Semidilute Solutions Research Articles

Sedimentation of large particles in a suspension of colloidal rods

The sedimentation at low Reynolds numbers of large, non-interacting spherical inclusions in networks of model monodisperse, slender colloidal rods is investigated. The influence of rod concentration, rod length, and inclusion stress on the inclusion’s creeping motion is investigated. The decrease in sedimentation speeds as a function of rod concentration is compared to the Stokes law, using the zero-shear viscosity from the Doi–Edwards theory for semi-dilute colloidal rod solutions. The experimental speeds display the same concentration dependence as the zero-shear viscosity and are, thus, strongly dependent on the rod length. The speed is, however, a fraction of 2 and 4 lower than expected for rods of 0.88 μm and 2.1 μm, respectively. The results for both rod lengths superimpose when plotted against the overlap concentration, hinting at an extra dependence on the entanglement.

Influence of hydrophobic and electrostatic interactions on counterion-dissociation in sodium carboxymethylcellulose - polyethylene glycol (PEG) solutions

Counterion dissociation/condensation and related phenomena of sodium carboxymethylcellulose have been investigated in water with varying hydrophobicity by conductance measurements. Alteration of the hydrophobicity of the media was accomplished by adding varying amounts of polyethylene glycol with different molar masses to the solutions. Analyses of the specific conductances measured as a function of sodium carboxymethylcellulose concentration were performed taking into account the de Gennes scaling model which describes the configuration of polyion chains in semidilute solutions. Results indicate that polyions are the chief transporter of the electricity in the investigated solutions and that a major fraction of the counterions is accompanied by the polyion chains and performs concerted movement towards the positive electrode. Increasing molar mass of the polyethylene glycol samples added to aqueous sodium carboxymethylcellulose solutions containing a given amount of the additive promotes counterion-dissociation, whereas increasing amount of the additive with a given molar mass promotes counterion-condensation. Relative influences of electrostatic and hydrophobic forces have been taken into consideration in order to elucidate the observed dissociation/condensation behavior of counterions of aqueous sodium carboxymethylcellulose solutions. Analyses of the results provided important insight regarding the possible alterations of the conformation of the polyions originating from the subtle balance of hydrophobic and electrostatic interactions in these solutions.

Breakup Dynamics of Semi-dilute Polymer Solutions in a Microfluidic Flow-focusing Device.

Droplet microfluidics involving non-Newtonian fluids is of great importance in both fundamental mechanisms and practical applications. In the present study, breakup dynamics in droplet generation of semi-dilute polymer solutions in a microfluidic flow-focusing device were experimentally investigated. We found that the filament thinning experiences a transition from a flow-driven to a capillary-driven regime, analogous to that of purely elastic fluids, while the highly elevated viscosity and complex network structures in the semi-dilute polymer solutions induce the breakup stages with a smaller power-law exponent and extensional relaxation time. It is elucidated that the elevated viscosity of the semi-dilute solution decelerates filament thinning in the flow-driven regime and the incomplete stretch of polymer molecules results in the smaller extensional relaxation time in the capillary-driven regime. These results extend the understanding of breakup dynamics in droplet generation of non-Newtonian fluids and provide guidance for microfluidic synthesis applications involving dense polymeric fluids.

Kinetically controlled cyclization in step-growth polymerization of AB2 macromonomer: Role of molar mass of macromonomer

