arXiv subjects

Peter D. Olmsted

Publications and source records attributed to Peter D. Olmsted.

At least 19 recordsLinked to original sources

arXiv2026

A Smoluchowski equation for a sheared suspension of frictionally interacting rods

In this work we develop constitutive equations for a dense, sheared suspension of frictionally interacting rods by applying Onsager's variational method as formulated by Doi. We treat both solid friction, of the Amontons-Coulomb form; and lubricated friction, which scales with relative tangential velocity at the contact point. Dissipation functions in terms of the rod angular velocity are derived via a mean field approach for each form of friction, and from these, a Rayleighian for dense suspensions of rigid rods under shear constructed. Derivatives of this Rayleighian with respect to rod angular velocity and velocity gradient give a Smoluchowski equation and stress tensor, respectively. We show that these are representable as perturbations to Doi's model for a sheared liquid crystal. We also suggest a form for the average number of contacts between rods as a function of volume fraction, aspect ratio, and nematic order parameter, generalizing Philipse's random contact equation for disordered packings.

cond-mat.soft↗

arXiv2026

Hydrodynamic cascade drives tumbling in sheared colloidal rod suspensions

Modeling the dynamics of colloidal rods remains a central challenge in soft-matter physics due to the anisotropic and long-ranged nature of their interactions. Hydrodynamic interactions in rods suspensions are often assumed to be screened or too week to play any role in semi-dilute regimes, yet we find here these assumptions to break down at shear rates and concentrations that are often attained in experiments. Using particle-based simulations and scaling analysis, we uncover a cascade of tumbling events driven by hydrodynamic coupling among neighboring rods. This collective dynamics disrupts flow alignment and leads to a pronounced increase in viscosity and normal stress differences, in qualitative agreement with recent experiments. The discovery of this hydrodynamically-promoted cascade effect calls for a revision of existing constitutive models for colloidal rods and highlights hydrodynamic coupling as a key mechanism governing collective dynamics in highly anisotropic suspensions.

cond-mat.soft↗

arXiv2026

Shear Banding in Simulations of Polymer Melts

Results from numerical simulations of polymers under shear flow are compared with predictions for shear banding based on a model coupling Rolie-Poly-like tube dynamics to the entanglement dynamics mediated by Convected Constraint Release (CCR). CCR is controlled by a parameter $β$, whose dependence on the bending stiffness $k_θ$ is calculated from the simulations. The model predicts shear banding for polymers whose equilibrium entanglement number $Z$ exceeds a critical value $Z_{c}$ that depends on $β$. The simulations are in semi-quantitative agreement with the model, with deviations that are attributed to approximations inherent in the model, and the inadequacy of tube models to describe partially-disentangled liquids in strong flow. These results may help determine which physical polymers could undergo shear banding.

cond-mat.soft↗

arXiv2026

Elastic turbulence in highly entangled polymers and wormlike micelles

We show theoretically that an initially homogeneous planar Couette flow of a concentrated polymeric fluid is linearly unstable to the growth of two-dimensional (2D) perturbations, within two widely used constitutive models: the Johnson-Segalman model and the Rolie-Poly model. We perform direct nonlinear simulations of both models in 2D to show that this instability leads to a state of elastic turbulence comprising several narrow shear bands that dynamically coalesce, split and interact. Importantly, we show that this 2D instability arises not only in fluids that have a non-monotonic constitutive curve, and therefore show shear banding in 1D calculations, but also in shear thinning fluids with a monotonic constitutive curve, for which an initially homogeneous base state is stable in 1D. For the former category, the high shear branch of the constitutive curve is unstable to 2D instability in both models, so that the high shear band may be turbulent. In the Rolie-Poly model, the low shear branch is also likewise unstable. Our work provides the first simulation evidence for elastic turbulence in highly entangled polymeric fluids. It also potentially explains rheo-chaotic states seen experimentally in shear banding wormlike micelles. We additionally demonstrate elastic turbulence within both models in the planar Poiseuille geometry.

