young_modulus_cryogel_theory: young_modulus_cryogel_theory

In tbgitoo/textureAnalyzerGels: Reading and analyzing texture analyzer data

young_modulus_cryogel_theory

Description

Theoretical calculation of the Young modulus of a cryogel

Usage

young_modulus_cryogel_theory(polymer_volume_fraction=0.01,E_polymer=10e6,structural_factor=1)

Arguments

polymer_volume_fraction	Volume fraction occupied by the polymer phase (rather than the pore space)
E_polymer	Intrinsic Young modulus of the polymer phase
structural_factor	Factor relating the actual mechanical response to the idealized cantilever situation. On the order of 1 for structurally fully intact gels, and 0.01-0.1 for gels where some of the bridges are not formed due to too low viscosity of the monomer

Details

To obtain an order-of-magnitude estimation of the cryogel macroscopic modulus, a following cantilever-based model is used, as described in Beduer 2015

Each pore structure is represented by a single cantilever of the following dimensions:
- Thickness given by polymer_volume_fraction*pore_size
- Length of pore_size/2
- Width given by pore_size/2

Such a cantilever has a spring constant given by:
k=E_polymer*beam_thickness^3*beam_width/4/beam_length^3
=E_polymer*polymer_volume_fraction^3*pore_size^3*pore_size/2/4/(pore_size^3/8)=E_polymer*polymer_volume_fraction^3*pore_size

The Young modulus can be calculated by considering full compression (e.g., compression by pore_size), and then reporting it to the area of a pore (e.g., pore_size^2):
E_cryogel = k*pore_size/pore_size^2=E_polymer*polymer_volume_fraction^3

Maybe a bit surprisingly the global modulus of the cryogel is independent of the pore size.

In reality, the gels tend to be weaker than the idealized calculation because some of the "bridges" are actually interrupted, and maybe also because the sheet-cantilever model simply supposes a too high connectivity. To account for this, it is possible to supply structural_factor, which is used to multiply the cryogel Young modulus (E_cryogel = E_polymer*polymer_volume_fraction^3*structural_factor).

Value

Macroscopic Young modulus of the cryogel

Author(s)

Thomas Braschler

References

Beduer A, Braschler T, Peric O, Fantner GE, Mosser S, Fraering PC , Bencherif SA, Mooney DJ, Renaud P: A compressible scaffold for minimally invasive delivery of large intact neuronal networks, Adv Healthc Mater, 2015, 4(2):301-12, https://doi.org/10.1002/adhm.201400250

Examples

young_modulus_cryogel_theory()

tbgitoo/textureAnalyzerGels documentation built on March 30, 2022, 4:53 a.m.