Semidilute Polymer Solutions Research Articles

Quantifying Properties of Polysaccharide Solutions.

We apply a scaling theory of semidilute polymer solutions to quantify solution properties of polysaccharides such as galactomannan, chitosan, sodium carboxymethyl cellulose, hydroxypropyl methyl cellulose, methyl cellulose, xanthan, apple pectin, cellulose tris(phenyl carbamate), hydroxyethyl cellulose, hydroxypropyl cellulose, sodium hyaluronate, sodium alginate, and sodium κ-carrageenan. In particular, we obtain the molar mass of the chain segment inside a correlation blob M g = B̂ 3/(3ν-1) c 1/(1-3ν) as a function of concentration c, interaction parameter B̂, and exponent ν. Parameter B̂ assumes values B̂ g, B̂ th and M 0/N A 1/3 l for exponents v = 0.588, 0.5 and 1, respectively, where M 0 is the molar mass of a repeat unit, l is the projection length of a repeat unit, and N A is the Avogadro number. In the different solution regimes, the values of the B̂-parameters are extracted from the plateaus of the normalized specific viscosity ηsp (c)/M w c 1/(3ν-1), where M w is the weight-average molecular weight of the polymer chain. The values of the B̂-parameters are used in calculations of the excluded volume v, Kuhn length b, and crossover concentrations c*, c th, and c** into a semidilute polymer solution, a solution of overlapping thermal blobs and a concentrated polymer solution, respectively. This information is summarized as a diagram of states of different polysaccharide solution regimes by implementing a v/bl 2 and c/c** representation. The scaling approach is extended to the entangled solution regime, allowing us to obtain the chain packing number, P̃ e. This completes the set of parameters {B̂ g, B̂ th, P̃ e} which uniquely describes the static and dynamic properties of a polysaccharide solution.

Interconnecting solvent quality, transcription, and chromosome folding in Escherichia coli

All cells fold their genomes, including bacterial cells, where the chromosome is compacted into a domain-organized meshwork called the nucleoid. How compaction and domain organization arise is not fully understood. Here, we describe a method to estimate the average mesh size of the nucleoid in Escherichia coli. Using nucleoid mesh size and DNA concentration estimates, we find that the cytoplasm behaves as a poor solvent for the chromosome when the cell is considered as a simple semidilute polymer solution. Monte Carlo simulations suggest that a poor solvent leads to chromosome compaction and DNA density heterogeneity (i.e., domain formation) at physiological DNA concentration. Fluorescence microscopy reveals that the heterogeneous DNA density negatively correlates with ribosome density within the nucleoid, consistent with cryoelectron tomography data. Drug experiments, together with past observations, suggest the hypothesis that RNAs contribute to the poor solvent effects, connecting chromosome compaction and domain formation to transcription and intracellular organization.

Nanoparticle dynamics in semidilute polymer solutions: Rings versus linear chains

We study the dynamics of nanoparticles in semidilute solutions of ring and linear polymers using hybrid molecular dynamics–multiparticle collision dynamics simulations. The dynamics of the monomers, the polymer centers-of-mass, and the nanoparticles coincide for these two architectures for solutions of the same monomer concentration. The long time diffusivities of the nanoparticles follow the predictions of a polymer coupling theory [Cai et al., Macromolecules 44, 7853–7863 (2011)], suggesting that nanoparticle dynamics are coupled to segmental relaxations for both polymer architectures examined here. At intermediate time scales, the nanoparticle dynamics are characterized by subdiffusive exponents, which markedly deviate from coupling theory and closely follow those of the polymers. Instead, the nanoparticle dynamics are strongly coupled to the polymer center-of-mass motions for both architectures, rather than to their segmental dynamics. The presence of ring concatenations does not affect the long-time diffusivity of the nanoparticles but leads to a slight decrease in the subdiffusive exponents of the nanoparticles and the polymer center-of-mass.

Dripping and jetting of semi-dilute polymer solutions co-flowing in co-axial capillaries

This work is focused on the mechanisms of the dripping and jetting flow modes of viscoelastic semi-dilute polyacrylamide aqueous solutions co-flowing with silicone oil in co-axial capillaries. A phase diagram of the dripping, jetting, and intermediate flow modes is established. It was found that in the dripping mode, the elongation velocity of the filament between the terminal droplet and the inner capillary is controlled solely by the continuous phase rate. At the same time, the decrease in the filament diameter is due to both stretching and outflow of the polymer solution into the terminal droplet. In the jetting mode, the thread diameter was found to evolve in three stages. In the first stage, the average jet velocity increases, whereas in the second and third stages, it becomes constant and corresponds to the velocity of the continuous phase. The transition from the second to the third stage is defined by the appearance of capillary waves resulting in the formation of the beads-on-string structure. In the third stage, the filament diameter between the neighbor beads decreases exponentially and is governed by the relaxation time, which strongly depends on polymer concentration, but does not depend on the continuous phase flow rate. A simple physical model was proposed for describing the evolution of dimensions of filaments and beads during development of jet capillary instability. The universal character of the evolution of filaments and beads sizes, which is independent of concentration of semi-diluted polymer solutions and flow rates of the continuous phase, is revealed.

