Scattering from solutions of star polymers

We study the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, ) from where the radius of the star can be extracted; the intermediate region () that carries the signature of the form factor of a star with f arms: ; and a high wavevector zone () where the local swollen structure of the polymers gives rise to the usual q ^-5/3 decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q ^-5/3 originating from the sea of blobs. Received: 3 September 1997 / Revised: 13 January 1988 / Accepted: 31 March 1998     

Dynamic and static light scattering study of the formation of cross-linked PMMA gels

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl metacrylate (EGDMA) was investigated in solution at different molar ratios R = [EGDMA]/[MMA] between 0 and 0.05. Initially mainly linear PMMA was formed with weight average molar mass 7.5 g/mol independent of R. At larger reaction extents branched polymers were formed and the systems gelled. The scattering intensity rose initially with the reaction extent, but reached a plateau value at larger reaction extents. The plateau value increased strongly with R. Dynamic light scattering showed the appearance of a slow relaxation not observed in linear PMMA solutions. The data can be interpreted by assuming that the excess scattering originates from the branching points and relaxes through self diffusion of the branched particles. The results agree with predictions of the percolation model for gelation and Rouse dynamics. Viscosity measurements corroborate this interpretation. Measurements on a progressively diluted sample quenched close to the gel point again showed quantitative agreement with the percolation model for gelation. Received 11 May 1998 and Received in final form 22 October 1998     

Critical behaviour in solutions of branched polymers and swollen gels as studied by static and dynamic light scattering

Summary We present results of static and dynamic light scattering study of the critical phenomena in semi-dilute solutions and gels of poly(methyl methacrylate) (PMMA) prepared by radical copolymerization of methyl methacrylate and ethylene dimethacrylate in the θ-solvent (4-heptanone). The correlation length ξ and the extrapolated zero-angle scattering intensityI _c,0 of the solutions with degree of cross-linkingf _c≤1% diverge at the pseudospinodal temperature with exponents ofv=0.5 and γ=1, respectively, characteristic of mean-field behaviour. The values ofv and y for samples withf _c≥1.5% are about 0.6 and 1.2, respectively, indicating that the phase transition in solutions of branched PMMA molecules and PMMA gels can be classified to the 3D Ising model. The pseudospinodal temperaturesT _s, for semi-dilute solutions of branched molecules and gels were found as a function of the degree of cross-linking,f _c. The time autocorrelation functions consist of two contributions of which the faster one is attributed to the cooperative motions of the polymer matrix, while the broad slow mode is due to the dynamics of the partly penetrating polydisperse clusters and can be interpreted in terms of a simple cluster diffusion model. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Structural evidence of charge renormalization in semi-dilute solutions of highly charged polyelectrolytes

We show experimentally that Manning counterion condensation also leads to a renormalization of the charge density at high concentrations of highly charged, flexible, hydrophilic polyelectrolytes. Investigations by small angle neutron and X-ray scattering of semi-dilute solutions of poly(acrylamide-co-sodium-2-acrylamido-2-methylpropane sulfonate) at different charge densities above the condensation threshold, show that the scattering function is invariant with the charge density. Received 16 June 1998     

Effects of ionic strength and charge annealing in star-branched polyelectrolytes

We have developed a scaling theory that describes the conformations of weak star-branched polyelectrolytes in dilute solutions. The dependences of the overall star size on the number of branches and on the ionic strength of the solution (tuned by the addition of low molecular weight salt) are analyzed. The intrinsic structure of the polyelectrolyte stars in salt-free and salt-added solutions is discussed in terms of concentration and elastic blobs. In contrast to neutral stars, the swollen corona of the polyelectrolyte star consists of blobs which are not closely packed. We have shown that the size of star polyelectrolytes is less sensitive to the variation in the ionic strength than the size of linear polyelectrolytes. The effects of the ionization-recombination balance in the star polyelectrolyte were taken into account. For polyelectrolytes with small ionization constant, the size of the star depends nonmonotonically on the number of branches and on the ionic strength of the solution due to recombination of counterions with charged monomers. Received: 10 November 1997 / Revised: 16 February 1998 / Accepted: 1st April 1998     

Nanostructures of colloidal complexes formed in oppositely charged polyelectrolyte/surfactant dilute aqueous solutions

Small-angle neutron scattering measurements were performed on dilute solutions of carboxymethylcellulose/DTAB complexes in water in order to determine their size, shape and internal structures. At low polymer content, the complexes are spherical, rather monodisperse and probably made of polymer chains intercalated between surfactant micelles. Moreover, we show that these micelles have a similar cubic arrangement than found in polymer/surfactant precipitates formed at higher surfactant concentrations. At larger polymer content, in the semi-dilute polyelectrolyte regime, the complexes are larger, softer and polydisperse. However, they possess a similar internal structure in both regimes. Carboxymethylcellulose/CTAB complexes are also large, soft and polydisperse but do not seem to exhibit well-defined internal structures.     

