Trapping Polymer Entanglements via Prolonged Initiation
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Trapping Polymer Entanglements via Prolonged Initiation
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  • Suyoung Lee
    Suyoung Lee
    Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
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  • Yan Huang
    Yan Huang
    Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
    More by Yan Huang
  • Jinyue Dai
    Jinyue Dai
    Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
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  • Haeji Kim
    Haeji Kim
    Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
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  • Junsoo Kim*
    Junsoo Kim
    Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
    *Email: [email protected]. Phone: +1 (847) 491-4322.
    More by Junsoo Kim
    Orcidhttps://orcid.org/0000-0001-7340-2770
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Macromolecules

Cite this: Macromolecules 2026, XXXX, XXX, XXX-XXX
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https://doi.org/10.1021/acs.macromol.5c03018
Published February 28, 2026

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Abstract

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Entanglements in polymer networks can be either trapped or transient, and their ratio is crucial to the mechanical properties of soft materials. Traditionally, entanglement formation has been mostly linked to chain length─polymers entangle when their lengths exceed the entanglement molecular weight─without independent control of the ratio between the two. Here, we demonstrate that the initiation rate significantly affects the fraction of trapped entanglements and the resulting mechanical properties. We hypothesize that more monomers grow in the presence of existing polymers as the initiation rate decreases, forming more trapped entanglements. To demonstrate this, we synthesize UV-curable, highly entangled polyacrylamide hydrogels in which the initiation rate varies with UV intensity. Upon swelling, transient entanglements can detangle, whereas trapped entanglements cannot, by which we characterize the fraction of entanglements. We observe that the swelling ratio of the same precursor decreases significantly as UV intensity decreases, indicating a higher fraction of trapped entanglements. Additionally, such hydrogels with many trapped entanglements exhibit superior fracture resistance due to their swell-resistance. Our work offers a kinetic approach to network topology design, expanding the material property space of polymer networks.

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1. Introduction

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Entanglements are a fundamental element of polymer structure. Entanglements can increase the modulus by constraining the polymer chains, (1−3) toughen the polymer networks by dissipating additional energy, (4) and increase the fracture and fatigue resistance by distributing the tension to entangled polymer chains. (5−7) Recent studies on highly entangled polymer networks highlight the importance of entanglements in various aspects of polymer development, such as mechanical durability (5−9) and degradation. (10) The ability to control entanglements is critical for the design of polymer network structures and their mechanical properties.
Entanglements can be trapped or transient. When entanglements cannot detangle without breaking polymer chains, they are called trapped entanglements, or topological entanglements. When entanglements can detangle upon sufficient time or tension, they are called transient entanglements. Upon deformation, transient entanglements slowly detangle and relax the stress, while trapped entanglements remain. (11−13) Upon swelling, many of the transient entanglements detangle, while trapped entanglements resist swelling. (14,15) In most polymer networks, both types of entanglement coexist, and their ratio significantly affects the dynamics of the mechanical properties of polymer networks. (16,17)
Traditionally, entanglements have been controlled by the length of polymer chains. When the molecular weight between two neighboring cross-links, referred to as the chain length, is greater than the entanglement molecular weight (Me), polymers can entangle between the two neighboring cross-links, resulting in trapped entanglements. (18−22) When the chain length is lower than Me, cross-links are denser than entanglements, resulting in a negligible number of entanglements within a polymer chain. The backbone length, the molecular weight between two dangling ends, also affects the entanglement structure. When the backbone length is comparable or shorter than the target chain length, the number of dangling chains becomes significant, reducing the number of trapped entanglements. (23)
Entanglements can be controlled by the stoichiometry of the precursor, because it determines the chain and backbone lengths. For example, as the cross-linker-to-monomer ratio decreases, the chain length increases, forming more trapped and transient entanglements. (24−26) When the cross-linker-to-initiators ratio is high, a significant number of dangling chains form, because initiators determine the backbone length and cross-linkers determine the chain length. (5) In this case, entanglements of the end of polymer backbones are transient. Also, the monomer concentration can affect chain length and alter the entanglement density. As the initiator-to-monomer ratio changes from 500:1 to 100,000:1, the molecular weight of the resulting polymers also increases, promoting trapped entanglements. (23,24,27,28) The concentration of monomer or polymer also influences the entanglements. As the concentration increases, the blobs of polymer chains inevitably overlap, increasing the total number of entanglements. (11,18−20,23,24,27−29)
The polymerization kinetics is another way to influence the backbone length and entanglements. For example, when the initiator-to-monomer ratio is high (∼1:100), the excess free radicals accelerate termination reactions, thereby reducing the backbone length. (30,31) This reduces the stability of the polymer network and decreases the modulus. (32) An uncontrolled and rapid gelation exhibits heterogeneous chain lengths, promoting the formation of entanglements compared to a slow but controlled gelation. (33,34)
In addition to precursor conditions, various synthesis conditions, such as the concentration of accelerators in thermal polymerization, (35−37) UV intensity in photo polymerization, (32,) and mixing during polymerization (38) can also influence the topology of polymer networks. However, the effects of these precursors and synthesis conditions on the formation of trapped versus transient entanglements remain largely unexplored. Despite the vast design space for tuning network topology, the relationship between synthesis conditions and network structure, particularly in terms of entanglement types, has been relatively understudied.

