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JOURNAL OF DIFFERENTIAL EQUATIONS 27, 320-358 (1978) A Spectral Theory for Linear Differential Systems* K~HEKT J. SACKER Depautmmt of Matfmnatics, University of Soutlrern California, Los .&g&s, California 90007 AND GEORGE R. SELL School of Mathematics, University of .VIimesota, Minneupolis, Minnesota 55455 Received October 15, 1976; revised May 23, 1977 This paper is concerned with continuous and discrete linear skew-product dynamical systems including those generated by linear time-varying ordinary differential equations. The concept of spectrum is introduced for a linear skew-product dynamical system. In the case of a system of ordinary differential equations with constant coefficients the spectrum reduces to the real parts of the eigenvalues. In the general case continuous spectrum can occur and under certain conditions it consists of finitely many compact intervals of the real line, their number not exceeding the dimension of the system. A spectral decomposi- tion theorem is proved which says that a certain naturally defined vector bundle is the sum of invariant subbundles, each one associated with a spectral sub- interval. This partially generalizes the Jordan decomposition in the case of constant coefficients. .4 perturbation theorem is proved which says that nearby systems have spectra which are close. Almost periodic systems are given special attention. I. INTRODUCTION Our primary objective in this paper is to study the dynamical behavior of solutions of linear differential systems. We wish to include in our theory, not only linear differential equations with constant coefficients, but also periodic and almost periodic equations as well as more general systems. The proper object of study, for this purpose, is a linear skew-product flow, which is a fiber- preserving flow on a vector bundle that is linear in each fiber. More concretely, consider a flow r on a product space W -7 X x 1, where 1’ is a Hausdorff space and X is a finite-dimensional linear space, i.e., X = R”l * This research was supported in part bye U.S. Army Grant DA-ARO-D-3 I -I 24-7 I - G176 (RJS) and NSF Grants GP-38955 and MCS 76-06003 (GRS). 320 0022-0396/78/0273-032OSO2.00/0 Copyright 0 1978 by :\cademrc Preys. Inc. All rights of reproduction ,n any form rcservrd.

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Page 1: Practicable activated aluminosilicates mortar

CERAMICSINTERNATIONAL

Available online at www.sciencedirect.com

http://dx.doi.org/0272-8842/& 20

nCorrespondinE-mail addre

(2014) 15027–15032

Ceramics International 40 www.elsevier.com/locate/ceramint

Practicable activated aluminosilicates mortar

Saad B.H. Faridn

University of Technology, Department of Materials Engineering, 10066 Baghdad, Iraq

Received 23 March 2014; received in revised form 22 June 2014; accepted 22 June 2014Available online 30 June 2014

Abstract

Alkali-activated aluminosilicates mortars were produced from recycled bricks, water glass, and commercial grade caustic soda flakes. The solidpart of the mortar was a mixture of recycled bricks and caustic soda powders. The liquid part consisted of diluted water glass. Explicitly, theliquid part did not contain the chemically aggressive high molarity sodium hydroxide. Six compositions are devised with different caustic sodaand water glass contents. Setting times for the mix pastes were measured; also, the pastes were cured under ambient conditions for 1, 7, 14, 21,and 28 days. Compressive strengths were measured for the cured pastes as function of the curing times. It is found that setting times and the speedof the compressive strength development depends on the ratio of the caustic soda to the water glass content; in addition, the setting time andcompressive strength were optimum at a given optimum value of this ratio. The cured pastes were characterized via X-ray diffraction, FTIR, andoptical microscopy. It is shown that the produced pastes were quartz and mullite composite in gel matrix, and the peak gel build up was occurredat the optimum value of the caustic soda to the water glass ratio.& 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Keywords: C. Mechanical properties; Alkali activation; Recycled materials

1. Introduction

The utilization of the recycled materials and decrease inenergy consumption in the production processes is a universalconcern of the current research activities. Thus, the alkali-activated cementitious aluminosilicates receive increasingattention as a green alternative to Portland cements in viewof the great reduction in CO2 emissions and the potential ofincorporating recycled materials as precursors [1–3]. Thedominant aluminosilicate precursor for the alkali activatedcement pastes is the metakaolin, prepared by calcination ofkaolin at around 700 1C [4]. Nevertheless, various aluminosi-licate material resources were investigated for it performanceas cementitious materials, e.g. volcanic ash and fly ashes fromdifferent resources [5–8].

