Extraction of the Volatile Oils of Dictyopteris membranacea Batters 1902 by Focused Microwave-assisted Hydrodistillation and Supercritical Carbon Dioxide: Empirical Kinetic Modelling Approach, Apparent Solubility and Rate Constants

Supercritical carbon dioxide extraction (SCCO2) and focused microwave-assisted hydrodistillation (FMAHD) were used comparatively to isolate the volatile oils of the brown alga Dictyopteris membranacea from the crude ether extract. The volatiles fractions were analysed by GC/MS, the major compounds were: dictyopterene A, 6-butyl 1,4-cycloheptadiene, 1-undecen-3-one, 1,4-undecadien-3-one, (3-oxoundec-4-enyl) sulphur, tetradecanoic acid, hexadecanoic acid, 3-hexyl-4,5-dithiacycloheptanone, and albicanol. A kinetics study of the extraction of the volatile fractions obtained by the two processes was carried out, an external calibration allowed to quantify the content of the main metabolites. Empirical models were applied to adjust the experimental kinetics values but also to determine the values of apparent solubilities for SCCO2 and the rate constants for FMAHD. The results obtained revealed that the SCCO2 process was characterized by the coexistence of three distinct phases. For FMAHD, the extraction mechanism included two steps.


Introduction
Volatiles of marine origin have been rarely studied although they could be used as a source of original flavouring agents in food and perfume industries 1 . The genus Dictyopteris is one of the few genera of odoriferous brown seaweeds. Literature reports that the major constituents identified in the essential oils obtained from algae of this genus were C11 hydrocarbons, known as sex pheromones of brown algae 2,3 , sulphur products such as 3-hexyl-4,5--dithiacycloheptanone (D. plagiogramma, D. australis 4 and D. membranacea 5 ), and sesquiterpene compounds (D. prolifera and D. undulata) 6,7 . Essential oil (EO) is traditionally obtained by steam distillation according to ISO-9235 (2013) norms. Currently, various methods can be used for the isolation and extraction of volatile oils from plant materials, which mainly include solvent extraction 8 , supercrit-ical fluid extraction (SFE) 9 and liquid-phase microwave-assisted process (MAP) extraction 10 . Extraction with supercritical carbon dioxide (SCCO 2 ) is a good alternative method to preserve the native essential oil components 11 . The thermodynamic (equilibrium) solubility of a compound could be determined by two main methods, static and dynamic 12 . It should be noted that SCCO 2 under optimum conditions, is usually a saturated (or almost saturated) solution of extract 13 . Therefore, the concentration of saturated solution in equilibrium with extracted plant is called "apparent solubility". It is an important parameter in the extraction kinetics and could be evaluated from the SFE kinetics data. The term "apparent solubility" is used to distinguish from the thermodynamic solubility, realized when the plant material is in contact with SF CO 2 for a long time to reach the equilibrium concentration, thereby, the apparent solubility is a fraction of the thermodynamic solubility in the SFE of many solutes contained in vegetable organisms 14 . Thus, the thermodynamic and apparent solubilities are usually quite identical for seed oils 15 . However, the thermody-namic solubility of volatile compounds is, often, higher than their apparent solubilities 16,17 . It should be noted that theoretical models (TM) as well as semi-empirical and empirical (SE-E) models were employed to predict the solubilities of solute in supercritical CO 2 . The model parameters are evaluated by minimizing the deviation between experimental data and model predictions using the method of least squares for the determination of the absolute average relative deviation (AARD) or the residual sum of squares (RSS). Some common semiempirical models are reported in literature, i.e., Chrastil 18 , Del Valle and Aguilera 19 , Modified Mendez Santiago-Teja 20 , Modified Bartle 21 , Adachi and Lu 23 , and Gordillo 24 . The microwave-assisted extraction (MAE) technique was developed and applied to the isolation of volatile and bioactive compounds from plant materials 25 . The main advantage of MAE is the reduction of extraction time and organic solvent production. The kinetics of microwave extraction processes have been reported in many research studies, several mathematical models were proposed to describe the kinetic data 26,27 . The described models were developed using Fick's second law of diffusion 28 , the empirical kinetic model fitting such as: First-order kinetic model 29 , second-order rate kinetic 30 , power law 31 , two-site kinetic model 32 , hyperbolic model (Peleg's model) 33 and Weibull's exponential model 34 . In a previous work 35 , we had reported the determination and the quantification of the chemical composition of the volatile fraction obtained by three extraction techniques from the crude extract of D. membranacea collected off the Mediterranean coast. The present study aimed to investigate the kinetics study and modelling analysis of the extraction of volatile fractions of D. membranacea, firstly by supercritical carbon dioxide at two different pressures, and secondly by focused microwave extraction. An external standard quantification was performed to investigate the evolution of the mass percent vs time of the main compounds in the oils obtained during kinetics study of both extraction techniques.

