Partial Solubility Parameters Research Articles

Determination of poly(ɛ-caprolactone) solubility parameters: Application to solvent substitution in a microencapsulation process

The evolution of regulation on chemical substances (i.e. REACH regulation) calls for the progressive substitution of toxic chemicals in formulations when suitable alternatives have been identified. In this context, the method of Hansen solubility parameters was applied to identify an alternative solvent less toxic than methylene chloride used in a microencapsulation process. During the process based on a multiple emulsion (W/O/W) with solvent evaporation/extraction method, the solvent has to dissolve a polymer, poly(ɛ-caprolactone) (PCL), which forms a polymeric matrix encapsulating or entrapping a therapeutic protein as the solvent is extracted. Therefore the three partial solubility parameters of PCL have been determined by a group contribution method, swelling experiments and turbidimetric titration. The results obtained allowed us to find a solvent, anisole, able to solubilize PCL and to form a multiple emulsion with aqueous solutions. A feasibility test was conducted under standard operating conditions and allowed the production of PCL microspheres.

Modeling the solid–liquid equilibrium in pharmaceutical‐solvent mixtures: Systems with complex hydrogen bonding behavior

AbstractA methodology is suggested for modeling the phase equilibria of complex chemical mixtures with an equation of state (EoS) for the case where only limited experimental data exist. The complex hydrogen bonding behavior is explicitly accounted for and the corresponding parameters are adopted from simpler molecules of similar chemical structure and/or are fitted to Hansen's partial solubility parameters. The methodology is applied to modeling the solubility of three pharmaceuticals, namely acetanilide, phenacetin, and paracetamol, using the nonrandom hydrogen bonding (NRHB) EoS. In all cases, accurate correlations were obtained. The prediction ability of the approach was evaluated against predictions from the COSMO‐RS model. A thorough discussion is made for the appropriate modeling of solid solubility considering the effect of the difference of the heat capacities of the solute in liquid and solid state, ΔCp = Cpl − Cps, in the determination of solid chemical potential and, also, of the polymorphism of drugs. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Investigation of thermodynamic properties of hyperbranched poly(ester amide) by inverse gas chromatography

AbstractThermodynamic properties of the hyperbranched poly (ester amide) (Hybrane® 1200) were investigated by inverse gas chromatography (IGC) using 19 different solvents as the probes at infinite dilution. Retention data of probes were used for an extensive characterization of the polymer, which includes the determination of the Flory‐Huggins interaction parameter, the weight fraction activity coefficient, the total, partial, and additive solubility parameters. The analysis of the results indicated that the additive value of the solubility parameter is lower than the value obtained from a standard procedure. Furthermore, the solubility parameter decreases with increase of temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2166–2172, 2008

Solubility Behavior of Pimozide in Polar and Nonpolar Solvents: Partial Solubility Parameters Approach

The solubility behavior of pimozide in individual solvents ranging from nonpolar to highly polar was studied. For understanding the solute-solvent interactions, the partial solubility parameters concept was utilized. Solutions containing excess drug were shaken in a water bath for 72 hours at 25 °C. After the solutions attained equilibrium, they were filtered and analyzed for drug content. A multiple regression method, using extended Hansen’s partial solubility parameters, was applied to verify the solubilities of pimozide in pure polar and nonpolar solvents and to predict its solubility in untested solvents. The three-parameter approach and the Flory-Huggins size correction term ‘B’ give predictions of solubilities with correlations up to 97%. The four-parameter approach involving proton-donor and proton-acceptor parameters was also used in fitting the solubility data. The correlations are appreciable (94%). Further, the ‘B’ term coupled with four-parameter approach was examined in order to improve the data representation, and resulted in a 1% improvement (98%) in the correlation when compared to the Flory-Huggins size-correction method. The solubility parameter obtained by this method is 10.43 H which is closer to the values obtained by theoretical methods, such as Fedors’ and Hoy’s. The resulting partial solubility parameters are δ2d=8.85 H, δ2p=2.17 H, δ2a=3.15 H, and δ2b=4.08 H, which give insights into the interaction capability of pimozide and are consistent with its chemical structure. Pimozide is a Lewis base as its δ2b>δ2a. The total solubility parameter of pimozide is assigned at 10.43 H. This work demonstrates for the first time the validity of the four-parameter approach coupled with the Flory-Huggins size-correction term and therefore the result is interesting.

