# 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.

## References

- Fu, S.-Y.; Sun, Z.; Huang, P.; Li, Y.-Q.; Hu, N. Some basic aspects of polymer nanocomposites: A critical review. Nano Mater. Sci.
**2019**, 1, 2–30. [Google Scholar] [CrossRef] - Alonso-Redondo, E.; Belliard, L.; Rolle, K.; Graczykowski, B.; Tremel, W.; Djafari-Rouhani, B.; Fytas, G. Robustness of elastic properties in polymer nanocomposite films examined over the full volume fraction range. Sci. Rep.
**2018**, 8, 16986. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bačová, P.; Rissanou, A.N.; Harmandaris, V.; Harmaris, V. Edge-Functionalized Graphene as a Nanofiller: Molecular Dynamics Simulation Study. Macromolecules
**2015**, 48, 9024–9038. [Google Scholar] [CrossRef] - Srivastava, S.; Schaefer, J.L.; Yang, Z.; Tu, Z.; Archer, L.A. 25th Anniversary Article: Polymer-Particle Composites: Phase Stability and Applications in Electrochemical Energy Storage. Adv. Mater.
**2013**, 26, 201–234. [Google Scholar] [CrossRef] - Kumar, S.K.; Krishnamoorti, R. Nanocomposites: Structure, Phase Behavior, and Properties. Annu. Rev. Chem. Biomol. Eng.
**2010**, 1, 37–58. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Giannelis, E.P. Polymer Layered Silicate Nanocomposites. Adv. Mater.
**1996**, 8, 29–35. [Google Scholar] [CrossRef] - Balazs, A.C.; Emrick, T.; Russell, T.P. Nanoparticle Polymer Composites: Where Two Small Worlds Meet. Science
**2006**, 314, 1107–1110. [Google Scholar] [CrossRef] - Devi, J.M. Aggregation of thiol coated gold nanoparticles: A simulation study on the effect of polymer coverage density and solvent. Comput. Mater. Sci.
**2014**, 86, 174–179. [Google Scholar] [CrossRef] - Ma, J.-Z.; Liu, Y.-H.; Bao, Y.; Liu, J.-L.; Zhang, J. Research advances in polymer emulsion based on “core–shell” structure particle design. Adv. Colloid Interface Sci.
**2013**, 197, 118–131. [Google Scholar] [CrossRef] - Chrissopoulou, K.; Andrikopoulos, K.S.; Fotiadou, S.; Bollas, S.; Karageorgaki, C.; Christofilos, D.; Voyiatzis, G.A.; Anastasiadis, S.H. Crystallinity and Chain Conformation in PEO/Layered Silicate Nanocomposites. Macromolecules
**2011**, 44, 9710–9722. [Google Scholar] [CrossRef] - Corbierre, M.K.; Cameron, N.S.; Sutton, M.; Laaziri, K.; Lennox, R.B. Gold Nanoparticle/Polymer Nanocomposites: Dispersion of Nanoparticles as a Function of Capping Agent Molecular Weight and Grafting Density. Langmuir
**2005**, 21, 6063–6072. [Google Scholar] [CrossRef] - Kotelyanskii, M.; Theodorou, D.N. Simulation Methods for Polymers; Marcel Dekker Inc.: New York, NY, USA, 2004. [Google Scholar]
- Dhoke, S.K.; Khanna, A. Study on electrochemical behavior of Nano-ZnO modified alkyd-based waterborne coatings. J. Appl. Polym. Sci.
**2009**, 113, 2232–2237. [Google Scholar] [CrossRef] - Laachachi, A.; Ruch, D.; Addiego, F.; Ferriol, M.; Cochez, M.; Cuesta, J.M.L. Effect of ZnO and organo-modified montmorillonite on thermal degradation of poly(methyl methacrylate) nanocomposites. Polym. Degrad. Stab.
**2009**, 94, 670–678. [Google Scholar] [CrossRef] - Dashtizadeh, A.; Abdouss, M.; Mahdavi, H.; Khorassani, M. Acrylic coatings exhibiting improved hardness, solvent resistance and glossiness by using silica nano-composites. Appl. Surf. Sci.
**2011**, 257, 2118–2125. [Google Scholar] [CrossRef] - Che, X.-C.; Jin, Y.-Z.; Lee, Y.-S. Preparation of nano-TiO2/polyurethane emulsions via in situ RAFT polymerization. Prog. Org. Coatings
**2010**, 69, 534–538. [Google Scholar] [CrossRef] - Zhu, A.; Shi, Z.; Cai, A.; Zhao, F.; Liao, T. Synthesis of core–shell PMMA–SiO2 nanoparticles with suspension–dispersion–polymerization in an aqueous system and its effect on mechanical properties of PVC composites. Polym. Test.