2. Hypothesis

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In this study, we hypothesize that the fraction of trapped entanglements significantly varies with the initiation rate of polymerization. Consider a precursor with a low solvent-to-monomer ratio to form dense entanglements and a low cross-linker-to-monomer ratio, such that the entanglements govern the elastic properties (Figure 1A). Assume that the resulting polymer chains are highly soluble in the precursor solution, so that the growing polymer chain has a free volume with monomers. When the initiation rate is high, initiators are triggered simultaneously, and polymers grow individually (Figure 1B). After polymerization is complete, polymer chains percolate via cross-links, forming a network with entanglements (Figure 1C). Note that the number of both trapped and transient entanglements of the fully cured polymer network is determined by the concentration of polymers. Upon swelling, most transient entanglements detangle, whereas trapped entanglements and cross-links resist swelling (Figure 1D). By contrast, when the initiation rate is low, initiators are gradually triggered (Figure 1E,F). Throughout this prolonged polymerization process, some polymer chains will grow using monomers inside the free volume. Since these polymer chains grow in the presence of polymer chains that are initiated earlier, they will form more trapped entanglements than individual growth (Figure 1G). Meanwhile, the monomer concentration in the overlapped region will decrease, allowing additional monomers to diffuse in. Consequently, compared to the fast initiation, where monomers inside the free volume primarily react at the end of the polymerization, more monomers will react in the presence of polymers, forming more trapped entanglements (Figure 1H). The resulting networks, whether formed through fast or slow initiation, will have a comparable total number of entanglements for the same polymer concentration, but the fraction of trapped entanglements is expected to be higher at slow initiation, which will decrease the swelling ratio (Figure 1I).

Figure 1

Figure 1. Control the fraction of trapped entanglements via prolonged initiation. (A) A precursor for highly entangled long-chain polymer networks. (B) Simultaneous triggering of initiators. (C) The fully cured polymer network with fast initiation. Entanglements are either trapped or transient. (D) A low fraction of trapped entanglements results in significant swelling. (E, F) Gradual triggering of initiators. Monomers are present inside the free volume. (G) Monomers inside the free volume polymerize in the presence of polymers, forming trapped entanglements. The monomer concentration at the overlapping region decreases, allowing additional monomers to diffuse in. (H) The resulting polymer network has the same concentration as (C) but a different fraction of trapped entanglements. (I) Limited swelling due to a high fraction of trapped entanglements.

