Dilute Concentration Regime Research Articles

Elastic interactions and stability of clay-filled lamellar phases

High aspect ratio clay particles dispersed in a lamellar matrix composed of a block copolymer or a lyotropic smectic are expected to orient with the lamellae. Under such conditions, the smectic medium transmits elastic forces among particles in addition to the usual forces produced by dispersion and electrostatic interactions. We compute these elastic forces and explore their influence on the thermodynamics of lamellar-clay dispersions. It turns out that the large aspect ratio of the clay implies a long range of interaction at the two particle level. Consequently, virial expansions break down at very low loadings of particles. We examine the thermodynamic behavior of assemblies of flexible and rigid clay plates in both dilute and semidilute concentration regimes. Our results should have implications for the design of nanocomposites formulated with block copolymers and lyotropic liquid crystals.

Collapse of flexible polyelectrolytes in multivalent salt solutions

The collapse of flexible polyelectrolytes in a solution of multivalent counterions is studied by means of a two state model. The states correspond to rodlike and spherically collapsed conformations. We focus on the very dilute monomer concentration regime where the collapse transition is found to occur when the charge of the multivalent salt is comparable (but smaller) to that of the monomers. The main contribution to the free energy of the collapsed conformation is linear in the number of monomers N, since the internal state of the collapsed polymer approaches that of an amorphous ionic solid. The free energy of the rodlike state grows as N ln N, due to the electrostatic energy associated with that shape. We show that practically all multivalent counterions added to the system are condensed into the polymer chain, even before the collapse.

Microstructures formed in aqueous solutions of a hydrophobically modified nonionic cellulose derivative and sodium dodecyl sulfate: a fluorescence probe investigation

The association behavior of hydrophobically modified ethyl hydroxyethyl cellulose (HM-EHEC) and its interaction with the anionic surfactant sodium dodecyl sulfate (SDS) has been studied in the dilute concentration regime. Steady-state fluorescence probe techniques have been utilized to obtain microstructural information of the system properties and combined with macroscopic bulk information from equilibrium dialysis experiments in order to determine binding isotherms of SDS to HM-EHEC. HM-EHEC was found to self-associate and form polymeric micelles in semi-dilute aqueous solutions. c ∗ for the self-association process was determined to be approximately 0.4%. The microviscosity of the polymeric micelles is much higher, and the micropolarity slightly higher, than that of ordinary SDS micelles. The onset of interaction between HM-EHEC and SDS was evidenced by a simultaneous strong increase in microviscosity and decrease in micropolarity upon successive addition of SDS. There is a minor, noncooperative SDS binding to the HM-EHEC starting from low concentrations of SDS (<5 mM) followed by a highly cooperative binding region at SDS concentrations ≥5 mM. The polymer–surfactant aggregates are rigid and hydrophobic with a maximum in microviscosity in the noncooperative binding region at a very low degree of SDS-adsorption.

Electrical conductivity of isotropic fibre suspensions

The electrical conductivity of a quiescent isotropic fibre suspension is measured for a concentration range nL 3 = 0.1 to 4, where n is the number density of fibres and L is the fibre length. In the dilute concentration regime, for which nL 3 ≪ 1, our experiments agree with available theoretical predictions.

