Topology Effect on Order–Disorder Transition of High-χ Block Copolymers

This work aims to systematically examine the topology effect on the self-assembly of block copolymers. Compositionally, symmetric polystyrene-block-polydimethylsiloxane block copolymers (BCPs) with different chain topologies (diblock, three-arm star-block, and four-arm star-block) and various molecular weights are synthesized. These purposely designed block copolymers are used as a model system to investigate the topology effect on order-to-disorder transition temperature (TODT) by temperature-resolved small-angle X-ray scattering experiments. An increase of the TODT is observed when the arm number of BCPs with equivalent arm length (i.e., molecular weight) is increased from one to four. Based on the random-phase approximation (RPA), Flory–Huggins interaction parameter (χ) is determined from the regression of the measured TODT. The observation by differential scanning calorimetry also demonstrates the shifting of the endothermic peak from the order-to-disorder transition of star-blocks to the higher temperature region, consistent with the scattering experiments and the RPA prediction.


Synthesis of Linear Diblock and Star-Block Copolymers of (PS-b-PDMS)n (n = 1, 3, 4).
Styrene (Acros Organics, 99%), hexamethylcyclotrisiloxane (D3, Sigma-Aldrich, 98%), secondary butyllithium (sec-Buli, Sigma-Aldrich, 1.4 M in cyclohexane), benzene (Chem-Lab, 99.7%) and tetrahydrofuran (THF, Carlo Erba, 99.9%) were meticulously purified to meet the high standards for anionic polymerization to synthesize polystyrene-blockpolydimethoxysilane (PS-b-PDMS). 1 Following the established techniques for synthesis of PS-b-PDMS, 1 the diblock (PS-b-PDMS)n (n = 1) was synthesized by utilizing styrene as a monomer (10 g, 0.096 mol) and sec-Buli as an initiator (2.40 mmol) in a non-polar environment (benzene 400 ml) and the reaction proceeded for 18 hours.After retrieving a small aliquot to trace the degreee of polymerization by size exclusion chromotagraphy (SEC) as shown in Figure S1 and vapor pressure osmometry (VPO), D3 (13 g, 0.17 mol) was introduced in the reacting flask and remained for another 18 hours in order to accomplish the ring opening of D3.Equal quantity of THF (400 ml) was added to the solution in order to propagate the polymerization of D3 for 4 hours at ambient conditions and then quenched to -20℃ holding for 10 days.After 10 days, the solution was divided into three separate flasks.
Chlorotrimethylsilane ((CH3)3SiCl, Sigma-Aldrich, 98%) was purified in advance and added in one of the flasks to terminate the reaciton.In the rest two flasks, coupling agents were stoichiometrically introduced to carry out the preparation of three-arm and four-arm star-block (PS-b-PDMS)n (n = 3, 4) based on the same source of the diblock precursor.In the case of three-arm star-block (PS-b-PDMS)n (n = 3), purified trichloromethylsilane (CH3SiCl3, Sigma-Aldrich, 98%) (0.4 mmol) was added to the solution to initiate the coupling reaction which lasted for approximately 1 month prior to termination with (CH3)3SiCl.Same protocol was adopted for the synthesis of the four-arm star-block (PS-b-PDMS)n (n = 4) by exploiting purified tetrachlorosilane (SiCl4, Sigma-Aldrich, 99%) (0.3 mmol) as the coupling reagent.
After termination, all synthesized materials were precipitated in cold methanol and subsequently transferred into a vacuum oven to remove residual solvents.In contrast to diblock, star-block PS-b-PDMS were further submitted to fractionation to remove all the by-products including homopolymers and precursor.Detailed procedures for the syntheses of the diblock and star-block copolymers from a diblock precursor have been reported by Ho and Avgeropoulos et al. 1 Eventually, the narrow-dispersed (PS-b-PDMS)n (n = 1, 3, 4) were prepared as evidenced by the SEC (Figure S1 and Table 1).Extensive characterizations by 1 H-NMR (Figure S2) and differential scanning calorimetry were carried out to determine the volume fraction and its thermal properties (Table 1).

Sample Preparation
All bulk samples of (PS-b-PDMS)n (n = 1, 3, 4) were prepared by the solution casting at ambient condition using cyclohexane (C6H12) which can be referred as a neutral solvent for both PS and PDMS segments.The concentration of polymer solution was fixed at 10 wt %.
Slow evaporation rate of solvent (< 0.1 ml/day) was applied to avoid of the formation of kinetically trapped morphologies.Subsequently, all bulk samples were detached from glass vials and then transferred to a vacuum oven for 1 day for removal of residual solvent.The ascast samples were sealed in quartz tubes under vacuum for the following thermal annealing at 100℃ for three days.

