Jetting of dilute polymer solutions

Light emitting devices containing conjugated polymers are conveniently fabricated using ink-jet printing. A common problem in the processing of these materials is that the Newtonian viscosity of the polymer solution is not sufficient to describe the jetting performance because the molecular weights and concentrations employed are such that the resulting solutions are elastic. These differences in fluid elasticity levels cannot be measured using traditional techniques like dynamic mechanical experiments or the first normal stress difference in shear, but strongly impact the jetting behavior of the liquid. In this study, a variety of polystyrene solutions in DECALIN having a shear viscosity of ~5 mPa s but different elasticity levels were examined for their jetting behavior. The jetting behavior of these solutions was studied visually using drop-on-demand jetting equipment and their rheology was characterized using a custom extensional rheometer designed for measuring the elasticity of such low viscosity liquids. If elasticity effects are absent as in Newtonian liquids (corresponding to a Trouton ratio of 3) satellite drops are formed resulting in loss of liquid and poor positioning. On the other hand, if elasticity effects are very large (Trouton ratios ≫4) separation problems occur at the nozzle with undesirable “tailing.” The optimum range for stable, efficient jetting occurs at Trouton ratios in a narrow band between 3 and ~5. A very slight degree of elasticity corresponding to a Trouton Ratio around four thus seems to be optimum for the jetting process. This appears to be the first time that such a design criterion has been outlined for this process. Such an approach complements thermal techniques for elucidating the role of molecular and flow properties on the processing behavior of polymeric systems.     

Shear thinning and polymer deformation in large flow fields

We theoretically investigate polymer deformation and shear thinning, i.e., a decrease of intrinsic viscosity, in a dilute polymer solution as a function of the applied shear rate $ \dot \gamma $. We use a bead-and-spring model with hydrodynamic interaction in the Rouse-Zimm framework, approximately accounting also for excluded-volume effects, and impose a constraint on the average mean-square spring length to prevent its stretching at large $ \dot \gamma $. When suitably normalized, both the intrinsic viscosity [η] and the components of the mean gyration tensor 〈SS〉 depend on the single variable $ \xi = {{\dot \gamma \tau _1^{\left( 0 \right)} } \mathord{\left/ {\vphantom {{\dot \gamma \tau _1^{\left( 0 \right)} } {N^{1 - v} }}} \right. \kern-\nulldelimiterspace} {N^{1 - v} }} $ where τ is the longest relaxation time for $ \dot \gamma = 0 $, N is the number of chain springs and v is the Flory exponent. The full shear-rate dependence is obtained numerically, and compared with analytical results obtained under free-draining conditions both for low and for very large shear rates. The shortcomings of the theory are also discussed, in particular a substantial stretching under shear of the central springs, where the intramolecular tension is largest, with a corresponding strong contraction of the end springs due to the average character of the constraint.     

Quasielastic scattering by dilute polymer solutions

The scattering law S( k ,w) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ω(k) of S( k ,w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse–Zimm model) using the “spring-bead” model ignoring memory effects. For small (ka\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} ? 1) and large (ka ? 1) values of k we find Ω = 0.195 k²/β α η₀ \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} and Ω = k²/βξ, respectively, indicating that the width is governed mainly by the viscosity η₀ for small k values and by the friction coefficient ξ for large k values. For intermediate k values which are of importance in neutron scattering we find that in the Rouse limit Ω = k⁴a²/12βξ. When the hydrodynamic effects are included, Ω(k) becomes 0.055 k³/βη₀. Using the Rouse–Zimm model, it is seen that the effect of pre-averaging the Oseen tensor is to underestimate the half-width Ω(k). The implications of the theoretical predictions for scattering experiments are discussed.     

Quasielastic scattering by dilute polymer solutions

The scattering law S(k, w) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ώ(κ) of S(k, w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse-Zimm model) using the “spring-bead” model ignoring memory effects. For small $ \left( {ka\sqrt N \ll 1} \right) $ and large (ka >> 1) values of k we find OHacgr; = 0.195 κ²/β aŋo,$ \sqrt N $ and OHacgr; = κ²/βξ respectively, indicating that the width is governed mainly by the viscosity ŋo for small κ values and by the friction coefficient ξ for large κ values. For intermediate κ values which are of importance in neutron scattering we find that in the Rouse limit Ώ = κ⁴a²/12βξ. When the hydrodynamic effects are included, Ώ(κ) becomes 0.055 κ³/βeng;o. Using the Rouse-Zimm model, it is seen that the effect of pre-averaging the Oseen tensor is to underestimate the half-width Ώ(κ). The implications of the theoretical predictions for scattering experiments are discussed.     

