<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">ACES</journal-id><journal-title-group><journal-title>Advances in Chemical Engineering and Science</journal-title></journal-title-group><issn pub-type="epub">2160-0392</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/aces.2023.132011</article-id><article-id pub-id-type="publisher-id">ACES-124347</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Chemistry&amp;Materials Science</subject></subj-group></article-categories><title-group><article-title>
 
 
  Physico-Chemical Study of the Adsorption of Carotenoids from Carrots on Raw and Modified Kaolinites
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Orléans</surname><given-names>Ngomo</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Etienne</surname><given-names>Dongo</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Joseph</surname><given-names>Sieliechi</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib></contrib-group><aff id="aff2"><addr-line>Department of Applied Chemistry, The National School of Agro-Industrial Sciences, University of Ngaoundere, Ngaoundere, Cameroon</addr-line></aff><aff id="aff1"><addr-line>Department of Organic Chemistry, Faculty of Sciences, University of Yaoundé I, Yaounde, Cameroon</addr-line></aff><pub-date pub-type="epub"><day>03</day><month>03</month><year>2023</year></pub-date><volume>13</volume><issue>02</issue><fpage>132</fpage><lpage>148</lpage><history><date date-type="received"><day>3,</day>	<month>February</month>	<year>2023</year></date><date date-type="rev-recd"><day>16,</day>	<month>April</month>	<year>2023</year>	</date><date date-type="accepted"><day>19,</day>	<month>April</month>	<year>2023</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  This study focuses on the adsorption at temperatures below 70
  &amp;#8451;
  
  , of 
  carotenoids from carrots on clay materials such as kaolinite in the raw state, activated with a 0.5
   
  M HCl solution or treated with a sodium solution of Al
  <sup>+</sup>
  . The kinetic study of carotenoid adsorption shows that equilibrium is reached after 30 minutes and the temperature has little influence on carotenoid adsorption. On the other hand, the quantities adsorbed at equilibrium increase with the initial concentration of carotenoids. The kinetic model that best describes the experimental data is that of the pseudo-second order, adsorption is made in two time. For the carotenoid adsorption isotherms, the best correlation is obtained with the Freundlich model. The low values 
  of the Freun
  dlich constants indicate that the adsorption is probably of a physical type. This conclusion is confirmed by the effective desorption of carotenoids observed during desorption experiments.
 
</p></abstract><kwd-group><kwd>Kaolinite</kwd><kwd> Carrots</kwd><kwd> Antioxidant</kwd><kwd> Cosmetic</kwd><kwd> Adsorption</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>Carotenoids are hydrocarbon compounds mainly synthesized by plants. They are responsible for the intensity of the yellow, orange and red colors of many plants and vegetables, their color is the result of the presence of a system of conjugated double bonds in the molecule. Carrots are another great source of carotenoids. In 2007, annual production was 20.601.214 tons [<xref ref-type="bibr" rid="scirp.124347-ref1">1</xref>] of which 33% was grown in China. Carrot cultivation is gaining momentum in Cameroon [<xref ref-type="bibr" rid="scirp.124347-ref2">2</xref>] . This crop is one of the most cultivated in peri-urban areas. Carrots are very perishable; however, it is observed that carrot extracts are used in beauty products [<xref ref-type="bibr" rid="scirp.124347-ref3">3</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref4">4</xref>] .</p><p>Indeed, solar radiation interacts with the substances contained in the air to produce singlet oxygen and other oxygenated species. These species can attack the skin. Carotenoids, when present in cosmetic formulations, are likely to react with oxidizing species. it is also necessary to determine the real oxidizing power of carotenoids. Cyclic voltammetry is the most widely used and also the most effective method for determining the antioxidant power of chemical substances [<xref ref-type="bibr" rid="scirp.124347-ref5">5</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref6">6</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref7">7</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref8">8</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref9">9</xref>] .</p><p>Carotenoids have double bonds that give them significant antioxidant power. This antioxidant power can be particularly valorized in beauty masks in cosmetics [<xref ref-type="bibr" rid="scirp.124347-ref10">10</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref11">11</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref12">12</xref>] . Carotenoids are very useful in dermatology to improve the general condition of the skin, they promote the synthesis of melanin, which is the pigment responsible for tanning, and the natural filter of ultraviolet rays [<xref ref-type="bibr" rid="scirp.124347-ref13">13</xref>] ; they attenuate the formation of peroxide radicals [<xref ref-type="bibr" rid="scirp.124347-ref14">14</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref15">15</xref>] facilitate the renewal of cutaneous tissues, attenuate scars and stretch marks and prevent the oxidation of lipids [<xref ref-type="bibr" rid="scirp.124347-ref16">16</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref17">17</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref18">18</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref19">19</xref>] . The antioxidant properties of carotenoids allow them to trap reactive oxidant particles in cell tissue responsible for premature skin aging, expression lines, dry and damaged skin [<xref ref-type="bibr" rid="scirp.124347-ref20">20</xref>] . However, they are quickly destroyed by solar radiation; for this purpose, the use through a clay support as a beauty mask will allow a slow and deep diffusion in the skin, which would increase their concentration and consequently increase their protective action of the skin.