**2008**, 27, 540–547. [Google Scholar] [CrossRef] - Wen, X.-F.; Li, M.-Z.; Pi, P.-H.; Chen, J.; Yang, Z.-R. Study of the physicochemical properties of silica powder and the stability of organic–inorganic hybrid emulsion in the presence of ethanol. Colloids Surf. A Physicochem. Eng. Asp.
**2008**, 327, 103–110. [Google Scholar] [CrossRef] - Kritikos, G.; Karatasos, K. Temperature dependence of dynamic and mechanical properties in poly(acrylic acid)/graphene oxide nanocomposites. Mater. Today Commun.
**2017**, 13, 359–366. [Google Scholar] [CrossRef] - España-Sánchez, B.L.; Ávila-Orta, C.A.; Padilla-Vaca, F.; Neira-Velázquez, M.G.; González-Morones, P.; Rodríguez-González, J.A.; Hernández-Hernández, E.; Rangel-Serrano, A.; Barriga-C, E.D.; Yate, L.; et al. Enhanced Antibacterial Activity of Melt Processed Poly(propylene) Ag and Cu Nanocomposites by Argon Plasma Treatment. Plasma Process. Polym.
**2014**, 11, 353–365. [Google Scholar] [CrossRef] - Babu, K.F.; Dhandapani, P.; Maruthamuthu, S.; Kulandainathan, M.A. One pot synthesis of polypyrrole silver nanocomposite on cotton fabrics for multifunctional property. Carbohydr. Polym.
**2012**, 90, 1557–1563. [Google Scholar] [CrossRef] [PubMed] - Palza, H. Antimicrobial Polymers with Metal Nanoparticles. Int. J. Mol. Sci.
**2015**, 16, 2099–2116. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nascimento, H.P.; Oliveira, M.D.; De Melo, C.P.; Silva, G.J.; Cordeiro, M.T.; Andrade, C.A. An impedimetric biosensor for detection of dengue serotype at picomolar concentration based on gold nanoparticles-polyaniline hybrid composites. Colloids Surfaces B Biointerfaces
**2011**, 86, 414–419. [Google Scholar] [CrossRef] [PubMed] - Pérez-López, A.M.; Rubio-Ruiz, B.; Sebastian, V.; Hamilton, L.; Adam, C.; Bray, T.L.; Irusta, S.; Brennan, P.M.; Lloyd-Jones, G.C.; Sieger, D.; et al. Gold-Triggered Uncaging Chemistry in Living Systems. Angew. Chem. Int. Ed.
**2017**, 56, 12548–12552. [Google Scholar] [CrossRef] - Shevach, M.; Fleischer, S.; Shapira, A.; Dvir, T. Gold Nanoparticle-Decellularized Matrix Hybrids for Cardiac Tissue Engineering. Nano Lett.
**2014**, 14, 5792–5796. [Google Scholar] [CrossRef] - Ribeiro, M.; Ferraz, M.P.; Monteiro, F.J.; Fernandes, M.H.; Beppu, M.M.; Mantione, D.; Sardon, H. Antibacterial silk fibroin/nanohydroxyapatite hydrogels with silver and gold nanoparticles for bone regeneration. Nanomed. Nanotechnol. Biol. Med.
**2017**, 13, 231–239. [Google Scholar] [CrossRef] [PubMed] - Li, Z.; Ye, E.; Lakshminarayanan, R.; Loh, X.J. Recent Advances of Using Hybrid Nanocarriers in Remotely Controlled Therapeutic Delivery. Small
**2016**, 12, 4782–4806. [Google Scholar] [CrossRef] [PubMed] - Bodelón, G.; Montes-García, V.; Fernández-López, C.; Pastoriza-Santos, I.; Pérez-Juste, J.; Liz-Marzán, L.M. Au@pNIPAM SERRS Tags for Multiplex Immunophenotyping Cellular Receptors and Imaging Tumor Cells. Small
**2015**, 11, 4149–4157. [Google Scholar] [CrossRef] - Xiao, C.; Wu, Q.; Chang, A.; Peng, Y.; Xu, W.; Wu, W. Responsive Au@polymer hybrid microgels for the simultaneous modulation and monitoring of Au-catalyzed chemical reaction. J. Mater. Chem. A
**2014**, 2, 9514–9523. [Google Scholar] [CrossRef] - Tang, F.; Ma, N.; Wang, X.; He, F.; Li, L. Hybrid conjugated polymer-Ag@PNIPAM fluorescent nanoparticles with metal-enhanced fluorescence. J. Mater. Chem.