Cyclization has been widely reported to compete with interchain growth and lead to limited degree of polymerization in step-growth polymerization of AB2 monomers. However, little attention has been paid to kinetical comparison between interchain growth and cyclization in preparation of long-subchain hyperbranched polymers (LHPs) from AB2 macromonomers in semi-dilute solution. This work aims to elucidate how cyclization influences the polymerization of AB2 macromonomers via kinetical competition with interchain growth and how molar mass of macromonomer affects this competition. The corresponding kinetics in semi-dilute solution is theoretically derived in consideration of cyclization. For a given mass concentration, interchain growth rate (rg), cyclization rate (rc) and their ratio (rg/rc) highly depend on the molar mass of macromonomer (M), following the scale rule of rg∝M−2, rc∝M−2.5 and rg/rc∝M0.5, respectively. It indicates that macromonomers with lower molar mass tend to generate products with lower degree of polymerization in terms of macromonomer (DPmacromonomer) and higher self-cyclized macromonomer ratio (CMMR) at a faster rate, while macromonomers with higher molar mass act oppositely. These proposed theories are further verified via the experimental investigation about the step-growth of AB2 polystyrene (PSt) macromonomers with different molar masses. The structural analyses of the resultant products from PSt macromonomers with a low molar mass of 2.5 k indicate a very low DPmacromonomer with a nearly complete conversion of focal A groups, which implies predominant position of cyclized compositions in resultant products, not only cyclized macromonomers (CMMs) but also cyclized long-subchain hyperbranched polymers (CLHPs). More importantly, experimental results show that conversion rate and CMMR increase but DPmacromonomer decreases sharply as molar mass of macromonomer decreases, which quite agrees with the theoretical inference.

Viscoelastic Nanocomposites of Wormlike Micelles of Surfactant and Aluminosilicate Clay Nanoplates

Viscoelastic nanocomposites based on a matrix of semidilute aqueous solutions of entangled wormlike (polymer-like) micelles of a cationic surfactant and aluminosilicate nanoplates of montmorillonite clay, efficiently acting as crosslinks, were prepared and studied. The produced materials represent a new type of a self-assembling nanocomposite system. The results of changes in viscoelastic properties of nanocomposites when adding clay nanoplates are well described by a proposed interaction model which implies adsorption of wormlike micelles by end-caps to the surfactant layer formed on the nanoplates surface.

Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features

Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position [Formula: see text] by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, [Formula: see text], in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions [Formula: see text] The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35-0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.

Conformation and Phase Behavior of Sodium Carboxymethyl Cellulose in the Presence of Mono- and Divalent Salts

We report a small-angle neutron scattering (SANS) study of semidilute aqueous solutions of sodium carboxymethyl cellulose (NaCMC), in the presence of mono- (Na+) and divalent salts (Mg2+, Ca2+, Zn2...

Molecular Weight Dependence of Associative Behavior in Polyimide/DMF Solutions

Eight 6FDA-TFDB polyimide (PI) samples with absolute molecular weights ranging from 1.25 × 105 g·mol−1 to 3.11 × 105 g·mol−1 are obtained by precipitation fractionation. Rheological experiments are conducted to determine the influence of molecular weight on the associating behavior of PI in N,N′-dimethylformamide (DMF) solutions in a broad volume fraction, including abnormal steady shear flow, solution heterogeneity, and scaling behavior. Abnormal flow behaviors, i.e., multi-region shear thinning and weak shear thickening, are studied, and these behaviors have not been reported in literature. The heterogeneity of PI/DMF solutions is examined by dynamic rheological test. By plotting ηsp versus ϕ/ϕη, four concentration regions of I–IV can be distinguished for all PI samples with various molecular weights. The scaling results in different concentration regions are in good agreement with the associative polymer theory proposed by Rubinstein and Semenov. The scaling exponents do not show molecular weight dependence in concentration regions I and II. In concentration regions III and IV, the scaling exponents change little when the molecular weight is below 242 k but increase when the molecular weight increases from 242 k to 311 k. This work can help us to understand polyimide solution properties from dilute to semidilute entangled solutions, and will guide the polyimide solution preparation for different processing.

