Counting 1° Loops in Star Polymer Networks

We first sought to examine the effect of monomer feed rate on the fraction of 1° loops in star polymer networks. We developed the star network disassembly spectrometry method as outlined in Fig. 3A for a gel prepared from bis-cyclooctyne A₂ and tetra-azide PEG star polymers B_4H and B_4D (10-kDa number-average molar mass, M_n; SI Appendix, sections SII and SVI). Mixing of these components leads to network formation via strain-promoted azide–alkyne cycloaddition (SPAAC) (36⇓⇓–39). The star polymers B_4H and B_4D possess photocleavable ortho-nitrobenzyloxycarbonyl (NBOC) groups (40, 41) near their termini that facilitate controlled network disassembly in response to UV light (358 nm). They also possess either hydrogen (B_4H) or deuterium (B_4D) labels between the azide and the NBOC groups. Consequently, network formation and disassembly leads to three possible labeled products: nn, ni, and ii (Fig. 3A). The ratios of these products (Fig. 3B) are uniquely dependent on the fraction of 1° loops per doubly reacted A₂, denoted here as ϕ_λ, and the amount of B_4H and B_4D used to form the network (x and 1 – x, respectively) according to Eqs. 1 and 2 (SI Appendix, section SIII.A)[nn][ii]=x2(1−ϕλ)+xϕλ(1−x)2(1−ϕλ)+(1−x)ϕλ,[1][ni][ii]=2x(1−x)(1−ϕλ)(1−x)2(1−ϕλ)+(1−x)ϕλ.[2]Notably, because star network disassembly spectrometry yields three disassembly products (nn, ni, and ii) regardless of f, this strategy should be universal to a range of f-functional star polymers with no additional complications from higher f junctions: a significant advance over our previous loop-counting methods.

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Fig. 3.

Star network disassembly spectrometry. (A) Chemical structures of compounds A₂, B_4H, and B_4D. Combining A₂ with a 1:1 mixture of B_4H and B_4D leads to A₂ + B₄ networks via SPAAC. Exposure of these materials to UV light induces network disassembly to yield three labeled products: nn, ni, and ii. (B) A representative mass spectrum showing the products nn, ni, and ii. The ratios of these products are uniquely dependent on ϕ_λ. (C) Plot of ϕ_λ versus [B₄] as obtained by experiments and rate theory. m, mass; z, charge.

We validated star network disassembly spectrometry using gels formed at various network concentrations. DMSO stock solutions of A₂ and 1 B_4H:1 B_4D (i.e., x = 0.5) and additional DMSO were mixed to achieve the desired concentration and a 1:1 ratio of functional groups A (cyclooctyne) and B (azide). The reactions were allowed to proceed under ambient atmosphere for 24 h to achieve maximal conversion (>98%; SI Appendix, section SIII.B). Then, the gels were exposed to UV irradiation (358-nm, 8-W bench-top lamp) for 5 h to generate the mixture of disassembly products shown in Fig. 3A. The distribution of nn, ni, and ii was obtained by electrospray ionization mass spectrometry (see Fig. 3B for example spectrum). Application of Eqs. 1 and 2 provided ϕ_λ as a function of network concentration (Fig. 3C). As expected, ϕ_λ decreased as polymer concentration increased, which reflects the intramolecular nature of 1° loop formation. A sol–gel transition occurred at ∼1.5 mM (1.5% m/v); below this concentration gelation was precluded by the large number of loops. The experimental results were compared with rate theory methods developed by us (23) (SI Appendix, section SIII.G). The experiment and theory are in excellent agreement. Taken together, these results show that star network disassembly spectrometry can be used to precisely and accurately count loops in star polymer networks.

Monomer Feed Rate and Network Topology

We next studied the impact of monomer addition rate on ϕ_λ in these materials. For these studies, 20 μL of a 40 mM A₂ solution was placed in a vial, to which 380 μL of 1.05 mM B₄ solution was added (1 μL/min) over 6.3 h via a digitally programmable syringe pump to reach 1:1 stoichiometry of functional groups and 1 mM (1% m/v) final concentration of B₄ (note: “B₄” refers to a 1:1 mixture of B_4H and B_4D). The reaction was monitored over time to determine ϕ_λ as a function of the percentage of B₄ added (Fig. 4A).

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Fig. 4.