Plant material and chemicals
The plant material was collected off the coasts of Algeria on the east of Tipaza (36°37' 12 '' NR, 2°39' 00 '' E). This sample belongs to Phaeophyceae Class, Dictyotales order, Dictyotaceae family, Dictyopteris genus and polypodioides (Stackhouse) Batters species 36 . D. membranacea is considered as the synonym for D. polypodioides which is currently the approved name 37 . The alga was air-dried under shade with no other treatment.

Preparation of crude extract
Extraction in batch mode (static) for one week at room temperature was performed in triplicate using a ratio of mass (g) of dried seaweed to volume of diethyl ether used as extraction solvent (mL) of 0.15. The solvent was removed using rotary evaporator under reduced pressure leading to an average mass of 3.5 g of crude extraction, corresponding to a yield of 1.2 %.

Preparation of volatile fractions
The volatile fractions were prepared from the crude extract using two extraction techniques, SCCO 2 and FMAHD.

Preparation of volatile fraction by supercritical carbon dioxide
The supercritical carbon dioxide extraction was performed on a HP 7680A extractor (Hewlett Packard, Les Ulis, France) equipped with a 7-mL stainless steel extraction vessel. About 300 mg of crude extract were mixed with a sufficient amount of 2-mm diameter glass beads, and heated to approximately 40 °C in a rotavapor set at slow speed, in the aim of obtaining a homogeneous thin layer of crude extract around the glass beads, thus generating a large contact surface with supercritical carbon dioxide. Thereafter, the glass beads coated with extracts were filled into the extractor. The mixture of oil and fluid leaving the extractor were trapped in a cylindrical tube filled with Tenax GC (60/80 Mesh, Interchim, Montluçon, France), the trap was cooled with a stream of carbon dioxide to maintain the trapping temperature of 0 °C. The oil was then extracted twice with 10 mL of an equivolume solution of dichloromethane/diethyl ether. The extraction temperature was fixed at 40 °C.
Under the optimized extraction conditions, two kinetics studies were carried out at pressures of 91 and 104 bars.

Preparation of volatile fraction by focused microwave-assisted hydrodistillation
The focused microwave-assisted hydrodistillatin was carried out in a Discover microwave oven manufactured by CEM (Matthews, NC, USA) equipped with a power modulator and an infrared temperature sensor. The algal extract was mixed with a precise water volume and poured into a pyrex tube topped with a Dean-Starck system allowing the recovery of the oil and water mixture. The ratio of algal extract mass/water volume was optimized in preliminary experiments; the best determined value was: 1 mg mL -1 . The kinetics study was carried out at a heating power of 120 W and 180 W.

Modelling and kinetics study of extraction processes by SCCO 2 and FMAHD
The kinetics study of the overall yield vs time was performed for both techniques SCCO 2 and FMAHD. Thus, the overall (cumulative) yield was evaluated by adding the mass of volatile oils extracted vs time. The experimental kinetic data were modelled using two semi-empirical models, the power law 31 (model 1), and the hyperbolic model 33 (model 2) described previously and given by equations 1-2, respectively.
Y: overall yield (mg of volatile oil/mg crude extract), t: time (min).