**2011**, 21, 16943–16948. [Google Scholar] [CrossRef] - Zhang, J.; Ma, N.; Tang, F.; Cui, Q.; He, F.; Li, L. pH- and Glucose-Responsive Core–Shell Hybrid Nanoparticles with Controllable Metal-Enhanced Fluorescence Effects. ACS Appl. Mater. Interfaces
**2012**, 4, 1747–1751. [Google Scholar] [CrossRef] - Tamayo, L.; Palza, H.; Bejarano, J.; Zapata, P.A. 8—Polymer Composites with Metal Nanoparticles: Synthesis, Properties, and Applications. In Polymer Composites with Functionalized Nanoparticles; Pielichowski, K., Majka, T.M., Eds.; Elsevier: Amsterdam, The Netherlands, 2019; pp. 249–286. [Google Scholar]
- Ding, Y.; Jiang, Z.; Saha, K.; Kim, C.S.; Kim, S.T.; Landis, R.F.; Rotello, V.M. Gold Nanoparticles for Nucleic Acid Delivery. Mol. Ther.
**2014**, 22, 1075–1083. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lai, C.-T.; Sun, W.; Palekar, R.U.; Thaxton, C.S.; Schatz, G.C. Molecular Dynamics Simulation and Experimental Studies of Gold Nanoparticle Templated HDL-like Nanoparticles for Cholesterol Metabolism Therapeutics. ACS Appl. Mater. Interfaces
**2017**, 9, 1247–1254. [Google Scholar] [CrossRef] - Zhou, P.; Jia, S.; Pan, D.; Wang, L.; Gao, J.; Lu, J.; Shi, J.; Tang, Z.; Hua-Jie, L. Reversible Regulation of Catalytic Activity of Gold Nanoparticles with DNA Nanomachines. Sci. Rep.
**2015**, 5, srep14402. [Google Scholar] [CrossRef] [Green Version] - Teranishi, T. Fabrication and electronic properties of gold nanoparticle superlattices. Comptes Rendus Chim.
**2003**, 6, 979–987. [Google Scholar] [CrossRef] - Kim, Y.; Johnson, A.R.C.; Hupp, J.T. Gold Nanoparticle-Based Sensing of “Spectroscopically Silent” Heavy Metal Ions. Nano Lett.
**2001**, 1, 165–167. [Google Scholar] [CrossRef] - Boisselier, E.; Astruc, D. Gold nanoparticles in nanomedicine: Preparations, imaging, diagnostics, therapies and toxicity. Chem. Soc. Rev.
**2009**, 38, 1759–1782. [Google Scholar] [CrossRef] [PubMed] - Lal, S.; Link, S.; Halas, N.J. Nano-optics from sensing to waveguiding. Nat. Photon.
**2007**, 1, 641–648. [Google Scholar] [CrossRef] - Lu, Y.; Yin, Y.; Li, Z.-Y.; Xia, Y. Synthesis and Self-Assembly of Au@SiO2Core−Shell Colloids. Nano Lett.
**2002**, 2, 785–788. [Google Scholar] [CrossRef] - Zhang, R.-C.; Sun, D.; Zhang, R.; Lin, W.-F.; Macias-Montero, M.; Patel, J.; Askari, S.; McDonald, C.; Mariotti, D.; Maguire, P. Gold nanoparticle-polymer nanocomposites synthesized by room temperature atmospheric pressure plasma and their potential for fuel cell electrocatalytic application. Sci. Rep.
**2017**, 7, 46682. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wang, Z.; Tao, P.; Liu, Y.; Xu, H.; Ye, Q.; Hu, H.; Song, C.; Chen, Z.; Shang, W.; Deng, T. Rapid Charging of Thermal Energy Storage Materials through Plasmonic Heating. Sci. Rep.
**2015**, 4, srep06246. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Edwardson, T.G.W.; Lau, K.L.; Bousmail, D.; Serpell, C.J.; Sleiman, H.F. Transfer of molecular recognition information from DNA nanostructures to gold nanoparticles. Nat. Chem.
**2016**, 8, 162–170. [Google Scholar] [CrossRef] - Govorov, A.O.; Zhang, W.; Skeini, T.; Richardson, H.; Lee, J.; Kotov, N.A. Gold nanoparticle ensembles as heaters and actuators: Melting and collective plasmon resonances. Nanoscale Res. Lett.
**2006**, 1, 84–90. [Google Scholar] [CrossRef] [Green Version] - Anker, J.N.; Hall, W.P.; Lyandres, O.; Shah, N.C.; Zhao, J.; Van Duyne, R.P. Biosensing with plasmonic nanosensors. Nat. Mater.
**2008**, 7, 442–453. [Google Scholar] [CrossRef] - Shinde, S.K.; Kim, D.-Y.; Saratale, R.G.; Syed, A.; Ameen, F.; Kim, D.-Y. A Spectral Probe for Detection of Aluminum (III) Ions Using Surface Functionalized Gold Nanoparticles. Nanomaterials
**2017**, 7, 287. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Alsawafta, M.; Badilescu, S.; Paneri, A.; Truong, V.-V.; Packirisamy, M. Gold-Poly(methyl methacrylate) Nanocomposite Films for Plasmonic Biosensing Applications. Polymers
**2011**, 3, 1833–1848. [Google Scholar] [CrossRef] - Betzer, O.; Meir, R.; Dreifuss, T.; Shamalov, K.; Motiei, M.; Shwartz, A.; Baranes, K.; Cohen, C.J.; Shraga-Heled, N.; Ofir, R.; et al. In-Vitro Optimization of Nanoparticle-Cell Labeling Protocols for In-vivo Cell Tracking Applications. Sci. Rep.
