Results and Discussion

We envisioned that the shape and size of bottlebrush polymers could be programmed by implementing a computer-controlled semibatch reactor setup in conjunction with a graft-through polymerization (Fig. 1, Left). With this approach, the flowrate profile of the solution of growing macromonomer would directly translate into the shape of the bottlebrush polymer, i.e., each flowrate profile will result in a unique polymer shape. The reactor setup consists of a syringe/syringe pump as the first reaction vessel, and a flask as the second vessel. In the first vessel, the macromonomers are synthesized via a controlled polymerization, while the solution is continuously fed into the second reaction vessel. The brush growth is immediately quenched upon addition to the second vessel, and the macromonomers are rapidly and quantitatively incorporated into the growing bottlebrush polymer via a graft-through polymerization. Over time, the length of the macromonomer increases in the first vessel, and the process results in a shaped bottlebrush polymer in the second vessel.

To implement the proposed shape-controlled synthesis, a few polymerizations selection criteria are considered. First, the two polymerizations should be fully compatible and orthogonal. Second, the macromonomer synthesis should be quenched readily in the second vessel. Third, the graft-through polymerization should have a very high rate of polymerization to prevent the accumulation and scrambling of macromonomers of different lengths. Grubbs third-generation (G3) catalyzed ROMP of norbornene-type monomers was selected for the graft-through polymerization (the backbone-forming reaction), as it results in very narrow polymer molecular weight dispersities at very high monomer conversion (24, 25). The ROP of lactide catalyzed by a 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) was selected for the brush synthesis as an orthogonal and quenchable polymerization (26).

The polymerization rates for both brush and backbone reactions were determined to ensure the control over the bottlebrush’s shape and size was maintained. The rate constant of ROP of lactide (k_p = 200 M⁻²⋅min⁻¹; SI Appendix, section 3) was determined and extremely narrow polymer dispersities were achieved (M_w/M_n = Ɖ < 1.1) (26). The narrow polymer dispersities are a key element for maintaining shape control, as a broad polymer distribution would reduce the shape resolution. The rates of polymerization of G3-initiated ROMP of macromonomers (nor-PLA) were measured over a broad range of molecular weights (SI Appendix, section 5). In all cases, the rates of polymerization were very fast (k_obs > 1.5 min⁻¹) compared with ROP (∼10²× faster). This large difference in polymerization rates is important to ensure that the macromonomer growth and thus the feed rate of macromonomers is slow enough so that the fast ROMP is able to maintain a high macromonomer conversion; i.e., prevent the accumulation and scrambling of brushes of various lengths in the ROMP pot.

To ensure the orthogonality of ROMP and ROP a study was conducted to explore the compatibility of both polymerizations in detail. A model system using nor2 [(bicyclo[2.2.1]hept-5-en-2-yl)methyl benzoate] as a monomer for ROMP was implemented to probe the effect of ROP reagents on ROMP (SI Appendix, section 4). Only DBU was identified to be an inhibitor. Therefore, DBU must be quantitatively scavenged out of solution upon addition to the second vessel (27). Boric acid was found to be very efficient in this role as it fully quenched ROP without affecting the ROMP (with respect to rate and polymer dispersity) prior to and post-DBU quenching. Finally, we demonstrated that ROMP remained controlled under semibatch conditions by slowly feeding a solution of 500 eq of nor2 to a solution of G3 over the course of 1 h. Full monomer conversion was achieved, and the isolated polymer had the same molecular weight, as in the batch experiment (M_n = 113 kg/mol, Ɖ = 1.03).

A key feature of the methodology is that the molecular shape is a direct result of the flowrate profile [ϑo(flow rate) vs. t(time)] of liquid from vessel 1 to vessel 2. We chose to target three specific geometric shapes (cone, ellipsoid, and concave elliptical cone) to establish the methodology. However, the method can in principle be used to synthesize any axisymmetric monotonic geometry. The flowrate equations/profiles were derived using a constraint that describes the relationship between brush length with respect to backbone position (i.e., shape). A unique feature of this is that each shape and size has a different characteristic flowrate profile. The constraint for a cone, for example, is a constant, “A” (Eq. 1), which embodies the cone angle. The flowrate equation for the cone is presented in Eq. 2. A detailed derivation of the flowrate equations for all of the targeted geometries can be found in SI Appendix, section 9.Constant≡A=NbrushNbb,[1]ϑo=(Nbrushsyn,maxNbbsyn,max)(V1A)(KROP)e−KROPt.[2]The flowrate equation is the only mathematical framework needed to synthesize shaped bottlebrush polymers. Additionally, it is possible to predict the polymerization outcomes (i.e., conversion of lactide and norbornene in both reaction vessels and M_n of brushes and bottlebrush polymers) at any time point by combining the flowrate equation with the rate laws, and the design equations for semibatch reactors (SI Appendix, section 9) (26, 28). The use of a mathematical framework to predict the polymerization outcomes provides a first-principle methodology for proving precise shape and size control. Each shape and size has its own flowrate equation and its own characteristic prediction profiles. A match between the experimental data and the predictions would validate a successful synthesis of a shaped bottlebrush, as no other macromolecule could have been synthesized. To that end, a MATLAB code was written to numerically solve the design equations (SI Appendix, section 10) and generate the predictions.

