# Interface and Interphase in Polymer Nanocomposites with Bare and Core-Shell Gold Nanoparticles

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{g}using atomistic and systematic coarse-grained models [88,93], or bead–spring models [94,95]. In addition, concerning the segmental dynamics of the macromolecules, relaxation times of segments at the vicinity of a solid surface strongly depend on the strength of the polymer/surface interactions [89,96]. For polymer chains supported by a solid substrate the size of the interface or interphase depends on the actual property under study [88].

## 2. Model and Simulation Method

_{2}and methyl CH

_{3}group represented as a single Van der Waals interacting site. Harmonic potential was used to describe the polyethylene bonds and angles whereas the OPLS force field (Appendix A Table A1) was used to describe the polyethylene dihedrals. For the Van der Waals interactions between the PE-PE (Appendix A Table A2) we used a spherically truncated 6–12 Lennard–Jones potential with cutoff distance R

_{c}= 10 Å [109]. The first gold nanoparticle with Wulff construction has 459 atoms with 2.51 nm diameter and the second has 3101 atoms with 5.02 nm diameter [111,112]. The interaction between the Au and PE is described via a Morse potential, which is taken from the literature and is based on detailed DFT calculations [88,93,116]. This potential is parametrized in order to describe with accuracy extensive DFT data regarding the adsorption energy of the ethylene on the Au surface as a function of distance for several different adsorption sites.

_{x}groups of PE were modeled via a 6–12 Lennard–Jones potential with cutoff distance R

_{c}= 10 Å (see Table A2 in Appendix A). For the S–CH

_{2}–CH

_{2}–CH

_{2}dihedral angle interactions the OPLS force field was used. The entire atomistic force field is given in Table A1 and Table A2 of the Appendix A. Tail corrections were applied to both energy and pressure. For the non-bonded interactions between PE-PE monomers, the Lorentz–Berthelot rules were used. The gold nanoparticles are frozen during the duration of the MD runs. This is not expected to be a crude assumption since the Au NPs are very stable under conditions (temperature and pressure) similar to those of the current simulations.

#### 2.1. Shape of Au NPs

_{2}[120], Au with adsorbed CO [112], Ag [121], and Pt in HCl [122].

#### 2.2. Generation and Equilibration of Model Systems

- (a)
- First, in order to obtain initial PE/grafted Au configurations, we added the anchors to the Au surface randomly by using a Monte Carlo algorithm in suitable positions according to the shape of the Au and taking into account the absorption sites of sulfur in the DFT calculations of alkanethiols adsorbed on Au.
- (b)
- Second, we equilibrate the hybrid system through energy minimization and long simulation runs. Energy minimization of the core/shell system was performed followed by MD simulation runs up to 10 ns in the NVT ensemble. Then, the Au nanoparticle, grafted or not, was placed at a close distance (about 0.5 nm) to several well-equilibrated polymer samples [109].
- (c)
- The final step of our “equilibration protocol” involves the execution of long MD simulations, of the order of 30 ns. Throughout this time we monitored the motion of the whole hybrid system. Our simulations run times were much higher than the relaxation times of the chains [109].

_{g}, values and checked the de-correlation of the end to end vector (ACF) of polymer chains. Furthermore, we performed several (3–5) different simulations by following the exact same procedure but starting with different initial configurations and we end with the same results.

#### 2.3. Analysis Method

## 3. Results

#### 3.1. Structural Properties

#### 3.1.1. Density Profiles

^{3}), though at different distances due to the different Au NP sizes. PE100/Au2 and PE100/Au5 systems exhibit the same behavior: a peak of rather similar height (but larger than the bulk value) is observed at a distance/radius of about 1.3 nm and 1.8 nm respectively, which denotes the attraction of the polymer atoms from the gold NP at short distances, due to vdW forces, while at longer distances the bulk density is attained. In the core/shell Au NP systems (PE100/Au5/g20 and PE100/Au5/g62), only few polyethylene chains can penetrate the anchors and reach the gold surface. We observe a similar behavior for the systems consisting of PE matrices of 22 mers per chain although in this case the average density is lower than that of the systems consisting of PE matrices of 100 mers per chain. The above values are in very good agreement with experimental data for bulk PE chains [123].

