Quench-induced ordering in diblock thin films

Diblock copolymers readily make regular repeating structures in their bulk phases.  The length scale and the symmetry of the pattern are determined by molecular parameters such as architecture (diblock/triblock, composition).  An important engineering goal is to establish these bulk patterns in thin films.  Such patterned polymer films can, through a variety of mechanisms, be used as templates for creating ordered surfaces with nanoscopic length scales.

A mechanism for controlling this pattern may be to impose a temperature gradient normal to the substrate.  Large temperature gradients should exist during not-so-well controlled quenches from high to low temperature.  Two effects have been studied through simulation:  the effect on the film order of maintaining a static surface-normal temperature gradient, and the possibility that this gradient could give rise to hydrodynamic flow in the layers.  The following pictures were grabbed from a simulation on symmetric diblocks subjected to the steady, convective (divergenceless) flow shown at the right.  At each time, the upper panel shows the situation when the peak convective velocity is 0.5 in dimensionless units, the middle panel shows the situation with a convective flow that is five times slower, and the lowest panel shows the quiescent layer, quietly arranging itself in uniform wetting layers.  Each panel was started with the same random initial configuration, and was subjected to the same sequence of order-parameter conserving noise.
 

 Short wavelength flow:       Long wavelength flow: 

You can download this animation in avi format.  Here is  another animation file showing what happens when the wavelength of the flow pattern is doubled, with everything else the same.

The boundary conditions are chosen so that the dark-"stained" portion of the diblock is attracted to both the upper and lower rigid surfaces, and laterally periodic boundary conditions have been enforced.  The diblocks are not quite strongly segregated.  The lattice used in the calculation is 30X90 units, but two repeat sequences have been plotted here.

At this point, the lateral order in the films is entirely a result of the externally applied flow.  The upper flow is strong enough so that the order which arises does not extend past a single convective cell, whereas the middle panels with the "slow" stirring show ordering that extends throughout the system.  Also, the middle panel order gets stuck, and releases its stresses at discrete times during the simulation.  When the flow is much weaker than the thermodynamic forces driving the pattern formation, this sort of stick-slip motion occurs.  The missing element at this point, and which I am currently working, is coupling the flow to the striped patterns, and determining if these circulating flows can be induced and controlled by adjusting the temperature gradient across the film.
 

time= 0005 

time= 0250 

time= 0500 

time= 0750 

time = 1000