The platinum group metal iridium is perhaps the most puzzling metal on Earth due to its property of being cleavable and a plastic solid simultaneously (1). This refractory face-centred cubic (fcc) metal (T_melt = 2446°C) serves as the structural material for applications under extremely hard conditions (2, 3) such as containers for fuel sources in radioisotope generators for deep space missions (4), or crucibles for growing oxide crystals for power lasers (5). Industrial technology for refining and processing iridium, based on traditional chemical refining methods (2, 6, 7), has been developed over the past 60 years (8–10). Based on these achievements, it has been shown that polycrystalline iridium exhibits limited plasticity due to intergranular fracture at room temperature, but its plasticity increases considerably under elevated temperatures (9–12). The segregation of non-metallic impurities on the grain boundaries was considered the cause of poor workability of polycrystalline iridium (12). This type of deformation behaviour agrees with empirical knowledge on deformation and fracture of metals (13, 14). On the other hand, single crystalline iridium behaved unusually: it cleaved under tension after considerable elongation (13, 15), but never failed under compression (16–18). At room temperature the fracture mode of iridium single crystals was attested as BTF (1, 15), while brittle intergranular fracture (BIF) was the fracture mode for polycrystalline iridium (11, 19). Analysis of the causes of cleavage in iridium has shown that it satisfies some empirical cleavage criteria (18–20) due to features in the elastic moduli in comparison with other fcc metals (18, 21). This fact leads to the conclusion that the inclination to cleavage is an intrinsic property of iridium, whereas impurities only reinforce it (18–20, 22, 23). However, the analysis of interatomic bonding in iridium has shown that BIF may also be considered as the intrinsic fracture mode of polycrystalline iridium (24).

The pyrometallurgical scheme for the refining of iridium, including: (a) oxidation induction melting; (b) electron beam melting; and (c) growing massive single crystalline workpieces by electron beam, became an alternative technology to manufacture ‘plastic’ iridium (25–27). Pyrometallurgical iridium demonstrated considerable plasticity prior to failure under tension in both the single crystalline state (28) and the polycrystalline state (29), while its elastic properties were the same as findings obtained earlier (30). It was confirmed that the intrinsic fracture mode of this ‘plastic’ iridium is BTF, while BIF is induced by harmful non-metallic impurities such as carbon and oxygen (31, 32). Indeed, the portion of BTF on the fracture surface of plastic iridium is considerably higher than BIF (33, 34). Deformation mechanisms and, hence, behaviour of pyrometallurgical iridium were the same as a normal fcc metal excepting the special fracture mode (35–38). Recent studies of deformation and fracture behaviour of iridium have shown that new participants achieved the technological level that allows ‘plastic’ iridium to be manufactured (39, 40), including iridium single crystals (41). Also, the old problem concerning the intrinsic fracture mode of polycrystalline iridium or the competition between BTF and BIF in iridium remains (42). Therefore, in the present paper, the deformation and fracture behaviour of iridium wires under tension at room temperature are considered in light of the discussion on this problem.

Pyrometallurgical iridium was used in this work. It was high purity metal, free of non-metallic contaminants such as carbon and oxygen. The refining procedure and, hence, impurities content were the same as the metal used in earlier work by our group: non-metallic elements <0.1 ppm; tungsten, molybdenum, niobium, iron, zirconium, copper, gadolinium, yttrium, gallium, nickel, palladium, zinc, magnesium, calcium –0.1–1 ppm; platinum, rhodium ~10 ppm (26, 27, 29, 38). Experience has shown that pyrometallurgical refining could be limited by the first and second procedures without loss of quality of the metal. Therefore, the operation of the growth of the massive single-crystalline iridium workpieces was not carried out in this work. The mechanical treatment of the pyrometallurgical iridium included: (a) forging the ingot into sheet at 1500–2000°C in air; and (b) rolling the sheet at ~800°C in air. The resulting metal could be processed like platinum. The cold drawing iridium wire, whose diameter varied from 2.7 mm to 0.5 mm, was prepared from this plastic metal. No long-term recrystallisation annealing of this wire was carried out because this procedure leads to embrittlement and failure of iridium wire due to BIF. Tensile testing was carried out with the help of an Autograph AG-X 50N tensile/compression tester (Shimadzu Corporation, Japan) (traverse rate of 1 mm min^–1) at room temperature. The lengths of working parts of iridium wire samples were 100 mm. The structure of the samples before and after testing was examined by conventional X-ray diffraction (XRD) technique on the D8 Advance diffractometer (Bruker Corporation, USA) with copper kα irradiation. Back surfaces of each sample before and after testing were documented on a light metallographic microscope. The fracture surfaces of samples were studied on the scanning electron microscope JSM-6390 (JEOL Ltd, Japan).

The first set of iridium samples consisted of 10 pieces taken from a commercial parcel of cold drawing thin iridium wire produced by UralInTech (Russia) having a diameter of 0.5 mm. The microstructure of this wire had a strongly deformed lamellar morphology, where the grains of the polycrystalline matrix practically disappeared (Figure 1). The main feature of this lamellar structure is the narrow highly elongated grains collected in a bunch like a rope. As a result, deformation tracks, such as slip bands or twin lamellae, could not be revealed on the surfaces of the samples after deformation. An XRD spectrum taken from the cold drawing iridium wire prior to testing is shown in Figure 2. There are two high narrow peaks ((200) and (220)) in the middle angles of the spectrum taken from the sample. No visible changes in the spectrum were revealed after tensile testing of the sample. It may be concluded that a stable drawing texture is formed in the iridium wire in comparison with an annealed polycrystalline sheet, which does not depend on further tensile deformation.

Fig. 1.

Fig. 2.

The second set of iridium samples consisted of 10 cold drawing wires with a diameter of 2.7 mm taken from the workpiece that was used to manufacture the thin plastic iridium wire. The Vickers microhardness of these samples in the undeformed state was about 7 GPa. The third set of iridium samples contained 10 cold drawing wires with a diameter of 2 mm. In contrast with the second set, these samples were annealed at 1000–1200°C for 20 min in a low vacuum and, as a result, their Vickers microhardness dropped up to 5 GPa. This operation is also used in the technological process for the manufacture of plastic iridium wire.

The stress-strain curves of the cold drawing iridium wires are shown in Figure 3 and some of their mechanical characteristics are collected in Table I. The back surfaces of the deformed samples are shown in Figure 4, while their fracture surfaces are given in Figure 5. It is clearly visible that the deformation behaviour of the samples from the first set (Figure 3, curve A) is similar to the behaviour of annealed copper wire (Figure 3, curve B). The long stage of plastic flow takes place after the short stage of material strengthening (Figure 3, curves A and B, respectively). Indeed, the total elongation of both materials may be estimated as considerable for a polycrystalline wire sample (30% for iridium and 43% for copper). In addition, there is a clearly visible advanced necking region on the back surfaces of the deformed samples (thinning of 20% for iridium and 55% for copper) (Figures 4(a) and 4(b) and Table I). However, in contrast with copper, iridium exhibits much higher yield stress and ultimate tensile strength (Table I). In spite of the features that are inherent to the ductile deformation behaviour, the fracture mode of the iridium samples from the first set is attested as BTF in the strongly deformed lamellar structure (Figure 5(a)). The same findings were obtained for cold drawing iridium wire with a diameter of 0.3 mm in the temperature range 20–800°C in (29).

Fig. 3.

Fig. 4.

Fig. 5.

The deformation behaviour of thick cold drawing iridium wire (Figure 3, curve C) can be attested as brittle: its stress-strain curve has an almost rectilinear profile, the yield stress is similar to the ultimate tensile strength, while the deformation prior to failure is small in comparison with the previous case. No necking was observed on the back surfaces of the deformed cold drawing thick iridium wires (Figure 4(c)). The fracture mode of the samples agrees with their brittle behaviour, it is BTF (Figure 5(b)). The short-term vacuum annealing of the thick cold drawing iridium wire at a temperature close to the point of recrystallisation of iridium leads to a change in mechanical behaviour from brittle to ductile. Indeed, the behaviour of the stress-strain curve becomes similar to annealed copper (Figure 3, curve D) when after a short stage of strengthening follows the plastic flow stage, while the yield stress and the tensile strength drop considerably (Table I). However, its deformation prior to failure is very small (Table I) for a plastic material and the neck is absent in the deformed samples (Figure 4(d)). The fracture mode does not change from brittle to ductile: it is attested as a mixture of BTF and BIF (Figure 5(c)).

It was shown that the deformation behaviour of cold drawing iridium wire under tension at room temperature depends on its structural state. Wire with grains of 50–100 μm behaves as a brittle material and exhibits BTF as the fracture mode. Vacuum annealing at 1000–1200°C causes a drop of yield stress of the iridium wire, but does not lead to significant increase of plasticity, while its fracture mode continues to be brittle. On the other hand, thin cold drawing iridium wire having a lamellar structure demonstrates considerable elongation prior to failure and clearly visible necking, despite BTF as its fracture mode. This finding gives the basis for the conclusion that such lamellar structure is the correct morphology for plastic polycrystalline iridium. It is important to note that this morphology is formed in the iridium workpiece under the cold drawing process, while a few short terms annealing at 1000–1200°C are included in the procedure after some rolling passes (29).

Earlier, it was shown that BIF is the impurities induced fracture mode of high purity polycrystalline iridium (31, 32). Indeed such non-metallic elements as carbon and oxygen contained in a low vacuum (10^–2 MPa) induce grain boundaries brittleness, but the kinetics of the process depends on the working temperature and its duration (31). For example, under annealing of 20 min at 1200°C, the portion of BIF on the fracture surface is considerably less than the portion of BTF, while after 24 h annealing BIF covers the whole fracture surface. It means that the regime of annealing of the cold drawing iridium wire used in this work is optimal because the hardness and the yield stress of the iridium workpiece are decreased, but the cohesion strength of grain boundaries does not drop.