</p><p>In addition, Cameroon has many clay deposits. In general, smectite-type clays are found in the North and Far North regions of Cameroon and, on the other hand, in southern Cameroon, kaolinite-type clays are found [<xref ref-type="bibr" rid="scirp.124347-ref21">21</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref22">22</xref>] . The adsorbent properties of clays can be used for this purpose; moreover, natural products play a critical role in cosmetics, giving it an image of safety and relief compared to synthetic products, especially in anti-aging products [<xref ref-type="bibr" rid="scirp.124347-ref23">23</xref>] .</p></sec><sec id="s2"><title>2. Material and Methods</title><sec id="s2_1"><title>2.1. Raw Materials</title><p>The carotenoid source consists of carrots (genus Dauca of Umbelliferae, species Dauca carota). They were harvested when ripe, sorted, washed several times with water; peeled and chopped using a stainless-steel scraper. We obtain fine fibers of one millimeter in diameter and about 5mm in length. These carrot fibers are then spread out on plastic racks and placed in an electric dryer (massa dry) at 40˚C for 24 hours. After drying, these fibers are stored in a black polyethylene bag. The clays were sampled in Douala in the littoral region and characterized by [<xref ref-type="bibr" rid="scirp.124347-ref24">24</xref>] and codified D0M for the raw, D05M for the clay activated with HCl 0.5N and DAl<sub>13</sub> for the sample bridged with Aluminum Chloride (illustrated on the schemes below).</p><disp-formula id="scirp.124347-formula1"><graphic  xlink:href="//html.scirp.org/file/5-3701200x2.png?20230419095536662"  xlink:type="simple"/></disp-formula></sec><sec id="s2_2"><title>2.2. Equipments</title><p>The characterization of the carotenoids was carried out by UV-Visible spectrophotometry using a Perkin Elmer brand spectrophotometer (lambda 35) controlled by a computer, thanks to the Winlab Software program. The spectra were obtained by automatic scanning between 190 nm and 1100 nm. Quartz cells with a 1 cm optical path were used for this purpose.</p><p>The antioxidant activity of the carotenoids was determined by cyclic voltammetry, using a Bio-Logic SAS, system of three conventional electrodes at room temperature (25˚C) in the CH<sub>2</sub>Cl<sub>2</sub> solution. For electrochemical measurements, a platinum electrode is considered as the working electrode, the platinum wire is the auxiliary electrode and the calomel saturated electrode is the reference electrode. Cyclic voltammograms are recorded from &#177;0.1 V to &#177;2.0 V; the speeds vary from 2 to 100 mV/S. The sample solution of pure β carotene is added to the experimental electrolyte in the electrochemical cell. The solution prepared is of low concentration (10<sup>−6</sup> mM). Voltammograms are recorded immediately after the electrodes are immersed in the solution.</p></sec><sec id="s2_3"><title>2.3. Technics Analysis</title><p>The β carotene solutions serving as reference are prepared from a standard solution obtained near the company Sigma-Aldrich (M) Pte. ltd. of 98% purity. Whose physicochemical characterizations and chemical structure are shown in <xref ref-type="fig" rid="fig1">Figure 1</xref> and in <xref ref-type="table" rid="table1">Table 1</xref>.</p><p>The calibration curve is determined by taking 2.5 mg of β carotene powder which is introduced into 50 ml of cyclohexane. Necessary dilutions make it possible to obtain solutions of 10, 20, 30, 40 and 50 mg/L of β carotenes. Thus, the β-carotene content can be calculated with respect to the equation of the calibration curve.</p><p>For studies of adsorption of carotenoids by clays, we have in a series of 100 ml Erlenmeyer flasks covered with aluminum foil, introduced masses (2 g) of</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Some characteristics of β carotene</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Chemical formula</th><th align="center" valign="middle" >Molecular weigth (g/mol)</th><th align="center" valign="middle" >λ<sub>max</sub> (nm)</th><th align="center" valign="middle" >Colour</th></tr></thead><tr><td align="center" valign="middle" >C<sub>40</sub>H<sub>56</sub></td><td align="center" valign="middle" >536.89</td><td align="center" valign="middle" >450</td><td align="center" valign="middle" >Red</td></tr></tbody></table></table-wrap><p>adsorbent to which we have added the same volume (5 ml) of carotenoid solution of variable concentration (0 to 50 mg/l). These closed bottles are placed on magnetic stirrers (IKA<sup>&#174;</sup> RCT basie safety control model) with a regulated stirring speed of 250 rpm for a predetermined contact time. At the end of this time, the contents of the flask are centrifuged at 1500 revolutions/minute, and analyzed by UV-Visible spectrophotometry at 450 nm. Each experimental value is the average of two trials. The number of carotenoids per grams is given by the following relationship (Equation (1)):</p><p>q t = ( C 0 − C t ) V m (1)</p><p>where: q<sub>t</sub> is the quantity of carotenoids per unit mass of adsorbent (in mg/g);</p><p>C<sub>0</sub> is the initial concentration of carotenoids (mg/L);</p><p>C<sub>t</sub> is the residual concentration at time t (mg/L);</p><p>V is the volume of adsorbate (L);</p><p>m is the mass of adsorbent (g).