Edited 2017 - changed recommended long life storage voltage and added comments on fast charging using some recent systems. RM.
What YOU do as regards several of these questions depends largely on what YOU are trying to achieve or test.
Discharge to cutoff is fully discharged (to whatever remaining % that voltage represents). That's the easy one :-)
Percent dropoff of current in tail sets final % of max possible charged reached. There was a superb table given here within last week or so. Can supply later if you don't find it.
Real Men™ plateau at 4.2V and tail down to 10% or even 5% of the constant current rate. This gets the battery full and knocks the stuffing out of it.
Others terminate the current tail at say 25% of cc value.
Optimum lifetime for ongoing usage is at about the end of the constant current phase. That makes it very easy to locate - charge at specified current until desired max voltage is reached, then charge at constant voltage as desired. Here "desired" is to stop immediately. This is the point at which batteries tend to give significantly longer whole of life mAh of storage without grossly reducing mAh capacity per cycle. This is liable to be the point where older "fast chargers" tell you they have finished. Actual % total claimed varies but probably 70% - 80% range.
Newer USB input fast chargers use the term differently. In the case of USB the maximum available charge current at 5V is 5A so that the battery MAY be able to be charged at ~= 6A for the CC part of the cycle using an efficient buck converter to drop voltage and raise current.
[For a buck converter: Vout x Iout = Vin x Iin x efficiency_of_conversion]
Some systems such as QuaqlComms Quick Charge system allow the use of higher charger voltages (9, 12, 20) with specifically designed equipment, so battery charging can be faster for a given voltage provided that the battery specification allows this.
Maximum charge rates for LiIon and LiPo batteries are usually C/1 = 1A per Ah of battery capacity.
At 5V, 5A a USB charger can charge a 6000 mAh 1 cell LiPO battery at max rate - so eg a 10,000 mAh single cell battery used in some larger tablets can not be charged at the allowed 10A ! rate.
For long life storage where actual stored capacity is unimportant, LiIon and LiPo cells should be stored at about 3.7V.
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Using cells without protection adds to the rich tapestry of life. As long as you don't mind the occasional scorch mark on the tapestry that's fine. Note that part of the protection is a one time high capacity fuse under the cap for when things get out of control. Undervoltage discharge destroys. Charging from below a certain voltage at full rate can get fun, I'm told. Charging at reduced rate can bring cell up, I'm told. Below another second level they say don't even think about it. I've had very poor success in trying to get LiIon to misbehave. I have a box of unprotected cells that are very uncooperative about venting with lame etc. Strange. Sony and Apple and even HP seem to be much better at it :-).
So, when the cell voltage is close to 4.2V the charging voltage will must be higher e.g. 4.5V, and this should not cause any damage to the cell. Is my understanding correct?
No. Your understanding is incorrect and your charger is suspect.
And/or your description is not quite complete and unambiguous.
For information on battery matters for most battery chemistries a good starting point is often the excellent site at Battery University.
NB: What I have written below is based both on experience and on input from a wide range of sources, including battery university.
Assume for following discussion a manufacturers spec of
Maximum current = CCmax (usually 1C for LiIon but may be other for specific cells).
Assume CCmax is 1C for the cell in question for convenience.
Actual spec will be as per datasheet and is temperature dependant and also depends on how many charge/discharge cycles you wish to achieve before the battery turns to mush and/or is reduced to say 70% of original capacity.
Maximum voltage of Vmax - usually 4.2V or less. Say 4.2V for now.
As for current, the maximum Voltage applied will affect cell longevity (and capacity on a given charge). Charging at a terminal voltage of much above 4.2V will shorten you cell life, may lead to metallic lithium plating out and can lead to the exciting and equipment eating "vent with flame" battery meltdown phenomenon.
Minimum current of Icv_min when charging at Vmax. This is the minimum that current should be allowed to fall to when charging in CV mode. When in CV mode, charging is terminated when current drops to this level. Icv_min is typically set at somewhere between 25% of Icc (early charge termination) and say 10% of Icc (maybe sometimes even 5% of Icc). The lower Icv_min is set the longer current trickles into the battery at Vmax in CV mode. Setting a low value of Icv_min adds slightly to the energy that can be stored in the battery on a given cyccle AND utterly tears the battery apart inside and shortens it life.
These two important points apply:
The maximum voltage AT the battery (1 cell) under maximum constant current CCmax is Vmax = 4.2V in this case.
BUT the maximum voltage AT the battery (1 cell) under ANY current is also Vmax.
If the battery will not accept Imax when Vmax is applied then CC mode is no longer appropriate. Charging should be CV (or terminated if Icharge at Vmax is <= Icv_min - see below)
An important point here is where you measure what you call "the charging voltage".
