Molecular insights into the damping mechanism of poly(vinyl acetate)/hindered phenol hybrids by a combination of experiment and molecular dynamics simulation

Abstract

The fundamental mechanism of the improved damping properties of poly(vinyl acetate) (PVAc), contributed by the introduction of hindered phenols, was systematically elucidated by two-dimensional infrared (2D IR) spectroscopy, dynamic mechanical analysis (DMA), differential scanning calorimeter (DSC), X-ray diffraction (XRD) and molecular dynamics (MD) simulation. The 2D IR results revealed the evolution of hydrogen bonds (H-bonds) from intermolecular H-bonds to H-bond networks of PVAc/hindered phenols. Note that subsequent DMA results revealed that the damping properties of PVAc exhibited two different degrees of improvement due to the addition of hindered phenol. Moreover, DSC results showed that all hybrids were miscible, as concentration fluctuations changed irregularly. In accordance with the XRD observation of only amorphous hindered phenols existing in the PVAc matrix, further MD simulation, based on an amorphous cell, characterized the number of H-bonds, the binding energy and the fractional free volume (FFV) of the hybrids. It was observed that the variation tendency of the simulation data was in accordance with the experimental results. Therefore, the damping mechanism of PVAc/hindered phenol hybrids was proposed through a detailed analysis on the synergistic effect of the number of intermolecular H-bonds and the binding energy between PVAc and the hindered phenol, as well as the FFV or dynamic heterogeneity.

---

1. Introduction

Nowadays, airborne noise and structural vibration control has become a fundamental concern in both industries and daily life. Viscoelastic polymers with the capacity of reducing unwanted noise and preventing vibration fatigue failure have therefore been widely used for acoustic and vibration damping.¹ The damping mechanism of the polymer is a reaction due to internal friction.² When the chain segments in a polymer backbone make de Gennes-like reptation motions,³ molecular vibrational energy is converted into heat energy, thus a loss peak appears in a certain temperature range in dynamic mechanical studies results. According to the damping theory,^4–6 the height and width of the loss peak are mutually linked. As a result, a loss peak that is both high and wide at the same time is unattainable for a homopolymer. However, in order to meet the requirements for applications, damping polymer materials should exhibit a high loss peak over a wide range. Therefore, efforts have been made to solve the issue by different methods, such as blending,⁷ co-polymerization,⁸ interpenetration network (IPN) polymers⁹ and gradient polymers,¹⁰ as well as the main concern of this paper: the use of hydrogen bonds (H-bonds) for the design of damping hybrids or so-called “self-assembled” materials.

During recent years, many efforts have been devoted for improving the damping properties of polymer hybrids through H-bonds and exploring their mechanisms. For example, rubber/hindered phenols or hindered amines, such as tetrakis[methylene-3-(3-5-di-tetra-butyl-4-hydroxyphenyl)propionyloxy]methane (AO-60),¹¹ triethylene glycolbis-[3-(3-tert-butyl-4-hydroxy-5-methyl phenyl)propionyloxy] (AO-70),¹¹ 3,9-bis[1,1-dimethyl-2-{b-(3-tert-butyl-4-hydroxy-5-methylphenyl)propionyloxy}-ethyl]-2,4,8,10-tetraoxaspiro[5,5]-undecane (AO-80),¹² 2,20-methylene bis(6-tert-butyl-4-methylphenol) (AO-2246),¹³ and N,N-dicyclohexyl-2-benzothiazolylsulfenamide (DZ),¹⁴ have been widely investigated as types of high performance damping materials.¹⁵ Moreover, in order to explore the damping mechanism in the hybrids, Zhao et al. first investigated the damping mechanism of the nitrile–butadiene rubber (NBR)/AO-80 hybrids in a quantitative manner with the help of molecular dynamics (MD) simulation and attributed the cause of maximum dynamic property to the largest number of H-bonds and the greatest binding energy, as well as the minimum fractional free volume (FFV), by combining the simulation results with experimental results.¹⁶ Subsequently, Song et al. also proposed a similar conclusion using the combination of MD simulation and experimental results of NBR/AO-60 hybrids.¹⁷ However, to our surprise, though the polymers with glass transition temperature (T_g) above ambient temperature play an important role in damping material fields, the predominant damping mechanism due to H-bonds in these polymer/hindered phenol systems have been hitherto rarely reported. Moreover, though the H-bond damping mechanism of polymer/hindered phenol hybrids had been widely studied, some mechanisms were still unclear. For example, the effect of intramolecular H-bonds on damping properties was not well understood. Therefore, in order to fabricate composites with high damping properties, it is necessary to investigate the mechanism of the formation of H-bonds at T_g values above ambient temperature for polymer/hindered phenol hybrids and their effects on the damping behavior of the hybrids.

