S1

Supplemental Material

Colloidal stability and mobility of extracellular polymeric substance amended hematite

nanoparticles

Sneha Pradip Narvekar, Thomas Ritschel*, Kai Uwe Totsche

Institute of Geosciences, Friedrich Schiller University Jena, Germany.

Corresponding Author*

Phone: 0049 - (0) 3641 – 948718; Fax: 0049 - (0) 3641 – 948742; email: thomas.ritschel@uni-

jena.de

List of Sections

S.1. Modeling aggregation kinetics 2

S.2. Closed-flow column system 6

S.3. Porous media contact efficiency 7

S.4. Synthesis of hematite 10

S.5. Characterization of EPS isolated from Bacillus subtilis 168 (DSM 402) 11

S.6. Concentrations of EPS sorbed on hematite nanoparticles 12

S.7. Effect of EPS on Aggregation Kinetics of HNP with NaCl 13

S.8. Effect of EPS on Aggregation Kinetics of HNP with CaCl2 14

S.9. Evaluation of interactions between the particles 15

S.10. Transport of solute through closed-flow column systems 16

S.11. Calculation of adsorption strength from breakthrough curves 17

S2

S.1. Modeling aggregation kinetics

Puertas and de las Nieves (1999) described the stability ratio in terms of total interaction energy

(or energy barrier) VT(H) by the following equation (Di Marco et al., 2007)

𝑊 = ∫ 𝛽 (𝐻) (𝐻 + 2𝑅𝐻)2. exp (

𝑉𝑇(𝐻)𝑘𝐵𝑇

) 𝑑𝐻⁄∞

0

∫ 𝛽 (𝐻) (𝐻 + 2𝑅𝐻)2. exp (𝑉𝐴(𝐻)𝑘𝐵𝑇

) 𝑑𝐻⁄∞

0

(1)

Here, H is the distance between the particle surfaces, β(H) is the hydrodynamic correction factor

(Overbeek, 1982), VT(H) is the total potential energy of interaction and VA(H) is the potential

energy of the van der Waals interaction.

DLVO interactions

The total interaction energy between the particles VT(H) is given by the equation,

𝑉𝑇(𝐻) = 𝑉𝐴(𝐻) + 𝑉𝐸(𝐻) (2)

Here 𝑉𝐸(𝐻) is the total potential energy of electrostatic double layer interactions.

The total potential energy of the van der Waals interaction is given by

𝑉𝐴(𝐻) = −

𝐴

6[

2𝑅𝐻2

𝐻(4𝑅𝐻 + 𝐻)+

2𝑅𝐻2

(2𝑅𝐻 + 𝐻)2+ 𝑙𝑛

𝐻(4𝑅𝐻 + 𝐻)

(2𝑅𝐻 + 𝐻)2]

(3)

Where A is the Hamaker constant of particles interacting in the water.

S3

The total potential energy by electrostatic double layer interaction is given by

𝑉𝐸(𝐻) = 2𝑅𝐻휀0휀𝑟𝜋 [

4𝐾𝐵𝑇

Ζ𝑒𝛾]

2

𝑒−𝜅𝐻 (4)

where 𝛾 is given by

𝛾 =

𝑒Ζ𝑒𝜓𝑑 2𝐾𝐵⁄ 𝑇 − 1

𝑒Ζ𝑒𝜓𝑑 2𝐾𝐵⁄ 𝑇 + 1

(5)

εo is the permittivity in vacuum, εr is the relative permittivity, KB is the Boltzmann constant, T is

the absolute temperature, Z is the valence of the electrolyte, κ is the Debye parameter, which

depends on the ionic strength of the solution, ψd is the diffusion potential related to and very close

(in value) to the zeta potential (Di Marco et al., 2007).

EDLVO interactions

Steric interactions

In the presence of steric forces, an additional term is added to the total interaction energy equation

(2)

𝑉𝑇(𝐻) = 𝑉𝐴(𝐻) + 𝑉𝐸(𝐻) + 𝑉𝑆(𝐻) (6)

The steric interaction energy comprised of two energies the osmotic energy Vosm and the elastic

energy Velas.

𝑉𝑆(𝐻) = 𝑉𝑜𝑠𝑚(𝐻) + 𝑉𝑒𝑙𝑎𝑠(𝐻) (7)

When the polymer brushes of the two parties overlap, osmotic pressure is built up due to an

increase in the concentration of the polymer resulting in repulsion between the two particles.

