Correlation Length Of Concentration Fluctuations Research Articles

Surface enrichment and interdiffusion in blends of semiflexible polymers of different stiffness.

A model for a mixture of two kinds of semiflexible polymers (A and B) with the same chain length (NA = NB = 32), but different persistence lengths, confined between parallel planar repulsive walls in a common good solvent is studied by molecular dynamics simulations. In the isotropic phase at low polymer concentrations, both polymers are repelled by the walls, and the system is anisotropic near the walls over a range controlled by the polymer linear dimensions. Close to the concentrations where in the bulk nematic order sets in, precursors of thick nematic layers at the walls are observed, strongly enriched by a stiffer component, which hence is depleted in the center of the slit pore. At larger concentrations, where in the bulk a uniformly mixed nematic phase occurs, the enrichment of B-chains at the walls is rather minor, extending over the scale of the transverse correlation length of concentration fluctuations, which is of the order of a few monomeric diameters only for the present model. In this ordered phase, both self-diffusion and interdiffusion of chains (in the direction perpendicular to the director) are found to be significantly slowed down in comparison to dilute solutions. Since equilibration times scale with the square of the slit thickness, incomplete equilibration is predicted when polymeric coatings on substrate containing polymers differing in stiffness are produced.

Carboxylic acids in aqueous solutions: Hydrogen bonds, hydrophobic effects, concentration fluctuations, ionization, and catalysis.

In the frequency range between 100 kHz and 2 GHz, ultrasonic absorption spectra have been measured for a series of carboxylic acids from formic to enanthic acid, including constitutional isomers. Also investigated have been the spectra for mixtures with water of short-chain formic, acetic, propionic, butyric, and isobutyric acid, in each case covering the complete composition range. The neat carboxylic acids feature two Debye-type relaxation terms with relaxation times between 5.6 and 260 ns as well as 0.14 and 1.4 ns, respectively, at room temperature. Depending on the composition, mixtures with water reveal an additional Debye relaxation term in the intermediate frequency range (acetic acid) or a term subject to a relaxation time distribution (propionic, butyric, and isobutyric acid). The relaxations of the neat acids are assigned to the equilibrium between monomers and single-hydrogen-bonded linear dimers and between linear and twofold-hydrogen-bonded cyclic dimers. The latter equilibrium is considerably catalyzed by hydronium and carboxylate ions. Several mixtures with water indicate one of the up to three Debye relaxations to reflect the protolysis of the organic acid. The term with underlying relaxation time distribution is due to noncritical fluctuations in the local concentrations. The Debye relaxations are evaluated to yield the parameters of the relevant elementary chemical reactions, such as the rate and equilibrium constants and the isentropic reaction volumes. A comparison of the correlation length of concentration fluctuations with data for other aqueous systems confirms the idea that the hydrophobic part of the organic constituent promotes the formation of a micro-heterogeneous liquid structure, whereas the hydrophilic moiety is of minor importance in this respect. The high-frequency limiting absorption suggests the equilibrium between conformers of linear dimers to contribute to the spectra well above the frequency range of measurements.

Partial Collapse and Reswelling of a Polymer in the Critical Demixing Region of Good Solvents

Using small-angle neutron scattering, we explored the conformational behavior of a polymer in a mixture of good solvents near their critical demixing temperature T(C). Experiments at full and zero average neutron contrast were used to study the correlation length of concentration fluctuations ξ and the radius of gyration R(g) of individual polymer coils as a function of temperature T. The results confirm a theoretically predicted partial collapse followed by reswelling of polymer coils to the original dimensions as T→T(C). Reswelling begins when ξ becomes comparable to the R(g) of the polymer.

Effect of Ionic Strength on Surface-Selective Patch Binding-Induced Phase Separation and Coacervation in Similarly Charged Gelatin−Agar Molecular Systems

Coacervate is defined as a polymer-rich dense phase, which remains in thermodynamic equilibrium with its low concentrated phase called the supernatant. The effect of ionic strength (I = 0-0.1 M NaCl) on the mechanism of surface patch binding-induced protein-polysaccharide interaction leading to complex coacervation, between agar (a polyanionic polysaccharide) and gelatin B (a polyampholyte protein), both having similar net charge, at a particular mixing ratio, [gelatin]/[agar] = 1, was studied at various temperatures (20-40 °C). The coacervation transition was probed by turbidity and zeta-potential measurements. The intermolecular association had the signature of surface-selective binding, and a model calculation could explain the potential energy of interactions operative in such processes. The thermo-mechanical features of the coacervates were found to be strongly dependent on ionic strength, which has been interpreted as originating from formation of salt-bridges between the biopolymers. The microstructure of the coacervate materials was analyzed using rheology and small angle neutron scattering (SANS) techniques, which probed the heterogeneity prevailing in the system that had characteristic length in the range 1.3-2.0 nm, and the same data yielded the correlation length of concentration fluctuations, which was estimated to lay in the range 2.4-4 nm. It is concluded that the coacervation transition driven by surface-selective binding is not influenced by the ionic strength of the solution, but the mobile ions participate in the structural organization of the interacting polyions in the coacervate.

