密度泛函理论在聚合物发泡领域中的应用研究进展

doi:10.19491/j.issn.1001-9278.2021.07.020

中国塑料 ›› 2021, Vol. 35 ›› Issue (7): 126-133.DOI: 10.19491/j.issn.1001-9278.2021.07.020

密度泛函理论在聚合物发泡领域中的应用研究进展

董星彤¹, 王向东¹, 孙晓红², 陈士宏¹()

^1.北京工商大学化学与材料工程学院，北京 100048
^2.北京工商大学人工智能学院，北京 100048

收稿日期:2021-03-08 出版日期:2021-07-26 发布日期:2021-07-21

Research Progress in Density Functional Theory Used in Field of Polymer Foaming

DONG Xingtong¹, WANG Xiangdong¹, SUN Xiaohong², CHEN Shihong¹()

^1.School of Chemical and Materials Engineering，Beijing Technology and Business University，Beijing 100048，China
^2.School of Artificial Intelligence，Beijing Technology and Business University，Beijing 100048，China

Received:2021-03-08 Online:2021-07-26 Published:2021-07-21
Contact: CHEN Shihong E-mail:shihong02@126.com

摘要/Abstract

摘要：

阐述了在发泡领域引入密度泛函理论的原因，综述了国内外对密度泛函理论的研究现状，详细介绍了密度泛函理论在高分子体系中尤其是在发泡领域中的发展与应用研究进展；总结了基于均相成核、非均相成核方法并结合不同动力学、热力学公式的创新的密度泛函模型，并对这些模型的应用进行了综述；将密度泛函模型与其他计算模型进行比对，以体现出其在聚合物发泡机理研究中的独特性。

关键词: 密度泛函理论, 聚合物发泡, 模型模拟, 密度分布, 气泡成核

Abstract:

This article introduced the reasons that the density functional theory was introduced into the field of foaming. The current research status of density functional theory at home and abroad was reviewed. The development and application of density functional theory in polymer systems were introduced， especially in the field of foaming. An innovative DFT model based on the homogeneous and heterogeneous nucleation combined with different dynamic and thermodynamic formulas was summarized. The applications of this DFT model were reviewed. Finally， a comparative analysis was presented for the DFT model and other computational models to reflect its uniqueness in the polymer foaming process.

Key words: density functional theory, polymer foaming, modeling simulation, density distribution, bubble nucleation

中图分类号:

TQ328

董星彤, 王向东, 孙晓红, 陈士宏. 密度泛函理论在聚合物发泡领域中的应用研究进展[J]. 中国塑料, 2021, 35(7): 126-133.

DONG Xingtong, WANG Xiangdong, SUN Xiaohong, CHEN Shihong. Research Progress in Density Functional Theory Used in Field of Polymer Foaming[J]. China Plastics, 2021, 35(7): 126-133.

