Size-dependent

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

Trevor D J, Whetten R L, Cox D M and Kaldor A 1985 Gas-phase platinum cluster reactions with benzene and several hexanes evidence of extensive dehydrogenation and size-dependent chemisorption J. Am. Chem. Soc. 107 518... 

Emory S R, Haskins W E and Nie S 1998 Direct observation of size-dependent optical enhancement in single metal nanoparticles J. Am. Chem. Soc. 120 8009-10... 

Given tire a size dependence of tire settling rate, sedimentation can be used for particle size analysis. Indeed, a quick... 

For tire purjDoses of tliis review, a nanocrystal is defined as a crystalline solid, witli feature sizes less tlian 50 nm, recovered as a purified powder from a chemical syntliesis and subsequently dissolved as isolated particles in an appropriate solvent. In many ways, tliis definition shares many features witli tliat of colloids , defined broadly as a particle tliat has some linear dimension between 1 and 1000 nm [1] tire study of nanocrystals may be drought of as a new kind of colloid science [2]. Much of die early work on colloidal metal and semiconductor particles stemmed from die photophysics and applications to electrochemistry. (See, for example, die excellent review by Henglein [3].) However, the definition of a colloid does not include any specification of die internal stmcture of die particle. Therein lies die cmcial distinction in nanocrystals, die interior crystalline stmcture is of overwhelming importance. Nanocrystals must tmly be little solids (figure C2.17.1), widi internal stmctures equivalent (or nearly equivalent) to drat of bulk materials. This is a necessary condition if size-dependent studies of nanometre-sized objects are to offer any insight into die behaviour of bulk solids. 

The definition above is a particularly restrictive description of a nanocrystal, and necessarily limits die focus of diis brief review to studies of nanocrystals which are of relevance to chemical physics. Many nanoparticles, particularly oxides, prepared dirough die sol-gel niediod are not included in diis discussion as dieir internal stmcture is amorjihous and hydrated. Neverdieless, diey are important nanoniaterials several textbooks deal widi dieir syndiesis and properties [4, 5]. The material science community has also contributed to die general area of nanocrystals however, for most of dieir applications it is not necessary to prepare fully isolated nanocrystals widi well defined surface chemistry. A good discussion of die goals and progress can be found in references [6, 7, 8 and 9]. Finally, diere is a rich history in gas-phase chemical physics of die study of clusters and size-dependent evaluations of dieir behaviour. This topic is not addressed here, but covered instead in chapter C1.1, Clusters and nanoscale stmctures, in diis same volume. 

We begin our discussion of nanocrystals in diis chapter widi die most challenging problem faced in die field die preparation and characterization of nanocrystals. These systems present challenging problems for inorganic and analytical chemists alike, and die success of any nanocrystal syndiesis plays a major role in die furdier quantitative study of nanocrystal properties. Next, we will address die unique size-dependent optical properties of bodi metal and semiconductor nanocrystals. Indeed, it is die striking size-dependent colours of nanocrystals diat first attracted... 

Obtaining high-quality nanocry stalline samples is the most important task faced by experimentalists working in tire field of nanoscience. In tire ideal sample, every cluster is crystalline, witli a specific size and shape, and all clusters are identical. Wlrile such unifonnity can be expected from a molecular sample, nanocrystal samples rarely attain tliis level of perfection more typically, tliey consist of a collection of clusters witli a distribution of sizes, shapes and stmctures. In order to evaluate size-dependent properties quantitatively, it is important tliat tire variations between different clusters in a nanocrystal sample be minimized, or, at tire very least, tliat tire range and nature of tire variations be well understood. 

Figure C2.17.9. Size-dependent changes in PXRD linewidtlis. PXRD can be used to evaluate tire average size of a sample. In tliese cases, different samples of nanocrystalline titania were analysed for tlieir grain size using tire Debye-Scherr fonnula. As tire domain size increases, tire widtlis of tire diffraction peaks decrease.

The striking size-dependent colours of many nanocrystal samples are one of tlieir most compelling features detailed studies of tlieir optical properties have been among tire most active research areas in nanocrystal science. Evidently, tire optical properties of bulk materials are substantially different from Arose of isolated atoms of tire... 

