Lattice Monte Carlo Simulations Of The Dynamics Of A Single Confined Polymer Chain

Polymer dynamics is one of the core problems in polymer physics. Due to recent studies of proteins and DNAs in the confining space, the dynamics of a confined polymer chain has become a hot topic. Though the physical model of a confined polymer chain is relatively simple, the theoretical treatment is extremely complicated and the mathematical approximations must be applied in the calculations. On the other hand, the confinement structure with the nanometer spatial scale is hard to fabricate experimentally. The typical dynamical times are in the magnitude of nanosecond and thus few measurement tools can be applied in the system. As an alternative, computer simulation can effectively and has been an important and useful method in this field.Based on lattice Monte Carlo simulations with the bond-fluctuation algorithm, we have systematically explored the characteristic dynamic behaviors of a free chain, a wall-grafted chain, and a confined chain in slit, square tube, and cubic pore confinements respectively. The main achievements and original contributions of this thesis can be summarized as follows:(1) The scaling behavior of the mean first-passage times of the end-to-end looping associated with two reactive terminal ends and the intrachain looping associated with a terminal end and an interior monomer for a free chain and a wall-grafted chain has been studied. The end-to-end looping time and the kinetic relaxation time of the end-to-end vector for a free self-avoiding chain are in full agreement with the Rouse dynamic behavior. The simulation results of the intrachain looping collapse into a universal scaling behavior and display a maximum for different chain lengths. By testing the phantom chain, we found that the peak was not caused by the excluded-volume effect. Following the derivation of the normal modes for a Gaussian chain, we calculated the relaxation time of the end-to-interior vector, which displayed a weak maximum at nearly the same location as the looping time. Therefore, it is the internal short-time dynamic modes complicating the situation and leading to the maximum. For the wall-grafted chain, due to the confinement of the grafting point and the depletion effect of the hard wall, the characteristic time of the end-to-end looping deviated from Rouse dynamic behavior. Furthermore, just because of that, the symmetry of the two terminal ends of a polymer chain was destroyed, and thus the looping processes for the grafting terminal end and the free terminal end displayed distinct scaling behavior. For the former, the maximum caused by the complicated internal dynamic modes still existed and the numerical value was one order magnitude larger than that of a free chain. While the peak disappeared for the latter and the looping time displayed a monotonic increase.(2) We have further observed the typical dynamic processes associated with three characteristic times: rotation time, diffusion time and the looping time of a self-avoiding polymer in three types of confinement: slit, square tube and cubic pore, and have discussed these three time scales in light of scaling theories. Special attention has been paid to the parameter regime where the characteristic confinement dimension is smaller than the radius of gyration of the unconfined polymer. We got a series of the scaling behavior of these three times, and in particular, for the strong tube confinement, the looping time and the rotation time displayed an exponential scaling law. Comparing the looping times under three different confinement dimensions, we found that the proper confinement lead to the faster looping dynamics, which was in agreement with the previous observations: a faster intrachain looping in the sphere pore and a faster protein folding in chaperonin and sphere. What's more, the looping time decreased with the confinement dimensions, which reflected a faster looping dynamics and proved the conclusion in another way that confinement lead to faster dynamics.(3) We also examined the thermodynamics of the polymer adsorption on a periodic potential surface and a periodic channel-structured surface. Two processes were detected: the polymer adsorption from the free space to the periodic potential surface and the localization from two adsorbing strips to one. The former corresponds to the sharp transitions of some thermodynamic parameters such as specific heat and the chain dimensions, yet it is not a first-order phase transition. From the simulation results, however, no phase transition behavior has been observed for the localization process.Upon basically finishing the simulations of this thesis, the author also tried to be trained experimentally and thus performed preparation of a sustained release carrier. The two contributions in the experiments are summarized as follows. (1) Microgel preparation conditions have been improved. Injectability is one of the key properties which determine whether the novel controlled release system could be accepted by the patients and the doctors. By the improvement of the traditional fabrication and post-fabrication techniques, we got the injectable microgel with small size. In addition, as to the redispersion problem of the vacuum-dried microgel, we synthesized a series of macromers with different block lengths of the lactide acid and studied the redispersion property of the microparticles fabricated from these macromers to get the most suitable one. (2) We have experimentally explored the activity loss of the released proteins from the microgel developed in our group. The potential factors have been studied and the real reason has been found finally. These investigations have laid a solid foundation for the further in-vitro and in-vivo experiments of this novel controlled release system.