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3. Materials and Experimental Methods

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3.1. Materials

Acrylamide (AAm), N,N′-Methylenebis(acrylamide) (MBAA), 2-Hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone (Irgacure 2959), and Deuterium Oxide (D2O) were purchased from Sigma-Aldrich Co. LLC. All compounds were used as received.

3.2. Preparation of the Precursor of Highly Entangled PAAm Hydrogel

To prepare the precursor, we use the water-to-monomer molar ratio (W) of 2, cross-linker-to-monomer molar ratio (C) of 10–5, and initiator-to-monomer molar ratio (I) of 4 × 10–6, otherwise noted. To match those conditions, we mixed 30 g of AAm with 15 mL of DI water in a 50 mL conical tube, then gently shook the mixture and heated it in a microwave oven for 15 s to completely dissolve AAm. We prepared stock solutions of the cross-linker (MBAA, 42.2 mM in DI water) and the photoinitiator (Irgacure 2959, 16.88 mM in anhydrous ethanol). Next, 0.1 mL of MBAA solution and 0.1 mL of Irgacure 2959 solution were dispensed to the prepared Acrylamide solution. The final precursor was sonicated under 30 °C for 3 min to remove the dissolved gas.

3.3. Photopolymerization

The molds consist of silicon rubber sheets (5787T71) as a spacer and glass plates (8476K15, 1/4″ thickness) as a substrate. All engineering materials were purchased from McMaster-Carr. The 125 mm × 125 mm spacer, with a 100 mm × 100 mm central cavity, was placed on a glass substrate without adhesive. The precursor was poured onto the mold and sealed with the other glass substrate. Two glass substrates were tightly fixed with binder clips. To cure the precursor, UV light was irradiated at different intensities and for different times. UV irradiation was performed at a wavelength of 365 nm, and the light intensity was measured using a UV light meter (Linshang Technology, LS125 with a UVALED-X0 probe). For high UV intensity (129–23 mW/cm2), the Ultraviolet Flood Exposure System (Inpro Technologies F300S) was utilized. For low UV intensity, a large UV lamp (Analytic Jena, UVP Cross-linker CL-3000) and a UV chamber with small UV lamps (8 each, Sankyo Denki, F8T5BL) were used to achieve UV intensities of 3.2 mW/cm2 and lower, respectively. After curing, the sample was weighed and submerged in water for more than 1 day to swell to equilibrium. The fully swollen sample was weighed again to measure the swelling ratio.

3.4. Mechanical Tests for Hydrogels

A hydrogel sample was cut into a dumbbell-shaped specimen and mounted on a universal testing machine (Instron 34TM). The specimens were aligned and clamped at the fully relaxed state. The strain rate was 0.1 s–1. The stress–strain curve was obtained from the recorded force and displacement data, where the engineering stress was calculated using the specimen’s initial cross-sectional area. The modulus and strength were calculated from the stress–strain curve: the modulus from the initial slope, and the strength from the maximum stress. To ensure repeatability, more than three specimens were tested under the same conditions. For rheological characterization, circular hydrogel samples (diameter: 25 mm) were prepared and tested using a rheometer (Anton Paar MCR302). The sample was carefully placed between the parallel plates of the rheometer, and the plate gap was adjusted to match the sample thickness. Oscillatory shear tests were performed under a constant strain amplitude of 1%. The angular frequency was swept from 0.1 to 100 rad/s at a controlled temperature of 25 °C. The storage modulus (G′) and loss modulus (G″) were recorded to evaluate the viscoelastic properties of the hydrogels.

3.5. DLS Analysis to Measure the Length of Synthesized Polymer Backbones

The samples were polymerized in water, without cross-linkers, at different UV intensities. The samples were then dried overnight at 60 °C, yielding crystalline solids. DI water is added to dissolve the sample to 1 mg/mL, and the solution is passed through 0.45 μm PVDF filters to remove aggregates or impurities. DLS was then performed at 25 °C on a microvolume DLS instrument (pUNk, Unchained Laboratories). Corrupted runs were rejected, and the Z-average hydrodynamic radius and polydispersity index were obtained by cumulant analysis.

