Academic literature on the topic 'Pseudo-ternary diffusion'

The rate equations for diffusion and chemical reaction have been solved for isothermal diffusion with the first-order reactionA → Bin stirred diaphragm cells. Provided pseudo-steady-state conditions are established in the diaphragms, the concentration differences across the diaphragm for the reactant and product are predicted to show damped oscillations in time for certain values of the solute diffusivities. Diffusion coefficients have been determined for aqueous solutions of trans-dichlorobis (ethane-1,2-diamine)cobalt(III) chloride in which the 1 : 1 salt slowly converts into a 1:2 salt through the reaction [Co(en)2Cl2]+ + Cl - → [Co(en)2Cl]2+ +2Cl- with k = 3.6×10-5 s-1 at 25°C. Supplementary ternary diffusion coefficients have been determined for aqueous solutions of potassium acetate + potassium sulfate, a ternary mixed electrolyte with ionic mobilities similar to those of the aqueous cobalt salts.

A general method for the determination of multicomponent diffusion coefficients is developed using the algebraic technique of matrix diagonalization. When linear combinations of measurements from several multicomponent diffusion experiments performed with different initial concentration gradients (but with the same final composition) are analyzed as simple binary data, particular combinations may be found that transform the multicomponent diffusion coefficient matrix D to diagonal form and thus yield time-invariant, pseudo-binary diffusion coefficients: the eigenvalues of D. Since the matrix that diagonalizes D is given by the coefficients used to form the linear combinations, D is easily recovered by the inverse transformation. The advantages of the eigenvalue method are briefly discussed. For testing purposes, ternary diffusion coefficients are determined from conductance measurements for dilute aqueous NaOH + NaCl mixtures. Diffusion of NaOH in aqueous NaCl is significantly more rapid than in pure water, and large coupled flows of NaCl are observed. The results are in close agreement with behavior predicted by Onsager–Fuoss theory.

This study aimed to develop a microemulsion formulation for topical delivery of Diacetyl Boldine (DAB) and to evaluate its cytotoxicity against melanoma cell line (B16BL6) in vitro. Using a pseudo-ternary phase diagram, the optimal microemulsion formulation region was identified, and its particle size, viscosity, pH, and in vitro release characteristics were determined. Permeation studies were performed on excised human skin using Franz diffusion cell assembly. The cytotoxicity of the formulations on B16BL6 melanoma cell lines was evaluated by MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-2H-tetrazolium bromide) assay. Two formulation compositions were selected based on the higher microemulsion area of the pseudo-ternary phase diagrams. The formulations showed a mean globule size of around 50 nm and a polydispersity index of <0.2. The ex vivo skin permeation study demonstrated that the microemulsion formulation exhibited significantly higher skin retention levels than the DAB solution in MCT oil (Control, DAB-MCT). Furthermore, the formulations showed substantially higher cytotoxicity toward B16BL6 cell lines than the control formulation (p < 0.001). The half-maximal inhibitory concentrations (IC50) of F1, F2, and DAB-MCT formulations against B16BL6 cells were calculated to be 1 µg/mL, 10 µg/mL, and 50 µg/mL, respectively. By comparison, the IC50 of F1 was 50-fold lower than that of the DAB-MCT formulation. The results of the present study suggest that microemulsion could be a promising formulation for the topical administration of DAB.

Acyclovir has low bioavailability mainly due to low solubility. This study aimed to formulate an optimized acyclovir (ACV) nanoemulsion gel for the slow, variable and incomplete oral drug absorption in patient suffering from herpes simplex viral infection. The dispersion solubility of acyclovir was studied in various oils, surfactants and co-surfactants and by constructing pseudo phase ternary diagram nanoemulsion area was identified. The optimized formulations of nanoemulsions were subjected to thermodynamic stability tests. After stability study, stable formulation was characterized for droplet size, pH determination, centrifugation, % drug content in nanoemulsion, Zeta Potential and Vesicle size measurement and than nanoemulsion gel were prepared and characterized for spreadability, measurement of viscosity, drug content, In-vitro diffusion, in-vitro release data. Span 40 was selected as surfactant, PEG 400 as co surfactant and castor oil as oil component based on solubility study. The in vitro drug release from acyclovir nanoemulsion gel was found to be considerably higher in comparison to that of the pure drug. The in-vitro diffusion of nanoemulsion gel was significantly good. Based on this study, it can be concluded the solubility and permeability of acyclovir can be increased by formulating into nanoemulsion gel. Keywords: Acyclovir, Nanoemulsion, In-vitro diffusion, Zeta potential, Stability

