Mass transfer kinetics of neodymium(III) extraction by calix[4]arene carboxylic acid using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamics and kinetics data are both important to explain the extraction property. In order to develop a novel separation technology superior to current extraction systems, many promising extractants have been developed including calixarene carboxylic acids. The extraction thermodynamics behavior of calix[4]arene carboxylic acids has been reported extensively. In this study, the mass transfer kinetics of neodymium(III) and the interfacial behavior of calix[4]arene carboxylic acid were investigated. RESULTS: The rate constant (K_ao) becomes constant when the stirring speed was controlled between 250 rpm and 400 rpm. The activation energy (E_a) was calculated to be 21·41 kJ mol^?1 or 88·17 kJ mol^?1 (dependent on temperature) from the slope of log K_ao against 1000/T. The linear relationship between the specific area and the extraction rate is the characteristic of an interfacial reaction control. The minimum bulk concentration of the extractant necessary to saturate the interface (C_min) is lower than 4·19 × 10^?4 mol L^?1. CONCLUSION: The effect of stirring speed, temperature, and species concentration on the extraction rate demonstrates that the extraction regime depends on the extraction conditions. The chemical reaction control governs the extraction regime at temperatures below 303 K and a mixed control regime occurs when the temperature is between 303 K and 318 K. The probable locale for the chemical reaction is at the liquid–liquid interface and the rate equation is deduced to be: ? d[Nd³⁺]_(a)/dt = k_f[Nd³⁺]_(a)[H₄A]_(o)^0·727[H⁺]_(a)^?0·978. The rate‐controlling step was suggested by the analysis of the experimental results. Copyright © 2008 Society of Chemical Industry     

Effect of Temperature on Kinetics and Adsorption Profile of Endothermic Chemisorption Process: –Tm(III)–PAN Loaded PUF System

Abstract

The sorption behavior of 3.18×10^?6 mol l^?1 solution of Tm(III) metal ions onto 7.25 mg l^?1 of 1‐(2‐pyridylazo)‐2‐naphthol (PAN) loaded polyurethane foam (PUF) has been investigated at different temperatures i.e. 303 K, 313 K, and 323 K. The maximum equilibration time of sorption was 30 minutes from pH 7.5 buffer solution at all temperatures. The various rate parameters of adsorption process have been investigated. The diffusional activation energy (ΔE_ads) and activation entropy (ΔS_ads) of the system were found to be 22.1±2.6 kJ mol^?1 and 52.7±6.2 J mol^?1 K^?1, respectively. The thermodynamic parameters such as enthalpy (ΔH), entropy (ΔS), and Gibbs free energy (ΔG) were calculated and interpreted. The positive value of ΔH and negative value of ΔG indicate that sorption is endothermic and spontaneous in nature, respectively. The adsorption isotherms such as Freundlich, Langmuir, and Dubinin–Radushkevich isotherm were tested experimentally at different temperatures. The changes in adsorption isotherm constants were discussed. The binding energy constant (b) of Langmuir isotherm increases with temperature. The differential heat of adsorption (ΔH_diff), entropy of adsorption (ΔS_diff) and adsorption free energy (ΔG_ads) at 313 K were determined and found to be 38±2 kJ mol^?1, 249±3 J mol^?1 K^?1 and –40.1±1.1 kJ mol^?1, respectively. The stability of sorbed complex and mechanism involved in adsorption process has been discussed using different thermodynamic parameters and sorption free energy.     

Synergistic extraction of rare earths(III) from chloride medium with mixtures of 1‐phenyl‐3‐methyl‐4‐benzoyl‐pyrazalone‐5 and di‐(2‐ethylhexyl)‐2‐ethylhexylphosphonate

