Viscoelastic Material Properties of Gelatin with Varying Water to Collagen mass Ratios

TL;DR

This study investigates how the water-to-collagen mass ratio $R_{H_2O}$ governs the viscoelastic properties of gelatin to validate its use as a soft-tissue analogue. Using compression tests across $R_{H_2O}=2:1$–$20:1$, the authors fit a Maxwell–Weichert model with three elastic moduli $(E_0,E_1,E_2)$ and two viscosities $(T_1,T_2)$ to obtain a relaxation modulus $E_r(t)=E_0+E_1 e^{-t/T_1}+E_2 e^{-t/T_2}$. They find that the elastic moduli decrease with $R_{H_2O}$ following a decreasing power law $E_i(R_{H_2O})=a_i (R_{H_2O})^{-b_i}$, while the relaxation times follow an increasing sigmoid $T_i(R_{H_2O})=rac{c_i}{1+ ext{exp}[-d_i(R_{H_2O}-f_i)]}+g_i$, enabling precise design of gelatin samples with target stiffness and time-scale behavior. The results span roughly two orders of magnitude in stiffness and more than an order of magnitude in relaxation time, offering a practical framework to tailor gelatin for soft-matter mechanics experiments and for ballistic gelatin analogs of human tissue. Such ratio-dependent characterizations provide a safe, inexpensive standard material for studying tissue mechanics and validating computational models in biomedical research.

Abstract

Gelatin is often used as an analog for studying soft and biological materials in order to understand the mechanics of behavior of biological tissue in events like traumatic brain injuries. The material properties of gelatin change with the ratio of water to gelatin powder used to make a given sample. Characterizing the relationship between this ratio and the material properties of gelatin is crucial to enable its use in mechanics experiments. In this work, compression tests were performed on a texture analyzer on samples which ranged from a 2:1 to 20:1 ratio of water to gelatin powder. In this range, instantaneous stiffnesses were well fit via power law in this ratio and decreased from 277 +/- 30 kPa to 4.34 +/- 0.64 kPa. The dominant (longest) timescales of the samples were well fit via a sigmoid function in this ratio and increased from 29.8 +/- 1.0 s to 621 +/- 92 s. The resulting ratio-property relationships offer a functional way to design gelatin samples for use in mechanics experiments.

Figures (8)

• Figure 1: (a) The hierarchical structure of gelatin. 1) Long amino acid chains are the base units of collagen. 2) The long chains are "woven" together into yarn-like collagen strands. 3) The strands are tangled and linked together, capturing water and forming gelatin. (b) Relative density of polymer networks for high and low water to collagen mass ratio $R_{H_2O}$. The graduated cylinders depict the relative amounts of water and gelatin powder (collagen) used.
• Figure 2: Maxwell--Weichert spring--damper model of gelatin. Initially during a step response, the viscous dampers react rigidly and the system responds with the instantaneous modulus $(E_0 + E_1 + E_2)$. As $t\to\infty$, the viscous dampers support none of the load, and the relaxation modulus decays to the quasi-static modulus $E_0$.
• Figure 3: Texture Analyzer compression experiment setup. Samples were lubricated with vegetable oil to mitigate sample barreling (which would increase error). They were then placed on the TA-90 Aluminum Test Platform and compressed via the TA-25 2-inch Compression Probe at 1 mm/s.
• Figure 4: A plot of a typical force and displacement curve for a gelatin sample in compression on the texture analyzer. During the "compress" stage (denoted in red) the crosshead moves down at a constant rate compressing the sample. During the "hold" stage (denoted in green) the sample is held at a constant strain. The stress response decreases due to viscoelastic effects. Finally, during the "reset" stage (denoted in yellow) the probe moves back up from the sample to its starting position.
• Figure 5: Relaxation modulus responses of one of each set of samples at roughly constant temperature ($19.9 \pm 0.5~^{\circ}\mathrm{C}$). (a) A semi-log plot of the relaxation modulus response of each sample to the step-response experiments. Values range over several orders of magnitude. (b) A plot of the normalized relaxation modulus with time. Notice the normalized curves seem to be bounded by a lower and upper limit.