S1

SUPPORTING INFORMATION

Impacts of Antiscalants on the Formation of Calcium Solids:

Implication on Scaling Potential of Desalination Concentrate

Tushar Jain†, Edgar Sanchez†, Emily Owens-Bennett‡,

Rhodes Trussell‡, Sharon Walker† and Haizhou Liu*†

† Department of Chemical and Environmental Engineering, University of California at

Riverside, Riverside, CA, 92521 USA

‡ Trussell Technologies, Inc. Pasadena, CA, 91101 USA

* Corresponding author, e-mail: haizhou@engr.ucr.edu, phone (951) 827-2076, fax

(951) 827-5696.

Submitted to Environmental Science: Water Research & Technology

Electronic Supplementary Material (ESI) for Environmental Science: Water Research & Technology.This journal is © The Royal Society of Chemistry 2019

S2

Table of Contents

Figure S1 Molecular structures of the three most widely used phosphonic antiscalants that

are examined in this study. ............................................................................................ S3

Figure S2 The negligible effect of pH buffer concentration on the precipitation of

Ca5(PO4)3OH(s) in presence of antiscalant EDTMP. ....................................................... S4

Text S1 Kinetics modeling of the precipitation of calcium solids .................................. S5

Figure S3 (A) Kinetic modeling on the precipitation of Ca5(PO4)3OH(s). ....................... S6

Figure S4 X-ray diffraction traces of samples. .............................................................. S7

Text S2 Calculations on calcium complexation with different antiscalants .................... S8

Table S1 Calcium-antiscalant complexes and their stability constants. ........................ S10

Figure S5 The impact of pH on the fraction of total dissolved calcium existing as free

calcium in the presence of each antiscalant. ................................................................. S11

Text S3 Calculations for net charge of different antiscalants at different pH ................ S12

Table S2 Protonation constants of NTMP, EDTMP and DTPMP ................................ S12

Figure S6 The impact of pH on the charge of each antiscalant. ................................... S14

Figure S7 Impact of the antiscalant DTPMP on the zeta potential of hydroxyapatite at

different pHs ............................................................................................................... S15

Figure S8 The effect of EDTMP dosage on the extension of induction time for CaSO4(s)

and CaCO3(s) precipitation. .......................................................................................... S16

Figure S9 The impact of varying dosage of EDTMP at different saturation indices on the

induction time for Ca5(PO4)3OH(s), CaCO3(s) and CaSO4(s) nucleation .......................... S17

Figure S10 Impact of saturation index of CaCO3(s) and CaSO4(s) on activation energy of

nucleation at varying EDTMP dose ............................................................................. S18

Figure S11 Impact of saturation index of CaCO3(s) and CaSO4(s) on critical radius of

nucleation at varying EDTMP dose ............................................................................. S19

S3

Figure S1 Molecular structures of the three most widely used phosphonic antiscalants that

are examined in this study.

NTMP: nitrilotris(methylenephosphonic acid);

EDTMP: ethylenediaminetetra(methylenephosphonic acid);

DTPMP: diethylenetriaminepenta(methylenephosphonic acid)

NTMP

DTPMP

EDTMP

S4

Figure S2 The negligible effect of tris(hydroxymethyl)aminomethane (TRIS) pH buffer

concentration on the precipitation of Ca5(PO4)3OH(s) in presence of antiscalant EDTMP.

Results showed that the presence of different TRIS buffer concentrations did not affect the

precipitation kinetics. [Ca2+] = 10 mM; [PO43-] = 31 mg P/L; saturation index = 14.8;

[EDTMP] = 3 µM; pH = 7.8; ionic strength = 100 mM.

S5

Text S1 Kinetics modeling of the precipitation of calcium solids

The backbone of the model is the Michaelis-Menten equation that gives the relationship

between the turbidity of the precipitation and the time of the precipitation reaction (Eqn.

1):

𝑇 = 𝑇#$% 𝑡

𝑡 +𝐾# (1)

Where, T is the turbidity of the precipitation (NTU) at time t (seconds), Tmax is the

maximum turbidity of the precipitation reaction (NTU) and Km is the Michaelis-Menten

half-velocity constant (seconds).

