Hydrogel

In the unswollen state, hydrogels can be modelled as highly crosslinked chemical gels, in which the system can be described as one continuous polymer network. In this case:

${\displaystyle G=N_{p}kT={\rho RT \over {\overline {M}}_{c}}}$

where G is the shear modulus, k is the Boltzmann constant, T is temperature, N_p is the number of polymer chains per unit volume, ρ is the density, R is the ideal gas constant, and ${\displaystyle {\overline {M}}_{c}}$ is the (number) average molecular weight between two adjacent cross-linking points. ${\displaystyle {\overline {M}}_{c}}$ can be calculated from the swell ratio, Q, which is relatively easy to test and measure.[19]

For the swollen state, a perfect gel network can be modeled as:[19]

${\displaystyle G_{swollen}=GQ^{-1/3}}$

In a simple uniaxial extension or compression test, the true stress, ${\displaystyle \sigma _{t}}$, and engineering stress, ${\displaystyle \sigma _{e}}$, can be calculated as:

${\displaystyle \sigma _{t}=G_{swollen}\left(\lambda ^{2}-\lambda ^{-1}\right)}$

${\displaystyle \sigma _{e}=G_{swollen}\left(\lambda -\lambda ^{-2}\right)}$

where ${\displaystyle \lambda =l_{current}/l_{original}}$ is the stretch.[19]

In order to describe the time-dependent creep and stress-relaxation behavior of hydrogel, a variety of physical lumped parameter models can be used.[19] These modeling methods vary greatly and are extremely complex, so the empirical Prony Series description is commonly used to describe the viscoelastic behavior in hydrogels.[19]

The most commonly seen environmental sensitivity in hydrogels is a response to temperature.[21] Many polymers/hydrogels exhibit a temperature dependent phase transition, which can be classified as either an Upper Critical Solution Temperature (UCST) or Lower Critical Solution Temperature (LCST). UCST polymers increase in their water-solubility at higher temperatures, which lead to UCST hydrogels transitioning from a gel (solid) to a solution (liquid) as the temperature is increased (similar to the melting point behavior of pure materials). This phenomenon also causes UCST hydrogels to expand (increase their swell ratio) as temperature increases while they are below their UCST.[21] However, polymers with LCSTs display an inverse (or negative) temperature-dependence, where their water-solubility decreases at higher temperatures. LCST hydrogels transition from a liquid solution to a solid gel as the temperature is increased, and they also shrink (decrease their swell ratio) as the temperature increases while they are above their LCST.[21]

Different applications call for different thermal responses. For example, in the biomedical field, LCST hydrogels are being investigated as drug delivery systems due to being injectable (liquid) at room temp and then solidifying into a rigid gel upon exposure to the higher temperatures of the human body.[21] There are many other stimuli that hydrogels can be responsive to, including: pH, glucose, electrical signals, light, pressure, ions, antigens, and more.[21]

There are many ways to fine-tune the mechanical properties of hydrogels. One of the most simple is to use different molecules for the backbone and crosslinkers of the hydrogel system, as different molecules will have different intermolecular interactions with each other and different interactions with the absorbed water.[21][22] Another method of modifying the strength or elasticity of hydrogels is to graft or surface coat them onto a stronger/stiffer support, or by making superporous hydrogel (SPH) composites, in which a cross-linkable matrix swelling additive is added.[23] Other additives, such as nanoparticles and microparticles, have been shown to significantly modify the stiffness and gelation temperature of certain hydrogels used in biomedical applications.[24][25][26]