| Reaction-diffusion systems are ubiquitous in nature. Cage-effect, gel-effect, glass-effect and so on produced by diffusion in the process of free-radical polymerisation effect on the produce process and the control of polymer quality. So it is important to study the diffusion in polymerization reaction.The study objects of diffusion are small molecular and macromolecule. For small moleculars, diffusion process in polymer solution have been described by the model of Maxwell-Fricke, Mackie-Meares, Modified Enskog and free volume theory, in which M-F model consider that polymer segments can not flow relative to solvent molecule and suspend in the continuously flowing solvent medium, so the model deviates when the concentration of polymer is high; M-M model bases on the same scale of solvent molecule and polymer segment in the cubic crystal lattices, and the mean increase in path length due to obstraction makes the model'deviated. M-E model bases on dynamic transference theory and momentum transference among hard balls is considered. The model provides a method of measuring solvent molecules, but the collision frequency among molecules for asymmetry molecules is overestimated; the free volume theory avoid the deviations and the model can be applied in the change of the concentration of polymers during the whole process of polverization. For macromolecules, diffusion process can be described by the model of Bueche theory, scale and reptation theory and free volume theory, in which Bueche theory is limited for need of precise viscosity data; Reptation theory considers polymer viscoelasticity and uses long chain model to calculate stress and strain, which can calculate self-diffusion coefficient; the free volume theory is not perfect. However, to the best of ourknowledge, the model of diffusion in the polymerization has not been studied by mesoscale simulation so far.In the present study, we carry out computer mesoscale simulations in two dimensions to study the kinetics of polymerization reaction with diffusion in based on the modified TDGL equation and using the cell dynamical scheme.There is a class of polymerisation where the number of propagating chains remains invariant throughout the course of reaction. Such a situation exists, for example, in ethylene oxide type poymerizations where the initiator concentration sets the number of propagating species. We assume that the rate constants for initiation and propagation are both constants, and the chain termination and transference are neglected. Initiator and monomer are presented as volume fraction at the beginning of reaction, the sum of which is 1 under impressive condition. Because the volume fraction of initiator fluctuates in each cell, diffusion occurs. Besides, the effect of entanglement is also considered. Then we induce the dispersive dynamic equations.The simulation results show that weight-average chain length and number-average chain length are both bigger if diffusion effect is considered, whereas the polydispersity index d is smaller. Due to the fluctuation of concentration of initiator in each cell at the beginning, the diffusion occurs. The concentration of each component exchanges with the corresponding component in the nearest and the next nearest cell, then the difference of the concentration of the same component in different cells decreases, which make molecular weight distribution narrow. Moreover, the value of d is irrelatedwith that of k1, and k with the same value of r in Louis Gold's theory results,while in our simulation the contrary result gained. The theoretical value of polydipersity index d is smaller than that of simulation with the same value of. It is because there is initial fluctuation of concentration of initiator, the distribution of the terminal molecular weight is wider than that of homogeneous system. Furthermore, on the base of reaction and diffusion, shear effect is also considered. As the simulation results show, molecular weight distribution is narrow with the increase of shear rate. |
PDF Full Text Request