**2015**, 5, 15400. [Google Scholar] [CrossRef] [Green Version] - Liu, M.; Li, Q.; Liang, L.; Li, J.; Wang, K.; Li, J.; Lv, M.; Chen, N.; Song, H.; Lee, J.; et al. Real-time visualization of clustering and intracellular transport of gold nanoparticles by correlative imaging. Nat. Commun.
**2017**, 8, 15646. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Park, J.H.; Lim, Y.T.; Park, O.O.; Kim, J.K.; Yu, J.-W.; Kim, Y.C. Polymer/Gold Nanoparticle Nanocomposite Light-Emitting Diodes: Enhancement of Electroluminescence Stability and Quantum Efficiency of Blue-Light-Emitting Polymers. Chem. Mater.
**2004**, 16, 688–692. [Google Scholar] [CrossRef] - Gupta, R.; Rai, B. Effect of Size and Surface Charge of Gold Nanoparticles on their Skin Permeability: A Molecular Dynamics Study. Sci. Rep.
**2017**, 7, srep45292. [Google Scholar] [CrossRef] [Green Version] - Ghosh, P.; Han, G.; De, M.; Kim, C.K.; Rotello, V.M. Gold nanoparticles in delivery applications☆. Adv. Drug Deliv. Rev.
**2008**, 60, 1307–1315. [Google Scholar] [CrossRef] - Remediakis, I.N.; López, N.; Nørskov, J.K. CO oxidation on gold nanoparticles: Theoretical studies. Appl. Catal. A Gen.
**2005**, 291, 13–20. [Google Scholar] [CrossRef] - Remediakis, I.N.; Lopez, N.; Nørskov, J.K. CO Oxidation on Rutile-Supported Au Nanoparticles. Angew. Chem. Int. Ed.
**2005**, 44, 1824–1826. [Google Scholar] [CrossRef] - Haruta, M. 4 Catalysis and applications of gold nanoparticles. In Studies in Surface Science and Catalysis; Anpo, M., Onaka, M., Yamashita, H., Eds.; Elsevier: Amsterdam, The Netherlands, 2003; pp. 31–38. [Google Scholar]
- Von White, G.; Mohammed, F.S.; Kitchens, C.L. Small-Angle Neutron Scattering Investigation of Gold Nanoparticle Clustering and Ligand Structure Under Antisolvent Conditions. J. Phys. Chem. C
**2011**, 115, 18397–18405. [Google Scholar] [CrossRef] - Jia, H.; Grillo, I.; Titmuss, S. Small Angle Neutron Scattering Study of Polyelectrolyte Brushes Grafted to Well-Defined Gold Nanoparticle Interfaces. Langmuir
**2010**, 26, 7482–7488. [Google Scholar] [CrossRef] - Jang, J.D.; Jeon, S.-W.; Yoon, Y.-J.; Bang, J.; Han, Y.S.; Kim, T.-H. Self-assembly of gold nanoparticles in a block copolymer aggregate template driven by hydrophobic interactions. Polym. Chem.
**2019**, 10, 6269–6277. [Google Scholar] [CrossRef] - Coelho, S.C.; Pereira, M.D.C.; Rangel, M.; Ivanova, G. Structural characterization of functionalized gold nanoparticles for drug delivery in cancer therapy: A NMR based approach. Phys. Chem. Chem. Phys.
**2015**, 17, 18971–18979. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhou, B.; Shen, M.; Banyai, I.; Shi, X. Structural characterization of PEGylated polyethylenimine-entrapped gold nanoparticles: An NMR study. Analyst
**2016**, 141, 5390–5397. [Google Scholar] [CrossRef] [PubMed] - Guo, C.; Yarger, J.L. Characterizing gold nanoparticles by NMR spectroscopy. Magn. Reson. Chem.
**2018**, 56, 1074–1082. [Google Scholar] [CrossRef] [PubMed] - Farea, M.O.; Abdelghany, A.M.; Oraby, A.H. Optical and dielectric characteristics of polyethylene oxide/sodium alginate-modified gold nanocomposites. RSC Adv.
**2020**, 10, 37621–37630. [Google Scholar] [CrossRef] - Mangal, R.; Srivastava, S.; Archer, L.A. Phase stability and dynamics of entangled polymer–nanoparticle composites. Nat. Commun.
