Abstract Alkyl Ketene Dimer (AKD) is a sizing agent commonly introduced into cellulose substrates during papermaking to improve its hydrophobicity. High-pressure impregnation of this solute with supercritical carbon dioxide (scCO2) into cellulose and other substrates can achieve excellent hydrophobicity of the substrate, and may be used as an alternative technique to traditional coating (sizing) methods. In this study, the solubility of AKD in scCO2 was modelled using Peng-Robinson equation of state (PR-EOS) with van der Waals mixing rules, and volume-translated PR-EOS (VTPR). Given the unavailability of AKD's experimental critical properties and vapor pressure data, group contribution estimation methods (GCEM) were used to determine these physical constants. Available experimental data from another research group, collected using cloud-point and extraction methods, was used to regress binary interaction parameters and compare the resulting model's capability in predicting solubility. The models for each experimental method predicted crossover pressures within a small range, but fitted the cloud-point experimental data much better than the extraction data, showing good agreement at pressures beyond 15 MPa and all temperatures investigated. The VTPR model showed the least agreement with experimental data. A relative standard deviation of 0.26 was obtained between modelled and experimental data for the cloud-point method, and 0.42 for the extraction method data. The models were confirmed with the Chrastil equation, and strongly demonstrated the linear relationships predicted by this expression. The models additionally predicted a change in temperature dependence around the critical density, with a common linear relationship independent of temperature being observed at densities below the critical value. This newly observed behavior, not predicted by the Chrastil equation, sets the groundwork for further fundamental investigations, while the developed models will assist the design of alternative sizing processes involving AKD and scCO2.

中文翻译：

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模拟烷基乙烯酮二聚体在超临界二氧化碳中的溶解度：Peng-Robinson、群贡献方法以及临界密度对溶解度预测的影响

摘要 烷基乙烯酮二聚体（AKD）是一种在造纸过程中通常引入纤维素基材以改善其疏水性的施胶剂。将此溶质与超临界二氧化碳 (scCO2) 高压浸渍到纤维素和其他基材中可以实现基材优异的疏水性，并可用作传统涂层（施胶）方法的替代技术。在本研究中，AKD 在 scCO2 中的溶解度使用具有范德华混合规则的彭-罗宾逊状态方程 (PR-EOS) 和体积平移 PR-EOS (VTPR) 建模。鉴于 AKD 的实验临界特性和蒸气压数据不可用，因此使用群贡献估计方法 (GCEM) 来确定这些物理常数。来自另一个研究小组的可用实验数据，使用浊点和提取方法收集，用于回归二元相互作用参数并比较所得模型在预测溶解度方面的能力。每种实验方法的模型都预测了小范围内的交叉压力，但比提取数据更适合浊点实验数据，在超过 15 MPa 的压力和所有研究温度下显示出良好的一致性。VTPR 模型与实验数据的一致性最小。浊点法的模拟数据和实验数据之间的相对标准偏差为 0.26，提取法数据的相对标准偏差为 0.42。这些模型通过 Chrastil 方程得到证实，并有力地证明了该表达式预测的线性关系。这些模型还预测了临界密度附近温度依赖性的变化，在低于临界值的密度下观察到与温度无关的共同线性关系。这种新观察到的行为，不是由 Chrastil 方程预测的，为进一步的基础研究奠定了基础，而开发的模型将有助于设计涉及 AKD 和 scCO2 的替代上浆工艺。