Nanopore Structure Buildup during Endodontic Cement Hydration

Jan 19, 2010 - of endodontic cement pastes during hydration, from the initial ... a widely used commercial endodontic cement paste and two more recent...
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J. Phys. Chem. B 2010, 114, 1767–1774

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Nanopore Structure Buildup during Endodontic Cement Hydration Studied by Time-Domain Nuclear Magnetic Resonance of Lower and Higher Mobility 1H Mirko Gombia,† Villiam Bortolotti,‡ Boris De Carlo,§ Romano Mongiorgi,§ Silvano Zanna,§ and Paola Fantazzini*,† Department of Physics, UniVersity of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy; DICAM, UniVersity of Bologna, Via Terracini 28, 40131 Bologna, Italy; and Dipartimento di Scienze della Terra e Geologico-Ambientali, UniVersity of Bologna, Piazza di Porta S. Donato 1, 40127 Bologna, Italy ReceiVed: July 29, 2009; ReVised Manuscript ReceiVed: January 2, 2010

Time-domain nuclear magnetic resonance (TD-NMR) of 1H nuclei has been used to monitor and model changes of endodontic cement pastes during hydration, from the initial reaction period up to hours and days. The 1H in the samples are divided into two major spin groups by fitting each free induction decay, acquired after the second pulse of an inversion recovery (I-R) pulse sequence with variable interpulse delay, by the sum of a quasi-Gaussian (signal from low mobility nuclei) and an exponential (from higher mobility nuclei). The extrapolations to zero time of the signals from the two spin groups give two sets of I-R data that have been analyzed to give quasi-continuous T1 distributions. After about a day, two clearly solid components appear. From a day to a few days, three liquid populations are identified, one of them mainly in the low-mobility spin group, which later merge, giving a single T1 or T2 peak. The rapid onset of the solid components, at the cost of the liquid, and the rapid changes of the relaxation time distributions of all components are clear indicators of the amount and kinetics of reaction products formation (C-S-H gel and Portlandite) and of the C-S-H micronanoporous structure buildup and evolution. At 30 days of hydration, the very short T1 and T2 liquid component (T1 = 200 µs and T2 = 50 µs) can be assigned to C-S-H intralayer water (thickness of the order of fractions of a nanometer) and the remaining liquid signal to interlayer water (thickness of the order of 1 nm). Comparisons are made among a widely used commercial endodontic cement paste and two more recent commercial pastes, with additive compounds to make the hydration process faster and to increase the workability. Parameters can be extracted from the data to characterize the different kinetics and nanostructure of the pore space formed up to 30 days. The parameters are in agreement with the expected effects of the additives, so the parameters can be used to optimize the formulation of new pastes, in order to improve their therapeutic performance. 1. Introduction Hydration of cements consists of a complex sequence of chemical-physical processes leading to the formation of a micronanoporous material having a significant resistance to compression. It starts when water is added to a powder of clinker grains, obtained by melting a mixture of limestone and clay at high temperature. The hydration kinetics and the pore-structure development and evolution can be studied by time domain nuclear magnetic resonance (TD-NMR) of 1H nuclei.1 Over the years, NMR diffusometry, relaxometry, and imaging have been applied to monitor these processes through the water selfdiffusion coefficient,2 relaxation times of the longitudinal (T1) and transverse (T2) components of the nuclear magnetization,2-12 and images of internal sections,13,14 respectively. In the present work, NMR relaxometry has been applied to study evolution of endodontic cement pastes over the first 30 days of hydration. The main properties of the NMR signal used are the following: (1) the proportionality of NMR signal to the number of 1H nuclei in the sensitive volume; (2) the dependence of longitudinal and transverse relaxation times on molecular correlation times, * To whom correspondence should be addressed. Tel: +39 051 20 95119. Fax: +39 051 20 95047. E-mail: [email protected]. † Department of Physics. ‡ DICAM. § Dipartimento di Scienze della Terra e Geologico-Ambientali.

allowing for separation of lower-mobility from higher-mobility 1 H nuclei on the basis of their free induction decay (FID) signals; (3) the dependence of the relaxation rate (reciprocal of relaxation time) of 1H nuclei of water completely filling a pore on the surface-to-volume (S/V) ratio of the pore under the assumptions that the bulk relaxation rates are negligible and the molecular diffusion time inside a pore is short compared with the relaxation times, the relaxation rate being associated with the S/V of the pore (1/T1,2 ) F1,2S/V), where F1,2 is the surface relaxivity; (4) the distribution of relaxation rates observed in a porous medium corresponds to a distribution of “pore sizes”, which can be computed in the form of a quasi-continuous distribution by mathematical algorithms for inversion of multiexponential decay (operation now usually called 1D inverse Laplace transform (1DILT)). Endodontic cements have a wide clinical application for conservative therapy. They must have good workability and proper mechanical and biological properties and hardening times. A cement widely used is the mineral trioxide aggregate (MTA), a Portland cement composed of tricalcium silicate (3CaO · SiO2), dicalcium silicate (2CaO · SiO2), tricalcium aluminate (3CaO · Al2O3), with added bismuth oxide.15-18 Special additives can be added to Portland cement to improve the properties of the cements for therapeutic use. It is of interest to set up methodologies to study and compare the kinetics of the