The low plasticity of the thick cold drawing iridium wire, which was strongly hardened during preliminary processing, may be explained by the supposition that its resource of plasticity is finally exhausted under tension as it takes place in iridium single crystals under the same experimental conditions (26, 37). As a result, the cleavage crack can appear on any dangerous macroscopic surface defect and, hence, such wire is prone to separation by the brittle route without necking. Following this logic, the thin cold drawing iridium wire should behave the same way; however, it exhibits ductile mechanical behaviour, except its fracture mode. One cause of this puzzling effect may be the special configuration of the defect structure of iridium, whose feature on the microscopic level is a lamellar morphology. Indeed, high purity polycrystalline iridium is able to undergo severe deformation under high-pressure torsion at room temperature when the nanocrystalline structure is forming in the material (38). It is puzzling, but in this case, the surface defects play the role of the initiation of cleavage in the neck region only (29). Indeed, iridium meets some empirical cleavage criteria (18–20). However, this effect should be considered as an artefact because in contrast with other cleavable solids iridium is a plastic material in both the single crystalline and polycrystalline states and its inclination to cleavage depends on the structural state.

The lamellar structure that forms in iridium wire during the cold drawing process provides the excellent mechanical properties of polycrystalline iridium under tension: it behaves like a ductile fcc-metal excepting the brittle fracture mode. It was shown that the inclination of iridium to cleavage depends on its structural state.

The lattice dynamical study of metallic crystals is an interesting field of research. Platinum group metals are highly valuable transition metals which have many useful properties. The electronic structure of the platinum metals is of impressive theoretical and practical importance. Dependable thermodynamic information is expected to give the crude material from which lattice dynamics, electronic conveyances and energy states can be deduced by genuine understudies of the solid state. In the present manuscript the author has used VTBFSM for theoretical calculation. The pioneering work of Kellerman (1) for ionic interactions in the alkali halides has attracted considerable attention theoretically as well as experimentally. Löwdin’s (2, 3) and Lundqvist’s (4–6) theory for ionic solids leads to the first important term as many body force which includes the three-body component. The Heitler-London theory and the free-electron approximations will employ the combined effects of VWI and TBI in RSM (7). The effects of VWI and TBI in the framework of ion polarisable RSM (IPRSM) are effective up to the second neighbour with short-range, VWI and TBI interaction. The experimental investigation for the phonon dispersion curve of platinum has been done with coherent inelastic neutron scattering, variation in Debye temperature and Raman spectra (8–10). The elastic constants and dielectric constants (11), physical and natural properties of platinum have been elucidated by expedient of theoretical models (12–16), which has also successfully described their interesting properties. After the failure of the Kellerman rigid-ion model (RIM) then Karo and Hardy (17) used a deformation dipole model, Woods et al. (7) and Dick and Overhauser (18) used a RSM to report lattice properties of alkali halides. The other most prominent model was also proposed by some researchers, among them Schröder’s (19) breathing shell model, Basu and Sengupta’s (20) deformable shell model and the three-body force shell model of Verma and Singh (21–23) and Singh et al. (24) for such halides. In consideration of the effect of VWI, reported by Upadhyaya et al. (25), excellent results have been procured between experiment and theory for ionic halides and semiconductors. The betterment of the present model VTBFSM over others can be realised from the fact that in the present model relatively fewer numbers of parameters have been able to interpret numerous and largely divergent physical properties of materials. This has to motivate the author to incorporate this model in the present study.

In the present paper the parameters including (C₁₁, C₁₂ and C₄₄), polarisabilities (α₁, α₂), and lattice constant by (26) have been theoretically calculated for platinum and given in Table I. By solving Equations (i) and (v) we can obtain the phonon spectra in the first Brillouin zone divided into evenly spaced miniature cells. The theoretical results were obtained by VTBFSM. We have used the computed vibration spectra to study the specific heat and infrared (IR)/Raman spectra in the present paper. The DOS have been obtained by computing the DOS of the frequencies from the knowledge of lattice vibrational frequency spectra. The values of frequencies are compatible with theoretical and experimental peaks and Cauchy-discrepancy for lattice dynamics of platinum.

In the Brillouin zone surface the calculated phonon dispersion curves for platinum are shown in Figure 1 by using first principles along two high symmetry directions (qqq) Г-X-Г. The parallel vibrational modes show real dispersion with a maximum cleave. The upper branch consists of longitudinal modes, while the lower one is the shear‐horizontal mode, along both the Г-X-Г directions. We find that the surface modes for clean platinum (qqq) undergo a few changes in L-T modes on the clean surface, near the zone boundaries and along the X-direction, are replaced only in the dispersion curves. This is because the zone boundaries are moderate and the next two surface modes are strengthened. The experimental reported results for dispersion relation are shown in Figure 1(b) (27). On comparing with the experimental result i.e. Figure 1(a) with Figure 1(b) good agreement can be observed.

Fig. 1.

The DOS vs. frequency curve for platinum theoretically calculated in the energy range from approximately –7.0 eV to 0.5 eV in bulk is shown as a solid line in Figure 2. The bulk DOS exhibits three main peaks that are accurately produced. The small observed differences are related to the shape of the main peaks. The differences between the calculated and observed values were found and discussed in Figure 2. There are very important features obtained from the DOS vs. frequency curve. The information about the surface and resonance states was found through these differences. Below the Fermi level E_F, resonance-states are expected to be obtained, mainly because these energies represent the continuum and few energy gaps exist at these energy values. The experimental reported DOS curve (28) may be compared with the present model i.e. Figure 2(a). Sharp peaks can be seen in Figure 2(a) while in Figure 2(b) the distortion in peaks can be seen which justifies the superiority of the present theoretical study.

Fig. 2.

The specific heat and Debye temperature Θ_D have been calculated as a function of temperature T from the lattice frequency spectra as shown in Figure 3. Debye temperature Θ_D is calculated from different frequency values. The specific heat value of platinum has been measured at extended temperature (0 K to 300 K). The calculated result is in reasonable agreement at moderate temperature and at very low temperature. The comparison can be seen through experimental results (27).

Fig. 3.

The varying investigated properties are distinctly shown in the present study by successful use of VTBFSM, which has provided the complete lattice description of platinum. It agrees well with the test of anisotropy factor A = 2C₄₄/(C₁₁–C₁₂) > unity and towards the high frequency end the higher peak is found. The determined model parameters in Table I were used to solve the secular equation for specified values of wave vectors in the first Brillouin zone, which is split up in an evenly spaced sample of (1000) wave vectors by Kellerman (1). From the symmetry, these 1000 points are reduced to 48 non-equivalent points at which the vibration frequencies have been obtained by solving the secular determinant. Debye temperature variations at different temperatures by Macfarlane et al. (26) and colossal dielectric constant (CDC) curves for platinum crystals have been computed by using VTBFSM model. By using the sampling technique the corresponding values of Θ_D have been compared with available experimental data (27–29) and the curve for Θ_D vs. absolute temperature (T) was plotted as shown in Figure 1 for platinum. In this temperature range one should take into account the temperature dependence of the frequency spectrum, this requires, however, knowledge of the phonon frequencies at more than one temperature. The variations of Θ_D with specific heats have been used to compute phonon frequencies in the first Brillouin zone and data points for different points were reported in Table II. The effect of anharmonicity is excluded so slight discrepancies between theoretical and experimental results at higher temperatures are seen, though the agreement is almost better with VTBFSM. The calculated (Θ_D–T) curve for platinum has given excellent agreement with the experimental values (8–10). The DOS curve is given in Figure 2 and data points are shown in Table III. The two-phonon Raman spectra are sensitised to the high-frequency side while the specific heats are sensitive to its lower side which is stated the reasonableness of VTBFSM for all wavelength range.

The exploration of model parameters, Debye temperature and DOS are reported by use of the present model VTBFSM for platinum. The conformity with experimental data (8–10) of our theoretical peak is very good for platinum. A successful explanation of spectra has provided the next best test of any model for their higher range of frequency. Small deviations were observed at the higher temperature side due to harmonic approximation in the Debye curve. Better agreement has been obtained with the available experimental data (16–20) and theoretical results. The motivation of this work is the availability of experimental (29) and theoretical (30, 31) work on platinum. Therefore, it may be concluded that the incorporation of VWI is requisite for the absolute interpretation of the phonon dynamical behaviour of platinum. Many researchers have also successfully reported theoretical results for alkali halides (32–42) by use of the present model. Hence, the present model may be understood to provide a powerful and simple approach for a comprehensive study of the harmonic as well as anharmonic elastic properties of the crystals under consideration. The only constraint of VTBFSM is the knowledge of certain experimental parameters needed that can be used as input data.

Platinum and its alloys are very important in industries such as the chemical and glass industries. Some of their main applications are as follows: a functional structural material in the aerospace industry; a catalyst in the nitric acid preparation industry; nozzles for preparing glass fibres; preparing crucibles and utensils that require special properties for use in chemical laboratories. Platinum-rhodium alloys with low rhodium content can also be used as brazing filler metals in metal welding. Although expensive, their high temperature stability and chemical inertia cannot be replaced by other materials (1, 2).

However, the strength and creep resistance of pure platinum would significantly reduce at high temperature because of sharp grain growth. Therefore, it is crucial to find a way to improve the high temperature creep resistance of platinum alloys (3). Many methods of strengthening platinum materials are known. Among these different methods, the best methods are solid solution strengthening and dispersion strengthening. The addition of rhodium has been found to have the best solid solution strengthening effect in high temperature use of platinum. With increasing rhodium content in platinum-rhodium alloys, the normal temperature strength, high temperature endurance strength, creep rupture life and creep activation energy of the alloy increases greatly, so platinum-rhodium alloys are widely used (4, 5). But the high-temperature mechanical properties of platinum-rhodium alloys fail to satisfy the requirement of industrial production with worsening service conditions. Therefore, dispersion-strengthened platinum-rhodium alloys were subsequently developed in Johnson Matthey, UK (6, 7), Engelhard Corporation, USA (8) and Heraeus, Germany (9) from the 1980s to 1990s. They were prepared by adding zirconium, yttrium or scandium oxide particles into the platinum-rhodium alloy under certain process conditions. At present, dispersion-strengthened platinum alloys such as zirconia grain stabilised (ZGS) platinum and oxide dispersion strengthened (ODS) platinum (10, 11), in which Y₂O₃ and ZrO₂ are two commonly used reinforcement particles, are used in industrial applications. According to the experimental results of Hu et al. (12), as the zirconium concentration increases, the platinum-rhodium alloy’s yield stress (0.2% offset) increases significantly, while the elongation decreases slightly. The work hardening rate of particle-reinforced samples increases with the increase of the volume concentration of dispersed particles, which is a typical behaviour of particle dispersion enhancement. In addition, based on a reformulation of the Orowan stress for particle strengthening and by superposing this stress to the matrix stress, a calculated flow stress is in good accord with the experimental value. Though the strength of these particle strengthened platinum alloys can be significantly improved, the further enhancement of the strength is difficult due to the lack of mechanism research and empirical development in the past (12, 13).

