Dumbbell Polymer Research Articles

Molecular conformations of dumbbell-shaped polymers in good solvent.

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.

Viscoelastic Properties of Dumbbell-Shaped Polystyrenes in Bulk and Solution

This study examined viscoeslastic properties of two flexible dumbbell-shaped polystyrene (PS) samples, D-30/120/30 and D-30/240/30, which possess the same ring size (MR ∼ 30 kg/mol) and different lengths of central linear chains (ML ∼ 120 and 240 kg/mol) in bulk and solution. In bulk, both dumbbell PS samples exhibited an extremely long entanglement plateau in dynamic oscillatory measurements, and their terminal relaxation behavior was not observed in our experimental window. In stress relaxation measurements, dumbbell samples in bulk exhibited considerably slower terminal relaxation than high-molecular-weight linear PS samples (M ∼ 10⁶ g/mol), and a clear difference between two dumbbell PS samples was observed in the long time regime, i.e., terminal relaxation of D-30/240/30 is much slower than that of D-30/120/30. These results suggest that (i) the dumbbell polymer forms a characteristic “network” where two rings on both ends in a molecule spontaneously thread the ring part of other dumbbell chains and (ii) this type of interchain interaction resulting in network formation becomes more dominant than usual entanglements similar to linear chains. The network of dumbbell chains starts to relax their stress when the intermolecular threading is released, and this release process tends to occur more frequently for the dumbbell with a shorter central chain, D-30/120/30, than that with a longer one, D-30/240/30. In dioctyl phthalate (DOP) solutions of D-30/240/30, where DOP is known as a θ-solvent for PS at 22 °C, in a relatively high concentration regime (i.e., 20–30 wt %), the solutions exhibited an entanglement plateau and higher viscosity than the corresponding linear PS solutions, suggesting that the characteristic entanglement originating from intermolecular threading of dumbbell chains is still dominant in the solution. On the contrary, in a lower-concentration regime (≤8 wt %), the D-30/240/30 solutions exhibited similar viscosities to the linear PS ones, wherein the dumbbell molecules behave like unentangled/isolated chains.

Machine-learning-based non-Newtonian fluid model with molecular fidelity.

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN^{2}), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN^{2} where models based on empirical closures show limitations.

Viscometric flow for a many-body dissipative particle dynamics (MDPD) fluid with Lees–Edwards boundary condition

Viscometric properties of polymer are explored by the many-body dissipative particle dynamics (MDPD) using Lees–Edwards boundary conditions. The equation of state for the MDPD system is modified by fitting the density correction to different values of the cut-off radius. Due to the many-body interactions in MDPD, the viscosity contributed from the conservative force increases considerably with increasing repulsive coefficient, density and cut-off radius, and cannot be ignored compared to the ‘standard’ DPD case. The influence of these parameters on the MDPD viscosity is investigated, and we propose an equation to predict the viscosity in MDPD model. Additionally, the dumbbell polymer suspension model is investigated in the MDPD fluid, and the relations concerning first normal stress difference and shear rate, the relaxation time and spring constant, are consistent to theoretical works. We conclude that the MDPD model can be used to investigate the dynamics of non-Newtonian droplets.

Synthesis and characterization of dumbbell-shaped polystyrene

A dumbbell-shaped polystyrene (PS) sample, where rings are attached on both ends of a linear chain, was anionically synthesized by a coupling reaction between highly-purified ring PS (R-30; Mw = 33.7 kg/mol) with two diphenylethylene (DPE) type vinyl groups and bifunctional living linear PS (L-80; Mw = 84.0 kg/mol). The crude coupling product obtained was confirmed to include a targeted dumbbell polymer in addition to unreacted L-80 and R-30, and a single-tail tadpole polymer as byproducts. To isolate the dumbbell polymer, successive size-exclusion chromatography (SEC) and interaction chromatography (IC) fractionations were performed. It was found out that the dumbbell chain (D-30/80/30; Mw = 147 kg/mol) with sufficiently high purity (99.9%) was separated from the tadpole polymer with a single-tail in IC mode just due to a small difference in their chain architectures, i.e., the presence of the small rings on either one or both chain ends of a linear chain. This is the first report on successful preparation of a dumbbell-shaped polymer with high molecular weight and high purity, and the present product must be suitable for investigation of accurate physical properties.

