Session T42: Focus Session: Theory and Simulation of Macromolecules II

Dynamics and rheology of living polymers

Molecular dynamics simulations are used to study the dynamics and stress relaxation in ``living'' polymers such as wormlike micelles (WLMs) of surfactants. These systems exhibit complex dynamical properties due to incessant chain scission and inter-chain recombination events over time scales that range from few ns to milliseconds. We study the structure and energetics of WLMs obtained from large-scale coarse-grained Molecular Dynamics simulations that consist of millions of atoms. Various dynamical properties such as the non-monotonic variation of the zero shear viscosity with salt concentration, as well as the recombination time and a possible reptation-based stress relaxation mechanism will be discussed.   

Extreme value statistics of work done in stretching a polymer in a gradient flow

We study the statistics of work on a finitely extensible polymer subjected to a gradient flow and thermal fluctuations. The flow breaks the detailed balance and stretches the polymer, the work to stretch the molecule is stored as elastic energy, which later dissipates with fluctuations of the molecule's elongation. The whole system is in a non-equilibrium dynamical state, which is sustained by the energy flow from the fluid to the molecule and back. We obtain the Large Deviation Function (LDF) of the work in the full range of appropriate flow, elasticity and thermal noise parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: ``near tails'' are linear in work and dominated by coiled polymer configurations, while ``far tails'' are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition. In our work, we use non-equilibrium work relations to study the extension of a polymer in a flow. Relations like these are becoming instrumental in studies of soft matter materials.   

Importance of chain tumbling and finite extension on the start-up and relaxation behavior of transient networks

Associative polymer networks are ubiquitous in tissue and biomedical engineering. However, the particular molecular attributes that contribute to the macroscopic behavior like shear thinning, self-healing, and yield stress are less well known. Here we incorporate chemical kinetics in the the Smoluchowski Equation capable of modeling the full network chain end-to-end distance distribution while tracking the fraction of looped, bridged, and dangling chains in the gel. In steady shear, we see the development of non-monotonic flow instabilities when the rate of chain association and dissociation are slower than the rate of chain relaxation. These instabilities arise due to a combination of chain finite extensibility and tumbling. During start-up of steady shear, the combination of these two phenomena also results in stress overshoots followed by multiple damped oscillations toward steady-state. The timescale of chain relaxation after the cessation of shear is dominated by the chain kinetics of association and dissociation as a function of the fraction of dangling chains present at any time post-shear.   

Mesoscopic Simulation Methods for Polymer Dynamics

We assess the accuracy and efficiency of mesoscopic simulation methods, namely Brownian Dynamics (BD), Stochastic Rotation Dynamics (SRD) and Dissipative Particle Dynamics (DPD), for polymers in solution at equilibrium and in flows in microfluidic geometries. Both SRD and DPD use solvent “particles” to carry momentum, and so account automatically for hydrodynamic interactions both within isolated polymer coils, and with other polymer molecules and with nearby solid boundaries. We assess quantitatively the effects of artificial particle inertia and fluid compressibility and show that they can be made small with appropriate choice of simulation parameters. We then use these methods to study flow-induced migration of polymer chains produced by: 1) hydrodynamic interactions, 2) streamline curvature or stress-gradients, and 3) convection of wall depletion zones. We show that huge concentration gradients can be produced by these mechanisms in microfluidic geometries that can be exploited for separation of polymers by size in periodic contraction-expansion geometries. We also assess the range of conditions for which BD, SRD or DPD is preferable for mesoscopic simulations. Finally, we show how such methods can be used to simulate quantitatively the swimming of micro-organisms such as E. coli.\\[4pt] In collaboration with Lei Jiang and Tongyang Zhao, University of Michigan, Ann Arbor, MI.   