Controlled monomer addition leads to reduction of loop defects in PEG gels prepared via SPAAC. (A) ϕ_λ as a function of batch mixing, slow addition, and STF addition of B₄ to A₂ (final concentration of B₄ is 1 mM for all samples). Slow addition and STF addition both provide a significant decrease in ϕ_λ. Rate theory calculations (open circles) follow a similar trend. (B) Effect of B₄ addition rate (u) on ϕ_λ. * denotes the predicted addition rate u = 2.75 μL/min below which ϕ_λ should not change significantly. This prediction is based on the reported second-order rate constant for DBCO and azide SPAAC (0.3 M^-1⋅s⁻¹). (C) SANS curves for gels prepared at B₄ = 5 mM using batch addition and STF addition. (D) Plots of Gʹ versus frequency for gels prepared at B₄ = 5 mM using batch addition versus STF addition. (E) Relationships between Gʹ, ϕ_λ, and the percentage of B₄ added slowly. (F) Representative tensile testing measurements of gels prepared at B₄ = 5 mM using batch addition and STF addition with 15% versus 50% of B₄ added slowly.

During the course of slow B₄ addition, ϕ_λ gradually decreased. Upon completion, a polymer network with ϕ_λ = 19% was obtained (Fig. 4A). Note that in Fig. 4A, at early stages of the network-forming reaction ϕ_λ is quite large. This observation highlights the fact that ϕ_λ is the fraction of loops on doubly reacted A₂. At early stages, there is very little doubly reacted A₂ (most A₂ molecules are either unreacted or reacted on only one end); what little does exist is likely to be a 1° loop. Importantly, at complete conversion the analogous batch-prepared material had ϕ_λ = 35%. Thus, slow addition afforded a material with nearly 50% fewer 1° loops. Rate theory calculations of ϕ_λ supported these experimental findings (Fig. 4A). This reduction in defects was reflected as a change in the material properties: slow addition produced elastic gels (solids) (Fig. 4B) whereas the batch process gave a fluid.

Next, we prepared a series of networks using different rates of B₄ addition (u). As shown in Fig. 4B, ϕ_λ decreases as u decreases until u approaches 2 μL/min, where ϕ_λ reaches a constant value. We developed a semiquantitative model to interpret the data (SI Appendix, section SIV.C). Given the reported second-order rate constant of this SPAAC reaction (0.3 M^-1⋅s⁻¹) (42), the model predicts that for u ≤ 2.75 μL/min there should be no further reduction in loop defects. The agreement between the predicted and observed data (Fig. 4B) supports our proposed mechanism (Fig. 2A). To provide further evidence, we used liquid chromatography and UV absorbance to quantify the fraction of dangling cyclooctynes as a function of the percentage of B₄ added via slow addition (SI Appendix, Fig. S4). As expected, the fraction of dangling A groups was very high at early stages in the reaction (due to a large excess of A₂ monomer) and it gradually decreased to undetectable levels as the addition proceeded. These dangling ends suppress loop formation and lead to loop-depleted networks (Fig. 2A).

Given that slow addition has the greatest impact on ϕ_λ during the earliest stages of network formation, we also investigated a “slow then fast” (STF) addition approach wherein the first 50% of B₄ solution was added slowly to yield soluble “A-rich” network fragments (Fig. 2A) and the second 50% was added in one portion to induce gelation. As shown in Fig. 4A, the STF method gave ϕ_λ = 21%, which is similar to the result obtained for complete slow addition (19%). Notably, STF addition provides a faster and more convenient way to reduce the number of loop defects that avoids concerns over gelation before complete monomer addition.

Having demonstrated both slow addition and STF addition methods as promising for tuning the number of loops at a concentration that does not produce gels upon batch mixing (1 mM, 1% m/v), we investigated whether the same methods could enable the synthesis of loop-depleted polymer networks at concentrations much higher than the gel point for the batch-synthesized material. Gels were prepared via slow addition and STF addition as described above but with concentrations adjusted to yield a final [B₄] of 5 mM (5% m/v) (note: this concentration is half that of the solubility limit of the B₄ star polymer; see SI Appendix). In the case of complete slow addition, the gel point was reached long before B₄ could be completely added, which led to a large amount of undesirable sol fraction. Thus, we focused on the STF method. As shown in Table 1, STF addition once again yielded networks with nearly 50% fewer 1° loops compared with batch synthesis.

