10.1098/rspa.2002.0975

Liesegang pattern development in carbonatingtraditional lime mortars

By Carlos Rodriguez-Navarro, Olga Cazalla,

Kerstin Elert and Eduardo Sebastian

Departamento de Mineralogıa y Petrologıa, Universidad de Granada,Fuente Nueva s/n, 18002 Granada, Spain

Received 17 October 2000; revised 12 November 2001; accepted 26 February 2002;published online 11 July 2002

Liesegang patterns, generally rings, bands, spheres or spirals, form in far-from-equilibrium systems in nature and in the laboratory by self-organized periodic pre-cipitation of sparingly soluble phases following a nonlinear reaction–diffusion process.Although Liesegang patterns have been known for more than hundred years, there isstill disagreement as to the mechanisms underlying this phenomenon. Most studieshave focused on Liesegang pattern formation in gels, quantitative studies of quasi-periodic patterns in non-conventional porous media (e.g. construction materials)being rare. Here, we report the development of ‘revert’ three-dimensional Liesegangpatterns (i.e. concentric ellipsoids) in traditional lime mortars undergoing carbon-ation. Portlandite (Ca(OH)2) in a quartz (SiO2) sand aggregate, transforms intocalcite (Ca(CO)3) in contact with atmospheric CO2, resulting in banded cementa-tion of the lime mortar. Surprisingly, well-developed Liesegang patterns only occur inmortars prepared using ‘aged’ lime putty, kept under excess water for years, followingan ancient Roman recipe to improve slaked lime quality; the carbonation of thesemortars being faster than in pattern-less ones. The smaller Ca(OH)2 particle size inthe long-term-aged putty enhances dissolution and increases the ion-concentrationproduct, while creating a higher volume of pores with r < 0.1 µm. These small porescan sustain very high supersaturation ratios with respect to CaCO3, resulting inhigher nucleation rates, a crucial fact for pattern development previously neglected.These results may have strong implications for the understanding of Liesegang pat-terns, as well as for the conservation of architectural heritage.

Keywords: Liesegang patterns; lime mortars; calcium hydroxide;calcite; supersaturation; architectural conservation

1. Introduction

The Liesegang phenomenon (Liesegang 1896) is a quasi-periodic self-organized (Nico-lis & Prigogine 1977; Ortoleva 1984a) precipitation (of a sparingly soluble product)occurring in the wake of a moving reaction front. Liesegang patterns, generally rings,bands or spheres, although there are more complex patterns such as spirals (Muller etal . 1982a), have been described in nature (Ortoleva et al . 1990; Fujikawa 1992; Kruget al . 1996) and in the laboratory (Stern 1954; Henisch 1988). Liesegang patterns arecharacterized by a series of simple geometric and spatiotemporal relationships (Dee

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2262 C. Rodriguez-Navarro and others

1986). In spite of their abundance, Liesegang patterns are formed only under specificphysical-chemical conditions (Kai et al . 1982; Chopard et al . 1994; Garcıa-Ruiz etal . 1996). A prerequisite for Liesegang pattern development is that the reactantscounter-diffuse. If convective or gravitatory flow of the reactants occurs, Liesegangpatterns are not developed (Garcıa-Ruiz et al . 1996). Generally, a diffusion-controlledtransport of the reactants is achieved in a saturated porous medium, porous gelsbeing among the best supports for Liesegang pattern development (Henisch 1988).However, periodic precipitation patterns have also been described in homogeneoussystems (Ortoleva 1982; Antal et al . 1998).

