The effect of nanoparticle softness on the interfacial dynamics of a model polymer nanocomposite

The introduction of soft organic nanoparticles (NPs) into polymer melts has recently expanded the material design space for polymer nanocomposites, compared to traditional nanocomposites that utilize rigid NPs, such as silica, metallic NPs, and other inorganic NPs. Despite advances in the fabrication and characterization of this new class of materials, the effect of NP stiffness on the polymer structure and dynamics has not been systematically investigated. Here, we use molecular dynamics to investigate the segmental dynamics of the polymer interfacial region of isolated NPs of variable stiffness in a polymer matrix. When the NP–polymer interactions are stronger than the polymer–polymer interactions, we find that the slowing of segmental dynamics in the interfacial region is more pronounced for stiff NPs. In contrast, when the NP–polymer interaction strength is smaller than the matrix interaction, the NP stiffness has relatively little impact on the changes in the polymer interfacial dynamics. We also find that the segmental relaxation time τ α of segments in the NP interfacial region changes from values lower than to higher than the bulk material when the NP–polymer interaction strength is increased beyond a “critical” strength, reminiscent of a binding–unbinding transition. Both the NP stiffness and the polymer–surface interaction strength can thus greatly influence the relative segmental relaxation and interfacial mobility in comparison to the bulk material.


INTRODUCTION
The addition of nanofillers to a polymer matrix is a growing trend in material science that allows for tuning the macroscopic properties of polymer-based composites by manipulating their nanoscale structure and composition. 1,2Silica nanoparticles (NPs) are common nanofillers that can improve the mechanical properties of polymer materials, such as Young's modulus and toughness, [3][4][5] and also lead to the emergence of new features, such as reproducing the optical properties of complex biomaterials, such as the chameleon's skin. 6The application potential of silica NP filled polymer composites is limitless, ranging from the pharmaceutical, 7,8 aerospace, 9,10 to automotive industries. 11,12The increased material performance that comes from this widening in the design space of chemical compositions can be anticipated to arise from a modification of interfacial interactions with the polymer matrix, but the origin of these property changes is not completely understood, since changes in polymer dynamics near the NP interfaces are hard to observe experimentally and anticipate theoretically.Molecular simulations offer opportunities to better understand these property changes, since this approach has the requisite spatial and temporal resolution to study interfacial dynamics.Here, we use this approach to study the effect of nanoparticle rigidity on the segmental dynamics in the interfacial region of the composite.Our analysis is restricted to the dilute limit to avoid complications that can arise when the interfacial zones of different particles overlap.
Many previous simulations [13][14][15] and experimental studies [16][17][18][19] have attempted to unravel the molecular mechanisms underlying the performance enhancements sometimes found when adding NPs to polymer matrices, and most of these studies have focused on the addition of stiff, nearly un-deformable NPs in a polymer matrix.The current literature has considered the effects of NP size, 20,21 concentration, [21][22][23] size dispersity, 24 polydispersity, 21 surface roughness, 22 and NP-polymer interaction. 19From the perspective of polymer melt structure, for instance, the presence of NPs with repulsive NP-polymer interaction apparently has little impact on local chain conformations, although the radius of gyration of chains increases somewhat in composites having attractive NPs. 25 This leads to a non-linear density gradient from the NP surface to the neat polymer matrix.In addition to local structural changes upon adding NPs, the segmental dynamics in the polymer matrix clearly change around the NPs, where we also observe, as in previous investigations, that there is no direct correlation between the density gradient and the mobility gradient around the NPs. 26,27In general, a reduced mobility of chain segments near an attractive NP surface is observed. 17However, the spatial extent of the interfacial mobility layer is modest in comparison to the size of a typical NP, extending to a distance of no more than ≈5 nm in amorphous glass-forming polymers. 28Nonetheless, this layer can sometimes exert a large influence on the properties of nanocomposites.
In practice, it is often difficult to disperse the NPs homogeneously in the polymer matrix, and this has led to a growing interest in using organic "soft" NPs, such as single chain polymer NPs, polymer-grafted NPs, or star polymers, where a judicious choice of the polymer topology and NP-polymer interaction can aid the relatively homogeneous dispersion of the NPs. 294][35][36][37] With the addition of soft NPs, the viscosity and the plateau modulus both tend to decrease with increasing NP concentration, accompanied by an intriguing breakdown of the Stokes-Einstein equation relating the rate of diffusion to the fluid viscosity. 32The incorporation of spherical NPs with a radius R ≈ 10 nm has been shown to increase the rate of diffusion of polymer chains (radius of gyration, Rg ≈ 20 nm) in the melt. 33More generally, this type of change is controlled by the relative size of the NPs to the polymer chains. 38However, there are significant complexities and the measurement of segmental dynamics in the interfacial region is inherently difficult. 21,39,40The mechanism behind the effect of soft NPs on the polymer dynamics is particularly poorly understood.
In the present work, we perform coarse-grained molecular dynamics (CG-MD) simulations of a single NP in a polymer matrix, where we tune both the softness of the NP at varying temperature and NP-polymer interaction strength.Slower polymer segmental interfacial dynamics are observed with a strongly attractive NP-polymer interaction, consistent with many prior studies. 26,27e show that the magnitude of this effect can be enhanced by increasing NP stiffness.A crossover is observed for threshold values of the NP stiffness and NP-polymer interaction strengths where the segmental dynamics compared to the pure polymer matrix changes from being faster to slower.This provides insights into the molecular origin of the structural and dynamical changes induced by adding soft NPs to polymer matrices that should be useful in the design of composite materials.Thus, while the density gradient cannot by itself predict the mobility gradient around NPs, changes in the interfacial mobility can signal changes in the interfacial density profile, possibly signaling the occurrence of molecular binding to the polymer matrix.The change in the density profile near the substrate is apparent in the case of polymer films supported on solid substrates. 41However, the observation of this type of density "anomaly," defined by a change in the sign of the derivative of the density near the solid interface, can be obscured in the case of non-spherical particles, and this complication is more pronounced in the case of the very soft particles studied here, which can spontaneously adopt deformed shapes.