S4

𝑉𝑜𝑠𝑚(𝐻) = 0 2δ ≤ H (8)

𝑉𝑜𝑠𝑚(𝐻) =4𝜋𝑎

𝑣1

(𝜙2)2𝑘𝐵𝑇 (1

2− 𝜒) (𝛿 −

𝐻

2)

2

δ ≤ H ≤ 2δ

(9)

𝑉𝑜𝑠𝑚(𝐻) =4𝜋𝑎

𝑣1

(𝜙2)2𝑘𝐵𝑇 (1

2− 𝜒) 𝛿2 (

𝐻

2𝛿−

1

4− 𝑙𝑛 (

𝐻

𝛿))

H < δ

(10)

Here χ is the Flory-Huggins solvency parameter, ϕ2 is the volume fraction of the EPS within the

brush layer, δ is the thickness of the brush layer and v1 is the volume of one solvent molecule.

When the two particles are at such a close distance (H=δ), some polymer molecules undergo

compression leading to loss of entropy for the polymers, which result in elastic repulsion between

the two particles.

𝑉𝑒𝑙𝑎𝑠(𝐻) = 0 δ ≤ H (11)

𝑉𝑒𝑙𝑎𝑠(𝐻) = 𝑘𝐵𝑇 (2𝜋𝑎

𝑀𝑤𝜙2𝛿2𝜌) (

𝐻

𝛿𝑙𝑛 (

𝐻

𝛿(

3 − 𝐻 𝛿⁄

2)

2

)

− 6 𝑙𝑛 (3 − 𝐻 𝛿⁄

2) + 3 (1 +

𝐻

𝛿))

H< δ (12)

Here Mw is the molecular weight of the EPS and ρ is the density of the EPS (Romero-Cano et al.,

2001)

S5

Acid-base interactions

EPS sorption can also affect the surface electron acceptor and electron donor properties. Hence,

acid-base interaction can also contribute to the total interaction energy. When acid-base interaction

contributes to total energy, the acid-base component is added to the total energy equation 2

𝑉𝑇(𝐻) = 𝑉𝐴(𝐻) + 𝑉𝐸(𝐻) + 𝑉𝐴𝐵(𝐻) (13)

The Acid-base energy between two particles is given by

𝑉𝐴𝐵(𝐻) = 𝜋𝑟𝜆Δ𝐺ℎ𝑜

𝐴𝐵𝑒𝑥𝑝 (𝐻𝑜 − 𝐻

𝜆)

(14)

here 𝜆 is the decay length of the molecules of the liquid medium, and Δ𝐺ℎ𝑜

𝐴𝐵 is the polar free

interaction energy between the particles at distance Ho which is the minimum equilibrium distance

due to Born repulsion, which is 0.157 nm (Li and Chen, 2012).

The derivation of equation 1 permits the comparison of predicted W values to the experimental

data of log W vs. electrolyte concentration. Some values such as Hamaker constant (A), Gibbs free

energy of acid/base interaction (Δ𝐺ℎ𝑜

𝐴𝐵), the volume fraction of the EPS with in the brush layer

(ϕ2), the thickness of the brush layer (δ) could not be derived independently. Hence these

parameters were fitted to the observed data using the Levenberg-Marquardt algorithm for local

optimization (Levenberg, 1944; Marquardt, 1963). The correlation between the fitting parameters

was also calculated. All the values used for different parameters are given in Table . Parameter

uncertainty was calculated as the 95 % confidence interval

S6

Table S1. Parameters used for the calculation of VT(H) by DLVO and EDLVO theories

Parameter Value

Hydrodynamic correction

factor (Overbeek, 1982)

β(H)

𝛽(ℎ) =6(ℎ

𝑎)

2+ 13(ℎ

𝑎) + 2

6(ℎ𝑎

)2

+ 4(ℎ𝑎

)

Debye parameter (Berg,

2010)

κ 1

√𝜀𝑟𝜀𝑜𝑅𝑇2𝐹2𝐶𝑜

Permittivity in vacuum εo 8.854 × 10−12 F/m

Relative permittivity εr 80.1

Absolute temperature T 293 K

Boltzmann constant KB 1.3806×10-23 m2 kg s-2 K-1

Gas constant R 8.3144

J K−1 mol−1

Faraday constant F 96485.3365 C mol−1

S.2. Closed-flow column system

Figure S1. Scheme of the closed-flow column set up

S7

S.3. Porous media contact efficiency

The transport data from these experiments are described using the colloidal filtration (CFT) theory

(Tufenkji and Elimelech, 2004) with corrections for the closed-flow transport regime. It calculates

the attachment efficiency of the porous media and the single collector contact efficiency.

The attachment efficiency (α) is the fraction of collisions between the particles and porous media

that result in the attachment.

