The 2df SDSS LRG and QSO survey: evolution of the luminosity function of luminous red galaxies to z=0.6

We present new measurements of the luminosity function (LF) of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) and the 2dF SDSS LRG and Quasar (2SLAQ) survey. We have carefully quantified, and corrected for, uncertainties in the K and evolutionary corrections, differences in the colour selection methods, and the effects of photometric errors, thus ensuring we are studying the same galaxy population in both surveys. Using a limited subset of 6326 SDSS LRGs (with 0.17 < z < 0.24) and 1725 2SLAQ LRGs (with 0.5 < z < 0.6), for which the matching colour selection is most reliable, we find no evidence for any additional evolution in the LRG LF, over this redshift range, beyond that expected from a simple passive evolution model. This lack of additional evolution is quantified using the comoving luminosity density of SDSS and 2SLAQ LRGs, brighter than M-0.2r - 5 log h(0.7) = - 22.5, which are 2.51 +/- 0.03 x 10(-7) L circle dot Mpc(-3) and 2.44 +/- 0.15 x 10(-7) L circle dot Mpc(-3), respectively (< 10 per cent uncertainty). We compare our LFs to the COMBO-17 data and find excellent agreement over the same redshift range. Together, these surveys show no evidence for additional evolution (beyond passive) in the LF of LRGs brighter than M-0.2r - 5 log h(0.7) = - 21 ( or brighter than similar to L-*).. We test our SDSS and 2SLAQ LFs against a simple 'dry merger' model for the evolution of massive red galaxies and find that at least half of the LRGs at z similar or equal to 0.2 must already have been well assembled (with more than half their stellar mass) by z similar or equal to 0.6. This limit is barely consistent with recent results from semi-analytical models of galaxy evolution.

Exploitation du potentiel sismique des étoiles naines blanches

Le but de cette thèse est d’explorer le potentiel sismique des étoiles naines blanches pulsantes, et en particulier celles à atmosphères riches en hydrogène, les étoiles ZZ Ceti. La technique d’astérosismologie exploite l’information contenue dans les modes normaux de vibration qui peuvent être excités lors de phases particulières de l’évolution d’une étoile. Ces modes modulent le flux émergent de l’étoile pulsante et se manifestent principalement en termes de variations lumineuses multi-périodiques. L’astérosismologie consiste donc à examiner la luminosité d’étoiles pulsantes en fonction du temps, afin d’en extraire les périodes, les amplitudes apparentes, ainsi que les phases relatives des modes de pulsation détectés, en utilisant des méthodes standards de traitement de signal, telles que des techniques de Fourier. L’étape suivante consiste à comparer les périodes de pulsation observées avec des périodes générées par un modèle stellaire en cherchant l’accord optimal avec un modèle physique reconstituant le plus fidèlement possible l’étoile pulsante. Afin d’assurer une recherche optimale dans l’espace des paramètres, il est nécessaire d’avoir de bons modèles physiques, un algorithme d’optimisation de comparaison de périodes efficace, et une puissance de calcul considérable. Les périodes des modes de pulsation de modèles stellaires de naines blanches peuvent être généralement calculées de manière précise et fiable sur la base de la théorie linéaire des pulsations stellaires dans sa version adiabatique. Afin de définir dans son ensemble un modèle statique de naine blanche propre à l’analyse astérosismologique, il est nécessaire de spécifier la gravité de surface, la température effective, ainsi que différents paramètres décrivant la disposition en couche de l’enveloppe. En utilisant parallèlement les informations obtenues de manière indépendante (température effective et gravité de surface) par la méthode spectroscopique, il devient possible de vérifier la validité de la solution obtenue et de restreindre de manière remarquable l’espace des paramètres. L’exercice astérosismologique, s’il est réussi, mène donc à la détermination précise des paramètres de la structure globale de l’étoile pulsante et fournit de l’information unique sur sa structure interne et l’état de sa phase évolutive. On présente dans cette thèse l’analyse complète réussie, de l’extraction des fréquences à la solution sismique, de quatre étoiles naines blanches pulsantes. Il a été possible de déterminer les paramètres structuraux de ces étoiles et de les comparer remarquablement à toutes les contraintes indépendantes disponibles dans la littérature, mais aussi d’inférer sur la dynamique interne et de reconstruire le profil de rotation interne. Dans un premier temps, on analyse le duo d’étoiles ZZ Ceti, GD 165 et Ross 548, afin de comprendre les différences entre leurs propriétés de pulsation, malgré le fait qu’elles soient des étoiles similaires en tout point, spectroscopiquement parlant. L’analyse sismique révèle des structures internes différentes, et dévoile la sensibilité de certains modes de pulsation à la composition interne du noyau de l’étoile. Afin de palier à cette sensibilité, nouvellement découverte, et de rivaliser avec les données de qualité exceptionnelle que nous fournissent les missions spatiales Kepler et Kepler2, on développe une nouvelle paramétrisation des profils chimiques dans le coeur, et on valide la robustesse de notre technique et de nos modèles par de nombreux tests. Avec en main la nouvelle paramétrisation du noyau, on décroche enfin le ”Saint Graal” de l’astérosismologie, en étant capable de reproduire pour la première fois les périodes observées à la précision des observations, dans le cas de l’étude sismique des étoiles KIC 08626021 et de GD 1212.