#### 3.1.2. Structure of PE Chains

**v**

^{1−3}vector, which connects two non-consecutive carbon atoms. The segmental orientation is quantified via the second rank bond order parameter [12,124] defined as:

**v**

^{1−3}one) and one that connects the center of the gold NP with the midpoint of the above (

**v**

^{1−3}) vector (see Figure A3 in Appendix A), and whereas brackets 〈 〉 denote statistical average. S

_{1–3}limiting values of −0.5, 0.0, and 1.0 correspond to perfectly parallel, random, and perpendicular vector orientations relative to the Au NP, respectively. For the limiting values we assume smooth plain surface.

**v**

^{1−3}for all systems with PE matrices consisting of 100 mers per chain is depicted in Figure 5. In all cases there is an obvious tendency of the segments of the polymer chain for an almost parallel orientation relative to the Au NP surface at short distances which is gradually randomized the further the distance. There is a decrease of the bond order parameter of the PE segments closest to the Au NP and the minimum values are about −0.4 for all hybrid systems. The same behavior is observed for the other model systems studied here as well.

_{dih}, of polymer chains at different distances from the gold NP. Results about the dihedral angle distributions of the PE chains are shown in Figure 6a for the PE100/Au2 system (“trans” corresponds to 0°, “gauche-” and “gauche+” to −60° and +60° respectively and “cis” to 180° degrees). For the first adsorption layer, defined via the first minimum in the density profile (0–30 Å, see Figure 3), a non-negligible enhancement of the trans states with a consequent reduction of the gauche ones is observed for PE22/Au2, PE22/Au5, PE100/Au2 and PE100/Au5 systems compared to the bulk case (Figure 6b). This observation reflects the more ordered PE chains close to the gold NP. Enhancement of “trans” population would be expected to affect the crystallinity of PE chains as well as the mechanical properties of the hybrid system. Such a behavior has been observed for PE adsorbed on planar carbon-based surfaces, such as graphite or graphene, where the structure of PE commensurate to the underlying crystal structure of the substrate [3,96,125,126]. Here the enhancement of “trans” population is rather weak.

_{g}) for the PE was calculated and found approximately 6 Å in the systems consisting of 22 monomers per chain (Appendix A Figure A4) and approximately 16 Å in the systems consisting of 100 monomers per chain (Appendix A Figure A5). These values are very close to the experimental data [127]. Moreover, we observed a small increment, about 5%, of the R

_{g}close to the surface area, as we expected. Such perturbation of the R

_{g}has been also observed in other polymer nanocomposite systems as for example PE with graphene [96].

#### 3.2. Dynamical Properties

#### 3.2.1. Orientational Dynamics

_{end-end}(t) at different radial adsorption layers are presented in Figure 7 for the hybrid PE100/Au5 system and the comparison with PE22/Au5 system in Appendix A Figure A6. In these figures corresponding data for a bulk PE system are also shown. It should be noted that we monitored the position of each vector only for the time period it belongs to the corresponding analysis regime in order to make these calculations. It is clear that in all systems slower PE chain dynamics at the vicinity of the Au nanoparticles is shown. In particular, PE chains in the first adsorption layers show much slower terminal dynamics compared to the bulk one. Then moving away from the Au NP surface up to a specific distance, we observed a more rapid decorrelation, whereas beyond this all curves coincide. We’ve also calculated the average value of the ACF for the entire system, which is almost identical with the bulk’s one.

