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CaCO3 vaterite microparticles for biomedical and personal care applications

Daria B. Trushina, Tatiana V. Bukreeva, Mikhail V. Kovalchuk, MariaN. Antipina

PII: S0928-4931(14)00242-2DOI: doi: 10.1016/j.msec.2014.04.050Reference: MSC 4606

To appear in: Materials Science & Engineering C

Received date: 16 January 2014Accepted date: 21 April 2014

Please cite this article as: Daria B. Trushina, Tatiana V. Bukreeva, Mikhail V. Kovalchuk,Maria N. Antipina, CaCO3 vaterite microparticles for biomedical and personal care ap-plications, Materials Science & Engineering C (2014), doi: 10.1016/j.msec.2014.04.050

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CaCO3 vaterite microparticles for biomedical and personal care applications

Daria B. Trushinaa,b

, Tatiana V. Bukreevac,d

, Mikhail V. Kovalchukc,d

, Maria N. Antipinaa*

a Institute of Materials Research and Engineering, A*STAR, Singapore, 117602 Singapore

b Lomonosov Moscow State University, Faculty of Physics, Moscow, 119991 Russia

c National Research Centre "Kurchatov Institute", Moscow, 123098 Russia

d A.V. Shubnikov Institute of Crystallography Moscow, 119333 Russia

*Corresponding author:

Email: antipinam@imre.a-star.edu.sg (Maria N. Antipina)

Tel. +65 68741974

Fax +65 68720785

Abstract

Among the polymorph modifications of calcium carbonate, the metastable vaterite is the most

practically important applied in regenerative medicine, drug delivery and a broad range of

personal care products. This manuscript scopes to review the mechanism of the calcium

carbonate crystal growth highlighting the factors stabilising the vaterite polymorph in the most

cost efficient synthesis routine. The size of vaterite particles is a crucial parameter for practical

applications. The options for tuning the particle size are also discussed.

Keywords

Calcium carbonate (CaCO3), biomineral, vaterite polymorph, co-precipitation, crystal growth.

1. Introduction

Vaterite is a mineral, a polymorph of calcium carbonate (CaCO3). Vaterite is usually colorless,

having spherical shape and porous inner structure. The diameter of a vaterite particle ranges from

0.05 to 5 μm. Like aragonite, vaterite is a metastable phase of CaCO3 at ambient conditions at

the surface of the earth. Being less stable than either calcite or aragonite, vaterite has a higher

solubility than either of these phases. Therefore, vaterite transforms to calcite or aragonite once it

is exposed to water. Temperatures below 60C facilitate the formation of calcite, and at the

higher temperatures, recrystallization to aragonite occurs [1, 2].

Despite being metastable, vaterite can still be found in nature, for instance, in mineral

springs. It usually occurs as a minority component of a larger structure or as a result of a

pathological process in humans and animals. Thus, vaterite is found in fish otoliths, freshwater

pearls, healed scars of some mollusk shells, gallstones and urinary calculi [3]. In those

circumstances, some impurities (metal ions or organic matter) may stabilize the vaterite and

prevent its transformation into calcite or aragonite.

Like other polymorphs of calcium carbonate, vaterite rapidly dissolves at acidic pH, and

thus it can undergo degradation both in vivo and in vitro. Biodegradation of vaterite may occur in

body fluids or some acidic extracells, or upon the cellular phagocytosis and absorption. Body

fluid contains a number of acidic metabolites, such as citrate, lactate and acid hydrolysis

enzymes, which provides acidic environment for dissolution of the material. After entering cells

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(mainly macrophages) by phagocytosis, vaterite particles are split into ions under the effect of

cytoplasmic and lysosomal enzymes, and then the degradation products, Ca2+

and CO32-

, can be

transferred to extracell. Ca2+

can then participate in the formation of new tissue without causing

organic damage and pathological tissue calcification [4].

Vaterite microparticles can be produced in a number of ways, however, the majority of

them is laborious, or require extreme conditions and special equipment. The main industrial

manufacturing method is based on CO2 bubbling through a calcium containing solution, also

referred as the Kitano approach [5-8]. Among the other popular methods are the double emulsion

approach [9], solvothermal growth in autoclave above 100°C [10], and biomineralization [4, 11,

12]. Synthesis is often carried out in a double jet reactor vessel [13] applying ultrasound [14-16]

or magnetic field [14, 17, 18]. The simplified method comprises mixing of saturated aqueous

stock solutions containing calcium and carbonate ions. The mixing method is highly cost

efficient, fast and easy to perform. Moreover, it may be scaled up for industrial production of

vaterite particles [19-23]. However, the mixing method may result in unwonted recrystallization

of vaterite to more stable polymorphs of calcium carbonate. Therefore, a detailed understanding

of the CaCO3 crystal growth process is essential for success in vaterite production.

Here we introduce the current opinions on the vaterite crystal growth and review the

conditions promoting the vaterite polymorph of calcium carbonate. Due to its biodegradability,

low cost and unique physical and chemical properties, vaterite is highly demanded in

biomedicine and is an essential component of a big variety of personal care products. Besides

being actively used in bone implants, abrasives, cleaners and absorbers, vaterite is playing a key

role in encapsulation and drug delivery. However, the size of the vaterite particles is often a

crucial parameter. Possible ways to influence the particle size are also discussed in the

manuscript.

2. Introduction to the CaCO3 crystal growth

The formation of a new solid phase is initiated through nucleation in supersaturated solution.

Solid state precipitates initially in an amorphous sediment of spherical granules with a diameter

10 nm - 70 nm [5, 17, 19, 20, 24, 25]. Then, the transformation and dissolution-recrystallization

processes result in a mixture of calcium carbonate crystalline hydrated forms (hexahydrate and

monohydrate) and three anhydrous crystalline polymorphs (vaterite, aragonite and calcite).

Vaterite nucleation and growth is of the special interest, and the vaterite particle formation

mechanism is a subject of on-going debate [25]. Two explanations for the formation of primary

polycrystalline vaterite spheres exist in the literature. The nano-aggregation concept claims that

the spheres are the result of rapid aggregation of initially formed nano-sized crystals [6, 16, 22,

26, 27]. However, only relatively insoluble substances develop high supersaturations, so that

precipitation can also be considered as crystallization of sparingly soluble substances. Thus, the

concept of classical spherulitic growth shown schematically in Figure 1, advocates that a sphere

of vaterite with polycrystalline features originates from the formation of a single nucleus

followed by branching of this small crystal (often mentioned as ripening of crystallites) [26, 28,

29]. It is also supposed that a final particle can be a result of both crystallization processes taking

place at a time [30].