Mass transport in polyelectrolyte solutions

The self-diffusion coefficients of the three components of a salt-free heavy-water solution of polymethacrylic acid, completely neutralized with tetra-methylammonium hydroxide, were measured over a broad concentration range. Three concentration regions were observed for the self-diffusion of both the polyions and the counterions. At polyion concentrations below 0.01 mol monomer kg-1, the dilute concentration regime for the polymer, the polyion self-diffusion coefficient approaches the self-diffusion coefficient of a freely diffusing rod upon dilution. At polyelectrolyte concentrations above 0.1 mol monomer kg-1, the self-diffusion coefficients of the solvent, the counterions and the polymer decreased with concentration, suggesting that this decrease is due to a topological constraint on the motions of the components. In the intermediate-concentration region, the self-diffusion coefficients of the polyions and the counterions are independent of the concentration. The polyion dynamic behaviour is, in the intermediate- and high-concentration regions, reasonably well described by that of a hard sphere, with a radius of 3.7 nm. A correct prediction for the solvent dynamics is given by the obstruction effect of this hard sphere on the solvent. The relative counterion self-diffusion coefficient is predicted almost quantitatively over the entire concentration range with the Poisson-Boltzmann-Smoluchowski model for the spherical cell, provided that the sphere radius and the number of charges are chosen appropriately (approximately the number of charges in a persistence length). Using this model, the dependence of the counterion self-diffusion coefficient on the ionic strength, polyion concentration and counterion radius is calculated quantitatively over a large concentration range.

Concentration Fluctuations in a Polymer Solution under a Temperature Gradient

We have performed small-angle Rayleigh light-scattering measurements in polymer solutions under various externally applied temperature gradients. Our experiments confirm the existence of an enhancement of the concentration fluctuations. The nonequilibrium concentration fluctuations are proportional to $(\ensuremath{\nabla}T{)}^{2}{/k}^{4}$, where $\ensuremath{\nabla}T$ is the applied temperature gradient, and $k$ is the wave number of the fluctuations. The measured strengths of the nonequilibrium fluctuations in the dilute and semidilute concentration regime agree with the strengths calculated from fluctuating hydrodynamics.

Dynamic light scattering of dilute PVA-borax aqueous solutions

Poly(vinyl alcohol)-borate (PVA-borate) complexes in dilute aqueous solutions were investigated by dynamic light scattering (DLS). Two relaxation modes obtained, were scattering vector-q2 dependent and diffusive. The amplitude of slow mode was independent of borax concentration. In the very dilute PVA concentration regime ( [PVA] < 5 g/L), the PVA di-diol-borate complexation was dominated by intra-molecular reaction, and the fast mode correlation length ςf which corresponds to the polymer chain dimension increased rapidly with borax concentrations lower than 0.06 M, and reached an asymptote in the higher borax concentration regime. However, for a dilute PVA aqueous solution with higher PVA content (i.e., [PVA] = 9 g/L), both intra-and inter-molecular PVA di-diol-borate complexations might happen. The chain expansion and shrinkage of PVA-borate complex with increasing borax concentration was observed due to the balance between the electrostatic repulsion of the charged diol-borate complexes and the intra-molecular crosslink induced by the intra-molecular di-diol-borate complexation.

Molar Mass Dependence of the Apparent Diffusion Coefficient of Flexible Highly Charged Polyelectrolytes in the Dilute Concentration Regime

In this study dynamic light scattering experiments have been performed on the flexible highly charged polyelectrolyte sodium poly(styrenesulfonate). The apparent diffusion coefficient was determined for five molar masses at a fixed ionic strength of 0.1 M at dilute polyelectrolyte concentrations. The apparent diffusion coefficients extrapolated to zero polyelectrolyte concentration were compared with theoretical D0 values calculated with a theoretical procedure based on the translational friction coefficient of the wormlike chain model of Yamakawa and Fujii. With the excluded volume theories of Fixman and Skolnick, and Barrett, the electrostatic persistence length according to Le Bret, and the counterion condensation theory of Manning, a satisfactory agreement was found for all molar masses. From the polyelectrolyte concentration dependence of the apparent diffusion coefficient, the diffusion second virial coefficient could be obtained. The molar mass dependence of the diffusion second virial coefficient was found to be linearly proportional to the molar mass and could be interpreted with small ion−polyion coupled mode theories.

