correction notice calcium carbonate …4 physical sciences division, pacific northwest national...

CORRECTION NOTICE

Calcium carbonate nucleation driven by ion binding in a biomimetic matrix revealed by in situ electron microscopy Paul J. M. Smeets, Kang Rae Cho, Ralph G. E. Kempen, Nico A. J. M. Sommerdijk and James J. De Yoreo

Nature Materials http://dx.doi.org/10.1038/nmat4193 (2015)

In the version of the Supplementary Information originally published online, the first two sentences in the second paragraph of the section ‘Setup of liquid cell assembly and liquid flow TEM holder’ should have read “PEEKTM tubing was used for the liquid flow holder (Fig. S1a). Either 1.25 mM CaCl2 (control experiment), or the Ca-PSS solution was filled in the syringe connected to tubing with inner diameter of 100 µm…” This error has been corrected in this file 10 February 2015.

© 2015 Macmillan Publishers Limited. All rights reserved

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT4193

NATURE MATERIALS | www.nature.com/naturematerials 1

Calcium carbonate nucleation driven by ion binding in a biomimetic matrix revealed by in situ electron microscopy

Paul J.M. Smeets1,2,3,4, Kang Rae Cho1, Ralph G.E. Kempen2, Nico A.J.M. Sommerdijk2,3* &

James J. De Yoreo4*

1 Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

2 Laboratory of Materials and Interface Chemistry and Soft Matter CryoTEM Unit, Eindhoven

University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands

3 Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513,

5600 MB Eindhoven, The Netherlands

4 Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352,

USA

*Correspondence and request for materials should be directed to JJDY and NAJMS,

([email protected]; [email protected])

Calcium carbonate nucleation driven by ion binding in a biomimetic matrix revealed by in situ electron microscopy


http://www.nature.com/doifinder/10.1038/nmat4193

2 NATURE MATERIALS | www.nature.com/naturematerials

SUPPLEMENTARY INFORMATION DOI: 10.1038/NMAT4193

Contents

Supplementary Methods and Materials ................................................................ 3 I. Synthesis of calcium-complexed poly(sodium 4-styrenesulfonate) (Ca-PSS) globules and

CaCO3 formation. ......................................................................................................................... 3

II. Transmission Electron Microscopy. ............................................................................................. 5

III. Atomic Force Microscopy. ........................................................................................................... 7

IV. Fourier Transform Infrared Microscopy. ...................................................................................... 8

V. Isothermal Titration Calorimetry. ................................................................................................. 8

VI. Dynamic Light Scattering and Zeta Potential Measurements. ..................................................... 9

VII. Scanning Electron Microscopy. .................................................................................................... 9

VIII. Confocal Raman Microscopy. .................................................................................................... 10

IX. Ion Selective Electrode Experiments. ......................................................................................... 10

Supplementary Data .............................................................................................. 12 I. Nucleation and growth of vaterite without PSS. ......................................................................... 12

II. Flow of the initial Ca-PSS solution into the liquid cell. ............................................................. 14

III. Size analysis of Ca-PSS globules and control solutions. ............................................................ 14

IV. Ca2+ concentration determination. .............................................................................................. 19

V. Nucleation and growth of amorphous calcium carbonate inside Ca-PSS globules. ................... 20

VI. Diffraction pattern analysis of ACC in globules and transformation into calcite at higherelectron dose. .............................................................................................................................. 23

VII. Growth of ACC in globules without electron beam influence. .................................................. 24

VIII. Determination of supersaturation from calcite growth rates....................................................... 26

IX. Determination of supersaturation and diffusivity from the diffusion equation. ......................... 27

X. Determination of carbonate concentration inside globules vs. vaterite without PSS. ................ 33

XI. Presence of vaterite in bulk solution besides ACC in Ca-PSS globules. .................................... 34

Supplementary Tables ........................................................................................... 37

Supplementary Discussion .................................................................................... 38 I. Effects of physical confinement on the mineralization inside the LP-TEM cell. ....................... 38

II. Surface charge comparison of mica and Si3N4. .......................................................................... 39

Supplementary Videos ........................................................................................... 40

Supplementary Literature ..................................................................................... 43

2

Supplementary Methods and Materials

I. Synthesis of calcium-complexed poly(sodium 4-styrenesulfonate) (Ca-PSS) globules

and CaCO3 formation.

i. Reagents – All reagents were from Sigma Aldrich and were used as received: Calcium

chloride dihydrate (powder, ACS reagent, ≥ 99%), poly(sodium 4-styrenesulfonate) (PSS,

powder, average Mw ~70000) and ammonium carbonate (powder, ACS reagent, ≥ 30% NH3

basis). Ultrapure water was prepared by degassing Milli-Q water (18.2 MΩ, Millipore, 25 °C)

using nitrogen gas to remove CO2 overnight.

ii. Ca-PSS Globule solution – A 100 mL 1.25 mM CaCl2 solution was added to a bottle with

0.05 g of PSS powder in it, whereafter the mixture was vigorously stirred in a sealed system

from the air. Then the solution was equilibrated for approximately 30 minutes before its use in

experiments. The amounts of solution used for the experiments varied, depending on the types of

the experiments (see Section II).

iii. CaCO3 formation by the ammonium carbonate diffusion method – The (NH4)2CO3

powder was used as source for increasing the carbonate concentration over time: CO2 and NH3

in the gas phase diffuse across the gas-liquid interface into the Ca2+-containing solution over

time. In a second and slower step, aqueous CO2 reacts with water to form carbonic acid, which

rapidly deprotonates into carbonate and bicarbonate ions. Next, calcium and carbonate are then

able to react with each other to form calcium carbonate

Ca2+ + CO32- CaCO3 (1)

At longer diffusion times, the concentration of the (bi)carbonate ions increases, and thus results

in an increase in supersaturation with respect to calcium carbonate1.

3





Contents

Supplementary Methods and Materials ................................................................ 3 I. Synthesis of calcium-complexed poly(sodium 4-styrenesulfonate) (Ca-PSS) globules and

CaCO3 formation. ......................................................................................................................... 3

II. Transmission Electron Microscopy. ............................................................................................. 5

III. Atomic Force Microscopy. ........................................................................................................... 7

IV. Fourier Transform Infrared Microscopy. ...................................................................................... 8

V. Isothermal Titration Calorimetry. ................................................................................................. 8

VI. Dynamic Light Scattering and Zeta Potential Measurements. ..................................................... 9

VII. Scanning Electron Microscopy. .................................................................................................... 9

VIII. Confocal Raman Microscopy. .................................................................................................... 10

IX. Ion Selective Electrode Experiments. ......................................................................................... 10

Supplementary Data .............................................................................................. 12 I. Nucleation and growth of vaterite without PSS. ......................................................................... 12

II. Flow of the initial Ca-PSS solution into the liquid cell. ............................................................. 14

III. Size analysis of Ca-PSS globules and control solutions. ............................................................ 14

IV. Ca2+ concentration determination. .............................................................................................. 19

V. Nucleation and growth of amorphous calcium carbonate inside Ca-PSS globules. ................... 20

VI. Diffraction pattern analysis of ACC in globules and transformation into calcite at higherelectron dose. .............................................................................................................................. 23

VII. Growth of ACC in globules without electron beam influence. .................................................. 24

VIII. Determination of supersaturation from calcite growth rates....................................................... 26

IX. Determination of supersaturation and diffusivity from the diffusion equation. ......................... 27

X. Determination of carbonate concentration inside globules vs. vaterite without PSS. ................ 33

XI. Presence of vaterite in bulk solution besides ACC in Ca-PSS globules. .................................... 34

Supplementary Tables ........................................................................................... 37

Supplementary Discussion .................................................................................... 38 I. Effects of physical confinement on the mineralization inside the LP-TEM cell. ....................... 38

II. Surface charge comparison of mica and Si3N4. .......................................................................... 39

Supplementary Videos ........................................................................................... 40

Supplementary Literature ..................................................................................... 43

2

Supplementary Methods and Materials

I. Synthesis of calcium-complexed poly(sodium 4-styrenesulfonate) (Ca-PSS) globules

and CaCO3 formation.

i. Reagents – All reagents were from Sigma Aldrich and were used as received: Calcium

chloride dihydrate (powder, ACS reagent, ≥ 99%), poly(sodium 4-styrenesulfonate) (PSS,

powder, average Mw ~70000) and ammonium carbonate (powder, ACS reagent, ≥ 30% NH3

basis). Ultrapure water was prepared by degassing Milli-Q water (18.2 MΩ, Millipore, 25 °C)

using nitrogen gas to remove CO2 overnight.

ii. Ca-PSS Globule solution – A 100 mL 1.25 mM CaCl2 solution was added to a bottle with

0.05 g of PSS powder in it, whereafter the mixture was vigorously stirred in a sealed system

from the air. Then the solution was equilibrated for approximately 30 minutes before its use in

experiments. The amounts of solution used for the experiments varied, depending on the types of

the experiments (see Section II).

iii. CaCO3 formation by the ammonium carbonate diffusion method – The (NH4)2CO3

powder was used as source for increasing the carbonate concentration over time: CO2 and NH3

in the gas phase diffuse across the gas-liquid interface into the Ca2+-containing solution over

time. In a second and slower step, aqueous CO2 reacts with water to form carbonic acid, which

rapidly deprotonates into carbonate and bicarbonate ions. Next, calcium and carbonate are then

able to react with each other to form calcium carbonate

Ca2+ + CO32- CaCO3 (1)

At longer diffusion times, the concentration of the (bi)carbonate ions increases, and thus results

in an increase in supersaturation with respect to calcium carbonate1.

