**4. Thermochemistry and setting kinetics**

to induce both liquid flow and mat discharge increases. This self-feeding loop gradually transforms the suspension to a packed bed at an increasing rate as evidenced by the exponential nature of the pressure vs. time curves of unstably flowing suspensions. Empirical attempts to tackle the filter-pressing issue shows that the injectability of CPCs is generally improved by decreasing the P/L ratio, the use of finer, round particles, the addition of electrically stabilizing groups, and the addition of viscous polymer solutions [96–101]. In addition to a large number of parameters relating to CPC composition, the injectability of a setting cement depends strongly on the post-mixing time interval relative to the cement setting time. In this regard, premixed CPCs that do not harden until being placed into the defect constitutes an advantage

Calcium phosphate cements are able to provide short-term biologically desirable properties and then be replaced by a new bone. In order to achieve optimum clinical results, an appropriate CPC resorption rate is an important parameter that may vary with the intended clinical applications. For critical applications close to vital organs like cranioplasty, rapid implant resorption and replacement by bone may not be an as important factor as implant stability and integrity, and even may not be desirable due to the sensitivity of the brain to local ionic concentration gradients. For other applications, such as periodontal bone defect repairs or sinus lift, the ability of the implant cement to be replaced quickly by bone is highly desirable. Studies on the in vivo evaluation of macroporous calcium phosphate cements revealed a higher bioresorption rate due to both a higher contact with body fluids and enhanced cellular activity due to particle degradation. When the bioresorbability of dense and macroporous α-tricalcium phosphate cement were compared, it was seen that pores formed by albumin foaming promoted bone ingrowth and replacement [103]. Introduction of macroporosity to the CPC causes a trade-off between strength and bioresorbability which should be compensated by some means of strength reinforcement such as incorporation of polymeric fibers.

The overall bioresorption behavior of calcium phosphate cement is a combination of a solution-mediated passive resorption process and a cell-mediated active resorption process. The resorption properties of bioceramics are generally believed to relate to the solubility of their constitutive phases. The much higher (3 orders of magnitude) solubility of brushite compared to hydroxyapatite translates as the much quicker resorption of brushite cements. An important in vivo characteristic of HA-forming CPC is that it does not dissolve spontaneously in a normal physiological fluid environment, yet is resorbable under cell-mediated acidic conditions. Although brushite is soluble in normal physiological fluids, studies have shown that resorption of brushite CPC was also essentially cell-mediated [3]. Phase changes often occur in brushite cements in vivo by a dissolution-reprecipitation reaction, which results in stable phases with lower solubility, thus slowing down degradation and hence bone regeneration kinetics. The kinetics of passive resorption depends on porosity of the samples, ionic substitutions, Ca:P ratio, crystallinity and pH of the cement-tissue interface. The active resorption is due to cellular activity; however, it is also related to the passive one. Serum pH near macrophages and osteoclasts can drop to 5 by the excretion of lactic acid, whereas near osteoblasts pH can become as high as 8.5 by the excretion of ammonia [12]. The micropores in hardened cements do not allow fast bone ingrowth and they are not interconnected unless special

in that the viscoelastic properties are independent of time prior to injection [102].

**3.4. Bioresorbability**

200 Cement Based Materials

Dissolution of the initial calcium phosphates and mass transport are the primary functions of the aqueous CPC setting solution, in which the dissolved reactants form a supersaturated microenvironment with regard to precipitation of the final product. The relative stability and solubility of various calcium phosphates is the major driving force for the setting reactions that occur in various cement formulations. Mixing of calcium phosphate precursors with aqueous setting solution induces various chemical transformations, where crystals of the initial calcium phosphates dissolve and precipitate into crystals of HA or brushite. When powders of calcium oxides are mixed with an acid-phosphate solution, they dissolve at various rates in the solvent and release calcium cations in the solution. These cations react with the phosphate anions at various rates within the solvent and form a precipitate of salt molecules. Thus, CPC setting is a result of the following three steps [112]:

Accordingly, HA is the least soluble salt down to a pH of 4.2; for pH values lower than this, DCP is the least soluble salt. Also, it can be observed for pH values lower than 8.5 that the most soluble salt is TTCP; and for pH values higher than 8.5 that the most soluble salt is DCPD. TTCP and DCP were used as the precursors in the first apatite CPC not fully coincidentally because these are the most soluble salts and thus would provide the greatest driving force for the HA-forming reaction. Since at a pH above 4.2, all other calcium phosphate compounds are more soluble than HA, they can be used as precursors for apatite cements. Although several calcium phosphate phases, such as OCP and whitlockite (not shown in figure), are more soluble than HA under neutral pH conditions, they have been found as the major phase in the cement products [126, 127]. This is because these metastable phases precipitate in preference to HA according to the Ostwald's rule of stages [128], and finally convert to HA. Homogeneous formation of HA at low concentrations is almost never observed due to the activation energy barrier for nucleation that should be overcome with high supersaturation. At the onset of precipitation, initial supersaturation is the thermodynamic driving force. It is demonstrated by Song *et al*. for a batch system that after the fast precipitation in the early stage, the following precipitation becomes very slow due to the decrease of supersaturation of the solution with the depletion of calcium and phosphate ions [129]. The fast precipitation cannot continue because there is no supply of extra calcium and phosphate ions. However at a semi-batch system such as that of a CPC, where time dependent dissolution of precursor calcium phosphates supplies ions for supersaturation, the fast precipitation can be kept provided that suitable pH value and concentrations of calcium and phosphate are present.

Calcium Phosphate Bone Cements

203

http://dx.doi.org/10.5772/intechopen.74607

**Figure 2.** Calcium ion concentration of various calcium phosphate compounds as functions of solution pH.


The conditions to form a CPC are governed by the rate of reactions that control each of these three steps. The growth kinetics is mainly controlled by phosphate incorporation step, and additives interfering with this step regulate precipitation and crystal growth. Adsorbed atoms from the solution have to be removed during crystal growth to accommodate the competing HPO<sup>2</sup> 4− ion; hence, dehydration or impurity de-adsorption is an important part of the activation barrier for growth and dissolution [113]. Since acid-phosphate reactants such as DCP, monocalcium phosphate monohydrate (MCPM), or orthophosphoric acid (PA) are generally soluble, their dissolutions rates are comparatively high, hence uncontrollable. The phosphate reaction between dissolved cations and anions described in step III is also inherently fast and may be kinetically constrained to the formation of intermediate precursor phases according to the Ostwald's rule of stages. Thus, the only reaction that can be controlled is the dissolution of calcium oxides given in step II. Particle size [114, 115], crystallinity [116], powder/liquid ratio [117], precursor chemistry [105], Ca:P ratio [118], temperature [44], surface charge [69], liquid pH [119], ionic strength [34], and concentration of stabilizing, setting promoting or retarding chemicals [120–122] may significantly affect the rate of dissolution and the consequent setting time of CPC. α-TCP is a calcium oxide that dissolves fast and also reacts fast. On the other hand β-TCP dissolution rate is too low in neutral water, so that it remains mostly unreacted in a solution with a slightly acidic phosphate source. For this reason appropriate calcium oxides, based on their solubility, should be selected in combination with suitable acid-phosphate counterparts to synthesize CPCs [123].

Relative stability of different calcium phosphate salts in equilibrium with their saturated solution for different pH values can be understood from **Figure 2** showing the solubility isotherms for the ternary system Ca(OH)<sup>2</sup> -H<sup>3</sup> PO<sup>4</sup> -H<sup>2</sup> O at 25°C according to the solubility constants given in literature [124]. These isotherms have a negative slope in the neutral and acid regions of the solubility diagrams which point to the fact that calcium phosphates become more soluble as the pH decreases. The gradient of the slopes indicates the solubility increase of the salt as the pH decreases. Therefore the isotherm slope is considered as a measure of the salt basicity and DCPD and DCP are acid salts in comparison to OCP, α-TCP, β-TCP, HA and TTCP because they have lower negative slopes [125]. The isotherms show that the amount dissolved at equilibrium depends on the pH of the solution and the thermodynamic solubility product of the compound which is a function of both crystal and solution chemistry and physical properties.