The synergistic effect of 1‐phenyl‐3‐methyl‐4‐benzoyl‐pyrazalone‐5 (HPMBP, HA) and di‐(2‐ethylhexyl)‐2‐ethylhexylphosphonate (DEHEHP, B) in the extraction of rare earths (RE) from chloride solutions has been investigated. Under the experimental conditions used, there was no detectable extraction when DEHEHP was used as a single extractant while the amount of RE(III) extracted by HPMBP alone was also low. But mixtures of the two extractants at a certain ratio had very high extractability for all the RE(III). For example, the synergistic enhancement coefficient was calculated to be 9.35 for Y³⁺, and taking Yb³⁺ and Y³⁺ as examples, RE³⁺ is extracted as RE(OH)A₂.B. The stoichiometry, extraction constants and thermodynamic functions such as Gibbs free energy change ΔG (?17.06 kJ mol^?1), enthalpy change ΔH (?35.08 kJ mol^?1) and entropy change ΔS (?60.47 J K^?1 mol^?1) for Y³⁺ at 298 K were determined. The separation factors (SF) for adjacent pairs of rare earths were calculated. Studies show that the binary extraction system not only enhances the extraction efficiency of RE(III) but also improves the selectivity, especially between La(III) and the other rare earth elements. Copyright © 2006 Society of Chemical Industry     

Degradation of acrylonitrile–ammonium itaconate copolymers

Acrylonitrile–ammonium itaconate copolymers were prepared by H₂O/dimethyl formamide suspension polymerization technique. Differential scanning calorimetry results of the degradation of acrylonitrile–ammonium itaconate copolymers in air are presented. The apparent activation energy of degradation of the copolymer was calculated using the Kissinger method. Effects of copolymerization conditions on the apparent activation energy of copolymer were studied. Increasing the dimethyl formamide concentration in the solvent mixture leads to a rapid increase in the degradation apparent activation energy of acrylonitrile–ammonium itaconate copolymer. The value of the degradation apparent activation energy of the copolymer synthesized in dimethyl formamide solvent increases up to 168.3 kJ mol^?1. The apparent activation energy decreases quickly along with an increase in ammonium itaconate concentration, and this change becomes less prominent as the weight ratio of ammonium itaconate/acrylonitrile goes beyond 6/94, ΔE_a = 89.4 ± 2.0 kJ mol^?1. The apparent activation energy shows a trend of increase with increasing copolymerization temperature. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1708–1711, 2005     

Hydride Transfer: A Dominating Reaction of Ozone with Tertiary Butanol and Formate Ion in Aqueous Solution

This article provides evidences that hydride transfer is an important primary step in ozone reactions of formate and tertiary butanol in aqueous media. In both systems, one argument is the fact that the free hydroxyl radical yields are relative low ((40 ± 4)% and (7 ± 0.8)% for formate and tertiary butanol, respectively). Another hint is the high exergonicity of these reactions: ΔG = –249 kJ mol^?1 for formate/ozone system and ΔG = –114 kJ mol^?1 for hydride transfer followed by a methyl shift in the reaction between tertiary butanol and ozone. In addition, the main product of tertiary butanol ozonolysis is butan-2-one [(89 ± 3)%], a compound that is formed only via hydride transfer. For the reaction of ozone with formate an activation energy of (54.6 ± 1.2) kJ mol^?1 and a pre-exponential term of (2.5 ± 1.2) × 10¹¹ were determined (in the presence of tertiary butanol as ^?OH scavenger) whereas for tertiary butanol the two activation parameters were (68.7 ± 1.9) kJ mol^?1 and (2.0 ± 1.5) × 10⁹, respectively.     

Extraction kinetics of cerium(IV) from sulfuric acid medium by the primary amine N1923 using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamic studies on Ce(IV) extraction with primary amine N1923 demonstrate that primary amine N1923 is an excellent extractant for separation of Ce(IV) from Re(III). In order to clarify the mechanism of extraction and to optimize the parameters in practical extraction systems used in the rare earth industry, the extraction kinetics was investigated using a constant interfacial area cell with laminar flow in the present work. RESULTS: The data indicate that the rate constant (k_ao) becomes constant when stirring speed exceeds 250 rpm. The apparent forward extraction rate is calculated to be 10^?1.70. The activation energy (E_a) was calculated to be 20.5 kJ/mol from the slope of log k_ao against 1000/T. The minimum bulk concentration of the extractant necessary to saturate the interface (C_min) is lower than 10^?5 mol L^?1. CONCLUSION: Studies of interfacial tension and the effects of stirring rate and specific interfacial area on the extraction rate show that the extraction rate is kinetically controlled, and a mass transfer model has been proposed. The rate equation has been obtained as: ? d[Ce(IV)]/dt = 10^?1.70[Ce(IV)] [(RNH₃)₂SO₄]^1.376. The rate‐controlling step has been evaluated from analysis of the experimental results. Copyright © 2007 Society of Chemical Industry     