To characterize structural and spectroscopic properties related to H-bonds, two of the most useful approaches are infrared spectroscopy, and, in particular, two-dimensional infrared (2D IR) spectroscopy^18–22 and MD simulations.^23,24 It is widely accepted that the formation of the H-bond X–H⋯Y results in weakening of both the bond of X–H and the bond adjacent to Y, thus leading to the decrease of vibration frequencies of the X–H and Y species. The decreased frequencies can be detected by IR spectroscopy, which provides unambiguous information about the formation of H-bonds. However, in some special cases, certain useful information on H-bonds cannot be easily “decoded” from the overlapping peaks in a conventional IR spectrum. In contrast, 2D IR correlation spectroscopy can extract information that cannot be obtained straight from one-dimensional IR spectroscopy, since the spectral resolution can be enhanced by spreading peaks along the second dimension.^25–28 Therefore, 2D IR correlation spectroscopy has become a powerful and versatile tool for elucidating subtle spectral changes induced by an external perturbation. On the other hand, MD simulation provides one of the most direct ways to theoretically investigate molecular behavior,²⁹ which is not accessible to experimental approaches in complex systems such as a system involving H-bond interactions.³⁰ Furthermore, in order to obtain useful insight into H-bond dynamics, it is important to establish the correlation between the simulation results of structural or vibrational properties and experimental results.³¹

Therefore, to investigate the detailed predominating H-bond damping mechanism in viscoelastic polymer/hindered phenol hybrids, Poly(vinyl acetate) (PVAc), with hydroxyl side groups acting as proton acceptors, was selected as the matrix in this paper. It is a typical amorphous and polar polymer with a T_g above ambient temperature, which is easy to process and has been commonly used as a damping material, such as for the use as backing material in loudspeaker production for damping noise vibrations.³² AO-70, with two hydroxyl end groups acting as proton donors, is incorporated into PVAc for the purpose of obtaining high damping hybrids. Furthermore, with the combination of experiment and MD simulation, the relationship between the H-bond structures and the damping properties of PVAc/AO-70 hybrids is interpreted in detail.

2. Experimental and simulation strategies

2.1. Materials

Poly(vinyl acetate) (PVAc) (grade G30) with a molecular weight of 4 × 10⁴–6 × 10⁴ g mol⁻¹ and a solid content of 100% was purchased from Wuxi Sincere Chemicals Co., Ltd (Wuxi, China). Triethylene glycolbis-[3-(3-tert-butyl-4-hydroxy-5-methyl phenyl)propionyloxy] (AO-70 or KY-2080), which was in the powder form, was obtained from Beijing Additive Research Institute (Beijing, China). Tetrahydrofuran (analytical grade) was purchased from Chengdu Kelong Chemical Reagent Factory (Chengdu, China). All materials were used without further purification, and the molecular structure of PVAc and AO-70 are shown in Fig. 1.

Fig. 1 Molecular structures of (a) AO-70 and (b) PVAc.

2.2. Sample preparation

PVAc/AO-70 binary hybrids were prepared as follows: (1) the as-received PVAc and AO-70 were dried in a vacuum oven at 50 °C for 24 h. (2) The dried PVAc was first hot sheared in a Haake internal mixer (Rheocord 90, Germany) at a rotor speed of 30 rpm for 1 min at 120 °C. (3) AO-70 powders with weight ratios of 0 phr, 6.25 phr, 12.5 phr, 25 phr, 37.5 phr and 50 phr were added to their respective samples of sheared PVAc. (4) The mixtures were mixed in the Haake internal mixer at a rotor speed of 60 rpm for another 8 min at 120 °C to prepare the binary hybrids. These are designated as PVAO-0 phr to PVAO-50 phr, respectively.

In order to get mixed samples for characterization, the hybrids were first dried at 60 °C for 12 h, then preheated at 120 °C for 10 min, hot-pressed at 120 °C for 5 min under 12 MPa, and then cool-pressed at room temperature under 12 MPa.

2.3. Characterization

2.3.1. Fourier transform infrared spectroscopy (FTIR). The temperature-dependent absorbance FTIR spectra of PVAc, AO-70 and the hybrids were recorded with a 2 cm⁻¹ spectral resolution on a Nicolet-IS10 (Thermo Electron Co., USA) spectrometer by signal averaging 20 scans. Two pieces of microscope KBr windows, which have no absorption bands in the MIR region, were used to prepare a transmission cell. Variable-temperature spectra, controlled by a temperature control instrument such as a programmed heating cell and a circulating water jacket cooling system, were collected between 20 and 120 °C with an increment of 5 °C. All samples were prepared via solvent casting from 20 g L⁻¹ tetrahydrofuran solution, dried in a vacuum oven at 60 °C for 12 h and protected by dried high-purity nitrogen gas during measurement. The baseline correction was performed by the automatic baseline correction function of the OMNIC 8.2 spectral collecting software (Thermo Fisher Scientific Inc., USA).

2.3.2 Two-dimensional (2D) correlation analysis. Spectra recorded at intervals of approximately 10 °C were selected in certain wavenumber ranges, and the generalized 2D correlation analysis was applied by the 2D Shige software composed by Shigeaki Morita (Kwansei-Gakuin University, Japan). In the 2D correlation maps, the red regions are defined as the positive correlation intensities, whereas the blue ones are regarded as the negative correlation intensities.

2.3.3 Dynamic mechanical analysis (DMA). Dynamic mechanical spectra were acquired through a dynamic mechanical analyzer (Q800, TA Instrument). The samples with sizes of 10 mm (length) × 10 mm (width) × 1 mm (thickness) were heated from −20 to 100 °C at a constant frequency of 10 Hz with controlled stress by 0.1% and a heating rate of 3 °C min⁻¹ under a single-cantilever mode.

