Discussion
The order of average molecular weights of a polymer is
Answer: A
The order is \(M_{z} \gt M_{w} \gt M_{v} \gt M_{n}\).
The averages weight the molecules differently. \(M_{n}\) counts every chain equally; \(M_{w}\) weights each chain by its mass, and \(M_{z}\) by its mass squared, so each is pulled further towards the heavy chains. For any sample that is not monodisperse this gives \(M_{z} \gt M_{w} \gt M_{n}\).
The viscosity average \(M_{v}\) depends on the Mark-Houwink exponent a, usually 0.5 to 0.8, and lies between \(M_{n}\) and \(M_{w}\) (it equals \(M_{w}\) when a = 1). The other orders put \(M_{n}\) above \(M_{w}\), or \(M_{v}\) outside that range, which cannot happen.
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