Thermodynamic properties and modeling of sorption isotherms for longer storage of Urtica urens leaves

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1 International OPEN ACCESS Journal Of Moern Engineering Research (IJMER) Thermoynamic properties an moeling of sorption isotherms for longer storage of Urtica urens leaves A. Lamharrar 1, A. Ilimam 2, M. Cherkaoui 3, L. Lahnine 4, M. Kouhila 5 1,2,3,4,5, Laboratory of Solar Energy an Meicinal Plants, Ecole Normale Supérieure, Cai Ayya University, Marrakesh, Morocco. 4 Equipe e Recherche Innovation e Développement Durable en Chimie Verte, Faculté es Sciences semlalia, Cai Ayya University, Marrakesh, Morocco Abstract: Moisture uilibrium ata of Urtica urens leaves by esorption an asorption ere etermine at 30, 40, an 50 C. The isotherms ere etermine by a static gravimetric metho for various temperature an humiity conitions. Five mathematical moels ere use to fit the experimental ata. A nonlinear least-squares regression program as use to evaluate the constants of the five esorption an asorption isotherm moels GAB an Moifie Halsey moels ere auate to escribe the sorption characteristics of the samples. Isosteric heats of esorption an asorption ere calculate by applying the Clausius-Clapeyron uation to the sorption isotherms at ifferent temperatures. It ecrease ith increasing moisture content. We recognize the linear relation exists beteen the enthalpy an entropy of the sorption reaction. Keyors: enthalpy, entropy, hysteresis, mathematical moels, sorption isotherm. I. INTRODUCTION The homeopathic remey Urtica urens leaves is prepare using the entire herb knon as annual nettle, hile it is in blossom an is use to treat a number of health conitions, especially nettle rash or hives. Commonly knon as arf nettle, annual nettle or small nettle, Urtica urens is a semi-ooy plant belonging to genus Urtica that gros annually. Traitionally, people have been using this herb as a meication for skincare as ell as alleviate skin inflammation or itchiness. In effect, scientists have especially stuie the herb Urtica urens for its potential in supporting the skin hen external irritants result in certain complaints [1]. The meicinal an aromatic plants have a great importance for both the pharmaceutical inustry an the traitional. The stability of a ehyrate meicinal plant is influence by its ater activity. This stability is mainly a consuence of the relationship beteen the uilibrium moisture content an its corresponing ater activity. Knolege of the sorption properties of foos is of great importance in meicinal plant, especially in the quantitative approach to the preiction of the shelf life of rie meicinal plant. Equations for moeling ater sorption isotherms are of special interest for many aspects of meicinal plant preservation by ehyration. In this stuy, temperatures of 30 C, 40 C, an 50 C ere chosen, to typify tropical storage conitions. Using an experimental approach, the uilibrium curves are etermine by the saturate salt solution metho. The experimental sorption curves are escribe by five ifferent moels to ientify the most appropriate mathematical moel for a better escription of the prouct uilibrium state: GAB s moel, moifie Henerson's moel, moifie Halsey s moel, moifie Osin s moel. Then, e investigate from the experimental ata the ater activity optimal for the storage of Urtica urens. Further analysis of sorption isotherm ata by application of thermoynamic principals can provie information regaring ifferential enthalpy or the isosteric heat of sorption an ifferential entropy. Differential enthalpy of sorption gives an inication of the amount of boun ater existing in the prouct. The ifferential entropy of material is proportional to the number of its available sorption sites at a specific energy level [2]. Subsuently e etermine the thermoynamic functions (ifferential enthalpy, ifferential entropy). Moreover, e recognize the linear relation exists beteen the enthalpy an entropy of the sorption reaction. II. MATERIALS AND METHODS 2.1 Experimental proceure The plant Urtica urens use in our stuy as collecte at Tahanouat, Marrakesh Morocco. The hygroscopic uilibrium coul be achieve by a ynamic or static metho. In the present ork, a static metho IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