Accordingly, HA is the least soluble salt down to a pH of 4.2; for pH values lower than this, DCP is the least soluble salt. Also, it can be observed for pH values lower than 8.5 that the most soluble salt is TTCP; and for pH values higher than 8.5 that the most soluble salt is DCPD. TTCP and DCP were used as the precursors in the first apatite CPC not fully coincidentally because these are the most soluble salts and thus would provide the greatest driving force for the HA-forming reaction. Since at a pH above 4.2, all other calcium phosphate compounds are more soluble than HA, they can be used as precursors for apatite cements. Although several calcium phosphate phases, such as OCP and whitlockite (not shown in figure), are more soluble than HA under neutral pH conditions, they have been found as the major phase in the cement products [126, 127]. This is because these metastable phases precipitate in preference to HA according to the Ostwald's rule of stages [128], and finally convert to HA. Homogeneous formation of HA at low concentrations is almost never observed due to the activation energy barrier for nucleation that should be overcome with high supersaturation. At the onset of precipitation, initial supersaturation is the thermodynamic driving force. It is demonstrated by Song *et al*. for a batch system that after the fast precipitation in the early stage, the following precipitation becomes very slow due to the decrease of supersaturation of the solution with the depletion of calcium and phosphate ions [129]. The fast precipitation cannot continue because there is no supply of extra calcium and phosphate ions. However at a semi-batch system such as that of a CPC, where time dependent dissolution of precursor calcium phosphates supplies ions for supersaturation, the fast precipitation can be kept provided that suitable pH value and concentrations of calcium and phosphate are present.

calcium phosphates dissolve and precipitate into crystals of HA or brushite. When powders of calcium oxides are mixed with an acid-phosphate solution, they dissolve at various rates in the solvent and release calcium cations in the solution. These cations react with the phosphate anions at various rates within the solvent and form a precipitate of salt molecules. Thus, CPC

**I.** The acid phosphates dissolve in water, release phosphate anions, and form an acid-phos-

**II.** The calcium oxides dissolve gradually in the low pH solution and release Ca2+ cations. **III.** The phosphate anions react with the newly released cations and form a coordinated net-

The conditions to form a CPC are governed by the rate of reactions that control each of these three steps. The growth kinetics is mainly controlled by phosphate incorporation step, and additives interfering with this step regulate precipitation and crystal growth. Adsorbed atoms from the solution have to be removed during crystal growth to accommodate the competing

Relative stability of different calcium phosphate salts in equilibrium with their saturated solution for different pH values can be understood from **Figure 2** showing the solubility isotherms

in literature [124]. These isotherms have a negative slope in the neutral and acid regions of the solubility diagrams which point to the fact that calcium phosphates become more soluble as the pH decreases. The gradient of the slopes indicates the solubility increase of the salt as the pH decreases. Therefore the isotherm slope is considered as a measure of the salt basicity and DCPD and DCP are acid salts in comparison to OCP, α-TCP, β-TCP, HA and TTCP because they have lower negative slopes [125]. The isotherms show that the amount dissolved at equilibrium depends on the pH of the solution and the thermodynamic solubility product of the compound which is a function of both crystal and solution chemistry and physical properties.

O at 25°C according to the solubility constants given


4− ion; hence, dehydration or impurity de-adsorption is an important part of the activation barrier for growth and dissolution [113]. Since acid-phosphate reactants such as DCP, monocalcium phosphate monohydrate (MCPM), or orthophosphoric acid (PA) are generally soluble, their dissolutions rates are comparatively high, hence uncontrollable. The phosphate reaction between dissolved cations and anions described in step III is also inherently fast and may be kinetically constrained to the formation of intermediate precursor phases according to the Ostwald's rule of stages. Thus, the only reaction that can be controlled is the dissolution of calcium oxides given in step II. Particle size [114, 115], crystallinity [116], powder/liquid ratio [117], precursor chemistry [105], Ca:P ratio [118], temperature [44], surface charge [69], liquid pH [119], ionic strength [34], and concentration of stabilizing, setting promoting or retarding chemicals [120–122] may significantly affect the rate of dissolution and the consequent setting time of CPC. α-TCP is a calcium oxide that dissolves fast and also reacts fast. On the other hand β-TCP dissolution rate is too low in neutral water, so that it remains mostly unreacted in a solution with a slightly acidic phosphate source. For this reason appropriate calcium oxides, based on their solubility, should be selected in combination with suitable acid-phosphate

setting is a result of the following three steps [112]:

phate solution of low pH.

