Sketch three repeating units of the polymer formed from (a) \(\mathrm{CH}_{2}=\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}\); (b) \(\mathrm{CH}_{2}=\mathrm{CHCN}\); (c) isoprene,

Understanding the concept of monomer identification is essential for grasping the fundamentals of polymer chemistry. A monomer is a single molecule which can bind chemically to other molecules to form a polymer. In the context of our exercise, the monomers given are (CH_{2}=C(CH_{3})_{2}), (CH_{2}=CHCN), and isoprene. Each of these contains a double bond, characteristic of many monomers used in addition polymerization.

Monomers are the building blocks of polymers and can be identified by this reactive feature, such as a double bond, which allows them to link up with one another. In polymerization, the distinct reactive sites that double bonds provide are utilized to form long chains or networks. To identify a monomer, check for unsaturation or functional groups that can undergo polymerization reactions. In our examples, the presence of vinyl groups (C=C) is the key indicator of a monomer that can polymerize to form a larger molecule.

The process of bond formation in polymers is a fascinating journey from small to macroscopic structures. When monomers join to form polymers, the covalent bonds between them rearrange. During addition polymerization, the double bonds (pi-bonds) break and new single bonds (sigma-bonds) form between monomers, extending the chain.

The breaking of the double bonds allows two monomers to connect, while still maintaining a strong covalent bonding through the newly created single bond. The original double bond in a monomer molecule, like those in (CH_{2}=CH-R), where R can be any side group, is the active site at which polymerization initiates. Typically, a catalyst or initiator is needed to break these double bonds under controlled conditions, enabling a sequential bonding that results in the polymer chain. This knowledge is vital when trying to visualize or predict the structure of the resulting polymer from a given set of monomers.

Sketching the structure of a polymer can often appear daunting, but it's an important skill for understanding the visual aspect of polymer chemistry. After identifying the monomers and understanding how they bond, the next step is to represent the polymer on paper. To begin, draw the monomer and then illustrate the breaking of the double bond. Consequently, extend the sketch by replicating the monomer structure to signify the addition of subsequent monomer units.

For the polymers given in our exercise, each repeating unit after the original monomer must be attached by linking through what was previously the double bond site. This is indicated by showing single bonds that now connect the repeating units. When drawing, remember to include all side groups and keep the orientation consistent for each repeating unit. The final structure for three repeating units will display how the repeating pattern continues in a larger polymer chain. Mastery of polymer structure sketching helps in understanding the physical properties and potential applications of the polymer.