On the measurement of the χ-parameter under the zero average contrast condition

Several methods for measuring directly the interaction parameter X as a function of polymer concentration are presented. These methods are applied to symmetric ternary mixtures of homopolymers and copolymers in solution under the zero average contrast condition. They can be used for an arbitrary concentration from dilute solution to the bulk and at any value of the scattering wavenumber q. Possible combinations of static and dynamic measurements are presented. © 1992 John Wiley & Sons, Inc.     

Characterization of ethylene/propylene copolymers by means of a GPC-4D technique

Copolymer composition and comonomer distribution are important magnitudes in polymer material that have a big effect on different kind of properties and consequently there are several ways to study.In this work several ethylene/propylene copolymers synthesized with two different metallocene catalysts and a Ziegler–Natta catalyst and covering a wide composition range were studied. Characterization was carried out by nuclear magnetic resonance (¹³C NMR) and by gel permeation chromatography with 4 detectors (GPC-4D): refractive index, viscosity, multi-angle light scattering and infrared detectors.Different behaviour in the comonomer distribution along the molecular weight was obtained for metallocene and for ZN copolymers as expected due to the differences between these catalytic systems. Nevertheless, Ziegler–Natta copolymers present more homogeneous comonomer distribution due to the synthesis method. Study of conformation of chains in solution was improved by defining the scaling law of R_g against the number of repeat units because it avoids the effect of the repetitive unit size. Both metallocene copolymer sets show similar dependence of q value with the copolymer composition, however Ziegler–Natta copolymers show different behaviour with q values independent on copolymer composition. This different behaviour has been related with the effects of the heterogeneity of the ethylene distribution and of the molecular weight of the samples.     

Rheological and structural properties of aqueous solutions of a hydrophobically modified polyelectrolyte and its unmodified analogue

Rheological methods and small angle neutron scattering (SANS) were used in the characterization of dilute and semidilute aqueous solutions, both with and without added salt, of anionic poly(vinyl alcohol) (PVA⁻) and its hydrophobically modified analogue (HM-PVA⁻). The rheological measurements showed that the concentration induced viscosification effect and elastic responses are considerably stronger for solutions of HM-PVA⁻ than in solutions of the unmodified polyelectrolyte. Over the considered polymer concentration domain, the solutions of PVA⁻ exhibit virtually Newtonian behavior, whereas strong shear thinning effects are observed in the HM-PVA⁻ solutions. The SANS results for HM-PVA⁻ solutions reveal a pronounced peak in the plot of scattering intensity versus scattering wavevector q at intermediate q values and the position of the maximum scales with polymer concentration as q_max∼c^0.28±0.02. This peak is suppressed in solutions of the unmodified polyelectrolyte and merely a shoulder in the scattering curve appears. Additionally, an “upturn” in the scattered intensity is observed at small q values and the magnitude of this effect depends on polymer concentration, hydrophobicity and salt addition. At large q values, the SANS results from HM-PVA⁻ solutions suggest morphological changes, from rod-like chains to a network of semiflexible chains, as the polyelectrolyte concentration increases.     

Dynamical relaxations in mixtures of different polymers and nonsymmetrical copolymers in solution

Dynamical relaxation properties of nonsymmetrical mixtures of homopolymers and of copolymers in solution are examined. In particular, examples of bimodal mixtures in solution, ternary mixtures of two different homopolymers and a solvent, and nonsymmetrical diblock copolymers in solution are examined. The frequencies of the eigenmodes Γ and Γ′, those of the cooperative mode Γ_T and the interdiffuse mode Γ_I are calculated for these systems. It is found that the variations of T_T and T_I, with the scattering wave number q are practically identical to those of Γ_T and Γ_I, respectively. This identity is rigorous only for mixtures or copolymers where the two polymer components are identical except for their contrast factors (i.e., indices of refraction or scattering lengths). Here, it is argued that the identification of the eigenmodes with the cooperative and interdiffuse modes can be extended qualitatively to mixtures of different polymers and to nonsymmetrical copolymers in solution.     