The FENE Dumbbell Polymer Model: Existence and Uniqueness of Solutions for the Momentum Balance Equation

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coeffcients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.

Rheological characterization in shear of a model dumbbell polymer concentrated solution

We investigate the linear and non-linear rheological behavior in shear of a concentrated solution of “dumbbell” polystyrene with long linear backbone and dense short brushes at both ends and compare it with corresponding linear polymers. This type of dumbbells has never been rheologically characterized before. In linear viscoelasticity, the dumbbell polymers show significant differences with conventional linear polymers. In particular, the reptation relaxation of the dumbbell is strongly slowed down. Furthermore, the addition of the side chains increases the friction so that the dumbbell lies above the η 0 vs. number of entanglements relation of linear samples. Transient shear rheology experiments on weakly entangled solutions show a retardation of the chain stretch relaxation of the dumbbell by a factor 2.5 vs. a linear polymer with the same Rouse time. Additionally, a second peak in the transient viscosity is observed at high shear rates.

On the existence and uniqueness of solutions of the configurational probability diffusion equation for the generalized rigid dumbbell polymer model

Kinetic phase-space theories (see [3]) have long been associated with successfully predicting the rheological properties of a variety of macromolecular fluids. Their cornerstone is the configurational probability density, essential to calculating the stress tensor. This function is a solution to the probability diffusion equation. In Section 2 we prove the existence and uniqueness of solutions to the corresponding evolutionary diffusion equation, in Section 3 to the stationary (time independent) equation; these problems, within the context of polymer dynamics theory, did not receive attention until now.

A General Method for the Synthesis and Isolation of Well-Defined Core Cross-Linked Multistar Assemblies: A Route toward Enhanced pH-Responsive Polymers

A general method for the synthesis of well-defined multistar assemblies (in which the stars contain cross-linked cores) involving the atom transfer radical polymerization (ATRP) of macroinitiators (MIs) and cross-linker with the use of telechelic macroinitiators (TMIs) as the connecting blocks is described. Isolation of each type of multistar assembly with a high degree of specificity was achieved via a simple fractional precipitation process. Selective degradation of the PMMA-based and PtBMA-based multistar assemblies into their individual star units via cleavage of the disulfide group within the connecting blocks confirmed the synthesis of well-defined, low-polydispersity PMMA-based tristar and dumbbell polymers and PtBMA-based tetrastar, tristar, and dumbbell polymers. Hydrolysis of the PtBMA-based assemblies afforded amphiphilic poly(methacrylic acid) (PMAA) multistar assemblies and dumbbell polymers with enhanced pH responsiveness over their single star analogues, with changes in dh of 42% and 30%, r...

Coupled flow-polymer dynamics via statistical field theory: Modeling and computation

Field-theoretic models, which replace interactions between polymers with interactions between polymers and one or more conjugate fields, offer a systematic framework for coarse-graining of complex fluids systems. While this approach has been used successfully to investigate a wide range of polymer formulations at equilibrium, field-theoretic models often fail to accurately capture the non-equilibrium behavior of polymers, especially in the early stages of phase separation. Here the “two-fluid” approach serves as a useful alternative, treating the motions of fluid components separately in order to incorporate asymmetries between polymer molecules. In this work we focus on the connection of these two theories, drawing upon the strengths of each of the approaches in order to couple polymer microstructure with the dynamics of the flow in a systematic way. For illustrative purposes we work with an inhomogeneous melt of elastic dumbbell polymers, though our methodology will apply more generally to a wide variety of inhomogeneous systems. First we derive the model, incorporating thermodynamic forces into a two-fluid model for the flow through the introduction of conjugate chemical potential and elastic strain fields for the polymer density and stress. The resulting equations are composed of a system of fourth order PDEs coupled with a non-linear, non-local optimization problem to determine the conjugate fields. The coupled system is severely stiff and with a high degree of computational complexity. Next, we overcome the formidable numerical challenges posed by the model by designing a robust semi-implicit method based on linear asymptotic behavior of the leading order terms at small scales, by exploiting the exponential structure of global (integral) operators, and by parallelizing the non-linear optimization problem. The semi-implicit method effectively removes the fourth order stability constraint associated with explicit methods and we observe only a first order time-step restriction. The algorithm for solving the non-linear optimization problem, which takes advantage of the form of the operators being optimized, reduces the overall simulation time by several orders of magnitude. We illustrate the methodology with several examples of phase separation in an initially quiescent flow.