We used Fourier transform infrared spectroscopy (FTIR), swelling measurements, and small-angle neutron scattering (SANS) to characterize gels prepared via STF and batch methods. The FTIR spectra (SI Appendix, Fig. S7) for these materials were indistinguishable, which suggests that STF does not lead to a significant change in the chemical composition of the network. The swelling ratio S, which is the ratio of the solvent-swollen gel divided by the dried gel, for the STF-formed material was significantly lower than that of the material formed via batch mixing (Table 1), which supports the notion that the STF-formed material has fewer topological defects. The SANS curves (Fig. 4C) were fitted using the following model, which combines a power law with an Ornstein−Zernike function (43):I(q)=Aqn+C1+(qξL)m+B,where q is the scattering vector, ξ_L is the network mesh size, n is a scaling exponent for scattering from the larger network structure, m is a scaling exponent for scattering from polymer chains, A and C are constants, and B the incoherent background. STF addition reduced ξ_L by ∼0.6 nm (Table 1). Given that the concentration of B₄ is below the overlap concentration of the 10-kDa four-arm PEG star polymer (ϕ* = 6 mM, 6% m/v) and that the A and B functional groups are present in equal stoichiometry, the observation of a decreased mesh size ξ_L is consistent with increased network homogeneity at short length scales, which is expected for a reduction in the fraction of 1° loops (44). We also note that STF addition leads to an increase in low-q scattering, which suggests that there may be some increase in long length-scale heterogeneities within the gel (45).

Using STF Addition to Improve and Tune Gel Mechanics

Next, we studied how the structural changes imparted by STF addition impact the bulk mechanical properties of these gels. Fig. 4D shows plots of the shear storage modulus G′ versus frequency for gels prepared at [B₄] = 5 mM (5% m/v) by batch monomer mixing and STF addition (note: three gels of each type were prepared and G′′ was omitted for clarity; SI Appendix, Fig. S8). Whereas both methods yielded elastic materials (as demonstrated by rheology and creep and recovery tests shown in SI Appendix, Fig. S12), the gels formed via STF addition consistently possessed ∼19% greater G′ values despite the fact that they were formed at exactly the same concentration and using the same components as the batch-formed gels (Table 1). This mechanical enhancement is due to the reduction in loop defects afforded by STF addition. Moreover, we note that STF addition gave similar improvements in G′ for gels formed above and below the overlap concentration (SI Appendix, Figs. S11 and S13). We can estimate the impact of 1° loops on G′ via the real elastic network theory (12):G=G0(1−83ϕλ),where G₀ is the modulus of an ideal network with no defects and G is the modulus of the real network. The measured ϕ_λ and G′ values correlated well (SI Appendix, Table S9), which further highlights the impact of 1° loops on the storage modulus. Moreover, tensile tests showed that STF addition yielded materials with greater tensile moduli relative to batch addition (Fig. 4F and SI Appendix, Fig. S10).

As shown in Fig. 4E, as the percentage of B₄ monomer that was added slowly was gradually increased, ϕ_λ decreased and G′ increased. Thus, through simply altering the amount of B₄ monomer added slowly, it was possible to finely tune the loop content of these networks, and thereby produce a series of gels of the same composition and concentration with an ∼19% variation in G′. Depending on the network structure and composition, the extent of this range will of course vary; nonetheless, alterations, and particularly enhancements, of even a few percent in modulus could be valuable in specific applications given the simplicity of STF addition and the fact that new network components are not needed.

To investigate the effect of the order of addition on gel properties, we prepared a series of gels by slowly adding a solution of A₂ to a solution of B₄ (the opposite order as studied above). Interestingly, although star network disassembly spectrometry showed that ϕ_λ was indeed reduced via this method, there was no enhancement of the mechanical properties of the gels compared with the batch-mixing case (SI Appendix, section SV). These observations suggest that inversing the order of addition leads to new defects [e.g., clusters of variable network density (46, 47) or higher order loops (12, 48)] that cancel the effect of reducing ϕ_λ. SANS analysis is consistent with this hypothesis: the mesh size for this gel was larger (4.32 ± 0.05 nm; SI Appendix, Table S11) than that for the batch-addition sample (2.83 ± 0.05 nm) despite its lower fraction of 1° loops.

Generality of STF Addition

We tested STF addition in other network-forming systems to demonstrate that the property enhancements observed above are general even in materials where we cannot directly count loops. First, another A₂ + B₄ network was prepared via thiol-maleimide conjugate addition of commercially available PEG components. In this hydrogel system, STF addition led to gelation at a concentration well below the gel point of batch-synthesized gels (SI Appendix, Fig. S18). Moreover, a doubling of Gʹ was achieved for gels prepared at 4.5 mM via STF versus batch (SI Appendix, Fig. S19).

