Semidilute Concentration Regime Research Articles

Continuous Crossover from the Dilute to Semidilute Concentration Regime in Spherically Confined Polymers

Continuous Crossover from the Dilute to Semidilute Concentration Regime in Spherically Confined Polymers

Rigid rod particle like viscoelastic responses of poly(vinylidene fluoride) in N-methylpyrrolidone solution

A systematic study was performed on the dynamic viscoelastic properties of N-methylpyrrolidone (NMP) solutions of poly(vinylidene fluoride) (PVDF) samples with a wide range of weight average molar masses (Mw) from 140 to 3300 kg mol−1 over a temperature range of −24 to 35 °C in the dilute to semidilute concentration (c) regime in this study. In previous studies under extremely dilute conditions, it was confirmed that PVDF molecules behave as isolated highly elongated rigid rods, and the average particle length (⟨L⟩) and diameter (⟨d⟩) for different PVDF samples were precisely determined. The fundamental viscoelastic parameters used to analyze the dynamics of PVDF molecules dissolved in NMP were precisely determined, including the zero-shear shear viscosity (η0), the steady state compliance (Je), the average relaxation time (τw), and the activation energy (E*v) of τw in this study. E*v increased stepwise above c values corresponding to the reciprocal of the intrinsic viscosity ([η]−1) for different solutions, independent of Mw, showing that contact or the formation of entanglements between PVDF molecules causes the increase in E*v. Je−1 was found to be proportional to the number density of PVDF molecules (ν = cNAMw−1, where NA denotes the Avogadro constant) over the entire investigated v range, irrespective of Mw and the presence of entanglements between PVDF molecules. The reduced specific viscosities, ηspNA⟨L⟩3(Mw[η])−1, were reasonably described as a universal function in the parameter ν⟨L⟩3 over the entire investigated range, and ηspNA⟨L⟩3(Mw[η])−1 ∝ (ν⟨L⟩3)3 was found over the region 102 < ν⟨L⟩3 < 103, irrespective of Mw.

Depletion interaction mediated by semiflexible polymers.

We present a simple mean-field theory to describe the polymer-mediated depletion attraction between colloidal particles that accounts for the polymer's chain stiffness. We find that for fixed polymer radius of gyration and volume fraction, the strength of this attraction increases with increasing chain stiffness in both dilute and semidilute concentration regimes. In contrast, the range of attraction monotonically decreases with chain stiffness in the dilute regime, while it attains a maximum in the semidilute regime. The obtained analytical expressions for the depletion interaction were compared with numerical self-consistent field lattice computations and shown to be in quantitative agreement. From the interaction potential between two spheres, we calculated the second osmotic virial coefficient B2, which appears to be a convex function of chain stiffness. A minimum of B2 as a function of chain stiffness was observed both in the numerical self-consistent field computations and the analytical theory. These findings help explain the general observation that semiflexible polymers are more effective depletants than flexible polymers and give insight into the phase behavior of mixtures containing spherical colloids and semiflexible polymers.

Orientation dynamics of anisotropic and polydisperse colloidal suspensions

Small-angle light scattering (SALS) is employed to determine in situ microstructural changes of polydisperse colloidal suspensions under capillary flow. Titanium dioxide (rod-like) bundles and kaolinite nanoclay (platelet) flake-like stacks of particles are suspended in a Newtonian fluid to explore the effects of shape anisotropy. Subjecting the systems to a startup test in a flow cell in Stokes's regime, the evolution of the anisotropy factor (AF), and the average orientation angle (χ) of particles vs strain is probed at different averaged Péclet (Pe¯) numbers. Dilute and semi-dilute concentration regimes are explored in a capillary flow. Moving in the vorticity direction, we show significant changes in χ due to the gradient in shear rate in the capillary flow, while no cross-sectional flow migration was exhibited. In these polydisperse colloidal suspensions, two characteristic stages are observed: initial particle alignment and subsequent orientational demixing. Probing the velocity–vorticity (xy) plane, an initial particle alignment in the flow direction at high Pe¯ (> 1) occurs, is demonstrated by an elliptical SALS pattern, and then, an increase in AF is observed due to particles' phase mixing. This behavior is then followed by a breakdown in structure and loss of particle alignment due to orientational demixing. The evolution of the average orientation angle of particles in the xy plane can be clearly observed through these two stages by the help of high-resolution SALS contours. These experimental findings provide novel insights into the flow–microstructure relationship of polydisperse colloidal suspensions for the optimization of many industrial processing schemes.