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According to the crystal growth theory, precipitation starts from nucleation. The initially

formed nuclei grow into crystallites. The crystal growth process occasionally entailed with the

formation of secondary nuclei causes significant changes in the initial concentrations of calcium

and carbonate ions in solution. The crystal growth itself is a complex process comprising two

elementary processes taking place either at some distance from the crystal surface or at the

crystal-solution interface. These elementary processes are 1) diffusion and/or convection of

growth units through the bulk toward the crystal-solution interface, and 2) surface integration

processes at the crystal-solution interface. The slowest of these consecutive processes determines

the overall crystal growth rate.

The solid phase thus formed (crystals) undergoes further changes in physical and

chemical properties. These secondary changes occur under conditions close to equilibrium

signifying the tendency of the system to establish equilibrium. Theoretically, precipitation

terminates when the crystals present in the system form one crystal which is in equilibrium with

the saturated solution. In practice, precipitation is completed when crystals reach a size that

causes sedimentation. The process that leads to equilibrium is called ageing and takes place

through several possible ways. Dissolution of small and simultaneous growth of large particles

(also referred as Ostwald ripening) and recrystallization are the mechanisms that probably

always occur in the early stages of the precipitate formation. Coagulation and agglomeration

followed by sintering change the initial dispersion of the system by formation of more stable

large aggregates (Fig 1).

The preference for vaterite formation exists when starting ionic activity product

lays between thermodynamic solubility product for amorphous calcium carbonate

KSP(ACC) and the solubility product for vaterite KSP(Vaterite) [26]. The logarithmic ion activity

Figure 1. Stages and pathways of precipitation processes [15].

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product of Ca2+

and CO32-

in the suspension at 25°C is shown as a function of time in Figure 2a.

Regions I, II and III in Fig. 2 correspond to unstable stage, metastable stage and stable stage,

respectively.

Figure 2. The change in logarithmic ion activity product of calcium and carbonate, log IAP, with

time at 25 ˚C (a) (plotted from [19]) ; the dependence of nucleation rate on supersaturation (b)

(plotted from [31]).

Under condition within the region I (unstable stage), calcium carbonate nanoparticles

randomly emerge as an amorphous sediment at all temperatures. Onwards, nanoparticles line up

along specific crystallographic orientations, resulting in a phase change from poorly crystalline

to crystalline. The crystalline CaCO3 begins to form around the time when the IAP curve shows

the “inflection point” (Figure 2a) [19]. As the crystals continue to precipitate, the supersaturation

status decreases causing the nucleation force to decrease as shown in Figure 2b, and the

subsequently formed nanoparticles begin to attach to each other in a crystallographically oriented

fashion, which is thermodynamically more stable than random attachment. The transformation of

amorphous calcium carbonate (ACC) is completed just before the steep decrease in the IAP, and

all ACC particles disappear forming clusters a few micrometres in diameter.

Figure 3. Plots of abundance of crystalline calcium carbonates at the early metastable stage as a

function of temperature (plotted from [19]).

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The polymorph composition of precipitated particles in the early metastable stage

presented as a function of temperature in Figure 3. Initial ACC transformed to the combination

of vaterite and calcite at low temperatures (14°C to 30°C). Vaterite polymorph occurs

predominantly at 30°C – 40°C. At intermediate temperatures (40°C to 50°C) the formation of all

three polymorphs is observed. Elevating the temperature above 60°C stabilize aragonite

polymorph of calcium carbonate.

The abundance of a certain modification also depends on supersaturation [11, 13, 19, 26].

The effect of supersaturation has been described by the Ostwald's law of stages: at sufficiently

high supersaturation the most soluble and the least stable form crystallizes first [32]. At the

beginning of the stage II, the system is supersaturated with respect to all polymorphic forms, thus

the least stable and higher-energy form of vaterite is the firstly to crystallize. The crystallization

of the vaterite form will proceed until the supersaturation value decreases down to reach the

solubility for this form (Figure 4a). At the same time, as the system is supersaturated with

respect to all forms, the crystallization of the second more soluble form (aragonite) begins.

Dissolving vaterite contributes to further crystallization of the aragonite form until completely

transformed [32]. Complete dissolution of vaterite induces steep decrease in the IAP value to

Ksp of the next polymorph (aragonite) with subsequent transformation to the most stable calcite

[19]. Figure 4b provides a range of respective Ksp values for the vaterite, aragonite and calcite

forms at different temperatures. It can be seen from Fig 4b that the solubility product of all forms

decreases at the higher temperatures that is quite uncommon for both organic and inorganic

substances.

Figure 4. The effect of supersaturation on the crystallization of polymorphs. The circles indicate

different supersaturations (a) (plotted from [32]); solubility of the anhydrous crystalline

polymorphs at 1bar (b) (plotted from [33]).

As the vaterite form has the highest solubility among the polymorphs and precipitates

first, it appears to be the most challenging to stabilize it nuclear and suspend the formation of

other modifications. During the metastable stage, all crystals are finally transformed to the most

stable modification of calcite at all temperatures as a result of water induced dissolution-

recrystallization process Figure 5. The implication of the theory reveals that by controlling the

supersaturation and harvesting crystals at an appropriate time, it should be possible to isolate the

certain polymorphic form [32].

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The stable stage corresponds to particles growth in size without further changes in

morphology. The value of IAP stabilizes at the solubility product of calcite and stable nuclei

grow occurs to a certain size (Fig. 2a) [23].

Figure 5. Schematic depiction of the formation of CaCO3 spherulites and the transformation

from amorphous phase to typical calcite [34].

Figure 6. Plot of the time required to reach the metastable stage (Tm) as a function of

temperature (plotted from [19]).

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Factors influencing the morphology of CaCO3 crystals are those affecting

supersaturation. Activity of the calcium and carbonate ions is connected with the ionic strength

and temperature. As shown in Figure 6, the time required to reach the metastable stage (Tm) of

the polymorph mix decreases with increasing temperature. Temperature is an important

parameter for bulk crystallizations as it allows to control the product solubility making possible

to obtain only the thermodynamically stable lowest-free-energy form at any given value [32].

