Section 12: Mineralized TissuesSection 12: Mineralized Tissues

2. Ionic solids; hydroxyapatite2. Ionic solids; hydroxyapatite

2/28/06

SolubilitySolubility of ionic solids of ionic solids

the solubility of a salt or ionic solid is a the solubility of a salt or ionic solid is a resultant of 2 tendencies:resultant of 2 tendencies:

aggregation or formation of the solid stateaggregation or formation of the solid state(crystallization, precipitation)(crystallization, precipitation)

favored by the strength of attraction between ions favored by the strength of attraction between ions (ion-ion interaction)(ion-ion interaction)

dispersion or formation of the dissolved statedispersion or formation of the dissolved state(dissolution)(dissolution)

favored by attraction between ions and solventfavored by attraction between ions and solvent(ion-dipole interaction)(ion-dipole interaction)

11

Types of ionic solidsTypes of ionic solids slightly soluble salts slightly soluble salts

stable in the solid state stable in the solid state ions:ions:

– have high charge density (have high charge density (e.g.e.g., Ca, Ca2+2+, Al, Al3+3+ , , POPO4433–– ) )

– pack so as to:pack so as to:maximize separation of same-charge maximize separation of same-charge

ions ions minimize separation of opposite-minimize separation of opposite-charge ionscharge ions

highly soluble salts highly soluble salts stable in the dissolved statestable in the dissolved state ions:ions:

– have low charge density (Nahave low charge density (Na++, NH, NH44++ ))

– pack relatively poorlypack relatively poorly– are attracted to Hare attracted to H22OO22

solid formation & dissolving described as a chemicalsolid formation & dissolving described as a chemicalequation:equation: dissolutiondissolution

[M(H[M(H22O)O)66]]++ + [X(H + [X(H22O)O)66]]-- M M++XX -- + 12 H + 12 H22O O

precipitationprecipitation the ions on the left side of the above equation are shown the ions on the left side of the above equation are shown

hydrated (aquo ions) with the common coordination # of 6hydrated (aquo ions) with the common coordination # of 6

[M(H[M(H22O)O)66]] + + : : ball & stickball & stick

Solid–solution transitionSolid–solution transition

33 space-fillingspace-filling

solid formation & dissolving described as a chemicalsolid formation & dissolving described as a chemicalequation:equation: dissolutiondissolution

[M(H[M(H22O)O)66]]++ + [X(H + [X(H22O)O)66]]-- M M++XX -- + 12 H + 12 H22O O

precipitationprecipitation the ions on the left side of the above equation are shown the ions on the left side of the above equation are shown

hydrated (aquo ions) with the common coordination # of 6hydrated (aquo ions) with the common coordination # of 6 usually ion'susually ion's

hydration statehydration statenot shown:not shown:MM++ + X + X

-- M M++XX ––

MX MX

[M(H[M(H22O)O)66]] + + : : ball & stick ball & stick space-fillingspace-filling

Solid–solution transitionSolid–solution transition

33

Solubility & rates ofSolubility & rates ofprecipitation & dissolution precipitation & dissolution the rates of these processes depend on the surface the rates of these processes depend on the surface

area of the solid, area of the solid, AAsolidsolid::

rateratedslndsln = k= kdslndsln((AAsolidsolid))rateratepptnpptn = k= kpptnpptn((AAsolidsolid)[M)[M++][X][X

–– ]]

[M[M++][X][X ––

] is often called the ] is often called the ion production product kkdslndsln & & k kpptnpptn are rate constantsare rate constants

at equilibrium,at equilibrium,

rateratedslndsln = rate= ratepptnpptn

k kdslndsln((AAsolidsolid)) = k= kpptnpptn((AAsolidsolid) [M) [M++]]eqeq[X[X ––

]]eqeq44

Solubility: KSolubility: Kspspdividing by kdividing by kpptnpptn((AAsolidsolid),),

kkdslndsln/k/kpptnpptn = [M = [M++]]eqeq[X[X ––

]]eqeq

this ratio of rate constants is an this ratio of rate constants is an equilibrium equilibrium constantconstant

KKspsp = [M = [M++]]eqeq[X[X ––

]]eqeq

this last equation states that this last equation states that at equilibrium at equilibrium the product of the product of the component ions is equal to a constant, termed the the component ions is equal to a constant, termed the solubility product constantsolubility product constant, K, Kspsp

the solution is said to be the solution is said to be saturatedsaturated there is no there is no net net dissolution or precipitation,dissolution or precipitation,

but in general the equilibrium is but in general the equilibrium is dynamicdynamic KKspsp: : a measure of solubilitya measure of solubility

larger values indicate greater solubilitylarger values indicate greater solubility55

