Studies of Osmotic Coefficients and Volumetric Behaviour on Aqueous Solutions of ~-Cyclodextrin at 298.15 K
Indi an Journal of Chemistry Vol. 43A , October 2004, pp. 2073-2080
Studies of osmotic coefficients and volumetric behaviour on aqueous solutions of ~-cyclodextrin at 298.15 K
Dilip H Dagade, Rahul R Kolhapurkar & Kesharsingh J Patit* Department of Chemistry, Shivaji Universi ty, Kolh apu r 416 004, Indi a Email: patilkcsharsin [email protected] Received 31 March 2004; revised 11 August 2004
The osmotic coefficient . solute activity coefficients and apparent molar vo lume are determined for ~-c y clodc x trin (~ -CD ) using the techniques of vapor press ure osmometry and digital densitometer in aqueous solutions (0.00 164 to 0.01308 1 mol kg' ) at 298.15 K. The th ermodyn ami c data of acti vities and partial molar volumes for so lvent and solute are computed usin g appropriate methodology and equations. Theories of dilute so lutions such as McMillan-Mayer and Flory- Hu gg in s arc
app li ed to es timate th e second vi rial coefficient (8*2) for ~-CD , the number of binding si tes and x12 interaction parameter. Usin g the parti al mol ar volume data at infinite dilution and 8*2 val ue, the contribution du e to solute-solvent and solute solute interactions in terms of attracti ve and repul sive components are estimated. The values or 8*2 and the components are compared with th e val ue s reponed for mono-saccharides. di saccharidcs an d other non-electrolytes. The results are discu ssed in terms of hydrophobic hydration and hydrophobic interaction. IPC Code: Int. Cl 7 GO IN 13/04
Thermodynamic methods are frequently employed in stabilized by weak van der Waals forces. Therefore, it the studies of the properties of natural biopolymers, was thought pertinent to obtain information about the nucleic acids and polysaccharides 111 aqueous interaction in solution phase where the solubility is so I uttons. t-3 . I n recent years a new fi1 e ld , limited. We report here the osmotic coefficient and supramolecular chemistry, has emerged in which the density measurement for aqueous ~-CD solutions at intermolecular interactions of the host-guest type are 298.15 K. The data are subjected to scrutiny by 3 14 generally studied .4. Among all potential hosts, the application of McMillan-Mayer as well as Flory 15 cyclodextrins are important because of their inclusion Huggins theories developed for solutions . complex forming ability which results in molecular encapsulation of the guest components. Materials and Methods A study of association between ~-CD and various ~-CD (98 % pure) procured from Merck 5 drugs has been made by microcalorimetric methods. Schushardt was dried at 100 oc under vacuum for Similarly, many spectroscopic methods are employed about 48 hours and used without further purification. 6 7 to determine the binding constants · . However, it is The analysis of the sample for water content was felt that no adequate attention has been given to made using Karl-Fischer titration method. It was understand the host-solvent interaction, although the found that the sample is well dried and has no disaccharides and polysaccharides interactions in measurable presence of water molecules. 13 All the 8 11 water have been understood in detail - • solutions were prepared on molality basis using Cycloamylases have hydrophobic cavities that can doubly glass distilled deionized water. NaCl salt of form inclusion complexes depending upon the AR grade (BDH) was dried under vacuum for 24 structure of guest molecules (functional group, charge hours at l20°C and used for calibration of osmometer. 