Читать книгу Introduction to Nanoscience and Nanotechnology - Chris Binns - Страница 35

The vapor pressure above a flat liquid surface within a closed container is [15]:

(2.2)

where n_s is the atomic density near the surface, E_f is the enthalpy of evaporation (or the energy required by a molecule to escape from the flat surface), θ is the sticking probability of a vapor phase molecule incident on the liquid surface, k is Boltzmann's constant and T is the temperature. Since the term kT varies slowly compared to the exponential term, for the present purposes, (2.2) can be simplified to:

(2.3)

where A includes all the constants in (2.2). If we now consider a curved liquid surface, say a drop, in equilibrium with its vapor, a molecule near the surface has, on average slightly fewer nearest neighbors because of the curvature. As a result, the enthalpy will decrease and the vapor pressure will be greater than above the flat surface. The enthalpy becomes dependent on the radius of the drop and it can be shown that [15] the enthalpy is (see Problem 3):

(2.4)

where E_c(r) is the radius‐dependent enthalpy for a curved surface, γ is the surface tension of the drop and v is the volume of the departing molecule. This equation is derived by working out how much the surface energy of a drop changes as a result of losing a molecule. The increased vapor pressure, p > p₀ of a drop compared to a flat surface is obtained by replacing E_f in Equation (2.3) with E_c(r) given by (2.4), that is:

(2.5)

This is known as the Kelvin equation. So now we can consider what happens if we have a vapor with a pressure p > p₀ (a supersaturated vapor) containing no liquid drops. If we introduce a drop with a radius r derived from (2.5) into this vapor, it will be stable because the rate of molecules evaporating from it will equal the rate of molecules incident on it from the vapor. If our initial drop is smaller than r however, it will shrink because it will evaporate molecules faster than acquiring them from the vapor. Similarly, a larger initial drop will grow. In a highly pure vapor, getting the initial stable size drops is a bottleneck because the only way they can form is by the simultaneous collision of a sufficient number of molecules (homogenous nucleation), which is a highly improbable event. If there are, however, preexisting particles (liquid or solid) in the supersaturated vapor, it quickly condenses onto these. In the case of clouds, these preexisting particles are called cloud condensation nuclei or CCNs.

Figure 2.9 Relative sizes of particles involved in clouds. Comparison of a CCN, a typical water droplet in a cloud and a raindrop. In order to get a visible comparison, a typical CCN has been compared to a small raindrop, which can be a factor of 10 larger. The CCNs are the preexisting particles that allow cloud droplets to form (see Advanced Reading Box 2.2). Normal cloud drops fall sufficiently slowly under gravity to be “suspended” (see Advanced Reading Box 2.1) but under certain circumstances can grow large enough to precipitate out as rain.

Under certain conditions, the cloud droplet can grow large enough to drop out of the cloud as rain. These raindrops contain the CCNs that started the water drop growing in the first place so, although there is a tendency to regard rainwater as pure it contains the particles that formed the original CCNs. If these contain sulfur the rain will be acidic to a degree and, as described below, there are natural processes that produce sulfur‐containing aerosol so a certain amount of acid rain is inherent in climate processes and has nothing to do with human activities. The relative sizes of CCNs, cloud droplets and raindrops are illustrated in Figure 2.9. Precipitating clouds are a mechanism for removing atmospheric aerosol and thus form a self‐regulating feedback system. An increase in the density of aerosol produces more CCNs, which produce more cloud, which in turn increases the rate at which particles are washed out back to the ground.

CCNs are an example of where it is the number density of particles that is important rather than the mass they contain. Each particle will act as a perfectly good CCN, although until recently, it had been thought that particles smaller than 50 nm, referred to as ultrafine aerosol particles or UAPs by atmospheric scientists, do not make efficient CCNs. It is not just size that has influence but also the material. For example, the growth of cloud droplets is profoundly affected if the CCNs are soluble in water and one mechanism is that soluble CCNs can change the surface tension of the water droplets condensing onto them thus changing the stable droplet size for a given water vapor pressure (see Advanced Reading Box 2.2).

Recently an experiment conducted in cloud formation above the Amazon rain forest provided new insight into the role of nanoparticles with sizes below 50 nm [16]. Large areas of the sky above the pristine rain forest have very low densities of aerosol particles, often measuring hundreds per cubic centimeter, which is similar to densities in preindustrial times. Within this environment lies the city of Manaus with 1.8 million inhabitants, which is a significant source of atmospheric nanoparticles with sizes below 50 nm that are carried in a plume by the North‐Easterly trade winds. Thus it was possible for the first time to isolate the effect of nanoparticles injected into preformed clouds.

Figure 2.10 Effect of nanoparticles on DCCs. In clouds that lack nanoparticles with sizes below 50 nm (UAP < 50) (left), the clouds are highly supersaturated above the cloud base with relatively few cloud droplets at high altitudes. With added UAP < 50 (right, red dots), an additional number of cloud droplets are nucleated above the cloud base, which enhances condensation, releasing additional latent heat at low and middle levels, thus intensifying convection, which drives more CCNs to higher altitudes. This increases the intensity of precipitation and electrification.

In particular, the study looked at the characteristics of deep convective clouds (DCCs) that are responsible for storms. Generally, these form in moist air when an atmospheric instability has initiated rising air that carries the moisture up into cooler air to form a supersaturated vapor. This will then condense into droplets in the presence of CCNs and the process releases latent heat into the surrounding air that increases the updraft driving more moisture into supersaturation. In very clean environments, in which CCNs are virtually absent at high altitudes, the process is self‐limiting. The effect of introducing nanoparticles into this situation was found to intensify the storm by the process illustrated in Figure 2.10. With the absence of the nanoparticles and a low density of larger CCNs, at high altitudes, the cloud droplets tend to remain at lower altitudes and form warm rain that reduces the droplet area available for condensation. Above the cloud base there is a very high level of supersaturation and injecting large numbers of nanoparticles with diameters less than 50 nm (UAP < 50) into this situation produces a significant increase in cloud droplets above the cloud base. The enhanced condensation generates latent heat that drives an updraft that carries larger CCNs to high altitudes and increases condensation and energy release, which further increases convection. This drives the cloud to higher altitudes, increases precipitation, and enhances storm electrification. Thus, the study showed that nanoparticles generated by human activity can significantly increase the intensity of storms in the tropics and this is important data to be fed into climate change models.