Inhibition of Spiral Growth and Dissolution at the Brushite (010

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Inhibition of Spiral Growth and Dissolution at the Brushite (010) Interface by Chondroitin 4-Sulfate Hang Zhai, Lijun Wang, and Christine V Putnis J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11531 • Publication Date (Web): 07 Jan 2019 Downloaded from http://pubs.acs.org on January 11, 2019

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The Journal of Physical Chemistry

Inhibition of Spiral Growth and Dissolution at the Brushite (010) Interface by Chondroitin 4-Sulfate

Hang Zhai,† Lijun Wang,*,† and Christine V. Putnis‡,§

College of Resources and Environment, Huazhong Agricultural University, Wuhan

†

430070, China ‡

Institut für Mineralogie, University of Münster, 48149 Münster, Germany §

Department of Chemistry, Curtin University, Perth, 6845, Australia

*

To whom correspondence should be addressed.

Lijun Wang College of Resources and Environment Huazhong Agricultural University Wuhan 430070, China Tel/Fax: +86-27-87288382 Email: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT

Modulating mineralization and demineralization of calcium phosphates (Ca-Ps) with organic macromolecules is a critical process for preventing human kidney stone disease. As a long unbranched polysaccharide of urinary glycosaminoglycans (GAGs), chondroitin 4-sulfate (Ch4S) has been shown to play an essential role in inhibiting the formation of kidney stones. However, the mechanism of the role of Ch4S remains poorly understood. Here, we used in situ atomic force microscopy (AFM) to observe the growth and dissolution of spirals on brushite (CaHPO4∙2H2O) (010) surfaces.

The

results show that Ch4S preferentially inhibits the [101]Cc step growth/dissolution by step pinning. This step-specific effect appears to be related to specific binding of Ch4S to Ca sites as the observed inhibition is not seen in other crystallographic directions where there are fewer Ca terminations. Moreover, Ch4S promotes an increase in terrace width of the [101̅]Cc by the modification of the interfacial energies of the step edge. These in vitro direct observations of Ch4S modulating brushite mineralization and demineralization reveal a dual control of both step kinetics and interfacial energy.

INTRODUCTION

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Kidney stones exhibit a complex composition consisting of organic compounds and inorganic calcium salts (oxalates, phosphates, sulfates and carbonates).1 At the initial stage of stone formation, more than half of kidney stones may occur with the formation of calcium phosphate (Ca-P) phases within the apical surface of renal papillae and the urinary space,2,

3

and brushite (CaHPO4∙2H2O) is present inside spherical

hydroxyapatite (Ca10(PO4)6(OH)2, HAP) with a radial distribution of acicular crystallites.4, 5 As the initial precipitating species, brushite may induce the heterogenous crystallization of HAP and calcium oxalates (CaOx) in Randall’s plaque.2 Thus, the inhibition of brushite mineralization and the promotion of brushite demineralization may lower the risk for kidney stones.6, 7 Prevention of kidney stones often involves the use of natural or synthetic macromolecules, including proteins,8, 9 peptides,10, 11 and polysaccharides,12, 13 through binding to the Ca-P or CaOx surfaces to inhibit crystal growth. As long unbranched polysaccharides, urinary glycosaminoglycans (GAGs) have been found to play an essential role in influencing stone formation.14-20 Normal urine contains about 2% GAGs which contain about 60% chondroitin sulfate (ChS).15, 16 Robertson et al.21 and Michelacci et al.22 demonstrated that ChS promoted crystal nucleation in artificial urine, and Ryan et al.23 reported that ChS had no effect on the deposition and aggregation of stone crystals; whereas in other published research,24-26 ChS was suggested to be a major inhibitor of crystal growth. In order to understand these inconsistent results, the influence of chondroitin 4-