12 effects etc.) and cavity diameter . Recently, we The densities were measured with the help of studied the presence of water in solid ~-CD and found Anton Paar oscillating tube digital densitometer that there are seven water molecules per ~-CD (Model DMA 60/602) at constant temperature 298. 15 molecule using Karl-Fischer and TGA-DT A ± 0.02 K. Water from Julabo F25 cryostat (having an 13 technique . It is proposed that these water molecules accuracy of ± 0.02 K) was circulated through the may be H-bonded with the etheric oxygen atoms of~ densitometer. The densitometer was calibrated with CD or may be in the form of spiral like cluster air (the appropriate humidity and pressure corrections 2074 INDIAN J CHEM, SEC A. OCTOBER 2004 were appli ed) and water. The reproducibility of 3 3 density measurements was better than ±5x 10· kg m- . .. . (2) The osmotic coefficients (
( V2 ) of B-CD at various concentrations were the presence of solute-solute interaction as difJ,. IS dm estimated usin g Eq. (l) negative. The osmotic coefficients of aqueous B-CD -v2 =-rrr. ,. + 111 [difJ,J- ... (1) dm solutions were determined over the range 0.00164 to 0.01308 mol kg·' at 298.15 K. The data are The calculations of partial molar volumes ( V, ) of represented by Eq. (3) water at different concentrations of B-CD were made usi ng Eq. (2) Table !- Density, ¢v· y2. v, .water activity. osmotic coefficient. and act ivity coefficient data for aqueous 13-CD sol utions at 298. 15 K Ill d ¢,. v2 v, ¢ G w y, Y2 L'.CE 1 kg m-3 3 1 1 mol kg' cm moJ' cm3mor 1 cm3mor 1 J mor 0.00 164 997.733 7 16.9 7 15.0 18069 1.0 12 14 0.999970 I .000000 I .02208 0.001 0.003 14 998.365 7 15 3 7 12. I 18. 070 I .02044 0.999942 0'.999999 I .04208 0.003 0.00487 999.096 7 13.7 709.6 18.070 1.02972 0.9999 10 0.999997 I .06376 0.007 0.00666 999.854 7 12.4 707.9 18.070 I .03955 0.999875 0.999995 I .08621 0.0 13 0.01004 1001 .286 7 10.7 707.3 18.070 I .05828 0.999809 0.999989 12839 0.028 0.01308 1002.565 7 10. I 709.5 IS 069 I .07532 0.999747 0.999982 I. 16747 0.047 DAGADE eta!.: OSMOTIC COEFFICIENTS & DENSITIES OF 0-CYCLODEXTRIN SOLUTIONS 2075 725 1.08 720 1.06 0 5 ~8 7 15 ~ 1.04 710 1.02 705 1.00 IL_------~------~------~ 700 L_------~------~------~ 0 0.005 O.QI 0.0 15 0.000 0.005 0.0 10 0.0 15 m / molkg-1 m /mol kg·' Fig. !-Apparent molar volume (¢v) of 0-CD as a function of Fig.2-Variation of osmotic coefficient (¢) of 0-CD in water as a molality (m) of 0-CD in water at 298. I 5 K. function of molality (m) of 0-CD at 298. I 5 K. The solvent activity coefficients were calculated water activity decreases slightly as a function of mole from experimental osmotic coefficient () data fraction of B-CD. following the procedure as described earlier for 18- The activity coefficient of solute (y2) has been 20 crown-6 (18C6)-H20 system and ustng the calculated using Eq. (6) expression , lny2 =(<1>-1)+ f(-1)dlnm ... (6) ... (4) 0 Since the osmotic coefficient expressed as a power series on the molality scale of the solute by Eq. (7) where Xt and x2 are the mole fractions of solvent and solute, respectively, and a 1 is water activity. Thus, the solvent activity coefficient y can be expressed as a II 1 = 1 + AJn; .. . (7) power senes tn the mole fraction of solute by the L 3 2 1 i = l expression "· where the coefficient A; can be obtained by the lny1 = Bx; +Cx ~ + ...... (5) method of least squares, Eq. (6) takes the form, after solving the integral, as The B and C coefficients appearing in Eq. 5 with its sign and magnitude are of special importance in understanding the thermodynamic behavior since they ... (8) are related to solute-sol vent association, solute-solute 2 22 interactions and solute size. 1. The data for the osmotic and activity coefficient for The data for the solute activity coefficient (y2) for aqueous B-CD solutions at 298.15 K are collected in aqueous B-CD solutions are collected in Table I and Table 1. The variation of osmotic coefficient of B-CD its variation as a function of molality of B-CD is in aqueous medium as a function of molality of B-CD shown in Fig. 3. It is observed that the increased y 2 at 298.15 K is shown in Fig. 2 which indicates that the as a function of concentration is similar to aqueous osmotic coefficient of B-CD in aqueous medium solutions of monofunctional nonelectrolytes23 and can 24 increases as the solute concentration increases. The be attributed to solute-solute association . 