Model with one particle embedded inside the specimen

model with one particle embedded inside the speciement

first part

First, we consider caseⅠ: when the particle with fixed size (Rparticle=1 μm) is embedded inside the hydrogel, letting the depth, where particle embedded, Δh vary.

Indentation response

The indentation responses of four models (Δh=-0.5 μm, -1 μm, -2 μm, and -3 μm) are plotted in Fig. 4 (a), in which the load is normalized against the indentation response of a pure hydrogel, with a maximum indentation depth of 1.5 μm.

result 1

It can be seen that the load-indentation response is sensitive to the depth the particle is embedded at, when it is directly underneath the indenter.

Comparison

When comparing the cases without particles and with the case of Δh=-0.5 μm, the reaction force in the case with one particle is much higher than in the former; the discrepancy becomes less significant when particle is embedded deeper under the indentation surface (absolute value of Δh becomes greater).

Indentation combinined with AFM

The indentation depth-dependent apparent modulus Eapp was then calculated with same Matlab program (using the Hertz model) as introduced in AFM experimental section, herein relation of modulus vs. indentation depth for four different models (Δh=-0.5 μm, -1 μm, -2 μm, and -3 μm) are summarized in Fig. 4-(b).

result2

At shallow indentation, Eapp in models with one particle inside the specimen, directly related to Δh, are higher than that of pure hydroge

Translation

首先，我们考虑情况Ⅰ:当固定大小的颗粒(Rparticle=1 μm)嵌入水凝胶中时，让颗粒嵌入的深度Δh变化。

Four different model

四种模型(Δh=-0.5 μm、-1 μm、-2 μm和-3 μm)的压痕响应如图4所示，其中载荷与最大压痕深度为1.5 μm的纯水凝胶的压痕响应归一化。

result 1

可以看出，当粒子处于压痕器的正下方时，载荷-压痕响应对粒子嵌入的深度很敏感。
对比无颗粒和Δh=-0.5 μm时，有颗粒时的反作用力远大于无颗粒时;颗粒嵌入压痕面下方越深，差异越小(Δh绝对值越大)。

AFM combining MATLAB

利用AFM实验部分介绍的相同Matlab程序(采用Hertz模型)计算压痕深度随表观模量Eapp，其中四种不同模型(Δh=-0.5 μm、-1 μm、-2 μm和-3 μm)模量与压痕深度的关系如图4所示。

result2

在浅压痕处，与Δh直接相关的单颗粒模型的Eapp高于纯hydroge模型。