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sulfate (Ch4S) (Figure 1) on a brushite (010) surface was investigated. Using an atomic force microscope (AFM) coupled with a fluid reaction cell, growth and dissolution were observed and recorded in situ in the presence of different concentrations of Ch4S (5500 ng/L, which is related to actual in vivo concentrations19). Based on our in situ AFM observations, Ch4S was found to preferentially bind to the [101]Cc steps to inhibit growth and dissolution through step pinning as well as morphology modification of the growth and dissolution spirals. Furthermore, contact angle measurements were conducted to reveal the energetic basis for inhibition of brushite growth and dissolution by Ch4S. The binding of Ch4S to steps increases the brushite-fluid interfacial energies, resulting in a delay for the formation of active steps on the brushite (010) face. These direct observations may further improve our understanding of the role of ChS in modulating pathological mineralization and demineralization and may provide clues to the design of effective therapeutic agents for the prevention of kidney stone formation.

EXPERIMENTAL SECTION

Reagents. All chemical reagents including pure reaction grade Ch4S were purchased from Sigma-Aldrich (St. Louis, Missouri). All experimental solutions were prepared using ultrahigh purity water (resistivity >18 MΩ·cm) that was obtained through a twostep purification treatment including a triple distillation (YaR, SZ-93, Shanghai, China) and deionization (Milli-Q, Billerica, MA). Brushite Crystal Synthesis. Brushite crystals were synthesized inside a silica-gel

4


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phase by using 4.3% sodium metasilicate solution (Na2SiO3) with 99.7% acetic acid (CH3COOH) to adjust the pH to 5.6-6.0 to form a gel. 1.0 M potassium dihydrogen phosphate (KH2PO4) solution was incorporated into the gel and 0.5 M calcium chloride (CaCl2) was added at the top of the tubes. All the gel tubes were kept at the room temperature (22 ± 2 ºC) for about 30 days.27 Brushite crystals were harvested and then characterized by Bruker D8X-ray diffraction (Billerica, Massachusetts), to identify the crystals as a single phase. In Situ Atomic Force Microscopy (AFM). Supersaturated and undersaturated solutions used in in situ AFM (NanoScope V-Multimode 8, Bruker) experiments were prepared by dropwise mixing 0.04 M CaCl2 and 0.04 M KH2PO4. 1.0 M sodium chloride (NaCl) was used to adjust the ionic strength (IS) to 0.15 M, and nitrogen (N2) was passed through the solution to exclude carbon dioxide (CO2). Ch4S was added before the pH was adjusted. The pH was then adjusted to 5.6 with 0.01 M potassium hydroxide (KOH) by a glass pH electrode with a single-junction Ag/AgCl reference electrode (Orion 4 Star ISE meter, Thermo) using Metrohm 888 Dosimat Plus (Herisau, Switzerland). The addition of Ch4S at various concentrations (5-500 ng/L) did not affects the pH (5.6) and ionic strength (IS, 0.15 M) of the final reaction solutions due to the fact that all concentrations of Ch4S chosen were about 1000 times lower than that of Ca2+ ions in supersaturated or undersaturated solutions. The relative supersaturation and undersaturation for brushite nucleation/growth and dissolution is given by σ = (IAP/Ksp)1/2 -1, where IAP is the ion activity product, and Ksp is the solubility product constant of brushite (1.87 × 10-7 mol2 L-2, 25 °C).28 The reaction

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solutions (Table S1) were continuously injected into the fluid cell of AFM at the rate of 10 mL/h with a high-precision springe pump (Razel Scientific Instruments model R100-E, Saint Albans, VT). All in situ AFM experiments were conducted under 25 ºC in contact mode. Si3N4 tips (NP-S10, Bruker) with spring constants ranging from 0.06 to 0.35 N/m and a tip radius of 10 nm were used with a scan rate of 4 Hz and a resolution of 512 × 512 pixels. The setpoint was decreased to 0.5 V to lower tip force in order to minimize possible tip-surface force interactions. Measurements were made on more than three repeated experiments on brushite crystals for each solution composition to ensure the reproducibility of results. Static Contact Angle () Measurements and Surface Free Energy Calculations. Drop Shape Analyzer-DSA100 (KRUSS, Hamburg, Germany) was used for static contact angle measurements. The brushite crystal surface-air interfacial energy (γS-air) was calculated as a proxy for crystal-liquid interfacial energy (γSL) with a wellestablished method.29 In brief, the  values of the brushite (010) surface pre-adsorbed with Ch4S at various concentrations (0, 5, 50, and 500 ng/mL) were measured with four different liquids including ultrahigh purity water, glycerol, formamide, and diiodomethane with known polar (γPL ) and dispersive (γdL ) surface energy (Table S2)30. The values of cos  are linearly related to a function of the known parameters of the testing liquids with the following expression31: γL (cos θ +1) 2√γdL

