Distribution of a polymer chain between two interconnected spherical cavities

doi:10.1088/1674-1056/abaedc

Abstract

The equilibrium distribution of a polymer chain between two interconnected spherical cavities (a small one with radius R_s and a large one with radius R_l) is studied by using Monte Carlo simulation. A conformational transition from a double-cavity-occupation (DCO) state to a single-cavity-occupation (SCO) state is observed. The dependence of the critical radius of the small cavity (R_sC) where the transition occurs on R_l and the polymer length N can be described by $ {R}_{{\rm{sC}}}\propto {N}^{1/3}{R}_{{\rm{l}}}^{1-1/3\nu } $ with ν being the Flory exponent, and meanwhile the equilibrium number (m_s) of monomers in the small cavity for the DCO phase can be expressed as m_s = N/((R_l/R_s)³ + 1), which can be quantitatively understood by using the blob picture. Moreover, in the SCO phase, the polymer is found to prefer staying in the large cavity.

Keywords: polymer phase transition free energy blob theory

Received: 06 July 2020
Revised: 29 July 2020
Accepted manuscript online: 13 August 2020

PACS:	82.35.Jk	(Copolymers, phase transitions, structure)
	82.35.Lr	(Physical properties of polymers)
	82.20.Wt	(Computational modeling; simulation)

Corresponding Authors: ^†Corresponding author. E-mail: chaowang0606@126.com ^‡Corresponding author. E-mail: luomengbo@zju.edu.cn

About author:

†Corresponding author. E-mail: chaowang0606@126.com

‡Corresponding author. E-mail: luomengbo@zju.edu.cn

* Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY20A040004) and the National Natural Science Foundation of China (Grant Nos. 11604232, 11674277, 11704210, and 11974305).

Cite this article:

Chao Wang(王超)†, Ying-Cai Chen(陈英才), Shuang Zhang(张爽), Hang-Kai Qi(齐航凯), and Meng-Bo Luo(罗孟波)‡ Distribution of a polymer chain between two interconnected spherical cavities 2020 Chin. Phys. B 29 108201

Fig. 1.

A 2D sketch of the simulation model. Two spherical cavities, a small one with radius R_s and a large one with radius R_l, are connected by a small hole with diameter D_h. The polymer is confined in the two cavities.

Fig. 2.

The SCO probability P_SCO as a function of R for different N. The radius where P_SCO = 0.5 is defined as the critical radius R_C. The inset shows the phase diagram for the symmetric twin-cavity system. The red line shows the radius of gyration (R_g0) of polymer in free space as a function of N.

Fig. 3.

The SCO probability P_SCO as a function of the radius of the small cavity R_s for different R_l (< R_C), where N = 60. The radius where P_SCO = 0.5 is defined as the critical radius R_sC.

Fig. 4.

Phase diagram for the asymmetric system, where N = 60. The inset shows the dependence of R_sC on $ {R}_{{\rm{l}}}^{9/4}{N}^{-3/4} $ for N = 40, 60, 80, 100, and 120. The solid black line is guide for eyes.

Fig. 5.

The relative probabilities of the whole polymer in the small cavity (P_s/P_SCO) and in the large cavity (P_l/P_SCO) in the SCO phase as functions of the radius of the small cavity R_s for different R_l, where N = 60.

Fig. 6.

The equilibrium number (m_s) of monomers in the small cavity as a function of R_s for different R_l (< R_C), where N = 60. The inset shows m_s/N as a function of (R_l/R_s)³ for different R_l and N. The solid red line is given by Eq. (12).