The preparation parameters such as the curing conditionsand the SiO2/Al2O3 molar ratio influence the degree of thereaction, the integrity of the microstructure, and the final

10.1016/j.ceramint.2014.06.10614 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

g author. Tel.: þ964 7805457828.ss: [email protected]

mechanical properties [9–11]. Moreover, adding up of silicadelays the pozzolanic reaction; consequently, an optimumvalue for Na2O/SiO2 should be attained [12].The mechanicaland thermal properties were enhanced with the additions of thenano silica. The preparation of the nano silica from burnedpods of ‘Delonix Regia’ and burned rice husk are among thevarious methods of synthesis of the nano silica. [13–14].Recycling of waste materials is one of the valuable

contributions of the alkali-activated cementitious aluminosili-cates. Recycled porcelain stoneware scraps were bonded viautilization of alkali-activated metakaolin to make ceramiccomposites. The scraps act as partially reactive filler, but thesurface reactivity were varied for various scraps, which leavethe door open for further investigations [15].The activated aluminosilicates were also suggested resolving

the problem of the growing construction waste. Crushed andground waste brick and concrete were used as startingaluminosilicate's materials. The utilized aluminosilicates wereactivated using industrial grade sodium silicate and sodiumhydroxide. A 28-day compressive strength of 40 MPa wereobtained for a certain mix [16]. The metakaolin and waste

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Table 1Chemical analysis of the recycled bricks powder and the prepared nano-silica.

Recycled bricks Nano Silica

SiO2 55.25 99.1Al2O3 35.98 0.35Fe2O3 1.26 0.05Na2O 0.44 –

K2O 0.42 –

CaO 0.24 0.25MgO 0.44 0.25TiO2 1.1 –

L.O.I 4.87 –

Table 2Specifications of the utilized sodium silicate.

Specification Value as received Values after adding5 wt% Silica

Na2O (wt%) 19.20 18.24SiO2 (wt%) 30.70 34.17SiO2/Na2O 1.60 1.87Density* (g/cm3) 1.64PH 13.5Viscosity*poise 20Appearance Clear liquid

nvalues at 25 1C.

S.B.H. Farid / Ceramics International 40 (2014) 15027–1503215028

concrete sludge mix was also used as a source of thealuminosilicates and found that the addition of silica fume(SF) can improve both the bending and compressive strengths[17].

A serious environmental problem is the accumulation of thefly ashes from municipal solid waste (MSW) incinerators.These fly ashes are contained toxic materials such as heavymetals; thus they are potentially harmful to the environment.Two different kinds of the incinerator fly ashes (IFA) wereincluded as 20 wt% in the starting materials of the alkali-activated metakaolin and the results show that the pollutantmobility was reduced via physical and chemical bonding [18].Higher percentages (50–70 wt%) of the ash were includedsuccessfully in another study [19]. It is shown that bothamorphous and crystalline fractions with a different degreeof reactivity are present in the fly ashes, which should beconsidered in the formulation of the cementitious material.Alkali-activation of metakaolin with (60 and 70 wt%) of ladleslag and incinerator fly ashes were prepared and characterized[20]. One of the outcomes of this study was that themorphology of the prepared pastes was very close to that ofthe pure metakaolin pastes, but the presence of calcium in thecase of ladle slag promotes the formation of calcium–alumi-nate–silicate–hydrate phase.

