Mechanical Properties of End-linked PEG/PDMS. Hydrogels

Transcription

1 Supporting Information Mechanical Properties of End-linked PEG/PDMS Hydrogels Jun Cui, Melissa A. Lackey, Gregory N. Tew* and Alfred J. Crosby* Department of Polymer Science and Engineering, University of Massachusetts Amherst, Massachusetts, 0003, USA

2 Materials 5-norbornene-2-carboxylic acid (99% exo), diisopropyl azodicarboxylate (DIAD), triphenylphosphine, poly(ethylene glycol) (PEG) (M n = 2.3 kda, according to H NMR), hydroxyl terminated polydimethylsiloxane (PDMS) (M n = 4.4 kda, according to H NMR), pentaerythritol tetrakis(3- mercaptopropionate) (PETMP), and 2-hydroxy-4 -(2-hydroxyethoxy)-2-methylpropiophenone (Irgacure 2959) were purchased from Sigma Aldrich, Acros Organics, Alfa Aesar, or Gelest and used without further purification. Swelling properties SI Figure. Swelling ratio (Q) as a function of the initial volume fraction of PDMS (φ PDMS,0 ). Standard deviations were calculated from at least three samples. 2

3 SI Figure 2. Swelling ratio (Q) as a function of the initial polymer volume fraction (φ 0 ), where the ratio of the initial volume fraction of PEG to PDMS (φ PEG,0 /φ PDMS,0 ) was. SI Table. Summary of the gel fraction, molecular weights between cross-links and elongation in extension for PEG/PDMS hydrogels with different compositions. Name Gel Fraction a M c (kda) b Extension Ratio PEG 00 PDMS ± PEG 70 PDMS ± PEG 50 PDMS ± PEG 30 PDMS ± a M c stands for the molecular weight between cross-links in the hydrophilic phase of the hydrogels. b Extension ratio shows the maximum extension ratio under tension. Mechanical measurements 3

4 SI Figure 3. Young s modulus (E) as a function of the volume fraction of the total polymer (φ ). Standard deviations were calculated from at least three samples. SI Figure 4. Young s modulus (E) as a function of the equilibrium volume fraction of PDMS in the PEG/PDMS hydrogels (red circles). Standard deviations were calculated from at least three samples. Blue dashed line represents the theoretical values of E predicted by the Guth-Gold model. 4

5 SI Figure 5. Relationship between the equilibrium volume fraction of PDMS (φ PDMS ) and the ratio of the initial volume fraction of the PEG to PDMS (φ PEG,0 /φ PDMS,0 = κ ). SI Figure 6. Universal plot of the normalized composite moduli predicted by the Voigt model (upper line) and Reuss model (lower line) as a function of the volume fraction ratio of the two components in 5

6 the composite (φ 2 /φ ). The value shown on each curve represents the modulus ratio of the two components (E 2 /E ). SI Figure 7. Plot of the normalized composite moduli predicted by the Voigt model (upper line) and the Reuss model (lower line) as a function of volume fraction ratio (φ 3 /φ ), which scales with the volume fraction ratio (φ 2 /φ ) as φ 3 /φ = 0.5( φ 2 /φ ).4. This is the scaling relationship for the PEG/PDMS hydrogels, where φ = φ PDMS, φ 2 = φ PEG + φ water and φ 3 = φ PEG. The value shown on each curve represents the modulus ratio of the two components (E 2 /E ). 6

7 SI Figure 8. Critical strain energy release rate (G c ) plotted as a function of the volume fraction of the total polymer (φ ). Standard deviations were calculated from at least three samples. SI Figure 9. The volume fraction of PEG in the PEG phase (φ PEG / water ) plotted as a function of the initial volume fraction of PDMS (φ PDMS,0 ). 7

8 SI Figure 0. The swelling ratio of PEG in the PEG phase (Q PEG/water ) and the swelling ratio of the hydrogels plotted as a function of the volume fraction of PDMS (φ PDMS ) at the equilibrium-swollen state. SI Figure. Representative plots of stress-strain relationship in tension for swollen PEG/PDMS hydrogels with different PEG to PDMS molar ratios. 8

9 SI Figure 2. Representative curves of compressive stress as a function of compressive strain for swollen PEG/PDMS hydrogels with different volume fractions of PEG and PDMS. The details of the composition for each hydrogel were shown in Table. SI Figure 3. Representative curves for cyclic stress-strain relationship of the 70/30 PEG/PDMS sample. For clarity, the curves are shifted on the strain axis, and the final strains are given on the plots. 9

10 SI Figure 4. Representative curves for cyclic stress-strain relationship of the 50/50 PEG/PDMS sample. For clarity, the curves are shifted on the strain axis, and the final strains are given on the plots. SI Figure 5. Representative curves for cyclic stress-strain relationship of the 30/70 PEG/PDMS sample. For clarity, the curves are shifted on the strain axis, and the final strains are given on the plots. 0

11 SI Figure 6. Representative curves for cyclic stress-strain relationship of the 0/90 PEG/PDMS sample. For clarity, the curves are shifted on the strain axis, and the final strains are given on the plots. Equations The Voigt model describes polymer composites with two components arranged parellel to the loading direction. In the PEG/PDMS hydrogels, the two components were the hydrated PEG phase with a volume fraction of φ PEG + φ water and the bulk PDMS phase with a volume fraction of φ PDMS. The Young s modulus of the hydrogels, E hydrogel was described in Equation S. In the PEG phase E of the hydrated PEG followed the scaling relationship as E E 0 φ 2,25, whereas in the PDMS phase E was assumed to be E of the PDMS in bulk, E PDMS E PDMS,0. Substituting these relationships into Equation S led to Equation S2. The ratio of φ PEG,0 to φ PDMS,0 was defined as κ and κ φ PEG /φ PDMS when the conversion of thiol-norbornene chemistry for the PEG and PDMS was the same. To simplify the equation, this relationship was substituted into Equation S2, leading to Equation S3 such that E hydrogel was decribed as a function of κ and φ PDMS. φ PDMS empirically scaled with κ as φ PDMS = 0.078κ.28 (SI Figure S4). Substituting this relationship into Equation S3 led to Equation S4, which represented the Voigt model, plotted in Figure 6.

12 E hydrogel = ( φ PEG + φ water )E PEG + φ PDMS E PDMS (S) φ E hydrogel = ( φ PEG + φ water )E PEG PEG,0 φ PEG + φ water φ PDMS E PDMS,0 (S2) E hydrogel = φ PDMS E PEG,0 κ 2.25 φ PDMS.25 + E PDMS,0 (S3) E hydrogel = 0.078κ.28 [ E PEG,0 κ 2.25 ( 2.8κ.28 ).25 + E PDMS,0 ] (S4) The Reuss model was used to describe polymer composites with two components arranged perpendicular to the loading direction. The same assumptions as the Voigt model were applied to derive Equations S5-S8. Equation S8 represented the Reuss model, plotted in Figure 6. E hydrogel = φ PEG + φ water E PEG E hydrogel = E PEG,0 + φ PDMS E PDMS φ PEG + φ water φ PDMS φ PEG E PDMS,0 φ PEG + φ water (S5) (S6) ( ) 3.25 φ PDMS = φ E PDMS + hydrogel E PEG,0 κ 2.25 E PDMS,0 (S7) ( ) κ.28 = 0.078κ.28 + E hydrogel E PEG,0 κ 2.25 E PDMS,0 (S8) 2