_{KWW}is the KWW relaxation time and β the stretch exponent, which describes the broadness of the distribution of the relaxation times (i.e., the deviation from the ideal Debye behavior β = 1). Then, the relaxation time, τ

_{end-end}, is calculated as the integral of the KWW curves through:

_{end-end}and the β exponent for PE chains of all the simulated systems are presented in Figure 8 and Figure 9. Bulk values are also shown in these figures. It is clear that the PE chains which are very close to the Au NP, have much slower orientational dynamics (longer terminal relaxation time τ

_{end-end}) and τ

_{end-end}is about 2–10 times longer than the bulk one. As expected polymer chains become more mobile as their distance from the gold nanoparticle increases, reaching a plateau, bulk-like regime, at distances of about 2.5–3.0 nm away from the Au NP. From the relaxation times reported in Figure 8 it is clear that the adsorbed polymer chains are (several times) slower than the ones in the bulk-like regime, however they are still mobile, as it is also shown below by probing the translational dynamics of polymer chains. In addition, β-exponent values of PE chains are smaller than the bulk value (~0.89), the black line shown in Figure 9, at the majority of all distances. The latter indicates a broader distribution of the polymer terminal dynamics, compared to the bulk one. Furthermore as was expected, the 100 mers PE systems have much slower relaxation times in comparison to those of the 22 mers PE systems (Appendix A Figure A7, Figure A8, Figure A9, Figure A10, Figure A11 and Figure A12).

#### 3.2.2. Translational Dynamics

_{2}or CH

_{3}group here) within region j, at time t and t + τ, respectively, and brackets 〈 〉 denote statistical average for all segments within the region j. Note, that in the analysis used here a segment contributes to the above MSD for a given time interval τ and for a radial region j, if and only if it was constantly present in that region in the entire course of time τ. Data on ΔR

_{j}(τ) for all (radial) adsorption layers, scaled with t

^{0.5}, for the PE100/Au5/g62 system is shown in Figure 10. We observed slower terminal dynamics of the polymer atoms closer to the Au NP atoms (mainly in the first adsorption layer) in comparison to the one of the atoms in the other layers. In contrast, chains which belong to the other regimes, (above the second layer) show quite similar dynamics, almost equal to the bulk one, the black line and the total average value of the entire system, the magenta line shown in Figure 10. All the simulated hybrid systems have a similar behavior. However, the PEs in PE22/Au2, PE22/Au5, PE22/Au5/g20 and PE22/Au5/g62 (see Appendix A Figure A13) are faster than the equivalent systems with PE matrices consisting of 100 mers per chain.

_{j}(τ) ∝ τ

^{1/2}. Our calculations using the data for bulk PE (PE100 system) showed that the Rouse regime was well-attained for the linear bulk chains, as it has been shown also in previous works [129,130,131]. Concerning the different adsorption spherical shells we extracted exponents less than 1/2. Those exponents indicate the variation from the Rouse behavior which is more pronounced close to the Au NP. This attributed to the fact that there is attraction of the PE monomers from the Au NP and from the grafted polymers. Furthermore, according to our analysis method, we calculated the MSD for the hybrid systems as long as the segments were within the spherical shells. Therefore the time frame window is not enough to reach the Rouse regime for the PE monomers that are close to the surface of the Au NP.

_{1}(τ), scaled with t

^{0.5}, is presented in Figure 11 for all simulated systems with PE matrices consisting of 100 mers per chain. We observe that the MSD, ΔR

_{j}(τ) in all systems for the 1st adsorption shell is smaller than the corresponding bulk one. Nevertheless, in qualitative agreement with the orientational segmental dynamics discussed above, chains in the first adsorption layer are still mobile.