</p><p>Desorption is the opposite phenomena of adsorption, by which the adsorbed molecules are detached from the substrate. Generally endothermic operation. The desorption studies were carried out using the method [<xref ref-type="bibr" rid="scirp.124347-ref25">25</xref>] modified. Indeed, after carrying out the adsorption, the clay on which the carotenoid is fixed is recovered, the solvent is introduced and kinetics are carried out in order to determine the time after which the maximum number of carotenoids has entered the solvent.</p></sec></sec><sec id="s3"><title>3. Results and Discussion</title><sec id="s3_1"><title>3.1. Characterization of β-Carotene</title><p><xref ref-type="fig" rid="fig2">Figure 2</xref> shows the determination of the maximum adsorption wavelength of carrot carotenes. <xref ref-type="fig" rid="fig3">Figure 3</xref> shows the calibration curve with a correlation coefficient close to 1.</p><p>According this figure, the maximum adsorption length wave is 450 nm in comparison to [<xref ref-type="bibr" rid="scirp.124347-ref26">26</xref>]</p><p>The cyclic voltammograms of carrot carotenoids at different scanning speeds are presented in <xref ref-type="fig" rid="fig4">Figure 4</xref>(a). It is observed that at low scanning speeds, of the potential (5, 10, 20 mVs<sup>−1</sup>), the curves are irregular. A more representative</p><p>voltammogram is obtained when the sweep rate is 50 mVs<sup>−1</sup>. However, a normal cyclic voltammogram is only obtained at the scan rate of 100mVs<sup>−1</sup> (<xref ref-type="fig" rid="fig4">Figure 4</xref>(b)). This mode of evolution of the voltammogram as a function of the scanning speed has been obtained by various authors on various organic compounds [<xref ref-type="bibr" rid="scirp.124347-ref27">27</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref28">28</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref29">29</xref>] . The voltammogram obtained at the speed of 100 mVs<sup>−1</sup> is similar to those of pure β carotenes [<xref ref-type="bibr" rid="scirp.124347-ref8">8</xref>] , however the peaks are less marked here. This difference can be attributed to the presence of lipids in the medium. The presence of a single anodic peak shows that the electrochemical oxidation reaction of β carotene takes place in a single step. In fact, it has been demonstrated [<xref ref-type="bibr" rid="scirp.124347-ref30">30</xref>] that the oxidation potential of β carotene (Car) and the radical cation (Car<sup>●</sup><sup>+</sup>) are so close that the two reactions take place simultaneously.</p><p>Car ↔ Car • + + e − ( E 1 ∘ = 0.54 ) et Car • + ↔ Car 2 + + e − ( E 2 ∘ = 0.54 )</p><p>The low values of E 1 ∘ and E 2 ∘ show that β-carotene has a high antioxidant</p><p>power [<xref ref-type="bibr" rid="scirp.124347-ref28">28</xref>] , the oxidation is determined as quasi-reversible according to the Nicholson-Shain criterion [<xref ref-type="bibr" rid="scirp.124347-ref31">31</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref7">7</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref8">8</xref>] . This antioxidant power is attributed to the presence of conjugated double bonds (<xref ref-type="fig" rid="fig1">Figure 1</xref> performed with AUTOLAB PGSTAT30 potentiostat with GPES software) in the structure of β-carotene.</p></sec><sec id="s3_2"><title>3.2. Carotene Adsorption Kinetics from Carrots on Clays</title><p>Carotene adsorption kinetics were performed to determine the contact time required to reach equilibrium for different adsorbents at different initial concentrations and different temperatures.</p><sec id="s3_2_1"><title>3.2.1. Effect of Contact Time on Adsorption Kinetics</title><p>The influence of the initial concentration of carotenes in the extract in solution on the kinetics of adsorption on raw, activated and bridged kaolinites was investigated at initial concentrations of 20 mg/L, 40 mg/L and 50 mg/L; the results obtained are shown in <xref ref-type="fig" rid="fig5">Figure 5</xref> (making by using sigma plot logician)</p><p><xref ref-type="fig" rid="fig5">Figure 5</xref> shows that the quantities of carotenes adsorbed per gram of adsorbent gradually increase with contact time and stabilize after approximately 30 minutes [<xref ref-type="bibr" rid="scirp.124347-ref32">32</xref>] . The same appearance has been observed by [<xref ref-type="bibr" rid="scirp.124347-ref33">33</xref>] . The type of treatment applied does not seem to have any influence on the adsorption kinetics of carotenes; on the other hand, there is an influence of the initial concentration on the quantities adsorbed at equilibrium. Indeed, the concentrations adsorbed at equilibrium increase with the initial concentrations regardless of the type of treatment applied as shown in <xref ref-type="table" rid="table2">Table 2</xref>. This increase in the quantity of</p><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Effect