Capillary breakup extensional rheometry of sodium carboxymethylcellulose solutions in water and propylene glycol/water mixtures

ABSTRACTThis article presents the results of capillary break‐up extensional rheometer experiments conducted for semidilute solutions of carboxymethylcellulose sodium salt (Na‐CMC) with degrees of substitution (DS) ranging from 0.62 to 1.04 in distilled water and propylene glycol (PG)/water mixtures. The partial aggregation of Na‐CMC chains with DS < 1 observed in aqueous solutions triggers an increase in apparent extensional viscosity and extension of break‐up time. The rheological properties of Na‐CMC solutions in propylene glycol/water mixture are determined by the solubility of the polymer and the physical crosslinking of chains. The disappearance of the elasto‐capillary regime during the filament thinning of Na‐CMC solutions with DS < 1 in propylene glycol/water mixture was linked to the physical crosslinking of polymer chains. The shape of the extensional viscosity curve for Na‐CMC solutions with DS = 1.04 in PG/water mixture was characteristic for semidilute polymer solutions with a low number of entanglements. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1537–1547

Uniaxial extensional viscosity of semidilute DNA solutions

The extensional rheology of polymeric liquids has been extensively examined through experiments and theoretical predictions. However, a systematic study of the extensional rheology of polymer solutions in the semidilute regime, in terms of examining the effects of concentration and molecular weight, has not been carried out so far. Prior studies of the shear rheology of semidilute polymer solutions have demonstrated that their behaviour is distinctively different from that observed in the dilute and concentrated regimes. This difference in behaviour is anticipated to be even more pronounced in extensional flows. In this work, the extensional rheology of linear, double-stranded DNA molecules, spanning an order of magnitude of molecular weights (25 to 289 kilobasepairs) and concentrations (0.03 to 0.3 mg/ml), has been investigated. DNA solutions are now used routinely as model polymeric systems due to their near-perfect monodispersity. Measurements have been carried out with a filament stretching rheometer since it is the most reliable method for obtaining an estimate of the elongational stress growth of a polymer solution. Transient and steady-state uniaxial extensional viscosities of DNA dissolved in a solvent under excess salt conditions, with a high concentration of sucrose in order to achieve a sufficiently high solvent viscosity, have been determined in the semidilute regime at room temperature. The dependence of the steady state uniaxial extensional viscosity on molecular weight, concentration and extension rate is measured with a view to determining if data collapse can be observed with an appropriate choice of variables. Steady state shear viscosity measurements suggest that sucrose-DNA interactions might play a role in determining the observed rheological behaviour of semidilute DNA solutions with sucrose as a component in the solvent.

Rheological Properties of Poly(acrylic acid) Complexes with Poly(sodium styrenesulfonate) in Semidilute Aqueous Solutions

Solutions of poly(acrylic acid) mixtures with poly(sodium styrenesulfonate) in water and in decimolar hydrochloric acid are studied by potentiometry, viscometry, and rotational rheometry. It is shown that, in a wide range of mixture compositions, thermosensitive polyelectrolyte complexes are formed via ion–dipole interactions of functional groups of polymers. The formation of complexes in the semidilute solution regime is accompanied by a significant increase in viscosity as compared with solutions of the initial polymers, which makes it possible to obtain systems with high viscosity without using large concentrations of polyelectrolytes. The dependence of viscosity on the composition of the mixture passes through a maximum corresponding to the most complete binding of the components of the complex, and the position of the maximum does not depend on the molecular weight of poly(sodium styrenesulfonate) and is determined by the ratio of the concentrations of the functional groups of the polymers. The frequency dependences of the storage modulus and the loss modulus demonstrate that the system experiences strong structuring in the process of complex formation.