3.6. Measurement of the Heat Flux from Gelation of PAAm Hydrogel

To quantify the heat flux generated during the photopolymerization of PAAm hydrogel, we placed three thermocouples (K type, Danoplus) on the molds: one on the top of the glass substrate, one at the bottom of the glass substrate, and one in the middle of the precursor. The two glass substrates have dimensions of 5″ × 5″ and a thickness of 1/4″ (8476K15, McMaster-Carr). A rubber sheet of the same outer dimensions was used as a spacer (5787T71, McMaster-Carr), with a central square cavity of 10 cm × 10 cm. This spacer was placed on one glass sheet, and the cavity was filled with either the PAAm hydrogel precursor or DI water. A second glass sheet was then placed on top and securely clamped. The temperatures measured by the three thermometers were recorded during polymerization (DP-373, Danoplus). The calculation of the heat flux based on the measured temperature is described in Section 4.1.

4. Results and Discussion

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4.1. Model Material System

To test our hypothesis, we use UV-curable polyacrylamide hydrogels as a model material system. The polymerization of acrylamide is highly exothermic and fast, and offers a high degree of polymerization. (39) Also, polyacrylamide is highly soluble in water, so that monomers readily diffuse into the free volume inside the blob of growing polymer chain. We will vary the initiation rate using the UV intensity. To confirm the relation between the initiation rate and UV intensity, we monitor the heat flux generated by polymerization at different UV intensities by using the molds as a calorimeter (Figure 2A). We place thermocouples below the bottom glass, within the precursor, and above the upper glass, and record the temperatures during polymerization, denoted as Tb, Tm, and Tt, respectively. Upon UV light, the absorption of the UV light by the glass molds and the precursor, as well as the exothermic reaction of polymerization generate thermal energy, which dissipates to the surroundings over time.

Figure 2

Figure 2. Measurement of the heat flux from hydrogel gelation. (A) The experiment setup for the heat flux measurement. (B) The temperature profile by polymerization and UV exposure. (C) The temperature of the precursor, Tm, over time upon UV exposure. (D) The heat flux generated by polymerization over time at different UV intensities.

