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Modeling mechano-chromatic lamellar gels

Wei Hong's picture

Consisting of alternating swelling and nonswelling polymeric layers (SLs and NLs), lamellar gels are 1D photonic crystals with tunable optical properties.  The lamellar structure induces a constraint between the SLs and the NLs, resulting in an anisotropic swelling behavior coupled with deformation.  The coupling gives rise to the mechano-chromatic effect, and quantitative understanding of it is the key to many applications.  This letter formulates a nonlinear continuum model for lamellar gels by considering the constrained swelling of SLs and the anisotropic deformation in both types of layers.  A finite-element method is further developed to simulate the response to non-uniform deformation.


Lianhua Ma's picture

Dear Wei, Thanks for posting your paper.  I had a look on this interesting paper and I have a question to be clarified. As you mentioned, the lamellar gel is a composite composed of two distinct regions: SLs and NLs. I noticed that you treated this composite as a homogeneous continuum, and derived the coupled constitutive relations by writing the total free energy density function. To my knowledge, the total free energy density for a composite should be given in terms of the volume fraction and the stretches of every phase. In Eq.(3) and(4), the SL and NL volume fractions were incorporated into the free energy function Wm and Wb. However, the SL volume fraction was missing in Eq.(2) Wn. I am not sure why the SL volume fraction and lamda0^3 (in the last log.term) were excluded? Maybe the effect of SL volume fraction was reflected by N (the number of HPN chains per reference volume)?




Wei Hong's picture

Dear Lianhua,

Glad that you are interested in this work.  You are absolutely correct.  Eq. (2) has a coefficient N, which is the number of polymer chains in the reference state.  Since we take the as-synthesized state as the reference state, N already includes the information of the SL volume fraction.

Happy New Year,


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