p

=

√γdS

+

√γPS

√γL

(

√γdL

)

(1)

where γL is the sum of γdL and γPL . √γdS and √γPS corresponds to the intercept and slope, respectively of Eq. 1 (Table S3). The γS-air for each brushite surface treated by 6


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different concentrations of Ch4S is given by the sum of the dispersive (γdS ) and polar (γPS ) components: γS-air = γdS + γPS (2)

RESULTS AND DISCUSION

Growth/Dissolution Spirals on the Brushite (010) Surface. Growth hillocks on the brushite (010) surface at dislocation sources, exhibited a typical triangular-shaped spiral along the [101]Cc, [1̅00]Cc, and [101̅]Cc directions (Figure 2A1) with the step height of about 0.76 nm (Figure 2A3), exactly matching half the size of the (010) lattice plane spacing.32 Similar to growth hillocks, dissolution occurred through the formation of spirals (Figure 2B1, B2) with monomolecular step depths of about 0.76 nm (Figure 2B3). Kinetics of Spiral Growth/Dissolution in the Absence and Presence of Ch4S. a) Growth. We measured the step spreading velocities of growth spirals in pure supersaturated solutions at σ ranging from 0.044 to 0.607 (Figure 3B). The growth in the system can be divided into three stages: stage I is a dead zone at low σ where steps exhibit zero velocity; stage II is a region where growth suddenly begins with a rapid rise in velocity above 𝜎+𝑑 of a critical supersaturation (𝜎+𝑑 = 𝜎+∗ = 0.11); stage III is a roughly linear region of relatively slow growth that appears to be a linear dependence of the motion rate of the [101]Cc step on σ; stage IV is a rapid growth region (i.e., it

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becomes steeper). Following the addition of Ch4S, roughening of the [101]Cc steps and rounding of corners intersecting the [101]Cc and [101̅]Cc steps were observed (Figure 3A1, A2). Consistent with changes in the spiral morphology, the presence of Ch4S resulted in the [101]Cc step speed clearly inhibited at stage III (Figure 3B), whereas there were no obvious changes in step rates of the [101̅]Cc and [1̅00]Cc (Figure S1A and B), suggesting a step-specific interaction. b) Dissolution. Brushite dissolution experiments were conducted in pure undersaturated solutions at σ ranging from -0.026 to -0.841. Etch pits occurred frequently with irregular morphologies increasing with time near equilibrium (σ = 0.026) that is close to 𝜎−𝑑 (Figure S2A). Triangular dissolution spirals formed at relatively high undersaturations (σ > -0.096) (Figures 2B1, 4A1 and S2B) with the same step directions as observed for the growth spirals (Figure 2A1 and A2), and these dissolution spirals were used for velocity measurements. However, opposite handedness of dissolution and growth spirals does not occur, i.e., the direction of step retreating during dissolution is not always opposite to that during growth.33 Moreover, in contrast to spiral growth, the required activation Gibbs energy for the formation of kinks by ions/building units leaving non-kink positions in a step during dissolution may be larger than the activation Gibbs energy required for new kinks being formed by ions attaching onto non-kink positions in a step.34 Specifically, the attachment barriers may primarily result from kink site desolvation, while detachment barriers may largely result from breaking ion-crystal bonds.35 The retreat velocity of the [101]Cc, [101̅]Cc and [1̅00]Cc step versus σ exhibited a

