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Question: The \[{\text{P}}\](PDI) of a polymer is: (\[{{\text{M}}_{\text{w}}}\]​​= weight average molecular ma...

The P{\text{P}}(PDI) of a polymer is: (Mw{{\text{M}}_{\text{w}}}​​= weight average molecular mass and Mn{{\text{M}}_{\text{n}}} ​​= number average molecular mass)
A.the product of Mn{{\text{M}}_{\text{n}}}and Mw{{\text{M}}_{\text{w}}}
B.the sum of Mn{{\text{M}}_{\text{n}}}and Mw{{\text{M}}_{\text{w}}}
C.the difference between Mn{{\text{M}}_{\text{n}}}and Mw{{\text{M}}_{\text{w}}}
D.the ratio between Mn{{\text{M}}_{\text{n}}}and Mw{{\text{M}}_{\text{w}}}

Explanation

Solution

To answer this question you should recall the concept of Polydispersity index of a polymer. It refers to the broadening of molecular weight distribution due to various arrangements of the constituent chains.

Complete step by step answer:
The larger the PDI, the more the array of constituent chains and broader the molecular weight. It is calculated using the ratio of weight average by number average molecular weight. It has special importance in the selection of the most suitable polymers in different applications. There is the use of photon correlation spectroscopy for determination of size by using the scattering of light by dispersed particles due to their Brownian motion.
The formula can be written as Polydispersity Index = MwMn{\text{ = }}\dfrac{{{{\text{M}}_{\text{w}}}}}{{{{\text{M}}_{\text{n}}}}}.
In case this value is more than 1 it means that the polymer has extra chains as compared to an actual molecular chain which is the case for trans-esterified polymers like cyclic oligomers or chain transfer products.
In case this value is 2 it refers to the fact that polymer growth is not in a controlled manner and oligomers concentration is more.

Hence, the correct option is option D.

Note:
For calculation of the mass of polymers we use osmotic pressure. The expression for osmotic pressure can be given by Π=iCRT\Pi = iCRT
where Π\Pi = Osmotic pressure, ii= Van’t Hoff Factor, CC= concentration, RR=Universal gas constant and TT=Temperature. As compared to other colligative properties, its magnitude is large even for very dilute solutions. The technique of osmotic pressure for determination of the molar mass of solutes is particularly useful for biomolecules as they are generally not stable at high temperatures and polymers have poor solubility.