Numerous theories have been proposed to explain the Liesegang phenomenon(Stern 1954; Dee 1986; Henisch 1988; Antal et al . 1998). Most of them are basedon Ostwald’s supersaturation theory (Ostwald 1897), which assumes that crystal-lization (in a supersaturated system) is discontinuous and therefore the spatial andtemporal arrangement of crystallization conditions determines the Liesegang rings orbands location. A mathematical model for this theory was first developed by Ostwald(1925) and completed by Prager (1956). Variations of this so-called pre-nucleationtheory have been proposed (Smith 1984; Dee 1986; LeVan & Ross 1987) to explainsome experimental results not contemplated in the original Ostwald model (e.g. pat-tern formation in the absence of reactant concentration differences, or the existenceof colloid precursors and/or precipitates between bands). However, pre-nucleationmodels fail in explaining the development of unusual Liesegang structures such ashelicoidal patterns (Muller et al . 1982a; Sydow & Plath 1998), speckled structuresand secondary banding (Feeney et al . 1983; Krug et al . 1996) and inverted or ‘revert’patterns (Packter 1955; Kanniah et al . 1981; Das et al . 1989). In the late 1970s it waspostulated that Liesegang patterns occur as a post-nucleation phenomenon (Feinnet al . 1978; Lovett et al . 1978; Venzl & Ross 1982; Kai et al . 1982; Feeney et al .1983; Ortoleva 1984a, b; Kirkaldy 1992). In the post-nucleation case, the reactionfront propagates continuously through the medium and colloid-size crystals appeardistributed in a homogeneous fashion initially. A feedback process involving growth,diffusion and surface-tension effects results in the pattern due to the development ofa Lifshitz–Slyozov instability (Lifshitz & Slyozov 1961). Ostwald ripening, i.e. growthof the larger crystals at the expense of the smaller, takes place (see Dunning (1973) fora detailed description of the Ostwald ripening phenomenon) and bands form wherelarger crystals concentrate. The post-nucleation model, also known as the competitiveparticle growth (CPG) model, as well as the so-called induced sol coagulation model(as a generalization of the CPG model (Gnaman et al . 1980)), may help explain casesnot contemplated by the Ostwald–Prager model (e.g. ‘revert’ Liesegang patterns).Much effort has been dedicated to developing a comprehensive unified model explain-ing all the observed spatial and temporal arrangements of Liesegang patterns; how-ever, the complexity and sometimes chaotic nature of this phenomenon have somehowobstructed it (Sultan & Sadek 1996). One of the most recent models incorporatesnucleation, growth and ripening, and claims to bridge the gap between a nucleation-growth-dominated regime (i.e. pre-nucleation model) and one where ripening is active(i.e. post-nucleation model) just by tuning a phenomenological parameter that char-acterizes the thickness of the Gibbs surface of a precipitate particle (Chacron &L’Heureux 1999). However, it assumes that a non-homogeneous particle-size distri-bution of the precipitate is needed for the onset of the post-nucleation regime (asopposed to the original CPG model). This assumption may imply that the pattern

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Liesegang patterns in lime mortars 2263

development is already triggered at the nucleation phase, apparently rendering thisunified model as a pre-nucleation model where coarsening (i.e. ripening) is contem-plated. The persisting controversy on the origins of Liesegang patterns, their visualattraction and apparent similarity to geologic and biologic structures, as well asthe theoretical challenge and scientific implications of this phenomenon, continue tostimulate research (Krug & Brandtstadter 1999). The study of its occurrence notsolely in classical laboratory experiments (i.e. precipitation in gel media), but also inother contexts (e.g. geologic settings, civil engineering or architectural works), seemsa promising way to gain a better understanding of this phenomenon.

Here, we report on three-dimensional Liesegang pattern formation (concentricellipsoids in prism-shaped samples) in traditional lime mortars undergoing carbon-ation. A Liesegang pattern develops when lime mortars are prepared using tradi-tional lime putties that have been aged by long-term storage under water (morethan 14 years), following a recipe used since Roman times (Ashurst 1990). Mortarsprepared using recently hydrated lime putty (less than 1 year of ageing) do not showpattern formation, or its development is very poor.

Lime-mortar carbonation, a key process determining the mortar’s performance asa building material, is a very slow process requiring years, and sometimes centuries,for its completion. It takes place when CO2 dissolves in water and reacts with dis-solved calcium hydroxide, which is the mortar binder, resulting in the precipitationof calcium carbonate via the following overall reaction (Moorehead 1985):

Ca(OH)2 + CO2 → CaCO3 + H2O. (1.1)

Lime mortars were traditionally used as building material for millennia (first recordsdated from 12 000 BC (Kingery 1988)) until Portland cement replaced lime as thebinder of choice in the 19th century (Ashurst 1990). However, the disadvantagesof Portland cement (Rodriguez-Navarro et al . 1998) and the increasing awarenessof the preservation of architectural heritage using traditional compatible materials,have resulted in a revival of lime-mortar technology and application (Ashurst 1990).Nevertheless, little research has been dedicated to the study of this material, itsproperties and performance. For instance, very little work has been dedicated tothe better understanding of the carbonation of calcium hydroxide in lime mortars(Moorehead 1985; Van Balen & Van Gemert 1994), and, to our knowledge, no dataexist on the formation of patterned structures through this process.