HPO<sup>2</sup>

202 Cement Based Materials

work and consolidate into a CPC

counterparts to synthesize CPCs [123].

for the ternary system Ca(OH)<sup>2</sup>

**Figure 2.** Calcium ion concentration of various calcium phosphate compounds as functions of solution pH.

Although the likelihood of precipitation of a particular calcium phosphate phase is ultimately determined by the thermodynamic driving force of formation, kinetic factors may be considerably more important in controlling the nature of the solids formed. Ostwald's Rule of Stages postulated in 1897 states that the crystal phase that nucleates in a supersaturated solution is not the phase that is thermodynamically stable at that temperature and pressure but rather another metastable phase that is closest in free energy to the parent phase [130]. There are also examples of phase transformations where a metastable phase exists but does not form due to immediate transformation into another phase. It is possible to observe the metastable intermediate by slowing down the kinetics of the reaction. According to the Ostwald's rule of stages, the nucleated phase is the phase that has the lowest free-energy barrier of formation of a critical radius *Rc* (having the lowest critical radius), rather than the phase that is thermodynamically stable (having the highest supersaturation). In classical nucleation theory [131], the free energy of formation ∆*G*, and the activation energy for nucleation ∆*G*<sup>∗</sup> are related to the surface energy *γ*, density *ρ*, and the difference between the chemical potentials of the products and the reactants ∆*μ* which is basically a function of the supersaturation *S* with respect to the precipitating phase, which is the driving force for nucleation:

$$
\Delta G = 4\pi R^2 \,\gamma + \frac{4}{3} \pi R^3 \,\rho \,\Delta \mu \tag{4}
$$

$$R\_c = \frac{-2\gamma}{\rho \,\Delta\mu} \tag{5}$$

Ca4 (PO4)

β − Ca3 (PO4)

7 Ca4 (PO4)

2 Ca4 (PO4)

3 Ca4 (PO4)

Ca4 (PO4)

3 Ca4 (PO4)

3 Ca4 (PO4)

Ca4 (PO4)

3 Ca4 (PO4)

ent such as CaCO<sup>3</sup>

Ca9(HPO4) (PO4)

2

+ Ca (H<sup>2</sup> PO4)

5

2

directly with TTCP to form PHA or CDHA according to the following reactions:

2

2

O + 2 Ca (H<sup>2</sup> PO4)

O + CaHPO<sup>4</sup>

2

O + Ca8 H<sup>2</sup> (PO4)

O + Ca (H<sup>2</sup> PO4)

The TTCP + DCPD and TTCP + DCP combinations have been the most studied [136]. They offer hardening at a suitable time at body or room temperature within a neutral pH range. From a theoretical standpoint, any calcium phosphate that is more acidic than HA can react

2

2

2

2

O + 3 Ca8 H<sup>2</sup> (PO4)

2

2

or Ca(OH)<sup>2</sup>

2

tensile strengths as high as 7.5 MPa [139].

O + 6 CaHPO<sup>4</sup>

2

2

Ca4 (PO4)

O + CaHPO<sup>4</sup> → Ca5 (PO4)

OH + 3H<sup>3</sup> PO<sup>4</sup> + 17 H<sup>2</sup> O → 9 CaHPO<sup>4</sup>

.H<sup>2</sup> O → 6 Ca5 (PO4)

.H<sup>2</sup> O → Ca9(HPO4) (PO4)

.2H<sup>2</sup> O → Ca5 (PO4)

.2H<sup>2</sup> O → 2 Ca9(HPO4) (PO4)

.5H<sup>2</sup> O → 4 Ca5 (PO4)

.5H<sup>2</sup> O → 4 Ca9(HPO4) (PO4)

+ H<sup>2</sup> O → 2Ca5 (PO4)

. [137, 138] Takagi *et al*. were the first to propose a calcium

O + CaHPO<sup>4</sup> → Ca5 (PO4)

O + 6 CaHPO<sup>4</sup> → 2 Ca9(HPO4) (PO4)

2

It is also possible to form HA from acid-base mixtures of calcium phosphates with a Ca/P lower than that of HA when an additional source of calcium ions instead of TTCP is pres-

phosphate cement formulation without TTCP. Different combinations of DCP and DCPD, α-TCP, amorphous calcium phosphate (ACP), calcium hydroxide and calcium carbonate have been prepared to obtain improvements in the setting time to as low as 5 minutes and

All brushite CPCs are obtained by an acid–base reaction. Because DCPD and DCP are the least soluble calcium phosphates under acidic pH (<4.2), they are the products formed by acidic CPC formulations. All other calcium phosphate phases being more soluble under these

6

6

O + 2 Ca3 (PO4)

3

3

3

3

5

3

5

3

5

5

.H<sup>2</sup> O + 7H<sup>2</sup> O → 4 CaHPO<sup>4</sup>

OH (8)

http://dx.doi.org/10.5772/intechopen.74607

Calcium Phosphate Bone Cements

205

.2H<sup>2</sup> O (9)

.2H<sup>2</sup> O (10)

OH + 3 H<sup>2</sup> O (11)

