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284   Carbon Nanotube Fibers and Yarns


          11.5.4  Power density (P)
          Power density is the time derivative of the energy (work) density. Power den-
          sity can be related to the speed at which the actuation can occur and this can
          be assumed to match the tensile actuation rate if the inertia effects are ignored.
                                        dE
                                    P =    m  =  Fv                  (11.10)
                                         dt
          where F=mg is the lifting force and v is the instantaneous velocity of the
          object in the hung weight experiment. The average power density (P) of an
          actuator may be calculated using Eq. (11.11)

                                             v (
                            (
                                                     3
                                                  /
                         PW /    g) =  E t m  or  PW m ) =  E t v    (11.11)
                           m
          where t correspond to actuation time (second, minute, or hour), and E m  and
          E v  are from Eq. (11.8).
          11.5.5  Efficiency (η)
          Definition: the ratio of output work over input energy.
                                         W
                                 η % () =  out  ×100 %               (11.12)
                                         W in
          where W out  ( J) and W in  ( J) correspond to the output work and input work, re-
          spectively. The input energy can be in the form of electricity, heat, radiation, etc.

          11.5.6  Other metrics

          Bandwidth refers to the range of frequencies that the actuator can be ex-
          cited continuously. Cycle life refers to the number of cycles that an actuator
          can survive before failure.
             Table 11.1 shows the performance metrics of some CNT yarn-based
          actuators.


          11.6  Potential applications

          By virtue of their remarkable actuation performance, CNT yarn-based actuators
          have been suggested to make a wide range of smart devices. It is important to
          note that the type and magnitude of the stimulus (e.g., current, solvent, heating,
          etc.) are important in selecting the best-suited actuator for a specific application.
             Smart window is a favorite demonstration example for researchers.
          Actuators made of single and plied twist-spun CNT yarns subjected to
          hydrophilic treatment can be activated by water absorption. Such a actu-
          ator fixed on the backside of a window frame can be used to open and
          close a window (Fig.  11.9A)  [50]. Driven by reversible water-induced
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