The depletion thickness in solutions of semi-flexible polymers near colloidal surfaces: analytical approximations.

We derive a simple, yet accurate approximate mean-field expression for the depletion thickness δsf of a solution of dilute semi-flexible polymers next to a hard surface. In the case of a hard wall this equation has the simple form δsf = δ0[1 − tanh(psf/δ0)], where psf accounts for the degree of flexibility and δ0 is the depletion thickness in the case of fully flexible polymers. For fixed polymer coil size, increasing the chain stiffness leads to a decrease in the depletion thickness. The approach is also extended to include higher polymer concentrations in the semidilute regime. The analytical expressions are in quantitative agreement with numerical self-consistent field computations. A remarkable finding is that there is a maximum in the depletion thickness as a function of the chain stiffness in the semidilute concentration regime. This also means that depletion attractions between colloidal particles reach a maximum for a certain chain stiffness, which may have important implications for the phase stability of colloid–polymer mixtures. The derived equations could be useful for the description of interactions in- and phase stability of mixtures of colloids and semi-flexible polymers.

Polymer Induced Gelation of Aqueous Suspensions of Cellulose Nanocrystals.

We investigated the gelation of cellulose nanocrystals (CNCs) in polyelectrolyte and neutral polymer solutions. Cellulose nanocrystals (CNCs) with half-ester sulfate groups produced by acid hydrolysis of wood pulp were used in this study. The microstructure of CNCs/polymer suspensions was investigated in semidilute concentration regimes by selecting carboxymethyl cellulose (CMC700) as an anionic polymer and poly(ethylene oxide) (PEO600) as a neutral polymer solution. Together with quartz crystal microbalance with dissipation monitoring (QCM-D), rheology, scanning electron microscopy (SEM), and cryo-transmission electron microscopy (cryo-TEM), we characterized CNCs-polymer interactions, the suspension microstructure, and the macroscopic gel flow. Significant viscosity increases at low shear rates coupled with high shear-thinning behaviors were observed in CNC colloid-CMC700 polymer mixtures, but not those CNCs in PEO600 solutions. The apparent differences between CNCs-CMC700 and CNCs-PEO600 mixtures were due to their chain confirmations. On the basis of the evaluations from STEM, cryo-TEM, and polarized optical microscopy, we proposed that the excess CMC700 molecules in solutions result in the depletion of CNCs and the formation of anisotropic domains.

Determination of a critical separation concentration for associative polymers in porous media based on quantification of dilute and semi-dilute concentration regimes

Hydrophobic interactions are an inherent property of associative polymers which results in the formation of molecular aggregates. The loss of hydrophobic interactions under reservoir conditions have been reported, and this results in increased fluid – rock interaction effect such as adsorption. However, existing adsorption studies only reports the interaction of individual molecules with rock surface without taking into account mechanically retained molecular aggregates in narrow pores. The implication of this is a reduction in associative effect between polymer molecules during transport in a porous media. In this work, the minimization of this phenomenon and sustenance of the interaction network was studied through a theoretically defined dimensionless parameter for the quantification of molecular interactions in the various polymer concentration regimes. It was established in this work that associative polymers exhibit a critical separation concentration during propagation in a porous media under given reservoir conditions. This critical separation concentration marks the concentration beyond which large molecular aggregates constituting the hydrophobic network is sterically excluded and retained in narrow pore spaces. This separation phenomenon was predicted to occur when the proportion of molecular interactions arising from hydrophobic and intramolecular interactions are equal. Thus, the balance in the molecular interactions in the semi – dilute concentration regime was identified as key in minimizing the loss of hydrophobic interactions to aggregate retention and optimizing its sustainability in a porous media. Consequently, a novel approach was developed based on this knowledge for the transport of associative polymers at which these hydrophobic interactions are sustained. It was demonstrated that propagating associative polymers using this approach ensured the sustainability at concentrations below the critical separation concentration tend to maximize the hydrophobic interaction network with minimal loss of polymer chains retention mechanisms.

