Question
Download Solution PDFIn a polymer of N monomer units, the root mean square separation between the two ends is proportional to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
→ The RMS separation between the two ends of a polymer chain is a measure of the average distance between the two ends, taking into account the statistical fluctuations due to the thermal motion of the chain. It is calculated by finding the square root of the sum of the squared distances between each pair of monomer units in the chain.
→ For a polymer chain consisting of N monomer units, the number of possible configurations or conformations of the chain is extremely large, and it is not possible to calculate the RMS separation analytically in most cases. However, it is possible to use statistical mechanics to estimate the RMS separation for a polymer chain in a given state.
Explanation:
→ The root mean square (RMS) separation between the two ends of a polymer chain of N monomer units can be expressed as:
RMS = \(\sqrt{N}\times a\)
where "a" is the average bond length between the monomer units.
This equation shows that the RMS separation is proportional to the square root of N.
This relationship arises because the polymer chain is essentially a random walk, where each step has a certain length (the bond length "a") and direction. The more steps there are (i.e., the larger the value of N), the more likely it is that the polymer chain will have taken a long, meandering path, resulting in a larger RMS separation.
Conclusion:
Therefore, we can conclude that the RMS separation between the two ends of a polymer chain is proportional to the square root of the number of monomer units in the chain.
Last updated on Jun 5, 2025
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