How to Distinguish a Repeat Unit from a Polymer Chain

An unbracketed polymer chain is drawn as:

\[ \ldots-\ce{CH2-CH(CH3)-CH2-CH(CH3)-CH2-CH(CH3)}-\ldots \]

Is the entire six-carbon backbone section one repeat unit, or does it contain several repeat units?

It contains three repeat units. The smallest complete pattern that repeats is \(\ce{-CH2-CH(CH3)-}\). The longer structure is simply a short section of the polymer chain containing three copies of that pattern.

This distinction is important when interpreting polymer structures. If you choose the wrong section, you can misidentify the polymer’s repeating structure, count the wrong number of units, or reconstruct an incorrect monomer.

01Repeat unit or short section of polymer chain?

The difference

A repeat unit, also called a repeating unit, is the smallest complete structural pattern that repeats along a polymer chain.

A short section of polymer chain is simply a portion of the larger molecule. It might contain one repeat unit, several repeat units, or even an incomplete section of a repeating pattern.

Consider polypropylene:

\[ \ce{[-CH2-CH(CH3)-]_{n}} \]

Its repeat unit is:

\[ \ce{-CH2-CH(CH3)-} \]

The complete polymer chain contains many copies of this structure joined together.

Notice that the monomer and repeat unit are not identical. Propene contains a carbon-carbon double bond, whereas the polymer’s repeat unit contains a carbon-carbon single bond.

Think about the repeating pattern

Imagine looking at a strip of wallpaper containing the same decorative pattern several times.

The entire strip is not one repeating pattern. Instead, you identify the smallest section that can be copied repeatedly to reproduce the strip.

A polymer works in a similar way. You identify the smallest complete arrangement of atoms that reproduces the structure when connected repeatedly.

There is one important difference: wallpaper patterns can sit next to each other without chemical consequences. Polymer units are joined by covalent bonds, so the atoms at the boundaries must connect correctly and satisfy their usual valencies.

What makes a repeat unit complete?

A proposed repeat unit must reproduce the polymer’s structure when copies are joined.

For polypropylene, consider these two possibilities:

• \(\ce{-CH(CH3)-}\)
• \(\ce{-CH2-CH(CH3)-}\)

The first structure contains a carbon with a methyl side group, but it does not reproduce the alternating arrangement of the polymer backbone.

The second contains both backbone carbon environments:

• A \(\ce{CH2}\) carbon.
• A \(\ce{CH(CH3)}\) carbon.

Joining copies of the second structure recreates the original chain.

This gives us a useful rule:

A repeat unit must reproduce the complete repeating arrangement, including the position of every side group.

02Understanding brackets, open bonds, and chain ends

Polymer structures often use square brackets and short lines extending from either end of the bracketed structure.

These symbols carry important information.

Consider:

\[ \ce{[-CH2-CH(Cl)-]_{n}} \]

This is the repeating unit of poly(chloroethene), commonly called PVC.

There are four things to recognise.

The dashes at the ends are particularly important. They represent bonds connecting the unit to neighbouring sections of the polymer chain.

They are not missing hydrogen atoms, and they do not represent unpaired electrons.

Open bonds are not actual chain ends

Compare the following two representations.

Representation A: A repeating unit

\[ \ce{[-CH2-CH(Cl)-]_{n}} \]

The two terminal dashes indicate that the structure continues into neighbouring repeat units.

Representation B: A simplified, finite hydrogen-capped chain

\[ \ce{H-CH2-CH(Cl)-CH2-CH(Cl)-H} \]

Here, the hydrogen atoms at the two ends are actual atoms attached to the terminal carbon atoms.

This second structure represents a finite model containing two repeat units, with hydrogen atoms satisfying the terminal carbon valencies.

The distinction is:

• Open bonds indicate continuation into the polymer chain.
• Explicit terminal atoms indicate actual chain ends in the molecule being represented.
• Three dots or an ellipsis indicate that part of the chain has been omitted from the drawing.

Why carbon valency matters

Carbon normally forms four covalent bonds.

When identifying a repeat unit, count all the bonds around each carbon, including the bonds connecting neighbouring repeat units.

For the PVC repeating unit:

\[ \ce{-CH2-CH(Cl)-} \]

Consider each carbon separately.

Both carbons satisfy their usual valency.

Remember that a double bond counts as two bonds when checking valency.

A structure that gives carbon five bonds is incorrect, even if its repeating pattern initially looks reasonable.

However, passing the valency check does not automatically prove that a proposed repeat unit is correct. It must also reproduce the actual connectivity of the polymer.

That is why you should use both the valency check and the join test.

03How the type of polymerisation affects the repeat unit

One common mistake is assuming that every polymer has a two-carbon repeating unit derived from an alkene.

That works for many familiar addition polymers, but it does not work for condensation polymers.

