The effect of temperature on the geopolymerization process of a metakaolin-based geopolymer

This paper describes the effect of different curing temperatures on the geopolymerization process, physical, mechanical and optical properties of a metakaolin-based geopolymer activated by alkali. The influence of different curing temperatures (within the range 30 to 90 °C) was studied systematically by means of differential scanning calorimetry (DSC), SEM, UV/Vis Spectrophotometry, Leaching analysis and Brunauer-Emmet-Teller method (BET). The results showed the existence of an optimum temperature at which the geopolymer presents the best physical and mechanical properties. The geopolymers cured at 30 and 90 °C presented high porosity, and were translucent to the Visible light, which makes possible to tailor this inorganic polymers for optical and photocatalytic applications.     

Thermosensitive solutions and gels consisting of poly(vinyl alcohol) and sodium silicate

We have investigated the transparency for visible light of a poly(vinyl alcohol) (PVA) aqueous solution in the presence of sodium silicates (SS). The transparency of the aqueous solution dramatically changed by varying temperature despite that neither aqueous solutions of PVA nor SS is sensitive to temperature. The aqueous solution showed a lower critical solution temperature (LCST) around 30 °C. The LCST depended on both concentrations of PVA and sodium silicate. Below the LCST, the transmittance was thermally irreversible. By a further increase in the temperature, the solution was separated into two phases consisting of a phase rich in solvent and that in solute; that is a coacervation. In the region of coacervation, the transmittance was thermally reversible. Reversible change in the transmittance was realized corresponding to stepwise temperature changes between 10 and 40 °C. A PVA gel swollen by the solution demonstrated transparency change in response to temperature changes as well as the solution.     

Mechanism of geopolymerization and factors influencing its development: a review

Geopolymerization is a developing field of research for utilizing solid waste and by-products. It provides a mature and cost-effective solution to many problems where hazardous residue has to be treated and stored under critical environmental conditions. Geopolymer involves the silicates and aluminates of by-products to undergo process of geopolymerization. It is environmentally friendly and need moderate energy to produce. This review presents the work carried out on the chemical reaction, the source materials, and the factor affecting geopolymerization. Literature demonstrates that certain mix compositions and reaction conditions such as Al₂O₃/SiO₂, alkali concentration, curing temperature with curing time, water/solid ratio and pH significantly influences the formation and properties of a geopolymer. It is utilized to manufacture precast structures and non-structural elements, concrete pavements, concrete products and immobilization of toxic metal bearing waste that are resistant to heat and aggressive environment. Geopolymers gain 70% of the final strength in first 3–4 h of curing.     

Electromagneto-thermoelastic fundamental solutions in a two-dimensional problem for short time

Summary. The model of the two-dimensional equations of generalized magneto-thermoelasticity in a perfectly conducting medium is established. The analysis is carried out in the uncoupled framework under the classical Lord–Shulman [3] and Green–Lindsay [6] theories of thermoelasticity. Fundamental solutions of the corresponding differential equations are obtained using the inverse Laplace transform in an approximate manner for small values of time. The behavior of these solutions is discussed when we apply a continuous source of heat to an infinite elastic body. Numerical results in the presence of a magnetic field are presented graphically along with a comparison of the three theories. A discussion concerning which of the three theories is the most physically acceptable is given, with the Green–Lindsay formulation emerging as the clear choice.     

Phase separation behaviour of a metal-organic derived sodium silicate glass

The phase separation behaviour of an 18.56 mol % Na₂O-SiO₂ glass prepared via the standard glass preparation technique and the metallic-organic derived (MOD) method have been studied and contrasted. Our results suggest that at this composition the miscibility temperature is significantly elevated when a MOD preparation procedure is used. The origin of this effect appears to be related to the enhanced water content in the glass prepared by the MOD procedure.     

On the fundamental solutions in micropolar elasticity with voids

Summary By means of an uncoupling representation, we derive the fundamental solution for the differential system of micropolar elasticity with voids in the steady vibration case. Reciprocity properties are also explored.     