## 4. Discussion and Conclusions

- Local structural and conformational features were analyzed at the level of both individual segments (atoms or bonds) and entire chains. Due to the intermolecular PE/Au NP (adhesive) interaction the local monomer PE mass density exhibits a maximum near the gold surface. At short distances chain segments tend to orientate almost parallel to the Au NP surface. This randomizes gradually as the chain segments move away from the interface. Furthermore, in the dihedral angle distribution at the PE/gold NP interface we observed an increase of “trans” population compared to the bulk one. This reflects the more ordered polymer chain structures.
- Orientational relaxation of PE chains in the hybrid systems at the segmental and terminal level was quantified through the time autocorrelation function of a segmental vector and the end-to-end vector of PE chain respectively. In all cases the PE chains which were closer to the Au NP had much slower orientantional dynamics (segmental relaxation time, τ
_{seg}, is about 10 times longer) in comparison to the bulk one. Moving away from the interface up to a specific distance, we noticed faster C_{1–3}(t) decorrelation, while beyond this, all curves coincide. Moreover, we observed broader distribution of the polymer orientational dynamics in comparison to the bulk one (smaller β-exponent values). - Translational segmental and center of masses dynamics of PE chains were examined by calculating the average mean-square displacement. Due to the polymer/gold nanoparticle interfaces, for all model hybrid systems, PE chains closer to the Au NP are slower, compared to the bulk one.

## Supplementary Materials

_{2}and the free CH

_{3}monomers. In red are the grafted CH

_{2}and CH

_{3}monomers.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Snapshot from MD simulation of hybrid polyethylene/grafted gold nanoparticle at 450 K. Au nanoparticle (2461 atoms, diameter of 5.04 nm) is shown. In yellow is the Au and in grey are the terminal CH

_{3}groups. In red are the grafted CH

_{2}and the grafted CH

_{3}monomers. The initial configuration of the grafted NP with the short anchored polymeric chains and with the long anchored polymeric chains.

Non-Bonded Interactions | ||||
---|---|---|---|---|

${V}_{LJ}\left({r}_{ij}\right)=4{\epsilon}_{ij}\left[{\left(\frac{{\sigma}_{ij}}{{r}_{ij}}\right)}^{12}-{\left(\frac{{\sigma}_{ij}}{{r}_{ij}}\right)}^{6}\right],r\le {R}_{c}$ Lennard-Jones | ||||

Atom Types | mass (g/mol) | σ (nm) | ε (kJoule/mol) | |

CH_{2} | 14.027 | 0.395 | 0.3824 | |

CH_{3} | 15.035 | 0.395 | 0.3824 | |

S–CH_{2} | 32.066–14.027 | 0.372 | 0.7219 | |

S–CH_{3} | 32.066–15.035 | 0.372 | 0.8761 | |

${V}_{Morse}\left({r}_{ij}\right)={\mathrm{D}}_{0}\left[{e}^{-2a\left(r-{r}_{0}\right)}-2{e}^{-a\left(r-{r}_{0}\right)}\right],r\le {R}_{c}$ Morse | ||||

Atom Types | mass (g/mol) | D_{0} (kJoule/mol) | α (nm^{−1}) | r_{0} (nm) |

Au–CH_{2} | 196.967–14.027 | 1.6885 | 11.69 | 0.4085 |

Au–CH_{3} | 196.967–15.035 | 1.6885 | 11.69 | 0.4085 |

Bonded Interactions | |||||
---|---|---|---|---|---|

${V}_{b}\left({r}_{ij}\right)=\frac{1}{2}{k}_{ij}^{b}{\left({r}_{ij}-{b}_{ij}\right)}^{2}$ | |||||

Bond | b (nm) | k^{b} (kJ/mol·nm^{2}) | |||

CH_{2}–CH_{2} | 0.154 | 100,000.00 | |||

CH_{2}–CH_{3} | 0.154 | 100,000.00 | |||

CH_{3}–CH_{2} | 0.154 | 100,000.00 | |||

S–CH_{2} | 0.181 | fixed | |||

${V}_{\mathsf{\alpha}}\left({\mathsf{\theta}}_{ijk}\right)=\frac{1}{2}{k}_{ijk}^{\mathsf{\theta}}{\left({\mathsf{\theta}}_{ijk}-{\mathsf{\theta}}_{ijk}^{0}\right)}^{2}$ | |||||

