Acid−Base and Metal Complexation Chemistry of Phosphino-polycarboxylic Acid under High Ionic Strength and High Temperature

Phosphino-polycarboxylic acid (PPCA), a phosphorus-labeled linear polymer, has been widely used for controlling scale formation in the oil/gas field and water treatment processes because of its strong scale-inhibiting capability, high thermal stability, and environmental acceptability. PPCA is similar to poly(acrylic acid) with about 1% (w/w) phosphorus added to facilitate analytical measurement. In this study, the thermodynamic properties of PPCA and Ca−PPCA complexes in aqueous solution have been studied by combining electrostatic theory with potentiometric titrations. The acid−base and calcium complex solution chemistry of PPCA has been determined from 0.01 to 5 m ionic strength and from 25 to 90 °C. For simplicity, PPCA is reduced to a hypothetical, averaged monoacid, HA, with the same concentration of the PPCA monomer. Both proton and calcium dissociation reactions are defined as 1:1 type hypothetical reactions. That is, HA ↔ H + + A - with p K H = pH − log(θ u /θ H ) and Ca(A···A) ↔ Ca 2+ + (A···A) 2 - with p K Ca = pCa − log(θ u /θ Ca ) where θ u stands for the dissociated fraction of HA, θ H stands for the protonated fraction, θ Ca stands for the calcium-complexed fraction, (A···A) 2 - is a unit of arbitrary combinations of two dissociated A - units, and pCa is the negative logarithm of the free calcium concentration. The corresponding constants for these two reactions, K H and K Ca, are determined from the acid/base titrations. These constants are then fitted with a linear electrostatic model: p K H = p K H,int + b elec θ u and p K Ca = p K Ca,int + 2 b elec θ u where K H,int and K Ca,int are intrinsic constants at ionic strength ( I ), and refer to the condition of zero dissociation, and b elec is an electrostatic factor determined from polyelectrolyte theory. Both p K H and p K Ca are expressed as a function of ionic strength and temperature through p K H,int, p K Ca,int, and b elec: p K H,int = 4.856 − 0.984 I 1/2 +0.253 I − 198.7/ T for proton dissociation, p K Ca, int = 3.968 − 2.671 I 1/2 + 0.750 I − 1102.3/ T for Ca−PPCA dissociation, and b elec = 2.778 − 1.081 I 1/2 + 0.226 I, where I stands for ionic strength in molality and T stands for temperature in Kelvin. The fitting results show that the electrostatic factor b elec is not significantly influenced by temperature, which is reasonable according to electrostatic theory. These results can be used to analyze the equilibria of PPCA in a solution, given pH, ionic strength, temperature, and total metal (Ca 2+ here) concentration.