Multi-fluid simulations of polymer dynamics

In many industrially important polymeric materials, a discrepancy exists between the time scale intrinsic to the system and processing time scales. As a consequence, models which go beyond equilibrium thermodynamics are required to understand the evolution of the microstructure of such materials. Building a tractable model to address such a system becomes especially challenging when process dynamics coexist with complex thermodynamic behavior such as micro- or macro-phase separation. Indeed, in many traditional simulation schemes (e.g. Brownian or molecular dynamics or dynamic field theories), cost constraints become prohibitive for 3D dynamic simulations as length and time scales increase. To address such problems, we explore a framework of meso-scale dynamic phase field models originally proposed by Brochard and de Gennes. Expanding on the ``two-fluid'' formalism of Doi and Onuki, we find that such models are capable of incorporating many phenomena relevant for industrially important polymer materials, including phase separation dynamics and viscoelastic fluid flow. In addition, we explore numerical methods capable of solving such models, with the goal of developing a framework for inexpensive ``multi-fluid'' simulations of polymer dynamics.   

Tightening the noose on tube models: a priori determination of equilibration time and other tube model parameters for 1,4-polybutadienes

Linear viscoelastic G' and G'' master curves for multiple linear, star, H, and comb 1,4-polybutadienes from the literature were compared and found with only one exception to agree well in the high frequency region, where G' and G'' exceed the plateau modulus, irrespective of molecular weight and branching structures. This agreement occurred despite variations of up to an order of magnitude in the horizontal shift factors used for generating master curves, probably due to small variations in the percentage of 1,2 linkages, which ranges from 6-10{\%} for typical 1,4-polybutadienes. Fitting high frequency data to the Rouse theory yields a ``universal'' equilibration time of around $\tau_e = 3.7e-07$ s at 25 C, regardless of chain architecture. From a study by Carella et al. (Macromolecules 17:2775, 1984), the plateau modulus for 1,4-polybutiene is expected to vary by only 2{\%} for 1,2 content ranging from 0.06 to 0.10, and a similar variability of the entanglement molecular weight over this range can be inferred for this range of 1,2 content. Accordingly, for typical 1,4-polybutadienes, with 1,4 content ranging form 6-10{\%}, all three canonical parameters of the tube model can be taken as fixed within a tight range, for 1,4-polybutadienes of any architecture, thus providing tight constraints on parameter adjustments that might be used to fit theories, such as tube theories, to rheological data.   

Plastic deformation of triblock elastomers by molecular simulation

The mechanical properties of thermoplastic elastomers (TPE) can be greatly enhanced by exploiting the complex morphology of triblock copolymers. A common strategy consists of confining chain ends into hard glassy regions that effectively crosslink a soft rubbery phase. We present molecular dynamics simulations that provide insight into key microscopic behaviour of the copolymer chains during deformation. First, a coarse-grained polymer model with an ABA type configuration and soft interactions is employed to achieve equilibrated spherical morphologies. Our model TPEs contain at least 30 spheres in order to ensure configurational averaging. Elastoplastic deformation with uniaxial extension or volume conserving shear is then studied after hard excluded volume interactions have been reintroduced. We consider trends of stress-strain curves for different chain lengths, and compare to equivalent homopolymeric systems. During deformation we simultaneously track the evolution of the number and shape of the minority spheres, the proportion of chains bridging from one sphere to another, as well as local plastic deformation. The simulations reveal strong differences between deformation modes, the evolution of sphere morphology and chain anisotropy.   

Entanglement effect in polymer melts by Dissipative Particle Dynamics (DPD)

Dissipative Particle Dynamics (DPD) is a mesoscale simulation method that has shown a very good potential in modeling different soft matter systems from colloidal suspensions to highly entangled polymers. Like any other simulation technique DPD is associated with some deficiencies, for instance in the case of entangled polymers soft repulsions used in DPD allow particle overlap which may result in topology violations that prevent the correct capturing of the entanglement effect. Therefore, in the present work in order to properly reproduce the dynamics and viscoelastic properties of polymers the soft repulsions between the particles are substituted with a repulsive potential between non-adjacent bonds of different FENE chains. Also, DPD is a coarse-grained simulation method that can be used to model time and length scales longer than atomistic models; however, due to the existence of an upper level limit for the level of coarse graining this method is not applicable for the whole mesoscopic range. Thus, this work represents a new approach for tuning the level of coarse-graining by adjusting the simulation parameters. The ability of the method in capturing the entanglement effects is validated by simulating dynamic and viscoelastic properties of polymers.   

