Dilute Polymer Solutions Research Articles

Cross-over in the dynamics of polymer confined between two liquids of different viscosity.

Using molecular dynamics simulations, we analysed the polymer dynamics of chains of different molecular weights entrapped at the interface between two immiscible liquids. We showed that on increasing the viscosity of one of the two liquids the dynamic behaviour of the chain changes from a Zimm-like dynamics typical of dilute polymer solutions to a Rouse-like dynamics where hydrodynamic interactions are screened. We observed that when the polymer is in contact with a high viscosity liquid, the number of solvent molecules close to the polymer beads is reduced and ascribed the screening effect to this reduced number of polymer-solvent contacts. For the longest chain simulated, we calculated the distribution of loop length and compared the results with the theoretical distribution developed for solid/liquid interfaces. We showed that the polymer tends to form loops (although flat against the interface) and that the theory works reasonably well also for liquid/liquid interfaces.

Определение дисперсной фазы буровых растворов на полимерной основе

The purpose of the article is determination of the volume of the polymer solution dispersed phase, estimation of their subordination degree to the power law of fluid flow, as well as determination of the rheological model of mud flow in order to calculate the pressure losses under fluid movement in the elements of the circulation system. Water-soluble polymers are widely used in the composition of drilling fluids and are also used independently as flushing fluids for drilling wells. Despite the wide application range of polymers, when drilling little attention is paid to the volume of the dispersed phase resulting from the dissolution of polymer in water. Particular interest is caused by so-called dilute solutions (term used in the theory of polymer solutions). They are little mentioned in drilling but their number of macromolecular coils of the polymer reaches such a value that they do not interact with each other when the fluid flows. Using a viscometric method, the molecular mass and the characteristic viscosity of each solution used for the dispersion phase volume determination are estimated. The parameters of the rheological power law are determined through the application of rotametric viscometry. As a result, it has been found out that the solutions of the considered polymers prepared for the study are referred to diluted. On example of one of them the possibility of determining the relative volume of macromolecular coils of polymer with the immobilized solvent (water) is shown. It is demonstrated that a change in the specified volume causes a change in the parameters of the rheological power law of researched solution flow. The proposed methods for determining the relative volume of the dispersed phase of drilling muds based on dilute polymer solutions allows to adjust the rheological properties of flushing fluids and set the parameters of the rheological power law describing the flow of pseudoplastic fluids.

Crystallization-Arrested Viscoelastic Phase Separation in Semiconducting Polymer Gels

Through a combination of rheological characterization and temperature-variable imaging methods, a novel gelation pathway in dilute solutions of a semiconducting polymer to achieve interconnected, crystalline networks with hierarchical porosity is reported. Upon rapid cooling, solutions of regioregular poly(3-hexylthiophene) (RR-P3HT) in ortho-dichlorobenzene formed thermoreversible gels. Temperature-variable confocal microscopy revealed cooling-induced structural rearrangement to progress through viscoelastic phase separation. The phase separation process arrested prematurely during the formation of micron-sized solvent-rich "holes" within the RR-P3HT matrix due to intrachain crystallization. Cryogen-based scanning electron microscopy of RR P3HT gels revealed the existence of an interfibrillar network exhibiting nano-sized pores. Remarkably, these networks formed to equal gel strengths when a third component, either small molecule phenyl C61 butyric acid methyl ester (PCBM) or non-crystallizing regiorandom (Rra)-P3HT, was added to the solution. Organic solar cells in which the active layers were deposited from phase-separated solutions displayed 45% higher efficiency compared to reference cells.

Elastic Alfven waves in elastic turbulence

Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed cel on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity.

Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous Stress

We study models of dilute rigid rod-like polymer solutions. We establish the global well-posedness of the Doi model for large data and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the viscous stress adds dissipation to high derivatives of velocity.

Convergence of the Freely Rotating Chain to the Kratky-Porod Model of Semi-flexible Polymers

The freely rotating chain is one of the classic discrete models of a polymer in dilute solution. It consists of a broken line of N straight segments of fixed length such that the angle between adjacent segments is constant and the $$N-1$$ torsional angles are independent, identically distributed, uniform random variables. We provide a rigorous proof of a folklore result in the chemical physics literature stating that under an appropriate scaling, as $$N\rightarrow \infty $$ , the freely rotating chain converges to a random curve defined by the property that its derivative with respect to arclength is a Brownian motion on the unit sphere. This is the Kratky-Porod model of semi-flexible polymers. We also investigate limits of the model when a stiffness parameter, called the persistence length, tends to zero or infinity. The main idea is to introduce orthogonal frames adapted to the polymer and to express conformational changes in the polymer in terms of stochastic equations for the rotation of these frames.