Counterion-binding and related phenomena in sodium alginate-sodium chloride-water ternary systems: A conductometric study

Counterion-binding and related phenomena in aqueous solution of the naturally-occurring anionic polyelectrolyte sodium alginate have been explored in absence as well as in presence of sodium chloride using electrical conductivity as the probe. In particular, the variations of the counterion-binding behavior as functions of polyelectrolyte concentration, added electrolyte concentration, and temperature were investigated. A phenomenological treatment of the data which considered the additivity of salt and polyelectrolyte conductivities taking into account the Debye-Hückel interactions using Manning's theoretical expressions for self-diffusion was performed. The results indicated a marked departure from additivity. The data were, therefore, analyzed on the basis of the de Gennes scaling model for the configuration of a polyion chain in semidilute solutions. Counterion-dissociation reached its maximum in absence of the added salt, whereas counterion-binding reached its maximum in presence of the highest amount of the added salt. In moderately saline media, however, counterion-binding was initially found to increase with polyelectrolyte concentration which then gradually leveled off indicating confinement of counterions within the domains of polyion chains at higher polyelectrolyte concentrations. Results indicated the existence of alginate ions as flexible chains in aqueous solutions. A subtle balance of the influences of the effective monomer charge and the effective monomer size played a pivotal role the polyion mobility. Possible conformational changes of the polyion chains caused by dilution led to changes in hydrodynamic resistance in the investigated solutions. The results also provided important insight as to the influence of the alterations of the hydration behavior of the counterions and the relative permittivity of the media on counterion-binding in the investigated systems.

Simulation of semidilute polymer solutions in planar extensional flow via conformationally averaged Brownian noise.

The dynamics and rheology of semidilute polymer solutions in strong flows are of great practical relevance. Processing applications can in principle be designed utilizing the relationship between nonequilibrium polymer conformations and the material properties of the solution. However, the interplay between concentration, flow, hydrodynamic interactions (HIs), and topological interactions which govern semidilute polymer dynamics is challenging to characterize. Brownian dynamics (BD) simulations are particularly valuable as a way to directly visualize how molecular interactions arise in these systems and are quantitatively comparable to single-molecule experiments. However, such simulations are often computationally intractable and are limited by the need to calculate the correlated Brownian noise via decomposition of the diffusion tensor. Previously, we have introduced an iterative conformational averaging (CA) method for BD simulations which bypasses these limitations by preaveraging the HI and Brownian noise in an iterative procedure. In this work, we generalize the CA method to flowing semidilute solutions by introducing a conformation dependent diffusion tensor and a strain dependent approximation to the conformationally averaged Brownian noise. We find that this approach nearly quantitatively reproduces both transient and steady state polymer dynamics and rheology while achieving an order of magnitude computational acceleration. We then utilize the CA method to investigate the concentration and flow rate dependence of polymer dynamics in planar extensional flows. Our results are consistent with previous experimental and simulation studies and provide a detailed view of broad conformational distributions in the semidilute regime. We observe interconversion between stretched and coiled states at steady state, which we conjecture occur due to the effect of concentration on the conformation dependent polymer drag. Additionally, we observe transient flow-induced intermolecular hooks in the startup of flow which lead to diverse and unique stretching pathways.

Wormlike Micelles of a Cationic Surfactant in Polar Organic Solvents: Extending Surfactant Self-Assembly to New Systems and Subzero Temperatures.

Wormlike micelles (WLMs) are long, flexible cylindrical chains formed by the self-assembly of surfactants in semidilute solutions. Scientists have been fascinated by WLMs because of their similarities to polymers, while at the same time, the viscoelastic properties of WLM solutions have made them useful in a variety of industrial applications. To date, most studies on WLMs have been performed in water (i.e., a highly polar liquid), while there are a few examples of "reverse" WLMs in oils (i.e., highly nonpolar liquids). However, in organic solvents with lower polarity than water such as glycerol, formamide, and ethylene glycol, there have been no reports of WLMs thus far. Here, we show that it is indeed possible to induce a long-tailed cationic surfactant to assemble into WLMs in several of these solvents. To form WLMs, the surfactant is combined with a "binding" salt, i.e., one with a large organic counterion that is capable of binding to the micelles. Examples of such salts include sodium salicylate and sodium tosylate, and we find self-assembly to be maximized when the surfactant and salt concentrations are near-equimolar. Interestingly, the addition of a simple, inorganic salt such as sodium chloride (NaCl) to the same surfactant does not induce WLMs in polar solvents (although it does so in water). Thus, the design rules for WLM formation in polar solvents are distinct from those in water. Aqueous WLMs have been characterized at temperatures from 25 °C and above, but few studies have examined WLMs at much lower (e.g., subzero) temperatures. Here, we have selected a surfactant with a very low Krafft point (i.e., the surfactant does not crystallize out of solution upon cooling due to a cis-unsaturation in its tail) and a low-freezing solvent, viz. a 90/10 mixture of glycerol and ethylene glycol. In these mixtures, we find evidence for WLMs that persist down to temperatures as low as -20 °C. Rheological techniques as well as small-angle neutron scattering (SANS) have been used to characterize the WLMs under these conditions. Much like their aqueous counterparts, WLMs in polar solvents show viscoelastic properties, and accordingly, these fluids could find applications as synthetic lubricants or as improved antifreezing fluids.

