管子模型
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摘要
高分子非线性流变学是发展高效、节能高分子材料及其加工技术的学科基础.针对缠结高分子流体,de Gennes、Doi和Edwards基于单链平均场近似建立了"管子模型".该模型奠定了现代高分子流体非线性流变学的基础,标志着人类描述缠结高分子流体步入了分子流变学时代.然而,"管子模型"过于简化的物理图像无法基于分子链本身和第一性原理,处理快速大形变条件下缠结高分子流体非线性流变学的一些问题;另一方面,"管子模型"无法统一描述近期的一些流变学实验现象.这就需要重新考虑现有的单链平均场假设和多链相互作用,建立分子流变学的新范式.本文介绍了"管子模型"及其修正理论的基本物理图像、概念及其发展历程,给出了该模型中核心方程的推导过程及其参数的物理意义,最后,对该领域的未来发展趋势以及面临的机遇和挑战进行了简明扼要的展望.希望通过本文能够加深读者对"管子模型"的认识和理解.
Nonlinear rheology for polymers is the foundational science underlying high efficiency and energysaving processing of polymeric materials. For chainlike polymers, complicated interchain interactions affect their dynamics and determine the structure-processing-property relationship. This interaction is often called the entanglement, and becomes the key issue in polymer rheology. To our knowledge, the rheological behavior of entangled polymers is based on the de Gennes-Doi-Edwards tube model(DE theory), which reduces the manychain interaction into a smooth confining tube and assumes the test chain undergoes the Rouse dynamics inside the tube. Some predictions based on the DE theory are in agreement with rheological results, for instance, the timestrain separated form of the reduced relaxation modulus. To overcome some obvious disadvantages and provide reasonable results, many improvements and refinements have also been made to the DE theory. However, the tube model is only an essential single-chain mean-field theory since its intuitive molecular picture is too simple the theory cannot be derived from first principles and lacks self-consistency. In brief, the tube model does not describe how entanglement arises and cannot address the problem of when, how, and why disentanglement occurs after the external deformation. The model is inadequate in describing the chain conformation under fast and large deformations, and fails to explain a number of experimental observations in recent studies, such as the shear banding and the nonquiescent relaxation which show remarkable strain localization phenomena. Therefore, it is necessary to reexamine the single-chain mean-field assumptions and to consider the many-chain interactions explicitly. In other words, the chain entanglement may involve active localized intermolecular interactions that should be preceived as network junctions, and the critical picture of barrier-free Rouse retraction is questionable.In this article, we provide a general introduction to the original tube model and its subsequent improvements, with an emphasis on the development, basic assumptions, and key concepts. We provide derivation of some key results and explain the physical meaning of the parameters. The article ends with an outlook of the challenges and opportunities in the theory for polymer rheology, hoping to motivate researchers to working on this field.
Nonlinear rheology for polymers is the foundational science underlying high efficiency and energysaving processing of polymeric materials. For chainlike polymers, complicated interchain interactions affect their dynamics and determine the structure-processing-property relationship. This interaction is often called the entanglement, and becomes the key issue in polymer rheology. To our knowledge, the rheological behavior of entangled polymers is based on the de Gennes-Doi-Edwards tube model(DE theory), which reduces the manychain interaction into a smooth confining tube and assumes the test chain undergoes the Rouse dynamics inside the tube. Some predictions based on the DE theory are in agreement with rheological results, for instance, the timestrain separated form of the reduced relaxation modulus. To overcome some obvious disadvantages and provide reasonable results, many improvements and refinements have also been made to the DE theory. However, the tube model is only an essential single-chain mean-field theory since its intuitive molecular picture is too simple the theory cannot be derived from first principles and lacks self-consistency. In brief, the tube model does not describe how entanglement arises and cannot address the problem of when, how, and why disentanglement occurs after the external deformation. The model is inadequate in describing the chain conformation under fast and large deformations, and fails to explain a number of experimental observations in recent studies, such as the shear banding and the nonquiescent relaxation which show remarkable strain localization phenomena. Therefore, it is necessary to reexamine the single-chain mean-field assumptions and to consider the many-chain interactions explicitly. In other words, the chain entanglement may involve active localized intermolecular interactions that should be preceived as network junctions, and the critical picture of barrier-free Rouse retraction is questionable.In this article, we provide a general introduction to the original tube model and its subsequent improvements, with an emphasis on the development, basic assumptions, and key concepts. We provide derivation of some key results and explain the physical meaning of the parameters. The article ends with an outlook of the challenges and opportunities in the theory for polymer rheology, hoping to motivate researchers to working on this field.
