Rubber
Natural rubber is a polymer is a polymer found in the sap of the rubber tree.  The rubber tree grows throughout the tropics primarily in Souteast Asia.  Chemically the polymer is CH2-C(CH3)=CH-CH2.  Natural rubber has long been known, but it only became valuable with the development of the vulcanizing process (heating in the presence of sulfur).  This process was developed by Charles Goodyear, and it gives a more rubbery and coherent substance.  The synthetic rubber industry did not grow significantly until the onset of WWII.  At the present time, over 75% of America's rubber is synthetic.  The most significant types of rubber are Buna-S and Buna-N.
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The Structure of Rubber
The chains in a normal piece of rubber are not arranged in a neat parallel array.  Instead, they are coiled up and tangled together in the manner shown below.
    The length between the ends of a chain may be only a tenth or a hundredth of the stretched length of the chain. These act as a tangle of coiled-up springs.  When the rubber is stretched, the "springs" are extended.  The rubber can be stretched to over ten times its original length before the chains are to their full length.  When the chains are stretched to their full length the rubber shows crystalline features because the chains are more-or-less parallel. Because the resistance to deformation is dependent upon the length of each chain, the rubber will become harder or stiffer when more links are added.  Temperature can have the same effect.  At low temperatures, rubber can become hard and brittle.  This is a serious problem for people driving in arctic climates.
    In some rubbers, the chains do not tangle with their neighbors.  In this case, very little energy is lost when the rubber is stretched and then released.  This rubber is then called resilient.  Balls made of this rubber will often rebound to the original height from which they were dropped.  For this reason, this type of rubber is often called "bouncy."  Rubber that does not have this property of resilience is often called "soggy."  Another term for lack of resilience is called "hysteresis loss."  In this type of rubber, much energy is lost when the rubber is strectched then released.  This energy is lost in the form of heat.  In many technilogical rubbers fillers, such as carbon, are added to increase hardness and decrease wear.  This also leads to an increase in hysteresis loss.
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Friction and Rubber
    The coefficient of rubber against most hard surfaces is between 1 and 4, but we will concern ourselves more with tires since that is the most useful application of rubber.
    When a tire rolls freely over a surface, adhesion is a minor concern, but when you try to accelerate, deccelerate, or turn adhesion becomes very important. In normal cases, the coefficient of friction between tire and road are between 1 and 2.  This changes dramatically when the road is wet.  The sliding friction can approach zero in the wet road scenario.  Tire manufacturers are constantly trying to come up with new ways to increase the friction on wet roads.  In order to reach this goal, they break up the surface of the tire into many small surfaces with a typical pattern; this allows the tire to squeeze the water from under itself.  Another approach is to put tiny cuts in the tire so that it acts as a windshield wiper and sweeps away the water.  This approach can produce quite high friction on wet roadways.  A newer approach suggests that tires with high hysteresis loss will have greater friction in this situation.  Experiments have shown that an improvement does occur in friction when using high hysteresis loss tires.