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This article focuses on the design and analysis of experiments with mixtures, very commonly involved in product development whenever a multicomponent system is concerned. Here, classical and computer-aided designs for mixture studies are introduced and discussed with various numerical examples. In fact, the strategies, which may be adopted by the experimenter for the construction of blending models in the region of interest, are quite different. The use of various methods and techniques for analysis and optimization are here illustrated by some case studies taken from practical experiences to analyse step by step the procedures adopted for the experimentation and the analysis of mixture data.

A novel approach based on the use of desirability functions is presented for the robustness assessment of liquid chromatographic separations as derived from computer-assisted methods development processes. The approach is based on generally accepted hypothesis that a robust separation procedure will be inert to small random variations of the operational variables, typically encountered in the day-to-day routine analytical practice. This means that peak positions along the chromatograms must keep standstill or move insignificantly when operational variables are not intentionally changed. Thus, the degree of peak positions variation as evaluated from mathematical retention models can be used to assess the robustness of the developed procedures before testing the actual performance experimentally. In the approach proposed, this assessment is obtained by fixing a bilateral partial desirability window around each peak in the simulated chromatogram. The whole chromatogram robustness is characterized by an overall desirability value calculated as the geometric mean of the partial desirability windows evaluation. An added advantage of this approach is that the robustness value calculated is normalized between zero and one and thus, easy to interpret. Thus, when chromatograms are simulated and small random variations are introduced into the operational factors of the model, values for the overall desirability close to one means that the procedure performs robustly. On the contrary, low values for the overall desirability clearly indicated a serious lack of robustness. When used in conjunction with the Pareto optimality approach, as shown here, this robustness assessment strategy allows testing several Pareto front solutions before the final experimental testing which is always needed. In this way, a dramatical reduction of the experimental effort is obtained. Although the approach is theoretically applicable to any chromatographic separation, examples of reversed phase liquid chromatographic procedures are used to show the performance of the proposed methodology.

Mixed-level supersaturated designs are designs in which the number of coefficients to estimate is greater than the number of experiments. This type of design is useful in the rapid preliminary investigation of a process with a large number of potentially relevant factors but with only a few of them having important effects. The purpose of this project was to determine the active parameters on a chemical process. A mixed-level supersaturated design of 12 experiments was carried out, allowing us to screen 17 two-level factors and 5 three-level factors. χ²-optimality of the design was confirmed. In order to verify the results, a 40-run matrix was built. One parameter was identified as very active in both analyses, and several others were suspected to have an effect on the process. Some differences were observed in the results, regarding the detection of the least influent factors. These are likely due to the loss of information generated by the reduction of runs in the supersaturated design, as this kind of design allows an important reduction of the number of experiments. Further studies should be considered to confirm the activity of some factors.

International audience; n this article, we apply supersaturated strategies to identify active factors in the field of numerical simulation. As the number of simulations is inferior to the number of studied factors, new resolution techniques are proposed and provide excellent results. Indeed, classical supersaturated treatments could not be applied to the high dimensional problem. We show that these designs are well adapted to the high dimensional problem while maintaining the number of simulations at reasonable levels. Very small-sized supersaturated designs show low reliability. Keywords: Hadamard matrix; Supersaturated designs; Screening; Computer experiments; Genetic algorithm; Sensitivity analysis

The cyclodimerisation reaction of butadiene leading to methylene-2-vinylcyclopentane catalysed by zerovalentnickel in presence of Threophos ligand has been optimised using the experimental research methodology. Thus, we obtain the cyclodimer with 70% of selectivity for a conversion rate of 90% and this in the following conditions: temperature 80°C; time 6 hours; [ligand]/[Ni0]=1; [butadiene]/[Ni0]=80; [methanol]/[Ni0]=50.

A series of benzene derivatives C6H5R with R ranging from the two extremes of the σ+ scale of H.C. Brown has been acylated with little FeCl3 catalyst at reflux temperature. Under these conditions the reaction is limited to activated substrates: with benzene and deactivated aromatics the yield is below 10%. A fractional factorial design is carried out with 5 parameters: temperature, % catalyst, time, ratio aromatic/acylation reagent and nature of catalyst in the case of acylation of benzene by benzoyl chloride with a Lewis acid catalyst (AlCl3 or FeCl3). The multivariate analysis shows that the important factors are: temperature, nature and ratio of catalysts; and also that the interaction % of catalyst-nature of catalyst and temperature-nature of catalyst are determinant. Acylation of benzene (and deactivated aromatics) with little Lewis acid catalyst will give acceptable yields if both a moderately active catalyst (FeCl3, ZnCl2) and a high temperature of reaction are used.

New chiral aminophosphinite ligands are readily prepared and their behaviour as homogeneous catalysts was investigated in the linear dimerization of butadiene and isoprene. This latter reaction has been optimised using experimental research methodology, leading to a conversion rate above 50%.