The role of the National Audit Office in Private Finance Initiative endurance

The Private Finance Initiative (PFI) has become one of the UK’s most contentious public policies. Despite New Labour’s advocacy of PFI as a means of achieving better value for money, criticisms of PFI have centred on key issues such as a lack of cost effectiveness, exaggerated pricing of risk transfers, excessive private sector profits, inflexibility and cumbersome administrative arrangements. Nevertheless, PFI has persisted as a key
infrastructure procurement method in the UK and has been supported as such by successive governments, as well as influencing policy in the Republic of Ireland and other European Nations. This paper explores this paradoxical outcome in relation to the role played in the UK by the National Audit Office (NAO). Under pressure to justify its support for PFI, the Blair government sought support for its policies by encouraging the NAO to investigate issues relating to PFI as well as specific PFI projects. It would have been expected that in fulfilling its role as independent auditor, the NAO would have examined whether PFI projects could have been delivered more efficiently, effectively or economically through other means. Yet, in line with earlier research, we find evidence that the NAO failed to comprehensively assess
key issues such as the value for money of PFI projects, and in so doing effectively acted as a legitimator of PFI policy. Using concepts relating to legitimacy theory and the idea of framing, our paper looks into 67 NAO private finance reports published between 1997 and 2011, with the goal of identifying the preferences, values and ideology underpinning the
NAO’s view on PFI during this period. Our analysis suggests that the NAO sought to legitimise existing PFI practices via a selective framing of problems and questions. Utilising a longitudinal approach, our analysis further suggests that this patterns of selective framing persisted over an extended time period during which fundamental parameters of the policy (such as contract length, to name one of the most important issues) were rarely addressed.
Overall the NAO’ supportive stance toward PFI seems to have relied on 1) a focused on positive aspects of PFI, such as on time delivery or lessons learned, and 2) positive comments on aspects of PFI that were criticised elsewhere, such as the lack of flexibility of underlying contractual arrangements. Our paper highlights the possibility that, rather than providing for a critical assessment of existing policies, national auditing bodies can
contribute to the creation of legitimatory environments. In terms of accounting research we would suggests that the objectivity and independence of accounting watchdogs should not be taken for granted, and that instead a critical investigation of the biases which can characterise these bodies can contribute to a deeper understanding of the nature of lobbying networks in the modern state.

