Phosphorus Substitution Research Articles

Boosted Lithium-Ion Transport Kinetics in n-Type Siloxene Anodes Enabled by Selective Nucleophilic Substitution of Phosphorus

HighlightsExtrinsic doping is proposed as a novel route to enhance the intrinsic properties of the two-dimensional oxidized Si nanosheet (namely, siloxene) anode for Li-ion batteries.Fabrication of P-doped n-type siloxene is revealed to be possible through selective nucleophilic substitution of Si atoms in siloxene with P atoms.Due to boosted charge transport kinetics, n-type siloxene (6.7 × 1019 P atoms cm-3) exhibits the excellent storage performance (594 mAh g-1 after 500 cycles) even at 2000 mA g-1.

Exploring the Influence of the Phosphorus-Heteroatom Substitution in Nicotine on Its Electronic and Vibrational Spectroscopic Properties.

The influence of phosphorus substitution of nitrogen in heterocyclic compounds on the vibrational spectroscopy as well as frontier molecular orbitals are analyzed. Nicotine with two nitrogen atoms in its structure is taken as the sample system to be studied computationally. By replacing the nitrogen atom in one or both rings of this molecule with phosphorus, three nicotine derivatives are created. The vibrational circular dichroism and infrared spectra of these four molecules in their monomer state, as well as the assemblies up to trimers are determined. The aforementioned spectra are calculated using static quantum chemical calculations employing a cluster-weighted approach. The calculated gas phase spectra of nicotine are compared to their respective experimental spectra. It is observed that the nicotine derivatives with phosphorus in the methylpyrrolidine ring have considerably different gas phase and bulk phase vibrational circular dichroism spectra when compared to nicotine. The phosphorus substitution reduces the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital as well as altering the polarizability and reactivity of the investigated molecules.

Template-Free Synthesis of Phosphorus/Nitrogen-Doped Mesoporous Titania Materials with Excellent Adsorption for Lysozymes.

Element-doped mesoporous titanium oxide has significant advantages in substance separation and adsorption due to its larger specific surface area and stronger hydrophobicity. However, its current synthesis methods have limitations such as complicated preparation process, high production cost, or not being environmentally friendly, and the synthesis of elementally doped titanium oxide materials by simple, low-cost, and green means is the research goal of this study. In this study, phosphorus-doped mesoporous titanium oxides (TiP) materials have been synthesized through a facile template-free method in an ethanol system, which were further modified by nitrogen doping with the use of urea as the nitrogen source. Both the synthesized TiP and P-N codoped sample (N-TiP) are amorphous with mesopores. It was revealed by FTIR and XPS spectra that the formation of Ti-O-P and -O-Ti-N bonds in the synthesized samples was due to the partial substitution of phosphorus for titanium in Ti-O-Ti bonds in mesoporous titanium oxide, while nitrogen replaced some oxygen in the -O-Ti-O bonds in the form of anions. The TiP sample was estimated by the BET method to have a relatively large surface area, up to 317 m2/g. The adsorption of TiP and N-TiP materials to lysozyme protein in a buffer solution at different pH values showed that the adsorption of TiP to lysozyme protein was larger, which was 32.68 μmol/g. It shows that TiP has potential as a multifunctional adsorbent.

Effects of phosphorus substitution on amorphous formation, crystallization behavior and magnetic properties of FeSiBCuNb alloys

Fe-Si-B-Cu-Nb nanocrystalline alloys exhibit excellent soft magnetic properties and have been increasingly applied in high frequencies ranging from several kHz to several hundred kHz, but the magnetic permeability needs further to design to meet the magnetic components under different frequencies. In the present work, the influences of phosphorus substitution on amorphous forming, crystallization behavior and soft magnetic properties of silicon-rich Fe-Si-B-Cu-Nb alloys were systematically investigated. It was found that the suitable addition of 1 at.% of P in Fe-Si-B-Cu-Nb alloy can significantly improve the amorphous forming ability, reduce the coercivity (Hc) of the annealed alloys and elevate the effective magnetic permeability (μe) at frequencies ranging from 1 to 30 kHz in spite of having fractional detriment to the alloy's thermal stability but still remaining a relatively broad annealing temperature region. Besides, the μe in high P-containing alloys becomes insensitive to frequencies at high frequencies region, which can attain frequencies-dependent constant magnetic permeability induced by composition design.

