Generalized characteristic ratio

The molecule is either fully flexible or semi-flexible. The fully flexible chains are generally harder to crystallize than semi-flexible chains [35]. In the latter part of the paper (Sect. 5), where we discuss crystallization from the melt, we consider a semi-flexible chain, the flexibility of which is adjusted to reproduce the characteristic ratio of real polyethylene. We there make the... 

Lipids are generally identified in paint samples by evaluating characteristic ratio values of FA amounts and comparing them with naturally or artificially aged reference paint layers. Molar or weight contents are obtained after quantification based on calibration curves. 

Let us compare the kinetics of the selective-solvent-induced collapse of protein-like copolymers with the collapse of random and random-block copolymers [18]. Several kinetic criteria were examined using Langevin molecular dynamics simulations. There are some general results, which seem to be independent of the nature of interactions or the kinetic criteria monitored during the collapse. Here, we restrict our analysis to the evolution of the characteristic ratio f = (Rgp/Rg ) that combines the partial mean-square radii of gyration calculated separately for hydrophobic and hydrophilic beads, k2n and Rg . This ratio takes into account both the properties of compactness and solubility for a heteropolymer globule [70] (compactness is directly related to the mean size of the hydrophobic core, whereas solubility should be dependent on the size of the hydrophilic shell). 

This characteristic ratio is essentially independent of the applied voltage and is therefore also independent of the electric field it is commonly called the dielectric constant of the material. Substituting for Q from Equation (2.2) in Equation (2.4), and adopting the more general vector notation,... 

The apparent concentrations thus obtained constitute, in certain specific cases (such as where matrix effects are negligible), a good approximation of the mass concentrations of the elements present in the sample. Nevertheless, in the majority of cases, calculations are required to correct for matrix effects because the influence of the matrix elements on the measured characteristic signal generally differs between the sample and the standard. The measured apparent concentration levels (A-ratios) then serve as a basis for an iterative process for correcting matrix effects. 

Pine charcoal burns in combination with ammonium perchlorate at F/O = 2 10 producing a yellow flame, but no sparks or fire dust. A mixture of pine charcoal, sulphur and potassium nitrate in the weight ratio 30 10 60 burns producing pretty. orange red fire dust. This characteristic is generally seen with other charcoals but pine charcoal produces the most pretty fire dust of all. On the other hand, the phenomenon shows that pine charcoal does not complete the reaction and produces less gas in black powder-type compositions. Therefore pine charcoal is used to produce fire dust and not to obtain force. 

The Equilibrium Chain Rigidity as Embodied in the Generalized Characteristic Ratio... 

The Generalized Characteristic Ratio C(q). For a very long chain (IV -> co) the function C(q) is the same for both transforms, and being a generalization of the classic characteristic ratio in Fourier chain coordinate space, it is conveniently denoted as the generalized characteristic ratio [11,21]. It is evaluated from... 

A general remark is in order concerning the adoption of C q) in the framework of the present Fourier representation. The characteristic ratio is usually evaluated on a nonperiodic chain, in contrast with the Fourier representation. In the case of short chains this may entail minor errors deriving from end effects, which vanish if N is large enough that <1(1).1(N)>o F [22]. 

Figure 2. Generalized characteristic ratio C q) plotted vs. qjn for three typical polymers polyethylene (PE) at 400 K [11, 21], atactic polystyrene (PS) at 300 K. [14], and poly(dimethyl-siloxane) (PDMS) at 350 K [15],...

The numerical value of Flory s characteristic ratio depends on the local stiffness of the polymer chain with typical numbers of 7-9 for many flexible polymers. The values of the characteristic ratios of some common polymers are listed in Table 2.1. There is a tendency for polymers with bulkier side groups to have higher C c, owing to the side groups sterically hindering bond rotation (as in polystyrene), but there are many exceptions to this general tendency (such as polyethylene). 

---