Zirconium and yttrium have good plasticity and corrosion resistance. Diffusion strengthening improves the metal strength through adding a second phase or multiple phases and the essence is the interaction of the second phase and the dislocation (13). Nevertheless, the two reinforcement particles, i.e. Y₂O₃ and ZrO₂, are usually thought be to the same as strengthening particles based on Orowan’s equation where the strength increment from the non-deformable dispersed particles is positively correlated with the particle spacing (14, 15). When making samples, we tried to add the yttrium content to 0.1%, and found that the ingot will crack during rolling, so we speculate that different deformation behaviours will have a huge impact on alloy strengthening.

In this study, two kinds of platinum alloys strengthened by Y₂O₃ and ZrO₂, respectively, were prepared and characterised by TEM. A number of differences in deformation behaviour of the two particles during processing were found. These findings are expected to lead to new insights into developing dispersion strengthened high strength platinum alloys.

Nominal composition of the investigated alloys is listed in Table I. The preparation processes have been described in previous research (13) and can be briefly summarised as follows: Pt-20 wt% Rh-0.015 wt% Y without and with 0.1 wt% Zr were smelted in a vacuum induction furnace at 1800–2000°C under argon atmosphere, then cast into a water-cooled copper mould to obtain ingots. The ingots were hot forged to 10 mm plates which were sheared into pieces, followed by mechanical milling to fine powder. The size distribution of the powder was measured using an LS-POP(6) laser particle size analyser (OMEC, China). 97% of the particles were distributed between 5 μm and 60 μm with an average particle size of 25 μm. The powder was sintered and exposed in air to internally oxidise at 1150°C for 4 h. The 30 mm sheets were obtained by hot forging at 1400°C, then rolled to 1 mm sheets at room temperature followed by annealing at 1150°C for 30 min. To prepare the TEM samples, the sheets from rolling-normal direction were mechanically ground to 50–70 μm, followed by argon ion milling at 5 kV until a hole appeared on the centre of the foil. TEM was used to examine the microstructure at 200 kV (JEM-2100 electron microscope (JEOL Ltd, Japan)) and at 300 kV (JEM-3000F field emission electron microscope (JEOL Ltd)). JEM-2100 was used to detect topography of the particles and energy-dispersive X-ray spectroscopy (EDS) was conducted to determine the components; JEM-3000F was used for high-resolution transmission electron microscopy (HR-TEM) observation to determine the structure of the particles. In this paper, Pt-20Rh-0.015Y is referred to as Alloy 1 while Pt-20Rh-0.015Y-0.1Zr is referred to as Alloy 2.

3.1 Thermomechanical Analysis

During preparation processes, especially at high temperature under oxidising atmosphere, the metals in the alloys may be oxidised and the possible oxides are PtO₂, Rh₂O₃, ZrO₂ and Y₂O₃. Their reaction equations are as follows (Equations (i)–(vi):

(i)

(ii)

(iii)

(iv)

(v)

(vi)

According to the Gibbs free energy theorem, a reaction can only occur when the Gibbs free energy is negative and the more negative the Gibbs free energy of a reaction, the more easily the reaction occurs. When the Gibbs free energy is greater than zero, the reaction cannot happen. Figure 1 is the oxidation tendency of platinum, rhodium, zirconium and yttrium, which indicates:

• ΔG of all the reactions increases as temperature increases

• Within the temperature range we calculated, ΔG of Y₂O₃·ZrO₂, Y₂O₃ and ZrO₂ are much smaller than those of Rh₂O₃, Rh₂O and RhO, which means the formation of Y₂O₃·ZrO₂, Y₂O₃ and ZrO₂ are much easier during processing

• ΔG of RhO, Rh₂O and Rh₂O₃ are very close to ΔG = 0 and even greater than 0 at the internal oxidation temperature (1423 K), thus the formation of RhO, Rh₂O and Rh₂O₃ are difficult and can be ignored.

Fig. 1.

The oxidation tendency of platinum, rhodium, zirconium and yttrium

For platinum, when the temperature rises from room temperature, platinum will react with oxygen and form a PtO₂ film on the metal surface. The thickness of PtO₂ would grow with the rise of temperature. When the temperature reaches about 500°C, this process would stop. If the temperature continues to rise, the PtO₂ film will be gradually vaporised. Meanwhile, the higher the temperature, the faster the gasification rate. Samples in this experiment were about 1200°C, the PtO₂ film formed by oxidation had been basically vaporised. Therefore, PtO₂ is not present in the samples.

Overall, according to the thermomechanical analysis, Y₂O₃, ZrO₂ and Y₂O₃·ZrO₂ are easily formed in the platinum-rhodium-(zirconium)-yttrium alloys. Platinum and rhodium are present as almost pure metals.

3.2 Microstructure and Energy-Dispersive X-ray Spectroscopy Analysis of Platinum-Rhodium-(Zirconium)-Yttrium

3.3 Analysis of Deformation Behaviour Between Zirconia and Yttria Particles

In platinum-rhodium-(zirconium)-yttrium alloys, yttrium and zirconium are easily oxidised into Y₂O₃, ZrO₂ and Y₂O₃·ZrO₂ and form corresponding oxides while platinum and rhodium are basically present as pure metals. ZrO₂ and Y₂O₃ particles have been observed in platinum-rhodium-zirconium-yttrium and platinum-rhodium-yttrium, respectively, and verified by EDS analysis and HR-TEM observations. The deformation behaviour of these two oxides is quite different during processing, though they have the same deformation history. The ZrO₂ particles maintained their spherical shape without any visible deformation, while the Y₂O₃ particles were compressed along the normal direction with two cracks forming on two sides of the particles. Insufficient hardness of Y₂O₃ and relatively lower interface strength between Y₂O₃ particles and matrix were supposed to be responsible for deformation of Y₂O₃ during processing.

But it is not for the pgms’ aesthetic or investment value that this collection of papers has been collated, rather to highlight the fascinating science of these incredible metals and their wide range of industrial uses. This special edition of the Johnson Matthey Technology Review will examine both the fundamental properties of these metals and their use in a variety of applications and fields.

The pgms are rare elements, occurring in economic quantities in only a few geographical locations. Demand is generally price inelastic, meaning that consumption volumes are often relatively insensitive to underlying metal prices (1). Importantly, the pgms are widely recovered and recycled; for example, through the recovery of catalytic convertors from end of life vehicles or through a closed-loop system where the catalyst that is installed in a chemical plant is recovered, sent for refining and ultimately reused. Sustainability not only of the metals themselves but also with regard to their end uses is why the pgms are so important, as described in two of the articles – European projects BIORECOVER and PLATIRUS.

The use of platinum, palladium and rhodium is dominated by the automotive sector where for several decades they have been a vital component in emission control catalysts. These three metals have been fundamental in removing carbon monoxide, hydrocarbons and nitrogen oxides from gasoline and diesel engine exhausts to dramatically improve air quality across the world, as detailed in several publications by one of our authors, Martyn Twigg, who in his long career was at the forefront of autocatalyst development (2–4).

In this special edition, Twigg and Emeritus Reader John Burgess from the University of Leicester, UK, have written a two-part commemoration of the late Professor Bob Gillard, discussing his remarkable life, work and contribution to the understanding of transition metal chemistry, particularly the chemistry of rhodium and other platinum group metal complexes.

The use of pgms by the chemical industry is of vital importance to a huge range of bulk and speciality products. One example of this is the oxidation of ammonia to produce nitric acid which has used platinum and rhodium in catalyst gauze for over 100 years (5). The latest work in this field will be discussed by Ashcroft in this special edition. Interestingly, the use of pgm for chemical catalysts has remained one of the more robust areas of demand during the coronavirus disease (COVID-19) pandemic. Nitric acid is used to manufacture both fertilisers for global crop production and explosives for the mining industry, which are essential for the supply of metals such as nickel and platinum and will be central to the future electrification of the automotive fleet.

The minor pgms ruthenium, iridium and osmium can often appear somewhat neglected despite their use in a huge number of applications. Iridium is prized for its high melting point which makes it ideal for use in crucibles to produce high purity metal oxide single crystals, used in medical scanners, light-emitting diode production and surface acoustic wave filters, amongst others. The behaviour and properties of iridium are the subject of two papers in this edition. Osmium is perhaps the least known of the metals given its more limited applications. However, Arblaster has remedied that with a paper discussing the thermodynamic properties of the densest element in the Periodic Table.

The pgms are among the most invaluable elements discovered. To sum up all their useful properties in one key attribute is that they enable the world to be a more sustainable place. Globally we are starting to undergo a monumental change in energy use and production, away from reliance on fossil fuels towards a cleaner, greener, more sustainable model (6). The move to hydrogen as an energy source is vital in the move to a net zero economy, a key example of which is the fuel cell vehicle. Johnson Matthey actually provided the platinum to William Grove when he demonstrated the first fuel cell in 1839 (7). Aside from the use of pgm in the catalyst of the vehicle itself, the production of hydrogen of suitable purity makes use of one of the key properties of palladium. Palladium has an intrinsic selectivity for hydrogen, which makes it an ideal choice for purification membrane technology. In this issue, Faizal et al. discuss the use of palladium in this vital application for the growing hydrogen economy.