cond-mat.soft↗

arXiv2025

Chain-length-dependent correlated molecular motion in polymers

We show how dynamic heterogeneities (DH), a hallmark of glass-forming materials, depend on chain flexibility and chain length in polymers. For highly flexible polymers, a relatively large number of monomers ($N_c\sim500$) undergo correlated motion at the glass transition temperature $T_g$, independent of molecular weight ($M$). In contrast, less flexible polymers show a complex $N_c(M)$ behaviour divided into three regimes, consistent with observation in both $T_g(M)$ and chain conformational structure. For short oligomers ($\lesssim$ 2 Kuhn steps), a transition from mainly $\it{inter}$molecular correlations and $N_c\sim 200$, to strongly $\it{intra}$molecular correlations and $N_c< 50$ (roughly the molecular size) is observed; for longer chains, $N_c$ increases weakly, before saturating. For poly(methyl methacrylate), a remarkable similarity is found between $N_c(M)$ and the $M$-dependent ratio of the activation barriers of the structural ($α$) and secondary ($β$) relaxations. Our results suggest a link between the DH length-scale and the number of $β$ relaxation events jointly-activated to facilitate the $α$ relaxation.

cond-mat.soft↗

arXiv2025

The roles of elasticity and dimension in liquid-gel phase separation

We compare six elastic models for polymer networks in the context of phase separation within a gel, including a new model that combines the finite extensible Arruda-Boyce model and the slip tube model for entangled chains. We study incompressible uniaxial stretch and compression, and three volume-changing constrained-dimension deformations, in which the material can only deform in the designated dimensions(s) while the constrained direction(s) remain(s) the same. Each model responds differently to large deformations, and our proposed model successfully describes both strain softening and strain hardening, which are both present in well-entangled elastomers. When considering phase separation, we show that the commonly-used neo-Hookean model fails to admit a common tangent construction for phase coexistence for 3D deformations. This can be resolved by using a model with finite extension, such as the Arruda-Boyce model. In constrained-dimension deformations, where the gel's volume is allowed to change, for elastic models in which phase coexistence is possible, the critical temperatures increases and the critical concentration decreases with increasing deformation dimensions. This strong dependence of the phase diagram on spatial dimension and geometry distinguishes phase separation elastic media from conventional phase separation.

cond-mat.soft↗

arXiv2025

Thermodynamics of microphase separation in a swollen, strain-stiffening polymer network

Elastic MicroPhase Separation (EMPS) provides a simple route to create soft materials with homogeneous microstructures by leveraging the supersaturation of crosslinked polymer networks with liquids. At low supersaturation, network elasticity stabilizes a uniform mixture, but beyond a critical threshold, metastable microphase-separated domains emerge. While previous theories have focused on describing qualitative features about the size and morphology of these domains, they do not make quantitative predictions about EMPS phase diagrams. In this work, we extend Flory-Huggins theory to quantitatively capture EMPS phase diagrams by incorporating strain-stiffening effects. This model requires no fitting parameters and relies solely on independently measured solubility parameters and large-deformation mechanical responses. Our results reveal that strain-stiffening enables metastable microphase separation within the swelling equilibrium state and why the microstructures can range from discrete droplets to bicontinuous networks. This works highlights the critical role of nonlinear elasticity in controlling phase-separated morphologies in polymer gels.

cond-mat.soft↗

arXiv2024

A fast transferable method for predicting the glass transition temperature of polymers from chemical structure

We present a new method that successfully predicts the glass transition temperature $T_{\! \textrm{g}}$ of polymers based on their monomer structure. The model combines ideas from Group Additive Properties (GAP) and Quantitative Structure Property Relationship (QSPR) methods, where GAP (or Group Contributions) assumes that sub-monomer motifs contribute additively to $T_{\! \textrm{g}}$, and QSPR links $T_{\! \textrm{g}}$ to the physico-chemical properties of the structure through a set of molecular descriptors. This method yields fast and accurate predictions of $T_{\! \textrm{g}}$ for polymers based on chemical motifs outside the data sample, which resolves the main limitation of the GAP approach. Using a genetic algorithm, we show that only two molecular descriptors are necessary to predict $T_{\! \textrm{g}}$ for PAEK polymers. Our QSPR-GAP method is readily transferred to other physical properties, to measures of activity (QSAR), or to different classes of polymers such as conjugated or bio-polymers.

