The species distribution of the H₂SO₃ as the function of pH was calculated by using the HYDRA/MEDUSA software package (Puigdomenech, 2015). The acid dissociation constants of H₂SO₃ are: pK_a1 = 1.91 and pK_a2 = 7.22. The total concentration of SO₃ ^2- used for calculation was 0.8 mm, which was calculated by considering the approximate inflowed 2.0 M Na₂SO₃ in 10 min (flow rate of 0.30 ml/h), diluted to 20 ml. Except neutralization, no other reactions were considered.

The recorded pH oscillations in the optimized semibatch BrO₃ ⁻ − SO₃ ^2– pH-oscillator driven PISA of PEG-b-PHPMA with different target degrees of polymerization (DP_targets) of HPMA are shown in Figure 1A (DP_target = 100) and Supplementary Figure S1 (DP_target = 65 and 130). The change of period times, amplitudes, and the minimal pH values in each pH oscillation periods, at composition DP_target = 100 are shown in Supplementary Figure S2. The period time of the pH oscillations stabilized within a narrow range from 8 to 10 min as reaction proceeded, while the amplitudes (ΔpH) kept decreasing from 3.5 to 2 pH units, and the minimal pH values (pH_min) increased from ∼3.75 to ∼4.25.

When polymerization was coupled with the pH oscillator, compared to the H⁺ concentration of the inflowed solution [c(Na₂SO₃) = 2.0 M and c(H⁺) = 0.06 M] in the pure BrO₃ ⁻ − SO₃ ^2– pH-oscillator (Supplementary Figure S3B), to maintain the original high amplitude pH oscillations, higher input of H⁺ (c(H⁺) = 0.31 M) was required. When this high concentration H⁺ (c(H⁺) = 0.31 M) was inflowed to the pure system, oscillations in the pH cannot be measured (Supplementary Figure S3A).

The conversion (%) of HPMA was determined by ¹H-NMR. Reaction mixture samples were collected at different times (labeled on the pH oscillation curve in Figure 1A). Here LX/UX indicates the lower or upper point in the X oscillatory cycle. The monomer conversion (%) vs. time (Figure 1B) was calculated two ways, from the decrease in the area of the monomer peak and from the increase in the area of the polymer peak in the ¹H-NMR spectra (Supplementary Figure S4). The final monomer conversion at 120 min calculated in from the increase in the area of polymer peak was 51% (Supplementary Table S1), while based on the decrease of the area of the monomer peak, the final conversion at 120 min was calculated to be 100%. Monomer evaporation (T = 40°C) was the potential reason for the difference in the conversions calculated in the two different ways.

An interesting, and expected, behavior consisting of a series of stepwise increases in monomer conversions (%) vs. time, is observed and indicates the presence of periodic polymerization in our system (Figure 1B). The two-way oxidation of SO₃ ^2– by BrO₃ ⁻ is known to be the source of the pH oscillations in the BrO₃ ⁻ − SO₃ ^2– pH-oscillator (Szántó and Rábai, 2005). The complete oxidation of HSO₃ ⁻ and H₂SO₃ to SO₄ ^2– produces H⁺ autocatalytically and provides a positive feedback (Table 1, R3 and R4). The partial oxidation of HSO₃ ⁻ to the relatively stable intermediate, S₂O₆ ^2– (Table 1, R5), consumes H⁺ which is the source of the delayed negative feedback in the pH oscillatory cycle with the contribution of the protonation of the inflowed SO₃ ^2–. Possible radical formation and consumption reactions are listed in Table 1 (R6–R11). The SO₃ ⁻*, HSO₃*, OH* are potential initiators (Mukherjee et al., 1966). Halogen atom endgroup has not been found in BrO₃ ⁻/SO₃ ^2– redox pair-initiated polymerization (Mukherjee et al., 1966). Both the positive (R3, R4) and negative feed-back processes (R5) involve free radical steps (R6, R7). A considerable difference in the amount of produced free radicals is expected during the H⁺ producing and consuming reactions, since the major route for the oxidation of the sulfite is known to be the complete oxidation, while only 1–2% of the initial SO₃ ^2– is oxidized to S₂O₆ ^2–. Our experiments completely support this. The polymerization is found to be faster as the pH decreases and slower, or negligible, when the pH increases (especially so after the first three periods of oscillation). To further characterize this system, a series of experiments were conducted at different starting pH values and at different temperatures (Figure 2 Supplementary FigureS5). Working at a lower temperature (T = 25°C) increases the period time of the oscillations and allowed us to perform more accurate sampling. Figures 2A, B show the pH change and the corresponding conversion (%) in time at a DP_target = 100 at 25°C at different initial pH values. When premixed PEG-CTA and HPMA were added to the bromate solution, without prior adjustment of the initial pH, the pH of the system immediately dropped from ∼5.5 (pH of 0.10 M NaBrO₃) to ∼4.5 (Figure 2A). Then, the pH quickly increased to >7.0 as the sulfite solution (Na₂SO₃ + H₂SO₄) was continuously inflowed at a steady flow rate (0.30 ml/h). Polymerization was not detected between the points L0 and U0. At point U0, the slow oxidization of HSO₃ ⁻ by the bromate ion is triggered and slowly produces H⁺ (R3). This reaction generates initiating radicals for the polymerization between U0 and U0′ indicated by the slow increase in the conversion (%). The increasing H⁺ concentration increases the concentration of the more reactive H₂SO₃ and R4 reaction is activated. The rate of R4 is much higher than the rate of R3. As the overall reaction rate increases, the concentration of free radicals also increases, which is clearly accompanied by an increment in the rate of polymerization between the U0′ and L1 points.