Angle | θ° (deg) | k^{θ} (kJ/mol * rad^{2}) | |||

CH_{2}–CH_{2}–CH_{2} | 114 | 519.611 | |||

CH_{3}–CH_{2}–CH_{2} | 114 | 519.611 | |||

CH_{2}–CH_{2}–CH_{3} | 114 | 519.611 | |||

S–CH_{2}–CH_{2} | 114 | 519.611 | |||

${V}_{opls}\left({\mathsf{\phi}}_{ijkl}\right)=\frac{1}{2}{{\rm K}}_{1}\left[1+\mathrm{cos}\left(\mathsf{\phi}\right)\right]+\frac{1}{2}{{\rm K}}_{2}\left[1-\mathrm{cos}\left(2\mathsf{\phi}\right)\right]+\frac{1}{2}{{\rm K}}_{3}\left[1+\mathrm{cos}\left(3\mathsf{\phi}\right)\right]+\frac{1}{2}{{\rm K}}_{4}\left[1-\mathrm{cos}\left(4\mathsf{\phi}\right)\right]$ | |||||

Dihedral | ${{\rm K}}_{1}$(KJ/mol) | ${{\rm K}}_{2}$(KJ/mol) | ${{\rm K}}_{3}$(KJ/mol) | ${{\rm K}}_{4}$(KJ/mol) | |

CH_{3}–CH_{2}–CH_{2}–CH_{2} | 4.276 | −1.12968 | 13.1545 | 0.00 | |

CH_{2}–CH_{2}–CH_{2}–CH_{2} | 4.276 | −1.12968 | 13.1545 | 0.00 | |

CH_{2}–CH_{2}–CH_{2}–CH_{3} | 4.276 | −1.12968 | 13.1545 | 0.00 | |

S–CH_{2}–CH_{2}–CH_{2} | 4.276 | −1.12968 | 13.1545 | 0.00 |

**Figure A2.**Mass monomer density profiles of PE chains as a function of distance from the center of the gold NP, r, for the systems: PE22, PE22/Au2, PE22/Au5, PE22/Au5/g20 and PE22/Au5/g62.

**Figure A3.**The definition of the θ angle for the calculation of the second rank bond order parameter S

_{1–3}of polyethylene chains for

**v**

^{1−3}vector. In blue is the PE and in yellow is the Au NP. The orange line connects two non-consecutive carbon atoms and the blue line connects the center of the gold NP with the midpoint of the orange line. In red is the θ angle.

**Figure A4.**Radius of gyration of PE chains, scaled with its bulk value (R

_{g/}R

_{g bulk}) as a function of r distance from the center of the Au NP. Data for the PE22, PE22/Au2, PE22/Au5, PE22/Au5/g20 and PE22/Au5/g62 systems are shown.

**Figure A5.**Radius of gyration of PE chains, scaled with its bulk value (R

_{g/}R

_{g bulk}) as a function of distance, r, from the center of the gold NP. Data for the PE100, PE100/Au2, PE100/Au5, PE100/Au5/g20 and PE100/Au5/g62 systems are shown.

**Figure A6.**Time ACF of the end-to-end vector of PE chains, C

_{end-end}(t), as a function of time for PE22/Au5 and PE100/Au5 systems. C

_{end-end}(t) values for the PE22/Au5 and PE100/Au5 systems, for various spherical shells are presented.

**v**

^{1−3}, at time t relative to its position at t = 0. Second, we calculate the second order Legendre polynomial (correlation function) for this vector, defined as:

_{1–3}(t) using a KWW function and derive the characteristic segmental relaxation time, τ

_{seg}and the corresponding β-exponent, by computing the integral below the KWW curve, similar to the analysis followed for the end-to-end vector ACFs.

**Figure A7.**Segmental relaxation times of PE chains, scaled with the value of bulk chains, τ

_{seg}/τ

_{seg bulk}, as a function of distance from the center of the Au NP, r, minus the half diameter of the NP, for all systems with PE matrices consisting of 100 mers per chain.