Orientational relaxation of ring polymers in dilute solutions.

The segmental relaxation dynamics of ring polymers in dilute solutions is investigated via optimized Rouse-Zimm theory. To the best of our knowledge, this is the first study that characterizes the orientational relaxation dynamics of ring polymers in dilute solutions. The orientational time autocorrelation functions are governed by two major processes that span a broad range of timescales: (i) local segmental motion at short times, independent of the ring size, and (ii) overall motion of the ring at long times that depends on the limiting ring size. Smaller rings relax faster than larger rings and their respective linear analogues. The hydrodynamic interactions decrease the higher relaxation rates corresponding to the local relaxation modes and increase the smaller relaxation rates which correspond to the collective relaxation modes. The spectral density is independent of frequency in the low frequency regime while it decreases with increasing frequency. Regardless of the ring size, the spin-lattice relaxation rate exhibits a single characteristic maximum as a function of frequency that shifts to a lower value with increasing strength of hydrodynamic interactions.

Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow.

The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer deformability. Brownian motion caused the droplet position to fluctuate with a distribution that primarily depended on the balance between inertial lift forces pushing the droplet outward and elastic forces from the polymers driving it inward. The droplet shape was controlled by the local shear rate, and so its average shape depended on the droplet distribution.

Measurement of flow properties and mean elastic stresses of dilute polymer solutions passing through small slits

We measured pressure drops and jet thrusts of dilute (100 ppm and 10 ppm) or ultra-dilute (1 ppm) aqueous solutions of polymer in flows through slits with width of 1.0 mm, 480 μm, and 122 μm owing to investigation of flow properties of dilute polymer solution passing through a small slit. Good agreement between the experimental results of water alone and the predictions was obtained within the experimental errors. However, the dilute and ultra-dilute polymer solutions exhibited lower values. To understanding the experimental results, we estimated mean elastic stresses via jet thrust method. Moreover, we clarified that power-law relationship between mean elastic stress and mean velocity, and it corresponded to the flow properties via the pressure drops.

Effect of Composition of Nitrile-Butadiene Rubber–Chlorinated Polyisoprene–Solvent System on the Structural and Dynamic Characteristics of the Film Material

The structure and properties of film materials obtained from solutions of nitrile-butadiene rubber and chlorinated polyisoprene taken at ratios of 100 : 0, 80 : 20, 50 : 50, 20 : 80, and 0 : 100 are examined. DSC, EPR, viscometry of dilute polymer solutions, FTIR spectrometry, and elastic-strength testing are applied. Methyl acetate, ethyl acetate, butyl acetate, acetone, and methyl ethyl ketone are used as solvents. It is shown that the introduction of up to 50 wt % chlorinated polyisoprene in the polymer blend weakly affects the glass-transition temperature, elastic modulus, degree of ozone oxidation, and molecular mobility, whereas a higher concentration of chlorinated polyisoprene provides marked changes in these parameters. The thermodynamic quality of the solvent determines the structural and dynamic parameters of the studied film materials.

Assessing structure/property relationships and synthetic protocols in the fabrication of poly(oxanorbornene imide) single-chain nanoparticles

We present the synthesis of poly(oxanorbornene imide) single-chain nanoparticles (SCNP) by intrachain radical polymerization of pendant methacryloyl units. Well-defined poly(oxanorbornene imide)s were first prepared via ring-opening metathesis polymerization (ROMP) of methacryloyl-containing monomers. Handling and polymerizing these monomers requires some special care to prevent undesired premature reaction of the methacryloyl groups. Addition of AIBN to dilute solution of the ROMP polymers triggers intrachain radical polymerization of pendant methacryloyl groups, folding the linear polymers into SCNP. Characterization by NMR spectroscopy and SEC confirmed SCNP formation and revealed structure/property relationships related to methacryloyl pendent length and percent incorporation.

Dimensions of catenated ring polymers in dilute solution studied by Monte-Carlo simulation.