Modified fundamental solutions for the scattering of elastic waves by a cavity: Numerical results

The boundary integral equation method is very often used to solve exterior problems of scattering of waves (elastic waves, acoustic waves, water waves and electromagnetic waves). It is known, however, that this method fails to provide a unique solution at the so-called irregular frequencies. This difficulty is inherent to the method used rather than the nature of the problem. In the context of elastodynamics. we proposed, in a recent work¹, two methods for eliminating these irregular frequencies. Both are based on modifying the fundamental solution. Here we present numerical results pertaining to the solutions of the modified and unmodified integral equations.     

Solution of potential flow problems by the modified method of fundamental solutions: Formulations with the single layer and the double layer fundamental solutions

This paper describes an application of the recently proposed modified method of fundamental solutions (MMFS) to potential flow problems. The solution in two-dimensional Cartesian coordinates is represented in terms of the single layer and the double layer fundamental solutions. Collocation is used for the determination of the expansion coefficients. This novel method does not require a fictitious boundary as the conventional method of fundamental solutions (MFS). The source and the collocation points thus coincide on the physical boundary of the system. The desingularised values, consistent with the fundamental solutions used, are deduced from the direct boundary element method (BEM) integral equations by assuming a linear shape of the boundary between the collocation points. The respective values of the derivatives of the fundamental solution in the coordinate directions, as required in potential flow calculations, are calculated indirectly from the considerations of the constant potential field. The normal on the boundary is calculated by parametrisation of its length and the use of the cubic radial basis functions with the second-order polynomial augmentation. The components of the normal are calculated in an analytical way. A numerical example of potential flow around a two-dimensional circular region is presented. The results with the new MMFS are compared with the results of the classical MFS and the analytical solution. It is shown that the MMFS gives better accuracy for the potential, velocity components (partial derivatives of the potential), and absolute value of the velocity as compared with the classical MFS. The results with the single layer fundamental solution are more accurate than the results with the double layer fundamental solution.     

The method of fundamental solutions for a biharmonic inverse boundary determination problem

In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation is investigated. This problem consists of determining an unknown boundary portion of a solution domain by using additional data on the remaining known part of the boundary. The method of fundamental solutions (MFS), in combination with the Tikhonov zeroth order regularization technique, are employed. It is shown that the MFS regularization numerical technique produces a stable and accurate numerical solution for an optimal choice of the regularization parameter. A. Zeb on study leave visiting the University of Leeds.     

Hydrolytic stability of sodium silicate gels in the presence of aluminum

Polycondensation in alkali silicate solutions comprises a fundamental process of the geopolymerization technology. Previous works had shown that the hydrolytic stability of sodium silicate gels depends on the SiO₂/Na₂O ratio. Sodium silicate gels totally insoluble in water can be produced at SiO₂/Na₂O molar ratios higher than 4.4. This article aims at elucidating the effect of tetra-coordinated aluminum addition on the hydrolytic stability of sodium silicate gels. According to the results, the aluminum addition stabilizes the sodium silicate gels in an aqueous environment. A sodium silicate gel with SiO₂/Na₂O molar ratio 3.48, which is totally soluble in deionized water at ambient temperature, can be transformed to insoluble sodium hydroaluminosilicates with the addition of tetrahedral aluminum at Al/Si molar ratios higher than 0.08. In addition, this article studies the structure of prepared sodium hydroaluminosilicates and draws very useful conclusions for the geopolymerization technology.     

Wet chemical etching of silicate glasses in hydrofluoric acid based solutions

The etching of silicate glasses in aqueous hydrofluoric acid solutions is applied in many technological fields. In this review most of the aspects of the wet chemical etching process of silicate glasses are discussed. The mechanism of the dissolution reaction is governed by the adsorption of the two reactive species: HF and HF ₂ ^- and the catalytic action of H⁺ ions, resulting in the breakage of the siloxane bonds in the silicate network. The etch rate is determined by the composition of the etchant as well as by the glass, although the mechanism of dissolution is not influenced. In the second part of this review, diverse applications of etching glass objects in technology are described. Etching of SiO₂ and doped SiO₂ thin films, studied extensively for integrated circuit technology, is discussed separately.     