3





The powder was put either in a parafilm-covered glass vial with three small holes (benchtop

experiments), inside a syringe connected to PEEKTM tubing towards a TEM liquid cell (TEM

experiments), or inside tubing connected to an AFM liquid cell (AFM experiments). The amount

of powder was roughly scaled to the surface area that the globule solution had in each of these

experiments because the CO2 diffusion rate is approximately linearly dependent on the surface

area of solution1. For example, in the benchtop experiment with a vial containing a solution

surface area of 6 cm2, approximately 1 g of (NH4)2CO3 was used, while in the TEM fluid cell

with a surface area of 0.25 cm2, approximately 0.05 g was used. In addition, diffusion barriers

were also kept roughly similar in their magnitude in each of these experiments since they were

also found to have a profound effect on the CO2 addition rate1: punctured holes in the parafilm

for the benchtop experiments had an area comparable to the PEEK tubing in the TEM

experiments. Therefore, approximately the CO2 diffusion rates should be also comparable

between the various used systems.

iv. CaCO3 benchtop diffusion experiments - Benchtop crystallization experiments were

carried out in a desiccator. A glass vial (diameter 28 mm) was filled with 5 mL Ca-PSS solution

and a backetched Si3N4/Si(100)/Si3N4 substrate (Si3N4 layer of 50-100nm), which was plasma-

cleaned for 1 minute, was placed on the bottom of the vial. Sealing of the vial was done with

parafilm, in which three small holes were punctured using a small needle. Two petri-dishes filled

with each 0.5 g (NH4)2CO3 were placed at the bottom of the desiccator and similarly covered

using parafilm with three small punctured holes.

Control experiments without the PSS were conducted according to the procedure

described above, but instead using only 1.25 mM CaCl2 as the mineralizing solution.

4

II. Transmission Electron Microscopy.

A JEOL 2100-F with a field emission gun was used at an acceleration voltage of 200 kV, in

combination with a commercially available liquid flow TEM holder from Hummingbird

Scientific. The dose rate was estimated 1 ± 0.5 x 103 e/Å2·s (see discussion main text).

i. Setup of liquid cell assembly and liquid flow TEM holder – Si square-shaped top and

bottom chips containing a Si3N4 layer of 50 nm in thickness were used, each containing a Si3N4

electron transparent membrane 200 by 50 µm in size. The bottom chip contained a spacer of 250-

500 nm in height. The top blank chip was oriented 90° with respect to the bottom chip to result

in a cross-over of Si3N4 electron transparent area of 50 by 50 µm for imaging (based on perfect

alignment). All Si3N4 surfaces of the chips that were exposed to fluid were washed with water

and plasma cleaned for one minute prior to use to render them hydrophilic and free of organic

contaminants.

PEEKTM tubing was used for the liquid flow holder (Fig. S1a). Either 1.25 mM CaCl2

(control experiment), or the Ca-PSS solution was filled in the syringe connected to tubing with

inner diameter of 100 µm and was infused at a flow rate of 100 µL/h into the assembled

cell, which initially contained 0.5 µL ultrapure water (Fig. S1b). Then, depending on the

goal of the experiments, for example, a second syringe containing ammonium carbonate was

connected to start the reaction, as stated above.

The PEEKTM tubing utilized for the diffusion experiments in the LP-TEM setup had a

larger diameter of 500 µm and a length of approximately 40 cm. Since the diffusion of gaseous

CO2 in air at 20°C and 1 atm is 0.160 cm2/s as previously reported2, it would take ~50 seconds to

reach the cell. After passing the gas-liquid interface, conversion into carbonic acid and

5





areas were chosen for diffraction analysis. Subsequently, a similar approach to this was taken for

imaging in bright field TEM mode.

iii. TEM image/video analysis – Image J was used to measure particle sizes utilizing the line

tool. The DiffTools suite was used in Digital MicrographTM to analyze electron diffraction data.

Videos were collected at either 5 frames per second (fps) or 10 fps using VirtualDub video

capture/processing utility (Avery Lee) (frame size: 1001 ± 1 × 666 ± 1 pixels).

Particle growth rate data was obtained using a MATLAB script by measuring sizes based

on intensity variations in pixels. The average radii of the growing particles (ACC or vaterite)

were obtained from a measured minimum Feret diameter (dF,max) and a maximum Feret diameter

(dF,min) by 𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = �(𝑑𝑑𝑑𝑑𝐹𝐹𝐹𝐹,𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚+𝑑𝑑𝑑𝑑𝐹𝐹𝐹𝐹,𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)/22

�. Here, the measured Feret diameters were in pixels, and the

error magnitude was ± 3 pixels (± 1.4 nm for the measurement of ACC size and ± 2.1 nm for the

measurement of vaterite size due to different magnifications used) for both dF,max and dF,min. This

procedure was followed since the measured particles appeared not perfectly spherical and the

error covered uncertainty of intensity variations.

III. Atomic Force Microscopy.

Experiments were performed on a Digital Instruments Multimode Nanoscope IIIa (Veeco

Metrology, Inc., Santa Barbara, CA) using a sealed glass fluid cell. All images were acquired at

room temperature in tapping mode using a Si3N4 cantilever (Bruker, NP-S) with a spring

constant of 0.12 N/m. Analysis was done with Nanoscope Analysis v.1.40 software, and for high

resolution quality of collected images a low pass filter was used.

7

subsequently into bicarbonate and carbonate ions takes place (as described in Section I) where

the kinetic rate is reported as 0.04 s-1 (or 25 s)3. Thus, we expect the diffusion process by itself

not to take much longer than a minute.

Figure S1 | LP-TEM setup.

(a) Schematic of the liquid flow holder with tubing configuration. (b) The side view of the cell assembly,

which contains a small o-ring under the bottom chip and on top of the top chip, while a large o-ring near

the outer edge hermetically seals the cell from the vacuum (o-rings are indicated in black). The spacer

(green) attached to the bottom chip is oriented 90° from the actual orientation, to display the liquid layer

which is being imaged in between the chips.

ii. Electron diffraction analysis – The samples investigated were highly beam-sensitive. To

obtain information about the crystallinity of the sample, unless stated otherwise, nonirradiated

6





As the surface of the Si3N4 substrates was too rough for accurate AFM height

measurements, having height variations larger than the globule dimensions, freshly cleaved

atomically flat mica was used. However, at the conditions used mica and Si3N4 substrates should

be similarly charged (see Supplementary Discussion II).

For diffusion experiments, the inlet and outlet of the liquid cell were connected with

tubing containing a small amount of fresh (NH4)2CO3 in the closed connected system.

IV. Fourier Transform Infrared Microscopy.

A Perkin Elmer Spectrum One Fourier Transform Infrared Microscopy (FTIR)

Spectrophotometer coupled with a HATR Sampling Accessory (ZnSe crystal) was used to

acquire spectra. Multiple acquisitions of 100 scans in each sample with a resolution of 4 cm-1

were taken at ambient conditions between 600-4000 cm-1.

V. Isothermal Titration Calorimetry.

Isothermal Titration Calorimetry (ITC) measures the change in heat (adsorbed or released) when

two solutions are mixed. Measurements were performed on a TA Instruments Nano ITC (New

Castle, DE) in an adiabatic jacket. Prior to solution injection, all solutions were degassed for 20

minutes. A 250 µL 0.15 mM PSS solution (or 250 µL Milli-Q water for control experiments)

contained in a syringe of total volume 250 µL was used as the titrant in the measurements

conducted with a sample cell of 1.1 mL in volume. The sample cell made out of 24k gold was

filled with either Milli-Q water (control experiments) or a 1.25 mM solution of CaCl2 and stirred

8

at 300 rpm to ensure homogeneous mixing. Injections of 5 µL were spaced by 250 seconds to

ensure equilibration. Data was acquired at 25 °C, where the data from the first injection was not

taken in account in the data analysis due to the possible error from dilution effects. Baseline

correction, integration of the heat flow peaks, normalization with respect to the amount of moles

of PSS, and data fitting using the independent-binding-sites model were done using TA

NanoAnalyze SoftwareTM. Dilution effects were taken into account by performing appropriate

measurements.

VI. Dynamic Light Scattering and Zeta Potential Measurements.

A Malvern Instruments Zetasizer Nano ZS containing a 633 nm laser was used for both DLS and

Zeta Potential determinations at a scattering angle of 173°. The sample was put in a clean

disposable sizing cuvette and equilibrated for 1 minute prior to measurements. Zeta Potential

measurements were performed with the use of a Dip cell kit (ZeN1002). The cuvettes and cell

were thoroughly cleaned and made dust-free using Nanopure water (Barnstead Nanopure

Diamond, 18.2MΩ).

VII. Scanning Electron Microscopy.

A Zeiss ULTRATM 55 field emission Scanning Electron Microscopy (SEM) was used at an

accelerating voltage of 3 kV. Samples with crystals either from the AFM experiments on mica or

benchtop experiments on Si/Si3N4 wafers were quenched in ethanol, dried and subsequently

transferred to a metal stub for analysis.

9





VIII. Confocal Raman Microscopy.

Crystals grown on Si/Si3N4 wafers from benchtop experiments were quenched in ethanol and

analyzed using a LabRAM ARAMIS Raman microscope (Horiba Scientific). A 100 x objective

microscope was used to image the crystals, and a laser of wavelength 532 nm was focused on the

crystal of interest on the substrate using a D2 filter with a hole size of 300 µm. An acquisition

time of one minute was used to obtain spectra with a resolution of 4 cm-1 in the range of 100-

2000 cm-1.

IX. Ion Selective Electrode Experiments.

A computer-controlled titration system (Titrando 809, Methrom, Switzerland) was used in

combination with a calcium ion selective electrode (Ca-ISE), pH electrode, and a Dosing unit

(Dosino 807, 2mL glass cylinder). The Dosing unit contained a 10 mM NaOH solution to ensure

a constant pH of the initial Ca-PSS solution (pH = 6.3).

i. Calibration of the ISE and pH electrode – The Ca-ISE calibration was performed by

correlating measured calcium potentials (U(Ca2+)) with known analytical Ca2+ concentrations,

(c(Ca2+)) by using a Nernstian approach. The potential can be deduced from an electrochemical

chain consisting of the Ca2+-ISE and a reference electrode (the pH electrode) and can be

described in diluted solutions (where the ionic strength I ≤ 10-2 M) as

𝑈𝑈𝑈𝑈(𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2+) = 𝑈𝑈𝑈𝑈0 + 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅2𝐹𝐹𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 �𝑐𝑐𝑐𝑐(𝐶𝐶𝐶𝐶𝑎𝑎𝑎𝑎2+)

𝑐𝑐𝑐𝑐⊗� (2)

10

where U0 is the electrode intercept, R the gas constant, T the temperature, F the Faraday

constant, and c⊗ the standard concentration4. Thus, by an electrode calibration the electrode

intercept U0 and the slope RT/2F for Nernstian behavior can be determined.