Temperature variations may change the rank order of the thermodynamic stability reflecting the

changes in the free energies of the polymorphs. Such a change in terms of solubilities is shown

in Figure 7. The change in rank order is characterized by a transition temperature Tc. From these

considerations it is clear that the thermodynamic stability of the polymorphs must be taken into

account in studies on crystallization of polymorphs [32].

Changes in the initial pH values have an impact on the ionic strength of the solution,

which is related to supersaturation. A higher pH leads to a higher concentration of carbonate ions

and a higher supersaturation. When the initial pH value is higher than 7 but is lower than 11, the

precipitation of calcium carbonate follows the ACC–vaterite pathway described above [35].

The vaterite abundance and its crystal size increase with higher initial concentrations of

Ca2+

and CO32-

ions. The change in its dominance with time for two solutions of different

supersaturation values is shown in Figure 8a. In spite of practically equal ion activity of calcium

and carbonate in the initial solutions in (A) and (B), the suspension which contains an excess of

Ca2+

(A) gives a higher vaterite abundance.

Figure 7. Schematic diagram illustrating the solubility relationship between two

polymorphic forms as a function of temperature close to the phase transition temperature Tc

(plotted from [32]).

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Figure 8. Plots of vaterite abundance as a function of time in metastable stage as 25 ˚C with

initial concentrations of calcium and carbonate (a). Initial concentrations: (A) 0.11 M CaCl2 –

0.10 M Na2CO3, (B) 0.10 M CaCl2 – 0.11 M Na2CO3 (plotted from [19]). Plots of the square root

of the growth rate as a function of the relative supersaturations and various ionic strengths (b)

[15].

Using a computer program, the rate of crystal growth was determined by numerical

differentiation and the growth kinetics was found to be parabolic (Fig. 8b) [15], which is in good

agreement with experimental data obtained elsewhere [33]. Surprisingly, a rather weak

dependence of the vaterite growth rate on the ionic strength was found [15].

3. Vaterite characterization and properties

3.1 Structure

Being a metastable polymorph, vaterite rarely exists in nature in the pure form, and large single

crystals of vaterite are difficult for obtaining in-vitro. Because of that, it has been a big challenge

to resolve the structure of vaterite for almost a century.

The most widely accepted fact is that vaterite has a hexagonal crystal symmetry [10, 14,

20, 29, 36, 37] and P63/mmc space group [16, 25, 38], with unit pseudo-cell parameters a' =

4.13Å, c' = 8.49Å. The specific gravity measurements reveal that this cell contains two CaCO3

(Z’=2) [25]. Five weak reflections also observed by (X-ray diffraction) XRD initially could not

be indexed, and were attributed to the true cell rotated by 30° about the c axis to the from the

main one, with lattice parameters a =

= 7.16Å, c = 2c' = 16.98Å, Z=12 [25]. The atomic

arrangement shown in Figure 9 is constructed based on the symmetry elements of space group

P63/mmc. This model posits 100% occupancy by the calcium and one-third occupancy by the

carbonate groups. When the carbon atom was placed in the centre of the prism and the vertical

carbonate group oriented so that each oxygen atom was equidistant from the two nearest calcium

atoms, the resultant calcium-oxygen interatomic distances were found to have the expected

values [25].

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In [38] another structure is suggested. The basic unit cell is essentially in agreement with

previous model but the site symmetry of the carbonate groups is different. It was emphasized

that additional spectral features observed in diffraction data (diffuse streaks along the c axis and

satellite reflections) are attributable to stacking faults perpendicular to the c axis, leading to

doubling or tripling of the c lattice parameter, as reflected in Figure 10.

The principal debate has arisen on whether the vaterite symmetry is hexagonal or

orthorhombic, although recently it was claimed that none of the proposed models is consistent

with Raman spectra indicated the presence of two or more carbonate groups in the asymmetric

unit [39]. Based on the spectroscopy data, it was proposed the possibility of at least three

structurally independent carbonate groups in the unit cell of vaterite.

A Raman spectrum of vaterite discussed in [39] is characterized by the presence of at

least eight relatively broad bands at frequencies corresponding to the external lattice modes

Figure 9. Vertical projection of

vaterite showing orientation of

carbonate group relative to calcium

atoms [25].

Figure 10. Structure of the vaterite unit cell [38].

Figure 11. Raman spectra of vaterite [39].

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whereas the other bands are split into two or three distinct peaks (Figure 11). Vaterite peaks in

Raman spectra often have high value of full width at half-maximum in comparison with other

polymorphs, that implies the crystal structure of vaterite is not well ordered. The peak

broadening is possibly affected result of the stacking faults, layer shifts or syntactic intergrowth

irregularities, making it difficult to determine the parameters of the crystal structure.

Different variations of the model were proposed, resulting in the unit cell with P6522 or

Ama2 space group or modified orthorhombic unit cell. Based on diffraction tomography and

transmission electron microscope data, two structures with very low symmetries (a monoclinic

unit cell and a triclinic one) were suggested in [40]. Taking into account all the diffraction data

obtained in the study, the lowest symmetries was hypothesized.

Nevertheless, the most recent report claims that vaterite should be considered as a

combination of two different crystal structures that coexist within a pseudo-single crystal [3].

The structure of vaterite crystal is possibly predominantly hexagonal with at least one other

coexisting minor crystallographic structure. The minor atomic structure, existing as nanodomains

within the major matrix, is still unknown. The coexistence of two structures of different

symmetries largely explains the amount of contradicting results previously obtained by different

research groups all over the world.

There are at least three different theoretical models equally well describing the vaterite

structure at room temperature. These distinct models, each comprising multiple structures, can

explain the disorder of vaterite in terms of different orientations of the carbonate anions, multiple

stacking sequences of the carbonate layers, and possible chiral forms. Hence, vaterite is not a

single “disordered” structure but should instead be considered as a combination of different

forms, and each form can exhibit rapid interchange between multiple structures that possess

similar average properties. Besides explaining the existence of several vaterite forms it suggests

that perhaps not all samples of vaterite might be the same, while still exhibiting similar

spectroscopic properties [41].

The polycrystalline nature of the vaterite particle compared to monocrystalline calcite is

evident from diffraction diagrams recorded from areas within the two particle slices displayed in

Figure 12a, and b [42]. Random orientation of the crystallites within the vaterite particle should

produce continuous circles on the diffraction diagram. The increased intensity at certain

positions along the circle points to a preferential alignment of the crystallites. The fact that these

diffraction spots are elongated indicates a certain degree of variation in the crystal orientation.

