# How does molecular weight effect glass transition temperature?

May 28, 2016

The glass transition temperature ${T}_{g}$ increases with molecular weight and asymptotically approaches a maximum value.

#### Explanation:

The glass transition temperature is the temperature range in which a polymer changes from a rigid “glassy” state to a more pliable “rubbery” state.

In polymer chemistry, the Flory–Fox equation relates the number-average molecular mass ${M}_{n}$ of a polymer to its glass transition temperature ${T}_{g}$:

color(blue)(|bar(ul(color(white)(a/a) T_g = T_(g,∞) -K/M_n color(white)(a/a)|)))" "

where

•  T_(g,∞) is the maximum value of ${T}_{g}$ that can be achieved at a theoretical infinite molecular mass
• $K$ is an empirical parameter that is related to the free volume present in the polymer sample.

The free volume is a measure of the room a polymer chain has in which to move in relation to the other polymer chains around it.

A polymer with long chains (high molecular mass) has less free volume than one with short chains.

Thus, low molecular mass gives lower values of ${T}_{g}$, and higher molecular mass causes ${T}_{g}$ to approach T_(g,∞) asymptotically.

We see this behaviour in a typical Flory-Fox plot:

In the above plot, T_(g,∞) ≈ "380 K".