In a previous paper, we showed that the preparation of sulfated diethanolamide of fatty acids is easy to carry out without organic solvents when using olive pomace oil as starting material; the reaction yield was, however, highly variable as a function of factor levels. The purpose of this research is to look for the optimal experimental conditions. We started by applying a supersaturated experimental design to screen for important factors among a list of 31 potentially influential factors in 18 experiments. Thus, we constructed a two-level supersaturated design as a half fraction of a 36-experiment Hadamard matrix and used it for this screening purpose. Multiple regression methods namely stepwise selection procedure, ridge regression and all-subset regressions were used to analyze the supersaturated design results according to a four step procedure. Results indicated that six factors, namely, molar ratio SO 3 /ester, amidation time, amide addition rate, alkali reagent, alkali concentration, and amidation temperature, were very influential factors. Three other factors were moderately influential: neutralization temperature, sodium methanoate amount, and methanol amount. In future research, these factors will be further studied in order to perform robustness tests of the process.

New cosmetic emulsion with biomimetic molecules have been investigated using experimental designs. For this purpose, six variables have been studied: the nature of surfactant (three mixture variables), the percentages of surfactant, co-surfactant and squalene, and five properties have been measured: stability, centrifugation, viscosity, pH, microscope analysis. Because of the complexity of the study, the optimization of these five responses has been carried out in two steps. First, a simple additive model has been postulated, in order to define a smaller domain of interest. A Doehlert, a grid and a simplex centriod designs have been built in order to generate candidate points. Exchange algorithm has allowed to extract a design with only 28 experiments. Results have shown that the percentage of squalene exhibits the greatest influence on the stability and on the viscosity of the emulsions. Secondly, a multiplicative model has been postulated using composite and simplex centroid design to generate candidate points. A set of 36 experiments has been selected. Conditions for the percentage of surfactant and co-surfactant, and for mixture variables have been determined in order to obtain a good compromise between the five responses. Finally, these studies have allowed to determine in the whole domain of interest an optimal formula composed only with biomimetic products and presenting good physico-chemical characteristics and stability.

The use of experimental designs in the field of numerical simulation improves global sensitivity analysis compared to Monte Carlo based method by decreasing the number of simulations. More particularly, supersaturated designs can be applied to decrease the number of calculations, because the number of simulations is inferior to the number of studied factors but its use is risky and depends on “parsimony principle”. This paper shows new supersaturated designs that use the a priori knowledge and thus overcome this difficulty.

The present research studies the optimization of the preparation of a hydrotrope (mixture of sodium toluenesulfonate and sodium xylenesulfonates) for liquid detergents using experimental designs. The preparation is carried out by selective sulfonation of toluene and xylene present in the BTX fraction of a natural gas. The optimization of five responses has been carried out in two steps. First, we carry out an asymmetrical screening design 2 1 3 6 //18 to select from seven factors, those factors which have significant influence on the amount of residual sodium sulfate in the product and on the total conversion of toluene and xylenes. Secondly, we carry out a Box–Behnken design to optimize three retained factors (temperature, molar ratio of acid to toluene plus xylenes, and the amount of desulfation agent), using response surface methodology. In addition, and in order to reach near-optimal sulfonation conditions, we use the desirability functions to optimize the five responses simultaneously. This allows us to determine for the whole process, sulfonation conditions leading to a high yield of toluene and xylene conversion and acceptable amounts of residual sodium sulfates and sodium benzenesulfonate.

The present research studies the formulation and optimization of a self-leveling composition for floor toppings. This formulation is, in particular, based on a fluoroanhydrite which is a by-product of a Tunisian plant for fluorhydric acid preparation; it also contains aggregates, a neutralizing agent, a hydration accelerator and, especially, a plasticizer prepared by sulfonation of the lignin extracted from the black liquor of a Tunisian esparto grass soda pulping process. The optimization of four responses (plasticity, compressive strength, initial and final setting times) has been carried out in two steps. First, we obtain a coarse composition with a relatively acceptable rheological properties. Second, we carry out a mixture design in the surroundings of the retained composition aimed at obtaining a product with the required characteristics formulated by the users of this kind of materials. To this end, the evolution of the plasticity and the setting times of the fresh mortar and the compressive strength of the hardened mortar in a four-component system with constraints were analyzed using a mathematically independent variable approach. Finally, and in order to reach a near-optimal composition, we use the desirability functions to optimize the four responses simultaneously. This allows us to determine the coordinates of a composition which is characterized by high plasticity, acceptable compressive strength and relatively rapid setting times.