**2015**, 6, 7198. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mijovic, J.; Lee, H.; Kenny, J.M.; Mays, J. Dynamics in Polymer−Silicate Nanocomposites As Studied by Dielectric Relaxation Spectroscopy and Dynamic Mechanical Spectroscopy. Macromolecules
**2006**, 39, 2172–2182. [Google Scholar] [CrossRef] - Papadimitriou, K.D.; Skountzos, E.N.; Gkermpoura, S.S.; Polyzos, I.; Mavrantzas, V.G.; Galiotis, C.; Tsitsilianis, C. Molecular Modeling Combined with Advanced Chemistry for the Rational Design of Efficient Graphene Dispersing Agents. ACS Macro Lett.
**2015**, 5, 24–29. [Google Scholar] [CrossRef] [Green Version] - Monti, S.; Carravetta, V.; Ågren, H. Decoration of gold nanoparticles with cysteine in solution: Reactive molecular dynamics simulations. Nanoscale
**2016**, 8, 12929–12938. [Google Scholar] [CrossRef] [PubMed] - Ndoro, T.V.M.; Voyiatzis, E.; Ghanbari, A.; Theodorou, D.N.; Boöhm, M.C.; Muüller-Plathe, F. Interface of Grafted and Ungrafted Silica Nanoparticles with a Polystyrene Matrix: Atomistic Molecular Dynamics Simulations. Macromolecules
**2011**, 44, 2316–2327. [Google Scholar] [CrossRef] - Allen, M.P.; Tildesley, D.J.; Banavar, J.R. Computer Simulation of Liquids. Phys. Today
**1989**, 42, 105–106. [Google Scholar] [CrossRef] - Doi, M.; Edwards, S.F. The Theory of Polymer Dynamics; Claredon: Oxford, UK, 1986. [Google Scholar]
- Karatasos, K. Self-Association and Complexation of the Anti-Cancer Drug Doxorubicin with PEGylated Hyperbranched Polyesters in an Aqueous Environment. J. Phys. Chem. B
**2013**, 117, 2564–2575. [Google Scholar] [CrossRef] [PubMed] - Karatrantos, A.V.; Clarke, N.; Kröger, M. Modeling of Polymer Structure and Conformations in Polymer Nanocomposites from Atomistic to Mesoscale: A Review. Polym. Rev.
**2016**, 56, 385–428. [Google Scholar] [CrossRef] - Harmandaris, V.; Angelopoulou, D.; Mavrantzas, V.G.; Theodorou, D.N. Atomistic molecular dynamics simulation of diffusion in binary liquid n-alkane mixtures. J. Chem. Phys.
**2002**, 116, 7656–7665. [Google Scholar] [CrossRef] - Milano, G.; Santangelo, G.; Ragone, F.; Cavallo, L.; Di Matteo, A. Gold Nanoparticle/Polymer Interfaces: All Atom Structures from Molecular Dynamics Simulations. J. Phys. Chem. C
**2011**, 115, 15154–15163. [Google Scholar] [CrossRef] - Rissanou, A.N.; Papananou, H.; Petrakis, V.S.; Doxastakis, M.; Andrikopoulos, K.S.; Voyiatzis, G.A.; Chrissopoulou, K.; Harmandaris, V.; Anastasiadis, S.H. Structural and Conformational Properties of Poly(ethylene oxide)/Silica Nanocomposites: Effect of Confinement. Macromolecules
**2017**, 50, 6273–6284. [Google Scholar] [CrossRef] - Fotiadou, S.; Karageorgaki, C.; Chrissopoulou, K.; Karatasos, K.; Tanis, I.; Tragoudaras, D.; Frick, B.; Anastasiadis, S.H. Structure and Dynamics of Hyperbranched Polymer/Layered Silicate Nanocomposites. Macromolecules
**2013**, 46, 2842–2855. [Google Scholar] [CrossRef] - Voyiatzis, E.; Rahimi, M.; Müller-Plathe, F.; Böhm, M.C. How Thick Is the Polymer Interphase in Nanocomposites? Probing It by Local Stress Anisotropy and Gas Solubility. Macromolecules
**2014**, 47, 7878–7889. [Google Scholar] [CrossRef] - Binder, K. Monte Carlo and Molecular Dynamics Simulations in Polymer Science; Oxford University Press: New York, NY, USA, 1995. [Google Scholar]
- Vogiatzis, G.G.; Theodorou, D.N. Structure of Polymer Layers Grafted to Nanoparticles in Silica–Polystyrene Nanocomposites. Macromolecules
**2013**, 46, 4670–4683. [Google Scholar] [CrossRef] [Green Version] - Tsourtou, F.D.; Alexiadis, O.; Mavrantzas, V.G.; Kolonias, V.; Housos, E. Atomistic Monte Carlo and molecular dynamics simulation of the bulk phase self-assembly of semifluorinated alkanes. Chem. Eng. Sci.
