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Description
Telechelic associating polymer networks consist of polymer chains terminated by endgroups that have a different chemical composition than the polymer backbone. When dissolved in a solution, the endgroups cluster together to form aggregates. Their lifetime depends on temperature. At the micelle transition the temperature is sufficiently low for these aggregates to be substantial in size. At low temperature, a strongly connected reversible network is formed and the system behaves like a gel. Telechelic networks are of interest since they are representative of biopolymer networks and are widely used in medical applications and consumer products. The material properties of these polymer networks pose complex and current problems in polymer physics. Many of the most basic questions concerning these networks, such as how they deform under stress, remain unanswered. Experiments under constant shear reveal a rich variety of non-Newtonian responses, including shear thinning and shear thickening. Within the shear thinning regime, shear banding is observed: when a constant shear is applied, the system forms two coexisting bands with different shear rates. The goal of this work is to study such systems using computer simulations. A hybrid molecular dynamics/Monte Carlo simulation is used for this purpose. First we investigate how the network topology of an ensemble of telechelic polymers changes with temperature using graph theory. The aggregates are considered as nodes and the polymer chains as links between them. Our analysis shows that the degree distribution of the system is bimodal and consists of two Poissonian distributions with different average degrees. The number of nodes in each of them as well as the distribution of links depend on temperature. By comparing the eigen-value spectra of the simulated gel networks with those of reconstructed networks, the most likely topology at each temperature is determined. Below the micelle transition the topology can be described by a robust bimodal network in which superpeer nodes are linked among themselves and all peer nodes are linked only to superpeers. At even lower temperatures the peers completely disappear leaving a structure of interconnected superpeers. Many real life networks exhibit a spatial dependence, i.e. the probability to form a link between two nodes in the network depends on the distance between them. The study of the eigenvalue spectra of the simulated gel revealed that spatial dependent networks show universal spectral properties. This led to an in-depth study of such spectra. When increasing spatial dependence in Erdös-Rényi, scale-free and smallworld networks, it is found that the spectrum changes. Due to the spatial dependence, the degree of clustering and the number of triangles increase. This results in a higher asymmetry (skewness). Our results show that the spectrum can be used to detect and quantify clustering and spatial dependence in a network. Next, we study the rheological response of the polymer network under constant shear. The transient stress response shows an overshoot, followed by fluctuations around a lower, average value. When different shear rates are applied, there is a region in which the average stress does not increase significantly. Within this plateau, shear banding occurs. Experiments suggest possible differences between both bands in several properties. The simulation allows for a study of these differences on the microscopical scale. The average aggregate size is lower in the high shear rate band, due to an increase in aggregates consisting of a single endgroup. There is an increase in dynamics and this is highest in the high shear band. These changes are gradual as a function of the distance between the moving walls, and we did not find a sharp increase at the interface. Next, we focus on structural changes of the sheared system as a whole, compared to the unsheared system. The aggregate size distribution becomes bimodal and preferential aggregate size formation decreases under shear. There is a decrease in links and a rearrangement of the structure under shear. This leads to larger aggregates that are connected by "stronger" links of high weight, consisting of multiple bridging chains. Such rearrangement is of importance in the observed decrease in stress in the transient stress response. The loop/bridge ratio increases, but only for high strain rates. Finally we investigate the relation between percolation and gelation. Since the junctions between the endgroups in our system are temporary, geometric percolation does not occur at the gelation temperature. To explain the rheological changes that occur around this transition, only the network made up of endgroups that have junctions that survive over longer times is important. The percolation threshold, the time where the system shows 50% probability to percolate, increases with decreasing temperature. Vogel-Fulcher-Tamman (VFT) theory predicts that this time will diverge at T = 0.29. This is in agreement with the gelation temperature obtained from earlier measurements of relaxation times. A master curve can be constructed for percolation probability and survival rate by empirically shifting them up to T = 0.6. The scaling factors follow the Williams-Landel-Ferry (WLF) equations and the T₀ from WLF corresponds to the one from VFT. This is in support of recent ideas that gelation phenomena and glass transition show similarities.