A structural, DFT and experimental investigation of the ring stability and ring-opening polymerization behaviour of cyclic thionylphosphazenes in the presence of Lewis acid catalysts

A series of cyclic thionylphosphazenes were prepared and density functional theory (DFT) calculations initiated to gain insight into their susceptibility to ambient ring-opening polymerization with Lewis acid catalysts (GaCl3, AlCl3). DFT analyses determined that PBE1PBE-GD3BJ provided the optimal calculated structures for 1, 5, 5’ and 8. The gauge-independent atomic orbital (GIAO) method (M05-2X-GD3//PBE1PBE-GD3BJ) provided a good approximation for the 31P NMR resonances. Energy calculations indicate that thionylphosphazene phosphorus substitution promotes heterolytic cleavage of the thionyl S–Cl bond, as does adduct formation with GaCl3 or AlCl3, suggesting that 4 has potential for GaCl3-catalyzed ROP reactions at ambient temperatures. The generation of thionylphosphazene cation from 1 with catalytic quantities of Lewis acids (10:1 GaCl3, AlCl3) initiates the ambient temperature ROP to poly(thionylphosphazene) (2) in a minimum amount of solvent. Polymerization/depolymerization studies of 1 and 2 in solution was found to be fully reversible in the presence of GaCl3.

Controlling atomic phosphorous-mounting surfaces of ultrafine W2C nanoislands monodispersed on the carbon frameworks for enhanced hydrogen evolution

Controllably mounting foreign atoms on the surfaces of earth-abundant electrocatalysts strongly improve their surface electronic properties for optimizing the catalytic performance of surficial sites to an unusual level, and provides a good platform to gain deep insights into catalytic reactions. The present work describes, employing ultrafine W2C nanoislands (average size: 2.3 nm) monodispersed on the N, P dual-doped carbon frameworks as a model system, how to regulate the atomic phosphorous-mounting effect on the surfaces of W2C to derive an active and stable P-mounting W2C (WCP) catalyst for both acidic and alkaline hydrogen evolution reaction (HER). Since in situ phosphorus substitution into carbon sites of preformed W2C nanoislands gradually proceeds from surfaces to solids, so that using a proper amount of phosphorus sources can readily control the surface mounting level to avoid the mass P-doping into the bulk. By this way, the activity per active site of WCP catalyst with robust stability can be optimized to 0.07 and 0.56 H2 s−1 at –200 mV overpotential in acid and base, respectively, which reach up to the several-fold of pure-phase W2C (0.01 and 0.05 H2 s−1). Theoretical investigations suggest that compared with solid P doping, the P mounting on W2C surface can more remarkably enhance its metallicity and decrease the hydrogen release barrier. This finding disclosed a key correlation between surface foreign atom-mounting and catalytic activity, and suggested a logical extension to other earth-abundant catalysts for various catalytic reactions.

Mössbauer studies of spin and charge modulations in BaFe2(As1−xPx)2

The BaFe2(As1-xPx)2 compounds with x = 0 (parent), x = 0.10 (under-doped), x = 0.31, 0.33, 0.53 (superconductors with Tc = 27.3 K, 27.6 K, 13.9 K, respectively) and x = 0.70, 0.77 (over-doped) have been investigated versus temperature using 57Fe M\"ossbauer spectroscopy. Special attention was paid to regions of the spin-density-wave (SDW) antiferromagnetic order, spin-nematic phase, and superconducting transition. The BaFe2(As0.90P0.10)2 compound exhibits a reduced amplitude of SDW as compared to the parent compound and preserved universality class of two-dimensional magnetic planes with one-dimensional spins. The spin-nematic phase region for x = 0.10 is characterized by an incoherent magnetic order. BaFe2(As0.69P0.31)2 shows coexistence of a weak magnetic order and superconductivity due to the vicinity of the quantum critical point. The charge density modulations in the BaFe2(As0.67P0.33)2 and BaFe2(As0.47P0.53)2 superconductors are perturbed near Tc. Pronounced hump of the average quadrupole splitting across superconducting transition is observed for the system with x = 0.33. The phosphorus substitution increases the Debye temperature of the BaFe2(As1-xPx)2 compound. Moreover, experimental electron charge densities at Fe nuclei in this material conclusively show that it should be recognized as a hole-doped system. The measured M\"ossbauer spectral shift and spectral area are not affected by transition to the superconducting state. This indicates that neither the average electron density at Fe nuclei nor the dynamical properties of the Fe-sublattice in BaFe2(As1-xPx)2 are sensitive to the superconducting transition. Theoretical calculations of hyperfine parameters determining the patterns of M\"ossbauer spectra of BaFe2(As1-xPx)2 with x = 0, 0.31, 0.5, and 1.0 are performed within the framework of the density functional theory.

