Surface Modification Design for Improving the Strength and Water Vapor Permeability of Waterborne Polymer/SiO2 Composites: Molecular Simulation and Experimental Analyses

Polymer-based nanocomposites properties are greatly affected by interfacial interaction. Polyacrylate nanocomposites have been widely studied, but few studies have been conducted on their interface mechanism. Therefore, there was an urgent demand for providing a thorough understanding of the polymethyl acrylate/SiO2 (PMA/SiO2) nanocomposites to obtain the desired macro-performance. In this paper, a methodology, which combined molecular dynamics simulation with experimental researches, was established to expound the effect of the surface structure of SiO2 particles which were treated with KH550, KH560 or KH570 (KH550-SiO2, KH560-SiO2 and KH570-SiO2) on the mechanical characteristic and water vapor permeability of polymethyl acrylate/SiO2 nanocomposites. The polymethyl acrylate/SiO2 nanocomposites were analyzed in binding energy and mean square displacement. The results indicate that PMA/KH570-SiO2 had the highest tensile strength, while PMA/KH550-SiO2 had the highest elongation at break at the same filler content; KH550-SiO2 spheres can significantly improve water vapor permeability of polyacrylate film.


Introduction
Nanoparticles have received significant attention from researchers in the fields of electronics, metallurgy, aerospace, chemical engineering, biology and medicine due to their unique properties [1][2][3][4][5][6][7][8][9][10]. However, on account of the high surface energy of nanoparticles and the fact that they usually do not contain active functional groups, the dispersion of nanoparticles in polymers is very poor, thus leading to weak reinforcing effects [11,12]. A number of studies have shown that most properties of composite materials depend on the nanoparticles dispersion in polymer matrix and their interfacial interaction [13][14][15]. Therefore, there are numerous examples have been proposed for improving the dispersion of nanoparticles in polymer matrix thus improving the interfacial interactions by grafting or surface modified materials on the surface of nanoparticles for functionalization [16][17][18]. Meanwhile, effects of surface structure of nanomaterials on the properties of composites are still the focus of research [19][20][21]. The procedure for preparing SiO 2 nanoparticles modified by KH570 as follows: About 5 mL ethanol solution of KH570 was gradually added to 100 mL SiO 2 nanoparticles ethanol dispersion under a magnetic stirrer. Then, the mixed solution was stirred at room temperature for 72 h. The mixed solution was centrifuged and washed with xylene, ethanol and deionized water several times, then SiO 2 nanoparticles modified by KH570 were attained via drying for 12 h at 60 • C (KH570-SiO 2 ).
The procedure for preparing SiO 2 nanoparticles modified by KH550, which is defined as KH550-SiO 2 (SiO 2 modified by KH560, which is defined as KH560-SiO 2 ) as follows: SiO 2 nanoparticles were ultrasonic dispersed into 100 mL of ethyl alcohol at 25 • C for 30 min, and the pH of the mixed solution dispersion reached 6 with glacial acetic acid. Then 5 mL of KH550 (or KH560) was added into the solution under the stirring at 60 • C for 6 h. The obtained solution was then centrifuged and washed by xylene, ethanol and deionized water for several times, and dried at 60 • C for 6 h to obtain KH550-SiO 2 (or KH560-SiO 2 ) nanoparticles.

Preparation of PMA/Modified-SiO 2 Nanocomposite and its Composite Film
Some modified-SiO 2 (2 wt% of PMA mass) and SDS were ultrasonic dispersed for 10 min at 75 • C. Then KPS and MA were added to the emulsion drop wisely, while the polymerization was conducted at 75 • C for 6 h.
Finally, the PMA/modified-SiO 2 composite emulsion was poured into polytetrafluoroethylene (PTFE) mold and laid on the horizontal surface until dried completely at room temperature to obtain PMA/modified-SiO 2 composite film. PMA/SiO 2 composite film was prepared in the same method.

Characterization and Measurements
The microstructures and morphology of all samples were measured by scanning electron microscope (SEM, S4800, Rigaku) and transmission electron microscope (TEM, Tecnai G2 F20, FEI). The chemical structures of all materials were analyzed by fourier transform infrared spectrum (FT-IR, VECTOR-22, Brucker) and Ultraviolet-visible-near infrared spectrophotometer (Cary 5000, Agilent). The thermal stability of the samples was studied by thermogravimetric analysis (TGA, STA409PC, Netzsch) at the nitrogen atmosphere from room temperature to 600 • C with a heating rate of 5 • C/min. The glass transition process of samples was characterized using a differential scanning calorimeter (DSC, Q5000 IR) The mechanical properties were tested by a servo material multi-functional high and low temperature control testing machine (AI-7000-NGD, Goodtechwill) at a loading rate of 100 mm/min according to QB/T 1331-1998. The water vapor transmission rate (WVP) was tested by a Water vapor transmittance tester (W3/060, Labthink) according to QB/T 1279-2012.