of the initial concentration on the quantity of carotenes adsorbed at equilibrium</title></caption><table><tbody><thead><tr><th align="center" valign="middle"  colspan="5"  >Quantities adsorbed (μmol/g)</th></tr></thead><tr><td align="center" valign="middle"  colspan="2"  ></td><td align="center" valign="middle"  colspan="3"  >Initials concentrations (mg/L)</td></tr><tr><td align="center" valign="middle" >Adsorbents</td><td align="center" valign="middle"  colspan="2"  >20</td><td align="center" valign="middle" >40</td><td align="center" valign="middle" >50</td></tr><tr><td align="center" valign="middle"  colspan="2"  >D0M</td><td align="center" valign="middle" >0.875 &#177; 0.018</td><td align="center" valign="middle" >1.651 &#177; 0.033</td><td align="center" valign="middle" >1.866 &#177; 0.037</td></tr><tr><td align="center" valign="middle"  colspan="2"  >D05M</td><td align="center" valign="middle" >0.951 &#177; 0.019</td><td align="center" valign="middle" >1.670 &#177; 0.033</td><td align="center" valign="middle" >1.951 &#177; 0.039</td></tr><tr><td align="center" valign="middle"  colspan="2"  >DAl<sub>13</sub></td><td align="center" valign="middle" >0.912 &#177; 0.018</td><td align="center" valign="middle" >1.729 &#177; 0.035</td><td align="center" valign="middle" >1.912 &#177; 0.038</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><p>carotenes adsorbed is however not proportional to the initial concentration, it is very strong between 20 mg/L and 40 mg/L and less marked between 40 mg/L and 50 mg/L; there is probably a trend towards saturation of the adsorption sites.</p><p>Acid activated clay performs best; however, it should be noted that the differences in the quantities adsorbed by all the adsorbents used here are small in all cases. Our sample of clay types 1:1 (kaolinites) absorbs for the initial concentrations of 20 mg/L for the raw, bridged and activated acid states respectively 0.875; 0.912 and 0.951 mmol/g for example indicates that it is not a structural phenomenon, but rather a surface interaction [<xref ref-type="bibr" rid="scirp.124347-ref34">34</xref>] . Acid activation causes a slight increase in specific surface area; the bridging leads to a deposit of polycations on the surface of the kaolinites and increase a little bit the basal spacing [<xref ref-type="bibr" rid="scirp.124347-ref35">35</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref36">36</xref>] . The samples are of different texture (specific surface and porosity) and the adsorbed quantities are not always closely related to the texture; it can therefore be concluded that the texture has no significant influence on the adsorption of carotenes.</p></sec><sec id="s3_2_2"><title>3.2.2. Influence of Temperature on Adsorption Kinetics</title><p>The adsorption kinetics of carotenes at temperatures of 25˚C, 45˚C and 65˚C were carried out. <xref ref-type="fig" rid="fig6">Figure 6</xref> make by using sigma plot logician show the evolution of the quantities of carotenes adsorbed as a function of time for an initial concentration of 40 mg/L.</p><p>By observing these curves, we notice that the adsorption is very strong in the first 10 minutes, followed by a gradual evolution until equilibrium. Overall, it can be seen that the adsorption of carotenes is practically not influenced by temperature (<xref ref-type="table" rid="table3">Table 3</xref>).</p><table-wrap id="table3" ><label><xref ref-type="table" rid="table3">Table 3</xref></label><caption><title> Effect of temperature on the quantity of carotenes adsorbed at equilibrium</title></caption><table><tbody><thead><tr><th align="center" valign="middle"  colspan="6"  >Quantities adsorbed (μmol/g)</th><th align="center" valign="middle" ></th></tr></thead><tr><td align="center" valign="middle" ></td><td align="center" valign="middle"  colspan="6"  >Temperature (˚C)</td></tr><tr><td align="center" valign="middle" >Adsorbents</td><td align="center" valign="middle"  colspan="3"  >25</td><td align="center" valign="middle" >45</td><td align="center" valign="middle" >65</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle"  colspan="2"  >D0M</td><td align="center" valign="middle" >1.652 &#177; 0.033</td><td align="center" valign="middle"  colspan="2"  >1.691 &#177; 0.034</td><td align="center" valign="middle"  colspan="2"  >1.730 &#177; 0.035</td></tr><tr><td align="center" valign="middle"  colspan="2"  >D05M</td><td align="center" valign="middle" >1.671 &#177; 0.033</td><td align="center" valign="middle"  colspan="2"  >1.691 &#177; 0.034</td><td align="center" valign="middle"  colspan="2"  >1.749 &#177; 0.035</td></tr><tr><td align="center" valign="middle"  colspan="2"  >DAl<sub>13</sub></td><td align="center" valign="middle" >1.730 &#177; 0.035</td><td align="center" valign="middle"  colspan="2"  >1.749 &#177; 0.035</td><td align="center" valign="middle"  colspan="2"  >1.769 &#177; 0.035</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap></sec><sec id="s3_2_3"><title>3.2.3. Modeling of Carotene Adsorption Kinetics</title><p>The modeling of kinetic data can reveal the different molecular steps involved in the process and thus elucidate the adsorption mechanism involved. Among the different models developed to describe the kinetics of adsorption in solution, three are used in most work. These are the pseudo first order models, the pseudo second order model, and the intraparticle diffusion model [<xref ref-type="bibr" rid="scirp.124347-ref37">37</xref>] - [<xref ref-type="bibr" rid="scirp.124347-ref42">42</xref>] . These three models were therefore used here to model the kinetics of carotene adsorption by raw or modified kaolinites.