AN INELASTIC NEUTRON SCATTERING STUDYOF THE WATER DYNAMICS IN CEMENT PASTE

I. PADUREANU 1, DORINA ARANGHEL1, GH. ROTARESCU1, FELICIA DRAGOLICI1,C. TURCANU1, ZH. A. KOZLOV2, V. A. SEMENOV3

1 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest 077125,Romania

2 Joint Institute of Nuclear Research, 141980, Dubna, Russian Federation3 Neutron Scattering Laboratory for Condensed Matter Study, Institute of Physics and Power

Engineering 249020, Obninsk, Russia

Received November 27, 2004

Inelastic neutron scattering (INS) was used to investigate the dynamics ofwater in a long aging cement matrix. The data were analyzed in terms of the dynamicscattering function S(Q, ε) and generalized vibration density of states G(ε). INS datawere collected across a wide range of wave-vector (Q) and energy transfers ε = ω , sothat both the translation and rotation motions of the water molecules were revealed byS(Q, ε) and G(ε). A representation of S(Q, ε) on a wave vector Q constant scale as afunction of energy transfer showed a non-Lorentzian behavior of the quasi-elastic line(QE), whereas the QE line shape in bulk water at room temperature was known to beLorentzian. It appeared from S(Q, ε) at constant ε that a nanometric structure was present.

1. INTRODUCTION

We previously investigated the inelastic neutron scattering spectra measuredon a hydrated cement paste in the presence of fresh precipitate of ferric hydroxideFe(OH)3, phosphate Fe2(PO)4, and NaCl [1]. Cementation is known as an attractiveoption, as far as processing is concerned, for the conditioning of radioactive waste.The Portland cement paste remains fluid long enough to allow safe processing. Itis a low temperature operation tolerant to water, and the set cement has adjustableproperties. The reaction between tricalcium silicate (C3S) and water is theprincipal factor in the setting and hardening of Portland cement. The chemicalreaction that takes place is a stepwise process, schematically rendered as [2]:

3 5 2 2 2 2Ca SiO (3 )H O (CaO) (SiO )(H O) (3 )Ca(OH)x yy x x+ + − → + −

In cement notation, the above equation reads:

3C S (3 )H C SH (3 )CHx yy x x+ + − → + −

with the cement-chemistry notation: C = CaO, S = SiO2, H = H2O.

Rom. Journ. Phys., Vol. 50, Nos. 5–6 , P. 561–574, Bucharest, 2005

562 I. Padureanu et al. 2

The variables x and y change during the reaction, especially at a very earlystage, and vary according to position on a nanometer scale [3]. Chemically,cement produces a reacting matrix with a porous microstructure. Knowing howthe microstructure develops is therefore desirable in order to assess thecompatibility of radioactive streams with cement and predict waste formperformance during storage and disposal. To improve the safety of disposal, itwould be necessary to immobilize these wastes into a long-term stable solidwaste form. Little is known so far on the chemical reactions taking place orproducts that are formed as cement mixes with solid or liquid waste and water.The precipitation products and their behavior during cementation are extremelyhard to study because of the system complexity (phase composition and structure)and the lack of nondestructive analytical methods. 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 techniques formonitoring the hydration of cementation materials [4]. Using QENS, it wasfound [5] that the translation dynamics of a water molecule’s center of masscould be described through the relaxing cage model [6] originally developed forsupercooled water. While the quasi-elastic method provides information onhydration reaction dynamics, a complementary method, known as small angleneutron scattering (SANS), informs us on the spatial evolution of the reactionproducts [7]. In a SANS experiment, the measured spectra contain informationabout the fractal behavior of the interfaces and the size distribution of thescattering particles [8]. An important feature of the SANS scattering function isthe power law behavior S(Q) ∼ Q–α which may point at fractal-like structures inregions of the dimension l ~ 1/Q [9, 10]. Using SANS, one can study structuresin the range of about 1 to 100 nm. Yet, the real stoichiometry is still unclear inthe calcium hydrosilicate gel (C-S-H), the amorphous nature of which makes itvery difficult to obtain information about its nanometric structure. The presenceof the gel is the principal factor in the setting and hardening of the cement paste.However, electron diffraction and electron microscopy experiments [11] haveshown the mesostructure of the cement paste to consist of nanocrystallineregions of the scale of ~ 50 Å or less. The importance of SANS for studying thestructure of fractals was emphasized in the paper [12].