Gas chromatography-mass spectrometry (GC/MS)
The GC/MS analysis was carried out on a gas chromatograph (HP-6890) coupled to a mass spectrometer (HP-5972) detector. A capillary column CP Sil 8 (30 m length, 250 µm i.d., 0.25 µm film thickness) was used in the separation. The analyses were performed on the electron ionization mode (EI) at 70 eV, the mass range m/z 40-550 and the ion source temperature used were, 280 and 250 °C, respectively. The samples (1.0 μL) diluted in ACOEt (1:10/v:v) were injected using the split mode (1:90) at injection temperature of 250 °C. Helium was used as the carrier gas at a flow rate of 1 mL min -1 . The GC oven was set initially at 90 °C and held for 3 min, increased to 220 °C by a linear ramp at 3 °C min -1 , and held for 10 min. The compounds were identified based on their mass spectra analysis and the following mass spectra database: Wiley 7N (Wiley), NBS 75K (HP), and Mass Finder 4. The identification of compounds was completed by comparing their mass spectra with those reported in literature 38,39 .

Quantitative analysis
The volatile oils extracted versus time for both extraction methods were analysed by GC/MS. The aim was to quantify the major compounds of the volatile oils, and, consequently, to perform a kinetics study of each compound. The quantification was conducted using suitable pure external standards. The choice of standards was based on their chemical similarity with the compounds of interest in the volatile oils. The calibration of the external standard was better suited than the internal standard for the quantification of small quantities, and required a single point measurement for the determination of the response coefficient, given by equation 3 40 . The single-point external calibration strategy is easy to process and quite accurate. However, it requires rigorous injection of the same volume of standard solution and sample (volatile oil) solution in the same conditions.
In equation 3, C st , C comp , A st , A comp are respectively, mass concentration, peak area of pure standards, and quantified compounds in volatile oil. The response coefficient (K rep ) is determined as the slope of the calibration straight-line resulting from the linear regression of the experimental data plot [C(i), A(i)] obtained by injection of a series of known concentration standard solutions.

Results and discussion
Kinetics study of the extraction of volatile fractions As specified previously, the experimental data of the kinetics study of the oil extraction by SCCO 2 and FMAHD were modelled using two semi-empirical models described by equations 1 and 2. Therefore, the best-fit values of the model parameters with the experimental data were determined by minimizing the residual square sum (RSS). Since the extraction mechanisms of SCCO 2 and FMAHD were quite different, it seemed more convenient to discuss the modelling results for both techniques separately.
Kinetics study and modelling of SCCO 2 As previously noticed, the kinetics study of oil extraction was carried out at two extraction pressures (91, 104 bars), and two flows of SCCO 2 , mainly 0.5 and 1.5 mL min -1 . The overall extraction curves (OEC) obtained by SCCO 2 are described first as overall yield (Y: mg oil/mg crude extract and/or Y/%)) vs time (min) (OEC time ) in Fig. 1 and 2. The model parameters, shown in Table 1 were obtained from Figs. 1-2, where Y ∞ (exp.) is the overall yield at infinite time, obtained for an exhaustive extraction for a sufficiently long time (t > 2.5 h). The RSS values, for fitting both models to kinetic data, were mainly between 0.017 and 0.44. For the used pressures and flow rates of SCCO 2 , model 2 seemed to fit well with the experimental data, most notably for the extraction pressure at 91 bars, characterized by low RSS values. The power law (model 1) seemed well characterised with experimental data for kinetic extraction at 91 bars, however, it showed poor fitting to the one obtained at 104 bars. Most likely, model 2 described the extraction mechanism more correctly than model 1. Likewise, model 2 show ed an asymptotic value of the yield at infinite time more correctly, mainly at the flow rate of 1.5 mL min -1 .   Careful examination of OEC ( Fig. 1-2) showed a typical kinetic curve observed for the extraction of natural products characterized by the coexistence of three distinct phases: constant extraction rate period (CER), falling extraction rate period (FER), and diffusion-controlled period (DC), which agreed with the reported literatures 41 .
The first line was identified as the constant extraction rate period (CER), it corresponded to the equilibrium solute concentration in the supercritical carbon dioxide phase, representing the apparent solubility, under specific extraction conditions 42 .