Figure S3A shows the experimental data for the precipitation of hydroxyapatite in absence

of antiscalant with time. The Michaelis-Menten type of model as described in equation 1

above is fit for the rapid-precipitation stage of the reaction. The constant, Tmax/Km gives the

rate constant of the precipitation (NTU/second). This kinetic model fits the precipitation of

all calcium solids very well. Figure S3B shows a typically data fitting on the precipitation

of hydroxyapatite with different NTMP and phosphate dosages.

S6

Figure S3 (A) Kinetic modeling on the precipitation of Ca5(PO4)3OH(s). [Ca2+] = 10 mM;

[PO43-] = 22 mg P/L; saturation index = 14.3; [NTMP] = 0 µM; pH = 7.8; [TRIS buffer] =

20 mM; ionic strength = 100 mM. (B) Michaelis-Menten model fitting for precipitation of

Ca5(PO4)3OH(s) at different saturation indices in the presence of varying dosages of NTMP.

[Ca2+] = 10 mM; [PO43-] = 20-32 mg P/L; saturation index = 14.3-14.9; [NTMP] = 0-6 µM;

pH = 7.8; ionic strength = 100 mM; [TRIS buffer] = 20 mM.

0

10

20

30

40

0 5 10 15 20

Turb

idity

(NTU

)

Time (minutes)

Model fit

Experimental data

A

0

20

40

60

80

0 5 10 15 20

Turb

idity

(NTU

)

Time (minutes)

[P] = 22 mg P/L; [NTMP] = 0 µM

[P] = 27 mg P/L; [NTMP] = 3 µM

[P] = 32 mg P/L; [NTMP] = 6 µM

B

S7

Figure S4 X-ray diffraction of precipitated solids. Three scale-forming calcium solids

were confirmed. (A) gypsum, (B) vaterite, (C) hydroxyapatite.

10 20 30 40 50 60 70 80 90

Inte

nsity

(a.u

.)

2 theta (degrees)

Gypsum sample

Gypsum standard

A

10 20 30 40 50 60 70 80 90

Inte

nsity

(a.u

.)

2 theta (degrees)

Vaterite sampleVaterite standard

B

10 20 30 40 50 60 70 80 90

Inte

nsity

(a.u

.)

2 theta (degrees)

Hydroxyaptite sample

Hydroxyapatite standard

C

S8

Text S2 Calculations on calcium complexation with different antiscalants

Mass balance for total calcium gives the equation below:

𝑇𝑂𝑇Ca = {Ca./} + {CaHL}34 + {CaH.L}.4 + {CaH3L}4 + ⋯+ {CaH6L}748

+ {CaOH}/ (2)

Where TOTCa is the total dissolved calcium concentration, and L is the Ligand

(NTMP in the above case, which has a negative six charges for its most deprotonated

species L).

𝛽7 = {CaH64;L}

{Ca./}{H}(74;){L} (3)

The speciation equilibrium for CaOH+, which has a pKa of 12.7 (Visual MINTEQ)

is calculated as below:

{CaOH/} = {Ca./}

104;..A

{H/} (4)

In addition, calcium-antiscalant complexes for NTMP, EDTMP and DTPMP are listed in Table S1.

𝑇𝑂𝑇Ca = {Ca./}B1 +CCaL84

Ca./ D +CCaHL34

Ca./ D + CCaH.L.4

Ca./ D + ECaH3L4

Ca./F

+ ECaH8LCa./

F + CCaOH/

Ca./ DG

(5)

𝑇𝑂𝑇Ca = {Ca./} H1 + 𝛽;{L} + 𝛽.{H/}{L} + 𝛽3{H/}.{L} + 𝛽8{H/}3{L}

+ 𝛽I{H/}8{L} +𝐾{H/}J

(6)

Let K1 + 𝛽;{L} + 𝛽.{H/}{L} + 𝛽3{H/}.{L} + 𝛽8{H/}3{L} + 𝛽I{H/}8{L} +L{MN}

O = 𝐵

S9

𝛼R$SN = 1𝐵 (7)

𝛼R$TUV = 𝛽;{L}𝐵 (8)

𝛼R$MTWV = 𝛽.{H/}{L}

𝐵 (9)

𝛼R$MSTSV = 𝛽3{H/}.{L}

𝐵 (10)

𝛼R$MWTV = 𝛽8{H/}3{L}

𝐵 (11)

𝛼R$MUT = 𝛽I{H/}8{L}

𝐵 (12)

𝛼XYZ[N = 𝐾

{𝐻/}𝐵 (13)

Where, 𝛼R$SN ,𝛼R$TUV , 𝛼R$MTWV, 𝛼R$MSTSV, 𝛼R$MWTV, 𝛼R$MUT and 𝛼R$]MN is the fraction of total dissolved calcium existing as Ca2+, CaL84, CaHL34, CaH.L.4, CaH3L4, CaH8L and CaOH/, respectively.