The reaction type helps you understand which atoms belong in the complete repeating structure.

Addition polymers

Addition polymers commonly form when alkene monomers join together.

The carbon-carbon double bond opens, allowing the monomers to connect through new carbon-carbon single bonds.

For example, ethene forms poly(ethene):

\[ \ce{nCH2=CH2 -> [-CH2-CH2-]_{n}} \]

The repeat unit contains the two carbon atoms originally present in one ethene molecule.

Other examples include:

Condensation polymers

Condensation polymers form when monomers with suitable functional groups join together, with elimination of a small molecule.

In common HSC examples, this is often water.

Two important types are:

• Polyesters, containing ester linkages, \(\ce{-C(=O)-O-}\).
• Polyamides, containing amide linkages, \(\ce{-C(=O)-NH-}\).

Unlike simple alkene-derived addition polymers, their repeating units often contain structural sections contributed by two different monomers.

For example, poly(ethylene terephthalate), or PET, contains the repeating unit:

\[ \ce{[-O-CH2-CH2-O-C(=O)-C6H4-C(=O)-]_{n}} \]

The \(\ce{C6H4}\) section represents a benzene ring with two substituents in the para positions.

The repeat unit contains:

• A section derived from ethane-1,2-diol.
• A section derived from benzene-1,4-dicarboxylic acid.

Both are needed to reproduce the complete polymer structure.

The important lesson is that you cannot identify a condensation polymer’s repeat unit simply by looking for two adjacent carbon atoms.

You must follow the complete backbone, including its functional groups.

04A reliable method for identifying a repeat unit

When you are given an unfamiliar polymer structure, use the following process.

Step 1: Trace the polymer backbone.

Identify the continuous chain of atoms running through the polymer.

Do not automatically assume that every atom inside the brackets belongs to the backbone. Some atoms may form side groups.

Step 2: Look for the smallest complete repeating pattern.

Compare consecutive sections of the chain.

Look for the arrangement of atoms and side groups that occurs repeatedly.

Step 3: Identify the polymerisation type.

Decide whether the structure is consistent with an addition polymer or a condensation polymer.

Look for features such as:

• A saturated carbon backbone with substituent groups.
• Ester linkages.
• Amide linkages.

Step 4: Perform the join test.

Imagine copying your proposed repeat unit twice.

Connect the right-hand open bond of the first copy to the left-hand open bond of the second.

Does the resulting structure match the original polymer chain?

If not, your proposed repeat unit is incomplete or incorrect.

Step 5: Check valency.

Check that each atom has an appropriate number of bonds.

For carbon, the total bond order should normally be four. For neutral oxygen in an ester, it should normally be two.

A correct answer must satisfy both the chemical bonding rules and the repeating pattern of the original polymer.

05Worked examples

06Questions and solutions

The following questions progress from straightforward identification to more demanding problems involving chain boundaries, valency, and competing repeat-unit representations.

Question 1

A section of an addition polymer is represented by:

\[ \ldots-\ce{CH2-CH(Cl)-CH2-CH(Cl)}-\ldots \]

Identify the repeat unit and state how many complete repeat units are shown.

Solution 1

The repeat unit is \(\ce{-CH2-CH(Cl)-}\), and two complete repeat units are shown.

The backbone alternates between two different carbon environments:

• \(\ce{CH2}\), containing two hydrogen atoms.
• \(\ce{CH(Cl)}\), containing one hydrogen atom and one chlorine atom.

These two carbon atoms together form the smallest complete pattern that reproduces the chain.

Therefore, the repeating unit is:

\[ \boxed{\ce{[-CH2-CH(Cl)-]_{n}}} \]

The chlorine atoms are side groups. They are attached to the backbone but do not form part of the continuous carbon chain.

A common mistake is to identify \(\ce{-CH(Cl)-}\) alone as the repeat unit because chlorine appears at regular intervals. However, copying that section would produce adjacent \(\ce{CH(Cl)}\) groups rather than the alternating arrangement in the original polymer.

Question 2

A simplified, hydrogen-capped polystyrene oligomer is represented by:

\[ \ce{H-CH2-CH(C6H5)-CH2-CH(C6H5)-H} \]

Assume that the two hydrogen atoms at the ends are actual terminal caps, not bonds to additional polymer units.

Identify:

(a) The repeat unit.

(b) The number of complete repeat units.

(c) Why the terminal hydrogen atoms should not be interpreted as open bonds connecting to neighbouring units.

Solution 2

The repeat unit is \(\ce{-CH2-CH(C6H5)-}\), and the finite structure contains two complete repeat units.

(a) Repeat unit

The backbone consists of alternating \(\ce{CH2}\) and \(\ce{CH(C6H5)}\) carbon atoms.

