[Paper Review] Towards rational design of power-law rheology via DNA nanostar networks

Nathaniel Conrad, Omar A. Saleh+1 more|arXiv (Cornell University)|Aug 28, 2023

Nanopore and Nanochannel Transport StudiesEngineering3 citations

TL;DR

This study demonstrates that DNA nanostar networks with tunable strong and weak bonds enable rational design of power-law rheology. By varying the ratio of strong to weak DNA bonds, the authors show that diffusive stress relaxation in a strong-bond subnetwork through a viscous weak-bond matrix yields frequency-dependent moduli scaling with exponents linked to fractal dimensions, validated by simulations and experiments.

ABSTRACT

We measure the rheology of transient hydrogels comprised of a single type of DNA nanostar that makes both strong and weak bonds. These gels exhibit power-law frequency-dependence of their storage and loss moduli, with scaling exponents that depend on the proportions of the two bonds. A diffusive stress-relaxation model, in which the strong-bond sub-network relieves stress by diffusing through an effective viscosity imposed by the weak bonds, explains the scaling of their moduli. The model has implications for the fractal dimensions of the strong-bond sub-network that are in good agreement with measurements and makes testable predictions for the viscoelasticity of other transient hydrogels. Overall, this work demonstrates the power of DNA nanotechnology to decipher, and potentially rationally design, power-law rheology.

Motivation & Objective

• To understand the origin of power-law rheology in transient hydrogels, which deviates from standard Maxwell behavior.
• To investigate how multiple relaxation timescales from distinct bond types (strong and weak) influence viscoelastic response.
• To develop a predictive model linking network topology, bond dynamics, and frequency-dependent moduli scaling.
• To validate the model using DNA nanostar systems with precisely controlled bond valence and strength.
• To establish a framework for rational design of complex biomaterials with tailored viscoelastic properties.

Proposed method

• Synthesized DNA nanostars with six arms, each bearing either strong (γ: TGCGCGCA), weak (α: CGATCG), or no (x) overhangs to control interparticle bonding.
• Formed hydrogels by thermal annealing of nanostar solutions, resulting in transient networks with dual-bond types.
• Performed oscillatory rheology in the linear viscoelastic regime across frequencies (0.1–10 Hz) and temperatures (5–50 °C), using time-temperature superposition to construct master curves.
• Applied a diffusive stress-relaxation (DSR) model where the strong-bond network relaxes via diffusion through a viscous medium defined by weak bonds.
• Used strain sweeps to estimate the elastic correlation length ξ(f), testing consistency with f⁻¹/³ scaling in the Zimm regime.
• Validated the DSR model by comparing experimental scaling exponents to simulations of 2D near-isostatic networks with known fractal dimensions.

Experimental results

Research questions

• RQ1 How do two distinct bond types (strong and weak) in a DNA nanostar network alter the frequency dependence of storage and loss moduli?
• RQ2 Can a diffusive stress-relaxation model explain the observed power-law scaling of moduli in such networks?
• RQ3 What is the relationship between the fractal dimension of the strong-bond subnetwork and the observed power-law exponents?
• RQ4 How does the ratio of strong to weak bonds affect the scaling of the elastic correlation length ξ with frequency?
• RQ5 To what extent do simulations of 2D near-isostatic networks support the DSR model and its predictions for G′ scaling?

Key findings

• Hydrogels with only one bond type (e.g., α₆ or x₃γ₃) exhibited Maxwell-like behavior with G′ ∼ f² and G′′ ∼ f, indicating single relaxation mode.
• Heterotypic networks with both strong and weak bonds displayed power-law scaling: G′ ∼ f¹/² and G′′ ∼ f¹/² in the α₄γ₂ and α₃γ₂ systems.
• The elastic correlation length ξ scaled as f⁻¹/³ in α₄γ₂ and α₃γ₂ gels, consistent with the diffusive stress-relaxation (DSR) model in the Zimm regime.
• Simulations of 2D near-isostatic networks predicted G′ ∼ f⁰.⁶⁰ in the Zimm limit and f⁰.⁴⁷ in the Rouse limit, matching experimental scaling exponents.
• The fractal dimension of stress-bearing chains (d_min ≈ 1.80) and the network’s fractal dimension (d_fr ≈ 1.86) were consistent with the observed scaling behavior.
• The DSR model successfully explained emergent broad relaxation dynamics not captured by simple addition of relaxation modes.