First to sub 7 nm half pitch phase separation in 1978 !

A long long time ago, in a land far far away.......I obtained 7 nm half pitch phase separation in a block copolymer as shown by the small
angle x ray scatter pattern below in Figure 1.   This was in a multi-block polymer with an individual repeat  length of (A+B) N = 30 repeat
units, and a chi of 0.2. When the chi dropped to 0.1 or N = 10 then there was no phase separation. The interaction parameter Chi is a
measure of incompatibility between repeating units of 2 polymers, the standard DSA material of PS/PMMA has a chi of 0.04 and a
solubility parameter difference of 0.4.

                      Figure 1 Small angle X ray scattering from a phase separated sample chi = 0.2 N = 30. Bragg spacing or
                                                                      period  of  the phases = 14 nm,

Of course, there was no thought of patterning using these materials, but It's rather fun to be in the patterning business 30 years later and
listen to the debate of can we get to 7 nm using block copolymers.

The structure that produced the x ray scattering is shown in Figure 2.


Figure 2 A schematic of partial phase separation of a multi-block polymer.

The incompatible blocks in a single chain group into different phases with the junction between the blocks pinned at the interface shown
in Figure 2. The volume fraction illustrates the presence of graded partial phase separation at the interface. The difference in atomic
weight between the periodic phases scatter X rays as shown on Figure 1, and show that the period of phase separation was 14 nm or a
“half pitch” 7 nm. The measured pitch was also consistent with theory. It turns out that the RMS end to end coil length as a function of
molecular weight is a number that was tabulated in the Polymer Handbook in 1974. The predicted pitch for the small angle x-ray example
above was 10nm, and the measured was 14 nm.  

At the top of this discussion I implied that there were intermediate degrees of phase separation between 2 phases and homo-polymer
like properties. Achieving partial phase separation was the objective of my Phd, and I tracked phase separation through dynamic
mechanical properties. At the glass transition point, mechanical loss factor or “tan delta “ goes through a sharp maximum over 10
degrees for a homo-polymer or a pure phase. As the materials started to phase separate I expected the mechanical damping peak  to
broaden and eventually to produce 2 separate peaks for the 2 phases.

I made a whole series of different polymers, varying composition, block length and incompatibility between the blocks. Figure 3 shows a
summary of all the data. Each graph shows 4 different compositions of a particular pair of materials (chi)  and block length (N)  of the low
Tg component. The left most (low Tg) plot in each group consists of > 90% low Tg block which behaves like a homo-polymer. The
remaining plots are for 75%, 50% and 25% low Tg component. The block length of the 2 materials are roughly equal for the 50%

The first column shows all chi = 0.2 with increasing block length. The second column shows a chi = 0.1 composition.

Figure 3 Change in phase separation for varying incompatability (Chi) and block length N, measured by mechanical loss factor (tan
delta). Each group consists of 4 compositions, >90%,75%,50% and 25%  of the low Tg component.  Column 1 shows a poly (aliphatic
ether-b- aromatic ester) chi = 0.2, with varying  A+B  block length 4,10,20,30 repeats. Column 2 shows a poly (aliphatic ester-b- aromatic
ester) chi = 0.1 block length 48 repeats.

The top grouping  has a very short block length (N=2) and  shows the Tg changing with temperature as the composition changes, with a
sharp homo-polymer like transition.

The bottom grouping (chi= 0.2, N= 30) shows two peaks for the 50:50 composition indicating phase separation. The 50:50 composition
produced the small angle x ray scattering in figure 1.  In between, at chi = 0.2 N = 10, the mechanical loss factor is close to that of a homo-
polymer, and  indistinguishable from data for chi = 0.1 and N = 24 shown in column 2 . At N = 20 chi = 0.2, a very broad peak in loss factor
shows partial phase separation.  The trends in Tg for the multiple peaks were consistent with phase separation. Finally the dominant
phase could be changed by changing the casting solvent. The mechanical loss curves showed the progression in phase separation just
as I had hoped.  Even more intriguing 2 different materials showed very similar phase separation at similar chi*N products as shown in
the 2 graphs in row 2 of Figure 3.

The presence of partial phase separation is predictable because pinning the junction between the blocks in a thin interface produces a
large entropy penalty, so a graded transition is thermodynamically favorable. The size of the interface was estimated by previous workers
by assuming a sine squared transition profile. I modified the model to handle multi-blocks, and make a better approximation for a large
transition fraction. The model suggested that for chi = 0.2 and N = 30 the transition fraction was around 80%.  A mechanical model for a
composite with such a transition fraction just showed the 2 peaks in loss factor  I observed in the Figure 2.

The thermodynamic model, mechanical model,  the x ray data, the phase size model, the mechanical data, and the Tg trend data were all
consistent in confirming the presence of block controlled phase separation with a large transition fraction.

The product chi*N measures the tendency of a given block polymer to phase separate, so there are some broad trends shown in these
data compared to typical DSA di block materials;

    1)        chi*N = 6 for the A+B length)  according to my model  will have
                a transition fraction of around  30%..  The literature rule for  pure phases  is > 10.

    2)        chi*N =  4  just produces 2 phases with a large transition fraction  (80%), and

    3)        chi*N <= 2 produces homogeneous films .

One other factor that is worth noting is that these blocks are made by condensation polymerization, so the blocks have a range of
molecular weights (poly-disperse) . The range of molecular weights might be expected to depress phase separation however these data
does seem to be generally consistent with results from mono-disperse materials such as PS/PMMA.

Along with the fun, there are some serious points to make about materials design for DSA. At these very low block lengths (Mw = 3-4000),
the properties of the block are very molecular weight dependent. In order to get handle-able materials, I made a multi-block polymers with
a total molecular weight of 50,000.  The important point for DSA materials is that as the total molecular weight drops below the
entanglement length of 20,000, the viscosity of the material drops sharply. I would expect the anneal time for defect free assembly to be
tightly coupled to viscosity.  The other factor that affects viscosity is the presence of phase separation in the melt. To anneal effectively, the
temperature must be selected to minimize viscosity while keeping the phases separated.

All the arcane details can be found in my PhD thesis and the paper I published, now scanned and linked here as the copyright has
expired !

M.P.C. Watts, E.F.T. White “Phase Separation And Mechanical Properties Of An Amorphous Poly(Ether-B-Ester),” Multiphase Polymers, A.
C.S. V 176, p153, 1978