Near-surface rheology and hydrodynamic boundary condition of semi-dilute polymer solutions.

Understanding confined flows of complex fluids requires simultaneous access to the mechanical behaviour of the liquid and the boundary condition at the interfaces. Here, we use evanescent wave microscopy to investigate near-surface flows of semi-dilute, unentangled polyacrylamide solutions. By using both neutral and anionic polymers, we show that monomer charge plays a key role in confined polymer dynamics. For solutions in contact with glass, the neutral polymers display chain-sized adsorbed layers, while a shear-rate-dependent apparent slip length is observed for anionic polymer solutions. The slip lengths measured at all concentrations collapse onto a master curve when scaled using a simple two-layer depletion model with non-Newtonian viscosity. A transition from an apparent slip boundary condition to a chain-sized adsorption layer is moreover highlighted by screening the charge with additional salt in the anionic polymer solutions. We anticipate that our study will be a starting point for more complex studies relating the polymer dynamics at interfaces to their chemical and physical composition.

Instabilities in freely expanding sheets of associating viscoelastic fluids.

We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structures. Upon impact, the weakly viscoelastic samples exhibit a behavior qualitatively similar to that of Newtonian fluids: a smooth and regular sheet forms, expands, and then retracts. By contrast, for highly viscoelastic fluids, the thickness of the sheet is found to be very irregular, leading to instabilities and eventually to the formation of holes. We find that the rheological properties of the material rule the onset of instabilities. We first provide a simple image analysis of the expanding sheets to determine the onset of instabilities. We then demonstrate that the Deborah number related to the shortest relaxation time associated with the sample structure following a high shear is the relevant parameter that controls the heterogeneities in the thickness of the sheet, eventually leading to the formation of holes. When the sheet tears-up, data suggest by contrast that the opening dynamics depends also on the expansion rate of the sheet.

Nonmonotonic dependence of comb polymer relaxation on branch density in semidilute solutions of linear polymers

The relaxation of comb polymers in semidilute solutions is studied using single-molecule fluorescence microscopy and Brownian dynamics simulations with long-range hydrodynamic interactions (HI). Unexpectedly, comb polymer relaxation is found to depend nonmonotonically on branching density, such that lightly branched chains relax faster than linear chains in semidilute solutions. These results challenge commonly held notions in the field and show that the dynamics of branched polymers in nondilute solutions is governed by a coupling between polymer architecture, long-range HI, and excluded volume interactions.

Positively charged poly (N-vinyl imidazole) gel-filled loose nanofiltration membranes: Performances and modelling analysis

Loose nanofiltration (NF) membrane with pore radius approaching 1 nm and positive charges can be valuable alternative to commercial available negatively charged polyamide NF membrane in specific applications, such as removal of hardness and heavy metal ions and selective separation of dyes/salts mixture. In this work, positively charged poly(N-vinyl imidazole) (PVI) gel-filled loose NF membranes were developed by asymmetric gel-filling upon an asymmetric ultrafiltration (UF) support via UV-initiated surface grafting polymerization and post-quaternization. Compared to the polyamide NF membranes, these membranes displayed a comparable salt rejection ability due to their stronger Donnan exclusion effect. A rigorous three-parameter transport model (TPM) considering steric, Donnan and dielectric exclusion on ions partitioning via effective pore radius (rp), membrane charge density (Xd) and averaged pore dielectric constant (εp), was used to analyze the membrane parameters. Then the gel conformation model (GM) treating confined gel as semi-dilute polymer solution with a characteristic correlation length (ξ) was applied to analyze these gel composites. The results suggest that the gel polymer volume fraction (φ) is decisive in the gel mesh size (viewed as membrane pore size) and gel permeability. Surface porosity of the asymmetric UF base is a limiting factor in membrane permeability. The joint modelling analysis can clarify the membrane structure-properties relationship, performance limits and potentials of the gel-filled NF membrane and hence facilitate structure design and optimization.

Time–Ionic Strength Superposition: A Unified Description of Chain Relaxation Dynamics in Polyelectrolyte Complexes

Addition of salt speeds up chain relaxation dynamics in polyelectrolyte complexes (PECs), and time-salt superposition (TSS) approaches to describe the linear viscoelastic response of PECs are well-established. However, TSS is carried out at fixed initial polyelectrolyte concentrations, and varying the initial polyelectrolyte concentration results in distinct TSS master curves. In this contribution, we show that accounting for the small ions that accompany the oppositely charged polyelectrolyte chains (designated as accompanying counterions) enables assimilation of these distinct TSS master curves into a single universal master curve. This approach, that we christen as time-ionic strength superposition (TISS), enables a unified description of the PEC viscoelastic response in terms of the solution ionic strength, that accounts for both the accompanying counterions and the added ions, and underlines the dynamic similarities between PECs and semidilute polymer solutions. The sticky electrostatic associations among the oppositely charged chains, however, contribute additional relaxation modes in the PECs. We demonstrate that the time scales of these additional relaxation modes are described quantitatively by a modified sticky Rouse model that accounts for the influence of solution ionic strength on electrostatic screening and chain friction.

