Self-consistent field theory and its applications in polymer systems

doi:10.1007/s11458-011-0251-8

Front Chem Chin

2011, Vol. 6

Issue (4) : 310-331 https://doi.org/10.1007/s11458-011-0251-8

REVIEW ARTICLE

Self-consistent field theory and its applications in polymer systems

Dadong YAN^1,2(

), Tongchuan SUO², Xinghua ZHANG^1,2, Xingkun MAN², Bing MIAO²

1. Department of Physics, Beijing Normal University, Beijing 100875, China; 2. Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China

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Abstract

This review article addresses the widely used self-consistent field theory (SCFT) in interacting polymer systems. The theoretical framework and numerical method of solving the self-consistent equations are presented. In this paper, different structures of polymer can be considered, such as homopolymer, block copolymer, polydisperse polymer and charged polymer. Several systems, micro/macro phase separation, interface, self-assembly, are presented as examples to demonstrate its applications in details. Besides, the fluctuation effects are considered. The first order is Gaussian fluctuation theory, which can be used to determine the stability of the mean-field solution and predict the kinetics of unstable structure. The derivation and applications of Gaussian fluctuation theory are presented as well.

Keywords self-consistent field theory (SCFT) Gaussian fluctuation theory self-assembly adsorption depletion polyelectrolyte confinement

Corresponding Author(s): YAN Dadong,Email:yandd@bnu.edu.cn

Issue Date: 05 December 2011

Cite this article:

Dadong YAN,Tongchuan SUO,Xinghua ZHANG, et al. Self-consistent field theory and its applications in polymer systems[J]. Front Chem Chin, 2011, 6(4): 310-331.

URL:

https://academic.hep.com.cn/fcc/EN/10.1007/s11458-011-0251-8
https://academic.hep.com.cn/fcc/EN/Y2011/V6/I4/310

Fig.1 Polymer segments distributions belong to tail, loop, and free part. The parameters are taken as =1000, , = 0.4 and / = 10.

Fig.2 Average tail length, , as a function of normalized particle radius, /, at different bulk concentrations of , 0.04, 0.1, 0.5, and 0.95, respectively. =1000; = 0.2.

Fig.3 The depletion potential (a, b) and depleted amount (c, d) between two spheres as a function of the separation in dilute (a, c) and semidilute (b, d) solutions. The parameters are taken as = 0.5, = 100, and / = 10.

Fig.4 Effect of surface curvature on the scaling law. and are obtained for fixed = 0.025 and =0.1, respectively. and decrease as increases when <2. As goes larger than 2, and nearly do not change with and approach the fixed values of the planar surface, i.e., 2/3. The insert is the dependence of . increases as increases and quickly converges to the result of the planar surface as goes larger than 2. ( is used as the Kuhn length here instead of .)

Fig.5 The dependence of the reduced critical radius, /. ( is the Kuhn length here.) The critical line separates the adsorption regime from the depletion regime for = 0.025 and = 0.1.

Fig.6 Cylindrical radius, (in unit of Kuhn length, ), dependence of the charge inversion ratio, /, in the Coulombic interaction dominated regime with = 0, = 0.1, = 0.5, = 0.1 and = 0. The insert is the detail for the crossover point of . Only moderate charge inversion (/ ≈ -2×10) happens in this case.

Fig.7 Charge inversion ratio, /, as a function of cylindrical radius, , (in unit of Kuhn length ) with = 0.1, = 0.025, =0.1, and = 0.1 for different short-range non-Coulombic interactions, . When <2, the magnitude of / increases with decreasing , and strong charge inversion / = -1.9 and -5.2 have been obtained in large surface curvature (=1) for = - 0.3 and -0.5, respectively. When >2, / nearly does change with .

Fig.8 Volume fractions of species A at the centers of critical nuclei, (0) as functions of for different polydispersity. For a given , higher polydispersity (small ) leads to lower (0). The parameters are taken as , =.

Fig.9 Volume fraction contributions of the polydisperse A species as functions of chain lengths, (/), for different polydispersity parameters (a) in homogeneous bulk, and (b) at the centers of critical nuclei. The parameters are taken as =2.5, , and =. Higher polydispersity leads to larger / for the peak position of (,0).

Fig.10 Two-dimensional phase diagram as a function of and for a diblock copolymer solution with =0.1, =0.2 and (a) =0.5, =200; (b) =0.5, =150; (c) =0.3, =150; (d) =0.18, =150. The ordered phases are denoted as follows: L=lamellae, H=hexagonally packed cylinders, G=gyroid, S=body-centered cubic spheres, S=face-centered cubic spheres. Dis=disordered phase. The subscript of each symbol refers to the core composition. The boundary between the regions of L+H and G in (d) should be considered just as a guide to the eye.

Fig.11 Ordered phases obtained using the generic spectrum approach for model linear ABC triblock copolymers with = = 35 and = 15. Blue, green, and red represent domains rich in A, B, and C blocks, respectively. Reproduced from Ref. [], Copyright ? 2008 American Physical Society.

Fig.12 Phase diagram of a model linear ABC triblock copolymer with = = 35 and = 15. Dotted lines are phase boundaries that are not determined exactly. Reproduced from Ref. [], Copyright ? 2008 American Physical Society.

Fig.13 Size dependence of the spinodal point () for the symmetric ( = 0.5) diblock copolymer melts confined between two parallel slabs with a distance of . The solid line represents the physical spinodal point determined from the most unstable mode with = 0. The dotted line obtained from the Gaussian fluctuation theory and the dashed line obtained from the Landau-Brazovskii model illustrate the zero point induced by the second-lowest fluctuation mode with = 1.

Fig.14 Size dependence of the spinodal point () for the symmetric ( = 0.5) diblock copolymer melts confined in a spherical pore with the radius of. The solid line and the dashed line are obtained from the Gaussian fluctuation theory and the Landau-Brazovskii model, respectively.

Fig.15 The order parameter, , as a function of for the symmetric diblock copolymer melts confined between two slabs with preferential surfaces of different surface strengths of and the separation distance =10. The solid, dashed, dotted and dash-dotted lines correspond to the cases of = 0, 0.1, 1 and 2, respectively.

Fig.16 The evolution of the order parameter, , with for = 3 = 9.6 and = 0.1. The jump of the order parameter happens around = 13.

Fig.17 The evolution of the spatial density distribution of block B, , with . = 9.6 and = 0.1.

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