The pgms: six of the rarest elements in the Periodic Table that have and continue to change the world around us. Metals that are driving forward sustainable technology and the move towards net zero, metals that will help drive the clean energy revolution, provide food to billions and facilitate communication and data sharing and storage across the globe to enable a more connected society.

Hydrogen purification by palladium-based membrane is one of the most well-known techniques for supplying high purity hydrogen to low temperature operated (1) PEFC in various electronic devices such as tablets, laptop computers and small vehicles. The compact methanol steam reformer that consists of a catalytic burner, reformer and hydrogen purification device in a single package was developed almost two decades ago (2). Over the years, various integrated systems, operating conditions and geometries have been investigated to obtain the optimum operating conditions for reliable performance (3–9). As a result, the compact reformer has several advantages (i.e. simple and compact) compared to complex systems with separated units (10).

Due to the difficulty and high risk of exposure to accidents, the transportation and storage of gaseous hydrogen are undesirable. Alternatively, the utilisation of alcohols is more practical due to their existence in a liquid form at ambient conditions. Methanol for instance has a relatively high hydrogen:carbon ratio and moderate reaction temperature compared to other alcohols (10, 11). Based on the two step equations of methanol steam reforming, the reaction between vaporised methanol and steam produces hydrogen and carbon dioxide along with carbon monoxide. However, the concentration of carbon monoxide in the electrode of PEFC must be equal to or less than 10 ppm (12). Otherwise, the carbon monoxide could deteriorate the electrode performance by reducing the active surface area for reaction and lowering the partial pressure of hydrogen (13–15).

Hydrogen purification by palladium based membrane is preferable rather than selective carbon monoxide methanation and selective carbon monoxide oxidation (16), in which very high purity of hydrogen and very high permeation flux can be obtained (17–19). PSA is an alternative technique to produce very high purity hydrogen (20). However, the high costs of installing PSA is not economical for small size (or small capacity) applications (21). In addition to the well-known inhibitive carbon monoxide produced from the aforementioned methanol steam reforming, carbon dioxide and excessive methanol from the same reaction (22), hydrogen sulfide (23, 24) and trace amounts of ammonia (20, 25) from coal gasification process, dehydrogenated methanol and ethanol (26) also affect adversely the performance of palladium membranes through its inhibitive mechanism.

Alloying palladium with other metals such as silver and copper is necessary during membrane fabrication to prevent embrittlement when the membrane is used under hydrogen atmosphere and below 573 K and 2 MPa (10). It was found that the maximum amount of permeated hydrogen is obtained when the silver content is 23% (27). In addition, the palladium/silver membrane shows better performance compared to the palladium/copper membrane from the viewpoint of hydrogen permeability. Consequently, there is growing interest in the palladium/silver membrane. In addition to these two types of alloys, the palladium-yttrium membrane has also been previously examined due to its superior hydrogen permeability. However, this type of membrane is not commercialised due to the expensive processes required to convert the palladium-yttrium alloy into the functional separation membrane (28).

Hydrogen permeation through palladium based membranes is based on the solution-diffusion mechanism (29). When a membrane with sufficient thickness is operated at sufficiently high temperature, the diffusion of hydrogen atoms through the metallic lattice becomes dominant, thus permeation flux can be estimated accurately by using Sieverts’ Law (30, 31) that is quantified in Fick’s First Law as follows, Equation (i):

(i)

where f is the hydrogen permeation mole flux, q is the hydrogen permeance coefficient, d is the membrane thickness, P_H2,1 is the hydrogen partial pressure at membrane surface of upstream (or retentate) side and P_H2,2 is the hydrogen partial pressure at membrane surface of downstream (or permeate) side. The Sieverts’ equation as shown by Equation (i) states that hydrogen permeation is governed by the difference in the square root of the hydrogen partial pressure between the upstream and downstream side.

Membrane temperature (22, 32) and membrane thickness (33–35) are among the important parameters that determine compliance with Sieverts’ Law. When the temperature of the membrane is sufficiently high, the adsorption and dissociation of hydrogen atoms at the membrane surface are very fast. Therefore, the diffusion of hydrogen atoms through the metallic lattice becomes a controlling step for permeation. In this case, the hydrogen permeation flux is found to be linear with respect to the difference in the square root of hydrogen partial pressures between the upstream and downstream side. For the case of the palladium/copper membrane, Ma found that Sieverts’ Law is valid only when the membrane temperature is set above 573 K (32), whereas for the palladium/silver membrane, the law can be applied even if the temperature is lower than 500 K (22).

The different findings by several groups of researchers had proven that there is no exact value of thickness that can be set as a limit for compliance with Sieverts’ Law. Ward and Dao (33) and Federico et al. (34) found that the membrane thickness should be higher than 10 μm in order to apply the Sieverts’ equation (Equation (i)). Other research groups discovered that the Sieverts’ Law is still valid even though the membrane thickness is below 10 μm (22, 35). These contrary findings are supposed to be caused by difficulty in quantifying various uncontrolled factors such as surface processes (36), surface poisoning (37) and grain boundaries (38).

For the case of pure hydrogen, hydrogen permeation is found to follow the correlation of Sieverts’ equation regardless of feed flow rate. However, for mixtures, when the feed flow rate of hydrogen becomes sufficiently high, the hydrogen permeation ratio (fraction of fed hydrogen that permeates membrane) (39) becomes low. Therefore, the hydrogen permeation flux can be predicted accurately by Sieverts’ equation (Equation (i)). Further, the term P_H2,1 in Equation (i) can be predicted from the bulk value of hydrogen mole fraction at the upstream side, which indicates that hydrogen partial pressures at the membrane surface and the bulk flow are uniform, as illustrated by Line 1 in Figure 1.

Fig. 1.

When a mixture of hydrogen with relatively low feed flow rate (or high permeation ratio) is used, the direct substitution of inlet hydrogen partial pressure (P_H2,in) value into the Sieverts’ equation causes an overestimation of P_H2,1 from the actual permeation flux. This indicates there is a nonuniformity of hydrogen mole fraction in the boundary layer near to membrane surface, as illustrated by Line 2 in Figure 1. In this case, several research groups (39–41) mentioned that the hydrogen permeation flux could start to affect the hydrogen concentration at the membrane surface, thus could trigger the phenomenon of concentration polarisation.

The concentration polarisation phenomenon causes the accumulation of the less permeable species and the depletion of the more permeable species in the boundary layer adjacent to the membrane, thus generating a concentration gradient in the boundary layer (42). Therefore, in such situation, an additional elementary step is essential for the solution-diffusion mechanism of the membrane. This involves the transportation of molecular hydrogen from (to) the bulk gas phase to (from) the gas layer adjacent to the surface at the upstream (downstream) side (33). As a consequence, if the inlet hydrogen partial pressure is directly substituted into the Sieverts’ equation (Equation (i)), the hydrogen partial pressure at the membrane surface of upstream side is overestimated, which causes a significant deviation from the actual permeation flux. Chen et al. observed that such deviation implies the level of concentration polarisation for a palladium based membrane (41). Based on the analytical study for multicomponent hydrogen mixtures, Caravella et al. confirmed that such deviation is caused by the effect of multicomponent external mass transfer (such as concentration polarisation) in addition to non-ideal diffusion through the membrane (43).

Technological advances in membrane materials, modification and fabrication (42) since the end of the 20th century have stimulated the fabrication of very thin membranes in order to substantially improve the permeation performance. Therefore, the phenomenon of concentration polarisation could not be avoided due to the use of membranes with minimal thickness. However, some researchers (44) have recommended installation of baffles in the membrane reactor to decrease the polarisation effect. For palladium based membranes, concentration polarisation has been extensively investigated in the past decade (40) although concentration polarisation had been investigated in the 1990s for separation of a gas-vapour mixture (45). Therefore, significant research interest in the theoretical understanding of the phenomenon has resulted in numerous methods for estimating hydrogen flux for such conditions.

Therefore, a comprehensive review of the transport phenomena for palladium based membranes is performed, particularly on concentration polarisation. In addition to the background of the scenario related to palladium based membranes already highlighted, current information on various parametric studies and theoretical approaches for predicting hydrogen permeation flux under the influence of concentration polarisation are covered. Therefore, this review presents critical scientific knowledge and current research on concentration polarisation. The coverage of the present review is significantly different from the published works of Adhikari and Fernando (46), Rei (47), Gallucci et al. (21), Al-Mufachi et al. (28), Li et al. (48), Conde et al. (49) and Peters and Caravella (50). Adhikari and Fernando comprehensively reviewed the classification of hydrogen purification membranes, along with the advantages and disadvantages of each type of membrane (46). The study emphasised the superior quality of palladium based membranes in producing ultra-high purity hydrogen due to very high selectivity (46). Similarly, Rei (47) reviewed the advances in permeation through palladium based membranes for the case of a hydrogen mixture based on case studies in Taiwan. Several discoveries on new phenomena of hydrogen permeation such as perturbation of hydrogen permeation due to palladium lattice expansion and hydrogen spillover in the membrane reactor have been described (47). Gallucci et al. also highlighted the problem of concentration polarisation in the membrane reactor, although this was not the main topic of the study (21). The authors mainly focused on the route of commercialisation and application of various types of membranes (21). The review of several palladium alloy membranes was presented by Al-Mufachi et al. (28). The paper highlighted the advantages and disadvantages of each type of membrane in terms of hydrogen permeability, tensile strength and fabrication costs (28). Subsequently, Li et al. reviewed the thermal and chemical stability of palladium based membranes which are considered the two most critical issues for the commercialisation of the membranes (48). In 2017, a review on palladium based membranes was performed by Conde et al. (49). The paper presented a review of the alloying elements for palladium based membranes and their effect on the membrane properties. Finally, a most recent overview by Peters and Caravella (50) has covered the scopes of manufacturing process of palladium membranes, membrane materials, membrane modules and reactor design, as well as applications of palladium based membranes.