The fraction of total dissolved calcium existing as Ca2+ as a function of solution pH is plotted in Figure S4.

S10

Table S1 Calcium-antiscalant complexes and their stability constants.

# Calcium ligand complexes with NTMP Logβi a (1) Ca./ +L^4 ↔ CaL84 7.6 (2) Ca./ +H/ +L^4 ↔ CaHL34 16.6 (3) Ca./ +2H/ +L^4 ↔ CaH.L.4 22.9 (4) Ca./ +3H/ +L^4 ↔ CaH3L4 28 (5) Ca./ +4H/ +L^4 ↔ CaH8L 32.1

Calcium ligand complexes with EDTMP Logβi b

(6) Ca./ +L^4 ↔ CaL84 9.29 (7) Ca./ +H/ +L^4 ↔ CaHL34 18.74 (8) Ca./ +2H/ +L^4 ↔ CaH.L.4 26.98 (9) Ca./ +3H/ +L^4 ↔ CaH3L4 33.72

(10) Ca./ +4H/ +L^4 ↔ CaH8L 39.21 Calcium ligand complexes with DTPMP LogK c

(11) Ca./ +H.Lc4 ↔ CaH.L^4 5.04 (12) Ca./ +H3LA4 ↔ CaH3LI4 4.41 (13) Ca./ +H8L^4 ↔ CaH8L84 3.78 (14) Ca./ +HILI4 ↔ CaHIL34 3.5 (15) Ca./ +H^L84 ↔ CaH^L.4 2.52 (16) Ca./ +HAL34 ↔ CaHAL4 1.89 (17) Ca./ +HcL.4 ↔ CaHcL 1.26 (18) Ca./ +HdL/ ↔ CaHdL/ 0.63

Calcium hydroxy complex LogK c (19) Ca./ +H.O ↔ CaOH/ +H/ -12.697

a Taken from reference (1), b Taken from reference (2), c Taken from reference (3).

S11

Figure S5 The impact of pH on the fraction of total dissolved calcium existing as free

calcium in the presence of each antiscalant.

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14

Frac

tion

of to

tal c

alci

um a

s fr

ee C

a2+

pH

DTPMP

EDTMP

NTMP

S12

Text S3 Calculations for net charge of different antiscalants at different pH

Mass balance on the speciation of an antiscalant gives the equation below:

𝑇𝑂𝑇L = L^4 + {HL}I4 + {H.L}84 + {H3L}34 +⋯+ {H7L}(e47)4 (14)

where L6- is the most deprotonated form of NTMP. TOTL is defined as the sum of the

concentration of all the species in the solution that contain an antiscalant, n is the charge

of the most deprotonated species and i varies from 0 to n.

Speciation constants for NTMP, EDTMP and DTPMP are shown in Table S2 below.

Table S2 Protonation constants of NTMP, EDTMP and DTPMP # NTMP pKa d

(1) HIL4 +H/ ↔ H^L 0.30 (2) H8L.4 +H/ ↔ HIL4 1.50 (3) H3L34 +H/ ↔ H8L.4 4.64 (4) H.L84 +H/ ↔ H3L34 5.86 (5) HLI4 +H/ ↔ H.L84 7.30 (6) L^4 +H/ ↔ HLI4 12.10

EDTMP pKa e

(7) H^L4 +H/ ↔ HAL 1.30 (8) HIL.4 +H/ ↔ H^L4 2.96 (9) H8L34 +H/ ↔ HIL.4 5.12

(10) H3L84 +H/ ↔ H8L34 6.40 (11) H.LI4 +H/ ↔ H3L84 7.87 (12) HL^4 +H/ ↔ H.LI4 7.85 (13) LA4 +H/ ↔ HL^4 13.01

DTPMP pKa f

(14) HdL4 +H/ ↔ H;fL 1.04 (15) HcL.4 +H/ ↔ HdL4 2.08 (16) HAL34 +H/ ↔ HcL.4 3.11 (17) H^L84 +H/ ↔ HAL34 4.15 (18) HILI4 +H/ ↔ H^L84 5.19 (19) H8L^4 +H/ ↔ HILI4 6.23 (20) H3LA4 +H/ ↔ H8L^4 7.23 (21) H.Lc4 +H/ ↔ H3LA4 8.30 (22) HLd4 +H/ ↔ H.Lc4 11.18 (23) L;f4 +H/ ↔ HLd4 12.58

d Taken from literature (4), e Taken from literature (2), f Taken from literature (5)