Prior to an experiment, the pH meter was initially calibrated utilizing pH 4.0, 7.0, and 9.0

Metrohm buffers. Subsequently, the Ca-ISE was calibrated by titrating in a 0.1 M CaCl2 solution

at a rate of 10 µL/min into 25 mL Milli-Q water at the same pH. In addition, the stirring rate was

kept constant.

ii. Determination of free calcium concentration in the Ca-PSS solution – The analysis was

performed by measuring the potential of the Ca-PSS solution (25 mL) in time at pH 6.3 after the

aforementioned calibration procedures. The potential U(Ca2+) was then correlated to the

concentration c(Ca2+) by Eq. (2).

11





Supplementary Data

I. Nucleation and growth of vaterite without PSS.

Figure S2 | Vaterite nucleation without PSS.

(a) Snapshot of grown structures in LP-TEM on the Si3N4 after ~10 minutes of diffusion which show a

clear diffraction contrast, indicative of crystals grown in solution (note that the beamstop pattern is

visible). (b) AFM height image after ~10 minutes of diffusion on mica showing larger entities in solution,

of which one is magnified in (c) displaying an apparent partial vaterite structure similar to Fig. 1c in the

main text. Scale bars 200 nm.

Nucleation and growth of vaterite were observed when imaging the CaCl2 solution

exposed to the vapor of the solid (NH4)2CO3 (Fig. S2, Supplementary Video VS1). Although the

electron beam undoubtedly has a profound effect on the observed occurrences (discussion main

text), additional benchtop experiments using Si3N4 as a substrate showed that indeed vaterite is

a b

c

12

the predominant CaCO3 polymorph formed under these conditions (Fig. S3a-c), while also some

calcite was observed (Fig. S3a).

Figure S3 | Benchtop experiments of CaCO3 crystal formation using a Si3N4 wafer.

(a,b) SEM micrographs of a typical sample from the benchtop experiments using a Si3N4 wafer after 1

day of diffusion. These show predominantly large crystals with a typical vaterite flower morphology,

clearly indicated by the higher resolution micrograph in (b). (c) Raman data indicates that vaterite is the

CaCO3 polymorph present in such an individual flower crystal, selected for Raman analysis by optical

microscopy (OM) (inset, scale bar 10 µm).

250 500 750 1000 1250

Ram

an in

tens

ity (a

.u.)

Wavenumbers (cm-1)

a b

c

268 30

1

751

1076

1091

741

13





II. Flow of the initial Ca-PSS solution into the liquid cell.

The total volume V of the inlet tubing with a total length L ≈ 50 cm and radius r = 50 µm in

which the Ca-PSS solution was injected is calculated by

𝑉𝑉𝑉𝑉 = 𝜋𝜋𝜋𝜋𝑟𝑟𝑟𝑟2𝐿𝐿𝐿𝐿 (3)

Thus, V = 3.93 µL. With a set flow rate at 100 µL/h for 145 s, the total pumped volume was 4.03

µL, surpassing the total volume capacity of the inlet tubing. This confirmed that the Ca-PSS

solution should have reached the liquid cell at this point.

III. Size analysis of Ca-PSS globules and control solutions.

Fig. S4 shows that in general a similar trend towards larger particle sizes of the globules is found

if going from the bulk solution (DLS) to a surface, being mica (AFM) or Si3N4 (TEM). The

particle sizes’ mode was 13 ± 3 nm intensity-based or 8 ± 1 nm volume-based (DLS; Fig. S4a),

30 ± 3 nm (AFM; Fig. S4b), and 20 ± 3 nm (TEM; Fig. S4c), respectively. The slight difference

of sizes measured in TEM and by DLS compared to those determined in AFM is partly due to

some contribution from the AFM tip size effect, and possibly due to a somewhat differently

charged surface (mica). Nonetheless, compared to the bulk measurements we expect the globules

to flatten onto the substrate, which is indeed confirmed by AFM height measurements in the next

Section. Furthermore, effects of confinement in the LP-TEM cell on the adsorption of the

globules onto the substrate are expected to be negligible (see Supplementary Discussion I).

14

Figure S4 | Ca-PSS globule size distributions.

Particle size distributions as determined by (a) DLS (primary y-axis: intensity-based; secondary y-axis:

volume-based), (b) AFM and (c) TEM measurements.

i. Height of the globules by the AFM measurements – In Fig. S5 several lines indicate the

presence of globules of different sizes (Fig. S5a,b). In general, their heights were between 0.7 nm

- 2.5 nm. In contrast to bulk solutions where DLS analysis is based on the assumption the

globules are spherical, the height measurements show that, as expected, the globules have a

flattened profile when adsorbed to a substrate. Because, as discussed above, the dimensions of

the cell are far above the regime in which confinement effects are expected, and because it is

observed for both Si3N4 and mica, the observed flattening must be a result of the affinity of the

globules for the substrate.

If we take a spherical globule in solution with a mean diameter of d = 10.5 nm in bulk

solution (based on intensity and volume distribution in Fig. S4a) we can calculate a volume of V

= 4π/3×(d/2)3 ≈ 606 nm3. A flattened globule with a spheroidal shape, a similar volume (V =

4π/3×(d/2)2×(h/2)) and a typical height h = 1.5 nm, would have a lateral diameter of d ≈ 28 nm,

which is in the range of the most observed (mode) diameters seen in both AFM and TEM.

15





Furthermore, it was noticed that the background in these samples of the mica substrate

(Fig. S5a,b) contained a roughened pattern compared to the control of 1.25 mM CaCl2 solution

on mica (Fig. S5c), whereas the latter displayed an atomically flat surface. Adsorption of a

monolayer of the same PSS molecule (Sigma-Aldrich, Mw 70,000 g/mol) has been reported to be

between approximately 0.5 and 1 nm in height5, in line with our data (0.5 nm seems to fit best).

Thus, this roughened pattern suggests PSS chain adsorption onto the mica.

Figure S5 | Height determinations of the Ca-PSS globules.

(a,b) AFM height images showing polyelectrolyte globules on a mica surface. (a) Height profiles along

the three colored lines are shown in the inset of (a). The blue and green line indicate four globules with

corresponding peaks in the inset, while the red line (I) shows a typical background profile. The orange

square in (a) is magnified in (b), where three smaller globules are displayed along the blue line with their

resultant peaks (blue) in the inset. For comparison, the black line (II) shows height profiles of the

background with their resultant peaks (black) in the same inset. (c) AFM height image from the control

solution containing only CaCl2 on mica, showing no particles on the surface. Lines (I – III) in the inset

show height profiles of the backgrounds along the lines I-III shown in (a-c) for their comparison.

16

ii. Control PSS solution – In Fig. S6a an AFM height image from solely the PSS solution

shows no clearly visible larger globules. Similarly, no globules were observed in TEM (Fig.

S6b). In addition, the line profile in Fig. S6a shows a similar height pattern to that of the

background (I) in the insets in Fig. S5a and Fig. S5c. This suggests that, similar to the Ca-PSS

solution, there was a layer of PSS adsorbed onto the mica surface.

Figure S6 | Adsorbed PSS layer on the surface in the PSS control solution.

(a) Typical AFM height image from the 0.5 g/L control PSS solution, showing a line with corresponding

height profiles along it (inset). (b) Typical LP-TEM image from the control PSS solution. Scale bar 50

nm.

iii. Globule formation at different concentrations of Ca2+ and PSS – In Fig. S7, AFM height

images show changes occurring with increased concentration of Ca2+ or PSS. Clearly, increasing

the Ca2+ concentration gives rise to an increased density of globules at the surface and, in

addition, larger size globules (Fig. S7b). This suggests that more PSS chains are incorporated

into the globule structure. The opposite effect is seen when increasing the PSS concentration: the

17





globule density becomes lower and individual globules seem to become smaller at the mica

surface (Fig. S7c).

Figure S7 | Globule formation at various concentrations of Ca2+ and PSS.

(a) [Ca2+] = 1.25 mM and [PSS] = 0.5 g/L (see also Fig. S5a); (b) [Ca2+] = 5 mM and [PSS] = 0.5 g/L; (c)

[Ca2+] = 1.25 mM and [PSS] = 1.0 g/L. The insets show the height profiles of the lines shown in the

images. In (c), the black and the pink arrow indicate globules of which the height profile is given in the

inset through the center of the globule (line not indicated due to very small size of globules).

18

IV. Ca2+ concentration determination.

Free Ca2+ concentration determination via an ion-selective electrode (Ca2+-ISE) showed a

concentration of 0.55 ± 0.07 mM (Fig. S8a). Since the total concentration of Ca2+ was 1.25 mM,

the Ca2+ bound by the polymer was 0.70 ± 0.07 mM (or in percentage 56 ± 6% of total

concentration Ca2+). The total concentration of PSS monomers in a 0.5 g/L solution of PSS

polymer (Mw = 70,000, DP = 340) was 2.43 mM. Therefore, the binding ratio is 1 Ca2+ : 3.5 ±

0.4 PSS monomers (SS). Since we know binding takes places with the SO3- group of such a

monomer, this corresponds to a ratio of 0.29 ± 0.3 Ca2+ : 1 SO3-. Isothermal Titration

Calorimetry (ITC) data (Fig. S8b) fitted by an independent-binding-sites model showed an

average stoichiometry of binding n = 0.010 (for N = 2 experiments), or in a different expression,

0.010 PSS (titrant) binding with 1 Ca2+ (analyte). This corresponds to 100 Ca2+ per PSS chain, or

0.29 Ca2+ : 1 SO3-, in line with values from Ca2+-ISE measurements and literature of calcium

binding to PSS (polymer Mw 1,000 kg/mol)6.