Interestingly, however, the broken ring pattern of electron diffraction obtained from a

micrometer-scale area exhibited 6-fold symmetry. For example, the diffraction rings of (110) and

(114) were composed of six bright and six dark segments (Figure 12c). That means that the

crystallographic direction of the nanocrystals in the mosaic is not random but roughly arranged

in the same orientation. The presence of texture in the vaterite sample supports the concept of

spherulitic growth but does not provide sufficient evidence, since a hypothetical ordered

aggregation process could give the same diffraction pattern.

High resolution TEM image (Figure 12d) displays the size of the individual crystallites.

The diffraction rings in Figure 12e are more continuous indicating less systematic orientation,

emphasizing the variability of the vaterite structure [42].

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Figure 12. Electron diffraction patterns of vaterite with a certain degree of variation in

crystal orientation (a) and calcite (b) [42]; electron diffraction pattern of vaterite with

nanocrystals arranged in the same orientation (c) [24]; a high-resolution image of primary

crystals of vaterite (d); electron diffraction diagram of vaterite with crystallites in random

orientation (e) [42].

Figure 13 reveals an XRD pattern of vaterite power obtained by solvothermal synthesis in

the presence of ethylene glycol. The powder XRD exhibits the characteristic reflections of

vaterite, which correspond to lattice planes hkl and d-spacings shown in Table 1 [16].

Figure 13. X-ray diffraction pattern of vaterite [10].

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Table 1. XRD data (hkl indices and corresponding d-spacings) for vaterite [16].

h k l dobs /Å

0 0 4 4.254

1 1 0 3.591

1 1 2 3.307

1 1 4 2.741

2 1 1 2.327

2 0 5 2.287

1 1 6 2.223

2 1 3 2.167

0 0 8 2.122

3 0 0 2.070

3 0 4 1.860

1 1 8 1.826

2 2 0 1.792

2 0 8 1.752

2 2 4 1.650

Diffractograms of vaterite spherulites composed of nanocrystalline sub-domains or grains

usually reveal relatively broad peaks of low intensity, which still can be analysed by the Scherrer

equation relating the grain size and peak width [20, 24]. The phase composition can be refined

from X-Ray diffractograms by Rietveld analysis [14, 29, 40].

3.2 Shape and morphology

The particle morphology may be the most uncertain characteristic because it displays a great deal

of variety. The main crystal structure of polycrystalline vaterite is hexagonal with typically a

spherical crystal habit like the one shown in Figure 14a [5, 9, 13, 17, 24, 43-47]. The spherical

form is also called framboid [5] or raspberry [27] (translation of ‘la framboise’ from French). A

detailed examination of particle surface showed that spheroids are composed of smaller single

crystal sub-units (Figure 14b) arranges with some degree of order as mentioned earlier. The most

common interior feature is the presence of grooves radiating from the centre of the particle as

radial fibre-like (or channel-like) structures (Figure 14c). Fracture cross-section images display

nanograins developed into oriented rods (Figure 14d). The deviation angle of each main bundle

of the oriented rods was roughly estimated to be about 60° (Figure 14e).

A so-called “sheaf of wheat” inner structure of spherulites was observed in [5, 48]. One

can imagine this structure as a bundle of fibres tied together at the centre, so that the ends fan

out. While the number of growing fibres increases their ends close off to form a sphere. The

particle growth scenario called “sphere-to-dumbbell-to-sphere” (Figure 14f) is currently one of

the most explored [21, 24, 29, 49].

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Figure 14. SEM-images of calcium carbonate vaterite crystals: top view (a), surface (b) [47],

interior (c) [43], cross-section (d) and detailed fibre-like structure (e) [24], possible particle

growth scenario (f) [24].

Besides the typical spheroidal structure, in vitro precipitation of vaterite often results in a

variety of complex shapes: fried-egg shape, different kinds of layered flower-like (Figure 15a, b)

or rosette-shaped structures (Figure 15c) united with 6-fold symmetry [24, 31, 36, 50, 51]. Figure

15d, e, and f represents a typical SEM image and a suggested formation scheme for such

hexagonal-shaped vaterite composed of small hexagonal units.

Figure 15. Vaterite particles of different shapes. Flower-like vaterite particle (a), a magnified

SEM image of the particle surface (b) [31], rosette-shaped vaterite (c) [36], hexagonal-shaped

vaterite and particle magnified surface (d) [24], possible growth mechanism (e) [31].

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Other reported shapes of vaterite [16, 35, 50, 52] are plates and lenses (Figure 16 a, and

b). Plate morphology is probably characteristic for the intermediate stage of cauliflower-like

particle growth, since other petals growing on plane regions can be seen (Fig 16b).

Figure 16. SEM- images of the vaterite particles of lens (a) [50] and plate (b) [52] shape.

However, the development mechanisms, resulting textures, and common features of all

different shapes are yet to be explored. Importantly, in minor cases, calcite could also have a

spherical habit [42], so the particle analysis must not rely solely on SEM images, but be

supplemented with the methods discovering more exhaustive information about the phase, e.g.,

XRD.

3.3 Porosity

High specific surface area and porosity of vaterite particles are of particular importance for their

practical applications. Brunauer–Emmett–Teller (BET) analysis reveals the specific surface area

of the vaterite framboids to be 3.2 - 8.8 m2g

-1 for different precipitation conditions [5, 43, 53-55].

Vaterite particles with the highest surface area 24.72 m2g

-1 were achieved via coprecipitation

with inulin [56]. Besides, the pore size distribution displayed average pore size 20-60 nm for the

particles with medium diameter of 4-6 µm [43]. Theoretical equation evidently indicates specific

surface area is subject to exponential decay with increasing particle size [5].

3.4 Absorption spectrum

Table 2. Assignment of the IR absorption bands of the three polymorphs [16].

IR absorption band

ν1, cm-1 ν2, cm

-1 ν3, cm

-1

Vaterite 1087 877 745

Aragonite 1080 866 706

calcite 1080 879 706

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Fourier transformation infrared spectroscopy (FTIR) is a very useful technique to identify the

polymorph composition of CaCO3 particles [21, 50, 57]. The absorption bands of the different

crystallographic varieties of CaCO3 are listed in Table 2. Pure vaterite exhibits the characteristic

vibrational bands at 1480, 1070, 1087, 877, 848 and 745 cm-1

, where the last three of the listed

bands are the most typical and informative [17, 18, 35, 53, 58]. The selected FTIR spectrum for

vaterite samples precipitated in mono-ethylene glycol solution at 40°C (Figure 17) shows

representative bands at 1088, 874 and 744 cm-1

attributing to the deformation modes of CO3 in

the vaterite polymorph [14]. The shifts of peak positions in FTIR spectra indicate interactions

between calcium ions and chemical groups of additional molecules in the reaction medium

(additives or impurities) [10, 14, 16, 18]. Shift magnitude directly corresponds to the strength of

such interactions.

