Maximum loss modulus

In general, the maximum loss modulus is the most appropriate value. This is the method prescribed by ASTM D4065. It is a reasonable criterion from a practical point of view because the upper use temperature of many amorphous polymers is the softening point. It is clear that by the transition midpoint (peak tan 5) the softening point has been exceeded. 

Dynamic storage modulus ( ) is the most important property to assess the load-bearing capability of a composite material. The ratio of the loss modulus (E") to be storage modulus (F) is known as a mechanical loss factor (tan S), which quantifies the measure of balance between the elastic phase and the viscous phase in a polymeric structure. This can relate to impact properties of a material. Generally, the tan S peak (at low frequency) is at a temperature 10-20 °C above the Tg as measured by dilatometer or differential thermal analysis (DTA). The temperature of maximum loss modulus E" is very close to Tg. 

Figure 4.16 Determination of the glass transition temperature. Different methods of calculation include onset of storage modulus decrease, inflection point (derivative maximum), loss modulus maximum, or tan 8 maximum.

Chains of polybutadiene were trapped in the network formed by cooling a butadiene-styrene copolymer until phase separation occurred for the styrene, effectively crosslinking the copolymer. At 25°C the loss modulus shows a maximum which is associated with the free chains. This maximum occurst at the following frequencies for the indicated molecular weights of polybutadiene ... 

The relaxation at the lowest temperature y relaxation) takes place below - I0O°C. The two polymers with shorter spacers (PDEB and PTEB) show weak relaxations overlapped with the )3 ones due to the low tanS values (0.03 and 0.04, respectively). Notwithstanding this, the y relaxation is clearly distinguished when using loss modulus plots, even in the case of PDEB, that shows the weakest maximum (see Fig. 16). For PTTB, tan6 values in the y relaxation interval are of the order of 0.05. 

It is usually considered that the y relaxation arises from crankshaft and kink movements of polymethylenic sequences, but the clear maximum of tanS and loss modulus for the three polybibenzoates here reported leads to the conclusion that the motion responsible of this relaxation also takes place when one of the methylenic... 

There are also some far-fetched proposals for the LST a maximum in tan S [151] or a maximum in G" [152] at LST. However, these expectations are not consistent with the observed behavior. The G" maximum seems to occur much beyond the gel point. It also has been proposed that the gel point may be reached when the storage modulus equals the loss modulus, G = G" [153,154], but this is contradicted by the observation that the G — G" crossover depends on the specific choice of frequency [154], Obviously, the gel point cannot depend on the probing frequency. Chambon and Winter [5, 6], however, showed that there is one exception for the special group of materials with a relaxation exponent value n = 0.5, the loss tangent becomes unity, tan Sc = 1, and the G — G" crossover coincides with the gel point. This shows that the crossover G = G" does not in general coincide with the LST. 

Tan landa, a damping term, is a measure of the ratio of energy dissipated as heat to the maximum energy stored in the material during one cycle of oscillation. For small to medium amounts of damping. G is the same as the shear modulus measured by other methods at comparable time scales. The loss modulus G" is directly proportional to the heat H dissipated per... 

Now these expressions describe the frequency dependence of the stress with respect to the strain. It is normal to represent these as two moduli which determine the component of stress in phase with the applied strain (storage modulus) and the component out of phase by 90°. The functions have some identifying features. As the frequency increases, the loss modulus at first increases from zero to G/2 and then reduces to zero giving the bell-shaped curve in Figure 4.7. The maximum in the curve and crossover point between storage and loss moduli occurs at im. 

In this contribution we present results obtained with tetra-ethyleneglycol diacrylate (TEGDA). This compound was chosen since its polymer shows an easily discernible maximum in the mechanical losses as represented by tan 5 or loss modulus E" versus temperature when it is prepared as a thin film on a metallic substrate. When photopolymerized at room temperature it forms a densely crosslinked, glassy polymer, just as required in several applications. Isothermal vitrification implies that the ultimate conversion of the reactive double bonds is restricted by the diffusion-limited character of the polymerization in the final stage of the reaction. Therefore, the ultimate conversion depends strongly on the temperature of the reaction and so does the glass transition. 

