本論文主要是以一種介觀尺度下的模擬方法－分散粒子動力學（Dissipative Particle Dynamics）來探討簡單的雙成份溶液中，改變系統中的斥力參數(Repulsive parameter)和濃度，可以分析得到其團聚(cluster)的數量和形狀。發現在斥力參數aow=30下，溶液濃度為C=4%與C=14%時，確實如文獻所發現的會以小團聚的現象存在，團聚大以2-50顆的大小存在。而當斥力參數高到24%時，進而發現會有一滲透(Percolation Threshold)的現象發生。接著我們以碎形維度(Fractal dimension)來探討在相同濃度與斥力參數之下，溶液中團聚的形狀。得知此溶液其最大團聚集和小團聚集的碎形維度是一樣的，即最大團形狀與小團無異。然而，隨著改變濃度區間在(2-20%)卻會使得碎形維度有上升的趨勢。進而使用了The Kirkwood-Buff Theory，藉由它能夠連接微觀的分子分佈得到巨觀的熱力學性質，我們得到在雙成份系統內，當斥力參數由小變大時， 的值為增加的趨勢；反之 則是減少。

This work is to investigate the microscale clusters and solvation characteristic in a completely miscible two-component system. In order to study the behavior of clusters, we perform Dissipative Particle Dynamics (DPD) simulation to obtain the effect of concentration on the clusters size and fractal dimension (df). It is known that the solvation molecules in aqueous solution cluster together despite solvent and solution being fully miscible in macroscale. The present results show that small clusters do exist. The cluster size and fractal dimension (df) increases with increasing solvent concentration from 8% to 16%. The fractal dimension is increasing from 1.7 to 2.0. When the solvent concentration is over 20%, the cluster size increases rapidly. The percolation threshold concentration of the solvent is 25%.
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The compressibility factor has been widely accepted and applied to evaluate the solvation ability. The compressibility relation is one of the simplest and most useful relations between a thermodynamic quantity and pair correlation function. Although solvation ability varies as the reciprocal compressibility, we found that the converse result for soft molecules and solvation ability is closely related to compressibility, partial molar volumes and Floury-Huggins parameter. Consequently, Ben-Naim definition is applied to determine the hydration ability. The Ben-Naim definition of solutions is originally formulated to obtain thermodynamic quantities from molecular distribution functions. It is the excess number of molecules of various species around a selected molecule is a important quantity in the analysis of the solvation number of mixture system. Our simulation results demonstrated that Ben-Naim definition is more accurately than compressibility factor.

1. M.P.Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford University Press Inc. (1987).
2. P. J. Hoogerburgge and J. M. V. Koelman, Europhysics Letters V19, 155 (1992).
3. Maddalena Venturoli, Mesoscopic models of lipid bilayers and bilayers with embedded proteins-A Dissipative Particle Dynamics study (2004).
4. Español, P., Warren, P., Europhysics Letters, 30, 191-196 (1995).
5. Fan, C. F., Olafson, B. D., Blanco, M., Hsu, S. L., Macromolecules, 25, 366 (1987).
6. Groot R. D., Warren, P. B. , J. Chem. Phys., 107, 4423-4435 (1997).
7. D. Frenkel, Understanding Molecular Simulation from algorithms to applications, Academic Press (1996).
8. D. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press, London 1997.
9. 梁雲芳、陳義裕, 科學發展, 370 (2003).
10. Arieh Ben-Naim, Molecular Theory of Solutions (2006).
11. Ben-Naim, A. Statistical Thermodynamics for Chemists and
Biochemists; Plenum Press: New York, 1992
12. S. Dixit, J. Crain etc. , NATURE, 416, 829-832 (2002).
13. M. Misawa, K. Mori, Journal of Chemical Physics, 121, 4716-4723 (2004)
14. Ivan L. Shulgin and Eli Ruckenstein, J. Phys. Chem. B, 110, 12707-
12713 (2006)