Scattering technique

Static Light, X-Ray, and Small-Angle Neutron Scattering 

In these experiments the time-averaged scattered intensity /, is measured as a function of the scattering vector q. The net detected intensity can be computed as the superposition of the signals from each scattering center (e.g., each monomer unit). According to the spatial arrangement of the scatterers, the individual scattered waves may interfere constructively or destructively at the detector. Thus, 7f(q) is proportional to the so-called static structure factor 5(q), which sums the waves with different phases from different locations. 5(q), in fact, reflects the spatial Fourier transform of the distribution of scatterers (i.e., the pair correlation function), and 

Also known as quasi-elastic light scattering, this technique monitors the tempord fluctuations in / (q) (Berne and Pecora, 1976 Chu, 1990). These fluctuations result from random thermal motions, which change the instantaneous spatial arrangement of molecules and thus the net scattered intensity. As these random motions result in microscopic concentration fluctuations, a mutual diffusion coefficient can be determined from the time constant of the decay of the time autocorrelation function of Liq, t). Rapid advances in laser and autocorrelator technology during the last two decades have made this experiment a routine characterization and research tool. 

Some basic scattering theory is reviewed here and in Appendix C, but an excellent resource for specific scattering and diffraction techniques is Modern X-ray Physics by Nielsen and McMorrow.  

TABLE 4.2 Approximate Wavelength Ranges for Different Scattering Techniques 

The structure factor in polymer solutions is a quantity that represents the scattering from the average distribution of the polymer chains as a function of the scattering vector q and can be represented by the formula 

The application of any of these methods depends on the information required and the availability of the instrument. These methods are described in detail in Chapter 19. 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A 0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

The true second virial coefficient can be calculated via A2 — A2 aPP(Mapp/Ma,). 

In the case of copolymers the heterogeneity parameters need to be considered in the analysis. If we assume an AB-copolymer the heterogeneity parameters are given by 

The deviations in composition (xAl — xA) are weighted by the z-statistical weights WjMj. The apparent molecular weight Mapp is given by 

A careful characterization of copolymers is quite time consuming and a combination of methods as discussed in Section 6.1 might be considered. In practice the situation is often complicated by an amphiphilic character of the copolymers, which leads additionally to micelle formation. 

In recent years, SNMS has evolved into an important tool for the characterisation of surfaces and thin films [210-217]. Mathieu et al. [217] have reviewed the different post-ionisation methods and the analytical use of SNMS in comparison with SIMS. A textbook is also available [5]. 

Industrial application of SNMS is still in its infancy. As opposed to the many SIMS applications for polymer/additive analysis cfr. Chp. 4.2.1), there appear to be no records (yet) of the use of SNMS or SIMS/SNMS for this purpose despite the desirable features of the (combined) technique. However, scarcity and cost of the equipment (as well as safety aspects for L-SNMS) play a major role in application to routine problems. Also, the SIMS-XPS combination is obviously a serious proven competitor in many instances. Another drawback in many applications is of course the fact that the surface is analysed rather than the bulk. In SNMS most progress can be expected from a combination of laser post-ionisation and sputter depth profiling. 

Principles and Characteristics Ion beam spectroscopy for polymer surface analysis comprises two general classes of experiments. One class uses a primary ion beam to generate secondary ions, which are then mass analysed. This technique, secondary ion mass spectrometry, has evolved into dynamic and static SIMS. Only the latter technique finds frequent application in polymer/additive analysis cfr. Chp. 4.2.1). The second class of ion beam spectroscopy measures the energy loss of a primary ion scattered from a surface. 

The most important interactions between ions and atoms are as follows  

ISS was first proposed for elemental identification in 1967 as a very surface-sensitive tool [218]. However, conventional noble gas ISS is matrix dependent and the exclusive first-layer specificity has been lost multiple scattering complicates the data. ISS has thus grown from a simple first layer detection scheme for elemental composition to an 

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The scattering techniques, dynamic light scattering or photon correlation spectroscopy involve measurement of the fluctuations in light intensity due to density fluctuations in the sample, in this case from the capillary wave motion. The light scattered from thermal capillary waves contains two observables. The Doppler-shifted peak propagates at a rate such that its frequency follows Eq. IV-28 and... 

Foam rheology has been a challenging area of research of interest for the yield behavior and stick-slip flow behavior (see the review by Kraynik [229]). Recent studies by Durian and co-workers combine simulations [230] and a dynamic light scattering technique suited to turbid systems [231], diffusing wave spectroscopy (DWS), to characterize coarsening and shear-induced rearrangements in foams. The dynamics follow stick-slip behavior similar to that found in earthquake faults and friction (see Section XU-2D). 

Chen S H, Chu B and Nossal R (eds) 1981 Scattering Techniques Appiied to Supramoiecuiar and Nonequiiibrium Systems (New York Plenum)... 

Chang T-C and DIott D D 1988 Picosecond vibrational cooling in mixed molecular crystals studied with a new coherent Raman scattering technique Chem. Phys. Lett. 147 18-24... 

Figure 4 Descriptive aspects of EXAFS Curves A-E are discussed in the text. Adapted from J. Stohr. In Emission and Scattering Techniques Studies of inorganic Molecules, Solids, and Surtees. (P. Day, ad.) Kluwer, Norwell, MA, 1981.

The dependence on target mass makes ion scattering techniques ideal for the study of multielement systems. By increasing the incident ion mass, the energy separation between different elements becomes larger. On the other hand, radiation-induced damage becomes a more important consideration. 

P. R. Watson./. Phys. Chem. Ref. Data. 19, 85, 1990. Compilation of structural data attained by MEIS and other ion scattering techniques. 

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