图/表 5

图1 不同过饱和度下的成核速率等温线

Fig.1 Nucleation rate isotherms under different supersaturations

图2 过饱和度?温度关系曲线

Fig.2 Supersaturation ratio of nucleation as a function of temperature

图3 非均相气泡成核示意图

Fig.3 Schematic diagram of heterogeneous nucleation

图4 CO2在PCL基体中的溶解度预测曲线及实验数据

Fig.4 Predicted and experimental CO2 solubilities in PCL matrix

图5 CO2?H2O发泡剂在PS基体中的发泡倍率预测曲线

Fig.5 Prediction curve of CO2?H2O induced PS swelling ratio

参考文献 57

1	NOFAR M，PARK C B.Poly （Lactic Acid） Foaming［J］.Progress in Polymer Science，2014，39（10）：1 721⁃1 741.
2	VOSEL S，ONISCHUK A，PURTOV P，et al.Classical Nucleation Theory［M］.New York： Aerosols Handbook，2012：503⁃528.
3	LIU W K，KARPOV E G，ZHANG S，et al.An Introduction to Computational Nanomechanics and Materials［J］.Computer Methods in Applied Mechanics & Engineering，2015，193（17/20）：1 529⁃1 578.
4	HALL L M，JAYARAMAN A，SCHWEIZER K S.Molecu⁃lar Theories of Polymer Nanocomposites［J］.Current Opi⁃nion in Solid State & Materials Science，2010，14（2）：38⁃48.
5	ROSSKY， PETER J. The Structure of Polar Molecular Liquids［J］. Annual Review of Physical Chemistry， 2003， 36（1）：321⁃346.
6	DOBRYNIN A V， RUBINSTEIN M. Theory of Polye⁃lectrolytes in Solutions and at Surfaces［J］. Progress in Polymer Science， 2005， 30（11）：1 049⁃1 118.
7	KIERLIK E， ROSINBERG M L. Perturbation Density Functional Theory for Polyatomic Fluids. III. Application to Hard Chain Molecules in Slitlike Pores［J］. Journal of Chemical Physics， 1994， 100（2）：1 716⁃1 730.
8	YETHIRAJ A， WOODWARD C E. Monte Carlo Density Functional Theory of Nonuniform Polymer Melts［J］. Journal of Chemical Physics， 1995， 102（13）：5 499⁃5 505.
9	HOOPER J B， SCHWEIZER K S. Theory of Phase Separation in Polymer Nanocomposites［J］. Macromolecules， 2015， 39（15）：5 133⁃5 142.
10	CAI J， LIU H， HU Y. Density Functional Theory and Monte Carlo Simulation of Mixtures of Hard Sphere Chains Confined in A Slit［J］. Fluid Phase Equilibria， 2002， 194（1）：281⁃287.
11	RIVERA O. Molecular Simulation of Liquid Crystals： Phase Equilibrium and the Solubility of Gases in Ordered Fluids［J］. 2016：2.
12	PROCTOR J E， MAYNARD⁃CASELY H E. Equations of State for Fluids［M］. Boca Raton： The Liquid and Supercritical Fluid States of Matter，2020：31⁃46.
13	CARNAHAN N F， STARLING K E. Intermolecular Repulsions and the Equation of State for Fluids［J］. Aiche Journal， 2010， 18（6）：1 184⁃1 189.
14	YE Z C， CAI J， LIU H L， HU Y. Density and Chain Conformation Profiles of Square⁃Well Chains Confined in A Slit by Density⁃Functional Theory［J］. The Journal of Chemical Physics， 2005，123（19）：194902.
15	DIAMANTONIS N I， ECONOMOU I G. Evaluation of Statistical Associating Fluid Theory （SAFT） and Perturbed Chain⁃SAFT Equations of State for the Calculation of Thermodynamic Derivative Properties of Fluids Related to Carbon Capture and Sequestration［J］. Energy & Fuels， 2011， 25（7/8）：3 334–3 343.
16	LAFITTE T， MENDIBOURE B， PINEIRO， MANUEL M， et al. Interfacial Properties of Water/CO₂： A Comprehensive Description through A Gradient Theory⁃SAFT⁃VR Mie Approach［J］. Journal of Physical Chemistry B， 2010， 114（34）：11 110⁃11 116.
17	CHEN H X， YE Z， PENG C， et al. Density Functional Theory for the Recognition of Polymer at Nanopatterned Surface［J］. Journal of Chemical Physics， 2006， 125（20）：3 157.
18	CHEN X， SUN L， LIU H， et al. A New Lattice Density Functional Theory for Polymer Adsorption at Solid⁃Liquid Interface［J］. Journal of Chemical Physics， 2009， 131（4）：537.