X-ray diffraction, differential scanning calorimetry [13], and more recentlyQENS have found that the hydrated cement paste contains C-S-H in a gel formand C-H in the form of colloidal particles imbedded in the C-S-H matrix. Thewater molecules incorporated in the colloidal particles appear immobile, whilethe water molecules dispersed in the C-S-H gel matrix behave as interfacialwater showing a slow dynamics different from that of bulk water. Over time, theinterfacial water in the C-S-H gel penetrates into the colloidal particles. This is acontinuous process increasing the immobile fraction of water [5, 14]. In this

3 Water dynamics in cement paste 563

case, the intermediate scattering function Fs(Q, t) is composed of an elasticcomponent, which is due to the immobile water inside the colloidal particle(a constant part), and a relaxing function resulting from the structural relaxationof the interfacial water [15].

In this paper we reported a new analysis of the inelastic neutron scatteringspectra in terms of the incoherent scattering function S(Q, ε) and generalizedvibration density of states across a wide range of wave vectors Q and energytransfers. In this way, both the translation and rotation of the water moleculewithin the cement matrix are revealed by S(Q, ε) and G(ε). The behavior ofS(Q, ε) at constant ε shows that a nanometric strucure is present.

2. THEORETICAL BACKGROUND

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

22

0

d ( , )d d

kb S Qk

σ = εΩ ε

Here b is the bound nuclear scattering amplitude; k, k0 are the absolute values ofthe wave vectors of the scattered and incident neutrons, respectively; ε is theenergy transfer in the scattering process; Q = (k0 – k) is the magnitude of themomentum transfer; and S(Q, ε) the dynamic structure factor. A symmetric form

( , )S Q ε is sometimes used, and the relation between S(Q, ε) and ( , )S Q ε is:

( , ) exp ( , )2 B

S Q S QK Tεε = − ε

Here KB is the Boltzman constant, and T is the absolute temperature of theinvestigated sample. Van Hove [16] showed that S(Q, ε) was related to the self-correlation function Gs(r, t) and pair time correlation function Gd(r, t) for atomicmotions, and since the sum G(r, t) = Gs(r, t) + Gd(r, t), we have:

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

S Q G r t i Qr t r tε = − επ ∫∫

Here G(r, t) consists of a self and interference term arising from Gs(r, t)and Gd(r, t), respectively. The latter functions are related to the self-dynamicstructure factor Ss(Q, ε) and the dynamic structure factor Sd(Q, ε), respectively.In the case of incoherent scattering, the cross section d2σ/dΩdε is determined bySs(Q, ε), and we can only get information on the self motion of the atoms.Coherent scattering provides information about the interference phenomena that

564 I. Padureanu et al. 4

are due to the collective motions of the atoms or molecules. As a rule, mostelements are both mixed coherent and incoherent scatterers. For this case, a totaldynamic structure factor is defined as given by the relation:

2 2 2( , ) ( , ) ( , )total total inc s coh cohb S Q b S Q b S Qε = ε + ε

The coherent scattering consists of a self and interference term, and wehave the relation

( ) ( ) ( ), , ,coh s dS Q S Q S Qε = ε + ε

These functions have the property that the ε integrals from –∞to +∞are:

( ), d 1sS Q+∞

−∞

ε ε =∫

( ) ( ) ( ), d 1cohS Q f Q S Q+∞

−∞

ε ε = + =∫

Here S(Q) is called the static structure factor. In many cases theexperimental data are analyzed in terms of the generalized density of states(GVDS), G(ε). From an incoherent scatterer G(ε) can be obtained in theharmonic one-phonon approximation (OPA).

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

2B

inc sF k T

S Q S Q Q G WM

⎛ ⎞εε = ε = ε −⎜ ⎟ε⎝ ⎠

Here, F(x) is the thermal population factor given by 1( ) (e 1)xF x −= − +1 (1 1);2

+ ± 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 be derivedby assuming the average of the coherent effective cross section due to thevariations of the final wave-vectors orientation:

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

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 ≅ε Ω ε ε ε −∫

with bcoh the coherent scattering length, and Q1 and Q2 the minimum andmaximum values of the wave vector transfer Q of neutrons scattered betweenangles θ1 and θ2. In the present experiment, the observed scattering spectraobtained from the neutron scattering process are dominated by the individualincoherent neutron cross section of the individual hydrogen atom. As is knownfrom the literature, the water molecule consists of two light hydrogen atoms and