引文
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2Dealy J M,Larson R G.Structure and Rheology of Molten Polymers:From Structure to Flow Behavior and Back Again.Munich:Hanser Publishers,2006.91-126,193-229,329-400,415-464
3Rubinstein M,Colby R H,Polymer Physics.New York:Oxford University Press,2003.30-53,197-252
4Wang Shiqing(王十庆).Sci China Chem(中国科学-化学),2010,53(1):151-156
5Kalathi J T,Kumar S K,Rubinstein M,Grest G S.Macromolecules,2014,47(19):6925-6931
6Casale A,Porter R S,Johnson J F.Polym Rev,1971,5(2):387-408
7Berry G C,Fox T G.Adv Polym Sci,1968,5:261-357
8Lodge T P.Phys Rev Lett,1999,83(16):3218-3221
9de Gennes P G.J Chem Phys,1971,55(2):572-579
10Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1978,74:1789-1801
11Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1978,74:1802-1817
12Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1978,74:1818-1832
13Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1979,75:38-54
14Graham R S,Likhtman A E,McLeish T C B,Milner S T.J Rheol,2003,47(5):1171-1200
15Wang S-Q,Wang Y,Cheng S,Li X,Zhu X,Sun H.Macromolecules,2013,46(8):3147-3159
16Lu Yuyuan(卢宇源),An Lijia(安立佳),Wang Jian(王健).Acta Polymerica Sinica(高分子学报),2016,(6):688-697
17Kaye A,Non-Newtonian Flow in Incompressible Fluids.Cranford:College of Aeronautics Press,1962.4-16
18Bernstein B,Kearsley E A,Zapas L J.Trans Soc Rheol,1963,7:391-410
19Larson R G,Constitutive Equations for Polymer Melts and Solutions.Stoneham:Butterworth Publishers,1988.29-49
20Green M S,Tobolsky A V.J Chem Phys,1946,14(2):80-92
21Lodge A S.Rheol Acta,1968,7(4):379-392
22Doi M.J Polym Sci,Part B:Polym Phys,1983,21(5):667-684
23Milner S,McLeish T.Phys Rev Lett,1998,81(3):725-728
24Viovy J L,Rubinstein M,Colby R H.Macromolecules,1991,24(12):3587-3596
25Rubinstein M,Colby R H.J Chem Phys,1988,89(8):5291-5306
26Ianniruberto G,Marrucci G.J Non-Newton Fluid Mech,1996,65(2):241-246
27Marrucci G.J Non-Newton Fluid Mech,1996,62(2-3):279-289
28Likhtman A E,Milner S T,McLeish T C B.Phys Rev Lett,2000,85(21):4550-4553
29Milner S T,McLeish T C B,Likhtman A E.J Rheol,2001,45(2):539-563
30Ruan Yongjin(阮永金),Wang Zhenhua(王振华),Lu Yuyuan(卢宇源),An Lijia(安立佳).Acta Polymerica Sinica(高分子学报),2017,(5):727-743
31Edwards S F.Proc Phys Soc,1967,92(575):9-16
32Edwards S F.British Polym J,1977,9(2):140-143
33Rouse P E.J Chem Phys,1953,21(7):1272-1280
34Likhtman A E,Sukumaran S K,Ramirez J.Macromolecules,2007,40(18):6748-6757
35Onogi S,Masuda T,Kitagawa K.Macromolecules,1970,3(2):109-116
36Osaki K,Kurata M.Macromolecules,1980,13(3):671-676
37Osaki K,Nishizawa K,Kurata M.Macromolecules,1982,15(4):1068-1071
38Archer L A.J Rheol,1999,43(6):1555-1571
39Archer L A,Sanchez-Reyes J,Juliani.Macromolecules,2002,35(27):10216-10224
40Tanner R I.Trans Soc Rheol,1973,17(2):365-373
41Gao H W,Ramachandran S,Christiansen E B.J Rheol,1981,25(2):213-235
