The loss modulus is a measure of energy dissipation, though as a modulus it is hardness or stiffness of a material. Upon heating both storage and loss modulus decrease because less force is required for deformation. In the region of the glass transition molecular segmental motions are activated, however motions occur with difficulty, described as molecular friction that dissipates much of the force. Therefore though the material is less stiff/hard, more force is dissipated as heat, increasing the loss modulus. Much less energy is stored since the molecules can move with the force giving a rapid decline in storage modulus. 

Because modulus means stiffness/hardness, that is resistance to deformation, intuitively it seems that both storage and loss modulus should decrease with temperature. However loss modulus must be interpreted as force/energy dissipation. The relative changes in storage and loss modulus are emphasised by their ratio, the loss tangent or damping factor, that is often used to locate glass transition temperature because of its sharpened emphasis, though really it is the loss modulus that is the physical manifestation of the glass transition temperature.

As temperature continues to increase above the glass transition molecular frictions are reduced, less energy is dissipated and the loss modulus again decreases. This higher temperature decrease in loss modulus results in a peak in loss modulus in the glass transition region. The glass transition region is special because it is a transition in molecular response revealed as a change in properties. Materials transition from glassy to leathery to rubbery in this temperature range. 

The loss modulus is calculate by G''=(stress/elongation)*sin delta. The elongation induced stress decrease with increasing temperature. You need less force to generate the same stress. In this case, the loss modulus decrease.

Thanks

Loss modulus decreases with increasing temperature.

So G" (T) = Stress(T) / Elong(T) * sin delta (T).  Well, the storage modulus is G' (T) = Stress(T) / Elong(T) * cos delta (T).

So the argument about stress decreasing with temperature, while partly right, does not address the question fully, since the argument equally applies to both G" (loss modulus) and G' (storage modulus).

What we need to pay attention to just as well is the loss tangent ("tan delta").  When you have a polymeric (either thermoplastic or thermoset), and your temperature exceeds the glass transition temperature, then you have a "rubbery" material with crosslinks (can be physical, like entanglements for thermoplastics and hydrogen bonding for polyurethane thermosets;  or can be chemical, as in vulcanized rubbers).

So a polymeric material, which is very viscoelastic in the glass transition zone (and therefore its "tan delta" shows a peak), becomes much more elastic above the Tg, where the tan delta decreases substantially.  Since G" = Stress / Elong * sin delta ==> a decrease in tan delta = decrease in sin delta, so G" decreases.  So that is the fuller picture.

---

Additional note: if you were to take a polymeric liquid with molecular weight that is substantially lower than the entanglement molecular weight (in which case, you might refer to it more appropriately as an oligomer), and do a DMA experiment, you will find that your G" will keep increasing as you go above the Tg [don't ask me why, but I actually did a test like that to convince myself one time what I already should have known!]   So the tan delta decreasing after the glass transition, is seen with rubbers and not liquids.  This is a key difference between polymeric glasses (glass-rubber transition) and small molecule glasses (glass-liquid transition).

The loss modulus is a measure of energy dissipation, though as a modulus it is hardness or stiffness of a material. Upon heating both storage and loss modulus decrease because less force is required for deformation. In the region of the glass transition molecular segmental motions are activated, however motions occur with difficulty, described as molecular friction that dissipates much of the force. Therefore though the material is less stiff/hard, more force is dissipated as heat, increasing the loss modulus. Much less energy is stored since the molecules can move with the force giving a rapid decline in storage modulus. 

Because modulus means stiffness/hardness, that is resistance to deformation, intuitively it seems that both storage and loss modulus should decrease with temperature. However loss modulus must be interpreted as force/energy dissipation. The relative changes in storage and loss modulus are emphasised by their ratio, the loss tangent or damping factor, that is often used to locate glass transition temperature because of its sharpened emphasis, though really it is the loss modulus that is the physical manifestation of the glass transition temperature.

As temperature continues to increase above the glass transition molecular frictions are reduced, less energy is dissipated and the loss modulus again decreases. This higher temperature decrease in loss modulus results in a peak in loss modulus in the glass transition region. The glass transition region is special because it is a transition in molecular response revealed as a change in properties. Materials transition from glassy to leathery to rubbery in this temperature range. 

Dear Dr. Verker:

Here, with due careful, it is interesting have in mind that increase the frequency of measurement have an equivalent effect to the decreasing the temperature of measurement.

i) Typically, the storage modulus depends on the molecular-motion of the main-chain of the polymer.

ii) During a heating cycle, when the temperature passes through its glass transition temperature the maximum in tan(delta) parameter occurs.

iii) In fact there is kind of phenomenon of resonance between the frequency of forced vibration selected in the analysis and the frequency of the diffusional motion ascribed to the main-chain or main backbone chain.

In this sense, there is a maximum being that left side of the maximum exhibits increasing and high side of the maximum decreasing.

Previous answers approach this event, despite that in my view, this question is a priori one of more complex for this area.

Kind regards

Marcos Nobre

The resonance phenomena between the force frequency and the strain imposed in the specimen is not related to the peak in loss modulus or tangent(delta). Resonance of the specimen is an aberration to the experiment, where the test frequency and specimen geometry factor and modulus impinge. Resonance results in a sudden high intensity response appearing like noise over a limited frequency range. Response can be removed or shifted by choosing a specimen with different dimensions; it usually occurs at higher frequencies. I suspected resonance in a specimen at 80 Hz in one experiment, it was repeatable until I changed the specimen dimensions. I liken it to the observer causing an unwanted distortion in the system being observed.