In a previous study, we presented a new method for preparing a mixture of sodium toluenesulfonates (STS), sodium xylenesulfonates (SXS), sodium benzenesulfonate (SBS) and Na 2 SO 4 by sulfonating the BTX fraction of a Tunisian natural gas. Such mixtures can be used as a hydrotrope agent for concentrated liquid detergents. In the present work, we performed a mixture design in order to study the effect of each of these four components on the clear point and the viscosity of a liquid detergent, and therefore, to determine the conditions allowing to improve the effectiveness of the hydrotrope. Twenty-eight combinations of the 4 components out of 51 candidate points are selected by the Nemrod-W software according to the D-optimal criterion to fit two polynomial models. The statistical study shows that the fitted models were adequate to describe the clear point and the viscosity responses. Optimal conditions allowing to lower the two responses are then looking for by examining the response surface both as a contour plot, and as three-dimensional surface plot and the response trace. We prove that Na 2 SO 4 exhibits a harmful negative effect, while SXS and STS exhibit, respectively, a strong and moderate positive effect on both clear point and viscosity responses. As expected, SBS has a harmful effect on the two responses but the magnitude of this effect is lesser than that predicted by the preliminary experiments carried out with SBS alone. This phenomenon is explained by the formation of heteroassociation between SBS, STS and SXS similar to what is found in surfactants. The effectiveness of the hydrotrope, obtained by sulfonation of the BTX fraction of the Tunisian natural gas, is really improved by removing sulfates either by adding lime to precipitate gypsum, or isopropanol to reduce the solubility of Na 2 SO 4 .

Background: The aim of this study was to determine the optimal composition of a new medium for long-term hypothermic heart preservation. Methods: The independent effects of 19 compounds were evaluated using an in vitro porcine model. Tissue viability was assessed by measuring the reduction of methyltetrazolium salt, oxygen consumption and energetic compound levels on myocardial biopsies after 24-, 48- or 72-hour incubation periods. Screening of several compounds at two concentrations was performed to greatly reduce the number of experiments. Results: Pyruvate, aspartic acid, chlorpromazine and polyethylene glycol displayed protective properties, whereas calcium (2 mmol/liter), nifedipine, mannitol, magnesium (16 mmol/liter) and reduced glutathione showed deleterious effects. On the basis of these data, the composition of a new preservation solution (Group 1, n = 6) was compared with St Thomas solution (Group II, n = 6) in an isolated, 24-hour pig heart preservation model. During reperfusion, left ventricular developed pressure and coronary blood flow were significantly higher (p < .01) in Group I, suggesting better preservation. Conclusions: Our technique allows for rapid and efficient screening of many compounds currently used in the composition of preservation solutions for cardiac surgery.

Les acides gras eicosapentaenoique et docosahexaenoique, derives de l'acide alpha-linolenique, ont une action fluidifiante sur le sang et sont recommandes dans les maladies cardio-vasculaires (infarctus du myocarde, atherosclerose) et le psoriasis. L'effet hypocholesterolemiant des acides gras polyinsatures dans l'alimentation a ete demontre et donc leur interet dans la prevention de l'atherosclerose. Chez le fœtus et le nourrisson, leur role dans le developpement du cerveau et de la retine est primordial.

The aim of this study was to prepare 5-iodo-2'-deoxyuridine (IdUrd) loaded poly(d,l-lactide-co-glycolide) (PLGA) microspheres with a reduced initial burst in the in vitro release profile, by modifying the drug grinding conditions. IdUrd particle size reduction has been performed using spray-drying or ball milling. Spray-drying significantly reduced drug particle size with a change of the initial crystalline form to an amorphous one and led to a high initial burst. Conversely, ball milling did not affect the initial IdUrd crystallinity. Therefore, the grinding process was optimized to emphasize the initial burst reduction. A first step allowed us to set qualitative parameters such as ball number (7) and cooling with liquid nitrogen to obtain a mean size reduction and a narrow distribution. In a second step, three parameters including milling speed, drug amount and time were studied by a response surface analysis. The interrelationship between drug amount and milling speed was the most significant factor. To reduce particle size it should be necessary to use a moderate speed associated with a sufficient drug amount (400-500 mg). IdUrd release from microparticles prepared by the o/w emulsion/extraction solvent evaporation process with the lowest crystalline particle size (15.3 microns) was studied. Burst effect could be reduced significantly. Concerning the first phase of drug release, the burst was 8.7% for 15.3 microns compared to 19% for 19.5 microns milled drug particles.