Morphological Observation
Ultrathin microsections (thickness lower than 60 nm) of the solution-cast and the thermally annealed (PS-b-PDMS)n (n = 1, 3 or 4) were prepared at -160℃ by a Leica EM UC6 microtome with accessory for cryo-microtome (Cryochamber EM FC7).Real-spacing images (TEM) were acquired from the ultrathin microsections without staining due to intrinsic massthickness contrast from PDMS to PS microdomains.TEM studies were performed on a JEOL-2100 Transmission electron microscopy (TEM) operating at an accelerating voltage of 200 kV.
For further examination of the intrinsic phase behaviors of (PS-b-PDMS)n (n = 1, 3 or 4) synthesized, four diblocks were prepared for real-space observation under TEM.As shown in  The measurements of the temperatures of order-disorder transition (TODT) obtained from solution casting by cyclohexane were studied by an in-situ temperature-resolved SAXS experiments.The measurements are divided into two stages.In the first stage, owing to the gap between the TODTs and vitrification of PS microdomains below the temperature of glass transition of PS (Tg PS ~67℃), a rapid heating rate at 20℃/min was set till reaching the approximately predicted temperature at TODT -60℃.Smaller interval between heating steps was set for the precise measurement for the TODTs.In the second stage, slower heating rate was set for 0.5℃/min capture the starting point of ODT.As shown in Figures 3 and S4, the S7 complete temperature window covers a wide range of 150℃ which is expected to be able to examine the ODTs of the high-χ BCPs before the occurrence of degradation.Clear step changes on the inverse intensity of the self-assembled diblocks can be observed; note that the discontinuity of profiles is attributed to the temperature limit of the heater for in-situ SAXS experiments.Similar procedures were applied to the three-arm and four-arm star-blocks.As shown in Figure S5 and S6, the uprising jumps to the temperature dependent curves unambiguously mark the occurrence of ODT.Plots of FWHM and inverse intensity were combined for precise determination of the measured TODTs of the self-assembled (PS-b-PDMS)n (n = 1, 3 or 4) which were summarized in Figure 7 and Table 2.  and B.

Setups for Prediction of ODTs by Random Phase Approximation (RPA)
3][4] For two-component systems, the inverse collective structure factor,  ̃ −1 , was written as follow: − , where is the product of the Fourier-space bond transition probabilities of all the segments that form the linear sub-chain bridging segments  and : with bγ denoting the statistical segment length of the monomer, γ, and if th monomer is of type α 0, otherwise The stability limit of the homogeneous phase (i.e., spinodal point) when the ODT occurs is determined by locating the point at which  ̃ diverges, or  ̃ −1 goes to zero.
For the incompressible melt of star-blocks, we assume that each AB-type star-block copolymer (BA)n chain is composed of n identical AB arms joined together through their A (i.e., PDMS) ends, and the B (i.e., PS) ends are free.The total degree of polymerization of one star-block copolymer chain is Nt = n(NA + NB).With these assumptions, one can carry out the integrals of Sαβ to get the expressions for the various Sαβ's: , , where   =  2   2 6   (α= A or B).
By setting n = 1, the equations above reproduce the results for a simple AB diblock copolymer:  By using RPA, we evaluate the spinodal curves for the (BA)n copolymer melts with  ranging from 1 (diblocks) up to 5 ((BA)5 star-blocks), with bA = bB = 1 chosen for simplicity.
The results are presented in the fA -N plane and displayed in Figure S8.It is clearly seen that the (N)spinodal at the same fA decreases as increasing  , indicating an increased TODT as increasing the number of arms of the star-block copolymers.

Figure S8
. Spinodal curves of the (BA)n star-block copolymer melts with different n.

Measurements of Latent Heat of Self-Assembled (PS-b-PDMS)n at ODTs
As demonstrated in previous study, the composition fluctuation inhomogeneity at ODTs can be measured by differential scanning calorimetry (DSC). 5More predictions of the latent heat of diblocks at the ODTs have been also investigated. 6,7 ere, we aim to study the topology effect on the phase behaviors of the self-assembled high- BCPs, especially for the difference on the degree of fluctuation on polymer chains.The heating and cooling rates for scanning of the DSC thermogram are fixed at 20℃/min, ranging from 150℃ to temperatures above the measured TODT by 10℃.Cyclic heating and cooling procedures were adopted for examination of the reversible ODTs.The heating and cooling curves are plotted in separated figures as shown in Figure S9.The summary of the measure latent heat of ODTs from the heating and cooling cycles are summarized in Table S1.The measurements of the latent heat at ODTs (∆HODT) were calculated from the first cycle during measurements at the heating and cooling rates of 20℃/min.

Figure S3 ,
Figure S3, the alternating dark and bright stripes evidenced the formation of lamellar

Figure S3 .
Figure S3.TEM micrographs of the of PS-b-PDMS with different molecular weights: (A)

Figure S4 .S8Figure S5 .Figure S6 .
Figure S4.Temperature dependence of inverse of maximum intensity (1/I(q*)) of the self- above, we can locate the spinodal at which min   ̃ −1 = 0 for a given set of {n, NA, NB, bA, bB}.It is known that the mean-field phase behavior of diblock copolymers modelled as the standard Gaussian chains only depends on the collective parameter Nγ, where Nγ is a reference degree of polymerization that can be chosen arbitrarily.Here, we choose Nγ to be the degree of polymerization of one single AB arm of the (BA)n copolymer, denoted as N. Different choices of {NA, NB} but with the same overall A volume fraction fA = NA/N will produce the same (N)spinodal.Therefore, we simply choose N = 1 and re-parameterize the polymer chain by {n, fA, bA, bB}.As an example, the  ̃ −1 () curves with{n, fA, bA, bB} = {3, 0.5, 1, 1} and three typical values of N, i.e. 10, 8.14 and 6, are shown in FigureS7.In particular, the minimum value of the curve corresponding to N = 8.14 is 0 and thus is identified as the (N)spinodal marking at the ODT.