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linear relationship (Figures 4B and S1C, D). When 50 ng/mL Ch4S was added into undersaturated solutions, the step retreat velocities along the [101]Cc direction were decreased, whereas the velocities of the [1̅00]Cc, and [101̅]Cc steps were hardly changed (Figure S1C and D). In addition, a new [1̅01̅]Cc step parallel to the [101]Cc step with more Ca2+ ions (Figure S3) was observed during the dissolution at σ ranging from 0.239 to -0.686 (Figure 4A2) (i.e., σ ≪ σd- ), suggesting that Ch4S tends to bind with Ca2+ along the [101]Cc and [1̅01̅]Cc steps.36 Mechanisms Explaining the Effect of Ch4S on Step Velocity and Morphology. In this study, the linear dependence between step velocity and supersaturation (v ≈ β(a − ae) was observed at stage III, where a and ae are the actual and equilibrium solute activities and β is the kinetic coefficient37 (Figure 3B). The velocity curves for surface growth or dissolution in the presence of Ch4S (Figure 5) have a shape that is at least qualitatively similar to that predicted by the Cabrera-Vermilyea (C-V) model of crystal growth inhibition.38 In the present study, a velocity dead-zone is present regardless of the absence or presence of Ch4S, suggesting that pure solutions actually contain some unknown, trace impurities that may be from chemicals used in the

preparation of

supersaturated solutions. This will generate different dead-zones (𝜎+𝑑1 = 0.11 and 𝜎+𝑑2 = 0.18 for the solutions in the absence and presence of 50 ng/mL Ch4S, respectively), but it does not influence the result that can be explained by the C-V model. At supersaturation beyond 𝜎+𝑑2 , the [101]Cc steps recover motion while they are roughening (Figure 3A2) due to step pinning.37 In the C-V model, effects of impurities on crystal growth are mainly through the

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adsorption at terraces, edges, and/or kinks of a growing surface, contributing to the formation of a barrier blocking the movement of the spreading step.37 The steps continue to advance around the blocked sites when the spacing (Li) between impurities is greater than the critical diameter of curvature for the step (2rc), as described by the Gibbs-Thomson (G-T) law,37, 39 through the equation Li =

1

(3)

BC0.5 i

where B is a proportionality coefficient and Ci is the bulk solution concentration of impurities/additives. In this study, step roughening was observed at [101]Cc step edges (Figure 3A2) and the ratio of step advancement velocity on impurity/additive spacing (𝑣𝑖 ) to the velocity in a pure system (𝑣0 ) is given by39, 40 𝑣𝑖 𝑣0

= (1-

2rc Li

)(1-EC0.5 i )

where the first term, (1-

(4) 2rc Li

) is the effect of step pinning, and the second, (1-EC0.5 i )

reflects the decrease of βi (the slope of the 𝑣𝑖 versus Ci in eq 4), and E is a proportionality constant reflecting a combination of geometric factors, probability of attachment, and the lifetime of the impurity/additive adsorbing on the surface. As a consequence, the C-V model makes a prediction of the presence of a “dead zone” where no growth occurs below a critical supersaturation (σ*) with an expression for39 vi v0

= (1-

σ* σ

)(1 - EC0.5 i )

(5)

Figure 5A reflects a linear dependence of

𝑣𝑖 𝑣0

and

1 𝜎

at a constant Ci , showing that the

C-V model gives a good fit to the AFM data in the presence of Ch4S. In terms of Ci , the expression is37

10


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vi v0

= (1 -

BC0.5 i σ

)(1 - EC0.5 i )

(6)