Thermodynamic considerations showed, according to the model, that Ca-PSS globule

formation by Ca2+ binding to the SO3- sites is exothermic (ΔG = -456 kJ mol-1) by an

enthalpically-driven mechanism.

Additionally, Ca2+-ISE measurements reveal no changes in free Ca2+ concentration over

time, indicating that the binding of Ca2+ with the SO3- groups of the PSS when the solutions are

mixed is instantaneous and stable. This binding mechanism is exothermic, and breaking up this

structure would involve rehydration of the Ca2+ bringing along a large energetic penalty.

Consequently, we do not expect these globules to change their composition upon binding of the

globules on the Si3N4 membrane.

19





Figure S8 | Calcium concentration determination in globules.

(a) Ca2+ ion selective electrode measurements displaying a constant value of free Ca2+ as measured in the

Ca-PSS solution vs. time. (b) ITC measurements. Upper panel: raw heat pulse data. Lower panel:

integrated heat pulses, normalized per mole of injectant. This shows a differential binding curve that is

adequately described by an independent-binding-sites model with fitting parameters given in the squared

box. The blue dotted line indicates the location of 1.25 mM CaCl2 and 0.5 g/L PSS in the graph.

V. Nucleation and growth of amorphous calcium carbonate inside Ca-PSS globules.

In Fig. S9 an additional example of nucleation and growth of ACC inside globules is shown

(ACC 2, used for growth rate analysis in Fig. 3b; ACC 1 is shown in Fig. 3a of the main text,

Fig. S10 and Supplementary Video VS4). Focus near the bottom membrane was achieved by

observing the silicon diffraction patterns in the corner of the chips: the Kikuchi lines from the top

chip were clearly visible, while absent in the bottom chip due to the present liquid layer through

a b

20

which the transmitting beam had to pass. Consequently, when we observed ACC growth near

focus, we noticed particles with black contrast.

Figure S9 | Nucleation and growth of ACC from Ca-PSS globules (ACC 2).

LP-TEM images extracted from Supplementary Video VS5 at ~1h diffusion, displaying (a) two Ca-PSS

globules before ACC nucleation (t = 0) in the red box. (b) ACC formed within one of the globules from

the red box in (a) through the nucleation and growth process at t = 19.6 s is shown within the blue box.

(c) The serial intermittent processes of the nucleation and growth of ACC in (b) are shown with snapshots

captured at (i) t = 0 s, (ii) 0.4 s, (iii) 1.6 s, (iv) 3.2 s, (v) 4.0 s, (vi) 5 s, (vii) 7.6 s, and (viii) 19.6 s. The

final snapshot (viii) is highlighted in blue, matching the area within the blue box at t = 19.6 s in image

(b). Scale bar 20 nm.

a b

c (i) (ii) (iii) (iv)

(v) (vi) (vii) (viii)

21





Figure S10 | Determination of average radius for ACC 1.

(a) LP-TEM image sequence of ACC 1 demonstrating the determination of the minimum Feret diameter

(dF,min in red) and maximum Feret diameter (dF,max in yellow) via a MATLAB script in order to calculate

an average radius R per frame (5 f/s). Included error was 3 pixels per measured diameter (see

Supplementary Methods and Materials II).

0.2 s 0.4 s 0.6 s 0.8 s

1.0 s 1.2 s 1.4 s 1.6 s

1.8 s 2.0 s 2.2 s 2.4 s

2.6 s 2.8 s 3.0 s 3.2 s

3.4 s 3.6 s 3.8 s 4.0 s

22

VI. Diffraction pattern analysis of ACC in globules and transformation into calcite at

higher electron dose.

Figure S11 | Intensity vs. q-space of the ACC diffraction pattern.

After radially integrating the diffraction pattern in the inset of Fig. 3C of the main text, comparison of

the intensity distribution in q-space gives a peak in the range of 2.6 nm-1 (~3.85 Å) to 2.8 nm-1 (~3.57

Å) – that is, around 2.7 nm-1 (~3.70 Å). This agrees well with the value from the radially integrated

diffraction pattern of ACC obtained by cryoTEM7.

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

Inte

nsity

(A.U

.)

q (nm-1)

23





Figure S12 | ACC transformation into calcite upon increased electron dose.

(a) LP-TEM image of ACC in globules exposed for several minutes to the electron beam after

approximately 50 minutes of diffusion. (b) Electron diffraction analysis of the image reveals a calcite

zone axis in the [001] direction. This image matches with an orientation pattern of calcite obtained using

PSS as an additive from literature8. The inset shows multiple spots per reflection indicated by the white

arrows, implying that the particles in (a) were growing similarly along the [001] direction with a slight

misalignment between one another. (c) Shows the calcite crystal structure where the [001] direction is

parallel to the electron beam (z-axis). Scale bar in (a) is 50 nm.

VII. Growth of ACC in globules without electron beam influence.

In Fig. S13, LP-TEM images obtained in pristine areas of the Ca-PSS solution using a single

dose of ~50-300 e/A2 (see also discussion main text) show globules formed after 45-50 minutes

of diffusion. It can be seen from the images that ACC has been growing inside the globules (Fig.

S13a-d), and diffraction analysis without previous beam exposure (Fig. S13e) confirmed the

amorphous nature of the ACC in such a globule (Fig. S13f), in line with previous observations.

(110)

(100)

[001]a b

(1 0)(0 0)

(010)( 10)

( 0)

c

24

Thus, this indicates that formation of ACC inside the globules is indeed an intrinsic

phenomenon, not driven by a beam effect. Note that the contrast is not as high as observed in

previous images, due to a varying liquid layer thickness in between the windows.

Figure S13 | ACC formation in globules without previous electron beam exposure.

(a-d) LP-TEM low dose images recorded after approximately 45 to 50 minutes of diffusion. All images

were recorded from previously unexposed areas of the Ca-PSS solution. (e) Diffraction pattern recorded

from a pristine area of the cell. (f) Post-diffraction imaging of the area in (e) in bright field TEM mode,

showing the diffraction pattern was taken from a single ACC particle (indicated by white arrow) within a

single globule. Scale bars are 50 nm.

a b c

d e f

25





VIII. Determination of supersaturation from calcite growth rates.

The supersaturation σ can be given by

𝜎𝜎𝜎𝜎 = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ��𝑎𝑎𝑎𝑎𝐶𝐶𝐶𝐶𝑚𝑚𝑚𝑚2+�∗�𝑎𝑎𝑎𝑎𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶32−

�

𝐾𝐾𝐾𝐾𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠� (4)

The growth of ACC at the surface can be expected to be controlled by similar physical processes

that control the kinetics of attachment and detachment on the surface of calcite (in other words

similar kinetic coefficients and thus barriers, which is true for a wide range of crystals9). Since

supersaturation is directly given by the relative on- and off- rates9, a similar supersaturation gives

a similar net attachment rate at a kink site regardless of the phase. While on calcite the latter is

limited to growth at acute and obtuse steps, the atomically rough10 and near-spherical ACC has

ubiquitous kink sites, and therefore the radial growth rate should be of the same magnitude as the

calcite step speed at high supersaturation where the steps are rough. This has been studied in

detail as function of supersaturation11-13.

From the growth rates of the two ACC particles in the main text (16-23 nm/s), we can

approximate σ to vary between 1.0 and 1.8 at 23.5 °C (Fig. S14)11. Thus, we estimate ACC

nucleation to occur at these levels of supersaturation relative to ACC.

Similarly, for vaterite the high curvature at the time of nucleation allows us to make the

same approximation as in the case of ACC to compare initial growth rates to a calcite

supersaturation. Therefore, we determine σ = 0.5 to σ = 0.6, i.e. vaterite nucleation (without PSS)

to occur at these levels of supersaturation relative to vaterite.

26

Figure S14 | Calcite step speeds at various supersaturation values.

Calcite step speed versus supersaturation for different temperatures at pH = 8.5, ionic strength 0.1 M and

[Ca2+] : [CO32-] = 1 : 1 for (a) the obtuse steps and (b) the acute steps. Data adapted from ref 11.

IX. Determination of supersaturation and diffusivity from the diffusion equation.

Since we observe the ACC growth only in lateral dimensions, we cannot acquire direct

information on the obtained heights. Since ACC particles reported often have a spherical shape,

this would (also energetically) be a logical choice. However, from rather noisy intensity profiles

along the particles we could not distinguish between the growth of a (hemi)sphere and growth of

a flat cylindrical plate on the substrate. In this section, we calculate and discuss the differences

between both cases in terms of supersaturation and diffusivity.

Diffusion equation in 3D for spherical symmetry: If we assume the ACC to grow in a

spherical fashion, the diffusion equation over a sphere14 of radius

𝑅𝑅𝑅𝑅 ≡ 𝑆𝑆𝑆𝑆𝐷𝐷𝐷𝐷0.5𝑡𝑡𝑡𝑡0.5 (5)

27





VIII. Determination of supersaturation from calcite growth rates.

The supersaturation σ can be given by

𝜎𝜎𝜎𝜎 = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ��𝑎𝑎𝑎𝑎𝐶𝐶𝐶𝐶𝑚𝑚𝑚𝑚2+�∗�𝑎𝑎𝑎𝑎𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶32−

�

𝐾𝐾𝐾𝐾𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠� (4)

The growth of ACC at the surface can be expected to be controlled by similar physical processes

that control the kinetics of attachment and detachment on the surface of calcite (in other words

similar kinetic coefficients and thus barriers, which is true for a wide range of crystals9). Since

supersaturation is directly given by the relative on- and off- rates9, a similar supersaturation gives

a similar net attachment rate at a kink site regardless of the phase. While on calcite the latter is

limited to growth at acute and obtuse steps, the atomically rough10 and near-spherical ACC has

ubiquitous kink sites, and therefore the radial growth rate should be of the same magnitude as the

calcite step speed at high supersaturation where the steps are rough. This has been studied in

detail as function of supersaturation11-13.

From the growth rates of the two ACC particles in the main text (16-23 nm/s), we can

approximate σ to vary between 1.0 and 1.8 at 23.5 °C (Fig. S14)11. Thus, we estimate ACC

nucleation to occur at these levels of supersaturation relative to ACC.

