摘要
本论文研究中开发非平衡态耗散粒子动力学模拟方法,实现了稳态剪切,振荡剪切以及顶盖驱动流场等一系列流场。利用非平衡态耗散粒子动力学方法,分别对环形二嵌段共聚物、线型二嵌段共聚物在剪切场的作用下的相行为,嵌段共聚物胶束在顶盖驱动流场下的形貌变化进行了研究。主要内容包括:
研究了本体中环形二嵌段共聚物的穿孔的层状相在简单剪切流场的作用下的相行为和流变学性质。确认了两种典型的相转变过程:(1)从穿孔层状相到层状相的转化,(2)从穿孔层状相到六方堆积柱状相的转化。发现剪切速率不仅对穿孔层状相最终形成的相态,起决定性的作用;而且还对最终形成的相的形貌有巨大的影响。通过序参量随时间的演化过程发现,剪切可以促进体系的演化,加快其达到稳定的状态。剪切粘度随着剪切速率的增加而减小,但是在剪切导致的柱状相出现时,有一个局部的升高。
利用非平衡态耗散粒子动力学方法研究了线型二嵌段共聚物层状相在振荡剪切作用下的相行为,发现剪切导致的层状相形貌是剪切振幅和频率共同作用的综合结果。我们在同一振幅的条件下,比较频率对取向选择的影响,确认了取向对频率的依赖关系。另外,我们还通过计算在相同振幅、不同频率下体系序参量来研究剪切导致的层状相相转变的动力学过程。在模拟中,剪切可以引起无序相到层状相的相转变。我们发现剪切可以使相转变临界点(χN)ODT降低。我们还研究了复合剪切粘度和复合模量在振荡剪切中的变化。
利用非平衡态耗散粒子动力学模拟方法,研究了溶液中线性二嵌段共聚物胶束在顶盖驱动流场的条件下的形态变化,研究了顶盖驱动流场对其相行为的影响。我们发现:在顶盖驱动流场和限制性的墙的共同作用下,线性两嵌段共聚物胶束的形貌和平衡态时的形貌有很大的区别。此外,限制性的墙与高分子链段之间的相互作用对嵌段共聚物聚集体的形貌有不可忽视的影响。
A key challenge in nanotechnology is to design and synthesize the soft materials with simple block copolymers, which are now widely used in industry and daily life for the sake of their novel self-assembly behavior and the periodic physical properties on nanoscale. As a fertile source of soft materials, block copolymers can self-assemble into various ordered structures in both melts and solutions. These stable and metastable microstructures are always under different external fields during industrial processing. It actually relies on the ability to couple an external bias field to some molecular or supermolecular features, and thus achieve directional control over the microstructures. Shearing, as one of the most efficient techniques of symmetry breaking, had been widely used to obtain (or choose) perfect long-range ordered microstructures in block copolymer systems.
Computer simulation method and experiments can be considered as the two convenient means while doing scientific researches. We use computer simulation to do scientific researches in this dissertation, because it is one of the powerful techniques to visualize the above-mentioned physical processes directly. It helps us understand and explore the laws inherent in these natural phenomena. We carry out the dissipative particle dynamics (DPD) simulations in order to study the topics mentioned above in detail, respectively. The DPD method includes soft interaction potential, where all the particles interact with each other through three pairwise forces: a conservative force, a dissipative force, and a random force. Compared with traditional molecular dynamics (MD) simulation method, the integration time step can be larger than that in MD. The time scale in DPD simulation can be at milliseconds. We can unite some molecules or polymer segments into one DPD bead due to the soft repulsion potential, thus the DPD model can be used to study the systems at micron length scale. Therefore, DPD is the simulation method that is based upon the mesoscopic scale at both length scale and time scale. The pairwise interactions in the DPD model also result in the momentum of the system being conserved. It is proper to adopt DPD to simulate the microphase separation of block copolymers, because hydrodynamic interaction (HI) is another characteristic in DPD model. DPD is one of the powerful tools to model the dynamic process of complex fluids. At present, DPD has been widely used in the research fields of Chemistry, Physics, Biology, and also Materials Science.
In our study, DPD method is used to study the microphase behavior of diblock copolymers which is far away from equilibrium state, such as the cyclic diblock copolymers under steady shear and the linear diblock copolymers subjected to the oscillatory shear. The polymer micelle in the lid-driven flow is also studied comprehensively by carrying out DPD simulations. The main results are as follows:
The dissipative particle dynamics simulation technique is used to study the microphase transitions of perforated lamellae of cyclic diblock copolymers under steady shear. The perforated lamellae are transformed to perfect lamellae, and the layer normal is aligned to the direction parallel to the gradient of the velocity under weak shear, whereas they undergo a phase transition to form perfect lamellae whose normal is aligned to the direction perpendicular to the gradient of the velocity due to strong shear. Subjected to the moderate shear, the perforated lamellae are transformed to hexagonally ordered cylinders. By examining the microphase morphologies in the shearing process, we find shear thinning in general, which is reflected by the reorientation of the lamellae, and shear-induced thickening when hexagonally ordered cylinders appear. The calculated shear viscosity basically decreases with increasing shear rate but shows a local maximum at the shear rate that induces hexagonally ordered cylinders.