Synthesis and Characterization of Model Dumbbell Polymers

High molecular weight dumbbell shaped polymers were prepared by atom transfer radical polymerization (ATRP) to grow branches from repeat units of end blocks of a symmetric triblock copolymer. The triblock copolymer itself was prepared by polymer-polymer coupling of a commercially obtained alpha,omega-end functionalized polystyrene as central block with end-functionalized poly(chloromethylstyrene) that we synthesized by nitroxide-mediated polymerization. Temperature gradient interaction chromatography (TGIC) enabled the estimation of the terminal hydroxyl functionality of the high molecular weight alpha,omega-difunctional polystyrene as 75%. Size exclusion chromatography (SEC) and H-1 NMR enabled the determination of molecular weights and verification of the structures of the intermediate and the cleaved products. Size exclusion chromatography coupled with light scattering (SEC-LS) and scanning force microscopy (SFM) were used to confirm that the desired dumbbell architecture was obtained.

Polymer dynamics in a model of the turbulent buffer layer

A Brownian dynamics study of bead–spring–chain polymer dynamics is undertaken in a model flow that captures key features of the buffer region of near-wall turbulence—wavy streamwise vortices superimposed on a mean shear. In this flow and in any Lagrangian chaotic flow, a Hookean dumbbell polymer will stretch indefinitely if and only if the Weissenberg number based on the largest Lyapunov exponent for the velocity field is ⩾12. In the flow investigated here, this criterion is found to be good predictor of when the stretch of finitely extensible chains approaches its maximum value. The chains become highly stretched in the streamwise streaks and relax as they move into and around the vortex cores, leading to large differences in stress in different regions of the flow. Hydrodynamic and excluded volume interactions between polymer segments have no qualitative effects once results are normalized for the change in relaxation time due to their inclusion. The results from the bead–spring–chain models are used to assess the utility of the simpler FENE-P model. Although the FENE-P model does not capture the hysteresis in stress that is seen with the bead–spring–chain models, it otherwise qualitatively captures the behavior of the bead–spring chains. Most importantly, large polymer stress in the flow is seen at the same spatial positions for both the FENE-P and the more detailed models.

Electronic structures of transition metal–C 60 coordination polymers (η 6-C 60) nM n (M=Sc, Ti, V, or Cr)

The electronic structures of a series of transition metal (M)–C 60 dumbbell polymers (η 6-C 60) n M n have been examined with the one-dimensional (1D) tight-binding crystal orbital (TBCO) method at the extended Hückel (EH) approximation level. The band structures for M=Sc, Ti, and V are metallic but that for M=Cr is semiconductive with a narrow bandgap, E G≈8.15×10 −3 eV. For all the polymers, there are five specific bands near the Fermi level, four of which show the interaction between the d atomic orbitals (AO) (d xy and d x 2− y 2 ; the coordinate axes are given in the text) of M and the π orbitals on C 60. The structural instability of the 1D polymer for M=Cr is discussed based on the very narrow bandgap.

Hydrodynamics of particulate motion in sinusoidal pores via a singularity method

AbstractAxisymmetric motions of suspended spheres and dumbbells through sinusoidally corrugated capillaries are considered as an illustrative model of particulate or macromolecular transport in porous media. Numerical simulations are carried out using a least‐squares singularity method, which is well suited to simulating creeping flows in the complicated, time‐evolving geometries associated with particle motion through nonrectilinear pores. The numerical method is applied to a representative closure problem, whose solution yields effective transport coefficients describing particulate flow in porous media. With reference to polymer‐induced mobility control in enhanced oil recovery, a hydrodynamic mechanism of mobility reduction is studied using a rigid dumbbell polymer model.

高分子アーキテクチャー;アレイ状高分子のセルロースに対する吸着に及ぼす影響

高分子アーキテクチャー;アレイ状高分子のセルロースに対する吸着に及ぼす影響