**2015**, 121, 32–50. [Google Scholar] [CrossRef] - Ginzburg, V.V. Polymer-Grafted Nanoparticles in Polymer Melts: Modeling Using the Combined SCFT–DFT Approach. Macromolecules
**2013**, 46, 9798–9805. [Google Scholar] [CrossRef] - Posel, Z.; Posocco, P.; Lísal, M.; Fermeglia, M.; Pricl, S. Highly grafted polystyrene/polyvinylpyridine polymer gold nanoparticles in a good solvent: Effects of chain length and composition. Soft Matter
**2016**, 12, 3600–3611. [Google Scholar] [CrossRef] - Lin, J.; Zhang, H.; Morovati, V.; Dargazany, R. PEGylation on mixed monolayer gold nanoparticles: Effect of grafting density, chain length, and surface curvature. J. Colloid Interface Sci.
**2017**, 504, 325–333. [Google Scholar] [CrossRef] - Hagita, K.; Morita, H.; Doi, M.; Takano, H. Coarse-Grained Molecular Dynamics Simulation of Filled Polymer Nanocomposites under Uniaxial Elongation. Macromolecules
**2016**, 49, 1972–1983. [Google Scholar] [CrossRef] [Green Version] - Patra, T.K.; Singh, J.K. Coarse-grain molecular dynamics simulations of nanoparticle-polymer melt: Dispersion vs. agglomeration. J. Chem. Phys.
**2013**, 138, 144901. [Google Scholar] [CrossRef] [PubMed] - Quan, X.; Peng, C.; Dong, J.; Zhou, J. Structural properties of polymer-brush-grafted gold nanoparticles at the oil–water interface: Insights from coarse-grained simulations. Soft Matter
**2016**, 12, 3352–3359. [Google Scholar] [CrossRef] - Matsuda, T.; Smith, G.D.; Winkler, R.G.; Yoon, D.Y. Stochastic Dynamics Simulations of n-Alkane Melts Confined between Solid Surfaces: Influence of Surface Properties and Comparison with Scheutjens-Fleer Theory. Macromolecules
**1995**, 28, 165–173. [Google Scholar] [CrossRef] - Johnston, K.; Harmandaris, V. Hierarchical simulations of hybrid polymer—Solid materials. Soft Matter
**2013**, 9, 6696–6710. [Google Scholar] [CrossRef] [Green Version] - Johnston, K.; Harmandaris, V. Hierarchical Multiscale Modeling of Polymer—Solid Interfaces: Atomistic to Coarse-Grained Description and Structural and Conformational Properties of Polystyrene—Gold Systems. Macromolecules
**2013**, 46, 5741–5750. [Google Scholar] [CrossRef] [Green Version] - Priestley, R.D.; Ellison, C.J.; Broadbelt, L.J.; Torkelson, J.M. Structural Relaxation of Polymer Glasses at Surfaces, Interfaces, and In Between. Science
**2005**, 309, 456–459. [Google Scholar] [CrossRef] [PubMed] - Harmandaris, V.A.; Daoulas, A.K.C.; Mavrantzas, V.G. Molecular Dynamics Simulation of a Polymer Melt/Solid Interface: Local Dynamics and Chain Mobility in a Thin Film of Polyethylene Melt Adsorbed on Graphite. Macromolecules
**2005**, 38, 5796–5809. [Google Scholar] [CrossRef] - Daoulas, K.C.; Harmandaris, V.A.; Mavrantzas, V.G. Detailed Atomistic Simulation of a Polymer Melt/Solid Interface: Structure, Density, and Conformation of a Thin Film of Polyethylene Melt Adsorbed on Graphite. Macromolecules
**2005**, 38, 5780–5795. [Google Scholar] [CrossRef] - Anastasiadis, S.H.; Karatasos, K.; Vlachos, G.; Manias, E.; Giannelis, E.P. Nanoscopic-Confinement Effects on Local Dynamics. Phys. Rev. Lett.
**2000**, 84, 915–918. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Johnson, K.; Harmandaris, V. Properties of short polystyrene chains confined between two gold surfaces through a combined density functional theory and classical molecular dynamics approach. Soft Matter
**2012**, 8, 6320–6332. [Google Scholar] [CrossRef] [Green Version] - Mischler, C.; Baschnagel, J.; Dasgupta, S.; Binder, K. Structure and dynamics of thin polymer films: A case study with the bond-fluctuation model. Polymers
**2002**, 43, 467–476. [Google Scholar] [CrossRef] - Aoyagi, T.; Takimoto, J.-I.; Doi, M. Molecular dynamics study of polymer melt confined between walls. J. Chem. Phys.