The aim of this research is to study and understand how Liesegang patternsform in carbonating traditional lime mortars, with a threefold goal. First, todetermine what is the mechanism of quasi-periodic calcium-carbonate precipitation(i.e. pre-nucleation versus post-nucleation phenomena). Second, to understand whya Liesegang pattern only occurs when the lime putty undergoes a certain amount ofageing. Third, to understand how this may affect the behaviour of the resulting car-bonated lime mortar. Some practical considerations of this research for understandingprocesses resulting in patterned structures and, in particular, their implications inarchitectural conservation are outlined.

2. Materials and methods

Two lime mortars were prepared: one using a traditional long-term-aged lime putty(14 years of ageing), and another one using a lime putty stored under water for

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2264 C. Rodriguez-Navarro and others

a shorter period of time (less than 1 year). Mortars were prepared by adding theaggregate, i.e. quartz sand, to the lime putty. The binder to aggregate ratio was 1:3.The water to binder ratio was 1:2. To facilitate CO2 access to the mortar pore system,samples (4 cm × 4 cm × 16 cm in size) were kept standing up (vertical position) in aventilated room. The room temperature and relative humidity (RH) were controlledat 18±5 ◦C and 60±5%, respectively. CO2 concentration in the room was estimatedto be the standard atmospheric concentration (i.e. 0.033 ± 0.001% by volume (Lide1996)). Further details on hydrated lime-crystal size and shape, as well as on lime-mortar preparation, were presented in an earlier publication (Cazalla et al . 2000).

The carbonation evolution over time was qualitatively evaluated impregnating themortar samples with a saturated phenolphthalein (C20H14O4) ethyl alcohol solution.Phenolphthalein, a pH indicator, shows red coloration at pH > 8.2 (i.e. areas whereCa(OH)2 is abundant), while it remains white at pH < 8.2 (i.e. areas where CaCO3is more abundant). Phenolphthalein was homogeneously sprayed on fresh mortarsurfaces of 4 cm × 4 cm × 4 cm cubes, cut perpendicular to the longest prism axis.Impregnation was performed on mortar samples with different carbonation times(i.e. 10, 49 days, 2, 6, 9 and 18 months). The degree of carbonation is proportionalto the degree of whiteness of the sample, normally showing an outer whitish ringwith a reddish core. Colour differences between calcite- and portlandite-rich areasevidence Liesegang pattern formation. Photographic images of the sample surfacetreated with phenolphthalein were scanned and digitally analysed using computerimage-processing software (Photoshop, v. 4.0). The image analysis allowed us tomeasure ring location and dimensions (width).

Portlandite crystal surface area and its evolution upon ageing was determined bymeans of N2 adsorption (Micromeritics Gemini) using the BET method (Brunaueret al . 1938). Special care was taken to avoid carbonation (keeping the samples in anN2 atmosphere and tightly sealed in plastic bags).

Partly carbonated aged lime putty was observed at high magnification by means oftransmission electron microscopy (TEM) (200 kV, Philips CM 20 coupled with EDXmicroanalysis). Diluted ethyl alcohol portlandite (plus calcium carbonate) suspen-sions were deposited in 3 mm diameter Cu grids. Samples were carbon coated prior toTEM observation. Gold-coated mortar samples with well-developed Liesegang pat-terns were observed at high magnification by means of scanning electron microscopy(SEM) (Zeiss DSM 950).

Small sample cubes (1 cm3) were collected from the mortar-sample surface after10 days of setting (i.e. minimum extent of carbonation), and their porosity andpore-size distribution were evaluated by means of mercury intrusion porosimetry(MIP) (Micromeritics Autopore 5410). The equilibrium moisture content (EMC)of each mortar type (after 10 days carbonation time) was evaluated by weighing4 cm3 sample cubes following 24 h drying in an oven at 110 ◦C and comparing thesevalues with their weight following exposure until equilibrium (i.e. constant weight)to a 19 ◦C, 69% RH atmosphere in an airtight box, where a saturated solution of KIwas placed.