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We simplify the thermal analysis of our system as follows. We disregard the temperature gradient within the precursor because it is much thinner (thickness ∼ 0.8 mm) than the glass mold (thickness ∼ 6.4 mm), and convection in the precursor further flattens the temperature gradient. When UV light is applied, the temperature profile builds over time by both UV absorption and polymerization (Figure 2B). To further simplify the analysis, we test two samples: precursor and water. The effects of UV absorption will be similar for both tests, because it is dominated by the glass, and the UV absorption coefficient of water is much lower than that of glass in the UVA range. (40,41) Therefore, the difference in the temperature profiles between the precursor and the water will reflect the contribution from the polymerization. (42) The heat flux contributed by polymerization can be calculated as Jb = −kg[(Tm,precursor – Tm,water) – (Tb,precursor – Tb,water)]/dg and Jt = −kg[(Tt,precursor – Tt,water) – (Tm,precursor – Tm,water)]/dg, respectively, where Jb is the heat flux toward bottom mold, Jt is the heat flux toward top mold, kg is the thermal conductivity of the glass mold (=1.15 W/mK), and dg is the thickness of the glass mold (Note S1). The thermal energy generated by polymerization is the sum of the heat fluxes, |Jb| + |Jt|.
We measure Tm,precursor, Tm,water, Tb,precursor, Tb,water, Tt,precursor, and Tt,water, as a function of time at UV intensities of 3.2 and 23 mW/cm2. The maximum values of Tm,precursor at two UV intensities are similar, suggesting that the thermodynamic properties of polymer chains at synthesis are independent of UV intensity (Figure 2C). Using the formula described above, we plot the heat flux due to polymerization as a function of time (Figure 2D). At 23 mW/cm2, the heat flux increases sharply at the early stage of UV exposure, with a negligible induction period, and then decreases rapidly after approximately 150 s. In contrast, at 3.2 mW/cm2, after the induction period of 1650 s, the heat flux increases gradually. The area under the curve is comparable for the two UV intensities (about 2873.7 kJ/m2 at 23 mW/cm2 and 3255.3 kJ/m2 at 3.2 mW/cm2), indicating that the number of monomers participating in polymerization is similar. These results demonstrate that polymerization proceeds rapidly at high intensity, whereas polymerization proceeds more slowly but gradually at low intensity. The raw data and additional analysis are presented in Figures S1–S2.
Next, we fully polymerize the precursor without cross-link, dilute the resulting polymer solution, and measure the radius of gyration using dynamic light scattering (DLS), to investigate how the initiation rate affects the polymerization reaction. In this diluted solution, polymers are well-separated, so the measured diameter corresponds to the backbone length (diameter ∼ length3/5, as water is a good solvent for PAAm). The results show that all samples at various UV intensities exhibit comparable sizes and deviations (Figure 3A). This observation suggests that most monomers and initiators react even at low UV intensities, and that the resulting polymer chains exhibit a similar distribution of chain lengths, which is consistent with the stoichiometry. Additionally, we measure the gel fraction─the mass ratio of fully dried, washed hydrogels to the used monomer (Figure 3B). At all UV intensities, the gel fraction is around 95%, indicating that most monomers polymerize and the gelation is unaffected by UV intensity. Overall, our model system exhibits similar degrees of polymerization, conversion, and gelation across UV intensities. Therefore, some structural properties of polymer networks known to be determined by stoichiometry, such as the chain length and the fraction of dangling chains relative to elastically effective polymer chains, are expected to be insensitive to the UV intensity, allowing us to focus on how UV intensity affects monomer diffusion.

Figure 3

Figure 3. Validation of the model material. (A) Polymer chain size at different UV intensities measured by DLS. (B) Gel fraction at different UV intensities.

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4.2. Swelling Ratio

We synthesize hydrogels using the same precursor at various UV intensities and exposure time (Figure 4A). We choose W = 2 to form dense entanglements, C = 10–5 to form long polymer chains, and I/C = 0.4 to minimize the fraction of dangling chains. In such a highly entangled, long-chain polymer network, entanglements determine elastic properties, such as modulus and swelling ratio. (5) The average chain length is fixed since C is fixed, and the total number of trapped and transient entanglements is also fixed since W is fixed. When the exposure time is short, the precursor does not cure and dissolves in water upon swelling (indicated by a dotted line). As the exposure time increases, the polymer chains percolate and show a finite swelling ratio. The swelling ratio decreases further with increasing UV exposure time, then plateaus, indicating that the precursor is fully cured. Also, as the UV intensity increases, the time to reach the plateau decreases, indicating that the UV intensity controls the initiation rate.

Figure 4

Figure 4. Swelling ratio of PAAm hydrogels synthesized at different UV intensities. (A) The swelling ratio as a function of the exposure time at various UV Intensities. (B) The swelling ratio of the fully cured samples as a function of the UV Intensity. (C) The swelling ratio as a function of the exposed energy. All samples were prepared with a precursor of W = 2, C = 10–5, and I = 4 × 10–6.

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We plot the swelling ratio of fully cured samples as a function of the UV intensity (Figure 4B). The swelling ratio of the fully cured sample with UV intensity of 1.8 mW/cm2 is 4.5, while that with the UV intensity of 129 mW/cm2 is 13.6. This significant difference in swelling ratio from the same precursor indicates that the fraction of trapped entanglements is highly sensitive to UV intensity. The swelling ratio plateaus at low UV intensities, suggesting that the swelling ratio of 4.5 is the lower limit set by the maximum density of trapped entanglements for this precursor. At the UV intensity of 0.5 mW/cm2, the precursor did not cure. These observations indicate that more trapped entanglements form at lower UV intensities, which supports our hypothesis that a low initiation rate promotes the formation of trapped entanglements.
We further plot the swelling ratio as a function of the exposed energy (UV intensity multiplied by the exposure time) (Figure 4C). As the UV intensity decreases from 129 to 3.2 mW/cm2, the required energy to reach the plateau decreases. However, from 3.2 to 0.8 mW/cm2, more energy is required to reach the plateau, while the swelling ratio remains nearly the same. Therefore, lowering the UV intensity beyond 3.2 mW/cm2 does not form further trapped entanglements but requires unnecessary energy to complete the curing process.