Extraction and mineral processing industries results inindustrial solid wastes that accompanied with the risk ofenvironmental pollution. The reuse of such materials in thesynthesis of cementitious paste is value-added approach in thefield of construction materials. The flotation tailings resultedfrom the mixed sulfide ores processing are solid wastes thancan cause the generation of acid mine drainage. Mixtures offlotation tailings and fired-coal fly ash were alkali activated toproduce environmental friendly materials that efficientlyimmobilize of the heavy metals contained in the flotationtailings [21]. Another common industrial waste is the red mudthat produced by the Bayer process in Alumina industry. Thered mud is highly alkaline, and its accumulation can causeserious environmental problems. Alkali-activated cementitiouspastes were synthesized after partials substitution of themetakaolin by the red mud and found that the final micro-structure and mechanical properties depend on the red mudcontents and the curing times [22]. The red mud and rice huskash were used produce alkali activated cementitious materialswithout incorporating metakaolin [23]. The compressivestrengths depend on the rice husk ash to the red mud ratiowith an optimum value of 20.46 MPa at the ratio of 0.5.Finally, a further progress in this area is the use of Bayerprocess liquors as a primary source of caustic sodiumaluminate in replace of diluted sodium hydroxide [24]. Thefly ash is utilized as a source of reactive silica and additionalalumina and the silica fume as an additional source of reactivesilica. High compressive strength of 43 MPa was accom-plished. The use of plant Bayer liquor to produce cementitiouspaste may represent an impurity removal process for the Bayerprocess.

The brick fragments and the rice husks are very abundantwaste in Iraq, which accumulated yearly with no serious

attempts to reuse these materials. In this study, the recycledbrick powder is shown as a substitute for the metakaolin andthe burned ‘Iraqi Anber’ rice husks as source of the nano silicathat can be utilized in syntheses of alkali-activated cementi-tious pastes. The usual utilization of high concentrations ofNaOH represents a difficulty in handling alkali-activatedcementitious materials and may limit its acceptance. The aimof this work is to employ alternative compositions andprocedure that makes the solid part contains the aluminosili-cates and solid NaOH. The liquid part consists of just dilutedwater glass, which makes handling of such mortars safe andeasy. Finally, the correlation between the compositions relatedsetting times of the cementitious pastes with the final com-pressive strengths is illuminated in this study.

2. Materials and methods

The starting materials include recycled brick fragments,which were originated from fired local clay, sodium silicates(water glass), and commercial sodium hydroxide as causticsoda flakes (NaOH 96% min). Table 1 shows the chemicalcomposition of the used recycled bricks. The water glass wasbrought from Al-Taji glass-manufacturing site of the ministryof industry located at Baghdad-Iraq. Table 2 shows thespecifications of the used water glass. The recycled brickfragments and the caustic soda flakes were grinded and milledvia a rotary blade mill, and the final particle size was 10–53 μm in the two cases. The solid part of the mortarwas prepared by dry mixing of the recycled bricks with thecaustic soda powders in rotating alumina jar for two hours. The

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Table 3The composition as wt% of the prepared mortars.

Composition/No. 1 2 3 4 5 6

Recycled bricks 70 70 70 70 70 70Caustic soda 9 9.75 9.9 10.6 11.2 12.75Water glass 12 10.5 10.2 8.8 7.6 4.5Tap water 9 9.75 9.9 10.6 11.2 12.75

S.B.H. Farid / Ceramics International 40 (2014) 15027–15032 15029

approximate inner dimensions of the alumina jar are 100 mmlength � 100 mm diameter. The powder filling volume was1/3 of that of the alumina jar. The milling balls were not used,and the output particle size was the same as the input size (10–53 μm). The temperature and humidity of the lab were readdigitally via thermo-hygrometer (CHEERMAN KT-903,China). The lab temperature was 25 1C and humidity was30%; thus no agglomeration for the mixed powders wasobserved.