3. Results and discussion

Following carbonation, phenolphthalein impregnation on freshly cut mortar surfacesevidenced Liesegang pattern formation and its evolution over time (figure 1). The

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Liesegang patterns in lime mortars 2265

(a) (b)

p

c

t = 10 days t = 28 days

t = 62 days t = 180 days

t = 270 days t = 545 days

Figure 1. Liesegang patterns in lime mortars. (a) Scheme of the pattern spatial arrangementin a lime mortar sample (c denotes calcite, p portlandite). (b) Snapshots of the ring evolutionversus carbonation time in the long-term-aged lime mortars after impregnation with saturatedphenolphthalein-ethyl alcohol solution on fresh mortar surfaces cut perpendicular to the longestprisms axis. Dark bands are due to massive presence of Ca(OH)2, while white bands indicatepresence of CaCO3.

pattern spatial arrangement followed the so-called ‘spacing law of Jablczynski’, a fun-damental characteristic of Liesegang patterns (Stern 1954; Dee 1986; Henisch 1988;Chopard et al . 1999). For large numerical order (n) of the rings, the position (or dis-tance from the diffusion front at time t = 0) of two consecutive bands (Xn and Xn+1)approaches a constant value (figure 2),

Xn+1

Xn→ 1 + p, (3.1)

where p is known as the spacing coefficient. The observed p value of 0.06 (for n > 6,when the p values are asymptotic) falls among the typical 0.05 < p < 0.4 (Das et al .

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2266 C. Rodriguez-Navarro and others

1.0

1.5

2.0

1.5

0 4 8n

0

0.5

1.0

1.5

2.0

2 6X

n+

1/X

n

∆X

n

Figure 2. Analysis of the pattern spatial arrangement. Xn+1/Xn (filled circles)and ∆Xn = (Xn+1 − Xn) (open circles) versus n.

1989). However, the pattern is not a direct, but a ‘revert’, one (Packter 1955), withdecreasing spacing between rings as n increases (figure 2).

The low p value in our experiment is consistent with a high ion concentrationproduct σ (σ = [CO2−

3 ][Ca2+]), as indicated by Chopard et al . (1999). Muller etal . (1982b) demonstrated that a Liesegang pattern only develops when a certain σthreshold has been reached. In fact, low reactant concentrations either do not resultin Liesegang pattern, or the resulting pattern shows a random arrangement (Kaiet al . 1983). Additionally, a significant difference between the concentration of theouter and the inner reactant ∆ (∆ = [CO2−

3 ]−[Ca2+]) enhances pattern development(Muller et al . 1982b; Kai et al . 1983). The limited solubility of Ca(OH)2 in water(2.5 × 10−2 mol dm−3 at 25 ◦C), which results in pH ∼ 12.4, and the high CO2solubility (as CO2−

3 ) in alkaline media (Somasundaran & Agar 1967), ensures a high∆ value in the lime mortar. However, enhanced dissolution of Ca(OH)2, resulting inhigher σ values, can be achieved in the long-term-aged lime mortars if compared withthe short-term-aged ones, due to the smaller size (Cazalla et al . 2000) and highersurface area of Ca(OH)2 crystals in the former. In fact, BET N2 surface area valuesfor long- and short-term-aged putties were 10.8 and 4.5 m2 g−1, respectively. Thelong-term-aged portlandite crystals are more reactive and soluble, as given by themodified Kelvin equation (Adamson 1990),

RT lnS

S0=

2γVm

ri, (3.2)

where S is the actual solubility of a crystal with radius ri, S0 is the bulk solubil-ity of the crystal, and γ and Vm are the crystal surface energy (surface tension)and molar volume, respectively. Rodriguez-Navarro et al . (1998) demonstrated thatCa(OH)2 crystals undergo significant size reduction (from greater than 1 µm to muchless than 1 µm) and habit modification (from prism to plate like) upon ageing, dueto differences in solubility between basal {0001} and prism {1010} faces, the latterbeing more soluble due to higher surface energy γ (i.e. γ{0001} < γ{1010}). Addi-tionally, they observed that secondary heterogeneous nucleation of nanometre-sizedplate-like Ca(OH)2 crystals also contributed to an overall crystal size reduction andspecific surface area increase. Higher σ values in mortars developing Liesegang pat-terns result in kinetically faster carbonation (i.e. the system is very far from equi-

