Size-Induced Polarization

The positive Cls-level shift is associated with a reduction in work function from the bulk value of 4.6. 3 eV for the single-layer GNR [84]. The work function reduction indicates the enhancement of edge polarization and charge densification by bond contraction. The fraction of surface and edge atoms increases and the number of layer is reduced. Hence, the associated work function reduction and the Cls shift evidence the coexistence of entrapment and polarization. 

Unlike other metals that demonstrate positive shift with size reduction, Zn 2pa/2 level in ZnO shifts oppositely—size reduction raises the core level. 0-passivation enhances the positive shift but hydrogen passivation shifts the core level adversely. 

Annealing under 100 % O2 at the ambient pressure lowers the PL peak from 2.46 to 2.15 eV [87]. 

As both the core level and bandgap depend on the crystal potential, bond contraction deepens the potential and polarization elevates it by screen weakening. Particle-size reduction enhances the polarization of the non-bonding electrons by the densely entrapped core electrons, which happens at the highly curved surfaces. 

The screening of the crystal potential by the 0-induced dipoles narrows the bandgap and shifts the core level negatively. However, hydrogenation annihilates the unpaired electron dipoles. The competition of polarization and entrapment determines both the bandgap and the CLS [88, 89]. 

---

DFT calculations of Cuboctahedral (CO-13, 55, 147) and Marks Decahedral (MD-13, 49,75) gold clusters [15] result in the LDOS shown in Fig. 13.3. The size-induced polarization is consistent with STM/S observations and BOLS prediction. Calculations also confirmed the BOLS expected lattice strain, charge transfer in real space from the inner to the outermost atomic layer, and valence charge polarization from the lower to the higher binding energies of the well-... 

Fig. 16.12 Normalized Zn-2p3/2 spectra showing a cluster size-induced polarization (upward shift) that screens in turn the crystal potential and shift the core level negatively [85]. b Annealing under the ambient of O.2IO2 + O.79N2 shifting the peak fiom 1,021.2 to 1,020.8 eV but under O.O3H2 + 0.97Ar ambient annihilates the polarization shifting the peak of 1,020.8-1,022.9 eV (Reprinted with permission from [86, 87])...

Eq. [4.3.1] corresponds only to flic electrostatic contribution to the solvation energy. In experiments where the charge distribution on a solute molecule is suddenly changed (e.g. during photoionization of the solute) this is the most important contribution because short range solute-solvent interactions (i.e., solute size) are essentially unchanged in such processes. The origin of W is the induced polarization in the solvent under the solute electrostatic field. 

Among different (like flexoelectric, flexomagnetic etc.) flexoeffects, the influence of flexoelectric effect on the nanosystem properties had been studied in most details. One can conclude that even rather moderate flexoelectric effect significantly renormalizes all the polar, piezoelectric and dielectric properties and the correlation radius in particular. The effect also suppresses the size-induced phase transition from ferroelectric to paraelectric phase and thus stabilizes the ordered phase in ferroic nanoparticles. 

Abstract Atomic undercoordination shortens and stiffens the remnant bonds to yield local quantum entrapment, densihcation, and polarization, which discriminate defects, skins, and nanostructures from the bulk, particularly in the size dependence and size-induced emergence behavior. 

Size reduction-induced polarization happens in compounds containing N, O, and F and metals with the outermost s-orbit filled with unpaired electrons like Ag, Au, Rh, while happens not to metals with such s-orbit that is empty or filled with paired electrons, such as Pt and Co. Such polarization of substance at the nanoscale creates properties that the bulk counterpart never demonstrates such as the dilute magnetism, catalysis, superhydrophobicity, fluidity, lubricity, as will be addressed in later section. 

The Hamiltonian determines and correlates the properties intrinsically, and therefore, it is appropriate to consider the change of all the properties relating to the Hamiltonian rather than separate one phenomenon at a time from another. The size-induced quantum entrapment and polarization modulates the Hamiltonian, and therefore, the entire band structure of nanostructured semiconductors [1] ... 

The size-induced quantum entrapment and polarization spits the valence band of metals to generate an artihcial bandgap, which turns a metal at the nanoscale to be an insulator [27]. The artihcial bandgaps for Au [28] and Pd [29] clusters increase when the number of Au and Pd atoms is reduced in the clusters. Figure 17.2 shows the evolution of the STS spectra for Pd and Si nanowires. 

On the other hand, an ultrafast liquid-jet UPS [33], shown in Fig. 35.2, resolved the bound (vertical binding as an equivalent of work function) energies of 1.6 and 3.3 eV for solvated electrons at the water skin and in the bulk solution, respectively. The bound energy decreases with the number of water molecules, indicating the size-induced strong polarization [34]. 

H-O bond contraction. Coulomb repulsion, and dual-process polarization drive the supersolidity with multiple features. The molecular separation doo = d + dn grows and molecular size d shrinks simultaneously at the skins because of the molecular under-coordination [21]. The H-0 bond contraction follows the rule of BOLS correlation the doo expansion results from the Coulomb repulsion between electron pairs on adjacent oxygen atoms [21, 24]. The polarization of water molecules in the molecular clusters [25, 26], surface skins, or ultrathin films of water is related to the molecule volume expansion because of the molecular charge conservation. The undercoordination-induced polarization lowers the work function of the bound electrons [6]. 

Discrimination by size and polarity in combination with colorimetric signaling was also observed for microporous materials—for example, when a pyrylium derivative is anchored to the inner pores of zeolite Beta. Zeolite Beta is characterized by a 3D channel system for which access to the pore voids is limited by 6.8 A aperture that is composed of 12 silicon atoms. A size-based discrimination was observed and only amines smaller than the pore openings induce color modulations. For amines of similar size, an additional discrimination by polarity that is induced by the hydrophobic environment of the inner zeolite was also found (Fig. 11). ... 

The relaxation-time spectrum correlates with the spectrum of pore geometrical properties. On this basis, Tong et al. (2006) used induced polarization measurements on shaly sands to derive capillary pressure curves. Transformation of the normalized decay curve (comparable to NMR processing) yields a relaxation-time spectrum. The relaxation-time spectrum reflects the pore-size distribution, and also contains information about pore-body and pore-throat cmitributions. Figure 8.45 shows an example. 

Tong, M., Wang, W., Jiang, Y., 2006. Determining capillary-pressure curve, pore-size distribution, and permeability from induced polarization of shaley sands. Geophysics 71 (3), N33-N40. 

In this equation, AG°CS is taken to be negligible for p- and y-cyclodextrin systems and to be constant, if there is any, for the a-cyclodextrin system. The AG W term is virtually independent of the kind of guest molecules, though it is dependent on the size of the cyclodextrin cavity. The AG dw term is divided into two terms, AG°,ec and AGs°ter, which correspond to polar (dipole-dipole or dipole-induced dipole) interactions and London dispersion forces, respectively. The former is mainly governed by the electronic factor, the latter by the steric factor, of a guest molecule. Thus, Eq. 2 is converted to Eq. 3 for the complexation of a particular cyclodextrin with a homogeneous series of guest molecules ... 

---