The compositions as wt% of the prepared mortars are shownin Table 3. The liquid part was prepared by the addition of tapwater to the used water glass with the amounts shown inTable 3. The cementitious pastes were prepared by mixing thesolid part with the liquid part by amounts shown in the tableand given the code (Set1). The setting time was measured foreach of the prepared pastes via Gillmore needles according toASTM C266 [25].

In order to enhance the understanding of the role ofcomposition on setting times, another two sets of mortars(Set2 and Set3) was prepared. To prepare Set2 and Set3 ofmortars, 5 wt% of silica was added first to the water glass,which changes the SiO2/Na2O ratio of the water glass from1.60 to 1.87 as shown in Table 2. In the case of Set2, the addedsilica was high purity α-cristobalite with average particle sizeof 9.04 mm; and, in the case of Set3, nano-silica with averageparticle size of about 81 nm is added. The particle sizes aremeasured via laser particle size analyzer (Shimadzu SALD-2101, USA). Set2 and Set3 of mortars were prepared againaccording to Table 3 and the setting times are measured.

The pastes then cured in ambient conditions for 1, 7, 14, 21,and 28 days for all the prepared sets of mortars. The averageambient temperature and humidity are 32 1C and 36% respec-tively. Compressive strengths are measured using a universaltesting machine (Time group Inc, China). The pastes werecasted in 27 mm inner diameter cylindrical molds. The moldswere prepared in advance by casting a mix of about 40 vol%RTV silicone and 60 vol% silica sand. The specimens were leftfor 1 day before removing from the molds. Grinding paperswere used to make the upper and lower bases parallel and tomake the length of the cylindrical specimens equals to 50 mm.After the targeted curing times were attained, the average ofthree tests is calculated for each specimen.

X-ray diffraction (Shimadzu-600, USA) was utilized toinvestigate the nano silica; which was prepared by combustionof the ‘Iraqi Anber’ rice husks. X-ray diffraction is also used toexamine the difference between the recycled bricks and aselected cured paste after curing for 28 days

The infrared spectra were performed using FTIR spectro-meter (Shimadzu, Kyoto Japan). The FTIR of the recycledbricks powder and that for a cured paste are compared; also,the peak position for a typical absorption peak is monitored forthe cured pastes for different compositions.Optical micrography (Microscopes, Inc. USA) is utilized to

examine the microstructure at the fracture surface of twoselected cured pastes. The open porosity was measured forselected samples according to ASTM C373 [26]. Finally, thecompressive strengths were measured for the cured pastes fordifferent compositions and curing times.

3. Results and discussion

As mentioned above, the mortar is designed so that liquidNaOH is avoided as starting material to overcome thedifficulty of handling high alkali solution even for a qualifiedworker. The caustic soda powder is the source of NaOH,which is included in the solid part of the mortar together withthe recycled bricks powder as the source for the aluminosili-cates. In the liquid part of the mortar, it can be seen fromTable 3 that the water contents equal to the correspondingquantities of the caustic soda. This is equivalent to addingabout M12.5 of NaOH solution to the recipe, which was withinthe range (12M–14M) usually found in the literature [9–11].The main concern of the current work is that how much time

is required for the setting of the pastes when solid and liquidpart is mixed, and the development of the compressive strengthof the produced mortars. Numerous experimentations wereperformed to test different compositions for the setting times. Itwas noticed that the setting times were correlated to therelative magnitudes of caustic soda to water glass. Accord-ingly, the mortar compositions were designed so that it coversa range of caustic soda to water glass weight ratios as shown inTable 3.It was understood that this correlation might numerically

change if the aluminosilicate source is altered and/or if theSiO2/Na2O ratio of the used water glass is changed. Therefore,the chemical composition of the used recycled brick powderand the specification of the utilized water glass are presentedfirst as shown in Tables 1 and 2 respectively.The results for X-ray diffraction are shown in Fig. 1. The