Figure 17. FT-IR spectra of vaterite [14].

3.5 Chemical and physical properties

Owing to the mass density (2.54 gcm-3

), solid vaterite is used in regenerative medicine [5] for

doping of implant scaffolds. Besides, calcium carbonate is quite inert and biocompatible. CaCO3

structure has good stability at neutral and alkaline pH but begins to dissolve at slightly acid

conditions opening an opportunity of using pH to trigger disassembly in practical applications

[44]. The solubility of calcium carbonate is different for different polymorphs and was found to

be Lg Ksp = -7.913 for vaterite at 25°C [23, 35, 55]. Moreover, the solubility of vaterite particles

is in direct relationship with the concentration of CO2 gas in water medium [59]. The increase of

CO2 content leads to the high CO32-

concentration in the solution, which, as discussed in [8],

increases the fraction of vaterite.

4. Facilitating vaterite formation

The morphology and polymorph composition of CaCO3 is very sensitive to synthesis conditions.

Many efforts have been made to favour growth of vaterite over the other calcium carbonate

polymorphs. Various experimental conditions are supposed to promote synthesis of this

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metastable phase. Among those, the use of highly saturated salts solutions, alkaline pH, and

temperature control induces the vaterite formation with high yield of stable particles [18, 23, 35,

49, 60].

The sources of calcium and carbonate ions have significant effect on the morphology and

phase of CaCO3. CaCl2 salt appears to be the most popular compound [9, 17-19, 30, 43, 61-64].

Ca(NO3)2 is less frequently used [22, 42, 54]. The most common source of carbonate ions is

sodium carbonate Na2CO3 [19, 43, 62, 42, 22, 30], other sources are sodium bicarbonate

NaHCO3 [54, 61, 63], ammonium carbonate (NH4)2CO3 [9, 4, 17, 64] and ammonium

bicarbonate NH4HCO3 [18].

Facilitating factors include the presence of certain additives in the aqueous medium,

which are thought to influence the crystallization of vaterite polycrystals by several different

mechanisms. Generally, interaction between added molecules and calcium and carbonate ions

individually lowers the concentration of freely available ions in bulk medium and decreases the

actual thermodynamic driving force for nucleation. Lower nucleation rate delays formation of

more stable polymorphs of aragonite and calcite promoting the vaterite fraction.

Additives can also influence the kinetics of crystal growth. The additive molecules may

have greater affinity with certain faces of a particular polymorph and will adsorb strongly onto

these faces, delaying the nucleation or retarding the growth of the affected polymorphs to the

advantage of others. Besides, it is mentioned that when the basicity of the basic additive

increases (e. g. urea, sodium hydroxide), the sizes of CaCO3 structures decrease [4, 10].

Vaterite precipitation is promoted by inorganic additives (for instance ammonia,

ammonium ions, nitric acid) [4, 12, 31, 50, 65], certain organic substances such as amino acids

[53, 63, 66], protein molecules (e.g., bovine serum albumin, ovalbumin, gelatin, casein,

polyglycine, fibrin, pelovaterin) [6, 11, 25, 53, 57, 61-63, 67-69], and sucrose [61]. Among

another high-molecular weight compounds polymers (poly(styrenesulfonate) [22, 24],

polyacrylic acid [23, 27, 64], polyvinylpyrrolidone [23, 34], poly(vinyl alcohol) [22, 23],

polycarboxylic acid [30], carboxymethyl inulin [56]), copolymers [58, 60], including double-

hydrophilic block copolymers (DHBCs) [13, 21, 49, 52], dendrimers [17, 70], and calixarene

[36] are the most frequently used. Besides, DHBCs and dendrimers were mixed with surfactants

[52, 70]. Moreover, ionic liquid surfactant can be utilized as an effective polymorph control

agent on its own [16, 35]. Different kinds of alcohols are also referred as the vaterite promoters

and stabilizers [4, 14, 21, 29, 37, 42, 59, 71].

4.1 Nitrogen containing compounds

A number of amino acids (lysine, glycine, alanine, glutamic acid, leucine) were found to

stabilize the vaterite polymorph [53, 66]. It is assumed that calcium ions are attracted by strong

electric field caused by shifting the negative charge of the C=O bond towards the oxygen atom.

The electrostatic interactions temporarily fixed Ca2+

ions near C=O groups that along with the

diffused carbonate ions toward the fixed Ca2+

initiate the vaterite critical nuclei formation.

Onwards, the amino acids interact with Ca2+

ions of the crystal surface with their side terminal

carboxyl groups or through hydrogen bonding. Crystallization in the presence of nitric acid,

organic amines, and tetrasodium etidronate resulted in vaterite nucleation as well [7, 65].

Biotic experiments [12] suggest that tight binding between amide groups and vaterite

surface via NH–O hydrogen bonds controls CaCO3 polymorph selection providing long-term

stabilization of vaterite.

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4.2 Proteins

Proteins like bovine serum albumin (BSA) have been successfully used to manipulate the

polymorphic phases [61, 67] and crystal morphology of calcium carbonate and have shown

strong influence on the oriented crystallization and growth. Moreover, the reduction of crystal

size by albumin is also reported [11, 63]. During the formation of vaterite spheres, the nucleation

and growth of the crystals might be affected by the protein through electrostatic matching, and

structural and interfacial molecular recognition. The role of BSA in the formation of vaterite

attributes to a big variety of functional groups: C=O, HO-, N-H, C-N, etc. [11, 61, 62, 67]. In

[11] it was demonstrated that ovalbumin from chicken egg white displayed a distinguished

stabilizing effect on the vaterite phase by ovalbumin adsorption onto the unstable surface of the

crystal. As an acidic protein, ovalbumin could capture Ca2+

through carboxylates at the periphery

of the protein, thereby leading to a local enrichment of calcium ions. Upon introduction of CO32-

and diffusion into the solution, their distributions would be enriched by Ca2+

ions around the

protein. According to the Ostwald rule, the metastable crystalline form may tend to precipitate

under a higher local supersaturation, resulting in the production of vaterite crystals around the

protein molecules. Furthermore, ovalbumin will adsorb onto the surface of vaterite crystals upon

their formation, thereby retarding its transformation into more stable crystalline forms.