2.3.4 Differential scanning calorimetry (DSC). The thermal properties of PVAc, AO-70, and the hybrids (5–7 mg) were measured using differential scanning calorimetry (Q20, TA Instrument). The nitrogen gas was purged throughout the measurements. The sample was first heated from room temperature to 120 °C (first heating) to eliminate heat history. Subsequently, the sample was cooled to −50 °C and heated again to 120 °C (second heating). All the heating and cooling rates were 10 °C min⁻¹. The glass transition temperature (T_g) was obtained from the second-heating scan, whereas the melting temperature (T_m) of the as-received AO-70 was obtained from the first-heating scan.

2.3.5 Wide-angle X-ray diffraction (WXRD). WXRD measurements were performed on an X'Pert Pro X-ray diffractometer (Philips) using Cu Kα radiation (λ = 0.154 nm, 40 kV, 40 mA) at room temperature, and the scanning rate was 8° min⁻¹.

2.3.6 Ultraviolet spectroscopy (UV). The UV spectra of the PVAc, AO-70, and the hybrids were obtained with a Shimadzu 1705 UV-visible spectrophotometer. The wavelength ranged from 200 to 1100 nm at a resolution of 1 nm. The linear correlation coefficient was greater than 0.999.

2.4. Simulation strategies for PVAc/AO-70 hybrids

MD simulation had been performed on the PVAc/AO-70 hybrids at ambient temperature (25 °C) using the software packages of Discover and Amorphous cell modules (Accelrys, Inc., San Diego, CA) with the Material Studio Modeling program (version 5.0). The COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies) force field, which was used for computing interatomic interactions, has been widely used to optimize and predict the structural, conformational, and thermophysical condensed phase properties of molecules such as polymers.³³ In the COMPASS force field approach, total energy E_T of the system is represented by the sum of bonding and nonbonding interactions, which is given as follows:

E_T = E_b + E_o + E_φ + E_loop + E_pe + E_vdw + E_q (1)

Here, the first five terms represent the bonded interactions, which correspond to energies associated with the bond, E_b; bond angle bending, E_o; torsion angle rotations, E_φ; out of loop, E_loop; and potential energy, E_pe. The last two terms represent non-bonded interactions, which consist of the van der Waals term, E_vdw, and electrostatic force, E_q.³⁴ Initial velocities were set by using the Maxwell–Boltzmann profiles at 25 °C. The Verlet velocity time integration method was used with a time step of 1 femtosecond (fs).³⁵

Using the rotational isomeric state (RIS) theory that describes the conformations of unperturbed chains, initially, the structures of AO-70 and PVAc polymer chains containing 50 repeat units³⁶ were built and energy-minimized. The lengths of the chain repeat units were chosen according to two criteria: (1) to keep cell size and computing time at a manageable level (one long chain would be a less realistic option than a few short chains) and (2) to ensure sufficient mobility of the chain to allow chain movements within the modelling time period.¹⁶ Cubic amorphous cells containing 4 PVAc polymer chains and different mass ratios of AO-70, as Table 1 shows, were constructed with the periodic boundary condition applied. The density from MD simulation and experimental results are also summarized in Table 1. The agreement of the simulated densities with the experimental values (ρ_MD − ρ_Exp < 0.004) indicates that the motion of the polymer chains in the hybrids can be expressed by MD simulation.

Table 1 Mass ratios and densities of PVAc/AO-70 hybrids by experiment and MD simulation

Sample Name	PVAO-0 phr	PVAO-6.25 phr	PVAO-12.5 phr	PVAO-25 phr	PVAO-37.5 phr	PVAO-50 phr
a Experiment mass ratio was obtained from the UV results.
Experiment mass ratio^a (phr)		9.45	13.85	28.19	39.23	50.71
MD simulation mass ratio (phr)		10.22	13.62	27.24	40.86	51.08
Experiment density (g cm^−3)	1.1880	1.1829	1.1807	1.1741	1.1666	1.1575
MD simulation density (g cm^−3)	1.1902	1.1825	1.1802	1.1703	1.1635	1.1565

---

Fig. 2 shows the process of MD simulation. After the construction of amorphous cells (Fig. 2(a)–(c)), the total system was energy-minimized with the steepest descent method, followed by the conjugate gradient method. Subsequently, in order to adjust the periodic box size and to obtain an energy equilibrated cell, the cell was equilibrated in the isothermal–isobaric (NPT) ensemble at 1 atm and 25 °C. This equilibration was performed for 1 nanosecond (ns) with the dynamics, followed by data accumulation running for another 1 ns, and the configurations were saved for every 5 picoseconds (ps) (Fig. 2(d)). Finally, the cell could be used to count the number of H-bonds (Fig. 2(e)) and to analyze the FFV (Fig. 2(f)), as well as the binding energy. The FFV of the equilibrated hybrids was determined by a grid scanning method.

Fig. 2 Models for MD simulation of PVAO hybrids (red atom is O, green atom is H, grey atom is C, and blue dashed line represents H-bonds).

3. Results and discussion

3.1. Hydrogen bonds in PVAO hybrids

Combining the chemical structures of AO-70 and PVAc shown in Fig. 1, multiple H-bonds might be formed between one type of proton donator (phenolic O–H groups in AO-70 (Fig. 1(1) and (2))) and two types of proton acceptors (ester C=O groups in both PVAc (Fig. 1(5)) and AO-70 (Fig. 1(3) and (4))) in PVAO hybrids. To confirm the existence of the aforementioned H-bonds, temperature-dependent IR absorbance in the O–H and C=O group regions of AO-70 and PVAO-50 phr were characterized, and the results are shown in Fig. 3.

