Local Dielectric Property Detection of the Interface between Nanoparticle and Polymer in Nanocomposite Dielectrics

The interface between nanoparticles and polymer matrix is considered to have an important effect on the properties of nanocomposites. In this experimental study, electrostatic force microscopy (EFM) is used to study the local dielectric property of the interface of low density polyethylene (LDPE)/TiO2 nanocomposites at nanometer scale. The results show that the addition of TiO2 nanoparticles leads to a decrease in local permittivity. We then carry out the finite element simulation and confirm that the decrease of local permittivity is related to the effect of interface. According to the results, we propose several models and validate the dielectric effect and range effect of interface. Through the analysis of DSC and solid-state NMR results, we find TiO2 nanoparticles can suppress the mobility of local chain segments in the interface, which influences the dipolar polarization of chain segments in the interface and eventually results in a decrease in local permittivity. It is believed the results would provide important hint to the research of the interface in future research.

Scientific RepoRts | 6:38978 | DOI: 10.1038/srep38978 phase. In this study, the 2ω phase shift signal Δ φ(2ω) is detected to avoid the impact of the work function difference between the probe and sample (Supplementary Note 2) and obtain the electrostatic force gradients 13,14 , which is related to the capacitance between the probe and the sample. Figure 1c shows the TEM image of LDPE/ TiO 2 nanocomposite and we find the diameter of the TiO 2 nanoparticle is about 100 nm. Figure 1d is the topography of test area and the average thickness is about 117 nm, which indicates nanoparticles will not be stacked together in the test area.
The results of local dielectric detection are shown in Fig. 2. Figure 2a and c show some bumps marked with red circles in the topography. The diameters of these bumps are consistent with TiO 2 nanoparticles and they just correspond to the areas with small |Δ φ(2ω)| shown in Fig. 2b and d. As similar bumps and the change of |Δ φ(2ω)| are not found in pure polyethylene, it is validated that these bumps are actually nanoparticles wrapped in polyethylene matrix. At the same time, we find |Δ φ(2ω)| of these bump is smaller than polyethylene matrix. Some other interesting conclusions can be drawn from Fig. 2e and f, |Δ φ(2ω)| signal of the special bump structure, marked with magenta circle on the top, is much stronger than that of polyethylene matrix. Because the probe scans at a lift height above the surface of sample in the second scan and the |Δ φ(2ω)| signal is not influenced by the topography, we suppose that the change in |Δ φ(2ω)| signal is caused by the change in dielectric properties of the materials. In order to confirm the speculation, we use the peak force tapping mode in the first scan and obtain the DMT modulus of the sample. After analysis (Supplementary Note 3, Fig. S4), we confirm the bump structure marked with magenta circle represents an "exposed" nanoparticle with "broken" wrapping layer, which may be caused by the process of ultrathin sections preparation. The exposed nanoparticle leads to the strong |Δ φ(2ω)| signal. Figure 2g and f reveal a special case of the "exposed" nanoparticle. The area, marked with blue circle on the lower left, also corresponds to strong |Δ φ(2ω)| signal. However, no obvious bump structure can be observed in topography in Fig. 2g. According to the analyses above, we suppose it corresponds to the case that nanoparticle is "just" exposed and no obvious bump structure is formed. Based on the analysis above, we summarize four cases that occur in the measurement, as shown in Fig. 2i,j,k and l. For convenience, they are named "matrix" (pure polyethylene without nanoparticle), "bump" (a complete bump with a nanoparticle wrapped in), "exposed bump" (a bump structure formed by an exposed nanoparticle) and "exposed area" (a "just exposed" nanoparticle without bump structure), respectively.
The electric field induces a polarization in the sample, and the electric potential difference between them can be expressed as where Δ Φ represents the work function difference between the probe and the sample. Without considering the surface charge, the electrostatic force can be written as 16 where C is the capacitance between the probe and the substrate. Because the van der Waals force is a kind of short-range force, while the electrostatic force is a kind of long-range force, when the probe is lifted, van der Waals force decreases rapidly 15,17 , the interaction force between the probe and sample is mainly the electrostatic force. The vibration state of the probe will be affected by interaction force, and the 2ω phase shift can be expressed as where Q and k are the quality factor and the elastic coefficient of the probe cantilever, respectively. If we keep V AC constant in the scanning process, |Δ φ(2ω)|is directly proportional to d 2 C/dz 2 , which is closely related to the permittivity of the sample. A well-accepted model of the probe/sample capacitance can be written as 18,19  (i,j,k and l) are four typical cases: "matrix", "bump", "exposed bump" and "exposed area".
