Size-dependencies of

To conclude this chapter we discuss the size-dependencies of the electric susceptibilities. The weak-coupling exciton theory and the oscillator sum rule indicate that transition dipole moments from the ground state to an excited state are proportional to vT, whereas interexcited state transition dipole moments are independent of size. This result indicates that is a linear function of L for long chains. 

---

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... 

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

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. 

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... 

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... 

In addition to the surface area of the particles, several other parameters have some influence on the necessary resin consumption, e.g. the type of the boards, thickness of the sanding zone, type and capacity of the blenders, separation and spraying of the glue resin (only wiping effect or spraying of the resin by air or liquid pressure), shape of the panicles for the same particle sizes, dependence of... 

Although the theoretical consideration above imply a positive size-dependence of aggregation, the particle size distributions observed can often be approximated by a size-independent kernel. 

Hollow carbon nanotubes (CNTs) can be used to generate nearly onedimensional nanostrutures by filling the inner cavity with selected materials. Capillarity forces can be used to introduce liquids into the nanometric systems. Here, we describe experimental studies of capillarity filling in CNTs using metal salts and oxides. The filling process involves, first a CNT-opening steps by oxidation secondly the tubes are immersed into different molten substance. The capillarity-introduced materials are subsequently transformed into metals or oxides by a thermal treatment. In particular, we have observed a size dependence of capillarity forces in CNTs. The described experiments show the present capacities and potentialities of filled CNTs for fabrication of novel nanostructured materials. 

In the case of a single patch, the size dependence of the system follows directly from the finite size scaling theory [133]. In particular, the critical point temperature scales with the system size as predicted by the equation... 

These two lengths have been discussed in detail by Point et al. [93] and Dosiere et al. [94]. They study the size dependence of the growth rate of polyethylene for very small crystals using a decoration technique. The accuracy of their measurements is carefully considered, and they conclude that there is no size dependence of the growth rates for all length scales measured (>200 nm). Several other claims that there is no size dependence do not seem justified by the number and accuracy of the measurements involved. As shown below, a detailed investigation of these facts would be extremely useful and would enable limits to be placed on the magnitudes of i and g. 

The size-dependence of the intensity of single shake-up lines is dictated by the squares of the coupling amplitudes between the Ih and 2h-lp manifolds, which by definition (22) scale like bielectron integrals. Upon a development based on Bloch functions ((t>n(k)), a LCAO expansion over atomic primitives (y) and lattice summations over cell indices (p), these, in the limit of a stereoregular polymer chain consisting of a large number (Nq) of cells of length ao, take the form (31) ... 

Crystallites "The Size Dependence of the Lowest Excited Electronic State" /. Chem. Phys., 80, 4403. 

A dynamic ordinary differential equation was written for the number concentration of particles in the reactor. In the development of EPM, we have assumed that the size dependence of the coagulation rate coefficients can be ignored above a certain maximum size, which should be chosen sufficiently large so as not to affect the final result. If the particle size distribution is desired, the particle number balance would have to be a partial differential equation in volume and time as shown by other investigators ( ). 

Figure 1.12 The three different types of cluster size dependence of catalytic conversion. Rates are considered normalized per exposed surface atom (schematic).

S. Link and M. A. El-Sayed, Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals. Int. Rev. Phy. Chem. 19(3), 409-453 (2000). 

As for the size dependence of nonlinear optical properties of semiconductor nanomaterials, detailed investigations are required from both the theoretical and experimental points of view. 

Here we summarize our investigations on the nonlinear optical properties of CdTe QDs in the nonresonant wavelength region, in which the size dependence of will be... 

Ionization potential of metal clusters is one of the factors affected by cluster size [33]. This study represents the most extensive effort so far to determine the size dependence of IP. The measurements on these clusters showed a decreasing IP with size with apparent oscillatory trend. Even-size particles had a relatively larger IP compared to their odd-size counterparts. The data show oscillatory behavior for small Na clusters with a loss of this oscillation for the larger Na clusters. The IP decreases with cluster size, but even at Nai4 the value 3.5 eV is far from... 

Figure 12. Size dependence of the photoemission data for gold nanoparticles at Fermi level (a), (bi), (62), and (c), respectively. Curve Si02 represents the emission from the support only. (Reprinted from Ref. [171], 2002, with permission from Elsevier.)...

---