The crowded magnetosphere of the post-common-envelope binary QS Virginis

We present high-speed photometry and high-resolution spectroscopy of the eclipsing post-common-envelope binary QS Virginis (QS Vir). Our Ultraviolet and Visual Echelle Spectrograph (UVES) spectra span multiple orbits over more than a year and reveal the presence of several large prominences passing in front of both the M star and its white dwarf companion, allowing us to triangulate their positions. Despite showing small variations on a time-scale of days, they persist for more than a year and may last decades. One large prominence extends almost three stellar radii from the M star. Roche tomography reveals that the M star is heavily spotted and that these spots are long-lived and in relatively fixed locations, preferentially found on the hemisphere facing the white dwarf. We also determine precise binary and physical parameters for the system. We find that the 14 220 ± 350 K white dwarf is relatively massive, 0.782 ± 0.013 M⊙, and has a radius of 0.010 68 ± 0.000 07 R⊙, consistent with evolutionary models. The tidally distorted M star has a mass of 0.382 ± 0.006 M⊙ and a radius of 0.381 ± 0.003 R⊙, also consistent with evolutionary models. We find that the magnesium absorption line from the white dwarf is broader than expected. This could be due to rotation (implying a spin period of only ˜700 s), or due to a weak (˜100 kG) magnetic field, we favour the latter interpretation. Since the M star's radius is still within its Roche lobe and there is no evidence that it is overinflated, we conclude that QS Vir is most likely a pre-cataclysmic binary just about to become semidetached.

The VLT-FLAMES Tarantula Survey: XVIII. Classifications and radial velocities of the B-type stars

We present spectral classifications for 438 B-type stars observed as part of the VLT-FLAMES Tarantula Survey (VFTS) in the 30 Doradus region of the Large Magellanic Cloud. Radial velocities are provided for 307 apparently single stars, and for 99 targets with radial-velocity variations which are consistent with them being spectroscopic binaries. We investigate the spatial distribution of the radial velocities across the 30 Dor region, and use the results to identify candidate runaway stars. Excluding potential runaways and members of two older clusters in the survey region (SL 639 and Hodge 301), we determine a systemic velocity for 30 Dor of 271.6 ± 12.2 km s^-1 from 273 presumed single stars. Employing a 3σ criterion we identify nine candidate runaway stars (2.9% of the single stars with radial-velocity estimates). The projected rotational velocities of the candidate runaways appear to be significantly different to those of the full B-type sample, with a strong preference for either large (≥345 km s^-1) or small (≤65 km s^-1) rotational velocities. Of the candidate runaways, VFTS 358 (classified B0.5: V) has the largest differential radial velocity (-106.9 ± 16.2 km s^-1), and a preliminary atmospheric analysis finds a significantly enriched nitrogen abundance of 12 + log (N/H) ≳ 8.5. Combined with a large rotational velocity (υ_e sin i = 345 ± 22 km s^-1), this is suggestive of past binary interaction for this star.

Localização em espaços interiores por luz visível para robôs móveis

Esta dissertação investiga a localização em espaços interiores através da comunicação por luz visível para robôs móveis, com base nos LEDs fixos nos edifícios, dando particular atenção à simulação e desenho do sensor, com vista ao desenvolvimento de um sensor de localização. Explica-se o crescimento da tecnologia LED e da constante necessidade de localização do homem em espaços interiores. Apresentado algumas características do LED e dos foto-detetores existentes. Com uma breve referencia a algumas das comunicações por luz visível de baixo débito possíveis de implementar. O desenvolvimento do protótipo do sensor inicia-se, principalmente, pela simulação de alguns dispositivos essenciais e das suas caraterísticas, como o emissor LED no controlo do ^angulo de meia potência (HPA) e a altura a que se encontra, e no recetor foto-díodo e a sua restrição de campo de visão (FOV). Simula-se o sensor pretendido com o número de foto-díodos necessários otimizando o espaço físico disponível e fazendo não só um refinamento no FOV mas também na distribuição espacial dos foto-díodos com funções predefinidas para a redução de incertezas de decisão de localização do robô. Estes resultados permitiram a construção física do sensor, desde o suporte para os foto-díodos, tendo em conta todas as medidas durante as simulações, e terminando com o desenvolvimento dos sensores e a sua integração completa. O tratamento de dados da leitura dos sinais recebidos do sensor são tratados por um microcontrolador, permitindo calcular parâmetros fundamentais no cálculo da posição. No final, os resultados teóricos bem como os práticos obtidos ao longo do desenvolvimento e possíveis propostas para trabalhos futuros que beneficiam desta investigação