Scientific RepoRts | 6:38978 | DOI: 10.1038/srep38978 where ε 0 is the permittivity of vacuum, R and θ 0 are the tip apex radius and conical tip angle of the probe, respectively, h and ε r are the local thickness and local relative permittivity of the sample. Because of the relationship between the 2ω signal and the permittivity, 2ω electrostatic force signal is also called dielectric force 20 . According to the analysis, a rough calculation is conducted to calculate relative permittivity by using EFM results, we choose several points in each typical area in Fig. 2e and f and obtain topography and |Δ φ(2ω)| data. The calculation results of average permittivity of "matrix", "bump" and "exposed bump" are 2.250, 1.944 and 2.546, respectively.
TiO 2 nanoparticle has a much larger permittivity than polyethylene. If the interface is not considered, the permittivity of bump, influenced by nanoparticle wrapped in polyethylene, should be larger than that of polyethylene matrix. However, the experiment and calculation results demonstrate that the permittivity of bump is actually lower. So we guess it is the effect of interface, which leads to the decrease of the permittivity.

Simulation of Local Dielectric Property.
In order to validate the speculation, we use finite element method to simulate several situations in the experiment. At the beginning, the interface is not considered. As "exposed area" can be seen as a special case of "exposed bump" (Supplementary Note 4, Figs S6 and S7), we focus on other three cases, including "matrix", "bump" and "exposed bump", and design models to carry out simulation, as shown in Fig. 3a,b and c. Since the actual vibration of the probe cannot be simulated, we adopt the method of altering the lift height of probe to calculate electrostatic force in different lift height, and electrostatic force gradient can be obtained from numerical differential calculation. As the phase shift signal |Δ φ(2ω)| is proportional to the electrostatic force gradient signal dF(2ω)dz as previously analyzed (Supplementary Note 2), we can use the value of dF(2ω)dz to represent |Δ φ(2ω)| in different cases.
The results of simulation are exhibited in Fig. 3d and e. The curves of electrostatic force and electrostatic force gradient decrease with the increase of the lift height. With a fixed lift height, the electrostatic force gradient of "exposed bump" is significantly larger than that of other two cases, which is consistent with experimental results. However, the electrostatic force gradient in "bump" is larger than "matrix", which is not consistent with experimental results.
Since the simulation results are inconsistent with experiment results without considering the interface, we guess that the interface may result in a decrease of the local permittivity. We introduce a layer of interface with low permittivity outside the nanoparticle and revise the model, as shown in Fig. 3f,g and 3h. Figure 3i and j reveal that with considering the interface, the electrostatic force gradient of "matrix" is larger than that of "bump", which is consistent with experimental results. In fact, the interface is usually regarded as a layer which has different microstructure from matrix. As a result, under some conditions, this special layer can be observed via TEM image, as shown in Fig. 4a and b, which may serve as direct evidence of the existence of the interface. are the local finite element models corresponding to three cases without considering the interface: "matrix", "bump" and "exposed bump", respectively. (d and e) are the simulation results of three models without interface. (f,g and h) are the local finite element models corresponding to three cases with interface: "matrix", "bump" and "exposed bump". (i and h) are the simulation results of three models with interface.
Since the |Δ φ(2ω)| signal is closely related to the capacitance between the probe and substrate, we analyze the capacitance structures of the models. The capacitance structures of "matrix", "bump" and "exposed bump" are exhibited in Fig. 4c,d and e. The total capacitance measured by the probe can be decomposed into several series and parallel-connected capacitance components. It is obvious that three models have three different types of capacitance structures.