cond-mat.soft↗

arXiv2024

Entanglement kinetics in polymer melts are chemically specific

We investigate the universality of entanglement kinetics in polymer melts. We compare predictions of a recently developed constitutive equation for disentanglement to molecular dynamics simulations of both united-atom polyethylene and Kremer-Grest models for polymers in shear and extensional flow. We confirm that entanglements recover on the retraction timescale, rather than the reptation timescale. We find that the convective constraint release parameter $β$ is independent of molecular weight, but that it increases with the ratio of Kuhn length $b_K$ to packing length $p$ as $β\sim (b_K/p)^α$, with an exponent $α=1.9$, which may suggest that disentanglement rate correlates with an increase in the tube diameter. These results may help shed light on which polymers are more likely to undergo shear banding.

cond-mat.soft↗

arXiv2022

Bonded straight and helical flagellar filaments form ultra-low-density glasses

We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semi-dilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are micron-long helices assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics, so that shape-diblocks become permanently jammed at exceedingly low densities. We also measure the rheological properties of semi-dilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semi-dilute fibrous suspensions.

cond-mat.soft↗

arXiv2022

A thermodynamically consistent constitutive equation describing polymer disentanglement under flow

We derive a thermodynamically consistent framework for incorporating entanglement dynamics into constitutive equations for flowing polymer melts. We use this to combine the convected constraint release (CCR) dynamics of Ianniruberto-Marriccui into a finitely-extensible version of the Rolie-Poly model, and also include an anisotropic mobility as in the Giesekus model. The reversible dynamics are obtained from a free energy that describes both a finitely-extensible conformation tensor and an ideal gas of entanglements along the chain. The dissipative dynamics give rise to coupled kinetic equations for the conformation tensor and entanglements, whose coupling terms describe shear-induced disentanglement. The relaxation dynamics of the conformation tensor follow the GLaMM and Rolie-Poly models, and account for reptation, retraction and CCR. We propose that the relaxation time $τ_ν$ for entanglement recovery is proportional to the Rouse time $τ_R$ which governs polymer stretch within the tube. This which matches recent molecular dynamics simulations, and corresponds to relaxing the entanglement number before the entire polymer anisotropy has relaxed on the longer reptation time $τ_d$. Our model suggests that claimed signatures of slow re-entanglement on the reptation time in step-strain experiments may be interpreted as arising from anisotropies in reptation dynamics.

cond-mat.soft↗

arXiv2022

Cooperative intramolecular dynamics control the chain-length-dependent glass transition in polymers

The glass transition is a long-standing unsolved problem in materials science. For polymers, our understanding of glass-formation is particularly poor due to the added complexity of chain connectivity and flexibility; structural relaxation of polymers thus involves a complex interplay between intra- and inter-molecular cooperativity. Here we study how the glass transition temperature Tg varies with molecular weight M for different polymer chemistries and chain flexibilities. We find that Tg(M) is controlled by the average mass (or volume) per conformational degree of freedom, and that a `local' molecular relaxation (involving a few conformers) controls the larger-scale cooperative alpha relaxation responsible for Tg. We propose that dynamic facilitation where a `local' relaxation facilitates adjacent relaxations, leading to hierarchical dynamics, can explain our observations including logarithmic Tg(M) dependences. Our study provides a new understanding of molecular relaxations and the glass transition in polymers, which paves the way for predictive design of polymers based on monomer-scale metrics.

cond-mat.soft↗

arXiv2022

Probing the nonequilibrium dynamics of stress, orientation and entanglements in polymer melts with orthogonal interrupted shear simulations

Both entangled and unentangled polymer melts exhibit stress overshoots when subject to shearing flow. The size of the overshoot depends on the applied shear rate and is related to relaxation mechanisms such as reptation, chain stretch and convective constraint release. Previous experimental work shows that melts subjected to interrupted shear flows exhibit a smaller overshoot when sheared after partial relaxation. This has been shown to be consistent with predictions by constitutive models. Here, we report molecular dynamics simulations of interrupted shear of polymer melts where the shear flow after the relaxation stage is orthogonal to the original applied flow. We observe that, for a given relaxation time, the size of the stress overshoot under orthogonal interrupted shear is larger than observed during parallel interrupted shear, which is not captured by constitutive models. Differences in maxima are also observed for overshoots in the first normal stress and chain end-to-end distance. We also show that measurements of the average number of entanglements per chain and average orientation at different scales along the chain are affected by the change in shear direction, leading to non-monotonic relaxation of the off-diagonal components of orientation and an appearance of a 'double peak' in the average number of entanglements during the transient. We propose that such complex behavior of entanglements is responsible for the increase in the overshoots of stress components, and that models of the dynamics of entanglements might be improved upon by considering a tensorial measurement of entanglements that can be coupled to orientation.