Determination of the apparent solubility
As reported previously, the mass transfer resistance between the extract and the supercritical carbon dioxide (SCCO 2 ) was sufficiently weak, meaning that the concentration equilibrium could be reached relatively quickly, considering the residence (equilibrium) time of SCCO 2 . This condition was verified by evaluating two extraction runs carried out at different solvent residence times, meaning at different solvent flow rate-to-feed ratios 42 . Thus, the experiment done on the yield variation vs residence time (Rt) (Fig. 3) revealed an almost constant evolution of the yield. This result confirmed that equilibrium was reached nearly instantaneously. We adopted (as recommended in the device manual) a residence time equal to 5 min for all the experiments. Under these conditions, constant extraction rate period (CER) was used to evaluate the apparent solubility. Thus, OEC was described secondly as overall yield (OEC O/F ) against the solvent-to-feed ratio q (g SCCO 2 /mg crude extract) (Fig. 4-5). The  Table 2.  Table 2, the SCCO 2 flow had no impact on the apparent solubility values, which were, however, greatly influenced by the pressure. Therefore, the apparent solubility increased about 6-fold when the pressure had been increased from 91 to 104 bars; this result is hardly surprising because of the close link between pressure and solubility. There are many reports on apparent solubility of extracts 43 , pure compounds 44 available in literature. However, we found the following values of apparent solubility, at 100 bars of plant volatile oils (mg g -1 ): Chamomile (1.8) 45 , Clove (2.3) 46 , Peppermint (5.8) 16 and St. John's Wort (4.2) 17 . We noticed, from Table 2, that the apparent solubility of alga volatile oil, at 91 bars, was quite similar in comparison to the ones of some terrestrial plants cited previously. This is probably due to a similarity in chemical composition.

Kinetics study and modelling for FMAHD
The kinetics study was carried out at two heating powers (120 W and 180 W), the OEC time are shown in Fig. 6. As for SCCO 2 , the parameters of models 1 and 2 that best fit the experimental kinetic data are given in Table 3.
Analysis of Table 3 suggested clearly that models 1 and 2 gave reasonably the best fit to experimental data, most notably model 2, which showed very good fit to extraction kinetics at 180 W, where RSS and the ratio of asymptotic yield (Y ∞ (exp)/Y ∞ (model) tended towards zero and 1, respectively. Analysis of experimental kinetic data (Fig. 6) revealed that the extraction mechanism could be split into two stages (Fig. 7), as reported in the literature 47 : a fast extraction stage (washing step), a) b) and a slow extraction stage (diffusion step). Thus, the OEC at 180 W (Fig. 7a) revealed the presence of the washing step for a short time, followed by the slow diffusion stage which took more time. Nevertheless, concerning the OEC at 120 W (Fig. 7b), we noticed the reverse phenomenon, the first stage occurred over a longer time, probably due to the low heating power provoking low volatilization of surface volatile oil. The first step included a washing stage for short time, then the diffusion stage joined the washing stage, both phenomena occurred simultaneously, which explains the relatively long time of the first stage. The second step occurred when the diffusion phenomena became the limiting step of the extraction process. The experimental data of both steps (washing and diffusion steps) could be fitted by linear interpolation, where the slope of the straight could be considered as the extraction rate constant of each step (Table 4).