10.1021/jp907248r  2010 American Chemical Society Published on Web 01/19/2010

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reactions leading to the formation of the pore structure, contributing to the determination of the therapeutic performance of the cement pastes. It is known that the most important reaction products in cement pastes are calcium hydroxide (Ca(OH)2, portlandite, CH in the cement chemists’ nomenclature) and a quasi-amorphous, poorly crystalline, calcium silicate hydrate, called C-S-H gel. Hyphens mean that there are no fixed chemical composition relationships among the oxides. It is generally believed that in the first 24 h of hydration Ettringite, an expansive salt containing water in stoichiometric proportions (Ca6Al2(SO4)3(OH)12 · 26(H2O)) and 30% of Portlandite are formed. After formation the Ettringite soon disappears. The C-S-H gel is assumed to be made of calcium silicate sheets, arranged rather randomly in some regions but in a more regular clay layer structure in others. Following ref 5, the spaces of the gel pores are considered to range from 10 nm down to less than 0.5 nm. Elsewhere,19,20 the thickness of the tightly bound gel water layers between the sheets is given as about 1-2 nm. In ref 11, the intrasheet porosity is considered to correspond to about a water layer, while other pore sizes are given in the range 1 nm to 10 µm. A recent computer simulation gives a model where C-S-H is made of somewhat irregular sheets, with water adsorbed not only in the interlayer regions (spacings a little over 1 nm) but also in the distorted intralayer regions around the silica monomers.21 In principle, 1H nuclei of water in capillaries (larger pores) and in C-S-H gels and in solid phases, such as hydroxyl groups of Portlandite and crystal water, can be resolved, thanks to the effect on T1 and T2 of molecular mobility and interactions at the pore surfaces. The appearance of an off-diagonal peak in a two-dimensional inverse Laplace transform (2D-ILT) T1-T2 and T2-T2 experiment led McDonald et al.6 to infer an exchange of hydrogen (or water) between compartments. In a 2D-ILT T2-T2 correlation study by the same authors,7-9 and reported in an extended review,12 they suggested an exchange between two different structures in the gel. One pore size was evaluated after 4 days of curing to be in the range 1.0-1.7 nm, and another in the range 7-30 nm (evaluated as 2.4 and 16 nm, respectively, in ref 12). In that study, the existence of a population of very low mobility protons was not investigated through the characteristic shape of their FID signal. Many materials give solidlike and liquidlike NMR signals, from lower and higher molecular mobility 1H nuclei, respectively. These nuclei can be distinguished by an analysis of FID signals. The solidlike nuclei give signal decay of quasi-Gaussian form with T2 ≈ 12-15 µs, which is 1-2 orders of magnitude shorter than the T2 for exponential decay of the liquidlike nuclei. In a study5 where white cement paste, basically Portland, was monitored as a function of hydration time from 15 min to 200 h, very low mobility nuclei could be distinguished on the FIDs. The growth or reduction, as well as the dynamic state and evolution, of five populations of 1H were monitored by means of a discrete-component analysis of relaxation curves and then associated with known hydration products. In that study only T2 relaxation was taken into account. Cement paste hydration has been studied by the evolution of T1 relaxation time distributions in the early stages of hydration.10 During the first few minutes of hydration at least two T1 values were found. The time evolution of the longest T1 value, followed for several hours, was shown to correlate with the known phases of the hydration process: initial reaction, induction, acceleration and deceleration period, and slow hydration reaction. In that

