STRUCTURE AND DYNAMICS OF CONFINED H2O AND D2OIN CEMENT PASTE MATRIX STUDIED BY QUASIELASTIC

AND INELASTIC NEUTRON SCATTERING

I. PADUREANU 1), D. ARANGHEL1), GH. ROTARESCU1), F. DRAGOLICI1), C. TURCANU1)

R. BRZOZOWSKI2), M. STEPINSKI2), P. J. SZALANSKI2), ZH. A. KOZLOV3),V. A. SEMENOV4)

1) IFIN-HH, P.O. Box MG-6, Bucharest-Mãgurele, RO2) University of Lodz, 90-236 Lodz, PL

3) Frank Laboratory of Neutron Physics, JINR, 141980, Dubna, RU4) Neutron Scattering Laboratory, IPPE, 249020 Obninsk, RU

padu@ifin.nipne.ro

Received December 3, 2004

Understanding the state of hydration water in cements, the dynamics of waterconfined in nanopore structures, and the two-step dynamic process similar to the onein glasses and known as β- and α-relaxation is a topic of high fundamental interest incondensed matter physics. Aside from being theoretically challenging, it also has abroad range of applications. The results of a scientific research conducted in theframe of an international cooperation at the European Union Center of Excellence(CEX-IDRANAP) of IFIN-HH are given in this paper. Quasi-elastic neutronscattering (QENS) and inelastic neutron scattering (INS) are very powerful tools forstudying the dynamics and structure of condensed matter from simple liquids to thevery exciting phenomena related to the supercooled state, nanostructure and fractalnucleation. QENS and INS experiments on hydrated cement pastes after a long agingtime were performed using the TOF spectrometer DIN 2PI at IBR–2 reactor, JINRDubna. Our experimental results confirmed the conclusions of the recent theoreticaland MD simulation papers on the existence of supercooled water confined in thematrix structure of cement. A wave vector transfer Q dependence of the dynamicstructure factor S(Q, ε) at constant energy transfers ε = ω revealed a nanometric

structure where the water molecules were trapped in the nanoporous matrix. Thewater dynamics resembled the relaxing cage model. In the short term, the orientationof the water molecule considered was fixed by H-bonds (H–B) to its neighbors andthe molecule performed harmonic oscillation around H–B. In the longer term, thebonds broke, the trap began to relax, and the molecule was able to reorient losingmemory of its initial orientation. The relaxation dynamics suggested the existence ofa fractal process.

INTRODUCTION

We previously investigated the inelastic neutron scattering spectra measuredon hydrated cement paste in the presence of fresh precipitate of ferric hydroxide

Rom. Journ. Phys., Vol. 50, Nos. 5–6 , P. 551–559, Bucharest, 2005

552 I. Padureanu et al. 2

Fe(OH)3, phosphate Fe2(PO)4, and NaCl [1]. As is already known, cementationis an attractive option from a processing point of view for radioactive wasteconditioning. The Portland cement paste remains fluid for a sufficiently longtime to allow safe processing. The operation takes place at low temperature andis tolerant to water; in addition, the set cement has adjustable properties. Thereaction between tricalcium silicate (C3S) and water is the principal factor in thesetting and hardening of the Portland cement. Chemically, the cement produces areacting matrix with a porous microstructure. Over the last decade, severalexperimental methods based on neutron scattering have emerged as newtechniques and powerful tools for characterizing complex microstructures.Quasi-elastic neutron scattering (QENS) is a new such technique for monitoringthe hydration of cementation materials [2]. Using QENS it was shown [3] thatthe translation dynamics of the center of mass of a water molecule could bedescribed by the relaxing cage model [4] developed for supercooled water. TheQENS technique has shown that the hydrated cement paste contains C-S-H in agel form and C-H in the form of colloidal particles imbedded in the C-S-Hmatrix. The water molecules incorporated in the colloidal particles appearimmobile while the water molecules dispersed in the C-S-H gel matrix behave asinterfacial water showing a slow dynamics, quite different from that of bulkwater. Over time, the interfacial water in C-S-H gel penetrates into the colloidalparticles. This is a continuous process increasing the immobile fraction of water[3, 5]. In this case, the intermediate scattering function (ISF), Fs(Q, t) derived fromthe incoherent dynamic structure factor Ss(Q, ε) is composed of an elasticcomponent due to the immobile water inside the colloidal particle (a constantpart) and a relaxing function deriving from the structural relaxation of theinterfacial water [6].

