Heating a monolayer atop a substrate with a laser This problem is briefly mentioned in various research papers I'm reading, but it's never addressed in detail. 
The monolayer is attached atop a substrate as shown below

The centre of the monolayer is heated by a laser coming from the top of the diagram. If the monolayer has a thermal expansion coefficient larger than the substrate by an order of 2, what will happen? And also, if the monolayer was graphene and had a negative expansion coefficient, what do you think will happen?
As far as my thinking goes for the larger coefficient scenario, and what is sort of suggested in research papers, is that the material on top will raise up and form a blister because it's expanding much faster than the substrate and has nowhere else to go. 
As for the graphene scenario, I'm not sure what the mechanism would be, a shrinking monolayer would go towards the laser spot, but if it's decreasing in size I'm unsure if it can manage to raise up and form a blister. I feel like it could possibly break apart?
Any suggestions appreciated! 
 A: Probably depends on how good the adhesion is between your monolayer film and the substrate. If the adhesion is very good then the fact that the film and substrate have different coefficients of expansion doesn't necessarily mean that the film will delaminate or form blisters. The film may simply accommodate itself to the different thermal coefficient of expansion of the substrate, which of course means that stresses will develop in the film and at the film-to-substrate interface. As long as the stresses don't become too high and if the adhesion is good, then there shouldn't be any problems with delamination. The film and interfacial stresses do tend to increase as the film thickness increases, so the fact that your films are only a monolayer thick helps the situation.
If you want to get quantitative, you could probably do a decent back-of-the-envelope estimate of the likely film stresses by noting how much your monolayer film will be compressed or stretched by the substrate over the expected temperature range, and then combining that with the effective Young's modulus of the film.