On the Laplace transform of a matrix of fundamental solutions for thermoelastic plates

The Laplace transform of a matrix D(x,t) of fundamental solutions for the partial differential operator describing the time-dependent bending of thermoelastic plates with transverse shear deformation is constructed, and its asymptotic behavior near the origin is investigated. The differential system is reduced to an algebraic one through the application of the Laplace and then Fourier transformations, and all possible cases of roots of the determinant of the latter system are considered. It is shown that in every case, the asymptotic expansion of near the origin has the same dominant term. This is an important step in the construction of boundary-element methods for the above time-dependent model because it determines the nature of the singularity of the kernel of the boundary-integral-equations associated with various initial-boundary-value problems for the governing system.     

The method of fundamental solutions for a time-dependent two-dimensional Cauchy heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the time-dependent two-dimensional Cauchy heat conduction problem, which is an inverse ill-posed problem. Data in the form of the solution and its normal derivative is given on a part of the boundary and no data is prescribed on the remaining part of the boundary of the solution domain. To generate a numerical approximation we generalize the work for the stationary case in Marin (2011) [23] to the time-dependent setting building on the MFS proposed in Johansson and Lesnic (2008) [15], for the one-dimensional heat conduction problem. We incorporate Tikhonov regularization to obtain stable results. The proposed approach is flexible and can be adjusted rather easily to various solution domains and data. An additional advantage is that the initial data does not need to be known a priori, but can be reconstructed as well.     

Frequency response analyses in vibroacoustics using the method of fundamental solutions

The method of fundamental solutions, one of the promising boundary-type meshless methods, is proposed as a direct procedure to formulate and analyze the vibroacoustic problem. The coupled system discussed in this study is composed of an acoustic-cavity and excited by an external force or an internal sound source harmonically. The wall of cavity consists of the beam or the plate components, respectively, in two- and three-dimensional problems. The two independent sub-systems interact at the interface simultaneously by satisfying the necessary equilibrium and compatibility conditions. The mathematical formulations described by the presented meshless method demonstrate straightforwardly the frequency responses of the vibroacoustic problems with no boundary integrals. General characteristics of the dynamic coupling effect are displayed, based on the systematic natural frequencies and mode shapes. Feasible results simulated by the presented numerical scheme are validated through meshless numerical experiments including the acoustic-wave propagation problems and the vibroacoustic problems.     

Crystalline phase formation in metakaolinite geopolymers activated with NaOH and sodium silicate

The effect of the NaOH content and the presence of sodium silicate activators on the formation of crystalline phases from metakaolinite-based geopolymers were studied by X-ray powder diffraction (XRD), Rietveld quantitative XRD, solid-state MAS NMR and SEM in samples synthesized with varying NaOH contents and different curing times at 40 °C. Geopolymers activated with NaOH alone with Si/Na ratios of 4/4 or less formed the crystalline zeolite Na–A (Na₉₆Al₉₆Si₉₆O₃₈₄·216H₂O), but at ratios >4/4 nanosized crystals of another zeolite (Na₆[AlSiO₄]₆·4H₂O) were formed. The Si/Na ratio of 4/4 produces a product of greatest crystallinity. The addition of sodium silicate in addition to NaOH significantly reduces crystallite formation. The network units of all the materials containing NaOH and sodium silicate are essentially the same, namely, tetrahedral [SiO₄] units coordinated through four bridging oxygens to four aluminium atoms [denoted as Q⁴ Si(4Al) units]. A templating function of the various silicate units of the sodium silicate molecules is suggested to occur in geopolymerization, which differs from the reaction route operating when NaOH alone is used as the activator. This templating function is responsible for the suppression of crystallization and the increase in strength of the geopolymers activated with sodium silicate.     