2076 INDIAN J CHElvl, SEC A, OCTOBER 2004 E The excess Gibbs free energy change (6-G ) has The value for the solute-solvent interaction NB,7 been calculated by using standard thermodynamic (where s:~ = -b1°1 ) for aqueous ~-CD solutions were equation 6-G E = RTl.xi In yi . The values obtained for calculated using Eq.(9). It is being compared with 6-GE are collected in Table I. For studied other similar non-electrolytes in aqueous solutions at concentration range 6-GE values are small but positive 298.15 K in Table 2. in aqueous ~-CD solutions. Similar type of results 11 The b1°1 is related to the potential of mean force W was obtained in case of 18C6 in aqueous medium. between one molecule of solute and one of solvent in However, the values obtained for 6-GE in case of 18C6 20 the pure solvent (including averaging of the force in CC1 medium are negative . . 4 over all rotational coordinates) by the expression Solute-solvent interactions The solute-solvent cluster integral b1°1 is related to ... (10) the pa11ial molecular volume of solute ( vg) at infinite dilution by where r is the distance between the centers of the molecules. The integral in Eq. (10) can split into two ... (9) parts as repulsive and attractive pa11 given by Eq. (11) as follows where k is the Boltzmann constant, T is the absolute temperature, and K is the isothermal compressibility 25 26 B,'~ ~ 4n 1[ 1- exp( -;;' )] ,' d, coefficient for pure solvent. ' 0.2 ~------, +![l-ex{ -;;l'd, ... (II) 0. 16 = 0. 12 where 0.08 '~ [ 0 ~----~-----~-----~ 0 0.005 0.0 1 0.0 15 S represents repulsive contribution and Table 2-Allractive contribution to solute-solve nt interaction coefficients at 298.15 K 3 3 3 3 10·3 X ~~ ~ 10' X RTK 10· x NB;~ 10' X NS 1o · x c-NctJA) 3 1 3 3 1 mm3mol· 1 mm mol' mm3mol' 1 llllll 1110!' I mm mol' ~-CD+ H20 7 18.9 I. I I 717.8 1977 1260 cell obiose+ H20 $ 2 12.0 1.1 I 210.9 405 194 sucrose+ H20 ' 2 11. 5 I. I I 210.4 476 266 glu cose+ H20 ' 11 2. 2 1.1 I Ill . I 358 246 I8C6+H20 # 223.2 I. II 222. 1 699 477 n Data fro m reference 20; ' Data from reference 21; s Data from reference 25 DAGADE et al.: OSMOTIC COEFFICIENTS & DENSITIES OF 0-CYCLODEXTRIN SOLUTIONS 2077 simplest potential function regards the molecule as high N<:PA value in solution phase is due to weak van rigid spheres. The B-CD molecule is assumed to be der Waals type of forces existing between the walled 27 spherical having a diameter of 15.4 ±0.4A . skeleton of -CH2 groups and the supported H-bonds For two hard spheres of diameters R1 and R2, one between etheric oxygen of the ring and clusters of water molecules inside the B-CD cavity. can estimate S as S = ~ ( R1 + R2 f. Using this value, the repulsive contribution to the solute-solvent Solute-solute interactions interaction is obtained as NS = 1977 cm3 mor', while The theory of McMillan-Mayer allows the formal the attractive contribution to the solute-solvent separation of effects for a solution which arise from interaction at 298.15 K has been obtained as, N<:PA = molecular pair, triplet, etc. interactions without taking into account solute-solvent effects. For such effects to = -1260 cm3mor'. NB;~- NS be included in a description of solution, the The values obtained for