The special peptide – pelovaterin, extracted from eggshells of a soft-shelled turtle, was

synthesized specifically to induce the nucleation and stabilization of the vaterite phase in

solution [69]. It is a glycine-rich peptide with 42 amino acid residues and three disulphide bonds.

Compared with proteins containing no phosphonate groups, phosphoproteins (ovalbumin,

casein) might have specific and prominent influences on mediating the mineralization process

[57]. It has been found that organophosphorus compounds adsorb to ionic crystals much more

strongly than other additives. They preferentially interact with kinks on the crystal nucleus

surface [57] and adsorb onto the sites of active growth [54] and thus efficiently inhibit the crystal

growth and lead to generation of the least stable vaterite. The effect of phosphonates on the

crystal habit must be related to the affinity of a compound to Ca2 +

, which influence the

crystallization rate and change the morphology of crystals [22, 54].

Besides proteins, some other compounds with phosphonate groups are also known to

facilitate the vaterite formation [7, 13].

In short, the vaterite stabilization and growth inhibitory effect of proteins is attributed to

the enriching of calcium ions around its molecules due to new bonds formation.

4.3 Polymers

It can be claimed that the growth of crystalline CaCO3 is a surface-controlled process, which

means that the adsorption of water-soluble polymers should have strong influence on both

velocity and habit of the crystal growth, changing their morphology and structure.

It was found that the presence of polyvinylpyrrolidone (PVP) lead to spherical vaterite

particles [23] (but has a very slight effect) and alters the surface morphology of vaterite at high

PVP concentrations [34]. The PVP easily absorb on the surface of the initially formed spheres of

amorphous CaCO3, and consequently, the loops and trains of the absorbed polymer molecules

make the cauliflower-shaped spherulites more incompact and rough [27, 34]. This could be

easily understood by referring to the hypothesis of the formation mechanism illustrated in Figure

18 [49].

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Polyacrylic acid (PAA) also known to control crystal size, quality, and shapes increasing

the induction time of vaterite [23]. Polymer inclusion in vaterite modifies the parameters of unit-

cell in the respective phases [27]. Taken in a low concentration, PAA completely dissociates in

water, and liberate protons into bulk solution: . In the resulting acidic

conditions, CaCl2 solubility is increased, giving rise to more Ca2+

and thus Ca2+

- polyelectrolyte

complexes as a result of chemical reaction: . The

complexes are formed rapidly, and it seems reasonable to hypothesize that this

reaction takes place wherever highly energetic sites are present. It is well known that vaterite

crystals predominately grow in the direction of their c-axes upon crystallization from

supersaturated solution, and highly energetic sites in vaterite occur preferentially on faces

parallel to the c-axes, i.e. where oxygen atoms from carbonate groups are most located.

Resultantly, the complex adsorbs preferentially on these faces block further growth to another

axes and prevent vaterite transformation [27]. Pores of the spherical vaterite particles are filled

by further vaterite growing under PAA complexes, giving rise to the raspberry shapes by

aggregation of several spheres (or to further development of each initial conglomerate under

PAA influence). The surface morphology (smooth or rough) and crystal interior (radiating

features) depend on the moment the polymer is interfering with the crystallization process and

polyelectrolyte chain length (Figure 19).

Figure 19. Schematic depiction of the CaCO3 spherulites formation with addition of a

polymer [64].

Figure 18. Proposed mechanism of vaterite formation: (a) The polymer-stabilized amorphous

nanoparticles; (b) formation of spherical vaterite precursors; (c) aggregation of the vaterite

nanoparticles [49].

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Ca2+

-activity measurements show that polymers are partially incorporated into the

forming crystals [30]. At that, the polymer contaminated CaCO3 particles exhibit strong

resistance towards aggregation into flocs and are stable to recrystallization process in water

attributed to the formation of a polymer shell [27, 30]. Particle stabilization can be of permanent

or temporary nature depending on the amount of polymer in the system. Temporary effect is

achieved when the amount of polymer is insufficient to cover the surface of all formed

nanoparticles. Uncoated nanoparticles will then undergo dissolution and recrystallization.

Sufficient amount of polymer enables permanent stabilizing effect [30].

The effect of polymers on the crystal habit is shown to be related with the affinity

between polymer and Ca2 +

and even distribution of polymer molecules over the volume of

CaCO3 crystals [22]. This mechanism is probably attributed to a variety of polymers. Among the

polymers employed for vaterite promotion, the PAA and polystyrene sulfonate (PSS) are

obviously the most effective in retention of spherical shape [22, 24, 64]. Anionic groups or lone

pair electrons in polymers are supposed to play a role in arranging calcium ions and regulating

the crystal form. Besides, the clusters can be formed by the addition of multivalent ions (like

Ca2+

) to polyacrylic acid [72-74]. At a certain point, the clusters become large enough to

precipitate out, which is known as the "gel point'' [72]. Therefore, the precipitation obtained from

the supersaturated solution in the presence of PAA may consist of both vaterite and calcium

polyacrylate clusters and the sample composition should be examined particularly carefully.

As for phosphorus containing polymers, sodium polyphosphate has been successfully

used [7]. Moreover, phosphonate groups in copolymers strongly promote vaterite formation and

their influence becomes significant with increasing the number of phosphonate groups [13].

4.4 Double-hydrophilic block copolymers

Double-hydrophilic block copolymers (DHBCs), consisting of a hydrophilic poly(ethylene

glycol) (PEG) block and a second hydrophilic moiety which strongly binds alkaline earth ions

effectively inhibiting the CaCO3 precipitation [49]. This was explained by the block copolymer

character and the related “sharing of responsibilities”: the COOH-functionalized block interacts

with nanocrystals or nuclei, whereas another block keeps the microcrystals in solution by steric

stabilization without interaction with the dissolved ions. Since both tasks do not interfere with

each other, both blocks can be independently optimized with respect to polymorph composition,

size, functionality and structure [13, 49]. And it is clear that an optimal functional block length

should exist [13, 21].

Copolymers with poly(ethylenimine)-poly(acetic acid) (PEG-PEIPA) functional block are

shown as very efficient templates to promote pure vaterite crystals of smaller size when used in

moderate concentration [13, 21].

