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Hierarchical porous Si can breath lithium without causing volume change

Sulin Zhang's picture

Electrochemical lithiation/delithiation causes 300% volume change in solid silicon. Whereas hierarchical porous Si synthesized by GM causes negligible apparent volume change when breathing lithium.  

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Sulin Zhang's picture

comments?

Shuze Zhu's picture

Dear Prof. Zhang, 

I enjoyed a lot reading this paper. The porous structure is a really cute solution. Intuitively this porous structure should be expanding in every direction geometrically but it is not. 

The model used in your simulation is a scaled-up model of the original structure without nano-scale nanopores. I am wondering if a scaled-down porous structure model could also demonstrate this zero expansion effect. Many thanks. 

Best,

Shuze

Sulin Zhang's picture

Thanks, Shuze, for your comment. I have been taking a couple of days off for Thanksgiving Holiday. So sorry for my tardy reply. 

We can always pick up a representative volume unit from the porous shell to study the phase-dependent constitute law (we have already done this using MD with reactive force field). However, it is computationally challenging by using a fine-scale model to simulate lithiatioin/delithiation behavior of the entire hierarchical porous sphere, i.e., including both the porous shell and the hollow core. In the paper, we used the phase-dependent (lithium concentration dependent) constitutive law obtained from MD simulations for the shell, and constructed a continuum model to simulate the cycling behavior. I am still deliberating whether it is worth publishing the MD data in a separate paper.  

Sulin Zhang's picture

Thanks, Shuze, for your comment. I have been taking a couple of days off for Thanksgiving Holiday. So sorry for my tardy reply. 

We can always pick up a representative volume unit from the porous shell to study the phase-dependent constitute law (we have already done this using MD with reactive force field). However, it is computationally challenging by using a fine-scale model to simulate lithiatioin/delithiation behavior of the entire hierarchical porous sphere, i.e., including both the porous shell and the hollow core. In the paper, we used the phase-dependent (lithium concentration dependent) constitutive law obtained from MD simulations for the shell, and constructed a continuum model to simulate the cycling behavior. I am still deliberating whether it is worth publishing the MD data in a separate paper.  

Zheng Jia's picture

Dear Prof. Zhang,

Thank you for posting this great paper, a very decent and inspiring piece. I have a question regarding the lithiation process of meso-porous lithiated silicon.

This paper clearly elucidates the big picture of the lithiation process of meso-porous silicon: the excessive volume change is accommodated by the shrinkage of meso-pores rather than the overall expansion of the whole silicon particle. In the simulation, the nano-pores are not directly modelled; their influence is considered through an expression Y=A(1-P)^3 as a stiffness descriptor. Consequently, what remains opaque is a clear mechanistic understanding on the physical process of shrinkage of each single nano-pore. As we know, compressing a spherical nano-pore uniformly until disappearance can be very energetically costly. I wonder what physical mechanism drives each nano-pore to disappear. In my mind, there might be two possible reasons:

1) Since the average size of the nano-pore is only 3.2nm and the porosity is high (~60%-70%), surface energy of the nano-pore inner surface may play a vital role here. In response to far-field compression, each nano-pore tends to shrink significantly to minimize its inner surface area. 2) Because of the high porosity, silicon shells between neighboring nano-pores are very thin in thickness. As a result, the meso-porous structure can be regarded as a thin-shell network. The far-field compression exerted by lithiation of outer part of silicon particle can easily cause buckling/collapse of the inner network structure and thus fill the nano-pores.

Here are just my 2 cents. I would like to ask for your insights on the reason why each silicon nano-pore disappears.

Sulin Zhang's picture

Dear Jia,

Thanks for your comments and great questions arised. 

We did not consider the compression effect from the nanoscale. Rather we were more enagaged in developing a physically sound phase-dependent constitutive law for the porous shell. We consider the shrinkage of the nanopore is due to the lithiation induced expansion of the nanocrystals. Considering the volume of the Si nanocrystals is 1, the volume of the nanopore takes up to 2 (with given porosity) in the pre-lithiation stage,  lithiation would generate an excessive volume of 3 that is sufficient to fill up the nanopores. 

Indeed the wave-like lithiation generates a clear interphase that separates the lithiated and unlithiated phases and seems to be sharp. This indicates incompatible strains and stresses in the lithiated and unlithiated phases. However, we did not consider the buckling effect of the porous network under the lithiation induced compressive stress. Our collaborator did not report/observe such a buckling phenomenon. But that does not mean buckling of the porous network does not occur - this is a great thought.  

 

 

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