## 1 Introduction  
The complexation of metal ions by polymer-supported reagents is important to many applications including recovery in environmental remediation [1], pre-concentration in analytical determinations [2], and pharmaceuticals [3]. The extent of complexation is determined by the stability of the complex. Depending on the ligand, complexation of metal ions can involve ion exchange or coordination. Metal ions can coordinate to neutral oxygen such as the phosphoryl oxygen [4] or nitrogen donors such as the pyridyl nitrogen [5], or bond ionically with ion exchange ligands such as carboxylate [6]. Differences in the strength of the coordinate covalent bond have been used to separate trivalent actinides from lanthanides [7]. More than one ligand can coordinate to metal ions and this is the basis of synergistic extraction [8].  
Phosphorus-based substituents form a versatile set of ligands which permit the synthesis of complexants with a wide range of metal ion affinities [9]. Immobilized phosphinic, phosphonic, and phosphoric acids are important ion-complexing reagents because of their ability to ion exchange with metal ions under dilute acid conditions and coordinate to metal salts through the phosphoryl oxygen under more acidic solutions. Hydrogen bonding has been found to increase the ionic affinities of neutral coordinating polymers: diethyl phosphate ligands immobilized onto polystyrene through polyol scaffolds have increased ionic affinities due to hydrogen bonding at the phosphoryl oxygen by the -OH groups of the polyol [10]. The affinity of the phosphoryl oxygen for divalent ions increased as their polarizability increased and was significant from 0.01 M HNO\({}_{3}\), but greatly decreased as the solution acidity increased.  
Having established the importance of hydrogen bonding between the phosphoryl oxygen and an -OH group on a neighboring polyol, the focus of subsequent study became the effect of hydrogen bonding between the phosphoryl oxygen and an acidic proton in the presence of a neighboring polyol from glycerol (Gly) and pentaerythritol (Penta), in the absence of a neighboring -OH using ethylene glycol (EG1) as a spacer from the polystyrene, and with only the acidic -OH in diprotic phosphonic acid (DPA). Figure 1 shows the structures of the monoprotic phosphorylated ethylene glycol (pEG1M), glycerol (pGlyM), and pentaerythritol (pPentaM), as well as DPA. A recent report has shown an effect of hydrogen bonding in the affinity for Eu\({}^{3+}\): monoprotic glycols have higher affinities compared to DPA due to decreased hydrogen bonding [11]. Given that the affinities for divalent transition metal ions by the purely coordinating diethyl ester resins decreased to negligible levels as acidity increased from 0.01 M HNO\({}_{3}\)[10], the objective of the current report was to determine whether divalent and trivalent metal ion affinities of phosphate ligands capable of ion exchange would be affected by hydrogen bonding and whether these polymers would have higher affinities than neutral coordinating phosphate ligands. These polymers are analogous to the neutral phosphates but with one -OEt group replaced by-OH. The metal sorption behavior for a set of divalent (Pb(II), Cd(II), Cu(II), and Zn(II)) and trivalent (Fe(III), Al(III), La(III), and Lu(III)) ions by the monoprotic polymers was compared to the coordinating polymers as well as the phosphonic acid. The metal ions were chosen as representative of a range of polarizabilities [12].