Polymer fluids atomistic models

A distinctly different approach, which has witnessed much progress recently, is large scale Monte Carlo and molecular dynamics computer simulations [4]. These studies provide many insights regarding the physics of model polymer fluids, and also valuable benchmarks against which approximate theory can be tested. However, an atomistic, off-lattice treatment of high polymer fluids and alloys remains immensely expensive, if not impossible, from a computational point of view. 

As a general comment on the recent polymer integral equation work, we note that applications to date have focused primarily on the structure (intra- and intermolecular) and equation of state (based on a virial or free energy route) of the simple hard core, tangent jointed chain model of polymer solutions and melts. How tractable and generalizable the various approaches are for treating semiflexible and/or atomistic models of macromolecular fluids is unclear for most theories. Little, or no, work has... 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

The molecular dynamics methods that we have discussed in this chapter, and the examples that have been used to illustrate them, fall into the category of atomistic simulations, in that all of the actual atoms (or at least the non-hydrogen atoms) in the core system are represented explicitly. Atomistic simulations can provide very detailed information about the behaviour of the system, but as we have discussed this typically limits a simulation to the nanosecond timescale. Many processes of interest occur over a longer timescale. In the case of processes which occur on a macroscopic timescale (i.e. of the order of seconds) then rather simple models may often be applicable. Between these two extremes are phenomena that occur on an intermediate scale (of the order of microseconds). This is the realm of the mesoscale Dissipative particle dynamics (DPD) is particularly useful in this region, examples include complex fluids such as surfactants and polymer melts. 

The outline of the paper is as follows. In Sect. 2 we describe the basic RISM and PRISM formalisms, and the fundamental approximations invoked that render the polymer problem tractable. The predicticms of PRISM theory for the structure of polymer melts are described in Sect. 3 for a variety of single chain models, including a comparison of atomistic calculations for polyethylene melt with diffraction experiments. The general problem of calculating thermodynamic properties, and particularly the equation-of-state, within the PRISM formalism is described in Sect. 4. A detailed application to polyethylene fluids is summarized and compared with experiment. The develojanent of a density functional theory to treat polymer crystallization is briefly discussed in Sect. 5, and numerical predictions for polyethylene and polytetrafluoroethylene are summarized. 

Dissipative particle dynamics (DPD) is a meshless, coarse-grained, particle-based method used to simulate systems at mesoscopic length and timescales (Coveney and Espafiol 1997 Espafiol and Warren 1995). In simple terms, DPD can be interpreted as coarse-grained MD. Atoms, molecules, or monomers are grouped together into mesoscopic clusters, or beads, that are acted on by conservative, dissipative, and random forces. The interaction forces are pairwise additive in nature and act between bead centers. Connections between DPD and the macroscopic (hydrodynamic, Navier-Stokes) level of description (Espanol 1995 Groot and Warren 1997), as well as microscopic (atomistic MD) have been well established (Marsh and Coveney 1998). DPD has been used to model a wide variety of systems such as lipid bilayer membranes (Groot and Rabone 2001), vesicles (Yamamoto et al. 2002), polymersomes (Ortiz et al. 2005), binary immiscible fluids (Coveney and Novik 1996), colloidal suspensions (Boek et al. 1997), and nanotube polymer composites (Maiti etal.2005). 

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