Solubility of carboxylic acids in a matrix of uncross-linked polystyrene

Solubility diagrams of a series of carboxylic acids in a matrix of linear polystyrene have been measured using a gravimetric method on samples immersed in solvent, as reported earlier [Bernardo G, Vesely D. Eur Polym J 2007;43:938–48]. The results show that the amount of solvent, swelling the polymer, reaches an equilibrium saturation which has a unique and reproducible value for each system and temperature. An analysis based on Flory–Huggins theory shows that all data presented here can be well interpreted with an interaction parameter in a simple form: χ = a + ( b/ T). An excellent fit can also be obtained using the van’t Hoff equation. An analysis based on total and partial (Hansen) solubility parameters has also been investigated.

Limitation observed in the application of the three dimensional solubility parameters to the coating formulation of poly (3-hydroxybutyrate-hydroxyvalerate) systems

Purpose: Poly (3-hydroxybutyrate-hydroxyvalerate) displayed high dipole-dipole interaction, a high hydrogen bonding but low polar interaction, and was therefore expected to be miscible with solvents/plasticizers that exhibit similar pattern of cohesive interaction. To determine the applicability, or otherwise of the theory of the three dimensional solubility parameters to the formulation of poly (3-hydroxybutyrate-hydroxyvalerate) polymeric coating system, and hence identify any limitation in the application of the theory. This aspect was investigated in the study. Method: The structural group contribution method was employed to compute the partial and total solubility parameters of the compounds – the biopol polymer, a series of organic solvents and plasticizers. The computed partial solubility parameters included: dipole-dipole (dd), polar (dp) and hydrogen bonding (dh). Following a standard procedure in the literatures, the dd and dp values were combined to form a composite solubility parameter, dv: where dv = &#8730 &#948d 2+&#948p 2. A plot of dh versus dv gave the energy maps, which depicted the energy levels of the various compounds and from which the miscibility of the compounds were predicted. The closer the position of the solvent or plasticizer to the polymer in the map, the greater, the probability of mixing. Cast films of the various polymeric formulations were made and examined for homogeneity by scanning electron microscopy. Results: It was possible to select suitable plasticizers that were miscible with the polymer by applying theory of solubility parameters. The prediction for the solvents was, however, erroneous and this may be attributable to the inability of the dv parameter to clearly reflect the differences between the dd and dp interactions of the polymer on the one hand and those of the various solvents in all situations on the other hand. This means that in certain instances, the dv values of the polymer and the solvents were similar even though their dd and dp interactions were dissimilar. Conclusion: The analysis of the data showed that the composite solubility parameter dv of compounds could be similar even though the actual energies of dd and dp interactions are different. This is a limitation in the application of the theory of the three dimensional solubility parameters. Keywords: keyword; keyword; keyword > Tropical Journal of Pharmaceutical Research Vol. 4 (1) 2005: pp. 355-362

Correlations between experimental and predicted equilibrium distribution coefficient of chlorobenzene and chlorophenol compounds in soil-water systems using partial solubility parameters

Many pesticides are degraded to become chlorinated aromatic compounds in soils. Equilibrium distribution of chlorobenzene and chlorophenol compounds in soil-water systems of Yangmingshan loam, Pingcheng silty clay loam and Annei silty loam was studied with the integral distribution equilibrium equation involving the partial solubility parameters of the chemicals. If the adsorption of chemicals on soils is partitioning in soil organic matter surrounding the soil mineral particles, the absorption constant (K d ) of a chemical in soil-water system could be stated as the distribution coefficient (or partition constant, K oc ) of the chemical in the two adjunct immiscible phases—water and soil organic matter. The distribution coefficient (K oc ) of chemicals calculated from the integral distribution equilibrium equation agrees well with the experimental adsorption coefficient (K d , or experimental K oc ) of chemicals determined in this study, for all the three different types of soils in water according to multiple-regression analysis. Reference data of Karger or Tijssen are employed to estimate the K oc for both polar and non-polar chemicals. The integral distribution equilibrium equation can exactly describe the distribution behavior of nonionic compound of chlorobenzenes and chlorophenols in soil-water systems.