Effect of nanoparticle stiffness on mobility interfacial zone
Since our main goal is to quantify the effect on the polymer segmental dynamics in the NP-polymer interfacial region when the stiffness of the nanoparticle is changed, along with other parameters, such as temperature and NP-polymer interaction strength (which are quantities investigated in our previous work 26,27 ), we focus on the limit of isolated NPs where the interfacial layers of different NPs do not interact.In our coarse-grained polymer model, NP stiffness is specified by a stiffness parameter k, defined by a harmonic potential of the bonds tethering the NP beads to their original location (see Fig. 1 and the "Methods" section for details).
We evaluate the self-intermediate scattering function Fs(q, t) and the relaxation time τα as a function of the distance r from the NP surface, as described in the Methods section.Figures 1(a) and 1(b) show the simulation setup, visualizing the segmental relaxation time in the vicinity of the NP for a weakly attractive NP-polymer interaction strength (εNP-P = 0.1) and a strongly attractive NP-polymer interaction strength (εNP-P = 1.5), respectively.Figures 2(a) and 2(b) show the variation of Fs(q, t) approaching the NP surface for weakly and strongly attractive NP-polymer interaction strength at a fixed T and k.3][44] From Fs(q, t), we can quantify the relaxation time τα(r), as described in "Methods" section.Figures 2(c) and 2(d) present the distance r dependence of the relative relaxation time τα(r)/τ far with varying k and T, respectively, where τ far is the value of the relaxation time in the bulk, far away from the NP surface.For an infinitely dilute system, τ far only depends on the temperature T and must correspond to the segmental relaxation time of the bulk material.In our simulations, we observe a relatively small deviation of τ far from the bulk limit estimate that depends on the strength of εNP-P, but not detectably on the NP stiffness parameter k, due to the finite size of the system.These finite size effects have been studied previously to understand the concentration dependence of polymer nanocomposites, since varying the box size changes the effective NP concentration. 14To make our analysis manageable, and to avoid unwarranted assumptions in the description of these finite size effects, we simply define τ far ≡ τα(r = 10).
The interfacial relaxation time can evidently be either much larger or much smaller at different strengths of the NP-polymer interaction, which has been reported in earlier works for hard NPs. 13,27,45,46We also see that τα(r)/τ far increases with increasing k at strong interaction, while k has little impact on the segmental relaxation time when the NP-polymer interaction is weak.Upon cooling, the interfacial relaxation time increases for a weak  2) and adjacent layers are represented in coherent colors.The segmental relaxation near the NP is greatly accelerated for a weakly attractive interaction, while the NP with strongly attractive interaction slows down the dynamics.Relaxation time with (c) increasing k (5, 25, 45, 65, 100, 200, 500) at T = 0.5 and (d) increasing T (0.5, 0.6, 0.7, 0.8) at k = 45.r = 5 corresponds to the NP surface, and distance r = 10 is the neat polymer matrix.The interfacial relaxation time increases with increasing k or decreasing T at strong interaction.For a weak NP-polymer interaction strength, the interfacial polymer segmental relaxation time increases upon cooling and is nearly independent of k.

