What is the real link between a very long molecule (or polymer, precisely) and a game like 3-6 year old wood-train ?
Did you know that Snake game (thanks to Nokia) could be a really good picture of the chemistrial model for polymer ?
Actually, it is very important to derive a mathematical tool to evaluate or predict the average length of a polymer created. Nevertheless, as a polymer is constituted by a lot of atoms (in order to form a kind of chain), it is quite difficult to measure it with classical methods !
And now, I will try to explain what are the main assumption of that model...But, if you read the end of that "post", you will see that a basic picture can explain it better ! ! Damn' !!
The solution, once again, is mathematical. Let's imagine a polymer of N atoms (single chain...). Of course, we know the distance between two immediate neighbours, let's call that L. A naive explaination is to say that the total lenght is L(N-1). That is true if the N atoms constitute a perfect line.
But honestly, who can assume that ?
(Un)Fortunately, the solution is quite different !! We have to consider the probability that the next neighbour will create a bond in the direction X (with the angle between the two directions is not alway 180° --> not a straight line !). Therefore, the total length (symbolized sometimes by the end-to-end vector) isn't L(N-1), but a L' (with L' < L(N-1)).
But, that model has no physical meaning if we doesn't introduce the effect of neighboring ! For example, that's not possible to cross the chain already created or it is easy to understand that it exist a maximum angle between two bonds... Can't imagine the mess !!!
Trust me, in that case, maths becomes quite tricky !
But in that case, there is a very good picture of that phenomenon :
--> Maximum angle between two bonds !!!
--> the polymer cannot cross itself !!
Science is fun, isn't it ? Thanks to Dave for that wondeful picture of Snake...(sure it was level 0)
Did you know that Snake game (thanks to Nokia) could be a really good picture of the chemistrial model for polymer ?
Actually, it is very important to derive a mathematical tool to evaluate or predict the average length of a polymer created. Nevertheless, as a polymer is constituted by a lot of atoms (in order to form a kind of chain), it is quite difficult to measure it with classical methods !
And now, I will try to explain what are the main assumption of that model...But, if you read the end of that "post", you will see that a basic picture can explain it better ! ! Damn' !!
The solution, once again, is mathematical. Let's imagine a polymer of N atoms (single chain...). Of course, we know the distance between two immediate neighbours, let's call that L. A naive explaination is to say that the total lenght is L(N-1). That is true if the N atoms constitute a perfect line.
But honestly, who can assume that ?
(Un)Fortunately, the solution is quite different !! We have to consider the probability that the next neighbour will create a bond in the direction X (with the angle between the two directions is not alway 180° --> not a straight line !). Therefore, the total length (symbolized sometimes by the end-to-end vector) isn't L(N-1), but a L' (with L' < L(N-1)).
But, that model has no physical meaning if we doesn't introduce the effect of neighboring ! For example, that's not possible to cross the chain already created or it is easy to understand that it exist a maximum angle between two bonds... Can't imagine the mess !!!
Trust me, in that case, maths becomes quite tricky !
But in that case, there is a very good picture of that phenomenon :
--> Maximum angle between two bonds !!!
--> the polymer cannot cross itself !!
Science is fun, isn't it ? Thanks to Dave for that wondeful picture of Snake...(sure it was level 0)
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