Open Access Article

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Guilong
Wang
*^{ab},
Chongda
Wang
^{b},
Jinchuan
Zhao
^{bc},
Guizhen
Wang
^{d},
Chul B.
Park
*^{b},
Guoqun
Zhao
*^{a},
Wouter
Van De Walle
^{e} and
Hans
Janssen
^{e}
^{a}Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, School of Materials Science and Engineering, Shandong University, Jinan, Shandong 250061, China
^{b}Microcellular Plastics Manufacturing Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5T3G8, Canada
^{c}Centre for Precision Engineering, School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
^{d}Key Laboratory of Chinese Education Ministry for Tropical Biological Resources, Hainan University, Haikou, Hainan 570228, China
^{e}KU Leuven, Department of Civil Engineering, Building Physics Section, Kasteelpark Arenberg 40 – Box 2447, BE-3001 Heverlee, Belgium

Received
3rd September 2018
, Accepted 3rd September 2018

First published on 13th September 2018

Correction for ‘Modelling of thermal transport through a nanocellular polymer foam: toward the generation of a new superinsulating material’ by Guilong Wang et al., Nanoscale, 2017, 9, 5996–6009.

The authors have noticed that the finite discretization for dθ

The authors have recalculated the data presented in the published paper by using a much finer discretization with 10000 intervals. With a much finer discretization, increased significantly at high void fractions compared to the original case. Subsequently, both λ_{rad} and λ_{eff} decreased obviously at high void fractions. Thus, the originally published Fig. 8 should be replaced by the updated version of Fig. 8 provided below. It should be noted that λ_{con} was not affected by discretization. Thus, the data in Fig. 8b was not changed.

Regarding the data presented in the originally published Fig. 9, λ_{eff}, λ_{rad}, and changed obviously at small cell sizes when using a much finer discretization in the calculations. Thus, this figure should be replaced by the updated version of Fig. 9 provided below. In the updated version of Fig. 9c, it should be noted that the behaviour of the radiative thermal conductivity as a function of the cell size changes significantly in comparison with the data presented in Fig. 9c of the published paper. In the updated version of Fig. 9c, the radiative thermal conductivity reduced first to a certain minimum level, and then increased gradually to a certain maximum value with decreasing cell size. This in turn led to the increase in the total thermal conductivity upon decreasing the cell size, as shown in the updated version of Fig. 9a, instead of it reaching a certain maximum value and subsequently decreasing with reducing cell size as shown in the original version of Fig. 9a. This phenomenon was due to the sharp decrease in the reflectance of the single cell wall with decreasing cell size (Fig. 9d), and increasing the number of cell walls could not offset the adverse impact on the total reflectance of IR waves.

As shown in the original versions of Fig. 9a and c, both λ_{eff} and λ_{rad} first decreased, then increased, and finally decreased again, upon reducing the cell size. Thus, both λ_{eff} and λ_{rad} showed maximum peak values. In order to explain the final downward trend of the two variables, it was stated in the published paper that the increase in the rate of the cell wall number (n) was much faster than the declining rate of the wavelength-averaged reflectance of the single cell wall . However, this was not true because n and were not compared over an equivalent numerical range. In fact, if an equivalent numerical range were to be employed, it would be found that the decrease in would be so fast that the increase in n could not offset its adverse impact on the total reflectance of IR waves. Subsequently, the maximum peak values that appeared in the original versions of Fig. 9a and c should not have existed, as shown in the updated versions of Fig. 9a and c. It was inferred that, as the cell size reduced indefinitely, would gradually approach zero and would approach one. According to eqn (41) shown in the published paper, the radiative thermal conductivity would finally approach its maximum value of , which is 257.5 mW m^{−1} K^{−1}.

When calculating with a much finer discretization, decreased significantly at high void fractions compared with the originally published data. Subsequently, both λ_{rad} and λ_{eff} increased significantly at high void fractions in comparison with the original data. Thus, Fig. 10 in the published paper should be replaced by the updated version of Fig. 10 provided below. Notably, it can be seen in the updated version of Fig. 10b that the maximum value of λ_{rad} could be up to 250 mW m^{−1} K^{−1}, which is much larger than the maximum value reported in the original version of Fig. 10b. Consequently, the maximum value of λ_{eff} reported in the updated version of Fig. 10a was also much larger than the maximum value reported in the original version of Fig. 10a.

For the same reason, Fig. 11 in the published paper should also be replaced by the updated version of Fig. 11 provided below. Notably, both λ_{rad} and λ_{eff} increased significantly at high void fractions in comparison with the original data. However, the change in discretization here did not change the variation trend of the variables. Moreover, the minimum effective thermal conductivity (λ^{Min}_{eff}) calculated for the different cases only changed slightly.

Fig. 12 in the published paper should also be replaced by the updated version of Fig. 12 provided below. Overall, the contour isotherms of the thermal conductivity did not exhibit any obvious changes in comparison with the original version of Fig. 12, except for the data at small cell sizes and high void fractions.

Also, the formulas (23)–(33) in the paper need to be corrected because the refraction angle, θ_{2}, which should be a complex number, was mistakenly processed as a real number when preparing the original article. However, these errors did not affect the calculation results, because θ_{2} had been correctly taken as a complex number in all previous modelling and calculation works.

The formula (23) in the article should be changed to the following:

(23) |

In the updated formula (23), u_{s} and υ_{s} are employed to simplify the notation, and their values are determined by u_{s} + iυ_{s} = (n_{s} + iκ_{s})cosθ_{2}. To calculate the complex refraction angle, θ_{2}, the formula (24) should be changed to:

(24) |

Accordingly, for the incident radiation wave with the electric vector perpendicular to the plane of incidence, formulas (25) and (26) which were used to determine ρ_{gs}, ρ_{sg}, ϕ_{gs}, and ϕ_{sg} should be respectively replaced with the following formulas:

(25) |

(26) |

Meanwhile, for the incident radiation wave with the electric vector parallel to the plane of incidence, formulas (27) and (28) should be respectively changed to the following:

(27) |

(28) |

The formula (29) used to calculate the transmittance of polymer film in the article should be changed to the following:

(29) |

For the incident radiation wave with the electric vector perpendicular to the plane of incidence, formulas (30) and (31) used to determine τ_{gs} and τ_{sg} should be respectively replaced with the following formulas:

(30) |

(31) |

Meanwhile, for the incident radiation wave with the electric vector parallel to the plane of incidence, formulas (32) and (33) should be respectively changed to the following:

(32) |

(33) |

In addition to the above corrections, eqn (36) in the published paper should be changed to the following:

(36) |

These errors do not affect the main conclusions of the paper. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

This journal is © The Royal Society of Chemistry 2018 |