Explosive dissolution and trapping of block copolymer seed crystallites

Enhanced control over crystallization-driven self-assembly (CDSA) of coil-crystalline block copolymers has led to the formation of intricate structures with well-defined morphology and dimensions. While approaches to build those sophisticated structures may strongly differ from each other, they all share a key cornerstone: a polymer crystallite. Here we report a trapping technique that enables tracking of the change in length of one-dimensional (1D) polymer crystallites as they are annealed in solution at different temperatures. Using the similarities between 1D polymeric micelles and bottle-brush polymers, we developed a model explaining how the dissolving crystallites reach a critical size independent of the annealing temperature, and then explode in a cooperative process involving the remaining polymer chains of the crystallites. This model also allows us to demonstrate the role of the distribution in seed core crystallinity on the dissolution of the crystallites.


Materials
Decane (99+ %) was purchased from Aldrich and used without further purification.
Platinum-divinyltetramethyldisiloxane complex in xylenes (Karstedt's catalyst) with a concentration of Pt of ~2 wt % was purchased from Aldrich.

Transmission electron microscopy
Bright-field transmission electron microscopy (TEM) images were taken using a Hitachi H-7000 instrument. Samples were prepared by placing one drop of solution on a Formvar-carbon coated grid, touching the edge of the droplet with a filter paper to remove excess liquid and allowing the grid to dry. We observed that the amount of micelles deposited on a TEM grid increased when the seed solution was left for a longer contact time on the TEM grid before removing excess liquid. A sample that contained fewer seeds in the solution (after dissolution) was thus left for a longer time on the TEM grid to compensate for the decrease in number density of micelles.
For each sample, micelle length distributions were determined by tracing more than 200 micelles or stained trapped seeds using the software ImageJ (NIH, US). The number average length of the micelles (or trapped stained seeds), L n , was calculated as  (1) where N i is the number of micelles of length L i , and N is the total number of micelles (or stained trapped seeds) examined for each sample. Q.E. APD avalanche photodiode module, interfaced to the ALV-5000/EPP multiple tau digital.
All measurements were carried out at 20 °C. SLS and DLS experiments were performed simultaneously in an unpolarized configuration, i.e., without any polarizer installed in front of the detector. The angular range consisted of scattering angles between 20º and 150º (at 5º intervals). Toluene was used as the standard in the SLS measurements.

Calculation of the mass percentage of seeds that survived the annealing procedure, %m ts (T a ) (eq.1 main text)
When no unimer is added to a solution of micelle fragments (seed crystallites or seeds), the unimer present when the solution is heated to T = T a is due only to the dissolution of the seeds.
A seed solution annealed at a temperature T a for a time t will contain a mass of seeds, m ts (T a ): where N agg/L , the linear aggregation number, describes the number of block copolymer (BCP) molecules per nanometer of seed length. L ts (T a ) is the number average length of the trapped seeds, M 0 , the weight average molecular weight of the BCP, and N ts (T a ) is the number of seeds remaining in the solution at T a . Note that no change in the magnitude of m ts (T a ) was observed when the sample was heated for more than 10 minutes.
The magnitude of N ts (T a ) depends on both the extent of seed dissolution, which decreases the number of seeds, and seed fragmentation, which causes an increase in the number of seeds.
At room temperature, all of the BCP is incorporated into micelles and no unimer remains in solution. N ts (T a ) can thus be evaluated experimentally as a function of the number of seeds in the solution at RT prior to annealing, N seeds,RT : where L seeds,RT is the number average length of the seeds at RT. N seeds,RT can also be calculated as a function of mass of seeds in solution at RT: L T m T m L T  (5) Note that N agg/L and M 0 cancel out in Supplementary Equation 5. We thus do not need to know the values of these two parameters.
Since no unimer was added to the solution, the total mass of BCP at any temperature is the same as that at RT: The mass percentage of seeds persisting in solution after annealing at T a for a time t is, The translational and rotational diffusion coefficients depend on the geometry of the rod considered. They have been evaluated for different types of rigid cylinders, i.e., with flat caps, spherical caps or even for tubes by Flamik and Aragon using a boundary element method (BE). 2,3 They can be expressed as a function of the ratio of the rod length to the hydrodynamic crosssectional diameter, p = L/d, and the solvent viscosity, η. For cylinders with spherical caps, the translational diffusion coefficients, D ∥ and D , are given by: Where T is the temperature, k is the Boltzmann constant, while X ┴ and X ║ , are the translational diffusion shape functions: The rotational diffusion coefficient D r is given by With the rotational diffusion shape, X r , given by: D app can also be obtained experimentally from the ratio  1 /q 2 , where  1 is the first cumulant calculated for each angle from the fitting of the autocorrelation decay with a cumulant expansion to second order (2-CUM).
To evaluate the hydrodynamic diameter of the seed cross-section, we first prepared a relatively concentrated solution (c = 6.0 mg mL -1 ) of PFS 53 -b-PI 637 micelles in decane, by

Calculation of L mic (T a ) as a function of T a (eq.6 main text)
In seeded growth experiments, one adds a given mass of unimer to a solution of seeds to extend their length. In self-seeding experiments, the unimer formed upon heating a micelle fragment solution comes from the dissolution of existing seeds, and, upon cooling to room temperature, this unimer adds to the seeds that survived the annealing step. There is thus a simple relationship between the length of the seeds regrown at room temperature, L mic (T a ), and the mass of unimer obtained by the dissolution of some of the seeds: 4 a a uni a mic ts ts a The mass of surviving seeds, m ts (T a ), is given by Supplementary Equation 2, while the mass of unimer formed at T a , is given by: If we assume that the distribution of dissolution temperatures of the seeds, f(T a ), can be represented by a normal distribution (Supplementary Figure 17), then where T d is the average dissolution temperature, and is the standard deviation of the distribution. Figure 17, the number of seeds dissolved at a given temperature is equal to the sum of all the seeds that dissolved below this temperature. The number of seeds that have survived at T a is thus given by:

As depicted in Supplementary
where N 0 is the total number of seeds in solution before dissolution.
Supplementary Equation 21 can be rewritten using the complementary error function, erfc(x): At mild temperatures (for T a ≤ 50 °C), the seeds do not dissolve to a significant extent, but they undergo a small extent of fragmentation, increasing the total number of seeds present in solution. From Supplementary Tables I and II  a. standard error of the mean determined by tracing more than 200 micelles for each annealing temperature. a. standard error of the mean determined by tracing more than 200 stained trapped seeds for each annealing temperature.