Simulation Methodologies
The reactant molecules were built in the Visualizer module of Material Studio 8.0 software (Accelrys Inc., San Diego, CA, USA). For the MD simulations, the Forcite and Amorphous cell modules of the Materials Studio suite of software were used. All the theoretical calculations were performed using the Condensed-Phase Optimized Molecular Potentials for Atomistic Simulation Studies COMPASS force field [41,42].

Construction of SiO 2 Nanoparticles
The xsd molecular model of SiO 2 is imported from MS software material library. After the unit cell model of silica is obtained, it is geometrically optimized to obtain a lower energy structure. Next, the silica particles with a radius of 1 nm (10 Å) are constructed, and a spherical silica nanoparticle with a surface saturated with unsaturated bonds between Si atoms and O atoms is obtained. Select the broken bond on the Si atom on the surface of the SiO 2 unit cell and combine it with -OH, and combine the broken bond on the surface O atom with the H atom. Increase the reliability, and optimize the structure to obtain a spherical SiO 2 model (Figure 1). Three different modifiers were grafted on the silica surface, and the three modifiers were KH550 (2a), KH560 (2b) and KH570 (2c). The structure of the modified surface was optimized, and the energy converged to 1 × 10 −4 kca1/mol. Figure 2 shows the structure of three modifiers, and Figure 3 shows the surface of modified-SiO2. In this paper, four identical silane coupling agent chains were grafted onto SiO2 sphere, and the grafted microspheres were optimized by the Smart method to optimize the energy to 1 × 10 −4 kca1/mol. In order to search for the optimal structure, the cell is then annealed at 0.1 MPa from the low temperature of 300 K to the upper temperature of 500 K for 200 ps to prevent the system to form being trapped at a local high energy minimum. Subsequently, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K.   Three different modifiers were grafted on the silica surface, and the three modifiers were KH550 (2a), KH560 (2b) and KH570 (2c). The structure of the modified surface was optimized, and the energy converged to 1 × 10 −4 kca1/mol. Figure 2 shows the structure of three modifiers, and Figure 3 shows the surface of modified-SiO 2 . In this paper, four identical silane coupling agent chains were grafted onto SiO 2 sphere, and the grafted microspheres were optimized by the Smart method to optimize the energy to 1 × 10 −4 kca1/mol. In order to search for the optimal structure, the cell is then annealed at 0.1 MPa from the low temperature of 300 K to the upper temperature of 500 K for 200 ps to prevent the system to form being trapped at a local high energy minimum. Subsequently, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K. Three different modifiers were grafted on the silica surface, and the three modifiers were KH550 (2a), KH560 (2b) and KH570 (2c). The structure of the modified surface was optimized, and the energy converged to 1 × 10 −4 kca1/mol. Figure 2 shows the structure of three modifiers, and Figure 3 shows the surface of modified-SiO2. In this paper, four identical silane coupling agent chains were grafted onto SiO2 sphere, and the grafted microspheres were optimized by the Smart method to optimize the energy to 1 × 10 −4 kca1/mol. In order to search for the optimal structure, the cell is then annealed at 0.1 MPa from the low temperature of 300 K to the upper temperature of 500 K for 200 ps to prevent the system to form being trapped at a local high energy minimum. Subsequently, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K.    Three different modifiers were grafted on the silica surface, and the three modifiers were KH550 (2a), KH560 (2b) and KH570 (2c). The structure of the modified surface was optimized, and the energy converged to 1 × 10 −4 kca1/mol. Figure 2 shows the structure of three modifiers, and Figure 3 shows the surface of modified-SiO2. In this paper, four identical silane coupling agent chains were grafted onto SiO2 sphere, and the grafted microspheres were optimized by the Smart method to optimize the energy to 1 × 10 −4 kca1/mol. In order to search for the optimal structure, the cell is then annealed at 0.1 MPa from the low temperature of 300 K to the upper temperature of 500 K for 200 ps to prevent the system to form being trapped at a local high energy minimum. Subsequently, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K.     To study the diffusion coefficient of H2O in composite systems, the MSDs of H2O in composite systems were analyzed. Some composite systems containing water molecules were constructed as follows (Supplementary Materials, Figure S1): PMA/SiO2 (KH550-SiO2, KH560-SiO2)/H2O: Amorphous cells containing composites of PMA polymer chains with 20 repeat units, one SiO2 (or modified-SiO2) nanoparticle (diameter 20 nm) and 10 H2O molecules were constructed, and periodic boundary conditions were applied.