</p><p>The velocity equations in their linear forms for the different models are as follows:</p><p>- Pseudo first order kinetics:</p><p>ln ( q e − q t ) = ln q e − k 1 t (2)</p><p>- Pseudo-second order kinetics:</p><p>t q t = 1 k 2 q e 2 + 1 q e t (3)</p><p>- The intra-particle diffusion model:</p><p>q t = k i n t t + α (4)</p><p>where: q<sub>e</sub> and q<sub>t</sub> are the quantities of adsorbed carotenes (mg/g) at equilibrium and at time t respectively.</p><p>k<sub>1</sub>, k<sub>2</sub> and k<sub>int</sub> are respectively the pseudo first order (min<sup>−1</sup>), pseudo second order (g/&#181;g∙min) and intraparticle diffusion (&#181;mol/(mg∙min<sup>1/2</sup>)) rate constants respectively.</p><p>α is a constant.</p><p>The values of k<sub>1</sub>, k<sub>2</sub>, k<sub>int</sub>, q<sub>e</sub> and the correlation coefficients R<sup>2</sup> are reported in <xref ref-type="table" rid="table4">Table 4</xref>.</p><p>The experimental data conform to the pseudo first order kinetic model if the linear regression ln(q<sub>e</sub> −q<sub>t</sub>) in function of t has a coefficient of determination R<sup>2</sup> &gt; 0.900.</p><p>In the case of the pseudo second order model, the linear regression t/q<sub>t</sub> in function of t must have an R<sup>2</sup> &gt; 0.900.</p><p>The data conforms to the intraparticle diffusion model if the R<sup>2</sup> of the q<sub>t</sub> versus</p><table-wrap id="table4" ><label><xref ref-type="table" rid="table4">Table 4</xref></label><caption><title> Kinetic parameters of raw and modified kaolinites with carrot extracts: initial concentration = 40 mg/L, clay mass = 2 g, extracted volume = 5 ml, T˚ = 25˚C</title></caption><table><tbody><thead><tr><th align="center" valign="middle"  rowspan="2"  >Clays</th><th align="center" valign="middle"  colspan="4"  >Pseudo first order</th><th align="center" valign="middle"  colspan="4"  >Pseudo second order</th><th align="center" valign="middle"  colspan="4"  >Intraparticule diffusion model</th><th align="center" valign="middle"  rowspan="2"  >q<sub>e</sub> exp (μmol/g)</th></tr></thead><tr><td align="center" valign="middle" >k<sub>1</sub> (min<sup>−1</sup>)</td><td align="center" valign="middle" >q<sub>e</sub> (μmol/g)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >χ<sup>2</sup></td><td align="center" valign="middle" >k<sub>2</sub> (μmol/g<sub>min</sub>)</td><td align="center" valign="middle" >q<sub>e</sub> (μmol/g)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >χ<sup>2</sup></td><td align="center" valign="middle" >k<sub>int</sub> (μmol/g<sub>min</sub><sup>1/2</sup>)</td><td align="center" valign="middle" >q<sub>e</sub> (μmol/g)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >χ<sup>2</sup></td></tr><tr><td align="center" valign="middle" >D0M</td><td align="center" valign="middle" >0.136</td><td align="center" valign="middle" >1.370</td><td align="center" valign="middle" >0.909</td><td align="center" valign="middle" >0.058</td><td align="center" valign="middle" >1.000</td><td align="center" valign="middle" >1.746</td><td align="center" valign="middle" >0.991</td><td align="center" valign="middle" >0.005</td><td align="center" valign="middle" >0.179</td><td align="center" valign="middle" >0.056</td><td align="center" valign="middle" >0.945</td><td align="center" valign="middle" >45.429</td><td align="center" valign="middle" >1.651</td></tr><tr><td align="center" valign="middle" >D05M</td><td align="center" valign="middle" >0.222</td><td align="center" valign="middle" >1.280</td><td align="center" valign="middle" >0.982</td><td align="center" valign="middle" >0.119</td><td align="center" valign="middle" >2.819</td><td align="center" valign="middle" >1.708</td><td align="center" valign="middle" >0.999</td><td align="center" valign="middle" >0.001</td><td align="center" valign="middle" >0.178</td><td align="center" valign="middle" >0.056</td><td align="center" valign="middle" >0.900</td><td align="center" valign="middle" >46.518</td><td align="center" valign="middle" >1.670</td></tr><tr><td align="center" valign="middle" >DAl<sub>13</sub></td><td align="center" valign="middle" >0.207</td><td align="center" valign="middle" >2.353</td><td align="center" valign="middle" >0.902</td><td align="center" valign="middle" >0.165</td><td align="center" valign="middle" >0.573</td><td align="center" valign="middle" >1.901</td><td align="center" valign="middle" >0.975</td><td align="center" valign="middle" >0.016</td><td align="center" valign="middle" >0.196</td><td align="center" valign="middle" >0.062</td><td align="center" valign="middle" >0.967</td><td align="center" valign="middle" >44.821</td><td align="center" valign="middle" >1.729</td></tr></tbody></table></table-wrap><p>regression is greater than 0.900.</p><p>In any case, we must always have an “Absolute Average Deviation” (AAD) close to 1 and in addition the value of the Chi-square (χ<sup>2</sup>) must be low.</p><p>The coefficient χ<sup>2</sup> has the expression:</p><p>χ 2 = ( q e x p − q c a l ) ∗ 2 q c a l (5)</p><p>where: q<sub>exp</sub> (&#181;mol/g) is the quantity of adsorbed carotenes, obtained experimentally;</p><p>q<sub>cal</sub> (&#181;mol/g) is the theoretical quantity of carotenes adsorbed.