Combining particle tracking microrheology and viscometry for the study of DNA aqueous solutions.

We use video particle tracking microrheology (VPTMR) in order to investigate the viscoelasticity of salmon DNA and correlate it to its steady-flow shear-thinning viscosity. Aqueous solutions of DNA are tested in a wide concentration range from the dilute to the semidilute unentangled concentration regime. The observed mean squared displacement shows power-law scaling with lag-time which is equivalent to power-law behavior of the complex modulus as a function of frequency that is, |G* (ω)| = S ∙ ω α . The relaxation exponent α changes abruptly with concentration in the semidilute regime from about 1 to about 0.5 which is the exponent predicted by the Rouse model. The quasi-property S follows the scaling of viscosity for uncharged polymers near θ-conditions in the semidilute regime that is, with νeff = 0.50 - 0.51. The shear-thinning exponent observed by viscometry increases gradually towards the value of 0.5 which has been predicted for Rouse chains under flow. Our findings are in agreement with recent studies of DNA solutions where DNA is treated as a model polymer and addresses the low-molar mass regime of DNA viscoelasticity. This work demonstrates that the combination of passive particle tracking with viscometry can provide a complete picture on the viscoelasticity of DNA-based biopolymer materials.

Oscillating grid turbulence in shear-thinning polymer solutions

Oscillating grid apparatuses are well known and convenient tools for the fundamental study of turbulence and its interaction with other phenomena since they allow to generate turbulence supposedly homogeneous, isotropic, and free of mean shear. They could, in particular, be used to study turbulence and mass transfer near the interface between non-Newtonian liquids and a gas, as already done in air-water situations. Although frequently used in water and Newtonian fluids, oscillating grid turbulence (OGT) generation has yet been rarely applied and never characterized in non-Newtonian media. The present work consists of a first experimental characterization of the flow properties of shear-thinning polymer (Xanthan Gum, XG) solutions stirred by an oscillating grid. Various polymer concentrations are tested for a single grid stirring condition. The dilute and semidilute entanglement concentration regimes are considered. Liquid phase velocities are measured by Particle Image Velocimetry. The existing mean flow established in the tank is described and characterized, as well as turbulence properties (intensity, decay rate, length scales, isotropy, etc.). OGT in dilute polymer solutions induces an enhanced mean flow compared to water, a similar decay behavior with yet different decay rates, and enhanced turbulence large scales and anisotropy. In the semidilute regime of XG, turbulence and mean flows are essentially damped by viscosity. The evolution of mean flow and turbulence indicators leads to the definition of several polymer concentration subregimes, within the dilute one. Critical concentrations around 20 ppm and 50 ppm are found, comparable to drag reduction characteristic concentrations.

Structure of polyvinylpyrrolidone aqueous solution in semi-dilute regime: Roles of polymer-surfactant complexation

The effect of sodium bis (2-ethylhexyl) sulfosuccinate (AOT) addition on the structure of polyvinylpyrrolidone (PVP) aqueous solution, in dilute and semi-dilute regimes, has been investigated at 25 °C. The intrinsic viscosity, Huggins constant, Flory exponent and the Mark-Houwink-Sakurada coefficient were deduced by viscosimetry. The structure of PVP (MW = 40.000 g/mol) aqueous solution in semi-dilute regime was described according the blob model. The monomer size, the density of monomer, the correlation length and the number of monomer in each blob were determined. The PVP-AOT interaction in water was studied in dilute and semi-dilute concentration regime of the polymer by electrical conductivity. A complexation occurs between polymer and surfactant independently on the concentration regime, where the complex nature depends on surfactant concentration. The overlapping concentration of PVP-AOT aqueous solution increases with increasing AOT concentration from 0 to 0.6 g/dl. The Flory exponent decreases from 0.545 to 0.509 and the Mark-Houwink-Sakurada coefficient decreases from 0.636 to 0.528 g/dl. The effect of AOT complexation with PVP in water was also discussed according the blob model. At the overlapping concentration, the density of monomers and the correlation length decrease with increasing surfactant concentration. The density of monomers increases from its value at the overlapping concentration as the polymer concentration increases at the semi-dilute regime. However, the monomer size, the correlation length and the number of monomer in each blob decrease from their values at the overlapping concentration as the polymer concentration increases.