Molecular Dynamics Simulation Process
After building PMA/SiO2 (or modified-SiO2) composite systems, the energy of each generated cell is minimized to a convergence value of 1.0 × 10 −4 kcal mol −1 by using the Smart Minimizer method to relax the state of minimal potential energy. Whereafter, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K. The cell is then annealed at 0.1 MPa from the low temperature of 300 K to the upper temperature of 500 K for 200 ps to prevent the system to form being trapped at a local high energy minimum [43]. Subsequently, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K, 500 ps of NPT (constant number of particles, pressure, and temperature) simulation is performed at 0.1 MPa and 2 ns of NVE (constant number of particles, volume, and energy) simulation is performed to further relax the polymer structure by using the Andersen Thermostat for temperature control and the Berendsen Barostat for pressure control [44,45] (Figure 5).
At last, the cell can be used to analyze properties of the system. In order to further verify the effect of the number of polymer chains on the properties of composites, a composite system with 30 polymer chains was studied ( Figure S2). The results show that the binding energy between the polymer and SiO2 is not significantly different from the data of the composite system of 20 polymer chains in the article, which is reasonable (Tables S1 and S2). This result indicates that the composite system of 20 polymer chains may basically match the experiment. With the increasing of the number of polymer chains, the performance of the composite system has not changed significantly.

Molecular Dynamics Simulation Process
After building PMA/SiO 2 (or modified-SiO 2 ) composite systems, the energy of each generated cell is minimized to a convergence value of 1.0 × 10 −4 kcal mol −1 by using the Smart Minimizer method to relax the state of minimal potential energy. Whereafter, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K. The cell is then annealed at 0.1 MPa from the low temperature of 300 K to the upper temperature of 500 K for 200 ps to prevent the system to form being trapped at a local high energy minimum [43]. Subsequently, 200 ps of NVT (constant number of particles, volume, and temperature) simulation is performed at 298 K, 500 ps of NPT (constant number of particles, pressure, and temperature) simulation is performed at 0.1 MPa and 2 ns of NVE (constant number of particles, volume, and energy) simulation is performed to further relax the polymer structure by using the Andersen Thermostat for temperature control and the Berendsen Barostat for pressure control [44,45] (Figure 5).
At last, the cell can be used to analyze properties of the system. In order to further verify the effect of the number of polymer chains on the properties of composites, a composite system with 30 polymer chains was studied ( Figure S2). The results show that the binding energy between the polymer and SiO 2 is not significantly different from the data of the composite system of 20 polymer chains in the article, which is reasonable (Tables S1 and S2). This result indicates that the composite system of 20 polymer chains may basically match the experiment. With the increasing of the number of polymer chains, the performance of the composite system has not changed significantly. System equilibrium is judged by temperature and energy balance. Figure 6 shows the trajectory temperature and energy fluctuation chart of 200 ps NVT in the MD equilibrium stage. From the Figure 5, the trajectory energy fluctuation of each frame is gentle, indicating that the system energy has reached equilibrium. The above two criteria showed that the PMA/SiO2 composite system has indeed reached equilibrium through MD simulation, and the subsequent analysis results are reliable. The remaining PMA and modified-SiO2 interaction systems could all reach the same conclusion.

Morphological and Structural Characterization of Modified-SiO2
Surface modification is essential for the synthesis and functionality of composites. FT-IR is often used to characterize surface modification. FT-IR spectra of SiO2 and modified-SiO2 are shown in Figure 7a. The characteristic peaks assigned to the stretching vibration of Si-O-Si at 1101 cm −1 are System equilibrium is judged by temperature and energy balance. Figure 6 shows the trajectory temperature and energy fluctuation chart of 200 ps NVT in the MD equilibrium stage. From the Figure 5, the trajectory energy fluctuation of each frame is gentle, indicating that the system energy has reached equilibrium. System equilibrium is judged by temperature and energy balance. Figure 6 shows the trajectory temperature and energy fluctuation chart of 200 ps NVT in the MD equilibrium stage. From the Figure 5, the trajectory energy fluctuation of each frame is gentle, indicating that the system energy has reached equilibrium. The above two criteria showed that the PMA/SiO2 composite system has indeed reached equilibrium through MD simulation, and the subsequent analysis results are reliable. The remaining PMA and modified-SiO2 interaction systems could all reach the same conclusion.

Morphological and Structural Characterization of Modified-SiO2
Surface modification is essential for the synthesis and functionality of composites. FT-IR is often used to characterize surface modification. FT-IR spectra of SiO2 and modified-SiO2 are shown in Figure 7a. The characteristic peaks assigned to the stretching vibration of Si-O-Si at 1101 cm −1 are The above two criteria showed that the PMA/SiO 2 composite system has indeed reached equilibrium through MD simulation, and the subsequent analysis results are reliable. The remaining PMA and modified-SiO 2 interaction systems could all reach the same conclusion.