The response of microstructure to processing in a series of poly(siloxaneimide) copolymers

Poly(siloxaneimide) (PSI) segmented copolymers exhibit organized microdomains if the blocks are sufficiently incompatible. As with neat diblock and triblock copolymers, the processing route employed to prepare films of PSI materials is expected to influence the dimensions and/or morphology of the resultant microstructure. In this work, small-angle neutron scattering (SANS) is utilized to characterize the disordered microstructure found in films of a series of PSI copolymers which are subjected to solvent casting and various thermal treatments. Microstructural dimensions such as the periodicity and correlation length are deduced from the Teubner-Strey (TS) model for disordered microemulsions. The scattering intensity of each copolymer up to q = 5.0 nm^?1, where q is the scattering vector, is found to scale as q^?2.8+?0.1. Results indicate that processing the materials as cast films or as melt-pressed films allowed to cool slowly has a small, but discernible, effect on microstructural characteristics. SANS profiles of films quenched from elevated temperatures reveal a clear transition in microdomain periodicity, which correlates well with the glass transition temperature of the imide microphase in these and other materials of similar chemical structure. © 1993 John Wiley & Sons, Inc.     

Comparative Study of Scattering and Osmotic Properties of Synthetic and Biopolymer Gels

Summary: The effect of monovalent/divalent cation exchange on the structure and osmotic properties of chemically cross-linked polyacrylate and DNA gels swollen in near physiological salt solutions has been investigated. Both systems exhibit a reversible volume phase transition in the presence of calcium ions. The small-angle neutron scattering spectra of these gels display qualitatively similar features. At low values of q surface scattering is observed, while in the intermediate q range the signal is characteristic of scattering from rod-like elements. At high values of q the scattering intensity is governed by the local (short-range) geometry of the polymer chains. The competition between monovalent and divalent cations has been studied by anomalous small-angle X-ray scattering (ASAXS). The ASAXS results reveal that the local concentration of the divalent counter-ions in the vicinity of the polymer chains significantly exceeds that of the monovalent counter-ions.     

Dynamics of end-grafted polystyrene brushes in theta solvents

The dynamics of the concentration fluctuations in end-grafted polystyrene brushes in a theta solvent (cyclohexane) are probed by evanescent wave dynamic light scattering at different wavevectors q and temperatures. When the solvent quality changes from marginal to poor, the relaxation function C(q, t) exhibits strong effects as compared with the smooth variation of the brush density profile. From a single exponential above 50 °C, C(q, t) becomes a two-step decay function. The fast decay is still assigned to the cooperative diffusion albeit slower than in the good solvent regime whereas the slow nonexponential and nondiffusive process might relate to microsegragated and/or chain dynamics in the present polydisperse brush. The relaxation function of the present three brushes with different grafting density reveals similarities and disparities between wet brushes and semidilute polymer solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3590–3597, 2006     

Ordering in Bio-Polyelectrolyte Chitosan Solutions

The scaling of the polyelectrolyte scattering peak in chitosan solutions, as deduced from the relation q_max∼c_p^α was studied by synchrotron SAXS as a function of the charge density of the polymer. We observe a variation in the α exponent corresponding to the limit of the ionic condensation, by varying the degree of acetylation of the polymer. The nature of the solution medium also affects the polyelectrolyte peak, and it is shown that in alcoholic/water mixtures, the lower dissociation of the acid induces a lower charge density, thus influencing the polyelectrolyte ordering.     

Structure of gum arabic in aqueous solution

Gum arabic, a natural polysaccharide derived from exudates of Acacia senegal and Acacia seyal trees, is a commonly used food hydrocolloid. The complex chemical structure of the gum has been widely studied revealing a multifraction material consisting mainly of a highly branched polysaccharide and a protein–polysaccharide complex (GAGP) as a minor component. This work investigates its mesoscopic structure in aqueous solution by small‐angle X‐ray and neutron scattering combined with cryotransmission electrons microscopy. Scattering measurements reveal an intricate shape composed of many spheroidal aggregates assigned to the polysaccharide with a small amount of larger coils. A scattering peak is observed at moderate to high concentrations, the spacing of which exhibits a c^?1/3 power law relation to polymer concentration (c). Upon addition of salt, this peak disappears, indicating its electrostatic nature. The large coils contribute a q^?2 power law at the low scattering vector (q) range. However, at low concentration in which the interaggregate peak is not observed, a q^?1 power law at the low q range indicates the possible existence of a fraction with a locally extended conformation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3265–3271, 2006     