The phenyl groups, \(\ce{C6H5}\), are side groups attached to the second carbon in each repeating pattern.

Therefore:

\[ \boxed{\ce{[-CH2-CH(C6H5)-]_{n}}} \]

(b) Number of repeat units

The chain contains two \(\ce{CH2}\) groups and two \(\ce{CH(C6H5)}\) groups.

These form two complete copies of the repeat unit.

Thus, the degree of polymerisation for this simplified model is:

\[ \boxed{n=2} \]

(c) Terminal hydrogen atoms

The hydrogen atoms at the ends are actual atoms attached to the terminal carbon atoms.

They complete the carbon valencies at the ends of this finite molecule.

By contrast, the open bonds in a general polymer repeat-unit representation indicate connections to neighbouring units.

The tempting mistake is to treat every line at the edge of a polymer drawing as an open continuation bond. You must first establish whether the structure represents an indefinite polymer chain or a finite molecule with explicit end groups.

The hydrogen-capped structure is a simplified model. Actual polystyrene chain-end groups depend on the polymerisation and termination chemistry.

Question 3

An idealised polypropylene chain contains 276 carbon atoms in its repeating structure. Ignore any additional atoms associated with chain-end groups.

Given that the repeat unit is:

\[ \ce{-CH2-CH(CH3)-} \]

calculate:

(a) The number of repeat units.

(b) The number of carbon atoms belonging to the polymer backbone.

Solution 3

The chain contains 92 repeat units and 184 backbone carbon atoms.

Step 1: Count the carbon atoms in one repeat unit.

The repeat unit is:

\[ \ce{-CH2-CH(CH3)-} \]

It contains:

• One carbon in \(\ce{CH2}\).
• One carbon in \(\ce{CH(CH3)}\).
• One carbon in the methyl side group, \(\ce{CH3}\).

Therefore, each repeat unit contains three carbon atoms in total.

Step 2: Calculate the number of repeat units.

Use:

\[ \text{Number of repeat units} = \frac{\text{Total carbon atoms}} {\text{Carbon atoms per repeat unit}} \]

Substitute:

\[ n=\frac{276}{3} \]

\[ \boxed{n=92} \]

Step 3: Calculate the number of backbone carbon atoms.

Each repeat unit contributes two carbon atoms to the backbone.

Therefore:

\[ N_{\text{backbone}}=92\times 2 \]

\[ \boxed{N_{\text{backbone}}=184} \]

The remaining 92 carbon atoms belong to the methyl side groups.

A common error is to divide 276 by two because the repeat unit has two backbone carbons. However, the question gives the total number of carbon atoms, including side groups. You must count every carbon in the repeat unit before calculating the degree of polymerisation.

Question 4

A polymer chain contains the following structural section:

\[ \begin{aligned} \ldots-\ce{NH-(CH2)6-NH-C(=O)-(CH2)4-C(=O)}\\ \ce{-NH-(CH2)6-NH-C(=O)-(CH2)4-C(=O)}-\ldots \end{aligned} \]

A student proposes that the repeat unit is:

\[ \ce{-NH-(CH2)6-NH-} \]

(a) Identify the complete repeat unit.

(b) Classify the polymer as a polyamide or polyester.

(c) State whether the polymer is formed through addition or condensation polymerisation.

(d) Explain why the student’s proposed repeat unit is incomplete.

Solution 4

The complete repeat unit is:

\[ \boxed{ \ce{[-NH-(CH2)6-NH-C(=O)-(CH2)4-C(=O)-]_{n}} } \]

The polymer is a polyamide formed through condensation polymerisation.

(a) Complete repeat unit

Trace the continuous backbone through both sections.

The first section is:

\[ \ce{-NH-(CH2)6-NH-} \]

The second section is:

\[ \ce{-C(=O)-(CH2)4-C(=O)-} \]

Together, they form the complete repeating pattern.

(b) Polymer classification

The polymer is a polyamide because its backbone contains amide linkages:

\[ \ce{-C(=O)-NH-} \]

This particular polymer is nylon 6,6.

(c) Polymerisation type

Nylon 6,6 is formed through condensation polymerisation in the standard HSC model.

The relevant monomers are:

• Hexane-1,6-diamine, \(\ce{H2N-(CH2)6-NH2}\).
• Hexanedioic acid, also called adipic acid, \(\ce{HOOC-(CH2)4-COOH}\).

Their functional groups react to form amide linkages, with water eliminated.

(d) Why the proposed repeat unit is incomplete

The student’s proposed structure contains only the diamine-derived section.

If copies of this section were joined directly together, the resulting chain would contain an N-N connection between neighbouring sections.

That is not the structure of the original polymer.

The actual polymer contains carbonyl groups between the diamine-derived sections. These groups form the amide linkages that connect the monomer residues.

The full repeat unit must therefore contain both sections.