Fig. 3 The temperature-dependent infrared spectrum of (a) AO-70 and (b) PVAO-50 phr in the range of 3700–3150 cm⁻¹ and 1780–1660 cm⁻¹ from 20 to 120 °C.

It is well accepted that temperature plays an important role in determining the extent of H-bonds. In general, the strength of H-bonds decreases with increase in temperature, resulting in decreased intensity and increased wavenumber of H-bonded IR peaks. For pure AO-70 (Fig. 3(a)), the peak at 3480 cm⁻¹ decreased and shifted to higher wavenumber while a new peak at 3590 cm⁻¹ stood out with increasing temperature, which could be attributed to the vibrations of H-bonded O–H and free O–H, respectively. Moreover, a distinct peak at 1735 cm⁻¹ and a latent shoulder peak at 1710 cm⁻¹ both decreased and shifted to higher wavenumbers with increasing temperature, which correspond to the vibration of free C=O and H-bonded C=O, respectively. Therefore, a H-bond between a phenolic O–H and ester C=O were shown to exist in AO-70. However, for PVAO-50 phr (Fig. 3(b)), only the decreasing peaks at 3480 and 1735 cm⁻¹, corresponding to the vibrations of H-bonded O–H and free C=O, respectively, could be observed with increasing temperature. As a result, one might come up with the following questions: (1) where was the peak location of the H-bonded C=O and (2) what kind of H-bond is formed in PVAO hybrids: intermolecular, intramolecular or both? In order to check out the latent peaks in the C=O region and clarify the H-bond relationship in PVAO hybrids, 2D IR, with higher sensitivity, was applied, and the results are shown below. The results for AO-70 and PVAO-6.25 phr were also taken into account for comparison.

The 2D IR correlation spectra were characterized by two independent wavenumber axes (ν1, ν2) and a correlation intensity axis. Two types of spectra, 2D synchronous and asynchronous, were generally obtained. In the synchronous spectra, diagonal positive peaks were referred to as “autopeaks,” which represent the overall extent of the temperature-induced fluctuation of spectral intensity with respect to the reference spectrum. The off-diagonal peaks were called “crosspeaks” and their presence indicated that the simultaneous changes occurred at two different wavenumbers. Positive crosspeaks demonstrated that the intensity variations of the two peaks at ν1 and ν2 were taking place in the same direction (both increase or both decrease) under the environmental perturbation, while the negative cross-peaks helped to infer that the intensities of the two peaks at ν1 and ν2 change in opposite directions (one increases, while the other one decreases) under perturbation. The asynchronous spectra had only off-diagonal peaks. The intensity of an asynchronous spectrum represented sequential or successive changes of spectral intensities observed at ν1 and ν2. A positive asynchronous peak at (ν1, ν2) indicated that the intensity at ν1 changed faster compared to that at ν2, while the negative asynchronous peak indicated the opposite phenomenon, and this feature is very useful in differentiating overlapped or latent peaks due to different spectral origins.³⁷

The synchronous and asynchronous maps for the heating process of AO-70 in the 3700–3200 cm⁻¹ and 1780–1660 cm⁻¹ region are shown in Fig. 4. In the synchronous map of 3700–3200 cm⁻¹ (Fig. 4(a)), two strong autopeaks developed at 3590 and 3480 cm⁻¹, indicating the prominent changes of free and H-bonded O–H with increase in temperature. The negative crosspeaks show that the heating-induced intensity variations of the peaks at 3590 and 3480 cm⁻¹ were simultaneously changed in an opposite direction. In the asynchronous map of 3700–3200 cm⁻¹ (Fig. 4(b)), the crosspeaks indicate that out-of phase spectral changes occurred at 3590 and 3480 cm⁻¹. The synchronous spectrum (Fig. 4(c)) in the 1780–1660 cm⁻¹ range is dominated by only one strong autopeak at 1735 cm⁻¹, which was attributed to the vibration of free C=O with increase in temperature. According to the crosspeaks in the asynchronous map of 1780–1660 cm⁻¹ (Fig. 4(d)), the existence of the peak at 1710 cm⁻¹, attributed to the vibration of H-bonded C=O, could be detected. Therefore, it was confirmed that the results of the above 2D IR analysis were strongly consistent with that of the temperature-dependent FTIR.

Fig. 4 2D IR correlation spectra of AO-70 obtained from 20 to 120 °C: (a) synchronous map of 3700–3200 cm⁻¹, (b) asynchronous map of 3700–3200 cm⁻¹, (c) synchronous map of 1780–1660 cm⁻¹ and (d) asynchronous map of 1780–1660 cm⁻¹.