5 Water dynamics in cement paste 565

a heavier oxygen atom with its center of mass very near to the position of theoxygen atoms. The scattering spectrum obtained from pure water according tothe OPA approach has to reflect the motions of the hydrogen atom, namely: thevibration of the H – atom around its equilibrium position, rotation around thecenter of mass, and the translation motion of the center of mass. A comparativestudy of the frequency spectra in pure water and the confined water or interfacialwater in the lattice of the cement is a challenging question able to explain therole of water on the microscopic and macroscopic properties of cement.

3. EXPERIMENTAL PROCEDURE

The samples were prepared of a well-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, using a DIN-2PI high-intensity time offlight spectrometer at the fast pulsed reactor IBR 2. The samples were enclosedin a rectangular aluminium cell in such a way as to avoid the loss of water or thecontamination of the paste because of the environment. Two incident neutronenergies were chosen at 4.439 meV and 10.476 meV that allowed obtaining aresolution in the range of 0.28÷0.5 meV (full width at half the maximum ofthe elastic line scattered from vanadium). The resulting Q range as it resultsfrom the cinematic space (energy and wave-vector (ε, Q) transfer), coveredexperiments for the two incident neutron energies 0.15 Å–1 < Q < 2.7 Å–1 and0.23 Å–1 < Q < 4.1 Å–1, respectively.

4. DATA ANALYSIS, RESULTS AND DISCUSSION

4.1. TOF SPECTRA

The INS TOF measurements were made over a kinematic space (Fig. 1)that was determined by the wave vector and energy (Q, ε) transfer. The resultingQ range covered in our experiment was from 0.26 Å–1 to 4.10 Å–1. The transferenergy was measured by time of flight over 6.99 m of flight path of the scatteredneutrons between the sample and He3 detectors.

The time-of-flight spectra measured over the dynamic variables shown inFig. 1 were scaled by their monitor counts, corrected for the experimentalbackground, and standardized by normalization to the scattering intensity fromthe vanadium sample.

Fig. 2 shows the TOF spectra from C + H2O at ambient temperature fordifferent scattering angles between 6° and 134°. Parameters N = 1024,

566 I. Padureanu et al. 6

Fig. 1

t0 = 706.33 µs/m, E0 = 10.476 meV, τ = 8 µs, L = 6.99 m. The TOF spectra werealso corrected for the effects resulting from the geometry and nuclear propertiesof the sample.

In an incoherent inelastic neutron scattering experiment where the sampleis dominated by the scattering contribution of the H – atoms, the doubledifferential scattering cross section is given by:

( )2

0

d ,d d 4

Hs

kN S Qk

σσ = εΩ ε π

Here N/2 means the quantity of water molecules in the scattering volume,and σH the total scattering cross section of the H atoms. The measured spectralintensity normalized to unity is fitted by the following equation:

( , ) ( , ) ( )I Q S Q Rε = ε ⊗ ε

where ( )R ε represents the normalized vanadium spectral intensity. Though thescattering intensity from our sample is dominated by the incoherent scattering, acontribution from other atoms is also present.

In a classical way, we assume the decoupling between vibration, rotations,and diffusion motions. Such approximation is justified at low temperatures.Within approximation the intensity ( , )I Q ε is [17]:

568 I. Padureanu et al. 8

( ) ( ) ( ) ( )2 2, exp / 3 , ,T RI Q Q u I Q I Qε = − ε ⊗ ε

where the first term is the Debye–Waller factor, ( ),RI Q ε accounts for the

hindered rotations and ( ),TI Q ε for the translation motions. The sign ⊗ denotes

the ε convolution, and 2u is the mean square amplitude of the vibrations.

( )( )22

( )1,( )

TQ

I QQ

Γε =π ⎡ ⎤ε + Γ⎣ ⎦

( ) ( ) ( ) ( ) ( ) 22 2

1

1, 2 1 1 / 1R i r ri

I Q i J Q a i i D i i D∞

=

ε = + ⋅ + ε + +⎡ ⎤⎣ ⎦π ∑2

20

( )1

DQQ

DQΓ =

+ τ

( ) 16l rD −τ =

06l D= τ

Here ( )QΓ is the width of the translational line, D is the self-diffusion, τ0 is

the residence time, τl is the hindered rotations characteristic time, a the oxygen-hydrogen intramolecular distance, and l is the mean square jump lengthaccording to the jump diffusion model [18].