S13

p𝐾Y,7 = −log B{He47/;L};47

{H/}{He47L}47G (15)

where L is the most deprotonated form of the ligand (NTMP, EDTMP or DTPMP), n is the

charge of the most deprotonated form of the ligand (n = 6, 8 and 10 for NTMP, EDTMP

and DTPMP, respectively) and i varies from 0 to n.

𝛼7 = {H/}e47 ∏ 𝐾Yn7

nof

∑ ({H/}e4q ∏ 𝐾Ynqnof )e

qof (16)

Where αi is defined as the fraction of TOTL that is in a form that has lost i protons, n is the

number of protons in the most protonated state, Ka0 = 1.0. Thus, for NTMP, the value of α

for the species H6L is defined as:

𝛼f = {H/}^

{H/}^ + {H/}I𝐾Y; + {H/}8𝐾Y;𝐾Y. + ⋯+𝐾Y;𝐾Y.𝐾Y3𝐾Y8𝐾YI𝐾Y^ (17)

Using the pKa values from Table S2 and equation (15), (16) and (17) the fraction of each

species is calculated at different pHs. Accordingly, the net charge of each antiscalant

molecule is calculated by using the equation below:

𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟𝑐ℎ𝑎𝑟𝑔𝑒𝑝𝑒𝑟𝑚𝑜𝑙𝑒 = }𝛼7𝑧7

7oe

7of

(18)

Where zi is the charge of species that has lost i protons, n is the number of protons in the

most protonated species.

S14

Figure S6 The impact of pH on the charge of each antiscalant. The charge is normalized

to the molar concentration of the antiscalant and shown as the ratio of charge to molar

concentration of antiscalant in the y-axis.

-12

-9

-6

-3

0

0 2 4 6 8 10 12 14

Net

ant

isca

lant

cha

rge/

mol

e

pH

NTMP

EDTMP

DTPMP

S15

Figure S7 Impact of the antiscalant DTPMP on the zeta potential of hydroxyapatite at

different pHs. [Ca2+] = 10 mM; [PO43-] = 26 mg P/L; saturation index = 14.2; [DTPMP] =

1 µM; ionic strength=100 mM; [TRIS buffer] = 20 mM.

-40

-30

-20

-10

0

10

20

2 4 6 8 10 12

Zeta

pot

entia

l (m

V)

pH

w/o DTPMP

w/ DTPMP

S16

Figure S8 The effect of EDTMP dosage on the extension of induction time for CaSO4(s)

and CaCO3(s) precipitation. Experimental conditions: (A) [Ca2+] = 37-80 mM; [SO42-] =

564 mM; ionic strength = 1 M pH = 7.8. (B) [Ca2+] = 10 mM; [CO32-] = 10-36 mM; pH =

7.8; ionic strength = 100 mM; [TRIS buffer] = 50 mM.

0

20

40

60

80

100

120

1.2 1.4 1.6 1.8

Indu

ctio

n tim

e (m

inut

es)

Saturation index

[EDTMP] = 0 µM

[EDTMP] = 1 µM

[EDTMP] = 2 µM

[EDTMP] = 3 µM

[EDTMP] = 9 µM

[EDTMP] = 21 µM

B

0

20

40

60

80

6 7 8 9 10 11

Indu

ctio

n tim

e (m

inut

es)

Saturation index

[EDTMP] = 0 µM

[EDTMP] = 1 µM

[EDTMP] = 6 µM

[EDTMP] = 9 µM

[EDTMP] = 11 µM

A

S17

Figure S9 The impact of varying dosage of EDTMP at different saturation indices on the

induction time for Ca5(PO4)3OH(s), CaCO3(s) and CaSO4(s) nucleation. (A) [Ca2+] = 10 mM;

[PO43-] = 18-30 mg P/L; pH = 7.8; ionic strength = 100 mM; [TRIS buffer] = 20 mM. (B)

[Ca2+] = 10 mM; [CO32-] = 10-36 mM; pH = 7.8; ionic strength = 100 mM; [TRIS buffer]

= 50 mM. (C) [Ca2+] = 37-80 mM; [SO42-] = 560 mM; ionic strength = 1 M; pH = 7.8.