4.3. Elastic and Fracture Properties

We measure the stress–strain curves of fully cured samples at various UV intensities at the fully swollen state to study the effects of the fraction of trapped entanglements on the elastic and fracture properties (Figure 5A). As UV intensity increases, the Young’s modulus decreases (Figure 5B). This observation corroborates that a lower UV intensity increases the fraction of trapped entanglements, since the trapped entanglements stiffen the polymer network. Furthermore, as UV intensity decreases, strength increases (Figure 5C) and work of fracture increases (Figure 5D). This observation aligns with other experimental results showing the effects of the density of trapped entanglements in PAAm hydrogels by using the precursor concentration as a variable. (5) The effects of the UV intensity on elastic and fracture properties are significant: modulus and strength by 6.2-fold and 4.7-fold, respectively, when the UV intensity changes from 129 to 3.2 mW/cm2. Thus, UV intensity is a critical synthesis parameter, along with precursor stoichiometry, for achieving a high load-bearing capacity. The stretchability and strength at 0.8 mW/cm2 drop rapidly, although the stress–strain curve overlaps with that at 1.8 mW/cm2. We do not have a clear understanding of this phenomenon.

Figure 5

Figure 5. Stress–strain curves of fully swollen, fully cured PAAm hydrogels at various UV intensities. (A) Stress–strain curves at different UV intensities. (B) Young’s modulus as a function of the UV intensity. (C) Strength as a function of the UV intensity. (D) Work of fracture as a function of the UV intensity. (E) Toughness at different UV intensities.

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We measure the toughness of PAAm hydrogels with different UV intensities. The hydrogels prepared at relatively high UV intensities, such as 129 and 23 mW/cm2, exhibit a toughness of about 800 and 1200 J/m2, respectively. By contrast, the sample prepared at 3.2 mW/cm2, which is expected to have more trapped entanglements, exhibits a toughness of about 1500 J/m2, more than double that of the high-UV-intensity sample (Figure 5E). Considering that the chain length is fixed by the fixed C value, we attribute this difference in toughness to the topological effects. For example, the trapped entanglements suppress swelling, so the sample with 3.2 mW/cm2 exhibits approximately twice the polymer content compared to those with 129 mW/cm2 at the fully swollen state. The toughness is known to scale with ϕ2/3, where ϕ is the polymer content in the gel. The values of toughness divided by ϕ2/3 are comparable across the UV intensity, indicating that the difference in toughness is due to the polymer fraction, which originates from the difference in the fraction of trapped entanglements (Figure S3).

4.4. Rheological Properties

We measure the storage modulus (G′) and loss modulus (G″) at various UV intensities as a function of the angular frequency (Figure 6A). The data show that both G′ and G″ increase as the UV intensity decreases, and G′ increases more than G″. Consequently, Tan δ of a sample with the UV intensity of 129 mW/cm2 shows the highest value, while the sample with the UV intensity of 3.2 mW/cm2 shows the lowest (Figure 6B). This observation can also be explained by a high fraction of trapped entanglements at low UV intensities, as trapped entanglements act as cross-links, increasing elasticity. (43−47) At the UV intensity of 129 mW/cm2, Tan δ does not follow the trends of lower UV intensities and abruptly increases, which indicates that the polymer network is not well percolated and excessively swollen.