From the perspective of the capacitance structure, we can easily draw the conclusion that, as for the complete interface in "bump", its relative permittivity and thickness will have significant influence on the dielectric response (Supplementary Note 4, Figs S8 and S9). As for the "incomplete" interface in "exposed bump", it seems that the completeness of the interface is the key factor for the interface effect which results in the discrepancy between the experimental and simulated results of "bump" and "exposed bump". A new model named "broken interface" has been designed to validate the speculation, as shown in Fig. 4f. The model represents a case that the interface has been partially removed while the nanoparticles has not been exposed. The completeness of the interface in "broken interface" is between "bump" and "exposed bump", if the effect of interface is related to its completeness, the dielectric response of "broken interface" should be between "bump" and "exposed bump" as well. The simulation results, shown in Fig. 4g and h, reveal that the electrostatic force gradient of "broken interface" is between "bump" and "exposed bump". In addition, compared with "bump", the capacitance components of "broken interface" is more similar to "exposed bump" (both have four series and parallel-connected capacitance components), so the electrostatic force gradient of "broken interface" is also larger than "matrix".
Considering the area around exposed area of the nanoparticle, although the interface has been partially removed during the process of ultrathin sections while the nanoparticles has not been exposed, forming a similar "broken interface" structure. Experimental results also reveal that the |Δ φ(2ω)| signal of the "broken interface" area is stronger than matrix (Supplementary Note 3, Fig. S4), which may serve as indirect evidence of the existence of the interface. In addition, it can also be inferred from the results that the interface effect is affected by its completeness, or the range, that is, "broken" interface may not work as well as "complete" interface. The conclusions above are summarized as the range effect of interface.

Microscopic Mechanism of Dielectric Effect of Interface.
In electromagnetics, the external electric field applied to dielectric materials will lead to polarization, which will form induced electric field and weaken external electric field. The permittivity of dielectric material is the ratio of the external electric field and actual internal electric field. That is, the permittivity is related to the polarization mechanism of the material. In the experiment, the polarization mechanism of TiO 2 nanoparticle is ionic polarization while the polarization mechanism of polyethylene matrix and the interface is dipole polarization. Dipolar polarization is closely related to the (c,d,e and f) are the capacitance structures of "matrix", "bump", "exposed bump" and "broken interface". (g and h) are the simulation results of four models. mobility of chain segments 21 , if the chain segments are bound, the dipolar polarization will be influenced and the permittivity decreases.
To study the effect of TiO 2 nanoparticles on the mobility of chain segments of LDPE, the spherulite microstructure of LDPE and nanocomposites are observed and the differential scanning calorimetry (DSC) and 1 H solid-state nuclear magnetic resonance (SSNMR) are conducted, the results are exhibited in Fig. 5.
The morphology of the etched cross sections of pure LDPE and nanocomposites are shown in Fig. 5a,b and c, the black holes represent the original location of TiO 2 nanoparticles, which were removed during the etching process. Figure 5a and b show that LDPE has well-defined spherulites with the average diameter of 8 μ m. With the addition of TiO 2 nanoparticles which act as the heterogeneous nucleating agents, the diameter of spherulites decreases to 3-4 μ m and their number increases. It is easy to draw a conclusion that nanoparticles can affect the crystallization of the polyethylene matrix, reduce the proportion of crystalline region and increase the proportion of interphase region between crystalline region and non-crystalline region 22 .