Deviation from equilibriumDeviation from equilibriumoften for salts often for salts in vivoin vivo, applicable ion product ≠ K, applicable ion product ≠ Kspsp , so under- , so under-standing these nonequilibrium conditions is also important:standing these nonequilibrium conditions is also important:

solutionsolution tendencytendency G'G'dslndsln G'G'pptnpptn in vivo process in vivo process conditioncondition favored favored

saturated:saturated: no net changeno net change 00 00 ion product ion product (equilibrium)(equilibrium) = K = Kspsp

supersaturated:supersaturated: precipitationprecipitation ++ –– mineralization:mineralization: ion product ion product MM++ + X + X–– MXMX formation of formation of > K > Kspsp bone, enamel bone, enamel

& calculus& calculus

undersaturated:undersaturated: dissolutiondissolution –– ++ demineralization:demineralization: ion product ion product MX MX MM++ + X + X–– caries, bonecaries, bone < K < Kspsp resorptionresorption

66

calcium & phosphate form a variety of saltscalcium & phosphate form a variety of saltsat pH at pH 7, the calcium phosphate solid7, the calcium phosphate solidwith the lowest solubility is with the lowest solubility is hydroxyapatitehydroxyapatite

empirical formula: empirical formula: CaCa1010(PO(PO44))66 (OH)(OH)22 despite its evident complexity, despite its evident complexity, at constant pHat constant pH a reasonable approximation of its solubility is obtained by a reasonable approximation of its solubility is obtained by the simple equation:the simple equation:

K'K'sp(HA)sp(HA) = [Ca= [Ca2+2+][P][Pii]]

where [Pi] = [Hwhere [Pi] = [H22POPO44––] + [HPO] + [HPO44

==] + [PO] + [PO4433––]]

in vitroin vitro, with only Ca, with only Ca2+2+, P, Pii in H in H22O, pH = 7, K'O, pH = 7, K'spsp 0.01 mM 0.01 mM 22

in solutions containing physiological concentrations of in solutions containing physiological concentrations of other ions, its solubility is higher:other ions, its solubility is higher: K'K'spsp = 0.7 mM = 0.7 mM22

Hydroxyapatite (HA): composition, KHydroxyapatite (HA): composition, Kspsp

77

by comparison, for a salt like NaCl, by comparison, for a salt like NaCl, KKspsp = 3 = 3××101077 mM mM 22

knowing the K'knowing the K'spsp and [ions], one can calculate the and [ions], one can calculate the tendencytendency of a fluid to dissolve mineral or form it of a fluid to dissolve mineral or form it

note that it is the note that it is the productproduct of the ions' concentrations of the ions' concentrations that mattersthat matters for example:for example: [Ca[Ca2+2+] ] ×× [P [Pii] = ion product] = ion product

mM mM mM mM mM mM 22

0.84 0.84 0.840.84 0.70.7 0.7 0.7 1.0 1.0 0.70.7 0.07 0.07 1010 0.70.7

despite differing ion concentrations, these 3 cases are despite differing ion concentrations, these 3 cases are at equilibrium under conditions where K'at equilibrium under conditions where K'spsp = 0.7 mM = 0.7 mM

22 88

K'K'spsp of HA compared to [Ca of HA compared to [Ca2+2+] [P] [Pii] ion product] ion product

Calcium & PCalcium & Pi i in vivoin vivo

Concentrations & ion products of calciumConcentrations & ion products of calcium & P & Pii in some biological fluids in some biological fluids

[Ca[Ca2+2+]×[P]×[Pii] = ion product] = ion product mM mM mMmM mM mM 22

ECF: adultECF: adult 1.21.2 1.31.3 1.61.6 childchild 1.21.2 1.91.9 2.32.3Saliva: low flow rateSaliva: low flow rate 11 55 55 high "high " 22 22 44

in all cases, ion product > K'in all cases, ion product > K'spsp, so the fluids are , so the fluids are supersaturatedsupersaturated with respect to HA with respect to HA (as long as the pH is close to 7)(as long as the pH is close to 7)

99

Conditions where ion product < K'Conditions where ion product < K'spsp as the pH of saliva drops toward 5, however, the as the pH of saliva drops toward 5, however, the

K'K'spsp of HA increases & becomes larger than the of HA increases & becomes larger than the ion product, i.e., saliva becomes ion product, i.e., saliva becomes undersaturatedundersaturated with respect to HA with respect to HA