Next, a network derived from 10-kDa eight-arm PEG amine (B_8NH2) and suberic acid bis(N-hydroxysuccinimidyl ester) (A_2NHS) was investigated (Fig. 5A). In this system, the sol–gel point occurs at [B_8NH2] = 2.25 mM (2.25% m/v) when both components are mixed in batch. Fig. 5B shows that when a solution of B_8NH2 was added slowly to a solution of A_2NHS, gels formed at concentrations as low as [B_8NH2] = 1.5 mM (1.5% m/v). Moreover, G′ values for gels formed via STF addition ([B_8NH2] = 2.5 mM, 2.5% m/v) were nearly six times greater than those formed via batch addition (1,300 Pa compared with 220 Pa, respectively) (Fig. 5C). We also note that when the gelation was performed above overlap concentration, a similar improvement in G′ was still observed (SI Appendix, Fig. S16). To further prove that STF addition leads to tunable mechanical properties in these f = 8 networks, we prepared 4 different sets of A_2NHS + B_8NH2 gels at the same concentration ([B_8NH2] = 5 mM (5% m/v) but with different amounts of B_8NH2 monomer added via the STF method (SI Appendix, Fig. S17). Similar to the studies described above, swelling ratio measurements and shear rheometry demonstrated that STF addition could produce gels at constant concentration with variable mechanical properties. Notably, compared with the A₂ + B₄ gels prepared by SPAAC, the range of storage moduli accessible in A_2NHS + B_8NH2 networks (from 9 to 15 kPa) is much larger, which suggests that STF addition may have a larger impact on high-f materials (49).

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Fig. 5.

Generality of loop control via STF addition. (A) Chemical structures of A₂ + B₈ network components. (B) STF addition of A_2NHS to B_8NH2 at 1.5 mM leads to gelation (Left), whereas batch addition at the same concentration does not produce a gel (Right). (C) Shear moduli for A₂ + B₈ gels formed via STF addition and batch addition at B_8NH2 = 2.5 mM. STF addition leads to an ∼sixfold enhancement in Gʹ. (D) Chemical structures of A₂ + B_∼24 (B_∼24 is a statistical copolymer) network components. (E) STF addition of A₂ to B_∼24 at 1.6 mM leads to gelation (Left), whereas batch addition at the same concentration does not produce a gel (Right). (F) Shear moduli for A₂ + B_∼24 gels formed via STF addition and batch addition at [B_∼24] = 2 mM. STF addition leads to an ∼fourfold enhancement in Gʹ. (G) Chemical structures of A₄ + B₄ Tetra-PEG network components. (H) STF addition of A_4NHS to B_4NH2 at 1 mM leads to gelation (Left), whereas batch addition at the same concentration does not produce a gel (Right). (I) Shear moduli for Tetra-PEG gels formed via STF addition and batch addition at B_4NHS = 1.5 mM. rad, radians.

Pendantly functionalized polymers are frequently used as precursors to polymer networks, and we hypothesized that our loop-control strategy would also be applicable to these materials as they are analogous to end-linked networks where the B_f monomer has a distribution of f values. Thus, we synthesized pendantly azido-functionalized random copolymer with a number average of 24 azide groups (B_∼24) using nitroxide mediated polymerization (Fig. 5D). Polymer networks were formed via SPAAC using this pendantly functionalized polymer and A₂ (Fig. 5D). Fig. 5 E and F shows that STF addition has a similar impact on these pendantly functionalized polymer networks, enabling an ∼400% increase in Gʹ for gels formed at [B_∼24] = 2 mM.

Finally, we examined STF addition in the context of an A₄ + B₄ star polymer end-linking reaction that cannot form 1° loops. Although these “Tetra-PEG” gels inherently have highly homogeneous network structures and excellent mechanical properties (50) (Fig. 5D), they still have cyclic defects such as secondary loops (51). We have previously shown that the number of 1° loops is coupled to the numbers of higher order loops (48), and that these higher order defects are also elastically defective (12). We suspected that STF addition may reduce higher order loop defects in Tetra-PEG gels (45). This notion is supported by the results presented in Fig. 5E. Whereas STF addition of Tetra-PEG components A_4NHS and B_4NHS at 1 mM (1% m/v) led to gelation, batch addition at this same concentration did not produce gels (Fig. 5E). Rheological analysis for Tetra-PEG gels formed at 1.5 mM (1.5% m/v) showed a >300% increase in G′ for STF addition compared with batch addition (Fig. 5F). When Tetra-PEG gels were prepared at higher concentration (5 mM) there was no discernible difference between batch addition and STF addition (SI Appendix, Fig. S21), which highlights the fact that higher order cyclic defects are not as detrimental to elasticity as 1° loops (12). Nonetheless, these data provide evidence that simple STF addition can reduce not only 1° loops but also higher order defects in polymer networks.

In summary, we have demonstrated semibatch monomer addition as a method for controlling the fraction of loops in polymer networks. The mechanism for this process was supported by an experimental method, star network disassembly spectrometry, that enables quantification of 1° loops in networks formed via end-linking of star polymers. STF addition is general to a range of network-forming systems, and it facilitates the synthesis of materials with enhanced and finely tuned mechanical properties. STF addition can even enable gelation below “normal” sol–gel transition points. These findings should prove useful for researchers interested in polymer networks in a range of industrial and academic settings.