Small Angle Scattering of X-Rays

Porosity plays a clearly important role in geology. It controls fluid storage in aquifers, oil and gas fields and geothermal systems, and the extent and connectivity of the pore structure control fluid flow and transport through geological formations, as well as the relationship between the properties of individual minerals and the bulk properties of the rock. In order to quantify the relationships between porosity, storage, transport and rock properties, however, the pore structure must be measured and quantitatively described. The overall importance of porosity, at least with respect to the use of rocks as building stone was recognized by TS Hunt in his “Chemical and Geological Essays” (1875, reviewed by JD Dana 1875) who noted:

> “Other things being equal, it may properly be said that the value of a stone for building purposes is inversely as its porosity or absorbing power.”

In a Geological Survey report prepared for the U.S. Atomic Energy Commission, Manger (1963) summarized porosity and bulk density measurements for sedimentary rocks. He tabulated more than 900 items of porosity and bulk density data for sedimentary rocks with up to 2,109 porosity determinations per item. Amongst these he summarized several early studies, including those of Schwarz (1870–1871), Cook (1878), Wheeler (1896), Buckley (1898), Gary (1898), Moore (1904), Fuller (1906), Sorby (1908), Hirschwald (1912), Grubenmann et al. (1915), and Kessler (1919), many of which were concerned with rocks and clays of commercial utility. There have, of course, been many more such determinations since that time.

There are a large number of methods for quantifying porosity, and an increasingly complex idea of what it means to do so. Manger (1963) listed the techniques by which the porosity determinations he summarized were made. He separated these into seven methods for …

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Characterization and Analysis of Porosity and Pore Structures

Protein Interactions in Solution Characterized by Light and Neutron Scattering: Comparison of Lysozyme and Chymotrypsinogen

To deepen our understanding of the principles determining the folding and functioning of globular proteins the determination of their three-dimensional structures must be supplemented with the characterization of their internal motions. Although dynamical events in proteins occur on time-scale ranging from femtoseconds to at least seconds, the physical properties of globular proteins are such that picosecond (ps) time-scale motions make a particularly important contribution to the internal fluctuations of the atoms from their mean positions.

Protein dynamics: comparison of simulations with inelastic neutron scattering experiments.

We present a systematic analysis of the aggregation number and shape of micelles formed by nine detergents commonly used in the study of membrane proteins. Small-angle X-ray scattering measurements are reported for glucosides with 8 and 9 alkyl carbons (OG/NG), maltosides and phosphocholines with 10 and 12 alkyl carbons (DM/DDM and FC-10/FC-12), 1,2-dihexanoyl-sn-glycero-phosphocholine (DHPC), 1-palmitoyl-2-hydroxy-sn-glycero-3-[phospho-rac-(1-glycerol)] (LPPG), and 3-[(3-cholamidopropyl)dimethylammonio]-1-propane sulfonate (CHAPS). The SAXS intensities are well described by two-component ellipsoid models, with a dense outer shell corresponding to the detergent head groups and a less electron dense hydrophobic core. These models provide an intermediate resolution view of micelle size and shape. In addition, we show that Guinier analysis of the forward scattering intensity can be used to obtain an independent and model-free measurement of the micelle aggregation number and radius of gyration. This approach...

Size and Shape of Detergent Micelles Determined by Small-Angle X-ray Scattering

We present small angle neutron scattering measurements on binary aqueous solutions of some short-chain amphiphiles (diols, triols, glycols and diglycols) at room temperature. The spectra were analysed in terms of the Teubner-Strey phenomenological formula which allows to obtain a measure for the amphiphilicity strength of each system (amphiphilicity factor fa). In some systems, however, other models, valid for micellar solutions, give also a good representation of the spectra. As a result, we find that, independently of the type of hydrophilic group side (oxydrilic or oxirane), these systems cover the entire accessible amphiphilicity scale ( -1 1) presumably are able to form micelle-like aggregates.

Small-angle neutron scattering studies of aqueous solutions of short-chain amphiphiles.

Structural properties of micellar solutions

A large number of experimental results have shown that macromolelcules in solution give rise to ordered (thyxotropic) structures, a noticeable role being played by a dynamic correlation. In the present paper we develop a semi-phenomenological model that can be solved analytically. The model is able to describe in a quantitative way both structural and dynamical properties of a thyxotropic solution. A careful experimental investigation is also carried out and the experimental results are compared to the theoretical prediction. In such a way the relevant parameters implied in the structure can be evaluated. Some implications concerning energy exchanges between proteins and the thermal bath are discussed.

Dynamical Behaviour of Structured Macromolecular Solutions

Small-angle neutron scattering has been performed on lysozyme solutions at different concentrations, both at the Intense Spallation Impulsed Source (ISIS), Rutherford-Appleton Laboratory) and at Orph\'ee (Laboratoire Leon Brillouin). The results show that, in addition to the large-scale structural properties revealed by light-scattering experiments elsewhere, there is also partial ordering on a molecular scale, with features similar to the large-scale ones, provided a suitable scaling of the spatial length is made. We obtained a careful evaluation of the shape and size of the lysozyme molecule that compares favorably with existing data, and achieved a quantitative description of the intracluster structural properties in terms of a preferred distance among macromolecules. In addition, comparison with results obtained for solutions in different chemical and physical conditions allows for some insight concerning the kinds of interactions responsible for the structure.

Small-angle neutron scattering in lysozyme solutions.

We performed both quasielastic and inelastic neutron scattering, the latter extending to 1000 meV exchange energy, in pure water and in a solution containing 10% lysozyme by weight. The results obtained are discussed in the framework of a structured model of the solution, as given by many previous investigations made with optical techniques. In the case of pure water, our data agree perfectly with the results of others. For the lysozyme solution we found a strongly reduced mobility of water that also shows a ``trapped'' behavior in finite-size regions. As for the vibrational spectra, which involve high energy and high momentum transfer, we show that an appropriate analysis can be made using the ``impulse approximation'' for both pure water and solution cases. Again, such an analysis indicates the existence of a peculiar collective behavior of the macromolecular solution.

R. Giordano

Papers

Small-angle neutron scattering studies of aqueous solutions of short-chain amphiphiles.

Structural properties of micellar solutions

Dynamical Behaviour of Structured Macromolecular Solutions

Small-angle neutron scattering in lysozyme solutions.

Quasielastic and inelastic neutron scattering in macromolecular solutions