**2001**, 115, 552–559. [Google Scholar] [CrossRef] - Rissanou, N.; Power, A.; Harmandaris, V. Structural and Dynamical Properties of Polyethylene/Graphene Nanocomposites through Molecular Dynamics Simulations. Polymers
**2015**, 7, 390–417. [Google Scholar] [CrossRef] [Green Version] - Hore, M.J.A.; Korley, L.T.J.; Kumar, S.K. Polymer-Grafted Nanoparticles. J. Appl. Phys.
**2020**, 128, 030401. [Google Scholar] [CrossRef] - Ge, T.; Grest, G.S.; Rubinstein, M. Nanorheology of Entangled Polymer Melts. Phys. Rev. Lett.
**2018**, 120, 057801. [Google Scholar] [CrossRef] [Green Version] - Peters, B.L.; Salerno, K.M.; Agrawal, A.; Perahia, D.; Grest, G.S. Coarse-Grained Modeling of Polyethylene Melts: Effect on Dynamics. J. Chem. Theory Comput.
**2017**, 13, 2890–2896. [Google Scholar] [CrossRef] - Modica, K.J.; Martin, T.B.; Jayaraman, A. Effect of Polymer Architecture on the Structure and Interactions of Polymer Grafted Particles: Theory and Simulations. Macromolecules
**2017**, 50, 4854–4866. [Google Scholar] [CrossRef] - Martin, T.B.; Jayaraman, A. Using Theory and Simulations to Calculate Effective Interactions in Polymer Nanocomposites with Polymer-Grafted Nanoparticles. Macromolecules
**2016**, 49, 9684–9692. [Google Scholar] [CrossRef] - Ndoro, T.V.M.; Böhm, M.C.; Müller-Plathe, F. Interface and Interphase Dynamics of Polystyrene Chains near Grafted and Ungrafted Silica Nanoparticles. Macromolecules
**2011**, 45, 171–179. [Google Scholar] [CrossRef] - Sgouros, A.P.; Theodorou, D.N. Atomistic simulations of long-chain polyethylene melts flowing past gold surfaces: Structure and wall-slip. Mol. Phys.
**2020**, 118, e1706775. [Google Scholar] [CrossRef] - Jabbarzadeh, A.; Atkinson, J.; Tanner, R. Nanorheology of molecularly thin films of n-hexadecane in Couette shear flow by molecular dynamics simulation. J. NonNewtonian Fluid Mech.
**1998**, 77, 53–78. [Google Scholar] [CrossRef] - Berro, H.; Fillot, N.; Vergne, P.; Tokumasu, T.; Ohara, T.; Kikugawa, G. Energy dissipation in non-isothermal molecular dynamics simulations of confined liquids under shear. J. Chem. Phys.
**2011**, 135, 134708. [Google Scholar] [CrossRef] - Bright, K.; Malpass, B.W.; Packham, D.E. Adhesion of Polyethylene to Metals. Nat. Cell Biol.
**1969**, 223, 1360–1361. [Google Scholar] [CrossRef] - Suresh, B.; Maruthamuthu, S.; Kannan, M.; Chandramohan, A. Mechanical and surface properties of low-density polyethylene film modified by photo-oxidation. Polym. J.
**2011**, 43, 398–406. [Google Scholar] [CrossRef] [Green Version] - Song, H.; Li, B.; Lin, Q.-B.; Wu, H.-J.; Chen, Y. Migration of silver from nanosilver–polyethylene composite packaging into food simulants. Food Addit. Contam. Part A
**2011**, 28, 1–5. [Google Scholar] [CrossRef] [PubMed] - Rissanou, A.; Harmandaris, V. Dynamics of Polymer/Graphene Interfacial Systems. Soft Matter
**2014**, 10, 2876–2888. [Google Scholar] [CrossRef] [Green Version] - Hautman, J.; Klein, M.L. Simulation of a monolayer of alkyl thiol chains. J. Chem. Phys.
**1989**, 91, 4994–5001. [Google Scholar] [CrossRef] - Barmparis, G.D.; Honkala, K.; Remediakis, I.N. Thiolate adsorption on Au(hkl) and equilibrium shape of large thiolate-covered gold nanoparticles. J. Chem. Phys.
**2013**, 138, 64702. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Barmparis, G.D.; Remediakis, I.N. Dependence on CO adsorption of the shapes of multifaceted gold nanoparticles: A density functional theory. Phys. Rev. B
**2012**, 86. [Google Scholar] [CrossRef] [Green Version] - Rissanou, A.N.; Harmandaris, V. Structural and Dynamical Properties of Polystyrene Thin Films Supported by Multiple Graphene Layers. Macromolecules
**2015**, 48, 2761–2772. [Google Scholar] [CrossRef] - Uz, M.; Bulmus, V.; Altinkaya, S.A. Effect of PEG Grafting Density and Hydrodynamic Volume on Gold Nanoparticle–Cell Interactions: An Investigation on Cell Cycle, Apoptosis, and DNA Damage. Langmuir
**2016**, 32, 5997–6009. [Google Scholar] [CrossRef] [Green Version] - Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys.
