침투성 구형 모델에 관한 분자 전산 연구: I. 상태 방정식

김춘호; 서숭혁; Chun-Ho Kim; Soong-Hyuck Suh

Polymer(Korea), Vol.35, No.4, 325-331, July, 2011

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침투성 구형 모델에 관한 분자 전산 연구: I. 상태 방정식

Molecular Simulation Studies for Penetrable-Sphere Model: I. Equation of State

김춘호, 서숭혁 ^†

계명대학교 화학공학과

Chun-Ho Kim, and Soong-Hyuck Suh^†

Department of Chemical Engineering, Keimyung University, 1000 Sindang-dong, Dalseo-ku, Daegu 704-701, Korea

E-mail:

초록

침투 가능한 구형 모델 유체의 상태 방정식을 고찰하고자 다양한 범위의 입자 충전 분율 φ 및 척력적 에너지 상수 ε* 에 대하여 분자 동력학 방법을 이용한 전산 모사를 수행하였다. 전산 모사로부터 얻어진 결과는 문헌에 보고된 고침투 근사식 및 저침투 근사식으로 알려진 두 가지의 한계적 이론식들과 직접 비교하였다. 낮은 척력적 에너지를 갖는 ε*<3.0의 경우 전산 모사 결과는 이들 두 이론식들과 일치하였으나, 반면 입자간 상호 포텐셜 에너지가 입자 자체 평균 운동 에너지의 두 배 이상 높은 척력적 에너지를 갖는 ε*≥3.0의 경우 이들 이론식들 모두 전산 모사 결과를 재현하지 못하였다. 이는 특히 높은 입자 밀도와 높은 척력적 에너지를 갖는 φ≥0.7 및 ε*＝6.0의 경우 입자들의 클러스터 형성 및 자체 입자 배제 부피에 따른 비연속적 크기 효과에 기인되었다.

Molecular simulations via the molecular dynamics method have been carried out to investigate an equation of state of penetrable-sphere model fluids over a wide range of packing fraction φ and finite repulsive energy ε*. The resulting simulation data are compared to theoretical predictions from the two limiting cases of high- and low-penetrability approximations available in the literature. A good agreement between theoretical and simulation results is observed in the case of ε*<3.0. However, for the highly repulsive energy systems of ε*≥ 3.0, where the potential energy barrier is more than two times higher than the particle kinetic energy, a poor agreement is found due to the clustering formation and the non-continuum size effects in the dense systems of φ≥ 0.7 and ε*＝6.0.

Keywords:equation of state;penetrable-sphere model;molecular dynamics simulation.

[References]

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Fernaud MJ, Lomba E, Lee LL, J. Chem. Phys., 112(2), 810 (2000)
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Choudhury N, Ghosh SK, J. Chem. Phys., 119(9), 4827 (2003)
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Zhou SQ, Ruckenstein E, J. Chem. Phys., 112(18), 8079 (2000)
Kim SC, Suh SH, J. Chem. Phys., 117(21), 9880 (2002)
Kim SC, Seong BS, Suh SH, J. Chem. Phys., 131, 134701 (2009)
Santos A, “Kinetic Theory of Soft Matter: The Penetrable Sphere Model”, in Rarefied Gas Dynamics, M. Capitelli, Editor, AIP Conf. Proc. No. 762, AIP, New York, 276 (2005)
Suh SH, Kim CH, Kim SC, Santos A, Phys. Rev. E., 82, 051202 (2010)
Carnahan NF, Starling KE, J. Chem. Phys., 51, 635 (1969)
Alder BJ, Wainwright TE, J. Chem. Phys., 31, 459 (1959)
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Allen MP, Tildesley DJ, Computer Simulation of Liquids, Clarendon, Oxford (1987)
Haile JM, Molecular Dynamics Simulation, John Wiley & Sons, Inc., New York (1992)
Widom B, J. Chem. Phys., 39, 2808 (1963)
Mayer C, Zaccarelli1 E, Stiakakis E, Likos CN, Sciortino F, Munam A, Gauthier M, Hadjichristidis N, Iatrou H, Tartaglia P, Lowen H, Vlassopoulos D, Nature.Mat., 7, 780 (2008)
Jusufi A, Likos CN, Rev. Mod. Phys., 81, 1753 (2009)

[Referenced By]

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[1] Likos CN, Phys. Rep., 348, 267 (2001)

[2] Marquest C, Witten TA, J. Phys. France., 50, 1267 (1989)

[3] Likos CN, Watzlawek M, Lowen H, Phys. Rev. E., 58, 3135 (1998)

[4] Schmidt M, J. Phys.: Condens. Matter., 11, 10163 (1999)

[5] Fernaud MJ, Lomba E, Lee LL, J. Chem. Phys., 112(2), 810 (2000)

[6] Schmidt M, Fuchs M, J. Chem. Phys., 117(13), 6308 (2002)

[7] Choudhury N, Ghosh SK, J. Chem. Phys., 119(9), 4827 (2003)

[8] Acedo L, Santos A, Phys. Lett. A., 323, 427 (2004)

[9] Malijevsky A, Santos A, J. Chem. Phys., 124, 074508 (2006)

[10] Santos A, Malijevsky A, Phys. Rev. E., 75, 021201 (2007)

[11] Malijevsky A, Yuste SB, Santos A, Phys. Rev. E., 76, 021504 (2007)

[12] Fantoni R, Giacometti A, Malijevsky A, Santos A, J. Chem. Phys., 133, 024101 (2010)

[13] Zhou SQ, Ruckenstein E, J. Chem. Phys., 112(18), 8079 (2000)

[14] Kim SC, Suh SH, J. Chem. Phys., 117(21), 9880 (2002)

[15] Kim SC, Seong BS, Suh SH, J. Chem. Phys., 131, 134701 (2009)

[16] Santos A, “Kinetic Theory of Soft Matter: The Penetrable Sphere Model”, in Rarefied Gas Dynamics, M. Capitelli, Editor, AIP Conf. Proc. No. 762, AIP, New York, 276 (2005)

[17] Suh SH, Kim CH, Kim SC, Santos A, Phys. Rev. E., 82, 051202 (2010)

[18] Carnahan NF, Starling KE, J. Chem. Phys., 51, 635 (1969)

[19] Alder BJ, Wainwright TE, J. Chem. Phys., 31, 459 (1959)

[20] Kim CH, Suh SH, Polymer(Korea)., submitted.

[21] Allen MP, Tildesley DJ, Computer Simulation of Liquids, Clarendon, Oxford (1987)

[22] Haile JM, Molecular Dynamics Simulation, John Wiley & Sons, Inc., New York (1992)

[23] Widom B, J. Chem. Phys., 39, 2808 (1963)

[24] Mayer C, Zaccarelli1 E, Stiakakis E, Likos CN, Sciortino F, Munam A, Gauthier M, Hadjichristidis N, Iatrou H, Tartaglia P, Lowen H, Vlassopoulos D, Nature.Mat., 7, 780 (2008)

[25] Jusufi A, Likos CN, Rev. Mod. Phys., 81, 1753 (2009)