Molecular dynamics polydisperse systems

Figure 2. Autocorrelation function of the end-to-end vector for a C-78 polymethylene melt (T = 450 , P = 1 atm) from different algorithms. The system has a uniform length distribution with polydispersity index of 1.08. For the MC runs, a common base combination of moves was used that consists of reptations (6%), rotations (6%), flips (6%), concerted rotations (32%), and volume move (0.5%). The rest of the moves were configurational-bias CB (49.5%, long dashed line), end bridge (49.5%, full line), and half CB (25%), half end bridge (24.5%, dotted line). The short dashed line corresponds to a NVM molecular dynamics simulation of the same system. The CPU time refers to an IBM/RS600 3CT machine [63].

Before going into details, let us make a brief statement that propagation in new controlled/living carbocationic systems has nearly the same mechanism as in the conventional systems discussed in Chapter 3, which consists of the electrophilic addition of carbenium ions to alkenes. The main difference is that carbenium ions are in dynamic equilibria with dormant species (covalent esters and onium ions). The correct choice of structures and concentrations of activators and nucleophilic additives as well as those of initiator allows for the preparation of polymers with predetermined molecular weights, low polydispersities, and controlled end functionality, including block copolymers (see Chapter 5). 

So far we have considered polymers made of bifunctional units. These may react by two ends, or functionalities. When the monomers are more than bifunctional, polymerization leads to branched stmctures, and eventually to a solid called a gel [48]. In this section we will consider this case. As we will see, every polymer has still a fractal behavior. In addition to this, there is a very broad distribution of molecular weights, called polydispersity. Because of this, what is observed is an effective dimension that depends also on the dimensirm of the distribution. This holds for many polydis-perse systems, with restrictions that will be discussed below. We will first present the distribution of molecular weights that is naturally found in the reaction bath. We will turn to dilute solutions, where the fractal dimension is smaller because of swelling. We will discuss the effective dimension that is observable. Then we will turn to the semidilute solutions and to the swollen gels. Finally, we will discuss the dynamics of these systems in the reaction bath. 

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