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## Über dieses Buch

It has been thirty years since one of the authors (EJD) began a collaboration with Professor Milton Kerker at Clarkson University in Potsdam, New York using light scattering methods to study aerosol processes. The development of a relatively short-lived commercial particle levitator based on a modification of the Millikan oil drop experiment attracted their attention and led the author to the study of single droplets and solid microparticles by levitation methods. The early work on measurements of droplet evaporation rates using light scattering techniques to determine the size slowly expanded and diversified as better instrumentation was developed, and faster computers made it possible to perform Mie theory light scattering calculations with ease. Several milestones can be identified in the progress of single microparticle studies. The first is the introduction of the electrodynamic balance, which provided more robust trapping of a particle. The electrodynamic levitator, which has played an important role in atomic and molecular ion spectroscopy, leading to the Nobel Prize in Physics in 1989 shared by Wolfgang Paul of Bonn University and Hans Dehmelt of the University of Washington, was easily adapted to trap microparticles. Simultaneously, improvements in detectors for acquiring and storing light scattering data and theoretical and experimental studies of the interesting optical properties of microspheres, especially the work on morphology­ dependent resonances by Arthur Ashkin at the Bell Laboratories, Richard Chang, from Yale University, and Tony Campillo from the Naval Research Laboratories in Washington D. C.

## Inhaltsverzeichnis

### 1. Background

Abstract
The advances in the science of microparticles that have occurred in the last three decades of the 20th Century involve a number of analytical and experimental tools. Theoretical analysis of the relevant phenomena and processes has been greatly aided by high-speed computers, which make it possible to perform extensive computations associated with light-scattering theory and to carry out numerical solutions of heat, mass and momentum transport problems. Advances in the solution of the Boltzmann equation have improved our understanding of transport in the transition regime between the continuum and free-molecule regimes. The experimental tools include: (i) elastic, quasi-elastic and inelastic light scattering techniques, (ii) instrumentation for isolating individual particles or trains of particles, (iii) spectroscopic methods for the chemical analysis of small amounts of matter, (iv) laser illumination, (v) efficient detectors, and (vi) high-speed data acquisition and data processing. The important interplay between theory and experiment is the subject of this book.
E. James Davis, Gustav Schweiger

### 2. Particle Levitation

Abstract
Although levitation based on clever illusion rather than physical principles has been a mainstay of the conjurer’s act, the physics of levitation makes it an important tool for the study of small amounts of matter ranging in size and mass from atomic ions to particulate matter with dimensions of dozens of micrometers and masses of order micrograms and droplets of order millimeters. As indicated in Chap. 1, the 1989 Nobel Prize for Physics shared by Dehmelt and Paul was given for their research on electrodynamically trapped ions, and as the technology of superconductors develops one hopes to see methods of levitation applied to highspeed ground transportation, to frictionless bearings and to other applications that rival the magician. Particle trapping already offers us ways to perform containerless processing and to examine numerous properties of matter. Suspension of microspheres has been used extensively to examine elastic and inelastic light scattering and is the basis for recent developments in the spectroscopy and mass spectrometry of microparticles.
E. James Davis, Gustav Schweiger

### 3. Elastic Light Scattering

Abstract
A major advantage in the study of microspheres is the power of light-scattering measurements and the theoretical interpretation of such data to yield precise determination of size, refractive index, molecular bond information, and composition. One example might suffice to excite the interest of the researcher in the area of cloud physics. By illuminating a microdroplet with a laser beam and recording the scattered light at right angle (or any other angle) to the beam as the object changes size and/or refractive index, the size and refractive index can be determined to one part in 105. Such measurements make it possible to determine evaporation or condensation rates with great precision, and a great variety of phenomena may be studied by working with microparticles and microdroplets.
E. James Davis, Gustav Schweiger

### 4. Basic Single Particle Measurements

Abstract
Direct measurements of forces acting on a microparticle are made by using the dc field of an electrostatic balance or an electrodynamic balance to counteract any vertical applied force, the most obvious force being gravity. But numerous other forces are of interest, including the aerodynamic drag force, Fd, the radiometric force, Fr, phoretic forces, Fph and magnetic forces, FH. Since the ac field exerts no time-average force on the levitated particle when it is at the null point of the balance chamber, a vertical force balance on a suspended particle yields
$${C_0}q{V_{dc}}/{z_0} = - mg + {F_d} + {F_r} + {F_{ph}} + {F_H},$$
(4.1)
where C0 and z0 are geometrical parameters (see Sect. 2.5), q is the Coulombic charge, Vdc is the levitation voltage, and mg is the particle weight. In the absence of forces other than gravity any particular force can be measured in terms of the particle weight by two simple experiments. If V0 is the dc voltage required to suspend the particle when only the gravitational force acts on it, Eq. (4.1) reduces to
$${C_0}q{V_{dc}}/{z_0} = - mg,$$
(4.2)
E. James Davis, Gustav Schweiger

