Using a core （142 nm） made of linear polystyrene （PS） chains as a seed, we further polymerized a thin layer of cross-linked PS shell （7 nm） on it in water to form a core-shell particle. Such a particle swells in...Using a core （142 nm） made of linear polystyrene （PS） chains as a seed, we further polymerized a thin layer of cross-linked PS shell （7 nm） on it in water to form a core-shell particle. Such a particle swells in toluene, which enables linear PS chains inside the core to gradually diffuse out through the porous shell. Using a combination of static and dynamic laser light scattering, we examined the chain diffusion process by following the change of the scattering intensity （i.e. the average molar mass of the particles）. For the first time, we have revealed that the diffusion exhibits three stages. In the first stage, the chain diffusion through the shell is even faster than their translational diffusion in a dilute solution. The three stages respectively correspond to the change of the solution in the core from concentrated to semidilute and then from semidilute to dilute.展开更多
By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1...By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1.2,3,4), Di(t) (i = 1,2), a12(t), a21(t), a23(t) and a32(t) are all positive periodic continuous functions with period w > 0, Ti(i = 1,2) are positive constants.展开更多
基金This work was financially supported by the Hong Kong Special Administration Region Earmarked(Grants No.CUHK4025/04P,2160242)the Chinese Academy of Sciences(Special Grant KJCX2-SW-H14)the National Natural Science Foundation of China(Key Grant 20574065).
文摘Using a core （142 nm） made of linear polystyrene （PS） chains as a seed, we further polymerized a thin layer of cross-linked PS shell （7 nm） on it in water to form a core-shell particle. Such a particle swells in toluene, which enables linear PS chains inside the core to gradually diffuse out through the porous shell. Using a combination of static and dynamic laser light scattering, we examined the chain diffusion process by following the change of the scattering intensity （i.e. the average molar mass of the particles）. For the first time, we have revealed that the diffusion exhibits three stages. In the first stage, the chain diffusion through the shell is even faster than their translational diffusion in a dilute solution. The three stages respectively correspond to the change of the solution in the core from concentrated to semidilute and then from semidilute to dilute.
基金Supported by the National Natural Science Foundation of China (No.19971026,10271044).
文摘By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1.2,3,4), Di(t) (i = 1,2), a12(t), a21(t), a23(t) and a32(t) are all positive periodic continuous functions with period w > 0, Ti(i = 1,2) are positive constants.