4.5 Dendrimers

Owing to spherical three-dimensional morphology and highly-functionalized terminal surface

dendrimers are successfully used as a central initiating core for vaterite particles formation [17,

70]. The commonly utilized poly(amido amine) (PAMAM) has enough amine branches (nitrogen

moieties) serving as the complexation sites to ions [17]. Another dendrimer, poly(propylene

imine), combined with a cationic surfactant was proposed as a template to attract carbonate ions

preferentially forming a stabilized surface ready to absorb more ions for subsequent vaterite

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formation [70]. Elsewhere [17] vaterite surface is stabilized by the carboxylate-terminated

dendrimer with a long lasting effect: incubation in water for 1 week did not change the crystal

morphology. Increasing the concentration of additive and the generation number of the

dendrimer, allows to reduce the size of vaterite particles from 5.8 down to 1.5µm [17]. These

results indicate a higher complexation ability of a higher generation of the PAMAM dendrimer

compare to that of a lower generation, since the particle size depends on the degree of the

dendrimer adsorption on primary nanoparticles.

4.6 Alcohols

Phase-pure vaterite founded to be promoted by OH-groups of polyols [10, 37, 42, 71]. Strong

electric field caused by OH-groups induces attraction to the nuclei changing the surface energy

of vaterite and making it more thermodynamically stable than the aragonite and calcite

modifications [10]. No phase-pure vaterite was achieved by adding alcohols with only one OH-

group [10, 29] except of ethanolamine favours the vaterite habit by NH2 functional group [65].

Alcohols with two or three hydroxyl groups (e.g., ethylene glycol (EG) and glycerol) offer an

enhanced solution density and reduced solubility of the carbonate [37, 42, 71]. Since vaterite has

relatively high solubility in water, non-aqueous solvents were suggested to benefit its

precipitation [14]. Decrease of the activation energy of nucleation by the interfacial molecular

recognition was pointed out as another factor facilitating vaterite precipitation [6, 37, 42].

Similar to polymers, polyols prolong the transformation time of metastable polymorphs (perform

the so-called kinetic stabilization) presumably by delaying the growth rate of the more stable

polymorphs [37] and thus hinder recrystallization to more stable phase. The presence of a co-

solvent also affects supersaturation, because of changes in the ion activity coefficients and

solubility of the calcium and carbonate salts [14, 37].

According to the classical nucleation theory, the smaller crystals are the result of higher

nucleation rates, provided that the same mass is precipitated [37, 59]. Admixture ethylene glycol

and glycerol to salts solutions increases nucleation rates resulting in smaller vaterite at a range of

temperatures [37]. Additionally, high local viscosity of the reaction medium containing glycerol

or other compounds, such as sucrose, ethanolamine precursors, gelatine or alginate hydrogels can

significantly limit the rate of diffusion for Ca2+

ions and effectively slow down the crystallization

[7, 21, 25, 61, 65, 75].

Summarising this paragraph, the factor facilitating stability of the vaterite phase and

promoting smaller particle size is a high amount of functional groups in the system achieved by,

e.g., high concentration of additives, using polymers of high molecular weight, or dendrimers

with a higher generation number [10, 17, 22, 23, 34, 53, 54, 56, 64].

4.7 Microorganisms

Some bacteria are capable to produce the CO2 and NH3 gases and transform the NH3 to the NH4+

and OH-. Since supersaturation is higher in more alkaline medium, the condition favourable for

vaterite precipitation is set. As a result, the vaterite formation occurs in the microenvironment

around the cells, and directly onto their surface.

Bacteria cell walls contain a number of surface functional groups, such as carboxyl,

hydroxyl and phosphate sites known to promote vaterite crystallization and stabilization. The

results of vaterite precipitation in the presence of different types of bacteria (common soil

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bacterium [12] and actinomycete [76]) suggest that bacterially mediated vaterite precipitation is

not strain-specific.

5. Application of vaterite

5.1 Personal care

Biological inertness, low toxicity and unique mechanical, physical and chemical properties of

precipitated vaterite microparticles benefit to a broad range of personal care products. Vaterite

crystals are commonly added to industrial personal care products with the purpose to improve

rheology, physical robustness and visual appearance. Vaterite particles can act as abrasives,

absorbents, anticaking agents, buffers, fillers, colorants, and emulsion stabilizers [65, 77, 78]

Besides, the use of CaCO3 material is safe for environment and extremely cost efficient.

Strong demand for spherical vaterites persists in the field of oral care. Among the other

CaCO3 polymorphs, vaterite demonstrates excellent cleaning properties without being

excessively abrasive. Vaterite microparticles of a certain size (0.2 – 4 µm) are reported to

improve cleaning and abrasive characteristics of dentifrice formulators, teeth whitening products

and mouthwashes [7]. Moreover, low cost of CaCO3 particles makes them a perfect substitute for

silica and dicalcium phosphate particles.

Other personal care products employing calcium carbonate particles as an abrasive

include facial cleansing soaps, exfoliating formulations, acne preventing wipes, bath soaps, bath

wash, makeup removers, baby wipes, diapers, powdered bleaches and all-purpose cleaners [77].

Abrasive properties of vaterite particles are gentle enough to be successfully utilized in paint

removals specially designed to clean delicate surfaces of lightweight metals and plastics.

Skin care, makeup and cosmetic products enjoy the properties of CaCO3 particles to

eliminate unwanted shine and create whiteness. Besides, as the vaterite particles of a certain size

can scatter UV light, they may serve in fabrication of sunscreens, face powders, blushes and

foundations [77]. Absorbent property of calcium carbonate is used in eyeshadows, blushes,

concealers, foundations, face powders, sunscreens, sun-tan lotions, self-tanning compositions,

bronzers, baby powders, diapers, deodorants and antiperspirants. Anticaking characteristics of

CaCO3 used a range of products from face powder and eyeshadow to laundry detergent,

bathroom cleaners and powdered bleach [77].

Vaterite is also known to maintain pH in aqueous medium. Buffering properties of

vaterite are often employed in non-ingestible formulations, such as lip gloss, nail polish, makeup

removal, different creams and lotions, teeth whitening agents and all-purpose cleaners.