Figure 6

Figure 6. Rheological properties of PAAm hydrogels synthesized at various UV intensities. (A) Storage (filled dots) and loss modulus (open dots), (B) Tan δ for various PAAm hydrogels synthesized at three different UV intensities.

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4.5. Stoichiometry of Precursors

We systematically vary the precursor conditions, including water-to-monomer molar ratio (W), cross-linker-to-monomer molar ratio (C), and initiator-to-monomer molar ratio (I), and investigate which conditions make the network topology and mechanical properties dependent on the UV intensity. We prepare PAAm hydrogels using precursors with various values of W at fixed C = 1 × 10–5 and I = 4 × 10–6, and measure the swelling ratio. At a UV intensity of 129 mW/cm2, the swelling ratio rapidly increases in W, and gelation fails at W = 20 (Figure 7A). As W increases, the concentration of monomers decreases, and most monomers grow individually with minimal overlaps, leading to a low fraction of trapped entanglements and a high swelling ratio. By contrast, at 3.2 mW/cm2, even at a high W value, many monomers can still grow in the presence of existing polymer chains and form trapped entanglements, resulting in a relatively low swelling ratio.

Figure 7

Figure 7. Swelling ratio of PAAm hydrogels depending on the precursor conditions. Swelling ratio as a function of (A) W, (B) C, and (C) I for various PAAm hydrogels synthesized at different UV intensities.

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Next, we measure the swelling ratio as a function of C at various UV intensities (Figure 7B). The C value determines the average chain length. Thus, the swelling ratio generally decreases in C. At C = 1 × 10–2, the molecular weight between neighboring cross-links is much lower than the entanglement molecular weight, so the polymer network is expected to have negligible trapped entanglements per chain. Thus, the swelling ratio is the lowest and is insensitive to UV intensity. At low C values, trapped entanglements contribute more to swelling resistance than cross-links, making the swelling ratio sensitive to the UV intensity. These observations confirm that the gelation kinetics by UV intensity is directly associated with the fraction of trapped entanglements in the polymer network.
Lastly, we measure the swelling ratio as a function of I at various UV intensities (Figure 7C). The initiation rate increases with increasing initiator concentration, as does the UV intensity. As a result, the swelling ratio increases with I at all UV intensities. However, the effects of I and UV intensity differ fundamentally in terms of stoichiometry. Since the initiator molecules consist of the ends of the backbone, the value of I determines the backbone length. The ends of the backbone are dangling chains as they do not cross-link with other chains. Particularly, when the value of I approaches the value of C, the fraction of dangling chains suddenly increases, and the fraction of trapped entanglements will decrease. Even at a UV intensity of 3.2 mW/cm2, the fully cured samples therefore exhibit excessive swelling at I > C = 1 × 10–5. Due to this difference, the curves at different UV intensities are not self-similar and cannot be combined into a master curve by shifting them. When the value I is sufficiently lower than C, the fraction of dangling chains is negligible, and the effects of the UV intensity on swelling become more pronounced.

5. Conclusions

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We show that the fraction of trapped entanglements in photopolymerized polymer networks can be significantly controlled by varying the UV intensity. At low UV intensity, polymerization initiates gradually, allowing more monomers to grow in the presence of existing polymers, forming additional trapped entanglements. At high UV intensity, by contrast, most initiators react at the initial stage, resulting in individual growth with fewer trapped entanglements. Hydrogels with dense trapped entanglements exhibit high swell resistance, as well as high fracture resistance, including strength, work of fracture, and toughness. Both UV intensity and initiator concentration can control the kinetics of initiation, but the former does not change the stoichiometry of the precursor, whereas the latter does. The ability to control the fraction of trapped entanglements expands the design space of polymer networks without requiring complex chemistry or stoichiometric adjustments, and enables the understanding and engineering of the mechanical properties of soft materials across various fields, from biomedical applications to soft devices. Further exploration to understand the relationship between the kinetics of synthesis processes and the formation of entanglements in other polymerization mechanisms, such as thermal and living polymerization, may pave the way for a new network topology.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.5c03018.

