Discharge Rate and Capacity

We experiment with two types of lithium-ion battery. One is the PP031012AB, with nominal capacity 19 mA-hr. The other is the 382030 with nominal capacity 150 mA-hr. The small one we consider suitable for implantation in mice, and the larger for implantation in rats.

The data sheets give a maximum charging current of 9 mA and 80 mA for the small and large batteries respectively. We begin by charging the small battery at 20 mA and the large one at 150 mA until the battery voltages reach 4.3 V. We discharge both with resistors, and we find that the battery capacity is roughly half nominal.

We now charge the batteries by the rapid-charge procedure specified by their data sheets. We supply 9 mA to the small battery and 150 mA to the large battery until their voltages reach 4.3 V, then we apply constant voltage of 4.3 V until the battery current drops to 10% of the rapid charge current. After two hours, both batteries appear to be fully charge. We discharge them with resistors. The graph below shows the small battery discharging through a 200-Ω resistor (A) and the large battery discharging through a 40-Ω resistor (B).


Figure: Charging and Discharging Lithium-Ion batteries. Lines A and B showing the discharge of the small battery through 200 Ω and the large battery through 40 Ω. Lines C and D show the small and large battery charging up to 4.3 V. Lines E and F another discharge with the same resistors. Line G is the large battery discharging through 20 Ω, and H is discharging through 10 Ω.
At 3.7 V the discharge currents (A and B) are 18 mA and 92 mA respectively. While discharging to 3.0 V, the small battery delivers 20 mA-hr and the large one delivers 160 mA-hr. The small battery discharges completely to 0.0 V through the 200-Ω resistor. The large battery is equipped with a protection circuit that disconnects it from the 40-Ω resistor when the battery voltage drops below 3.0 V.

We recharge the large battery at 150 mA (C) and the small battery at 9 mA (D). We discharge through the same resistors (E and F). The large battery provides 162 mA-hr but the small battery provides only 11 mA-hr. The small battery has been damaged by its complete discharge to 0.0 v. We re-charge the large battery and discharge it through 20 Ω (G). At 3.7 V, the discharge current is 185 mA. The battery provides 148 mA-hr. We re-charge and discharge through 10 Ω (H). At 3.7 V, the discharge current is now 370 mA and the battery still provides us with 130 mA-hr.

Lithium-ion battery data denote the nominal capacity of a battery in mA-hr with the letter C. For our large battery, C = 150 mA-hr. The rapid charge current is 1.0C mA = 150 mA. The maximum discharge current is 160 mA, which is 1.1C mA. The smaller battery has C = 19 mA-hr, but its rapid charge current is only 0.5C, or 9 mA, and its maximum discharge current is also 0.5C.

It takes one or two hours to charge a lithium-ion battery to its nominal capacity 1.0C. When we discharge at 1.0C mA, the capacity drops to 0.9C mA-hr, and discharging at 2.0C mA, the capacity drops to 0.8C mA-hr. If we allow the battery to discharge completely to 0.0 V, it loses over half its capacity. Thus we can draw 38 mA continuously from our 19 mA-hr miniature lithium-ion battery and still obtain 15 mA-hr of battery life.

High-Index Fiber

We receive from Fiberoptics Technology several hundred meters of 0.016" clad rod, F2/8250. We measure its outer diameter as 390 μm. Its core is Schott F2 glass and its cladding is Schott 8250. The core occupies 83% of the fiber cross-sectional area. We have a 355-μm diameter core with a 17-μm layer of cladding. The rod is so thin we can bend it in a 10-cm radius, and the core has refractive index 1.63, so we will call it high-index optical fiber.

We take a 5-cm length of fiber and polish both ends. We try to use hot-glue to hold the fiber in a ferrule, which is our usual method with silica glass, but when we try to remove the hot glue with a propane flame, the glass melts. The F2 glass melts at only 434°C compared to 1100°C for the silica we usually work with. Our flame-based tapering machine will not taper this glass. We will have to develop a lower-temperature heater to take the fiber just above its glass temperature for tapering. We will have to devise a reliable method for polishing the flat end of the fiber without the use of hot glue. For now, we did the best we could holding it between finger and thumb.

We clean the fiber and coat it with NO13685 adhesive. This adhesive has the consistency and appearance of water when applied, and cures to a tacky solid in UV light. Its refractive index is 1.3685. We lower this fiber onto a green EZ500 LED. We pre-cure the coating, then add clear epoxy to hold the fiber in place, and cure further while blowing nitrogen over the exposed coating. (The coating cures to a non-tacky, flexible solid only in the absence of oxygen.) We turn on the LED and take a photograph of the fiber base with our microscope, shown below on the left.