New experimental data obtained by INS on hydrated and deuteratedlong-aging cement pastes are presented in this paper. The INS spectra wereanalyzed in terms of the incoherent dynamic structure factor Ss(Q, ε) and ISF forthe hydrated and, respectively, dynamic structure factors Sd(Q, ε) and Fd(Q, t)for deuterated samples across a wide range of wave vectors Q and energytransfers. The generalized vibration density of states G(ε), ISF and S(Q, ε)revealed new features of the translational and rotational motions of H2O andD2O water molecules in the cement matrix. The behavior of S(Q, ε) at constant

ω showed that a nanometric structure was present.

THEORETICAL BACKGROUND

The basic formalism connects the correlation functions of atomic motionswith the double differential neutron scattering cross section d2σ/dΩdε by:

3 Structure and dynamics of confined H2O and D2O in cement 553

22

0

d ( , )d d

kb S Qk

σ = εΩ ε

Here b is the bound nuclear scattering amplitude; k, k0, E, E0 are theabsolute values of the wave vectors and the energies of the scattered and incidentneutrons; ε = ω = E – E0 is the energy transfer in the scattering process; Q == (k0 – k) is the magnitude of the wave-vector transfer and S(Q, ε) the dynamicstructure factor. It was shown by van Hove [7] that S(Q, ω) is related to theself-correlation function Gs(r, t) and the pair time-correlation function Gd(r, t)for atomic motions, or to the sum G(r, t) = Gs(r, t) + Gd(r, t).

1( , ) ( , )exp ( )d d2

S Q G r t i Qr t r tω = − ωπ ∫∫

Here G(r, t) consists of a self and an interference term arising from Gs(r, t)and respectively Gd(r, t). The latter functions are related to the incoherentdynamic structure factor, Ss(Q, ω) and Fs(Q, t), and the dynamic structure factorSd(Q, ω) and Fd(Q, t), respectively.

( ) ( ) [ ]1, , exp d2

S Q F Q t i t t+∞

−∞

ω = ωπ ∫

From an incoherent scatterer, the density of states G(ε) can be obtained inthe harmonic one-phonon approximation (OPA).

2( / )( , ) ( , ) ( )exp( 2 )

2B

inc sF k T

S Q S Q Q G WM

⎛ ⎞ωω = ω = ε −⎜ ⎟ω⎝ ⎠

Here, F(x) is the thermal population factor given by ( )F x =1 1(e 1) (1 1),

2x −= − + ± exp( 2 )W− is the Debye-Waller factor, and M is the mass

of the scattering unit. On the other hand, for a coherent scatterer, G(ε) can bederived from a method based on the averaging of the coherent effectivecross-section due to the orientation variations of the final wave vectors:

( ) ( ) ( ) ( )( )( )

2

1 21

4 422 2 12, 0

exp 2d dsin dd d d 8 exp 1

coh

B

Q Qb W Gk M Q K T

θ

θ θθ

−− εσ σ= θ θ ≅ω Ω ω ε ω −∫

where bcoh is the coherent scattering length, and Q1 and Q2 are the minimum andmaximum values of the wave vector transfer Q of neutrons scattered betweenangles θ1 and θ2.

554 I. Padureanu et al. 4

EXPERIMENTAL PROCEDURE

The samples were prepared from a known quantity of dry C3S powdermixed with distilled water to produce a paste with 0.60 water/C3S weight ratio.The inelastic neutron scattering experiment was carried out at the Frank NeutronPhysics Laboratory (FLNP) in Dubna, by using a DIN-2PI high-intensity time-of-flight spectrometer at the fast pulsed reactor IBR 2. The samples were closedinto rectangular aluminum cells to avoid loss of water and paste contaminationunder influence of the environment. Two incident neutron energies, 4.439 meVand 10.476 meV were chosen leading to a resolution in the range of 0.28÷0.5 meV(full width at half maximum of the elastic line scattered from vanadium). TheQ ranges covered in the experiment for the two incident neutron energies were0.15 Å–1 < Q < 2.7 Å–1 and 0.23 Å–1 < Q < 4.1 Å–1, respectively.