Morphological and Structural Characterization of Modified-SiO 2
Surface modification is essential for the synthesis and functionality of composites. FT-IR is often used to characterize surface modification. FT-IR spectra of SiO 2 and modified-SiO 2 are shown in Figure 7a. The characteristic peaks assigned to the stretching vibration of Si-O-Si at 1101 cm −1 are observed in the spectrum of SiO 2 . After modification with silane coupling agent, there appeared absorption peaks at 1705 cm −1 (C=C stretching vibration) in the spectrum of KH570-SiO 2 , as well as peaks at 1730 cm −1 (-C-H-asymmetric stretching vibration), 1623 cm −1 (N-H in-plane bending vibration) in the spectrum of KH550-SiO 2 . The peak at 2977 cm −1 reveals the existence of -CH 3 or -CH 2 -on SiO 2 surface. These may suggest that silane coupling agent is successfully grafted onto the SiO 2 surface.
Polymers 2020, 12, x FOR PEER REVIEW 7 of 16 observed in the spectrum of SiO2. After modification with silane coupling agent, there appeared absorption peaks at 1705 cm −1 (C=C stretching vibration) in the spectrum of KH570-SiO2, as well as peaks at 1730 cm −1 (-C-H-asymmetric stretching vibration), 1623 cm −1 (N-H in-plane bending vibration) in the spectrum of KH550-SiO2. The peak at 2977 cm −1 reveals the existence of -CH3 or -CH2-on SiO2 surface. These may suggest that silane coupling agent is successfully grafted onto the SiO2 surface. To reveal the chemically bonding between SiO2 and the silane coupling agent, UV absorption spectrum of the modified-SiO2 was characterized. It can be seen in Figure 7b that there is a small shift in the position of the absorption peak, which may be attributed to changes in the surface structure of SiO2.
SEM images (Figure 8) present that the as-prepared SiO2 and modified-SiO2 samples are uniform in size with spherical shape, and the average size was about 80 nm. Meanwhile, SiO2 are well dispersed (See Figure 8a). Nevertheless, the modified-SiO2 are not particularly well dispersed ( Figure  8b-d), which may be caused by self-polymerization of the silane coupling agent.  Figure 9 shows the TEM image of PMA and PMA/SiO2 composite latex particles. As shown in Figure 9a, the pristine PMA latex particles display a well-defined spherical morphology and the latex particle size is 100-200 nm. The black phase which are SiO2 particles are on the surface of latex particles (the fuzzy layers). SiO2 is located onto the surface of latex particles (Figure 9b), KH550-SiO2 To reveal the chemically bonding between SiO 2 and the silane coupling agent, UV absorption spectrum of the modified-SiO 2 was characterized. It can be seen in Figure 7b that there is a small shift in the position of the absorption peak, which may be attributed to changes in the surface structure of SiO 2 .

Morphological and Structural Characterization of PMA/SiO2 Composite Emulsion and Film
SEM images (Figure 8) present that the as-prepared SiO 2 and modified-SiO 2 samples are uniform in size with spherical shape, and the average size was about 80 nm. Meanwhile, SiO 2 are well dispersed (See Figure 8a). Nevertheless, the modified-SiO 2 are not particularly well dispersed (Figure 8b-d), which may be caused by self-polymerization of the silane coupling agent.  To reveal the chemically bonding between SiO2 and the silane coupling agent, UV absorption spectrum of the modified-SiO2 was characterized. It can be seen in Figure 7b that there is a small shift in the position of the absorption peak, which may be attributed to changes in the surface structure of SiO2.
SEM images (Figure 8) present that the as-prepared SiO2 and modified-SiO2 samples are uniform in size with spherical shape, and the average size was about 80 nm. Meanwhile, SiO2 are well dispersed (See Figure 8a). Nevertheless, the modified-SiO2 are not particularly well dispersed ( Figure  8b-d), which may be caused by self-polymerization of the silane coupling agent.  Figure 9 shows the TEM image of PMA and PMA/SiO2 composite latex particles. As shown in Figure 9a, the pristine PMA latex particles display a well-defined spherical morphology and the latex particle size is 100-200 nm. The black phase which are SiO2 particles are on the surface of latex particles (the fuzzy layers). SiO2 is located onto the surface of latex particles (Figure 9b), KH550-SiO2  Figure 9 shows the TEM image of PMA and PMA/SiO 2 composite latex particles. As shown in Figure 9a, the pristine PMA latex particles display a well-defined spherical morphology and the latex Polymers 2020, 12, 170 8 of 16 particle size is 100-200 nm. The black phase which are SiO 2 particles are on the surface of latex particles (the fuzzy layers). SiO 2 is located onto the surface of latex particles (Figure 9b), KH550-SiO 2 is onto the surface of latex particles (Figure 9c), and KH560-SiO 2 is also on the surface of latex particles (Figure 9d). There are more KH550-SiO 2 and 560-SiO 2 particles are on the surface of latex particles, this is mainly because that stronger hydrogen bonds or electrostatic interactions is formed between modified-SiO 2 nanoparticles and latex particles, compared with SiO 2 nanoparticles. KH570-SiO 2 nanoparticles which enter the interior of PMA latex particles seem less clear (Figure 9e), and other nanoparticles appear on the latex particle surface as black phase [46]. Different surface modification between the above four SiO 2 sources explains the difference in the distribution of SiO 2 nanoparticles.