HA thus has a tendency or potential to dissolveHA thus has a tendency or potential to dissolve this is a this is a necessarynecessary but but not sufficientnot sufficient condition for condition for

caries formation; a number of additional factors caries formation; a number of additional factors determine the actual rate and extent of dissolutiondetermine the actual rate and extent of dissolution

K'

K' spsp

[[ HH++]]

Variation of Variation of K'K'spsp with with [H[H++]]

1010 1010 CaCa2+2+ + 6 + 6 POPO4433–– + 2 + 2 OHOH –– ↔↔ CaCa1010(PO(PO44))66(OH)(OH)22

Effect of pH on solubilityEffect of pH on solubility for most simple salts (for most simple salts (e.g.e.g., NaCl),, NaCl),

solubility does not vary with pHsolubility does not vary with pH because the salt's ions don't react with Hbecause the salt's ions don't react with H++ or OH or OH –– in in

the physiological pH rangethe physiological pH range because OHbecause OH –– is not part of crystal structure is not part of crystal structure

for many other salts (for many other salts (e.g.e.g., phosphate salts),, phosphate salts), solubility is solubility is pH-dependentpH-dependent because Pi forms are acids/bases with each [form] because Pi forms are acids/bases with each [form]

being pH-dependent due to these pKbeing pH-dependent due to these pKaa values: values: HH22POPO44

–– HH ++ + HPO + HPO44== pKpKaa = 7 = 7

HPOHPO44== H H ++ + PO + PO44

33–– pKpKaa = 12 = 12 because OHbecause OH –– is a component ion of the crystal is a component ion of the crystal

1111

Crystal structure: generalCrystal structure: general unit cell:unit cell: repeating unit of a crystal repeating unit of a crystal

smallest sample of a crystal smallest sample of a crystal that includes an example of that includes an example of all of the interionic all of the interionic distances & angles distances & angles which occur in the which occur in the entire crystal entire crystal relatively simple relatively simple

example: example: NaClNaCl unit cell hasunit cell has

4 Na4 Na++ & 4 Cl & 4 Cl–– ionsions((lighterlighter spheres)spheres)

1212

HA crystals in enamel rodsHA crystals in enamel rods

4

300x

packing of rods in enamelhydroxyapatite crystallite200 x 500 x 1000 Å

hexagonal prisms that are small & variable in sizehexagonal prisms that are small & variable in size small size means small size means

large surface area/weightlarge surface area/weight

1313

HA crystal structureHA crystal structure

composed of unit cellscomposed of unit cells~10~1055 unit cells/crystallite unit cells/crystallite

composed of ionscomposed of ions polar surfacepolar surface ion exchange with ion exchange with

fluids at interfacefluids at interface adhesion of substances adhesion of substances

due to polar interactionsdue to polar interactions

50×50×

hydroxyapatitehydroxyapatitecrystallitecrystallite200 × 500 × 1000 200 × 500 × 1000 ÅÅ

hydroxyapatitehydroxyapatiteunit cellunit cell9.4 × 9.4 × 6.9 Å9.4 × 9.4 × 6.9 Å

60º

1414

complexcomplex18 ions/unit cell:18 ions/unit cell:

CaCa1010(PO(PO44))66(OH)(OH)22

formation difficultformation difficultsupersaturation supersaturation

likely likely unit cells pack tounit cells pack to maximize attractive maximize attractive interactions interactions ions shared betweenions shared between

unit cellsunit cells interlocking cellsinterlocking cells

HA unit cellHA unit cellstructurestructure

OH PO4

Ca

1515

2 unit cells stacked together2 unit cells stacked together ions at unit cellions at unit cell

surface interdigitate surface interdigitate with complementary with complementary spaces on adjacent spaces on adjacent unit cells unit cells (knobs into grooves)(knobs into grooves)[molecular LEGOs][molecular LEGOs]

ion sharingion sharingCaCa2+2+ & P & Pii ions ionson faces are shared on faces are shared with adjacent with adjacent unit cellunit cell

HA unit cell structureHA unit cell structure

1616

this view shows how 2 OHthis view shows how 2 OH–– ions ( ions (arrowsarrows) are shared ) are shared between 2 adjacent unit cellsbetween 2 adjacent unit cells

HA unit cell structure: ion sharingHA unit cell structure: ion sharing

1717

OHOH–– ions shared with 3 adjacent unit cells (total=4) ions shared with 3 adjacent unit cells (total=4)8 OH8 OH–– shown ÷ 4 = 2/unit cell shown ÷ 4 = 2/unit cell

HA unit cell structure: ion sharingHA unit cell structure: ion sharing

1818

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3. Mineralization & fluoride3. Mineralization & fluoride

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