Elastomere Friction - The Best Friend international

10 L.Busse,A.LeGal,andM.Klüppel
Fig. 5 T-sweeps for the loss modulus G ′′ .
effect is minimal for weakly filled samples (S2K), moderate for medium filled
ones (S4K, S6K) and dominant for highly filled sample S8K.
Looking at the loss modulus G ′′ in Figure 5, the increase with filler content
is obvious, too, but more proportional to the filler amount than in the T-sweep
of G ′ . In both cases, the increase is smaller for low temperatures, as chain
mobility is limited anyway under these circumstances.
According to the time-temperature-superposition principle (TTS), temperature
influence can be replaced by frequency influence, where cold rubber
equals high frequency treatment and causes a glassy state with high stiffness,
whereas a warm elastomer dominated by rubber matrix/ filler is connected
to low frequencies. Indeed, by applying various frequencies at discrete temperatures
on the sample, we get a bunch of branches for the moduli that can
be constructed to a master curve for the whole frequency range over several
decades by shifting the branches horizontally in order to form a continuous
curve. Above the glass transition temperature, the shift factors obey the
WLF relationship as shown in Figure 6, with WLF constants C1 = −3.85
and C2 =91.2 ◦ CatTref =20 ◦ C to match the room temperature of friction
measurements. Below about −45 ◦ C, the relative shift between the branches
decreases.
These horizontal factors were extracted from the unfilled sample S0K
(Figure 7), but are valid also for the filled samples. For high temperatures,
the branches of filled samples are also vertically dispersed, so vertical shift
factors need to be applied as well, independently for G ′ and G ′′ . The TTS is
not valid anymore for filled elastomers in this temperature range, because the
filler-filler bond instead of the polymer matrix then dominates the viscoelastic
behaviour [19]. Shift factors for log G ′ and log G ′′ with linear slope in the