Quantitative properties

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. 

Quantitative descriptions of the structural dependence of properties are called structure-property quantitative relationships (SPQR). The four types of these relationships are ... 

In an attempt to relate the grain size in a metal to its mechanical properties quantitatively, Fetch and Hall (9 and references therein) proposed an expression relating grain size d with hardness H in a metal. Hardness is defined in this case as the yield stress, the stress at which value the material experiences the onset of permanent deformation. Thus,... 

The fact that most triphosphates of polyvalent cations which are difficultly soluble in water are soluble in excess of triphosphate, and that such polyvalent cations (e.g. Ca++) are either not precipitated or not quantitatively precipitated by the usual reagents from solutions of their salts containing triphosphate, has become of great commercial importance in water softening (90). The term sequestration is used in this connection. Numerous publications have appeared which are not mentioned in detail here, and which attempt to determine this property quantitatively. In general, the effect is attributed to the formation of relatively stable ion pairs or complexes, the stability of which is defined by the formation constants K or K. ... 

The method presented in this chapter serves as a link between molecular properties (e.g., cavities and their occupants as measured by diffraction and spectroscopy) and macroscopic properties (e.g., pressure, temperature, and density as measured by pressure guages, thermocouples, etc.) As such Section 5.3 includes a brief overview of molecular simulation [molecular dynamics (MD) and Monte Carlo (MC)] methods which enable calculation of macroscopic properties from microscopic parameters. Chapter 2 indicated some results of such methods for structural properties. In Section 5.3 molecular simulation is shown to predict qualitative trends (and in a few cases quantitative trends) in thermodynamic properties. Quantitative simulation of kinetic phenomena such as nucleation, while tenable in principle, is prevented by the capacity and speed of current computers however, trends may be observed. 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

Once the health-effect endpoint and data points describing the exposure concentration-duration relationship have been selected, the values are plotted and fit to a mathematical equation from which the AEGL values are developed. There may be issues regarding the placement of the exponential function in the equation describing the concentration-duration relationship (e.g., C x t = k vs C X t = k2 vs X E = k3>. It is clear that the exposure concentration-duration relationship for a given chemical is directly related to its pharmacokinetic and pharmacodynamic properties. Hence, the use and proper placement of an exponent or exponents to describe these properties quantitatively is highly complex and not completely understood for all materials of concern. 

Measurement of the silicon spin lattice relaxation times also indicates a large difference between the local chain motions of phase I and phase II. The T1 value is 5.5 s for phase II silicon nuclei, whereas phase I nuclei have a Ti value of 3.2 h (iO), one of the longest relaxation times observed for silicon nuclei. Unfortunately, as a result of these tremendous differences in motional properties, quantitative data for the entire PDHS sample cannot... 

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