Based on these published review articles, it can be said that the subject of transport phenomena, particularly on the concentration polarisation, is the novelty for the present review. This paper presents coverage of recent research features and technological advances on the transport phenomena of palladium based membranes. It also presents the various prediction methods applicable to hydrogen permeation under the influence of concentration polarisation that could serve as a future reference for researchers and industrial practitioners.

In this section, a review of case studies on concentration polarisation is presented. The various studies and types of membrane used for each study are presented in Table I, whereas the parameters considered for studying such phenomena are listed in Table II. Based on Table I, it is evident that most common membranes are tubular, as illustrated by the various configurations in Figures 2(a)–2(c). The studies by Faizal et al. (55, 60) examined the phenomenon of concentration polarisation for flat sheet type membranes, which are widely used in compact reformers for hydrogen production (4–5, 65–66). The common configuration for a flat sheet type membrane is illustrated by Figure 2(d). It is interesting to note that various configurations and fluid flow conditions have been considered for studying concentration polarisation. Based on Table II, it is evident that the most common varied parameters for concentration polarisation are operating pressure, hydrogen mixture composition, feed flow rate and Reynolds number as well as membrane temperature. However, several studies have focused on geometry improvement to suppress concentration polarisation, as elaborated in this section.

Fig. 2.

In the early 21st century, Hou and Hughes were among the earliest groups who observed the concentration polarisation during an experiment involving hydrogen permeation with a palladium based membrane (67). The authors confirmed the existence of the concentration polarisation phenomenon during their experiment for a membrane with a thickness of 5 μm to 6 μm. However, the effect was not severe due to the relatively high feed gas velocity, which was a 5% decrease in hydrogen concentration for the various mixing ratios of the binary mixture of hydrogen and nitrogen (67).

Zhang et al. (51) were one of the pioneer groups who comprehensively investigated the concentration polarisation phenomenon specifically for palladium based membranes. The effect of various parameters such as pressure, temperature, feed gas flow rate and permeability was investigated experimentally. Also, the parameters were interpreted through mathematical modelling particularly for tubular membranes with porous ceramic supports. The authors found that when the feed gas flow rate is increased, the concentration polarisation is weakened, resulting in higher hydrogen permeation. For instance, for the case of membrane temperature of 723 K, when the feed flow rate was 5 ml s⁻¹ (equivalent to 5 × 10⁻⁶ m³ s⁻¹), the concentration polarisation degree for hydrogen (ratio of hydrogen permeation flux with concentration polarisation to hydrogen permeation flux without concentration) was around 0.54. However, when the feed flow rate was increased to around 14 ml s⁻¹ (equivalent to 14 × 10⁻⁶ m³ s⁻¹), the concentration polarisation degree for hydrogen became 1, that is no effect of concentration polarisation on hydrogen permeation flux was found. Furthermore, the authors reported that the observed phenomena are mainly due to the higher removal rate of accumulated nitrogen in the boundary layer at higher feed flow rates (51). However, an increase in pressure at the retentate or upstream side (at constant permeated pressure) increases concentration polarisation, as clearly described by the mathematical modelling developed in the study. Based on their study, at constant temperature of 723 K, for the case of pressure of 2 atm (equivalent to 202.6 kPa), the concentration polarisation degree for hydrogen already reached a value of 1 (no effect of concentration polarisation) when the feed flow rate was around 14 ml s⁻¹ (equivalent to 14 × 10⁻⁶ m³ s⁻¹). However, for the case of higher pressure of 4 atm (equivalent to 405.2 kPa), the concentration polarisation degree for hydrogen still not reached value of 1 even though feed flow rate was increased to 32 ml s⁻¹ (equivalent to 32 × 10⁻⁶ m³ s⁻¹). Based on the model, the observed trend is related to the proportional relation between the mass transfer coefficient of the retentate side and the diffusion coefficient, which is reciprocal to operating pressure (51). Therefore, the findings of Zhang et al. corroborated the previous findings by Morguez and Sanchez (68), which reported that the effect of selectivity is less significant compared to feed gas flow rate, pressure and permeability (68). The authors also observed that the temperature range used in their experiment did not trigger the concentration polarisation phenomenon. However, the authors did not rule out the possibility of concentration polarisation when the hydrogen permeation rate is enhanced due to the increase in temperature (51).

Pizzi et al. performed an experimental study for ultra-thin (~2.5 μm thickness) palladium/silver membranes deposited on ceramic supports. The authors observed that pronounced concentration polarisation occurred regardless of the composition mixture (52). As a result, the phenomenon was evident despite the concentration of nitrogen in a binary mixture of H₂:N₂ being relatively very low (12 vol%) (52). For this case, it was found that when Sieverts’ driving force is set to 0.8 bar^0.5 (equivalent to 253 Pa^0.5), the hydrogen permeate flux is only 0.26 mol s⁻¹ m⁻², that is significantly lower if compared to the permeate flux obtained when the concentration polarisation effect is negligible (permeate flux of 0.68 mol s⁻¹ m⁻²).

The lack of extensive studies on the detailed mechanism of concentration polarisation specifically for palladium based membranes prompted Catalano et al. (40) to explore this research area. The findings of Catalano et al. demonstrated a similar trend with that of Zhang et al. (51) in terms of the effect of feed flow rate, and Pizzi et al. (52) in terms of the effect of mixture composition on the concentration polarisation phenomena. Compared to previous research, a fundamental investigation on the ternary mixture of H₂:N₂:CH₄ (volume ratio of 50:25:25) was also conducted for the first time. The findings showed that the permeation flux was marginally less than the flux for the binary mixture of H₂:N₂ (volume ratio of 50:50) but almost similar to the H₂:CH₄ (volume ratio of 50:50) mixture. Therefore, the findings reveal that there was a very slight decrease in permeation flux, which occurred when nitrogen was replaced with methane (40). In this case, previous researchers have confirmed that the inhibitive effect caused by methane is very minimal, thus can be neglected (69). Based on the findings of Catalano et al. (40) and Jung et al. (69), it is evident that the severity level of concentration polarisation is independent on number of species (binary or ternary) in the non-inhibitive hydrogen mixture. Catalano et al. also have interpreted the level of concentration polarisation for various operating conditions using a dimensionless polarisation number, which is defined as the ratio of gas phase to membrane sensitivity factor (40). The polarisation number of much higher than 1 (S>>1) means concentration polarisation is dominant, whereas when the number is much less than 1 (S<<1), resistance by the metal membrane controls the entire permeation process. The authors discovered that for both cases of ternary and binary hydrogen mixtures with feed flow rates of 1 Nl min⁻¹ to 3 Nl min⁻¹ and relatively low inlet hydrogen concentration (50 vol% H₂), the concentration polarisation becomes dominant, that is S>>1. However the value of S is reduced when hydrogen concentration or feed flow rate is increased. As example, for the case of binary mixture of H₂:N₂ (50 vol% H₂ and 50 vol% N₂) with operating temperature and total pressure of 673 K and 600 kPa, respectively, when the feed flow rate was increased from 1 Nl min⁻¹ to 3 Nl min⁻¹, S reduced significantly from 6 to 2.5.

Most of the studies on concentration polarisation elaborated previously used palladium based membrane with support that influences the hydrogen permeation process (70). Conversely, Caravella et al. (53) examined the concentration polarisation phenomenon on self-supported palladium-based membrane in which case the effect of support was eliminated. In addition to the previous studies, other researchers (40, 51–52), have analysed the broader range of upstream hydrogen molar fraction, total upstream pressure, downstream total pressure, operating membrane temperature, membrane thickness and permeability to develop polarisation maps as a very useful guide for membrane reactor designer. The term concentration polarisation coefficient (CPC) was introduced in the maps as a demonstration for the level of concentration polarisation. Here, when the value of CPC is 0, it means no polarisation occurs while the value of 1 indicates the occurrence of total or maximum polarisation. Additional parameters were considered in this study that were not covered by the other previous researchers, namely: operating temperature, permeance, total downstream pressure and membrane thickness. Furthermore, the analysis demonstrated that the severity of concentration polarisation increases when the temperature and permeance are increased whereas the total downstream pressure and membrane thickness are reduced (53). As example, when Reynolds number, hydrogen retentate molar fraction, temperature, pressure at retentate side and pressure at permeate side were set to 2100, 0.40, 500°C, 1000 kPa and 200 kPa, respectively, the CPC increased significantly from around 0.13 to around 0.65 (thus concentration polarisation effect become stronger) when membrane thickness was reduced from 50 μm to 5 μm. Similar to the assertion by Morgues et al. (68), Caravella et al. (53) also found that the hydrogen flux itself plays a significant role during concentration polarisation.

Caravella et al. extended their analytical study to cover the concentration polarisation phenomena for a hydrogen mixture that contains well-known inhibitive species of carbon monoxide (22, 71–76). In this study (54), the authors simultaneously considered the effects of concentration polarisation and inhibition by carbon monoxide by merging their previously introduced approach (53) and the approach by Barbieri et al. (77). Similar to their previous study (53), the authors introduced a parameter so-called permeation reduction coefficient (PRC) that includes both polarisation and carbon monoxide inhibitive effects simultaneously. Interestingly, it was found that when the polarisation and carbon monoxide inhibition occur at the same time, the hydrogen permeation flux obtained is lower compared to the flux obtained when both phenomena occurred separately. This is mainly due to the polarisation of the inhibitor carbon monoxide toward the membrane surface, which increases the carbon monoxide partial pressure at the surface (54). The researchers found that for binary mixture of hydrogen and carbon monoxide, when operating temperature, membrane thickness, Reynolds number, hydrogen upstream molar fraction, total upstream pressure and downstream pressure are set to approximately 647 K, 60 μm, 1200, 0.60, 1000 kPa and 200 kPa, respectively, the permeating flux for the cases of polarisation only, inhibition by carbon monoxide only, and simultaneous polarisation and inhibition are around 85 mmol m⁻² s⁻¹, 71.5 mmol m⁻² s⁻¹ and 67 mmol m⁻² s⁻¹ (54). The inhibition of carbon monoxide under the influence of concentration polarisation is expected since the low feed flow rate is generally applied, for instance, during steam reforming for application in small portable electrical devices (8, 66).

