Malin Edvardsson Jun 5, ’18 3 min

What is Dissipation?

Talking about QCM-based instrumentation, one often comes across the concepts of ‘dissipation’ or ‘damping’. What do these concepts mean, and why are they relevant?

Dissipation, damping and energy loss

‘Dissipation’, or “energy dissipation”, to be more precise, refer to the energy that is lost from the system under study. The QCM is a harmonic oscillator and like all real-world oscillators, it is damped.

An oscillator that is not forced to oscillate by an external force, it will gradually oscillate with lower and lower amplitude and eventually, the oscillation will die out. This damping of the oscillation amplitude that we are considering here comes from frictional losses, which could be internal friction in the oscillator itself or in the surrounding medium (air, water, etc). The friction causes oscillatory energy to be dissipated as heat, hence the name Dissipation.

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Dissipation contains information about the material under study

In the case of QCM, the induced energy losses will mainly originate from materials in contact with the oscillating sensor surface. All material in contact with the surface will induce energy losses. The phenomenon is particularly pronounced in the presence of bulk liquids or at the deposition of soft films. During the oscillation, liquids and soft films in contact with the surface will be deformed, which results in energy being lost from the system. When the sensor surface is in contact with air or vacuum, the induced energy losses are comparatively small. The same goes for the losses induced by the deposition of thin and rigid layers. Thin and rigid layers do not deform during the oscillation, and the losses are therefore smaller than those induced by soft and/or thick layers. Consequently, a high dissipation indicates that we have soft or viscous material in contact with the surface, while a low dissipation indicates that the material at the surface is rigid and follows the oscillation.

The definition and the relation between the dissipation and the Q-factor

An important parameter describing the characteristics of an oscillator is the quality factor, or Q factor. This is a dimensionless parameter that describes the damping of the oscillation at resonance, by relating the amount of energy stored to the amount of energy lost. The dissipation, D, which is the inverse of the Q factor, is the sum of all energy losses in the system per oscillation cycle. It can also be defined as the energy dissipated per oscillation, divided by the total energy stored in the system.   

Q = 2π ⋅ (energy stored)/(energy lost per cycle) = 1/D             (1)

As can be concluded from Eq. 1, a high Q factor indicates that the energy loss is small and that the oscillation will persist for a long time, and vice versa, Figure 1. The higher the Q the lower the damping and the longer the oscillation will keep on going.

Dissipation tuning fork and jello

Figure 1. In the case of a tuning fork (left), the dissipation is low, and the oscillation will persist for a long time. In the case of Jello, the energy dissipation is higher, and the oscillation will die out faster.

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