The hydrogen diffusivities of acrylonitrile butadiene rubber (NBR) composites with different types and contents of carbon black (CB) fillers were investigated in the exposure pressure range of 0.5–10 MPa using a volumetric analysis system. These measured diffusivities exhibited distinct pressure-dependent behavior. The diffusivities of unfilled NBR and NBR composites containing medium-thermal CB filler decreased from 39.7 × 10−11 m2/s to 9.4 × 10−11 m2/s as the pressure increased. On the other hand, the pressure-dependent diffusivities of NBR composites containing high-abrasion furnace, fast-extrusion furnace and semireinforcing furnace CB fillers revealed left-biased unimodal shaped curves, with peak values ranging from 19.7 × 10−11 m2/s to 5.6 × 10−11 m2/s. To model this observed behavior, the diffusion resistance theory with a heterogeneous NBR–CB composite and a fractal porous structure for H2 was introduced. The theoretical parallel diffusion resistance model was found to coexist independently as the surface, Knudsen, and bulk diffusion phases. This theoretical multiphase modeling was applied to the measured diffusivities, determining diffusion resistance parameters for each phase. The obtained individual parametric characteristics for each diffusion were interpreted by considering the CB filler content and volume fraction of the filler. As a result, the diffusivities calculated by multiphase diffusion modeling were in quite agreement with the measured diffusivities for all investigated specimens, where the determined squared correlation coefficient (R2) by fitting process was in the range from 0.69 to 0.97.

中文翻译：

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不同填料丁腈橡胶-炭黑复合材料分形多孔结构中压力依赖性氢扩散率的多相建模


使用体积分析系统研究了不同类型和含量的炭黑（CB）填料的丁腈橡胶（NBR）复合材料在0.5-10 MPa的暴露压力范围内的氢扩散率。这些测量的扩散率表现出明显的压力依赖性行为。随着压力的增加，未填充的 NBR 和含有中热 CB 填料的 NBR 复合材料的扩散率从 39.7 × 10−11 m2/s 下降到 9.4 × 10−11 m2/s。另一方面，含有高磨损炉、快速挤压炉和半增强炉炭黑填料的 NBR 复合材料的压力相关扩散系数显示出左偏单峰形曲线，峰值范围为 19.7 × 10−11 m2/s 至5.6 × 10−11 平方米/秒。为了模拟这种观察到的行为，引入了异质 NBR-CB 复合材料和 H2 分形多孔结构的扩散阻力理论。理论平行扩散阻力模型被发现作为表面、克努森和体扩散相独立共存。该理论多相模型应用于测量的扩散率，确定每个相的扩散阻力参数。通过考虑CB填料含量和填料体积分数来解释所获得的每次扩散的单独参数特征。结果，通过多相扩散模型计算的扩散率与所有研究样本的测量扩散率非常一致，其中通过拟合过程确定的平方相关系数（R2）在0.69至0.97的范围内。