ARTICLE
scitation.org/journal/jcp3][44] The τα(r)/τ far ratio is always larger than 1 for a "strong" NP-polymer interaction strength (which slows down the dynamics at the interface) and lesser than 1 for a "weak" NP-polymer interaction strength (which accelerates the dynamics at the interface).The deviation between the segmental relaxation time near the interface and far-away polymer matrix generally becomes more pronounced at lower temperatures.In particular, for both weak and strong interactions, the ratio τα(r)/τ far at small r deviates strongly from 1 at low T, but converges to a value near 1 at high T.
An insensitivity of the interfacial mobility layer to the NP-polymer interaction strength is also apparent in the work of Zhang et al. investigating nanocomposites with highly stiff NPs 26,27 and thin films with rigid walls. 47This insensitivity of the mobile interfacial layer thickness to the boundary interaction stiffness and boundary rigidity seems to be robust, but recent work has shown that the mobile interfacial layer thickness near the solid substrate in supported polymer films depends strongly on the polymer topology. 48,49The thickness of the mobile interfacial layer then seems to be predominantly a physical characteristic of the polymer matrix material.

Stiffness dependence of dynamics of the interfacial region
We next discuss how a combination of temperature, NP-polymer interaction, and NP stiffness can influence the interfacial dynamics of the polymer surrounding the NP, both accelerating and slowing down the dynamics.It is already appreciated that varying the interfacial interaction strength can change the interfacial dynamics from faster than the surrounding polymer matrix (weak interfacial interactions) to slower than the polymer matrix (strong interfacial interactions).We show that the point at which this crossover occurs can be modulated by the NP stiffness parameter k.To emphasize this qualitative change in the interfacial mobility gradient, we focus on the relative mobility change in the interfacial layer, defined as the difference in the relaxation time between the innermost layer and the polymer matrix far from the NP, divided by the polymer matrix value.By denoting τα inter as the relaxation time of the innermost layer, this "relative mobility change," δτα = , increases with increasing k, and it has a stronger k dependence for a stronger NP-polymer interaction, as shown in Fig. 3(a).Our observations are evidently qualitatively consistent with the experimental observations of Dadmun et al., 33,35,36 in which faster polymer diffusion was observed with the addition of softer NPs.Direct quantitative comparison with these experiments is not possible because the mobility of the whole chain is not simply related to the polymer segmental dynamics. 28igure 3 shows that δτα can change sign for fixed moderate values of the interaction strength εNP-P = (0.75, 0.5) and a fixed T when the NP stiffness is varied over a large range, while no sign change on δτα is observed when εNP-P is relatively large or small.In Fig. 3(b), we further observe that if the NP stiffness is fixed to a moderate value, k = 45, and εNP-P is varied over a large range, δτα changes sign near εNP-P = 0.5, regardless of T. This crossover in the interfacial dynamics was reported in a previous study of supported thin polymer films and polymer nanocomposites containing rigid NPs, 26,27,43,45 although this phenomenon was not emphasized in these prior works.
The softness dependence of the "crossover energy" εc at which δτα changes sign is similar to the effect of rigidity on the binding transition between polymers in solution. 50,51In Fig. 4(a), we see an increase in the segmental density profile near the NP interface when the pair energy εNP-P is increased.This change in the density profile passing through εc has been observed previously in supported polymer films, 41,44 and the density changes are similar to those expected for a polymer binding transition.Figure 4(b) provides evidence that the nanoparticles deform considerably when they are very soft, allowing the polymer segments to invade the average domain occupied by the NP, much like a polymer interpenetrating other polymers in the melt.This interpenetration phenomenon greatly complicates the interpretation of the spherically averaged density profiles and the observation of the density kink tentatively associated with the binding of the NP to the polymer matrix.Further details on the interfacial density gradient (Figs.S1 and S2) and polymer radius of gyration (Figs.S3  and S4) are discussed in the supplementary material.The NP shape change is also shown in Fig. S1(a).It was also observed that the sign of the Tg shift in thin supported films occurred for values of εNP-P, near where the density "kink" occurred near the supporting substrate.
The variation δτα for the soft NPs has some features that are different from previous observations on supported films where a crossover value of the boundary stiffness parameter kc was observed for fixed values of εNP-P. 44We see that the effect of varying the NP stiffness on δτα is likewise strong for a highly attractive interaction  between the NP and the polymer matrix.The magnitude of δτα is generally positive, while there is virtually no variation of δτα when the attractive interaction between the NP and the matrix is weak and is negative when the stiffness is varied over a large range.This unexpected trend in δτα is attributed to the change in the shape of the NP as its stiffness is varied, which starts closer to the center of the softer NP, because more beads would be much closer to the center.The influence of the polymer-nanoparticle interaction strength on the dynamics of the outer layer of the NP is illustrated in Fig. S5 of the supplementary material.Changes in the segmental density profile near the NP surface and mobility gradient in the interfacial region are clearly more subtle for soft NPs because of the capacity of their interfaces to "crumple" in response to changes in εNP-P.
