[cityboy9x]

The formular of polymer is many monomers link together, and it's written as "n" monomers. For example Polypropylene:

In the example, there are n monomers C3H6 linked together in Polypropylene chain; and n is a positive integer certain value. In the chain, one middle monomer links to 2 monomers on either side by 2 single bonds.

So, what is the beginning and the ending of the polymer chain? It means, the monomers in the beginning and the ending of the chain, how there are?

It's becase 1 middle monomer links with 2 monomers on the left and the right of it, so in the beginning and the ending, there's one side of the monomer, so how the beginning and the ending monomer organize and link?

[mjc123]

It depends how the polymer is made - specifically, on how the polymerisation reaction is initiated and how it is terminated.
For example, if you have a radical polymerisation initiated by a peroxide ROOR, which splits into two RO· radicals:
RO· + CH₂+CHCH₃  ROCH₂CH^·CH₃  RO[CH₂CHCH₃]_nCH₂CH^·CH₃
so you have RO at one end. If termination is by recombination
2RO[CH₂CHCH₃]_nCH₂CH^·CH₃  RO----CH₂CH(CH₃)-CH(CH₃)CH₂----OR
and you have RO at both ends. If termination is by disproportionation
2RO[CH₂CHCH₃]_nCH₂CH^·CH₃  RO[CH₂CHCH₃]_nCH=CHCH₃ + RO[CH₂CHCH₃]_nCH₂CH₂CH₃ 
and you get some chains with an alkyl and some with an alkenyl termination. If by transfer
RO[CH₂CHCH₃]_nCH₂CH^·CH₃ + CH₂=CHCH₃ RO[CH₂CHCH₃]_nCH=CHCH₃ + CH₃CH^·CH₃
and you initiate a new chain with an isopropyl group at the beginning.
Anionic living polymerisation with e.g. sec-butyllithium will give a sec-butyl group at one end and an anion at the other
s-BuLi + CH₂=CHCH₃    s-Bu[CH(CH₃)CH₂]_nCH(CH₃)CH₂^-Li⁺
Workup with a protic solvent will protonate the anion.
For condensation polymerisation, if you have AXA + BYB, with A groups in excess, you get molecules of the form A[XY]_nXA, i.e. all the terminal groups are A. Self-polymerisation of AXB will give AX_nB.
Having made the polymer in one of these (or other) ways, if the terminal groups are reactive you can then manipulate them to give different terminal groups.

[cityboy9x]

My polymer chain is simple, and not begin with RO, A, B group or anything else. Because the formular is simple: -(C_xH_y)-_n. So it must begin and end with C_xH_y. For example the Polypropylene:

As this formular, the chain not begins or ends with any group but (C₃H₆). So, in this situation, how the chain begins and ends?

It's becase 1 middle monomer C₃H₆ links with 2 monomers on the left and the right of it with 2 single bonds, so in the beginning and the ending, there's one side of the monomer, so how the beginning and the ending monomer organize and link? It's mean the beginning and the ending monomers, how they links to the next momoner, because in their formular (C₃H₆), there're only single bonds, but they only can link to one next monomer, not to the either side?

[DrCMS]

Just asking the exact same question again without trying to understand the answer already given will not get you anywhere.

[mjc123]

My polymer chain is simple, and not begin with RO, A, B group or anything else.

How do you know? How was it made? Or are you not talking about a real polymer chain at all, but just a notional one consisting purely of C₃H₆ groups and nothing else? If so, there's no answer to your question, because such a thing doesn't exist. Propylene doesn't spontaneously polymerise, it has to be initiated by something. Also, propylene is a stable, stand-alone molecule. It can form bonds to other things by opening the C=C double bond - but it must form two bonds, not just one. C₃H₆ cannot be the terminal group of a polymer chain. Generally speaking, the terminal groups cannot be the same as the repeat unit, for precisely the reason that the repeat unit must form two linkages and the terminal group one. A real polymer never exactly has the formula [repeat unit]_n, but usually it is safe to ignore the terminal groups because they constitute only a tiny fraction of the mass of the material, at least for high polymer.

[Arkcon]

As this formular, the chain not begins or ends with any group but (C₃H₆). So, in this situation, how the chain begins and ends?

Why can't the polymer begin and end with a hydrogen atom?  mjc123: gave you a very thorough answer, adressing a variety of co-polymers.  But the answer is the same, something terminates the chain.

It's becase 1 middle monomer C₃H₆ links with 2 monomers on the left and the right of it with 2 single bonds, so in the beginning and the ending, there's one side of the monomer, so how the beginning and the ending monomer organize and link? It's mean the beginning and the ending monomers, how they links to the next momoner, because in their formular (C₃H₆), there're only single bonds, but they only can link to one next monomer, not to the either side?

You're saying:  middle monomer, and two monomers on either side, so how the beginning and ending link ...  But, I'm sorry, I can't follow you.  You change fonts and colors, I guess to make the statements look important, but you're not saying anything.

[AWK]

Search for Ziegler-Natta polymerization mechanisms

[Enthalpy]

The formulas for polymers don't represent the end groups, but these differ from the repeating group. The end groups may be indicated in the text instead, like "hydroxy-terminated".

[Corribus]

Polymer formula is an approximation also because of the presence of branching, defects, oxidation points, etc.

[cityboy9x]

How do you know? How was it made? Or are you not talking about a real polymer chain at all, but just a notional one consisting purely of C3H6 groups and nothing else? If so, there's no answer to your question, because such a thing doesn't exist. Propylene doesn't spontaneously polymerise, it has to be initiated by something. Also, propylene is a stable, stand-alone molecule. It can form bonds to other things by opening the C=C double bond - but it must form two bonds, not just one. C3H6 cannot be the terminal group of a polymer chain. Generally speaking, the terminal groups cannot be the same as the repeat unit, for precisely the reason that the repeat unit must form two linkages and the terminal group one. A real polymer never exactly has the formula [repeat unit]n, but usually it is safe to ignore the terminal groups because they constitute only a tiny fraction of the mass of the material, at least for high polymer.

Thank you mjc123! My curricurlum doesn't teach me about that, so I don't now about the problem. So I think that in the formula, the repeat unit represent the beginning and the ending of the chain!
When I asked this question to my teacher and classmates, they couldn't answer this question. They told me it can be that the beginning make a bond with the ending, so polymer has circle-structure? I don't think so! At that time. I didn't think the problem is so complicated. Now I understand more about the problem.
Thank you mjc123 again! Your first reply answer my question exactly, but your second reply answer the problem in my mind!

[mjc123]

You can get cyclic species in some polymerisations, e.g. an AX_nB oligomer of the right size may react with itself to give cyclo-X_n. Less likely, I think, in olefin polymerisations.