The phenomenon of concentration polarisation was featured by the two-dimensional numerical method for tubular type (39) and flat sheet type (78) membranes. In general, for permeation with tubular type membrane under concentration polarisation influence, the direction of hydrogen concentration decrease for binary mixture of H₂:N₂ is from the region around the leading edge (inlet part) to the tailing edge (outlet part) (39). This phenomenon is featured by Figure 3, in which dimensionless hydrogen concentration gradient decreases from the leading edge to the tailing edge of the membrane surface regardless of hydrogen volume percentage. However, for the case with vertical flow towards flat sheet type membrane surface, the hydrogen concentration is highest at the centre of the membrane, and decreases in radial direction, as shown by Figure 4 (78). These studies investigated the hydrogen concentration distribution around the membrane surface for various important parameters such as operating pressure, hydrogen molar fraction, feed flow rate (or Reynolds number) and membrane permeance. The qualitative simulated results reveal that the hydrogen concentration decreases at the membrane surface due to the effect of hydrogen flux itself during the phenomena. However, the severity level of concentration polarisation for the various parameters above is generally similar to the values described quantitatively by previous experimental and analytical studies (40, 51–54). Chen et al. introduced an important parameter called hydrogen permeation ratio (HPR) to indicate the level of concentration polarisation (39). The HPR is defined as the ratio of hydrogen permeation rate across the membrane to the hydrogen feed rate at the inlet. The authors concluded that a decrease in value of HPR indicates that the severity of concentration polarisation is diminished. As an example, for the case of binary mixture of H₂:N₂ (H₂ mole fraction of 0.50) with pressure difference and membrane permeance of 30 atm and 10⁻⁴ mol m⁻² s⁻¹ Pa^−0.5, respectively, HPR decreased from 96 to 3 when Reynolds number was increased from 20 to 2000, thus severity of concentration polarisation is significantly reduced (39). It is interesting to note that when the aforementioned four important parameters (operating pressure, hydrogen molar fraction, feed flow rate and membrane permeance) were set in such a way to cause the effect of concentration polarisation to become very significant, the hydrogen concentration gradient is very high at the leading edge of the membrane (in the region near to the inlet) and then decays faster. Due to this phenomenon, there was almost no driving force for permeation in most of the remaining membrane length, as demonstrated by Figure 5 (refer to the case of permeance (K) of 10⁻³) (39). Figure 5 also demonstrates that when the permeance is increased, the tendency for concentration polarisation to occur increases. Based on Nagy et al. (79), a convex shape can be observed for the hydrogen concentration curve in a boundary layer during concentration polarisation phenomena, once the convective flow starts to play a role in the diffusive flow of the layer (80, 81). Based on these numerical simulation studies, Chen et al. also asserted that the concentration polarisation phenomenon is not significant when the hydrogen permeation ratio (H₂ permeation rate:H₂ feed rate) is less than 30%. It is important to note that even if the concentration polarisation can be improved (and more hydrogen flux can be obtained), the HPR that indicates hydrogen recovery becomes smaller, and this becomes a shortcoming for the membrane performance (39).

Fig. 3.

Fig. 4.

Fig. 5.

Subsequently, Chen et al. extended their numerical simulation to the tubular type membrane with simultaneous use of feed flow and sweep flow (41) under concentration polarisation influence. The advantage of using sweep flow to improve hydrogen permeation flux (and to abate concentration polarisation) has been confirmed by previous researchers (6, 7, 82–84). When the sweep flow rate at the permeated side is increased, the hydrogen partial pressure at the membrane surface of the permeated side can be reduced, thus hydrogen permeation flux increases (and concentration polarisation is weakened) due to increase in hydrogen partial pressure difference (7, 83). For instance, in the case of countercurrent mode with the use of sweep gas in the shell side (outside tubular membrane and inside shell), the improvement in hydrogen flux was improved by 12.3% when the sweep flow rate was increased from 2.713 mol s⁻¹ to 4.3408 mol s⁻¹, thus indicating the importance of sweep flow rate in improving hydrogen flux. In this case, the optimum flow rate of sweep gas can be estimated from the arctangent function (41, 85) of feed gas flow rate, once the flow rate or Reynolds number of the feed gas is specified. Here, the flow rate of sweep gas is considered optimum when the flow rate can give the maximum hydrogen permeation flux and sufficiently high hydrogen recovery (up to 95% H₂ recovery) could be maintained (41). It is interesting to note that the coupling between feed gas and sweep gas will give better separation performance when countercurrent mode is applied (5, 41). It is also interesting to note that whether the feed gas is issued in the lumen side (inside tubular membrane) or the shell side (outside tubular membrane and inside the shell) during countercurrent mode, the difference in hydrogen flux for both configurations is negligible. Therefore, this implies the independence of hydrogen flux on the position of the feed flow. Also, the difference in hydrogen permeation flux between cocurrent mode and countercurrent mode can be reduced by increasing the feed flow rate. Similar to the feed flow rate, a decrease in the sweep flow rate causes the effect of concentration polarisation to become stronger.

Part II (86) continues the discussion and provides the conclusions.

Miguel et al. examined the decrease in the hydrogen concentration along the membrane length of a finger-like configuration (1–3) for the case of binary hydrogen mixtures with inhibitive carbon monoxide or carbon dioxide, by replacing the terms of feed partial pressure of inhibitive species and the difference in the square root of hydrogen partial pressure in the Sieverts’ Langmuir equation (4) with the average partial pressure of inhibitive species and logarithm mean driving force (5), respectively. In this case, the authors obtained an excellent concordance between the predicted results obtained from their rearranged Sieverts’ Langmuir equation with the actual hydrogen permeation flux (2), which proved the existence of concentration polarisation during the permeation.

With the apparent advantage of using sweep gas during hydrogen permeation (6), Chen et al. have further investigated the concentration polarisation phenomena under sweep gas and baffles implementation (7). The flows of feed gas and sweep gas were in the form of countercurrent mode. It is interesting to note that higher hydrogen flux can be obtained from the membrane when a smaller diameter of the shell (smaller distance between the shell and tubular membrane) is used. As an example, when the pressure difference, temperature, mass flow rate of feed gas and Reynolds number of flow at the permeate side were set to 9 atm, 623 K, 267.48 mg s⁻¹ and 1000, respectively, the hydrogen flux for the cases of large, medium and small shell were 0.88 mol m⁻² s⁻¹, 0.96 mol m⁻² s⁻¹ and 1.03 mol m⁻² s⁻¹, respectively. This is due to the reduction of boundary layer thickness, as demonstrated by the numerical results (7). Besides, the introduction of baffles to the shell side causes disturbance to the boundary layer and more hydrogen is directed towards the membrane surface. Therefore, concentration polarisation is weakened and more permeated hydrogen can be obtained. Interestingly, due to the trade-off between the installation cost and slight improvement in permeation performance when more baffles are installed, one baffle installation has been recommended (7). In this case, Coroneo et al. also have asserted there should be an optimum number of baffles installed after observing just a slight improvement in permeated flow when the number of baffles is increased, from around 38% (two baffles configuration) to just around 46% (three baffles configuration) (8).

Further investigation by Chen et al. (9) then discovered the optimum baffles configuration for minimising concentration polarisation while obtaining maximum hydrogen recovery. In this case, the authors emphasised the importance of concentrating hydrogen at the membrane surface through the flow contraction mechanism. The optimum conditions for baffle installations are as follows: (a) installation of single baffle at shell wall; (b) installation at the leading edge of the membrane and (c) use of a sufficiently high ratio of baffle length to shell radius (ratio of 0.75) (9).

Faizal et al. (10) investigated the effect of hydrogen partial pressure and feed flow rate on the level of concentration polarisation for flat sheet palladium/silver membrane, despite widespread research interest in tubular type membranes. A third degree polynomial equation has been introduced as a tool to predict hydrogen permeation flux for such geometry. Based on the predicted profile of hydrogen mole fraction at the membrane surface, the difference between the predicted average hydrogen mole fraction at the membrane surface and hydrogen mole fraction at the inlet becomes larger at higher inlet hydrogen partial pressure. For the case of a binary mixture of H₂:N₂ (inlet hydrogen mole fraction of 0.75), when operating temperature, feed mole flux and hydrogen partial pressure at downstream (permeate) side were set to 623 K, 0.40 mol m⁻² s⁻¹ and 0.10 MPa, respectively, the aforementioned difference increased from 9% to 20% when inlet hydrogen partial pressure was increased from 0.150 MPa to 0.225 MPa. Therefore, the concentration polarisation was strengthened. Compared to the previous studies, the changes in the concentration polarisation level concerning the inlet hydrogen partial pressure and feed flow rate are similar qualitatively (10).

Chen et al. performed experimental studies on a H₂:N₂ mixture permeation test using high permeance tubular palladium based membranes (palladium and palladium/copper membrane with porous stainless steel) (11). Here, the thickness applied was from 6–7 μm. Similar to the previous study on ultrathin high permeance palladium/silver membrane with ceramic support (thickness of 2.5 μm) (12), the authors revealed that concentration polarisation was most affected by the concentration of the hydrogen feed, notably when the hydrogen concentration was decreased from 75 vol% to 50 vol%. The severity of concentration polarisation becomes higher even though the hydrogen partial pressure difference has been set to the same value. In this case, it can be noticed that in order to obtain the same hydrogen partial pressure difference, when the hydrogen partial pressure at the permeated side is set constant, higher total upstream pressure is necessary for smaller feed hydrogen fraction, and this increases the levels of concentration polarisation. Within their selected operating condition, feed flow rate and hydrogen partial pressure difference cause concentration polarisation as well, but with minor influence compared to the feed hydrogen concentration factor (11). Zhao et al. performed a permeation test for a mixture that was almost similar to coal gasification product (<40% H₂ and <40 ppm H₂S) to simultaneously determine the effect of sulfur contamination and concentration polarisation. The authors found that the influence of concentration polarisation was dominant for the mixture with lower hydrogen composition (50% mole fraction) especially at a low feed flow rate due to the minor effect of sulfur poisoning in the specified condition (13).

