Reinforcement of Rubber and Filler Network Dynamics at Small Strains

Abstract

Carbon black particulate reinforcement of rubber is examined in terms of linear viscoelasticity and the dynamics of the filler particle network. First, it is demonstrated that for the case of purely hydrodynamic reinforcement, the dynamics of the filled rubber are equivalent to those of the corresponding unfilled material. A breakdown in thermorheological simplicity is observed with the onset of filler networking in reinforced compounds. The dynamics of the filler network are initially examined by strain sweep/recovery experiments performed on uncrosslinked materials. The role of the surface activity of carbon black in defining the rate and magnitude of flocculation is explored and various models to describe this process are reviewed. The dynamics of carbon black filler networks in crosslinked materials are probed using small strain torsional creep experiments. Physical ageing (structural relaxation) of filled compounds at temperatures well above the glass transition temperature of the rubber matrix is observed and the ageing rate is found to scale with the level of filler networking in the various compounds. Physical ageing is the result of non-equilibrium, slow dynamics, which sheds light on the physical origin of the filler network. Furthermore, the implications of physical ageing of highly filled rubbers on typical linear viscoelastic time–temperature superposition experiments are discussed.

Appendices

Appendix 1: Torsional Creep Equipment and Experiments

Torsional creep apparatus is illustrated in Fig. 14.

Fig. 14

Torsional creep rig setup, showing two different views of the equipment

Filled rubbers were compression moulded into cylinders of 150 mm length and 12 mm diameter. To minimise straining caused by sample handling, the mould design included thin flanges of excess crosslinked material attached to either side of the sample cylinder. This allowed the sample to be removed from the mould and subsequently handled without excessive pre-straining. Silicone-based mould release agent was also applied to the sample moulds prior to curing to lubricate removal of the samples from the mould. Cylindrical samples were then bonded by one end-face to a steel plate and by the other to a threaded screw using Loctite 480 adhesive. Once bonded in place, the flanges could then be trimmed from the sample using a scalpel. The samples were attached to the inertia bar via a screw thread and located and fixed to the bottom of the pendulum using an electromagnet locator system. Two aluminium plates were located at each end of the inertia bar and the bar was counter-balanced in the vertical direction using a pulley system. The central cylinder of the inertia bar seen in Fig. 14 had a diameter of 15 mm and a length of 65 mm. The arms and sensor target panels were constructed of stainless steel, giving the inertia bar a total length of 240 mm. Small steel side arms were attached at the extremities of the inertia bar projecting along the torsional plane of motion. One of these side arms passed through a wound copper coil. Passing a small, constant current through the coil induced a small, constant torsional force across the sample. The consequent elastic and inelastic creep displacements were measured by a non-contact displacement sensor for 1,000 s, after which the force was removed by cutting the current to the coil. The magnitude of the applied current depended on the sample in question. For the more compliant samples (N990, N990g), a current of 20 mA was required to produce an initial elastic deformation and creep behaviour that could be resolved by the sensor. For the stiffer samples (N330, N330g, N134, N134g), a current of 80 mA was required. Strain–time data were calculated from the raw voltage–time output by suitable calibration of the non-contact displacement sensor and calculation of the torsional strain, γ, in the sample by Eq. (5):

$$ \gamma =\theta \left(\frac{r_{\max }}{l}\right) $$

(5)

where θ is the angular deflection in radians, r _max is the radius at the extremity of the sample cylinder and l is the length of the cylinder. Maximum torsional creep strain values were found to be in the range of 0.009–0.04%, depending on the compound, which is well below the onset of non-linear effects.

The torsional stress applied to the samples during the creep experiments was calculated by calibrating the force exerted by the copper coil on the side arm as a function of coil current. Force was converted to torsional stress, τ, using Eq. (6):

$$ \tau =\frac{T_qd}{2I} $$

(6)

where T _q is the torque, d is the diameter of the sample cylinder and I is the second moment of area of the cylinder. Values of τ were used to convert shear strain into compliance.

Appendix 2: Free Vibration Experiments

The small strain linear viscoelastic storage moduli of the CB-filled compounds were determined by applying a small excitation across the sample cylinders via the inertia bar. The subsequent decay in free vibration was recorded by a non-contact displacement sensor. The vibration trace was analysed using Eq. (7):

$$ {G}^{\prime }=\left(\frac{2I{f}^2}{\pi}\right)\left(\frac{l}{r^4}\right) $$

(7)

where I is the inertia of the pendulum, f is the frequency of oscillation, l is the length of the sample cylinder and r is the cylinder radius. The strain range of these experiments was between 0.001 and 0.01% shear strain (relative to the exterior radius of the cylinder), which is well below the onset strains of non-linear responses.