0.8

1.6

2.4

3.2

4.5 4.7 4.9 5.1Lo

g (t i

nd) (

seco

nds)

1/SI2 (1×10-3)

[EDTMP] = 0 µM

[EDTMP] = 0.5 µM

[EDTMP] = 1.0 µM

[EDTMP] = 2.0 µM

[EDTMP] = 3.0 µM

[EDTMP] = 4.0 µM

A

2.7

3.1

3.5

3.9

0.5 1.0 1.5 2.0

Log

(t ind

) (se

cond

s)

1/SI2

[EDTMP] = 0 µM [EDTMP] = 1 µM

[EDTMP] = 2 µM [EDTMP] = 3 µM

[EDTMP] = 9 µM [EDTMP] = 21 µM

B

0.0

0.5

1.0

1.5

2.0

6 11 16 21 26

Log

(t ind

) (se

cond

s)

1/SI2 (1×10-3)

[EDTMP] = 0 µM

[EDTMP] = 1 µM

[EDTMP] = 6 µM

[EDTMP] = 9 µM

[EDTMP] = 11 µM

C

S18

Figure S10 Impact of saturation index of CaCO3(s) and CaSO4(s) on activation energy of

nucleation at varying EDTMP dose. (A) [Ca2+] = 10 mM; [CO32-] = 10-36 mM; pH = 7.8;

ionic strength = 100 mM; [TRIS buffer] = 50 mM. (B) [Ca2+] = 37-80 mM; [SO42-] = 564

mM; pH = 7.8; ionic strength = 1 M.

0

2

4

6

8

6 7 8 9 10 11

Act

ivat

ion

ener

gy (J

) ×10

-20

Saturation index

[EDTMP] = 0 uM

[EDTMP] = 1 uM

[EDTMP] = 6 uM

[EDTMP] = 11 uM

[EDTMP] = 16 uM

B

0

2

4

6

8

10

12

14

0.7 0.9 1.1 1.3

Act

ivat

ion

ener

gy (J

) ×10

-25

Saturation index

[EDTMP] = 0 uM

[EDTMP] = 3 uM

[EDTMP] = 9 uM

[EDTMP] = 16 uM

[EDTMP] = 21 uM

A

S19

Figure S11 Impact of saturation index of CaCO3(s) and CaSO4(s) on critical radius of

nucleation at varying EDTMP dose. A: Experimental conditions for CaCO3(s): [Ca2+] = 10

mM; [CO32-] = 10-36 mM; [EDTMP] = 0-21 µM; pH = 7.8; Ionic strength = 100 mM;

TRIS= 50 mM; B: Experimental conditions for CaSO4(s): [Ca2+] = 37-80 mM; [SO42-] =

564 mM; [EDTMP] = 0-16 µM; ionic strength = 1M; pH = 7.8.

0.6

0.8

1

1.2

1.4

1.6

1.8

0.7 0.9 1.1 1.3

Rcr

itica

l(m

) ×10

-11

Saturation index

[EDTMP] = 0 uM

[EDTMP] = 3 uM

[EDTMP] = 9 uM

[EDTMP] = 16 uM

[EDTMP] = 21 uM

A

4

5

6

7

8

9

6 7 8 9 10 11

Rcr

itica

l(m

) ×10

-10

Saturation index

[EDTMP] = 0 uM

[EDTMP] = 1 uM

[EDTMP] = 6 uM

[EDTMP] = 11 uM

[EDTMP] = 16 uM

B

S20

References

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2 Popov, K.; Rönkkömäki, H.; Lajunen, L. H. Critical evaluation of stability constants of

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3 Gillard, R. D.; Newman, P. D.; Collins, J. D. Speciation in aqueous solutions of di-

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complexes. Polyhedron 1989, 8 (16), 2077-2086.

4 Powell, K. J.; Pettit, L. D. IUPAC stability constants database. Academic Software 1997,

Otley.

5 Tomson, M. B.; Kan, A. T.; Oddo, J. E. Acid/base and metal complex solution chemistry

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1994, 10 (5), 1442-1449.