As a continuation of their previous study (10), Faizal et al. (14) investigated the concentration polarisation phenomena for various binary hydrogen mixtures with different inlet hydrogen mole fraction (0.70–0.80) and species (nitrogen, argon, helium and carbon dioxide). It is interesting to note that a mixture of hydrogen and argon was used due to different chemical characteristics, whereas the mixture of hydrogen and helium was used due to the different binary diffusivity compared to the hydrogen mixture that contained nitrogen (14). The authors compared the analytical results calculated by using their previously introduced theoretical equation that takes into account the effect of hydrogen permeation itself (10) with the actual hydrogen permeation flux. The study demonstrated an excellent concordance between the estimated hydrogen permeation flux and the actual flux regardless of inlet hydrogen mole fraction and species, thus elucidates the significant effect of hydrogen permeation itself on the decrease in hydrogen concentration at the membrane surface during concentration polarisation. Therefore, it is interesting to note that the severity of concentration polarisation is determined by feed flow rate and inlet hydrogen mole fraction, but not the different chemical characteristics and binary diffusivity of the mixtures (14).

Nakajima et al. reduced the boundary layer thickness to abate concentration polarisation by improving physical geometry of a reactor vessel containing a tubular palladium/silver membrane (15). In this case, the reduction of boundary layer thickness was performed by narrowing the path between the membrane surface and the inner surface of the vessel shell (15). For instance, by narrowing the path from 23.9 mm to 16.6 mm, the amount of produced hydrogen can be improved by around 25% even though there is only a 2% increment in methane conversion during hydrogen production from natural gas (for feed flow rate of 9 Nml min⁻¹ cm⁻²) (15). Such improvement is due to the reduction in distance between the inner surface of the vessel and the membrane surface, which has also been observed through the previous numerical simulation performed by Chen et al. (7).

As an alternative to the numerical simulation technique performed by Chen et al. (6, 16), the profiles of average axial concentration and concentration at the membrane surface can also be obtained by determining an analytical solution of the governed ordinary differential equation (ODE) (17). Further discussion on the analytical solution is presented in the following section.

In 2018, Kian et al. investigated the concentration polarisation phenomenon for the case of various ternary mixtures (18). They found the hydrogen permeation behaviour for ternary mixtures is similar to the case of binary mixtures, in which competitive adsorption becomes dominant when strong inhibitive carbon monoxide is used in the ternary hydrogen mixture (H₂:CO₂:CO) while concentration polarisation starts to play a significant role when methane is used instead of carbon monoxide. In the same year, Helmi et al. also proved the concentration polarisation phenomenon for the case of a fluidised membrane reactor (19). The good agreement between the developed model that considers concentration polarisation (so called ‘1D/k_d’) with experimental results elucidates that this phenomenon becomes more significant when lower inlet hydrogen mole fraction and higher inlet velocity are used (19). Based on the comprehensive review of the research scenarios in the previous paragraphs, it is evident that concentration polarisation is an undesirable phenomenon. This is because the ability of the membrane to permeate a very high amount of hydrogen cannot be fully utilised. However, it is unavoidable due to the advances in membrane technology that cause the fabrication of very thin membranes. Consequently, the external mass transfer becomes the permeation controlling step instead of diffusion in the metallic lattice. Although the development of compact devices with sufficiently high hydrogen recovery is possible, the concentration polarisation level becomes high due to the significant effect of permeation itself during the permeation.

In brief, several techniques have been introduced to address such disadvantages and effectively reduce the severity of concentration polarisation. For example, baffles may be implemented (7, 8) in the membrane reactor and the path between membrane surface and inner vessel wall may be narrowed (7, 15) to reduce the boundary layer at the membrane surface (15). The implementation of a spherical particles bed between tubular membranes in a membrane reactor has been confirmed to reduce the effect of concentration polarisation, due to the increase in the interparticle velocity and the increase in the Reynolds number between the particles and membrane surfaces (20). Helmi et al. have used fluidising particles inside a fluidised membrane reactor to significantly reduce the concentration polarisation effect due to better mixing of gases (21). The permeation system with microchannel configuration (22, 23) also has been suggested as a technique for concentration polarisation abatement due to the ability to decrease boundary layer thickness near to the membrane surface (22, 24). The combined usage of baffles and perforated pipe to reduce concentration polarisation effect has been demonstrated by Peters et al. (25) due to the creation of turbulence. Recently, an integrated compact system that consists of combustor, prereformer, reformer and hydrogen separator (palladium membrane) in a single module was developed by Wunsch et al. for small hydrogen demand applications (26). Since the height of the integrated system was relatively very small (12.4 mm) with eleven plates arranged in a stack, the concentration polarisation effect could be minimised, thus improving hydrogen yield as well as hydrogen productivity (26).

In 2008, Chen et al. introduced a constant concentration method with the aim to characterise the membrane by eliminating the effect of concentration polarisation (27). Based on this method, the tubular membrane reactor was filled with non-H₂ species first and followed by H₂ to obtain the desired hydrogen partial pressure without allowing any permeation. Once permeation began, the hydrogen that permeated out of the membrane was made up or replaced by the fresh hydrogen from the pressurised tank to maintain the hydrogen partial pressure at the retentate side. Therefore, the variation of hydrogen concentration at the membrane surface could be eliminated (27). However, this technique is not practical for industrial application since the flow stream at the upstream side of industrial membrane reactor is usually in plug flow, and not perfectly mixed flow, in which concentration polarisation usually could be triggered.

Extensive studies on concentration polarisation phenomena have been performed by Caravella et al. (28) and Catalano et al. (12). Caravella et al. (28) have created concentration polarisation maps which are very useful for hydrogen purification system design. Here, the maps are a two-dimensional graph of concentration polarisation coefficient versus hydrogen retentate molar fraction that was derived based on Equation (i):

(i)

where H₂flux (elementary steps) is the hydrogen permeation flux that is calculated by considering all the permeation elementary steps (external mass transfer, superficial adsorption, diffusion through the palladium-based bulk and superficial desorption) (29), in which in this case, involved complex procedures. Meanwhile, the concentration polarisation coefficient (CPC) is a concentration polarisation coefficient that becomes as an indicator for concentration polarisation level. The values of CPC were obtained by solving Equation (i) for various operating conditions and the values were plotted with respect to hydrogen retentate molar fraction. Here, when the value of CPC is 0, it means no concentration polarisation occurs while the CPC value of 1 indicates maximum level of concentration polarisation that has been defined as ‘total polarisation’ in their study. Π^Membrane is the membrane permeance that can be obtained from permeation test for pure hydrogen. Meanwhile, DF^Bulk is bulk driving force that can be obtained from the difference in square root of hydrogen partial pressure between the feed side and permeate side when the effect of concentration polarisation is negligible. For those who want to evaluate the concentration polarisation level by using these maps, only knowledge of the operating condition of the membrane reactor is required. The CPC can be determined manually from the maps. Finally, hydrogen permeation flux can be predicted by substitution of the CPC value into Equation (i) and followed by solving the equation. Despite the simplicity of this prediction method, the determined CPC actually does not account for the remaining length (and remaining area) of the tubular membrane where no permeation occurs anymore due to very fast decay of driving force at the region around the inlet. This situation occurs when concentration polarisation becomes significant (16), thus hydrogen concentration is overestimated when the aforementioned CPC value is used. This weakness was then solved through the introduction of the powerful parameter so called effective average CPC (EAC) (30). The determination of EAC is stated as follows, Equation (ii):

(ii)

where L, z and CPC are the membrane length, membrane axial abscissa and concentration polarisation coefficient, respectively. Here, the local value of CPC for each position on the membrane in z-direction is determined analogously as was introduced previously (28). Meanwhile, the hydrogen concentration profile and the respective profile of hydrogen permeation flux can be obtained by simultaneously solving the external mass transfer and hydrogen permeation equations (30). Here, the calculation of mass transfer coefficient is as reported by Caravella et al. (29). Finally, Equation (ii) can be solved to obtain the value of EAC. Based on the previous individual elaboration on the prediction techniques using CPC (28) and EAC (30), it can be said that the use of EAC is more desirable, since it has the ability to represent the real behaviour of a hydrogen permeation device. It is interesting to note that once the EAC maps have been prepared, similar to the previous technique of using the CPC maps (28), the hydrogen permeation flux can be estimated by simply substituting the value of the EAC obtained from the maps into Equation (ii).

Similarly, Catalano et al. (12) concluded the existence of non-negligible resistance to hydrogen transport in the gaseous phase itself, in addition to resistance caused by the membrane. For the case of a hydrogen mixture, the authors demonstrated a significant deviation from Sieverts’ Equation (Equation (iii)) when the hydrogen partial pressure of the bulk gas is substituted into the equation. To compensate for this situation, semi-empirical equations were developed for a tubular type membrane (membrane thickness of 2.5 μm) as follows (12), Equations (iv) and (v):

(iii)

(iv)

(v)

where N_H2,int is the hydrogen flux crossing the membrane interface and is defined as the hydrogen flux within the gas-metal interface, k_G is the mass transport coefficient, p_ret is the pressure at the retentate side, p_H2,int is the hydrogen partial pressure at gas-metal interface, p_H2,ret is the hydrogen partial pressure at retentate side, p_H2,per is the hydrogen partial pressure at permeate side and is the hydrogen permeance obtained from pure hydrogen experiment. It is interesting to note that once the value of k_G is obtained by solving Equations (iv) and (v) simultaneously and by using experimental data of N_H2,int, the same value of k_G can then be used to estimate hydrogen permeation flux for the cases with different hydrogen partial pressure difference.