Control of pH- and temperature-responsive behavior of mPEG-b-PDMAEMA copolymers through polymer composition

A series of poly(ethylene glycol) monomethyl ether-block-poly(2-(dimethylamino)ethyl methacrylate) (mPEG-b-PDMAEMA) diblock copolymers were synthesized using atom transfer radical polymerization to achieve controlled polymer molecular weight and narrow molecular weight distribution. The thermoresponsive properties of the mPEG-b-PDMAEMA diblock copolymers in aqueous buffered solutions were determined using UV-Visible spectroscopy and dynamic light scattering. The cloud point, a soluble-to-insoluble transition, was observed for all mPEG-b-PDMAEMA diblock copolymer solutions. Increasing either the mPEG or PDMAEMA molecular weight resulted in a decrease in observed cloud points as a function of pH and polymer concentration. Changing the mPEG molecular weight determined whether a second, higher temperature, thermal transition was observed as a function of pH and polymer concentration. Controlling the thermoresponsive properties of mPEG-b-PDMAEMA diblock copolymers through polymer composition, concentration, and pH enables the tailoring of these copolymers for applications ranging from non-viral gene delivery to use as a strengthening agent in paper.     

Collective dynamics of terminally anchored polymer chains

Thermal fluctuations of the segment density profile of a polymer brush were probed by dynamic light scattering in the evanescent wave configuration; the time correlation functions of concentration fluctuations with wavevector q were measured. It is found that there is a preferred wavelength of the order of the brush thickness, L₀, of these fluctuations with a concurrent slowing down of their thermal decay rate. A theory is presented for the small-amplitude deformation of the free surface of a parabolic brush in solution; a maximum in the respective structure factor of the concentration fluctuations is predicted at q* L₀ ∼ O(1), in agreement with the experiment.     

Quasielastic scattering of neutrons from freely jointed polymer chains in dilute solutions

Starting with Kirkwood's Fokker–Planck equation for the polymer configuration-space distribution function and using the Zwanzig–Mori projection operator technique we have calculated the scattering law S_(q,w) for a freely jointed model polymer chain in a dilute solution. When memory effects are neglected, the theory predicts a Lorentzian for S_(q,w) with a halfwidth Ω_(q), which we have determined as a function of the momentum transfer q for all values of q. The results are compared with recent neutron scattering experiments on deuterated polytetrahydrofuran and polystyrene in dilute solution in CS₂. It is found that the observed q dependence of Ω(q) is represented satisfactorily by the present theory with a bond length b of about 6.3 Å for polystyrene and 3.8 Å for polytetrahydrofuran, and a friction coefficient ζ = 4πη0b where η₀ is the viscosity of the solvent.     

Aggregation phenomena

We report on low-angle static light scattering measurements on colloidal aggregation of polystyrene latex particles. Measurements have been performed both at low and high monomer concentrations. Pure diffusion limited cluster aggregation (DLCA) have been investigated in the dilute regime. The predicted power-law growth of the radius has been observed. Spurious effects due to the presence of gravity are reported.Measurements on the high concentration samples show an unexpected and quite novel phenomenon. A peak in the scattering pattern whose position q_m moves towards smaller q-values and whose height grows in time has been observed. We have found that the scattering distributions can be scaled onto the same master curve with a scaling law strongly reminiscent of that working in the completely different case of spinodal decomposition.     

Aggregation behavior of thermo-responsive poly(2-oxazoline)s at the cloud point investigated by FCS and SANS

We have studied different thermo-responsive poly(2-oxazoline)s with iso-propyl (iPrOx) and n-propyl (nPrOx) pendant groups in aqueous solutions, where they exhibit lower critical solution temperature behavior. This paper focuses on the effect of the degree of polymerization, n, the concentration, c, in the dilute regime, and the presence of hydrophobic moieties. The cloud points were investigated as a function of the degree of polymerization, n, and of the polymer concentration, c. The aggregation behavior near the cloud point was studied by temperature-resolved small-angle neutron scattering and fluorescence correlation spectroscopy, i.e., a combination of ensemble and single molecule methods. We found that at the cloud points, large aggregates are formed and that the cloud points depend strongly on both, n and c. Diblock copolymers from iPrOx and nPrOx form large aggregates already at the cloud point of PnPrOx, and, unexpectedly, no micelles are observed between the cloud points of the two blocks. Gradient copolymers from iPrOx and n-nonyl-2-oxazoline (NOx) display a complex aggregation behavior resulting from the interplay between intra- and intermolecular association mediated by the hydrophobic NOx blocks. Above the cloud point, an intermediate temperature regime with a width of a few Kelvin was found with small but stable polymer aggregates. Only at higher temperatures, larger aggregates are found in significant number.     