DATA ANALYSIS, RESULTS, AND DISCUSSION

The experimental data were analysed in the (Q, ω) space in terms of( , )Q constS Q =ε and ( , ) .constS Q ω=ε Fig. 1 and Fig. 2 show the inelastic dynamic

Fig. 1. – C+H2O-Dynamicstructure factor at constant ε.

structure factor ( , )sS Q ε and ( , )dS Q ε at constant ε obtained from INSmeasurements on hydrated and deuterated cement pastes, respectively. At verysmall ε values such as ε < 0.6 meV, the static structure and its relaxation aftervery long times can be described by an average structure factor calculated from ahard-core sphere rigid potential. The diameter of the spheres can be chosen in therange 7.4÷8.4 Å to get a good fitting of the experimental results. After shorterrelaxation times, the first peak located in the above indicated range did not change

5 Structure and dynamics of confined H2O and D2O in cement 555

Fig. 2. – C+H2O-Dynamicstructure factor at constant ε.

its position, but remained centered at a Q value corresponding to a nanocrystallinecluster with an average diameter of about 7.5 Å. The dimension of the rangeordered regions was about 25 Å for all relaxation times investigated in theexperiment. Our data indicate the existence of a local structure extended to 25 Åand composed of crystallites with an average typical diameter of 7.5 Å÷8.4 Å.

From the Q dependence of ( ),S Q ε at constant ε, we concluded that theextended order to 25 Å could not be described in terms of a hard sphere clusterhaving dimension integers. This could suggest that, during the relaxationprocess, a model based on fractals is more consistent with what is currentlyknown of the hydrated cement structure. The origin of the fractal structure ofC-S-H/D gels can be seen as a process of aggregation of individual colloidalparticles into an extended cluster structure. This process known as diffusion-limited aggregation was investigated in [16]. The size of the cluster, as indicatedby our estimations from Figs. 1 and 2, is 7.5–8.4 Å (s ~ RD). Taking into accountthe density-weighted mean radius, we obtain a D value 2 < D < 3. This isinterpreted as a fractal volume applied to porous materials over a certainlength scale.

The dynamic structure factors are the time Fourier transforms of thecorresponding ISF. The ISFs for hydrated (C + H2O) and deuterated (C + D2O)cement pastes at Q = 1 Å–1 and T = 293 K are shown in Figs. 3 and 4 as afunction of time in logarithmic scale. The spatial Fourier transform of the VanHove correlation function is written as

( ) ( ) ( )2 2 / 3, e , ,Q uF Q t R Q t T Q t−=

where the first term is assumed to be the Debye-Waller factor due to the vibrationsof H/D atoms around its equilibrium position; R(Q, t) represents the ISF of therotational motion of H/D atoms with respect to the center of mass (CM) of thewater molecule; and T(Q, t) the ISF of the translational motion of cement.

556 I. Padureanu et al. 6

Fig. 3. – C+H2O-Intermediatescattering function.

Fig. 4. – C+D2O-Intermediatescattering function.

Extensive calculations of these functions by means of MD on supercooledwater were presented in [9]. The experimental results from fragile glass-formingliquids showed that, on supercooling, each molecule or atom experienced ahigher degree of confinement in a potential well, called a cage, due to neighboringatoms. Within the cage, the confinement showed a behavior as a plateau of thedynamic structure in the intermediate time range. The considered moleculeremained trapped in the cage for long times as the sample approached atemperature Tc called the temperature of structural arrest in the mode-couplingtheory (MCT) [10]. The investigation which tested MCT using moleculardynamics (MD) found that MCT prediction were satisfied by supercooled singlepoint charge (SPC / E) water [11, 12]. At ambient pressure, the bulk water can besupercooled only down to about 235 K. Our experimental results (Figs. 3 and 4)