Solubility parameter of drugs for predicting the solubility profile type within a wide polarity range in solvent mixtures

The solubility enhancement produced by two binary mixtures with a common cosolvent (ethanol–water and ethyl acetate–ethanol) was studied against the solubility parameter of the mixtures ( δ 1) to characterize different types of solubility profiles. Benzocaine, salicylic acid and acetanilide show a single peak in the least polar mixture (ethanol–ethyl acetate) at δ 1 = 22.59, 21.70 and 20.91 MPa 1/2, respectively. Phenacetin displays two solubility maxima, at δ 1 = 25.71 (ethanol–water) and at δ 1 = 23.30 (ethyl acetate–ethanol). Acetanilide shows an inflexion point in ethanol–water instead of a peak, and the sign of the slope does not vary when changing the cosolvent. The solubility profiles were compared to those obtained in dioxane–water, having a solubility parameter range similar to that covered with the common cosolvent system. All the drugs reach a maximum at about 90% dioxane ( δ 1 = 23 MPa 1/2). A modification of the extended Hildebrand method is applicable for curves with a single maximum whereas a model including the Hildebrand solubility parameter δ 1 and the acidic partial solubility parameter δ 1a is required to calculate more complex solubility profiles (with inflexion point or two maxima). A single equation was able to fit the solubility curves of all drugs in the common cosolvent system. The polarity of the drug is related to the shape of the solubility profile against the solubility parameter δ 1 of the solvent mixtures. The drugs with solubility parameters below 24 MPa 1/2 display a single peak in ethanol–ethyl acetate. The drugs with δ 2 values above 25 MPa 1/2 show two maxima, one in each solvent mixture (ethanol–water and ethanol–ethyl acetate). The position of the maximum in ethanol–ethyl acetate shifts to larger polarity values (higher δ 1 values) as the solubility parameter of the drug δ 2 increases.

Relationship between swelling of hydroxypropylmethylcellulose and the Hansen and Karger partial solubility parameters

A model that relates the equilibrium swelling of hydroxypropylmethylcellulose to the partial solubility parameters of both the polymer and the solvents is proposed to interpret and correlate the experimental data. The non-specific interactions are expressed as the dispersion δd and polar δp solubility parameters of Hansen, or as a combination of both. Hydrogen bonding is represented by the acidic δa and the basic δb Karger solubility parameters. The results are compared with models including the same parameters for non-specific interactions (δd and δp) and the Hansen hydrogen bonding parameter δh. Equilibrium swelling of this hydrophilic polymer that is widely used in drug formulation is measured in pure solvents covering a wide polarity range. In a qualitative way, swelling increases in solvents with higher Hildebrand solubility parameters and stronger hydrogen bonding capability, and it decreases in non-polar solvents. Single polarity indexes, such as the Hildebrand solubility parameter or the partition coefficient (PC), do not fit well the overall experimental data. The best correlations were obtained with the proposed model, providing at the same time an interpretation consistent with the physical meaning of the terms included in the equation. Swelling increases as the non-specific interactions of the polymer and the solvents become alike, and as the Lewis acid-base interactions of the polymer (1) and the solvent (2) represented by the products δ1aδ2b and δ1bδ2a become greater. Conversely, hydrogen bonding self association of the solvents (the product δ1aδ1b) lowers swelling. The results show that the Karger hydrogen bonding parameters provide a better approach than the Hansen hydrogen bonding parameter to correlate the swelling behavior of a hydrophilic polymer. © 2005 Wiley-Liss, Inc. and the American Pharmacists Association.

Hydrophilic solutes in modified carbon dioxide extraction—prediction of the extractability using molecular dynamic simulation

Super- and subcritical carbon dioxide (CO 2) extractions of crude drugs were simulated by molecular modelling to predict the extractability of different hydrophilic plant constituents under various extraction conditions. The CO 2 extraction fluids were simulated either with pure CO 2 or with solvent modified CO 2 at different pressures and temperatures. Molecular modelling resulted in three different solubility parameters: the total solubility parameter δ and the partial solubility parameters δ d for the van der Waals and δ EL for the polar forces. Thus, δ EL enabled the estimation of the polarity of the extraction fluids and the solute molecules. If the value of δ EL of the extraction fluid reached the value of the solute molecule in the crude drug, i.e. minimum extraction value, the compound was soluble at the distinct extraction conditions. For a further increase in yield of the hydrophilic solutes, the polarity of the extraction fluid had to be increased, too. That means δ EL of the fluid exceeded the minimum extraction value. All simulations were verified by CO 2 extractions of the secondary roots of Harpagophytum procumbens (harpagoside, stachyose) and the seeds of Aesculus hippocastanum (aescin). CO 2 extractions of the flowers of Matricaria recutita ((−)-α-bisabolol) were obtained from literature data. These four constituents with different properties, like molecular size and the allocation of polar functional groups were extracted, analysed, simulated and the extract content was correlated with the extraction fluid used, respectively.