The aim of this study was to prepare, in a reproducible manner, poly( d , l -lactide-co-glycolide) (PLGA) biodegradable microparticles with high encapsulation yield of nerve growth factor (NGF), a neurotrophic factor of interest in the treatment of neurodegenerative diseases. Human serum albumin (HSA) was co-encapsulated with NGF by the w/o/w emulsion solvent evaporation/extraction method to stabilize the primary emulsion and to protect NGF. The encapsulation yield optimization was first carried out with HSA alone since it was the major component in the final microspheres, as compared to NGF. The effects of ten process factors on HSA entrapment in PLGA microspheres were examined using a fractional factorial design. Four major factors were identified. The presence of carboxymethylcellulose sodium or mannitol in the internal aqueous phase, the increase of the internal aqueous volume and the concentration of HSA led to a decrease of the encapsulation yield. Two main factors, namely the internal aqueous phase volume and the proportion of acetone in the organic phase, previously identified as a predominant factor, were studied through a response surface methodology. The observed range of HSA encapsulation yield was 87.4–100%. NGF was encapsulated according to the optimal conditions found for the entrapment of HSA. The encapsulation yield was then 97.3±5.0%.

Many preliminary studies contain a large number of potentially relevant factors, but often only a few are believed to have actual effects. To isolate influential factors ( screening ) in an efficient way, special experimental strategies are needed, such as the supersaturated designs or the techniques of group screenin. For investigating k factors, these supersatured designs are composed of n observations where n ≪ k + 1. They are useful in situations in which the number of active factors is very small compared to the total number of factors being considered; more specifically, in practice experiments with simulated systems.

An optimization procedure for multi-step temperature programmed capillary GC was investigated for the detailed hydrocarbon analysis of gasoline. A set of twelve responses, represented by the value of the resolution of the most difficult separations, was selected from several isothermal analyses. The variation of these responses versus the temperature programming conditions was then modeled using a Doehlert matrix for experimental design. Optimal experimental conditions for the twelve responses were then obtained from a response surface optimization. The predicted and experimental resolutions were in good agreement.

An experimental design was carried out to determine the influence of sample weight, final temperature, initial gas pressure, heating rate, residence time and nature of the pyrolysis atmosphere on the yield and composition of pyrolysis shale oil. The study involved discontinuous pyrolysis procedures. The most influential factors were determined and the first-order interactions between them were analysed. The results obtained were exploited, using response surface methodology, to optimize the experimental conditions of pyrolysis. The main finding is that the percentages of the oils (>240% of the Fischer assay which provides 70 lt−1 of oil) and their quality (asphaltenes, paraffins, etc.) are very satisfactory.

Enzymatic hydrolysis (commercial enzyme) was applied to crushed bones in a batch reactor. The extraction was modeled using a Doehlert design. The effects of temperature (five levels ranging from 40 to 60°C), pH (seven levels from 5.7 to 7.5), enzyme concentration (seven levels from 20 to 80 g.kg -1 protein), hydrolysis time (seven levels from 30 to 180 mn) and protein concentration (three levels from 60 to 90 g.kg -1 mixture) were studied. Response surface methodology (RSM) predicted changes in protein yield and hydrolysis degree. Duration and enzyme concentration were the most important parameters, whereas pH and temperature exhibited no significant effects. Inhibition was observed over 80 g.kg -1 of protein concentration.

Multilinear regression is applied when experimenters wish to investigate the relationship between a block of predictor variables ( X ), whose values are fixed by the experimenter, and one or more responses ( Y ), measured at each experiment. The objective is to find a mathematical equation relating X and Y , by means of regression coefficients. Regression analysis is said to give good results when a squared multiple regression coefficient R 2 close to 1 is obtained and when the sum of squares of residuals (differences between experimental value of the response and computed value) is small. However, it must be noted that a bad choice of the experiments renders the obtained regression equation meaningless. In this paper an example of correct and incorrect use of multilinear regression is presented in detail the quality of the coefficients and the goodness of the prediction depend on the experimental design, and the value of R 2 gives no information at all about them. A set of criteria useful to judge the quality of an experimental plan, before carrying out any experiment, is proposed.

International audience; Optimal fractions of resolution V design matrices proposed by Rechtschaffner in 1967 are developed and applied as supersaturated designs in screening experiments. Rechtschaffner matrices allow evaluation of all main factors and two-factor interactions, which in many real-world studies are of practical significance. However, the number of experimental runs increases rapidly with the number of factors in the matrices, which are therefore impractical for more than 5-6 factors. On the contrary, saturated fractions based on Hadamard matrices, which are commonly applied in screening studies, cannot evaluate the interaction effects. Here, a procedure for selecting the optimum fractions of Rechtschaffner matrices is presented and provides supersaturated matrices that are well adapted to a variety of problems, thus allowing the development of screening studies with a relatively small number of experiments. The procedures developed to derive the size-reduced matrices and to evaluate the active factors are discussed and compared in terms of efficiency and reliability, by means of simulation studies and application to a real problem. These fractions are the first supersaturated design matrices capable of estimating interaction effects. Additionally, one important advantage of these supersaturated matrices is that they enable development of follow-up procedures in cases of inconclusive results, by enlarging the matrix and eventually resolving the full Rechtschaffner matrix of departure when it is necessary to evaluate the active factors and their interactions. (C) 2012 Elsevier B.V. All rights reserved.