To compare an experiment directly with our predictions, we performed the synthesis of a conical-shaped polymer (Nbrushmax=50, Nbb=185) multiple times, quenching the polymerizations at different reaction time points by simultaneously halting the flow of macromonomer and injecting vinyl ether to stop ROMP. The crude polymer mixtures were analyzed by gel permeation chromatography (GPC) and NMR spectroscopy to determine the system outcomes (Fig. 2 and SI Appendix, section 6). First, the conversion of lactide and lactide buildup proceeded as predicted, which confirms that the macromonomers fed out of the syringe had the desired conical profile. Second, no residual macromonomer was detected in the graft-through polymerization vessel at any time point (macromolecule conversion >98%, SI Appendix, section 11 for detection limit) providing proof of rapid incorporation of the macromonomers into the growing bottlebrush, thus ensuring that no scrambling of brushes of different lengths occurs. Third, the experimental and the predicted bottlebrush molecular weights were in close agreement, and all bottlebrush polymers had narrow molecular weight distributions (Ɖ < 1.1). Altogether the strong agreement between prediction and experiment validates the shape and size control of the process.

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Fig. 2.

Process flow diagram with predicted (line) and experimental (dots) data for the synthesis of conical bottlebrush.

The precision and flexibility of the methodology was further illustrated by synthesizing a series of conical-shaped bottlebrush polymers with different sizes, backbone lengths, and cone angles (Table 1 and SI Appendix, section 6). In all cases, the predicted parameters (molecular weights and conversions) matched the experimental values well, no residual macromonomers are detected, and the polymers remained narrowly dispersed (Ɖ ≤ 1.12). Next, the methodology was expanded to ellipsoid and concave elliptical cone shapes (Table 1). This was achieved by simply implementing the corresponding flowrate equations. Once again, NMR and GPC were used to analyze the products of the reactions. Narrow molecular weight distributions and strong agreement with predictions establish the exquisite control over shape and size. To further validate the methodology, atomic force microscopy (AFM) images of a conical-shaped polymer were collected. The size and shape observed are consistent with theoretical calculations of size (Fig. 3 and SI Appendix, section 13).

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Fig. 3.

AFM height maps for PLA cone bottlebrush on silicon surface. The blue line in the plot is the theoretical shape profile for the imaged bottlebrush.

The generality of the synthetic strategy was further showcased by expanding the chemical versatility of the process. The anionic ROP of cyclic siloxanes for the synthesis of PDMS brushes was used in place of the ROP of lactide (29). A detailed kinetic analysis and chemical compatibility study was performed, which identified trimethylsilyl chloride (TMSCl) as an effective quenching agent (SI Appendix, section 7). Polydimethylsiloxane (PDMS) conical bottlebrushes were successfully synthesized with narrow molecular weight distributions (Ɖ ≤ 1.2) and no detectable unreacted macromonomer was observed (Table 1 and SI Appendix, section 7).

Finally, as a second example illustrating the chemical versatility of the process, a compositional asymmetric cone was synthesized (30⇓–32). This was achieved by cofeeding two macromonomers synthesis reaction mixtures, one for PLA and one for PDMS, into a single vessel of G3, boric acid, and TMSCl (Fig. 4 and SI Appendix, section 8). Analysis of the crude reaction mixture confirmed that the experimental conversions matched the predicted values, while maintaining a narrow polymer dispersity (Ɖ = 1.19). The precision of the synthesis of this complex molecular object exemplifies the chemical flexibility and shape control of the methodology. Moreover, this one-step synthesis was completed in less than 2 h, using exclusively commercially available reagents.

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Fig. 4.

Synthesis of a compositional asymmetrical cone composed of PLA and PDMS arms.