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Appendix.
Building a prototype.
This appendix is a preliminary design for building a IMAT prototype using an IMAT.
Assume we have 5 materials in "cubes" of 50 µm side (Figure A-1) .
Figure A-1
The injectors can have the configuration of Figure A-2, in this configuration the ratio is 14:1 and isolator-1 cannot attach to the other materials. That is the piezoelectric film is free to move. The "x" show the empty conduit for moving the material.
Figure A-2
Other configuration more easily built is in Figure A-3. In this configuration the ratio is 32:1, the only assumption is that isolator-2 cannot bind to the conductor material.
Figure A-3
This figures show in profile the bimorph piezoelectric film, to calculate the approximate length the equation (1) [Pennwalt 87] can be used, where V is the voltage, d
31
is the piezoelectric constant, t is the thickness of the piezoelectric material and L is the length needed.
Now the width of the conduit is selected. If the width is 50 µm, the same as the "cubes",then the "cubes" can have a difficult time moving, because of this, a postprocess which can expand the width in 10-20% is needed, perhaps using an etching procedure or build a machine to grind the conduits. That is feasible because the conduits are accessible for one side of the machine. Additionally this machine is probably needed for periodic cleaning maintenance of the conduits.
Taking the final width of the conduit as 60 µm, then Æx = 60 µm, suppose V = 100 volts and d
31
= 50 x 10
-12
C/N this value is in between PVDF (plastic, Kynar) and BaTiO
3
(ceramic) . With these values L = 6.32 mm. This value assumes that the film closes all of the conduit. That is not necessary if the tip of the film touches the side of the last cube and presses into the wall then the column of cubes stop moving. For this case a tip displacement of only 10 µm is required and L = 2.58 mm; using L = 5 mm is a conservative approximation.
Assuming a work area of 10 cm per side, a ratio of 100:1 (symmetric in X and Y) and using 10 materials at the time; with these values 20 sections of 5 mm each are required, each section with 10 transversal injectors (one for each of 10 materials) and 200 longitudinal injectors for a total of 2000 injectors per section.
For controlling 2000 injectors, a matrix of 50 by 40 electrodes is proposed, that is 90 conductors per section. Because the piezoelectric film is a capacitor, cycles of charge/discharge of the capacitors are needed, using 100 Hz as a work frequency and 10 times more, that is 1 kHz as a multiplexing frequency for 40 lines, then a 40 kHz frequency using 50 control lines can control the 2000 injectors.
Figure A-4 shows how the top of the piezoelectric film can join a reservoir of material (here 2x3) in top of this is a feeder channel (here 4x3) , the film extend two electric connections to the top of the assembly. Two transversal cuts are show also.