42Likhtman A E,McLeish T C B.Macromolecules,2002,35(16):6332-6343
43Graham R S,Henry E P,Olmsted P D.Macromolecules,2013,46(24):9849-9854
44Auhl D,Ramirez J,Likhtman A E,Chambon P,Fernyhough C.J Rheol,2008,52(3):801-835
45Lodge A S.Rheol Acta,1989,28(5):351-362
46Ravindranath S,Wang S Q.Macromolecules,2007,40(22):8031-8039
47Cheng S,Lu Y,Liu G,Wang S Q.Soft Matter,2016,12(14):3340-3351
48Wang S Q,Ravindranath S,Boukany P,Olechnowicz M,Quirk R P,Halasa A,Mays J.Phys Rev Lett,2006,97(18):187801(1-4)
49Boukany P E,Wang S Q,Wang X.Macromolecules,2009,42(16):6261-6269
50Lu Yuyuan(卢宇源),Li Liangbin(李良彬),Yu Wei(俞炜),An Lijia(安立佳).Acta Polymerica Sinica(高分子学报),2018,(12):1558-1562
51Wang S Q.Nonlinear Polymer Rheology:Macroscopic Phenomenology and Molecular Foundation.Hoboken:John Wiley&Sons,2018.4-415
52Inoue T,Uematsu T,Yamashita Y,Osaki K.Macromolecules,2002,35(12):4718-4724
53Huang Q,Hengeller L,Alvarez N J,Hassager O.Macromolecules,2015,48(12):4158-4163
54Nielsen J K,Hassager O,Rasmussen H K,McKinley G H.J Rheol,2009,53(6):1327-1346
55Wang Z,Lam C N,Chen W R,Wang W,Liu J,Liu Y,Porcar L,Stanley C B,Zhao Z,Hong K,Wang Y.Phys Rev X,2017,7(3):031003(1-16)
56Xu W S,Carrillo J M Y,Lam C N,Sumpter B G,Wang Y.ACS Macro Lett,2018,7(2):190-195
57Hsu H P,Kremer K.ACS Macro Lett,2017,7(1):107-111
58Kr?ger M,Hess S.Phys Rev Lett,2000,85(5):1128-1131
59Kremer K,Grest G S.J Chem Phys,1990,92(8):5057-5086
2Dealy J M,Larson R G.Structure and Rheology of Molten Polymers:From Structure to Flow Behavior and Back Again.Munich:Hanser Publishers,2006.91-126,193-229,329-400,415-464
3Rubinstein M,Colby R H,Polymer Physics.New York:Oxford University Press,2003.30-53,197-252
4Wang Shiqing(王十庆).Sci China Chem(中国科学-化学),2010,53(1):151-156
5Kalathi J T,Kumar S K,Rubinstein M,Grest G S.Macromolecules,2014,47(19):6925-6931
6Casale A,Porter R S,Johnson J F.Polym Rev,1971,5(2):387-408
7Berry G C,Fox T G.Adv Polym Sci,1968,5:261-357
8Lodge T P.Phys Rev Lett,1999,83(16):3218-3221
9de Gennes P G.J Chem Phys,1971,55(2):572-579
10Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1978,74:1789-1801
11Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1978,74:1802-1817
12Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1978,74:1818-1832
13Doi M,Edwards S F.J Chem Soc,Faraday Trans 2,1979,75:38-54
14Graham R S,Likhtman A E,McLeish T C B,Milner S T.J Rheol,2003,47(5):1171-1200
15Wang S-Q,Wang Y,Cheng S,Li X,Zhu X,Sun H.Macromolecules,2013,46(8):3147-3159
16Lu Yuyuan(卢宇源),An Lijia(安立佳),Wang Jian(王健).Acta Polymerica Sinica(高分子学报),2016,(6):688-697
17Kaye A,Non-Newtonian Flow in Incompressible Fluids.Cranford:College of Aeronautics Press,1962.4-16
18Bernstein B,Kearsley E A,Zapas L J.Trans Soc Rheol,1963,7:391-410
19Larson R G,Constitutive Equations for Polymer Melts and Solutions.Stoneham:Butterworth Publishers,1988.29-49