Similarly, for vaterite the high curvature at the time of nucleation allows us to make the

same approximation as in the case of ACC to compare initial growth rates to a calcite

supersaturation. Therefore, we determine σ = 0.5 to σ = 0.6, i.e. vaterite nucleation (without PSS)

to occur at these levels of supersaturation relative to vaterite.

26

Figure S14 | Calcite step speeds at various supersaturation values.

Calcite step speed versus supersaturation for different temperatures at pH = 8.5, ionic strength 0.1 M and

[Ca2+] : [CO32-] = 1 : 1 for (a) the obtuse steps and (b) the acute steps. Data adapted from ref 11.

IX. Determination of supersaturation and diffusivity from the diffusion equation.

Since we observe the ACC growth only in lateral dimensions, we cannot acquire direct

information on the obtained heights. Since ACC particles reported often have a spherical shape,

this would (also energetically) be a logical choice. However, from rather noisy intensity profiles

along the particles we could not distinguish between the growth of a (hemi)sphere and growth of

a flat cylindrical plate on the substrate. In this section, we calculate and discuss the differences

between both cases in terms of supersaturation and diffusivity.

Diffusion equation in 3D for spherical symmetry: If we assume the ACC to grow in a

spherical fashion, the diffusion equation over a sphere14 of radius


27





with S a dimensionless ‘reduced radius’, D the diffusivity, and t the time, can be given as

𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) − 𝛷𝛷𝛷𝛷(∞) ≡ 𝐴𝐴𝐴𝐴 𝐴 𝐴𝐴𝐴𝐴(𝑆𝑆𝑆𝑆) (6)

where 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) is the concentration at the radius S and 𝛷𝛷𝛷𝛷(∞) the concentration at infinity. Here,

F(S) is given as function of S

𝐴𝐴𝐴𝐴(𝑆𝑆𝑆𝑆) = 𝑆𝑆𝑆𝑆−1𝑒𝑒𝑒𝑒−14𝑆𝑆𝑆𝑆

2− 1

2𝜋𝜋𝜋𝜋12 �1 − erf �1

2𝑆𝑆𝑆𝑆𝑆𝑆 (7)

with A

𝐴𝐴𝐴𝐴 = 12𝑞𝑞𝑞𝑞𝑆𝑆𝑆𝑆3 exp �1

4𝑆𝑆𝑆𝑆2𝑆 (8)

where q is the volume fraction of solvent or impurity in the old phase at the surface of the new

one. According to Frank14, in the ideal case that solvent or impurity is totally expelled from the

new phase (ideal crystallization), then

𝑞𝑞𝑞𝑞 = 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) (9)

Thus for the latter, we can write

𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) = 11+𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒𝑀𝑀𝑀𝑀′ (10)

and furthermore

𝛷𝛷𝛷𝛷(∞) = 11+𝐶𝐶𝐶𝐶∞𝑀𝑀𝑀𝑀′ (11)

with M’ = 0.001 × MCaCO3 (molar mass in g/mol of CaCO3) and Ce and C∞ in moles of Ca per

liter of solution so that M’Ce and M’C∞ are in kg/L. Then both concentrations are in kg of water

per kg of solution.

28

After substitution of (10) and (11) into (6), and rearranging we can find

𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

= �1+�1+ 1

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

1−�1+ 1𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)� (12)

from which we can subsequently determine the supersaturation in the case of spherical growth by

𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠 = ln �𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� = ln �

1+�1+ 1𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

1−(1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒) 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)� (13)

With MCaCO3·H2O = 118 g/mol and Ce = 2.8 × 10-2 mol/L for a 1:1 mixture of CaCl2 and NaHCO3

(pH = 8.4), we get M’Ce = 3.3 × 10-3 and 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) = 0.997. The values of S and F(S) can be

approximated by a constant for the two ACC particles (Fig. S15). Here, S from Eq. (5) is

determined from our average radius vs. time, and the diffusivity of water (2.3 × 10-5 cm2/s).

Obtaining the value of S, we can derive A = 4.1 × 10-13 from Eq. (8) and Eq. (9). Since

both AF(S) and M’Ce are << 1, we can approximate

�1 + 1𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆) ≈ 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

(14)

and

11−(1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒)𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

≈ 1 + 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆) (15)

Using Eq. (14) and Eq. (15) and substituting those approximations into Eq. (13) we find

𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠 = ln �𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� ≈ ln �1 + 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒+ 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆) + [𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)]2

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� (16)

29





with S a dimensionless ‘reduced radius’, D the diffusivity, and t the time, can be given as

𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) − 𝛷𝛷𝛷𝛷(∞) ≡ 𝐴𝐴𝐴𝐴 𝐴 𝐴𝐴𝐴𝐴(𝑆𝑆𝑆𝑆) (6)

where 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) is the concentration at the radius S and 𝛷𝛷𝛷𝛷(∞) the concentration at infinity. Here,

F(S) is given as function of S

𝐴𝐴𝐴𝐴(𝑆𝑆𝑆𝑆) = 𝑆𝑆𝑆𝑆−1𝑒𝑒𝑒𝑒−14𝑆𝑆𝑆𝑆

2− 1

2𝜋𝜋𝜋𝜋12 �1 − erf �1

2𝑆𝑆𝑆𝑆𝑆𝑆 (7)

with A

𝐴𝐴𝐴𝐴 = 12𝑞𝑞𝑞𝑞𝑆𝑆𝑆𝑆3 exp �1

4𝑆𝑆𝑆𝑆2𝑆 (8)

where q is the volume fraction of solvent or impurity in the old phase at the surface of the new

one. According to Frank14, in the ideal case that solvent or impurity is totally expelled from the

new phase (ideal crystallization), then

𝑞𝑞𝑞𝑞 = 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) (9)

Thus for the latter, we can write

𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) = 11+𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒𝑀𝑀𝑀𝑀′ (10)

and furthermore

𝛷𝛷𝛷𝛷(∞) = 11+𝐶𝐶𝐶𝐶∞𝑀𝑀𝑀𝑀′ (11)

with M’ = 0.001 × MCaCO3 (molar mass in g/mol of CaCO3) and Ce and C∞ in moles of Ca per

liter of solution so that M’Ce and M’C∞ are in kg/L. Then both concentrations are in kg of water

per kg of solution.

28

After substitution of (10) and (11) into (6), and rearranging we can find

𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

= �1+�1+ 1


1−�1+ 1𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)� (12)

from which we can subsequently determine the supersaturation in the case of spherical growth by

𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠 = ln �𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� = ln �


� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

1−(1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒) 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)� (13)

With MCaCO3·H2O = 118 g/mol and Ce = 2.8 × 10-2 mol/L for a 1:1 mixture of CaCl2 and NaHCO3

(pH = 8.4), we get M’Ce = 3.3 × 10-3 and 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) = 0.997. The values of S and F(S) can be

approximated by a constant for the two ACC particles (Fig. S15). Here, S from Eq. (5) is

determined from our average radius vs. time, and the diffusivity of water (2.3 × 10-5 cm2/s).

Obtaining the value of S, we can derive A = 4.1 × 10-13 from Eq. (8) and Eq. (9). Since

both AF(S) and M’Ce are << 1, we can approximate

�1 + 1𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆) ≈ 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒

(14)

and

11−(1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒)𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

≈ 1 + 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆) (15)

Using Eq. (14) and Eq. (15) and substituting those approximations into Eq. (13) we find

𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠 = ln �𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� ≈ ln �1 + 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒+ 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆) + [𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)]2

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� (16)

29





Figure S15 | Linear approximations for S and F(S) for ACC 1 and ACC 2.

Values of S and F(S) for ACC 1 (black) and ACC 2 (red) with a linear fit (dashed; green for ACC 1 and

blue for ACC 2) showing S and F(S) can be fairly well approximated by an average of 9.4 × 10-5 and 1.1

× 104 respectively.

Recognizing that in Eq. (16) only the first two terms are significant, and AF(S) and M’Ce << 1,

we can simplify

𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠 = ln �𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� ≈ 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒 (17)

which gives a supersaturation σs = 1.4 × 10-6.

30

Obviously this is an odd value for a supersaturation, from which we can conclude the

diffusion analysis for radial growth cannot be applied to the geometry of our experiments in a

straightforward manner. The only way S can be so much in error is if the diffusivity D is orders

of magnitude lower. Consequently, if the supersaturation estimates obtained in Section VIII are

used, AF(S) can be determined from Eq. (13) to be 5.6 × 10-3 (σ = σs = 1.0) and 1.6 × 10-2 (σ = σs

= 1.8). Since these are only a function of S (Eq. (7) and (8)) we find S to be 1.1 × 10-1 (σ = σs =

1.0) and 2.0 × 10-1 (σ = σs = 1.8). Here it can be observed that S is already at least three orders of

magnitude higher. If Eq. (5) is rearranged to give

𝐷𝐷𝐷𝐷 = 𝑅𝑅𝑅𝑅2

𝑆𝑆𝑆𝑆2𝑡𝑡𝑡𝑡 (18)

then, using the values of R and t from the measurements gives diffusivities (units in cm2/s) of D

= 1.63 × 10-11 ± 2.68 × 10-12 (σ = 1.0, ACC 1), D = 1.73 × 10-11 ± 9.11 × 10-12 (σ = 1.0, ACC 2),

D = 5.22 × 10-12 ± 8.56 × 10-13 (σ = 1.8, ACC 1), and D = 5.54 × 10-12 ± 2.91 × 10-12 (σ = 1.8,

ACC 2) (Supplementary Table S1).

Interestingly, if we take the growth rates of vaterite and calculate its diffusivity in a

similar manner by estimating the supersaturation (σ = 0.5 to σ = 0.6), we find no substantial

difference in D (D = 1.50 × 10-11 ± 3.21 × 10-12 (σ = 0.5, vaterite 1) and D = 1.18 × 10-11 ± 2.52 ×

10-12 (σ = 0.6, vaterite 1)). This suggests that the PSS does not influence the diffusivity in a

significant manner. Moreover, the changes in estimated diffusivity over time can be attributed to

a synergistic effect of variation in both the Ca2+ content, as well as CO32- levels through the

polymer and the solution.