In the present investigation, a nanoemulgel of minocycline was formulated and optimized for an improved drug delivery and longer retention time in the targeted area. Combining eucalyptus oil, Tween 20, and Transcutol HP, different o/w nanoemulsions were formulated by the oil phase titration method and optimized by pseudo-ternary phase diagrams. The morphology, droplet size, viscosity, and refractive index of the thermodynamically stable nanoemulsion were determined. Furthermore, optimized nanoemulsion was suspended in 1.0% w/v of Carbopol 940 gel to formulate the nanoemulgel, and for this, pH, viscosity, and spreadability were determined and texture analysis was performed. To compare the extent of drug penetration between nanoemulsion and nanoemulgel, ex vivo skin permeation studies were conducted with Franz diffusion cell using rat skin as the permeation membrane, and the nanoemulgel exhibited sustained-release behavior. It can be concluded that the suggested minocycline-containing naoemulgel is expected to treat acne rosacea more effectively.

Objective: The objective was to improve the bioavailability, stability of formulation, and skin permeability of Duloxetine HCl.Method: Microemulsion was prepared with oleic acid as oil, water, and Smix ratio of tween 20 to propylene glycol (1:3). Pseudo-ternary phase diagrams were constructed to determine the region of existence of microemulsions prepared using oil titration method. Optimization of formulations was done based on the in vitro diffusion studies. The microemulsion was gelled using carbopol 934p and HPMCK 100 as the gelling agent.Result: After the analysis of different evaluation parameter and drug release, the F3 batch was selected as a promising formulation for delivery of duloxetine HCl as a microemulsion gel for transdermal drug delivery with 79.607% drug release in 10 h.Conclusion: It was observed that transdermal microemulsion gel can be formulated successfully for duloxetine HCl with improved bioavailability. Among the other batches, the F3 batch was selected as an optimized batch because all the evaluation parameters results are satisfactory. From stability data, the formulation was found to be stable as no phase separation or turbidity was observed in the formulation after 3 months.

The purpose of the present work was to develop nanoemulsion-based formulations of mirtazapine for intranasal delivery using a spray actuator to target the brain for treating depression. Research on the solubility of medications in different oils, surfactants, co-surfactants, and solvents has been done. Using pseudo-ternary phase diagrams, the various ratios of the surfactant and co-surfactant mix were computed. Thermotriggered nanoemulsion was formulated using different concentrations of poloxamer 407 (i.e., 15%, 15.5%, 16%, 16.5% up to 22%). Similarly, mucoadhesive nanoemulsion using 0.1% Carbopol and water-based plain nanoemulsions were also prepared for comparative assessment. The developed nanoemulsions were analyzed for physicochemical properties, i.e., physical appearance, pH, viscosity, and drug content. Drug-excipient incompatibility was determined by Fourier transform infrared spectral (FTIR) analysis and differential scanning calorimetry (DSC). In vitro drug diffusion studies were conducted for optimized formulations. Among the three formulations, RD1 showed the highest percentage of drug release. Ex vivo drug diffusion studies were conducted on freshly excised sheep nasal mucosa with Franz diffusion cell simulated nasal fluid (SNF) for all three formulations up to 6 h, and the thermotriggered nanoemulsion (RD1) showed 71.42% drug release with 42.64 nm particle size and a poly dispersity index of 0.354. The zeta potential was found to be −6.58. Based on the above data, it was concluded that thermotriggered nanoemulsion (RD1) has great potential to be used as an intranasal gel for treating depression in patients. It can offer great benefits by reducing dosing frequency and improving bioavailability of mirtazapine by direct nose-to-brain delivery.

