Neutron scattering static

Those Warren-Cowley parameters have been determined in situ above the order-disorder transition temperature by diffuse neutron scattering. From these experimentally determined static correlations, the first nine effective pair interactions have been deduced using inverse Monte Carlo simulations. 

If the crossover points Q (x) are determined from Fig. 45, taking the x-values at half-step height, Q (x) = 1/1 (x) = (0.7 + 0.2)x is obtained in the case of the PS system. This has to be compared with static value Qs (x) = 1.6x, derived from the same polymer solvent system by elastic neutron scattering [103], As long as no corresponding data from other polymer solvent systems are available, the final decision as to whether static and dynamic scaling lengths coincide or not, is still open. 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

For both polymer systems the static structure factors were investigated using small angle neutron scattering and the results interpreted in terms of RPA theory. Figure 6.6 displays the temperature-dependent static structure factor obtained from a PE-PEE melt (sample IV). 

However, it seems that possibilities of this model to explain some of the experimental results were not fully explored. Also, this model shows some weaknesses. First, it predicts a value of Tc in DKDP (310 K) that is higher than the experimental value (229 K). Second, the calculated rate of the proton transfer in the PE phase is too low to explain the width of the CP in the neutron scattering spectra of KDP [62]. Third, and most important, because the model assumes that dipoles of PO4 groups lie along the c-axis, it cannot to explain static and dynamic properties of the transverse polarization fluctuations, whose importance in the phase transition mechanism has been supported by several experimental results [8,20,28,31-33]. 

Turbidity measurements, static and dynamic light scattering, and a brief introduction to x-ray and neutron scattering (Chapter 5)... 

Abbreviations C, coexistence curve S, static light scattering D, dynamic light scattering T, turbidity N, coherent neutron scattering V, shear viscosity E, electrical conductance I, interfacial phenomena (ellipsometry). d Deuterated 1-octanol. 

Measurements of static light or neutron scattering and of the turbidity of liquid mixtures provide information on the osmotic compressibility x and the correlation length of the critical fluctuations and, thus, on the exponents y and v. Owing to the exponent equality y = v(2 — ti) a 2v, data about y and v are essentially equivalent. In the classical case, y = 2v holds exactly. Dynamic light scattering yields the time correlation function of the concentration fluctuations which decays as exp(—Dk t), where k is the wave vector and D is the diffusion coefficient. Kawasaki s theory [103] then allows us to extract the correlation length, and hence the exponent v. 

The cross-section in Eq. (1 illustrates another distinguishing feature of inelastic neutron scattering for vibrational spectroscopy, i.e., the absence of dipole and polarizability selection rules. In contrast, it is believed that in optical and inelastic electron surface spectroscopies that a vibrating molecule must possess a net component of a static or induced dipole moment perpendicular to a metal surface in order for the vibrational transition to be observed ( 7,8). This is because dipole moment changes of the vibrating molecule parallel to the surface are canceled by an equal image moment induced in the metal. 

It should be noted here that the conclusion about s-wave nature of the SC order parameter is consistent with conclusion about s-wave symmetry of the SC order parameter in the bulk and d-wave symmetry at the surface of the sample of the cuprates [17]. It was noted in [17] that most conclusions about d-wave symmetry was obtained in experiments (e.g. ARPES ones) on the cuprates in which mainly surface phenomena have been used. In this sense, the resistive measurements on the cuprates (see, e.g. [4]) are essentially bulk in the nature. In addition, the electron scattering (in resistivity measurements) is sensitive to the spin disorder in the system (magnetic contribution in the electrical resistivity appears, see Sec.l). Moreover, the electron scattering permits probe not only static magnetic order but dynamical (short-lived) ones because of short characteristic times as compared e.g. with usual neutron scattering. 

The internal structure of polyelectrolyte block copolymer micelles such as their core radius Rc and micellar radius Rm can be determined by a variety of methods involving static and dynamic light scattering (SLS, DLS), small-angle X-ray (SAXS) and neutron scattering (SANS) as well as imaging techniques such as transmission electron microscopy (TEM) or atomic force mi-... 

Fig. 9 Density profiles of PEE-PSSH micelles for varying salt concentrations. The profiles were obtained by a combination of static and dynamic light scattering, small-angle neutron scattering and cryo-TEM [49]...

The radial distribution function plays an important role in the study of liquid systems. In the first place, g(r) is a physical quantity that can be determined experimentally by a number of techniques, for instance X-ray and neutron scattering (for atomic and molecular fluids), light scattering and imaging techniques (in the case of colloidal liquids and other complex fluids). Second, g(r) can also be determined from theoretical approximations and from computer simulations if the pair interparticle potential is known. Third, from the knowledge of g(r) and of the interparticle interactions, the thermodynamic properties of the system can be obtained. These three aspects are discussed in more detail in the following sections. In addition, let us mention that the static structure is also important in determining physical quantities such as the dynamic an other transport properties. Some theoretical approaches for those quantities use as an input precisely this structural information of the system [15-17,30,31]. 

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