Figure 2B shows the pH and the conversion (%) in time when the initial pH value of the bromate solution was set to pH∼3.5 (by adding H₂SO₄ to the solution of bromate, PEG-CTA and HPMA). The pH of the reaction mixture started to increase as the sulfite solution (Na₂SO₃ + H₂SO₄) was inflowed but in a much slower rate, than in the previous case and slow polymerization was detected immediately from point L0 initiated by the radicals generated in R7. After the system’s pH reaches a critical value (pH = 4–4.5) the polymerization was temporarily interrupted, indicating that the increase in pH here is predominantly caused by the protonation of the continuously inflowed sulfite, and the radical generation is negligible until point U1 is reached [Note that, the calculated species distribution of H₂SO₃-HSO₃ ⁻-SO₃ ²⁻ vs. pH (Supplementary Figure S7) shows a similar pH value of ∼4.5, above which H₂SO₃ is no longer available.] Then during the pH drop phase the polymerization is initiated, and from point U1 to U1′ its rate was found to be relatively slower and from U1′ to L1 faster [An experiment at T = 40°C with the adjustment of the starting pH to 3.8 was also run and, similarly, stepwise increases in the conversion (%) were detected (Supplementary Figures S5, S6)].

Following the conversion (%) in time for the complete working pH range of the pH oscillator, let us not only identify the ranges of each period when polymerization takes place in the system, but also to determine the relatively faster, slower and negligibly slow phases, providing proof of our assumption for the periodic radical formation and polymerization (Figure 2C). The formation of the initiating radicals (SO₃ ⁻*, HSO₃*, and OH*) is switched ON and OFF by the BrO₃ ⁻ − SO₃ ^2– pH oscillator. This is in contrast with B-Z-assisted periodic polymerization, in which the initiating malonyl radicals are always available and periodic termination by BrO₂* occurs (Pojman et al., 1992; Washington et al., 1999).

The DP of the purified final PEG-b-PHPMA product was also determined by ¹H-NMR (DP = 54, Supplementary Figure S8A) and GPC (DP = 46, Supplementary Figure S8B and Supplementary Table S1), the latter is close to the conversion calculated from the ¹H-NMR spectrum of the final reaction mixture sampled at 120 min (DP = 51, Figure 1B, Supplementary Figure S4 and Supplementary Table S1). The dispersity (Đ) of the final PEG-b-PHPMA was calculated to be 1.97 using GPC (Supplementary Table S1).