[1]	Simon S M, Blobe G 1991 Cell 65 371 DOI: 10.1016/0092-8674(91)90455-8
[2]	Lingappa V R, Chaidez J, Yost C S, Hedgpeth J 1984 Proc. Natl. Acad. Sci. USA 81 456 DOI: 10.1073/pnas.81.2.456
[3]	Gabashvili I S, Gregory S T, Valle M, Grassucci R, Worbs M, Wahl M C, Dahlberg A E, Frank J 2001 Mol. Cell 8 181 DOI: 10.1016/S1097-2765(01)00293-3
[4]	Laemmli U K, Favre M 1973 J. Mol. Biol. 80 575 DOI: 10.1016/0022-2836(73)90198-8
[5]	Levy S L, Craighead H G 2010 Chem. Soc. Rev. 39 1133 DOI: 10.1039/b820266b
[6]	Reisner W, Pedersen J N, Austin R H 2012 Rep. Prog. Phys. 75 106601 DOI: 10.1088/0034-4885/75/10/106601
[7]	Lacroix J, Pelofy S, Blatche C, Pillaire M J, Huet S, Chapuis C, Hoffmann J S, Bancaud A 2016 Small 12 5963 DOI: 10.1002/smll.201503795
[8]	Dorfman K D, King S B, Olson D W, Thomas J D P, Tree D R 2013 Chem. Rev. 113 2584 DOI: 10.1021/cr3002142
[9]	Sriram K K, Yeh J W, Lin Y L, Chang Y R, Chou C F 2014 Nucleic Acids Res. 42 e85 DOI: 10.1093/nar/gku254
[10]	Glasgow J, Tullman-Ercek D 2014 Appl. Microbiol. Biotechnol. 98 5847 DOI: 10.1007/s00253-014-5787-3
[11]	Chen J X, Chen Y G, Kapral R 2018 Adv. Sci. 5 1800028 DOI: 10.1002/advs.201800028
[12]	Cui R F, Chen Q H, Chen J X 2020 Nanoscale 12 12275 DOI: 10.1039/D0NR01211D
[13]	Kasianowicz J J, Brandin E, Branton D, Deamer D W 1996 Proc. Natl. Acad. Sci. USA 93 13770 DOI: 10.1073/pnas.93.24.13770
[14]	Deamer D, Akeson M, Branton D 2016 Nat. Biotechnol. 34 518 DOI: 10.1038/nbt.3423
[15]	Yuan Z S, Liu Y M, Dai M, Yi X, Wang C Y 2020 Nanoscale Res. Lett. 15 80 DOI: 10.1186/s11671-020-03308-x
[16]	Steinbock L J, Radenovic A 2015 Nanotechnology 26 074003 DOI: 10.1088/0957-4484/26/7/074003
[17]	Tyson J R, ONeil N J, Jain M, Olsen H E, Hieter P, Snutch T P 2018 Genome Res. 28 266 DOI: 10.1101/gr.221184.117
[18]	He Y, Tsutsui M, Fan C, Taniguchi M, Kawai T 2011 ACS Nano 5 5509 DOI: 10.1021/nn201883b
[19]	Liu X, Zhang Y, Nagel R, Reisner W, Dunbar W B 2019 Small 15 1901704 DOI: 10.1002/smll.v15.30
[20]	Mulero R, Prabhu A S, Freedman K J, Kim M J 2010 J. Assoc. Lab. Autom. 15 243 DOI: 10.1016/j.jala.2010.01.009
[21]	Smith D E, Tans S J, Smith S B, Grimes S, Anderson D L, Bustamante C 2001 Nature 413 748 DOI: 10.1038/35099581
[22]	Meller A, Nivon L, Branton D 2001 Phys. Rev. Lett. 86 3435 DOI: 10.1103/PhysRevLett.86.3435
[23]	Sakaue T, Raphaël E, de Gennes P G, Brochard-Wyart F 2005 Europhys. Lett. 72 83 DOI: 10.1209/epl/i2005-10190-3
[24]	Markesteijn A P, Usta O B, Ali I, Balazs A C, Yeomans J M 2009 Soft Matter 5 4575 DOI: 10.1039/b909208k
