The Dynamics of Polymer Solutions at Finite Concentrations

J. Ravi Prakash

Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia

Many important phenomena in both industrial and biological contexts involve polymer solutions at finite concentrations–in the so-called semidilute regime. However, the behaviour of polymer solutions is presently well understood only in the dilute and concentrated solution limits. I review the investigations of the dynamics of semidilute solutions in our group, through experiments and computer simulations, over the past few years. The experiments probe the linear and non-linear viscoelastic behaviour of solutions of polystyrene and DNA in a wide range of molecular weights, temperatures and concentrations. The dependence of the zero-shear rate viscosity on concentration is observed to display universal behaviour that can be understood within the framework of the blob theory for semidilute polymer solutions [1, 2]. Further, the shear rate dependence of viscosity at various temperatures and concentrations can be collapsed onto master curves when understood in terms of a relaxation time that depends on concentration [3]. Computational prediction of the static and dynamic properties of semidilute polymer solutions requires the simulation of a large system of polymer chains interacting with each other through excluded volume and hydrodynamic interactions. We describe the development of a Brownian dynamics simulation algorithm that uses a fast implementation of the Ewald summation method to predict the behaviour of flowing polymer solutions at finite concentrations [4]. In particular, we use the algorithm to examine the response of single chains in a semidilute solution when subjected to a step-strain deformation followed by cessation of flow [5,6]. A systematic comparison of simulation predictions is carried out with the experimental observations of Schroeder’s group, who have recently used single molecule techniques, in the context of semidilute solutions flowing in a cross-slot cell, to investigate the stretch-relaxation of individual λ-phage DNA chains.

Figure. 1. Data collapse for three DNA samples across molecular weights, concentrations, and solvent quality, when 𝜂"is scaled by 𝜂$ 𝑀 and 𝛾 by the relaxation time of a correlation blob [3].

Figure. 2. Top two panels highlight the stretch and relaxation of DNA in planar extensional flows and simulation snapshots. Bottom panel is a comparison of experiment and simulation [5,6].

References

1. A. Jain, B. Duenweg, and J. R. Prakash, Phys. Rev. Lett., 109, 088302 (2012). 2. S. Pan, D. A. Nguyen, T. Sridhar, P. Sunthar, J. R. Prakash, J. Rheol., 58, 339-368 (2014). 3. S. Pan, D. A. Nguyen, B. Duenweg, P. Sunthar, T. Sridhar, J. R. Prakash, J. Rheol., 62, 845-867 (2018). 4. A. Jain, C. Sasmal, R. Hartkamp, B.D. Todd, J. R. Prakash, Chem. Eng. Sci., 121, 245–257 (2015). 5. K. Hsiao, C. Samsal, J. R. Prakash, C. M. Schroeder, J. Rheol., 61, 151–167 (2017). 6. C. Sasmal, K. Hsiao, C. M. Schroeder, J. R. Prakash, J. Rheol., 61, 169–186 (2017).

January/February 2017

JOURNAL OFRHEOLOGY®

Volume 61 • Issue 1 • Pages 1-186

AVAILABLE ONLINEhttp://scitation.aip.org/joro/

ISSN 0148-6055JORHD2

Published by The Society of Rheologythrough AIP Publishing LLC

AVAILABLE ONLINEhttp://scitation.aip.org/joro/

ISSN 0148-6055JORHD2

Published by The Society of Rheologythrough AIP Publishing LLC

10-3 10-2 10-1 100 101 102 103

100

101

25 kbp, z = 1.78: c = 0.441 mg/ml (c/c* = 8.65) c = 0.441 mg/ml (c/c* = 7.14) c = 0.441 mg/ml (c/c* = 6.18)48.5 kbp, z = 1.73: c = 0.05 mg/ml (c/c* = 1.22) c = 0.08 mg/ml (c/c* = 1.95) c = 0.128 mg/ml (c/c* = 3.05)165.6 kbp, z = 1.65: c = 0.038 mg/ml (c/c* = 1.92) c = 0.059 mg/ml (c/c* = 2.98)

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25 kbp

165.6 kbp-0.33

-0.4

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7.3 Results and Discussion 156

10-3 10-2 10-1 100 101 102 10310-1

100

101

102

-0.39

λ-DNA, z = 0.54, c/c*: 1.48 2.31 3.7 z = 0.89, c/c*: 1.09 1.74 2.72 4.35 z = 1.32, c/c*: 1.22 1.95 3.05 z = 1.73, c/c*: 1.35 2.16 3.38

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T4 DNA, z = 0.51, c/c*: 1.27 1.97 3.13 z = 1, c/c*: 1.58 2.46 3.92 z = 1.65, c/c*: 1.92 2.98 z = 2.43, c/c*: 2.11 3.28

25 kbp, z = 0.33, c/c*: 5.13 4.23 3.66 z = 0.6, c/c*: 6.04 4.99 4.32 z = 1.37, c/c*: 7.88 6.5 5.63 z = 1.78, c/c*: 8.65 7.14 6.18

T4, 25 kbp and !-DNA

Figure 7.15: Concentration, temperature and molecular weight collapse. Widerange of c/c� (1.09 to 8.65), temperatures (15 to 44.6�C) or z (0.51 to 2.43) andmolecular weights (25–165.6 kbp) can be collapsed onto a single master curveplotting the data this way. Terminal slope of the entire data range was close to-0.4. The � values used are the �eff values as explained in the text.

10-3 10-2 10-1 100100

101

102

1>>!"# !

-0.47 ± 0.01

z = 0.6: c/c* = 6.04 c/c* = 4.99 c/c* = 4.32

z = 1.37: c/c* = 7.88 c/c* = 5 c/c* = 5.63

z = 1.78: c/c* = 8.65 c/c* = 7.14 c/c* = 6.18

z = 0.05: c/c* = 3.9 c/c* = 3.22 c/c* = 2.79

z = 0.33: c/c* = 5.13 c/c* = 4.23 c/c* = 3.66

25 kbp DNA

z = 0.05, 0.33, 0.6, 1.37 and 1.78

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