OH + 2 H<sup>2</sup> O (12)

OH + 13 H<sup>2</sup> O (14)

OH + 2 H<sup>2</sup> O (13)

OH (15)

OH + H<sup>2</sup> O (16)

OH + 4 H<sup>2</sup> O (17)

OH + 14 H<sup>2</sup> O (18)

OH (19)

where

and

$$
\Delta \mu = -kT \text{InS} \tag{6}
$$

and 
$$S = \frac{\text{Ion activity product}}{\text{Solubility product} \left(K\_{\eta}\right)}\tag{7}$$

The ionic activity product of a calcium phosphate phase is the product of the concentration of the constituent ions and their activity coefficients. The activity coefficients are also complex functions of the interactions between ions in the solution as expressed by the Pitzer's thermodynamical model for electrolytes [132], hence ionic strength. Brown and Chow have shown that the thermodynamic solubility product depends on the purity of the calcium phosphate, which in turn, depends on the method of preparation [133]. Substitute ions like fluoride, carbonate and magnesium influence the structure of the calcium phosphates and therefore have specific effects on their solubilities [134].

Generally two types of CPC setting reactions are observed, the most common one is the setting reaction that occurs according to an acid-base reaction, i.e., a relatively acidic calcium phosphate phase reacts with a relatively basic one to produce a more or less neutral calcium phosphate salt [135]. Typical examples are the cement of Brown and Chow, where TTCP (basic) reacts with DCP (slightly acidic) to form PHA (slightly basic), the cement of Lemaitre where β-TCP, (slightly basic) reacts with MCPM (acidic) to form DCPD (neutral), and a variation of Lemaitre's formulation where MCPM is substituted by PA while β-TCP is replaced by CDHA according to the reactions:

$$\text{Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + \text{CaHPO}\_4 \rightarrow \text{Ca}\_5\text{(PO}\_4\text{)}\_3\text{OH} \tag{8}$$

$$\beta-\text{Ca}\_3\text{(PO}\_4\text{)}\_2 + \text{Ca}\text{(H}\_2\text{PO}\_4\text{)}\_2\text{H}\_2\text{O} + 7\text{H}\_2\text{O} \rightarrow 4\text{CaHPO}\_4\text{2H}\_2\text{O}\tag{9}$$

$$\text{Ca}\_8\text{(HPO}\_4\text{)(PO}\_4\text{)}\_5\text{OH} + 3\text{H}\_3\text{PO}\_4 + 17\text{H}\_2\text{O} \rightarrow 9\text{CaHPO}\_4\text{2H}\_2\text{O} \tag{10}$$

The TTCP + DCPD and TTCP + DCP combinations have been the most studied [136]. They offer hardening at a suitable time at body or room temperature within a neutral pH range. From a theoretical standpoint, any calcium phosphate that is more acidic than HA can react directly with TTCP to form PHA or CDHA according to the following reactions:

Although the likelihood of precipitation of a particular calcium phosphate phase is ultimately determined by the thermodynamic driving force of formation, kinetic factors may be considerably more important in controlling the nature of the solids formed. Ostwald's Rule of Stages postulated in 1897 states that the crystal phase that nucleates in a supersaturated solution is not the phase that is thermodynamically stable at that temperature and pressure but rather another metastable phase that is closest in free energy to the parent phase [130]. There are also examples of phase transformations where a metastable phase exists but does not form due to immediate transformation into another phase. It is possible to observe the metastable intermediate by slowing down the kinetics of the reaction. According to the Ostwald's rule of stages, the nucleated phase is the phase that has

rather than the phase that is thermodynamically stable (having the highest supersaturation). In classical nucleation theory [131], the free energy of formation ∆*G*, and the activation energy for

cal potentials of the products and the reactants ∆*μ* which is basically a function of the supersatura-

∆*μ* = −*kTlnS* (6)

*<sup>S</sup>* <sup>=</sup> *Ionic activity product* \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Solubility product* (*Ksp*) (7)

The ionic activity product of a calcium phosphate phase is the product of the concentration of the constituent ions and their activity coefficients. The activity coefficients are also complex functions of the interactions between ions in the solution as expressed by the Pitzer's thermodynamical model for electrolytes [132], hence ionic strength. Brown and Chow have shown that the thermodynamic solubility product depends on the purity of the calcium phosphate, which in turn, depends on the method of preparation [133]. Substitute ions like fluoride, carbonate and magnesium influence the structure of the calcium phosphates and therefore have