International audience; A supersaturated design is a design for which there are fewer runs than effects to be estimated. Although two-level supersaturated designs are becoming increasingly popular, mixed-level designs are scarcely used. Mixed-level designs are needed when the response is based on a polynomial response surface model or in situations where factors are nominal variables (with more than two modalities). The aim of this study is to explore the construction of mixed-level supersaturated designs and to evaluate their performance from the analysis of peppermint oil using a gas chromatographic method as application. This experimental setup requires the study of seven factors at two levels and five factors at three levels. Different building methods are tested from asymmetric or symmetric supersaturated designs. The mixed-level supersaturated designs obtained are compared from the point of view of a priori criteria with the aim of evaluating which criteria are better suited to judge the quality and fitness for purpose of these experimental designs. Finally, the results of the supersaturated designs are compared to the complete classical design. (C) 2011 Elsevier B.V. All rights reserved.

Mathieu, D., Puech-Costes, E., Maurette, M.-T. and Phan Tan Luu, R., 1993. The simplex method applied to the detection and following of a discontinuity. Chemometrics and Intelligent Laboratory Systems , 20: 25–34. We present a new application of the so-called simplex method often used in optimization. It is proposed here as a method for following a contour or discontinuity. The method ensures that all the experiments performed are situated within the required accuracy from the investigated curve. The accuracy depends on the size of the simplex. The method can also be used to follow the meanders of a contour. Traditional methods (parallel sequences or lines radiating from a point) are inadequate when the curve studied is tangential to the lines. Several examples from the study of mixtures and other typical situations are presented.

The toxicity of three heavy metals, Cd, Cu and Zn, and the detoxifying role of Ca have been studied for the brown algaCystoseira barbata formaaurentia after a 4-week laboratory culture. The experimental design was based upon a complete factorial design 2k, which seems to be the first time it has been used in algal physiology. It was demonstrated that these three elements, applied jointly, act on weight-growth, chlorophyll a, c and carotenoid synthesis and Cd, Cu and Zn uptake. Cd and Zn act in synergy or in antagony, depending on their exogenous concentrations, on chlorophyll a and on carotenoid synthesis. Zn is antagonistic towards Cd and Cu on weight-growth in the combination Cd-Cu-Zn. From different element combinations, the protective role of Ca appears evident on weight-growth (Cd-Zn-Ca and Cu-Ca), chlorophyll a (Cd-Cu-Ca and Cu-Zn-Ca), chlorophyll c (Cd-Ca), carotenoid synthesis (Cd-Cu-Ca and Cu-Zn-Ca), Cd and Cu uptake (Cd-Cu-Ca) and Zn uptake (Cu-Zn-Ca). This role is confirmed by cytological investigations. This is apparently the first report concerning a Ca interaction with toxicity of heavy metals applied in combinations. However, the mechanisms of tolerance remain unknown.

In this paper, we review a comparison of the empirical and chemiometrical approaches to the modelization of the effects of solvent on a number of NMR, IR and UV–visible spectral properties. The solvents have first been characterized by the π*, α and β scales, which describe respectively the polarity–polarisability, the acidity, and the basicity by hydrogen bond; the 17 most representative, with orthogonal parameters, have been chosen. An attempt has been made to rationalize the observed effects on the observed properties by using simple linear empirical models like the π*, α, and β parameters of Kamlet, Taft, and Abboud; [Formula: see text] of Reichardt; and A and B of Swain. Furthermore, an analysis of the main components has been applied to these effects and to the properties examined; it appears that the quality of the correlations obtained is generally satisfactory and can be compared to the quality that can be observed with the empirical approach. Key words: solvent effect, empirical approach, chemiometrical approach. [Journal translation]

International audience; Experimental design is known to be a powerful tool that permits to identify the most active factors in an experiment. Many works have shown that this technique can also be applied to the domain of numerical simulation. In the present paper, we show that experimental design-based methods are suitable for sensitivity analysis studies in photochemical models. Such a method is presented and applied to a simple photochemical model of Titan's atmosphere. The key reactions that control the concentration of the main hydrocarbons of the model are identified. Comparison with a global sensitivity method is discussed. We show that experimental design-based methods permit to significantly reduce the number of simulations to identify the key reactions in complex kinetic models.