The 2D IR maps of PVAO-6.25 phr and PVAO-50 phr are depicted in ESI (Fig. 1-S and Fig. 2-S,† respectively). For PVAO-6.25 phr, in the synchronous maps of O–H and C=O regions, two autopeaks developed at 3590 and 1735 cm⁻¹, indicating the prominent changes of the groups with increase in temperature. In the asynchronous map of O–H group region, two symmetrical crosspeaks confirmed the presence of free and H-bonded O–H groups at 3590 and 3480 cm⁻¹, respectively. In the asynchronous map of C=O group region, the presence of two peaks (1735 and 1723 cm⁻¹) could be distinguished, which were assigned to the vibration of free and H-bonded C=O group, respectively. Therefore, by a comparison with AO-70, it could be concluded that the intermolecular H-bonds between PVAc and AO-70 were formed, while no intramolecular H-bonds were detected in PVAO-6.25 phr. After adding 50 phr AO-70 to PVAc, in the synchronous maps of the O–H and C=O regions, the autopeaks developing at 3480, 1723 and 1735 cm⁻¹ indicated considerable changes in H-bonded O–H, C=O and free C=O with increase in temperature, and the negative crosspeaks supported that the heating-induced intensity variations of the peaks at 3480 and 3590, as well as 1723 and 1735 cm⁻¹, were taking place in the opposite direction. In the asynchronous map of the O–H region, the two symmetrical crosspeaks indicate that out-of phase spectral changes occurred at 3590 and 3480 cm⁻¹. In the asynchronous map of the C=O region, three peaks (1735, 1723 and 1710 cm⁻¹) could be distinguished. By comparing the spectra of AO-70 and PVAO-6.25 phr, the peak at 1723 cm⁻¹ could be assigned to the vibration of intermolecular H-bonded C=O between PVAc and AO-70, while the peak at 1710 cm⁻¹ could be attributed to the intramolecular H-bonded C=O of AO-70.

Therefore, based on the 2D IR analysis, the schematic diagram of H-bonds in PVAO hybrids was put forward and shown in Fig. 5. When small amounts of AO-70 were added to PVAc, the H-bonds between O–H groups of AO-70 and C=O groups of PVAc were only formed in the hybrids. However, with more AO-70 added to PVAc, the intramolecular H-bonds between the O–H and C=O groups of AO-70 coexisted with the intermolecular H-bonds between AO-70 and PVAc. Thus, an H-bond network was formed in the hybrids with high amounts of AO-70.

Fig. 5 Schematic diagram of intermolecular H-bond (H-bond(a)) and intramolecular H-bond (H-bond(b)) in hybrids with black thick lines, blue short lines and black dashed lines denoting PVAc polymer chains, AO-70 small molecules and H-bonds, respectively.

3.2. Dynamic mechanical analysis

As mentioned above, H-bonds play an important role in determining the damping properties of hybrids containing hindered phenols. To explore the effect of H-bonding evolution on the damping properties of PVAO hybrids, the temperature dependence of the loss factor (tan δ) and the storage modulus of the hybrids are depicted, and the results are shown in Fig. 6. The detailed DMA results are also summarized in Table 2. For DMA results, high values of tan δ and wide temperature ranges of tan δ greater than a constant value indicate good damping properties of the material. For PVAO hybrids (Fig. 6(a)), on the one hand, the only tan δ peak, corresponding to the T_g of PVAc, gradually shifted to lower temperature with increasing amount of AO-70, indicating that AO-70 had plasticizing effects on PVAc. For example, compared with pure PVAc having a T_g at about 60 °C, the T_g of PVAO-50 phr shifted almost 15 °C to about 45 °C, which is beneficial for damping materials, because the temperature at which damping materials are used is usually near ambient temperature. One the other hand, the maximum value of tan δ and the temperature range of tan δ values greater than 1 increased with increase in amount of AO-70 (Fig. 6(a) and Table 2), which showed that AO-70 could effectively improve the damping properties of PVAc. However, the improvement could be divided into two stages. For the maximum value of tan δ, the value increased rapidly with increase in the amount of AO-70 from 0 to 25 phr, whereas the value showed a slight increase with further increase in the AO-70 amount. The temperature ranges of tan δ values greater than 1 showed a similar trend with the maximum value of tan δ. Related to the H-bonding evolution in PVAO hybrids, the different improvements could be reasonably attributed to the intermolecular and intramolecular H-bond changes in the hybrids. The storage modulus indicates the capability of a material to store mechanical energy and resist deformation. The loss of storage modulus from low temperature to high temperature may indicate the secondary transition and the glass transition of a polymer, respectively. In Fig. 6(b), every storage modulus curve displays two transitions corresponding to the movement of the side groups of PVAc (the lower temperature one) and the PVAc polymer chain (the higher temperature one), except for that of PVAO-37.5 phr, for which only the glass transition corresponding to the movement of the PVAc polymer chain could be observed. The value of the storage modulus in the low temperature region (before the glass transition) also gradually decreased with the increasing amount of AO-70, except for PVAO-37.5 phr, which exhibits the maximum value of storage modulus. All of these phenomena could also be reasonably attributed to the H-bonding evolution in the hybrids, especially the changes between intramolecular and intermolecular H-bonds. In order to explore the predominating H-bond damping mechanism in the hybrids, a quantitative analysis of the evolution of H-bonds by molecular dynamics simulation are given in the following part, where the number of H-bonds, the binding energy and the fractional free volume are discussed.

Fig. 6 Temperature dependence of (a) loss factor (tan δ) and (b) storage modulus of PVAO hybrids.