Structure–property relationships of the thermal gelation of partially hydrolyzed polyacrylamide/polyethylenimine mixtures in a semidilute regime

In this work, the structure–property relationships of the thermal gelation of partially hydrolyzed polyacrylamide (PHPA) and polyethylenimine (PEI) mixtures were investigated under realistic conditions of temperature (80 °C) and salinity (total dissolved solids = 3.4 g/l) of the Algerian reservoir (Tin Fouye Tabankort) prior to a conformance control application. The reactants were characterized with regard to their hydrolysis degree or branching degree using 13C-nuclear magnetic resonance, and viscosity–average molecular weights ($$ \bar{M}_{\text{v}} $$) were estimated using the Mark–Houwink equation and intrinsic viscosities measurements. The polymers had molecular weights that varied from 5 to 10 × 106 g/mol for PHPAs with initial hydrolysis degrees between 6 and 20 mol%, while the molecular weights of the PEI were between 2 and 67 × 104 g/mol with a constant branching degree of 57–59. Consequently, the effect of steady shear on the gelation time was investigated followed by the effect of reactant concentrations, the polymer and cross-linker molecular weights, the polymer’s hydrolysis degree, the temperature and the initial pH. All experiments were conducted in a semidilute concentration regime while maintaining practical initial gelant viscosities. As a result, the gelation time was found to decrease with reactant concentrations, molecular weights and temperature (Ea = 62 kJ/mol) and to increase with hydrolysis degree.

Characterizing droplet breakup rates of shear-thinning dispersed phase in microreactors

A two-phase flow predictive model with the integration of conservative level-set method (LSM) and Carreau-Yasuda constitutive equation was developed herein. The LSM was chosen as a potential interface capturing scheme for elucidating the interfacial phenomena including insight into the mechanism of shear-thinning droplets. In present paper, the dynamics of shear-dependent droplet emergence, growth, detachment and translocation in a Newtonian microsystem were examined via computational fluid dynamics (CFD) analysis. Dilute sodium carboxymethylcellulose (Na-CMC) solution was treated as dispersed phase (70 mPa.s < ηo < 10.2644 Pa.s) whereas the olive oil (68 mPa.s) was designated as continuous phase. Visualisation experiments were carried out and these laboratory data were used to validate the simulation results. Detailed 2D simulations were presented to examine systematically the impact of fluid properties on the droplet breakup rate at predefined flow rate ratio, Q of 0.05. The results yielded an inflection point in the dependence of droplet breakup rate on Na-CMC concentration was found in between the dilute and semi-dilute concentration regimes. This inflection point displays a non-monotonic profile which is mainly caused by the considerable viscosity effect of Na-CMC polymer when its concentration increases above a critical value (C > C*˜0.40 wt%). This striking behaviour highlights the importance of rheological effects in flows with a shear-dependent fluid under various flow conditions. The viscous effect of Na-CMC fluids substantially affects the manipulation over the droplet pinch-off time and production rate. Thus, it necessitate the control of the shear rate by adjusting the flow conditions and aspect ratio of microchannels.