[25]	Li X, Pivkin I V, Liang H 2013 Polymer 54 4309 DOI: 10.1016/j.polymer.2013.06.022
[26]	Klushin L I, Skvortsov A M, Hsu H P, Binder K 2008 Macromolecules 41 5890 DOI: 10.1021/ma800619n
[27]	Reisner W, Pedersen J N, Austin R H 2012 Rep. Prog. Phys. 75 106601 DOI: 10.1088/0034-4885/75/10/106601
[28]	Cifra P, Benkova Z, Bleha T 2009 J. Phys. Chem. B 113 1843 DOI: 10.1021/jp806126r
[29]	Cifra P 2009 J. Chem. Phys. 131 224903 DOI: 10.1063/1.3271830
[30]	Fu Y, Wu F, Huang J H, Chen Y C, Luo M B 2019 Chin. J. Polym. Sci. 37 1290 DOI: 10.1007/s10118-019-2291-3
[31]	Benkova Z, Cifra P 2012 Macromolecules 45 2597 DOI: 10.1021/ma202730c
[32]	Benkova Z, Cifra P 2013 Biochem. Soc. T. 41 625 DOI: 10.1042/BST20120279
[33]	Manneschi C, Angeli E, Ala-Nissila T, Repetto L, Firpo G, Valbusa U 2013 Macromolecules 46 4198 DOI: 10.1021/ma4000545
[34]	Chen J Z Y 2007 Phys. Rev. Lett. 98 088302 DOI: 10.1103/PhysRevLett.98.088302
[35]	Wang C, Wu F, Zhao B, Chen Y C, Luo M B 2020 Macromolecules 53 1694 DOI: 10.1021/acs.macromol.9b02645
[36]	Muthukumar M 2001 Phys. Rev. Lett. 86 3188 DOI: 10.1103/PhysRevLett.86.3188
[37]	Turner S W P, Cabodi M, Craighead H G 2002 Phys. Rev. Lett. 88 128103 DOI: 10.1103/PhysRevLett.88.128103
[38]	Matsuyama A, Yano M, Matsuda A 2009 J. Chem. Phys. 131 105104 DOI: 10.1063/1.3225140
[39]	Shojaei H R, Muthukumar M 2017 J. Chem. Phys. 146 244901 DOI: 10.1063/1.4986961
[40]	Yang Z Y, Zhang D, Zhang L X, Chen H P, Ateeq-ur-Rehman, Liang H J 2011 Soft Matter 7 6836 DOI: 10.1039/c1sm05523b
[41]	Zhou X L, Guo F C, Li K, He L L, Zhang L X 2019 Polymers 11 1992 DOI: 10.3390/polym11121992
[42]	Chen E, Fan Y, Zhao G, Mao Z, Zhou H, Liu Y 2020 Chin. Phys. B 29 018701 DOI: 10.1088/1674-1056/ab5941
[43]	Benkova Z, Rispanova L, Cifra P 2020 Polymers 12 1064 DOI: 10.3390/polym12051064
[44]	Rispanova L, Benkova Z, Cifra P 2018 Polymers 10 1301 DOI: 10.3390/polym10121301
[45]	Benkova Z, Rispanova L, Cifra P 2017 J. Chem. Phys. 147 134907 DOI: 10.1063/1.4991649
[46]	Benkova Z, Rispanova L, Cifra P 2017 Polymers 9 313 DOI: 10.3390/polym9080313
[47]	Kong C Y, Muthukumar M 2004 J. Chem. Phys. 120 3460 DOI: 10.1063/1.1642588
[48]	Nykypanchuk D, Strey H H, Hoagland D A 2005 Macromolecules 38 145 DOI: 10.1021/ma048062n
[49]	Cifra P 2005 Macromolecules 38 3984 DOI: 10.1021/ma050147g
[50]	Cifra P, Linse P, Nies E 2005 J. Phys. Chem. B 112 8923 DOI: 10.1021/jp801782p
[51]	Milchev A, Klushin L, Skvortsov A, Binder K 2010 Macromolecules 43 6877 DOI: 10.1021/ma1003826
[52]	Sakaue T, Raphaël E 2006 Macromolecules 39 2621 DOI: 10.1021/ma0514424