The influence of electrostatic interaction on the structure and the shear modulus of heat-set globular protein gels.

Gels formed by the globular protein β-lactoglobulin after heat denaturation were studied using light scattering, turbidity and shear oscillation measurements. The structure of the gels was characterized in terms of the amplitude and the correlation length of concentration fluctuations. The strength of electrostatic interactions was varied by changing the pH in the absence of added salt or by changing the NaCl concentration at pH 7. A very strong increase of the heterogeneity of the gels was observed when decreasing the pH towards the isoelectric point or when increasing the salt concentration. The structural change was interpreted in terms of a decrease of the net repulsion between the growing aggregates leading to increased concentration fluctuations and finally microscopic phase separation. The elastic shear modulus increased with decreasing pH and showed a maximum as a function of the NaCl concentration. No direct correlation between the change in the structure and the elastic modulus was found.

Thermodynamic instability in supersaturated lysozyme solutions: effect of salt and role of concentration fluctuations.

Experimental and theoretical work has suggested that protein crystal nucleation can be affected by the separation of two metastable liquid phases with different local concentrations, or more specifically by critical density fluctuations. We measure the amplitude and correlation length of local concentration fluctuations by light scattering for supersaturated solutions of hen egg-white lysozyme (at pH 4.5 and at different NaCl concentrations, up to 7% w/v). By extrapolating the critical divergent behavior of concentration fluctuation amplitude versus temperature, we determine the spinodal line, that is the limit of stability. Cloud-point measurements are used to determine liquid-liquid coexistence, consistent with previous work. In the present work, which is an extensive study of off-critical fluctuations in supersaturated protein solution, we observe a nonclassical scaling divergent behavior of the correlation length of concentration fluctuations, thus suggesting that off-critical fluctuations may have a role in crystallization kinetics. To appropriately fit the spinodal data, an entropic term must be added to the van der Waals or to the adhesive hard-sphere model. We interpret this contribution as due to the salt-induced modulation of protein hydration.

Effect of Screening of Intermicellar Interactions on the Linear and Nonlinear Rheology of a Viscoelastic Gel

We report our studies of the linear and nonlinear rheology of aqueous solutions of the surfactant cetyl trimethylammonium tosylate (CTAT) with varying amounts of sodium chloride (NaCl). The CTAT concentration is fixed at 42mM and the salt concentration is varied between 0mM to 120mM. On increasing the salt (NaCl) concentration, we see three distinct regimes in the zero-shear viscosity and the high frequency plateau modulus data. In regime I, the zero-shear viscosity shows a weak increase with salt concentration due to enhanced micellar growth. The decrease in the zero-shear viscosities with salt concentration in regimes I I and III can be explained in terms of inter-micellar branching. The most intriguing feature of our data however, is the anomalous behavior of the high frequency plateau modulus in regime II (0.12 $\le \frac{[NaCl]}{[CTAT]} \le$ 1. 42). In this regime, the plateau modulus {\it increases} with an increase in NaCl concentration. This is highly counter-intuitive, since the correlation length of concentration fluctuations and hence the plateau modulus $G_{\circ}$ are not expected to change appreciably in the semi-dilute regime. We propose to explain the changes in regime II in terms of the unbinding of the organic counterions (tosylate) from the CTA$^{+}$ surfaces on the addition of NaCl. In the nonlinear flow curves of the samples with high salt content, significant deviations from the predictions of the Giesekus model for entangled micelles are observed.

Binary Contacts in Semidilute Solution: Good and ϑ Solvents

In this paper we show that the concentration dependence of the plateau shear elastic modulus and of the viscosity can be understood if two lengths, the correlation length of concentration fluctuations and the tube diameter, are considered. To interpret the temperature variation of the viscosity and of the self-diffusion coefficient with the solvent quality, one has to take into account the local viscosity to which monomers are sensitive. This concentration dependent local viscosity, deduced from neutron spin-echo measurements, is independent of the polymer molecular weights, solvent viscosities and Θ temperatures. The local viscosity decreases to reach the solvent viscosity value at high temperature, that is, under good solvent conditions. The role of the macroscopic concentration on a local scale, seems to indicate that, in semidilute Θ solutions, the polymers are transparent to each other, as far as dynamic properties are concerned.