An explanation for these size-dependent optical properties, tenned quantum confinement , was first outlined by Bms and co-workers in the early 1980s, [156, 158, 159, 160 and 161] and has fonned the basis for nearly all subsequent discussions of these systems. Though recent work has modified and elaborated on this simple model, its basic predictions are surjDrisingly accurate. The energy of the lowest-lying exciton state is given by the following simple fonnula ... 

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

The ability to control pressure in the laboratory environment is a powerful tool for investigating phase changes in materials. At high pressure, many solids will transfonn to denser crystal stmctures. The study of nanocrystals under high pressure, then, allows one to investigate the size dependence of the solid-solid phase transition pressures. Results from studies of both CdSe [219, 220, 221 and 222] and silicon nanocrystals [223] indicate that solid-solid phase transition pressures are elevated in smaller nanocrystals. 

Vossmeyer T et al 1994 CdS nanoolusters synthesis, oharaoterization, size dependent osoillator strength, temperature shift of the exitonio transition energy and reversible absorbanoe shift J. Phys. Chem. 98 7665... 

Brus L E 1984 Electron-electron and electron-hole Interactions In small semiconductor crystallites the size dependence of the lowest excited electronic state J. Chem. Phys. 80 4403-9... 

Mittleman D M ef a/1994 Quantum size dependence of femtosecond electronic dephasing and vibrational dynamics in CdSe nanocrystals Phys. Rev. B 49 14 435... 

Cerullo G, De Silverstri S and Banin U 1999 Size-dependent dynamics of coherent acoustic phonons in nanocrystal quantum dots Phys. Rev. B 60 1928... 

Castro T ef a/1990 Size-dependent melting temperature of individual nanometre-sized metallic clusters Phys. Rev. B 42 8548... 

Lai S L ef a/1996 Size-dependent melting properties of small tin particles nanocalorimetric measurements P/iys. Rev. Lett. 77 99... 

Toibert S H and Aiivisatos A P 1993 Size dependence of the soiid-soiid phase transition in CdSe nanocrystais Z. Rhys. D 26 56... 

Tolbert S H and Aiivisatos A P 1994 Size dependence of a first order solid-solid phase transition the wurtzite to rock salt transformation in CdSe nanocrystais Science 265 373... 

Chen C C et al 1997 Size dependence of structural metastability in semiconductor nanocrystais Science 276 398... 

Siepmann JI and IR McDonald 1993a. Domain Formation and System-size Dependence in Simulatio of Self-assembled Monolayers. Langmuir 9 2351-2355. 

Note that the rate law in this case depends only on kj and any size dependence for this constant would not cancel out. 

The rate of spray is deterrnined by propellant concentration, the solvent used, and valve and vapor pressure. The pressure must be high enough to dehver the product at the desired rate under the required operating conditions. For example, a windshield ice remover that is likely to be used around 0°C must be formulated to provide an adequate pressure at that temperature. Spray dryness or wetness and droplet size depend upon propellant concentration. 

Sulfides. The main sulfide of indium is I1I2S2 [12030-24-9], which can be prepared by heating the metal with sulfur or by precipitation from weak acid solutions of indium salts by H2S. Precipitated I1I2S2 varies in color from yellow to red-brown, and in crystal size depending on formation conditions. It dissolves in acids and sodium sulfide solution. Other reported sulfides of indium ate InS [12030-14-7], a red-brown soHd In2S [12196-52-0], and In S [12142-00-5]. 

During Stage II the growing particles maintain a nearly constant monomer concentration. The concentration of monomer is particle-size dependent, with smaller particles having lower concentrations (28). 

Drops coalesce because of coUisions and drainage of Hquid trapped between colliding drops. Therefore, coalescence frequency can be defined as the product of coUision frequency and efficiency per coUision. The coUision frequency depends on number of drops and flow parameters such as shear rate and fluid forces. The coUision efficiency is a function of Hquid drainage rate, surface forces, and attractive forces such as van der Waal s. Because dispersed phase drop size depends on physical properties which are sometimes difficult to measure, it becomes necessary to carry out laboratory experiments to define the process mixing requirements. A suitable mixing system can then be designed based on satisfying these requirements. 

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