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.

Inverse integral transformation method to derive local viscosity distribution measured by optical tweezers.

Complex fluids have a non-uniform local inner structure; this is enhanced under deformation, inducing a characteristic flow, such as an abrupt increase in extensional viscosity and drag reduction. However, it is challenging to derive and quantify the non-uniform local structure of a low-concentration solution. In this study, we attempted to characterize the non-uniformity of dilute and semi-dilute polymer and worm-like micellar solutions using the local viscosity at the micro scale. The power spectrum density (PSD) of the particle displacement, measured using optical tweezers, was analyzed to calculate the local viscosity, and two methods were compared. One is based on the PSD roll-off method, which yields a single representative viscosity of the solution. The other is based on our proposed method, called the inverse integral transformation method (IITM), for deriving the local viscosity distribution. The distribution obtained through the IITM reflects the non-uniformity of the solutions at the micro scale, i.e., the distribution widens above the entanglement concentrations of the polymer or viscoelastic worm-like micellar solutions.

Concentration Dependence of the Extensional Relaxation Time and Finite Extensibility in Dilute and Semidilute Polymer Solutions Using a Microfluidic Rheometer

We investigated the composition dependence of the finite extensible nonlinear elastic (FENE) constant of poly(ethylene oxide) (PEO) solutions by the Tikhonov regularization method with the measured...

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.

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.

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.

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.

Soft Interactions Modify the Diffusive Dynamics of Polymer-Grafted Nanoparticles in Solutions of Free Polymer.

We examine the dynamics of silica particles grafted with high molecular weight polystyrene suspended in semidilute solutions of chemically similar linear polymer using X-ray photon correlation spectroscopy. The particle dynamics decouple from the bulk viscosity despite their large hydrodynamic size and instead experience an effective viscosity that depends on the molecular weight of the free polymer chains. Unlike for hard-sphere nanoparticles in semidilute polymer solutions, the diffusivities of the polymer-grafted nanoparticles do not collapse onto a master curve solely as a function of normalized length scales. Instead, the diffusivities can be collapsed across two orders of magnitude in free polymer molecular weight and concentration and one order of magnitude in grafted molecular weight by incorporating the ratio of free to grafted polymer molecular weights. These results suggest that the soft interaction potential between polymer-grafted nanoparticles and free polymer allows polymer-grafted nanoparticles to diffuse faster than predicted based on bulk rheology and modifies the coupling between grafted particle dynamics and the relaxations of the surrounding free polymer.

Viscoelastic effects on dynamics of concentration fluctuations in semi-dilute polymer solution in the good solvent regime

The relaxation processes of the concentration fluctuations in semi-dilute polystyrene (PS) dioctyl phthalate (DOP) solution are investigated by using dynamic light scattering (DLS) in the good solvent regime. Slow modes were found in the dynamic structure factors in the good solvent regime as found in its theta condition. They were almost independent of wavenumber, implying that the slow modes originate from the viscoelastic effects arising in dynamically asymmetric two component systems where the stress and diffusion are coupled. In order to clarify whether the viscoelastic effect indicates the slow modes, the dynamical structure factors were calculated by using Doi-Onuki (DO) theory, where the viscoelastic effects are considered in the dynamics of the concentration fluctuations of binary systems, and the calculated structure factors were compared with experimental ones. In contrast to the theta condition, the deviation was found between the calculated structure factors and experimental ones at longer time region. This deviation originates from the estimation of the osmotic compressibility from the small-angle X-ray scattering. On the other hand, interdiffusion coefficient and cooperative diffusion coefficient from calculated dynamical structure factors agree with those from experimental dynamical structure factors, indicating that both diffusion coefficients are insensitive to the relaxation process at longer time.

A generalised Phan–Thien—Tanner model

In this work we propose a novel generalised form of the Phan–Thien and Tanner (PTT) model by considering a new functional form of the nonlinear expression characterizing the destruction of physical network junctions and entanglements. This new function of the trace of the stress tensor is given by the generalized Mittag–Leffler function, and contains the familiar exponential form of the original Phan–Thien and Tanner model as a limiting case, but affords additional fitting flexibility through the inclusion of one or two additional fitting constants. We perform fits to experimental data in shear and extension and show that this generalized expression allows a better description of the rheological responses for a range of complex materials such as polymer melts and semidilute polymer solutions. By using an appropriate information criterion, we also demonstrate that the resulting generelized model remains parsimonious but provides improved fits of real world data.