Polymer Lennard-Jones

Figure 4. Demixing temperatures for Lennard-Jones polymer in Lennard-Jones solvent at P, = 2 as a function of polymer concentration for 16-mers (circles) and 64-mers (triangles). Temperature and pressure units are relative to the critical solvent properties. The Lennard-Jones interaction potential energy is cut at 2.5a and shifted [80].

Finitely extensible nonlinear elastic Lennard-Jones polymers... 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

We have studied, by MD, pure water [22] and electrolyte solutions [23] in cylindrical model pores with pore diameters ranging from 0.8 to more than 4nm. In the nonpolar model pores the surface is a smooth cylinder, which interacts only weakly with water molecules and ions by a Lennard-Jones potential the polar pore surface contains additional point charges, which model the polar groups in functionalized polymer membranes. 

Concluding this section, one should mention also the method of molecular dynamics (MD) in which one employs again a bead-spring model [33,70,71] of a polymer chain where each monomer is coupled to a heat bath. Monomers which are connected along the backbone of a chain interact via Eq. (8) whereas non-bonded monomers are assumed usually to exert Lennard-Jones forces on each other. Then the time evolution of the system is obtained by integrating numerically the equation of motion for each monomer i... 

As we discussed in the section on the structural properties of amorphous polymers, the relative size of the bond length and the Lennard-Jones scale is very different when comparing coarse-grained models with real polymers or chemically realistic models, which leads to observable differences in the packing. Furthermore, the dynamics in real polymer melts is, to a large extent, determined by the presence of dihedral angle barriers that inhibit free rotation. We will examine the consequences of these differences for the glass transition in the next section. 

In an early attempt to model the dynamics of the chromatin fiber, Ehrlich and Langowski [96] assumed a chain geometry similar to the one used later by Katritch et al. [89] nucleosomes were approximated as spherical beads and the linker DNA as a segmented flexible polymer with Debye-Huckel electrostatics. The interaction between nucleosomes was a steep repulsive Lennard-Jones type potential attractive interactions were not included. 

We now present results from molecular dynamics simulations in which all the chain monomers are coupled to a heat bath. The chains interact via the repiflsive portion of a shifted Lennard-Jones potential with a Lennard-Jones diameter a, which corresponds to a good solvent situation. For the bond potential between adjacent polymer segments we take a FENE (nonhnear bond) potential which gives an average nearest-neighbor monomer-monomer separation of typically a 0.97cr. In the simulation box with a volume LxL kLz there are 50 (if not stated otherwise) chains each of which consists of N -i-1... 

Block copolymer micelles with their solvent swollen corona are a typical example of soft spheres having a soft repulsive potential [61]. The potential has been derived by Witten und Pincus for star polymers [62] and is of form u(r) ln(r). It only logarithmically depends on the distance r and is therefore much softer compared to common r x-potentials such as the Lennard-Jones potential (x=12). The potential is given by... 

Figure 7(c). Normalized steady state radial distribution of difference stress contributed by Lennard-Jones interactions, for a simple liquid Nb = 0 (solid line) and polymer melts with Nb — 1,3 and 11 (dashed lines). Reduced density p — 0.9 for all cases. The results for the polymer melts are indistinguishable to within the statistical scatter of the simulations. 

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