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

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

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

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

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 structure. Upon impact, 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 formation of holes. We find that material rheological properties 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 a Deborah number related to the shortest relaxation time associated to 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.Comment: accepted for publication in Soft Matte

Constraint Release mechanisms for H-Polymers moving in Linear Matrices of varying molar masses

We investigate the influence of the environment on the relaxation dynamics of well-defined H-polymers diluted in a matrix of linear chains. The molar mass of the linear chain matrix is systematically varied and the relaxation dynamics of the H-polymer is probed by means of linear viscoelastic measurements, with the aim to understand its altered motion in different blends, compared to its pure melt state. Our results indicate that short unentangled linear chains accelerate the relaxation of both the branches and the backbone of the H-polymers by acting as an effective solvent. On the other hand, the relaxation of the H-polymer in an entangled matrix is slowed-down, with the degree of retardation depending on the entanglement number of the linear chains. We show that this retardation can be quantified by considering that the H-polymers are moving in a dilated tube at the rhythm of the motion of the linear matrix