What type of sensor technologies exist to determine the chemical composition of a polymer? Let's say I have several pieces of trash and each is made with a different type of material like:


Plastic bottle : High Density Polyethylene (HDPE) 
Cereal box : Paperboard &amp; Epichlorohydrin
Shrink Wrap : Polyolefin
Kitchen utensil : Melamine-resin
Textiles : Urea-formaldehyde
Crown Cork Bottle Cap : Metal and Plastisol lining
Rock
Plasterboard 
Coffee cup : Ceramic and Glaze (silica + metal oxides)


My objective is to build a system complete with sensors that automatically determines the material (chemical makeup) of each object. Are there material sensors currently on the market that can identify all of the materials that make up these objects?
You can identify many polymers without any clever sensor technologies at all but by following a number of simple physical tests. Sensor technology might help for some of the very fine distinctions, but if you can make a broad categorisation first with simple physical tests then that is what you should do.

And, of course, most plastic opponents are actually labelled with symbols to aid in recycling so you can often just look to identify the chemical nature of the polymer. For reference the symbols are shown below (V identifies chlorine-containing polymers like PVC):



The steps required to identify polymers, if you don't have a label, involve some simple physical tests. First identify whether the polymer is elastic or hard. Then identify whether it is a thermoplastic or a thermoset (by using a hot object like a soldering iron to see whether it remelts). Then a variety of tests can be applied: does it float in water or not? Does it burn and if so how does it behave and what does the flame look like?

One flowchart for this is available here as a pdf. Another simpler one is here also as a pdf but sufficient to distinguish the major classes of polymer. There are even interactive versions of such flowcharts such as this one (flash).

Included below is another version originally produced by the major, but now defunct, British chemical company ICI:



￼￼