Session Q3: Simple Views on Polymer Dynamics: Symposium Honoring P G de Gennes

Quasielastic scattering -- theory and experiment hand in hand

In his early career de Gennes worked with colleagues at the CEA Saclay and was familiar with the new possibilities offered for studying materials using neutron scattering techniques. He published a number of papers in this field, two of the most influential being in the field of polymer dynamics where he developed theoretical descriptions of quasi-elastic scattering from single polymer chains in solution. The first results were based on the Rouse model of a polymer chain with no dynamic interaction with the solvent. The second paper appearing a few years later extended the theory to take account of hydrodynamic interactions with the solvent (the so-called Zimm model). These papers appeared at the time when high resolution quasi-elastic scattering techniques were being developed at a number of neutron sources and were influential in driving some of the first experimental investigations of polymer dynamics using neutrons. As dynamic light scattering developed, particularly from large biological molecules the theory was also applied here. The subsequent development of the reptation model for polymer molecules in the dense phase, and the publication by de Gennes of the scattering law expected from a reptating chain also coincided with developments in experimental techniques, in particular the neutron spin-echo technique. This technique allowed the scattering from single polymer molecules in dense phases to be observed and provided some of the first direct experimental tests of the reptation model. Quasielastic scattering and particularly neutron spin-echo techniques have been continually developing in subsequent decades, and both local side group dynamics and main chain motion have been investigated in detail, as well as collective motions in these glass forming materials. Interpretation of the data has been considerably advanced by the parallel development of modelling, particularly molecular dynamic simulations. New neutron sources with even higher fluxes currently being commissioned include QENS in their portfolio of instruments so that we can anticipate further experimental investigation of polymer dynamics, to compare to ever more sophisticated modelling.   

The Coil-Stretch Transition after more than 30 years

From the seminal paper of DeGennes (1974), there has been a long debate over the nature of polymer dynamics surrounding the ``critical point'' in flow strength where local fluid line extension rates (and the resulting drag created on a linear polymer) dominate over the entropic restoring force -- the so-called coil-stretch transition. This debate has now essentially ended as a result of recent single molecule experiments and large scale molecular simulations which demonstrate that, for steady extensional flow, the basic tenets DeGennes put forth were correct, albeit with certain details which DeGennes did not foresee. However, for flows which are either not steady or which contain significant vorticity, there are qualitatively different features which have now been suggested and remain essential to understand. For example, molecular simulations of planar mixed flows demonstrate that conformational fluctuations play a key role in the coil-stretch transition especially for flows that are ``near shear''. Finally, the application of the DeGennes' ideas to turbulent drag reduction are far from clear, and new large scale molecular simulations have shed some light on polymer dynamics in this important application.   

Dynamics of Entangled Polymers

The effect of entanglements on polymer dynamics is one of the most interesting and most challenging areas of polymer physics. In 1967 Edwards introduced the confining tube model for polymer networks in which the effect of permanent entanglements from surrounding chains on a given one was replaced by the confining tube potential. In 1971 de Gennes proposed reptation model, suggesting that entangled chains diffuse along their confining tubes. This ingenious idea provided a simple explanation for strong molecular weight dependence of relaxation time and self-diffusion coefficient of entangled linear polymers. In 1975 de Gennes put forward the concept of constraint release that takes into account modifications of the confining tube caused by the motion of surrounding chains forming this tube. In the same paper de Gennes showed that dynamics of entangled branched polymers, such as stars, is qualitatively different from that of entangled linear polymers. Branch points do not allow these molecules to reptate along their confining tubes, as linear molecules do, but instead stars can only relax and move by a highly entropically unfavorable process of arm retraction. I will describe the development and modification of ideas put forward in de Gennes' original models of dynamics of entangled linear and branched polymers. Some details of de Gennes' constraint release model were modified and the concept of tube dilation was introduced couple of years later. For the following quarter of century scientists are debating whether constraint release or tube dilation is the dominant mechanism for relaxation of branched and linear polymers. The shape of the entropic potential for the arm retraction mechanism of branched polymers proposed by de Gennes was modified by Doi and Kuzuu in 1980. This potential is acting along the primitive path -- the axis of the confining tube, and the resulting relaxation time of the branched polymers strongly depends on the precise definition of this primitive path. Unfortunately, the primitive path is still not clearly defined by any of the existing models and scientists are still arguing which definition is better. I will describe these and other challenges and open questions remaining in the field of entangled polymer dynamics.   

Interdiffusion and disentanglement of polymer brushes

In the spirit of this symposium, I will briefly survey some of the main ideas on interdiffusion and interfacial relaxation put forward by de Gennes, then consider some recent experimental developments. A very attractive feature of the central tenets of polymer physics introduced by de Gennes is their versatility in different physical situations, so that a discussion of, for example, friction, will in a natural way involve reptation. A particular case in point concerns the relaxation of interdiffused, compressed polymer brushes undergoing shear, as when they are used as lubricating layers. Here the useful concept is, unexpectedly, that of relaxation of entangled star-branched polymers, introduced by de Gennes over 30 years ago for a totally different purpose: The main idea -- and conceptually a beautifully simple one - is that in order for an entangled chain emanating from a fixed branch point to relax, it needs to retract back along its `tube' and dissipate the stress by re-equilibrating in a new configuration. Compression of two polymer brushes, whether in a good solvent or in the melt, creates a model interdiffused interface, whose dynamic properties can be analyzed based on such star-branched relaxation models, and the talk will describe some recent results on these systems.