International audience; In this paper, we describe the optimization procedure for the quantitative assay of naphthodianthrones in St. John's Wort dry extract by reversed phase liquid chromatography. Lately, a project for European Pharmacopoeia monograph including an HPLC assay for the active moieties in St. John's Wort dry extract was published with a view to provoking reactions from other researchers. We therefore decided to use different chemometric approaches to evaluate the influence of both analytical and preparative factors to demonstrate the robustness of the optimized method. An asymmetric screening design was built in order to evaluate the weight of each level for each factor – the sonication duration, the light exposure duration, the flow rate and the type of column – on the response: the total hypericin content. Considering the results so obtained, we were compelled to modify some parameters. Thus we built a screening design to apprehend the reliability of the new sample pre-treatment process, the interpretation and identification of active factors were performed according to various methods. We used a third chemometric approach: a sequential bifurcation to check out the method's robustness. In a second step, an eluent compatible with Mass Spectrometry detection was determined by a combined design. To cope with both separation and analysis time, desirability functions were used. Optimal conditions are finally given by ternary system at an optimized temperature (40°C) and all the naphthodianthrones are separated in 10min on conventional endcapped octadecyl silica gel column.

International audience; An optimization procedure for the reversed- phase liquid chromatography (RPLC) assay of naphtho- dianthrones in St John ’ s wort extract from the European Pharmacopoeia project is described. The results obtained from two screening designs showed that light exposure, recommended in the monograph as sample pretreatment, does not permit one to obtain a reproducible quantification of the main ingredients. Improvement of the method robustness implies the need to overcome the problem of light exposure, to subsequently quantify protonaphthodian- thrones and to perform the separation on octadecyl (ODS)- bonded phase at optimized flow rate. The method robustness was checked by using a bifurcation sequential approach investigating the influence of 13 factors. The eluent recommended in the monograph is a ternary mixture of methanol, phosphate buffer and ethyl acetate. For the sake of simplicity, the phosphate buffer was substituted by an acetate buffer. The best composition of the ternary mixture was determined by a combined design including three mixture variables and the temperature as an indepen- dent variable. Chromatographic parameters were modelled in terms of analysis time, resolution and asymmetry. Desirability functions permit one to cope with these parameters and to determine the best compromise. The naphthodianthrones were separated on a conventional endcapped octadecyl silica gel column eluted by a ternary mobile phase at 40 °C in 10 min.

A formulation process, based on the inversion phase of an emulsion, was used to prepare lipid nanocapsules. Triglycerides, lecithin, salted water and hydroxy stearate of poly(ethylene glycol) were used in the preparation. The amounts of each that allowed nanocapsules to be formed described a feasibility domain within a ternary diagram. The size distribution of various nanoparticulate carriers has already been shown to influence their applications. An experimental mixture design inside the feasibility domain has been used in order to approximate, through an empirical model, the influence of the quantitative composition of nanocapsules on their size distribution. Reduced cubic polynomial equations successfully modelled the evolution of responses in terms of particle average diameters and coefficients of variation. The results were presented using an analysis of response surface showing a scale of possible particle sizes between 20 and 95 nm and a coefficient of variation between 11 and 40%. Furthermore, this technique showed that the proportion of hydrophilic surfactant had a major influence on the average diameter and the size distribution of the particles decreasing when its proportion increased. On the contrary, the coefficient of variation and the average diameter slightly increase with the proportion of triglycerides. Such a tool offers major advantages to design the formulation of particles as a function of the required size distribution.

An energy, volume and mass (EVM) model, involving four physico-chemical descriptor variables, i.e. van der Waals energy, internal energy, volume, and mass, to successfully predict the glass transition temperatures ( T g ) of aliphatic acrylate and methacrylate polymers, has been previously described. The EVM model is as good, or better, as the previous models in terms of accuracy of calculated T g values of polymers. However, the classical EVM approach is still limited by the validity of the experimental data that were used to derive the regressor coefficients of the quantitative structure–properties relationship (QSPR). In fact, one major problem is the large variation in the experimental T g values that were reported in the literature. Deciding which values to use for modelling the relationship and the evaluation set of polymers is a problem to tackle with. For these reasons, an a priori design approach to the selection of a database of acrylate and methacrylate polymers for the evaluation of the EVM model has been adopted. In particular, the selection of the molecules to be considered was performed by two computed-assisted procedures based on the exchange algorithm for obtaining D -optimal design and the uniform method for finding experimental designs characterized by a stable structure. Based on the a priori design criteria, the selection of the optimal and uniform designs was “carried out”, in particular according to G -optimality.

