Discussion
The ‘unperturbed dimension’ of the polymer chain is represented as,
\[ (\overline{r_{o}^{2}})^{1/2} \propto \bar{l}(n)^{1/2} \]
where,
\((\overline{r_{o}^{2}})^{1/2}\) = root-mean square end-to-end distance
\(\bar{l}\) = average length of a segment
\(n\) = number of segments in the chain
Using the above information, root-mean square end-to-end distance of a branched polyethylene would be _________________ when compared with that of the linear polyethylene of the same molecular weight and the same number of segments.
Answer: C
The root-mean-square end-to-end distance of the branched polyethylene is lower.
The relation \((\overline{r_{o}^{2}})^{1/2} \propto \bar{l}\,n^{1/2}\) applies to the segments that lie along the path between the two chain ends. In a linear chain all n segments are on that path. In a branched chain of the same molecular weight, some segments sit in side branches, so the main chain from end to end has fewer segments and a smaller end-to-end distance. Branched molecules are more compact for the same mass, which is also why they show a lower intrinsic viscosity.
'Same' would hold only if every segment were in the backbone, and 'higher' reverses the effect. 'Exactly √2 times' has no basis: the factor depends on how much of the chain is in branches.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development