Daniel J. Read

Mixing virtue and vice: combining the immediacy effect and the diversification heuristic

Many of the most significant choices that people make are between vices, which exchange small immediate rewards for large delayed costs, and virtues, which exchange small immediate costs for large delayed rewards. We investigate the consequences of making a series of such choices either simultaneously or sequentially. We made two predictions. First, because many alternatives chosen under simultaneous choice will only be experienced following a delay, and because hyperbolic time discounting predicts that people will prefer delayed virtues but immediate vices, we predicted that people would choose more virtues in simultaneous than sequential choice. Second, due to the tendency to diversify portfolios of choices, we predicted a greater mix of virtues and vices in simultaneous than sequential choice. These predictions were confirmed in two experiments involving real choices; one between ‘highbrow’ and ‘lowbrow’ movies, and the other between ‘instant-win’ and ‘prize-draw’ lottery tickets. We conclude by posing the question of whether simultaneous or sequential choice results in decisions that more closely approximate what people ‘really’ want. Copyright

Computational linear rheology of general branch-on-branch polymers

We present a general algorithm for predicting the linear rheology of branched polymers. While the method draws heavily on existing theoretical understanding of the relaxation processes in entangled polymer melts, a number of new concepts are developed to handle diverse polymer architectures including branch-on-branch structures. We validate the algorithm with experimental examples from model polymer architectures to fix the parameters of the model. We use experimentally determined parameters to generate a numerical ensemble of branched metallocene-catalyzed polyethylene resins. Application of our algorithm shows the importance of branch-on-branch chains in the system and predicts the linear rheology with good quantitative agreement over a wide range of branching density and molecular weight.

Linking models of polymerization and dynamics to predict branched polymer structure and flow.

The complex flow behavior of a branched polymer can be predicted from its chemical structure. We present a predictive scheme connecting the topological structure of highly branched entangled polymers, with industrial-level complexity, to the emergent viscoelasticity of the polymer melt. The scheme is able to calculate the linear and nonlinear viscoelasticity of a stochastically branched “high-pressure free radical” polymer melt as a function of the chemical kinetics of its formation. The method combines numerical simulation of polymerization with the tube/entanglement physics of polymer dynamics extended to fully nonlinear response. We compare calculations for a series of low-density polyethylenes with experiments on structural and viscoelastic properties. The method provides a window onto the molecular processes responsible for the optimized rheology of these melts, connecting fundamental science to process in complex flow, and opens up the in silico design of new materials.

Enduring pain for money: decisions based on the perception and memory of pain

We examine the relationship between memory for, and decisions about, pain. We test whether peoples willingness to accept pain (WTAP) in exchange for money depends on whether they experienced a sample of a similar pain either moments earlier, or one week earlier. Inspired by Leventhal et al.s two-factor theory of pain, we also manipulated whether subjects focused on, or were distracted from, their pain sensations. As predicted, although the distraction group displayed less WTAP than the sensation-focus group immediately after the initial experience, one week later they displayed greater WTAP. We also elicited WTAP and ratings of estimated pain intensity from a group of subjects who were given a description of the pain-induction procedure but did not actually experience it. These subjects exhibited greater WTAP, but similar ratings of pain intensity, compared with subjects who had experienced the pain either one week or moments earlier. Copyright

Bubble dynamics in viscoelastic fluids with application to reacting and non-reacting polymer foams

Abstract The effects of fluid viscoelasticity on the expansion of gas bubbles in polymer foams for the cases of reactive and non-reactive polymers are investigated. For non-reactive polymers, bubble expansion is controlled by a combination of gas diffusion and fluid rheology. In the diffusion limited case, the initial growth rate is slow due to small surface area, whereas at high diffusivity initial growth is rapid and resisted only by background solvent viscosity. In this high Deborah number (De) limit, we see a two stage expansion in which there is an initial rapid expansion up to the size at which the elastic stresses balance the pressure difference. Beyond this time, the bubble expansion is controlled by the relaxation of the polymer. In the model for reactive polymer systems, the polymer molecules begin as a mono-disperse distribution of a single reacting species. As the reaction progresses molecules bond to form increasingly large, branched, structures each with a spectrum of relaxation modes, which gel to form a viscoelastic solid. Throughout this process gas is produced as a by-product of the reaction. The linear spectrum for this fluid model is calculated from Rubinstein et al. [Dynamic scaling for polymer gelation, in: F. Tanaka, M. Doi, T. Ohta (Eds.), Space–Time Organisation in Macromolecular Fluids, Springer, Berlin, 1989, pp. 66–74], where the relaxation spectrum of a molecule is obtained from percolation theory and Rouse dynamics. We discretise this linear spectrum and, by treating each mode as a mode in a multimode Oldroyd-B fluid obtain a model for the non-linear rheology. Using this model, we describe how the production of gas, diffusion of gas through the liquid, and evolution of the largest molecule are coupled to bubble expansion and stress evolution. Thus, we illustrate how the rate of gas production, coupled to the rate of gas diffusion, affects the bubble size within a foam.