The phase morphologies of symmetric linear diblock copolymers subjected to the oscillatory shear are investigated with the aid of dissipative particle dynamics simulations. The frequency dependent reorientations of the lamellar phase (LAM) have been identified. We find that the parallel orientation of LAM, i.e., the lamellar normal is parallel to the velocity gradient appears at high shear frequency, whereas the perpendicular orientation of LAM the lamellar normal being perpendicular to the velocity gradient takes place at low shear frequency. In both of the cases, the reorientations undergo similar processes: the original LAM phase prepared in equilibrium breaks down rapidly, and it takes a very long time for the perfectly oriented LAM being reformed. Moreover, the shear-induced isotropic to lamellar phase transitions are observed when the oscillatory shear amplitude is large enough. It indicates that the shear amplitude plays a dominant role in the order-disorder transition. The viscosity and the modulus of the melt are found to be dependent on the shear amplitude and the shear frequency in a complex way.
The morphology variations of the micelles under lid-driven flow are studied via dissipative particle dynamics simulations. The morphologies of the micelles under flow are different from that in equilibrium. The weak lid-driven flow has hardly changed the morphologies of micelles. We find the worm-like micelles under moderate lid-driven flow. In the strong lid-driven flow, smaller micelles are observed. The properties of the walls are also a dominant factor influencing the micelle morphologies.
引文
[1] Moraweltz H. Polymer: The origins and growth of a science[M]. New York: John Wiley and Sons, 1985.
[2] Furukawa Y. Inventing Polymer Science[M]. Philadelphia: University of Pennsylvania Press, 1998.
[3]刘凤崎,汤心颐,高分子物理[M].北京:高等教育出版社,1995.
[4]何曼君,陈维孝,董西侠,高分子物理[M].上海:复旦大学出版社,1990.
[5] Pan C Y, Hong C Y. Chapter3. Synthesis and Characterization of Block Copolymer Prepared via Controlled Radical Polymerization Method[A].
[6] Hamley I W, Development in Block Copolymer Science and Technology[M], London: John Wiley&Sons, 2004, pp: 1-17.
[7] de Moel K. Comb-Shaped Supramolecules: A concept for Functional Polymeric Materials[D]. University of Groningen, 2001.
[8] Pispas S, Hadjichristidis N, Mays J W. Micellization of Model Graft Copolymers of the H andΠ-Type in Dilute Solution[J].Macromolecules, 1996, 29: 7378-7385.
[9] Dido S P, Lee C, Poehan D J, et al. Synthesis and Characterization and Morphology of Model Graft Copolymers with Trifunctional Branch Points[J]. Macromolecules, 1996, 29: 7022-7028.
[10] Floudas G, Hadjichristidis N, Iatrou H, et al. Microphase Separation IN Super-H-Shaped Block Copolymer Colloids[J]. Macromolecules,1998,31: 6943-6950.
[11] Iatrou H, Willner L, Hadjichristidis N, et al. Aggregation phenomena of Model PS/PI Super-H-Shaped Block Copolymers: Influence of the Architecture[J]. Macromolecules, 1996, 29: 581-591.
[12] Lee C, Dido S P, PoulosY, et al. H-Shaped Double Graft Copolymer: Effect of Molecules Architecture on Morphology[J]. J. Chem. Phys., 1997, 107:6460-6469.
[13] Bates F S, Fredrickson G H. Block copolymer thermodynamics: theory and experiment[J]. Annu. Rev. Phys.Chem., 1990, 41: 525-557.
[14] Fredrickson G H, Bates F S. Dynamics of Block Copolymers: Theory and Experiment[J]. Annu. Rev. Mater. Sci., 1996, 26: 501-550.
[15]姜世梅,沈家骢,嵌段共聚物自组装及其纳米图案化,韩志超,结构材料化学进展[M].北京,化学工业出版社: 2005.
[16] Thurn-Albrecht T, Steiner R, DeRouchey J. Nanoscopic templates from oriented block copolymer films[J]. ADVANCED MATERIALS, 2000, 12: 1138-1169.
[17] Hamley I W. The Physics of Block Copolymers[M]. Oxford, Oxford University Press: 1998.
[18] L. Leibler, Theory of Microphase Separation in Block Copolymers[J]. Macromolecules, 1980, 13: 1602-1617.
[19] Lee M, Cho B K, Zin W C. Supramolecular structures from rod-coil block copolymers[J]. Chem. Rev., 2001,101: 3869-3892.
[20] Thurn-Albrecht T, Schotter J, K?stle G A et al. Ultrahigh-density nanowire arrays grown in self-assembled diblock copolymer templates[J]. Science, 2000, 290: 2126-2129.
[21]马余强,软物质的自组织[J].物理学进展, 2002,第22卷, 73-98页.
[22] Bucknall D G, Anderson H L. Polymers get organized[J]. Science, 2003, 302: 1904-1905.
[23] Hamley I W. Nanostructure fabrication using block copolymers[J]. Nanotechnology, 2003, 14:R39 - R54.
[24] Riess G. Micellization of block copolymers[J]. Prog. Polym. Sci., 2003, 28: 1107-1170.
[25] Lodge T P, Bang J, Li Z, et al. Introductory Lecture Strategies for controllingintra- and intermicellar packing in block copolymer solutions: Illustrating the flexibility of the self-assembly toolbox[J]. Faraday Discuss., 2005, 128, 1-12.
[26] Kita-Tokarczyk K, Grumelard J, Haefele T, et al. Block copolymer vesicles-using concepts from polymer chemistry to mimic biomembranes[J]. Polymer, 2005, 46: 3540-3563.
[27] Nakashima K, Bahadur P. Aggregation of water-soluble block copolymers in aqueous solutions: Recent trends[J]. Adv. Colloid Interface Sci., 2006, 123-126: 75-96.
[28]许鑫华,叶卫平.计算机在材料科学中的应用[M].北京:机械工业出版社,2003.
[29]殷敬华,莫志深,现代高分子物理学[M].北京:科学出版社, 2001.
