tailieunhanh - Electroactive Polymers for Robotic Applications - Kim & Tadokoro (Eds.) Part 6

Tham khảo tài liệu 'electroactive polymers for robotic applications - kim & tadokoro (eds.) part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Ferroelectric Polymers for Electromechanical Functionality 93 displacement d so a torque or moment may exist. The torque consists of two components F sinớ and F- sinớ acting on the dipole as shown in Figure . The torque will tend to align or orient the dipole in the direction of the applied electric field 12 . As is well known torque is a quantity which is defined as a cross product of the force F and length vector d T d X F Using scalar notation the total torque is given by the following equation T F d 2 sinớ F_ d 2 sinớ Fd sinớ Since the force F is given by qE the torque is rewritten as T qEd sinớ where q is the charge. Using the relation u qd therefore T pE sinớ The incremental work dw which must be done to align the dipole by an angle d0 is dw Td0 Integrating this equation we obtain w d M pE ịsmSdỡ -ựE cosớ Here the amount of work or energy which is needed to align a dipole at an angle Ỡ to an applied electric field E is given. Thus a dipole I inclined by an angle 0 to an electric field E has a potential energy w given by w Lid cosd or the scalar product w Ịi- E. The alignment or orientation of the dipole under an electric field is called polarization. However even in the presence of an electric field dipoles are still under the influence of thermal motion amounting to an energy kT where k is the Boltzman constant X 10 J-K and T is temperature. Therefore the torque aligning the dipoles in the field direction is always counteracted by thermal energy to some extent. Polarizability and Polarization Polarization P is defined as a vector quantity expressing the magnitude and direction of the electric dipole moment per unit volume. In the absence of the external electric field the polarization is equal to the charge per unit area on the 94 J. Su surface of the material. In general there are four fundamental components of polarization electronic atomic orientational and interfacial or space charge polarizations 13 . .