This is properly measured at the cell electrodes as close to the cell internals as possible. In practice anywhere on the (usually) weld-attached tabs should be OK as at the max allowed current the voltage drop across the tabs should be minimal. As long as the voltage at the actual cell is <= Vmax then the voltage at other points in the charger may be > Vmax if the charger design requires it.
Consider: Apply a "true" constant current source to a discharged LiIon cell.
There will be lead resistance external to the cell so the voltage elsewhere to the system may be higher than at the battery terminals. Ignore that for now - comment on this at end.
For a discharged LiIon battery the terminal voltage will be somewhere around 3V and will slowly rise as CC is applied.
After about 40 to 50 minutes of charging a LiIon cell at 1C (= CCmax in this case) from fully discharged the TERMINAL voltage will reach 4.2V. This is where you stop applying CC and apply a CV of Vamx (= 4.2V in this case) at whatever current it takes to keep the voltage at 4.2V (up to a maximum of CCmax.)
The following paragraph may sound a little complex but it is important.
It does make sense - read and understand if you care about the answer to the question that you asked.
It is a fallacy to think that you must apply a higher voltage at the cell to get it to accept CCmax when Vcell is at Vmax.
This IS true if the battery is fully charged or is charged above the point in the cycle where Vcell first reaches Vmax when charging at CCmax.
BUT that is because you are then trying then to do something which is outside the proper charging "envelope".
IF a LiIon cell will not accept CCmax when Vmax is applied it should be charged at not above Vmax until Ibattery falls to Icv_min.
If you apply Vmax and Ibattery is below Icv_min then the battery is fully charged and you should remove Vcharge. Leaving a battery connected indefinitely to a voltage source of Vmax when Icharge is less than Icv_min will damage the battery and reduce or greatly reduce its cycle life.
Charging voltage is removed when Icharge falls below Icv_min to prevent potentially irreversible electrochemical reactions and to prevent Lithium metal "plating out".
If Vmax is set at 4.15V then charge capacity is reduced noticeably but cycle life is extended.
If Vmax is set at 4.1V charge capacity is significantly reduced and cycle life is significantly extended.
The loss of capacity per cycle that occurs when Vmax is reduced leads to an overall INCREASE in total lifetime capacity as the extension in life cycles rises faster than the per cycle capacity falls. If you care mainly about highest capacity per charge set Vmax as high as allowed and accept low cycle life.
If you can tolerate say 80% to 90% of max possible capacity per cycle, set Vmax lower and get more overall energy storage before replacement.
The graph below from Battery University article How to Prolong Lithium-based Batteries shows what happens when Vmax is increased above 4.2V.
At the end are 3 tables from the same battery University page which show the effects on cycle life from varying various parameters (depth of discharge, temperature, Vmax)
Internal voltage versus terminal voltage:
There will be internal resistance in the cell so the "real" potential in the cell proper during charging at CC will be less than at the terminals. At CV the internal voltage will approach the external voltage as Icharge "tapers off".
IF you want to play 'fast and loose' with all manufacturers' specs and all advice given you can assume that you can 'allow' for this resistance and guestimate a true internal voltage which is lower than the terminal voltage. May the force be with you and with your battery, and may it live long and prosper - but, it probably won't.
Three excellent tables from Battery University showing how cycle life varies with various parameters.
Best Answer
It usually does, but it's not necessary. That's the way commercial chargers work, to get the fastest charge while staying within the no-damage parameters.
One common regime that chargers use is to charge to 4.2v, then turn off until the voltage has fallen to 4.1v, then recharge to 4.2v.
For my money, 'providing enough charge over time' to keep the cell at 4.1v would be kinder if that charge was delivered steadily and the cell never exceeded 4.1v, than if it was provided in bursts and the cell cycled between 4.1v and the higher more damaging 4.2v. The first option is of course a continuous trickle charge.
However, I'm not a battery manufacturer, and I've yet to find data from any of them that discusses longevity under sub-maximum voltage trickle charge conditions. An immense amount of effort has been put into characterising rechargeable cells to get fastest charge rates and largest usable capacity (which, let's face it, is where the volume and the money is), and rather less into using them more gently.
To your specific charging conditions of 4v 100mA. If 100mA is less than the battery's max charge current, then your CI phase will be OK. Once the cell gets to 4v, the charging current will fall. I expect it would fall to essentially nothing.
I would risk keeping it on CV at 4v indefinitely, taking appropriate precautions to mitigate fire risk. You might be tempted to do the same. You will not find any reputable sources that will tell you this is OK. I will not be responsible for your cells if you do this, and find they degrade more quickly than you hoped.
It would be interesting for someone, perhaps you, to test a few cells with differing lower voltage trickle charge regimes and report the results, perhaps quarterly over a five or 10 year period. I've considered it, but am unlikely to get around to it.