Mid-infrared photonic sensors based on metamaterial structures

In this work three different metallic metamaterials (MMs) structures such as asymmetric split ring resonators (A-SRRs), dipole and split H-shaped (ASHs) structures that support plasmonic resonances have been developed. The aim of the work involves the optimization of photonic sensor based on plasmonic resonances and surface enhanced infrared absorption (SEIRA) from the MM structures. The MMs structures were designed to tune their plasmonic resonance peaks in the mid-infrared region. The plasmonic resonance peaks produced are highly dependent on the structural dimension and polarisation of the electromagnetic (EM) source. The ASH structure particularly has the ability to produce the plasmonic resonance peak with dual polarisation of the EM source. The double resonance peaks produced due to the asymmetric nature of the structures were optimized by varying the fundamental parameters of the design. These peaks occur due to hybridization of the individual elements of the MMs structure. The presence of a dip known as a trapped mode in between the double plasmonic peaks helps to narrow the resonances. A periodicity greater than twice the length and diameter of the metallic structure was applied to produce narrow resonances for the designed MMs. A nanoscale gap in each structure that broadens the trapped mode to narrow the plasmonic resonances was also used. A thickness of 100 nm gold was used to experimentally produce a high quality factor of 18 in the mid-infrared region. The optimised plasmonic resonance peaks was used for detection of an analyte, 17β-estradiol. 17β-estradiol is mostly responsible for the development of human sex organs and can be found naturally in the environment through human excreta. SEIRA was the method applied to the analysis of the analyte. The work is important in the monitoring of human biology and in water treatment. Applying this method to the developed nano-engineered structures, enhancement factors of 10^5 and a sensitivity of 2791 nm/RIU was obtained. With this high sensitivity a figure of merit (FOM) of 9 was also achieved from the sensors. The experiments were verified using numerical simulations where the vibrational resonances of the C-H stretch from 17β-estradiol were modelled. Lastly, A-SRRs and ASH on waveguides were also designed and evaluated. These patterns are to be use as basis for future work.

