Re: If plastic wrap sticks by static cling, why does it stick to itself?

You are quite correct.  If plastic wrap stuck by static cling, it would not 
stick to itself.

First, suppose the entire sheet of plastic wrap was charged the same sign, 
say positive.  That positive charge would induce a negative charge in other 
objects, such as the food you were trying to cover.  It would tend to stick 
to things, especially metals.  But it would strongly repel any part of 
itself, making it difficult to fold over.  It certainly would not stick to 
itself at all.  It would be nearly impossible to handle, too: you couldn't 
package it in a roll, and a stack of plastic-wrap boxes would tend to fly 
apart due to the net charge on each one.  In general, you can assume that 
everything you buy in the grocery store has equal amounts of positive and 
negative charge.

All right, suppose they made one face of the plastic wrap positive and the 
other negative.  If the charges were not equal, we'd be back to the first 
case.  If they were equal, I think there would be no electric fields or 
forces outside the plastic wrap.  Just as in the case of a parallel-plate 
capacitor, a charge outside the plastic wrap would feel an equal attraction 
to the positive face and repulsion from the negative face.  No forces, no 
sticky.  The exception is that the very edges of a piece would have 
"fringing fields" where the cancellation wasn't perfect.  The edges would 
be sticky in a very narrow band, comparable to the thickness of the sheet. 
 But some simple experiments with plastic wrap show that the whole face 
is sticky, with the edges no more so than the middle.

Next trick: suppose they made a pattern of positive and negative charges on 
each face, say a checkerboard.  If you put the plastic wrap up against a 
jar, each positive square would induce a region of negative charge in the 
glass next to it.  Each negative square in the plastic wrap would induce a 
positive charge in the glass next to it.  So the plastic wrap would stick 
to other objects.  If you brought two sheets of plastic wrap close to each 
other, though, the positive squares might be on top of the negative squares 
(very attractive) or they might be on top of the other positive squares 
(very repulsive).  Although I haven't simulated it, my instinct is that the 
repulsive areas and attractive areas would balance out to give no 
stickiness.  At least you would see strange patterns of sticky and 
non-sticky areas depending on how much you rotated the top sheet before 
pressing it down on the bottom sheet.  So that doesn't seem to fit the 
facts, either.

Fortunately a fellow Mad Scientist has also weighed in on the issue, who 
knows what plastic wrap is.  (I only know what it isn't.)  See 
this answer 
for more details.

To summarize his explanation, the stickiness of plastic wrap is similar to 
the stickiness of tape: they add a small amount of a soft, mobile additive 
to the plastic wrap, kind of like the adhesive layer on tape.  When two 
sheets of plastic wrap contact each other, patches of this additive move 
around to "glue" the sheets together.

Hope this answers your question.

Deron Walters
Rice University