Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model which is critically assessed in view of its successes and shortcomings, whereas alternative approaches are briefly discussed. Finally, intriguing experimental findings and controversial issues that merit consistent explanation, such as shear banding instabilities, multiple stress overshoots in transient simple shear and enhanced steady-state elongational viscosity in polymer solutions, are discussed, whereas future directions such as branch point dynamics and anisotropic monomeric friction are outlined.Comment: 25 pages, accepted for publication in Journal of Physics Condensed Matter (August 2015

Transition from confined to bulk dynamics in symmetric star-linear polymer mixtures

We report on the linear viscoelastic properties of mixtures comprising multiarm star (as model soft colloids) and long linear chain homopolymers in a good solvent. In contrast to earlier works, we investigated symmetric mixtures (with a size ratio of 1) and showed that the polymeric and colloidal responses can be decoupled. The adopted experimental protocol involved probing the linear chain dynamics in different star environments. To this end, we studied mixtures with different star mass fraction, which was kept constant while linear chains were added and their entanglement plateau modulus ($G_p$) and terminal relaxation time ($\tau_d$) were measured as functions of their concentration. Two distinct scaling regimes were observed for both $G_p$ and $\tau_d$: at low linear polymer concentrations, a weak concentration dependence was observed, that became even weaker as the fraction of stars in the mixtures increased into the star glassy regime. On the other hand, at higher linear polymer concentrations, the classical entangled polymer scaling was recovered. Simple scaling arguments show that the threshold crossover concentration between the two regimes corresponds to the maximum osmotic star compression and signals the transition from confined to bulk dynamics. These results provide the needed ingredients to complete the state diagram of soft colloid-polymer mixtures and investigate their dynamics at large polymer-colloid size ratios. They also offer an alternative way to explore aspects of the colloidal glass transition and the polymer dynamics in confinement. Finally, they provide a new avenue to tailor the rheology of soft composites.Comment: 9 Figure

Capital Flows, Capital Account Liberalisation and the Mediterranean Countries

This paper examines questions related to possible capital account liberalisation in the Mediterranean countries. First, we provide an overview of the extent to which these countries have capital controls along with their exchange rate regimes and some basic macroeconomic aggregates. Second, we examine the case for capital account liberalisation, along with the prerequisites for successful liberalisation. Here we consider issues such as sequencing and possible benefits of synchronisation. Finally, we examine the experience with capital flows – both FDI and other capital flows. We explain these flows and use the past experience of these countries to draw some conclusions for the successful opening up of the capital account.capital account liberalisation, Mediterranean countries, capital flows

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) is steady state attainable during uniaxial extension? (ii) what is the respective transient response in simple shear? and (iii) how does stress relax upon cessation of extension or shear? To accomplish our goal we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry (FSR) and cone-partitioned plate (CPP) shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the Branch-on-Branch (BoB) algorithm. The data indicates that the extensional viscosity reaches a steady state value, whose dependence on extension rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rate-independent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong ‘elastic memory’ of the material. These results are 2 described by BoB semi-quantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than 3 entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers

Crystal-to-crystal transition of ultrasoft colloids under shear

Ultrasoft colloids typically do not spontaneously crystallize, but rather vitrify, at high concentrations. Combining in-situ rheo-SANS experiments and numerical simulations we show that shear facilitates crystallization of colloidal star polymers in the vicinity of their glass transition. With increasing shear rate well beyond rheological yielding, a transition is found from an initial bcc-dominated structure to an fcc-dominated one. This crystal-to-crystal transition is not accompanied by intermediate melting but occurs via a sudden reorganization of the crystal structure. Our results provide a new avenue to tailor colloidal crystallization and crystal-to-crystal transition at molecular level by coupling softness and shear

Structure and dynamics of nondilute polyfluorene solutions

The rotational and translational diffusion dynamics of newly synthesized polyfluorenes were studied by dynamic light scattering over a broad concentration range up to the lyotropic state. On the basis of small-angle neutron scattering and translational diffusion measurements in dilute solutions. the single polymers were described as wormlike chains with a low persistent length l = 7 +/- 0.5 nm and cross-section diameter d = 1.8 +/- 0.5 nm. In the semidilute concentration regime, the rate of increase of the cooperative diffusion and the osmotic pressure with c/c* (c* being the overlap concentration) was lower than for linear flexible chains in good solvent. The intermediate scattering function displayed a second process assigned to chain relaxation, in reasonable agreement with the longest relaxation time obtained from shear rheometry. The bimodal shape of the orientation correlation function, which is a characteristic feature of shape persistent polymers and exhibits a peculiar dependence on the scattering angle, was also observed in this model system. The fuzzy cylinder model adequately represented the concentration dependence of the osmotic modulus and the chain orientation time, conforming to the wormlike nature of these polymers

Analysis of dynamic mechanical response in torsion

We investigate the dynamic response of industrial rubbers (styrene-butadiene random copolymers, SBR) in torsion and compare against common small amplitude oscillatory shear measurements by using a torsion rectangular fixture, a modified torsion cylindrical fixture, and a conventional parallel plate fixture, respectively, in two different rheometers (ARES 2kFRTN1 from TA Instruments, USA and MCR 702 from Anton Paar-Physica, Austria). The effects of specimen geometry (length-to-width aspect ratio) on storage modulus and level of clamping are investigated. For cylindrical specimens undergoing torsional deformation, we find that geometry and clamping barely affect the shear moduli, and the measurements essentially coincide with those using parallel plates. In contrast, a clear dependence of the storage modulus on the aspect ratio is detected for specimens having rectangular cross section. The empirical correction used routinely in this test is based on geometrical factors and can account for clamping effects, but works only for aspect ratios above a threshold value of 1.4. By employing a finite element analysis, we perform a parametric study of the effects of the aspect ratio in the cross-sectional stress distribution and the linear viscoelastic torsional response. We propose a new, improved empirical equation for obtaining accurate moduli values in torsion at different aspect ratios, whose general validity is demonstrated in both rheometers. These results should provide a guideline for measurements with different elastomers, for which comparison with dynamic oscillatory tests may not be possible due to wall slip issues

Tailoring the flow of soft glasses by soft additives

We examine the vitrification and melting of asymmetric star polymers mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a {\it single} glass, in which the small component is fluid in the glassy matrix of the big one and a {\it double} glass, in which both components are vitrified. Addition of small star polymers leads to melting of {\it both} glasses and the melting curve has a non-monotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems.Comment: 4 pages, 4 figures, accepted in Phys. Rev. Let