Modelling and quantitative kinetics study of the main compounds of the volatile oil
The volatile fractions isolated during SCCO 2 and FMAHD kinetics studies were submitted to GC/MS analysis in the aim to carry out a quantitative kinetics study of the main compounds in both oils; the quantification was done as explained previously. The chemical composition of volatile oils obtained by SCCO 2 and FMAHD were slightly different. Thus, the SCCO 2 oil was characterized by the presence of three chemical classes, previously identified in the essential oils of Dictyopteris genus 3-5 as C11 hydrocarbons, sulphur compounds, fatty acids and derivatives, as shown in the chromatographic profile (Fig. 8a). In addition, the analysis of the FMAHD oil revealed the presence of the same three chemical classes of components as in SCCO 2 oil, and surprisingly, a large amount of sesquiterpenoids (Fig. 8b), the complete identification of both oil compositions is reported in our previous work 35 . The experimental conditions of quantification carried out as described previously are given in Table 5.  The latter includes the concentration of stock solutions, retention times of the standards used, calculated response factor, retention times of the quantified compounds and their chemical classes.
As explained previously and based on the calibration parameters of standards (Table 5), the OEC time of the main metabolites were determined for SCCO 2 at p = 91 and 104 bars. The cumulative overall yield was calculated relatively to the mass of the volatile fraction. By way of non-exhaustive illustration, the OEC time at 91 and 104 bars of dictyopterene A and 6-butyl-1,4-cycloheptadiene are given in Fig. 9. The OEC of the main metabolites were valorised to deduce graphically their apparent solubility (Table 6) in the same way as for the volatile fraction, e.g., the apparent solubilities of dictyopterene A and 6-butyl-1,4-cycloheptadiene are  Fig. 10. The review of apparent solubility data for the main metabolites (Table 6) reveals the increase in dictyopterene A and 6-butyl-1,4-cycloheptadiene solubilities about 4 times, and between 7 and 14 times for the other metabolites, when the pressure had been increased from 91 to 104 bars. The increases in solubility versus the extraction pressure of extracts and metabolites has been reported in several studies 14,48 , so that the driving force for mass transfer would be larger at high pressure than at low pressure. According to the literature review, the apparent solubilities of natural crude extracts, pure secondary metabolites and pharmaceutical drugs increase between 4 and 10 times by raising the pressure to about 10 bars 50,51 . In the present study, the high increase in apparent solubility of 3-hexyl-4,5-dithiacycloheptanone, tetradecanoic acid and hexadecanoic acid ( Table 6) may have been due to their nonpolar character and consequently their high solubility in supercritical carbon dioxide 52 .
In the same context, the volatile fraction extracted by FMAHD was quantified by GC/MS analysis, using the calibration parameters of standard (Table 5), and led to the obtention of OEC time of the main metabolites (Fig. 8). The OEC time of dic-tyopterene A and albicanol are given in Fig. 11. It is clear that the same phenomenon of extraction process of volatile fraction (Fig. 7), with the intervention of two extraction steps (washing and diffusion), was met in this case as well, and conduct to the measurement of the rate constants of both steps for the main metabolites ( Table 7). The review of the results obtained revealed that the rate constants of washing step were higher than were those of diffusion step. However, as regards the four metabolites,  i.e., 1-undecen-3-one, 1,4-undecadien-3-one, tetradecanoic acid and hexadecanoic acid, the ratio of rate constant of washing and diffusion steps ranged between 1.6 -3.3. Nevertheless, dictyopterene A and albicanol showed a ratio of 8.6 and 9.3, respectively. This result could be related to the high volatility of both metabolites, therefore, their easy heteroazeotropic steam distillation. It must be pointed out that the OEC time of the main sulphur metabolite, i.e., 3-hexyl-4,5-dithiacycloheptanone, was interpolated by straight line, possibly suggesting that both steps occurred simultaneously, which was probably due to the long-time and low speed taken by the washing step.

Conclusion
The volatile fractions were prepared from crude ether extract of Dictyopteris membranacea by SCCO 2 and FMAHD. The kinetics studies of the volatile fraction extraction were performed and  conducted to the OEC time . Two empirical models were used to best-fit the kinetic experimental data, thus leading to the determination to the model's parameters, and then valorised in the determination of apparent solubilities for SCCO 2 and the rate constants for FMAHD. The volatile fractions collected during the kinetics studies were submitted to GC/MS analysis associated to an external standard quantification to determine the mass content of the main metabolites in the oils, and consequently the OEC time for each metabolite. The OEC time was exploited in the determination of the apparent solubilities, and the rate constant of the main metabolites for SCCO 2 and FMAHD, respectively.