[30]董建华,国家自然科学基金委员会化学科学部组编.高分子科学前沿与进展II[M].北京:科学出版社, 2006.
[31] Helfand E. Theory of inhomogeneous polymers: Fundamental of the Gaussian-random walk model[J]. J. Chem. Phys., 1975, 62: 999 -1005.
[32] Fredrickson G H, Helfand E. Fluctuation effects in the theory of microphase separation in block copolymers[J]. J. Chem. Phys., 1987, 87: 697-705.
[33] Bates F S, Fredrickson G H. Block copolymers-designer soft materials[J]. Phys. Today, 1999, 52: 32-38.
[34] Matsen M W, Bates F S. Origins of complex self-assembly in block copolymers[J]. Macromolecules, 1996, 29: 7641-7644.
[35] Matsen M W, Schick M. Stable and unstable phases of a diblock copolymer melt[J]. Phys. Rev. Lett., 1994, 72: 2660-2663.
[36] Mansky P, Harrison C K, Chaikin P M, et al. Nanolithographic templates from diblock copolymer thin films[J]. Appl. Phys. Lett., 1996, 68: 2586-2588.
[37] Park M, Harrison C, Chaikin P M, et al. Block Copolymer Lithography: Periodic Arrays of ~1011 Holes in 1 Square Centimeter[J]. Science, 1997, 276:1401-1404.
[38] Huang E, Russell T P, Harrison C, et al. Using Surface Active Random Copolymers To Control the Domain Orientation in Diblock Copolymer Thin Films[J]. Macromolecules, 1998, 31: 7641-7650.
[39] Rosa C D, Park C, Thomas E L, et al. Microdomain patterns from directional eutectic solidification and epitaxy[J]. Nature, 2000, 405: 433-437.
[40] Li R R, Dapkus P D, Thompson M E, et al. Dense arrays of ordered GaAs nanostructures by selective area growth on substrates patterned by block copolymer lithography[J]. Appl. Phys. Lett., 2000, 76, 1689-1691.
[41] Black C T, Guarini K W, Milkove K R, et al. Integration of self-assembled diblock copolymers for semiconductor capacitor fabrication[J]. Appl. Phys. Lett., 2001, 79: 409-411.
[42] Krausch G, Magerle R. Nanostructured Thin Films via Self-Assembly of Block Copolymers[J]. Adv. Mater., 2002, 14: 1579-1583.
[43] Wang H, Newstein M C, Krishnan A, et al. Ordering Kinetics and Alignment of Block Copolymer Lamellae under Shear Flow[J]. Macromolecules, 1999, 32: 3695-3711.
[44] Riise B L, Fredrickon G H, Larson R G. Rheology and Shear-Induced Alignment of Lamellar Diblock and Triblock Copolymers[J]. Macromolecules, 1995, 28: 7653-7659.
[45] Koopi K A, Tirrell M , Bates F S. Shear-Induced Isotropic-to-Lamellar Transitions[J]. Phys. Rev. Lett., 1993, 70: 1449-1452.
[46] Qiao L, Ryan A J, Winey K I. Acorrelation between Lamellar Contranction and Applied Shear Stress in Diblock Copolymer[J]. Macromolecules, 2002, 35: 3596-3600.
[47] Noguchi H, Gompper G. Fluid Vesicle with Viscos Membranes in Shear Flow[J]. Phys. Rev. Lett., 2004, 93: 258102.
[48] Abkarian M, Viallat A. Vesicles and red Blood cells in Shear Flow[J]. Soft Matter, 2008, 4: 653-657.
[49] Kalra V, Mendez S, Escobedo F, et al. Coarse-grained molecular dynamics simulation on the placement of nanoparticles within symmetric diblock copolymers under shear flow[J]. J. Chem. Phys., 2008, 128: 164909.
[50] Cates M E, Milner S T. Role of Shear in the Isotropic-to-Lamellar Transition[J]. Macromolecules, 1989, 62: 1856-1859.
[51] Morozov A N, Fraaije J G E M. Phase Behavior of Ring Diblock Coplymer Melt in Equilbrium and under Shear[J]. Macromolecules, 2001, 34: 1526-1528.
[52] Allen M P, Tildesley D J. Computer Simulation of Liquids[M]. Oxford: Clarendon, 1987.
[53] van Gunsteren W F, Berendsen H G X. Computer simulation of molecular dynamics: Methodology, applications, and perspectives in chemistry[J]. Angew. Chem. Int. Ed. Engl., 1990, 29: 992-1023.
[54] Frenkel D, Smit B. Understanding Molecular Simulation: From Algorithms to Applications[M]. San Diego: Academic Press, 1996.
[55] Leach A R. Molecular Modeling Principles and Applications[M]. Essex: Longman, 1996.
[56]杨小震,高分子的计算机模拟,高分子科学的今天与明天[M].北京:化学工业出版社, 1994, 182-193。
[57] Wilson S. Chemistry by Computer[M]. New York: Plenum Press, 1986.
[58] Slater J C. Quantum Theory of Molecular and Solids[M]. New York: McGraw-Hill, 1974.
[59] Wang X L, Lu Z Y, Li Z S. Molecular Dynamics Simulation Study on Controlling the Adsorption Behavior of Polyethylene by Fine Tuning the Surface Nanodecoration of Graphite[J]. Langmuir, 2007, 23: 802-808.
[60] Qian H J, Lu Z Y, Chen L J, et al. Computer simulation of cyclic blockcopolymer microphase separation[M]. Macromolecules, 2005, 38: 1395-1401.
[61] Groot R D, Madden T J. Dynamic simulation of diblock copolymer microphase separation[J]. J. Chem. Phys., 1998, 108: 8713-8724.
