The Five Minute Polymer Property Videocast: The Crystalline Melting Point – Transcript

As people seem to like transcripts of the video podcast, here it is. Most of the material in this videocast is taken from van Krevelen’s book.^[1]

Besides the glass transition temperature, the second transition temperature that we need to worry about in connection with polymers is the melting point. Thermodynamically, the melting point is a pure first order transition, at which the energies of the solid and that of the liquid phase are in equilibrium. Or, to put it in an equation: at the melting point, DH_m, the enthalpy of fusion is equal to T_m x DS_m, DS_m being the entropy of fusion. It should be noted, that this first order behaviour is in sharp contrast to the other transition temperature, the glass transition temperature. Thermodynamically, the latter is neither first nor second order as
the amorphous state is thermodynamically never at equilibrium and therefore normal state variables do not apply.

Besides the molecular structure of the polymer, there are a number of other factors that influence the melting point.

1. Pressure
The melting point of a polymer at a given pressure p can be estimated from its melting point in vacuum, the zero pressure melting point, plus the product of constant s_m x the pressure p. For flexible aliphatic polymers, s_m has a value of 0.175 K/MPa, whereas for semi rigid and rigid polymers, the value is 0.5 K/MPa.

2. Molecular Mass
Like the glass transition temperature, the melting point, too, is dependent on the molecular weight and increases asymptotically to a high polymer limit. This behaviour is captured in the well-known Flory equation, where T_m is the melting point, T_m(infin) is the melting point at high molecular weight limit, DH_m is the heat of fusion per structural unit and P_n is the degree of polymerisation. Intuitively, this behaviour can be understood, as the molecular weight correlates with the length of the crystallizable segments in the polymer. Beyond a certain threshold, the maximum melting point will be reached and any further increases in molecular weight become ineffectual.

3. Molecular Asymmetry
As a general rule, highly symmetric structural units elevate, asymmetric ones depress the melting point. Again this comprehensible from crystal packing considerations: polymers with symmetric structures will be able to pack more tightly in a crystal than asymmetric ones. The consequence is that more energy will be required to break up the crystal lattice, leading to an increase in melting points.

4. Tacticity
Tacticity is a variation on the same theme and we can derive some empirical rules, which hold for most polymers. Consider the repeat unit fragment on the slide above.If P is a hydrogen atom and Q any other group such as a methyl group, for example, then the rule that the melting points of isotactic polymers is higher than those of syndiotactic polymers generally holds. If, on the other hand P is not a hydrogen atom and has a different structure than Q, the syndiotactic polymer usually has the higher melting point.

5. The relationship between the glass transition temperature and the crystalline
melting point.
When plotting the experimental glass transition temperatures of polymers contained in the PoLyInfo database against the corresponding crystalline melting point, we can see that there is an approximately linear relationship, albeit with large deviations.

Early on it was observed by a number of scientists that for most polymers, the ratio of
the glass transition temperature and the crystalline melting point is approximately 2/3,
i.e. approximately 0.67. Boyer later refined this somewhat and claimed that the ratio for most symmetrical polymers is 1/2 and 2/3 for unsymmetrical ones. Unsymmetrical polymers in this context are polymers, having two non-identical main chain substituents. However, even with this refinement, there are still significant deviations from this rule. Further refinement yielded the following rules:

The majority of both symmetrical and unsymmetrical polymers have Tg/Tm ratios between 0.56 and 0.76, with a maximum number of values centered around 2/3.

Polymers with ratios below 0.5 are usually highly symmetrical, with short repeating units. These usually only consist of one or two main chain atoms, carrying substituents of only a single atom. They are usually very crystalline.

Polymers with ratios above 0.76 are unsymmetrical and all have relatively complex structures. They can be highly crystalline.

6. Copolymers
A discussion of the factors determining the melting points and T_g/T_m ratio would merit a separate presentation and anybody interested in delving deeper into the subject should refer to van Krevelen and other textbooks. At this point suffice it to say, that for random copolymers the melting point is usually depressed w.r.t. to the
corresponding homopolymers and intermediate between them. T_g/T_m ratios are
usually high.
Block copolymers can have high melting points, particularly if one of the blocks is crystallizable and of sufficient length. T_g/T_m ratios are usually low.

References
[1] van Krevelen, D. W.; Properties of Polymers: Their Correlation with Chemical Structure; Elsevier 1990 (3rd Edition)

The Five Minute Polymer Property Videocast: The Crystalline Melting Point

Now (almost) by definition, one has an awful lot of people knowing an awful lot about computers in a polymer informatics group, but rather less about polymers. One of the “educational” things that we therefore started here was the “polymer property of the week.” At each meeting of the polymer group, someone prepares a five minute talk about a particular polymer property that they happen to find sexy on that day and presents it to the rest of the group.

I think some of this material is interesting and useful to the polymer community at large and hence I have experimented with getting it into a videocast format, which you can either watch on your computer or download from Google Video directly onto your iPod without any fuss (hence I didn’t upload to YouTube). So please go ahead and watch it and tell me what you think….at this stage things are very experimental and I would be grateful for constructive feedback.