Effect of Potassium-Ion-Triggered Double Helix Aggregation on Shakedown Behavior of κ-Carrageenan/Polyacrylamide Hydrogel

Abstract

This study investigates the effect of potassium ion (K⁺) concentration on double helix aggregation in κ-carrageenan-based hydrogels, which significantly influences their shakedown behavior. The shakedown behavior of κ-carrageenan/polyacrylamide (PAAm) hydrogels was characterized by the evolution of maximum stress and energy dissipation during cyclic load. The experimental results indicate that higher K⁺ concentrations significantly improve the maximum stress in the steady state, but barely influence the energy dissipation in the steady state. The improved maximum stress can be explained by the higher density of double helix aggregation. The steady energy dissipation elucidates that the K⁺ concentration does not affect the breaking-recovering balance of the sacrificial network in cyclic loading. These results provide mechanistic insights into how ion-triggered double helix aggregation influences the shakedown behavior of κ-carrageenan-based hydrogels.

Keywords: double helices; fatigue damage; shakedown behavior; κ-carrageenan hydrogel.

Figure 1

The schematics of the network structure in hydrogel without K⁺ cations (C00), with 10 mM K⁺ cations (C10), and with 80 mM K⁺ cations (C80).

Figure 2

Tensile mechanical properties of the κ-carrageenan/PAAm hydrogel with various K⁺ concentrations. (a) Stress–stretch curves of hydrogel with varying K⁺ cation concentrations, labeled as C00, C10, C20, C30, C40, and C80, respectively. (b) Effects of K⁺ concentration on elastic modulus. (c) Effects of K⁺ concentration on fracture energy.

Figure 3

The yield behavior of the κ-carrageenan/PAAm hydrogel during the uniaxial tensile test. (a) The stress–stretch curve of C80 hydrogels. (b) Pictures demonstrating the yielding phenomenon during the tensile test of C80. Labels i–iv represent the correspondence between the stress–stretch curve and the picture. (c) Illustration of the C80 network structure before yielding and during yielding.

Figure 4

Viscoelastic behavior of the C80 hydrogels. (a) Stress–stretch curves measured at different loading rates. (b) Cyclic loading–unloading tests performed at different loading rates.

Figure 5

Cyclic fatigue damage of κ-carrageenan/PAAm hydrogel. (a) Experimental setup of fatigue test. (b) The loading curve of fatigue test, where the applied stretch λ is plotted as a function of cycles N. (c) Shakedown behavior, which involves stress S versus stretch λ curves over N cycles of the applied stretch. (d–k) Fatigue damage test of the κ-carrageenan/PAAm hydrogel under cyclic loads with maximum stretches of λ_max = 1.5 and λ_max = 2.0. The stress–stretch curves of (d,h) C00, (e,i) C10, (f,j) C20, and (g,k) C80.

Figure 6

The evolution of the maximum stress S_max in the shakedown behavior of a κ-carrageenan/PAAm hydrogel. (a,b) S_max of the C00, C10, C20, and C80 samples in each cycle under the maximum stretches λ_max = 1.5 and λ_max = 2.0. (c) S_max measured during the 1st cycle of the cyclic load. (d) The shakedown ratio of S_max, ϕ_S, of these hydrogels.

Figure 7

The evolution of the energy dissipation U_hys in the shakedown behavior of a κ-carrageenan/PAAm hydrogel. (a,b) U_hys of C00, C10, C20, and C80 samples in each cycle under the maximum stretches λ_max = 1.5 and λ_max = 2.0. (c) U_hys measured during the 1st cycle of the cyclic load. (d) The shakedown ratio of U_hys, ϕ_U, of these hydrogels.

Figure 8

Pure shear test of κ-carrageenan/PAAm hydrogel. (a) The geometry of a sample for pure shear test. (b) The stress–stretch curves of pure shear samples with a notch and without a notch. The sample with a notch ruptures at a critical stretch λ_c. The energy density W(λ_c) at the critical stretch is obtained from the area under the stress–stretch curve of the sample without a notch.