Based on the preceding discussion, we hypothesize that the crossover in the sign of the interfacial changes in the dynamics and the associated changes in the interfacial segmental density may be directly linked to a binding-unbinding transition between the NP and the polymer matrix. 52,53The density changes near such a transition are much more subtle in polymer melts than in polymer solutions, where the binding transition signals a sharp change in the local density gradient near the boundary, whose location can have an appreciable temperature dependence.Interestingly, the effect of the substrate stiffness on the binding of polymers to surface transitions at low polymer concentration ("polymer adsorption") has apparently never been investigated either experimentally or by simulation before.We infer from recent simulation observations showing a strong effect of molecular rigidity on the strength of molecular binding 50,51 that boundary stiffness should likewise have an appreciable influence on the strength of molecular binding of isolated polymers in solution and polymer melts to substrates.Despite recent efforts to extend the binding-unbinding transition for polymer chains beyond the limits of the dilute regime, 52,53 the problem remains open, and this possibility of a binding transition underlying these changes in the interfacial density and dynamics deserves further study.A precise mapping of the dependence of εc on substrate stiffness, NP size, polymer segmental and topological structure, and temperature is a practically important problem, but this task is beyond the scope of the present work.
Effect of NP stiffness on the Debye-Waller factor, ⟨u 2 ⟩ Along with the polymer segmental dynamics, we track the effect of NP stiffness on the picosecond caging dynamics associated with the fast β-relaxation. 54From the layer-resolved mean square displacement (MSD) of the beads of the polymer (modeling statistical segments of the polymer rather than atoms in our coarse-grained polymer model), we extract the "Debye-Waller parameter" ⟨u 2 ⟩ as the value of the MSD at tcage = 1 or a timescale of the order of 1 ps in laboratory units.This timescale corresponds to the typical order of magnitude of the β-relaxation time τ β in atomic and molecular liquids. 55In qualitative physical terms, ⟨u 2 ⟩ quantifies the average "amplitude" of segmental motion arising from thermal agitation of the particles on a caging timescale.However, it should be noted that the magnitude of ⟨u 2 ⟩ in cooled liquids is heavily weighted by relatively rare "mobile" particles on a ps timescale (a kind of dynamic heterogeneity) so that ⟨u 2 ⟩ is not just a measure of the scale of "cage-rattling" around a mean position, as in crystals at low temperatures. 54Figures 5(a) and 5(b) indicate the layer-resolved mean square displacement of the polymer statistical segments for a relatively weak and strong NP-polymer interaction strength, respectively.With a strong NP-polymer interaction, the mean amplitude of atomic motion near the inner layer (which can be taken as an inverse measure of local stiffness 56 ), is diminished compared to segments far away from the NP boundary.In the weak interaction case, the interfacial dynamics is correspondingly accelerated.As in our discussion above of the relaxation time gradient near the surface of the NPs in Fig. 2, we see that the effect of the width of the gradient on ⟨u 2 ⟩ is remarkably insensitive to both the NP rigidity and the NP-polymer interaction strength, while the magnitude of the change depends on these molecular variables.
4][65] The predictive power of this metric has become invaluable in the energy renormalization coarse-graining scheme developed for glass-forming systems. 66,67The interfacial gradient of ⟨u 2 ⟩ is also related to the variation of activation energies and local stiffness. 49Figures 5(c) and 5(d) show the effect of varying NP stiffness, surface interaction, and temperature on ⟨u 2 ⟩ as a function of the distance away from the center of the NPs.Evidently, the effect of the NP stiffness k is more pronounced when the polymer-surface interaction is strongly attractive, while the temperature effect is noticeable when the polymer-surface interaction is weakly attractive.The amplitude of the motion of the polymer segments in the interfacial region compared to the "bulk" fluid (corresponding to distances far away from the center of the isolated NP) is evidently larger when the NPs are stiffer.This trend is not obvious since we might have expected the structural relaxation time to monotonically increase as the segments become more localized in both the localization model 68 and the model of Leporini et al. 57,69 relating ⟨u 2 ⟩ to the structural relaxation time τα determined from the intermediate scattering function.This counterintuitive trend can be understood from the fact that it is the value of ⟨u 2 ⟩ relative to its value at a reference temperature or the value of ⟨u 2 ⟩ at Tg (or similar reference temperature) that is important.Previous work on metallic glass alloys has shown that ⟨u 2 (T)⟩ at the onset temperature TA for non-Arrhenius relaxation correlates strongly with the fragility of glass-formation 61 and it is natural to expect TA to depend on k.The quantification of this effect requires a systematic study of the relaxation time gradient and ⟨u 2 ⟩ over a large range of T and this task is left for future work.
The difference between the mobility in the interfacial region from the bulk-like region far away from the NP surface generally becomes more pronounced at lower temperatures, although this difference becomes small at a characteristic value of the interaction strength εNP-P between the polymer matrix and the NP where the attractive and repulsive interactions nearly compensate.The interfacial dynamics compared to the bulk changes profoundly at this "critical" value of εNP-P, similar to a binding-unbinding transition.

