The Formation of Condensed Phases

V. Molinier, P. J. J. Kouwer, J. Fitremann, A. Bouchu, G. Mackenzie, Y. Queneau, and J. W. Goodby, Shape dependence in the formation of condensed phases exhibited by disubstituted sucrose esters, Chem. Eur. J., 13 (2007) 1763-1775. 

As mentioned in the introduction, the discussion starts from a macroscopic system composed of 1 identical particles. Among the particles there exists an attractive interaction that is responsible for the formation of condensed phases. The particles on the other hand possess a certain degree of freedom of motion in any direction within the system, as required by the liquid state. Because no preferred distribution of particles can be assumed, the system seems on average to be totally homogeneous and isotropic. This leads to an essential simplification of the problem. 

The dispersion energy is the universal attractive glue that leads to the formation of condensed phases. It is additive at second order in perturbation theory, and the form of the three-body term that arises at third order (the tripledipole dispersion term) is also well known from perturbation theory. This Axilrod-Teller term " was the only addition to the pair potential for argon that was required to quantitatively account for its solid and liquid state properties. This may be grounds for optimism that other nonadditive dispersion terms are negligible. Whether this can be extended to less symmetrical organic molecules and their typical crystalline and liquid environments has not yet been established however. 

The droplet current / calculated by nucleation models represents a limit of initial new phase production. The initiation of condensed phase takes place rapidly once a critical supersaturation is achieved in a vapor. The phase change occurs in seconds or less, normally limited only by vapor diffusion to the surface. In many circumstances, we are concerned with the evolution of the particle size distribution well after the formation of new particles or the addition of new condensate to nuclei. When the growth or evaporation of particles is limited by vapor diffusion or molecular transport, the growth law is expressed in terms of vapor flux equation, given by Maxwell s theory, or... 

In these experiments the supersaturated state was produced physically for a single condensable substance. Gas-phase chemical reactions may also lead to the formation of condensable species, and several may be present simultaneously. This occurs in air pollution and in the commercial synthesis of tine particles. 

A as a Function of pH and 7r. Since the area/molecule could not be ascertained from the 7r-A isotherm of a desorbing film, the A values were calculated by extrapolating kinetic data (Equation 2) to zero t (8). Abrupt phase transitions occurred with palmitic acid films, and the 7r of the phase transition varied directly with pH (Figure 4). The anomalous decrease in A that was found immediately before film expansion (Figure 4) suggested partial ionization and the formation of condensed acid soaps (6, 8, 28). Since fatty acid monolayers are partially ionized in the condensed state (8), the apparent pKa of the fatty acid could not be esti-... 

Atoms, groups of atoms, ions, molecules, macromolecules, and particles always are subject to forces between them. These interaction forces may cause chemical reactions to occur, i.e., cause the formation of other molecular species, but they are also responsible for the existence of condensed phases (solids and liquids), for adherence of a liquid to a solid surface, or for aggregation of particles in a liquid. In short, all structures form because of interaction forces. Generally, formation of a structure causes a decrease in entropy, and this may counteract the tendency of formation, depending on its magnitude compared to that of the energy involved. 

One of the proposed theories applied successfully to the formation of gas-phase carbon from benzene is the droplet condensation mechanism. This "condensation theory", revised recently by Lahaye et al. (2), explains the formation of soot aerosols during benzene pyrolysis. The authors obtained an excellent agreement between the theory and experimental results. 

Atmospheric gas-phase reactions may lead to the formation of condensable products, which subsequently associate with the atmospheric aerosol. The best-known reaction of this kind is the oxidation of S02 to H2S04 and its neutralization by ammonia to form sulfate salts. 

The molecular structure not only determines the adsorbate-substrate interactions but also the lateral interactions between the adsorbed molecules. Attractive adsorbate-adsorbate interactions, for example, due to van der Waals forces between molecules with long hydrocarbon chains, result in the formation of condensed, often ordered ad-layer phases ( self-assembled monolayers, see Chapter 2.1 in Volume 10), in which the strength of adsorption is increased. Reciprocally, repulsive interactions (e.g. dipole-dipole interactions) weaken the adsorption. 

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