Let us proceed further to the analysis of the dynamic structural factor( ),S Q ε as a function of the variables measured in the experiment and defined in

Fig. 1. To this end, we plotted ( ),S Q ε on a Q constant scale as a function of

,ε = ω and on a ε constant scale as a function of Q.

4.2. ( , )Q constS Q =ε

Fig. 3 shows the ( ),S Q ε behavior at various Q values within the range

0.4 Å–1 = Q = 4 Å–1. As can be seen, ( ),S Q ε reveals two distinct parts, namely:one part which is related to the QENS scattering describing the translationalmotions and another which is responsible for the rotational motions. In the rangeQ < 1 Å, ( ),S Q ε essentially depicts the translational part. Therefore, in order todetect the translational parameters, one has to analyze the data at small Q range.The rotational motions begin to play an important role for the range Q > 1 Å–1,and the rotational relaxation dynamics parameters are determined.

9 Water dynamics in cement paste 569

Let us denote with ( ),TS Q ε the structure factor accounting for the

translational part and with ( ),RS Q ε the one for the rotational part. It becomesclear that the decoupling approximation holds good at smaller Q, while for aQENS data analysis a reasonable level of accuracy is acceptable. In the case ofbulk water, the single particle dynamics, ( ), ,TS Q ε can usually be calculated by

a jump diffusion model, just as the rotational dynamics ( ),RS Q ε is calculatedfrom rotational diffusion models [18]. In our case, the experimental data shownin Fig. 3 as a function of energy transfer, ε, one has to emphasize that the QENScovers an energy range from 0 to about 2 meV while INS covers energies higherthan 0. However, as shown in [19], the two simple models quoted above are poorapproximations for low temperature water. These models involve four parameters

2 ,u D, τ0, and DR that can be derived from fitting the normalized experimentaldata [18, 20, 21].

Several authors found these models were not valid for supercooled water[22, 23]. The translational contribution to the QENS line shape of usual water atroom temperature is typically lorentzian, known in the literature as “free water”.An analysis of the data shown in Fig. 3 for Q < 1 Å–1, led to the conclusion thatlorentzian is a bad approximation. In addition, the width of the translational lineis about constant against the wave vector Q. This conclusion agrees with theresults reported in [17], where the width weakly depends on Q2 in thesupercooled water region. It therefore becomes reasonable to accept that thewater molecules in a cement paste can be divided into two parts: immobile, orbound, water and mobile but glassy water. As cement ages, the glassy waterdecreases, and the immobile function increases.

The decoupling between rotation and translation modes, as shown by( ),S Q ε in Fig. 1 for Q > 1 Å–1, is yet another argument for the existence of

supercooled water confined in the hydrated cement paste. From a classical pointof view, it has been known for some time that in liquid water, the decoupling isnot correct at room or higher temperatures when rotational and diffusion motionsare coupled. This approximation is only justified at low temperatures.

The main conclusions derived from the ε dependence on ( ),S Q ε atvarious Q values can be summarized as follows:

– A very good decoupling of the translational and rotational motions shown by( ),S Q ε for Q > 1 Å–1. This approximation is only valid for low-temperature

water.– A constant Q dependence on the ε width of the translational part of ( ),S Q ε is

in agreement with the supercooled water dynamics earlier observed at lowtemperatures such as T = –20°C.

570 I. Padureanu et al. 10

– As for water dynamics in the porous cement structure, from the non-Qdependence of ε for ( ), ,TS Q ε we reach the conclusion that, in the presentcase of long-age cement, what we are dealing with is only immobile, orbound, water.