[1]	Tailoring of thermal expansion and phase transition temperature of ZrW₂O₈ with phosphorus and enhancement of negative thermal expansion of ZrW_1.5P_0.5O_7.75 Chenjun Zhang(张晨骏), Xiaoke He(何小可), Zhiyu Min(闵志宇), and Baozhong Li(李保忠). Chin. Phys. B, 2023, 32(4): 048201.
[2]	Topological phase transition in network spreading Fuzhong Nian(年福忠) and Xia Zhang(张霞). Chin. Phys. B, 2023, 32(3): 038901.
[3]	Coexisting lattice contractions and expansions with decreasing thicknesses of Cu (100) nano-films Simin An(安思敏), Xingyu Gao(高兴誉), Xian Zhang(张弦), Xin Chen(陈欣), Jiawei Xian(咸家伟), Yu Liu(刘瑜), Bo Sun(孙博), Haifeng Liu(刘海风), and Haifeng Song(宋海峰). Chin. Phys. B, 2023, 32(3): 036804.
[4]	Liquid-liquid phase transition in confined liquid titanium Di Zhang(张迪), Yunrui Duan(段云瑞), Peiru Zheng(郑培儒), Yingjie Ma(马英杰), Junping Qian(钱俊平), Zhichao Li(李志超), Jian Huang(黄建), Yanyan Jiang(蒋妍彦), and Hui Li(李辉). Chin. Phys. B, 2023, 32(2): 026801.
[5]	Magnetocaloric properties and Griffiths phase of ferrimagnetic cobaltite CaBaCo₄O₇ Tina Raoufi, Jincheng He(何金城), Binbin Wang(王彬彬), Enke Liu(刘恩克), and Young Sun(孙阳). Chin. Phys. B, 2023, 32(1): 017504.
[6]	Prediction of flexoelectricity in BaTiO₃ using molecular dynamics simulations Long Zhou(周龙), Xu-Long Zhang(张旭龙), Yu-Ying Cao(曹玉莹), Fu Zheng(郑富), Hua Gao(高华), Hong-Fei Liu(刘红飞), and Zhi Ma(马治). Chin. Phys. B, 2023, 32(1): 017701.
[7]	Configurational entropy-induced phase transition in spinel LiMn₂O₄ Wei Hu(胡伟), Wen-Wei Luo(罗文崴), Mu-Sheng Wu(吴木生), Bo Xu(徐波), and Chu-Ying Ouyang(欧阳楚英). Chin. Phys. B, 2022, 31(9): 098202.
[8]	Effect of f-c hybridization on the $\gamma\to \alpha$ phase transition of cerium studied by lanthanum doping Yong-Huan Wang(王永欢), Yun Zhang(张云), Yu Liu(刘瑜), Xiao Tan(谈笑), Ce Ma(马策), Yue-Chao Wang(王越超), Qiang Zhang(张强), Deng-Peng Yuan(袁登鹏), Dan Jian(简单), Jian Wu(吴健), Chao Lai(赖超), Xi-Yang Wang(王西洋), Xue-Bing Luo(罗学兵), Qiu-Yun Chen(陈秋云), Wei Feng(冯卫), Qin Liu(刘琴), Qun-Qing Hao(郝群庆), Yi Liu(刘毅), Shi-Yong Tan(谭世勇), Xie-Gang Zhu(朱燮刚), Hai-Feng Song(宋海峰), and Xin-Chun Lai(赖新春). Chin. Phys. B, 2022, 31(8): 087102.
[9]	Characterization of topological phase of superlattices in superconducting circuits Jianfei Chen(陈健菲), Chaohua Wu(吴超华), Jingtao Fan(樊景涛), and Gang Chen(陈刚). Chin. Phys. B, 2022, 31(8): 088501.
[10]	Hard-core Hall tube in superconducting circuits Xin Guan(关欣), Gang Chen(陈刚), Jing Pan(潘婧), and Zhi-Guo Gui(桂志国). Chin. Phys. B, 2022, 31(8): 080302.
[11]	Exchange-coupling-induced fourfold magnetic anisotropy in CoFeB/FeRh bilayer grown on SrTiO₃(001) Qingrong Shao(邵倾蓉), Jing Meng(孟婧), Xiaoyan Zhu(朱晓艳), Yali Xie(谢亚丽), Wenjuan Cheng(程文娟), Dongmei Jiang(蒋冬梅), Yang Xu(徐杨), Tian Shang(商恬), and Qingfeng Zhan(詹清峰). Chin. Phys. B, 2022, 31(8): 087503.
[12]	Structural evolution and bandgap modulation of layered β-GeSe₂ single crystal under high pressure Hengli Xie(谢恒立), Jiaxiang Wang(王家祥), Lingrui Wang(王玲瑞), Yong Yan(闫勇), Juan Guo(郭娟), Qilong Gao(高其龙), Mingju Chao(晁明举), Erjun Liang(梁二军), and Xiao Ren(任霄). Chin. Phys. B, 2022, 31(7): 076101.
[13]	Topological phase transition in cavity optomechanical system with periodical modulation Zhi-Xu Zhang(张志旭), Lu Qi(祁鲁), Wen-Xue Cui(崔文学), Shou Zhang(张寿), and Hong-Fu Wang(王洪福). Chin. Phys. B, 2022, 31(7): 070301.
[14]	Structural evolution and molecular dissociation of H₂S under high pressures Wen-Ji Shen(沈文吉), Tian-Xiao Liang(梁天笑), Zhao Liu(刘召), Xin Wang(王鑫), De-Fang Duan(段德芳), Hong-Yu Yu(于洪雨), and Tian Cui(崔田). Chin. Phys. B, 2022, 31(7): 076102.
[15]	Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Chin. Phys. B, 2022, 31(7): 070502.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Distribution of a polymer chain between two interconnected spherical cavities

Cite this article:

Online attention