利用耗散粒子動力學探討星形高分子溶液的滲透壓及維里係數

Osmotic pressure and virial coefficients of star polymer solutions : dissipative particle dynamics

房哲名(Che-Ming Fang)

指導教授 ： 曹恒光

國立中央大學/工學院/化學工程與材料工程學系/碩士(2008年)

摘要

本篇論文主要以一種介觀尺度下的模擬方法-分散粒子動力學(
Dissipative Particle Dynamics )來探討於good solvent中線性與星形高分子的滲透壓、第二維里係數( second virial coefficient, B2 )、第三維里係數( third virial coefficient, B3 )變化以及證明DPD模擬於滲透壓實驗的可行性。
本文利用半透膜將系統分為兩部份針對稀薄( dilute )溶液及半稀薄( semi-dilute )溶液兩種溶液之滲透壓進行討論。由模擬結果可得，線性高分子在稀薄溶液中，B2、迴旋半徑(radius of gyration, Rg)的關係式 ;在半稀薄溶液中，Π與Φ的關係式Π~Φ2.7，由於軟球模型之因此值大於理論值9/4。對星形高分子而言，於稀薄溶液中，一樣遵守 關係式；在半稀薄溶液中，Π~λΦα。λ與α值與手臂數有關但與手臂長度無關。當手臂數增加，α值會由2.70增加至3.07，這個結果與實驗結果吻合。

關鍵字

耗散粒子動力學 ； 滲透壓 ； 維里係數

並列摘要

The osmotic pressure Π and virial coefficients ( B2 and B3 ) of linear and star polymers in good solvents are studied by dissipative particle dynamics simulations.
The dependence of the osmotic pressure on the concentration c is directly caculated by considering two reservoirs separated by a semi-
permeable, fictitious membrane. For linear polymers with chain length N, our simulation results confirm the scaling relations that B2 ~ N3ν in the dilute regime and Π ~ c2.70 in the semi-dilute regime. The exponent is greater than 9/4 due to the nature of soft beads. For star polymers, the scaling relations become B2 ~ Rg3 in dilute regime and Π λcα in semi-dilute regime. Both the prefactor λ and exponent α vary with the arm number but is independent of the arm length. As the arm number is increased, the exponent may rise from 2.7 to 3.07, which is qualitatively consistent with the experimental result.

並列關鍵字

osmotic pressure ； scaling law ； DPD ； virial coefficient

參考文獻

1. A. Evilevitch, , L. Lavelle, C. M. Knobler, E. Raspaud, and W. M. Gelbart, Osmotic pressure inhibition of DNA ejection from phage, PNAS 100, 9292, 2003.

2. P. J. Hoogerbrugge and J. M. V. A. Koelman, Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics, Europhys. Lett. 19, 155, 1992.

3. P. Español and P. Warren, Statistical Mechanics of Dissipative Particle Dynamics, Europhys. Lett. 30, 191, 1995.

4. M. P. Allan & D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).

5. R. D. Groot and T. J. Madden, Dynamic simulation of diblock copolymer microphase separation, J. Chem. Phys. 108, 8713, 1998.