α = −

2

3

dc

(1 − f)Lηoln (

c

ci)

(15)

here dc is the average diameter of the porous media, f is the porosity, L is the length of the column,

c/ci is the ratio of the concentration of nanoparticles in the column at the end of the transport

experiment to the concentration of nanoparticles expected after imminent dilution due to the water

of saturation in the columns and η0 is the theoretical single collector contact efficiency developed

by Tufenkji and Elimelech (2004). All the parameters used for the calculation of attachment

efficiency and the single collector contact efficiency are given in Table 2.

Table S2. Parameters used for the calculation of attachment efficiency and the single collector contact

efficiency

Parameter Values

Porosity (f) 0.48

Diameter of porous media (dc) 0.0025 m

Diameter of particles (dp) 1.81E-07 m

Length of the column (L) 0.1 m

Fluid approach velocity (U) 1.0865E-06 m/s

Boltzmann constant (kB) 1.3806488 × 10-23 m2 kg s-2 K-1

S8

The actual single collector removal efficiency (η), which is generally lower than the single

collector contact efficiency (η0), is given by

η = αη0 (16)

Moreover, the particle deposition rate coefficient 𝑘d is given by

kd =

3

2

(1 − f)

dcfUαη0

(17)

here U is the approach velocity of the medium.

The single collector contact efficiency (η0) is calculated by

η0 = 2.4As1/3

NR−0.081NPe

−0.715NvdW0.052 + 0.55AsNR

1.675NA0.125

+ 0.22NR−0.24NG

1.11NvdW0.053

(18)

Here,

As = 2(1 − γ5) (2 − 3γ + 3γ5 − 2γ6)⁄ (19)

γ = (1 − f)1 3⁄ (20)

Absolute temperature (T) 298 K

Hamaker constant (glass)A132 1.93E-20 J

Hamaker constant (biofilm and EPS)A132 3.31E-21 J

Particle density (𝛒𝐩) 2400 kg/m3

Fluid density (𝛒𝐟) 1000 kg/m3

S9

NR =dp

dc⁄ (21)

NPe =Udc

D∞ (22)

D∞ =kBT

3πμdc (23)

NvdW=

A132kBT

(24)

NA =A132

3πμUdp2 (25)

NG =1

9

dp2(ρp − ρf)g

2μU (26)

S10

S.4. Synthesis of hematite

Figure S2. Characteristics of synthesized HNP (A) X-ray diffraction of synthesized HNP compared with

reference hematite (Maslen et al., 1994) (The American Mineralogist Crystal Structure Database) (Downs,

2003) (B) FTIR spectra of synthesized HNP (C) SEM image of uncoated HNP.

Around 500 ml (14g/L iron) of hematite solution was synthesized by adding 60 ml 1.0 M ferric

nitrate to 700 ml water.

S11

S.5. Characterization of EPS isolated from Bacillus subtilis 168 (DSM 402)

Figure S3. FTIR spectrum of isolated EPS showing presence of lipids, proteins, polysaccharides and

nucleic acids

Table S3. Properties of EPS isolated from Bacillus subtilis 168 (DSM 402)

Concentration

Total carbon 383.7 ± 1.45 mg/g

Total nitrogen 45.3 ± 1.64 mg/g

Total carbohydrates 657 ± 32.52 mg/l

Total proteins 170 ± 18.87 mg/l

Zeta potenial -39 ± 14 mV

S12

S.6. Concentrations of EPS sorbed on hematite nanoparticles

The concentration of EPS sorbed on the hematite was estimated by centrifuging the solutions at

10,000 rpm for 10 mins at 4°C. The supernatant and the precipitate were analyzed for carbon and

iron concentrations by elemental analyzer (CNS analyzer, Euro EA, Eurovector, Italy) and

phenanthroline method (Saywell and Cunningham, 1937) respectively. The presence of iron in the

supernatant indicated that HNP could not be separated from the solution quantitatively, especially

in case of colloidally stable suspensions. Thus, the amount of carbon measured in the precipitate

may only serve as a general indicator for EPS adsorbed to hematite surfaces. A general increase in

the amount of EPS present on the surface is seen with increasing loadings of EPS. Table 4 gives

concentrations of EPS sorbed on HNP. Other methods of separation such as aggregation of HNP

using high concentration of salts was not used since salts can also precipitate colloidal EPS

molecules.

Table S4. Concentration of EPS adsorbed on HNP surfaces.