Gombia et al. paper, T2 relaxation and FID analysis for solid-liquid separation were not used. In an extensive study,11,12 T1 relaxation data were obtained by inversion recovery (I-R) at 12 T both in static conditions and by the magic angle spinning (MAS) technique, used to suppress the effect of dipole-dipole interactions. Static T1 relaxation data at 3 months of hydration were inverted to T1 distributions by the software CONTIN, and by a discrete method analysis, “curve peeling,” obtaining five well-separated peaks, discussed in terms of a discrete pore-size distribution. MAS spectra combined with I-R measurements allowed them to assign the T1 peak at 1 ms to 1H of silanol (Si-OH, hydroxyl group attached to a silicon atom), probably located within the layers of C-S-H. The longest one (T1 ≈ 103 ms) was assigned mainly to 1H of the Ca(OH)2 group of Portlandite crystals. The intermediate T1 peaks were assigned to moving 1H species of Ca-OH and Si-OH bonds, fast diffusing inside different classes of C-S-H pores.11 In this work T2 relaxation and FID analysis for solid-liquid separation were not used. In the present paper, the changes have been studied of both T1 and T2 quasi-continuous distributions during hydration from 1 h to 30 days. A separation of components has been made on the FIDs to distinguish the T1 evolution of lower and higher mobility 1H nuclei, in the style of Pintar et al.,4,5 giving a sort of 2D analysis on a physical basis (solid-liquid separation). Also the dependence of the observed T2 on the CPMG pulse spacing (diffusion time) has been studied to give further insight into diffusion in the pore system. In such a way, a complete analysis of the evolution of both T1 and T2 relaxation time distributions for solidlike and liquidlike populations has been performed over 30 days for MTA cement. Two other endodontic cements, recently commercialized in Italy, with specific additives, have been compared with MTA. The observed differences show that this kind of analysis can help one not only to better set up the TD-NMR methodologies on cements but also to determine parameters that are easy to measure and able to distinguish properties of cement pastes for endodontic applications. 2. Materials and Methods Samples. Samples of Portland cement powder adapted for endodontic use were analyzed. A detailed analysis was performed on the commercial product MTA (ProRoot MTA, Mineral Trioxide Aggregate, Dentsply Tulsa Dental Products, Tulsa, OK). Two other pastes recently commercialized in Italy were compared with MTA. All three pastes are based on Portland cement with added Bi2O3, but MTA samples are of a different source than the others. The other two are based on white Portland cement (WPC). TECH BIOSEALER standard (ISASAN s.r.l., Como, Italy) (WPC-CaCl2) has the further additives phyllosilicate and CaCl2; in TECH BIOSEALER fluoridated (WPC-NaF) besides bismuth oxide and phyllosilicate, also CaSO4 and NaF are added. Bismuth oxide is added for radio-opacity; CaCl2 is added because it tends to cause expansion and increases the rate of setting, NaF is added because it gives F- ions to the structure of the enamel of the tooth, and moreover it is known by practice that it makes the paste better workable for a longer time; the phyllosilicate is a filler and places water molecules at the disposal of the reactions; CaSO4 controls the setting and slows down the hydration. Samples were prepared by adding 250 mg of water to 500 mg of powder, mixed at the bottom of a 10 mm external diameter glass NMR tube. The tube was sealed with Parafilm,

Endodontic Cement Nanopore Structure by TD-NMR and the measurements were performed at times after preparation from about 1 h to 30 days. TD-NMR Data Acquisition. NMR measurements were performed at 20 MHz (0.47 T) and 25 °C by a homemade relaxometer based on a Spinmaster console (Stelar, Mede, Italy) and a Jeol electromagnet. Longitudinal relaxation curves (T1) were acquired by inversion-recovery (I-R) pulse sequences (πx - ti - (π/2)x - FID acquisition). The signal was acquired with 128 ti values (I-R times) chosen in geometrical progression from 50 µs up to 1.4 s, with 512 points at 0.5 µs intervals on each FID, starting at 15 µs (dead time) after the end of the π/2 pulse (number of scans 16). Transverse relaxation curves (T2) were acquired by CPMG pulse sequences with different echo spacings (TE ) 40, 100, 200, 400, 1000 µs) (maximum number of echoes 8000, number of scans 256). The duration of π/2 pulse was 3.6 µs. All curves were acquired using phase-cycling procedures. TD-NMR Data Analysis. All experimental relaxation curves were inverted from data time to quasi-continuous relaxation time distributions by the inversion algorithm UPEN22-26 implemented in UpenWin software.27 The UPEN algorithm, differently from others, varies the smoothing factor with relaxation time, in order to maintain the penalty roughly constant, so reducing the features in the distributions not required by the data to be there. Almost all FIDs, obtained at different I-R times ti, showed the presence of at least two 1H spin groups distinguishable through the different decay shape: quasi-Gaussian (fast decay, solidlike) and exponential decay (slower decay, liquidlike). In principle, the different behaviors can be ascribed to different (1H or molecular) mobility. The algorithm applied was settled on over the course of time, when we observed these two 1H populations in biological samples (wood, bone, and collagen).26,28,29 The algorithm gives estimates of four parameters: T2g, the time constant of the fitted Gaussian or quasi-Gaussian decay; X2, its corresponding amplitude extrapolated to FID time ) 0; T2FID, the T2 corresponding to the slope of the fitted exponential decay; X1, its corresponding extrapolated amplitude. The ratio R ) X2/X1, is also calculated. Special attention has been devoted to reduce the introduction of scatter in the computed results, by forming stacks of FIDs on which computations were made, and to take into account potential changes in the FID slopes of the liquidlike component with FID time and with I-R time ti, due to possible T2 multiexponential decays. In the presence of only one quasi-Gaussian population and only one exponential population, an accurate determination of the two extrapolated signal amplitudes at each ti can be obtained, to produce separate files for input to UpenWin software,27 giving as output the quasicontinuous T1 distributions (1D-ILT), for both spin groups. 3. Results Results on all endodontic samples examined confirmed the general characteristics observed in the sample of MTA, the hydration of which was monitored in detail from 1 h to 30 days after water addition. The FIDs of MTA paste show the evolution of two spin groups (each later divided into more than one component) separated on the basis of their FID decay times, at least a factor 20 apart, that we have studied using the four parameters described above and the quasi-continuous T1 distributions of both spin groups. Figure 1 shows, on semilogarithmic plots, a few stacks of FIDs for the first (1 h (Figure 1a)) and the last (30 days (Figure 1b)) measurements. In Figure 1b it is seen that the FIDs for the fast relaxing group at short, and long I-R times do not have the same shape. This is a clear indicator of the presence of more than one solidlike component,