This example shows why identifying a repeating fragment is not enough. You must check that joining the proposed units recreates the actual polymer backbone.

Question 5

A polyester contains the following chain fragment. All benzene rings are para-substituted.

\[ \begin{aligned} \ldots-\ce{O-CH2-CH2-O-C(=O)-C6H4-C(=O)}\\ \ce{-O-CH2-CH2-O-C(=O)-C6H4-C(=O)}\\ \ce{-O-CH2-CH2-O-C(=O)-C6H4-C(=O)}-\ldots \end{aligned} \]

Three proposed repeat-unit representations are:

Candidate A

\[ \ce{[-O-CH2-CH2-O-]_{n}} \]

Candidate B

\[ \ce{[-O-CH2-CH2-O-C(=O)-C6H4-C(=O)-]_{n}} \]

Candidate C

\[ \ce{[-C(=O)-C6H4-C(=O)-O-CH2-CH2-O-]_{n}} \]

A student argues that Candidate A must be correct because it identifies the smallest section that appears repeatedly.

Another student argues that only Candidate B can be correct because the repeat unit must begin at an oxygen atom.

Evaluate both arguments.

In your answer:

(a) Identify which candidates are valid complete repeat units.

(b) Explain why Candidate A is incomplete, even though it satisfies the usual valency of oxygen.

(c) Explain the relationship between Candidates B and C.

(d) State the number of complete repeating cycles visible in the supplied chain.

(e) Identify the type of polymerisation.

Solution 5

Candidates B and C are both valid complete repeat units. Candidate A is incomplete, even though its atoms can satisfy normal oxygen valency. There are three complete repeating cycles, and the polymer is formed through condensation polymerisation.

This question tests an important distinction: a section that appears repeatedly is not necessarily a complete repeat unit.

(a) Which candidates are valid?

Candidate B is valid:

\[ \ce{[-O-CH2-CH2-O-C(=O)-C6H4-C(=O)-]_{n}} \]

It contains one complete sequence of the ethylene glycol-derived section and the terephthalate-derived section.

Candidate C is also valid:

\[ \ce{[-C(=O)-C6H4-C(=O)-O-CH2-CH2-O-]_{n}} \]

It contains exactly the same repeating arrangement, but the starting point has been shifted.

Both representations reproduce the original chain when copies are joined.

(b) Why Candidate A is incomplete

Candidate A is tempting because the section:

\[ \ce{-O-CH2-CH2-O-} \]

appears repeatedly in the chain.

However, it represents only the ethylene glycol-derived section, not the complete repeating pattern.

Use the join test.

If you copy Candidate A and connect the right-hand open oxygen to the left-hand open oxygen of the next copy, the resulting chain contains:

\[ \ce{-CH2-CH2-O-O-CH2-CH2-} \]

This introduces an O-O bond.

The original polymer instead contains an ester connection:

\[ \ce{-CH2-CH2-O-C(=O)-} \]

The connectivity is different.

Importantly, the O-O bond in the proposed structure is not automatically invalid because of valency. Each oxygen can still have two bonds.

This is the crucial point: a structure can satisfy normal valency and still be the wrong repeat unit because it does not reproduce the polymer’s actual bonding pattern.

Candidate A identifies a recurring section, but not the complete repeating unit.

(c) Why Candidates B and C are both valid

The beginning of a repeat unit does not have to be fixed at one particular atom.

A regular polymer chain allows you to choose different starting positions along the same repeating sequence.

For Candidate B, the unit begins at the oxygen of the ethylene glycol-derived section and ends at the second carbonyl carbon.

When copies are joined, the carbonyl carbon connects to the oxygen at the beginning of the next unit.

This recreates the ester linkage.

For Candidate C, the unit begins at the carbonyl carbon and ends at the oxygen of the ethylene glycol-derived section.

When copies are joined, that terminal oxygen connects to the next carbonyl carbon.

This also recreates the ester linkage.

The two structures are simply different boundary choices for the same complete repeating pattern.

(d) Number of complete repeating cycles

The supplied chain contains three complete ethylene glycol-derived sections and three complete terephthalate-derived sections.

Each pair forms one complete repeating cycle.

Therefore:

\[ \boxed{3\text{ complete repeat units}} \]

(e) Type of polymerisation

The polymer is a polyester formed through condensation polymerisation.

Its backbone contains ester linkages, \(\ce{-C(=O)-O-}\), connecting the diol-derived and dicarboxylic-acid-derived sections.

The correct classification follows from the functional groups and backbone connectivity, not simply from the presence of repeating carbon atoms.

Once you can identify a complete repeat unit, the next useful skill is reconstructing the original monomer or monomers. The method depends on whether the polymer formed through addition or condensation polymerisation.

For the next step, see How to Find Monomers from a Polymer’s Repeating Unit.