[62] Rekvig L, Hafskjold B, Smit B. Chain Length Dependencies of the Bending Modulus of Surfactant Monolayers[J]. Phys. Rev. Lett., 2004, 92: 116101.
[63] Wang X L , Qian H J, Chen L J. Dissipative Particle Dynamics Simulation on the Polymer Membrane Formation by Immersion Precipitation[J]. J. Membr. Sci., 2008, 311: 251-258.
[64] Yamamoto S, Hyodo S-A, Budding and fission dynamics of two-component vesicles[J]. J. Chem. Phys., 2003, 118: 7937-7943.
[65] Laradji M, Sunil Kumar P B. Dynamics of Domain Growth in Self-Assembled Fluid Vesicles[J]. Phys. Rev. Lett., 2004, 93: 198105.
[66] Roe R J. ed. Computer Simulation of Polymers[M]. New Jersey: Prentice Hall, 1991.
[67] Doyama M, Kihara J, Tanaka M, et al. ed. Computer Aided Innovation of New Material[M]. New York: North Holland, 1993.
[68] Flory P J, Principles of Polymer Chemistry[M]. New York: Cornell Univ. Press, 1953.
[69] Feller W. An Introduction to Probability Theory and its Applications[M]. New York: John Wiley & Sons, 1957.
[70] Zhao Y, Liu Y T, Lu Z Y. The sensitive influence of the segment sequence and the molecular architecture on the morphology diversity of the multicompartment micelles: a dissipative particle dynamics simulation study[J]. Polymer, 2008, 49: 4899-4909.
[71] Li Z W, Chen L J, Zhao Y, et al. Ordered Packing in Soft Discoidal System[J]. J. Phys. Chem. B, 2008, 112(44): 13842-13848.
[72] Liu H, Xue Y H, Qian H J, et al. A Practical Method to Avoid Bond Crossing inTwo-dimensional Dissipative Particle Dynamics Simulations[J]. J. Chem. Phys., 2008, 129: 024902.
[73] Qian H J, Chen L J, Lu Z Y, et al. Surface Diffusion Dynamics of a Single Polymer Chain in Dilute Solution[J]. Phys. Rev. Lett., 2007, 99: 068301.
[74] Li Z W, Lu Z Y, Sun Z Y, et al. Calculating the Equation of State Parameters and Predicting the Spinodal Curve of Isotactic Polypropylene/Poly(ethylene-co-octene) Blend by Molecular Dynamics Simulations Combined with Sanchez-Lacombe Lattice Fluid Theory[J]. J. Phys. Chem. B, 2007, 111(21): 5934-5940.
[75] He Y D, Qian H J, Lu Z Y, et al. Polymer translocation through a nanopore in mesoscopic simulations[J]. Polymer, 2007, 48(12), 3601-3606.
[76] Clementi E, Corongiu G, Bhattacharya D, et al. Selected topics in ab initio computational chemistry in both very small and very large chemical systems[J]. Chem. Rev., 1991, 91: 679-699.
[77] Liu T W. Flexible polymer chain dynamics and rheological properties in steady flows[J]. J. Chem. Phys., 1989, 90: 5826-5842.
[78] Zylka W, ?ttinger H C. A comparison between simulations and various approximations for Hookean dumbbells with hydrodynamic interaction[J]. J. Chem. Phys., 1989, 90: 474-480.
[79] Grassia P, Hinch E J F. Computer simulations of polymer chain relaxation via Brownian motion[J]. J. Fluid Mech., 1996, 308: 255-288.
[80] Doyle P S, Shaqfeh E S G, Gast A P. Dynamic simulation of freely draining flexible polymers in steady linear flows[J]. J. Fluid Mech., 1997, 334: 251-291.
[81] Hoogerbrugge P J, Koelman J M V A, Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics[J]. Europhys. Lett. 1992, 19: 155-160.
[82] Espa?ol P, Warren P B. Statistical Mechanics of Dissipative Particle Dynamics[J]. Europhys. Lett. , 1995, 30: 191-196.
[83] Groot R D, Warren P B. Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation[J]. J. Chem. Phys., 1997, 107: 4423-4435.
[84] Chen S, Doolen G D, Lattice Boltzmann method for fluid flows[J]. Annu. Rev. Fluid Mech., 1998, 30: 329-364.
[85] Fraaije J G E M, van Vlimmeren B A C, Maurits N M, et al. The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts[J]. J. Chem. Phys., 1997, 106: 4260-4269.
[86] van Vlimmeren B A C, Maurits N M, Zvelindovsky A V, et al. Simulation of 3D mesoscale structure formation in concentrated aqueous solution of the triblock polymer surfactants (ethylene oxide)(13)(propylene oxide)(30)(ethylene oxide)(13) and (propylene oxide)(19)(ethylene oxide)(33)(propylene oxide)(19). Application of dynamic mean-field density functional theory[J]. Macromolecules, 1999, 32: 646-656.
[87] Fredrickson G H, Ganesan V, Drolet F. Field-theoretic computer simulation methods for polymers and complex fluids[J]. Macromolecules, 2002, 35: 16-39.
[88] John D, Anderson J R. Computational Fluid Dynamics: The Basics with Applications[M]. McGraw-Hill Companies, Inc., 2002.
[89] Liu W, Qian H J, et al. A dissipative particle dynamics study on the morphology changes of diblock copolymer lamellar microdomains due to steady shear[J]. Phys. Rev. E, 2006, 74: 021802.
[90] Revenga M, Zuniga I, Espa?ol P, et al. Boundary Model in DPD[J]. Int. J. Mod. Phys. C, 1998, 9(8): 1319-1328.