Generally two types of CPC setting reactions are observed, the most common one is the setting reaction that occurs according to an acid-base reaction, i.e., a relatively acidic calcium phosphate phase reacts with a relatively basic one to produce a more or less neutral calcium phosphate salt [135]. Typical examples are the cement of Brown and Chow, where TTCP (basic) reacts with DCP (slightly acidic) to form PHA (slightly basic), the cement of Lemaitre where β-TCP, (slightly basic) reacts with MCPM (acidic) to form DCPD (neutral), and a variation of Lemaitre's formulation where MCPM is substituted by PA while β-TCP is replaced by CDHA

tion *S* with respect to the precipitating phase, which is the driving force for nucleation:

are related to the surface energy *γ*, density *ρ*, and the difference between the chemi-

(having the lowest critical radius),

<sup>3</sup> *πR*<sup>3</sup> *ρ* ∆*μ* (4)

*<sup>ρ</sup>* <sup>∆</sup>*<sup>μ</sup>* (5)

the lowest free-energy barrier of formation of a critical radius *Rc*

<sup>∆</sup>*<sup>G</sup>* <sup>=</sup> <sup>4</sup>*πR*<sup>2</sup> *<sup>γ</sup>* <sup>+</sup> \_\_4

*Rc* <sup>=</sup> <sup>−</sup>2*<sup>γ</sup>* \_\_\_\_

specific effects on their solubilities [134].

according to the reactions:

nucleation ∆*G*<sup>∗</sup>

204 Cement Based Materials

where

and

$$7\,\mathrm{Ca\_4(PO\_4)\_2O} + 2\,\mathrm{Ca(H\_2PO\_4)\_2H\_2O} \rightarrow 6\,\mathrm{Ca\_5(PO\_4)\_3OH} + 3\,\mathrm{H\_2O} \tag{11}$$

$$2\text{ Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + \text{Ca(H}\_2\text{PO}\_4\text{)}\_2\text{H}\_2\text{O} \rightarrow \text{Ca}\_4\text{(HPO}\_4\text{)(PO}\_4\text{)}\_5\text{OH} + 2\text{ H}\_2\text{O}\tag{12}$$

$$\text{Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + \text{CaHPO}\_4\\2\text{H}\_2\text{O} \rightarrow \text{Ca}\_5\text{(PO}\_4\text{)}\_3\text{OH} + 2\text{ H}\_2\text{O}\tag{13}$$

$$2\text{ Ca}\_4\text{(PO}\_4\text{)}\_2\text{ O} + 6\text{ CaHPO}\_4\\2\text{H}\_2\text{O} \rightarrow 2\text{ Ca}\_8\text{(HPO}\_4\text{)}\_5\text{OH} + 13\text{ H}\_2\text{O}\tag{14}$$

$$\text{Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + \text{CaHPO}\_4 \rightarrow \text{Ca}\_5\text{(PO}\_4\text{)}\_3\text{OH} \tag{15}$$

$$\text{3Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + 6\text{CaHPO}\_4 \rightarrow 2\text{Ca}\_4\text{(HPO}\_4\text{)(PO}\_4\text{)}\_5\text{OH} + \text{H}\_2\text{O}\tag{16}$$

$$3\,\text{Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + \text{Ca}\_8\text{H}\_2\text{(PO}\_4\text{)}\_6\text{5H}\_2\text{O} \rightarrow 4\,\text{Ca}\_5\text{(PO}\_4\text{)}\_3\text{OH} + 4\,\text{H}\_2\text{O}\tag{17}$$

$$3\text{ Ca}\_4\text{(PO}\_4\text{)}\_2\text{ O} + 3\text{ Ca}\_8\text{H}\_2\text{(PO}\_4\text{)}\_6\text{5H}\_2\text{O} \rightarrow 4\text{ Ca}\_8\text{(HPO}\_4\text{)(PO}\_4\text{)}\_5\text{OH} + 14\text{ H}\_2\text{O}\tag{18}$$

$$\text{Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + 2\text{ Ca}\_3\text{(PO}\_4\text{)}\_2 + \text{H}\_2\text{O} \rightarrow 2\text{Ca}\_5\text{(PO}\_4\text{)}\_3\text{OH} \tag{19}$$

It is also possible to form HA from acid-base mixtures of calcium phosphates with a Ca/P lower than that of HA when an additional source of calcium ions instead of TTCP is present such as CaCO<sup>3</sup> or Ca(OH)<sup>2</sup> . [137, 138] Takagi *et al*. were the first to propose a calcium phosphate cement formulation without TTCP. Different combinations of DCP and DCPD, α-TCP, amorphous calcium phosphate (ACP), calcium hydroxide and calcium carbonate have been prepared to obtain improvements in the setting time to as low as 5 minutes and tensile strengths as high as 7.5 MPa [139].