As a continuity of the previous study (28), Caravella et al. (31) considered simultaneously both concentration polarisation and inhibition by carbon monoxide species in their model, by introducing the permeation reduction coefficient. Similar to the prediction technique introduced previously (28), the permeation reduction coefficients were plotted for different operating conditions, or so called ‘permeation reduction maps’. The simple relation for the permeation reduction coefficient as shown by Equation (vi) was derived from definitions of CPC and inhibitive coefficient (IC), that were obtained from previous studies by Caravella et al. (28) and Barbieri et al. (4), respectively through complex calculation steps, Equation (vi):

(vi)

where PRC is the permeation reduction coefficient, CPC is the concentration polarisation coefficient and IC is the inhibition coefficient. To predict the hydrogen permeation flux for certain operating conditions, the value of PRC is determined manually from the ‘permeation reduction maps’ and then the value is substituted into Equation (vii) as follows:

(vii)

where J_H2 is the hydrogen permeation flux, PRC is the permeation reduction coefficient, Π^Sieverts is the permeance which is similar to the hydrogen permeance coefficient, obtained from pure-hydrogen test. Meanwhile, is the bulk driving force for hydrogen permeation, that is bulk difference in square root of hydrogen partial pressures between the retentate and permeate side.

As one of the solutions for the difficulty in obtaining a general relation that consists of several interdependent parameters as has been mentioned by Morgues et al. (32), Faizal et al. (10, 14, 33) have introduced a theoretical approach for hydrogen permeation through a flat sheet palladium based membrane after observing a significant deviation between the actual permeation flux and the estimated flux by Sieverts’ equation (Equation (iii)) when inlet hydrogen concentration was used (33). As asserted by previous researchers on the significant effect of permeation flux during concentration polarisation phenomena (6, 12, 16), the term of hydrogen partial pressure at membrane surface of upstream side in the Sieverts’ equation (Equation (iii)) has been modified to consider the effect of hydrogen permeation flux during permeation. The modification of Equation (iii) leads to the formation of Equation (viii) as follows (14):

(viii)

where f_p is the estimated hydrogen permeation mole flux, q is the hydrogen permeance coefficient, d is the membrane thickness, f_H2,in is the mole flux of hydrogen from inlet (feed flow rate of hydrogen divided by effective membrane surface area), f_in is the mole flux of the mixture from inlet (feed flow rate of mixture divided by effective membrane surface area), P_in is the total pressure at inlet (total upstream pressure) and p_H2,2 is the hydrogen partial pressure at membrane surface of the downstream side. In order to predict f_p, the values of operating parameters are substituted into Equation (viii) and followed by solving the equation for f_p. Surprisingly, the modified equation as shown by Equation (viii) can estimate accurately hydrogen permeation flux for any noninhibitive binary hydrogen mixture with different chemical characteristics and binary diffusivity, along with any hydrogen concentration and with any mole flux of mixture from the inlet. For instance, when the mole flux of mixture from the inlet is increased, the effect of concentration polarisation is weakened. Therefore, the estimated flux obtained from Equation (viii) approaches the flux obtained from Equation (iii) due to the weaker effect of f_p. The introduced method is supposed to be very useful for reactors with similar type of membrane used (34–36).

To prevent membrane damage due to mechanical stress, the palladium/silver tubular membrane was created in the form of a ‘finger-like’ configuration, thus allowing the free elongation and contraction of the membrane (2). For this kind of configuration, the way to predict hydrogen permeation flux is supposed to be similar to that for the tubular type membrane with common configurations (Figures 2(a) and 2(b) in Part I (37)) because the hydrogen mixture similarly flows horizontally along the membrane length for both cases. In the research performed by Miguel et al. (2), a model to simultaneously consider both concentration polarisation and inhibition by carbon monoxide or carbon dioxide has been introduced based on the logarithm-mean driving force (for considering concentration polarisation effect) and correction factor due to inhibitive effect (4). Compared to the approach by Barbieri et al. (4), the model introduced by Miguel et al. could provide more accurate results for the simultaneous occurrence of both phenomena. This is because the previous approach by Barbieri et al. (4) only considers the feed hydrogen partial pressure for prediction. However, the model introduced by Miguel et al. is semi-empirical and therefore, experimental data is necessary in order to determine certain parameters in the correction factor. The combination of correction factor and rearranged Sieverts’ equation forms the rearranged Sieverts’-Langmuir equation as shown below (2), Equation (ix):

(ix)

where the term is the correction factor due to adsorption of inhibitive species on the membrane surface and the term is the rearranged Sieverts’ equation.

Here, is the hydrogen permeation flux, α is the Sieverts’-Langmuir reduction factor, K_i is the Langmuir’s adsorption constant for species (CO or CO₂), is the average partial pressure of species (CO or CO₂) between the feed and retentate sides, L_H2 is the hydrogen permeance or hydrogen permeation coefficient, δ is the membrane thickness and ΔP_ln is the logarithm mean driving force that is determined based on theory of heat exchanger for parallel flow case (2, 5). It is important to note that the values of α and K_i for carbon monoxide and carbon dioxide are dependent on operating temperature, thus these values need to be fitted with experimental data first before using Equation (ix) to estimate hydrogen permeation flux.

A prediction method for hydrogen permeation capacity (length of membrane for hydrogen permeation) has been introduced by Xie et al. (38) through computer programming. The investigation was performed analytically for seven important scenarios with a different flow pattern on both sides (upstream and downstream side). In this case, the concept is similar to that performed by Faizal et al. (10, 14, 33), in which the effect of hydrogen permeation rate is taken into account when determining hydrogen partial pressure at the membrane surface of the upstream side, as shown by the following Equation (x) (example for the scenario with plug flow at upstream side, and no sweep gas):

(x)

where P_H (x) is the hydrogen partial pressure of an infinitesimal permeation capacity (infinitesimal membrane length for permeation), dx in the high pressure (upstream) side, M₁ is the feed flow rate of hydrogen at upstream side, M₂ is the feed flow rate of nonpermeable gas at upstream side, P₁ is the total pressure of upstream side and M_x is the hydrogen permeation rate through a membrane for length from 0 to x. Then, the local hydrogen permeation rate through the infinitesimal permeation capacity dx can be predicted by substituting Equation (x) into the Sieverts’ equation as follows, Equation (xi):

(xi)

where C is the constant for membrane and P₂ is the total pressure of downstream side. In their study, Equation (xi) is rearranged and then followed by integration of x with respect to M_x in order to predict the permeation capacity (membrane length for separation) x as shown by Equation (xii):

(xii)

Differently to other techniques, the technique introduced by Xie et al. (38) is used to estimate the value of x instead of M_x.

Recently, algebraic functions that can be used to predict the profiles of hydrogen permeation flux under the influence of the concentration polarisation phenomenon have been introduced (17). Concentration polarisation is accounted through the use of an effectiveness factor which was derived in the previous study (39). The effectiveness factor is the ratio of actual permeation flux over the calculated flux based on the average concentration, and it is a function of separation parameter that represents the ratio of diffusive to permeation flux. The effectiveness factor and separation parameter that obeys Sieverts’ Law can be expressed as Equation (xiii) and Equation (xiv), respectively (2):

(xiii)

(xiv)

where (Equation (xv)):

(xv)

Here, η is the effectiveness factor, is the hydrogen partial pressure at membrane surface of retentate side,  is the hydrogen partial pressure at membrane surface of permeate side, is the average hydrogen partial pressure at retentate side, Γ is the separation parameter, D is the diffusion coefficient of hydrogen in the gaseous phase, Sh is the Sherwood number, d is the characteristic length, p^ret is the pressure at retentate side, K_H2 is the hydrogen permeability and c_tot is the total molar density. To predict the profile of hydrogen permeation flux, the algebraic functions presented by Nekhamkina et al. (17) need to be solved.

The background of the scenarios related to palladium based membranes has been elaborated. It was found that concentration polarisation becomes unavoidable in parallel with advances in membrane technology. The scenario of parametric studies on the concentration polarisation phenomenon specifically for palladium based membranes was reviewed comprehensively. Based on the present review, it is evident that an increase in total upstream pressure, membrane temperature and permeance promotes concentration polarisation. The same trend is also achieved when the feed flow rate, inlet hydrogen concentration, total downstream pressure and membrane thickness are reduced. When the ratio of hydrogen permeation rate to hydrogen feed rate at the inlet becomes sufficiently high, the effect of hydrogen permeation flux on the hydrogen concentration decrease at the membrane surface becomes significant, thus concentration polarisation becomes strong. Therefore, it can be said that an increase in hydrogen recovery percentage leads to a stronger tendency for concentration polarisation to occur, and as a consequence, larger deviation from the hydrogen permeation flux estimated by Sieverts’ equation could be observed. For both tubular type and flat sheet type membranes, when concentration polarisation is triggered, the hydrogen concentration decreases in the horizontal direction (from the leading edge to the tailing edge) and radial direction, respectively. Furthermore, the existence of inhibitive species such as carbon monoxide in the hydrogen mixture somehow causes the membrane performance in terms of hydrogen permeation flux to become worse due to the simultaneous occurrence of concentration polarisation and inhibition by carbon monoxide. Meanwhile, the concentration polarisation level does not depend on the number of noninhibitive species, chemical characteristics of noninhibitive species or binary diffusivity in the hydrogen mixture (binary or ternary mixture).

Several techniques have been identified to effectively abate concentration polarisation such as coupling of upstream flow with sweep flow in countercurrent mode, installation of baffles in the appropriate number, size and position, and by narrowing the space for upstream flow, that is reduction of the distance between the shell and membrane. Basically, the aforementioned techniques were implemented to increase the hydrogen concentration at the membrane surface of upstream side, thus concentration polarisation could be reduced.

Finally, several estimation methods for hydrogen permeation flux have been reported for different membrane configurations. Several methods are empirical, in which experimental data is necessary to obtain certain coefficients while some of the methods can be used by just substituting the operating parameters into the introduced equation.

For future work, it is suggested that the methods to estimate hydrogen permeation flux for the application of steam reforming should be intensively developed for various operating conditions. In this case, the detailed chemical kinetics must be considered to obtain the accurate mixture composition near the membrane surface. The competitive adsorption by excessive steam and excessive vaporised alcohols (methanol for instance) in addition to carbon monoxide during the occurrence of steam reforming reaction should also be taken into account in the future development of estimation methods.