The external mass transfer of basic and acidic dyes on wood

The parameters affecting the initial adsorption rates of Astrazone Blue dye (Basic Blue 69) on to wood have been studied. A simple model has been proposed to determine the external mass transfer coefficients and these have been compared with values obtained using a more complex procedure. The external mass transfer coefficient, β, has been shown to vary linearly with agitation and initial dye concentration using log-log coordinates; furthermore β is independent of particle size. The effect of temperature has been studied and the activation energy for the process is 44 ± 2 kJ mol^?1. Similar correlations were obtained for the adsorption of Telon Blue dye (Acid Blue 25) on wood. Using log-log correlations, the external mass transfer coefficient was found to vary with (rev min^?1)^0.14, C₀^?0.27; and a small dependence on particle size was also observed. The activation energy for the external mass transfer process was 25 ± 2 kJ mol^?1.     

Heavy Metal Removal and Neutralization of Acid Mine Waste Water ‐ Kinetic Study

The influence of the apatite on the efficiency of neutralization and on heavy metal removal of acid mine waste water has been studied. The analysis of the treated waste water samples with apatite has shown an advanced purification, the concentration of the heavy metals after the treatment of the waste water with apatite being 25 to 1000 times less than the Maximum Concentration Limits admitted by European Norms (NTPA 001/2005). In order to establish the macro‐kinetic mechanism in the neutralization process, the activation energy, Ea, and the kinetic parameters, rate coefficient of reaction, k_r, and k_t were determined from the experimental results obtained in “ceramic ball‐mill” reactor. The obtained values of the activation energy Ea >> 42 kJ mol^?1 (e.g. Ea = 115.50 ± 7.50 kJ mol^?1 for a conversion of sulphuric acid η_H2SO4 = 0.05, Ea = 60.90 ± 9.50 kJ mol^?1 for η ^H2SO4 = 0.10 and Ea = 55.75 ± 10.45 kJ mol^‐1 for η ^H2SO4 = 0.15) suggest that up to a conversion of H2SO4 equal 0.15 the global process is controlled by the transformation process, adsorption followed by reaction, which means surface‐controlled reactions. At a conversion of sulphuric acid η ^H2SO4 > 0.15, the obtained values of activation energy Ea < 42 kJ mol^‐1 (e.g. Ea = 37.55 ± 4.05 kJ mol^‐1 for η ^H2SO4 = 0.2, Ea = 37.54 ± 2.54 kJ mol^‐1 for η ^H2SO4 = 0.3 and Ea = 37.44 ± 2.90 kJ mol^‐1 for η ^H2SO4 = 0.4) indicate diffusion‐controlled processes. This means a combined process model, which involves the transfer in the liquid phase followed by the chemical reaction at the surface of the solid. Kinetic parameters as rate coefficient of reaction, kr with values ranging from (5.02 ± 1.62) 10‐4 to (8.00 ± 1.55) 10‐4 (s^‐1) and transfer coefficient, kt, ranging from (8.40 ± 0.50) 10‐5 to (10.42 ± 0.65) 10‐5 (m s^‐1) were determined.     

Studies on two‐dimensional coordination polymer cadmium phosphate and its high efficient adsorption of Pb(II) ions from aqueous solutions

The two‐dimensional coordination polymer cadmium phosphate with the morphology of rectangle layers was prepared by solid‐state template reaction at room temperature, and was characterized by XRD, FTIR, and TEM techniques. The as‐synthesized sample is a layered cadmium phosphate material, in which the structure is poly (CdPO₄^?) anion framework with ammonium ions and water species residing in the space between the layers, and cadmium ions are coordinated by the phosphate oxygen atoms. This article also presents the adsorption of Pb(II) ions from aqueous solution on the as‐synthesized coordination polymer cadmium phosphate, and the results showed that this inorganic polymer adsorbent had good adsorption capacity. It could reach to the saturation adsorption capacity within an hour, and its excellent adsorption capacity for Pb(II) was 5.50 mmol/g when the initial solution concentration was 1.68 × 10³ μg/mL at T = 278K. Moreover, the adsorption kinetics and adsorption isotherms were studied, it revealed that the adsorption kinetics can be modeled by pseudo second‐order rate equation wonderfully. The apparent activation energy (E_a), ΔG, ΔH, and ΔS were 3.16 kJ mol^?1, ?13.97 kJ mol^?1, ?11.84 kJ mol^?1, and 7.66 J mol^?1 K^?1, respectively. And it was found that Langmuir equation could well interpret the adsorption of the as‐synthesized coordination polymer cadmium phosphate for Pb(II) ions. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Kinetics of Denaturation and Effects of Surfactants and Polyethylene Glycol on Soybean Esterase (Glycine max L) Stability

