Polymer beads, representation

Fig. 7.1 Schematic representation of linear versus dendritic polymers linear (left) and hyperbranched (middle) polymers, perfect dendrimer (right). The amount of terminal groups is indicated below each structure. These architectures can also be attached to a cross-linked polymer bead to obtain a high-loading hybrid material.

Such supports can be dealt with in generic reaction schemes as a special type of superatom. Often, a pictorial representation is used. A polymer bead may be conveniently represented by an s orbital in common chemistry software packages. Few standards have been developed for the representation of other supports, but a filled structure designates a solid support and an open structure may be used for a soluble support. 

Figure 3.1. Schematic representation of a styrenc-divinylbenzene copolymer. The divinylbenzene cross-links the linear chain of the styrene polymer. A high percentage of divinylbenzene produces a more rigid polymer bead.

Fig. 4.56 Schematic representation of emulsion polymerization. Large monomer droplets are stabilized by surfactant molecules in water. Excess surfactant forms micelles into which monomer molecules diffuse. Initiator molecules interact predominantly with the numerous small micelles (larger surface area) where the monomer polymerizes, resulting in a suspension of polymer beads in water.

Figure B3.3.11. The classical ring polymer isomorphism, forA = 2 atoms, using/ = 5 beads. The wavy lines represent quantum spring bonds between different imaginary-time representations of the same atom. The dashed lines represent real pair-potential interactions, each diminished by a factor P, between the atoms, linking corresponding imaginary times.

Fig. 6. Bead-spring and elastic dumbbell representation of a polymer chain in solution...

Usually, MD methods are applied to polymer systems in order to obtain short-time properties corresponding to problems where the influence of solvent molecules has to be explicitly included. Then the models are usually atomic representations of both chain and solvent molecules. Realistic potentials for non-bonded interactions between non-bonded atoms should be incorporated. Appropriate methods can be employed to maintain constraints corresponding to fixed bond lengths, bond angles and restricted torsional barriers in the molecules [117]. For atomic models, the simulation time steps are typically of the order of femtoseconds (10 s). However, some simulations have been performed with idealized polymer representations [118], such as Bead and Spring or Bead and Rod models whose units interact through parametric attractive-repulsive potentials. 

The failure of the Rouse theory was attributed to the pathological nature of medium motions in entangled systems, and not any special defect in the Rouse representation of the polymer chain itself. For Rouse chains in a deforming continuous medium, the frictional force depends on the systematic velocity of the bead relative to the medium. The frictional force on a bead is therefore a smootly... 

Figure 1. Schematic representation of operation of heterogeneous liquid crystal light shutters A) glass beads in a liquid crystal film, B) liquid crystal imbibed in a microporous film, C) encapsulated liquid crystal, D) polymer dispersed liquid crystals.

Figure 3-13. Bead-and-spring representation of a real polymer molecule in dilute solution.

Fig. 13 Mapping scheme of a PSS polymer onto a generic charged bead-spring model with an implicit solvent representation and counterions. Figure adapted from [116]...

An orthogonal set of approximations involves the structural representation of the polymer. As an example. Fig. 1 shows four different ways in which the structure of polyisoprene might be represented in an MD or BD simulation. The top structure (a) is an atomic representation of the polyisoprene repeat unit. The second structure (b) results from coUapsing all the hydrogens onto their parent carbons (the united atom approximation). The third structure (c) further collapses the three carbon centers in the fairly rigid double bond unit into a single pseudo-atom. Any of these three structures might be used in a simulation of local polymer dynamics. The fourth structure (d) shows a bead-... 

Fig. 2 (A) Schematic representation of the Zimm model, which takes into account hydrodynamic interactions. The beads affect (through the solvent) the motion of a bead which is distant from them along the chain (not connected directly to them by means of springs). (B) Schematic representation of the reptation model. A given, long polymer chain moves in the tube formed by other chains...

---