</p><p>Of the three kinetic models that have been tested with the experimental adsorption data, it can be said through the R<sup>2</sup> ≥ 0.9 that the adsorption responds equally well to the pseudo first order, pseudo second order models (similar to [<xref ref-type="bibr" rid="scirp.124347-ref43">43</xref>] ) and to the intra-particle diffusion (<xref ref-type="table" rid="table4">Table 4</xref>).</p><p>However, by comparing the calculated q<sub>e</sub> values of the different models to the experimental q<sub>e</sub>, the pseudo second order model responds better than the pseudo first order and intraparticle diffusion models to the adsorption of β-carotenes.</p><p>The fact that the experimental data conforms to the pseudo-second-order model implies that the adsorption takes place in two steps. Our experimental data are also consistent with the intraparticle diffusion model, it is deduced that the two stages of carotenoid adsorption are respectively the diffusion of carotenoids from the solution to the clay surface and the interaction at the surface.</p><p>For the intraparticle diffusion model, the curves generally have three characteristic zones which represent the initial curve zone, the linear zone and the plateau zone. First, the rising curve is the diffusion of the adsorbate through the solution onto the outer surface of the adsorbent or the molecule-solute bond diffusion layer. The second zone represents gradual adsorption, a stage where intra-particle diffusion is at the limit speed (adsorption-desorption dynamism). The third zone represents the final equilibrium, the stage where intra-particle diffusion begins to drop, due to the extremely low concentration of solute remaining in the solution; this third stage exists when the initial concentration of β carotene is high [<xref ref-type="bibr" rid="scirp.124347-ref40">40</xref>] . The intra-particle diffusion model was used to determine the limiting velocity during the adsorption process. If intra-particle diffusion occurs, q<sub>t</sub> as a function of will be linear; and if the points pass through the origin, then the rate limiting process is only due to intra-particle diffusion. In this study, the intra-particle diffusion line does not pass through the origin, suggesting that intra-particle diffusion is applicable to this system but was not the only rate-limiting step for step of adsorption.</p></sec></sec><sec id="s3_3"><title>3.3. Adsorption Isotherm</title><p>The kinetic study showed that the adsorption equilibrium is reached after 30 minutes. A contact time of 45 minutes was chosen to construct the adsorption isotherms.</p><sec id="s3_3_1"><title>3.3.1. Carotene Adsorption Isotherms</title><p><xref ref-type="fig" rid="fig7">Figure 7</xref> (make by using sigma plot logician) show the adsorption isotherms of</p><p>carrot carotenoids on raw and modified kaolinites.</p><p>It is observed that the raw clay which adsorbs less carotenes and even the adsorption is more effective at 45˚C than at 25˚C.</p></sec><sec id="s3_3_2"><title>3.3.2. Modeling of Adsorption Isotherms</title><p>Langmuir, Freundlich, Temkin and Dubinin-Raduchkevich models are regularly used to model adsorption isotherms in solution [<xref ref-type="bibr" rid="scirp.124347-ref44">44</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref45">45</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref46">46</xref>] . We applied these models to our experimental results.</p><p>The linear form of the Langmuir equation has the expression:</p><p>C q = 1 K L q m + 1 q m C (6)</p><p>where:</p><p>C is the adsorbate concentration at equilibrium (&#181;g/ml);</p><p>q<sub>m</sub> is the quantity of adsorbate adsorbed at equilibrium (&#181;g/mg);</p><p>b is the amount of adsorbate adsorbed to the monolayer (mg/g);</p><p>K<sub>L</sub> is Langmuir’s equilibrium adsorption constant (ml/&#181;g).</p><p>Carotene adsorption will follow Langmuir’s equation if the coefficient of determination of the linear regression C q in function of C is greater than 0.900.</p><p>Another essential characteristic of the Langmuir isotherm is the non-dimensional constant called the separation factor or equilibrium parameter R<sub>L</sub>, defined by [<xref ref-type="bibr" rid="scirp.124347-ref47">47</xref>] by the equation:</p><p>R L = 1 / ( 1 + K L C 0 ) (7)</p><p>where:</p><p>K<sub>L</sub> is Langmuir’s constant and C<sub>0</sub> the initial carotenoid concentration (mg/L). The values of R<sub>L</sub> indicate the types of isotherms to be as well favorable (0 &lt; R<sub>L</sub> &lt; 1), unfavorable (R<sub>L</sub> &gt; 1) as linear (R<sub>L</sub> = 1) or irreversible (R<sub>L</sub> = 0).</p><p>The linear form of the Freundlich equation is:</p><p>ln ( q e ) = ln K F + 1 n ln C (8)</p><p>The experimental data will conform to the Freundlich model if the linear regression lnq<sub>e</sub> as a function of lnC<sub>e</sub> has an R<sup>2</sup> ≥ 0.900.</p><p>where:</p><p>- K<sub>F</sub> is a constant relating to the adsorption capacity of the adsorbate.</p><p>- n is the Freundlich constant which indicates the degree of affinity between the adsorbent and the adsorbate. The affinity is very strong when n is greater than 10, it is medium for n between 0 and 10 and low for n &lt; 1.</p><p>The linear form of the Temkin isotherm has the expression:</p><p>q = B ln A + B ln C (9)</p><p>Similarly, the experimental data will conform to the Temkin model if the linear regression q as a function of lnC has a coefficient of determination R<sup>2</sup> greater than 0.900.