The imaginary part of the modulus, also called the loss modulus, is a damping term which determines the dissipation of energy as heat upon deformation. G"/G is called the dissipation factor and is proportional to the ratio of energy dissipated per cycle to the maximum potential energy stored during a cycle. 

In addition to knowing the temperature shift factors, it is also necessary to know the actual value of ( t ) at some temperature. Dielectric relaxation studies often have the advantage that a frequency of maximum loss can be determined for both the primary and secondary process at the same temperature because e" can be measured over at least 10 decades. For PEMA there is not enough dielectric relaxation strength associated with the a process and the fi process has a maximum too near in frequency to accurately resolve both processes. Only a very broad peak is observed near Tg. Studies of the frequency dependence of the shear modulus in the rubbery state could be carried out, but there... 

A coincidence between r and Tf, accompanied by the formation of a maximum of energy losses (peak of the loss modulus G" or of the loss factor tan <5 = G7G ), can be achieved by varying either the period Tf at constant temperature (isothermal experiment) or t (by changing the temperature) at the constant period Tf (isochronous experiment). The latter procedure is experimentally easier to implement and is therefore more frequently used. 

The effect of the side chain bulkiness has been further studied on a series of chloro derivatives of poly(ethyl methacrylate)(PEMA). Though poly(2-chloroethyl methacrylate) exhibits69 a pronounced peak at Ty = 117 K, poly(2,2,2-trichloroethyl methacrylate), poly(2,2,2-trichloro-l-methoxyethyl methacrylate), and poly(2,2,2-trichloro-l-ethoxyethyl methacrylate) do not show (Fig. 6) any low-temperature loss maximum above the liquid nitrogen temperature157. However, these three polymers probably display a relaxation process below 77 K as indicated by the decrease in the loss modulus with rising temperature up to 100 K. Their relaxation behavior seems to be similar to that of PEMA rather than of poly(2-chloroethyl methacrylate) which is difficult to explain. 

The temperature dependence of the loss modulus, at 1 Hz of MT0.9I0.ij plotted in Fig. 91, shows quite a broad peak with a maximum around - 110 °C. Such a behaviour is very surprising, compared to the results obtained by dielectric relaxation (Fig. 76) where a broad peak is also observed from - 120° to about 50 °C, centred around - 60 °C. 

Before considering the various mechanical properties, it is important to notice that the transition of these copolyamides, as shown by the dynamic mechanical loss modulus, E", in Figs. 84 and 85 for the xTyl -y and MTyIi y series, respectively, occurs at quite low temperatures. Indeed, for the first series the ft peak maximum occurs at - 60 °C at 1 Hz, and at - 110 °C for the second series. From this point of view, these copolyamides look more like BPA-PC (Sect. 4) than PMMA (Sect. 3). 

Thus, mechanical measurements such as DMA or TBA are more common with the latter being used on reactive systems to gather reaction kinetics data [120]. These methods relate changes in the responsive modulus of the material to an impressed sinusoidal vibration. From this Tg, the physical thermomechanical behavior of the system can be related by a quantity termed tan 8 (storage modulus/loss modulus) which passes through a maximum at the Tg. These relaxations occur at certain frequencies at characteristic temperatures. 

TDI Polyurethanes. Two 2,4-T-lP samples with different hard-segment concentrations were studied and found to display a broad a-relaxation maximum, also characterized by a decline in storage modulus of about two and one half orders of magnitude, as shown in Figure 5, a plot of storage and loss modulus vs. temperature at 11 Hz. The position... 

The dynamic mechanical properties of four 2,6-T-2P samples containing from 19 to 43 wt% hard segments are summarized in Figure 10. A low temperature s relaxation is apparent at about — 70°C for all compositions examined. The transition temperatures of these loss maxima and the associated activation energies are given in Table III. A second process, the c relaxation, can be noted as a shoulder on the high temperature side of the 8-loss maximum. The conclusion of this relaxation is marked by a change in slope of the loss modulus vs. temperature plots... 

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