Steady shear viscosity of semi-dilute bubbly suspensions

The steady shear viscosity of bubbly suspensions is known to depend upon the suspending fluid viscosity, the bubble volume fraction and a dimensionless number (the capillary number) accounting for the deformability of the bubbles under a viscous stress. However, experimental data on bubbly suspensions in the literature are scarce and present two main shortcomings: (i) the studied systems are polydisperse, which leads to arbitrariness in the definition of a capillary number, and (ii) there is a lack of data for capillary numbers of order unity, where bubbles are slightly deformable. This leads to the absence of clear conclusion on the relevance of the existing theoretical models. In order to make significant progress, an original device is designed to produce monodisperse suspensions of bubbles in a highly viscous Newtonian fluid. The steady shear viscosity of the bubbly suspensions is measured in the dilute and semi-dilute concentration regimes (volume fraction of bubbles between 2% and 18%) using a Couette geometry with a 20-bubbles-wide gap, for capillary numbers ranging between 0.01 and 10. The new obtained data are shown to be much more accurate than data previously reported in the literature. Experimental data are in very good agreement with the model of Frankel and Acrivos (1970), originally developed for dilute suspensions, in the whole range of studied volume fractions.

Chain conformation, rheological and charge properties of fucoidan extracted from sea cucumber Thelenota ananas: A semi-flexible coil negative polyelectrolyte

As a bioactive and functional polysaccharide, sea cucumber fucoidan has received increasing attention. Chain conformation and physicochemical properties of fucoidan extracted from Thelenota ananas (Ta-FUC) was investigated by utilizing HPSEC-MALLS-Visc-RI, microelectrophoresis and steady shear measurements. The conformation parameter αs (0.61±0.02), the Mark-Houwink-Kuhn-Sakurada exponent αη (0.92±0.01), αh (0.64±0.01) and the Smidsrød-Haug stiffness parameter B (0.036±0.010) consistently manifested that Ta-FUC adopted a semi-flexible coil conformation in NaCl solution. Based on a wormlike cylinder model, stiffness parameters, including persistence length q (13.27±0.80nm) and cylinder diameter d (0.79nm), were calculated. This polysaccharide demonstrated shear-thinning rheological behaviour, and critical concentration from dilute to semidilute concentration regime was determined as 3.6mg/ml. Ta-FUC exhibited as a negative polyelectrolyte in wide pH and ionic strength ranges. These molecular characteristics and physicochemical properties would facilitate further application of Ta-FUC as a functional ingredient in food.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

Novel Structural Changes during Temperature-Induced Self-Assembling and Gelation of PLGA-PEG-PLGA Triblock Copolymer in Aqueous Solutions.

The thermoresponsive amphiphilic block copolymer poly(d,l-lactic acid-co-glycolic acid)-block-poly(ethylene glycol)-block-poly(d,l-lactic acid-co-glycolic acid) (PLGA-PEGn -PLGA), which exhibits a reversible temperature-induced sol-gel transition at higher polymer concentrations in aqueous solution has attached a great deal of interest because of its potential in biomedical applications. In the present work, the length of the hydrophobic PLGA blocks is kept constant, whereas the length of the hydrophilic PEG block is altered and this variation has a pronounced impact on the phase behavior of the aqueous samples and the structure of the polymer. A short PEG block promotes gelation at a low temperature, whereas a longer PEG block shifts the gelation point to higher temperature. By using a combination of turbidity, rheology, and small angle neutron scattering (SANS) methods, the authors have revealed dramatic temperature effects. In dilute solution, the SANS experiments expose asymmetric ellipsoid structures for the copolymer with the short PEG-spacer, whereas spherical core-shell structure is observed for the polymer with long PEG-spacer. In the semidilute concentration regime, SANS measurements disclose similar profiles for the two copolymers. In a broad temperature interval, the transition from spherical core-shell micelles to cylindrical structure and packing of cylinders is observed.

