Abstract In the last two decades, Mesoporous Silica Nanoparticles (MSNs) were given a substantial interest due to their unique properties and wide range of applications. The size is a key feature which determines the use of MSNs. Transmission Electron Microscopy (TEM) is a standard technique for MSNs’ size determination. Despite reliable, yet it has some drawbacks, being time consuming, destructive and requires complex sample preparation. Therefore, this work aims at introducing Low-angle X-ray Scattering (LAXS) as a time-saving, non-destructive and inexpensive tool for the determination of the size of MSNs. Different sizes of MSNs are prepared using different concentrations of ammonium hydroxide (catalyst) and their corresponding LAXS profiles are recorded. LAXS profile parameters (peak position and area under peak) are found to exhibit a strong linear dependence on the size of MSNs determined using the standard TEM technique. Moreover, the pore sizes calculated from LAXS profiles show linear dependence on the size of MSNs. For MSNs in the range from 60 to 170 nm, two mathematical linear fitting equations are introduced for the determination of the size of MSNs by direct substitution using LAXS profile parameters. One more equation is introduced for the calculation of the size of MSNs directly from their pore size.

中文翻译：

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用于测定介孔二氧化硅纳米颗粒尺寸的低角度 X 射线散射

摘要 在过去的二十年里，介孔二氧化硅纳米颗粒 (MSNs) 由于其独特的性质和广泛的应用而受到广泛关注。大小是决定 MSN 使用的关键特征。透射电子显微镜 (TEM) 是 MSN 尺寸确定的标准技术。尽管可靠，但它也有一些缺点，即耗时、破坏性和需要复杂的样品制备。因此，这项工作旨在引入低角 X 射线散射 (LAXS) 作为一种省时、无损且廉价的工具，用于确定 MSN 的大小。使用不同浓度的氢氧化铵（催化剂）制备不同尺寸的 MSN，并记录其相应的 LAXS 剖面。发现 LAXS 剖面参数（峰位置和峰下面积）对使用标准 TEM 技术确定的 MSN 的大小表现出很强的线性依赖性。此外，从 LAXS 剖面计算的孔径显示出对 MSN 大小的线性依赖性。对于 60 到 170 nm 范围内的 MSN，引入了两个数学线性拟合方程，用于通过使用 LAXS 剖面参数直接替换来确定 MSN 的大小。另一个方程被引入用于直接从其孔径计算 MSN 的大小。引入了两个数学线性拟合方程，用于通过使用 LAXS 剖面参数直接替换来确定 MSN 的大小。另一个方程被引入用于直接从其孔径计算 MSN 的大小。引入了两个数学线性拟合方程，用于通过使用 LAXS 剖面参数直接替换来确定 MSN 的大小。另一个方程被引入用于直接从其孔径计算 MSN 的大小。