2 Thermoynamic properties an moeling of sorption isotherms for longer storage is use [3]. The metho is base on the use of saturate salt solutions to maintain a fixe relative humiity Rh. The mass transfers beteen the prouct an the ambient air are assure by natural iffusion of the ater vapour. The atmosphere surrouning the prouct has a fixe relative humiity for every orking temperature impose on the system. Six salts ere chosen { KOH, (MgCl 2, 6H 2 O), K 2 CO 3, NaNO 3, KCl an (BaCl 2, 2H 2 O)} so as to have a range of ater activity of [4]. The experimental apparatus consiste of six glass jars of 1 liter each ith an insulte li. Every glass jar as fille to quarter epth ith a saturate salt solution. Duplicate samples each of 0.4 g (±0.0001g) for esorption an 0.1 g (±0.0001g) for asorption ere eighe an place into the glass jars. The eight recoring perio as about 3 ays. This proceure continue until the eight as constant. The uilibrium moisture content of each sample as etermine in a rying oven at 105 C for 24 h. The hygroscopic uilibrium Urtica urens leaves as reache in then ays for esorption an eighth ays for asorption. 2.2 Moelling uations The relationship beteen uilibrium moisture content, ater activity, an temperature for Urtica urens leaves as preicte in literature by several mathematical moels [5]. In our stuy five moels have been applie: GAB s moel, moifie Henerson's moel, moifie Chung-Pfost moel, moifie Halsey moel, an moifie Osin s moel. The uations expressing those moels are given belo in table 1. X represents uilibrium moisture content (%MS); a ater activity; A, B, an C coefficients, epenant to the temperature or not, to etermine by smoothing the experimental curves of sorption an θ the temperature in C. The correlation coefficient (r) as one of the primary criteria for selecting the best uation to fit the four moels to the experimental ata. In aition to r, the statistical parameters mean relative error (MRE) as a percentage as use to etermine the quality of the fit [6]. Levenberg-Marquart nonlinear optimization metho using appropriate softare is use for the calculation of moel coefficients that escribe the uilibrium curves an their statistical parameters: the correlation coefficient (r) an mean relative error (MRE). r= N 2 i,pre i,exp i=1 N 2 i=1 MRE = X X i,exp -X -X X i,exp - X (1) N i,exp i,pre N (2) X 100 i=1 i,exp Where: X i,exp i th Experimental moisture content (%.b) X i th Preicte moisture content (%.b) i,pre N.b number of ata points. ry basis GAB Table 1: Mathematical moels use in our stuy Moel s name Expression of the moel References A B C a X = 1-B a 1-B a +B C a [7] Moifie Henerson Moifie Chung-Pfost Moifie Halsey Moifie Osin -ln(1-a ) X = A( B) -A a exp exp-cx θ B X (-exp(a B. ) ln(a ) a X (A B. ) 1 a 1/c (1/c) C [8] [9] [10] [11] IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

3 Thermoynamic properties an moeling of sorption isotherms for longer storage 2.3 Determination of the optimum conitions for storage The stuy of the sorption isotherms enables us to kno the optimal relative uilibrium moisture for the conservation of a prouct as ell as the ater content of uilibrium to reach at the en of the rying. Also, it affors users ith accurate information on ho to hanle a prouct uring storage an conservation [12]. For this purpose, the optimal ater activities of conservation (a op ) ere ogge. The hole of the experimental points is gathere on the same graph. Then, e moel the isotherm of sorption by a polynomial uation of the thir egree. The part closes to horizontality correspons to the zone of better stability of the prouct. This process of calculation consists in making a polynomial ecomposition of the uilibrium moisture content X, for the hole of the experimental results, accoring to the ater activity. This makes it possible to calculate the value for hich the erivative secon of X is cancelle inflection point an consuently optimal relative humiity for conservation. 2.4 Differential enthalpy an ifferential entropy of sorption The ifferential enthalpy or isosteric heat of sorption ( the soli material. The net isosteric heat of sorption ( heat of vaporization of ater ( Hvap h H ) associate ith the sorption process. vap ) inicates the state of absorbe ater by ) represents the quantity of energy exceeing the h H H (3) The net isosteric heat of sorption can be calculate from the experimental ata using the Clausius- Clapeyron uation [13]: (ln a ) -h (4) 1/ T R X This relation ruires etermining the isotherms at various temperatures in orer to calculate the variation logarithmic curve of the ater activity accoring to the reverse of the temperature, for a ater content fixe. Hoever, starting from the moifie uations, it is possible to obtain the analytical expression of the heat of sorption h. This approach assumes that isosteric heat H oes not vary ith the temperature [14]. The relationship beteen the net isosteric heat h an the ifferential entropy S of sorption is given by: h ΔS (-ln a ) X = - R. T R The experimental sorption isotherm ata as plotting in the form of ln(a ) versus 1 T (5) for specific moisture content (X ). We etermine h from the slope h an S from the intercept S. R R Applying this at ifferent moisture contents alloe etermining the epenence on 2.5 Enthalpy-Entropy Compensation Theory entropy an. Accoring to the theory of compensation, the linear relationship beteen the enthalpy S for a specific reaction are given by: h T. S G (6) h S h an the The isokinetic temperature (T ) is a characteristic property of the foo surface hose imension is absolute temperature. It represents the temperature to hich all the reactions of the series procee to the same rate. The free energy ( G ) provies a criterion to evaluate if the process of the ater sorption is spontaneous ( G ) or not ( G ). This process is repeate for several values of uilibrium relative humiity ith an aim of unerlining the relation beteen the ifferential entropy of sorption an the uilibrium moisture content of the stuie prouct. The isokinetic temperature (T ) an constant ( ) G IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