Manipulating and Separating Polymers and Particles at the Microscale using Conformation-dependent Electrophoretic Mobility

Many separation techniques rely on different physical or chemical characteristics of the objects being separated. This includes separations based on size, total charge, or strength of interaction with a substrate. Recently there are many contexts in which it is important to manipulate or separate objects with different deformabilities. The deformability of an object is also important because it is related to the rheological response. We have developed a coarse-grained Brownian dynamics simulation model that incorporates the change in electrophoretic mobility of rigid as well as flexible objects with conformation. The model incorporates the effect in a computationally efficient way, and has been validated by comparing with experiments with double-stranded DNA. In this talk, we will describe the results of computer simulations using the new model in which we quantify the stretch and residence time of polymers in a combination of electric field gradients and pressure-driven flow. The coupling of the stretch and mobility leads to a new way trap and manipulate biomaterials. A comparison of the simulations with single molecule experiments will also be shown.   

Long-time diffusivity of DNA chains in nanochannels: A Brownian dynamics study

The simplest approach to calculate the diffusivity of any polymer chain is to use the double sum Kirkwood formula, which is based on preaveraging approximation of diffusion tensor. The error due to the preaveraging approximation has been reported by a number of researchers in the context of free solution by computing both Kirkwood diffusivity $D^{(K)}$ (also known as short-time diffusivity) and long-time diffusivity $D_L$. In nanochannels, the main approach to compute the diffusivity is the Kirkwood formula. However, the error due to the preaveraging approximation is not known in a confined system. We use Brownian dynamics simulation algorithm with excluded volume and hydrodynamic interactions to calculate both short-time and long-time diffusivities of DNA chains in nanochannels, and compare them for a range of channel sizes and DNA chain sizes. Our results indicate that the long-time diffusivity is always smaller than the short-time diffusivity, which is consistent with the result obtained in free solution using linear response theory $D_L < D^{(K)}$ [M. Fixman, Macromolecules $\textbf{14}$, 1710 (1981)]. We show that this preaveraging error decreases as channel size decreases. Even for weakly confined channels, errors are found to be about 1 $\%$ for chains up to 40 $\mu$m.   

Nanovoid formation in cross-linked epoxy and poly(dicyclopentadiene) networks during high strain rate deformation

Cross-linked polymer networks are widely used as structural and protective materials under extremes of temperature, pressure, or strain rate. In particular, substantial effort has been devoted to improving the high strain rate impact resistance of epoxy resins. Although epoxy resins are widely used in applications requiring impact resistance, epoxy resins with the strength and stiffness necessary in structural applications typically have poor toughness. Recent work showed that other chemistries in cross-linked polymers can overcome this trade-off between strength and toughness. Specifically, cross-linked polydicyclopentadiene (pDCPD) was found to have exceptional performance compared to epoxy resins, which is related to the high toughness of pDCPD. Based on the physicochemical properties of epoxy and pDCPD, it was hypothesized that the excellent toughness of pDCPD was due to the formation and growth of nanovoids during impact events. Void growth dissipates energy that otherwise would contribute to failure. We use atomistic molecular dynamics simulations to quantify void formation in these cross-linked polymer networks and to examine the molecular-level properties of the voids. Our findings suggest methods to increase void formation and growth, which may improve toughness.   

Modelling poly(p-phenylene teraphthalamide) at Extreme Tensile Loading using Reactive Potentials

Aromatic polyamides classified as rigid-rod polymers due to orientation of their monomers. Because of their excellent mechanical and thermal properties, aramids are widely used in the industry. For example DuPont's brand Kevlar, for its commercial aromatic polyamide polymer, due to wide usage of this polymer in ballistic applications, habitually used as a nickname for bulletproof vests. In order to engineer these ballistic fabrics, material properties of aramid fibers should be studied. In this work we focused on the poly(p-phenylene teraphthalamide) PPTA fiber, known as brand name Kevlar. We employed Reactive potentials to simulate PPTA polymer under tensile loading. We first simulated both amorphous and crystalline phases of PPTA. We also introduced defects with varying densities. We further analysed the recorded atomic positions data to understand how tensile load distributed and failure mechanisms at extreme tensile loads.