Ni-based superalloys are widely used in jet engine applications. Bond coats are applied to these alloys for protection during service in a very harsh environment at high operating temperature. The addition of Pt to the -NiAl bond coat increases the cyclic oxidation resistance and the service life by reducing sulphur segregation between the bond coat and thermally grown oxide (TGO). However, it also increases the rate of interdiffusion of Ni and Al, leading to an increase in the thickness of the interdiffusion zone (IDZ) developed between the bond coat and superalloy. This results in an unwanted loss of Al from the bond coat, leading to a decrease in the service life of the turbine blade. Hence, it is important to understand the diffusion-controlled growth and microstructural evolution of IDZ at elevated temperature based on quantitative diffusion analysis. The composition-dependent interdiffusion coefficients (not the average over a composition range) could not be estimated experimentally following the conventional diffusion couple technique in multicomponent systems. The equations for the estimation of the interdiffusion coefficients in multicomponent systems are established based on the Onsager formalism. However, the number of independent equations required for the estimation of these data could not be achieved experimentally in a system with more than three components. Therefore, all the quantitative diffusion analyses are conducted in binary and ternary systems. In a binary system, both interdiffusion and intrinsic diffusion coefficients can be estimated. However, we can estimate only the interdiffusion coefficients in a ternary system. The intrinsic diffusion coefficients cannot be estimated following the Kirkendall marker experiments because of stringent requirements, which cannot be fulfiled experimentally. Since most of the inhomogeneous bulk materials in applications are multicomponent in nature, the lack of an experimental method for estimation of these diffusion coefficients in systems with more than three components makes it impossible to understand many physicomechanical properties based on quantitative analysis. To circumvent this problem, the pseudo-binary diffusion couple in the multicomponent system is explored. In a pseudo-binary diffusion couple, only two components develop the diffusion profiles while maintaining the compositions of other components as constant making it possible to estimate the diffusion coefficients in a multicomponent system by removing various complications. However, this method is still at the nascent stage and we cannot estimate the cross interdiffusion coefficients, which are essential for understanding the influence of thermodynamic parameters on diffusional interactions between the components. Therefore, we have developed the concept of the pseudo-ternary diffusion couple method in which only three components develop the diffusion profiles keeping other components as the constant facilitating the estimation of both main and cross interdiffusion coefficients. The benefits of using both pseudo-binary and pseudo-ternary diffusion couple methods in inhomogeneous multicomponent systems are demonstrated in this study by estimating different types of composition-dependent diffusion coefficients. The steps and analyses for utilizing the pseudo-binary and pseudo-ternary methods are first described in the Ni-Co-Fe-Mo system by producing ideal diffusion profiles fulfiling the concepts behind these methods. Subsequently, the discussion is extended to the Ni-Co-Cr system for the estimation of the tracer diffusion coefficients. Steps are also suggested to avoid the complications of developing non-ideal pseudo-binary diffusion profiles. These methods are easy to adopt for research engineers. Most importantly, these allow validating the data calculated following newly proposed numerical methods by different groups, which otherwise would not be possible earlier. The tracer diffusion coefficients estimated following the radiotracer method could compare the data estimated indirectly following the newly proposed method. However, these are available now only in very few multicomponent systems. Therefore, this study is extended to the Ni-Co-Fe-Cr system for the sake of comparison of the data estimated following the pseudo-binary method with tracer diffusion coefficients measured by the radiotracer method. Along with the interdiffusion coefficients, the intrinsic diffusion coefficients are also estimated for all the components by designing the pseudo-binary couples such that Ni and Co develop the diffusion profiles keeping Fe and Cr constant in one couple, and Fe and Cr develop the diffusion profiles keeping Ni and Co constant in another couple. We have proposed the relations for calculating the tracer diffusion coefficients considering the vacancy wind effect by utilizing the thermodynamic details. A very good match was found with the data estimated directly following the radiotracer method at the equiatomic composition. Since the PB method cannot explain the diffusional interactions between the components, which plays an important role in the evolution of diffusion profiles, the concept of the pseudo-ternary diffusion couple is demonstrated in the Ni-Co-Fe-Mo system. The pseudo-ternary diffusion profiles can be intersected since the diffusion paths are restricted in two dimensions compared to the situation in which all the components develop the diffusion profiles and difficult to intersect even two diffusion paths in a multicomponent space. The modifications of the equations for estimating the diffusion coefficients in this type of diffusion couple is proposed for estimating the main and cross interdiffusion coefficients, which was otherwise impossible during the last many decades. As a next step, we have utilized these methods to estimate the composition-dependent diffusion coefficients in the B2-Ni(CoPt)Al system to understand the diffusion process based on quantitative analysis, which was not possible earlier. We found that the PB-interdiffusion coefficients of Ni and Al decrease in Co's presence but an increase in the presence of Pt. The thermodynamic driving forces show an opposite trend with respect to the composition as compared to the changes in the interdiffusion coefficients. The PT-methods indicate that the main interdiffusion coefficients increase significantly in the presence of Pt. On the other hand, the cross interdiffusion coefficients change marginally, causing a minor change in these components' diffusional interactions. These indicate a dominating role of the Pt(Co)-induced modifications of point defect concentrations. The estimated diffusion coefficients are utilized to explain the increase in the thickness of the IDZ between the B2-Ni(Pt)Al bond coat and the single crystal superalloy René N5. Further, to understand the nature of the precipitates formed in IDZ, The electron probe micro analyser (EPMA) and transmission electron microscopy (TEM) analyses are carried out. It reveals that the precipitates are rich in refractory elements. The partial or complete replacement of Pt with Pd in B2-NiAl is examined by studying the interdiffusion zone's growth rate and the spallation of the oxide layer during thermal cycling. The quantitative diffusion analysis following the PB method indicates that the PB interdiffusion coefficient of Ni and Al decreases in the presence of Pd. This reflects the decreased growth rate of the interdiffusion zone and, therefore, can be considered beneficial compared to the Pt modified bond coat. On the other hand, the spallation of the oxide layer is high in the presence of Pd. However, a partial replacement of Pt with Pd leads to superior spallation resistance against thermal cycling along with the absence of deleterious PtAl2 phase during pack cementation. The combination of Pt and Pd reduces the Al loss caused by the growth of IDZ and forms a stable oxide layer. So, this combination of Pt+Pd modified bond coat is beneficial for gas turbine applications.