Le premier article concernant la planification d’experiences en formulation Planification d’experiences en formulation : criblage de ce traite a ete consacre a l’expose et a la mise en œuvre des techniques destinees a la selection des ingredients d’une formule et a la mise en evidence, parmi les facteurs qui caracterisent un procede de fabrication, de ceux qui ont un reel effet sur les proprietes du produit final. Ce second article est consacre a la mise au point d’une formule, qui correspond a son optimisation et constitue souvent l’etape suivante. Elle necessite l’utilisation d’un modele mathematique previsionnel afin de pouvoir simuler le comportement des proprietes etudiees dans le domaine experimental. Le fait que les proportions d’un melange ne puissent varier de facon independante, puisque leur somme est constante et egale a 1, oblige l’experimentateur a utiliser des matrices d’experiences et des modeles mathematiques specifiques. Ces techniques, connues sous le nom de matrices et modeles de Scheffe, sont donc presentees ici. Cependant, de nombreuses circonstances rendent souvent impossible la mise en œuvre de ces outils. Les domaines experimentaux sont en effet generalement soumis a de nombreuses contraintes sur les proportions des composants, dues a des necessites techniques (instabilite du melange), sanitaires (norme a respecter), economiques (composant couteux), etc. Nous etudierons donc l’impact de ces contraintes sur la forme du domaine experimental et les techniques de planification « sur mesure » qui doivent alors etre utilisees. Parfois, les techniques citees plus haut (matrices et modeles de Scheffe, ou matrices sur mesure) sont « seulement » inappropriees. C’est notamment le cas de l’etude du comportement d’un melange autour d’une composition donnee, particulierement lors de l’optimisation d’une formule deja fabriquee, et que nous etudierons dans le paragraphe intitule « Modelisation au voisinage d’une formule donnee ». Outre la composition de la formule, l’experimentateur doit aussi prendre en compte des facteurs dits « de process », tels que la temperature de moulage, la vitesse d’extrusion, le temps de sechage, etc. Nous consacrerons a ce probleme un paragraphe complet intitule « Problemes mixtes facteurs/composants », dans lequel nous montrerons aussi comment peut etre pris en compte un composant en tres faible quantite. Enfin, la planification des experiences ne serait pas complete sans l’analyse et l’interpretation des resultats. Nous illustrerons un grand nombre de techniques d’analyse, selon le type de probleme presente, en mettant surtout l’accent sur les methodes graphiques. En particulier, nous montrerons la mise en œuvre de la technique dite de la « desirabilite » qui permet de trouver le meilleur compromis entre plusieurs proprietes parfois contradictoires. Nous rappelons au lecteur que cette presentation se compose de deux articles : Planification d’experiences en formulation : criblage : Planification d’experiences en formulation : criblage [J 2 241] : Planification d’experiences en formulation : optimisation auxquels se rattache un fascicule de documentation : [Doc. J 2 242] : Planification d’experiences en formulation. Pour en savoir plus

Les techniques de planification d’experiences sont des outils incontournables de la formulation. Pratiquement toutes les methodes y sont applicables a un moment ou a un autre : choix d’un « ingredient » dans un ensemble de produits, mise au point de la composition d’un melange, des conditions de fabrication, optimisation d’une propriete ou recherche d’un compromis entre plusieurs proprietes, etc. Mais, malgre un nombre croissant de publications consacrees aux plans d’experiences, de nombreux outils sont encore meconnus ou peu utilises. Apres avoir decide de la nature des differentes familles d'ingredients devant entrer dans la composition de la formule finale (antioxydant, durcisseur, liant, etc.), l'experimentateur dispose souvent, pour chacune d'entre elles, d'un nombre plus ou moins important de produits susceptibles d'etre utilises. C'est a leur selection que nous nous attacherons dans cet article. Nous distinguerons deux cas. Dans le premier, que nous appellerons « criblage des facteurs independants », l'experimentateur desire savoir, au sein de chaque famille, quels sont les produits qui ont le meme comportement, quels sont les plus performants, afin de n'en retenir qu'un seul. Au cours de cette meme etape, il peut simultanement mettre en evidence quels sont, parmi les facteurs qui caracterisent le procede de fabrication, ceux qui ont un reel effet sur les proprietes du produit final. Dans le second cas, que nous designerons sous le nom de « criblage des composants en melange », l'experimentateur envisage la possibilite d'introduire dans la formule un melange de plusieurs produits d'une meme famille (melange de liants, par exemple), sous reserve que chacun ait un interet specifique. Un second article Planification d’experiences en formulation : optimisation de cette rubrique sera consacre a la mise au point d’une formule, qui correspond a son optimisation et constitue souvent l’etape suivante. Par souci pedagogique, nous avons deliberement choisi d’illustrer les differentes techniques presentees dans ces deux articles en nous appuyant sur un seul probleme tire du domaine de la galenique : la fabrication de comprimes. Certains des resultats experimentaux sont reels, d’autres sont simules a partir de veritables experimentations, l’objectif essentiel des exemples etant de montrer la mise en œuvre des outils de planification d’experiences et non de determiner de reelles conditions de fabrication. Les raisons essentielles de ce choix sont les suivantes : limiter au minimum l’introduction de chaque nouvel exemple ; montrer que le meme probleme peut etre aborde et resolu de multiples facons, et qu’un changement, apparemment leger, de l’enonce peut conduire a un choix de strategie tres different ; introduire une continuite entre differentes etapes possibles d’une meme etude. Il est en effet exceptionnel qu’un probleme de formulation soit resolu en une seule etape. Comme nous venons de le signaler dans l’introduction, cette presentation se compose de deux articles : [J 2 240] : Planification d’experiences en formulation : criblage Planification d’experiences en formulation : optimisation : Planification d’experiences en formulation : optimisation auxquels se rattache un fascicule de documentation : [J 2 242] : Planification d’experiences en formulation. Pour en savoir plus . Pour une presentation detaillee de l’ensemble des techniques de planification et d’analyse utilisees dans cet article, consulter les references [1] a [5]. Les ouvrages generaux presentant certaines methodes specifiques (melanges, surfaces de reponses, etc.) sont cites dans les references [6] a [8]. Quatre articles generaux consacres aux melanges sont cites aux references [9] a [12]. Plusieurs articles presentant des exemples voisins sont references dans le texte et detailles en [Doc. J 2 242] . La plupart des matrices d’experiences et des traitements decrits dans cet article necessitent l’emploi d’un logiciel specialise (cf. [Doc. J 2 242] ).