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Liesegang patterns in lime mortars 2267

0

0.04

0.08

0.12

0.16

0.001 0.01 0.1 1 10 100 1000r (µm)

log

dv/d

r (c

m3

g−1)

Figure 3. Lime mortars pore-size distribution. Porosimetry plots (differential intrusion volumeversus pore radius) for the short-term-aged (dotted line) and the long-term-aged (solid line)lime mortars.

1.0

1.5

2.0

2.5

0.001 0.01 0.1 1r (µm)

S

1 × 100

1 × 104

1 × 108

1 × 1012

J/J 0

Figure 4. Supersaturation (S) and nucleation rate (J/J0) versus pore size (r) for the systemH2O–CaCO3. For a given pore size, a curve indicates increased S values that can be sustainedin a pore of radius r, with respect to an initial S = 1 in the bulk solution (i.e. in pores withr � 1 µm). The second curve indicates the variation of nucleation rate for S = 2, with respectto pore size. Note the exponential increase as r → 0. Values calculated after Kashchiev &Van Rosmalen (1995).

librium), as revealed by X-ray diffraction data showing that long-term-aged limemortars carbonate four times faster than short-term-aged ones (Cazalla et al . 2000).

Mercury intrusion porosimetry (MIP) analysis of non-carbonated mortars (fig-ure 3) shows that long-term-aged lime putty mortars have a higher amount of poreswith r < 0.1 µm than short-term-aged ones, having both an almost identical openporosity (27 ± 0.5%). This seems to be due to the smaller size of the Ca(OH)2crystals in the long-term-aged hydrated lime. The role of small pores in Liesegangpattern development seems to be crucial: CaCO3, having a molar volume of the

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2268 C. Rodriguez-Navarro and others

(a) (b)

c

p

p

c100 nm 2 µm

Figure 5. (a) TEM photomicrograph of partly carbonated aged lime putty. Colloidal (spherical)calcium carbonate (c) and hexagonal plate-like portlandite (p) crystals can be observed. (b) SEMphotomicrograph of large sparitic calcite rombohedra in a calcite-rich band developed in thecarbonated ‘aged’ lime mortar.

condensed phase Vc bigger than the molar volume of the solute in aqueous solutionVs (Vc − Vs = 7.5 × 10−29 m3), undergoes a significant increase in both supersat-uration and nucleation rate in pores with r < 1 µm, due to the Laplace effect ofcurvature (Kashchiev & Van Rosmalen 1995). Figure 4 shows how calcite supersat-uration and nucleation rates in the system CaCO3–H2O increase as the pore sizedecreases. High supersaturation and nucleation rates induce the formation of numer-ous randomly distributed far-from-equilibrium nanometre-sized colloidal calcite par-ticles (Cole & Kroone 1959; Ogino et al . 1987; Cazalla et al . 2000), following themovement of the reaction–diffusion front toward the sample core. Figure 5a shows aTEM photomicrograph of the colloid-size calcium carbonate particles formed uponpartial carbonation of aged lime putty. These calcium carbonate particles are similarto those reported to form upon carbonation of calcium hydroxide in Portland cement(Grudemo 1962). It is not clear whether they are amorphous calcium carbonate par-ticles, microcristalline calcite or a metastable precursor such as monohydrocalcite(Jimenez-Lopez et al . 2001). Such small particles have very large surface-to-volumeratio, and hence interfacial energy can play a significant role (Ortoleva 1994). In par-ticular, grain solubility will strongly depend on particle size, as indicated by (3.2).Colloid-size calcium carbonate will evolve and transform into well-crystallized calcitethrough Ostwald ripening (figure 5b). According to the CPG model (Feeney et al .1983; Ortoleva 1994), this is the ideal scenario for the onset of a Lifshitz–Slyozovcoarsening instability (i.e. deviation of the local average particle size), which tendsto amplify itself, leading to a self-organization mechanism for creating patterns ofprecipitate content.