Rheological study of in-situ crosslinkable hydrogels based on hyaluronanic acid, collagen and sericin

The elaboration of chemically crosslinked hydrogels based on collagen (C), hyaluronanic acid (HA) and sericin (S) with different polymer ratios was investigated by in-situ rheology. This reaction was performed via amide or ester bond reaction activated by carbodiimide, in pure water. Prior to molecule crosslinking, the rheological behaviour of the biopolymers (alone or in mixture) was characterized in a semi-dilute concentration regime. Both flow and dynamic measurements showed that uncrosslinked collagen alone appears to be rather elastic with yield stress properties, whereas uncrosslinked HA alone appears to be rather shear thinning and viscoelastic in agreement with entangled polymer behaviour. Sericin exhibited Newtonian low viscosity behaviour according to its very low molar mass. Before crosslinking, HA exhibited viscoelastic behaviour at concentrations above the critical entangled concentration (C*) in the mixtures, thus HA shows promise as a matrix for future crosslinked networks, whereas sericin did not significantly modify the rheology. During the reaction, followed by rheology, the kinetics were slower for pure HA systems compared with the mixtures (i.e., with added collagen and/or to a lesser extent sericin). At the same time, the final network of hydrogels (i.e., the elastic modulus) was more structured in the mixture based systems. This result is explained by ester bonds (the only possibility for pure HA systems), which are less favourable and reactive than amide bonds (possible with sericin and collagen). The presence of collagen in the HA matrix reinforced the hydrogel network. SEM studies confirmed the structure of the hydrogels, and in vitro degradability was globally consistent with the effect of the selected enzyme according to the hydrogel composition. All the elaborated hydrogels were non-cytotoxic in vitro.

Tailoring Polyacrylonitrile Interfacial Morphological Structure by Crystallization in the Presence of Single-Wall Carbon Nanotubes

In order to improve stress transfer between polymer matrixes and nanofillers, controlling the structure development in the interphase region during composite processing is a necessity. For polyacrylonitrile (PAN)/single-wall carbon nanotubes (SWNT) composites, the formation of the PAN interphase in the presence of the SWNT as a function of processing conditions is studied. Under these conditions, three distinct interfacial coating morphologies of PAN are observed on SWNT. In the semidilute polymer concentration regime subjected to shearing, PAN extended-chain tubular coatings are formed on SWNT. Dilute PAN/SWNT quiescent solutions subjected to cooling yields hybrid periodic shish-kebab structures (first observation for PAN polymer), and dilute PAN/SWNT quiescent solutions subjected to rapid cooling results in the formation of an irregular PAN crystalline coating on the SWNT.

Use of dynamic light scattering to determine second virial coefficient in a semidilute concentration regime

The present work discusses an alternative procedure to obtain static light scattering (SLS) parameters in a dilute and semidilute concentration regime from a dynamic light scattering (DLS) instrument that uses an avalanche photodiode (APD) for recording the scattered intensity signal. An APD enables one to perform both SLS and DLS measurements by photon counting and photon correlation, respectively. However, due to the associated recovery time, the APDs are susceptible to saturation (above 1000kcps), which may limit the measurements in systems that scatter too much light. We propose an alternative way of obtaining the SLS parameters with instruments that use APD for recording signal intensities.

Self-similar assemblies of globular whey proteins at the air–water interface: Effect of the structure

We investigated the structure of heat-induced assemblies of whey globular proteins using small angle neutron scattering (SANS), static and dynamic light scattering (SLS and DLS), and cryogenic transmission electron microscopy (Cryo-TEM). Whey protein molecules self-assemble in fractal aggregates with a structure density depending on the electrostatic interactions. We determined the static and dynamic properties of interfacial layer formed by the protein assemblies, upon adsorption and spreading at the air–water interface using surface film balance and interfacial dilatational rheology. Upon spreading, all whey protein systems show a power-law scaling behavior of the surface pressure versus concentration in the semi-dilute surface concentration regime, with an exponent ranging from 5.5 to 9 depending on the electrostatic interactions and the aggregation state. The dilatational modulus derived from surface pressure isotherms shows a main peak at 6–8 mN/m, generally considered to be the onset of a conformational change in the monolayer, and a second peak or a shoulder at 15 mN/m. Long-time adsorption kinetics give similar results for both the native whey proteins and the corresponding self-similar assemblies, with a systematic effect of the ionic strength.