Asymmetrical designs are now widely used in the industrial world. However, the traditional methods to construct them are very poor and difficult to handle. To construct experimental design in ‘non-standard’ occurrences, algorithmic methods, such as Fedorov's or Mitchell's algorithms, are broadly used. But in case of high dimensionality, this class of algorithms cannot be used. In this paper, a new technique based on the genetic algorithm for constructing experimental designs is described.

A statistical treatment has allowed us to demonstrate the impossibility of calculating the magnetic susceptibilities and the anisotropies of the C—C and C—H bonds from the collection of chemical shifts reported by Simon and co-workers (22) as we have found the model of McConnell and the ApSimon to be inconsistent with experimental values.Nevertheless, we have been able to determine the values and confidence limits for the magnetic anisotropies of the C=C and C=O bonds and the electric field term for the C=O bond.

Application of modem methods of building experimental matrices gives a selection of 16 experiments amongst a set of 384 possible ones for studying the influence of three factors : the substituent (described by σI and [math]), the alkyl bromide (described by αap ), and the temperature on the rates of quaternization of 4-substituted pyridines in acetone. The kinetic measurements corresponding to the 16 selected experiments allow the calculation of 4 principal effects and 11 interaction terms. Among the last ones, the most significant are discussed with assistance of two — and three-dimensional diagrams. The validity of the proposed model is discussed (analysis of the variance).

L'utilisation d'une matrice factorielle fractionnaire de seulement seize experiences permet d'etudier l'effet de sept facteurs (volume du recipient, concentrations en cyanure et en carbonate d'ammonium, volumes d'eau et d'ethanol, temperature et temps de reaction) sur le rendement en cyclohexane spirohydantoine. La strategie experimentale et les resultats sont compares avec ceux d'une publication recente utilisant la methode d'optimisation du Simplex, montrant une connaissance plus precise de la reaction apres une matrice factorielle. The only sixteen experiments of a fractional factorial design have been necessary to study the influence on the yield of cyclohexanospirohydantoin of the seven following factors: flask volume, cyanide and ammonium carbonate concentrations, quanities of water and ethanol, temperature and reaction time. The experimental strategy and results are compared with a recently published Simplex optimization, showing a better knowledge of the reaction after using a factorial design.

Binary, ternary, and quaternary mixtures of four nematogenic compounds, 2-hydroxy-4,4′-dihexoxy-α,α′-dimethylbenzalazine, 4′-butyl-2-hydroxy-4-octoxy-α,α′-dimethylbenzalazine, S-4′-butoxy-2-hydroxy-4-(2-rnethylbutoxy)-α,α′-dimethylbenzalazine, and 2-hydroxy-4′-nitro-4-octoxy-α,α′-dimethylbenzalazine, were studied. In the mixtures with a nitro group a SA-induced phase appeared.These systems of mixtures were studied using the Scheffé algorithm. A comparative study of the prediction methods of the eutectic points was made.

In order to test the hypothesis that structural characteristics in a Free-Wilson type model can be used to describe heterocyclic substituents, a set of heterocyclic compounds (eighteen carboxaldehydes and their corresponding carboxylic acids) containing only one heteroatom was prepared and some spectroscopical properties were used as experimental responses. Fedorov's algorithm has been used to choose D-optimal designs. The validity of this methodology is discussed.

Using the isomeric ratio of RR,SS to RS,SR of a series of 2-aminoethanols obtained by the LiAlH4 reduction of 24 α-iminoketones we propose a mathematical model with 7 coefficients for the effect of substituent on the stereochemical course of the reaction. The values of these coefficients obtained by multilinear regression analysis are in agreement with the previously proposed mechanism for reduction but allow for some additional conclusions. The use of modern methods for the construction of experimental matrices allows us to choose 10 from a total of 24 experiments and shows that information of the same quality can be obtained from this subset.