Diffusion Coefficient of Nanoparticles in Semidilute Polyelectrolyte Solutions Based on Mode Coupling Theory†

doi:10.7503/cjcu20150642

Abstract

Abstract:

A theoretical formalism based on mode-coupling theory(MCT) was established to study the long-time diffusion coefficient of nanoparticles in polyelectrolyte solutions. By introducing an approximate summation form for Γ_pp (k,t), D_micro can be calculated straightforwardly and it is necessary to investigate explicitly how D depends on the concentration c of the polymer solution and the nanoparticle size R. For illustration, the theoretical approach is taken to analyze the diffusion of polystyrene nanoparticles in semidilute polyacrylamide solutions which has been studied in detail experimentally. As a result, our theoretical results show very good quantitative agreements with the experimental data in many aspects, such as the strong dependence on c, the large deviation from Stokes-Einstein relation particularly for small particles. Such good agreements clearly demonstrate the validity of our MCT framework, which may serve as a good starting point to study many more complex dynamical behavior associated with polymer solutions.

Key words: Polyelectrolyte solution, Long-time diffusion coefficient, Stokes-Einstein relation, Mode coupling theory, Nanoparticles

CLC Number:

O643

TrendMD:

DONG Yunhong, CHEN Anpu, ZHAO Nanrong. Diffusion Coefficient of Nanoparticles in Semidilute Polyelectrolyte Solutions Based on Mode Coupling Theory^†[J]. Chem. J. Chinese Universities, 2015, 36(11): 2251.

Figures/Tables 4

Table 1 Basic parameters for PAM(molecule weight 8×106)

N	σ⁽⁰⁾/nm	$R g 0$ /nm	$R c 0$ /nm	c^*/(g·L¹)
775	27.8	316	775	0.1

Table 1 Basic parameters for PAM(molecule weight 8×106)

N	σ⁽⁰⁾/nm	$R g 0$ /nm	$R c 0$ /nm	c^*/(g·L¹)
775	27.8	316	775	0.1

Table 2 Macroviscosity felt by nanoparticle with radius R=1000 nm and microviscosity felt by nanoparticle with radius R=200 nm in PAM solution[23]

c/(g·L^-1)	η_macro/(Pa·s)	η_micro/(Pa·s)
0.42	0.33	0.028
1.1	2.33	0.21
2.1	9.20	0.52
4.2	33.28	1.80

Fig.1 Diffusion coefficient D for nanoparticle with radius R=200 nm in PAM solution at different concentrations

Table 3 Comparison of diffusion coefficients based on MCT and S-E relation

R/nm	$D$ /( $μ m 2 · s - 1$ )	c/(g·L^-1)
R/nm	$D$ /( $μ m 2 · s - 1$ )	0.42	1.1	2.1	4.2
200	D_MCT	1.1×10^-2	1.65×10^-3	6.10×10^-4	1.73×10^-4
	D_Exp	1.1×10^-2	1.67×10^-3	6.67×10^-4	1.67×10^-4
	D_S-E	2.8×10^-3	4.70×10^-4	1.20×10^-4	3.30×10^-5
1000	D_MCT	6.15×10^-4	1.02×10^-4	2.56×10^-5	7.02×10^-6
	D_Exp	—	—	1.80×10^-5	—
	D_S-E	5.6×10^-4	9.40×10^-5	2.36×10^-5	6.60×10^-6

Table 3 Comparison of diffusion coefficients based on MCT and S-E relation

R/nm	$D$ /( $μ m 2 · s - 1$ )	c/(g·L^-1)
R/nm	$D$ /( $μ m 2 · s - 1$ )	0.42	1.1	2.1	4.2
200	D_MCT	1.1×10^-2	1.65×10^-3	6.10×10^-4	1.73×10^-4
	D_Exp	1.1×10^-2	1.67×10^-3	6.67×10^-4	1.67×10^-4
	D_S-E	2.8×10^-3	4.70×10^-4	1.20×10^-4	3.30×10^-5
1000	D_MCT	6.15×10^-4	1.02×10^-4	2.56×10^-5	7.02×10^-6
	D_Exp	—	—	1.80×10^-5	—
	D_S-E	5.6×10^-4	9.40×10^-5	2.36×10^-5	6.60×10^-6

References 24

[1]	Jeon I. Y., Baek J. B., Materials, 2010, 3, 3654—3674
[2]	Szymanski J., Weiss M., Phys. Rev. Lett., 2009, 103(3), 038102
[3]	Saxton M. J., Biophys. J., 2007, 92(4), 1178—1191
[4]	Ponnapati R., Karazincir O., Dao E., Ng R., Mohanty K. K., Krishnamoorti R., Ind. Eng. Chem. Res., 2011, 50(23), 13030—13036
[5]	Metin C. O., Bonnecaze R. T., Nguyen Q. P., SPE Res. Eval. Eng., 2013, 16(3), 327—332
[6]	Cu Y., Saltzman W. M., Nat. Mater, 2009, 8(1), 11—13
[7]	Holyst R., Bielejewska A., Szymanski J., Wilk A., Patkowski A., Gapinski J., Zywocinski A., Kalwarczyk T., Kalwarczyk E., Tabaka M., Ziebacz N., Wieczorek S. A., Phys. Chem. Chem. Phys., 2009, 11, 9025—9032
[8]	Koenderink G., Sacanna H. S., Aarts D. G., Philipse A. P., Phys. Rev. E, 2004, 69(2), 021804
[9]	Michelman-Ribeiro A., Horkay F., Nossal R., Boukari H., Biomacromolecules, 2007, 8(5), 1595—1600
[10]	Kohli I., Alam S., Patel B., Mukhopadhyay A., Appl. Phys. Lett., 2013, 102, 203705
[11]	Jee A. Y., Curtis-Fisk J. L., Granick S., Macromolecules, 2014, 47(16), 5793—5797
[12]	Cheng Y., Prudhomme R. K., Thomas J. L., Macromolecules, 2002, 35(21), 8111—8121
[13]	Kalwarczyk T., Ziebacz N., Bielejewska A., ZaboklickaE., Koynov K., Szymański J., Wilk A., Patkowski A., Gapiński J., Butt H. J., Hozyst R., Nano Lett., 2011, 11(5), 2157—2163
[14]	Ziebacz N., Wieczorek S. A., Kalwarczyk T., Fiakowski M., Holyst R., Soft Matter, 2011, 7, 7181—7186
[15]	Kohli I., Mukhopadhyay A., Macromolecules, 2012, 45(15), 6143—6149
[16]	Dong Y. H., Feng X. Q., Zhao N. R., Hou Z. H., J. Chem. Phys., 2015, 143, 024903
[17]	Yamamoto U., Schweizer K. S., J. Chem. Phys., 2011, 135, 224902
[18]	Kirkpatrick T. R., Wolynes P. G., Phys. Rev. A, 1987, 35, 3072
[19]	Schweizer K. S., Saltzman E. J., J. Chem. Phys., 2003, 119, 1181
[20]	Chatterjee A. P., Schweizer K. S., J. Chem. Phys., 1998, 109, 10464
[21]	Colby R. H., Rheologic Acta, 2010, 49, 425—442
[22]	Dobrynin A. V., Colby R. H., Rubinstein M., Macromolecules, 1996, 28, 1859—1871
[23]	Khorasani F. B., Skutvik R. P., Krishnamoorti R., Conrad J. C., Macromolecules, 2014, 47(15), 5328—5333
[24]	Pronk S., Lindahl1 E., Kasson P. M., Nature Communications, 2014, 5, 3034