Dynamic Light Scattering of a Flexible Highly Charged Polyelectrolyte in the Dilute Concentration Regime

The diffusion behavior of the flexible highly charged polyelectrolyte sodium poly(styrenesulfonate) has been studied extensively with dynamic light scattering in the dilute concentration regime. The apparent diffusion coefficient was determined for one molar mass and five ionic strengths at dilute polyelectrolyte concentrations. The apparent diffusion coefficients extrapolated to zero polyelectrolyte concentration were compared with theoretical D0 values calculated with a theoretical procedure based on a wormlike chain model, including the persistence length, the excluded volume, and counterion condensation. A satisfactory agreement was found. From the polyelectrolyte concentration dependence of the apparent diffusion coefficient, the diffusion second virial coefficient could be obtained. The ionic strength dependence of the diffusion second virial coefficient kd was found to be linearly proportional to 1/cs, in agreement with the prediction of small ion−polyion coupled mode theories.

On the correlation between the viscosity of partially hydrolyzed polyacrylamide solution and the diffusion coefficient in the semidilute concentration regime

AbstractThe solution viscosity of neutral polyacrylamide (PAM), the partially hydrolyzed polyacrylamide (70% HPAM), and polyacrylic acid (PAA) were measured concurrently with the apparent diffusion coefficient in the dilute and semidilute concentration regimes. We identified the scaling relation η − ηs = A/D in the semidilute regime, where η is the solution viscosity, ηs is the solvent viscosity, D is the coefficient of the slow diffusion mode obtained from dynamic light scattering, and A is a prefactor found to have a unique value of ∼1.0 × 10−8 cP cm2/s. The scaling relation as well as the prefactor are independent of the the ionic strength, the solvent quality, the molecular weight, the charge density, the polyelectrolyte, and salt concentrations. For the neutral PAM, the product [η – ηs]D is proportional to the polyelectrolyte concentration Cp, consistent with Rouse theory and previous experimental findings.

Laser Light Scattering of Model Casein Solutions: Effects of High Temperature

Static and dynamic light scattering studies of sodium cascinate solution in a Pipes-KCl buffer at pH 6.75 and a constant ionic strength in the dilute concentration regime are presented. In the absence of calcium ions, a bimodal distribution with comparable scattering intensity contributions has been consistently observed by using the CONTIN method to analyze the dynamic light scattering data. However, based on the weight fraction of submicelles and that of the aggregates, the casein solution remains overwhelmingly in the submicellar form with sizes in the 20-nm range. The calcium-induced aggregation of these casein submicelles appears to be a time-dependent process. After reaching equilibrium, two aggregate fractions of different average sizes (about 90 and 350 nm) bare been detected in the casein solution. Casein submicelles are generally stable at high temperatures. But, a prolonged ultrahigh-temperature treatment (10 min at 140°C) can fully transform casein submicelles into very large aggregates. Calcium-induced aggregates exhibit reduced thermal stability. Modification of casein with iodoacetic acid to block the SH groups gives the protein a stronger resistance to calcium-induced aggregation, but significantly reduces its stability at high temperatures when the calcium ions are present.

Aggregation Trends in Some Macromolecules by Photon Correlation Spectroscopy

The experimental results for heat aggregation behavior in some macromolecules of significant biological importance, e.g., phycobilisomes (PBS) and insulin are reported. The heat aggregation studies on PBS were performed only in the neutral medium pH 7.5 and very dilute concentration regime (0.23 to 1.8 gL-1). The aggregation and dissociation trends in PBS were found to be linear with temperature upto 55°C. Insulin also in very dilute concentration showed the linear aggregation tendency with temperature up to 35°C but on temperature reversal (self-cooling) insulin showed the hysteresis like behavior unlike the PBS. The hysteresis like behaviour at pH 7.5 was found to be predominantly large. In both cases the polydispersity observed in correlation spectra was quite low.