The DSC melting curves of the LDPE and LDPE/TiO 2 samples with different nanoparticle loading are shown in Fig. 5d. Table 1 summarizes the melting peak temperature T m , melting enthalpies Δ H m , crystallinity X c and crystal thickness L c of two samples, among them L c is calculated by using Thomson-Gibbs equation 23,24 : where σ (93 mJ/m −2 ) is the fold surface free energy, ∆h f 0 (293 J/g −1 ) is the melting enthalpies of 100% crystal-core polyethylene and T m 0 (410 K) is its equilibrium melting point, ρ c (1 g/cm 3 ) is the density of crystal polyethylene. It is obvious that the melting peak temperature increases with the increase of nanoparticles, indicates that TiO 2 nanoparticles act as the heterogeneous nucleating agents, increase crystallization temperature and accelerate the formation of crystal nucleus 25,26 . However, DSC crystallinity decreases with the increase of nanoparticles, which means both of them can suppress the crystallization of polyethylene. The reason for the decrease of crystallinity  is likely to be the absorption of nanoparticles on polyethylene chain segments and the space steric effect of nanoparticles, meanwhile, the bound chain segments make it difficult to crystallize, as a result, large spherulites are almost impossible to be formed, just as shown in SEM images. In addition, the crystal density may decrease as the crystal thickness increases and the crystallinity decreases. The 1 H wide-line solid-state NMR spectra and fitting results of LDPE is exhibited in Fig. 5e. The analysis of SSNMR spectrum is based on the extent of constrained molecular motion in different polymer domains 27,28 . The 1 H wide-line spectrum can be decomposed into three components by fitting the spectrum to the sum of a Gaussian function, a Lorentzian function and a combined Gaussian and Lorentzian function 28 , representing the rigid phase, the amorphous phase and the intermediate phase, respectively (Supplementary Note 5, Table S3). The phase composition can be obtained via calculating the proportion of each spectrum integration, as shown in Table 2.
NMR rigid region proportion is significantly higher than DSC crystallinity. We know that 1 H SSNMR test is based on the mobility of molecular chain segments while DSC is based on the melting enthalpies of crystalline regions. Some chain segments near nanoparticles and structured chain segments of crystalline phase do not form lattice so they cannot contribute to the melting enthalpies of crystalline region, however, their motion are hindered with the effect of nanoparticles and structured chain segments, as a result, they behave like chain segments of crystalline phase and contribute to the proportion of rigid phase.
The result of Δ X = X rigid − X c reveals the existence and change of bound chain segments in LDPE and its nanocomposites. In pure LDPE, Δ X is completely contributed by bound chain segments near crystalline phase, which are divided to non-crystalline phase in DSC experiment. After the addition of nanoparticles, Δ X is mainly contributed by bound chain segments around nanoparticles. The increasing of Δ X means that the quantity of bound chain segments increases with the increment of nanoparticles.
NMR rigid phase proportion decreases after the addition of TiO 2 nanoparticles, compared with pure LDPE. This is mainly due to the decrease in DSC crystallinity, which contribute to the NMR rigid phase proportion. In contrast, the amorphous phase proportion increases as nanoparticles affect the crystallization process, increase the number of spherulites and reduce their size. However, with the increment of nanoparticle loading, the bound effect of nanoparticles makes more chain segments of polyethylene transfer from amorphous phase to rigid phase, so the proportion of rigid phase increases and the proportion of amorphous phase decreases.
We can also easily draw some conclusions via half-peak width Δ υ H of each phase. Δ υ H is inversely proportional to the apparent spin-spin relaxation time of proton T 2 * , which is an important parameters related to the molecular motion. The increase of half-peak width of rigid, intermediate and amorphous phase is found with the increment of TiO 2 nanoparticle loading, suggesting that T 2 * decreases and the mobility of the chain segments is more hindered 27,28 , which is also consistent with previous analysis.
The DSC and NMR results prove that TiO 2 nanoparticles can suppress the mobility of local chain segments in the interface [29][30][31] , the reason may be the TiO 2 nanoparticles form hydrogen bonds with polyethylene and coupling agent molecules, the hydrogen bond has strong attractive force, which will hinder the mobility of local chain segments 32 . As a result, the bound chain segments surrounding the nanoparticle form the interface and influence the local dipolar polarization, eventually the permittivity of the interface decreases (Supplementary Note 5, Table S4).

Conclusions
In summary, we report an experimental measurement of the local dielectric property detection of LDPE/TiO 2 nanocomposites. We design a series of finite element models and carry out simulation. The experimental and simulated results validate that the interface is the key factor which causes the decrease of local permittivity. The effect is named the "dielectric effect" of interface. Meanwhile, the interface needs a sufficient range to play a role, when the interface reduces, the dielectric effect is weaken as well. The conclusion above is summarized as the range effect of interface. Further researches show that interface has different microstructure. With the influence of TiO 2 nanoparticles, the mobility of chain segments in the interface is suppressed, which influences the dipole polarization and eventually lead to the decrease in local permittivity. The experiment develops an effective method for investigating local dielectric properties of polymer nanocomposites and inspire the study on interface in the future.

