Objects (like combs) can be charged by rubbing as charged particles, particularly electrons, are transferred from one object to other. This can be seen as the object (comb) attracts small bits of paper. After some time, the charge on the body seems to disappear. How does this charge disappear without any external influence?
[Physics] How does an object regain its neutrality after being charged by rubbing
electrostatics
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The effect in which two objects get charged by rubbing and remain charged is called the triboelectric effect,
where the root "tribo" means friction in Greek (The Greek word $\tau\rho\iota\beta\omega$ means 'to rub'). Friction is actually unnecessary: contact is enough in principle.
This effect shouldn't be confused with the (Volta or Galvani) "contact potential" between metals which only exists as long as the two metals remain in contact, and especially not with "contact electrification" which was a name of a scientifically incorrect theory of electricity at the end of the 18th century that attempted to overgeneralize the interpretation of the triboelectric effect. "Electrophorus" was a gadget, first produced by Volta, that used the triboelectric effect.
The cause of the triboelectric effect is adhesion - the atoms on the surface literally form chemical bonds. Materials such as fur are ready to lose electrons and become positively charged while the materials such as ebonite or glass gain electrons and become negatively neutral. To get some idea about which atoms are likely to lose or gain electrons, it's useful to know their electronegativity:
http://en.wikipedia.org/wiki/Electronegativity#Electronegativities_of_the_elements
The redder atom, the higher electronegativity, and the more likely it is for the atom to gain electrons and become negatively charged. That's especially true for light halogens (fluorine, chlorine) and oxygen. That's partly why glass - with lots of $SiO_2$ - likes to get negatively charged in the triboelectric effect. Even sulfur (40% of ebonite) has a higher electronegativity than e.g. carbon and hydrogen that are abundant in the fur which is why fur loses electrons and becomes positively charged.
Of course, the actual arrangement of the atoms in the molecules matters, too. So this overview of the periodic table was just an analogy, not a reliable way to find out the results of the triboelectric effect.
I've never done the experiment with the plastic film, but as child I remember that if I rubbed a balloon on my pullover it would stick to the wall. The reason is the one you suggest. When you run the balloon on your pullover you charge it. When you bring the balloon close to the wall the charge on the ballon polarises the surface of the wall, i.e. it repels like charges and attracts unlike charges, so the surface of the wall acquires a charge opposite to the balloon. The opposite charges on the ballon and the surface of the wall attract, so the balloon sticks to the wall.
The problem with using this to fix pictures to the wall is that the charge gradually leaks away so the balloon/picture will fall off. My recollection is that the balloon would stay stuck to the wall for about an hour.
As you say, objects may be charged by rubbing them and this is called triboelectricity. Alternatively you can charge objects by touching them with something else that is charged. Because like charges repel, if you touch a charged object to an uncharged object there will be a tendancy for the charge to spread over both objects. To what extent this happens depends on the conductivity of the objects. I imagine the plastic film is a poor conductor and this is why you have to rub the Fun-Fly-Stick all over it.
I had never heard of the Fun-Fly-Stick but a quick Google suggests it's a type of Van de Graaff generator.
Best Answer
Charged objects have an electric field in their vicinity. The air will always contain a small number of ionized particles - this can be a result of cosmic radiation, local electrical activity, or just the chemistry of molecules. Now if your comb is positively charged, negatively charged ions will be attracted to it and positive ones will be repelled. Over time, this results in a neutralization of the charge on the comb.
The question then becomes - what is the major contributor to the conductivity of the air? A 1988 research report by Hugh R Carlon, Electrical properties of atmospheric moist air: a systematic, experimental study had the following in its abstract:
Reproducing figure 3 from that paper:
you can see that they measured a charge carrier density that is logarithmically dependent on relative humidity - and charge carrier density scales with conductivity (all other things being equal).
This is the reason, incidentally, that most ESD (electrostatic discharge) damage occurs in winter: when the air outside is cold, the relative humidity inside (where it is warm) will be low; thus the conductivity is low, and objects have a chance to build up charge without it leaking away so quickly.
One more figure from the same paper, showing the discharge current measured for different voltages, at different levels of humidity. Once again, it is hard to escape the conclusion that ionization of moisture in the air is responsible for the conductivity (and thus for the discharging of your statically charged comb):
Incidentally, in a dusty environment (see @Boris's answer) you may observe neutral dust particles being attracted to the comb (because of polarization of the particle) - but once it touches, it either sticks, or it will "jump away", having acquired a small amount of charge and therefore being now repelled. In so doing, these particles can be responsible for some charge leakage. But in clean air, moisture is the key component of conductivity.