The objective of this work was to evaluate the kinetics and thermodynamics parameters and the effects of anionic, cationic and nonionic surfactants and polyethylene glycol on the activity and stability of a crude esterase extracted from soybeans (Glycine max L.). The activation energy for thermal inactivation was calculated from the Arrhenius plot was found to be 59.4 kJ mol^?1 and the ΔH* 56.82 kJ mol^?1 at 40 °C, which was the optimum temperature for enzyme activity. The ΔS* and ΔG* of the enzyme were found to be 61.67 kJ mol^?1 and 15.50 J mol^?1 K^?1, respectively, at the optimum temperature. The activity was only enhanced by the cationic surfactants cetyltrimethylammonium bromide and tetradecylmethylammonium bromide at a concentration of 3.0 mM. The anionic surfactant showed a positive effect on enzyme activity at the concentrations of 1.5 and 3.0 mM. Aqueous PEG (polyethylene glycols) solutions activated the esterase, and maximum activation (170 %) occurred with the addition of 6 kDa PEG. PEG with molecular weights of 0.4 and 10 kDa enhanced enzyme stability at 40 °C.     

Kinetic Study of an Effective Pb(II) Transport through a Bulk Liquid Membrane Containing Calix[6]arene Hexaester Derivative as a Carrier

The article describes transport of Pb(II) through bulk liquid membrane (BLM) containing calix[6]arene hexaester derivative (1) as a carrier. The effect of various parameters such as temperature, carrier concentration, stirring speed and type of solvent on the Pb(II) transport efficiency of the carrier through BLM was evaluated. The activation energy values for the extraction and re-extraction were found as 56.33 kJ mol^?1 and 14.79 kJ mol^?1, respectively. These values demonstrate that the process is diffusionally controlled by Pb(II). Observations indicate that the membrane entrance and exit rate constants (k₁, k₂) increase with increasing stirring speed as well as carrier concentration and decrease with increasing temperature. The effect of solvent on k₁ and k₂ was found to be in the order of CH₂Cl₂ > CHCl₃ > CCl₄.     

Kinetic study of the reaction between hydroxyl-terminated polybutadiene and isophorone diisocyanate in bulk by quantitative FTIR spectroscopy

A kinetic study of the reaction between a hydroxyl-terminated polybutadiene (HTPB) and isophorone diisocyanate (IPDI) was carried out in the bulk state by using quantitative Fourier transform infrared (FTIR) spectroscopy. The reaction is shown to obey a second-order rate law, being first order in both the HTPB and IPDI concentrations. The activation parameters obtained from the evaluation of kinetic data are ΔH‡ = 41.1 ± 0.4 kJ mol, ΔS‡ = −198 ± 2 J K⁻¹ mol⁻¹ and E_a = 43.8 ± 0.4 kJ mol⁻¹, which are quite different from the solution values. However, they are in agreement with the results obtained on propellants by torsional braid measurements. The large negative value of the activation entropy is indicative of an associative mechanism, which is in accord with the second-order rate law for the polyurethane formation. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1979–1983, 1997     

Isothermal and nonisothermal melt‐crystallization kinetics of syndiotactic polystyrene

Analyses of the isothermal and nonisothermal melt kinetics for syndiotactic polystyrene have been performed with differential scanning calorimetry, and several kinetic analyses have been used to describe the crystallization process. The regime II→III transition, at a crystallization temperature of 239°, is found. The values of the nucleation parameter K_g for regimes II and III are estimated. The lateral‐surface free energy, σ = 3.24 erg cm^?2, the fold‐surface free energy, σ_e = 52.3 ± 4.2 erg cm^?2, and the average work of chain folding, q = 4.49 ± 0.38 kcal/mol, are determined with the (040) plane assumed to be the growth plane. The observed crystallization characteristics of syndiotactic polystyrene are compared with those of isotactic polystyrene. The activation energies of isothermal and nonisothermal melt crystallization are determined to be ΔE = ?830.7 kJ/mol and ΔE = ?315.9 kJ/mol, respectively. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2528–2538, 2002     