Heat aggregation studies of phycobilisomes, ferritin, insulin, and immunoglobulin by dynamic light scattering

Dynamic laser light scattering studies on the heat aggregation behavior of phycobilisomes (PBS), ferritin, insulin, and immunoglobulin (IgG) in dilute aqueous solutions has been reported. Except for PBS, results are reported for heat aggregation trends in these proteins for three different pH environments (4.0, 7.5, 9.1). For PBS, studies were performed only in the neutral buffer medium (pH 7.5). The experiments were performed in the very dilute concentration regime (between 0.23 and 1.8 gL-1). For all these samples heat aggregation and dissociation trends were found to be linear with temperature. Upon temperature reversal (self-cooling), hysteresis-like behavior observed in insulin was found to be predominantly large at pH 7.5. PBS, ferritin, and IgG showed no such behavior at any of three pH values, and retraced their path of aggregation while dissociating on temperature reversal. Heat aggregation and dissociation processes in ferritin were found to be independent of pH. The IgG samples showed smooth aggregation tendency only up to 35 degrees C in the buffer media pH 4.0 and 9.1, whereas for pH 7.0 the same could be observed until 60 degrees C. Low polydispersity in the correlation spectra was observed in case of all these samples.

Orientational dispersion of fibers in extensional flows

A kinetic theory is presented that predicts the dispersion of particle orientation, solely as a result of hydrodynamic interactions, about the principal axis of extension in uniaxial and planar extensional flows. The mean-squared displacement of the orientation vector is calculated in both the asymptotic dilute and semidilute concentration regimes. In the dilute regime (where nL3≪1, with n the fiber number density and L the fiber length) it is found that the mean-squared displacement is O[nL3/ln2(r)], where r is the fiber aspect ratio. For semidilute suspensions (where nL3≫1) it is predicted that the dispersion is O[ln(nL3)/nL3]. Thus the dispersion increases as the concentration is increased from infinite dilution and then ultimately decreases in the semidilute regime. The physical reasons for this behavior are discussed and, in particular, the semidilute scaling is demonstrated to be a consequence of the short-range particle screening that develops in semidilute suspensions [Phys. Fluids A 1, 3 (1989); 2, 7 (1990)]. The effect of this orientational dispersion on the material properties of fiber composites is also considered.

The hydrodynamic stress in a suspension of rods

A theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers. The theory is based on a diagrammatic representation of the multiple scattering expansion for the averaged Green’s function as developed in the authors’ previous work on the heat and mass transfer properties of fiber dispersions [Phys. Fluids A 1, 3 (1989)]. The ‘‘best one-body approximation’’ is used to calculate the wavenumber-dependent, ensemble-averaged stress for both aligned and isotropically oriented fiber dispersions. Both the dilute and semidilute concentration regimes are considered. The effective viscosity is calculated as a limit unit of the previously obtained wavenumber-dependent properties. In the semidilute concentration regime the scaling form originally suggested by Batchelor [J. Fluid Mech. 46, 813 (1971)] is recovered for both orientation distributions and its relation to short range ‘‘screening’’ is discussed. Corrections to this result in a ‘‘semidilute expansion’’ for small volume fraction are calculated and the dependence of these corrections on orientation distribution and particle shape is demonstrated.

Shear rate dependence of the viscosity of cellulose nitrate solutions in the dilute concentration regime revisited

AbstractA detailed rheological study of cellulose nitrate in ethylacetate had been carried out in the dilute concentration (c) regime, covering a degree of polymerization (DP) range between 300 &lt; DPη &lt; 7000 and shear rates (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}) between 100 s−1 &lt; \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} &lt; 2000 s−1. The results show a strong dependence of the transition Newtonian to non‐Newtonian behavior on the three variables \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}, DP, and c, similar to that found recently on solutions of synthetic polymers. Emphasis has been put on the critical concentrations corresponding to the standard shear rate 1000 s−1 to correspond to the standard conditions (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} ≅ 1000 s−1; 0.3 &lt; [η] · c &lt; 0.6; DS = 2.90 ± 0.02) proposed for the determination of the intrinsic viscosity [η] of cellulose nitrates. It is shown that solutions with concentrations adjusted according to the above given conditions still exhibit Newtonian behavior, up to the highest range of DP. It follows, therefore, that applying the standard conditions, an extrapolation to \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = 0 as has been proposed often for the intrinsic viscosity determination of cellulose nitrate is not advisable and results in considerable error. Considering the relationship between [η] and DP, the present results indicate that the decrease of the exponent (a) from a = 1.0 to a = 0.76, taking place above a DP ≅ 1000, is not a consequence of the applied shear rate but rather of the molecular properties of the solutes themselves.