19	FRAAIJE J， NATH S K， REMERIE K， et al. Phase Evolution Theory for Polymer Blends with Extreme Chemical Dispersity： Parameterization of DDFT Simulations and Application to Poly（propylene） Impact Copolymers［J］. Macromolecular Theory and Simulations， 2011， 20（2）：133⁃145.
20	EVANS R. Density Functionals in the Theory of Non⁃Uniform Fluids［J］. Fundamentals of Inhomogeneous Fluids， 1992， 90：85⁃175.
21	WU J. Density Functional Theory for Chemical Engineering： From Capillarity to Soft Materials［J］. Aiche Journal， 2006， 52（3）： 1 169⁃1 193.
22	LUTSKO J F. Recent Developments in Classical Density Functional Theory［J］. Advances in Chemical Physics， 2010， 144（1）：1.
23	HAATAJA M， GRÁNÁSY， LÁSZLÓ， LWEN H. Classical Density Functional Theory Methods in Soft and Hard Matter［J］. Journal of Physics Condensed Matter an Institute of Physics Journal， 2010， 22（36）：360301.
24	SCHMIDT M， BURGIS M， DWANDARU W S B， et al. Recent Developments in Classical Density Functional Theory： Internal Energy Functional and Diagrammatic Structure of Fundamental Measure Theory［J］. Condensed Matter Physics， 2012， 15：43603.
25	MARSHALL B D， CHAPMAN W G. Higher Order Classical Density Functional Theory for Branched Chains and Rings［J］. Journal of Physical Chemistry B， 2011， 115（50）：15 036⁃15 047.
26	JAIN S， DOMINIK A， CHAPMAN W G. Modified Interfacial Statistical Associating Fluid Theory： A Perturbation Density Functional Theory for Inhomogeneous Complex Fluids［J］. Journal of Chemical Physics， 2007， 127（24）：094506.
27	ZAWADA A， KACZMAREK⁃KĘDZIERA A， BARTKOWIAK W. On the Potential Application of DFT Me⁃thods in Predicting the Interaction⁃Induced Electric Properties of Molecular Complexes. Molecular H⁃Bonded Chains as a Case of Study［J］. Journal of Molecular Mode⁃ling， 2012， 18（7）：3 073⁃3 086.
28	JESSIC A， HUGHE S， ERI C， et al. A Classical Density⁃Functional Theory for Describing Water Interfaces［J］. The Journal of Chemical Physics， 2013， 138（2）：24 509⁃24 509.
29	王岗，陈静波. 聚合物发泡成型研究进展［J］. 精密成形工程， 2016，8（1）：21⁃26.
	WANG G， CHEN J B. Progress in Polymer Foaming Mold［J］. Journal of Netshape Forming Engineering， 2016，8（1）：21⁃26.
30	JACOBS L J M， KEMMERE M F， KEURENTJES J T F. Sustainable Polymer Foaming Using High Pressure Carbon Dioxide： A Review on Fundamentals， Processes and Applications［J］. Green Chemistry， 2008（10）： 731⁃738.
31	WANG X， MI J， ZHONG C. Density Functional Theory for Crystal⁃Liquid Interfaces of Lennard⁃Jones Fluid［J］. The Journal of Chemical Physics， 2013， 138（16）：164704.
32	SANTOS A. Chemical⁃Potential Route： A Hidden Percus⁃Yevick Equation of State for Hard Spheres［J］. Physical Review Letters， 2012， 109（12）：120601.
33	叶贞成，刘洪来，胡英. 非均匀流体密度泛函理论研究进展［J］. 中国科技论文在线， 2006，1（1）：1⁃12.
	YE Z C， LIU H L， HU Y. Progress on the Density Functional Theory of Nonuniform Fluid［J］. Sciencepaper Online， 2006，1（1）：1⁃12.
34	周迪. 均相与非均相气泡/液滴成核密度泛函理论研究［D］. 北京：北京化工大学， 2012.
35	ZHOU D， ZENG M， MI J G， et al. Theoretical Study of Phase Transition， Surface Tension， and Nucleation Rate Predictions for Argon［J］. Journal of Physical Chemistry B， 2011， 115（1）：57⁃63.
36	SINHA S， BHABHE A， LAKSMONO H， et al. Argon Nucleation in A Cryogenic Supersonic Nozzle［J］. Journal of Chemical Physics， 2010， 132（6）：154506.
37	DAMMER S M， LOHSE D. Gas Enrichment at Liquid⁃Wall Interfaces［J］. Physical Review Letters， 2006， 96（20）：206101.
38	LEE J， ALURU N R. Mechanistic Analysis of Gas Enrichment in Gas–Water Mixtures near Extended Surfaces［J］. The Journal of Physical Chemistry C， 2011，115（35）： 17 495–17 502.
39	BYKOV T V， ZENG X C. Heterogeneous Nucleation on Mesoscopic Wettable Particles： A Hybrid Thermodyna⁃mic/Density⁃Functional Theory［J］. The Journal of Chemical Physics， 2002， 117（4）：1 851⁃1 868.
