"The simplest answer that I can give to the question is that pressure-sensitive adhesives (which are polymers) are 'tacky' or 'sticky' because they are essentially very high viscosity liquids that also have some elastic characteristics--in technical terms, they are 'viscoelastic.' This property means that they exhibit some of the characteristics of liquids, and so they will 'wet' a surface to which they are pressed. But then, because of their elasticity, they will resist separation when stressed. Thus, 'stickiness' is strictly a physical (viscoelastic) phenomenon, not a chemical one."
Benjamin E. Russ is a research assistant in the University of California at San Diego's applied mechanics and engineering sciences department. He adds a few details:
"There are two fundamentally different components of tape's sticky nature; adhesion and cohesion. Adhesion is the binding force between two different materials, whereas cohesion is the binding force between two similar materials. When two materials are brought into contact with each other, the surface molecules interact, giving rise to attractive forces that may be physical, chemical or electrostatic (corresponding to adsorption, covalent bonding or van der Waals forces, respectively). When the molecules are similar, as in the case of two 'glue molecules,' the cohesive force causes the glue to stick to itself. When the molecules are dissimilar, as in the case of a glue molecule and a molecule of the substrate (the surface the glue is sticking to), the adhesive force holds the glue to the substrate. Hence, the 'stickiness' of tape is caused by a combination of the molecular forces of the glue material sticking to itself as well as holding onto the substrate."
Researchers in the Industrial Tape and Specialty Division at 3M offer some more thorough information:
"There is no chemical bonding or reaction between a pressure-sensitive adhesive and the substrate, the surface to which it bonds. A pressure-sensitive adhesive is a sticky, viscous, liquidlike material that adheres to a surface using only pressure. To function well, it should have good adhesion to a surface and good cohesion, or internal strength. For good adhesion, it is important that the adhesive can readily flow out on the surface. The degree, or freeness, of the flow often determines the intensity of adhesion. Degree of flow depends on the difference between the surface energy of the material and the surface energy of the adhesive. Pressure-sensitive adhesives tend to flow out on materials having a high surface energy--for instance, metals, glass and plastics such as acrylic, polycarbonate and nylon. Pressure-sensitive adhesives tend not to flow out as easily on low surface-energy materials such as polyethylene, polypropylene and Teflon.
"Mechanisms for adhesion include both mechanical adhesion and specific adhesion. Mechanical adhesion occurs when the adhesive flows into the texture of the substrate. Specific adhesion includes electrostatic forces, van der Waals forces and acid-base interactions that take place between the adhesive and the substrate. In the case of acrylic pressure-sensitive adhesives, the intensity of the bond typically increases over time. This growing degree of 'stickiness' occurs because of the long time it takes for the adhesive to flow onto and into the surface texture, and for the adhesive polymer to align with the surface to create the interactions."