4 Thermoynamic properties an moeling of sorption isotherms for longer storage ere calculate using linear regression. The isokinetic temperature T represents the slope of the linear function beteen the ifferential entropy an the ifferential enthalpy of sorption [2]. III. RESULTAS AND DISCUSSION 3.1 Asorption an esorption isotherms The uilibrium moisture content increases ith ecreasing temperature at constant ater activity (Fig 1). The sorption isotherms present the characteristic S-shape curve (Type II), typical of sorption isotherms of many plants an foo materials [3, 4, 5]. Fig. 1: Sorption isotherms of Urtica urens leaves at 30, 40 an 50 C The presentation of asorption an esorption experimental ata in the same plot sho that the plant oes not have the same hygroscopic uilibrium behaviour (fig 2). The phenomenon of esorption-asorption is irreversible. For the same constant relative moisture, the ater content of esorption is higher than that of asorption. Inee, there exists a phenomenon of hysteresis. This characteristic is visible for Urtica urens plant. Fig.2: Sorption hysteresis phenomenon of Urtica urens leaves Several hypotheses have been put to explain hysteresis. One of it is an analogy ith a sponge. When the pores o not contain any more ater, asorption oes not make it possible to recover the totality of initial ater since this one imprisons air in the pores. Another hypothesis states that hysteresis in the sorption isotherm is a consuence of variation in the fraction of boun ater present in the asorption an esorption processes. The boun fraction being alays larger on esorption than on asorption [15]. 3.2 Moelling of sorption experimental ata The results of non linear regression analysis of fitting the sorption uations to experimental ata of Urtica urens leaves as at three temperatures are presente in Tables 2 an 3. For all the moels teste, parameters A, B an C are foun to be temperature epenent. For esorption isotherms, GAB moel is foun IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

5 Thermoynamic properties an moeling of sorption isotherms for longer storage to be the best estimator for preicting the uilibrium moisture of the Urtica urens leaves. This moel gives the highest correlation coefficient (r) of an mean relative error MRE ( %) at = 40 C. For asorption isotherms, moifie Halsey moel is foun to be the best estimator for preicting the uilibrium moisture of Urtica urens leaves. This moels gives the highest (r) of an the MRE ( %) at = 50 C. Table 2: Estimate moel coefficients, r, MRE of five uation moel fitte to esorption isotherm of Urtica urens leaves Moel s name ( C) A B C r MRE (%) 30 C GAB 40 C C C C Moifie Henerson 50 C C C Moifie Chung-Pfost 50 C C Moifie Halsey 40 C C C Osin Moifié 40 C C Table 3: Estimate moel coefficients, r, MRE of five uation moel fitte to asorption isotherm of Urtica urens leaves Moel s name ( C) A B C r MRE( %) 30 C GAB 40 C C C C Moifie Henerson 50 C C C Moifie Chung-Pfost 50 C C Moifie Halsey 40 C C C Moifie Osin 40 C C Measurement of optimal ater activity of Urtica urens leaves A quality prouct eserves quality treatment. The heat an process engineering specialists must provie users ith accurate information on ho to hanle a prouct uring storage an conservation. For this purpose, the optimal ater activities of conservation ( a op ) ere etermine. The sorption isotherm curve can be escribe as a polynomial uation of the thir egree, the central part or "stage" is the best area of prouct stability (fig 3). IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