  • Raw data of the graphs in the main figures; Heat flux from hydrogel gelation at various UV intensities; Temperature profiles in the heat flux measurement; Toughness of PAAm hydrogels divided by φ2/3 at different UV intensities; Heat flux analysis (PDF)

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Author Information

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  • Corresponding Author
  • Authors
    • Suyoung Lee - Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
    • Yan Huang - Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
    • Jinyue Dai - Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
    • Haeji Kim - Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, United States
  • Author Contributions

    Suyoung Lee: Hydrogel fabrication, Formal Analysis, Investigation, Validation, Writing─drafting, reviewing and editing. Yan Huang: Toughness measurement, Gel fraction measurement Jinyue Dai: DLS analysis Haeji Kim: Hydrogel fabrication Junsoo Kim: Supervision, Conceptualization, Methodology, Formal Analysis, Validation, Writing─drafting, reviewing and editing.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was primarily supported by the National Science Foundation’s MRSEC program (DMR-2308691) at the Materials Research Center of Northwestern University. This work was also supported by start-up funds from Northwestern University.

References

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  • Abstract

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    Figure 1

    Figure 1. Control the fraction of trapped entanglements via prolonged initiation. (A) A precursor for highly entangled long-chain polymer networks. (B) Simultaneous triggering of initiators. (C) The fully cured polymer network with fast initiation. Entanglements are either trapped or transient. (D) A low fraction of trapped entanglements results in significant swelling. (E, F) Gradual triggering of initiators. Monomers are present inside the free volume. (G) Monomers inside the free volume polymerize in the presence of polymers, forming trapped entanglements. The monomer concentration at the overlapping region decreases, allowing additional monomers to diffuse in. (H) The resulting polymer network has the same concentration as (C) but a different fraction of trapped entanglements. (I) Limited swelling due to a high fraction of trapped entanglements.

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    Figure 2

    Figure 2. Measurement of the heat flux from hydrogel gelation. (A) The experiment setup for the heat flux measurement. (B) The temperature profile by polymerization and UV exposure. (C) The temperature of the precursor, Tm, over time upon UV exposure. (D) The heat flux generated by polymerization over time at different UV intensities.

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    Figure 3

    Figure 3. Validation of the model material. (A) Polymer chain size at different UV intensities measured by DLS. (B) Gel fraction at different UV intensities.

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    Figure 4

    Figure 4. Swelling ratio of PAAm hydrogels synthesized at different UV intensities. (A) The swelling ratio as a function of the exposure time at various UV Intensities. (B) The swelling ratio of the fully cured samples as a function of the UV Intensity. (C) The swelling ratio as a function of the exposed energy. All samples were prepared with a precursor of W = 2, C = 10–5, and I = 4 × 10–6.

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    Figure 5

    Figure 5. Stress–strain curves of fully swollen, fully cured PAAm hydrogels at various UV intensities. (A) Stress–strain curves at different UV intensities. (B) Young’s modulus as a function of the UV intensity. (C) Strength as a function of the UV intensity. (D) Work of fracture as a function of the UV intensity. (E) Toughness at different UV intensities.

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    Figure 6

    Figure 6. Rheological properties of PAAm hydrogels synthesized at various UV intensities. (A) Storage (filled dots) and loss modulus (open dots), (B) Tan δ for various PAAm hydrogels synthesized at three different UV intensities.

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    Figure 7

    Figure 7. Swelling ratio of PAAm hydrogels depending on the precursor conditions. Swelling ratio as a function of (A) W, (B) C, and (C) I for various PAAm hydrogels synthesized at different UV intensities.

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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.5c03018.

    • Raw data of the graphs in the main figures; Heat flux from hydrogel gelation at various UV intensities; Temperature profiles in the heat flux measurement; Toughness of PAAm hydrogels divided by φ2/3 at different UV intensities; Heat flux analysis (PDF)


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