Diffusion Behavior of Water Molecules in Hydrogels with Controlled Network Structure
Authors: Fujiyabu Takeshi , Li Xiang , Sakai Takamasa 
Published: February 2020

Hydrogels have attracted attention as biomaterials because of the similar property to biological soft tissues. One of the applications of hydrogels for biomaterials is drug release carrier. For the application, it is important to understand and to control the diffusion behavior of molecules in hydrogels.
There are three major models describing diffusion behavior of small molecules in the polymer solution. First is the Ogston model, in which polymer network is considered to behave as an obstacle preventing the diffusion of particles. Second is the hydrodynamic model, in which the existence of polymer increases the effective viscosity and decreases diffusion speed of particles. Third is the free volume model, in which particles diffuse passing through free volume of solvent and polymer. Although the validity of these models has been investigated by many researchers, there is no clear experimental evidence to support any models. Thus, even now, many models are left without validation. The muddling of models was assisted by the heterogeneity in conventional hydrogels. To understand the diffusion behavior of small molecules in a hydrogel, the validation of these models using a homogeneous hydrogel is necessary.
Recently, we have developed a homogeneous hydrogel, Tetra-PEG gel, by combining two kinds of tetra-armed pre-polymers. It has been revealed that Tetra-PEG gel has an extremely homogeneous network structure, and network structure parameters (polymer volume fraction : φ
0, molecular weight between crosslinks : M
w, binding ratio : p) of Tetra-PEG gel can be controlled independently.
In this study, we investigated the effect of network structures on the self-diffusion coefficient of water molecules (D) in Tetra-PEG gels and in pure water (D
0) by Pulsed field-gradient spin-echo Nuclear Magnetic Resonance (PGSE-NMR). The values of D/D
0 decreased as an exponential function with an increase in φ
0 (0 - 0.15), and was independent of M
w (10k, 20k g/mol) (Figure 1). This result well agreed with three models, and the difference among three models was negligible. On the other hand, D/D
0 decreased with a decrease in p (0 - 1) (Figure 1). This result was not reproduced by any three models, suggesting these models were not valid to describe diffusion behavior of small molecules in a hydrogel.
Here, we tested another model proposed by M. Tokita et al. In the model, the diffusion of probe molecules is mainly determined by the correlation length of the polymer network (blob size : ξ) and the hydrodynamic radius of the probe molecules (R
h) as, D/D
0 = exp(-R
h/ξ). In Figure 2, D/D
0 in Tetra-PEG gels were plotted against 1/ξ. The values of xwere estimated by our previous small angle neutron scattering experiment. As shown in the figure, all the data including p-tune results fall onto a guide showing D/D
0 = 0.97exp(-2.8/ξ). The experimental values of the front coefficient (0.97) and R
h (2.8Å) were close to the theoretical value (1.0) and the hydrodynamic radius of a water molecule (3.0Å), respectively. These results suggest that Tokita’s model is the correct model to describe the diffusion behavior of small molecules in a hydrogel.

Figure 1