# Correction: Cooperative strings in glassy nanoparticles

M. Arutkin, E. Raphael, J. A. Forrest, Thomas Salez

► To cite this version:

M. Arutkin, E. Raphael, J. A. Forrest, Thomas Salez. Correction: Cooperative strings in glassy nanoparticles. Soft Matter, 2017, 13 (18), pp.3457-3458. 10.1039/c7sm90062g. hal-01577372

HAL Id: hal-01577372

https://hal.science/hal-01577372v1

Submitted on 6 Jan 2025

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Cite this: *Soft Matter*, 2017, **13**, 3457

DOI: 10.1039/c7sm90062g

rsc.li/soft-matter-journal

# Correction: Cooperative strings in glassy nanoparticles

Maxence Arutkin,ª Elie Raphaël,ª James A. Forrestabc and Thomas Salez*abcd

Correction for 'Cooperative strings in glassy nanoparticles' by Maxence Arutkin et al., *Soft Matter*, 2017, **13**, 141–146.

The authors would like to correct errors in the legends of the published Fig. 2 and Fig. 3. The correct versions of Fig. 2 and Fig. 3 are shown below.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Predicted surface mobile-layer thicknesses $h_m$ of spherical polystyrene nanoparticles as a function of temperature $T$, according to eqn (16) and (17), for different sphere radii as indicated. We used the bulk glass-transition temperature $T_g^{bulk} = 371$ K,⁶⁹ and the onset temperature $T_c = 463$ K.⁵⁷,⁷⁰ We fixed the molecular size $\lambda_v = 3.7$ nm, and the Vogel temperature $T_v = 322$ K, to the values previously obtained for the thin-film geometry.³¹ Note that we replaced the $+\infty$ bound by 25 in eqn (16), and checked that it provides sufficiently precise numerical estimates. For comparison, the dashed line indicates the flat-interface result used for the thin-film geometry.³¹</figcaption></figure>

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<footnote>ª Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI ParisTech, PSL Research University, 75005 Paris, France. E-mail: thomas.salez@espci.fr</footnote>

<footnote>ᵇ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada</footnote>

<footnote>ᶜ Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada</footnote>

<footnote>ᵈ Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Hokkaido 060-0808, Japan</footnote>
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<figure><img src="image_6.png" /><figcaption>Fig. 3 Comparison between experimental data (symbols) for the reduced glass-transition temperature $T_g(R)$ of spherical polystyrene nano-particles$^{35,37,40}$ of radius $R$, and the theory (line) given by eqn (19) – that invokes eqn (16) through $F(v) = f(2^{-1/3}v)$. The fixed parameters are the bulk glass-transition temperature $T_g^{bulk} = 371$ K,$^{69}$ and the onset temperature $T_c = 463$ K.$^{57,70}$ The two adjustable parameters are the molecular size $\lambda_v = 3.7$ nm, and the Vogel temperature $T_v = 322$ K, that were fixed to the values previously obtained for the thin-film geometry.$^{31}$ Note that we replaced the $+\infty$ bound by 25 in eqn (16), and checked that it provides sufficiently precise numerical estimates.</figcaption></figure>

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.