4.3. ( , ) constS Q ε=ε

In the case of age-dependent water dynamics in hydrated cement pastes, aparticularly interesting topic refers to the existence of nanometric structures. Ithas been proven that C-S-H, the principal factor in the setting and hardening ofcement pastes, appears as a semicrystalline amorphous material in X-raydiffraction [24]. Other experiments based on small angle neutron scattering SANS[25] have shown the presence of a bimodal distribution of the colloidal particleswith a main component about 50 Å in diameter and a second component 100 Åin diameter. Transmission electron microscopy [26] has confirmed that these dimen-sions do not change during the hardening process, and each nanocrystalline regionhas a locally homogeneous structure with short-range ordered regions on a scaleof about 10 Å. We here present new experimental data to be compared to theearlier findings. The inelastic structure factor ( , )S Q ε at constant ε, as obtainedfrom our INS measurements, is shown In Fig. 4. At very small ε values such asε < 0.6 meV, the static structure and its relaxation after very long times can bedescribed by an average structure factor calculated from a hard-core sphere rigidpotential. The diameter of the spheres can be chosen within the range 7.4÷8.4 Åto get good fitting of the experimental results, as shown in Fig. 4. For shorterrelaxation times, the first peak located in the above-indicated range does notchange its position. It remains centered at a Q value corresponding to a nano-crystalline cluster of about 7.5 Å in average diameter. Another conclusion derivedfrom the data presented in Fig. 4 concerns the dimension of the short-rangeordered regions, which is about 25 Å for all relaxation times investigated in theexperiment. Our data support the idea of a local structure, extending to 25 Å andcomposed of crystallites with an average typical diameter of 7.5 Å÷8.4 Å.The main conclusion of this section could be summarized like this:

– The INS experiments on long-age cement pastes show the existence of a localstructure on a range of about 25 Å with nanocrystralites the diameter of whichis around 8 Å. This local order can be described by a hard sphere rigid pairinteraction potential.

4.4. PHONON DENSITY OF STATES (DOS), ( )G ε

Finally, the data are analyzed in terms of the generalized frequencydistribution G(ε). The shape line of this spectrum clearly shows that it is dominated

572 I. Padureanu et al. 12

by the water dynamics inside the cement matrix. From previous papers [27], itwas concluded, based on the spectra near the melting point, that the vibratingmotions in water closely resembled the motions found in ice. Thus the frequencyspectra derived from neutron spectra observed in H2O at +2°C and ice at –3°Cshowed an exact coincidence. Empirically, it is found that in the temperaturerange (0–100)°C the product 3/ 2

max .E T const⋅ = , where Emax is the energy ofthe peak in eV and T is the temperature in °K. As the temperature is raised, thepeak of the high-energy vibratory mode hindered motions is shifted towardslower energies. The frequency spectrum consists of two distinct parts: a low-lying part of the spectrum in the energy range ε < 50 meV and another one atε > 50 meV. For low temperatures close to the ice state, the hindered rotationspeak at about 80 meV. This spectral part derived from the neutron spectrameasured on C + H2O is very similar to earlier results obtained on ice.A calculation of the dispersion relations in ice [27], using the elastic constants ofice, led to the conclusion that acoustic vibrations were concentrated in an energyrange around 7 meV, and optical vibrations around 20–25 meV. Compared withthe observed spectrum for ice, the position of the peak in the case of C + H2O isabout the same at 80 meV, but is more smeared out. In the case of water and ice,the low-lying part of the spectrum (ε < 50 meV) is smeared when thetemperature rises and the peak of hindered rotations at ~ 80 meV is shiftedtowards lower energies. Thus for T = 365 K, the position of this peak is at about50 meV. From these observations on water, we can conclude on the existence inthe case of cement of two types of water, namely:

Fig. 5

13 Water dynamics in cement paste 573

– The hydration water, a “glassy water” similar to the supercooled bulk water,as indicated by the existence of the peak at about 80 meV.

– A bound water associated with the peak at about 40–50 meV similar to theshifting in bulk water of the hindered rotation peak from 80 meV to within40–50 meV, as the temperature increases.

– In the low-lying energy range ε < 50 meV the spectral peculiarities forsupercooled water in the cement matrix are similar to those for normal water.

– The existence of a shoulder in C + H2O at about 126.28 meV shows that waterdynamics in this case is characteristic for lower temperatures than shown inthe results of [27].

5. CONCLUSIONS

The quasielastic line is clearly non-Lorentzian in contradiction to theobservations for bulk water at room temperature. The non-experimental behaviorled to the conclusion that the relaxation dynamics of the water molecules at roomtemperature in the cement paste is similar to the situation found in supercooledbulk water [28]. The hydration water in cement was therefore interpreted as“glassy water,” which shows an age dependence. An elastic component developsover time showing that a fraction of the glassy water is converted to bound water.

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Fig. 2