**1995**, 117, 1–19. [Google Scholar] [CrossRef] [Green Version] - Alexiadis, O.; Harmandaris, V.; Mavrantzas, V.G.; Site, L.D. Atomistic Simulation of Alkanethiol Self-Assembled Monolayers on Different Metal Surfaces via a Quantum, First-Principles Parametrization of the Sulfur−Metal Interaction. J. Phys. Chem. C
**2007**, 111, 6380–6391. [Google Scholar] [CrossRef] - Barmparis, G.D.; Lodziana, Z.; Lopez, N.; Remediakis, I.N. Nanoparticle shapes by using Wulff constructions and first-principles calculations. Beilstein J. Nanotechnol.
**2015**, 6, 361–368. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Billinge, S.J.L.; Levin, I. The Problem with Determining Atomic Structure at the Nanoscale. Science
**2007**, 316, 561–565. [Google Scholar] [CrossRef] [Green Version] - Hadjisavvas, G.; Remediakis, I.N.; Kelires, P.C. Shape and faceting of Si nanocrystals embedded ina−SiO2: A Monte Carlo study. Phys. Rev. B
**2006**, 74, 165419. [Google Scholar] [CrossRef] [Green Version] - Herring, C. Some Theorems on the Free Energies of Crystal Surfaces. Phys. Rev.
**1951**, 82, 87–93. [Google Scholar] [CrossRef] - Vilé, G.; Baudouin, D.; Remediakis, I.N.; Copéret, C.; López, N.; Pérez-Ramírez, J. Silver Nanoparticles for Olefin Production: New Insights into the Mechanistic Description of Propyne Hydrogenation. ChemCatChem
**2013**, 5, 3750–3759. [Google Scholar] [CrossRef] - Li, Q.; Rellán-Piñeiro, M.; Almora-Barrios, N.; Garcia-Ratés, M.; Remediakis, I.N.; López, N. Shape control in concave metal nanoparticles by etching. Nanoscale
**2017**, 9, 13089–13094. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pearson, D.S.; Strate, G.V.; Von Meerwall, E.; Schilling, F.C. Viscosity and self-diffusion coefficient of linear polyethylene. Macromolecules
**1987**, 20, 1133–1141. [Google Scholar] [CrossRef] - Turzi, S.S. On the Cartesian definition of orientational order parameters. J. Math. Phys.
**2011**, 52, 053517. [Google Scholar] [CrossRef] - Sgouros, A.P.; Vogiatzis, G.G.; Megariotis, G.; Tzoumanekas, C.; Theodorou, D.N. Multiscale Simulations of Graphite-Capped Polyethylene Melts: Brownian Dynamics/Kinetic Monte Carlo Compared to Atomistic Calculations and Experiment. Macromolecules
**2019**, 52, 7503–7523. [Google Scholar] [CrossRef] - Gulde, M.; Rissanou, A.N.; Harmandaris, V.; Müller, M.; Schäfer, S.; Ropers, C. Dynamics and Structure of Monolayer Polymer Crystallites on Graphene. Nano Lett.
**2016**, 16, 6994–7000. [Google Scholar] [CrossRef] - Flory, P.J.; Volkenstein, M. Statistical mechanics of chain molecules. Biopolymers
**1969**, 8, 699–700. [Google Scholar] [CrossRef] - Williams, G.; Watts, D.C. Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Trans. Faraday Soc.
**1970**, 66, 80–85. [Google Scholar] [CrossRef] - Harmandaris, V.A.; Mavrantzas, V.G.; Theodorou, D.N. Atomistic Molecular Dynamics Simulation of Polydisperse Linear Polyethylene Melts. Macromolecules
**1998**, 31, 7934–7943. [Google Scholar] [CrossRef] - Harmandaris, V.A.; Mavrantzas, V.G.; Theodorou, D.N.; Kröger, M.; Ramírez, J.; Öttinger, H.C.; Vlassopoulos, D. Crossover from the Rouse to the Entangled Polymer Melt Regime: Signals from Long, Detailed Atomistic Molecular Dynamics Simulations, Supported by Rheological Experiments. Macromolecules
**2003**, 36, 1376–1387. [Google Scholar] [CrossRef] - Paul, W.; Smith, G.D.; Yoon, D.Y. Static and Dynamic Properties of an-C100H202Melt from Molecular Dynamics Simulations. Macromolecules
**1997**, 30, 7772–7780. [Google Scholar] [CrossRef] - Smith, G.D.; Bedrov, D. Dispersing Nanoparticles in a Polymer Matrix: Are Long, Dense Polymer Tethers Really Necessary? Langmuir
**2009**, 25, 11239–11243. [Google Scholar] [CrossRef] [PubMed]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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