Transient entanglements and clusters in dilute polymer solutions

A convenient method to monitor polymer dissolution is to measure the pressure drop created by passing a polymer solution through a capillary constriction rheometer. In this work, we studied the dissolution of polyethylene oxide (PEO) and cationic starch (C‐starch). We found that for freshly dissolved and entangled PEO, the main contribution to the overall pressure drop is due to the contraction and expansion of PEO entanglements at the entrance and exit of the capillary, and that the friction in the capillary plays a minor role. On the other hand, for well‐dissolved PEO, because of the absence of PEO entanglements, the loss of pressure is mainly due to friction. At high velocities the contraction and expansion coefficient for freshly dissolved PEO was more than 20 times higher than for well‐dissolved PEO, resulting in a three times higher overall pressure drop. C‐starch consists of amylopectin (～ 85%) and amylose and is known to contain clusters when freshly dissolved, likely formed from the globular amylopectin molecules. For C‐starch, the main contribution to the overall pressure drop is due to friction. Entrance and exit effects contribute only 10% to the overall pressure drop, which might be due to the linear amylose molecules in C‐starch. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 253–262, 2008     

Viscosities of dilute polymer solutions in nematic liquids

A nematic fluid is characterized by five friction coefficients. When dilute polymer coils are added to the fluid, all these coefficients are modified. Three Miesowicz viscosities (measured under an aligning magnetic field) and two coupling coefficients between orientation and flow are discussed. In our calculation, elastic dumbbells are used to model the flexible polymer chains. The results are written in terms of two size parameters R_∥ and R_⊥ and two chain friction coefficients λ_∥ and λ_⊥ (the label ∥ refers to a direction parallel to the nematic axis). This could be compared to other experiments (such as translational diffusion) which measure λ_∥ and _⊥ directly. They may give useful estimates of coil conformation in nematic solvents.     

Shear banding in semidilute entangled polymer solutions

Shear banding in semidilute polymer solutions and other soft materials is one of the most intensely debated topics in current rheology. By means of rheo-optical experiments, physical modeling, and numerical simulations, researchers have started to develop a more thorough understanding of this flow instability within the past few years. Nevertheless, much effort is still required to identify the exact microscopic mechanisms leading to shear band formation and to clarify whether the phenomenon is universal for polymers. For this purpose, basic rheological characteristics, such as the appearance of a stress overshoot during start-up of a simple shear flow, have to be revisited and better related to the dynamics of the polymeric network.     

Computer simulation of dilute polymer solutions in transient elongational flows

The behaviour of polymer molecules in solution flowing through a succession of contraction‐expansion zones was simulated using the Brownian dynamics method. The velocity profile of the flow field calculated previously, assuming that the flow modification in dilute polymer solution is negligible, was used. In the vicinity of the cell symmetry axis the flow can be described as an oscillatory elongational planar flow. The dumbbell with conformation‐dependent friction and elastic coefficients was chosen as a model for the polymer chain. When the initial state of the polymer chain entering the first contraction zone had corresponded to a gaussian coil the initial increase in the polymer deformation along the flow direction was observed. After some time independent of the flow rate, the amplitude of deformation gradually decreased to the stationary value further in the cell where the polymer deformation followed the flow oscillations. The amplitude of the deformation oscillations showed the critical behaviour: they increased for flow rates less than a critical value and did not change with further increase in the flow rate.     

Thermodynamics and viscosities of dilute polymer solutions in binary solvents

Experiments aimed at comparison of calculated and experimental intrinsic viscosities of PS and PMMA in some binary solvents used as eluents in chromatography are performed. The intrinsic viscosities are determined in mixed solvents of different thermodynamic qualities, including a θ solvent, in a wide composition range. The analysis of the thermodynamic and rheological theoretical equations for ternary systems allowed the interpretation of anomalies observed on the experimental curves of intrinsic viscosity versus solvent composition.     