Exploitation du potentiel sismique des étoiles naines blanches

Le but de cette thèse est d’explorer le potentiel sismique des étoiles naines blanches pulsantes, et en particulier celles à atmosphères riches en hydrogène, les étoiles ZZ Ceti. La technique d’astérosismologie exploite l’information contenue dans les modes normaux de vibration qui peuvent être excités lors de phases particulières de l’évolution d’une étoile. Ces modes modulent le flux émergent de l’étoile pulsante et se manifestent principalement en termes de variations lumineuses multi-périodiques. L’astérosismologie consiste donc à examiner la luminosité d’étoiles pulsantes en fonction du temps, afin d’en extraire les périodes, les amplitudes apparentes, ainsi que les phases relatives des modes de pulsation détectés, en utilisant des méthodes standards de traitement de signal, telles que des techniques de Fourier. L’étape suivante consiste à comparer les périodes de pulsation observées avec des périodes générées par un modèle stellaire en cherchant l’accord optimal avec un modèle physique reconstituant le plus fidèlement possible l’étoile pulsante. Afin d’assurer une recherche optimale dans l’espace des paramètres, il est nécessaire d’avoir de bons modèles physiques, un algorithme d’optimisation de comparaison de périodes efficace, et une puissance de calcul considérable. Les périodes des modes de pulsation de modèles stellaires de naines blanches peuvent être généralement calculées de manière précise et fiable sur la base de la théorie linéaire des pulsations stellaires dans sa version adiabatique. Afin de définir dans son ensemble un modèle statique de naine blanche propre à l’analyse astérosismologique, il est nécessaire de spécifier la gravité de surface, la température effective, ainsi que différents paramètres décrivant la disposition en couche de l’enveloppe. En utilisant parallèlement les informations obtenues de manière indépendante (température effective et gravité de surface) par la méthode spectroscopique, il devient possible de vérifier la validité de la solution obtenue et de restreindre de manière remarquable l’espace des paramètres. L’exercice astérosismologique, s’il est réussi, mène donc à la détermination précise des paramètres de la structure globale de l’étoile pulsante et fournit de l’information unique sur sa structure interne et l’état de sa phase évolutive. On présente dans cette thèse l’analyse complète réussie, de l’extraction des fréquences à la solution sismique, de quatre étoiles naines blanches pulsantes. Il a été possible de déterminer les paramètres structuraux de ces étoiles et de les comparer remarquablement à toutes les contraintes indépendantes disponibles dans la littérature, mais aussi d’inférer sur la dynamique interne et de reconstruire le profil de rotation interne. Dans un premier temps, on analyse le duo d’étoiles ZZ Ceti, GD 165 et Ross 548, afin de comprendre les différences entre leurs propriétés de pulsation, malgré le fait qu’elles soient des étoiles similaires en tout point, spectroscopiquement parlant. L’analyse sismique révèle des structures internes différentes, et dévoile la sensibilité de certains modes de pulsation à la composition interne du noyau de l’étoile. Afin de palier à cette sensibilité, nouvellement découverte, et de rivaliser avec les données de qualité exceptionnelle que nous fournissent les missions spatiales Kepler et Kepler2, on développe une nouvelle paramétrisation des profils chimiques dans le coeur, et on valide la robustesse de notre technique et de nos modèles par de nombreux tests. Avec en main la nouvelle paramétrisation du noyau, on décroche enfin le ”Saint Graal” de l’astérosismologie, en étant capable de reproduire pour la première fois les périodes observées à la précision des observations, dans le cas de l’étude sismique des étoiles KIC 08626021 et de GD 1212.

Effects of fundamental structure parameters on dynamic responses of submerged floating tunnel under hydrodynamic loads

This paper investigates the effects of structure parameters on dynamic responses of submerged floating tunnel (SFT) under hydrodynamic loads. The structure parameters includes buoyancy-weight ratio (BWR), stiffness coefficients of the cable systems, tunnel net buoyancy and tunnel length. First, the importance of structural damp in relation to the dynamic responses of SFT is demonstrated and the mechanism of structural damp effect is discussed. Thereafter, the fundamental structure parameters are investigated through the analysis of SFT dynamic responses under hydrodynamic loads. The results indicate that the BWR of SFT is a key structure parameter. When BWR is 1.2, there is a remarkable trend change in the vertical dynamic response of SFT under hydrodynamic loads. The results also indicate that the ratio of the tunnel net buoyancy to the cable stiffness coefficient is not a characteristic factor affecting the dynamic responses of SFT under hydrodynamic loads.

The role of paved surfaces in the Urban Heat Island phenomenon: Assessment of fundamental thermal parameters and finite element analysis for UHI mitigation