Quantitative diffusion analysis in multicomponent metallic systems has been a formidable task historically and despite decades of research, most of the diffusivity estimations were limited to interdiffusion and some intrinsic diffusion coefficients in binary systems and interdiffusion coefficients in a few ternary systems until recently. The experimental complications associated with the need to intersect (n-1) serpentine diffusion paths in the n dimensional space for determining the 〖(n-1)〗^2 interdiffusion coefficients lead to various approaches like average diffusivity, square root diffusivity estimations that approximate a representative value of the diffusivity across a composition range from a single experiment. However, these values are not material constants and do not provide any information about the atomic interactions. This lack of diffusivity data in multicomponent systems has hampered the development of mobility databases essential for various simulations and physico-chemical studies of materials. This work resolves the issues with quantitative multicomponent diffusion analysis via several newly proposed methods that solves the issue of intersecting diffusion paths through the application of special constrained diffusion paths. The equations necessary to apply these methods are derived and their application is discussed mathematically and applied experimentally to the model alloy system, the NiCoFeCr equiatomic multiprincipal element alloy to compare with available radiotracer data measured for this system. The work first employs the pseudo-binary diffusion couple approach that develops a rectilinear diffusion path in the multicomponent space to the NiCoFeCr system to estimate the tracer coefficients from the intrinsic coefficients at the marker plane. The mathematical formulations derived for the same justify its namesake and the obtained tracer coefficients can be used to back calculate the intrinsic and interdiffusion coefficients. The pseudo-ternary method improves on the shortcomings of the pseudo-binary diffusion couple method and enables the estimation of tracer coefficients of three components by crossing two constrained diffusion paths in a 2d plane in addition to the main and cross interdiffusion coefficients. The body diagonal method originally proposed for determination of interdiffusion coefficients is modified here to determine the tracer coefficients of all components using only two diffusion profiles thus reducing the errors associated with crossing (n-1).paths per the original approach. This work then explores the possibilities of crossing dissimilar constrained diffusion paths by crossing pseudo ternaries of different types. Strategically crossing a rectilinear pseudo-binary diffusion path with a serpentine conventional (body diagonal) diffusion path overcomes all the previous drawbacks of pseudo binary, pseudo ternary and body diagonal methods to determine the full set of diffusivities at any desired composition and generalizes the constrained diffusion path approach to any order multicomponent system. The obtained tracer coefficients show a good match with the diffusivities measured in radio tracer experiments. Finally, based on the ideas from the constrained diffusion path experiments in the NiCoFeCr system, a constrained path approach is devised to measure the diffusivities in an Al based NiCoFeCr multiprincipal element alloy system which was not possible earlier due to unavailability of radio isotopes and the complexities of interdiffusion experiments in higher order systems. The obtained tracer diffusivities, show an excellent match with the trends extrapolated from lower order systems. Calculated intrinsic and interdiffusion coefficients demonstrate the importance of vacancy wind effect as well as the issues with using diffusivities having different dependent components to make predictions on diffusion trends among different elements.

A computational approach has been undertaken to design and assess potential Fe-Cr-Ni-Al systems to produce stable nanostructured corrosion-resistant coatings that form a protective, continuous scale of alumina or chromia at elevated temperatures. Phase diagram computation was modeled using the Thermo-Calc® software and database [1, 2] to generate pseudo-ternary Fe-Cr-Ni-Al phase diagrams to help identifying compositional ranges without undesirable brittle phases. Computational modeling of the grain growth process, sintering of voids, and interface toughness determination by indentation, assessed micro-structural stability and durability of the nanocoatings fabricated by a magnetron-sputtering process. Interdiffusion of Al, Cr, and Ni was performed using the DICTRA® diffusion code [3] to maximize the long-term stability of the nanocoatings. The computational results identified a new series of Fe-Cr-Ni-Al coatings that maintain long-term stability and a fine-grained microstructure at elevated temperatures. The formation of brittle sigma phase in Fe-Cr-Ni-Al alloys is suppressed for Al contents in excess of 4 wt.%. Grain growth modeling indicated that the columnar-grained structure with a high percentage of low-angle grain boundaries is resistant to grain growth. Sintering modeling indicated that the initial relative density of as-processed magnetron-sputtered coatings could achieve full density after a short thermal exposure or heat-treatment. Interface toughness computation indicated that Fe-Cr-Ni-Al nanocoatings exhibit high interface toughness in the range of 52–366 J/m2. Interdiffusion modeling using the DICTRA software package indicated that inward diffusion could result in substantial to moderate Al and Cr losses from the nanocoating to the substrate during long-term thermal exposures.