Dynamics Of Semidilute Polymer Solutions Research Articles

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.

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.

Direct observation of DNA dynamics in semidilute solutions in extensional flow

The dynamic behavior of semidilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semidilute solutions are characterized by large fluctuations in polymer concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In nonequilibrium flows, it is generally thought that polymer chains can “self-entangle” in semidilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress in the field, we still lack a complete molecular-level understanding of the dynamics of polymer chains in semidilute solutions. In this work, we use single molecule techniques to investigate the dynamics of dilute and semidilute solutions of λ-phage deoxyribonucleic acid in planar extensional flow, including polymer relaxation from high stretch, transient stretching dynamics in step-strain experiments, and steady-state stretching in flow. Our results are consistent with a power-law scaling of the longest polymer relaxation time τ∼(c/c*)0.48 in semidilute solutions, where c is the polymer concentration and c* is the overlap concentration. Based on these results, an effective excluded volume exponent ν ≈ 0.56 was found, which is in good agreement with recent bulk rheological experiments. We further studied the nonequilibrium stretching dynamics of semidilute polymer solutions, including transient (1 c*) and steady-state (0.2 c* and 1 c*) stretching dynamics in planar extensional flow using an automated microfluidic trap. Our results show that polymer stretching dynamics in semidilute solutions is a strong function of concentration. In particular, a decrease in transient polymer stretch in semidilute solutions at moderate Weissenberg number (Wi) compared to dilute solutions is observed. Moreover, our experiments reveal a milder coil-to-stretch transition for semidilute polymer solutions at 0.2 c* and 1 c* compared to dilute solutions. Interestingly, a unique set of molecular conformations during the transient stretching process for single polymers in semidilute solutions is observed, which suggests transient stretching pathways for polymer chains in semidilute solutions are qualitatively different compared to dilute solutions due to intermolecular interactions. Taken together, this work provides a molecular framework for understanding the nonequilibrium stretching dynamics of semidilute solutions in strong flows.

Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: A study of a benchmark flow problem

The complex flow behaviour of semi-dilute (15 < c/ c * < 22.5) polydisperse polyethylene oxide (PEO) aqueous solutions flowing through a planar microfluidic geometry with an 8:1:8 contraction–expansion is systematically studied. The molecular weight and distribution of the PEO samples are analysed by Gel Permeation Chromatography (GPC). Full rheometric characterizations using various techniques including piezoelectric axial vibrator (PAV) measurements at frequencies as high as 6700 Hz are carried out for one semi-dilute PEO solution. Complex flows over a wide range of elasticity numbers (20 ⩽ El ⩽ 120), Weissenberg numbers (7 ⩽ Wi ⩽ 121) and Reynolds numbers (0.08 ⩽ Re ⩽ 4.5) are characterized using micro-particle image velocimetry (μ-PIV) and pressure drop measurements. The evolution of vortex formation and dynamics has been visualized through a step-flow-rate experiment. The effect of El on vortex stability has been studied. Various flow dynamics regimes have been quantified and are presented in a Wi–Re diagram. The experimental results reveal that the elastic behaviour of polymer solutions is very sensitive to high molecular weight polymer in the polydisperse polymer samples, and the contraction ratio and the aspect ratio of flow geometry are the important design parameters in controlling the non-linear dynamics of semi-dilute polymer solutions in microfluidics.

Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: effects of flow geometry

The non-linear dynamics of a semi-dilute (c/c* = 15) polydisperse polyethylene oxide (PEO) solution in microfluidics are studied experimentally using benchmark contraction–expansion flow geometries with three contraction–expansion ratios (4:1:4, 8:1:8 and 16:1:16) and two narrow channel lengths (L c/D h = 53 and 5.3, where L c is the length of the narrow channel and D h is its hydraulic diameter). Complex flows over a range of elasticity numbers (El), Weissenberg numbers (Wi) and Reynolds numbers (Re) are characterized using micro-particle image velocimetry ( $\upmu$ -PIV) and pressure drop measurements. The evolution of vortex formation and dynamics has been visualized through a step-flow-rate experiment. Various flow dynamics regimes have been quantified and are presented in a Wi–Re diagram. The experimental results reveal that the contraction ratio can result in qualitatively different vortex dynamics of semi-dilute polymer solutions in microfluidics, whereas the length of the narrow channel merely affects the dynamics at a quantitative level. A single elasticity number, if defined by the size of the narrow channel, is not sufficient to account for the effects of contraction ratio on the non-linear vortex dynamics.