Figure 5B shows that the above equation fits to step velocities along the [101]Cc direction. We, therefore, conclude that the interaction of Ch4S-[101]Cc step is reasonably described by the C-V model, and this phenomenon was absent for both [ 1̅ 00]Cc and [ 101̅ ]Cc steps (Figure S1), suggesting the presence of step-specific interactions by the negative carboxyl (-COO-) and sulfonyl hydroxide (-SO3-) groups of Ch4S binding to the calcium-terminated [101]Cc polar steps (Figure S3)41 through the geometry and stereochemistry of Ch4S matched to this polar step.25 Step Density Changes. In addition to inhibition of the step velocity of the [101] Cc by Ch4S, the step density (λ) of the [101̅]Cc was also changed due to the change of 1

terrace width (w = λ).42 In pure growth solutions at 𝜎 = 0.344, the average width of each terrace of the [101̅]Cc was 256.6 ± 21.5 nm (n = 3) (Figure 6A1), whereas the addition of 5 ng/mL Ch4S in supersaturated solutions (𝜎 = 0.344), the average terrace width increased to 371.9 ± 18.8 nm (n = 3) (Figure 6A2). This change was enhanced after the increase of Ch4S concentrations to 50 ng/mL (Figure 6A3). With increasing supersaturation to 0.555 in the presence of 50 ng/mL Ch4S, the effect of Ch4S on the step width eventually disappeared (Figure 6B1), and increasing Ch4S concentrations to 500 ng/mL slowed its disappearance down (Figure 6B2). The same phenomenon occurred during dissolution on the [101̅]Cc steps (Figure 6C1-D2). According to spiral growth mechanisms, terrace width changes due to both changes in surface energies and redistribution of step velocities,43,44 which are expressed in eq.6, wi = vi ∑3i = 1

lci sin (αi, i+1 )

(7)

vi+1

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Each corresponding edge of a spiral exhibits critical length 𝑙𝑐𝑖 and forms an angle 𝛼𝑖,𝑖+1 with the previous edge of the spiral.43 For the [101̅ ]Cc steps, the spreading velocities were not significantly changed (Figure S1). Thus, only 𝑙𝑐𝑖 affects wi , and the value of 𝑙𝑐𝑖 is given by45 lci =

2γstep Ω

(8)

kB Tσ

where Ω is the volume per growth unit in the solid, γstep is the free energy of the step edge, kB is the Boltzmann constant, and T is absolute temperature. The measured γS-air as a rough proxy for γSL (Figure 7B) suggests that Ch4S dramatically increases γSL because γS-air indicates the hydrophilicity of the substrate and a larger γS-air correlates with a smaller γSL .29 Moreover, because of γSL correlating with the mean value of the free energies of the step edges of all crystal faces, a higher γSL is associated with a higher step edge free energy (γstep ) that will delay the formation of new steps.

CONCLUSION

In the present study, we used in situ AFM to investigate the effect of Ch4S on spiral growth and dissolution of the brushite (010) surface. Ch4S inhibits the [101]Cc step growth/dissolution through step pinning. This effect appears to be related to specific binding of Ch4S to Ca sites as the observed inhibition is not seen in other crystallographic directions where there are fewer Ca terminations. Moreover, terrace width of the [101̅]Cc is increased by Ch4S due to the modification of the interfacial energies of the step edge. Previous results have shown three aspects of crystallization

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affected by Ch4S: nucleation, deposition/aggregation, and growth. This study addresses the role and mechanism of inhibition during crystal face growth and dissolution, and the findings provide possible implications concerning the role of Ch4S during nucleation and deposition/aggregation. Actually, Ch4S can also inhibit the nucleation of brushite (Figure S4). A fundamental understanding of brushite mineralization and demineralization in the presence of Ch4S macromolecules can be essential for the elucidation of the mechanisms of kidney stone prevention, although the exact role of Ch4S in modulating kidney stone formation in vivo may be more complicated. This study may provide insights into a broader application of Ch4S in inhibiting kidney stone formation, however more in vitro and in vivo research will be needed in the future.

ASSOCIATED CONTENT

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. AFM experimental conditions (Tables S1); Surface free energy (𝛾𝑆−𝑎𝑖𝑟 ) of brushite preadsorbed with Ch4S (Tables S2 and S3); Spreading velocities of the [1̅00]Cc and [101̅]Cc steps (Figure S1); Brushite dissolution at σ = -0.026 or -0.096 (Figure S2); Brushite structure (Figure S3) and the bulk nucleation (Figure S4).