The reported results and the above discussion suggest two possible scenarios forLiesegang rings development. The first scenario, based on a pre-nucleation model,involves pattern formation by the onset of cyclic supersaturation–crystallization–depletion events, which may involve late-stage coarsening through Ostwald ripening(Dee 1986; Smith 1984). Once a sufficient supersaturation is reached, resulting inlocalized high nucleation rates, calcite crystals will precipitate. Reactant concentra-tion depletion around the precipitation front will prevent further calcite nucleation.The reaction–diffusion front will move toward the sample core until appropriate

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Liesegang patterns in lime mortars 2269

supersaturation conditions for calcite precipitation are reached again, resulting inthe development of successive calcite-rich rings separated by bands without calciteprecipitate. Against this hypothesis for Liesegang ring formation in carbonating limemortar is the fact that pre-nucleation models do not explain inverted or ‘revert’ pat-terns (Feeney et al . 1983).

The other scenario, based on a post-nucleation model, involves pattern formationthrough a two-step mechanism. First, a very high supersaturation, inducing highnucleation rates (favoured by the small size of the aged lime mortar pores), resultsin the formation of nanometre-sized colloidal (microcrystalline) calcite or monohy-drocalcite (Jimenez-Lopez et al . 2001). The formation of amorphous calcite (Oginoet al . 1987) cannot be ruled out either. In many systems (e.g. CaCO3–H2O) at lowtemperature (ca. 25 ◦C), mineral precipitation often occurs though the Ostwald steprule, which consist of a sequential precipitation event where metastable solid phasesnucleate and are progressively replaced by more-stable ones (Morse & Casey 1988;Jimenez-Lopez et al . 2001). Therefore, in a second stage, colloid-size (or amorphous)calcite, or metastable microcrystalline calcite precursors such as monohydrocalcite,will undergo Ostwald ripening. The onset of a Lifshitz–Slyozov instability duringthis stage will induce the formation of bands of precipitate content (larger, more-stable calcite crystals). The larger calcite particles will develop at the expense of thesmallest in well-localized areas (i.e. rings or bands) defining the observed pattern.The sharp X-ray diffraction Bragg peaks of calcite (Cazalla et al . 2000) confirmthat these crystals are no longer colloidal once the Liesegang pattern is fully devel-oped. This is also consistent with SEM observations of large (greater than 2 µmin size) sparitic calcite rombohedra in calcite-rich bands (figure 5b). Therefore, thepost-nucleation model for Liesegang pattern development could better explain allthe observed characteristic of the pattern. In particular, the post-nucleation modelcan predict revert pattern formation (Feeney et al . 1983).

In a previous paper (Cazalla et al . 2000), a brief description of patterned structuresformed upon lime mortar carbonation was outlined. However, due to the lack of adetailed analysis of both the pattern spatial arrangement and the leading role ofsmall pores in supersaturation and colloid-size calcium carbonate precipitation, itwas postulated that the mechanism responsible for the pattern development wasof the Ostwald supersaturation–depletion type. However, in lieu of the new datapresented here, it seems more plausible that the mechanism triggering the patterndevelopment is an instability in the process of Ostwald ripening. Nevertheless, it isbelieved that the very high supersaturation reached in pores with a radius of lessthan 0.1 µm, resulting in high nucleation rates, is crucial to understand Liesegangpattern formation according to both the pre- and post-nucleation models (see alsoHenisch 1988; LeVan & Ross 1987; Xie et al . 1999).

A larger volume of pores with r < 0.1 µm enhances capillary condensation of waterin the 14-year-old lime mortar (its EMC is 0.0046 g cm−3 at 69% RH and 19 ◦C) ifcompared with the short-term-aged lime mortar (0.0022 g cm−3 EMC value). Theseresults are consistent with the Kelvin equation (Gregg & Sing 1982),

RT lnP

P0= −2γV

rcos φ, (3.3)

where P is the equilibrium partial pressure of water vapour in a capillary of radiusr at the temperature T (K), P0 is the saturated vapour pressure over a flat water

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2270 C. Rodriguez-Navarro and others

surface, γ and V are the surface tension and molar volume of the liquid water,respectively, R is the gas constant and φ is the contact angle between liquid waterand pore surface.