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Figure 1. A selection of FID stacks obtained in inversion-recovery measurements on the commercial endodontic cement MTA hydrated at 1 h (a) and 30 days (b) after water addition to the powder. FID signals are shown on a log scale. Twelve stacks of 10 FIDs each were formed starting at the shortest recovery times. The figure for the 30 days measurement displays the stacks corresponding to I-R times 0.07, 0.28, 0.57, 1.17, 2.37, and 4.80 ms. The initial portions of the FIDs after 30 days show the typical behavior of the low-mobility 1H nuclei of the so-called “solidlike” component, which has different shape at short and long I-R times, indicating at least two solid signal sources, having widely different T1 values. The exponential portions of the FIDs represent the liquidlike component due to 1H of water molecules.

having different T1 values. That means that each FID at each I-R time should be fitted by a different function, because each component contributes to the FIDs with different weights as the I-R time increases. To determine both T2g and T2FID from the FID at each I-R time would have the disadvantage of increasing scatter in the computed results, so the same T2g is used at all I-R times, and a T2FID varying smoothly with I-R time is used. Also, one should keep in mind that some spin populations might be attributed by the two-component computation partially to the solidlike group and partially to the liquid one, as will be discussed later. The signal amplitude of the quasi-Gaussian spin group increases rapidly during the first 2 days and continues to increase gradually. Figure 2a shows the extrapolated signal amplitudes for the solidlike (X2) and liquidlike (X1) and their sum (the total signal) over time for sample MTA. The total signal is about constant for more than 2 days, in agreement with the constant mass of the paste. Only on the third day does the total signal decrease, and the total mass is only 3 mg less at 30 days. The rapid increase of the solidlike and the parallel decrease of the liquidlike signal are due to the chemical reactions leading to the formation of the solid matrix at the cost of the liquid water molecules initially added to the cement powder, as already described in ref 5 with a progressive conversion of 1H nuclei from a high mobility phase (liquid water) to lower mobility ones. After 30 days, the ratio R ) X2/X1 is about 20%, as shown in the inset of Figure 2a, where a local maximum appears at about 2 days, shortly followed by a local minimum at about 3 days. At first glance, these features could be ascribed to data

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Figure 3. (a) Experimental longitudinal relaxation curves and (b) quasicontinuous T1 distributions of the solidlike group at 1 h, 9 h, 3.5 days, 30 days. The multiexponential data in (a) are inverted to distributions of relaxation times in (b) by the algorithm UPEN. Areas in the distributions are proportional to the numbers of 1H nuclei contributing to the signal, showing a progressive increase of signal and distribution complexity, as the hydration proceeds. The ordinate is an approximation to (dM)/(d ln T1), where M is the extrapolated signal per Neper (factor of e) of relaxation time.

Figure 2. (a) NMR signal vs hydration time, after solid-liquid separation by fitting each FID to the sum of a Gaussian (solidlike) and a single exponential (liquidlike). The NMR signals represented are the solidlike (X2), the liquidlike (X1), and their sum, extrapolated to zero delay time. The insert shows their ratio. The solidlike is formed over time at the cost of the liquidlike. (b) Time constants of the decay of the solidlike (T2g) (×10) and liquidlike (T2FID) groups vs hydration time. T2g decreases gradually from 15.1 µs down to 13.5 µs. T2FID decreases very rapidly in the first day, and its behavior follows the known periods of hydration, shown approximately in the expanded plot (c).