attractive and repulsive thermodynamic properties at infinite dilution must be contributions to the solute-solvent interaction in water known and expressed in terms of model for the for B-CD and other nonelectrolytes are collected in solvated state. Table 2. The comparison of the values for various According to McMillan-Mayer theory for a nonelectrolytes shows that, the attractive contribution solution of a solute in solvent, the osmotic pressure, 1 is more for B-CD than for other nonelectrolytes in n, is given b/ water. It has been explained that such a value for N<:PA depends upon the number of H-bonding sites n . 2 • 3 -=n+B?n +B n + ...... (13) available in case of solutions of carbohydrates in kT - 3 water. 25 It is observed that the attractive contribution increases in the order cellobiose < glucose < sucrose In this expression n is the number density, and < 18C6 < B-CD. The low value for cellobiose is s; s; attributed to its compact structure, while a similar are the osmotic second and third virial coefficients effect is being reflected in the solubility behavior of respectively (these refer to solute molecules only). s; these non-electrolytes in water. The solubility of and s; can be calculated from experimental activity sucrose and cellobiose are 2.6 (ref. 28) and 0.612 data and the partial molar volume of solute and (ref.25) mol dm-3 at 298.15 K respectively. The solvent as availability of hydroxyl group, the number of intramolecular hydrogen bonds per molecule in crystal and the magnitude of N<:PA show that sucrose ... (14) has high solubility than glucose (because, glucose has 4 hydroxyl groups and sucrose has 8 hydroxyl groups). In case of cellobiose, it has same number of hydroxyl groups as that of sucrose, but all are used up for H-bonding and hence it has 8 H-bonds per molecule. In sucrose, out of 8 hydroxyl groups one hydroxyl group is not involved at a ll in intramolecular ... (15) or intermolecular H-bonding which renders comparatively better solubility in water. 25 The strong 0 -o attractive interaction between l8C6 and water also where, "" and V 2 are the partial molar volumes of reveals that it is much more soluble than sucrose (i.e. solvent and solute respectively at infinite dilution. B in all proportions) because of its tendency to form and Care the coefficients in Eq. (5), in thi s expression bridged H-bonds and si ngle H-bonds with two solvent activity coefficient (y1) is expressed as power monomeric water molecules.20 Similarly, th e series in the mole fraction of B-CD at 298.15 K. attractive interactions are found to be hi gh between B While b and g in Eq. (15) are the coefficients in CD and water, it can be attributed to large Eqs 16 and 17 hydrophobic hydration. However, its solubility is limited in water because of intramolecular H-bonding existing in a solute molecul e. It is suggested that the . .. (16) 2078 INDIAN J CHEM, SEC A, OCTOBER 2004 - -o in aqueous B-CD solutions are collected in Table 3. V 2 = V 2 + gC2 + hC~ . .. (17) Similar values for other non-electrolytes have also been incorporated in Table 3 for comparison. The 1 2 Here V and V are the partial molar volumes of value for A 2min for aqueous B-CD solutions is found to 3 1 solvent and solute respectively at concentration C2 be -3420 cm mor which is a measure of pairwise (molarity). The coefficients a, b, g and h have been interactions between two B-CD molecules in water. evaluated using the partial molar volume and molarity The comparison of values in Table 3 shows that the data of aqueous B-CD solutions at 298.15 K. attraction contribution to solute - solute interactions Using the above equation for s;, the values of the between two molecules is maximum in B-CD pairwise interaction for many non-electrolytes