Scaling in the aggregation behaviour of zinc-free insulin studied by small-angle neutron scattering

Summary The aggregation behaviour of zinc-free insulin has been studied by small-angle neutron scattering as a function of protein concentration,pH, and ionic strength of the solution. The distance distribution functions for the 12 samples have been obtained by indirect Fourier transformation. The weight-averaged molecular mass and thez-averaged radius of gyration were determined. Both quantities vary systematically with the experimental conditions. They increase with decreasingpH and with increasing ionic strength. The radius of gyration scales as a power law of the weight-average mass with the exponent 0.44. A similar scaling is found for a set of oligomers structures based on the crystal structure of zinc-free insulin. The mass distribution between the oligomers was determined by a model based on these oligomers. The results from this model and the Fourier transformations have been compared to an equilibrium model recently introduced by Kadimaet al. The model takes into account the variation of the effective charge of the monomer withpH and ionic strength. The neutron scattering results agree well with the predictions of the model. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Small-angle neutron scattering from micellar solutions

Micellar solutions are the suspension of the colloidal aggregates of the sur-factant molecules in aqueous solutions. The structure (shape and size) and the interaction of these aggregates, referred to as micelles, depend on the molecular architecture of the surfactant molecule, presence of additives and the solution conditions such as temperature, concentration etc. This paper gives the usefulness of small-angle neutron scattering to the study of micellar solutions with some of our recent results.     

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

The dispersion state of sodium-sulphonated polystyrene ( NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c^* is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c^* and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c ^*), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c ^*), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c ^*, NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. Received 14 May 1999 and Received in final form 15 March 2000     

Scattering properties of salt-free wormlike micellar solutions

Static and dynamic light scattering and conductivity experiments were carried out on salt-free aqueous micellar solutions of cetyltrimethylammonium n-hexane sulfonate (CTAC_6SO_3) and cetyltrimethylammonium n-heptane sulfonate (CTAC_7SO_3) as a function of surfactant concentration. This study confirms the analogy between the behavior in the semi-dilute regime of elongated micellar systems and “classical” polyelectrolyte solutions. Time-resolved scattering experiments performed after a variation of concentration from about twice the overlap volume fraction to less than half of it revealed the existence of a structural relaxation with a characteristic time of several hours. Received 21 December 1999     

Small angle neutron scattering from micellar solutions

Small angle neutron scattering (SANS) is an ideal tool for studying structures of macromolecules and colloidal solutions. A number of micellar solutions have been studied in our laboratory using a home built SANS spectrometer. This paper gives an introduction to the technique of SANS and gives a brief survey of the results obtained at Trombay.     

Interactions between poly(diallyldimethylammonium chloride) and poly(acrylic acid) in dependence on polymer concentration

Summary The phase diagram of the ternary system,i.e. poly(diallyldimethylammonium chloride), poly(acrylic acid, sodium salt), and water was investigated by varying the molecular weight of the components. In general, a range of phase separation is surrounded by a one-phase system. The range of phase separation can be subdivided into a region of flocculation and/or coacervation in contrast to stable symplex dispersions. By increasing the molecular weight of the components the range of phase separation is increased and phenomena of flocculation followed by coacervation were observed predominantly. Above a molecular weight of 10 000 g/mol the transition to concentrated macroscopic homogeneous one-phase systems was observed at a constant ionic strength of 2 mol/l coinciding with the ?critical ionic strength? for Coulombic interactions in this system. That means the transition to concentrated one-phase systems can be understood by the disappearance of Coulombic forces above a system-specific ionic strength resulting in a quite additive behaviour of the mixtures with regard to the components. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Hydrodynamics of fractal aggregates

Summary The scaling of the ratio of the hydrodynamic radius to the radius of gyration of fractal aggregates is probed by numerical simulations for several different algorithms. In common with previous work it is found that this ratio shows a significant and long-lasting finite-size effect for particle-cluster aggregates, but a much less significant finite-size effect for hierarchical cluster-cluster aggregates. Simple theoretical models which reproduce the behaviour are discussed. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Scaling concept applied to the defect formation caused by interactions between melittin and phosphatidylcholine (PC) model membranes

Summary A simple computer model of defection process caused by interactions between melittin and phosphatidylcholine (PC) model membrane has been proposed. It leads to a scaling formula which connects the average diameter (or linear size parameter) of the affected domain with the reciprocity of the number of such domains. Some preliminary investigations show the scaling exponent to be a small fractional number between ca. 0.3 and 0.1, depending on the number of possible infection directions and the type of lattice taken as a lipid matrix. Such small values of the scaling exponent can roughly be interpreted in terms of random tesselations on a plane (like random Voronoi networks), and the whole process displays a statistical self-similarity. The values obtained seem to be, however, small comparable to the scaling exponents characteristic for the faulting process occurring during the earthquake propagation. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

A lattice-gas hamiltonian for micellar binary solutions

An explicit Ising-spin lattice Hamiltonian is proposed as a model for studying the phase diagrams of micellar binary solutions on the micellar length scale. Incorporating many essential features, it can be used to check the validity of a previously suggested scenario for nonuniversality at the consolute point.     