Kinetic and Thermodynamic Studies of Emulsion Polymerization of a Sugar Monomer by Calorimetry with Compensation Heating and Differential Cooling

The kinetic and thermodynamic features of free‐radical batch emulsion polymerization of a sugar monomer (3‐MDG) and butyl acrylate (BA) were investigated in a power compensation calorimeter. The homopolymerizations as well as the copolymerization have been studied. The overall activation energy of 3‐MDG homopolymerization was 140 ± 3.8 kJ · mol^?1, the polymerization enthalpy was ΔH_MDG = ?51.6 ± 1.9 kJ · mol^?1 and the calculated adiabatic temperature rise was ΔT_ad = 78.5 K. The effects of the initiator and the emulsifier concentrations on the 3‐MDG/BA batch copolymerization kinetics and on the colloidal properties of the final sugar latexes were studied at 60 °C. At higher emulsifier and initiator concentration, respectively, the polymerization rate increases and the particle size decreases, but the trends do not conform to the Smith‐Ewart theory. Polydisperse sugar latex particles with a mean diameter in the range of 50–67 nm were obtained.

Relationship between the activation energy and the conversion for BA (open symbols) and 3‐MDG (solid symbols).     

Kinetic Studies on Oxirane Cleavage of Epoxidized Soybean Oil by Methanol and Characterization of Polyols

The kinetics of the oxirane cleavage of epoxidized soybean oil (ESO) by methanol (Me) without a catalyst was studied at 50, 60, 65, 70 °C. The rate of oxirane ring opening is given by k[Ep][Me]², where [Ep] and [Me] are the concentrations of oxiranes in ESO and methanol, respectively and k is a rate constant. From the temperature dependence of the kinetics thermodynamic parameters such as enthalpy (ΔH), entropy (ΔS), free energy of activation (ΔF) and activation energy (ΔE _a) were found to be 76.08 (±1.06) kJ mol⁻¹, −118.42 (±3.12) J mol⁻¹ k⁻¹, 111.39 (±2.86) kJ mol⁻¹, and 78.56 (±1.63) kJ mol⁻¹, respectively. The methoxylated polyols formed from the oxirane cleavage reaction , were liquid at room temperature and had three low temperature melting peaks. The results of chemical analysis via titration for residual oxiranes in the reaction system showed good agreement with IR spectroscopy especially the disappearance of epoxy groups at 825, 843 cm⁻¹ and the emergence of hydroxy groups at the OH characteristic absorption peak from 3,100 to 3,800 cm⁻¹.     

Kinetic Studies of n-Butylparaben Degradation in H2O2/UV System

This work reports the experimental results of kinetics study of n-butylparaben (BP) degradation in H₂O₂/UV systems. A pseudo–steady-state and competition kinetic approaches were used to determine the reaction rate constants between the BP and ^?OH. In competition kinetics atrazine (2.30?×?10⁹ M^?1?s^?1) was used as a reference compound. The measured rate constants for ^?OH reaction with BP ranged from (3.84 ± 0.12)?×?10⁹ M^?1?s^?1 to (8.56 ± 0.90)?×?10⁹ M^?1?s^?1 depending on solution pH and temperature. Values of the rate constant obtained using different methods were in good agreement. The calculated activation energy was equal to 19.01 ± 1.02 kJ mol^?1.     

Supercritical water oxidation of quinoline in a continuous plug flow reactor—part 2: kinetics