Zn-Co phosphide porous nanosheets derived from metal-organic-frameworks as battery-type positive electrodes for high-performance alkaline supercapacitors

Excellent electrode materials are often desired to improve the overall performance of supercapacitors and conversion components, especially electrode materials synthesized by anion replacement to achieve high electrochemical performance. Herein, a zinc–cobalt phosphide electrode material with excellent electrical conductivity is synthesized through a metal–organic framework (MOF)-derived method, followed by phosphating in a tube furnace. As a result, an exchange of phosphorus ions and oxygen ions occurs, yielding a high specific capacitance of 2115.5 F g-1 at 1 A g-1, as well as a superior rate capacity of 1086.5 F g-1 at 50 A g-1. After 7000 cycle tests, 80.3% of the initial specific capacitance is maintained. Phosphorus substitution leads to a narrowed band gap, resulting in outstanding electrical conductivity, as confirmed through density functional theory (DFT) calculations. Subsequently, the self-assembled Zn0.33Co0.67P//Bi2O3 alkaline supercapacitor exhibits a high energy density of 83.05 Wh kg-1 (248.9 F g-1 at 1 A g-1) at a power density of 775.02 W kg-1. Meanwhile, a capacitance retention of 84.6% after 8000 cycles at a current density of 5 A g-1 is obtained. The outstanding performances of the electrode material in terms of electrical conductivity and electrochemical activity provide a new method for the design of high energy density alkaline supercapacitors (SCs).

Tailoring Electronic and Magnetic Properties of Graphene by Phosphorus Doping.

The electronic and magnetic properties of graphene can be modulated by doping it with other elements, especially those with a different number of valence electrons. In this article, we first provide a three-dimensional reconstruction of the atomic structure of a phosphorus substitution in graphene using aberration-corrected scanning transmission electron microscopy. Turning then to theoretical calculations based on the density functional theory (DFT), we show that doping phosphorus in various bonding configurations can induce magnetism in graphene. Our simulations reveal that the electronic and magnetic properties of P-doped (Gr-P) and/or phosphono-functionalized graphene (Gr-PO3H2) can be controlled by both the phosphorus concentration and configurations, ultimately leading to ferromagnetic (FM) and/or antiferromagnetic (AFM) features with the transition temperature up to room temperature. We also calculate core-level binding energies of variously bonded P to facilitate X-ray photoelectron spectroscopy-based identification of its chemical form present in P-doped graphene-based structures. These results may enable the design of graphene-based organic magnets with tailored properties for future magnetic or spintronic applications.

Effects of mineral phosphorus fertilizer reduction and maize straw incorporation on soil phosphorus availability, acid phosphatase activity, and maize grain yield in northeast China

ABSTRACT The partial substitution of mineral phosphorus (P) fertilizer by crop straw can mitigate its consumption and losing risk to the environment. However, the changes in soil P availability, acid phosphatase (AcP) activity, and grain yield under mineral P fertilizer reduction and crop straw incorporation remain poorly understood. This study evaluated the effects of a 20% reduction in mineral P fertilizer plus maize straw addition on soil P availability, AcP activity, and maize grain yield, as well as their relationships in a 5-year continually planted maize field in northeast China. Results showed that five years of continuous 20% of mineral P fertilizer reduction and maize straw incorporation significantly increased soil NaHCO3-Po and NaOH I-Pi concentrations, and did not decrease soil labile inorganic P concentration and grain yield compared to the treatment where 100% mineral P fertilizer was applied without straw addition. Additionally, there were significant positive correlations between soil AcP activity, labile inorganic P concentration, and grain yield, indicating AcP might play an important role in maintaining soil P availability and grain yield. Overall, the addition of maize straw can effectively replace 20% of the mineral P fertilizer and could be used as an appropriate fertilization practice in northeast China.