fluctuations, but the appearance in that period of a component with variable T2 has been reported,5 which could be compatible with the observed behavior. Figure 2b shows the evolution of the two time constants T2g and T2FID for MTA. The first might be considered as constant within the limits of the instrumental and computation resolution, but, the computed value shows a slow systematic decrease from the initial 15.1 µs down to 13.5 µs after 30 days. Over the same period of time the exponential time constant T2FID decreases from 850 to 300 µs. In Figure 2c the plot is expanded, in order to display T2FID in the course of the first four hydration steps, indicated approximately by the vertical lines: the initial reaction, the induction, the acceleration, and the deceleration periods. Because of the large liquid signal amplitude, T2FID is a robust parameter useful to monitor the changes of the environment of the liquidlike 1H nuclei. It should be noted that the FID decay of the liquidlike group is not single-exponential and that T2FID, although robust, depends on the FID interval used. A more detailed analysis is obtained by quasi-continuous relaxation time distributions of both spin groups. Figure 3a

shows a selection of I-R relaxation curves of the solidlike group during hydration. In Figure 3b the corresponding 1D-ILT T1 distributions are shown. At 1 h only one low peak is observed, from about 0.3 to 10 ms. At 9 h there is a single wide peak, extending from about 0.1 to 100 ms. At 1 day (not shown in the figure) a second peak starts to be visible at longer T1 values (hundreds of milliseconds), with significant amplitudes up to about 1 s. In the course of time the amplitudes of these two broad features increase. At 3.5 days the broad peak at shorter times is split into two peaks, centered at about 0.2 ms and about 5 ms and the peak centered at a few hundred milliseconds is increased in amplitude. At 30 days a broad distribution with some structure is observed from 40 µs to 10 ms and the amplitude of the peak at hundreds of milliseconds is further increased. More detailed T1 and T2 analysis will show that what our solid-liquid separation assigned to the solidlike group is made up of three components, one of which (the signal centered at 0.2 ms at 3.5 days) is actually a short-T2 liquid. The three components are growing in time and have T1 in three different ranges. Figure 4a,b shows a selection of T1 1D-ILT distributions of the liquidlike group of sample MTA. The very sharp T1 peak centered at about 60 ms at 1 h shifts to shorter times and maintains the same shape (with reduced area, in agreement with the reduced X1 signal) for many hours. The small liquid signal at times longer than 100 ms is due to water inside a few very large pores. Figure 4b is a magnification of a selection of distributions from 1 day to 30 days. At 1 day Figure 4b shows two resolved peaks in the range 0.4-10 ms. The features of the UPEN algorithm support strongly the valid resolution of these two peaks, that merge into only one as the hydration

Endodontic Cement Nanopore Structure by TD-NMR

Figure 4. Quasi-continuous relaxation time distributions for the liquidlike group of the same sample of Figure 1. (a) A selection of T1 distributions from 1 h to 30 days. The peaks shift to shorter times. (b) Magnification of a selection of the T1 distribution from 1 day to 30 days. At 1 day two peaks are observed that meld into only one after 3 days. (c) The same as for (a) is seen for T2 distributions obtained by CPMG pulse sequences with the shortest echo spacing available (40 µs). Areas in the distributions are proportional to the numbers of 1H nuclei contributing to the liquidlike signal. For T1 distributions the total signal is twice that of the corresponding T2 signal, being proportional to relaxing magnetization after inversion for T1 and to equilibrium magnetization for T2. (d) Magnification of a selection of T2 distributions from 1 day to 30 days. As CPMG T2 for liquids must be as large as or larger than T2 values from FIDs, the observed values shorter than T2FID at 30 days (about 300 µs) demonstrate that a fraction of the so-called “solidlike” spins are really liquid with very short T2.

proceeds, and the amplitude of the higher-T1 peak is more and more reduced. At 3.5 days almost all the signal is represented by only one wide nearly rectangular peak, which then gradually

