Combining Diffusion NMR and Small-Angle Neutron Scattering Enables Precise Measurements of Polymer Chain Compression in a Crowded Environment

Swomitra Palit, Lilin He, William A. Hamilton, Arun Yethiraj, and Anand Yethiraj

Phys. Rev. Lett. 118, 097801 – Published 3 March 2017

Abstract

The effect of particles on the behavior of polymers in solution is important in a number of important phenomena such as the effect of “crowding” proteins in cells, colloid-polymer mixtures, and nanoparticle “fillers” in polymer solutions and melts. In this Letter, we study the effect of spherical inert nanoparticles (which we refer to as “crowders”) on the diffusion coefficient and radius of gyration of polymers in solution using pulsed-field-gradient NMR and small-angle neutron scattering (SANS), respectively. The diffusion coefficients exhibit a plateau below a characteristic polymer concentration, which we identify as the overlap threshold concentration $c^{⋆}$ . Above $c^{⋆}$ , in a crossover region between the dilute and semidilute regimes, the (long-time) self-diffusion coefficients are found, universally, to decrease exponentially with polymer concentration at all crowder packing fractions, consistent with a structural basis for the long-time dynamics. The radius of gyration obtained from SANS in the crossover regime changes linearly with an increase in polymer concentration, and must be extrapolated to $c^{⋆}$ in order to obtain the radius of gyration of an individual polymer chain. When the polymer radius of gyration and crowder size are comparable, the polymer size is very weakly affected by the presence of crowders, consistent with recent computer simulations. There is significant chain compression, however, when the crowder size is much smaller than the polymer radius gyration.

Received 20 September 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.097801

Physics Subject Headings (PhySH)

Diffusion Excluded volume interaction Polymer conformation changes

Macromolecules

Nuclear magnetic resonance Small angle neutron scattering

Polymers & Soft Matter

Authors & Affiliations

Swomitra Palit¹, Lilin He², William A. Hamilton³, Arun Yethiraj⁴, and Anand Yethiraj^1,*

¹Department of Physics and Physical Oceanography, Memorial University, St. John’s, Newfoundland A1B3X7, Canada
²Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Instrument and Source Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA

^*ayethiraj@mun.ca

Comments & Replies

Comment on “Combining Diffusion NMR and Small-Angle Neutron Scattering Enables Precise Measurements of Polymer Chain Compression in a Crowded Environment”

C. Le Coeur, J. Teixeira, and S. Longeville

Phys. Rev. Lett. 123, 239801 (2019)

Palit et al. Reply:

Swomitra Palit, Lilin He, William A. Hamilton, Arun Yethiraj, and Anand Yethiraj

Phys. Rev. Lett. 123, 239802 (2019)

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Vol. 118, Iss. 9 — 3 March 2017

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Figure 1
The osmotic pressure of pure PEG in water (no crowder) is well described by a phenomenological scaling form (solid black line, from Cohen et al. [25]). The solution is dilute when $c^{scale} \equiv c_{p} / c^{#} \leq 0.2$ , and in the semidilute entangled regime when $c^{scale} \geq 6$ (dashed red line): the crossover regime (green hashed region) is in between ( $0.2 < c^{scale} < 6$ ). The expected scaling of the self-diffusion coefficient in the dilute (blue hashed) and semidilute (red hashed) regimes [30] is $D \sim c_{p}^{0}$ and $D \sim c_{p}^{- 7 / 4}$ .
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Figure 2
Self-diffusion: (a) Diffusion coefficient of PEG ( $M_{w} = 20 000$ ) polymer in water as a function of polymer concentration $c_{p}$ , in the absence of the crowder, Ficoll70, as well as for several Ficoll70 volume fractions $Φ_{F}$ ( $λ = R_{g} / R_{c} = 1.09$ ). A good fit to exponential behavior is possible, in all cases, above a characteristic PEG concentration, $c^{⋆}$ , with an extrapolated value $D^{⋆}$ . Below this PEG concentration, a plateau is observed at $D (0, Φ_{F})$ . (b) A log-log plot of $D_{PEG}$ vs $c_{p}$ shows the plateau, and also that a power law cannot fit the data in the crossover regime. (c) Dependence of characteristic PEG concentration $c^{⋆}$ as a function of $Φ_{F}$ for three polymer molecular weights ( $M_{w} = 20 000$ , $M_{w} = 42 800$ , and $M_{w} = 132 000$ ), corresponding to $λ = 1.09$ , 1.78, and 2.85. The solid blue curves may be treated as a guide to the eye. (d) From the phenomenological exponential decay in (a), a second characteristic concentration $c_{2}$ is obtained (for each $Φ_{F}$ ).
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Figure 3
Universal behavior in the dynamics: Using the values $D^{⋆}$ , $c^{⋆}$ , and $c_{2}$ (all functions of only $Φ_{F}$ ) from each fit, all the diffusion results (as a function of $c_{p}$ and $Φ_{F}$ ) are replotted in dimensionless form, $Y = (c_{2} / c^{⋆}) \ln [D (c_{p}, Φ_{F}) / D^{⋆}]$ as a function of a scaled polymer concentration $X = c_{p} / c^{⋆}$ . For all three polymers, there is good collapse onto one master plot that shows a sharp transition at $X = 1$ (see inset) from a polymer-dilute plateau to an exponential concentration dependence of the diffusion coefficient.
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Figure 4
Diffusion vs SANS: A comparison of $R_{g}^{2}$ from diffusion (blue, $c_{p} < 0.005 g / {cm}^{3}$ ) and SANS ( $c_{p} > 0.005 g / {cm}^{3}$ ) for PEG-water solution ( $Φ_{F} = 0$ ) confirms that the overlap concentration deduced from diffusion ( $c_{Diff}^{⋆} = 0.005 g / {cm}^{3}$ ) is also meaningful as the thermodynamic overlap concentration $c^{⋆}$ .
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Figure 5
SANS: (a) $R_{g} (c_{p}, Φ_{F})$ vs polymer concentration $c_{p}$ for $λ = 1.09$ . $R_{g}$ is fit to Eq. (2) assuming that the $c^{⋆}$ is the same as for the diffusion experiment. The blue asterisks reflect the value that would be obtained by a naive extrapolation of $R_{g}$ from the crossover regime. (b) The fit shows that $R_{g} (0, Φ_{F})$ in the “polymer-dilute” limit exhibits at most a weak dependence on Ficoll70 volume fraction $Φ_{F}$ . (c) $R_{g}$ dependence on packing fraction $Φ_{F}$ for three polymer molecular weights, corresponding to $λ = 1.09$ , 1.78, and 2.85 respectively. Results are compared with simulations from Kang et al. [12].
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