The investigation of shear banding polymer solutions in die extrusion geometry

This computational study investigates the shear banding phenomenon of semidilute entangled polymer solutions in an extrusion flow. A recently developed nonequilibrium thermodynamic two-fluid model in which shear banding is associated with stress-induced migration was employed. The interfoam solver of the viscoelastic package RheoTool v.2.0, an open-source toolbox based on OpenFOAM v.4.0, was utilized to solve the free-surface flow problem. The PIMPLE algorithm was used for the pressure-velocity coupling, and the convection terms were discretized using the high-resolution scheme CUBISTA. We gradually increased the uniform inlet velocity to reach the shear banding regime. As observed for the Giesekus model, the extrudate swell ratio initially decreases from the Newtonian case with increasing Deborah number. However, the slope’s subsequent increase is reduced, which may be due to both the impact of shear banding and the use of a single set of relaxation times. The velocity profiles in the die change from parabolic to plug-like while entering into the shear banding regime. At the die exit region where the die wall meets the free surface, the material’s boundary condition is changed from the no-slip surface to free surface, which leads to uniform velocity and stress profiles at the downstream. The polymers are pushed toward the wall in the low-shear-rate regime where Fickian diffusion is dominant. The trend in the shear banding regime is the opposite where the stress-induced migration is dominant. An important observation is that the shear banding effect on the polymer concentration is minor compared to the significant changes occurring in the die expansion region. We suggest using a broader spectrum of relaxation times in future mixed-flow calculations.

Instabilities in micro-contraction flows of semi-dilute CTAB and CPyCl solutions: rheology and flow instabilities

The flows of two semi-dilute surfactant solutions (CTAB and CPyCl) through several micro contractions/expansions are experimentally investigated, following an extensive rheological characterization in both shear and extensional flows. The shear rheology of the solutions shows strong shear thinning and shear banding, whereas Small Amplitude Oscillatory Shear and Capillary Break-up Extensional Rheometry indicate that they have high shear and extensional elasticities. Flow visualizations and micro-particle image velocimetry measurements show that the surfactant solutions exhibit three established types of flow patterns in contraction flows: Newtonian-like, asymmetric and disordered. Newtonian-like flow occurs at low flow rates and is preceded by a long transient flow in experiments starting from rest, which seems to be related to shear banding and the alignment of wormlike micelles. The asymmetric flow regime occurs at moderate flow rates and is characterized by an asymmetric upstream central jet with two adjacent vortices, features that change non-periodically, but slowly, in time. This flow pattern seems to be related with the high elasticity of the semi-dilute solutions. The disordered flow pattern is similar to the asymmetric flow in terms of broad characteristics, but the flow asymmetry changes with time much faster than in the asymmetric flow regime, resembling a chaotic-like flow. The disordered flow seems to be related with the breakdown of micellar structures. We concluded also that the flows in both the asymmetric and disordered flow regimes are globally stable in terms of flow patterns, but locally unstable in terms of flow characteristics, with power spectra of the velocity fluctuations having slopes that differ from those typically encountered in elastic turbulence.