Towards a better understanding of the parameter Ei/ E in the characterization of polar liquids

In the two previous papers [Stengele, A., Rey, St., Leuenberger, H., 2001. A novel approach to the characterization of polar liquids. Part 1: pure liquids. Int. J. Pharm. 225, 123–134; Stengele, A., Rey, St., Leuenberger, H., 2002. A novel approach to the characterization of polar liquids. Part 2: binary mixtures. Int. J. Pharm. 241, 231–240] it was shown, that the Clausius–Mossotti–Debye equation for the quasi-static dielectric constant ( ɛ) can be extended to liquids if the parameter E i / E is introduced. E i corresponds to the local mean field due to close molecule–molecule interactions after the application of an external electric field E. In the present paper, it is demonstrated that the value of E i / E at room temperature can be (1) related to the density of hydroxy groups and the density of the square of the dipole moment per molar volume for polar liquids and (2) also to the total ( δ t) and partial solubility parameter, for polar ( δ p) and hydrogen bond forming molecules ( δ h).

A new method to determine the partial solubility parameters of polymers from intrinsic viscosity

A modification of the extended Hansen method, formerly used to determine the partial solubility parameters of drugs and non-polymeric excipients is tested with a polymer for the first time. The proposed method relates the logarithm of the intrinsic viscosities of the polymer in a series of solvents and solvent mixtures with the Hansen (three parameter model) and Karger (four parameter model) partial solubility parameters. The viscosity of diluted solutions of hydroxypropyl methylcellulose (HPMC) was determined in pure solvents and binary mixtures of varying polarity. The intrinsic viscosity was obtained from the common intercept of the Huggins and Kraemer relationships. The intrinsic viscosity tends to increase with increasing the solubility parameter of the medium. The results show that hydrogen bonding and polarity of the polymer largely determine polymer–solvent interactions. The models proposed provided reasonable partial and total solubility parameters for the polymer and enable one to quantitatively characterize, for the first time, the Lewis acid–base ability of a polymer thus, providing a more realistic picture of hydrogen bonding for solvent selection/compatibility and to predict drug–polymer interactions. Combination of the dispersion and polar parameters into a single non-specific solubility parameter was also tested. The results extend earlier findings and suggest that the models are quite versatile and may be applied to drugs, non-polymeric and polymeric excipients.

Partial solubility parameters of poly( d, l-lactide-co-glycolide)

During production of microparticles by the polymer incompatibility method a polymer solution is demixed. Therefore, investigations into solubility are often carried out when the suitability of a polymer is examined. Solubility parameters can be used to quantify the solubility. For polylactide and polyglycolide as commonly employed copolymers for microparticles the solubility parameters have rarely been documented. This study aimed to determine solubility parameters and partial solubility parameters for different proportions of lactide to glycolide for poly( d, l-lactide-co-glycolide) (PLGA). The employed methods were compared and solubility maps established. Finally the accuracy of the results was discussed for different polymer batches which were used for production of microparticles. Although the turbidity titration method was found to be the most precise, it was not possible to sufficiently explain the differences between three polymer batches during microparticle production.