Enhanced CO2 and Ca(OH)2 dissolution into the larger amount of condensedwater in the long-term-aged lime mortar accelerates the carbonation process. Thelarge amount of pores with r > 1 µm connected to the areas with smaller pores in thelime mortar (Cazalla et al . 2000) ensures that CO2 reaches in a rapid and efficientway the areas where water condenses, not affecting the reaction rate (Van Balen &Van Gemert 1994). Under these conditions, the carbonation of the mortars showingLiesegang patterns will be fastest and most extensive. This has strong implicationsfor the performance of the lime mortar. More rapid and extended carbonation inthe long-term-aged lime putty mortars developing Liesegang patterns will result inbetter mortar performance in a shorter time. This makes understandable an ancientRoman law stating that lime putty should be stored underwater (aged) for at leastthree years before its use as a building material (Ashurst 1990). Traditional long-term-aged lime putties are therefore recommended for specific architectural heritageconservation interventions where sufficient mortar strength development in a shortperiod of time is required.

In summary, the development of Liesegang patterns in the carbonating traditionalaged lime mortars starts with the dissolution of Ca(OH)2 and the diffusion andsolubilization of CO2 as CO2−

3 in the water condensed in the mortar pore system.CO2−

3 readily reacts with Ca2+ from the already dissolved Ca(OH)2, resulting incolloid-size calcium carbonate precipitation once a certain supersaturation thresh-old has been reached in pores with r < 0.1 µm. Ostwald ripening will promote theformation of bands where larger calcite crystals concentrate. The diffusion–reactionfront will propagate deeper into the mortar pore system, allowing further colloidalcalcite precipitation and the onset of Ostwald ripening phenomena. The wake of themoving reaction front toward the sample core finally results in the described alter-nating CaCO3-rich and Ca(OH)2-rich rings. It should be mentioned that, accordingto Ortoleva et al . (1986), Ortoleva (1987) and Sultan et al . (1990), the continuousflow of the outer reactant toward the sample core (i.e. CO2 in our system) will tendto regularize band spacing, therefore contributing to the full development of theLiesegang pattern.

Calcite precipitation results in volume increase and porosity reduction, i.e. poreslarger than 1 µm in diameter are significantly reduced upon carbonation, the totalporosity reduction being greater than or equal to 12% (Moorehead 1985). Hencethe carbonation of lime mortars is a self-limiting process in which CO2 uptake anddiffusion decreases as the process progresses toward the sample core, which mayexplain the revert nature of the Liesegang pattern.

4. Conclusions

This study demonstrates the paramount importance of pores with radius less than0.1 µm in the development of Liesegang patterns, their role not only being limited toensure that diffusion is the transport mechanism, but also to enhance supersaturationand nucleation rates, i.e. they ensure that the system is very far from equilibriumand follows a nonlinear evolution. The high supersaturation results in very highnucleation rates and the development of colloid-size precipitates that may undergo

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Liesegang patterns in lime mortars 2271

Ostwald ripening, which, in turn, is a prerequisite for Liesegang pattern developmentaccording to a post-nucleation model.

These results may explain why Liesegang patterns form in some porous mediaand not in others, even if all other parameters are equal (Henisch 1988). They mayalso help us to understand the formation of Liesegang patterns, as well as other self-organized periodic structures in many porous natural media undergoing cementation,from kidney cysts (Krueger et al . 2000) to sedimentary rocks (Ortoleva 1993, 1994).

This work was supported by a grant from the Spanish Government (DGYCIT) under con-tract PB96-1445 and by the Research Group RNM-0179, as well as the Consejerıa de Culturaof the Junta de Andalucıa (IAPH). We are grateful to the Getty Conservation Institute (LosAngeles, CA) for N2 BET analyses. TEM and SEM analyses were performed at the ServiciosTecnicos de Apoyo a la Investigacion of Granada University. We thank Professor G. S. Scherer,Dr J. Garcıa-Ruiz and Dr J. Cartwright for their valuable comments and suggestions. Threeanonymous referees are also acknowledged for their constructive criticism and suggestions.

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