AUTHOR INFORMATION

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Corresponding Author *Phone/Fax: +86-27-87288382. E-mail:

[email protected]

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (41471245 and 41071208) and the Fundamental Research Funds for the Central Universities (2662017PY061 and 2662015PY206). C.V.P. acknowledges funding through the EU seventh Framework Marie S. Curie ITNs: Minsc; CO2 react; and Flowtrans.

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28. Dorozhkin, S. V. Calcium orthophosphates. J. Mater. Sci. 2007, 42 (4), 1061-1095. 29. Giuffre, A. J.; Hamm, L. M.; Han, N.; De Yoreo, J. J.; Dove, P. M. Polysaccharide chemistry regulates kinetics of calcite nucleation through competition of interfacial energies. Proc. Natl. Acad. Sci. U. S. A. 2013, 110 (23), 9261-9266. 30. Kaelble, D. H. Dispersion-polar surface tension properties of organic solids. J. Adhesion 1970, 2 (2), 66-81. 31. Owens, D. K.; Wendt, R. C. Estimation of the surface free energy of polymers. J. Appl. Polym. Sci. 1969, 13 (8), 1741-1747. 32. Curry, N. A.; Jones, D. W. Crystal structure of brushite, calcium hydrogen orthophosphate dihydrate: A neutron-diffraction investigation. J. Chem. Soc. A 1971, 3725-3729. 33. Adobes-Vidal, M.; Shtukenberg, A. G.; Ward, M. D.; Unwin, P. R. Multiscale visualization and quantitative analysis of L-cystine crystal dissolution. Cryst. Growth Des. 2017, 17, 1766-1774. 34. Christoffersen, J.; Christoffersen, M. R. Spiral growth and dissolution models with rate constants related to the frequency of partial dehydration of cations and to the surface tension. J. Cryst. Growth 1988, 87, 41-50. 35. Joswiak, M. N.; Doherty, M. F.; Peters, B. Ion dissolution mechanism and kinetics at kink sites on NaCl surfaces. Proc. Natl. Acad. Sci. U.S.A. 2018, 115, 656-661. 36. Qin, L.; Wang, L. J.; Wang, B. S. Role of alcoholic hydroxyls of dicarboxylic acids in regulating nanoscale dissolution kinetics of dicalcium phosphate dihydrate. ACS Sustain. Chem. Eng. 2017, 5, 3920–3928.

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37. De Yoreo, J. J.; Wierzbicki, A.; Dove, P. M. New insights into mechanisms of biomolecular control on growth of inorganic crystals. CrystEngComm 2007, 9 (12), 1144-1152. 38. Thomas, T. N.; Land, T. A.; DeYoreo, J. J.; Casey, W. H. In situ atomic force microscopy investigation of the {100} face of KH2PO4 in the presence of Fe (III), Al (III), and Cr (III). Langmuir 2004, 20 (18), 7643-7652. 39. Wang, L. J.; De Yoreo, J. J.; Guan, X.; Qiu, S. R.; Hoyer, J. R.; Nancollas, G. H. Constant composition studies verify the utility of the Cabrera−Vermilyea (CV) model in explaining mechanisms of calcium oxalate monohydrate crystallization. Cryst. Growth Des. 2006, 6 (8), 1769-1775. 40. Miura, H. Phase-field modeling of step dynamics on growing crystal surface: step pinning induced by impurities. Cryst. Growth Des. 2015, 15 (8), 4142-4148. 41. Qin, L.; Zhang, W.; Lu, J.; Stack, A. G.; Wang, L. J. Direct imaging of nanoscale dissolution of dicalcium phosphate dihydrate by an organic ligand: Concentration matters. Environ. Sci. Technol. 2013, 47(23), 13365-13374. 42. Li, M.; Zhang, J.; Wang, L. J.; Wang, B.; Putnis, C. V. Mechanisms of modulation of calcium phosphate pathological mineralization by mobile and immobile smallmolecule inhibitors. J. Phys. Chem. B 2018, 122 (5), 1580-1587. 43. Sizemore, J. P.; Doherty, M. F. A new model for the effect of molecular imposters on the shape of faceted molecular crystals. Cryst. Growth Des. 2009, 9 (6), 26372645. 44. Sizemore, J. P.; Doherty, M. F. A stochastic model for the critical length of a spiral