Diffusion equation in 2D for cylindrical symmetry: Since the globule height determined using

AFM in Fig. S5a,b and Fig. S7a is only a few nanometers, it is possible that the ACC growth can

31





be more accurately approximated by the growth of a cylinder in lateral dimensions.

Consequently for this case, crystal growth is controlled by two-dimensional diffusion and we can

define according to Frank14 for a cylinder of radius


and height h (with again S a dimensionless ‘reduced radius’, D the diffusivity, and t the time), the

diffusion equation as

𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) − 𝛷𝛷𝛷𝛷(∞) ≡ 𝐴𝐴𝐴𝐴2 ∗ 𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆) (20)

As in the spherical case above, here 𝛷𝛷𝛷𝛷(𝑆𝑆𝑆𝑆) is the concentration at the reduced radius S and 𝛷𝛷𝛷𝛷(∞)

the concentration at infinity. F2(S) is given as function of S where

𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆) ≡ −12

Ei �− 14𝑆𝑆𝑆𝑆2� (21)

which for small values of S can be expanded to

𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆) = ln �1.4984𝑆𝑆𝑆𝑆

� − 12�12𝑆𝑆𝑆𝑆�

2+ 1

2∙2∙2!�12𝑆𝑆𝑆𝑆�

4− 1

2∙3∙3!�12𝑆𝑆𝑆𝑆�

6+ ⋯ (22)

Furthermore, A2 is defined as

𝐴𝐴𝐴𝐴2 = 12𝑞𝑞𝑞𝑞𝑆𝑆𝑆𝑆2 exp �1

4𝑆𝑆𝑆𝑆2� (23)

in which q represents once again the amount of the diffusing entity expelled on the formation of

unit volume of the new phase. In the ideal case that solvent or impurity is totally expelled from

the new phase (ideal crystallization) we can write for the supersaturation in 2D cylindrical

growth (in a similar manner as derived from Eq. (9) – Eq. (13))

32

𝜎𝜎𝜎𝜎𝑐𝑐𝑐𝑐 = ln �𝐶𝐶𝐶𝐶∞𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� = ln �


� 𝐴𝐴𝐴𝐴2𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆)

1−(1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒) 𝐴𝐴𝐴𝐴2𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆)� (24)

with M’Ce = 3.3 × 10-3 as addressed in the spherical case. Thus, the fraction that 𝜎𝜎𝜎𝜎𝑐𝑐𝑐𝑐 varies from

𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠 can be expressed using Eq. (17) as

𝜎𝜎𝜎𝜎𝑐𝑐𝑐𝑐𝜎𝜎𝜎𝜎𝑠𝑠𝑠𝑠

=

ln�1+�1+ 1

𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� 𝐴𝐴𝐴𝐴2𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆)

1−�1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� 𝐴𝐴𝐴𝐴2𝐹𝐹𝐹𝐹2(𝑆𝑆𝑆𝑆)�

ln�1+�1+ 1


1−�1+𝑀𝑀𝑀𝑀′𝐶𝐶𝐶𝐶𝑒𝑒𝑒𝑒� 𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹(𝑆𝑆𝑆𝑆)�

(25)

In the case of S = 1.1 × 10-1 that was found for σs = 1.0, we can now obtain for this value of S via

Eq. (22) and Eq. (23) A2F2(S) = 1.6 × 10-2. Therefore via Eq. (24) we can determine σc = 1.79.

Since at this value of S we determined AF(S) to be 5.6 × 10-3 (σs = 1.0), the ratio σc/σs in Eq. (25)

takes the value of 1.79. Similarly, for the value of S = 2.0 × 10-2 at σs = 1.8, we obtain σc = 2.61

and σc/σs = 1.45.

To find the diffusivity D in the 2D case for cylindrical growth where σ = σc = 1.0 and σ =

σc = 1.8 as determined in Section VIII, we have S = 5.9 × 10-2 and S = 1.1 × 10-3 respectively.

Since D ∝ S-2 (Eq. (18)), values for the diffusivity are approximately 3.6 (σ = σc = 1.0) to 3.1 (σ

= σc = 1.8) times higher than those reported for spherical symmetry growth in Supplementary

Table S1; i.e. Dc = 3.6 Ds (σ = 1.0) and Dc = 3.1 Ds (σ = 1.8).

X. Determination of carbonate concentration inside globules vs. vaterite without PSS.

To estimate our carbonate concentrations, the supersaturation σ as described in Eq. (4) is used. σ

is dependent on the solubility product for ACC Ksp,ACC , besides our known Ca2+ concentration

33





bound by PSS (0.70 ± 0.07 mM, see Section IV). A value of 10-6.393 M2 for Ksp,ACC was reported

by Brěcević & Nielsen15, however, recent literature describes the finding of a lower Ksp under

differently used experimental conditions16,17. Nevertheless, as a first estimate we take the

solubility product of ACC from the literature. Furthermore, we assume the ionic strength I to be

< 0.01 as a fair assumption. This is because when we have cNa+ = 2.43 mM, cCa2+ = cCa2+free =

0.55 mM and cCl- = 2.5 mM, if cCO32- becomes < 10 mM, the ionic strength becomes I < 0.01 at

pH 9.0 and T = 25°C according to the MINTEQ18 program. Thus this gives 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶32− ≈ 𝑐𝑐𝑐𝑐𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶32− and

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2+ ≈ 𝑐𝑐𝑐𝑐𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2+, and as a result we can estimate 𝑐𝑐𝑐𝑐𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶32− to be 1.41 - 1.73 mM (σ = 1.0) and 3.14 -

3.84 mM (σ = 1.8), corresponding to a Ca2+ : CO32- ratio of approximately 1 : 2 to 1 : 5.

Since the difference between the normal growth rate of vaterite and the step speed of

calcite is within the range of step speeds for calcite at a given supersaturation19, we can expect a

low supersaturation when the observed growth rates are low. Therefore, the carbonate

concentrations related to vaterite (without PSS) are expected to be significantly lower than for

the ACC growth. Indeed, when we use cCa2+free = 1.25 mM and Ksp,V = 10-6.393 M2 as the vaterite

solubility product15, we get a Ca2+ : CO32- ratio of 1 : 0.013 (σ = 0.5) and 1 : 0.014 (σ = 0.6).

XI. Presence of vaterite in bulk solution besides ACC in Ca-PSS globules.

In situ AFM showed nucleation of large µm-sized structures on the surface after longer diffusion

time. They were easily moved by the AFM tip due to their weak binding to the surface and

sudden increase in the tapping imaging force due to their abrupt large height fluctuations (Fig.

S16a,e). Therefore, often only partial particles (white) appeared in the images collected by the

upscan (Fig. S16a,e). While removed from the surface, the structures left imprints on the places

34

they were located, which were lower in thickness by one or two layers of PSS than the

surrounding area (Fig. S16b,c). Their morphology appeared spherical, oval and peanut-shape

like, while Raman analysis for these entities revealed a vaterite polymorph (Fig. S16d) in

agreement with TEM results. In SEM imaging, the µm-sized vaterite could be shown with their

intact morphology (Fig. S16f). Note that sizes and densities of these structures are significantly

different from those of TEM results, due to a limited volume effect in the TEM cell. However,

the phase and formation after similar diffusion times seem very consistent.

35





Figure S16 | Vaterite nucleation and growth after longer diffusion time.

(a) Three subsequent in situ AFM (amplitude) images (i-iii) of the Ca-PSS solution after 2 hours of

diffusion. Image (ii) shows that large structures were present in solution (scale bars 1 µm). They were

moved by the AFM tip rather easily, leaving a spherical-like or peanut-like imprint (iii). (b) AFM (height)

image of (iii). (c) Height profiles along the lines shown in (b). (d) Raman spectrum of crystals on a Si3N4

wafer after similar diffusion times, which were quenched in ethanol. Numbered peaks are corresponding

to a vaterite structure, and the peak at 520 cm-1 is that of Si. The inset shows the crystal used for Raman

analysis in the center. (e) AFM (amplitude) image with larger scan size including the area shown in (a)

inside the red box. It shows that the micron-sized entities appeared all over the substrate and left imprints.

(f) SEM image of the grown crystals on mica such as the ones shown in (a), (b) and (e), which were

quenched in ethanol. Scale bars in (e) and (f) are 5 µm.

a b(i) (ii) (iii)

e

0.0 0.5 1.0 1.5 2.0 2.5-1.0

-0.5

0.0

0.5

Heig

ht (n

m)

Width (nm)

c

f

250 500 750 1000 1250

Inte

nsity

(a.u

.)

Wavenumbers (cm-1)

268

301

1076

1091

d

36

Supplementary Tables

Table S1 | ACC growth rate data based on spherical symmetry. Radius vs. time (left columns), values of S and D for σ = 1.0 (middle columns)

and σ = 1.8 (right columns) for ACC 1 and ACC 2.