Table 2 Temperature-loss factor values of PVAO hybrids

Sample name	Maximum value of loss factor		Temperature range of loss factor greater than 1
	Value	T/°C	T1/°C	T2/°C	△T/°C
PVAO-0 phr	2.564	58.80	49.08	77.67	28.59
PVAO-6.25 phr	2.618	55.21	44.84	76.27	31.43
PVAO-12.5 phr	2.891	53.64	43.28	79.45	36.17
PVAO-25 phr	3.032	52.15	41.75	78.54	36.79
PVAO-37.5 phr	3.086	48.72	39.19	77.05	37.86
PVAO-50 phr	3.129	46.14	36.10	74.06	37.96

---

3.3 Compatibility and microstructure

To further confirm the T_g variation observed above and to investigate the compatibility in the hybrids, the DSC traces of AO-70 and PVAO hybrids were obtained, and the results are shown in Fig. 7. The as-received AO-70 powder was crystalline and had a melting temperature of around 82 °C. After the as-received AO-70 was heated to 120 °C and quenched to −50 °C with a rate of 10 °C min⁻¹, amorphous AO-70 with a T_g of around 7 °C was obtained (Fig. 7(a)). In the PVAO hybrids (Fig. 7(b)), the shift of the only T_g, attributed to the T_g of PVAc, showed a similar variation trend with that of the DMA results. Moreover, neither the melting peak nor glass transition peak of AO-70 was observed in the hybrids, indicating that AO-70 was miscible with PVAc in all hybrids.

Fig. 7 DSC curves of (a) AO-70 and (b) PVAO hybrids.

Table 3 gives a summary of the T_g in terms of T_gm and the width of T_g, denoted by ΔW_Tg = T_gf – T_gi for PVAO hybrids, where T_gi, T_gm, and T_gf represent the onset, middle and end point of the glass transition region, respectively, and the value of ΔW_Tg is related to the extent of composition fluctuations and dynamic heterogeneity in miscible blends.³⁸ The ΔW_Tg of the hybrids were higher than that of pure PVAc, which indicated the higher dynamic heterogeneity of the hybrids with the addition of AO-70. Moreover, for the hybrids, the ΔW_Tg decreased first, followed by a gradual increase with increase in the amount of AO-70. As strong intermolecular associations (H-bonds) between the components have been found to suppress concentration fluctuations and couple partially (at least) the segmental motions of the two components,^39–41 PVAO-25 phr, whose ΔW_Tg value was the lowest, might have the strongest H-bonds or H-bond networks and lowest dynamic heterogeneity of AO-70 in PVAc matrix.

Table 3 Summary of the thermal properties of PVAO hybrids

Sample name	Tgm (°C)	Tgi (°C)	Tgf (°C)	ΔWTg (°C)
PVAO-0 phr	39.82	36.54	42.32	5.78
PVAO-6.25 phr	31.92	29.02	37.09	8.07
PVAO-12.5 phr	28.97	25.92	34.42	8.50
PVAO-25 phr	27.36	24.74	31.60	6.86
PVAO-37.5 phr	25.12	20.49	27.83	7.34
PVAO-50 phr	21.75	17.20	25.12	7.92

---

Fig. 8 shows the XRD traces of AO-70 and PVAO hybrid. The as-received and amorphous AO-70 displayed typical crystalline and amorphous characteristics, respectively. For PVAO-50 phr, the trace was similar to that of pure PVAc and no crystalline features were detected in the hybrid, suggesting the existence of only the amorphous AO-70 in PVAO hybrids.

Fig. 8 X-ray diffraction curves of AO-70 and PVAO hybrids.

3.4. Analysis of H-bonds in PVAO hybrids by MD simulation

Since only amorphous hindered phenols existed in the PVAc, MD simulation based on an amorphous cell was used to obtain detailed quantitative information about H-bonds in the PVAO hybrids. The simulation results of the pair correlation function, the number of H-bonds, as well as the H-bond predominant binding energy and FFV in the optimized amorphous cell, are shown below.

The pair correlation function g(r), which is related to the probability of finding another atom at a distance r from a specific atom, has been widely applied in studying H-bonds. In general, the distances between atoms of 2.6–3.1, 3.1–5.0, and above 5.0 Å belong to H-bonds, strong vdw forces, and weak vdw forces, respectively.⁴² Fig. 3-S (in ESI†) presents the pair correlation function results of H (in AO-70) and O (in PVAc and AO-70) in the optimized amorphous cell of PVAO-25 phr. The peak of the correlation function of H and O lies in the range of 2–3.2 Å, suggesting a high probability for the two atoms in that distance to form a H-bond interaction.

Table 4 lists the average number of intramolecular and intermolecular H-bonds in different PVAO hybrids calculated from the optimized amorphous cells. Five repeated cells obtained by the repeated MD simulation condition were used to obtain the number of H-bonds in those cells, and then the average number of H-bonds in the different hybrids was obtained. The numbers of H-bonds (a) and (b) both increased with increasing amount of AO-70, and the number of H-bonds (a) was larger than that of H-bonds (b) in all hybrids, indicating that H-bonds (a) were easier to form and play a more important role in the hybrids. Moreover, the H-bonds (b) were not detected in PVAO-6.25 and PVAO-12.5 phr, which is consistent with the 2D IR results. Moreover, the H-bonds showed big changes from PVAO-25 phr to PVAO-50 phr, indicating the probability of achieving the percolation threshold corresponding to the H-bond network by increasing the amount of AO-70.