Sharp Crossover of the Susceptibility in Polymer Solutions near the Critical Demixing Point

We have observed a sharp and nonmonotonic crossover of the susceptibility (osmotic compressibility) from mean-field to Ising critical behavior in semidilute solutions of polystyrene in deuterocyclohexane as the temperature decreases from the $\ensuremath{\Theta}$ region down to the critical temperature of the phase separation. We describe this crossover in terms of a competition between the long-range but finite intramolecular correlations of monomers in the polymer chain and the diverging correlation length of concentration fluctuations.

Temperature-concentration dependence of the correlation length of concentration fluctuations in liquid binary systems

An analysis is made of the correlation length of the concentration fluctuations in liquid binary systems over a wide range of temperature and composition. A quantitative relationship is obtained between the correlation length, the concentration, and the temperature. It is shown that the correlation length is determined by regions of different thermodynamic stability of a homogeneous solution, bounded by binodal and spinodal curves.

Hydrogen-bond effects induced by alcohol on the structure and dynamics of ionic reverse micelles

In this work we report how the structure of Zn(AOT) 2/H 2O/d-cyclohexane microemulsions is affected by the presence of alcohol (normal pentanol) molecules as cosurfactant. The systems are investigated by small-angle neutron scattering (SANS) and by Fourier transform IR (FTIR) spectroscopy. The SANS technique allows the study of the evolution of the size, the shape and the possible correlation length of concentration fluctuations as a function of water and alcohol content. Moreover FTIR spectra, in the OH stretching region, is quite sensitive to the structural changes of the water, induced by the polarization effects of the polar heads of the micelle surface and the positive counterions and by the presence of the alcohol.

Phase Separation Studies of Confined Thin Film Polymer Blends

ABSTRACTUsing video-optical microscopy and image analysis software, the morphological development of phase separation of polystyrene (PS) and poly(vinyl methyl ether) (PVME) blends is monitored for film thickness ranging from 200 to 700nm's. In the current studies, films are confined between glass slides. For blends having a PS volume fraction of 0.30 (the critical composition), the area fraction of the PS-rich minority phase, A, decreases more rapidly as film thickness decreases. At long times, the final A achieves a constant value which is less than the bulk value. The correlation length of concentration fluctuations increases more rapidly than the bulk scaling prediction, which suggests that wetting plays a significant role in the phase separation kinetics of thin films. Because of confinement, the shape of the PS-rich phase is anisotropic, flattened along the film direction. The confinement restricts the phase growth perpendicular to the film plane, and thus hinders the development of phase separation at very late stages.

Neutron and light scattering studies of polymer blends and block copolymers

AbstractThe structure of compatible polymer mixtures and its temperature dependence can be well described in many cases by the mean‐field approximation. Deviations with regard to the temperature dependence of the correlation length of concentration fluctuations can be explained by taking into account the spatial structure of the interaction potential. Concentration fluctuations and the microphase separation in diblock copolymers are in good agreement with theories based on the random phase approximation. In the two‐phase region the temperature dependence of the scattered X‐ray or neutron intensity is governed by the difference in the thermal expansion coefficients of the two components of the diblock copolymer. Photon correlation spectroscopy (PCS) yields valuable information on the concentration dependence of the mutual diffusion coefficient DAB.

Critical demixing in fluid bilayers of phospholipid mixtures. A neutron diffraction study

Critical lateral demixing in fluid bilayers of lecithins differing in chain length by four CH2 groups is established for the first time by small angle neutron scattering, exploiting the high scattering contrast between deuterated and protonated lipids. Good agreement with the Ornstein–Zernicke theory allows one the estimation of the correlation length of concentration fluctuations. The interesting aspect of critical demixing phenomena is their possible role in membrane processes such as facilitated trans-membrane transport, long range protein–protein interaction, and the control of enzyme activity.

Temperature‐Jump Experiments with a Binary Critical Mixture Near the Critical Temperature

AbstractThe time course of turbidity of critical isobutyric acid/water mixtures is measured after perturbing the internal equilibrium of the mixture by a small temperature jump (e.g. δT ≃ 0.05 K). The experiments are carried out as function of the temperature distance from the critical temperature (0.1 K < T – Tc < 0.6 K). A mechanism for the relaxation of turbidity change is proposed having a relaxation time of the order of ζ2 D−1 with ζ = ζ0ϵ−v and D = D0ϵ−v (ζ = correlation length of concentration fluctuations, D = mutual diffusion coefficient, v = 2/3, ϵ = (T* – Tc)/Tc, T* = T + δT/2). The experimental data are in qualitative agreement with the proposed mechanism.