Method
Materials Preparation. In this study, TiO 2 nanoparticles (anatase crystal forms) were supplied by Aladdin Industrial Corporation. Low density polyethylene (LDPE) pellets were obtained from ExxonMobil, which were additive-free, melt flow 3.5 g/10 min, density 0.924 g/cm3 and melting point 124 °C. The coupling agent, (3-Aminopropyl) triethoxy-silane (code name KH550), was chosen to modify the nanoparticles to reduce   agglomeration. The chemical reaction temperature was 100 °C, lasting 12 hours. With the effect of toluene, polar groups on the surface of nanoparticles, such as hydroxyl, and the coupling agents join together and generate small molecules (Supplementary Note 1, Fig. S1). The modified TiO 2 nanoparticles were blended with LDPE in a HAPRO torque rheometer with 60 ml Roller-cone mixer. The rotor speed was 60 rpm and the mixing time is 10 minutes. Film samples with different thickness were obtained by using compression melding at the temperature of 140 °C, lasting 10 minutes under the pressure of about 15 MPa. After that, the films were cooled to the room temperature under the same pressure. All films (Supplementary Note 1, Table S1) were annealed in the vacuum oven at 90 °C for 12 hours to eliminate the thermal history and internal stress. The FTIR spectra and XRD patterns prove that the preparation of nanocomposites was successful (Supplementary Note 1, Fig. S2). TEM image shows that TiO 2 nanoparticles with an average diameter of about 100 nm have good dispersion in nanocomposites, as shown in Fig. 1c. Local Dielectric Property Detection with EFM. The local dielectric property detection is implemented by a Bruker Dimension Icon Scanning Probe Microscope. The conductive probe is a Pt/Ir coated probe.
The ultrathin sections of LDPE/TiO 2 nanocomposite with the average thickness of about 100 nm are placed on the gold-plated silicon wafer. Several micro-areas are chosen where the local dielectric property detection is carried out (Supplementary Note 3, Table S2).
Finite Element Simulation. The simulation models of local dielectric property detection are established by using finite element software COMSOL (Supplementary Note 4, Fig. S5). The DC (2 V) and AC (amplitude 3 V) voltage was applied to the probe, the frequency of AC voltage was set to a 1 kHz. The electrostatic force was calculated and then decomposed into DC component, ω component and 2ω component. 2ω component of the electrostatic force was selected for further calculation, just corresponding to the principle of measurement.
The model of probe, with the tip apex radius of 20 nm, the conical tip angle of 25°and the length of 12.5 μ m, is built according to the parameters of an actual probe. The thick of sample is 150 nm and the diameter of TiO 2 nanoparticle is 100 nm, which are based on the results of topography scanning and TEM, respectively. The permittivity of TiO 2 nanoparticle and LDPE matrix is set to 80 and 2.25 respectively.
According to the experimental results, three basic models, including "matrix", "bump" and "exposed bump" are constructed. The bump with the height of 5 nm and the diameter of about 50 nm, and the exposed bump with the height of 7 nm and the diameter of about 50 nm are set with reference to the results of topography scanning. The simulation results are shown in Fig. 3d and e.
As the simulation results of basic models are not consistent with EFM results, the interface is introduced. The thickness of interface is set to 20 nm, referring to the classical multi-core model of interface 6 , the permittivity of the interface is set to 1.6, and the simulation results are exhibited in Fig. 3i and j. Effect of Nanoparticles on the Aggregation Structure of Polyethylene. The samples for SEM observation were broken in liquid nitrogen in order to obtain the cross sections. The thickness of samples was about 1 mm. The cross sections were etched at room temperature for 4 hours in a 1% w/v solution of potassium permanganate in 5 parts concentrated sulphuric acid to 2 parts orthophosphoric acid to 1 part water 33 . Then the cross sections were sputter-coated with gold in order to avoid charge accumulation.
The differential scanning calorimetry (DSC) experiment is conducted to study the crystallinity of LDPE and LDPE/TiO 2 samples under nitrogen atmosphere at a heating/cooling rate of 10 K/min between 300 and 430 K.