All brushite CPCs are obtained by an acid–base reaction. Because DCPD and DCP are the least soluble calcium phosphates under acidic pH (<4.2), they are the products formed by acidic CPC formulations. All other calcium phosphate phases being more soluble under these pH conditions, can be used as precursors for the DCPD- or DCP-forming cements. Although DCP is the more stable of the two phases, it is kinetically constrained to have a higher nucleation activation energy and can only form under certain conditions as explained earlier. After setting, the pH of the cement paste slowly changes towards the equilibrium pH [140]. Up to now, several formulations have been proposed, including β-TCP + MCPM, β-TCP + H<sup>3</sup> PO<sup>4</sup> , and TTCP + MCPM + CaO [51, 99, 141].

The second type of setting reaction is defined as hydrolysis of a metastable calcium phosphate when the reactant and the product have the same Ca/P molar ratio. Typical examples are ACP, α-TCP, and TTCP which form CDHA upon contact with an aqueous solution:

$$\text{Ca}\_{\text{x}}\text{H}\_{\text{y}}\text{(PO}\_{4}\text{)}\_{\text{z}}\text{nH}\_{\text{z}}\text{O} + \text{H}\_{\text{z}}\text{O} \rightarrow \text{Ca}\_{\text{z0-x}}\text{(HPO}\_{4}\text{)}\_{\text{x}}\text{(PO}\_{4}\text{)}\_{\text{ę-x}}\text{(OH)}\_{\text{z-x}} + \text{nH}\_{\text{z}}\text{O} \tag{20}$$

$$\text{3 } a-\text{Ca}\_3\text{(PO}\_4\text{)}\_2 + \text{H}\_2\text{O} \rightarrow \text{Ca}\_8\text{(HPO}\_4\text{)(PO}\_4\text{)}\_5\text{OH}\tag{21}$$

Similarly, many carboxyl group containing acids and salts have significant effect on hydroxyapatite microstructure and in general setting kinetics of calcium phosphate cements. A number of α-hydroxylated carboxylic acids and salts readily form calcium complexes as well as relatively insoluble and often amorphous Ca-carboxylate compounds [56]. These include glycolic, citric, tartaric, malonic, malic, succinic, lactic and maleic acids. Upon application of precompaction, compressive strength of TTCP-DCP cement increased fourfold to 184 MPa with sodium citrate concentration up to 500 mM compared to plain water and citric acid cement liquid [144]. Sodium citrate addition changed the surface zeta potentials of TTCP and DCP to −50.6 and −50.1 mV with 50 mM sodium citrate from −15.0 and −18.4 mV with

The powder of the original calcium phosphate cement formulation proposed by Brown and Chow consists of an equimolar mixture of TTCP and DCP. The setting reaction of calcium phosphate cements starts with ordered dissolution of the salts in the aqueous system. This

petal or needle-like crystals after initial setting is responsible for the adherence and interlocking of the crystalline grains, which result in hardening [26]. Detailed investigations of the setting of various CPC formulation using various molar ratios, particle sizes, P/L ratios reveal that the reaction proceeds by complete dissolution of the acidic phases DCP or MCPM and partial dissolution of the basic TTCP or β-TCP particles. The specific surface area and the resulting solubility of the basic phase has a much greater effect on the setting rate as increasing its specific surface area leads to an increase in pH, and results in a sharp rise in the solubility of the acidic particles and the supersaturation of HA in the solution [40]. For apatite cement setting is controlled by the dissolution of reactant particles in the first 4-h period, and since the rate of dissolution is proportional to the surface area of the particles which is basically constant in CPC specimens in the earlier stage, the precipitation rate of HA is linear with time. HA forms among the reactant particles which enhances the joint of solids, or around the particles which reduces the distance between grains [42]. Setting is controlled by diffusion through the HA layer at later stages. At 24 hours, the crystals are completely formed, being highly compacted in some areas of high density and well separated in areas with more porosity. Precipitated HA either in stoichiometric or calcium deficient form, nucleate and grow on TTCP particles, thereby reducing their dissolution rate at the final stages [145]. When such a shell is formed around the reactants, the rate of HA formation is controlled by the transport of water and ions through the shell and decrease with an increase of its thickness. Since the densities of DCP and HA are different, the hydration of the residual DCP engulfed by the shell to HA leads to volume expansion and internal

Liu *et al*. describes the thermodynamics of apatite cement setting clearly [118]. Calcium phosphate cement setting reactions are generally exothermic reactions consisting of several steps. In the short initiating period, water is absorbed and wets the surface of the grains upon mixing calcium phosphate powder with water. This is a physical exothermic process. In the inducing

3− ions, which precipitate in the form of HA. Epitaxial enlargement of

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http://dx.doi.org/10.5772/intechopen.74607

water.