Uniaxial extensional rheology of well-characterized comb polymers

We present a detailed systematic investigation of the transient uniaxial extensional response of a series of well-characterized, anionically synthesized comb polystyrenes and polyisoprenes. The comb architecture consists of a linear chain backbone with multiple branches of equal molar mass, and represents an excellent model branched polymer. The linear viscoelastic response has been studied already in great detail. Our results indicate that the strain hardening becomes more important as the Hencky strain rate is increased. In general, the larger the number of entanglements of the segments between branches and/or of the branches, the stronger the strain hardening and the smaller the characteristic rate for its onset. The key molecular parameter appears to be the number of entanglements per branch. By varying it, one can tailor the amount and onset of strain hardening. This can be rationalized by accounting for the combined effect of backbone tube dilation and extra friction, brought about by the branches. ...

A full-chain constitutive model for bidisperse blends of linear polymers

We develop a full-chain tube-based constitutive model [along the lines of Graham et al. J. Rheol. 47, 1171 (2003)] for the nonlinear rheology of bidisperse blends of long and short linear polymers. For a test chain in the blend, we use the physical picture of a fat tube, representing long-lived entanglements with long chains, and a thin tube, representing entanglements with all chains. The model includes the processes of reptation, contour length fluctuation (CLF), constraint release, and stretch relaxation. In the linear rheology regime, we identify a new relaxation process: CLF along the fat tube contour, achieved via a combination of chain motion along the thin tube, and local constraint release of the thin tube as it explores the width of the fat tube. This process is sufficiently fast to relax a significant portion of the long chains before reptation. It provides an explanation of the decrease in terminal time of long chains upon dilution with short chains in a framework where motion along the thin t...

Numerical prediction of nonlinear rheology of branched polymer melts

In a recent short communication [Read, D. J. et al., Science 333, 1871 (2011)], we showed that a computational scheme can describe the nonlinear flow properties for a series of industrial low-density polyethylene (LDPE) resins starting from the molecular architecture. The molecular architecture itself is determined by fitting parameters of a reaction kinetics model to average structural information obtained from gel-permeation chromatography and light scattering. Flow responses of these molecules in transient uniaxial extension and shear are calculated by mapping the stretch and orientation dynamics of the segments within the molecules to effective pom-pom modes. In this paper, we provide the details of the computational scheme and present additional results on a LDPE and a high-density polyethylene resin to illustrate the dependence of segmental maximum stretch variables on the flow rate.

Pom-pom-like constitutive equations for comb polymers

In analogy with the pom-pom model, we introduce a simple model for comb polymers with multiple side-arms attached to a linear backbone by considering a set of coupled equations describing the stretch in the individual interbranch backbone segments. The stretch equations predict a sudden onset of backbone stretch as the flow rate is increased. Drag-strain coupling smooths this transition to some extent. For a series of well characterized polyisoprene and polystyrene combs, we find good agreement with the experimentally determined transient stress growth coefficients in uniaxial extension.

Convective constraint release with chain stretch: Solution of the Rouse-tube model in the limit of infinite tubes

This article derives a constitutive equation for entangled polymer melts and solutions, including the effects of convective constraint release (CCR) and chain stretch. It uses a model for CCR based upon the conjecture that constraint release events produce local hops of the tube, giving rise to a dynamical equation similar to the Rouse model. This equation is solved in the limit of infinite tubes. Although the solution in this limit ignores chain-end effects, the method presented has the following advantages; (i) it is less computationally expensive to implement than a full “finite chain” solution, (ii) it retains separate variables for chain stretch and tube orientation, allowing for straightforward modification of the equations to include different stretch dynamics, and (iii) it allows the possibility of smoothly changing the characteristics of the tube (such as tube diameter) upon deformation. In the latter context, this article explores the consequences of possible changes to the tube characteristics (tube diameter, persistence length, and CCR hop length) in response to chain stretch. It is found that the CCR-stretch equations are highly sensitive to the nature of the tube upon deformation, and in particular to the lower lengthscale cutoff used to describe the CCR process. The effect of CCR on chain stretch is explicitly derived from the microscopic model. The behavior of the constitutive equations is described for steady states under shear and startup under steady shear (where the results are compared against experiment).This article derives a constitutive equation for entangled polymer melts and solutions, including the effects of convective constraint release (CCR) and chain stretch. It uses a model for CCR based upon the conjecture that constraint release events produce local hops of the tube, giving rise to a dynamical equation similar to the Rouse model. This equation is solved in the limit of infinite tubes. Although the solution in this limit ignores chain-end effects, the method presented has the following advantages; (i) it is less computationally expensive to implement than a full “finite chain” solution, (ii) it retains separate variables for chain stretch and tube orientation, allowing for straightforward modification of the equations to include different stretch dynamics, and (iii) it allows the possibility of smoothly changing the characteristics of the tube (such as tube diameter) upon deformation. In the latter context, this article explores the consequences of possible changes to the tube characteristics ...