Dynamics of branched polymers: motion, scattering and rheology (original) (raw)
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Theoretical Molecular Rheology of Branched Polymers in Simple and Complex Flows: The Pom-Pom Model
Physical Review Letters, 1997
The nonlinear rheological constitutive equation of a class of multiply branched polymers is derived using the tube model. The molecular architecture may be thought of as two q-arm stars connected by a polymeric "crossbar." The dynamics lead to a novel integrodifferential equation which exhibits extreme strain hardening in extension and strain softening in shear. Calculations of flow through a contraction predict that the degree of long-chain branching controls the growth of corner vortices, in agreement with experiments on commercial branched polymers. [S0031-9007(97)04103-3]
Dynamics of Branched Polymers: A Combined Study by Molecular Dynamics Simulations and Tube Theory
Macromolecules, 2013
We present large-scale computer simulations of entangled polymers with symmetric star-like and Cayley tree-like architectures. Unlike the usual observation for repational behaviour of linear chains, the simulated systems exhibit a strong dispersion, over several decades, of the relaxation times after the local reptative ('Rouse in tube') regime. Relaxation is dramatically slowed down by approaching the branch point from the outer segments. This is consistent with the expected retraction mechanism for strongly entangled branched polymers. In order to describe fluctuations around the branch point, we introduce a Rouse-like model adapted to star-like polymers and incorporate entanglements by means of localizing springs. Model predictions for localization of the branch point are compared with simulations with fixed arm ends, which suppress retraction and tube dilution. Strikingly, the simulations reveal a localization of the branch point weaker than expected. This suggests the presence of early constraint-release effects that are not captured by the standard mechanism of tube dilution. We quantify, as a function of time, the strength of such effects and the fraction of relaxed material directly from the simulations with free ends. This allows us to renormalize the tube diameter and entanglement time in our model as time-dependent quantities. With this renormalization, the model provides an excellent description of the early relaxation of the branch point.
A Monte Carlo simulation study of branched polymers
The Journal of Chemical Physics, 2006
simulations are presented for the static properties of highly branched polymer molecules. The molecules consist of a semiflexible backbone of hard-sphere monomers with semiflexible side chains, also composed of hard-sphere monomers, attached to either every backbone bead or every other backbone bead. The conformational properties and structure factor of this model are investigated as a function of the stiffness of the backbone and side chains. The average conformations of the side chains are similar to self-avoiding random walks. The simulations show that there is a stiffening of the backbone as degree of crowding is increased, for example, if the branch spacing is decreased or side chain length is increased. The persistence length of the backbone is relatively insensitive to the stiffness of the side chains over the range investigated. The simulations reproduce most of the qualitative features of the structure factor observed in experiment, although the magnitude of the stiffening of the backbone is smaller than in experiment.
Macromolecules, 2014
Relaxation of branched polymers under tube based models involve a parameter p 2 characterizing the hop-size of relaxed side-arms. Depending on assumptions made in rheological models (e.g. about the relevant tube diameter for branchpoint hops) p 2 had been set to values varying from 1 to 1/60 in the literature. From large-scale molecular dynamics simulations of melts of entangled branched polymers of different architectures, and from experimental rheological data on a set of well-characterized comb polymers with many (∼ 30) side-arms, we estimate the values of p 2 under different assumptions in the hierarchical relaxation scheme. Both the simulations and the experiments show that including the backbone friction and considering hopping in the dilated tube provides the most consistent set of hopping parameters in different architectures.
Linear Rheological Response of a Series of Densely Branched Brush Polymers
Macromolecules, 2011
We have examined the linear rheological responses of a series of welldefined, dense, regularly branched brush polymers. These narrow molecular weight distribution brush polymers had polynorobornene backbones with degrees of polymerization (DP) of 200, 400, and 800 and polylactide side chains with molecular weight of 1.4 kDa, 4.4 kDa, and 8.7 kDa. The master curves for these brush polymers were obtained by time temperature superposition (TTS) of the dynamic moduli over the range from the glassy region to the terminal flow region. Similar to other long chain branched polymers, these densely branched brush polymers show a sequence of relaxation. Subsequent to the glassy relaxation, two different relaxation processes can be observed for samples with the high molecular weight (4.4 and 8.7 kDa) side chains, corresponding to the relaxation of the side chains and the brush polymer backbone. Influenced by the large volume fraction of high molecular weight side chains, these brush polymers are unentangled. The lowest plateau observed in the dynamic response is not the rubbery entanglement plateau but is instead associated with the steady state recoverable compliance. Side chain properties affect the rheological responses of these densely branched brush polymers and determine their glassy behaviors.
Shear induced ordering in branched living polymer solutions
Soft Matter, 2010
We present a coarse-grained model for the dynamics of living polymer solutions which explicitly includes solvent hydrodynamics. We show that lamellar and columnar structures emerge when the solution is subjected to simple shear. In the absence of shear, the model predicts a fluid-gel transition as a function of polymer concentration. At a threshold concentration, the selfintermediate scattering function indicates Zimm-like dynamics at large wave vectors and diffusive dynamics at small wave vectors. The kinetics of scission and recombination clearly demonstrates the existence of mean field and diffusion controlled regimes for the dynamics of living polymers at low and high concentrations respectively.
Arm Retraction Potential of Branched Polymers in the Absence of Dynamic Dilution
Physical Review Letters, 2005
We study the stress relaxation of model polymer networks containing low contents of star shaped and linear dangling polymers. As compared with their melts, the behavior of star and dangling polymers leads to a dynamic response with unprecedented large relaxation times. By comparing data of star melts with those corresponding to stars and dangling chains residing in polymer networks, we were able to identify the effects of dynamic dilution clearly. Since in polymer networks the dynamic dilution effect is suppressed, we were able by the first time to experimentally test the validity of the potential for arm retraction proposed by Pearson and Helfand.
2012
It has been a long held ambition of both industry and academia to understand the relationship between the often complex molecular architecture of polymer chains and their melt flow properties, with the goal of building robust theoretical models to predict their rheology. The established key to this is the use of well-defined, model polymers, homogeneous in chain length and architecture. We describe here for the first time, the in silico design, synthesis, and characterization of an architecturally complex, branched polymer with the optimal rheological properties for such structure−property correlation studies. Moreover, we demonstrate unequivocally the need for accurate characterization using temperature gradient interaction chromatography (TGIC), which reveals the presence of heterogeneities in the molecular structure that are undetectable by size exclusion chromatography (SEC). Experimental rheology exposes the rich pattern of relaxation dynamics associated with branched polymers, but the ultimate test is, of course, did the theoretical (design) model accurately predict the rheological properties of the synthesized model branched polymer? Rarely, if ever before, has such a combination of theory, synthesis, characterization, and analysis resulted in a "yes", expressed without doubt or qualification.