Morphological and Structural Characterization of PMA/SiO 2 Composite Emulsion and Film
Polymers 2020, 12, x FOR PEER REVIEW 8 of 16 is onto the surface of latex particles (Figure 9c), and KH560-SiO2 is also on the surface of latex particles (Figure 9d). There are more KH550-SiO2 and 560-SiO2 particles are on the surface of latex particles, this is mainly because that stronger hydrogen bonds or electrostatic interactions is formed between modified-SiO2 nanoparticles and latex particles, compared with SiO2 nanoparticles. KH570-SiO2 nanoparticles which enter the interior of PMA latex particles seem less clear (Figure 9e), and other nanoparticles appear on the latex particle surface as black phase [46]. Different surface modification between the above four SiO2 sources explains the difference in the distribution of SiO2 nanoparticles. The dispersion of SiO2 particles in the PMA film before and after modification can be observed by SEM, as shown in Figure 10. The untreated SiO2 particles aggregated severely in PMA film with the size equivalenting about to 500 nm (Figure 10b). The KH560-SiO2 particles have better dispersibility in PMA, and good interfacial adhesion with PMA film. Which is better than those of the unmodified particles (Figure 10c). Nevertheless, there are still some aggregates in PMA film. KH550-SiO2 particles are well dispersed as small aggregates (Figure 10d). When PMA film was filled with KH570-SiO2 particles, the nanoparticles are uniformly dispersed in PMA film, and it is difficult to see the aggregate of the nanoparticles (Figure 10e). The interfacial compatibility between KH570-SiO2 nanoparticles and PMA film is well.
The unmodified-SiO2 particles aggregate in PMA film on account of their high polar surface energy. The poor compatibility of aggregated SiO2 particles with the PMA film is due to the hydrophilic surface. When SiO2 particles are modified with KH560, their surface is covered by long alkyl chain, which gives the particles a well interfacial compatibility to PMA film [47]. The interface compatibility between KH550-SiO2 particles and PMA film is a bit better, which introduce the amidogen group. The KH570-SiO2 particles can form chemically bond with PMA matrix through double bond polymerization. Good compatibility makes better dispersion of SiO2 particles in PMA film. The dispersion of SiO 2 particles in the PMA film before and after modification can be observed by SEM, as shown in Figure 10. The untreated SiO 2 particles aggregated severely in PMA film with the size equivalenting about to 500 nm (Figure 10b). The KH560-SiO 2 particles have better dispersibility in PMA, and good interfacial adhesion with PMA film. Which is better than those of the unmodified particles ( Figure 10c). Nevertheless, there are still some aggregates in PMA film. KH550-SiO 2 particles are well dispersed as small aggregates (Figure 10d). When PMA film was filled with KH570-SiO 2 particles, the nanoparticles are uniformly dispersed in PMA film, and it is difficult to see the aggregate of the nanoparticles (Figure 10e). The interfacial compatibility between KH570-SiO 2 nanoparticles and PMA film is well.
The unmodified-SiO 2 particles aggregate in PMA film on account of their high polar surface energy. The poor compatibility of aggregated SiO 2 particles with the PMA film is due to the hydrophilic surface. When SiO 2 particles are modified with KH560, their surface is covered by long alkyl chain, which gives the particles a well interfacial compatibility to PMA film [47]. The interface compatibility between KH550-SiO 2 particles and PMA film is a bit better, which introduce the amidogen group. The KH570-SiO 2 particles can form chemically bond with PMA matrix through double bond polymerization. Good compatibility makes better dispersion of SiO 2 particles in PMA film. Polymers 2020, 12, x FOR PEER REVIEW 9 of 16  Figure 11 reveals the tensile strength and elongation at break of PMA/SiO2 nanocomposites, in which SiO2 is modified by different silane coupling agents. As everyone knows, the interfacial interaction between polymer and nanoparticles has a greater influence on the tensile strength of composites [20]. The weak interfacial interaction between polymer and nanoparticles results in less stress being transferred from polymer to nanoparticles [47]. The stronger the interfacial interaction between polymer and nanoparticles, the greater the stress transmitted by the polymer to the nanoparticles, resulting in higher tensile strength. As can be seen in Figure 11a, the tensile strength of PMA/modified-SiO2 film is higher than that of PMA/SiO2 film. And, the tensile strength of PMA/KH570-SiO2 film have the highest value than that of other films. The dispersion and interfacial interaction between polymer and nanoparticles have a great influence on elongation at break of nanocomposites [48,49]. Good dispersibility and proper interfacial interaction can enhance the value of elongation at break, while excessive strong interfacial interaction can reduce it. The elongation at break of composite films is shown in Figure 11b, compared with  Figure 11 reveals the tensile strength and elongation at break of PMA/SiO 2 nanocomposites, in which SiO 2 is modified by different silane coupling agents. As everyone knows, the interfacial interaction between polymer and nanoparticles has a greater influence on the tensile strength of composites [20]. The weak interfacial interaction between polymer and nanoparticles results in less stress being transferred from polymer to nanoparticles [47]. The stronger the interfacial interaction between polymer and nanoparticles, the greater the stress transmitted by the polymer to the nanoparticles, resulting in higher tensile strength. As can be seen in Figure 11a, the tensile strength of PMA/modified-SiO 2 film is higher than that of PMA/SiO 2 film. And, the tensile strength of PMA/KH570-SiO 2 film have the highest value than that of other films.  Figure 11 reveals the tensile strength and elongation at break of PMA/SiO2 nanocomposites, in which SiO2 is modified by different silane coupling agents. As everyone knows, the interfacial interaction between polymer and nanoparticles has a greater influence on the tensile strength of composites [20]. The weak interfacial interaction between polymer and nanoparticles results in less stress being transferred from polymer to nanoparticles [47]. The stronger the interfacial interaction between polymer and nanoparticles, the greater the stress transmitted by the polymer to the nanoparticles, resulting in higher tensile strength. As can be seen in Figure 11a, the tensile strength of PMA/modified-SiO2 film is higher than that of PMA/SiO2 film. And, the tensile strength of PMA/KH570-SiO2 film have the highest value than that of other films. The dispersion and interfacial interaction between polymer and nanoparticles have a great influence on elongation at break of nanocomposites [48,49]. Good dispersibility and proper interfacial interaction can enhance the value of elongation at break, while excessive strong interfacial interaction can reduce it. The elongation at break of composite films is shown in Figure 11b, compared with The dispersion and interfacial interaction between polymer and nanoparticles have a great influence on elongation at break of nanocomposites [48,49]. Good dispersibility and proper interfacial interaction can enhance the value of elongation at break, while excessive strong interfacial interaction can reduce it. The elongation at break of composite films is shown in Figure 11b, compared with KH550-SiO 2 , the addition of KH570-SiO 2 reduced the elongation at break of the film, which is consistent with the strong interfacial interaction between PMA and KH570-SiO 2 .