20Green M S,Tobolsky A V.J Chem Phys,1946,14(2):80-92
21Lodge A S.Rheol Acta,1968,7(4):379-392
22Doi M.J Polym Sci,Part B:Polym Phys,1983,21(5):667-684
23Milner S,McLeish T.Phys Rev Lett,1998,81(3):725-728
24Viovy J L,Rubinstein M,Colby R H.Macromolecules,1991,24(12):3587-3596
25Rubinstein M,Colby R H.J Chem Phys,1988,89(8):5291-5306
26Ianniruberto G,Marrucci G.J Non-Newton Fluid Mech,1996,65(2):241-246
27Marrucci G.J Non-Newton Fluid Mech,1996,62(2-3):279-289
28Likhtman A E,Milner S T,McLeish T C B.Phys Rev Lett,2000,85(21):4550-4553
29Milner S T,McLeish T C B,Likhtman A E.J Rheol,2001,45(2):539-563
30Ruan Yongjin(阮永金),Wang Zhenhua(王振华),Lu Yuyuan(卢宇源),An Lijia(安立佳).Acta Polymerica Sinica(高分子学报),2017,(5):727-743
31Edwards S F.Proc Phys Soc,1967,92(575):9-16
32Edwards S F.British Polym J,1977,9(2):140-143
33Rouse P E.J Chem Phys,1953,21(7):1272-1280
34Likhtman A E,Sukumaran S K,Ramirez J.Macromolecules,2007,40(18):6748-6757
35Onogi S,Masuda T,Kitagawa K.Macromolecules,1970,3(2):109-116
36Osaki K,Kurata M.Macromolecules,1980,13(3):671-676
37Osaki K,Nishizawa K,Kurata M.Macromolecules,1982,15(4):1068-1071
38Archer L A.J Rheol,1999,43(6):1555-1571
39Archer L A,Sanchez-Reyes J,Juliani.Macromolecules,2002,35(27):10216-10224
40Tanner R I.Trans Soc Rheol,1973,17(2):365-373
41Gao H W,Ramachandran S,Christiansen E B.J Rheol,1981,25(2):213-235
42Likhtman A E,McLeish T C B.Macromolecules,2002,35(16):6332-6343
43Graham R S,Henry E P,Olmsted P D.Macromolecules,2013,46(24):9849-9854
44Auhl D,Ramirez J,Likhtman A E,Chambon P,Fernyhough C.J Rheol,2008,52(3):801-835
45Lodge A S.Rheol Acta,1989,28(5):351-362
46Ravindranath S,Wang S Q.Macromolecules,2007,40(22):8031-8039
47Cheng S,Lu Y,Liu G,Wang S Q.Soft Matter,2016,12(14):3340-3351
48Wang S Q,Ravindranath S,Boukany P,Olechnowicz M,Quirk R P,Halasa A,Mays J.Phys Rev Lett,2006,97(18):187801(1-4)
49Boukany P E,Wang S Q,Wang X.Macromolecules,2009,42(16):6261-6269
50Lu Yuyuan(卢宇源),Li Liangbin(李良彬),Yu Wei(俞炜),An Lijia(安立佳).Acta Polymerica Sinica(高分子学报),2018,(12):1558-1562
51Wang S Q.Nonlinear Polymer Rheology:Macroscopic Phenomenology and Molecular Foundation.Hoboken:John Wiley&Sons,2018.4-415
52Inoue T,Uematsu T,Yamashita Y,Osaki K.Macromolecules,2002,35(12):4718-4724
53Huang Q,Hengeller L,Alvarez N J,Hassager O.Macromolecules,2015,48(12):4158-4163
54Nielsen J K,Hassager O,Rasmussen H K,McKinley G H.J Rheol,2009,53(6):1327-1346
55Wang Z,Lam C N,Chen W R,Wang W,Liu J,Liu Y,Porcar L,Stanley C B,Zhao Z,Hong K,Wang Y.Phys Rev X,2017,7(3):031003(1-16)
56Xu W S,Carrillo J M Y,Lam C N,Sumpter B G,Wang Y.ACS Macro Lett,2018,7(2):190-195
57Hsu H P,Kremer K.ACS Macro Lett,2017,7(1):107-111
58Kr?ger M,Hess S.Phys Rev Lett,2000,85(5):1128-1131
59Kremer K,Grest G S.J Chem Phys,1990,92(8):5057-5086