Small angle neutron scattering from micellar solutions of triton X-100

Micellar solutions of non-ionic surfactant triton X-100 (8% by weight) show phase separation at cloud pointT _cp ～ 335 K. This paper reports results of small angle neutron scattering (SANS) experiments from this solution as a function of temperature between 298 and 332 K. The range of wave-vector transferQ, covered in these experiments is from 0.02 to 0.15 Å^?1. It is seen that as one approachesT _cp, the neutron scattering cross section diverges in the region of lowQ (<0.06 Å^?1) while it is independent of temperature in region of largeQ(>0.06 Å^?1). We believe that the divergence of scattering at lowQ with an increase in temperature is because of changes in the structure factorS(Q) of the solution. The measured distributions have been analyzed using four different models for inter-micellar potential. The models used to calculate the structure factorS(Q) are (1) mean spherical approximation (MSA) with Yukawa tail for attractive potential, (2) MSA with an attractive square well potential, (3) random phase approximation (RPA) with an attractive square-well potential and (4) Sticky hard sphere model (attractive square-well potential with Percus-Yevick approximation). The strengths of the attractive potential required to fit the SANS data are (?6.6 to ? 14.4)/kt for model (1), (? 6.6 to ? 15.0)/kt for model (2), (? 3.8 to ? 7.3)/k _B T for model (3) and (?2 to ?2.7)/kt for model (4). On the basis of reasonableness of the derived strength of the potential near the phase separation temperature and its relative temperature dependence, it is concluded that present data favour the Sticky hard sphere model.     

Small angle neutron scattering study of two nonionic surfactants in water micellar solutions

Two classic nonionic surfactants — C₁₄E₇ (heptaethylene glycol monotetradecyl ether) and C₁₀E₇ (heptaethylene glycol monodecyl ether) were investigated in heavy water solution for concentration c = 0.17% (dilute regime) at different temperatures in the range t = 10–35°C by small angle neutron scattering (SANS) method. In the case of C₁₄E₇ surfactant — for all temperatures at c = 0.17% there are two axial ellipsoidal micelles with longer axis 15 nm at 10°C and 49.5 nm at 35°C in investigated solutions. For C₁₀E₇ surfactant at the same concentration of solution and temperature — two axial ellipsoidal micelles were observed, too. The longer axis is equal to 7.5 nm at 10°C, 9 nm at 20°C and at 35°C this axis is equal to 12 nm. Micelles of C₁₀E₇ nonionic surfactant are smaller than those of C₁₄E₇ surfactant in the same experimental conditions.      

Mobility fluctuations and electrophoretic light scattering from macromolecular solutions

We discuss the origins and the effects of mobility fluctuations of rigid, globular macromolecules on a solution's electrophoretic light scattering spectrum. Assuming a dilute solution, a modified van Hove self-correlation function is calculated via van Kampen's time-ordered cumulant method and the results are compared with less rigorous approaches. The consequences of generalizing to dynamic external fields are briefly considered.     

Birefringence and scattering of light in colloidal solutions of magnetite in kerosene

The birefringence and dynamic and static scattering of light in colloidal solutions of magnetite nanoparticles in kerosene with different concentrations of the solid phase have been investigated. It is shown that these solutions contain both individual colloidal particles about 12 nm in diameter and their aggregates up to 100?600 nm in diameter. The largest aggregates are formed in solutions with the lowest concentration (on the order of 0.001 vol % or lower). The presence of relatively large aggregates makes it possible to observe specific features of optical anisotropy relaxation in these solutions, which are related to the non-Rayleigh character of light scattering from magnetite-particle aggregates.     

Light scattering and fluorescence probe studies on micellar properties of Triton X-100 in KCl solutions

The effect of KCl on micelle formation and structure of Triton X-100 (TX-100) was investigated by using combined static and dynamic light scattering measurements, together with the fluorescence probe technique. An analysis of the light scattering data, including hydrodynamic radius and micellar aggregation number, accounted for both micelle growth and hydration. Fluorescence studies using pyrene as a probe were carried out to determine the critical micelle concentration (CMC) as a function of solution composition. In addition, with the aim of gaining information on the possible changes in the micro-environmental properties of TX-100 micelles, fluorescence probe studies, including intermolecular pyrene excimer formation and fluorescence polarization of coumarin 6 associated with micelles, were carried out. It was found that the addition of electrolyte induces a decrease in the CMC and an increase in both aggregation number and hydration. However, complementary data of partial specific volume and cloud point of the surfactant suggested that the main contribution to micellar hydration is due to water mechanically trapped in the micelle. Fluorescence measurements do not indicate changes in the micellar micropolarity, probably due to modifications of the solubilization site of the probe caused by the micellar growth. Both pyrene excimer formation and fluorescence polarization of coumarin 6 revealed an increase in microviscosity with electrolyte addition, which is consistent with increased micellar hydration.     

Soret effect in interacting micellar solutions

We show that electrostatic effects have a dramatic influence on thermal diffusion of charged micelles. In the dilute regime, the Soret coefficient strongly decreases with the solution ionic strength, and scales as the square of the Debye-Hückel length. Yet, collective effects yield a reversed scenario even at fairly low surfactant concentration. We find that single-particle behavior can be explained using an interfacial tension mechanism proposed by Ruckenstein, which also fairly accounts for collective effects and opens the way to a general picture of thermal diffusion in disperse systems.     

Thermal diffusion in ionic micellar solutions

Thermal diffusion studies of complex fluids may have a deep impact on determining the microscopic origins of the Soret effect, allowing in particular for a clear distinction between single-particle and collective effects. We show for instance that electrostatic interactions have a dramatic influence on the thermal diffusion of charged surfactant micelles. In the dilute regime, the Soret coefficient strongly decreases with increasing solution ionic strength and scales as the square of the Debye-Hückel screening length. Yet, collective effects yield a reversed scenario even at fairly low surfactant concentrations. We find that the single-particle behaviour can be explained using an interfacial tension-driven mechanism originally proposed by Ruckenstein. Interparticle interactions drastically change the Soret coefficient mainly owing to their effects on the solution's osmotic compressibility. The proposed mechanism can be extended to other kinds of solvent-particle interaction and may open up the way to a general picture of thermal diffusion in disperse systems.