Water Vapor Permeability of PMA/SiO 2 and PMA/Modified-SiO 2 Composite Films
Water vapor permeability is an important index when emulsion products are used in coatings requiring air permeability. The water vapor permeation rate is primarily assumed by the diffusion process and adsorption/desorption process, which are influenced by the composition and structure of the polymer chains. The soft polymer chains of polyacrylate can give more free volume for the passage of water vapor molecules, although hydrophobic segments of polyacrylate are detrimental to the adsorption process [50].
The effects of functionalized SiO 2 on water vapor permeability of as-obtained films are shown in Figure 12a. Compared with pure PMA film (Figure 12a), water vapor transmission rate of composite films is improved. It is evident that by blending the KH550-SiO 2 or KH560-SiO 2 nanoparticles in the PMA film, water vapor permeability of PMA/SiO 2 nanocomposite films increases significantly. This is mainly attributed to the fact that KH550-SiO 2 and KH560-SiO 2 contain a hydrophilic amino group or an epoxy group to facilitate water vapor transmission through the film. It can be seen that the water vapor transmission rate of PMA/SiO 2 and PMA/KH570-SiO 2 composite films are higher than that of PMA composite film, which is mainly result from that: On the one hand, there is a large number of interfacial pores between SiO 2 nanoparticles and PMA film, which provides a good channel for water vapor molecules. On the other hand, an enhancement in the amount of hydrophilic groups in film leads to an increase in water vapor permeability [51]. The surface of SiO 2 nanoparticles contains a large amount of hydroxyl groups, which increases the number of hydrophilic groups inside the film.
Polymers 2020, 12, x FOR PEER REVIEW 10 of 16 KH550-SiO2, the addition of KH570-SiO2 reduced the elongation at break of the film, which is consistent with the strong interfacial interaction between PMA and KH570-SiO2.

Water Vapor Permeability of PMA/SiO2 and PMA/Modified-SiO2 Composite Films
Water vapor permeability is an important index when emulsion products are used in coatings requiring air permeability. The water vapor permeation rate is primarily assumed by the diffusion process and adsorption/desorption process, which are influenced by the composition and structure of the polymer chains. The soft polymer chains of polyacrylate can give more free volume for the passage of water vapor molecules, although hydrophobic segments of polyacrylate are detrimental to the adsorption process [50].
The effects of functionalized SiO2 on water vapor permeability of as-obtained films are shown in Figure 12a. Compared with pure PMA film (Figure 12a), water vapor transmission rate of composite films is improved. It is evident that by blending the KH550-SiO2 or KH560-SiO2 nanoparticles in the PMA film, water vapor permeability of PMA/SiO2 nanocomposite films increases significantly. This is mainly attributed to the fact that KH550-SiO2 and KH560-SiO2 contain a hydrophilic amino group or an epoxy group to facilitate water vapor transmission through the film. It can be seen that the water vapor transmission rate of PMA/SiO2 and PMA/KH570-SiO2 composite films are higher than that of PMA composite film, which is mainly result from that: On the one hand, there is a large number of interfacial pores between SiO2 nanoparticles and PMA film, which provides a good channel for water vapor molecules. On the other hand, an enhancement in the amount of hydrophilic groups in film leads to an increase in water vapor permeability [51]. The surface of SiO2 nanoparticles contains a large amount of hydroxyl groups, which increases the number of hydrophilic groups inside the film.