obtained nano silica was amorphous as shown in the figure.The figure also shows the diffraction pattern of the recycledbrick powder and a selected cured paste after curing for 28days. The recycled bricks powder was composed of mulliteand quartz, which are the expected crystalline phases thatresult from firing of clays. The same phases occur afterpreparation of the paste and curing. The difference is thatsome degree of smearing occurs to the diffraction peaks and abackground hump in the range 15–301 representing theoccurrence of an amorphous phase. These two features indicatethat the pozzolanic reaction took place but did not consume allthe available aluminosilicates, which result in a compositematerial of quartz and mullite with a gel matrix.Fig. 2 displays the measured setting times of the prepared

pastes (Set1) versus the caustic soda to water glass ratios. It is

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Fig. 1. Cu-Kα1 diffractograms for the prepared nano-silica, the recycled brickpowder, and the cured paste with with optimum caustic soda to water glassratio (0.75).

Fig. 2. Setting times for the prepared pastes as function of their caustic soda/water glass ratio.

Fig. 3. Comparison between the setting times as function of their caustic soda/water glass ratio for Set1, Set2, and Set3 of the prepared pastes.

Fig. 4. Comparison of the FTIR spectra for the recycled brick with that of thecured paste for 28 days (from Set1) with optimum caustic soda to water glassratio (0.75).

S.B.H. Farid / Ceramics International 40 (2014) 15027–1503215030

understood that using Na2O/SiO2 ratio is common and easierto read. In this work, caustic soda to water glass ratio is used toindicate a mix of solid and liquid components. The figureshows that the relation is not linear, but, the setting time has itminimum value (4.5 min) at an optimum caustic soda to waterglass weight ratio (0.75). It is expected that a balanced SiO2

content that assist gel formation be achieved at this ratio. Inorder to confirm this explanation, Set2 and Set2 of mortarswere prepared with the addition of micro and nano silicarespectively.

Fig. 3 compares the setting times of the three prepared setsof pastes. It can be noticed that, when adding the micro silica(Set2), the optimum caustic soda to water glass ratio (at theminimum setting time) was higher, i.e. the addition of SiO2 tothe water glass need to be balanced with higher caustic sodacontent. In the case of adding nano-silica (Set3) to the waterglass, the required caustic soda to water glass ratio is againhigher than that of (Set2) to achieve the minimum setting time.This can be explained in terms of that the nano-silica reactsfaster than the micro silica. This makes SiO2 molecules moreavailable in early times of reaction, thus, needs more NaOH toachieve balanced contents. Accordingly, in an alkali environ-ment, the available SiO2 control the speed of the gel built up

that makes the setting times depends on caustic soda to waterglass ratio. Recalling that the available SiO2 molecules in Set2was higher than that in Set1 and Set3 was higher than that inSet2, Fig. 3 shows that the minimum setting times wereincreased with the increase of the available SiO2 molecules.This type of behavior can be found in the literature, e.g. [4,27],which were mentioned that the setting times were increasedwith increasing SiO2/Al2O3 ratio of the starting mixtures.

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S.B.H. Farid / Ceramics International 40 (2014) 15027–15032 15031

Fig. 4 compares the FTIR spectra for the recycled brickpowder with the paste (Set1) of the optimum caustic soda towater glass ratio and 28 days curing. The main mulliteabsorption band at 1087 cm�1 is shifted toward 1056 cm�1.This shift was explained in [28] as originated from thechemical attack of the alkali. The chemical attack results in achange of the local chemical environment of Si–O bond due tothe formation of a new product. In reference [28], the shift was78 cm�1, which was larger than that of this study (31 cm�1).The difference may be attributed to different starting materialsand composition weight percentages.