CONCLUSION
This study investigates how the addition of deformable filler nanoparticles in polymer matrices compares with their hard NP counterparts, since the effect of NP stiffness on the structure and dynamics of polymer matrices has not been investigated from a molecular point of view in connection to glassy segmental dynamics.In particular, we simulate polymer nanocomposite systems with isolated model deformable NPs, and study the impact of NP stiffness, together with the NP-polymer interaction strength and tempera-ture, on the interfacial polymer segmental dynamics.The polymer segmental relaxation becomes larger or smaller for relatively large or small polymer-surface interaction strengths, which we suggest may have its origin in a NP-polymer binding transition. 52,53Increasing NP stiffness magnifies this effect and shifts the location of this crossover.1][72][73][74][75] Above or below the dynamical crossover, the segmental relaxation time can be much larger or smaller than its bulk value and essentially no gradient exists near the crossover point.A small change in the density profile near the surface can be seen above and below the crossover. 26,27With stronger NP-polymer interaction, a densification of monomers at the interface correlates with lower mobility, while an opposite trend is observed with higher stiffness.We attribute this opposite trend to the change in shape of the NP, which is affected by the NP stiffness.Both the NP stiffness and the NP-polymer interaction can help to manipulate the dynamical crossover.The composition and chemical functionality of soft NP surfaces become then tunable parameters to control the interface dynamics and viscoelastic behavior of NP-filled polymer composites.
The picosecond caging dynamics of the polymer have also been tracked.The impact of the NP stiffness k on these dynamics is less pronounced at a weaker attractive interaction, while the effect of temperature is more pronounced.When the NPs are stiffer, the relative change of the picosecond motion compared to that at the far end of the polymer matrix from the NP is amplified with a stiffer NP.These results provide further evidence of general trends in the nanoscale glassy dynamics found before in thin films and in the interfcail regions of rigid nanoparticles, and offer a rational strategy for tuning the macroscopic thermomechanical properties of NP-filled polymer composites.Future studies with more realistic soft nanoparticles and in the regime of high NP-concentration will be important to bridge the gap between the nanoscale dynamics observed here and the emergent properties of the whole composite.