Water Resistance of PMA/SiO2 and PMA/Modified-SiO2 Composite Films
Under normal circumstances, water absorption of the composite film is used to reflect its water resistance, and the higher the water absorption rate, the worse the water resistance. It can be seen from Figure 12b that compared with PMA film, water absorption of PMA/KH550-SiO2 and PMA/KH560-SiO2 composite films show higher value than that of PMA. While water absorption of PMA/SiO2 and PMA/KH570-SiO2 composite films show lower value than those of PMA, and the PMA/KH570-SiO2 composite film has the lowest water absorption. This is mainly due to the fact that KH550-SiO2 and KH560-SiO2 contain a hydrophilic amino group and an epoxy group to facilitate water vapor transmission through the film, while PMA/KH570-SiO2 contains a hydrophobic C=C which is not favorable for water vapor transmission through the film. Under normal circumstances, water absorption of the composite film is used to reflect its water resistance, and the higher the water absorption rate, the worse the water resistance. It can be seen from Figure 12b that compared with PMA film, water absorption of PMA/KH550-SiO 2 and PMA/KH560-SiO 2 composite films show higher value than that of PMA. While water absorption of PMA/SiO 2 and PMA/KH570-SiO 2 composite films show lower value than those of PMA, and the PMA/KH570-SiO 2 composite film has the lowest water absorption. This is mainly due to the fact that KH550-SiO 2 and KH560-SiO 2 contain a hydrophilic amino group and an epoxy group to facilitate water vapor transmission through the film, while PMA/KH570-SiO 2 contains a hydrophobic C=C which is not favorable for water vapor transmission through the film.

Thermal Properties of PMA/SiO 2 Composite Films
TGA curves of as-prepared films are shown in Figure 13. Compared with PMA film, the T 5 of PMA/SiO 2 and PMA/modified-SiO 2 increased.

Thermal Properties of PMA/SiO2 Composite Films
TGA curves of as-prepared films are shown in Figure 13. Compared with PMA film, the T5 of PMA/SiO2 and PMA/modified-SiO2 increased. The corresponding characteristic heat data for all samples is shown in Table 1. By comparing, heat-resistance index of the PMA/SiO2 and PMA/modified-SiO2 composite films obviously increased. This is mainly because that the addition of SiO2 nanoparticles causes entanglement of polymer chain, which slows down the decomposition of the molecular chain. The heat-resistance index of PMA/modified-SiO2 composite films is higher than that of PMA/SiO2. In addition, the heat-resistance index of PMA/KH570-SiO2 composite film is the highest. This is mainly ascribed to the stronger interface interaction between PMA and KH570-SiO2 [52,53].

Binding Energy Analysis
Molecular dynamics simulations are currently effective methods for verifying the strength of interfacial interactions. The strength of the interaction between the PMA film and the SiO2 particles can be reflected by the amount of binding energy between them. Generally, the greater the binding energy, the stronger the interaction force between PMA film and SiO2 particles. As a result, the simulation of the binding energy between PMA film and SiO2 (or modified-SiO2) particles can be used to study the interaction mechanism. The binding energies of PMA/SiO2 and PMA/modified-SiO2 composite materials can be used by: The corresponding characteristic heat data for all samples is shown in Table 1. By comparing, heat-resistance index of the PMA/SiO 2 and PMA/modified-SiO 2 composite films obviously increased. This is mainly because that the addition of SiO 2 nanoparticles causes entanglement of polymer chain, which slows down the decomposition of the molecular chain. The heat-resistance index of PMA/modified-SiO 2 composite films is higher than that of PMA/SiO 2 . In addition, the heat-resistance index of PMA/KH570-SiO 2 composite film is the highest. This is mainly ascribed to the stronger interface interaction between PMA and KH570-SiO 2 [52,53].