[91] Pivkin I V, Karniadakis G E. A new method to impose no-slip boundary conditions in dissipative particle dynamics[J]. J. Comput. Phys. 2005, 207: 114-128.
[92] Fan X J, N Phan-Thien, Yong N T, et al. Microchannel flow of a macromolecular suspension[J]. Phys. Fluids, 2003, 15: 11-21.
[93] You L Y, Chen L J, Qian H J, et al. Microphase Transitions of Perforated Lamellae of Cyclic Diblock Copolymers under Steady Shear[J]. Macromolecules, 2007, 40(14): 5222-5227.
[94] You L Y, He Y D, Zhao Y, et al. The complex influence of the oscillatory shear on the melt of linear diblock copolymers[J]. J. Chem. Phys., 2008, 129: 204901.
[95] Rapaport D C. The Art of Molecular Dynamics Simulation[M]. Cambridge: Cambridge University Press, 1995.
[96] Ciccotti G, Hoover G. Eds. Molecular-Dynamics Simulation of Statistical-Mechanics Systems[M]. Amsterdam: North-Holland, 1986.
[97] Frisch U, Hasslacher B, Pomeau Y. Lattice-Gas Automata for the Navier-Stokes Equation[J]. Phys. Rev. Lett., 1986, 56: 1505-1508.
[98] Benzi R, Succi S, Vergassola M. The lattice Boltzmann equation: theory and applications[J]. Phys. Rep., 1992, 222: 145-197.
[99] Succi S, Benzi R, Massaioli F. a Review of the Lattice Boltzmann Method[J]. Int. J. Mod. Phys. C, 1993, 4: 409-415.
[100] Swift M R, Orlandini E, Osborn W R. Lattice Boltzmann simulations of liquid-gas and binary fluid systems[J]. Phys. Rev. E, 1996, 54: 5041-5052.
[101] Koelman J M V A, Hoogerbrugge P J. Dynamic simulations of hard-sphere suspensions under steady shear[J]. Europhys. Lett., 1993, 21: 363-368.
[102] Kong Y, Manke C W, Madden W G, et al. Simulation of a confined polymer in solution using the dissipative particle dynamics method[J]. Int. J. Themophys.,1994, 15: 1093-1101.
[103] Schlijper A G, Hoogerbrugge P G, Manke C W. Computer simulation of dilute polymer solutions with the dissipative particle dynamics method[J]. J. Rheol., 1995, 39: 567-579.
[104] Dünweg B, Paul W. Brownian dynamics simulations without Gaussian random numbers[J]. Int. J. Mod. Phys. C, 1991, 2: 817-827.
[105] Tuckerman M E, Martyna G J. Understanding Modern Molecular Dynamics: Techniques and Applications[J]. J. Phys. Chem. B, 2000, 104: 159-178.
[106] Novik K E, Coveney P V. Finite-difference methods for simulation models incorporating nonconservative forces[J]. J. Chem. Phys., 1998, 109: 7667-7677.
[107] Pagonabarraga I, Hagen M H J, Frenkel D. Self-consistent dissipative particle dynamics algorithm[J]. Europhys. Lett., 1998, 42: 377-382.
[108] Gibson J B, Chen K, Chynoweth S. The equilibrium of a velocity-Verlet type algorithm for DPD with finite time steps[J]. Int. J. Mod. Phys. C, 1999, 10: 241-261.
[109] Vattulainen I, Karttunen M, Besold G, et al. Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models [J]. J. Chem. Phys., 2002, 116: 3967-3979.
[110] Nikunen P, Karttunen M, Vattulainen I. How would you integrate the equations of motion in dissipative particle dynamics simulations? [J]. Comp. Phys. Comm., 2003, 153: 407 -423.
[111] Dünweg B. Advanced Simulations for Hydrodynamic Problems: Lattice Boltzmann and Dissipative Particle Dynamics[R], In Attig N, Binder K, Grubmüller H, K. Kremer, editors, Computational Soft Matter: From Synthetic Polymers to Proteins, Lecture Notes[I]. Jülich, John von Neumann Institute for Computing, NIC Series, 2004, Vol. 23, ISBN 3-00-012641-4: pp. 61-82.
[112] Schneider T, Stoll E. Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions[J]. Phys. Rev. B., 1978, 17: 1302-1322.
[113] Chandrasekhar S, Stochastic Problems in Physics and Astronomy[J]. Rev. Mod. Phys., 1943, 15: 1-89.
[114] Risken H. The Fokker-Planck Equation[M]. Berlin: Springer-Verlag, 1984.
[115] Dünweg B. Langevin methods, In Dünweg B, Landau D P, Milchev A I, editors, Computer Simulation of Surfaces and Interfaces[M]. Dordrecht: Kluwer, 2003.
[116] Gardiner C W. Handbook of Stochastic Methods[M]. Berlin: Springer-Verlag, 1983.
[117] Groot RD, Rabone KL. Mesoscopic Simulation of Cell Membrane Damage, Morphology Change and Rupture by Nonionic Surfactants[J]. Biophysical Journal, 81(2): 725– 736.
[118] Sun H. Ab initio characterizations of molecular structures, conformation energies, and hydrogen-bonding properties for polyurethane hard segments[J]. Macromolecules, 1994, 26: 5924-5936.
[119] Ashurst WT, Hoover W G. Argon Shear Viscosity via a Lennard-Jones Potential with Equilibrium and Nonequilibrium Molecular Dynamics[J]. Phys. Rev. Lett., 1973, 31: 206-208.
[120] Ashurst WT, Hoover W G. Dense-fluid Shear Viscosity via Nonequilibrium Molecular-dynamics[J]. Phys. Rev. A, 1975, 11: 658-678.