</p><p>Where: B = R T b (J/mol), is the Temkin constant related to the adsorption energy;</p><p>A is the equilibrium constant corresponding to maximum equilibrium (ml/mg);</p><p>R is the universal gas constant (8.314 J/mol K);</p><p>T is the absolute temperature of the solution (K).</p><p>The linear form of the Dubinin–Radushkevich equation is:</p><p>ln q = ln q D R − β ε 2 .</p><p>q is the quantity adsorbed per gram of adsorbent (mol/g);</p><p>q<sub>DR</sub> is the monolayer adsorption capacity (mol/g);</p><p>β is the sorption energy constant relative to the average sorption energy per mol of adsorbate that is transferred to the adsorbent surface.</p><p>ε is the Polanyi potential and has the expression</p><p>ε = R T ln ( 1 + 1 C ) (10)</p><p>E: Sorption energy (kJ/mol) If 1 &lt; E &lt; 8, then the adsorption is physical; and if 8 &lt; E &lt; 16, we have chemical adsorption.</p><p><xref ref-type="table" rid="table5">Table 5</xref> shows about the values of R<sup>2</sup> that the numerical data of the adsorption of carotenoids by various adsorbents conform to the Langmuir model which is based on the homogeneous surface and also to the Freundlich and Dubinin Radushkevich models, which admit a heterogeneous surface. The analysis of the adsorbents showed that these materials are heterogeneous. We can however admit a homogeneous distribution of the adsorption sites, as justification for the conformity of the experimental results with the Langmuir model, similar observation was done by [<xref ref-type="bibr" rid="scirp.124347-ref37">37</xref>] .</p><p>The R<sub>L</sub> values obtained are between 0.174 and 0.004 both at 298K and 318K for the adsorption of carotenes on the different clays. This indicates that the adsorption process is favorable for most cases.</p><p>The disparate values of the quantity (q<sub>m</sub>) of carotenes adsorbed in the monolayer deduced from the Langmuir model show the limits of application of this model to the adsorption of carotenoids. Acid activated clay performs best, followed by bridged clay.</p><p>The values of n in the Freundlich equation are all less than 1, indicating poor affinity between carotenoids and clays. This low affinity is best expressed by the interaction energies obtained by the Temkin (B &lt; 1) and dubinin-Radushkevich (1 &lt; E &lt; 8) models. These very low values of B and E suggest that the adsorption of carotenoids by our clays is of a physical type with a very strong contribution from Van der Walls bonds. The involvement of Hydrogen bonds would indeed have induced stronger interaction energies of the order of 20 - 40 KJ∙mol<sup>−1</sup>.</p><p>The mechanism would include the interactions of double bonds of the carbon chain of the carotenes with the acid sites (Lewis and Br&#246;nsted) of the adsorbents [<xref ref-type="bibr" rid="scirp.124347-ref48">48</xref>] .</p></sec></sec><sec id="s3_4"><title>3.4. Adsorption-Desorption Isotherms</title><p>Desorption experiments are of great practical importance in the application of face masks because it gives long-term insight into the stability of the adsorbed constituent. <xref ref-type="fig" rid="fig8">Figure 8</xref> (make by using sigma plot logician) show the adsorption-desorption isotherms of carotenoids on raw, activated and bridged kaolinites. These isotherms show hysteresis manifested by a difference between the</p><table-wrap id="table5" ><label><xref ref-type="table" rid="table5">Table 5</xref></label><caption><title> Values of Langmuir, Freundlich, Temkin and Dubinin-R constants. for the adsorption of carotenes from carrots on raw clays, activated and bridged with AlCl<sub>3</sub></title></caption><table><tbody><thead><tr><th align="center" valign="middle"  rowspan="2"  >Clays</th><th align="center" valign="middle"  rowspan="2"  >T (˚K)</th><th align="center" valign="middle"  colspan="4"  >Langmuir model</th><th align="center" valign="middle"  colspan="3"  >Freundlich model</th><th align="center" valign="middle"  colspan="3"  >Temkin model</th><th align="center" valign="middle"  colspan="4"  >Dubinin-Radushkevich model</th></tr></thead><tr><td align="center" valign="middle" >K<sub>L</sub> (ml/&#181;g)</td><td align="center" valign="middle" >R<sub>L</sub></td><td align="center" valign="middle" >q<sub>m</sub> (&#181;mol/g)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >K<sub>F</sub> (mg/ (g(mg/l)<sup>1/n</sup>))</td><td align="center" valign="middle" >n</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >A (ml/mg)</td><td align="center" valign="middle" >B (J/mol)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >q<sub>DR</sub> (molg<sup>−1</sup>)</td><td align="center" valign="middle" >E (kJmol<sup>−1</sup>)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle"  rowspan="2"  >D0M</td><td align="center" valign="middle" >298</td><td align="center" valign="middle" >0.194</td><td align="center" valign="middle" >0.114</td><td align="center" valign="middle" >0.924</td><td align="center" valign="middle" >0.993</td><td align="center" valign="middle" >0.204</td><td align="center" valign="middle" >0.768</td><td align="center" valign="middle" >0.985</td><td align="center" valign="middle" >0.948</td><td align="center" valign="middle" >0.651</td><td align="center" valign="middle" >0.947</td><td align="center" valign="middle" >44.949</td><td align="center" valign="middle" >1.000</td><td align="center" valign="middle" >0.992</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >318</td><td align="center" valign="middle" >0.191</td><td align="center" valign="middle" >0.116</td><td align="center" valign="middle" >1.328</td><td