### 5. Continuum Transport Processes

Abstract
Evaporation and condensation phenomena in clouds determine the aerosol size and rate of production of rain, and in industrial applications condensation following nucleation of molecular clusters can produce undesirable fogs such as sulfuric acid mists or very desirable nanophase particles such as ceramic precursors. Evaporation and condensation processes are also responsible for the formation of hazes such as those produced by terpenes and other volatile organic compounds which evaporate from pine trees and condense in the atmosphere over forested areas or become oxygenated organic acids due to photochemical reaction in the atmosphere. Combustion processes generate soot, flyash and other particulate matter that is an environmental hazard. In addition, combustion processes that generate SO2, H2S or NOX lead to the formation of acid rain. The rate at which particles settle out of the atmosphere or are transported to a surface by convective motion of the surrounding fluid is a fluid mechanical issue, and heat and mass transfer rates can be affected by such convection. The mechanics of aerosols have been thoroughly examined in the treatise by Fuchs (1964), and more recent work on the motion of particles in gases and on the dynamics of aerocolloidal systems, including coagulation, deposition and re-suspension, have been reviewed by Williams and Loyalka (1991) in their monograph. We shall confine our attention to phenomena and properties associated with the single particle.
E. James Davis, Gustav Schweiger

### 6. Non-Continuum Processes

Abstract
This chapter examines the theory and applications of the interactions between a low density gas and microparticles when the gas cannot be considered to be a continuum. In the past two decades significant progress has been made in the relevant theory and in the experimental tools needed to complement that theory. The combination of theory and experiment is important, for measurements are needed to determine the characteristics of mass, momentum and energy exchange between gas molecules and ’engineering’ surfaces. In his development of the dynamical theory of gases Maxwell (1860a,b) recognized the difficulty of specifying the appropriate boundary conditions at a surface, and he modeled the molecular interaction as intermediate between two limiting cases: (i) specular reflection of molecules and (ii) accommodation of the molecules to the surface such that they leave following a law of random distribution of directions independent of the velocity of the impinging molecules. He introduced the concept of the accommodation coefficient as the fraction of molecules that accommodate to the surface. Thus, if αm is the fraction of molecules that fully accommodate to the surface, (l-αm is the fraction that undergo specular reflection.
E. James Davis, Gustav Schweiger

### 7. Thermodynamic and Transport Properties

Abstract
Droplet levitation makes it possible to explore a number of thermodynamic phenomena that are not easy to study in bulk systems. For example, studies of concentrated electrolyte solutions by conventional methods are limited by the fact that crystallization generally occurs at relatively low supersaturations due to the presence of foreign particles and surfaces that promote heterogeneous nucleation. Containerless processing, that is, droplet levitation offers the possibility of suppressing heterogeneous nucleation thereby allowing a high degree of supersaturation to be reached before homogeneous nucleation leads to crystallization.
E. James Davis, Gustav Schweiger

### 8. Inelastic Light Scattering

Abstract
If light interacts with matter without changing its frequency, the process is called elastic scattering because the photons change only their direction and not their energy. The scattered light has the same frequency as the incident light. Rayleigh scattering is one particular elastic scattering process. The key assumption in Rayleigh’s theory is that the scattering particles are small enough compared to the wavelength of the incident light to consider the electric field independent of space within the particles, as was pointed out in Sect. 3.5. In most cases light scattering by molecules can be considered to be Rayleigh scattering.
E. James Davis, Gustav Schweiger

### 9. Spectroscopies and Mass Spectrometry

Abstract
Three types of spectroscopy commonly used for bulk material and two novel spectroscopic methods have been applied to the chemical characterization of microparticles with more or less success. In addition, single particle mass spectrometry has reached a high level of sophistication for both laboratory studies and field measurements.The theories of Raman and fluorescence spectroscopies as applied to microparticles are examined in Chap. 8, and the applications are considered in this chapter together with mass spectrometry and less conventional spectroscopies. The unconventional spectroscopies include photothermal and photophoretic spectroscopies.
E. James Davis, Gustav Schweiger

### 10. Particle Chemical Reactions

Abstract
There are several aspects of chemical reactions associated with microparticles that are of considerable interest. Among these are homogeneous gas-phase reactions which produce clusters that grow and coagulate to form nanometer or larger size particles, reactions between reactive gases and pre-existing droplets and solid particles, and precipitation reactions that occur in solutions to produce microcrystals. An elementary example of a gas phase process that produces particulate matter is the reaction between vapors of ammonia and hydrochloric acid to form ammonium chloride smokes when they come in contact.
E. James Davis, Gustav Schweiger

### 11. Phoretic and Radiometric Phenomena

Abstract
There are a number of forces associated with microparticles that are either not encountered or are negligible in macroscopic systems, and some of these can be much larger than the gravitational force. For example, if you sit in a darkened room with a beam of light slanting down through an opening in a curtain or window shade, you might notice one of these interesting forces. Small dust particles can often be seen to move up the beam toward the light source. Although convection of the air in the room might well cause such motion, the phenomenon can be observed in still air. Ehrenhaft (1909, 1910, 1917, 1918) recognized that a small particle suspended in a gas can move either toward the light source or in the direction of propagation of the beam. He attributed the phenomenon to a firstorder electromagnetic effect, but this photophoretic force, as Ehrenhaft called it, is now understood to be caused by a radiometric force. Absorption of electromagnetic energy by the particle can produce anisotropic internal heating, and molecular collisions with the surface result in a net momentum transfer that causes a force on the particle. If the particle is illuminated from one direction and the back of the particle is heated, thereby producing a force towards the light source, the process is called negative photophoresis. When the net force is away from the source it is positive photophoresis.
E. James Davis, Gustav Schweiger

### Backmatter

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