Evaporation kinetics

C. M. Marques, M. S. Turner, M. E. Cates. End-evaporation kinetics in living polymer systems. J Chem Phys 99 7260-7266, 1993. 

Tyndall, G. W. and Waltman, R. J., Thermodynamics of Confined Perfluoropolyether Film on Amorphous Carbon Surface Determined from the Time-Dependent Evaporation Kinetics," J. Phys. Chem. B, Vol. 104,2000, pp. 7085-7095. 

Control of the evaporation kinetics of vapour diffusion trials... 

The relaxation of isolated, pairs of and ensembles of steps on crystal surfaces towards equilibrium is reviewed, for systems both above and below the roughening transition temperature. Results of Monte Carlo simulations are discussed, together with analytic theories and experimental findings. Elementary dynaniical processes are, below roughening, step fluctuations, step-step repulsion and annihilation of steps. Evaporation kinetics arid surface diffusion are considered. 

In the following, relaxation by evaporation kinetics and surface diffusion will be discussed. Results of simulations of nearest-neighbor SOS models and analytic theories are to be compared to experimental findings. A short summary concludes the article. 

Figure 1. Monte Carlo configuration of an isolated step below the roughening transition temperature TR 1.24J ofthe standard SOS model, at t= 2000 MCS, using evaporation kinetics.

So far, we tacitly assumed that the upper and lower terraces next to the step are below their roughening transition temperature. By fixing the boundary heights of the terraces, away from the step, at, say, level 0 for the lower and level 1 (in units of the lattice spacing) for the upper terrace, one can study the time evolution of the step width w, defined, for instance, as the second moment of the gradient of the step profile also above roughening. Then one obtains s =1/4 for terrace diffusion and 1/2 for evaporation kinetics, as predicted by the continuum description of Mullins and confirmed by our Monte Carlo simulations. 

In the case of evaporation kinetics, continuum theory predicts, e.g., that the amplitude of the wire decays with f, with w= 1/5. Simulations, for rather small systems, show strong deviations. The simulated profile shapes also differ appreciably from the predicted ones, even when conservation of mass at the surface is taken into account, especially near the top. The differences may be traced back to the fact that the mo-... 

In marked contrast, the classical continuum theory by mullins describes the sim-ulational data (profile shapes and amplitude decay) above roughening for wires even with small geometries surprisingly well, both for surface diffusion and evaporation-condensation The agreement may be a little bit fortuituous, because of a compensation of the competing effects of the anisotropic surface tension and anisotropic mobility, whereas continuum theory assumes isotropic quantities. In any event, the predicted decay laws with w= 1/4 for surface diffusion and w= 1/2 for evaporation kinetics are readily reproduced in the simulations. 

Below roughening, pronounced lattice effects show up in the simulations, as in the case of wires. The meandering of the top(bottom) steps and the islanding on the top(bottom) terrace leads to slow and fast time scales in the decay of the amplitude. The profile shapes near the top(bottom) broaden at integer values of the amplitude and acquire a nearly sinusoidal form in between. Again, these features are not captured by the continuum theory. For evaporation kinetics, continuum theory suggests that the decay of the profile amplitude z scales like z t,L) = where g =... 

Below roughening, the relaxation is driven by the lowering of the line tension of the curved steps. For evaporation kinetics, continuum theory and simulations show a shrinking of the bumps in the late stages of the decay. At small amplitudes, the radially symmetric profile scales with z r,t) Z(V ct + r )), where r is the distance from the center, and c is a constant. The continuum theory fails to describe the layerwise relaxation monitored in the simulations. ... 

As this ratio (Fig. 3) tends to decrease with increasing temperature, the best separations are achieved at the lowest temperatures, which on the other hand, lead to low evaporation rates. The refining temperature is a compromise between the ratio of the vapour pressures and evaporation kinetics e.g. 1120 °C Am, and 1600 °C for Cm evaporation and 900 °C for Am and 1300 °C for Cm condensation ... 

Evaporation Kinetics in Short-Chain Alcohols by Optical Interference 238... 

Marques, C.M., Turner, M.S., and Cates, M.E. "End-evaporation kinetics in living-polymer systems".. Chem. Phys. 99, 7260-7266 (1993). 

We now turn to the question of the evaporation kinetics of silicate systems. Figure 7 compares the evaporation rates in nominal vacuum P 10 torr) of forsterite (from Wang et ah, 1999) and the CMAS liquid shown in Figure 6. Forsterite evaporates congruently, while in the case of... 