[121] Tenenbaum A, Ciccotti G, Gallico R. Stationary Non-equilibrium State by Molecular-dynamics– Fourier Law[J]. Phys. Rev. A, 1982, 25: 2778-2788.
[122] Evans D J, Morriss G P. Non-Newtonian molecular dynamics [J]. Comput Phys. Rep., 1984, 1, 297-343.
[123] Gosling E M, McDonald I R., Singer K. Caculation by Molecular-dynamics of Shear S Viscosity of a simple fluid[J]. Mol. Phys., 1973, 26: 1475-1484.
[124] Ciccotti G, Jaccui G, McDonald I R. Transport Properties of Molten Alkali-Halides[J]. Phys. Rev. A, 1975, 13: 426-436.
[125] Ciccotti G, Jaccui G, McDonald I R. Thought-experiments by Molecular-dynamics [J]. J. Stat. Phys., 1979, 21: 1-22.
[126] Lees A W, Edwards S F. The computer study of transport processes under extreme conditions [J]. J. Phys. C: Solid State Phys., 1972, 5: 1921-1928.
[127] Rychkov I. Block copolymers under shear flow[J]. Macromol. Theory Simul., 2005, 14: 207-242.
[128] Hoover W G, Evans D F, Hickman R B, et al. Lennard-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics[J]. Phys. Rev. A, 1980, 22: 1690-1697.
[129] Evans D J, Morriss G P. Nonlinear-response theory for steady planar Couette flow[J]. Phys. Rev. A, 1984, 30: 1528-1530.
[130] Ladd A J C. Equations of motion for non-equilibrium molecular dynamics simulations of viscous flow in molecular fluids[J]. Mol. Phys., 1984, 53: 459-463.
[131] Soddemann T, Dünweg B, Kremer K. Dissipative particle dynamics: A useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations[J]. Phys. Rev. E, 2003, 68: 046702
[132] Spenley N A. Scaling laws for polymers in dissipative particle dynamics[J]. Europhys. Lett., 2000, 49: 534-540.
[133] Bates F S, Schulz M F, Khandpur A K, et al. Fluctuations, conformational asymmetry and block copolymer phase behaviour[J]. Faraday Discuss., 1994, 98: 7 - 18.
[134] Hajduk D A, Harper P E, Gruner S M. The Gyroid: A New Equilibrium Morphology in Weakly Segregated Diblock Copolymers[J]. Macromolecules, 1994, 27: 4063-4075.
[135] Fredrickson G H. Stability of a catenoid-lamellar phase for strongly stretched block copolymers[J]. Macromolecules, 1991, 24: 3456-3458.
[136] Olvera de la Cruz M, Mayers A M, Swift B W. Transition to lamellar-catenoid structure in block-copolymer melts[J]. Macromolecules, 1992, 25: 944-948.
[137] Hamley I W, Bates F S. Harmonic corrections to the mean-field phase diagram for block copolymers[J]. J. Chem. Phys., 1994, 100: 6813-6817.
[138] Thomas E L, Anderson D M, Henkee C S, et al. Periodic area-minimizing surfaces in block copolymers[J]. Nature, 1988, 334: 598-601.
[139] Almdal K, Koppi K, Bates F S, et al. Multiple ordered phases in a block copolymer melt [J]. Macromolecules, 1992, 25: 1743-1751.
[140] Mani S, Weiss R A, Cantino M E, et al. Evidence for a thermally reversible order–order transition between lamellar and perforated lamellar microphases in a triblock copolymer[J]. Eur. Polym. J., 2000, 36: 215-219.
[141] Loo Y L, Register R A, Adamson D H, et al. A Highly Regular Hexagonally Perforated Lamellar Structure in a Quiescent Diblock Copolymer[J]. Macromolecules, 2005, 38: 4947-4949.
[142] Lai C J, Loo Y L, Register R A. Dynamics of a Thermoreversible Transition between Cylindrical and Hexagonally Perforated Lamellar Mesophases[J]. Macromolecules, 2005, 38: 7098-7104.
[143] Borsali R, Benmouna M. Dynamic scattering from cyclic diblock-copolymer chains in solution[J]. Europhys. Lett., 1993, 23: 263-269.
[144] Borsali R, Lecommandoux, S, Pecora R, et al. Scattering Properties of Rod?Coil and Once-Broken Rod Block Copolymers[J]. Macromolecules, 2001, 34: 4229-4234.
[145] Marko J F. Microphase separation of block copolymer rings[J]. Macromolecules, 1993, 26: 1442-1444.
[146] Jo W H, Jang S S. Monte Carlo simulation of the order–disorder transition of asymmetric cyclic diblock copolymer system[J]. J. Chem. Phys., 1999, 111: 1712.
[147] Koopi K A, Tirrell M, Bates F S, et al. Lamellae orientation in dynamically sheared diblock copolymer melts[J]. J. Phys. II 1992, 2: 1941-1959.
[148] Kannan R M, Bates F S. Evolution of Microstructure and Viscoelasticity during Flow Alignment of a Lamellar Diblock Copolymer[J]. Macromolecules, 1994, 27: 1177-1186.
[149] GuptaV K, Krishnamoorti R, Kornfield J A, et al. Role of Strain in Controlling Lamellar Orientation during Flow Alignment of Diblock Copolymers[J]. Macromolecules, 1996, 29: 1359-1362.
[150] Chen Z R, Kornfield J A, Smith S D, et al. Pathways to macroscale order in nanostructured block copolymers[J]. Science, 1997, 277: 1248-1253.
[151] Ohta T, Kawasaki K. Equilibrium morphology of block copolymer melts[J]. Macromolecules, 1986, 19: 2621-2632.