cond-mat.soft↗

arXiv2021

Microscopic interactions and emerging elasticity in model soft particulate gels

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.

cond-mat.soft↗

arXiv2020

Fluctuating viscoelasticity based on a finite number of dumbbells

Two alternative routes are taken to derive, on the basis of the dynamics of a finite number of dumbbells, viscoelasticity in terms of a conformation tensor with fluctuations. The first route is a direct approach using stochastic calculus only, and it serves as a benchmark for the second route, which is guided by thermodynamic principles. In the latter, the Helmholtz free energy and a generalized relaxation tensor play a key role. It is shown that the results of the two routes agree only if a finite-size contribution to the Helmholtz free energy of the conformation tensor is taken into account. Using statistical mechanics, this finite-size contribution is derived explicitly in this paper for a large class of models; this contribution is non-zero whenever the number of dumbbells in the volume of observation is finite. It is noted that the generalized relaxation tensor for the conformation tensor does not need any finite-size correction.

cond-mat.soft↗

arXiv2019

Scission of flexible polymers in contraction flow: predicting the effects of multiple passages

When injected through a contraction, high molecular weight polymer solutions exhibit a sharp increase of apparent viscosity which originates from stretching polymer chains above a critical extension rate. This chain stretching can also induce polymer scission, which then decreases the extensional viscosity. In practice, the two phenomena are difficult to separate. Moreover, these phenomena are often observed in situation where flow instabilities appear. In order to disentangle the two effects we have measured the pressure-flux relation for polymer solutions passing through a hyperbolic contraction. The ratio of the pressure drop to that of the (Newtonian) solvent has a maximum due to the competition between polymer extension and scission. We find a geometry-dependent relation between the flow rates at which the maximum occurs for successive passages in a given contraction, which appears to be independent of molecular weight, concentration, solvent quality and viscosity, and can be used to predict the scission under successive passes.

physics.flu-dyn↗

arXiv2018

Effects of passive phospholipid flip-flop and asymmetric external fields on bilayer phase equilibria

Compositional asymmetry between the leaflets of bilayer membranes modifies their phase behaviour, and is thought to influence other important features such as mechanical properties and protein activity. We address here how phase behaviour is affected by passive phospholipid \textit{flip-flop}, such that the compositional asymmetry is not fixed. We predict transitions from "pre flip-flop" behaviour to a restricted set of phase equilibria that can persist in the presence of passive flip-flop. Surprisingly, such states are not necessarily symmetric. We further account for external symmetry-breaking, such as a preferential substrate interaction, and show how this can stabilise strongly asymmetric equilibrium states. Our theory explains several experimental observations of flip-flop mediated changes in phase behaviour, and shows how domain formation and compositional asymmetry can be controlled in concert, by manipulating passive flip-flop rates and applying external fields.

cond-mat.soft↗

arXiv2017

Frustration and thermalisation in an artificial magnetic quasicrystal

We have created and studied artificial magnetic quasicrystals based on Penrose tiling patterns of interacting nanomagnets that lack the translational symmetry of spatially periodic artificial spin ices. Vertex-level degeneracy and frustration induced by the network topology of the Penrose pattern leads to a low energy configuration that we propose as a ground state. Topologically induced emergent frustration means that this ground state cannot be constructed from vertices in their ground states. It has two parts, a quasi-one-dimensional rigid "skeleton" that spans the entire pattern and is capable of long-range order, and "flippable" clusters of macrospins within it. These lead to macroscopic degeneracy for the array as a whole. Magnetic force microscopy imaging of Penrose tiling arrays revealed superdomains that are larger for more strongly coupled arrays. The superdomain size is larger after AC-demagnetisation and especially after annealing the array above its blocking temperature.

cond-mat.dis-nn↗