Table 4 Average number of H-bonds in different PVAO hybrids by MD simulation

Sample name	PVAO-6.25 phr	PVAO-12.5 phr	PVAO-25 phr	PVAO-37.5 phr	PVAO-50 phr
No. of H-bonds (a)	1	2	4	4	7
No. of H-bonds (b)	0	0	1	2	2

---

How well two components were mixed with each other could be reflected by the binding energy (E_binding), which was defined as the negative of the intermolecular interaction energy (E_inter) between the two components,⁴³ and E_inter could be evaluated by the total energy (E_total) of the mixture and those of the individual components in the equilibrium state. Thus, the E_binding between AO-70 and PVAc could be determined as follows:

E_binding = −E_inter = −(E_total − E_AO-70 − E_PVAc) (2)

where E_total, E_AO-70 and E_PVAc are the total energy values of the PVAO hybrid, AO-70 and PVAc, respectively. E_PVAc is a constant (−2215.03 kcal mol⁻¹) because the number of PVAc chains were fixed in the amorphous cell.

The binding energies of the PVAO hybrids are shown in Table 5. Negative E_total values indicated that the interaction between PVAc and AO-70 was favorable to lower the energy; therefore, the hybrids were stable. With increase in the amount of AO-70, the E_binding increased first, followed by a decrease and reached the maximum value at 12.5 phr and the minimum value at 50 phr, indicating the best and worst mixing between AO-70 and PVAc due to the variation of H-bonds in PVAO-12.5 phr and PVAO-50 phr, respectively. Moreover, H-bonds between AO-70 and PVAc were more stable than that of only AO-70.

Table 5 Binding energies of PVAO hybrids with different AO-70 amounts

Sample name	Etotal (kcal mol^−1)	EAO-70 (kcal mol^−1)	Ebinding (kcal mol^−1)
PVAO-6.25 phr	−2571.40	−243.59	−112.78
PVAO-12.5 phr	−2686.11	−325.56	−145.52
PVAO-25 phr	−2944.44	−653.19	−76.22
PVAO-37.5 phr	−3268.63	−978.43	−75.17
PVAO-50 phr	−3486.01	−1226.77	−44.21

---

According to the Williams–Landel–Ferry (WLF) equation based on the free volume theory,⁴⁴ FFV, which was commonly used to characterize the efficiency of chain packing and the amount of free space in a polymer matrix, the packing is greatly affected by H-bonds and in turn affects the damping properties. A common definition of FFV is:

where V and V* are the specific volume and occupied volume, respectively.

Fig. 9 depicts the free volume and FFV results of the PVAO hybrids calculated by MD simulation. With increase in the amount of AO-70, the FFV decreases first and reaches a minimum value at PVAO-25 phr due to the formation of the optimal H-bond network in PVAO-25 phr, and then a great increase occurs at PVAO-50 phr, which is attributed to the destruction of the H-bond network.

Fig. 9 (a) Free volume and (b) fractional free volume of PVAO hybrids calculated by MD simulation.

According to the above quantitative analysis and experiment results, a detailed analysis on the synergistic effects of the relevant influencing factors on the damping mechanism of the PVAO hybrids could be put forward. For PVAO-6.25 phr and PVAO-12.5 phr, the rapid increase in the damping properties was mainly attributed to the intermolecular H-bonds between PVAc and AO-70 and the predominant H-bond binding energy between them. In addition to the intermolecular H-bonds, the rapid increase in the damping property for PVAO-25 phr could be mainly attributed to the most ideal H-bond network, resulting in the most compact chain packing of the hybrids, which causes more friction energy dissipation. PVAO-37.5 phr did not show obvious improvement in the damping property compared with that of PVAO-25 phr, though the number of intramolecular H-bonds in PVAO-37.5 phr was higher than that of PVAO-25 phr while other factors were almost the same, indicating that intramolecular H-bonds in AO-70 had little effect on the damping property of the hybrids. For PVAO-50 phr, even though the number of intermolecular H-bonds was the highest, the damping property showed only a slight improvement, because the largest amount of AO-70 leads to the relatively high FFV and lowest binding energy in PVAO-50 phr, which causes less friction energy dissipation.

4 Conclusions

The fundamental mechanism of the improved damping property of PVAc contributed by the introduction of AO-70 was systematically elucidated by the combination of experiment and MD simulation. Since AO-70 and PVAc could form both intra- and inter-molecular H-bonds, the inter-molecular H-bonds combined with their predominating binding energy and FFV, as well as the ideal H-bond network were the main contribution to the improvement of the damping properties. Moreover, the intra-molecular H-bonds had little or negative effects on the damping properties, and the destruction of the H-bond network also had negative influences on the damping properties of the hybrids.

Therefore, it has been indicated that there is an optimum ratio of AO-70 to PVAc for achieving the proper damping properties. These fundamental studies are expected to provide some useful information for the design and fabrication of high-performance polymeric damping materials.

Acknowledgements

Financial supports of the National Natural Science Foundation of China (51273132, 51227802 and 51121001) and the Program for New Century Excellent Talents in University (NCET-13-0392) are gratefully acknowledged.