align="center" valign="middle" >0.960</td><td align="center" valign="middle" >0.112</td><td align="center" valign="middle" >0.630</td><td align="center" valign="middle" >0.992</td><td align="center" valign="middle" >1.696</td><td align="center" valign="middle" >0.464</td><td align="center" valign="middle" >0.911</td><td align="center" valign="middle" >35.684</td><td align="center" valign="middle" >1.000</td><td align="center" valign="middle" >0.982</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle"  rowspan="2"  >D05M</td><td align="center" valign="middle" >298</td><td align="center" valign="middle" >0.687</td><td align="center" valign="middle" >0.035</td><td align="center" valign="middle" >2.418</td><td align="center" valign="middle" >0.931</td><td align="center" valign="middle" >0.406</td><td align="center" valign="middle" >0.909</td><td align="center" valign="middle" >0.913</td><td align="center" valign="middle" >3.958</td><td align="center" valign="middle" >0.358</td><td align="center" valign="middle" >0.978</td><td align="center" valign="middle" >8.423</td><td align="center" valign="middle" >1.066</td><td align="center" valign="middle" >0.922</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >318</td><td align="center" valign="middle" >3.113</td><td align="center" valign="middle" >0.008</td><td align="center" valign="middle" >1.787</td><td align="center" valign="middle" >0.979</td><td align="center" valign="middle" >0.647</td><td align="center" valign="middle" >0.909</td><td align="center" valign="middle" >0.985</td><td align="center" valign="middle" >53.802</td><td align="center" valign="middle" >0.184</td><td align="center" valign="middle" >0.909</td><td align="center" valign="middle" >1.182</td><td align="center" valign="middle" >1.539</td><td align="center" valign="middle" >0.985</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle"  rowspan="2"  >DAl<sub>13</sub></td><td align="center" valign="middle" >298</td><td align="center" valign="middle" >0.510</td><td align="center" valign="middle" >0.047</td><td align="center" valign="middle" >0.160</td><td align="center" valign="middle" >0.962</td><td align="center" valign="middle" >0.525</td><td align="center" valign="middle" >0.814</td><td align="center" valign="middle" >0.980</td><td align="center" valign="middle" >0.866</td><td align="center" valign="middle" >0.530</td><td align="center" valign="middle" >0.917</td><td align="center" valign="middle" >3.219</td><td align="center" valign="middle" >1.165</td><td align="center" valign="middle" >0.906</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >318</td><td align="center" valign="middle" >0.642</td><td align="center" valign="middle" >0.037</td><td align="center" valign="middle" >2.966</td><td align="center" valign="middle" >0.955</td><td align="center" valign="middle" >0.077</td><td align="center" valign="middle" >0.283</td><td align="center" valign="middle" >0.903</td><td align="center" valign="middle" >2.960</td><td align="center" valign="middle" >0.561</td><td align="center" valign="middle" >0.993</td><td align="center" valign="middle" >26.414</td><td align="center" valign="middle" >1.000</td><td align="center" valign="middle" >0.984</td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><p>adsorption and desorption isotherms. This lack of similarity between adsorption and desorption isotherms due to hysteresis has been observed on French clays [<xref ref-type="bibr" rid="scirp.124347-ref49">49</xref>] [<xref ref-type="bibr" rid="scirp.124347-ref50">50</xref>] . The desorption isotherms are below the adsorption isotherms, indicating that the adsorption of carotenoids is partial and reversible. This reversibility justifies the low interaction energies found previously.</p><p>Desorption is physical, however, by comparing the adsorbed and desorbed quantities, it appears from this table that the desorbed quantity represents on average 50% of the adsorbed quantity</p></sec></sec><sec id="s4"><title>4. Conclusion</title><p>Experimental carotenoid adsorption data from carrots on crude and modified kaolinites agree equally well with pseudo-first-order, pseudo-second-order and intra-particle diffusion models according the R<sup>2</sup>; however, by comparing the calculated qe values of the different models to the experimental qe, the pseudo second order model responds better, Therefore the adsorption takes place in two steps. The quantities adsorbed are proportional to the initial concentrations. The increase in the initial concentration leads to an increase in the quantity of β carotene fixed on the clay substrates under the study conditions. In addition, at high temperature, the adsorption rate is not significantly greater and the number of adsorbed carotenoids is substantially similar. Amongst the four model (Langmiur, Freundlich, Temkin and Dubinin-R.) for carotenoid adsorption equilibrium data from carrots in cyclohexane studied, the Freundlich model describe better adsorption with maximum adsorption at the monolayer. Sorption experiments confirm that adsorption is physical.</p></sec><sec id="s5"><title>Conflicts of Interest</title><p>The authors declare no conflicts of interest regarding the publication of this paper.</p></sec><sec id="s6"><title>Cite this paper</title><p>Ngomo, O., Dongo, E. and Sieliechi, J. (2023) Physico-Che- mical Study of the Adsorption of Carotenoids from Carrots on Raw and Modified Kaolinites. 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