We close this section by describing an experimentally calibrated parametrization for the evaporation kinetics of CM AS liquids. A similar parametrization for forsterite could be constructed from data and thermodynamic considerations found in the papers by Nagahara and Ozawa (1996), T suchiyama etal. 998,1999), W ang etal. (1999), and the more recent experimental data by Kuroda and Hashimoto (2002). Because of their use in constraining the thermal history of the type B CAIs, we will focus on the parametrizations for CMAS liquids. The following formula for the dependence of the evaporation rate of a type B CAI-like liquid is taken from Richter et al. (2002) ... 

We can illustrate how evaporation kinetics provides constraint on the thermal history of chondrules by discussing a set of Chainpur chondrules recently studied by Alexander and Wang (2001). 

Hashimoto A. (1988) Evaporation kinetics of REE oxides. Lunar Planet. Sci. XIX. Lunar and Planetary Institute, Houston, pp. 459-460. 

Hashimoto A. (1990) Evaporation kinetics of forsterite and implications for the early solar nebula. Nature 347, 53-55. 

Wang J., Davis A. M., Clayton R. N., and Hashimoto A. (1999) Evaporation of single crystal forsterite evaporation kinetics, magnesium isotope fractionation, and implications of mass-dependent isotopic fractionation of a diffusion-controlled reservoir. Geochim. Cosmochim. Acta 63, 953-966. 

Monte Carlo simulations have been used in some cases to study kinetics of clusters. For example, evaporation kinetics lends itself to this method. The method has been used to study kinetics of passage between pairs of adjacent minima, a subject discussed in a bit more detail later. A Monte Carlo study has described how a cluster of CO2 molecules containing a single 12 molecule relaxes when the extra electron is suddenly removed from the foreign molecule. ... 

There are only two experimental strategies that have the potential to yield reliable predictive results for nebulized aerosols. The first is to measure the droplets in their fully hydrated state. This can be done either immediately as they exit the mouthpiece, using a real-time sizing instrument, or by reducing the evaporation kinetics sufficiently to allow measurement downstream with an offline techniqne snch as inertial cascade impaction. The second is to completely dry the aerosol, size the dry particles, and then calculate back to obtain the original size distribntion. Measuring the aerosol at intermediate hydration states between these two extremes is obviously problematic because the hydration state would have to be measured in order to correct the size distribution back to the original inhaled size. 

Solvent evaporation will only play a dominant role in microsphere hardening kinetics when the extraction capacity of the continuous phase has been saturated and when the diffusion rate of organic solvents from the dispersed phase to the continuous phase is fast compared with the solvent evaporation kinetics. In solvent extraction, the amount and composition of the continuous phase are chosen so that the entire volume of the solvent can be dissolved. ... 

P.S. Kuts, C. Strumillo, 1. Zbicinski, Evaporation kinetics of single droplets containing dissolved biomass. Drying Technology, 14 (1996) 2041-2060. 

For the self-assembly driven by solvent evaporation, the narrow size distribution of building blocks is not the only requirement for achieving long-range order in the particles ensemble. Other conditions, such as solvent composition, temperature and evaporation kinetics are also very important. Fast drying procedure for less than 10s has been carried out in the suspensions of Ni nanoparticles (9 nm) in pentane deposited on amorphous carbon substrate. As a result, the two-dimensional densely packed monolayer of nanoparticles has been obtained. Deposition of the same particles of nickel from its suspension in mixed 80 % hexane with 20 % octane followed by slow evaporation (about 5 min) of liquid leads to 3D superlattice of Ni nanoparticles [344]. In addition, the wettability of the substrate by the suspension affects the superlattice morphology. If the nanoparticles suspension wets the sub-... 

Furthermore, modeling of the esterification reaction was attempted in the presence of silica nanoparticles during the formation of aliphatic polyester nanocomposites. From the experimental data, it was found that on increasing the Si02 content in esterification, the rate of water production decreases [47]. In addition, it was clear that the total quantity of water released does not depend on the nanoparticle concentration. This suggests that the existence of the particles does not influence the esterification reaction itself. Their main effect is to adsorb the produced water before it evaporates, altering in this way the water evaporation curve. The simplest model for this phenomenon is to assume very fast water adsorption/desorption kinetics on the Si02 particles. In this case, the evaporation kinetics must be explicitly taken into account because it is no more very fast compared to the other phenomena that occur. 

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