Enthalpic effect of polyacrylonitrile on the concentrated solutions in dimethyl sulfoxide: Strong thixotropic behavior and formation of bound solvents

ABSTRACTThe effect of dipole–dipole interaction by nitrile groups of PAN on the bound state of solvent molecules and the concentrated solution properties in DMSO was investigated. Variation of a solution viscosity exhibited three overlap concentrations, C1*, C2*, and C3*, at 2.7, 8.6, and 16.3 wt%, respectively, representing the transition of concentration regions in the order of dilute, unentangled‐semi dilute, entangled‐semi dilute, and concentrated regions. The two‐dimensional mapping of FT‐IR analysis and dielectric measurement confirmed that the intermolecular interaction of PAN was suddenly enhanced at the C*s, inducing polarization to DMSO. In the ice‐melting process of PAN solutions, two different melting peaks (Tm2 and Tm3) of DMSO newly appeared at each C2* and C3*, suggesting the different types of bound solvents. In the concentrated solutions, the saturated dielectric constant and the strongly delayed evaporation of the solvent even at the boiling point of DMSO along with strong thixotropic behavior were indicative of the stronger confinement state of bound DMSO than in the semidilute solutions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1080–1089

Steady streaming flows in viscoelastic liquids

We discuss experimental investigations on steady streaming flows of dilute and semi-dilute polymer solutions in microfluidic devices. The effect of non-Newtonian behavior on steady streaming for different model fluids is determined by characterizing the evolution of the inner streaming layer as a function of oscillation frequency using particle tracking velocimetry. We find that steady streaming velocity profiles in constant-viscosity elastic liquids are qualitatively similar to those in Newtonian liquids. Steady streaming velocity profiles in elastic liquids with strong shear thinning, however, display two unique features: (i) a non-monotonic evolution of the inner streaming layer with increasing frequency, first growing then decreasing in width, and (ii) a clear asymmetry in the flow profile at high frequencies.

Flow blurring atomization of Poly(ethylene oxide) solutions below the coil overlap concentration

Atomization of polymer solutions has important technological implications across many fields. Here, we investigated the atomization dynamics of diluted, polymer solutions using Flow Blurring (FB) technology. Aqueous solutions of poly(ethylene oxide) [PEO] of viscosity-averaged molecular weight in the range 100000 g/mol – 4000000 g/mol and varying concentrations were sprayed with a FB atomizer having an orifice diameter (D) of 700μm and a liquid feed-tube-to-orifice separation (H) of 100μm. The solutions belong to the dilute regime, where polymer coil overlap does not occur, that is φ=cmMvMe<φcrit (Modesto-López, Pérez-Arjona, & Gañán-Calvo, 2019). Shear viscosity measurements indicated that the solutions had viscosities of the order of that of the solvent and exhibited a Newtonian-like behavior. However, during the atomization, and due to the relatively high shear stress induced in the atomizer, the solutions exhibit extensional rheology, which most likely arises from the stretching of the polymer chains in-flight. Although initially the atomization resulted in formation of filaments, these broke up into droplets at relatively short distances from the atomizer discharge orifice as elucidated by images from ultra-high speed videos. The phenomenon is in contrast with that observed in FB-based atomization of semi-diluted polymer solutions with concentrations larger than the polymer coil overlap concentration, c∗. FB atomization of the diluted solutions resulted in a decrease in droplet size with increasing the gas-to-liquid mass ratio (GLR). The approach herein aims at understanding the droplet formation dynamics of viscoelastic, polymer solutions with FB, for applications in large-scale synthesis of materials.

Study of Flow-Driven Translocation of Flexible Polymer Chains through Cylindrical Nanopores in Unentangled Semidilute Solutions

This work reports our effort in clarifying the effect of solution concentration (C) on polymer translocation in semidilute solutions. By studying the translocation behavior of mono- and polydispers...