Glass transitions in ionic polymers

The glass transitions of an ionic polymer in bulk have been studied as a function of the counterion for various homo- and copolymers. It is shown that the glass transition temperature can vary by as much as 530°C., from ?10°C. for the nonionic material to +520 for Ca²⁺ or Zn²⁺ substituted polymer. From simple electrostatic considerations, it is shown that a linear correlation should exist beween the glass transition and the ratio of the cation charge, q, to the internuclear distance, a, between cation and chain anion; for this particular material (the polyphosphate chain) the relation is T_g = 625(q/a) ?12 where q is in units of one electron and a is in A. If the data are interpreted in the light of the Gibbs-DiMarzio theory, it is seen that both the chain stiffness and the intermolecular energy increase in an approximately parallel manner as q/a increases.     

On the Chirality of Torus Curves and Knots

As is well known, a (p, q) torus knot is topologically equivalent to a (q, p) torus knot. The sign of the writhe number, which characterizes the topological chirality, must evidently be the same in both cases. We here show by an analytic criterion related to the torsion that a (p, q) torus curve and a (q, p) torus curve have opposite chirality, although they are not enantiomers. An erratum to this article can be found at     

The effect of different polymer length on water droplets of reverse AOT microemulsion

We study the effect of polyethylene glycol (PEG) on the dynamic and structure of water droplets at the reverse sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) microemulsion. The mixture of water and oil with anionic surfactant AOT can form microemulsion. The dynamic of microemulsion in the presence of PEG is investigated by photon correlation spectroscopy technique. We mainly focus on the variation of the translational diffusion behaviour as a function of the polymer concentration and polymer length scale. By increasing the content of the lowest PEG length scale (M_n = 285), the dynamic of microemulsion slows down. In addition, one relaxation process is distinguished for all polymer concentration. However, for the two higher polymer length scale (M_n = 2200 and 6000), two relaxations are observed and the dynamic of microemulsion speeds up. We used the small angle X-ray scattering technique to monitor the size and the polydispersity of the mixture system (AOT microemulsion/PEG).     

Effect of Hydrophilic/Hydrophobic Block Ratio and Temperature on the Surface and Associative Properties of Oxyethylene and Oxybutylene Diblock Copolymers in Aqueous Media

Recent development in dispersion science and technology demands block copolymers with a variable block length and composition. To highlight that purpose, the surface active, associative, colloidal, and thermodynamic behavior of three diblock copolymers having different hydrophilic to hydrophobic ratio is reported here. Using surface tension and light scattering measurements, the micellization and adsorption behavior of polyoxyethylene and polyoxybutylene diblock copolymers of the type E_mB_n have been analyzed. Critical micelle concentration (CMC) and related thermodynamic parameters like free energy (ΔG_mic), enthalpy (ΔH_mic), and entropy (ΔS_mic) of micellization were calculated from CMC value using the closed association model. Likewise, the surface active parameters, like surface excess concentration (Γ₂), area per molecule (A₂), and thermodynamic parameters such as free energy (ΔG_ads), enthalpy (ΔH_ads), and entropy (ΔS_ads) of adsorption of polymer at the air/water interface, were also calculated at various temperatures. Static and dynamic light scattering techniques were employed for the determination of the weight-average molar (M_w), association number (N_w), polymer–water interaction (A₂), and micellar size in terms of hydrodynamic radii (R_h) of copolymer micelles. The effect of block length and solution temperature on the surface and micellar properties of these copolymers was also investigated.     

Distribution functions and dynamical properties of stiff macromolecules

An analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky-Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well-known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q^8/3tp^1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.