Interaction between two simple ring chains catenated in a molecule was estimated by a Metropolis Monte Carlo simulation, and the result was compared with a model. We employed catenated ring chains in this study; they were composed of two simple ring chains, and the topology was kept as . The temperature dependence of the distance between two ring chains in a molecule was discussed using Flory's scaling exponent, ν, in R g ∝ N ν , where R g is the radius of gyration of a simple ring chain catenated in a molecule. In the simulation, the topology of the component rings and their links were kept because chain crossing was prohibited. The excluded volume of chains was screened by the attractive force between polymer segments, and the strength of the attractive force depends on temperature, T. At the θ temperature for trivial ring polymers, where the condition ν = 1/2 holds, their trajectories can be described statistically as a closed-random walk, i.e., a closed-phantom chain model. The temperature at which interaction between trivial ring polymers, i.e., inter-molecular interaction, is repulsive; trivial ring polymer molecules show the excluded volume generated with keeping their own topology, 01. A catenated molecule is composed of two simple rings, and so forth a component ring can be affected by the existence of the counterpart rings. Under that temperature, the mean-square distance between two rings in a catenated molecule, ⟨L 2⟩, was obtained and compared with that of the simple model composed of two circles in three-dimensions, where interaction between circles is set as zero. It has been found that the simulated ⟨L 2⟩ values were constantly larger than those of the model owing to the excluded volume of rings in a molecule.

Conformationally averaged iterative Brownian dynamics simulations of semidilute polymer solutions.

The dynamics of semidilute polymer solutions are important to many polymer solution processing techniques such as fiber spinning and solution printing. The out-of-equilibrium molecular conformations resulting from processing flows directly impact material properties. Brownian dynamics (BD) simulations are a standard technique for studying this connection between polymer conformations in solution and processing flows because they can capture molecular-level polymer dynamics. However, BD simulations of semidilute polymer solutions are computationally limited by the calculation of hydrodynamic interactions (HIs) via an Ewald summed diffusion tensor and stochastic Brownian displacements via the decomposition of the diffusion tensor. Techniques based on the Cholesky decomposition scale with the number of particles N as O(N 3) and approximations in the literature have reduced this scaling to as low as O(N). These methods still require continuous updating of the diffusion tensor and Brownian displacements, resulting in a significant constant per-time step cost. Previously, we introduced a method that avoids this cost for dilute polymer solutions by iterative conformational averaging (CA) of intramolecular HIs. In this work, we extend the CA method to semidilute solutions by introducing a grid-space average of intermolecular HIs and a pairwise approximation to the Brownian displacements based on the truncated expansion ansatz of Geyer and Winter. We evaluate our method by first comparing the computational cost with that of other simulation techniques. We verify our approximations by comparison with expected results for static and dynamic properties at equilibrium and use our method to demonstrate the concentration dependence of HI screening.

On convergent schemes for two-phase flow of dilute polymeric solutions

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a recent micro-macro bead-spring model for two-phase flow of dilute polymeric solutions derived by methods from nonequilibrium thermodynamics ([Grün, Metzger, M3AS 26 (2016) 823–866]). The model consists of Cahn-Hilliard type equations describing the evolution of the fluids and the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three spatial dimensions for the velocity and the pressure of the fluids with an elastic extra-stress tensor on the right-hand side in the momentum equation which originates from the presence of dissolved polymer chains. The polymers are modeled by dumbbells subjected to a finitely extensible, nonlinear elastic (FENE) spring-force potential. Their density and orientation are described by a Fokker-Planck type parabolic equation with a center-of-mass diffusion term. We perform a rigorous passage to the limit as the spatial and temporal discretization parameters simultaneously tend to zero, and show that a subsequence of these finite element approximations converges towards a weak solution of the coupled Cahn-Hilliard-Navier-Stokes-Fokker-Planck system. To underline the practicality of the presented scheme, we provide simulations of oscillating dilute polymeric droplets and compare their oscillatory behaviour to the one of Newtonian droplets.

Reversible Assembly of Terpyridine Incorporated Norbornene-Based Polymer via a Ring-Opening Metathesis Polymerization and Its Self-Healing Property.