**Figure A8.**The stretch exponent β, as extracted from the fit of C

_{1–3}(t) ACF with a KWW, as a function of distance from the center of the Au NP, r, minus the half diameter of the NP, for all systems with PE matrices consisting of 100 mers per chain. Black lines represent β values of bulk PE.

**Figure A9.**Segmental relaxation times of PE chains, scaled with the value of bulk chains, τ

_{seg}/τ

_{seg bulk}, as a function of distance from the center of the Au NP, r, minus the half diameter of the NP, for all systems with PE matrices consisting of 22 mers per chain.

**Figure A10.**The stretch exponent β, as extracted from the fit of C

_{1–3}(t) ACF with a KWW, as a function of distance from the center of the Au NP, r, minus the half diameter of the NP, for all systems with PE matrices consisting of 22 mers per chain. Black lines represent β values of bulk PE.

**Figure A11.**Terminal relaxation times of PE chains derived for the end-to-end vector ACF, C

_{end-end}(t), scaled with the value of bulk chains, τ

_{end-end}/τ

_{end-end bulk}, as a function of distance from the center of the Au NP, r, minus the half diameter of the NP for all systems with PE matrices consisting of 22 mers per chain.

**Figure A12.**The stretch exponent β, as extracted from the fit with KWW functions, of

**v**

^{end−end}characteristic vector based on C

_{end-end}(t) time autocorrelation as a function of r (distance from the center of the Au NP) minus the half diameter of the NP, for all systems with PE matrices consisting of 22 mers per chain. Black lines represent β values of bulk PE.

**Figure A13.**Segmental MSD of PE chains for the first adsorption spherical shell, ΔR

_{1}, scaled with t

^{0.5}. Data for the PE22/Au2, PE22/Au5, PE22/Au5/g20 and PE22/Au5/g62 systems are shown, together with data for the bulk PE22 system.

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**Figure 1.**Snapshots from the model systems: (

**a**) The PE22/Au5 hybrid system. In yellow is the Au, in blue are the CH

_{2}monomers and in green are the CH

_{3}monomers. (

**b**) Au NP, of d = 5.02 nm (in yellow are the Au atoms and in grey the edge Au atoms), and a PE 100 mer chain. (

**c**) The PE100/Au5/g62 hybrid system. In blue are the free CH

_{2}and the free CH

_{3}monomers. In red are the grafted CH

_{2}and CH

_{3}monomers.

**Figure 2.**(

**a**) A sketch of the analysis scheme in spherical shells. (

**b**) Inside view of the Figure 2a.

**Figure 3.**Mass monomer density profiles of polyethylene as a function of r (distance from the center of the gold NP) for the systems: PE100, PE100/Au2, PE100/Au5, PE100/Au5/g20 and PE100/Au5/g62.

**Figure 4.**Mass monomer density profiles of polyethylene as a function of r (distance from the center of the gold NP). Au5/g20 and PE100/Au5/g62 systems. The density profile was decomposed to free polyethylene chains and grafted polyethylene chains.

**Figure 5.**Second rank bond order parameter S

_{1–3}of polyethylene chains for

**v**

^{1−3}vector, as a function of distance from the center of the Au NP, r, for all PE/Au systems with PE matrices consisting of 100 mers per chain.

**Figure 6.**(

**a**) Torsional angles distribution of PE chains for various distances from the center of the gold NP for the PE100/Au2 system and the corresponding PE bulk curve. (

**b**) Torsional angles distributions of all model systems for PE chains belonging in the first adsorbed layer, i.e., being closer to the Au NP. The corresponding curves for bulk PE are also shown.

**Figure 7.**The reorientation time autocorrelation function (ACF) C

_{end-end}(t) as a function of time for the end-to-end vector of polyethylene for PE100/Au5 system. PE chains are analyzed across various shells from the Au NP.