σ = 1.0; AF(S) = 5.6*10-3 σ = 1.8; AF(S) = 1.6*10-2

ACC 1 ACC 2 ACC 1 ACC 2 ACC 1 ACC 2

t (s) R (nm) t (s) R (nm) S D (cm2/s) S D (cm2/s) S D (cm2/s) S D (cm2/s)

0.4 2.32 0.2 1.43 1.11E-01 1.09E-11 1.11E-01 8.28E-12 1.97E-01 3.47E-12 1.97E-01 2.65E-12

0.6 3.52 0.4 3.25 1.11E-01 1.66E-11 1.11E-01 2.12E-11 1.97E-01 5.32E-12 1.97E-01 6.77E-12

0.8 4.44 0.6 4.41 1.11E-01 1.98E-11 1.11E-01 2.61E-11 1.97E-01 6.33E-12 1.97E-01 8.34E-12

1 4.65 0.8 4.79 1.11E-01 1.74E-11 1.11E-01 2.30E-11 1.97E-01 5.56E-12 1.97E-01 7.36E-12

1.2 5.48 1 5.92 1.11E-01 2.01E-11 1.11E-01 2.82E-11 1.97E-01 6.43E-12 1.97E-01 9.02E-12

1.4 5.87 1.2 7.60 1.11E-01 1.98E-11 1.11E-01 3.87E-11 1.97E-01 6.34E-12 1.97E-01 1.24E-11

1.6 5.53 1.4 8.05 1.11E-01 1.54E-11 1.11E-01 3.72E-11 1.97E-01 4.92E-12 1.97E-01 1.19E-11

1.8 6.08 1.6 7.93 1.11E-01 1.65E-11 1.11E-01 3.16E-11 1.97E-01 5.28E-12 1.97E-01 1.01E-11

2 6.67 1.8 9.58 1.11E-01 1.79E-11 1.11E-01 4.10E-11 1.97E-01 5.72E-12 1.97E-01 1.31E-11

2.2 7.24 2 8.83 1.11E-01 1.91E-11 1.11E-01 3.13E-11 1.97E-01 6.12E-12 1.97E-01 1.00E-11

2.4 6.85 2.2 8.98 1.11E-01 1.57E-11 1.11E-01 2.95E-11 1.97E-01 5.02E-12 1.97E-01 9.42E-12

2.6 7.61 2.4 10.21 1.11E-01 1.79E-11 1.11E-01 3.49E-11 1.97E-01 5.72E-12 1.97E-01 1.12E-11

2.8 7.68 2.6 11.35 1.11E-01 1.70E-11 1.11E-01 3.98E-11 1.97E-01 5.42E-12 1.97E-01 1.27E-11

3 7.95 2.8 11.36 1.11E-01 1.69E-11 1.11E-01 3.71E-11 1.97E-01 5.41E-12 1.97E-01 1.18E-11

3.2 8.14 3 11.60 1.11E-01 1.66E-11 1.11E-01 3.61E-11 1.97E-01 5.32E-12 1.97E-01 1.15E-11

3.4 7.86 3.2 11.08 1.11E-01 1.46E-11 1.11E-01 3.09E-11 1.97E-01 4.68E-12 1.97E-01 9.86E-12

3.6 7.76 3.4 11.42 1.11E-01 1.35E-11 1.11E-01 3.09E-11 1.97E-01 4.30E-12 1.97E-01 9.87E-12

3.8 7.90 3.6 11.62 1.11E-01 1.32E-11 1.11E-01 3.02E-11 1.97E-01 4.23E-12 1.97E-01 9.65E-12

4 7.56 3.8 10.42 1.11E-01 1.15E-11 1.11E-01 2.30E-11 1.97E-01 3.67E-12 1.97E-01 7.35E-12

4 10.71 1.11E-01 2.31E-11 1.97E-01 7.37E-12

4.2 10.45 AVERAGE 1.63E-11 1.11E-01 2.09E-11 AVERAGE 5.22E-12 1.97E-01 6.69E-12

4.4 11.70 STDEV 2.68E-12 1.11E-01 2.50E-11 STDEV 8.56E-13 1.97E-01 7.99E-12

4.6 11.10 1.11E-01 2.16E-11 1.97E-01 6.89E-12

4.8 11.96 1.11E-01 2.40E-11 1.97E-01 7.66E-12

5 10.14 1.11E-01 1.65E-11 1.97E-01 5.29E-12

5.2 11.45 1.11E-01 2.03E-11 1.97E-01 6.49E-12

5.4 10.41 1.11E-01 1.62E-11 1.97E-01 5.17E-12

5.6 12.43 1.11E-01 2.22E-11 1.97E-01 7.10E-12

5.8 10.29 1.11E-01 1.47E-11 1.97E-01 4.69E-12

6 11.49 1.11E-01 1.77E-11 1.97E-01 5.66E-12

6.2 11.48 1.11E-01 1.71E-11 1.97E-01 5.46E-12

6.4 12.17 1.11E-01 1.86E-11 1.97E-01 5.95E-12

6.6 10.95 1.11E-01 1.46E-11 1.97E-01 4.67E-12

6.8 10.77 1.11E-01 1.37E-11 1.97E-01 4.39E-12

7 12.23 1.11E-01 1.72E-11 1.97E-01 5.49E-12

7.2 11.19 1.11E-01 1.40E-11 1.97E-01 4.47E-12

7.4 13.27 1.11E-01 1.92E-11 1.97E-01 6.12E-12

7.6 12.75 1.11E-01 1.72E-11 1.97E-01 5.50E-12

7.8 12.99 1.11E-01 1.74E-11 1.97E-01 5.56E-12

8 11.78 1.11E-01 1.39E-11 1.97E-01 4.46E-12

8.2 12.28 1.11E-01 1.48E-11 1.97E-01 4.73E-12

8.4 12.77 1.11E-01 1.56E-11 1.97E-01 4.99E-12

8.6 12.12 1.11E-01 1.37E-11 1.97E-01 4.39E-12

8.8 12.55 1.11E-01 1.44E-11 1.97E-01 4.60E-12

9 11.90 1.11E-01 1.26E-11 1.97E-01 4.04E-12

9.2 12.12 1.11E-01 1.28E-11 1.97E-01 4.10E-12

9.4 12.22 1.11E-01 1.28E-11 1.97E-01 4.09E-12

9.6 11.62 1.11E-01 1.13E-11 1.97E-01 3.62E-12

9.8 12.56 1.11E-01 1.29E-11 1.97E-01 4.14E-12

10 12.94 1.11E-01 1.35E-11 1.97E-01 4.31E-12

10.2 13.32 1.11E-01 1.40E-11 1.97E-01 4.47E-12

10.4 12.61 1.11E-01 1.23E-11 1.97E-01 3.93E-12

10.6 12.45 1.11E-01 1.18E-11 1.97E-01 3.76E-12

10.8 12.20 1.11E-01 1.11E-11 1.97E-01 3.54E-12

11 12.93 1.11E-01 1.22E-11 1.97E-01 3.91E-12

11.2 11.81 1.11E-01 1.00E-11 1.97E-01 3.20E-12

11.4 13.07 1.11E-01 1.21E-11 1.97E-01 3.85E-12

11.6 12.59 1.11E-01 1.10E-11 1.97E-01 3.52E-12

11.8 12.09 1.11E-01 9.97E-12 1.97E-01 3.19E-12

12 11.68 1.11E-01 9.14E-12 1.97E-01 2.92E-12

12.2 12.22 1.11E-01 9.84E-12 1.97E-01 3.15E-12

12.4 11.64 1.11E-01 8.79E-12 1.97E-01 2.81E-12

12.6 11.62 1.11E-01 8.62E-12 1.97E-01 2.76E-12

12.8 12.24 1.11E-01 9.41E-12 1.97E-01 3.01E-12

13 13.12 1.11E-01 1.07E-11 1.97E-01 3.40E-12

13.2 11.48 1.11E-01 8.04E-12 1.97E-01 2.57E-12

13.4 12.01 1.11E-01 8.65E-12 1.97E-01 2.77E-12

13.6 11.76 1.11E-01 8.18E-12 1.97E-01 2.61E-12

13.8 12.95 1.11E-01 9.77E-12 1.97E-01 3.12E-12

14 12.95 1.11E-01 9.64E-12 1.97E-01 3.08E-12

14.2 13.19 1.11E-01 9.86E-12 1.97E-01 3.15E-12

14.4 12.50 1.11E-01 8.73E-12 1.97E-01 2.79E-12

14.6 12.10 1.11E-01 8.07E-12 1.97E-01 2.58E-12

14.8 12.91 1.11E-01 9.06E-12 1.97E-01 2.90E-12

15 13.80 1.11E-01 1.02E-11 1.97E-01 3.27E-12

15.2 14.26 1.11E-01 1.08E-11 1.97E-01 3.44E-12

15.4 12.82 1.11E-01 8.59E-12 1.97E-01 2.75E-12

15.6 13.01 1.11E-01 8.73E-12 1.97E-01 2.79E-12

15.8 12.59 1.11E-01 8.08E-12 1.97E-01 2.58E-12

16 13.63 1.11E-01 9.34E-12 1.97E-01 2.99E-12

16.2 12.90 1.11E-01 8.26E-12 1.97E-01 2.64E-12

AVERAGE 1.73E-11 AVERAGE 5.54E-12

STDEV 9.11E-12 STDEV 2.91E-12

37





Supplementary Discussion

I. Effects of physical confinement on the mineralization inside the LP-TEM cell.

Effects of confinement might be expected due to the geometry of the experimental LP-TEM cell

in which the fluid layer thicknesses are hundreds of nm to microns. Effects of confinement on

nucleation could be manifest in three ways. The first is through a similarity in cell dimensions to

critical nucleus size20 and the second is by structuring of the liquid layer through proximity to the

cell membranes21,22. However, the cell dimensions are orders of magnitude above the ~1-10 nm

critical sizes of the crystalline phases17, as well as the ~10Å thickness of the hydration layers.

The third is through what is better described as the effect of “small volume” rather than

confinement. As shown in studies using both polycarbonate pores23 and phospholipid vesicles24,

small volumes can dramatically extend the lifetime of ACC. Tester et al.24 concluded this effect

arises because nucleation probabilities scale with volume and, based on measured rates on

surfaces, volumetric rates of crystalline CaCO3 nucleation are expected to be exceedingly

small17,25. Therefore once ACC forms, the probability of replacement by crystalline phases is

insignificant on the timescale of the experiments. This scenario seems unlikely in the case of our

experiments, because previous experiments using the same LP-TEM cells – in which calcium

and carbonate buffers were mixed to create supersaturated conditions – documented the

formation of the crystalline phases of CaCO3, as well as the transformation of ACC to crystalline

CaCO3 via both direct transformation and dissolution/re-precipitation on the timescale of ~1-10

minutes26. Consequently, the stabilization of ACC in our experiments must be dominated by the

effect of the PSS-globules.

