Nanoscale size criterion for modifier selection in polymer composites for vibration damping

2.1. Materials

The primary objects of this study were nanodispersed particles of the following classes:

1) Carbon-based: graphite, ultradispersed diamonds (UDDs), carbon nanotubes (CNTs), shungite, carbon fibers (CFs).

2) Metal-containing: oxides and salts of organic acids.

3) Silicon-containing: mica, tripoli, opal, clays.

4) Fluorinated compounds: ultra-dispersed polytetrafluoroethylene (UPTFE).

All materials were sourced from industrial enterprises in Belarus and the Russian Federation. Nanosized components were produced through mechanical grinding and thermal treatment at temperatures ranging from 400 to 1200 °C.

2.2. Characterization techniques

The structure and properties of dispersed particles were investigated using the following methods:

– Infrared (IR) spectroscopy: Specord instrument, 400-4000 cm^–1 range.

– Electron paramagnetic resonance (EPR) spectroscopy: Bruker spectrometer, X-band (9.5 GHz).

– X-ray diffraction (XRD) analysis: DRON 3.0 diffractometer, CuKα radiation.

– Differential thermal analysis (DTA): Q-1500 derivatograph, 10 K/min heating rate.

– Scanning electron microscopy (SEM): ISM-50A, Nanolab-7, 15-30 kV accelerating voltage.

– Atomic force microscopy (AFM): NT-206, contact mode.

The energy state of nanosized modifiers was assessed using thermally stimulated current (TSC) spectroscopy over the temperature range 300-600 K at a heating rate of 5 K/min.

2.3. Technological treatments

Modifier particles were subjected to:

– Thermal treatment: 373–473 K for 1-3 hours in air atmosphere.

– Laser treatment: ${\lambda }_0=$ 1.06 μm, pulse duration 2×10^–6 s, energy density 10-50 J/cm².

– Mechanochemical activation: Planetary ball mill, 300-500 rpm, 0.5-2 hours.

3.1. Theoretical foundation of the nano-state criterion

For any substance, there exists a critical size L₀ below which characteristic parameters are influenced by the size factor. Following the concept developed by Professor V. A. Liopo [2-6], [8], [9], the critical nanoparticle size is determined by the Debye temperature ${\theta }_D$ according to: $L_0=$ 230·${\theta }_D$^–1/2 [nm], where ${\theta }_D$ is expressed in Kelvin. When particle size $r>L_0$, the particle exhibits bulk phase parameters with no size effects; when $r<L_0$, the substance behaves as a nano-object with properties differing from the bulk phase.

Table 1 presents the characteristic temperatures and maximum nanocrystal sizes for elemental substances.

Analysis of $L_0$ values reveals significant variation across different materials, ranging from 29.0 nm for neon to 5.3 nm for diamond. These values differ substantially from the commonly accepted arbitrary range of 1-100 nm, emphasizing the need for material-specific criteria.

3.2. Validation across material classes

The formula’s adequacy was verified for halide compounds (Table 2) and semiconductor materials (Table 3).

The data demonstrate systematic variation in $L_0$ with composition, confirming that particle size, composition, habitus, and structure collectively influence the modifying effect through changes in energy state.

3.3. Morphological evidence of nano-state formation

SEM and AFM analysis revealed characteristic surface layer morphologies incorporating nanoscale components across all particle classes (Fig. 1).

Fig. 1Characteristic morphology of dispersed particles

a) Clays

b) Carbon nanotubes (CNTs)

c) Metal oxides

d) Ultrafine polytetrafluoroethylene (UPTFE)

e) Metal particles

f) Clays

g) Carbon nanotubes (CNTs)

c) Metal oxides

j) Ultrafine polytetrafluoroethylene (UPTFE)

e) Metal particles

Technological treatments substantially modified surface layer morphology, increasing nanoscale constituent content (Fig. 2). Laser treatment produced the most pronounced effect, generating surface features with dimensions below the calculated $L_0$ threshold.

Fig. 2Morphology of colloidal graphite C-1

a) Initial state

b) After thermal treatment (423 K, 2 h)

c) After laser treatment (${\lambda }_0=$1.06 μm, 2×10⁻⁶ s)

3.4. Energy state characterization

TSC spectroscopy revealed nonlinear current-temperature dependence with extrema in temperature ranges characteristic of each modifier type (Fig. 3). The spectra exhibited transformation with changes in dimensional parameters and treatment intensity.

A characteristic feature of dispersed particles suitable for polymer matrix modification is the presence of uncompensated charge states with anomalously long relaxation times exceeding 10³ s, confirmed by EPR spectroscopy.

From the perspective of vibration-damping material design, these extended relaxation times are of particular significance. In polymer composites, the ability of a modifier to retain uncompensated energy and exhibit slow relaxation processes directly influences the viscoelastic response of the matrix under dynamic loading. The nanoscale particles ($r<L_0$) act as centers of local internal stress and sites for physical crosslinking, promoting the formation of a rigid but flexible interfacial layer. When mechanical vibrations propagate through the composite, this layer facilitates the conversion of mechanical energy into thermal energy through internal friction and chain segment relaxation. Thus, the enhanced energy state of subcritical particles serves as the fundamental driver for creating an interfacial structure capable of effective mechanical energy dissipation, which is essential for vibration-damping components.

A characteristic feature of dispersed particles suitable for polymer matrix modification is the presence of uncompensated charge with relaxation times exceeding 10³ s, confirmed by EPR spectroscopy. Particles below the $L_0$ threshold exhibited spin concentrations 2-3 orders of magnitude higher than their bulk counterparts.

Fig. 3Characteristic TSC spectra: 1 – clay; 2 – PTFE; 3 – CNTs; 4 – UDD

3.5. Implications for vibration-damping materials

The established dimensional criterion enables rational selection of modifiers for polymer composites intended for vibration-damping applications. Particles with $r<L_0$ exhibit enhanced surface energy ($\gamma =$ 50-200 mJ/m²) and increased interfacial adhesion work ($W_a=$ 80-150 mJ/m²), promoting the formation of viscoelastic interphase layers with optimal damping characteristics (tan $\delta =$ 0.1-0.3 at 20-80 °C).

The presence of nanoscale components in the surface layer is the crucial factor determining modifier activity in structure formation processes [10-15]. Activation technology must ensure formation of nanoscale components enabling dominant interfacial processes to proceed with required intensity for specific compositions and processing conditions [1], [2], [4], [8], [9].