CALCULATION OF THE THERMODYNAMIC CHARACTERISTICS OF Fe – P SYSTEM BY METHOD OF MOLECULAR DYNAMICS

The problem of dephosphorization of iron-carbon alloys is relevant for the metallurgical industry, since a high concentration of phosphorus contributes to the appearance of a number of extremely undesirable phenomena. A lot of experimental work has been devoted to solving this problem, but it has still not been completely possible to cope with it. Any field experiments aimed at studying the process of phosphorus removal, require considerable material and time costs, but at the same time do not guarantee getting the desired result. Therefore, to search for new approaches to solving this problem, it is much more rational to use numerical simulation methods involving the computational capabilities of modern computers. At present, computer experiments are the same recognized research method as theoretical research and real experiment. To study the behavior of phosphorus atoms in iron using a numerical experiment, it is necessary to build a computational model and test it by calculating various characteristics whose values are known in advance. In this paper, the method of molecular dynamics was chosen as the method of computer simulation. Using this method, one can conduct experiments with given atomic velocities and describe dynamics of the studied processes. To describe the interparticle interaction, we used the potential calculated in the framework of the immersed atom method. The study was conducted on a computational cell simulating α-iron crystal with phosphorus substitution atoms. The constructed model demonstrated satisfactory results when calculating the known characteristics of the simulated system. Dependences of changes in such characteristics as temperature coefficient of linear expansion, melting point, latent heat of melting and heat capacity on the concentration of phosphorus atoms, as well as in some cases on magnitude of the applied external pressure were established. Calculations showed that, for example, the phosphorus concentration of 0.5 % leads to an increase in the average thermal coefficient of linear expansion by 9 %, a decrease in temperature and latent heat of fusion by 5 % and a heat capacity by 7 %.

Calculation of the Thermodynamic Characteristics of Fe–P System by the Molecular Dynamics Method

The problem of dephosphorization of iron-carbon alloys is relevant for the metallurgical industry, since a high concentration of phosphorus contributes to the appearance of a number of extremely undesirable phenomena. A lot of experimental work has been devoted to solving this problem, but it has still not been completely possible to cope with it. Any field experiments aimed at studying the process of phosphorus removal require considerable material and time costs, but at the same time do not guarantee getting the desired result. Therefore, to search for new approaches to solving this problem, it is much more rational to use numerical simulation methods involving the computational capabilities of modern computers. At present, computer experiments are the same recognized research method as theoretical research and real experiment. To study the behavior of phosphorus atoms in iron using a numerical experiment, it is necessary to build a computational model and test it by calculating various characteristics whose values are known in advance. In this paper, the method of molecular dynamics was chosen as the method of computer simulation. Using this method, one can conduct experiments with given atomic velocities and describe dynamics of the studied processes. To describe the interparticle interaction, we used the potential calculated in the framework of the immersed atom method. The study was conducted on a computational cell simulating α-iron crystal with phosphorus substitution atoms. The constructed model demonstrated satisfactory results when calculating the known characteristics of the simulated system. Dependencies of changes in such characteristics as temperature coefficient of linear expansion, melting point, latent heat of melting and heat capacity on the concentration of phosphorus atoms, as well as in some cases on magnitude of the applied external pressure, were established. Calculations showed that, for example, the phosphorus concentration of 0.5% leads to an increase in the average thermal coefficient of linear expansion by 9%, a decrease in temperature and latent heat of fusion by 5% and a heat capacity by 7%.

Surface treated nickel phosphide nanosheet with oxygen as highly efficient bifunctional electrocatalysts for overall water splitting

The development of high catalytic activity, earth-abundant, low-cost, and long-term stability electrocatalysts is highly desirable. In this study, oxygen surface treated Ni2P nanosheets as bifunctional catalysts for both hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) is proposed based on density functional theory calculations. The mechanism of the enhanced electrocatalytic performance was investigated by considering oxygen adsorption and substitution of surface phosphorus on the Ni2P nanosheets surface. The results show that six O adsorption and six O substitution Ni2P exhibit excellent electrocatalytic performance because of their tuned Gibbs free energy and overpotential for hydrogen/oxygen evolution reaction being just −0.21 eV/0.27 V and − 0.15 eV/0.45 V, respectively. Additionally, due to the reducing of total potential, the catalysts can present better OER performance in alkaline media. The bicatalytic activities of O adsorption and O substitution can be well-explained by an amendatory p band-center model, which is also suitable for a broad class of surface engineering systems. This theoretical study not only provides vital insights into the enhanced mechanism of the bifunctional activities of water splitting but also helps to prescribe the principles for designing high performance multifunctional electrocatalysts.