Influence of some factors affecting the stationary value of the electric birefringence of aqueous solutions of poly(styrene sulphonates) in the presence of 0.01 mol dm–3 NaCl

The stationary values of the electric birefringence obtained by applying rectangular pulses to aqueous Na-poly(styrene sulphonates)–0.01 mol dm–3 NaCl solutions have been studied for five different samples of polyelectrolytes ranging from Mw= 1.8 × 105 to 12 × 105 g mol–1. The corresponding Kerr constants determined at low electric field strengths were not linearly dependent on the polyelectrolyte concentration in the concentration region explored, which covered both the the dilute and semi dilute regimes. The specific Kerr constant at infinite dilution increased with molar mass to the power 0.7. In the semi-dilute regime a scaling law was found of the form (K/K*)∼(C/C*)0.8, where K* is the Kerr constant in the dilute concentration regime extrapolated to the critical concentration C*. This concentration and molar mass dependence cannot yet be fully understood in terms of proposed theories. The study of the field strength dependence of the electric birefringence indicates that smaller parts of the chain contribute to the orientation mechanism responsible for the induced macroscopic anisotropy. It is likely that progressive deformation of the more or less flexible chains by high electric fields also plays a role.

An empirical correlation for polymer self‐diffusion data in the dilute and semidilute concentration regimes

AbstractAn expression is presented which can be used to correlate and predict, in an empirical fashion, polymer self‐diffusion coefficients in solution over a wide range of concentrations and molecular weights, and whose parameters can be established with a minimal amount of data. Predictions thus made have been found to agree well with the limited amount of available experimental data over the entire concentration‐molecular weight spectrum studied to date. This is in marked contrast to other available expressions, whose validity is confined to a narrow range of concentrations and/or molecular weights.

Elastic neutron scattering results on C 24Rb(D 2) x in the dilute concentration regime

We have studied the structure of D 2 molecules physisorbed in an oriented pyrolytic C 24Rb sample at 80 K by elastic neutron scattering. The low temperature diffraction pattern of pristine C 24Rb changed dramatically upon sorption of D 2 molecules, and is consistent with the assumption of deuterium molecules decorating lattice gas-like interstitial sites within the alkali intercalant layer. These are presumably triangular sites associated with the alkali low temperature close-packed superstructure.

Application of scaling concepts to sedimentation phenomena in semidilute macromolecular solutions

AbstractSedimentation velocity data on polystyrene in a good solvent (toluene) and in a theta solvent (cyclopentane), over a large concentration range are reported. Under good‐solvent conditions the exponent β in the apparent scaling law describing the concentration dependence of the sedimentation coefficient (s ∝ cβ) in the semidiiute region is found to be concentration dependent. However, a power law fit to data for the highest molecular weight (M = 20.6 × 106) in the concentration region (c &lt; 2 kg m−3) yields a value β = −0.59, somewhat smaller than that (−0.54) predicted theoretically. This discrepancy and the observed curvature in logs vs. logc at higher concentrations are discussed. Under theta‐solvent conditions, on the other hand, the concentration dependence of s in the semidilute regime can be represented by a simple power law, with β = −1.0, in excellent agreement with the theoretical prediction. The crossover concentration c*, separating the dilute and semidilute concentration regimes, was found to be well defined and located at c = 1/[η]. c* varies with molecular weight as M−0.73 and M−0.50 under good‐solvent and theta‐solvent conditions, respectively.