Capillary electrophoresis of RNA in dilute and semidilute polymer solutions

We report separations of RNA molecules (281-6583 nucleotides) by capillary electrophoresis in dilute and semidilute solutions of aqueous hydroxyethylcellulose (HEC) ether in varying buffers. RNA mobility and peak band widths are examined under both nondenaturing and also denaturing conditions. From studies of sieving polymer concentration and chain length, it is found that good separations can be obtained in semidilute solutions as well as in dilute solutions. The dependence of RNA mobility on its chain length is consistent with separation by a similar to transient entanglement mechanism in dilute solutions. In semidilute entangled solutions the separation proceeds by segmental motion.     

Excluded-volume effects in dilute polymer solutions. IV. Polyisobutylene

Statistical radii of gyration, second virial coefficients, and intrinsic viscosities of sharp fractions (M?_w/M?_n ≈ 1.1) of polyisobutylene (PIB) covering a wide range of molecular weight (1.6 × 10⁵ to 4.7 × 10⁶) were determined in isoamyl isovalerate (IAIV) at a number of temperatures ranging from 20 to 60°C, in n-heptane at 25°C, and in cyclohexane at 25°C by light-scattering and viscosity measurements. It was found that IAIV at 22.1°C is a theta solvent for PIB. Analysis of the data by the methods described in preceding papers of this series indicated that, except for minor differences, the conclusions derived from similar studies with polychloroprene, polystyrene, and poly-p-methylstyrene hold equally for solutions of the typical linear polymer investigated here. In particular, no decisive evidence for the drainage effect was found.     

Comparison of theory and experiment for diffusion in dilute polymer solutions

Results from a number of theories for the concentration dependence of the mutual diffusion coefficient in dilute polymer solutions are examined, and clarifications are made as to what forms of the equations for these theories should be used in comparisons with experimental diffusivity data. An evaluation of the available theories for the concentration dependence of the diffusivity under theta conditions is carried out using experimental diffusivity data taken using sharp fractions of polystyrene. It is concluded that the Pyun—Fixman theory appears to provide the most promising method for estimating the concentration dependence of the mutual diffusion coefficient in dilute polymer solutions at the present time.     

Effect of solvent on depolarized light scattering in dilute polymer solutions

An optical model of a system in which both polymer segments and solvent molecules are described as point dipoles has been used to calculate the intensity of light depolarized in scattering. The final expression consists of six terms, the physical meaning of which is briefly discussed. An approximation procedure has been worked out for the calculation of two interaction terms due to deviations of the local field in solution from the Lorentz–Lorenz field; the terms have been calculated for simple models of flexible and rigid molecules. Their dependence on molecular weight appears to be approximately the same as the intrinsic anisotropy of the polymer molecule; their contribution is nonzero even for a solvent isorefractive with the polymer.     

Application of the porous-sphere hydrodynamic model to dilute polymer solutions

The porous-sphere model of Debye–Brinkman–Bueche is applied to predict the limiting frictional coefficient f₀ and intrinsic viscosity [η] of polystyrene fractions in tetrahydrofuran and random protein coils in 6M guanidine hydrochloride. Following the formulation of Wiegel and Mijnlieff, the molecular permeability is modeled to increase exponentially as the square of the distance from the center of the molecule. A method is developed to obtain this permeability from the translational diffusion coefficient. The experimental values of f₀ and [η] are in satisfactory agreement with the calculated values. Also, this analysis predicts values of the Mandelkern–Flory–Scheraga parameter for flexible coils which are significantly smaller than the minimum values permitted by the Kirkwood–Riseman theory. This is in accord with the experimental evidence.     

Phase separation in dilute polymer solutions at high‐rate extension

In this article the demixing instability and phase segregation in unentangled polymer solutions of semiflexible chains at high‐rate uniaxial extension above the coil to stretched coil transition was studied. Orientation of the stretched chains was described in terms of an effective potential field. Based on the free energy analysis it was shown that the flow‐induced orientation of polymer segments could drastically reduce the energy of their steric repulsion. As a result attraction between the chains gain more importance, and this effect lead to the demixing process and eventual segregation of polymer from the solvent if the strain rate exceeds some critical value. A mean‐field theory was developed to study this flow‐induced phase separation effect. The phase diagrams of the system showing the spinodal and binodal transitions at different extension rates were calculated and discussed. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1066–1073