Isovalent Substitution Effects of Arsenic on Structural and Electrical Properties of Iron-Based Superconductor NdFeAsO0.8F0.2

In this paper, nominal compositions of NdFeAsO0.8F0.2, NdFeAs0.95Sb0.05O0.8F0.2 and NdFeAs0.95P0.05O0.8F0.2 were prepared by one step solid state reaction method. The structural, electrical and morphological properties of samples were characterized through the XRD pattern, the 4 probe method and SEM, respectively. The crystal structure of our samples was tetragonal with P4/nmm:2 symmetry group. Also, the (x, y, z) and occupancy of ions and lattice parameters were changed by isovalent substitution of Phosphorus P and Antimony Sb in the NdFeAsO0.8F0.2 sample. The alfa and beta bond angles and Fe-As bond length are changed from the corresponding value of alfa and beta regular FeAs4 tetrahedron by isovalent doping p/As and Sb/As, that they are effective on the superconductivity transition temperature. The microstrain and crystalline size of samples were studied by the Williamson Hall method. The superconducting critical temperatures were attained at 56K and 46K for NdFeAsO0.8F0.2, NdFeAs0.95Sb0.05O0.8F0.2, respectively. The NdFeAs0.95P0.05O0.8F0.2 showed the structural transition temperature at 140K. It seems that there is a relation between the superconductivity and shrinkage of the crystal lattice. The flake type of grains was observed by SEM pictures of samples.

The influence of phosphorus substitution by molybdenum on the chemical composition and certain properties of the zinc metaphosphate glass

xMoO3-50ZnO-(50-x)P2O5, i.e. (1-x/50)Zn(PO3)2-(x/50)ZnMoO4, glasses were prepared up to x = 25. It has been proved that the glasses are not a mixture of boundary components, but that chemical reactions taking place in the melt during synthesis produce in equilibrium a more complicated chemical mixture. Molybdenum is incorporated into the glass structure as a molybdate(2-) and also as complex cations, a colorless molybdenyl MoO4+ (d0 system) and blue colored MoO3+ (d1). The chemical model of the studied glasses was designed indicating that the glassy matrix gradually changes with increasing molybdenum content from pure anionic metaphosphate to the cationic-anionic network with the help of molybdenyl cation strongly bonded by four covalent donor-acceptor bonds with non-bonding phosphate oxygens. The compositional dependencies of some physical properties agree with the proposed chemical model. The melts or glasses of chemical compositions near the glass-forming border are less stable and immiscibility of glass phases was found.

Novel sodium superionic conductor of the Na1+yTi2SiyP3-yO12 series for application as solid electrolyte

In the search for new materials to be used as solid electrolytes, this paper discusses the substitution of phosphorus with silicon in the NaTi2(PO4)3 NASICON (Na-Super Ionic Conductor) compound, giving rise to the Na1+yTi2SiyP3-yO12 series. In fact, the substitution of P+5 for Si+4 enables the increase in the Na+ charger carrier concentration. The solid electrolytes are synthetized by the glass-ceramic route, which consists in the controlled crystallization of a precursor glass subjected to specific heat treatment. Experimental results indicate that precursor glasses are successfully crystallized in compositions containing y ≤ 1.2. X-ray diffraction patterns show the formation of NASICON phase in the Na1+yTi2SiyP3-yO12 glass-ceramics for y ≤ 0.8. However, with further addition of silicon, the major crystalline phase obtained is the Na(TiO)(PO4) phase. Surprisingly, the electrical characterization reveals that the y = 1.0 sample, whose main phase is the non-NASICON Na(TiO)(PO4), exhibits the lowest activation energy (0.31 eV) and the highest ionic conductivity of 1.0 × 10−4 S cm−1 at room temperature and 1.7 × 10−2 S cm−1 at 300 °C. Rietveld refinement and electrical conductivity results suggest that the increased ionic conductivity in the Na(TiO)(PO4) phase is due to the inclusion of some Si+4 ions in its structure, thus forming a new and highly Na(TiO)((Si)PO4) conductive phase.