[152] Qi S Y, Wang Z G. Kinetics of phase transitions in weakly segregated block copolymers: Pseudostable and transient states[J]. Phys. Rev. E, 1997, 55: 1697.
[153] Laradji M, Shi A C, Noolandi J. Stability of Ordered Phases in Diblock Copolymer Melts[J]. Macromolecules, 1997, 30: 3242-3255.
[154] Matsen M W. Cylinder?Gyroid Epitaxial Transitions in Complex Polymeric Liquids[J]. Phys. Rev. Lett., 1998, 80: 4470-4473.
[155] Fried H, Binder K. The microphase separation transition in symmetric diblock copolymer melts: A Monte Carlo study[J]. J. Chem. Phys., 1991, 94: 8349-8366.
[156] Pakula T, Karatasos K, Anastasiadis S H, et al. Computer Simulation of Static and Dynamic Behavior of Diblock Copolymer Melts[J]. Macromolecules, 1997, 30: 8463-8472.
[157] Guo H X, Kremer K. Molecular dynamics simulation of the phase behavior oflamellar amphiphilic model systems[J]. J. Chem. Phys., 2003, 119: 9308-9320.
[158] Guo H X. Shear-induced parallel-to-perpendicular orientation transition in the amphiphilic lamellar phase: A nonequilibrium molecular-dynamics simulation study[J]. J. Chem. Phys., 2006, 124: 054902.
[159] Schultz A J, Hall C K, Genzer J. Computer simulation of copolymer phase behavior[J]. J. Chem. Phys., 2002, 117: 10329-10338.
[160] Groot R D, Madden T J, Tildesley D J. On the role of hydrodynamic interactions in block copolymer microphase separation[J]. J. Chem. Phys., 1999, 110: 9739-9749.
[161] Luo K F, Yang Y L. Orientational phase transitions in the hexagonal cylinder phase and kinetic pathways of lamellar phase to hexagonal phase transition of asymmetric diblock copolymers under steady shear flow[J]. Polymer, 2004, 45: 6745-6751.
[162] de Gennes P G, Prost J. The Physics of Liquid Crystals[M]. Oxford: Clarendon Press, 1993.
[163] Bates F. S. Polymer-polymer Phase Behavior[J]. Science, 1991, 251: 898-905.
[164] Chen P, Vi?als J. Lamellar Phase Stability in Diblock Copolymers under Oscillatory ShearFlows[J]. Macromolecules, 2002, 35: 4183-4192.
[165] Patel S S, Larson R G, Winey K I, et al. Shear Orientation and Rheology of a Lamellar Polystyrene-Polyisoprene Block Copolymer[J]. Macromolecules, 1995, 28: 4313-4318.
[166] Gupta V K, Krishnamoorti R, Kornfield J A, et al. Evolution of Microstructure during Shear Alignment in a Polystyrene-Polyisoprene Lamellar Diblock Copolymer[J]. Macromolecules 1995, 28: 4464-4474.
[167] Maring D, Wiesner U. Threshold Strain Value for Perpendicular Orientation in Dynamically Sheared Diblock Copolymers[J]. Macromolecules, 1997, 30: 660-662.
[168] Pinheiro B S, Hajduk D A, Gruner S M, et al. Shear-Stabilized Bi-axial Texture and Lamellar Contraction in both Diblock Copolymer and Diblock Copolymer/Homopolymer Blends[J]. Macromolecules, 1996, 29: 1482-1489.
[169] Larson R G. The Structure and Rheology of Complex Fluids[M]. New York: Oxford University Press, 1999.
[170] de Moel K, M?ki-Ontto R, Stamm M, et al. Oscillatory Shear Flow-Induced Alignment of Lamellar Melts of Hydrogen-Bonded Comb Copolymer Supramolecules[J]. Macromolecules, 2001, 34: 2892-2900.
[171] Stangler S, Abetz V. Orientation behavior of AB and ABC block copolymers under large amplitude oscillatory shear flow[J]. Rheol. Acta, 2003, 42: 569-577.
[172] Zryd J L, Burghardt W R. Steady and Oscillatory Shear Flow Alignment Dynamics in a Lamellar Diblock Copolymer Solution[J]. Macromolecules, 1998, 31: 3656-3670.
[173] Saito S, Matsuzaka K, Hashimoto T. Structures of a Semidilute Polymer Solution under Oscillatory Shear Flow[J]. Macromolecules, 1999, 32: 4879-4888.
[174] Kim H Y, Lee D H, Kim J K. Effect of oscillatory shear on the interfacial morphology of a reactive bilayer polymer system[J]. Polymer, 2006, 47: 5108-5116.
[175] Hyun K, Kim S H, Ahn K H, et al. Large amplitude oscillatory shear as a way to classify the complex fluids[J]. J. Non-Newton. Fluid, 2002, 107: 51-65.
[176] Hyun K, Nam J G, Wilhellm M, et al. Large amplitude oscillatory shear behavior of PEO-PPO-PEO triblock copolymer solutions[J]. Rheol. Acta, 2006, 45: 239-249.
[177] [177] Kodama H, Doi M. Shear-Induced Instability of the Lamellar Phase of a Block Copolymer[J]. Macromolecules, 1996, 29: 2652-2658.
[178] Luo K, Yang Y. Lamellar Orientation and Corresponding Rheological Properties of Symmetric Diblock Copolymers under Steady Shear Flow[J]. Macromolecules, 2002, 35: 3722-3730.
[179] Malevanets A, Yeomans J M. Lattice Boltzmann simulations of complex fluids: viscoelastic effects under oscillatory shear[J]. Faraday Discuss., 1999, 112: 237-248.
