Low angle X-ray scattering

As discussed in Section 3.3.2, there is an inverse relationship between scattering angle 0 and the ratio of the size of the scattering structure to the wavelength of radiation which is used. Most scattering equations may be expressed in terms of a reduced variable of the form  

For convenience in accumulating data over a long time period, the use of an automatic angular advance and data accumulation system is desirable. 

With slit collimation, higher resolution may be obtained with much less loss of intensity. Such cameras are, for example, of the Rigaku-Denki and Kratky type, the latter employing an ingenious U-bar collimating system which permits resolution up to several thousand angstroms. While slit cameras may not readily be used to characterise degrees of partial orientation, a compromise is possible with cameras of 

High collimation cameras of the Franks, Eliott, - and Bonse-Hart types make use of total reflection of the X-rays at a glancing angle for collimation. These provide higher resolution with less intensity loss than the Kratky system for studies of spacings above about 1000 A. 

The quantity (p—p) is the equivalent of introduced in Section 3.3.2. For a two-phase system of phases of volume fractions v, and w 2 and electron densities pi and pj, it is given by  

---

Characterization. When siHca gel is used as an adsorbent, the pore stmcture determines the gel adsorption capacity. Pores are characterized by specific surface area, specific pore volume (total volume of pores per gram of solid), average pore diameter, pore size distribution, and the degree to which entrance to larger pores is restricted by smaller pores. These parameters are derived from measuring vapor adsorption isotherms, mercury intmsion, low angle x-ray scattering, electron microscopy, gas permeabiHty, ion or molecule exclusion, or the volume of imbibed Hquid (1). 

Low angle X-ray scattering in solution Non-destructive Time-consuming 5... 

The chemistry of the iron core is most interesting, in the light of the experiments mentioned above with respect to the hydrolytic polymers of Fe (III). The molecular structure of the iron core obtained from crystalline ferritin by treatment with concentrated sodium hydroxide has recently been investigated using low angle X-ray scattering patterns (44). These authors have proposed a structure quite similar to that of Green rust II ... 

LB films prepared from mixtures of ethylnedithiodiocta-decylthio tetrathiafulvalene with m-tricosenoic acid (or with stearic acid), transferred to substrates, and exposed to iodine vapor Absorption and infrared spectra and low-angle X-ray scattering Lateral d.c. conductivity was determined to be 0.2-1 Scm"1 736, 737, 738... 

The heptamolybdate anion and its protonated forms, [H Mo7024](6-"), n = 1-3, predominate in solutions of pH3-ca. 5.5. The structure of the anion, Figure 6, has been determined in sodium, potassium, ammonium and isopropylammonium salts, and has been confirmed in solution by low angle X-ray scattering.34 The anion structure can be viewed as ... 

Aqueous solutions of molybdate and arsenate, pH 3-5, contain [AsMo903i(H20)3]3 and an As2Mo6 anion.71 The exact structure of the latter ion in solution is in some doubt, although the tetramethylammonium sodium salt contains the anion shown in Figure 15. Low angle X-ray scattering measurements of aqueous molybdoarsenate solutions are not compatible with this structure and the anion may be hydrated in a fashion similar to that observed for the analogous... 

X-ray Scattering. Each sample was analyzed by a low-angle X-ray scattering technique in the laboratory of Wershaw and Pinkney (JO). 

X-ray Scattering. The results of the low-angle X-ray scattering analyses are reported in Table VI. By comparing the results obtained... 

Analysis of low angle X-ray scattering data gives a value for the radius of gyration at infinite dilution of 18.3 A (254)- The scattering curve can best be explained on the basis of a cylinder or prolate ellipsoid... 

This property remains difficult to define and to estimate. The value of 0.6 g/g quoted above from low angle X-ray scattering appears high. In a careful study of sedimentation behavior as a function of salt concentration, Cox and Shumaker 263) concluded that the preferential... 

R D Luggar, J A Horrocks, R D Speller, G J Royle and R Lacey (1995) Optimization of a low angle x-ray scatter system for explosives detection. SPIE 2511, 46-55. 

The study by low-angle X-ray scattering, electron microscopy, and differential scanning calorimetry of the mesophases obtained by dissolution of BSB copolymers in preferential solvents for the polystyrene block and of dry BSB copolymers obtained by slow evaporation of the solvent from the mesophases has allowed to establish the respective effect of different factors which control the structure of the mesophases and their geometrical parameters. It has been shown that the nature, concentration, polymerization of the solvent, and temperature have the same effect on BSB copolymers as on SB copolymers35,88-91. ... 

Using anionic polymerization in THF solution and with diphenylmethylsodium as initiator, Grosius et al.2ls have synthetized block copolymers poly(vinyl-2-pyridine)-poly(vinyl4-pyridine). They have studied by low-angle X-ray scattering the structure of a copolymer V 2 P V 4 P with molecular weight of the blocks 15000 and 8000 respectively. In octanol, they have found a lamellar and a cylindrical structure as a function of solvent concentration. In THF, dioxan, and benzene they have only found a cylindrical structure. 

Figure 13 shows a simplified model of HSA based on its amino acid sequence (37,38) and results from chemical and enzymatic fragmentation studies (41,42,43,44) and low-angle X-ray scattering (45). Much... 

The basic experimental problem was the determination of the rate of growth of platinum particles on an eta-alumina support. The method that these authors wished to use to detect the growth was low-angle x-ray scattering. The difficulty in this experiment is the scattering from the alumina-air interface, which is large. 

A possible solution is to fill the pores with a material that is volumetrically isoelectronic with alumina. These authors, however, found it more convenient to squeeze the pores out of the alumina. The scattering of the alumina could be reduced to the point where it was negligible. Figure 3 shows the low-angle x-ray scattering through pressed alumina as a function of the pressure to which the sample had been subjected. At 100,000 atm., the difference between air and... 

Figure 3. Effect of pressure on the low angle x-ray scattering of eta-alumina...

Figure 4. Low-angle x-ray scattering of platinum particles on an alumina support...

It is generally accepted that aluminum is tetrahedrally coordinated in aluminosilicate glasses and melts, provided that cations such as alkali metals or alkaline earth metals are present in sufficient amounts to charge compensate the replacement of Si by AF+ [i.e., Si + —> AP" -t- (1/ )M" +, where monovalent or divalent M ions occur in nonframework sites associated with the tetrahedral aluminosilicate framework]. Experimental data for aluminosilicate glasses derived from both low-angle x-ray-scattering experiments and EXAFS studies show that as aluminum is substituted for silicon, the average T (tetrahedrally coordinated ion) -O bond... 

Scattering with other radiation 7.2.2.1 Low angle X-ray scattering... 

Low angle X-ray scattering is an experimentally demanding technique and it is certainly not one of standard tools of the biochemical, or even biophysical laboratory. 

---