Figure: High-Index Fiber with NO13865 Coating. Left: first attempt, note the epoxy holding the fiber onto the LED. Right: after cleaning the fiber with acetone and re-coating.

In the left-hand picture we see light escaping from the bottom of the fiber, from dirt beneath the coating, and from the meniscus of the epoxy where it encloses the fiber. The fiber tip emits 19% of the LED light (2.6 mW of green light from a total of 13.6 mW generated with 30-mA forward current). We wipe the fiber repeatedly with acetone. The coating comes off and we continue to clean the fiber until hardly any signs of dirt remain. We coat the fiber again, and cure the coating. We obtain the photograph on the right. The fiber tip now emits 24% of the LED light (3.2 mW). The signs of dirt on the coated fiber are greatly reduced, but we still see the same ring of light at the limit of the epoxy.

If we assume light is distributed uniformly across the 480-μ square area of the EZ500, then 43% of its light should enter our 355-μm fiber core and 9% should enter its cladding. The core of index 1.63, combined with the coating of index 1.3865, gives us a numerical aperture of 0.87, so we expect 76% of the light in the core to reach the tip. The cladding has index 1.487, and is combined with the same coating, so it has numerical aperture 0.58 and we expect 34% of the light in the cladding to reach the tip. Adding these up, we expect to get 36% of the LED light at the fiber tip. We see only 24%.


Figure: A 5-cm Coated Fiber on Green EZ500.

The photograph above shows that the light leaking from the exposed length of the fiber is small compared to the light emitted by the tip. Our close-ups of the base of the fiber, however, show a ring of light being lost from the fiber at the limit of the epoxy. It could be that the coating was improperly cured and the epoxy penetrated to the fiber glass along the epoxy meniscus. The epoxy has index 1.5, which reduces the numerical aperture of the cladding to 0.00 and the core to 0.61. A sufficiently lengthy contact between the epoxy and the glass would reduce the fraction of light reaching the tip from 36% to 16%.

Another potential loss of power at the tip is poor polishing of the fiber ends. In the past, we have observed 10% loss of power due to slight imperfections in the polish. The polish on the ends of this fiber is far from perfect.

Nevertheless, we are now seeing 24% of the LED light at the fiber tip, which is better than our previous record of 17%. When combined with our new and more efficient blue LEDs, this fiber would give us 7.2 mW at the fiber tip for a 30-mA LED current.

In the future, we will try the MY132 coating, with refractive index 1.325. This alone will increase our theoretical coupling efficiency from 36% to 42%. We may also find that the LED light is concentrated towards its center, as we did before, where a 300 μm fiber captured 9/5 as much light as we expected. Thus we might obtain up to 75% of the LED light at the tip.

UPDATE: [26-APR-13] Spoke to Adam at Norland Products and decided to try NO1625 and NO164 adhesives to glue the base of the fiber to the LED. These adhesives have refractive index 1.625 and 1.64 respectively, so they should fill scratches in the fiber base and give us a reliable optical connection between the silicon surface and the core glass.

UPDATE: [03-MAY-13] We achieve 30% capture efficiency with the F2-core fiber and a 460-nm EZ500. The LED emits 27 mW at 30 mA forward current and we see 8.2 mW at the far end of an 8-cm fiber coated with black epoxy. Only the 355-μm core carries light. Its numerical aperture with the cladding is 0.67. We expect 43% of the LED light to enter the fiber, and 45% of this light entering to reach the other end, for a total capture efficiency of 19%. With the fiber offset from the LED center, so as to avoid the cathode pad, we get 24%. But when we center the fiber, which requires that we smash down the cathode bond wire, we get 30%.

Lithium-Ion Batteries

The Implantable Lamp (A3024A) is powered by a BR1225 lithium primary cell. Its nominal voltage is 2.7 V and its nominal capacity is 48 mA-hr. It cannot be recharged, and we anticipate that its capacity when providing 10 mA will be closer to 24 mA-hr, because its nominal discharge current is only 30 μA. The A3024A provides 30 mA at 5.0 V for its lamp using a 90% efficient inductive boost regulator. But the battery's internal resistance is of order 40 Ω, and this resistance limits the continuous lamp current to 8.2 mA. The A3024A is equipped with a 1-mF capacitor bank in parallel with the battery, and this capacitor bank allows the boost regulator to flash the lamp for up to 10 ms. The volume of the capacitor bank is roughly the same as the volume of the battery. When we flash the lamp for 10-ms bursts every 100 ms, the battery voltage drops to 1.8 V as it provides an average current of 10 mA. We expect this current to exhaust the battery in 2.4 hrs.