EPS: HNP

suspension

Carbon concentrations

(%C)

Iron concentrations

(mg/l)

Supernatant Precipitate Supernatant

HNP 5:1 27.41 7.95 20.63

HNP 2:1 8.70 5.41 6.29

HNP 1:5 3.47 3.86 1.89

S13

S.7. Effect of EPS on Aggregation Kinetics of HNP with NaCl

Figure S4. Aggregation profiles of a) HNP b) HNP 2:1 c) HNP 5:1 with different NaCl concentrations

Hyd

rod

yn

am

ic d

iam

ete

r (n

m)

200 400 600 800 1000 1200 1400 1600 18000

Time (seconds)

2000

1500

1000

500

HNP

5 mM10 mM15 mM

20 mM

25 mM30 mM

35 mM 40 mM

60 mM80 mM

100 mM 150 mM

200 mM

Hyd

rod

yn

am

ic d

iam

ete

r (n

m)

Time (seconds)

200 400 600 800 1000 1200 1400 1600 18000

3000

2500

2000

1500

1000

500

40 mM60 mM

80 mM100 mM

150 mM200 mM

250 mM300 mM

400 mM450 mM

500 mM600 mM

800 mM

HNP 5:1A

HNP 2:1

Hy

dro

dyn

am

ic d

iam

ete

r (n

m)

3000

2500

2000

1500

1000

500

Time (seconds)200 400 600 800 1000 1200 1400 1600 18000

10 mM

20 mM30 mM

40 mM

60 mM80 mM

100 mM 160 mM

200 mM300 mM400 mM

500 mM

600 mM

700 mM800 mM

900 mM

B

C

S14

S.8. Effect of EPS on Aggregation Kinetics of HNP with CaCl2

Figure S5. Aggregation profiles of a) HNP b) HNP 2:1 c) HNP 5:1 with different CaCl2 concentrations

Hyd

rod

yn

am

ic d

iam

ete

r (n

m)

2500

2000

1500

1000

500

Time (seconds)200 400 600 800 1000 1200 1400 1600 18000

HNP 5:1

0.5 mM 1 mM1.5 mM

2 mM 5 mM10 mM

15 mM 20 mM30 mM

40 mM 60 mM80 mM

A

Hyd

rod

yn

am

ic d

iam

ete

r (n

m)

Time (seconds)

3000

2500

2000

1500

1000

500

HNP 2:1

200 400 600 800 1000 1200 1400 1600 18000

0.1 mM0.2 mM0.4 mM

0.6 mM 1 mM

1.2 mM1.5 mM 2 mM

2.5 mM 4 mM

5 mM10 mM

15 mM 20 mM 25 mM

30 mM40 mM

60 mM 80 mM

100 mM

B

HNP

Hy

dro

dy

na

mic

dia

me

ter

(nm

)

Time (seconds)200 400 600 800 1000 1200 1400 1600 18000

2500

2000

1500

1000

500

0 mM 20 mM

40 mM60 mM

80 mM

100 mM 150 mM

200 mM250 mM

C

S15

S.9. Evaluation of interactions between the particles

Figure S6. Comparison of experimentally observed W and DLVO fitted W values

S16

S.10. Transport of solute through closed-flow column systems

Figure S7. A typical breakthrough curve obtained by simulations (Ritschel and Totsche, 2016)

In closed-flow columns, a typical breakthrough in the supply vessel consists of oscillations (a

continuous increase and decrease) in the concentration of the solute, which finally stabilizes when

an equilibrium state is reached. This is due to flow of the solute through the column several times

until the dispersion, diffusion and mixing leads to a stable concentration in the supply vessel

(Ritschel and Totsche, 2016).

S17

S.11. Calculation of adsorption strength from breakthrough curves

In closed-flow mode transport experiments, the distribution of a mobile compound between the

solid and the aqueous phase can also be expressed in terms of a dimensionless sorption or retention

coefficient 𝑆, which is given in close relation to the classical retardation factor as

𝑆 = 1 −𝜌𝐾

𝜃, (27)

where ρ is the bulk density of the porous medium, 𝐾 is the distribution coefficient between the

aqueous and the solid phase and θ is the volumetric water content of the porous medium (e.g.

Toride et al., 2003). A value of unity corresponds to conservative transport, where no sorption or

retention occurs and values higher unity are found in case of reactive transport. Ritschel and

Totsche (2016b) derived a way to calculate 𝑆 from the relative dilution 𝑑 observed in the mixing

vessel for reactive transport and the volumetric dilution 𝑑v caused by the mixture of solutes in

column and mixing vessel in closed-flow experiments according to

𝑆 =𝑑v(𝑑−1)

𝑑(𝑑v−1) . (28)

As 𝑑 is easily derived from breakthrough data and 𝑑v is calculated from the column geometry

according to

𝑑v =𝑉𝑚

𝑉𝑚+𝜃𝑉𝑐, (29)

where 𝑉𝑚 is the volume of the mixing vessel and 𝑉𝑐 is the volume of the column, we also calculated

𝑆 according to equation (6) for the different HNP suspensions.

S18

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