J. Phys. Chem. B, Vol. 114, No. 5, 2010 1771 becomes more rounded and shifts to shorter times. A low tail extending to times as short as 0.1 ms is seen at all times after 3 days. The T2 distributions from CPMG (Figure 4c,d) show a parallel behavior that confirms the trend. The T2 curve for 1 day has a sharp shoulder at just under 2 ms but not the two fully resolved peaks shown for T1 in Figure 4b, which has a sharp minimum at about 3 ms. It may be that diffusion in local inhomogeneous fields has decreased T2 more for the sharp peak at about 3.5 ms, presumably representing larger pores, than for the shoulder at about 1 ms, thus preventing resolution of separate components. In principle, CPMG distributions should represent only signal from liquid. Already at 1 day a tail is observed at short T2, down to 40 µs, whose amplitude increases with hydration time and includes times shorter than T2FID. That means that CPMG pulse train shows the presence of a signal from a liquid with T2 shorter than the T2FID used to define the liquid from our solid-liquid separation. This signal should be from the abovementioned short-T2 nuclei, with T2 values intermediate between the lowest mobility (truly solid) nuclei, with T2g about 12-15 µs, and those assigned to the much larger liquidlike component, with T2FID > 300 µs at all hydration times. The tail at very short T1 in Figure 4b must be part of this short-T2 liquid population included in the solidlike FID component in Figure 3b; otherwise it would have T1 < T2, not physically acceptable. In fact, a more detailed analysis of one set of FID data (at 3.5 days) shows that, in addition to the Gaussian (or modified Gaussian) signal (truly solid) and the exponential (liquid) signal with T2FID ) 430 µs, there is another FID component that is an exponential with T2 of the order of 50 µs and T1 about 200 µs. A component (fitted as a Gaussian, defined as time for decay to one-half), arising at about half a day and settling after 2 days to about 60 µs has been reported.5 Also, by 2D analysis, a tail with T2 of the order of 50 µs and T1 of about 200 µs has been reported.6,7,11,12 This component would contribute to both solidlike and liquidlike in our two spin groups, computed for solid-liquid separation and producing files for T1 analysis, although, since its FID decay is exponential rather than approximately Gaussian, it should be classified as liquid. All this supports the conclusion that the peak at short T1 in Figure 3b is part of the above-mentioned short-T2 liquid component and should really be combined with the liquid distribution. The formation of more than one liquid peak, observed at one day and merging into a single peak after a few days, is consistent with the hypothesis that liquid populations of 1H, not in fast exchange, are present from a day to a few days. After 30 days all the liquid is represented by only one wide peak, with T1 from 0.1 ms to a few ms, including the “solid” peak at short T1 in Figure 3b. In order to investigate possible effects of diffusion inside the pore system, CPMG data were acquired at increasing echo spacings TE. For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, neglecting the bulk fluid relaxation rate, the transverse relaxation rate R2 ) 1/T2 from CPMG data is given by (τγg)2D/3, where γ is the magnetogyric ratio, τ is TE/2, and D is the molecular self-diffusion coefficient. However, in porous media diffusion is not unrestricted nor is the magnetic field gradient constant. There may be significant pore-scale local gradients due to susceptibility differences between fluid and solid matrix,26,30-36 whose contributions to R2 may depend linearly on τ for small τ.26,30,31,36 Thus, plots of R2 against τ often show better linear fits to the data, and better extrapolations of the data to τ ) 0 for small τ values in porous media than do plots against τ2.

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Figure 7. T2FID of the liquidlike groups vs hydration time for MTA and the two cement pastes with additives. T2FID decreases more rapidly for WPC-CaCl2 than for WPC-NaF or MTA. This is consistent with the known effect of the addition of CaCl2 used to make the hydration faster. Figure 5. Quasi-continuous T2 distributions for the liquidlike group, acquired by CPMG at five echo spacings (40, 100, 200, 400, 1000 µs), shown at 1 h, 1day, 3 days, and 30 days. The line forms are clearly identified in the figure at 1 h, by noting that T2 decreases with echo time. For the first few hours the distributions shift to shorter T2 values with increasing echo spacing because of diffusion in inhomogeneous fields. The shift is strongly reduced as the gel formation proceeds.

Figure 6. R2gm (reciprocal of the geometric-mean time, T2gm) vs τ (halfecho spacing) for the data of Figure 5. At 1 h the first points lie close to a linear fit, as expected for molecular diffusion inside local field gradients due to susceptibility difference between water and pore matrix. The plots show that the effect of diffusion is very small already at 1 day of hydration. The decrease in rate at small τ for longer hydration times is because the echoes are at times too long to represent the small component with FID T2 of the order of 50 µs. The behavior of the data at 30 days and large τ is due to the inadequate coverage by the data when the T2 values become shorter than or comparable with the time of the first data point.

Figure 5 shows the T2 distributions obtained for five different TE values, at 1 h, 1 day, 3 days, and 30 days. A dependence on τ is observed at 1 h, corresponding to the diffusion of the liquid phase inside large pores. The dependence on τ is weaker as the hydration time increases. Figure 6 shows the plots of the reciprocal of the geometric-mean relaxation time 1/T2gm, where T2gm ) exp〈ln T2〉, against τ for all the measurements of Figure 5. Despite the use of only one parameter to represent a distribution of relaxation times, a trend that initially is closer to linear than quadratic is shown at 1 h and for the first few hours (not shown), suggesting diffusion of water molecules inside a distribution of internal field gradients. At hydration times longer than a few hours the FID component with T2 of the order of 50 µs become significant, so that the later time for the first data point at increased TE leads to a loss of signal. The result is an initial decrease of the rate plotted in Figure 6, especially for the 30-days data, where this very short T2 component is largest and where the T2 of the main peak is the shortest. The τ ) 0.5 ms data at 30 days have the first data