Nowadays the environmental issues and the climatic change play fundamental roles in the design of urban spaces. Our cities are growing in size, many times only following immediate needs without a long-term vision. Consequently, the sustainable development has become not only an ethical but also a strategic need: we can no longer afford an uncontrolled urban expansion. One serious effect of the territory industrialisation process is the increase of urban air and surfaces temperatures compared to the outlying rural surroundings. This difference in temperature is what constitutes an urban heat island (UHI). The purpose of this study is to provide a clarification on the role of urban surfacing materials in the thermal dynamics of an urban space, resulting in useful indications and advices in mitigating UHI. With this aim, 4 coloured concrete bricks were tested, measuring their emissivity and building up their heat release curves using infrared thermography. Two emissivity evaluation procedures were carried out and subsequently put in comparison. Samples performances were assessed, and the influence of the colour on the thermal behaviour was investigated. In addition, some external pavements were analysed. Albedo and emissivity parameters were evaluated in order to understand their thermal behaviour in different conditions. Surfaces temperatures were recorded in a one-day measurements campaign. ENVI-met software was used to simulate how the tested materials would behave in two typical urban scenarios: a urban canyon and a urban heat basin. Improvements they can carry to the urban microclimate were investigated. Emissivities obtained for the bricks ranged between 0.92 and 0.97, suggesting a limited influence of the colour on this parameter. Nonetheless, white concrete brick showed the best thermal performance, whilst the black one the worst; red and yellow ones performed pretty identical intermediate trends. De facto, colours affected the overall thermal behaviour. Emissivity parameter was measured in the outdoor work, getting (as expected) high values for the asphalts. Albedo measurements, conducted with a sunshine pyranometer, proved the improving effect given by the yellow paint in terms of solar reflection, and the bad influence of haze on the measurement accuracy. ENVI-met simulations gave a demonstration on the effectiveness in thermal improving of some tested materials. In particular, results showed good performances for white bricks and granite in the heat basin scenario, and painted concrete and macadam in the urban canyon scenario. These materials can be considered valuable solutions in UHI mitigation.

Reduced variance in monozygous twins for multiple MR parameters : implications for disease studies and the genetic basis of brain structure

Twin studies offer the opportunity to determine the relative contribution of genes versus environment in traits of interest. Here, we investigate the extent to which variance in brain structure is reduced in monozygous twins with identical genetic make-up. We investigate whether using twins as compared to a control population reduces variability in a number of common magnetic resonance (MR) structural measures, and we investigate the location of areas under major genetic influences. This is fundamental to understanding the benefit of using twins in studies where structure is the phenotype of interest. Twenty-three pairs of healthy MZ twins were compared to matched control pairs. Volume, T2 and diffusion MR imaging were performed as well as spectroscopy (MRS). Images were compared using (i) global measures of standard deviation and effect size, (ii) voxel-based analysis of similarity and (iii) intra-pair correlation. Global measures indicated a consistent increase in structural similarity in twins. The voxel-based and correlation analyses indicated a widespread pattern of increased similarity in twin pairs, particularly in frontal and temporal regions. The areas of increased similarity were most widespread for the diffusion trace and least widespread for T2. MRS showed consistent reduction in metabolite variation that was significant in the temporal lobe N-acetylaspartate (NAA). This study has shown the distribution and magnitude of reduced variability in brain volume, diffusion, T2 and metabolites in twins. The data suggest that evaluation of twins discordant for disease is indeed a valid way to attribute genetic or environmental influences to observed abnormalities in patients since evidence is provided for the underlying assumption of decreased variability in twins.

Information provision and network performance represented by Macroscopic Fundamental Diagram

The existence of the Macroscopic Fundamental Diagram (MFD), which relates network space-mean density and flow, has been shown in urban networks under homogeneous traffic conditions. Since the MFD represents the area-wide network traffic performances, studies on perimeter control strategies and an area traffic state estimation utilizing the MFD concept has been reported. The key requirements for the well-defined MFD is the homogeneity of the area wide traffic condition, which is not universally expected in real world. For the practical application of the MFD concept, several researchers have identified the influencing factors for network homogeneity. However, they did not explicitly take drivers’ behaviour under real time information provision into account, which has a significant impact on the shape of the MFD. This research aims to demonstrate the impact of drivers’ route choice behaviour on network performance by employing the MFD as a measurement. A microscopic simulation is chosen as an experimental platform. By changing the ratio of en-route informed drivers and pre-trip informed drivers as well as by taking different route choice parameters, various scenarios are simulated in order to investigate how drivers’ adaptation to the traffic congestion influences the network performance and the MFD shape. This study confirmed and addressed the impact of information provision on the MFD shape and highlighted the significance of the route choice parameter setting as an influencing factor in the MFD analysis.

