Exploring the Math of Glucose Polymers: Understanding 6^n

In summary, the conversation discusses the possible number of polymers that can be produced from n glucose monomers. It is mentioned that glucose molecules do not react at random and there are certain positions that are more prone to react during polymerization. The question is posed as to how many different polymers can be produced from n monomers connected in a specific way. The answer is not clear and may involve mathematical formalism and combinatorics.
  • #1
bo reddude
24
1
Homework Statement
not homework, just curious
Relevant Equations
(CH2O)_n
Let's say you have n glucose monomers. (C6H12O6) n

You want to find out how many possible polymers exist in combining those n number of glucose molecules randomly.

So glucose_1 has 6 OHs that can combine with glucose_2 which also has 6 OHs. Starting with glucose_1's first carbon C1, at that position, you can have 6 different OHs from glucose_2 attaching to it.

Since glucose_1 has 5 other OHs, and each of those OHs can have 6 different OH from glucose_2 attaching to it, you have total of 36 different configuration of glucose dimers.
what happens if you were to think about all possible combination of glucose polymer of arbitrary length n?

It seems like 6^ n, but I can't work out the details in trying to explain it. What's the mathematical formalism involved in this?

Thanks for any help.
 
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  • #2
This is more math and combinatorics than chemistry.

In chemistry glucoses don't react at random -OH, in the dominating hemiacetal structure some positions are much more prone to react during polymerization.
 
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Likes BillTre
  • #3
Is there a way to cross post to the math forum on here?
 
  • #4
Thread moved
 
  • #5
thank you
 
  • #6
To all math people wondering what the question is:

1681112387146.png


This star (let's call it a "monomer") can be connected to identical stars by linking any of the ends with any other end of any other star (this would be roughly what chemists call "condensation", and the product is "polymer" - don't treat these terms too seriously as chemical terms here, I am using them for brevity and ignoring details). Assume each star can connect only to two others. Question is, how many different "polymers" can be produced from n "monomers".

Supposedly OP can add some details, the question was originally posted in chemistry - but that's not how the glucose really react, so could be there are some additional limits on how these abstract representation can behave.
 
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Likes BvU
  • #7
no one wants to try and answer this question?
 

1. What is the significance of 6^n in the math of glucose polymers?

The number 6 represents the number of carbon atoms in a glucose molecule, and the exponent n represents the number of glucose units in a polymer chain. This math equation helps us understand the structure and properties of glucose polymers.

2. How does the number of glucose units affect the properties of a glucose polymer?

The number of glucose units, represented by the exponent n, determines the length of the polymer chain. Longer chains tend to have higher molecular weights and are more rigid, while shorter chains are more flexible. This affects the solubility, viscosity, and other physical and chemical properties of the polymer.

3. What is the relationship between 6^n and the branching of glucose polymers?

The exponent n also represents the degree of branching in a glucose polymer. A higher value of n indicates a more linear polymer, while a lower value indicates more branching. Branching affects the polymer's properties, such as its ability to form gels or films, and its digestibility.

4. How does understanding 6^n help in the production of glucose polymers?

By understanding the math behind glucose polymers, scientists can design and control the properties of these polymers for specific applications. For example, they can manipulate the value of n to produce polymers with desired molecular weights, branching, and properties.

5. What are some real-world applications of glucose polymers?

Glucose polymers have a wide range of applications, such as in food and beverage industries as thickeners, stabilizers, and fat replacers. They are also used in the production of biodegradable plastics, adhesives, and pharmaceuticals. Additionally, glucose polymers play a crucial role in the human body as glycogen, the storage form of glucose in animals and humans.

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