Scattering Behaviour

In practice, p is adjusted in the numerical calculations until the calculated Mapp agrees with the measured one. All other quantities, for instance the molecular-weight dependence of (S2)z, or the shape of the scattering curve, and the whole dynamic scattering behaviour, are now fully determined if the effective bond length is known. 

Fig. 18. Reciprocal particle-scattering factors of star-molecules with polydisperse rays, where f denotes the number of rays per molecule. The same functions are obtained also for the ABC-type polycondensates, where nb denotes the number of branching points per molecule. The case f = 1 or nb = 0 is identical to linear chains obeying the most probable lengths distribution. It also represents the scattering behaviour of randomly branched f-functional polycondensates 1...

One particular strength of SANS over SAXS is the differing scattering behaviour of isotopes towards neutrons, which is particularly pronounced for the hydrogen isotopes H and D. The true value of the SANS technique for structure analysis of dendrimers is due to this phenomenon. Thus, by deuterium label-... 

Flow cytometry has been applied to the study of the formation of the bio-polymer poly-h-hydroxybutyrate (PHB). While the formation of the polymer can be detected by changes in the light scattering behaviour of cells [ 145], its ac-... 

When such a system is oriented, where y corresponds to the angle between Q and the cylindrical axis, two specific cases can be defined for the scattering behaviour. For the first, where the vector Q is parallel to the cylindrical axis (y = 0) the scattering will be only a function of the axial length. Thus for a single isolated cylinder... 

The easiestexample for establishing the relationship between the structure of a sample and its scattering behaviour is the case of monoatomic liquid [93]. In this section, the static neutron scattering function (static structure factor) will be derived. In a simple homogeneous monoatomic liquid the probability to find a certain atom in volume element d3r at the position r is given by P(r)dir. Since the liquid is homogeneous P(r = and... 

Figure 5.1. Scattering behaviour of a fringed micelle or a block co-polymer. At large q values the asymptotic behaviour of a single chain can be measured. (Reprinted with permission from refs. 20 and 21)...

Advanced TCSPC techniques have resulted in a number of spectacular applications in different fields of time-resolved spectroscopy. Nevertheless, a large number of potential applications clearly could benefit from TCSPC but do not use or do not fully exploit the capabilities of the currently available techniques and devices. This may be due in part to the continuing misperception that TCSPC is unable to reeord high photon rates, to achieve short acquisition times, or to reveal dynamie effeets in the fluorescence or scattering behaviour of the systems investigated. Another obstacle may be that TCSPC users often do not take the effort to understand the advanced features of the technique and consequently do not make the most effieient use of the devices they have. 

The influence of the size of the solute molecule on the scattering behaviour becomes significant when the dimensions of the molecule are greater than 2/20. 

Adler, M. Some finite-dimensional systems and their scattering behaviour. Comm, Math, Phys, 55 (1977). 

Rq depends on the scattering behaviour of the single particles as well as on the particle concentration. For dilute suspensions, one gets ... 

Obviously, aU data points in the range of qRg,es = 1—4- lie essentially on one curve. That means that all aggregates of the examined fumed silica product belong to the same class of aggregates and obey approximately a universal scattering behaviour. The experimental correlation of Fig. 4.25 can be approximated for qRg es - 4 with the following equation ... 

Exact, analytical expressions for the scattering of very small ellipsoids were already derived by Lord Rayleigh (1897). Other particle shapes may require numerical solutions for Rayleigh scattering. Note that the calculation of the orientation averaged scattering behaviour benefits from symmetry relations (Bohren and Huffman 1983, pp. 154-157). 

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