Model development of aqueous diffusion softening transition in thermoplastic polyurethane cellulose nanocrystal composites

Cellulose: A Review of Water Interactions, Applications in Composites, and Water Treatment

“…More recently, some work by Bortner’s group has demonstrated that diffusion into a polymer matrix–CNC composite is increased with the addition of CNCs into a PU/CNC composite and that the dry and wet state mechanical properties can be modeled using percolation and Harpin–Kardos models, respectively. The percolation model is governed by the equation ,, bold-italicE ′ = false( 1 − 2 ψ + normalΨ X normalr false) E normals ′ E normalr ′ + false( 1 − X normalr false) ψ E r ′ 2 false( 1 − X normalr false) E r ′ + false( X normalr − normalΨ false) E s ′ with ψ = X r true( X normalr − X normalc 1 − X normalc true) 0.4 where E ′ is the storage modulus of the composite, E s ′ and E r ′ are the experimentally determined moduli of the matrix and the reinforcing phase, respectively, X r is the volume fraction of the reinforcing phase, X c is the critical per...…”

“…More recently, some work by Bortner's group 138 has demonstrated that diffusion into a polymer matrix−CNC composite is increased with the addition of CNCs into a PU/ CNC composite and that the dry and wet state mechanical properties can be modeled using percolation and Harpin− where E′ is the storage modulus of the composite, E s ′ and E r ′ are the experimentally determined moduli of the matrix and the reinforcing phase, respectively, X r is the volume fraction of the reinforcing phase, X c is the critical percolation volume fraction, and ψ is the volume fraction of the reinforcing phase that take part in load transfer. It is worth going back to the original papers on these models, specifically the Takayanagi model, 139 and the further developments by Ouali et al 140 for multiphase polymers, although their equation is largely based on the former.…”

“…More recently, some work by Bortner’s group has demonstrated that diffusion into a polymer matrix–CNC composite is increased with the addition of CNCs into a PU/CNC composite and that the dry and wet state mechanical properties can be modeled using percolation and Harpin–Kardos models, respectively. The percolation model is governed by the equation ,, with where E ′ is the storage modulus of the composite, E s ′ and E r ′ are the experimentally determined moduli of the matrix and the reinforcing phase, respectively, X r is the volume fraction of the reinforcing phase, X c is the critical percolation volume fraction, and ψ is the volume fraction of the reinforcing phase that take part in load transfer.…”

Dispersibility Characterization of Cellulose Nanocrystals in Polymeric-Based Composites

“…Pritchard et al calculated the theoretical storage modulus through the percolation network model agrees with the actual modulus, indicating good dispersion. 242 These results imply good dispersibility of the CNC in the matrix, while the deviation of higher content is related to the agglomeration of the CNC. 159 In addition, Wang et al corresponded the signal intensity of each point in the Raman mapping images to the volume fraction of nanofillers and then calculated the local storage modulus value of each point to obtain the distribution of local storage modulus in the composite material.…”

“…Pritchard et al. calculated the theoretical storage modulus through the percolation network model agrees with the actual modulus, indicating good dispersion . These results imply good dispersibility of the CNC in the matrix, while the deviation of higher content is related to the agglomeration of the CNC .…”