The results of a detailed investigation into the kinetics of quinoline oxidation in supercritical water are presented. The novel kinetic data presented were obtained in a continuously operated, plug flow reactor where parameters such as temperature, pressure, residence time and stoichiometric ratio of oxidant to quinoline were investigated and detailed in the companion paper (Pinto LDS, Freitas dos Santos LMF, Al‐Duri B and Santos RCD, Supercritical water oxidation of quinoline in a continuous plug flow reactor—part 1: effect of key operating parameters. J Chem Technol Biotechnol). An induction time was experimentally observed, ranging from 1.5 to 3.5 s, with longer times observed in experiments carried out at lower temperatures. A pseudo‐first‐order rate expression with respect to quinoline concentration (with oxygen excess) was first adopted and the activation energy of 234 kJ mol^?1 and a pre‐exponential factor of 2.1 × 10¹⁴ s^?1 were estimated. Furthermore, an integral power rate model expression was established, attributing a reaction order for quinoline as 1 and for oxygen as 0.36. An activation energy and pre‐exponential factor for this model were determined as 224 kJ mol^?1 and 3.68 × 10¹⁴ M^?0.36 s^?1, respectively. A global rate expression was then regressed for the quinoline reaction rate from the complete set of data. The resulting activation energy was 226 ± 19 kJ mol^?1 and the pre‐exponential factor was 2.7 × 10^{13 ± 2} M^?0.1 s^?1. The reaction orders for quinoline and oxygen were 0.8 ± 0.1 and 0.3 ± 0.1, respectively. It was shown that the least‐squares regression method provided the best‐fit model for experimental results investigated in this study. Copyright © 2006 Society of Chemical Industry     

Solvent extraction studies of Sm(III) from nitrate medium and separation factors of rare earth elements with mixtures of sec‐octylphenoxyacetic acid and 1,10‐phenthroline

BACKGROUND: Liquid–liquid extraction is widely used for the separation of rare earths, among which synergistic extraction has attracted more and more attention. Numerous types of synergistic extraction systems have been applied to rare earths with high extraction efficiency and selectivities. In the present study, mixtures of sec‐octylphenoxyacetic acid (CA12, H₂A₂) and 1,10‐phenanthroline (phen, B) have been used for the extraction of rare earths from nitrate medium. The stoichiometry of samarium(III) extraction has been studied using the methods of slope analysis and constant molar ratio. The possibility of using synergistic extraction effects to separate rare earths has also been studied. RESULTS: Mixtures of CA12 and phen display synergistic effects in the extraction of rare earth elements giving maximum enhancement coefficients of 5.5 (La); 13.7 (Nd); 15.9 (Sm); 24.5 (Tb); 45.4 (Yb) and 12.3 (Y). Samarium(III) is extracted as SmHA₄B₃ with mixtures of CA12 and phen instead of SmHA₄ when extracted with CA12 alone. The calculated logarithm of the equilibrium constant is 6.0 and the thermodynamic functions, ΔH, ΔG, and ΔS, have been calculated as 4.3 kJ mol^?1, ? 33.7 kJ mol^?1 and 129.7 J mol^?1 K^?1, respectively. CONCLUSION: Mixtures of CA12 and phen exhibit synergistic effects on rare earth elements. Graphical and numerical methods have been successfully used to determine their stoichiometries. The different synergistic effects may provide the possibility of separating yttrium from heavy lanthanoids at an appropriate ratio of CA12 and phen. Copyright © 2010 Society of Chemical Industry     

Kinetic and thermodynamic investigation of Arthrospira (Spirulina) platensis fed‐batch cultivation in a tubular photobioreactor using urea as nitrogen source

BACKGROUND: Fed‐batch culture allows the cultivation of Arthrospira platensis using urea as nitrogen source. Tubular photobioreactors substantially increase cell growth, but the successful use of this cheap nitrogen source requires a knowledge of the kinetic and thermodynamic parameters of the process. This work aims at identifying the effect of two independent variables, temperature (T) and urea daily molar flow‐rate (U), on cell growth, biomass composition and thermodynamic parameters involved in this photosynthetic cultivation. RESULTS: The optimal values obtained were T = 32 °C and U = 1.16 mmol L^?1 d^?1, under which the maximum cell concentration was 4186 ± 39 mg L^?1, cell productivity 541 ± 5 mg L^?1 d^?1 and yield of biomass on nitrogen 14.3 ± 0.1 mg mg^?1. Applying an Arrhenius‐type approach, the thermodynamic parameters of growth (ΔH* = 98.2 kJ mol^?1; ΔS* = ? 0.020 kJ mol^?1 K^?1; ΔG* = 104.1 kJ mol^?1) and its thermal inactivation ( kJ mol^?1; kJ mol^?1 K^?1; kJ mol^?1) were estimated. CONCLUSIONS: To maximize cell growth T and U were simultaneously optimized. Biomass lipid content was not influenced by the experimental conditions, while protein content was dependent on both independent variables. Using urea as nitrogen source prevented the inhibitory effect already observed with ammonium salts. Copyright © 2012 Society of Chemical Industry