Dynamics, polymer

The dynamical behavior of macromolecules in solution is strongly affected or even dominated by hydrodynamic interactions [6,104,105]. Erom a theoretical point of view, scaling relations predicted by the Zimm model for, e.g., the dependencies of dynamical quantities on the length of the polymer are, in general, accepted and confirmed [106]. Recent advances in experimental single-molecule techniques provide insight into the dynamics of individual polymers, and raise the need for a quantitative theoretical description in order to determine molecular parameters such as diffusion coefficients and relaxation times. Mesoscale hydrodynamic simulations can be used to verify the validity of theoretical models. Even more, such simulations are especially valuable when analytical methods fail, as for more complicated molecules such as polymer brushes, stars, ultrasoft colloids, or semidilute solutions, where hydrodynamic interactions are screened to a certain degree. Here, mesoscale simulations still provide a full characterization of the polymer dynamics. 

We will focus on the dynamics of polymer chains in dilute solution. In order to compare simulation results with theory - in particular the Zimm approach [6, 107] - and scaling predictions, we address the dynamics of Gaussian as well as selfavoiding polymers. 

The excluded volume leads to swelling of the polymer structure compared to a Gaussian chain, which is difficult to fully account for in analytical calculations [73]. 

The dynamics of the chain monomers is determined by Newtons equations of motion between the collisions with the solvent. These equations are integrated using the velocity Verlet algorithm with the time step Atp. The latter is typically smaller than the collision time At. The monomer-solvent interaction is taken into account by inclusion of the monomer of mass ntm = pm in the collision step [68,73], compare Sect. 7.1. Alternatively, a Lennard-Jones potential can be used to account for the monomer-MPC particle interaction, where a MFC particle is of zero interaction range [19,108]. 

The equilibrinm properties of a polymer are not affected by hydrodynamic interactions. Indeed, the resnlts for various equilibrium quantities - such as the radius of gyration - of MPC simulations are in excellent agreement with the results of molecular dynamics of Monte Carlo simulations without explicit solvent [73]. 

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Doi M and Edwards S F 1986 The Theory of Polymer Dynamics (Oxford Clarendon)... 

SPACEEIL has been used to study polymer dynamics caused by Brownian motion (60). In another computer animation study, a modified ORTREPII program was used to model normal molecular vibrations (70). An energy optimization technique was coupled with graphic molecular representations to produce animations demonstrating the behavior of a system as it approaches configurational equiHbrium (71). In a similar animation study, the dynamic behavior of nonadiabatic transitions in the lithium—hydrogen system was modeled (72). 

Doi, M. and Edwards, S.F., The Theory of Polymer Dynamics. Clarendon Press, Oxford, 1986. 

Finally, we want to describe two examples of those isolated polymer chains in a sea of solvent molecules. Polymer chains relax considerably faster in a low-molecular-weight solvent than in melts or glasses. Yet it is still almost impossible to study the conformational relaxation of a polymer chain in solvent using atomistic simulations. However, in many cases it is not the polymer dynamics that is of interest but the structure and dynamics of the solvent around the chain. Often, the first and maybe second solvation shells dominate the solvation. Two recent examples of aqueous and non-aqueous polymer solutions should illustrate this poly(ethylene oxide) (PEO) [31]... 

M. Cates. Reptation of living polymers Dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 20 2289-2296, 1987. 

J. G. van Alsten, B. B. Sauer, D. J. Walsh. Polymer dynamics at the melt/solid interface Experimental evidence of reduced center of mass mobility. Macromolecules 25 4046-4048, 1992. 

Flow-induced degradation is intimately related to the nonequilibrium conformation of polymer coils and any attempt to interpret the process beyond the phenomenological stage would be incomplete without a sound understanding of chain dynamics. To make the paper self-contained and to provide a theoretical basis for the discussion, we have included some fundamental models of polymer dynamics in the next section which may also serve as a guideline for future work in the field of polymer degradation in flow. For the first-time reader, however, this section is not absolutely necessary. Further, any reader familiar with molecular rheology or interested only in experimental results can skip this section, only to go back whenever a reference is needed. 

The static properties of an isolated chain constitute a good starting point to study polymer dynamics many of the features of the chain in a quiescent fluid could be extrapolated to the kinetics theories of molecular coil deformation. As a matter of fact, it has been pointed out that the equations of chain statistics and chain dynamics are intimately related through the simplest notions of graph theory [16]. 

Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, Oxford, chapters 4 5... 

Polymer Dynamic shear modulus (frequency > 1 Hz) S/MPa Quasi-static Young s modulus (frequency 0.01 Hz) E/MPa Ratio 3S/E... 

This area of research is still at its beginning and many aspects are not resolved. This includes in particular the structure and conformation of polymers at an interface as well as the modification of polymer dynamics by the interface. We have given several examples of the potential of surface and interface analytical techniques. They provide information on surface roughness, surface composition, lateral structure, depth profiles, surface-induced order and interfacial mixing of polymers on a molecular and sometimes subnanometer scale. They thus offer a large variety of possible surface and interface studies which will help in the understanding of polymer structure and dynamics as it is modified by the influence... 

Within the Rouse model for polymer dynamics the viscosity of a melt can be calculated from the diffusion constant of the chains using the relation [22,29,30] ... 

Ediger, M. D. and Adolf, D, B. Brownian Dynamics Simulations of Local Polymer Dynamics. VoU 16, pp. 73-110. 

It is known that polymer dynamics is strongly influenced by hydrodynamic interactions. When viewed on a microscopic level, a polymer is made from molecular groups with dimensions in the angstrom range. Many of these monomer units are in close proximity both because of the connectivity of the chain and the fact that the polymer may adopt complicated conformations in solution. Polymers are solvated by a large number of solvent molecules whose molecular dimensions are comparable to those of the monomer units. These features make the full treatment of hydrodynamic interactions for polymer solutions very difficult. 

Hybrid MPC-MD schemes are an appropriate way to describe bead-spring polymer motions in solution because they combine a mesoscopic treatment of the polymer chain with a mesoscopic treatment of the solvent in a way that accounts for all hydrodynamic effects. These methods also allow one to treat polymer dynamics in fluid flows. 

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