Compaction mechanism and tablet strength of unlubricated and lubricated (silicified) microcrystalline cellulose

This paper describes the differences in compaction properties between microcrystalline cellulose (MCC) and microcrystalline cellulose co-processed with colloidal silicon dioxide (SMCC). The different compaction parameters are not only compared for the pure materials, but also for the lubricated powders with magnesium stearate. Neither magnesium stearate, nor colloidal silicon dioxide, facilitates extensively the densification of (silicified) microcrystalline cellulose during compaction. The difference in tablet relaxation of MCC and SMCC indicates a small negative effect of colloidal silicon dioxide on the interparticle bonding strength of unlubricated MCC. However, for lubricated MCC a larger increase in tablet relaxation at a high compression speed was found than for lubricated SMCC tablets. Accordingly, the decrease in tablet strength was larger for the MCC tablets than for the SMCC tablets when lubrication was applied. The examination of the tablet strengths of tablets compressed from physical mixtures of MCC with increasing concentrations of colloidal silicon dioxide proved the slightly negative influence of silicon dioxide on the tablet strength of unlubricated MCC tablets and the positive effect of colloidal silicon dioxide addition on the tensile strength of lubricated MCC tablets. Co-processing of MCC with colloidal silicon dioxide showed no extra contribution on the tablet strength of lubricated tablets above the physical mixtures. The interactions between the different materials were further supported by the interaction parameters based on partial solubility parameters.

Application of solubility parameters to the formulation of acrylate methacrylate film coating systems

AbstractIn order to optimize the formulation of the acrylate methacrylate (AMA) coating systems, the partial solubility parameters of AMA and those of various coating solvents and plasticizers have been computed using the group contribution method of Van Krevelan and Hoftyzer. The data were analyzed in accordance with the three‐dimensional solubility parameters whereby δh (the hydrogen‐bonding component) was plotted against the sum of δd (the dipole–dipole component) and δp (the polar component). The data were also analyzed according to a two‐dimensional solubility parameters whereby δh was plotted vs δp to obtain the energy maps for the various compounds. With the three‐dimensional analysis, the position of the reference polymer in the energy map was centrally located and was flanked by plasticizers and solvents that were shown experimentally to be compatible with the polymer. On the other hand, the two‐dimensional analysis displaced the location of the reference polymer in the energy map leftward to the Y axis, and was not flanked by plasticizers and solvents that were compatible with it. The results show that the concept of the three‐dimensional solubility parameters was more applicable to the theoretical selection of plasticizers and solvents for the polymer studied. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1339–1344, 2003

Physico-chemical determinants of dermal drug delivery: effects of the number and substitution pattern of polar groups

The aim of this study was to investigate the effect of number and substitution pattern of –OH groups of a set of phenols on the in vitro permeation of heat-separated human epidermis. The diffusion was calculated from Log( D/ x)=log k p−0.59 log K oct+0.024 ( D, diffusion coefficient; x, pathlength; k p, permeability coefficient (cm/h); and K oct, octanol–water partition coefficient). The main factors reducing D were the dipolar and hydrogen bonding capabilities of the permeants quantified as their Hansen partial solubility parameters δ p and δ h. These parameters are significantly reduced by the degree of symmetry of the molecule, so that phloroglucinol (1,3,5-benzenetriol), with three –OH groups, diffuses more rapidly that phenol. When symmetry is absent, as in 1,2,4-benzenetriol, the number of –OH groups results in very slow diffusion. D/ x (cm/h) was related to the combined solubility parameter δ a defined as √( δ p 2+ δ h 2) by: ( D/ x)=0.0024−0.000065 δ a ( n=7, R 2=0.70, P=0.012).

Determination of partial solubility parameters of five benzodiazepines in individual solvents

Three and four component partial solubility parameters for diazepam, lorazepam, oxazepam, prazepam and temazepam were determined using the extended and expanded Hansen regression models. A comparison was made also with solubility parameters calculated by the group contribution method proposed by Van Krevelen. Although a limited number of solvents was used, the results from the present study indicate that the partial solubility parameters obtained from the experimental regression models clearly reflect the structural differences in these five structurally related molecules. High R 2-values were observed in the regression models (0.932≤ R 2≤0.984), except for lorazepam (0.606≤ R 2≤0.825). This was attributed to difficulties in obtaining reliable values of the temperature and heat of fusion due to thermal decomposition of this compound. Introduction of the Flory–Huggins size correction parameter did not improve the R 2- and F-values in any of the regression models used.