I grew up in an age before thermal analysis, and had to resort to something known as a torsion-pendulum to measure modulus vs. temperature of filled polymeric materials.   It was actually from those days that the tan delta came into vogue for describing the loss curve that one could construct on top of the modulus curve, both vs. temperature.  That work occurred at the "natural" frequency, which was whatever the sample delivered in response to an initial force.  We of course measured that frequency carefully, as a function of temperature. 

I always viewed this as a simple resonance process, since one readily observed (as temperature increased) the total loss in response of the pendulum at some temperature, followed by a regain in response at still higher temperatures.  We always saw the peak in the loss curve occurring around the middle of the decline of the modulus curve above Tg which was 10 deg C or so above the Tg. 

It somehow seemed reasonable that this was resonance process, because molecular translational motion (endothermal) was just starting at Tg. But since we did not typically vary the geometry of the sample much, I cannot comment on Dr. Shanks' observation above. 

So the remaining question is of course, what causes the loss of response at higher temperatures (or analogously frequencies), followed by the regain of response?  My physics professors suggested that complex systems simply fell into and out of "resonance" as a peculiarity of the whole system.  The amplification of the tan delta (loss modulus) was seen as analogous to the amplification of sound in a resonating system, which would rise and fall as one component increased in speed. 

But none of that addressed the question of "why?"  The observation that sample geometry can alter the "resonance" suggests that a more satisfying answer is needed.   

The original question has been expanded into issues caused by specimens displaying their resonant frequency.

Dr F. Louis Floyd described the portion pendulum technique for DMA where a torsional strain is imposed and upon release the specimen freely (without any imparted force) oscillates at its resonant frequency and damping is measured from the logarithmic decay of the oscillation amplitude.

Typical DMA instruments operate with a forced oscillation via an external (to the specimen) sinusoidal force. Still the specimen will have a natural resonant frequency due to its modulus and dimensions. When the applied sinusoidal frequency and the specimen natural frequency coincide then chaotic response is observed. The damping factor becomes an acceleration factor. This behaviour was demonstrated in the famous video of a bridge with the frequency of a severe wind coinciding with the natural frequency of the bridge whose oscillations became larger until it destructed. Damping elements are included in structures in Earthquake regions to dampen oscillations of the structures in the event of an Earthquake, rather than the opposite where oscillations in resonance could increase until destruction.

I have searched for publications giving an alternate or better explanation, their are not many, however attach a paper by Placet and Foltête (DOI:10.1051/epjconf/20100641004) on their DMA and resonant factors.

 Dr.  Robert ,

At present i am working on viscoelastic characterization of Epoxy based polymers. I have  used Zener model (maxwel in parallel with  a spring). I have evaluated model parameters at various temperatures. I have  found the E and Eta  values of maxwel model initially increases  with temperature at glassy region and  then it decreases. where as E of individual spring decreases with the increase in temperature. is it analogous to loss modulus increasing with temperature at glassy state???

Please give  me  reference paper so that in my paper i can cite that article.

Dear Kavitha Rao, We use creep measurements for viscoelastic characterisation:

Genovese, A. and Shanks, R. A. (2007). "Time-temperature creep behaviour of poly(propylene) and polar ethylene copolymer blends." Macromolecular Materials and Engineering 292(2): 184-196.

and modulated temperature – thermomechanical analysis:

Shanks, R. A. (2011). "Linear thermal expansion, thermal ageing, relaxations and post-cure of thermoset polymer composites using modulated temperature thermomechanometry." Journal of Thermal Analysis and Calorimetry 106: 151-158.

I am unsure if this is of any help to the original question, but I think that the resonance phenomenon discussed by Marcos Augusto Lima Nobre is in regard to the dynamic nature of the molecular motions rather that the general specimen resonance.

From my understanding, and I think also in accordance with the original answer of Pr. Shanks, the bell shaped nature of the loss modulus curve would be the result of something akin to internal friction losses. At the onset of the relaxation phase, the number of motion increases sharply and the sum of all losses increases, although individually losses may at some point be getting lesser for each individual motion. The net result being an increase in loss modulus. However, past a certain point, the increase in molecular mobility gets lesser and lesser and the losses incurred by each motions keep on decreasing, ultimately leading in a decrease in the loss modulus.

Now, back to the point of Pr. Lima Nobre. My understanding is that the 'internal friction' itself might not be a monotonically decreasing function of temperature but perhaps also some kind of bell shaped function because the mechanical and thermal excitations incurs a kind of resonance phenomenon on the molecular level motions (although no resonance occurs at the macroscopic level).

Best regards,

Laurent

(Note to Prs. Shanks and Lima Nobre: I hope I've paraphrased your comments correctly, but please take no offense if I did not and feel free to correct me.)

One thing that I have found in my accelerated life analysis using DMA and Heat Flow Microcalorimetry is that the plasticizers must be considered during the temperature changes - not just the base polymer - loss of the lower molecular weight plasticizers, interaction within the plasticizers and interaction of the base polymer with the plasticizer and basic aging of the plasticizer.  This is naturally dependent on the functional groups of the polymerics involved. This happens with temperature as well as mechanical stresses.