Dynamics in polymer melts

The dynamics of a generic linear, ideal Gaussian chain - as described in the Rouse model [38] - is the starting point and standard description for the Brownian dynamics in polymer melts. In this model the conformational entropy of a chain acts as a resource for restoring forces for chain conformations deviating from thermal equilibrium. First, we attempt to exemphfy the mathematical treatment of chain dynamics problems. Therefore, we have detailed the description such that it may be followed in all steps. In the discussion of further models we have given references to the relevant literature. 

Fig. 11). It is, therefore, highly probable that the bulky filler particles impose geometrical hindrances (entropy constraints) for the chain dynamics at the time scale of the NMR experiment (of the order of 1 ms). This effect may be compared with the effect of transient chain entanglements on chain dynamics in polymer melts. It should be remarked that the entanglements density estimated for PDMS melts by NMR is close to its value fi om mechanical experiments [38]. Therefore, it can be assimied that topological hindrances from the filler particles can also be of importance in the stress-strain behavior of filled elastomers. 

Lin, Y.H. (1985) Explanation for slip melt fracture in terms of molecular dynamics in polymer melts, /. Rheol, 29, 605-37. 

Entanglements constitute a major feature of the dynamics in polymer melts. Due to their strong interpenetration, which increases with the molecular weight, polymer molecules are highly entangled. Since the chains are linearly connected objects which cannot cross each other, their individual motions become constrained and for the chain as a whole it is therefore impossible to move freely in all directions. 

Macrocycles have been of fundamental interest for quite some time. Polymer physicists are fascinated by macrocyclic polymers due to their appealing topology and interesting properties (Zimm and Stockmayer, 1949). The lack of chains ends has, for example, been predicted to lead to different chain dynamics in polymer melts and concentrated solutions (Klein, 1986 Rubinstein, 1986). This cyclic topology also leads to a reduced radius of gyration (Zimm and Stockmayer, 1949) and intrinsic viscosity (Yamakawa, 1969) for macrocycles relative to their linear counterparts of the same molecular weight. 

The five time regions are based on the reptation theory proposed by De Gennes [46,47] and Doi and Edwards [48,49] for bulk dynamics of polymer melts and concentrated polymer solutions, and are discussed in detail in Chapter 3 of Ref. [1]. 

We can therefore conclude that differences in the structural relaxation between bead-spring and chemically realistic models can be attributed to either the differences in packing that we discussed above or the presence of barriers in the dihedral potential in atomistic models. To quantify the role of dihedral barriers in polymer melt dynamics, we now examine high-temperature relaxation in polymer melts. 

Dynamics Simulations of the Thermal Glass Transition in Polymer Melts a-Relaxation Behavior. 

Rotational Barriers in Polymer Melt Chain Dynamics. 

Phase Space in Polymer Melts A Comparison of Parallel Tempering and Conventional Molecular Dynamics Simulations. 

Discussions of dynamic phenomena in polymer melts are frequently based on assumptions about a structure of the system, which was earlier taken to be... 

Leonov AI (1994) On a self-consistent molecular modelling of linear relaxation phenomena in polymer melts and concentrated solutions. J Rheol 38( 1) 1—11 Liu B, Diinweg B (2003) Translational diffusion of polymer chains with excluded volume and hydrodynamic interactions by Brownian dynamics simulation. J Chem Phys 118(17) 8061-8072... 

The orientation of bonds is strongly affected by local molecular motions, and orientation CF reflect local dynamics in a very sensitive way. However, the interpretation of multimolecular orientation CF requires the knowledge of dynamic and static correlations between particles. Even in simple liquids this problem is not completely elucidated. In the case of polymers, the situation is even more difficult since particules i and j, which are monomers or parts of monomers may belong to the same chain or to different Chains. Thus, we believe that the molecular interpretation of monomolecular orientation experiments in polymer melts is easier, at least in the present early stage of study. Experimentally, the OACF never appears as the complicated nonseparated function of time and orientation given in expression (3), but only as correlation functions of spherical harmonics... 

In this paper we will concentrate on the diffraction techniques (SANS and reflectometry), and hence static measurements. However, it should be pointed out that through inelastic scattering, aspects of polymer dynamics are accessible. In particular, it has been possible to access single chain dynamics in bulk systems, deformation and relaxation of polymer melts under shear, shed new light on viscoelasticity in polymer melts, and obtain direct information on polymer reputation and particle fluctuations. 

A unique strength of solid-state NMR is its ability to probe molecular dynamics with site selectivity.9132 In this section, we present some specific examples that illustrate the considerable insight into dynamic processes provided by advanced solid-state NMR experiments applicable to as-synthesized samples, i.e., without the requirement for isotopic labeling. These examples focus on well-defined processes that are fast as compared to the time scale of the H DQ MAS experiment, this being on the order of 10-6 to 10 4 s. In addition, it should be noted that the extraction of dipolar couplings by following the buildup of DQC in a H DQ MAS experiment has been shown to provide insight into the complex dynamic processes in polymer melts,172 block copolymers,173 and elastomers.174... 

The Rouse limit applies to unentangled polymer melts because hydrodynamic interactions are screened in melts (just as excluded volume interactions are screened in melts). Polymer dynamics in the melt state (with no solvent) are described by the Rouse model, for short chains that are not entangled. 

The Rouse model is the simplest molecular model of polymer dynamics. The chain is mapped onto a system of beads connected by springs. There are no hydrodynamic interactions between beads. The surrounding medium only affects the motion of the chain through the friction coefficient of the beads. In polymer melts, hydrodynamic interactions are screened by the presence of other chains. Unentangled chains in a polymer melt relax by Rouse motion, with monomer friction coefficient C- The friction coefficient of the whole chain is NQ, making tha diffusion coefficient inversely proportional to chain length ... 

Paul, W. Molecular dynamics simulations of the glass transition in polymer melts. Polymer 45,3901-3905 (2004)... 

A review of rheo-optical techniques by Sherman et al. (1996) notes that there has been an increase in the use of rheo-optic set-ups both for FT-IR dichroism and for dynamic IR dichroism spectroscopies for polymer melts and polymer blends. Skytt et al. (1996) highlight the use of simultaneous measurement of the transient or steady-state rheological properties and IR dichroism to characterize orientation in polymer melts. However, there is little reference to dual spectroscopic-rheological techniques for reactive polymer systems in the literature. 

More recently, a new, viscoelastic-plastic model for suspension of small particles in polymer melts was proposed [Sobhanie et al., 1997]. The basic assumption is that the total stress is divided into that in the matrix and immersed in it network of interacting particles. Consequently, the model leads to non-linear viscoelastic relations with yield function. The latter is defined in terms of structure rupture and restoration. Derived steady state and dynamic functions were compared with the experimental data. 

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