Session B4: Dynamics of Polymers on Multi-Length Scales: Solutions

Dynamics in Multicomponent Polyelectrolyte Solutions

Double-network hydrogels (DN-gel) prepared from the combination of a moderately cross-linked anionic polyelectrolyte (poly(2-acrylamido-2-methyl-1-propanesulfonic acid), PAMPS) and an un-cross-linked linear polymer (polyacrylamide, PAAm) solution show strong mechanical properties far superior to that of their individual constituents [1]. To determine the origin of the superior properties of DN-gels, we investigated the structure and the chain dynamics of model PAMPS/PAAm solution blends using small-angle neutron scattering and neutron spin-echo measurements [2]. Akcasu's dynamic scattering theory for a multicomponent system [3] is modified to include polyelectrolytes, and the resulting equation describes well the neutron spin-echo results over the entire wavevector range covered in our experiments. Parameters such as effective solvent viscosity were deduced from the measured data using the modified Akcasu equation. Both the relaxation time at large length scales (10-100 nm) and the segmental diffusion coefficient at short length scales (0.1-1 nm) or the effective solvent viscosity show good accordance with the macroscopic rheological behavior of the solution blends. \\[4pt] [1] J.P. Gong et al., Adv. Mater. \textbf{15}, 1155 (2003). \\[0pt] [2] S. Lee et al., Macromolecules \textbf{42}, 1293 (2009). \\[0pt] [2] A.Z. Akcasu, in \textit{Dynamic Liht Scattering, The Method and Some Applications}; W. Brown Ed. (Oxford University Press, London 1992).   

Simulating the dynamics of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics

Two well--established and complementary methodologies to simulate the dynamics of polymers in solution are (i) Brownian Dynamics (BD), and (ii) Molecular Dynamics coupled dissipatively to a lattice Boltzmann background (MD/LB). The talk gives a brief introduction into both methods, and then presents results of a recent comparative study that applied both methods to the same model of a single chain that moves in a solvent under the influence of thermal noise. Emphasis is put on the question how to map the parameters onto each other, in particular those that are crucial for the dynamics. The agreement of static properties is perfect, as it must be. The dynamic properties agree very well, if for the MD/LB case the effects of finite box size are eliminated by extrapolation. We also find that proper thermalization of all MD/LB degrees of freedom (including the so--called ``kinetic modes'') is necessary. Small deviations between BD and MD/LB remain as a result of the different simulation methodologies. Finally, the computational efficiency of the two methods is compared. For the single--chain system, BD is clearly much faster, while scaling estimates suggest that the opposite is true for semidilute solutions. References: \begin{itemize} \item Tri T. Pham, Ulf D. Schiller, J. Ravi Prakash, and B. D\"unweg, J. Chem. Phys. {\bf 131}, 164114 (2009). \item B. D\"unweg and A. J. C. Ladd, Adv. Polym. Sci. {\bf 221}, 89 (2009). \end{itemize}   

Dynamics on Multiple Time and Length Scales in Complex Fluids Formed by Conjugated Polymers

Even though tremendous effort takes place to incorporate conjugated polymers into device applications, there is a significant gap in performance of the optimal desired devices developed. While the photo physics of highly conjugated polymers has been intensively investigated, the factors that affect the conformation and assembly and the dynamics on multiple length scales, that ultimately control the electro-optical response, have not been resolved. Using poly(\textit{para}phenyleneethynylene)s (PPE) as a model system for conjugated polymers, our studies have identified the driving forces for different association modes of PPEs as a function of their chemical structure and their interactions with solvents. X-ray and neuron scattering, probing dimensions from 0.1 to 100nm, revealed that PPEs dissolved in toluene form a rich variety of complex fluids. At high temperature the molecules are isolated and assume extended configuration. As the temperature decreases, the molecules associate and eventually form gels of different nature. In higher concentrations ordered phases are formed. Inelastic Neutron Back Scattering together with Neutron Spin Echo were used to study the dynamics on multiple length scales at the different complex fluids, exploring processes of 5-100 nano seconds. The dynamic scattering function incorporates the center of mass diffusion together with intramolecular motions. With decreasing temperature the PPE molecules aggregate and their center of mass diffusion is hindered. At the gellation transition the center of mass diffusion is no longer observed where as the intramolecular dynamics is retained in all phases. Cooperative dynamics of the solvent and PPE molecules has been observed in both molecular solution and micellar phase. The phases formed by PPEs are optically active where the dynamic processes affect directly their optical characteristics.   

Dynamics of Semiflexible Polymers in Solution

Biopolymers as individual filaments or assembled into solutions and networks are highly versatile materials with a large variety of different mechanical properties. At the same time they are interesting model systems that allow for the test of fundamental concepts of statistical mechanics and soft matter physics. The challenge is to understand how macroscopic material properties emerge from the intriguing interplay between entropy, filament elasticity and topological constrains on a molecular scale. In this talk we review recent progress in our understanding of the conformations and dynamics of single filaments from the single filament level up to the level of complex mutli-component networks. We critically review standard theories like the tube model and the reptation idea and show how new concepts like ``floppy modes'' emerge for stiff biopolymer systems. In addition to their physical relevance these concepts also contribute to our understanding of the functional principles of the cytoskeleton.   

Shear Banding and Flow Instabilities in Entangled Polymer Solutions

Entangled polymer solutions relax their stress by the reptation mechanism, in which polymers slither or ``reptate'' along their length. The original theory for this, due to Doi and Edwards (DE), has successfully captured many features of polymer dynamics. For applied shear rates much faster than the reptation time, the original DE theory predicts an instability due to the alignment of the ``tubes'' that constrain the polymer. This instability could lead to shear banding, in which the fluid can break into regions flow at different shear rates. For decades this had not been observed in entangled polymers, and DE theory has been modified to incorporate crucial missing physics, which could eliminate the original instability. Recent experiments by a number of groups on polymer solutions show macroscopic flow inhomogeneities consistent with the original DE instability and shear banding, but have been interpreted in other ways. I will discuss the predictions of the DE and related theories for flow inhomogeneities under strong flow conditions, and show that many, \textit{but not all}, of the recent experiments can be explained with no more new physics than is contained within DE theory. Note that most verifications and fittings of data to constitutive models (such as the DE model) assume homogeneous flow conditions: an important conclusion of this work is that one must study fully inhomogeneous flow to accurately validate these models.