Complex fundamental solutions and complex variables boundary element method in elasticity

The CVBEM for elasticity problems in its basic formulations (direct, indirect and displacement discontinuity (DD) ones) is presented. It is based on the use of complex fundamental solutions. The complex boundary integral equations (CBIEs) arising from the basic CVBEM formulations are considered. It was shown that the developed theory includes the main CBIEs obtained by using the different approaches. Besides, new real and complex integral equations were obtained. The revealed links between real variables BEM (RVBEM) and CVBEM serve to mutual enrichment of these two approaches.     

Implementation of a process analytical technology system in a freeze-drying process using Raman spectroscopy for in-line process monitoring

The aim of the present study was to propose a strategy for the implementation of a Process Analytical Technology system in freeze-drying processes. Mannitol solutions, some of them supplied with NaCl, were used as models to freeze-dry. Noninvasive and in-line Raman measurements were continuously performed during lyophilization of the solutions to monitor real time the mannitol solid state, the end points of the different process steps (freezing, primary drying, secondary drying), and physical phenomena occurring during the process. At-line near-infrared (NIR) and X-ray powder diffractometry (XRPD) measurements were done to confirm the Raman conclusions and to find out additional information. The collected spectra during the processes were analyzed using principal component analysis and multivariate curve resolution. A two-level full factorial design was used to study the significant influence of process (freezing rate) and formulation variables (concentration of mannitol, concentration of NaCl, volume of freeze-dried sample) upon freeze-drying. Raman spectroscopy was able to monitor (i) the mannitol solid state (amorphous, alpha, beta, delta, and hemihydrate), (ii) several process step end points (end of mannitol crystallization during freezing, primary drying), and (iii) physical phenomena occurring during freeze-drying (onset of ice nucleation, onset of mannitol crystallization during the freezing step, onset of ice sublimation). NIR proved to be a more sensitive tool to monitor sublimation than Raman spectroscopy, while XRPD helped to unravel the mannitol hemihydrate in the samples. The experimental design results showed that several process and formulation variables significantly influence different aspects of lyophilization and that both are interrelated. Raman spectroscopy (in-line) and NIR spectroscopy and XRPD (at-line) not only allowed the real-time monitoring of mannitol freeze-drying processes but also helped (in combination with experimental design) us to understand the process.     

Regularized solutions with a singular point for the inverse biharmonic boundary value problem by the method of fundamental solutions

Two numerical methods for the Cauchy problem of the biharmonic equation are proposed. The solution of the problem does not continuously depend on given Cauchy data since the problem is ill-posed. A small noise contained in the Cauchy data sensitively affects on the accuracy of the solution. Our problem is directly discretized by the method of fundamental solutions (MFS) to derive an ill-conditioned matrix equation. As another method, our problem is decomposed into two Cauchy problems of the Laplace and the Poisson equations, which are discretized by the MFS and the method of particular solutions (MPS), respectively. The Tikhonov regularization and the truncated singular value decomposition are applied to the matrix equation to stabilize a numerical solution of the problem for the given Cauchy data with high noises. The L-curve and the generalized cross-validation determine a suitable regularization parameter for obtaining an accurate solution. Based on numerical experiments, it is concluded that the numerical method proposed in this paper is effective for the problem that has an irregular domain and the Cauchy data with high noises. Furthermore, our latter method can successfully solve the problem whose solution has a singular point outside the computational domain.     

Synthesis of highly ordered and hydrothermally stable mesoporous materials using sodium silicate as a precursor

Highly ordered mesoporous silica and aluminosilicate materials with extremely high hydrothermal stability have been synthesized successfully at a high hydrothermal treatment temperature of 200 °C by using inexpensive sodium silicate and sodium aluminate as the silica source and alumina source, respectively. The resultant mesoporous materials possess a hexagonal mesostructure and extraordinary stability towards the steam treatment at 800 °C for 2 h. In addition, the direct incorporation of Al into the mesoporous framework can further enhance the hydrothermal stability of ordered mesoporous materials. Our contribution provides a commercially important approach to synthesize ordered mesoporous materials with highly hydrothermal stability, which may find potential applications for the catalytic cracking in the petroleum industry.