References

1. A. A. Gusev, K. Feldman and O. Guseva, Macromolecules, 2010, 43, 2638–2641.
2. L. H. Sperling, Introduction to physical polymer science, John Wiley & Sons, 2005.
3. P.-G. de Gennes, J. Chem. Phys., 1971, 55, 572–579.
4. L. Sperling and J. Fay, Polym. Adv. Technol., 1991, 2, 49–56.
5. D. Fradkin, J. Foster, L. Sperling and D. Thomas, Polym. Eng. Sci., 1986, 26, 730–735.
6. M. Maekawa, M. Nitta and C. Kako, J. Soc. Automot. Eng. Jpn., 1990, 44, 49.
7. S. Thomas and A. George, Eur. Polym. J., 1992, 28, 1451–1458.
8. F. Li, J. Hasjim and R. C. Larock, J. Appl. Polym. Sci., 2003, 90, 1830–1838.
9. C.-L. Qin, W.-M. Cai, J. Cai, D.-Y. Tang, J.-S. Zhang and M. Qin, Mater. Chem. Phys., 2004, 85, 402–409.
10. C. Qin, D. Zhao, X. Bai, X. Zhang, B. Zhang and Z. Jin, et al., Mater. Chem. Phys., 2006, 97, 517–524.
11. C. Wu, T. A. Yamagishi, Y. Nakamoto, S. I. Ishida, S. Kubota and K. H. Nitta, J. Polym. Sci., Part B: Polym. Phys., 2000, 38, 1496–1503.
12. C. Wu and S. Akiyama, J. Polym. Sci., Part B: Polym. Phys., 2004, 42, 209–215.
13. Q. Liu, H. Zhang and X. Yan, Iran. Polym. J., 2009, 18, 401–413.
14. H. Kaneko, K. Inoue, Y. Tominaga, S. Asai and M. Sumita, Mater. Lett., 2002, 52, 96–99.
15. Y. Gao, X. Wang, M. Liu, X. Xi, X. Zhang and D. Jia, Mater. Des., 2014, 58, 316–323.
16. B. Qiao, X. Zhao, D. Yue, L. Zhang and S. Wu, J. Mater. Chem., 2012, 22, 12339–12348.
17. M. Song, X. Zhao, Y. Li, S. Hu, L. Zhang and S. Wu, RSC Adv., 2014, 4, 6719–6729.
18. M. Cho, Chem. Rev., 2008, 108, 1331–1418.
19. S. Woutersen and P. Hamm, J. Phys.: Condens. Matter, 2002, 14, R1035–R1062.
20. M. Fayer, Annu. Rev. Phys. Chem., 2009, 60, 21–38.
21. Y. S. Kim and R. M. Hochstrasser, J. Phys. Chem. B, 2009, 113, 8231–8251.
22. W. Zhuang, T. Hayashi and S. Mukamel, Angew. Chem., Int. Ed., 2009, 48, 3750–3781.
23. Y. Tamai, H. Tanaka and K. Nakanishi, Macromolecules, 1996, 29, 6750–6760.
24. Y. Tamai, H. Tanaka and K. Nakanishi, Macromolecules, 1996, 29, 6761–6769.
25. I. Noda, A. Dowrey, C. Marcott, G. Story and Y. Ozaki, Appl. Spectrosc., 2000, 54, 236A–248A.
26. I. Noda, Vib. Spectrosc., 2004, 36, 143–165.
27. Y. Wu, J.-H. Jiang and Y. Ozaki, J. Phys. Chem. A, 2002, 106, 2422–2429.
28. T. Amari and Y. Ozaki, Macromolecules, 2002, 35, 8020–8028.
29. O. Alexiadis and V. G. Mavrantzas, Macromolecules, 2013, 46, 2450–2467.
30. J. Huang, D. Häussinger, U. Gellrich, W. Seiche, B. Breit and M. Meuwly, J. Phys. Chem. B, 2012, 116, 14406–14415.
31. M. Pagliai, F. Muniz-Miranda, G. Cardini, R. Righini and V. Schettino, J. Phys. Chem. Lett., 2010, 1, 2951–2955.
32. Z. Wang, R. L. Whitby, M. Rousseau, S. Nevill, G. Geaves and S. V. Mikhalovsky, J. Mater. Chem., 2011, 21, 4150–4155.
33. H. Sun, J. Phys. Chem. B, 1998, 102, 7338–7364.
34. S. Zhu, L. Yan, D. Zhang and Q. Feng, Polymer, 2011, 52, 881–892.
35. M. Khalili, A. Liwo, A. Jagielska and H. A. Scheraga, J. Phys. Chem. B, 2005, 109, 13798–13810.
36. T. Spyriouni and C. Vergelati, Macromolecules, 2001, 34, 5306–5316.
37. P. Wu, Y. Yang and H. Siesler, Polymer, 2001, 42, 10181–10186.
38. Z. Yang and C. D. Han, Macromolecules, 2008, 41, 2104–2118.
39. K. A. Masser and J. Runt, ed. Macromol. Symp, Wiley Online Library, 2009, 2009, pp. 221–227.
40. S. Zhang, R. Casalini, J. Runt and C. Roland, Macromolecules, 2003, 36, 9917–9923.
41. D. Fragiadakis and J. Runt, Macromolecules, 2009, 43, 1028–1034.
42. X. Ma, W. Zhu, J. Xiao and H. Xiao, J. Hazard. Mater., 2008, 156, 201–207.
43. M. Solimannejad and I. Alkorta, J. Phys. Chem. A, 2006, 110, 10817–10821.
44. C. Wu, Polymer, 2010, 51, 4452–4460.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra06644h

---