Student focus and prioritization of design parameters in first-year engineering design projects

BACKGROUND Research on engineering design is a core area of concern within engineering education and a fundamental understanding of how engineering students approach and undertake design is necessary in order to develop effective design models and pedagogies. Understanding the factors related to design experiences in education and how they affect student practice can help educators as well as designers to leverage these factors as part of the design process. PURPOSE This study investigated the design practices of first-year engineering students’ and their experiences with a first-year engineering course design project. The research questions that guided the investigation were: 1. From a student perspective, what design parameters or criteria are most important? 2. How does this perspective impact subsequent student design practice throughout the design process? DESIGN/METHOD The authors employed qualitative multi-case study methods (Miles & Huberman, 1994) in order to the answer the research questions. Participant teams were observed and video recorded during team design meetings in which they researched the background for the design problem, brainstormed and sketched possible solutions, as well as built prototypes and final models of their design solutions as part of a course design project. Analysis focused on explanation building (Yin, 2009) and utilized within-case and cross-case analysis (Miles & Huberman, 1994). RESULTS We found that students focused disproportionally on the functional parameter, i.e. the physical implementation of their solution, and the possible/applicable parameter, i.e. a possible and applicable solution that benefited the user, in comparison to other given parameters such as safety and innovativeness. In addition, we found that individual teams focused on the functional and possible/ applicable parameters in early design phases such as brainstorming/ ideation and sketching. When prompted to discuss these non-salient parameters (from the student perspective) in the final design report, student design teams often used a post-hoc justification to support how the final designs fit the parameters that they did not initially consider. CONCLUSIONS This study suggests is that student design teams become fixated on (and consequently prioritize) certain parameters they interpret as important because they feel these parameters were described more explicitly in terms how they were met and assessed. Students fail to consider other parameters, perceived to be less directly assessable, unless prompted to do so. Failure to consider other parameters in the early design phases subsequently affects their approach in design phases as well. Case studies examining students’ study strategies within three Australian Universities illustrate similarities with some student approaches to design.

Exploration of the fundamental equilibrium behaviour of calcium exchange with weak acid cation resins

This study evaluated the complexity of calcium ion exchange with sodium exchanged weak acid cation resin (DOW MAC-3). Exchange equilibria recorded for a range of different solution normalities revealed profiles which were represented by conventional “L” or “H” type isotherms at low values of equilibrium concentration (Ce) of calcium ions, plus a superimposed region of increasing calcium uptake was observed at high Ce values. The loading of calcium ions was determined to be ca. 53.5 to 58.7 g/kg of resin when modelling only the sorption curve created at low Ce values,which exhibited a well-defined plateau. The calculated calcium ion loading capacity for DOWMAC-3 resin appeared to correlate with the manufacturer's recommendation. The phenomenon of super equivalent ion exchange (SEIX) was observed when the “driving force” for the exchange process was increased in excess of 2.25 mmol calcium ions per gram of resin in the starting solution. This latter event was explained in terms of displacement of sodium ions from sodium hydroxide solution which remained in the resin bead following the initial conversion of the as supplied “H+” exchanged resin sites to the “Na+” version required for softening studies. Evidence for hydrolysis of a small fraction of the sites on the sodium exchanged resin surface was noted. The importance of carefully choosing experimental parameters was discussed especially in relation to application of the Langmuir–Vageler expression. This latter model which compared the ratio of the initial calcium ion concentration in solution to resin mass, versus final equilibrium loading of the calcium ions on the resin; was discovered to be an excellent means of identifying the progress of the calcium–sodium ion exchange process. Moreover, the Langmuir–Vageler model facilitated standardization of various calcium–sodium ion exchange experiments which allowed systematic experimental design.