were detected at the interface solid/liquid. The values are identical to those for indicating a common source for the donor-acceptor portions The increased y l value for the branched structure 3 indicates that in this particular case both oxygen atoms are exposed to the perfluorinated surface. 

Dispersion Forces The dipolar interaction forces between any two bodies of finite mass, including the Keesom forces of orientation among dipoles, Debye induction forces, and London forces between two induced dipoles. Also referred to as Lifshitz—van der Waals forces. 

The objections to the Hamaker theory were overcome by Lifshitz and his coworkers [Lifshitz 1956, Dzyaloshinskii 1961] using the bulk optical properties of the interacting bodies. The approach employed by Lifshitz uses the so-called Lifshitz-van der Waals constant h that depends only on the materials involved provided the separation distance is relatively small. Under some conditions the constant h can be related to the Hamaker constant by... 

---