Binding Energy Analysis
Molecular dynamics simulations are currently effective methods for verifying the strength of interfacial interactions. The strength of the interaction between the PMA film and the SiO 2 particles can be reflected by the amount of binding energy between them. Generally, the greater the binding energy, the stronger the interaction force between PMA film and SiO 2 particles. As a result, the simulation of the binding energy between PMA film and SiO 2 (or modified-SiO 2 ) particles can be used to study the interaction mechanism. The binding energies of PMA/SiO 2 and PMA/modified-SiO 2 composite materials can be used by: where E total is the energy of the PMA/SiO 2 or PMA/modified-SiO 2 , E PMA is the energy of PMA, and E SiO 2 is the energy of SiO 2 particles, E modified-SiO 2 is the energy of modified-SiO 2 particles. The binding energies between PMA and SiO 2 (or modified-SiO 2 ) are given in Table 2. The total energy of the PMA/SiO 2 (modified-SiO 2 ) system, the energy of PMA, and the energy of SiO 2 (modified-SiO 2 ) are presented in Table 2.
The binding energy of PMA/KH550-SiO 2 reaches a higher value than PMA/SiO 2 , showing the strongest interfacial interaction between PMA film and KH550-SiO 2 particles. A higher binding energy shows good compatibility between PMA film and KH550-SiO 2 particles. As the KH560-SiO 2 was added into PMA, the binding energy of the PMA/KH560-SiO 2 film is better than that of PMA/KH550-SiO 2 film, a sign of well compatibility of PMA film with KH560-SiO 2 particles [54].

MSD (Mean Square Displacement) and Diffusion Coefficient (D) of Water in Composite System
The diffusion coefficient (D) of water molecules in nanocomposite reflects the water vapor permeability of nanocomposite. The higher the diffusion coefficient is, the better the water vapor permeability is. To study the diffusion coefficient of H 2 O in films, the MSDs of H 2 O in the films were analyzed ( Figure 14). Diffusivity was calculated by using the slope of MSD diagram (Figure 14a) [55].
The results show that the diffusivity changes as the change of fillers (Figure 14b). The addition of SiO 2 (modified-SiO 2 ) nanoparticles improves the diffusivity of H 2 O molecules in PMA films. The addition of SiO 2 nanoparticles results in bigger voids at the interface of PMA/SiO 2 (modified-SiO 2 ) film, which facilitates the rapid passage of H 2 O molecules. The diffusion coefficient of water molecules in PMA/KH550-SiO 2 composite system is the best. And after that, the order of diffusion coefficient of water molecules in composite systems from high to low is PMA/KH560-SiO 2 , PMA/KH570, PMA and PMA/SiO 2 , respectively. This is consistent with the results of the water vapor permeability of the previous films.
where Etotal is the energy of the PMA/SiO2 or PMA/modified-SiO2, EPMA is the energy of PMA, and ESiO2 is the energy of SiO2 particles, Emodified-SiO2 is the energy of modified-SiO2 particles. The binding energies between PMA and SiO2 (or modified-SiO2) are given in Table 2. The total energy of the PMA/SiO2 (modified-SiO2) system, the energy of PMA, and the energy of SiO2 (modified-SiO2) are presented in Table 2.
The binding energy of PMA/KH550-SiO2 reaches a higher value than PMA/SiO2, showing the strongest interfacial interaction between PMA film and KH550-SiO2 particles. A higher binding energy shows good compatibility between PMA film and KH550-SiO2 particles. As the KH560-SiO2 was added into PMA, the binding energy of the PMA/KH560-SiO2 film is better than that of PMA/KH550-SiO2 film, a sign of well compatibility of PMA film with KH560-SiO2 particles [54].

MSD (Mean Square Displacement) and Diffusion Coefficient (D) of Water in Composite System
The diffusion coefficient (D) of water molecules in nanocomposite reflects the water vapor permeability of nanocomposite. The higher the diffusion coefficient is, the better the water vapor permeability is. To study the diffusion coefficient of H2O in films, the MSDs of H2O in the films were analyzed ( Figure 14). Diffusivity was calculated by using the slope of MSD diagram (Figure 14a) [55].
The results show that the diffusivity changes as the change of fillers (Figure 14b). The addition of SiO2 (modified-SiO2) nanoparticles improves the diffusivity of H2O molecules in PMA films. The addition of SiO2 nanoparticles results in bigger voids at the interface of PMA/SiO2 (modified-SiO2) film, which facilitates the rapid passage of H2O molecules. The diffusion coefficient of water molecules in PMA/KH550-SiO2 composite system is the best. And after that, the order of diffusion coefficient of water molecules in composite systems from high to low is PMA/KH560-SiO2, PMA/KH570, PMA and PMA/SiO2, respectively. This is consistent with the results of the water vapor permeability of the previous films.

Conclusions
In this study, experimental methods combined with molecular simulation ways have been successfully applied to study the microstructure-property relationship in various polyacrylate/ modified-SiO 2 composite systems. To investigate the effect of different surface structures on mechanical property and water vapor permeability of resultant PMA/SiO 2 nanocomposite films, SiO 2 particles were treated with polysiloxane (KH550, KH560 and KH570). Different functional groups on the surface of SiO 2 lead to different interfacial interactions with PMA, which give different mechanical properties of composite films. At the same time, due to the different hydrophilic and hydrophobic surface of SiO 2 , water vapor permeability of composite film is different. It can be used to study the interfacial interaction and microstructure-property relationships of polyacrylate-based nanocomposites, thus guiding the design of high performance polyacrylate-based nanocomposites.

Conflicts of Interest:
The authors declare no conflict of interest.