Objective

The purpose of this study is to develop a mathematical model for efficient prediction of the packing density of different filler formulations in dental resin composites (DRCs), and to study properties of DRCs at the maximum filler loading (MFL), thereby providing an effective guidance for the design of filler formulations in DRCs to obtain excellent properties.

Methods

The packing density data generated by discrete element model (DEM) simulation were used to re-derive the parameters of 3-parameter model. The modifier effect was also induced to modify the 3-parameter model. DRCs with 10 filler formulations were selected to test properties at the MFL. The packing densities of binary and ternary mixes in DRCs were calculated by 3-parameter model to explore the regularity of composite packing.

Results

The predicted packing density was validated by simulation and experimental results, and the prediction error is within 1.40 vol%. The optimization of filler compositions to obtain a higher packing density is beneficial to enhancing the mechanical properties and reducing the polymerization shrinkage of DRCs. In binary mixes, the maximum packing density occurs when the volume fraction of small fillers is 0.35−0.45, and becomes higher with the reduction of particle size ratio. In ternary mixes, the packing density can reach the maximum value when the volume fractions of large and small fillers are in the 0.5−0.75 and 0.15−0.4 ranges, respectively.

Significance

The modified 3-parameter model can provide an effective method to design the multi-level filler formulations of DRCs, thereby improving the performance of the materials.

中文翻译：

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有效预测牙科树脂复合材料中无机填料的填充密度以获得优异的性能

客观的

本研究的目的是建立一个数学模型来有效预测牙科树脂复合材料 (DRCs) 中不同填料配方的堆积密度，并研究 DRCs 在最大填料负载 (MFL) 下的性能，从而提供有效的指导用于设计 DRC 中的填料配方以获得优异的性能。

方法

离散元模型 (DEM) 模拟生成的堆积密度数据用于重新推导 3 参数模型的参数。还引入了修改器效应来修改 3 参数模型。选择具有 10 种填料配方的 DRC 来测试 MFL 的性能。通过三参数模型计算DRCs中二元和三元混合物的堆积密度，探索复合填料的规律性。

结果

通过模拟和实验结果验证了预测的堆积密度，预测误差在1.40 vol%以内。优化填料组成以获得更高的填充密度有利于提高 DRC 的机械性能和降低聚合收缩率。在二元混合物中，当小填料的体积分数为 0.35-0.45 时出现最大堆积密度，并随着粒径比的减小而增大。在三元混合物中，当大、小填料的体积分数分别在0.5-0.75和0.15-0.4范围内时，堆积密度可以达到最大值。

意义

修正后的三参数模型可以为设计DRCs的多级填料配方提供一种有效的方法，从而提高材料的性能。