7 Structure and dynamics of confined H2O and D2O in cement 557

showed the ISF for both hydrated and deuterated samples in (Q, t) space to decayfrom a single exponential, which is typical of a liquid behavior, to a two-stepprocess typical of a glass-like behavior. Around Tc interpreted as the temperatureof the structural arrest, ISF decayed rapidly to a plateau region called β relaxationregime, and then decayed slowly to zero, called α relaxation regime. Thisdynamic picture is fully supported by our data. The H/D dynamics in H2O andD2O confined in the cement matrix upon supercooling for t < 0.2 ps is similar tothe dynamics in the ordered solids. From Figs. 3 and 4 we also can see that thedynamics of hydrated and deuterated samples were very similar. The H/Drelaxation function shows a small first bump centered around 0.1 ps associatedwith a significant harmonicity in the dynamics at short times [13] and discussedin [14]. A second bump is observed at t ~ 1 ps in agreement with the MD studyof supercooled water [9]. According to the latter paper, this bump reflects thestrength of the translational-rotational coupling.

Finally, we present an analysis of the data in terms of the generalizedfrequency distribution ( )G ε shown in Figs. 5 and 6. The shape lines of these

Fig. 5. – C+H2O-Densityof states.

spectra clearly show that they are dominated by the H2O and D2O dynamicsinside the cement matrix. Earlier papers [15] concluded that near the meltingpoint the vibrating motions in water closely resembled the motions in ice. Thus,the frequency spectra derived from neutron spectra observed in H2O at +2°C andice at –3°C showed an exact coincidence. Empirically, it was found that in thetemperature range (0–100)°C the product 3/ 2

max .E T const⋅ = , where maxE is theenergy of the peak in eV and T is the temperature in K. As the temperature israised, the peak of the high-energy vibratory modes hindered motions shifts

558 I. Padureanu et al. 8

Fig. 6. – C+D2O-Densityof states.

towards lower energies. The frequency spectrum consists of two distinct parts,the low-lying part of the spectrum in the energy range ε < 50 meV and anotherfor ε > 50 meV. For low temperatures close to ice state, the hindered rotationspeak is located at about 80 meV. This spectral part derived from the neutronspectra measured on C + H2O is very similar to the earlier results obtained forice. A calculation of the dispersion relations in ice [15], using the elasticconstants of ice, allowed to conclude that the concentration of acousticvibrations is in an energy range around 7 meV and of the optical vibrationsaround 20–25 meV. Unlike the observed spectrum for ice, in the case ofC + H2O, the position of the peak is about the same at 80 meV, but appearssmeared out. In the case of water and ice, the low-lying part of the spectrum,ε < 50 meV is smeared when the temperature rises and the peak of hinderedrotations at ~ 80 meV is shifted towards lower energies. Thus for T = 365 K theposition of this peak is about 50 meV. From these observations on water, weconcluded on the existence in the case of cement of two types of water, namely:– The hydration water in cement – a “glassy water” similar to the situation in

supercooled bulk water reflected by the existence of the peak at about81.4 meV; and

– A bound water associated to the peak at about 40–50 meV similar to the effectof shifting of the hindered rotation peak from 80 meV to the peak range within40–50 meV in the bulk water, as the temperature is increased.

– The existence of a shoulder at about 126.28 meV in C + H2O shows the waterdynamics in this case corresponds to a lower temperature than that presentedin [15].

– In the case of C + D2O the hindered rotations peak is located at 84 meV and ashoulder at 142 meV is also observed. This could be an indication that D2O ismuch more supercooled in the cement matrix than H2O.

9 Structure and dynamics of confined H2O and D2O in cement 559

CONCLUSIONS

– The dynamic structure factor S(Q, ε) at constant energy transfer reveals ananometric structure of the hydrated and deuterated cement matrix.

– An extended structure order up to 25 Å consisting of clusters with an averagesize 7.5–8.4 Å suggests the idea of a process based on fractal approach.

– The time dependence of the dynamic function F(Q, t) is in agreement withMCT theory and the MD study of the supercooled water.

– The ISF for H2O and D2O confined in the cement matrix reveals a two-stepprocess interpreted as β relaxation regime and α relaxation at longer times.These observations are in satisfactory agreement to the MCT theory and MDsimulation for supercooled bulk water.

– The density of state G(ε) suggests that the degree of confinement is higher forD2O than for H2O.

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