40	WENNBERG C L， MURTOLA T， PALL S， et al. Direct⁃Space Corrections Enable Fast and Accurate Lorentz⁃Berthelot Combination Rule Lennard⁃Jones Lattice Summation［J］. Journal of Chemical Theory & Computation， 2015， 11（12）：5 737⁃5 746.
41	ZHOU D， MI J， ZHONG C. Theoretical Study of Dissolved Gas at A Hydrophobic Interface［J］. Journal of Physical Chemistry C， 2012， 116（4）：3 042–3 049.
42	JOHNSTON K P， ECKERT C A. An Analytical Carnahan⁃Starling⁃van der Waals Model for Solubility of Hydrocarbon Solids in Supercritical Fluids［J］. Aiche Journal， 2010， 27（5）：773⁃779.
43	MITCHELL L A， SCHINDLER B， DAS G， et al. 376124 Development and Application of the SAFT⁃FMT⁃DFT Approach for Adsorption Equilibrium［C］// AICHE Annual Conference. Atlanta： The Journal of Physical Chemistry C， 2014：1 457⁃1 463.
44	SANTOS A， ROHRMANN R D. Chemical⁃Potential Route for Multicomponent Fluids［J］. Physical Review E， 2013，87（5）： 052138.
45	TANG Y. On the First⁃Order Mean Spherical Approximation［J］. Journal of Chemical Physics， 2003， 118（9）：4 140⁃4 148.
46	KENTARO K A， DAISUKE Y B， HIROFUMI S A. The Development of a Revised Version of Multi⁃Center Molecular Ornstein⁃Zernike Equation［J］. Chemical Phy⁃sics Letters， 2012， 531（4）：223⁃228.
47	PENG B， YU Y X. A Density Functional Theory with A Mean⁃Field Weight Function： Applications to Surface Tension， Adsorption， and Phase Transition of a Lennard⁃Jones Fluid in A Slit⁃Like Pore［J］. Journal of Physical Chemistry B， 2008， 112（48）：15 407⁃15 416.
48	YUTA A， KAZUHIRO F. Modified Benedict⁃Webb⁃Rubin Equation of State for the Modified Lennard⁃Jones Fluid［J］. Journal of the Physical Society of Japan， 2014， 83（3）， 034601.
49	曾鸣. 受限流体与材料表面性质密度泛函理论研究［D］.北京：北京化工大学， 2011.
50	WEMHOFF A P. Extension of the Neoclassical Theory of Capillarity to Advanced Cubic Equations of State［J］. International Journal of Thermophysics， 2010， 31（2）：253⁃275.
51	RENYI R， ZHANG A， ALEXEI W， et al. Nucleation and Growth of Nanoparticles in the Atmosphere［J］. Chemical Reviews， 2012， 112（3）： 1 957⁃2 011.
52	BYKOV T V， ZENG X C. Homogeneous Nucleation at High Supersaturation and Heterogeneous Nucleation on Microscopic Wettable Particles： A Hybrid Termodyna⁃mic/Density⁃Functional Theory［J］. Journal of Chemical Physics， 2006， 125（14）：144515.
53	MARMUR A， KRASOVITSKI B. Line Tension on Curved Surfaces： Liquid Drops on Solid Micro⁃ and Nanospheres［J］. Langmuir， 2002， 18（23）：8 919⁃8 923.
54	DJIKAEV Y， WIDOM B. Geometric View of the Thermodynamics of Adsorption at A Line of Three⁃phase Contact［J］. Journal of Chemical Physics， 2004， 121（12）：5 602⁃5 610.
55	INDEKEU J O， KOGA K， WIDOM B. How Much Does the Core Structure of a Three⁃Phase Contact Line Contribute to the Line Tension near A Wetting Transition［J］. Journal of Physics Condensed Matter an Institute of Physics Journal， 2011， 23（19）：194101.
56	ZENG M， MI J， ZHONG C. Wetting Behavior of Sphe⁃rical Nanoparticles at a Vapor⁃liquid Interface： A Density Functional Theory Study［J］. Physical Chemistry Chemical Physics， 2011， 13（9）：3 932⁃3 941.
57	LUO Y W， XIN C L， SUN J， et al. Study on the Foaming Behavior of PS⁃CO₂ by Using Water or Ethanol as Co⁃Blowing Agent［J］. Advanced Materials Research， 2013， 748：112⁃116.

[1]	朱伟林;何亚东;罗祎玮;吴申康;信春玲. 挤出发泡片材褶皱分析及模拟计算[J]. 中国塑料, 2016, 30(09): 48-53 .
[2]	陈挺; 张广成;马瑞. 应力发白对AN/MAA共聚物气泡成核的影响[J]. 中国塑料, 2008, 22(10): 0-0 .

密度泛函理论在聚合物发泡领域中的应用研究进展

Research Progress in Density Functional Theory Used in Field of Polymer Foaming

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 5

参考文献 57

相关文章 2

编辑推荐

Metrics

本文评价