Adsorption of Eu(III) on titanate nanotubes studied by a combination of batch and EXAFS technique

The effects of pH,contact time and natural organic ligands on radionuclide Eu(Ⅲ) adsorption and mechanism on titanate nanotubes(TNTs) are studied by a combination of batch and extended X-ray absorption fine structure(EXAFS) techniques.Macroscopic measurements show that the adsorption is ionic strength dependent at pH < 6.0,but ionic strength independent at pH > 6.0.The presence of humic acid(HA) /fulvic acid(FA) increases Eu(Ⅲ) adsorption on TNTs at low pH,but reduces Eu(Ⅲ) adsorption at high pH.The results of EXAFS analysis indicate that Eu(Ⅲ) adsorption on TNTs is dominated by outer-sphere surface complexation at pH < 6.0,whereas by inner-sphere surface complexation at pH > 6.0.At pH < 6.0,Eu(Ⅲ) consists of ～ 9 O atoms at REu?O ≈ 2.40  in the first coordination sphere,and a decrease in NEu-O with increasing pH indicates the introduction of more asymmetry in the first sphere of adsorbed Eu(Ⅲ).At long contact time or high pH values,the Eu(Ⅲ) consists of ～2 Eu at REu-Eu ≈ 3.60  and ～ 1 Ti at REu-Ti ≈ 4.40 ,indicating the formation of inner-sphere surface complexation,surface precipitation or surface polymers.Surface adsorbed HA/FA on TNTs modifies the species of adsorbed Eu(Ⅲ) as well as the local atomic structures of adsorbed Eu(Ⅲ) on HA/FA-TNT hybrids.Adsorbed Eu(Ⅲ) on HA/FA-TNT hybrids forms both ligand-bridging ternary surface complexes(Eu-HA/FA-TNTs) as well as surface complexes in which Eu(Ⅲ) remains directly bound to TNT surface hydroxyl groups(i.e.,binary Eu-TNTs or Eu-bridging ternary surface complexes(HA/FA-Eu-TNTs)).The findings in this work are important to describe Eu(Ⅲ) interaction with nanomaterials at molecular level and will help to improve the understanding of Eu(Ⅲ) physicochemical behavior in the natural environment.     

Full characterization of the embedding relations between α-modulation spaces

In this paper, we consider the embedding relations between any two a-modulation spaces. Based on an observation that the a-modulation space with smaller a can be regarded as a corresponding decomposition space associated with a-covering for larger a, we give a complete characterization of the Fourier multipliers between a-modulation spaces with different a. Then we establish a full version of optimal embedding relations between a-modulation spaces.