Fig. 5 is a plot of the FTIR peak positions of the cured pastes(Set1) with different caustic soda to water glass ratio and 28 dayscuring; compared with the original value of mullite at 1087 cm�1.The figure shows an increasing shift of the absorption band towardlower values with increasing of the caustic soda to water glassratio. The maximum shift (31 cm�1) takes place at the optimumvalue of this ratio (that give the minimum setting time). Afterward,increasing this ratio lead to deficiency in SiO2 content, decreasinggel formation and FTIR shifts.

The optical micrographs for the fracture surface of two curedpastes (Set1) shown in Fig. 6. The first micrograph (a) is for thecured paste for 28 days with caustic soda to water glass ratio of 2.0,

Fig. 5. Peak positions of a typical FTIR absorption band for the cured pasteswith different caustic soda to water glass ratio.

Fig. 6. Optical micrograph for the fracture surface of the cured pastes (Set1) for 28 dwater glass ratio¼0.75.

and the second micrograph (b) is for the cured pastes for 28 dayswith the optimum caustic soda to water glass ratio (0.75). Themicrographs show gray solid grains, dark pore space, and brightareas indicative for the formation of the gel. Upon comparison ofthe two micrographs, it is obvious that at the optimum value ofcaustic soda to water glass ratio results in extra gel phase and thusmore packed microstructure. This conclusion is also supported bythe open porosity measurement where the value of the openporosity was 7.6% for the first case and 4.5% for the second case.The alkali attack did not totally consume the starting aluminosi-licate material, but the produced gel provides a matrix for thecomposite.The results for compressive strength measurements for the cured

pastes (Set1) versus the curing time are shown in Fig. 7. Explicitly,the caustic soda to water glass ratio, shown in the legend, has adominant effect on compressive strengths at all curing times. Theratio of (2.0) that needed the longest curing time, (Fig. 2) showsalmost linear developing of the compressive strength with curingtimes. The linear relation is expected as an approximation for slowgrowth phenomena; on the other hand, the optimum ratio of (0.75)shows the higher slope of compressive strength developmentversus the curing times. This is reasonable as the mortar systemhas its balanced composition. After 14 days of curing, the strengthdevelopment speed begins to decrease and almost reaches a plateau

ays. (a) Caustic soda to water glass ratio¼2.0 and (b) optimum caustic soda to

Fig. 7. Compressive strengths for the cured pastes (Set1) versus the curingtimes, for different caustic soda to water glass ratios as shown in the legend.

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S.B.H. Farid / Ceramics International 40 (2014) 15027–1503215032

near 28 curing days. This can be explained in terms of that the gelphase covers most of the grain boundaries it can reach after 14days of curing. Then, the gel phase begins to fill the pores instead,resulting in slower strength development. Generally, the compres-sive strengths increased with the curing times and reach a plateau.This behavior of compressive strengths with curing times can befound in other literature e.g. [4,27,29]. In addition, the role of theincrease of the gel phase was shown to have a decisive effect ondeveloping of the mechanical strength [30], which is coherent withthe results of the compressive strengths in this work.

As a final point, the starting aluminosilicates that can be utilizedfor alkali-activated mortars may be different in composition andphases; e.g., the fly ashes with various alumina and silica contents.Thus, the numerical values obtained in this work for setting timesand compressive strengths should change with different ingredi-ents. Accordingly, further work is needed to relate the setting timesand strength development of the alkali-activated mortars to theactivator composition and alumina content of the starting materials.

4. Conclusions

A methodology is constructed for the synthesis of activatedaluminosilicates mortar that based on alkali activation. Themethodology includes NaOH with the solid part, which over-comes the difficulty of handling high molar alkali solution.

The setting time and strength development of the mortardepend on the ratio of NaOH to the available free silicacontent. Monitoring this ratio may aid future work ofmodeling.

The obtained compressive strengths were increased withthe increase of the gel build up, which yields bettermicrostructure packing. The setting times may representan early estimation of the compressive strength develop-ment speed, which may help in design of improvedmicrostructure packing.

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