Effects of Polymer Chain Length and Stiffness on Phase Separation Dynamics of Semidilute Polymer Solution

Three-dimensional dissipative particle dynamics (DPD) simulations were performed to investigate the phase separation dynamics of semidilute polymer solutions with different polymer chain length and stiffness. For the polymer solution composed of shorter and more flexible chains, a crossover of the domain growth exponent from 1/3 to 2/3 was observed during the course of phase separation, indicating that the growth mechanism altered from diffusion to interfacial-tension driven flow. When the chain flexibility was kept the same but the chain was lengthened to allow for the chain entanglement to occur, the growth exponent changed to 1/4 in the diffusion-dominating coarsening regime while the growth exponent remained 2/3 in the flow-dominating regime. When the chain length was kept short but the stiffness was increased, the growth exponent became 1/6 in the diffusion-dominating regime and little effect was observed in the flow-dominating coarsening regime. The slow down of the phase separation dynamics in the diffusion-dominating coarsening could be explained by that the polymer chains could only perform wormlike movement when chain entanglements occurred or when the chain motion was limited by chain stiffness during phase separation. Moreover, when both the effects of chain length and stiffness were enhanced, polymer networks composed of longer and stiffer chains appeared and imposed an energy barrier for phase separation to occur. As a result, the polymer solution with stiffer and longer chains required a larger quench depth to initiate the phase separation and caused the delay in crossover of the coarsening mechanism from diffusion to flow.

Time domain effects in the single-chain dynamics of semidilute and concentrated polymer solutions

Single-chain dynamics in semidilute polymer solutions is Zimm-like on short time scales and Rouse-like on long time scales. The crossover is due to time-dependent screening of hydrodynamic interactions. We present a generalized Zimm theory for polymer dynamics in an elastic polymer network. We show that the coupled equations of motion of the polymer network–fluid system lead to a generalized Oseen tensor with a time-dependent hydrodynamic screening length. The time correlation function of the Rouse modes, monomer mean-square displacements and the single-chain dynamical structure factor are calculated.

Multiple Relaxations of Concentration Fluctuations in Entangled Polymer Solutions

We have investigated by dynamic light scattering the dynamics of semidilute polymer solutions in a good solvent, specifically polystyrene in benzene. We have shown that, using state-of-the-art instrumentation and data analysis techniques, it is possible to identify in the spectra of relaxation times three very weak slow modes with a combined amplitude of less than 5%, in addition to the dominant cooperative diffusion component (first mode). The results are compared with the predictions of Semenov's theory of dynamics of semidilute solutions in good solvents. The slowest component (fourth mode) was identified as the diffusion of clusters with characteristic size in the range of 100 nm. The third, broad mode corresponds to the reptation process, and finally the second mode is diffusive, with a decay time independent of molecular weight. It is about an order of magnitude slower than the cooperative diffusion and is tentatively assigned to dynamics corresponding to the interentanglement spacing. The three slow relaxation processes only appear for solutions having their concentration or molecular weight above the entanglement limit, ce or Me,c. For M = 770 000 we obtain ce ≅ 4.0c*, with c* being the usual overlap concentration and for a fixed concentration, of 0.05 g/mL we obtain Me,c ≅ 12Mc*, with Mc* being the overlap molecular weight for this concentration.

Neutron spin echo investigations on the segmental dynamics in semidilute polymer solutions under Θ- and good solvent conditions

Semidilute polymer solutions can be considered as transient networks of lifetime, τ g, and of average meshsize, ξ. ξ depends on the polymer concentration, c, and the solvent conditions. If the segmental diffusion of such systems is studied on timescales t ⪡ τ g using the neutron spin echo technique, different relaxation modes and continuous transitions between them are identified by varying the magnitude of the scattering vector, q. Under good solvent conditions, a crossover from single chain Zimm dynamics, as valid in dilute solutions on the entire intramolecular length scale, to the collective many chain diffusion is found at qξ( c) ≈ 1. The corresponding relaxation rates, Ω(q), vary from Ω(q) ∼ q 3 to Ω(q) q 2. In Θ-solvents, the many chain regime was not accessible. However, due to the existence of self-entanglements, which introduce an additional length scale ξ i ( c) < ξ( c), the crossover from disentangled (Ω(q) ∼ q 3) to entangled single chain relaxation (Ω(q) ∼ q) becomes visible.

Shear-Enhanced Structure and Dynamics in Semidilute Polymer Solutions

AbstractWe present elastic light scattering measurements of a semidilute polymer solution under shear flow. The basic symmetries observed in the shear-enhanced structure factor agree with the predictions of recently proposed theoretical models. The enhancement appears to be due to a coupling between the polymer concentration and shear flow through the concentration-dependent viscosity and normal stress coefficients. We also found an unexpected long wavelength peak in the shear-enhanced structure factor. Transient scattering measurements upon the cessation of shear have revealed the origin of this peak. The polymer solution demonstrates two modes of relaxation for concentration fluctuations in equilibrium due to a coupling between collective diffusion and stress relaxation. The transient scattering measurements indicate that the mechanism that couples the concentration fluctuations to the shear flow, and thereby enhances concentration fluctuations, selectively enhances only the slower of the two equilibrium modes. This selective enhancement generates the long wavelength peak in the shear-enhanced structure.

Dynamics of semidilute polymer solutions: hydrodynamic screening

En partant des equations de Ginsburg Landeau en fonction du temps, influence de cet effet sur la dynamique des solutions polymeres. Revue des theories existantes