Role of sorbent surface functionalities and microporosity in 2,2′,4,4′-tetrabromodiphenyl ether sorption onto biochars

The study provides insight into the combined effect of sorbent surface functionalities and microporosity on2,2 ′,4,4 ′-tetrabromodiphenyl ether （BDE-47） sorption onto biochars. A series of biochars prepared underdifferent conditionswere used to test their sorption behaviorswith BDE-47. The extents of sorption behaviorswere parameterized in terms of the single-point adsorption equilibrium constant （Koc ） at three equilibrium concentration （C e ） levels （0.001Sw （solubility）, 0.005Sw , and 0.05Sw ）whichwasdetermined using the Freundlich model. To elucidate the concentration-dependentdominant mechanisms for BDE-47 sorption onto biochars, K ocwas correlatedwith four major parameters using multiple parameter linear analysis accompaniedwith significance testing. The results indicated that at low concentration （Ce = 0.001Sw ）, the surface microporosity term,which represented a pore-filling mechanism, contributed significantly to this relationship,while as concentrationwas increased to higher levels, surface functionality related to surface adsorption began to take thedominant role,whichwas further confirmed by the results of Polanyi-based modeling. Given the above results, adual mode model based on Dubinin-Radushkevich andde Boer-Zwikker equationswas adopted to quantitatively assess the changes of significance of surface adsorption aswell as that of pore fillingwith sorption processdevelopment. In addition, UV spectra of four typical aromatic compoundswhich represented the key structural fragments of biochars before and after interactionswith BDE-47were analyzed todetermine the active functional groups and supply complementary evidence for thedominant interaction force for surface adsorption, based onwhich π-π electron-donor-acceptor interactionwas proposed to contribute greatly to surface adsorption.

HIERARCHICAL STOCHASTIC FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS

In this paper, the hierarchical approach is adopted for series representation of the stochastic nodal displacement vector using the hierarchical basis vectors, while the Karhunen- Loire series expansion technique is employed to discretize the random field into a set of random variables. A set of hierarchical basis vectors are defined to approximate the stochastic response quantities. The stochastic variational principle instead of the projection scheme is adopted to develop a hierarchical stochastic finite element method （HSFEM） for stochastic structures under stochastic loads. Simplified expressions of coefficients of governing equations and the first two statistical moments of the response quantities in the schemes of the HSFEM are developed, so that the time consumed for computation can be greatly reduced. Investigation in this paper suggests that the HSFEM yields a series of stiffness equations with similar dimensionality as the perturbation stochastic finite element method （PSFEM）. Two examples are presented for numerical study on the performance of the HSFEM in elastic structural problems with stochastic Young＇s Modulus and external loads. Results show that the proposed method can achieve higher accuracy than the PSFEM for cases with large coefficients of variation, and yield results agreeing well with those obtained by the Monte Carlo simulation （MCS）.