Surface-engineered cobalt oxide nanowires as multifunctional electrocatalysts for efficient Zn-Air batteries-driven overall water splitting

Active sites engineering of electrocatalysts is an essential step to improve their intrinsic electrocatalytic capability for practical applications. Here, we demonstrate a facile surface phosphidisation into cobalt oxide (Co3O4) nanowires to boost their active sites, where phosphorus substitution for oxygen atoms greatly increases the number of cobalt (II) cations (Co2+) and oxygen vacancies (VO) active sites. First-principles calculations combined with high-resolution X-ray photoemission spectroscopy, electron spin resonance and X-ray absorption spectroscopy characterization identify that the phosphorus heteroatoms and VO alter the electron density of surface Co atoms in Co3O4 nanowires, resulting in the conversion of cobalt (III) cations (Co3+) to more active Co2+. As a result, the multifunctional catalysts of Co3O4 nanowires exhibit superior catalytic performance in overall water splitting with a low cell voltage of 1.61 V at 10 mA cm−2 and zinc-air batteries with a high open-circuit voltage of 1.41 V and power density of 72.1 mW cm−2. Particularly, two-series-connected Zn-air batteries powerfully drive an electrolyzer system without any additional electrode materials. These experimental and theoretical findings offer a promising approach to constructing active sites in non-precious metal catalysts for efficient and stable electrocatalytic activity.

Self-supported nanoporous cobalt phosphosulfate electrodes for efficient hydrogen evolution reaction

The morphology and crystallographic surface can influence the catalytic HER activity of electrocatalyst. With sufficient active sites and surface area, nanoporous materials with three-dimensional interconnected porous networks have shown the promising application in electrocatalyst. In this work, we report a simple method that can synthesize the self-supported nanoporous cobalt phosphosulfate (CoP|S) electrocatalyst. Theoretical calculation shows that the phosphorus substitution by sulfur can control the electronic structures of the active sites and accelerate charge transfer of CoP, therefore improving HER activity. The experimental study shows that nanoporous CoP|S electrodes present the improved HER performance compared with CoP in alkaline media and acidic media, respectively.

Solution-phase phosphorus substitution for enhanced oxygen evolution reaction in Cu2WS4.

Transition metal phosphides are among the most promising materials for achieving efficient electrocatalytic performance without the use of rare or expensive noble metals. However, previous research into phosphides for the hydrogen evolution reaction (HER) or oxygen evolution reaction (OER) has focused on high-temperature vapor-phase processes, which are not practical for large-scale applications. Here, we introduce a simple, one-step solution-phase method of phosphide synthesis by modifying Cu2WS4 using triphenylphosphine (TPP), which serves to substitute S with P and transform the normally inactive basal plane of Cu2WS4 into a defect-rich, activated basal plane. The OER activity was significantly enhanced by phosphorus substitution, with the resulting Tafel slope of the sample with ∼8 at% phosphorus reaching 194 mV dec−1, a result close to that of the best OER catalyst (RuO2, 151 mV dec−1). The sample possessed stable OER performance, showing no degradation in current density over ∼24 hours (500 cycles), proving the robust and stable nature of the phosphorus substitution. These results open the possibility for further phosphide catalyst development using this low-cost, solution-phase method.

Gradual reduction of the superconducting transition temperature of H3S by partial replacing sulfur with phosphorus

Recently, using the first-principles calculations based on the virtual crystal approximation (VCA), it has been reported that hydrogen sulfide with low phosphorus substitution possesses higher critical temperature (280 K), compared to experimentally studied H3S (203 K). Herein, using the supercell method for doping, we discuss the correctness of this result through study of superconducting properties of H3S1-xPx mixture. We proved that electron-phonon coupling constants and superconducting transition temperatures (Tc) calculated using supercell approach deviate from these one obtained earlier within the framework of the virtual crystal approximation. In particular, supercell method indicates that Tc is shifted towards lower values in comparison to experimental measurements of H3S which is the evidence for failure in increasing Tc of hydrogen sulfide through partial phosphorus substitution. Moreover, the obtained trend of critical temperature as a function of pressure, in contrast to VCA approach, is consistent with experimental results.