**Figure 8.**Relaxation time of the end-to-end vector of PE chains, scaled with the value of bulk chains, τ

_{end-end}/τ

_{end-end bulk}, as a function of distance from the center of the Au NP, r, minus the half diameter of the NP, for all systems with PE matrices consisting of 100 mers per chain.

**Figure 9.**The stretch exponent β, as extracted from the fit with KWW functions, of the end-to-end vector ACF, C

_{end-end}(t), as a function of distance from the center of the Au NP, r, minus the half diameter of the NP for all systems with PE matrices consisting of 100 mers per chain. Black lines represent β values of bulk PE chains.

**Figure 10.**Segmental MSD of PE chains along r (distance from the center of the gold NP), ΔRj, scaled with t

^{0.5}Data for the PE100/Au5/g62 system, for various spherical shells, and the total MSD of the PE100 and PE100/Au5/g62 systems are shown.

**Figure 11.**Segmental MSD of PE chains for the first adsorption spherical shell, ΔR

_{1}, scaled with t

^{0.5}. Data for the PE100/Au2, PE100/Au5, PE100/Au5/g20 and PE100/Au5/g62 systems are shown, together with data about the MSD of the entire PE100 and PE100/Au5 systems.

Name | Au NP Diameter | Au Atoms | Free PE Chains | Au/PE w/w% | Au/PE v/v% | Grafted PE Chains | Grafted PE Mers/Chain |
---|---|---|---|---|---|---|---|

PE100/Au2 | 25.1 Å | 459 | 1200 | 4.9 | 0.2 | - | - |

PE100/Au5 | 50.2 Å | 3101 | 1200 | 37.6 | 1.7 | - | - |

PE100/Au5/g20 | 50.4 Å | 2461 | 1200 | 29.7 | 1.7 | 53 | 20 |

PE100/Au5/g62 | 50.4 Å | 2461 | 1200 | 29.7 | 1.7 | 53 | 62 |

PE100 | - | - | 240 | - | - | - | - |

PE22/Au2 | 25.1 Å | 459 | 5040 | 5.8 | 0.4 | - | - |

PE22/Au5 | 50.2 Å | 3101 | 5040 | 38.8 | 1.6 | - | - |

PE22/Au5/g20 | 50.4 Å | 2461 | 5040 | 30.8 | 1.6 | 53 | 20 |

PE22/Au5/g62 | 50.4 Å | 2461 | 5040 | 30.8 | 1.6 | 53 | 62 |

PE22 | - | - | 420 | - | - | - | - |

**Table 2.**The width of the interface in PE/au NP nanocomposites defined via different properties for the systems with 100 mers PE chains.

Property | Bare Au NPs | Grafted Au NPs |
---|---|---|

Density | 0.5–1.0 nm | 1.7–3.0 nm |

Structural | 0.5–1.0 nm | 0.5–1.3 nm |

Local (segmental) dynamics | 1.0–2.0 nm | 0.5–1.5 nm |

Global dynamics | 3.0–4.0 nm | 1.0–2.0 nm |

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**MDPI and ACS Style**

Power, A.J.; Remediakis, I.N.; Harmandaris, V.
Interface and Interphase in Polymer Nanocomposites with Bare and Core-Shell Gold Nanoparticles. *Polymers* **2021**, *13*, 541.
https://doi.org/10.3390/polym13040541

**AMA Style**

Power AJ, Remediakis IN, Harmandaris V.
Interface and Interphase in Polymer Nanocomposites with Bare and Core-Shell Gold Nanoparticles. *Polymers*. 2021; 13(4):541.
https://doi.org/10.3390/polym13040541

**Chicago/Turabian Style**

Power, Albert J., Ioannis N. Remediakis, and Vagelis Harmandaris.
2021. "Interface and Interphase in Polymer Nanocomposites with Bare and Core-Shell Gold Nanoparticles" *Polymers* 13, no. 4: 541.
https://doi.org/10.3390/polym13040541