METHODS
In this work, we assumed a dilute dispersion of "soft" NPs in the polymer matrix.Our study of the dilute limit allows us to avoid interaction effects between NPs so that we may focus exclusively on the interfacial zone around the NPs.Following our previous studies, 13,27,46,76,77 we construct the PNC model with a single polyhedral NP under the periodic boundary conditions.Polymer chains are modeled using the Kremer-Grest spring-bead model, 78 with bonded monomers linked via a finitely extensive nonlinear elastic (FENE) potential with R 0 = 1.5 σ and the force constant k b = 30 ε/σ 2 , where σ and ε are the parameters of the Lennard-Jones potential used for the non-bonded monomer-monomer interactions.Each chain has N = 20 monomers with mass m and diameter σ.The idealized NP consists of icosahedral shells using 356 Lennard-Jones (LJ) particles, corresponding to an inscribing sphere with radius of 5.0σ. 46Each particle of the NP is tethered to its ideal equilibrium position by a spring force.We tune the NP stiffness via the spring constant k in a range of 5-1000.All the pairwise interactions in the system are the LJ potential with a cutoff at rC = 2.5σ ⋅ εij between monomers εNP-P and between NP particles εNP-NP being 1ε and 2ε, respectively, while the value between NP particles and monomers εNP-P is in the range of 0.1ε to 1.5ε.The size parameter between NP and monomer is σNP-P = 1σ.
All simulations are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) 79 with standard LJ reduced units, where mass, length, temperature, and time are in units of m, σ, ε/kB, and τLJ = σ √ m/ε, respectively.kB is Boltzmann's constant.For a simple polymer like polystyrene (PS), our system can be loosely mapped to physical units 80 by taking σ = 1 nm, τLJ = 1 ps and ε = 7.7 kJ/mol, leading to the glass transition temperature Tg close to 370 K.All simulations are conducted over a temperature range 0.5 ≤ T ≤ 0.8 above Tg, which is in the range 0.3-0.4 for this model along an isobaric path at low pressure P = 0.1.A small value of pressure is chosen since atmospheric pressure is quite small.Using the mapping of LJ units described by Liu et al. 81 would yield P ≈ 2 MPa.While this is larger than atmospheric pressure, the quantitative difference in our findings between this and P = 0 is small, and the qualitative conclusions are unaffected.We equilibrate systems using the isothermal-isobaric ensemble (NPT ensemble) for at least 3000 τLJ, from which the mean volume V is determined.We carry out data production runs using the volume determined from the equilibration step in the canonical ensemble (NVT ensemble) to avoid complications in the analysis introduced by a fluctuating simulation volume in an NPT ensemble.The equilibration time is extended in cases at low T and high εNP-P, such as, at T = 0.5, εNP-P = 1.5, which is considered as strongly attractive interaction, so that the system is equilibrated for at least 100 times the segmental relaxation time.In the slowest case, the equilibration time needed is 240 000 τLJ.The segmental dynamics are quantified using the self-intermediate scattering function FS(q, t) ≡ 1 N ⟨∑ N j=1 e −iq⋅[r j (t)−r j (0)] ⟩, where q is the scattering vector, rj is the position vector of polymer beads j, and N is the total number of polymer beads.To better describe the time dependence, we fit the simulation data of Fs(q, t) within each shell to a phenomenological relaxation functional form 26 FS(q, t) = (1 − A)e −(t/τ s ) 3/2 + Ae −(t/τ α ) β , where the vibrational relaxation time is assumed to be a constant τs = 0.29 (of the order of 10 −13 s in laboratory units).The characteristic segmental relaxation time τα can also be estimated as the time FS(q 0 , t) = 0.2 ⋅ q 0 is the position of the first peak in the structure factor S(q).The dependence of τ the fitting parameter A of Eq. ( 2) is discussed in Fig. S6 of the supplementary material.To quantify the dynamics gradient from the NP surface to polymer, we divided the outer space into shells with a fixed thickness 0.5 and compute FS within each shell.The polymer beads are sorted into shells based on their location at time t = 0.