6 Thermoynamic properties an moeling of sorption isotherms for longer storage Fig.3: Determination of optimal ater activity for conservation of Urtica urens leaves This calculation metho consists of ecomposing polynomial of uilibrium moisture content X, for all the experimental results for each prouct base on ater activity (uation 7). The values of the optimal ater activity conservation of Urtica urens leaves ( a op = ) are in perfect agreement ith the results obtaine for other proucts [16, 17]. The optimal ater activities are range in ( ). X = a a a (7) 3.4 Enthalpy an entropy of sorption The net isosteric heat of sorption ( h ) values are calculate from the uilibrium moisture ata at ifferent temperatures using Clausius-clapeyron uation (4). The variation of the heats sorption of Urtica urens leaves ith uilibrium moisture content is shon in figure 4. The net isosteric heat of esorption an asorption of Urtica urens leaves can be expresse mathematically as a polynomial function of uilibrium moisture content: Desorption : Δh = X X X (8) S Asorption : Δh S = X M X (9) The ifferential entropy ( S ) is plotte as a function of moisture content in figure 4. Once again, the entropy ata isplay a strong epenence on moisture content. The experimental esorption an asorption ata, respectively, conform to polynomial relation as represente by the uations: Desorption : ΔS = X X X (10) Asorption : ΔS = X X X (11) Fig.4: Net isosteric heat an ifferential entropy of sorption of Urtica urens leaves as a function of uilibrium moisture content IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

7 Thermoynamic properties an moeling of sorption isotherms for longer storage 3.5 Enthalpy-entropy compensation theory The h an S values for asorption an esorption, at given moisture contents, ere calculate by linear regression uation using uation 5. It as assume that, at specific moisture content, i not vary ith temperature. Figure 5, shos a linear relation, ith a correlation of etermination (r S =1). This inicates that the compensation exists. The parameters T an G (Equation 6) ere calculate from the ata by linear regression, an the values are etaile in table 4 h an Fig.5: Compensation theory of enthalpy/entropy Table 4: Characteristic parameters for h / S Relationship T β(k) -1 ΔG β(j.mol ) esorption asorption IV. CONCLUSION It s no iely accepte that sorption ata provie valuable information for inustrial rying in orer to preserve an store the seasonal plants an make them available to consumers all year roun. The sorption ata may be use not only for the ientification of the optimum resiual moisture content of the final prouct, but also for the calculation of the rying time of hygroscopic substances. The moisture sorption curves of Urtica urens leaves ere experimentally investigate at three temperatures 30, 40 an 50 C. The isotherms have a sigmoi shape (Type II) hich is common for many hygroscopic proucts. The hysteresis phenomenon as istinctly observe. Among the sorption moels chosen, the GAB moel as the best moel escribing the uilibrium moisture ata for esorption, an the moifie Halsey moel as the most suitable to estimate asorption isotherms. The optimal ater activities of conservation ere etermine. Net isosteric heat of sorption an ifferential entropy values of Urtica urens leaves ere foun to be a polynomial function of moisture content for esorption an asorption. Enthalpyentropy compensation theory coul be successfully applie to the moisture sorption behaviour of Urtica urens leaves. REFERENCES [1] C. Marrassini, C.Aceveo, J. Miño, G. Ferraro an S. Gorzalczany, Evaluation of antinociceptive, antinflammatory activities an phytochemical analysis of aerial parts of Urtica urens L. Phytotherapy Research, 24(12), 2010, [2] N. Arsalan, an H. Togrul, The fitting of various moels to ater sorption isotherms of tea store in a chamber uner controlle temperature an humiity, Journal of Store Proucts research, 42(2), 2006, [3] A. Lamharrar A. Ilimam, an M. Kouhila, L. Themoynamic properties an moisture isotherms of Artemisia herba-alba Rev. Energ. Ren, 10(3), 2007, [4] A. Jamali, M. Kouhila, L. Ait Mohame, A. Ilimam, an A. Lamharrar, Moisture asorption-esorption isotherms of Citrus reticulata leaves at three temperatures, Journal of Foo Engineering, 77(1), 2006, IJMER ISSN: ijmer.com Vol. 4 Iss.12 Dec

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