Moreover, there is a number of food products where vaterite serves as a pH buffer, i.e. salad

dressings, water-based flavored drinks (e.g., energy drinks, sports drinks, electrolyte drinks),

canned fruits, vegetables and meats. Some emulsion based food products (e.g., salad dressings)

also enjoy a phase stabilizing property of vaterite particles [77].

5.2 Biomedical applications

Vaterite and other calcium-based inorganic nanostructured materials are extensively applied in

regenerative medicine and tissue engineering as bone cements and substitute materials, dental

implants, and scaffolds. [4, 79-82]. Better mechanical strength compared to polymer materials,

makes vaterite doped implants promising for strengthening the bone and dental tissues. Vaterite

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degrades in vivo at sites with acidic pH, thus replenishing calcium in a living organism and

promoting tissue regeneration [4, 79, 81].

It is well known that tooth and bone are the naturally organic/inorganic composites

having calcium phosphate, hydroxyapatite, calcium silicate, and calcium carbonate in the

structure. Hydroxyapatite and calcium phosphate are proved to be the most similar materials to

bone mineral that predetermined their extensive use in clinical bone graft procedures.

Importantly, their simplest synthesis method is based on replacement of carbonate group to

phosphate group in vaterite [4]. The characteristic features of new bone formation was found to

be identical in implants of either calcium carbonate or hydroxyapatite - percentage of the pore

space occupied by bone at 4 weeks after implantation was the same, and the marrow cells were

detected in pore areas of both implants [79]. But in contrast to hydroxyapatite, porous CaCO3

implants with or without marrow cells showed some degradation – the material has a potential to

completely degrade. Previous studies have shown that porous CaCO3 completely degrades after 3

months when placed in a bone forming a defect [79]. The carbonate surface can be modified with

hydroxyapatite to control the rate of biodegradation.

Vaterite-based materials with pore microstructure and high surface area can be used as

preservative containers for growth factors [80]. Being added to the scaffolds, they will promote

proliferation and differentiation of cells towards osteoblasts. Moreover, vaterite being in contact

with body fluid dissolves immediately, supplying calcium ions, while part of it re-crystallizes as

the most stable calcite. Simultaneously released carbonate ions neutralize pH at the inflamed site

of implantation [80].

Highly porous vaterite particles have been extensively used in pharmaceutical

applications as encapsulating carriers for various drugs [9, 44, 62, 83]. The structure and surface

morphology open up an opportunity to absorb a large range of biomolecules. Spherical CaCO3

with an enzyme immobilized into pores was demonstrated as a platform for the design of

biosensors [47]. High porosity of the vaterite beads is a key feature that leads to good adsorption

ability to silver and gold nanoparticles. Vaterite surface enhanced with nanoparticles is attractive

for developing biomarker sensing at concentrations corresponding to healthy and diseased

individuals (for glycose detection e.g.) [84]. Based on their high birefringence vaterite particles

can be used in the fields of microrheology, microfluidics and micromanipulation at the single

molecule level [20].

Triggered by the early studies by Volodkin et al. [43, 85-87], the employment of vaterite

microparticles have promoted a significant breakthrough in the area of encapsulation and

delivery of drugs by Layer-by-Layer (LbL) assembled capsules.

Figure 20. CLSM images of L929 cells incubated with FITC-BSA-loaded (Dex/PAr)3

microcapsules: (a) Cross-section fluorescence image with z-axis fluorescence projection at

the cross-plane displayed (windows at the bottom and on the right), scale-bar: 20 µm. (b)

Overlap of fluorescence mode and bright-field mode, scale-bar: 20 µm. (c) 3D

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fluorescence image from the top view, frame length, and width: 210 µm; height: 13 µm

[88].

Vaterite is found to co-precipitate a number of therapeutics, such as nucleic acids,

enzymes, antibodies and proteins. Subsequent coating with polymer multilayers and CaCO3

dissolution result in LbL capsules loaded with the co-precipitated compound [43, 89]. Moreover,

it was observed that CaCO3-assisted encapsulation results in a higher loading efficiency for some

type of compounds [90, 91]. Promising attempts of in vitro and in vivo delivery by 2-4 µm

microcapsules templated on vaterite particles for disease treatment and vaccination have been

shown [89, 92]. An important feature of Lbl capsules made of synthetic and natural

polyelectrolytes in different combinations is their tunable biodegradability [93]. Recent studies

have also revealed that capsules shape is a crucial parameter influencing the cellular uptake.

Elongated objects can be effectively and quickly internalized intercellularly compared with other

configurations. Thus fabrication of anisotropic particles and polyelectrolyte multilayer capsules

templated on them are of a special interest [94].

Although such capsules still can enter the living cells and deliver the therapeutics (Figure

20) [92, 95], we believe that the effect would be much stronger if the size of their CaCO3

templates was reduced. Thus, new ways to achieve smaller vaterite particles co-precipitating

biologically active molecules are to be discovered.

6. Conclusion

Owing to biodegradability and unique physical and chemical properties, vaterite polymorph of

calcium carbonate is extensively used in biomedicine and added to a wide range of personal care

products. The most cost efficient way to produce the CaCO3 microparticles is spontaneous

precipitation by mixing of two concentrated solutions of calcium and carbonate salts. Being a

metastable polymorph, vaterite may transform to either calcite or aragonite in this process. Here

we have reviewed the most accepted suggestions on the mechanism of calcium carbonate crystal

growth focusing on various factors promoting the vaterite polymorph. It has been proven that

high supersaturation, ambient temperature, and alkaline pH facilitate the formation of vaterite

over more stable modifications. Moreover, various inorganic and organic additives particularly

those bearing carboxylic, phosphonate, sulfonate, hydroxyl, carboxylate and amino groups are

responsible for the vaterite morphology. The process is tunable: changing the concentration of

additive, molecular weight and the amount of functional groups allows controlling the growth

rate, crystal habit and stability, particle size and surface morphology. Thus, synthesis conditions

can be configured to allow stable vaterite particles which fulfil the size requirement in each

particular application.

Among a number of application areas of the vaterite polymorph, polymeric Layer-by-

Layer drug delivery is may be the most novel and fast progressing one. Vaterite microparticles

have already enabled to achieve high loading efficiency for a range of therapeutics and analytes.

Reduction of size of the co-precipitated vaterite polycrystals is envisioned to increase the rate of

intracellular uptake for the corresponding capsules.

7. Acknowledgment

Daria Trushina thanks A*Star Graduate Academy (Singapore) and Russian Foundation for Basic

Research (Grant № 14-03-31889) for support.

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