point at 1.6 × T2gm, not adequately defining the relaxation of even the longer components. The linear fit of the initial points of the data corresponding to the first few hours gives R2(τ) ) (0.30τ + 0.07) ms-1; the intercept represents the rate in the absence of diffusion in the gradient, due only to the surface effect, and gives R2surf = 0.07 ms-1 and T2surf =15 ms. A strong decrease of the self-diffusion coefficient2 with hydration after a few hours has been described in cement paste in a study where the diffusion coefficient was measured by the pulsed field gradient technique. Figure 7 shows the T2FID values in logarithmic scale for MTA and the two TECH BIOSEALER samples. WPC-CaCl2 does not show an induction period. WPC-NaF shows a very brief induction period, less than for MTA. WPC-CaCl2 presents a strong acceleration in the first 5 h, while WPC-NaF is less accelerated. The large values of the initial T2FID (about 2 times the MTA value) presumably indicates the presence of larger spaces occupied by water, a feature that is preserved even at long times. Figure 8 compares the final T1 distributions at 30 days for MTA and the two samples with additives. The liquid distributions (Figure 8a) for WPC-CaCl2 and WPC-NaF are shifted to longer times than that for MTA. The shapes are different; in particular, WPC-NaF shows a substantial longlasting tail up to more than 1 s. WPC-CaCl2 shows a more complex structure, suggesting two unresolved components. The distributions for the “solid” (Figure 8b) present the same general characteristics, each with a large peak at long T1 values, an intermediate peak in the range of milliseconds and a tail at short times, which may represent the short-T2 liquid component. It can be noted in both Figure 8a,b that signal (areas under distributions) are larger for cement pastes with additives than for the MTA sample. 4. Discussion The principal features shown by our NMR data are the rapid onset of the solid signal, at the cost of the liquid, and the rapid changes of their relaxation time distributions. The results are consistent with the formation and evolution, in this 30-day period of hydration, of the most solid components and of the C-S-H gel, with pores in the cement varying in size over orders of magnitude during hydration. The known information about products formation and pore sizes within the hydrating cement can help in trying to associate the observed features of the distributions with components and pore space structure. In principle, T1 and T2 distributions for fully water-saturated porous systems can be related to the surface-to-volume ratio distributions of the pore space. The small liquid signal in Figure

Endodontic Cement Nanopore Structure by TD-NMR

Figure 8. Quasi-continuous T1 distributions of MTA and the two cement pastes with additives after 30 days of hydration for both liquidlike (a) and solidlike (b) populations. Areas in the distributions are proportional to the numbers of 1H nuclei contributing to the signal.

4 at times longer than 100 ms is clearly due to the largest pores. By considering the remaining peaks the ratio T1/T2 can be evaluated. The ratio T1/T2 is 2-3 at 1 day and at 30 days, and at 1 h it is 4-5, using the value T2surf ≈ 15 ms, corresponding to the τ ) 0 extrapolation in Figure 6. The liquid peak with FID T2 of the order of 50 µs has T1 about 200 µs, a factor of about 4. These ratios are compatible with the values observed for water confined in porous media when relaxation is due to surface effects. The change of the shapes of the liquid distributions and the shift, during the hydration process, toward shorter relaxation times of the signal from water molecules (Figures 4) reflects the gradual formation of the pore space of the C-S-H gel. The evolution shown is in agreement with the progressive buildup of the network of the pore structure of the gel, with higher and higher surface-to-volume ratios, leading to shorter and shorter relaxation times, as the process of setting and hardening proceeds. The creation of solidlike components at the cost of the liquidlike (Figure 2a) corresponds to the expected progressive production of Portlandite, crystal water, and the gel. Even if T1 and T2 proceed in parallel, the correlation of relaxation time and pore size is more reliable for T1, since T2 is affected by other mechanisms such as diffusion in inhomogeneous fields. By assuming a surface relaxivity37 in the range 0.5-2.5 µm/s for T1, one gets a characteristic pore size estimation for the MTA sample peak at 1 h (T1 ≈ 60 ms) in the ranges: 30-150 nm plate spacing for planar, 60-300 nm pore radius for cylindrical, or 90-450 nm pore radius for spherical geometries. Pore size estimation can be done also using T2 data, namely the value T2surf, not affected by diffusion, and the value of transverse surface relaxivity F2 ≈ 3 µm/s (F2 > F1) estimated for cement from the data reported in ref 7. The results give estimates of the characteristic pore sizes in the range 45-135 nm for the three geometries, consistent with T1-based estimations. Eleven hours after water addition, the T1 of the peak of the liquid of MTA is decreased by an order of magnitude, from 60