**5. Phase evolution during setting**

stress which is harmful to the compressive strength.

supplies Ca2+ and PO<sup>4</sup>

$$3\text{ Ca}\_4\text{(PO}\_4\text{)}\_2\text{O} + 3\text{ H}\_2\text{O} \rightarrow \text{ Ca}\_8\text{(HPO}\_4\text{)(PO}\_4\text{)}\_5\text{OH} + 3\text{Ca(OH)}\_2\tag{22}$$

Chemical composition of calcium phosphate cements may include all ionic compounds of naturally occurring minerals in human body. The list of possible additives includes the following cations: Na+ , K<sup>+</sup> , Mg2+, Ca2+, H<sup>+</sup> , Sr2+, Si4+, Fe2+, Ag+ , and anions: PO<sup>4</sup> 3−, HPO<sup>4</sup> 2−, H<sup>2</sup> PO4−, CO<sup>3</sup> 2−, HCO<sup>3</sup> − , SO<sup>4</sup> 2−, HSO<sup>4</sup> − , Cl<sup>−</sup> , F<sup>−</sup> , SiO<sup>4</sup> 4−. Therefore, mixed-type cements consisting of calcium phosphates and other calcium salts like gypsum, calcium sulfate hemihydrate, calcium pyrophosphate, calcium polyphosphates, calcium carbonate, calcium oxide, calcium hydroxide, calcium aluminate, calcium silicate, strontium phosphate, as well as cements made of ion substituted calcium phosphates such as Ca2 KNa(PO<sup>4</sup> ) 2 , NaCaPO<sup>4</sup> , Na3 Ca<sup>6</sup> (PO<sup>4</sup> ) 5 , magnesium-substituted calcium deficient hydroxyapatite (CDHA), strontium-substituted CDHA are possible [142].

CO<sup>3</sup> 2− ions have the most significant effect on CPC microstructure such that incorporation of carbonate in the apatite cement causes a decrease in the precipitated crystallite size and reduces the setting rate as well as the attained compressive strength. According to the study by Khairoun *et al*. CaCO<sup>3</sup> addition extended the initial setting times but significantly shortened the final setting times of single component HA cement. Furthermore its accelerating effect was more pronounced at higher concentrations [137]. Morphological studies reveal that the size and shape of the crystallites change from long needles to smaller rods to tiny spheroids [18, 102]. Carbonate ions can incorporate into apatite and substitute for PO<sup>4</sup> 3− or OH− in the apatite crystal structure and subsequently change its properties. It is reported that the supersaturation required for precipitation of slightly carbonated apatite was higher than that of apatite in simulated body fluid [143]. Carbonate ions disturb the crystallization of the growing apatite crystallites to such an extent that, depending upon the amount of carbonate added, the material may give an amorphous X-ray diffraction pattern. A submicron structure of interconnected microcrystals are responsible for the improved final mechanical properties of the cement formulation with addition of calcium carbonate. Moreover, carbonate ions cause the bonding in the apatite to become weaker and more isotropic, which results in the small spheroidal crystals and in faster dissolution rates [42].

Similarly, many carboxyl group containing acids and salts have significant effect on hydroxyapatite microstructure and in general setting kinetics of calcium phosphate cements. A number of α-hydroxylated carboxylic acids and salts readily form calcium complexes as well as relatively insoluble and often amorphous Ca-carboxylate compounds [56]. These include glycolic, citric, tartaric, malonic, malic, succinic, lactic and maleic acids. Upon application of precompaction, compressive strength of TTCP-DCP cement increased fourfold to 184 MPa with sodium citrate concentration up to 500 mM compared to plain water and citric acid cement liquid [144]. Sodium citrate addition changed the surface zeta potentials of TTCP and DCP to −50.6 and −50.1 mV with 50 mM sodium citrate from −15.0 and −18.4 mV with water.