We induced a terpyridine moiety into a norbornene-based polymer to demonstrate its self-healing property, without an external stimulus, such as light, heat, or healing agent, using metal–ligand interactions. We synthesized terpyridine incorporated norbornene-based polymers using a ring-opening metathesis polymerization. The sol state of diluted polymer solutions was converted into supramolecular assembled gels, through the addition of transition metal ions (Ni2+, Co2+, Fe2+, and Zn2+). In particular, a supramolecular complex gel with Zn2+, which is a metal with a lower binding affinity, demonstrated fast self-healing properties, without any additional external stimuli, and its mechanical properties were completely recovered.

Specific formation of hydrophobic aggregates of ionic thermoresponsive polymers with oppositely charged ionic surfactants under extremely dilute conditions

Cationic and anionic thermoresponsive polymers were synthesized and the formation of their hydrophobic aggregates with ionic surfactants was studied at extremely low polymer concentrations. Alongside the hydrophobic interactions, electrostatic interactions between the ionic groups of the polymers and surfactants played a major role in the formation of the hydrophobic aggregates. In the absence of an ionic surfactant, extremely dilute (i.e., 0.01 wt %) polymer solutions did not become turbid, even when they were heated above the phase-transition temperature. However, above the phase-transition temperature, the polymer solutions became turbid upon the addition of a specific concentration of an ionic surfactant with the opposite charge. In contrast, no increase in the turbidity was observed when an ionic surfactant with the same charge was added to the solution, regardless of the concentration of the ionic surfactant. Even below the phase-transition temperature, the application of a fluorescent probe that responded to the hydrophobicity of its environment revealed that the ionic thermoresponsive polymers formed a hydrophobic environment with oppositely charged surfactants owing to the electrostatic and hydrophobic interactions, even though hydrophobic precipitates were not observed. Thus, the electrostatic interactions between polymers and surfactants played crucial roles in the formation of hydrophobic aggregates under extremely low concentration of the polymers as well as the hydrophobic interactions did.

Controllable synthesis and AIE properties of fluorescent polyesters

For the potential application of functional polyesters in biomedical field, a series of side-chain functional fluorescent polyesters have been designed and prepared through the polymerization of AIE-functionalized carbonate monomer TPETC. The controllable nature of TPETC’s ROP and ROCP using different organocatalysts has been proved. In the dilute solution of these AIE polyesters, the structure of the polymers themselves, concentration of the polymer solution and other external conditions would obviously affect the aggregation of the side groups (TPE derivatives), and thus affecting the AIE phenomenon of the polymers. The structure of polymer chain had certain influences to the distribution and movements of side-groups, and these influences were reflected by the fluorescence intensity here. It is expected that this conclusion would provide a new perspective for the inner characteristics of dilute polymer solutions and broaden the application of AIE macromolecules.

Boundary layer of elastic turbulence

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As has been established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically the statistics of the polymer conformation, which is highly non-uniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of the mean flow to the magnitude of the flow fluctuations. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.

Elongational Stress and Velocity of Dilute Polymer Solutions Flowing into Small Apertures

Elongational Stress and Velocity of Dilute Polymer Solutions Flowing into Small Apertures

Rheological consequences of wet and dry friction in a dumbbell model with hydrodynamic interactions and internal viscosity.

The effect of fluctuating internal viscosity and hydrodynamic interactions on a range of rheological properties of dilute polymer solutions is examined using a finitely extensible dumbbell model for a polymer. Brownian dynamics simulations are used to compute both transient and steady state viscometric functions in shear flow. The results enable a careful differentiation of the influence, on rheological properties, of solvent-mediated friction from that of a dissipative mechanism that is independent of solvent viscosity. In particular, hydrodynamic interactions have a significant influence on the magnitude of the stress jump at the inception of shear flow, and on the transient viscometric functions, but a negligible effect on the steady state viscometric functions at high shear rates. Zero-shear rate viscometric functions of free-draining dumbbells remain essentially independent of the internal viscosity parameter, as predicted by the Gaussian approximation, but the inclusion of hydrodynamic interactions induces a dependence on both the hydrodynamic interaction and the internal viscosity parameter. Large values of the internal viscosity parameter lead to linear viscoelastic predictions that mimic the behavior of rigid dumbbell solutions. On the other hand, steady-shear viscometric functions at high shear rates differ in general from those for rigid dumbbells, depending crucially on the finite extensibility of the dumbbell spring.