38

II. Surface charge comparison of mica and Si3N4.

For Si3N4, the point of zero charge depends greatly on the method of preparation and

stoichiometry of the material27. The Si3N4 surface tends to hydrate into a surface of primary

amine (SiNH2) groups and silanol (SiOH) groups, which concentrations are dependent on the

deposition process used. The primary amines can be protonated (SiNH3+; pKa ~10) and the

amphoteric silanol groups can be deprotonated/protonated (SiO-/SiOH2+; pKa ~2), which ratio on

the surface can be used to estimate the point of zero charge (pHpzc) at a certain pH according to

Harame’s two-site model28. Reported values of pHpzc for planar surfaces and long channels were

3 – 628-31. Taking this into account, when the surface is exposed to the Ca-PSS solution (pH =

6.3), we can expect the surface to have mostly (deprotonated) silanol groups and thus an overall

negative charge (as in cleaved mica). Next, plasma cleaning gives rise to significant oxidation of

the Si3N4 surface and renders the surface hydrophilic32. Indeed, from Raman analysis of the TEM

wafer used for benchtop experiments (Fig. S17), the band at 970 cm-1 could be assigned to Si-

OH stretching mode of surface hydroxyls33, while significant Si-N modes seem absent.

Figure S17 | Si3N4 membrane surface chemistry.

Raman spectra of the TEM wafer used for benchtop experiments, showing clear peaks at 520 cm-1 (Si)

and a band 970 cm-1 (Si-OH stretch).

250 500 750 1000 1250Ram

an in

tens

ity (a

.u.)

Wavenumbers (cm-1)

520

970

39





Supplementary Videos

VS1. Rapid vaterite nucleation without PSS. Video was recorded at 10 fps and is shown in

real time. Scale bar 50 nm.

VS2. Example of CaCO3 growth focused on a single vaterite particle. Video was recorded

at 10 fps and was sped up to play 3 times normal speed (i.e. 30 fps). Note the initial

nucleation was only observed after taking an image (Fig. 1ai) and the video recording

started from approx. 3s (Fig. 1aii). Scale bar 50 nm.

40

VS3. Adsorption of Ca-PSS globules onto the Si3N4 window. Video was recorded at 10 fps

in real time, only starting from 142 s up to 158 s after flowing in the Ca-PSS solution,

since the largest part of the original video was imaging of water. Scale bar 200 nm.

VS4. Nucleation and growth of ACC 1 inside a Ca-PSS globule. Video was recorded at 5

fps and slowed down 5 times (i.e. 1 fps). Scale bar 20 nm.


fps and plays in real time. Scale bar 20 nm.

41





Supplementary Videos

VS1. Rapid vaterite nucleation without PSS. Video was recorded at 10 fps and is shown in

real time. Scale bar 50 nm.

VS2. Example of CaCO3 growth focused on a single vaterite particle. Video was recorded

at 10 fps and was sped up to play 3 times normal speed (i.e. 30 fps). Note the initial

nucleation was only observed after taking an image (Fig. 1ai) and the video recording

started from approx. 3s (Fig. 1aii). Scale bar 50 nm.

40

VS3. Adsorption of Ca-PSS globules onto the Si3N4 window. Video was recorded at 10 fps

in real time, only starting from 142 s up to 158 s after flowing in the Ca-PSS solution,

since the largest part of the original video was imaging of water. Scale bar 200 nm.


fps and slowed down 5 times (i.e. 1 fps). Scale bar 20 nm.


fps and plays in real time. Scale bar 20 nm.

41





42

Supplementary Literature

1 Ihli, J., Bots, P., Kulak, A., Benning, L. G. & Meldrum, F. C. Elucidating Mechanisms of Diffusion-Based Calcium Carbonate Synthesis Leads to Controlled Mesocrystal Formation. Advanced Functional Materials 23, 1965-1973 (2012).

2 Marrero, T. R. & Mason, E. A. Gaseous Diffusion Coefficients. Journal of Physical and Chemical Reference Data 1, 3-118 (1972).

3 Stumm, W. & Morgan, J. J. Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters (Wiley, 1996).

4 Kellermeier, M., Picker, A., Kempter, A., Cölfen, H. & Gebauer, D. A Straightforward Treatment of Activity in Aqueous CaCO3 Solutions and the Consequences for Nucleation Theory. Advanced Materials 26, 752-757 (2014).

5 Zhu, M., Schneider, M., Papastavrou, G., Akari, S. & Möhwald, H. Controlling the Adsorption of Single Poly(styrenesulfonate) Sodium on NH3

+-Modified Gold Surfaces on a Molecular Scale. Langmuir 17, 6471-6476 (2001).

6 Verch, A., Gebauer, D., Antonietti, M. & Colfen, H. How to control the scaling of CaCO3: a "fingerprinting technique" to classify additives. Physical Chemistry Chemical Physics 13, 16811-16820 (2011).

7 Pouget, E. M. et al. The Initial Stages of Template-Controlled CaCO3 Formation Revealed by Cryo-TEM. Science 323, 1455-1458 (2009).

8 Schenk, A. S. On the Structure of Bio-Inspired Calcite Polymer Hybrid Crystals. Dr. thesis, University of Potsdam (2011).

9 Dove, P. M., De Yoreo, J. J. & Weiner, S. Biomineralization 57-93 (Mineralogical Society of America, 2003).

10 Raiteri, P. & Gale, J. D. Water Is the Key to Nonclassical Nucleation of Amorphous Calcium Carbonate. Journal of the American Chemical Society 132, 17623-17634 (2010).

11 Wasylenki, L. E., Dove, P. M. & De Yoreo, J. J. Effects of temperature and transport conditions on calcite growth in the presence of Mg2+: Implications for paleothermometry. Geochimica et Cosmochimica Acta 69, 4227-4236 (2005).

12 Teng, H. H., Dove, P. M. & De Yoreo, J. J. Kinetics of calcite growth: surface processes and relationships to macroscopic rate laws. Geochimica et Cosmochimica Acta 64, 2255-2266 (2000).

13 Larsen, K., Bechgaard, K. & Stipp, S. L. S. The effect of the Ca2+ to activity ratio on spiral growth at the calcite surface. Geochimica et Cosmochimica Acta 74, 2099-2109 (2010).

14 Frank, F. C. Radially Symmetric Phase Growth Controlled by Diffusion. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 201, 586-599 (1950).

43





15 Brečević, L. & Nielsen, A. E. Solubility of amorphous calcium carbonate. Journal of Crystal Growth 98, 504-510 (1989).

16 Gebauer, D., Völkel, A. & Cölfen, H. Stable Prenucleation Calcium Carbonate Clusters. Science 322, 1819-1822 (2008).

17 Hu, Q. et al. The thermodynamics of calcite nucleation at organic interfaces: Classical vs. non-classical pathways. Faraday Discussions 159, 509-523 (2012).

18 Felmy, A. R., Girvin, D. C. & Jenne, E. A. MINTEQ--a Computer Program for Calculating Aqueous Geochemical Equilibria. (U.S. Environmental Protection Agency, 1984).

19 Andreassen, J.-P. Growth and aggregation phenomena in precipitation of calcium carbonate. Dr. thesis, Norwegian University of Science and Technology (2001).

20 Hedges, L. O. & Whitelam, S. Patterning a surface so as to speed nucleation from solution. Soft Matter 8, 8624-8635 (2012).

21 Kilpatrick, J. I., Loh, S.-H. & Jarvis, S. P. Directly Probing the Effects of Ions on Hydration Forces at Interfaces. Journal of the American Chemical Society 135, 2628-2634 (2013).

22 Cheng, L., Fenter, P., Nagy, K. L., Schlegel, M. L. & Sturchio, N. C. Molecular-Scale Density Oscillations in Water Adjacent to a Mica Surface. Physical Review Letters 87, 156103 (2001).

23 Stephens, C. J., Ladden, S. F., Meldrum, F. C. & Christenson, H. K. Amorphous Calcium Carbonate is Stabilized in Confinement. Advanced Functional Materials 20, 2108-2115 (2010).

24 Tester, C. C. et al. In vitro synthesis and stabilization of amorphous calcium carbonate (ACC) nanoparticles within liposomes. CrystEngComm 13, 3975-3978 (2011).

25 Hamm, L. M. et al. Reconciling disparate views of template-directed nucleation through measurement of calcite nucleation kinetics and binding energies. Proceedings of the National Academy of Sciences 111, 1304-1309 (2014).

26 Nielsen, M. H., Aloni, S. & De Yoreo, J. J. In situ TEM imaging of CaCO3 nucleation reveals coexistence of direct and indirect pathways. Science 345, 1158-1162 (2014).

27 Raiteri, R., Margesin, B. & Grattarola, M. An atomic force microscope estimation of the point of zero charge of silicon insulators. Sensors and Actuators B: Chemical 46, 126-132 (1998).

28 Harame, D. L., Bousse, L. J., Shott, J. D. & Meindl, J. D. Ion-sensing devices with silicon nitride and borosilicate glass insulators. IEEE Transactions on Electron Devices 34, 1700-1707 (1987).

29 Bousse, L. & Mostarshed, S. The zeta potential of silicon nitride thin films. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 302, 269-274 (1991).

44

30 Firnkes, M., Pedone, D., Knezevic, J., Döblinger, M. & Rant, U. Electrically Facilitated Translocations of Proteins through Silicon Nitride Nanopores: Conjoint and Competitive Action of Diffusion, Electrophoresis, and Electroosmosis. Nano Letters 10, 2162-2167 (2010).

31 Bousse, L. J., Mostarshed, S. & Hafeman, D. Combined measurement of surface potential and zeta potential at insulator/electrolyte interfaces. Sensors and Actuators B 10, 67-71 (1992).

32 Stine, R., Cole, C. L., Ainslie, K. M., Mulvaney, S. P. & Whitman, L. J. Formation of Primary Amines on Silicon Nitride Surfaces: a Direct, Plasma-Based Pathway to Functionalization. Langmuir 23, 4400-4404 (2007).

33 Galeener, F. L. & Mikkelsen, J. C. Vibrational dynamics in 18O substituted vitreous SiO2. Physical Review B 23, 5527-5530 (1981).

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correction notice calcium carbonate …4 physical sciences division, pacific northwest national...

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