Analysis of poly(bisphenol A carbonate) by size exclusion chromatography/matrix-assisted laser desorption/ionization. 2. self-association due to phenol end groups

We report here a case of apparent failure of the size exclusion chromatography/matrix-assisted laser desorption/ionization (SEC/MALDI) method to provide polymer fractions with narrow molar mass distribution, showing that intermolecular chain association is responsible for this phenomenon. Poly(bisphenol A carbonate) (PC) chains terminated with hydroxyl groups undergo self-association by hydrogen bonding, providing macromolecular aggregates with higher hydrodynamic volume. These aggregates are eluted through SEC columns at the same volume as higher molar mass chains, which remain non-associated. Thus, self-association affects negatively the SEC fractionation experiments, and even the sharpest SEC fractions contain a heterogeneous mixture of PC chains of different size. When the off-line SEC/MALDI procedure is applied, the SEC fraction is diluted in the matrix which, being a dissociating medium (carboxylic acid) for hydrogen-bonded aggregates, suppresses the chains' self-association. Therefore, the MALDI spectra of these PC fractions indicate a polydisperse character, with irregular bimodal distributions of peaks. As a consequence, in the presence of chain association, the SEC/MALDI method for the calculation of molar masses of polymers cannot be directly applied. In the present case we have found that, under opportune experimental conditions, self-association in polycarbonates can be avoided, so that nearly monodisperse SEC fractions can be obtained and the SEC/MALDI method can be applied. Our results also show that MALDI is a very sensitive technique for the detection of association of polymers in dilute solutions. Copyright 1999 John Wiley & Sons, Ltd.     

Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

We present an analytical self-consistent-field (SCF) theory for a neutral polymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This model mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. The equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the grafted chains) as well as the overall adsorbed amount and the adsorbate density profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the adsorbate in the solution. We demonstrate that, when the grafting density is varied, the overall adsorbed amount always exhibits a maximum, whereas the root-mean-square brush thickness either increases monotonically or passes through a (local) minimum. At high grafting densities the chains are loaded by adsorbed aggregates preferentially in the distal region of the brush, whereas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending on the relative strength of the excluded volume interactions between unloaded and loaded monomers both the degree of loading of the chains and the polymer density profile are either continuous or they exhibit a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists of unloaded and weakly extended chains and occupies the region proximal to the surface, whereas a more dilute phase consisting of highly loaded and strongly extended chains forms the periphery of the brush. Received 26 November 1998 and Received in final form 2 April 1999     

Glass like magnetic alternating field susceptibility behavior of structurally frozen ferrofluids

Four ferrofluids, distinct in size distribution and aggregate structure, were investigated. The relaxation time ,related to the temperature of susceptibility maximum, was fitted to a Vogel-Fulcher law. A mean ordering temperature, T₀, was calculated using magnetic particle parameters derived from the structure. It is assumed that at T₀ the particle moments of particle clusters correlate, leading to a spin glass-like transition. Hence, then dynamic slows down considerably, as indicated by a strong broadening of relaxation-time distribution. T₀ roughly agrees with the energy of competing interaction between particle moments, as calculated from the structure of particle aggregates. Differences between particle arrangements clearly influence the dispersion and absorption, particularly within the cluster phase. Received 15 July 1998     

Effect of PMMA on crystallization behavior and hydrophilicity of poly(vinylidene fluoride)/poly(methyl methacrylate) blend prepared in semi-dilute solutions

Films of poly(vinylidene fluoride) (PVDF)/poly(methyl methacrylate) (PMMA) blend were derived from a special procedure of casting semi-dilute solutions. Hydrophilic character and crystallization of PVDF were optimized by variation of PMMA concentration in PVDF/PMMA blends. It was found that a PVDF/PMMA blend containing 70 wt% PMMA has a good performance for the potential application of hydrophilic membranes via thermally induced phase separation. The films presented β crystalline phase regardless of PMMA content existed in the blends. Thermal analysis of the blends showed a promotion of crystallization of PVDF with small addition of PMMA which induced larger lamellar thickness of PVDF, leading to the largest spherulitic crystal of PVDF (10 wt% PMMA) is about 8 μm. SEM micrographs illustrated no phase separation occurred in blends, due to the high compatibility between PVDF and PMMA.     