[180] Huang Z.-F, Vi?als J. Orientation selection in lamellar phases by oscillatory shears[J]. Phys. Rev. E, 2006, 73: 060501.
[181] Willemsen S M, Hoefsloot H C J, Iedema P D. Mesoscopic simulation of polymers in fluid dynamics problems[J]. J. Stat. Phys., 2002, 107: 53-65.
[182] Lísal M, Brennan J K. Alignment of Lamellar Diblock Copolymer Phases under Shear: Insight from Dissipative Particle Dynamics Simulations[J]. Langmuir, 2007, 23: 4809-4818.
[183] Komatsugawa H, NoséS. Nonequilibrium molecular dynamics simulations of oscillatory sliding motion in a colloidal suspension system[J]. Phys. Rev. E, 1995, 51: 5944-5953.
[184] Komatsugawa H, NoséS. Nonequilibrium phase diagram of a polydisperse system: A molecular dynamics study[J]. J. Chem. Phys., 2000, 112: 11058-11064.
[185] Chen L J, Qian H J, Lu Z Y, et al. The effects of Lowe–Andersen temperature controlling method on the polymer properties in mesoscopic simulations[J]. J. Chem. Phys., 2005, 122: 104907.
[186] Raos G, Moreno M, Elli S. Computational Experiments on Filled Rubber Viscoelasticity: What Is the Role of Particle?Particle Interactions?[J]. Macromolecules, 2006, 39: 6744-6751.
[187] Jiang W H, Huang J H, Wang Y M, et al. Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics[J]. J. Chem. Phys., 2007,126: 044901.
[188] Nikunen P, Vattulainen I, Karttunen M. Reptational dynamics in dissipative particle dynamics simulations of polymer melts[J]. Phys. Rev. E, 2007, 75: 036713.
[189] Zhang Y, Wiesner U. Symmetrical Diblock Copolymers Under Large-Amplitude Oscillatory Shear Flow Entanglement Effect[J]. J. Chem. Phys., 1995, 103: 4784-4793.
[190] Zhang Y, Wiesner U. Symmetrical Diblock Copolymers Under Large-Amplitude Oscillatory Shear Flow: Dual Frequency Experiments[J]. J. Chem. Phys., 1997, 106: 2961-2969.
[191] Chen Z.-R, Issainan A K, Kornfield J A, et al. Dynamics of Shear-Induced Alignment of a Lamellar Diblock: A Rheo-optical, Electron Microscopy, and X-ray Scattering Study[J]. Macromolecules, 1997, 30: 7096-7114.
[192] Hajduk D A, Tepe T, Takenouchi M, et al. Shear-induced ordering kinetics of a triblock copolymer melt[J]. J. Chem. Phys., 1998, 108 : 326-333.
[193] Balsara N P, Hammouda B, Kesani P K, et al. In-Situ Small-Angle Neutron Scattering from a Block Copolymer Solution under Shear[J]. Macromolecules, 1994, 27: 2566-2573
[194] Huang C, Muthukumar M. Effect of shear on order-disorder and order-order transitions in block copolymers[J]. J. Chem. Phys., 1997, 107: 5561-5568.
[195] Morriss G P, Evans D Viscoelasticity in two dimensions[J]. J. Phys. Rev. A, 1985, 32: 2425-2430.
[196] Li X, Tang P, Zhang H, et al. Mesoscopic dynamics of inhomogeneous polymers based on variable cell shape dynamic self-consistent field theory[J]. J. Chem. Phys., 2008, 128: 114901.
[197] Adams J L, Graessley W W, Register R A. Rheology and the Microphase Separation Transition in Styrene-Isoprene Block Copolymers[J].Macromolecules, 1994, 27, 6026-6032.
[198] Balsara N P, Dai H J, Watanable H, et al. Influence of Defect Density on the Rheology of Ordered Block Copolymers[J]. Macromolecules, 1996, 29: 3507-3510.
[199] XüJ P, Chen W D, Ji J, et al. Novel Biomimetic Polymeric Micelles for Drug Delivery[J]. Chem. J. Chinese University, 2007, 28: 394-396.
[200] Li Z, Kesselman E, Talmon Y, et al. Multicompartment micelles for ABC miktoarm stars in water[J]. Science, 2004, 306: 98~101.
[201] Zhou Z, Li Z, Ren Y, et al. Micellar Shape Change and Internal Segregation Induced by Chemical Modification of Tryptych BlockCopolyer Surfactant[J]. J. Am. Chem. Soc., 2003, 125: 10182~10183.
[202] Kubowicz S, Baussard J.-F, Lutz J.-F.et al. Multicompartment micelles formed by self-assembly of linear ABC triblock copolymers in aqueous medium[J]. Angew. Chem. Int. Ed., 2005, 44: 5262~5265.
[203] Zhong C L, Liu D H. Understanding Multicompartment Micelles Using Dissipative Particle Dynamics Simulation[J]. Macromol Theory Simul., 2007, 16: 141~157.
[204] Willemsen S M, Hoefsloot H C J, Iedema P D. No-Slip Boundary Condition in Dissipative Particle Dynamics[J]. Int. J. Mod. Phys. C[J], 2000, 11: 881~890.
[205] Fedosov D A, Pivkin I V, Karniadakis G E. Velocity limit in DPD simulations of wall-bounded flows[J]. J. Comput. Phys., 2008, 227: 2540~2559.
[206] Cui Y Y, Zhong C L, Multicompartment Micellar Solutions in Shear: A Dissipative Particle Dynamic Study[J]. Macromol. Rapid Commun., 2006, 27: 1437~1441.