J. Phys. Chem. B, Vol. 114, No. 5, 2010 1773 to 10 ms. The formation of the two liquid T1 peaks observed at the end of the first day is consistent with the hypothesis of two populations of liquid 1H in addition to the one with very short T1 and T2, without fast exchange of water molecules between them in a relaxation time. The computation of the characteristic pore sizes using these data at 24 h for the peak at longer time (T1 ≈ 6 ms) gives estimates in the range 3-45 nm for the three geometries considered before. The corresponding values for the shorter T1 peak (T1 ≈ 1.2 ms) are 5 times smaller. T1 is an order of magnitude smaller for the liquid component with FID T2 of the order of 50 µs and would give sheet spacings of a half nanometer or less (that may correspond to intralayer spaces of the gel), but the above use of relaxivity values depends on the assumption that most of the pore fluid is not in layers bound on the surfaces of very small pores or closely spaced sheets. Some exchange has been hypothesized6-9 between two liquid compartments on the basis of 2D T1-T2 and T2-T2 relaxation measurements that show off-diagonal peaks with T2 of the order of 50 µs. Our data suggest exchange between the short-T2 liquid component and one or both of the much larger liquid components with much longer T2. Although our data have been obtained at about 0.5 T, the assignment of the features of the solid distributions can be made by making use of the results obtained by high-resolution MAS analysis (refs 11 and 12) at 12 T on a sample hydrated 3 months. The T1 peak of the solidlike group, after about a day, at about 300 ms in Figure 3b, with a substantially modified Gaussian FID shape with undershoot evident in the lowest curve of Figure 1, and not in exchange with any other component (because no other component has similar T1), can be attributed to 1H of Portlandite and/or possibly crystal water molecules. The distribution observed after a few days in the range 1-10 ms in Figure 3b, with closely Gaussian FID shape, is also clearly solid and can be attributed to 1H of CaOH or SiOH bonds, presumably in the gel structure. In summary, our results show that the sources of 1H signal (excluding the very large pores) can be divided into at least five compartments, which number changes during hydration, although each FID is split into only two groups to produce files for T1 analysis. The liquid T1 distribution shown in Figure 4a,b shows two resolved liquid peaks from 1 to 3 days and shows nearly rectangular distributions for the next several days, suggesting unresolved peaks. Thus, the main liquid signal seems to be from water confined in at least two separate compartments, at least from about a day to about a week. In this picture the two peaks seen in Figure 4a,b, with average T1 a factor about 5 apart at 1 day, correspond to two classes of pores, not in fast exchange, the sizes and relaxation times of which are gradually decreasing with hydration time. Exchange/diffusion has been shown also by self-diffusion measurements,2 and sizes are reported as about 2 and 16 nm in ref 12. The third liquid component, with T2 of the order of 50 µs and T1 a little over 200 µs, discussed earlier, is then ascribable to the component appearing at about 10 h in ref 5 and associated with water in thin C-S-H intralayer spaces, sizes of which were estimated to be less than 0.5 nm. These three liquid components are resolved by T1 at about 1 day (with much of the shortest component masquerading as solidlike at about 0.2 ms in Figure 3b) but form a continuous distribution from about 0.1 ms to about 5 ms after about 2 weeks. The peaks are due to signal from pores whose dimensions are in the range of nanometers, and the tail at very short T1 is very likely to be part of the water in intralayer spaces of the size of a fraction of nanometer, as discussed above. This

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picture fits well with the model presented in ref 21 where the interlayer spacing seems to be somewhat irregular, with a continuous distribution. The solid component with longer T1 can be attributed to 1H of Portlandite and/or possibly crystal water molecules. The remaining solid component can be attributed to 1H of CaOH or SiOH in the gel. The measurements of the two WPC pastes with additives show that the robust T2FID parameter is able to characterize the different kinetics. The absence of an induction period and the strong acceleration observed in the first 5 h in WPC-CaCl2 are consistent with the expected effects of the CaCl2 additive. WPCNaF is less accelerated, and this is consistent with the effect of the CaSO4 additive. The T1 distributions of the liquid signals at 30 days are different, and in particular WPC-NaF shows a longlasting tail, while WPC-CaCl2 shows a structure suggesting two unresolved components. This structure seems to indicate that the setting of this cement is still in progress at 30 days, unlike the other two. The additive that initially accelerates the hydration, now at this stage slows it down. The distributions for the “solid” present the same general characteristics as MTA, but suggest different relative amounts of the two solid components described above. Figure 7 shows that the initial T2FID of the pastes with additives is about double that of MTA. Also, the areas under the distributions in Figure 8a,b for the pastes with additives are much larger than for MTA. All this is presumably because of water in the added phyllosilicates. In conclusion, with time-domain NMR it is possible not only to monitor changes of the nanostructure of the endodontic cement paste and the reaction product formation but also to quantify the kinetics of products and nanostructure formation. The faster evolution of the gel formation in the WPC-CaCl2 paste due to the addition of CaCl2 is well monitored, as are the differences in the final pore space structure of the gels after 30 days of hydration. The determination of these parameters can be used to compare and optimize endodontic cement pastes, in order to improve their therapeutic performances. Acknowledgment. The authors thank R. J. S. Brown for useful discussions and F. Peddis for technical assistance. Supporting Information Available: In order to better distinguish the data at different times in Figure 4, a and c, the same figures are available in color. It can be seen that, at hydration times substantially less than 1 day, the T1 distributions are essentially zero below 2-3 ms and the T2 distributions are essentially zero below 1 ms. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kimmich, R. NMR Tomography, Diffusometry, Relaxometry; Springer-Verlag: Heidelberg, Germany, 1997.

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