As far as I understand, Polymers are long molecules made of smaller monomers which are Alkenes. But polymers don't have double bonds, so they are saturated. What is the difference between Alkanes and Polymers structures.
The first one is an Alkane, but if the chain was much longer, it would be structurally the same as the Polymer (Second image).
Some points to note: You said polymers are saturated. This generalization is not true in many cases, e.g. polystyrene, nylon, and much more. Alkanes are always saturated.
Alkanes can have branchings. The ones you have in mind are called normal alkanes, in which no carbon has higher order than two. An alkane can have any kind of branching, as long as it is saturated.
Now, maybe the most important one: polymers are made of so-called monomers. All polymers can be constructed from exactly one monomer (even co-polymers). An alkane which is sort-of tree-like randomly branched, will not have such an unit.
A normal alkane has some similarities with polymers, tho. As others mentioned it, the size is the deciding factor there. A normal alkane with a carbon count of 10000 is for sure a polymer.
There are two types of common polymers that are basically just alkanes with very long chains: polyethylene and polypropylene. But there are a large number of other polymers that are made of much more complex parts.
The essential differences between a polymer like polypropylene or polyethylene and an alkane are the size of the molecule and the purity of the molecules. Polymers are big, really big, often containing from thousands to hundreds of thousands of carbons. And, they are often made of mixtures rather than a pure alkane of a fixed number of carbons. These properties arise from the mechanisms of their creation which usually involve long chains of reaction where small molecules (monomers such as ethylene or propylene) are joined together often via a radical reaction to create long chains. These reactions can't be controlled precisely enough to give a single product so a mix of products with a distribution of chain lengths and "branchiness" usually results. To some extent the branchiness can be controlled and this yields different grades of polymer (some clever catalysts can give much more control of chain length).
The properties of polymers differ from those of alkenes mainly because of the size of the molecules. Though you can get some idea of the types of property to expect by following the properties of progressively larger alkanes. Small alkanes are gases, middle-sized alkanes are volatile liquids, larger alkanes (dozens of carbons) are often waxy solids. Polyethylene is just like an extreme version of the waxy solid (depending a little on how it is processed).
For answering the question, it makes sense to look at the definition of the term polymer as recommended by the International Union of Pure and Applied Chemistry (IUPAC) that they give in their Gold Book. It says a polymer is...
A substance composed of macromolecules.
So the word polymer does not refer to individual molecules although it is colloquially used like that. Then, a macromolecule is defined as:
A molecule of high relative molecular mass, the structure of which essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass.
The concept of the repeating units is already described in the other answers. Here, I would like to focus more on the question what is meant by a high molecular mass. This is covered by the first note on the IUPAC macromolecule definition:
In many cases, especially for synthetic polymers, a molecule can be regarded as having a high relative molecular mass if the addition or removal of one or a few of the units has a negligible effect on the molecular properties. [...]
So focussing now on your example, we can have a look at the boiling point of some alkanes:
| Alkane | boiling point [°C] |
|---|---|
| n-butane | 0 |
| n-pentane | 36 |
| n-hexane | 69 |
| n-heptane | 98 |
| n-octane | 126 |
As you can see, the physical property of the boiling point changes considerably with the number of carbons per molecule and with the molecular mass, so these low molecular mass alkanes are no macromolecules, and an ensemble of these molecules will not be a polymer.
Now, for the example of polyethylene I found a nice paper, unfortunately behind a paywall.[1] It shows a graph of melting temperatures of n-paraffins and polyethylene as a function of number of carbons per molecule. The melting temperature inceases at low carbon counts, but levels off around approx. 1,000. This would correspond to a polyethylene macromolecule with 500 repeating units with a molecular mass of around 14,000 g/mol which could be considered the lower molecular mass limit for polyethylene. This limit is far from being a strict limit, there is always some ambiguity, but for all practical purposes this is sufficient.
When I was a student, we were taught that as a rule of thumb, macomolecules will have molecular masses above around 20,000 g/mol, so the estimation above fits in quite well.
Molecules with lower molecular masses which still are composed of repeating units would be called oligomer molecules, and ensembles of these molecules would be called oligomer. So an alkane like dodecane could be considered as a low molecular mass oligoethylene.