X-ray spectroscopy of the metal-insulator transition in YbGdTe and YbLaTe

We report extended X-ray absorption fine structure (EXAFS) of Yb_1-xGd_xTe and Yb_1-xLa_xTe, two solid solutions which show an insulator-metal transition (IMT) as a function of x for a high donor concentration . The results are correlated to transport experiments and X-ray diffraction data, to analyse the IMT in relation to the structure at both a local and a macroscopic scale. A bimodal distribution is found for rare earth-Te nearest distances in these compounds crystallized in the fcc structure. In particular, we find the less rigid Yb-Te bond can be used as a local probe for the wavefunction of the electrons introduced by La or Gd donors, hence a new insight on the metal-insulator transitions which are of a different nature in the two solid solutions. Received: 23 March 1998 / Revised and Accepted: 12 July 1998     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

Magnetic properties of small Yttrium clusters

The magnetic properties of small Y_N clusters are studied by using a tight-binding Hubbard Hamiltonian in the unrestricted Hartree-Fock approximation. Several types of cluster geometries are considered in order to see the effects of the size and symmetry of the structures on the magnetic properties. The average magnetic moments are found to be constant over large domains of variations in the interatomic distance, a fact that can be explained by the existing closed shell electronic configurations at least for one spin direction in all our magnetic solutions. Small energy gains upon the onset of magnetization are obtained, which reveals the low stability of the magnetic solutions. Our results contradict the prediction of a magnetic-nonmagnetic transition at a large cluster size (about 90 atoms) for these kinds of systems. Received: 27 April 1998 / Received in final form: 23 June 1998 / Accepted: 17 July 1998     

Memory of silica aggregates dispersed in smectic liquid crystals: Effect of the interface properties

Previous studies on nematic liquid crystals containing silica particles indicated memory effects that might be due to hydrogen bonds between the individual silica particles. We made smectic liquid crystal dispersions containing silica particles with various surface properties. Using a neutron scattering technique we studied the interfacial surface effects on the structure of the silica aggregates, and on the smectic layer alignment. Our observations indicate that the stability of the memory correlates to the number of OH groups on the silica surfaces. The observations imply that, with fine-tuning of the OH content of the silica surfaces, various types of memory devices can be designed. We considered three different effects that can memorise the alignment of the liquid crystal. Measurements on tilted SmC phases indicate that surface effects become important only after repeated heating-cooling cycles, as the average size of the aggregates decrease. Received 31 July 1998 and Received in final form 17 December 1998     

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     

Sensitive Spectroscopic Detection of Large and Denatured Protein Aggregates in Solution by Use of the Fluorescent Dye Nile Red

The fluorescent dye Nile red was used as a probe for the sensitive detection of large, denatured aggregates of the model protein β-galactosidase (E. coli) in solution. Aggregates were formed by irreversible heat denaturation of β-galactosidase below and above the protein’s unfolding temperature of 57.4°C, and the presence of aggregates in heated solutions was confirmed by static light scattering. Interaction of Nile red with β-galactosidase aggregates led to a shift of the emission maximum (λ _max) from 660 to 611 nm, and to an increase of fluorescence intensity. Time-resolved fluorescence and fluorescence correlation spectroscopy (FCS) measurements showed that Nile red detected large aggregates with hydrodynamic radii around 130 nm. By steady-state fluorescence measurements, it was possible to detect 1 nM of denatured and aggregated β-galactosidase in solution. The comparison with size exclusion chromatography (SEC) showed that native β-galactosidase and small aggregates thereof had no substantial effect on the fluorescence of Nile red. Large aggregates were not detected by SEC, because they were excluded from the column. The results with β-galactosidase demonstrate the potential of Nile red for developing complementary analytical methods that overcome the size limitations of SEC, and can detect the formation of large protein aggregates at early stages.     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

Random copolymers at a selective interface: Many chains with excluded volume interactions

We investigate numerically, using the bond-fluctuation model, the adsorption of many random AB-copolymers with excluded volume interactions at the interface between two solvents. We find two regimes, controlled by the total number of polymers. In the first (dilute) regime, the copolymers near the interface extend parallel to it, while in the second regime they extend perpendicular to it. The density at the interface and the density in the bulk depend differently on the total number of copolymers: In the first regime the density at the interface increases more rapidly than in the bulk, whereas the opposite is true in the second regime. Received 4 March 1998 and Received in final form 22 September 1998     

Homogeneous and inhomogenous polyacrylamide gels as observed by small angle neutron scattering: A connection with elastic properties

Small angle neutron scattering of polyacrylamide solutions and gels is presented for different polymer and cross link concentrations. The gels are analyzed in connection with their elastic properties. For less than 11% of polymer concentration and for small cross link contents , it was found that the gels are no more heterogeneous than the solutions. This corresponds to the range of where the elastic modulus increases with . For larger cross link contents when the elastic modulus decreases if increases, the sample appears to be strongly heterogeneous with a large size distribution of the inhomogeneities. The results are compared with the recent model of Oshmyan and Benguigui of the elastic properties of the polyacrylamide gels. Thus a relation can be proposed between the observation of the inhomogeneities by scattering and the mechanical properties Received 30 December 1997 and Received in final form 26 June 1998     

Unbounded fluctuations in transport through an integrable cavity

We derive a semiclassical scheme for the conductance through a rectangular cavity. The transmission amplitudes are expressed as a sum over families of trajectories rather than a sum over isolated trajectories. The contributing families are obtained from the evaluation of a finite number of continued fractions. We find that, contrary to the chaotic case, the conductance fluctuations increase with the incoming energy and the correlation function exhibits a singularity at the origin. Received 17 July 1998 and Received in final form 23 November 1998