The pH and monomer conversions vs. time curves recorded in experiments when the system was in its non-oscillatory regime (Figure 3). The higher or lower input H⁺ concentrations make the system operate in a low or high pH steady state (Figures 3A, B). Figure 3A shows the pH change curve, and corresponding monomer conversion curve, when the inflowed solution had a lower H⁺ concentration [c(H⁺) = 0.21 M]. R3 and R4 (Table 1) could not be triggered, and the pH value kept growing until it was close to the pH of the inflowed solution. No polymerization was observed during the experiment because the oxidation of the unprotonated SO₃ ^2‒ by BrO₃ ⁻ is negligibly slow (Figure 3A and Supplementary Figure S9A). However, some reactions, such as disproportionation reactions and ester bond cleavage of monomers, may have occurred, especially in highly basic conditions (pH > 10), as can be inferred from the complicated structure of the -CH(OH)-CH₃ peak at ∼1.2 ppm and the decrease in the height of double bond peaks at 5.7 and 6.2 ppm shown in the ¹H-NMR spectra (Supplementary Figure S9A). A higher H⁺ input (c(H⁺) = 0.50 M) can also bring the system out of the oscillatory regime. The pH of the system increased quickly once sulfite solution was continuously pumped in. Then the autocatalytic oxidation of sulfite by bromate brought the pH quickly down to a value of pH < 4 and the pH stayed at the acidic steady state (Figure 3B). Although oscillations did not occur, radical formation was not stopped due to the ongoing R3, R4 and R5, when the pH < 4. Most of the polymerization happened during the pH drop phase in the first 30 min. The final monomer conversion at 120 min was much lower (<30%) than in the oscillatory regime (Supplementary Figure S9B). Experiments under the same conditions as in the original semibatch reactor (Figure 1) were also conducted in a batch reactor (Figure 3C), when a 0.60 ml solution (the same volume inflowed in 2 h to a semibatch reactor) of sulfite and H⁺ [c(Na₂SO₃) = 2.0 M and c(H⁺) = 0.31 M] was added all at once, the pH quickly dropped to an acidic state, and polymerization stopped once all the sulfite was consumed and the conversion was much lower, < 15% (Figure 3C and Supplementary Figures S9C).

Finally, the dynamical evolution as a collective system of the self-assembled objects generated during polymerization induced self-assembly driven by pH oscillatory chemistry was studied by monitoring the size and morphology changes of the generated self-assembled structures using DLS and SEM/TEM respectively (Figure 4) (The reaction conditions were the same as in Figure 1.) Figure 4A shows the change in the average size of self-assembled aggregates from ∼138 nm at 15 min to 1–1.5 μm at 60 min, and to ∼5 μm at 120 min. The formed vesicles were stable, but some precipitation was observed after 2–3 days.

PEG-b-PHPMA diblock copolymers, consisting of similar length of the stabilizing hydrophilic PEG-block and similar length of the hydrophobic core forming PHPMA blocks, as our final polymer, but synthesized by light-induced initiation has been reported to form only nanoscale spheres (Ren and Perez-Mercader, 2017). The essential presence of high concentration salt in the BrO₃ ⁻ − SO₃ ^2– pH oscillator, especially the continuously supplied Na₂SO₃ and the produced Na₂SO₄, can contribute to giant vesicle formation of PEG-b-PHPMA synthesized by pH oscillatory chemistry (Figures 4D1, D2). The increasing ionic strength makes entropic forces become more favorable to exclude hydrophobic structures, resulting in a shift toward higher order morphologies (Zhou et al., 2017). The solubility of hydroxyl group containing polymers, such as poly(vinyl alcohol) (PVA), has been reported to be greatly reduced by the addition of salt, and low concentrations of Na₂SO₄ serves as a precipitant for PVA (Gupta et al., 2012). The turbidities of purified PEG₄₃-b-PHPMA₅₁ suspensions were seen to gradually increase from pure water to NaBrO₃ solution and to the mixed solution of NaBrO₃ + Na₂SO₃ + H₂SO₄ (Supplementary Figure S10). The gradual increase in salt concentration can change the volume fraction of the hydrophobic tail and can lead to a higher packing parameter, which promotes the formation of giant vesicles (Scheme 1B and Figure 4). Vesicle budding and division were also seen in both TEM (Figure 4C) and SEM (Figures 4D1, D2) images. A possible reason for this evolution is the autonomously generated chemical gradient through the membrane by the continuously increasing salt concentration and by the difference in chemical reactions outside of the vesicles and entrapped by the vesicles.

Beside micelles and vesicles, other type of intermediate morphologies, such as worms and jellyfish, oligolamellar vesicles have been reported previously in the polymerization-induced self-assembly of HPMA using PEG macro-CTA at a very narrow range of the phase diagrams (Warren et al., 2014). Such kind of self-assembled objects were not observed during the pH oscillator-driven PISA of PEG-b-PHPMA. The reason of the absence of these morphologies could be the lower level of control on the degree of the polymerization and the higher dispersity of the resulting copolymer.

As indicated by an energy dispersive spectroscopy analysis (EDS), the observed objects in the 120-min sample contain the element carbon, thus proving that they are made of polymer (Supplementary Figure S11).