Proposition of group molar constants for sodium to calculate the partial solubility parameters of sodium salts using the van Krevelen group contribution method

The aim of this study is to propose, for the first time, a set of group molar constants for sodium to calculate the partial solubility parameters of sodium salts. The values were estimated using the few experimental partial solubility parameters of acid/sodium salt series available either from the literature (benzoic acid/Na, ibuprofen acid/Na, diclofenac Na) or determined in this work (salicylic acid/Na, p-aminobenzoic acid/Na, diclofenac), the group contribution method of van Krevelen to calculate the partial parameters of the acids, and three reasonable hypothesis. The experimental method used is a modification of the extended Hansen approach based on a regression analysis of the solubility mole fraction of the drug ln X 2 against models including three- or four-partial solubility parameters of a series of pure solvents ranging from non-polar (heptane) to highly polar (water). The modified method combined with the four-parameter model provided the best results for both acids and sodium derivatives. The replacement of the acidic proton by sodium increased the dipolar and basic partial solubility parameters, whereas the dispersion parameter remained unaltered, thus increasing the overall total solubility parameter of the salt. The proposed group molar constants of sodium are consistent with the experimental results as sodium has a relatively low London dispersion molar constant (identical to that of –OH), a very high Keesom dipolar molar constant (identical to that of –NO 2, two times larger than that of –OH), and a very high hydrogen bonding molar constant (identical to that of –OH). The proposed values are: F (Na)d=270 (J cm 3) 1/2 mol −1; F (Na)p=1030 (J cm 3) 1/2 mol −1; U (Na)h=17 000 J mol −1. Like the constants for the other groups, the group molar constants proposed for sodium are certainly not the exact values. However, they are believed to be a fair approximation of the impact of sodium on the partial solubility parameters and, therefore, can be used as such in the group contribution method of van Krevelen.

Partial Solubility Parameters of Lactose, Mannitol and Saccharose Using the Modified Extended Hansen Method and Evaporation Light Scattering Detection.

The modified extended Hansen method was tested for the first time to determine partial solubility parameters of non-polymeric pharmaceutical excipients. The method was formerly tested with drug molecules, and is based upon a regression analysis of the logarithm of the mole fraction solubility of the solute against the partial solubility parameters of a series of solvents of different chemical classes. Two monosaccharides and one disaccharide (lactose monohydrate, saccharose and mannitol) were chosen. The solubility of these compounds was determined in a series of solvents ranging from nonpolar to polar and covering a wide range of the solubility parameter scale. Sugars do not absorb at the UV-vis region, and the saturated solutions were assayed with a recent chromatographic technique coupled to an evaporative light scattering detector. This technique was suitable to determine the concentration dissolved in most solvents. The modified extended Hansen method provided better results than the original approach. The best model was the four parameter equation, which includes the dispersion delta d, dipolar delta p, acidic delta a and basic delta b partial solubility parameters. The partial solubility parameters obtained, expressed as MPa1/2, were delta d = 17.6, delta p = 28.7, delta h = 19, delta a = 14.5, delta b = 12.4, delta T = 32.8 for lactose, delta d = 16.2, delta p = 24.5, delta h = 14.6, delta a = 8.7, delta b = 12.2, delta T = 32.8 for mannitol and delta d = 17.1, delta p = 18.5, delta h = 13, delta a = 11.3, delta b = 7.6, delta T = 28.4 for saccharose. The high total solubility parameters delta T obtained agree with the polar nature of the sugars. The dispersion parameters delta d are quite similar for the three sugars indicating that the polar delta p and hydrogen bonding parameters (delta h, delta a, delta b) are responsible for the variation in the total solubility parameters delta T obtained, as also found for drugs. The results suggest that the method could be extended to determine the partial solubility parameters of other non-polymeric pharmaceutical excipients.

Partial solubility parameters of chlorobenzene and chlorophenol compounds at equilibrium distribution in two immiscible phases

Partial solubility parameters of chlorobenzene and chlorophenol compounds at equilibrium distribution in two immiscible phases such as soil-water system were studied. An integral distribution equilibrium equation is derived from the concept of partial solubility parameters and Flory-Hungins equation. Twelve chlorobenzenes and nineteen chlorophenols were employed in this study and their partial solubility parameters including dispersion( ( δ d),and polar van der Waals ( δ p), as well as their electron acceptor and donor solubility parameters ( δ a and δ b) were calculated.Hildebrand's solubility parameter(δ) of the compounds was also obtained by using boiling point and formula.HPLC was performed by octadecyl-bonded phase as the stationary phase with methanol or acetonitrile as the mobile phase to determine the capacity factor k′ of all compounds for the calculation of δ a and δ b.