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edge. J. Cryst. Growth 2010, 312, 785−792. 45. Li, S.; Wu, S.; Nan, D.; Zhang, W.; Wang, L. J. Inhibition of pathological mineralization of calcium phosphate by phosphorylated osteopontin peptides through step-specific interactions. Chem. Mater. 2014, 26 (19), 5605-5612.

Figure 1. Chondroitin 4-sulfate (Ch4S) molecule consisting of glucuronic acid (GlcA) and N-acetylgalactosamine (GalNAc-4S).

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Figure 2. Spiral growth and dissolution features on the brushite (010) surfaces. AFM (A1, B1) deflection and (A2, B2) height images showing the (A1, A2) growth and (B1, B2) dissolution spiral in a hillock with steps spreading along the [101]Cc, [101̅] Cc, and [1̅00] Cc directions. Scale bars = 1 µm. (A3, B3) Height profiles along lines 1 → 2 in (A2, B2) showing the monomolecular heights of 0.76 nm.

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Figure 3. Time sequence of AFM images of a growth spiral in supersaturated solutions (σ = 0.397) (A1) without and (A2) with 50 ng/mL Ch4S, showing roughening of the [101]Cc steps by Ch4S. Scale bar = 1 µm. (B) Spreading velocities of the [101]Cc steps of growth spirals in the absence and presence of Ch4S in supersaturated solutions (σ = 0.044 - 0.607). Dashed lines divide the spreading velocities into 4 stages. Arrows in (B) indicate different dead-zones with 𝜎+𝑑1 = 0.11 (black) and 𝜎+𝑑2 = 0.18 (blue) for the supersaturated solutions in the absence and presence of 50 ng/mL Ch4S, respectively.

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Figure 4. Time sequence of AFM images of a dissolution spiral in an undersaturated solution (σ = -0.385) in the (A1) absence and (A2) presence of 50 ng/mL Ch4S. Arrow in A2 indicates the newly expressed the [1̅01̅]Cc steps. Scale bar = 1 µm. (B) Retreat velocities of the [101]Cc, [1̅00]Cc and [101̅]Cc steps of dissolution spirals in the absence and presence of 50 ng/mL Ch4S in undersaturated solutions (σ = -0.096 - -0.841).

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Figure 5. (A) Relative step velocity (v/v0) for [101]Cc steps as a function of (A) 1/σ and (B) concentrations of Ch4S. The fitted dashed lines in (A, B) are calculated with eq 5 and 6, respectively.

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Figure 6. AFM images of (A1-A3) growth spirals and (C1-C3) dissolution spirals in the absence and presence of Ch4S, demonstrating the effect of Ch4S on terrace widths along the [101̅] Cc direction during the (B1, B2) growth and (D1, D2) dissolution. Scale bars = 1 µm.

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Figure 7. Measurements of surface free energy in air 𝛾𝑆−𝑎𝑖𝑟 . (A) Fitting contact angles of the brushite (010) surfaces adsorbed with various concentrations of Ch4S by eq 1. (B) 𝛾𝑆−𝑎𝑖𝑟 calculated by eq 2 with fitting parameters including the intercept (√𝛾𝑆𝑑 ) and the slope ( √𝛾𝑆𝑝 ), showing a decrease of 𝛾𝑆−𝑎𝑖𝑟 with the increase of Ch4S concentrations.

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TOC Graphic

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Inhibition of Spiral Growth and Dissolution at the Brushite (010

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