The LIR1220 lithium-ion secondary cell is slightly thinner than the BR1225, has nominal output voltage 3.6 V, output resistance only 2 Ω, and can be re-charged. With its low output resistance, it can supply continuous power to the lamp without the need for a capacitor bank. Its capacity, however, is only 8 mA-hr. Consider instead the PP031012AB lithium-ion battery with capacity 19 mA-hr. Its rectangular shape occupies only 0.25 ml, compared to the 0.31 ml of the circular BR1225. When flashing the lamp 10 ms out of every 100 ms, the battery voltage will remain close to 3.6 V, and the battery will need to supply an average of only 5 mA to the boost regulator. The battery's capacity is 19 mA-hr at a discharge current of 20 mA. Here our average current is 5 mA but the peak current is 50 mA. We expect a slight decrease in capacity as a result, perhaps to 15 mA-hr. Even so, we can flash the lamp for 3.0 hrs with this battery, compared to 2.4 hrs with the BR1225. Furthermore, we can turn on the lamp continuously, although we should be aware that doing so will reduce our battery capacity.

The Implantable Sensor with Lamp (ISL), as we specified in our Technical Proposal, will combine a subcutaneous transmitter, an implantable lamp, and a microprocessor into one circuit that may be implanted in a rat. We are aiming to keep its volume less than 4 ml. Suppose we equip the ISL with a TE382030 battery pack. Its volume is 2.3 ml (30 mm × 20 mm × 3.8 mm), which leaves us 1.7 ml for the circuit, which will be sufficient because we no longer need space for a capacitor bank. The battery has capacity 150 mA-hr when delivering 150 mA continuously. It could flash the lamp with current 30 mA for 10 ms out of every 100 ms for 30 hrs, or it could turn the lamp on continuously for 3.0 hrs. Alternatively, with some lower-resistance lamp leads, we could increase the lamp current to 50 mA, thus boosting the optical power at the fiber tip, and we would still be able to turn on the lamp continuously for 1.8 hrs.

Lithium-ion batteries discharge themselves slowly. Even if we draw no current from them, they lose roughly 5% of their charge in the first month and 2% per month thereafter. This self-discharge, combined with their lower total capacity compared to the lithium primary cells, will shorten their shelf-life to a few months. If we could recharge the batteries before implantation, we could be sure of obtaining the maximum operating life after implantation. If we could recharge the battery while it is implanted, we could greatly extend the duration of our experiments.

The head fixture of the ISL offers us an opportunity to recharge a battery while implanted. Suppose we contrive to place upon the head fixture a sufficiently small, two-way, water-resistant socket. In addition to the L+ and L− leads required by the lamp, we run a B+ lead to the battery positive terminal on the ISL circuit. The B+ and L− wires connect to the two-way socket in the head fixture. When we want to recharge the battery, we connect two flexible leads with pins on the end to the head fixture. These leads in turn connect to an especially-designed battery charger, which we connect to our LWDAQ. The charger measures the resistance of the charging leads and monitors the battery voltage during a rapid charge cycle that will take roughly one hour to complete.

In both the mouse-sized Implantable Lamp and the rat-sized Implantable Sensor with Lamp, it appears that the lithium-ion battery pack provides us with a smaller, longer-lasting, and more capable power supply, even if we do not recharge them. Thus we believe we should switch to lithium-ion batteries for the ISL development regardless of whether or not we can devise a way to recharge the batteries while implanted. Furthermore, we will add a single pad to the ISL circuit that will allow connection to the battery positive terminal, so we can re-charge the battery before encapsulation, and allow for the possibility of recharging through a separate B+ lead to the head fixture.

UPDATE: [24-APR-13] We take an old cell-phone lithium-ion battery and solder wires to its terminals. This is a PBR-55D by Pantech, capacity 1000 mA-hr with nominal voltage 3.7 V. We use a 10 Ω power resistor as a load and a bench power supply as a charger. We have no difficulty charging and discharging the battery, and we find its output resistance to be 1.0 Ω. Further investigation reveals that the standard quick-charge time for lithium-ion batteries is 2.5 hrs. We begin with constant current charging at 0.5C/hr, where C is the battery capacity. When the battery voltage reaches 4.2 V, we switch to constant voltage charging until the charge rate drops to 0.05C/hr.