SUPPLEMENTARY MATERIAL
The effect of the nanoparticle stiffness on the density profile around the nanoparticle, the spatial variation of the polymer radius of gyration, the effect of varying stiffness parameter k on NP deformation, and the effect on the strength of the α relaxation are discussed in the supplementary material.This material is available free of charge at http://pubs.acs.org.

FIG. 1 .
FIG. 1. Visualization of the gradient of relaxation time τα around the NP at stiffness k = 500 and temperature T = 0.5 for systems having either (a) weakly ε NP-P = 0.1 or (b) strongly ε NP-P = 1.5 attractive interaction, compared to the pure polymer relaxation time τ far .The interfacial polymer dynamics speed up with weak interaction, while they are slowed down with strong attractive interaction.The NP beads are colored in yellow.

FIG. 2 .
FIG. 2.Layer-resolved self-intermediate scattering function Fs(q, t) at temperature T = 0.5 and variable NP stiffness k = 45 for systems having either (a) weakly ε NP-P = 0.1 or (b) strongly ε NP-P = 1.5 attractive interaction.Symbols are the collected data for each layer.Lines are the fit defined by Eq. (2) and adjacent layers are represented in coherent colors.The segmental relaxation near the NP is greatly accelerated for a weakly attractive interaction, while the NP with strongly attractive interaction slows down the dynamics.Relaxation time with (c) increasing k(5, 25, 45, 65, 100, 200, 500) at T = 0.5 and (d) increasing T (0.5, 0.6, 0.7, 0.8) at k = 45.r = 5 corresponds to the NP surface, and distance r = 10 is the neat polymer matrix.The interfacial relaxation time increases with increasing k or decreasing T at strong interaction.For a weak NP-polymer interaction strength, the interfacial polymer segmental relaxation time increases upon cooling and is nearly independent of k.

FIG. 3 .
FIG. 3. Relative mobility change δτα with (a) varying NP stiffness k at T = 0.7 and different ε NP-P and (b) varying ε NP-P at k = 45 and different T.There is a critical value of k at a fixed ε NP-P and a critical value of ε NP-P at a fixed k at which the dynamics at the interface switch from being faster to being slower than the bulk dynamics.Lines are a guide for the eye.

FIG. 4 .
FIG. 4. Density profile for polymer chains with (a) varying ε NP-P at k = 45 and T = 0.7 and (b) varying NP stiffness k at T = 0.7 and ε NP-P = 0.5.r is the distance from the NP center.The icosahedral NP has radius of r = 5, while r = 10 is the neat polymer matrix.

FIG. 5 .
FIG. 5. Layer-resolved dynamics of polymer beads at (a) weak interaction and (b) strong interaction.Symbols are the collected data for each layer.Layers are shown in coherent colors.Radial averaged Debye-Waller factor ⟨u 2 ⟩ for the polymer (c) with varying k at a fixed temperature T = 0.5 and (d) with varying T at a fixed k = 45 where r is the radial distance from the center of the NP and ⟨u 2 ⟩ is the value of mean square displacement at t = 1 = tcage.