have molecules than others. The order of magnitude are been tabulated by Kauzrnann et al. 21 They have also B-CD > 18C6 > sucrose > glucose > cellobiose. It is estimated the attractive and repulsive components for tempting to interpret the maximum value for A 2min in the osmotic second virial coefficients for many non terms of presence of maximum number of functional electrolytes in water. For osmotic second virial groups. However, as indicated earlier, it may be due coefficient, the mjnimum attractive (A 2m; 11 ) an . to the presence of hydrophobic interaction (or mjnimum repulsive contributions (R2 111; 11 ) have been attraction) between pair of B-CD molecules. calculated using Eqs 18 and 19. Additionally, in B-CD molecule the -OH groups on Cz-atom of one glucose unit and Cr atom of ... (18) neighboring glucose unit are hydrogen bonded with each other. Such an interpretation is evidenced when one compares the Nct> A contribution to s; and s;~ ... (19) (Tables 2 and 3). It is observed that the solute-solute attractive contribution to (i.e. between two B-CD where, f is the factor which is measure of the s; molecules) is considerably more than the solute ellipticity of the molecule and V2° is the molar solvent attractive contribution to s;~ (i.e. B-CD and volume of pure solute. For B-CD, it is assumed that it water). Alternatively, this indicates that hydrophobic exists as a spherical entity in aqueous medium and interactions persist even up to the lowest hence f is unity. The minimum attractive and minimum repulsive concentration studied between B-CD molecules. contributions to the osmotic third virial coefficient, In order to ascertain the reliability of our data of osmotic virial coefficients, we processed the data i.e. A J min and R J min respectively have been calculated n by using Eqs 20 and 21. other way i.e. a plot of versus 3 .. . (20) (concentration in g cm- ) is made and shown in Fig. 4 . The intercept of the said plot yielded the value of reciprocal of molecular weight, while the slope value .. . (21) gave the measure of osmotic second virial coefficient. It is pleasing that the calculated molecular weight is The data of osmotic second and third virial obtained as 1127 g mor 1 (formula weight = 1135 g 1 coefficients as well as their minimum attractive and mor ). Similarly, the value of osmotic second virial repulsive contributions to solute - solute interactions coefficient value is obtained as 5874 cm3 mol' 1 which Tabl e 3-Attracti ve contributions to solute-so lute interaction coeffi cients at 298.15 K 2 NB; N 8; - A2min R 2min - ;\3min R 3min ~-CD+ H20 6296 83 30941 3420 2876 3162568 5168373 Cellobiose+H, Os 267 355 622 Sucrose+H ,o ' 286 87000 558 783 360000 447000 Glu cose +H~ o · 117 403 520 18C6+H,oii 278 226998 615 893 498048 271051 # Data from reference 20; • Data from reference 2 1; $ Data from reference 25 DAGADE et al.: OSMOTIC COEFFICIENTS & DENSITIES OF ~-CYCLODEXTRIN SOLUTIONS 2079 10 0.980 9.7 0.978 0 -<$. E 9.4 - 0.976 !:'- ::::. -<$. '-'"" -= ~ 9.1 >< ,; 0.97 4 c 0 8.8 0.972 8.5 L__----~---~----__._ ____j 0.970 '----~---'------'-----'------' 0.000 0.005 0.0 10 0.0 15 0.020 0.000 0.002 0.004 0.006 0.008 0.0 10 C /gcm-J 2 (I • ¢, ) Fig. 4--Extrapolation of the osmoti c pressure (IT) - concentrati on Fig. 5-Variation of (I n aw-ln !fiw)l( l-1/1.. ) as a function of solute (C2) rati o to infinite dilution for a sample of ~-CD in water at volume fraction (1-!fiw) for the estimation of X12 (Fiory-Huggins 298. 15 K. interaction parameter) in aqueous solutions of ~-CD at 298.15 K. is also in close agreement with that obtained usmg theory of solutions to the activity data, indicate that in 3 1 Eq. (14) (i.e. 6296 cm mol' ). aqueous solutions, in the solubility range both We treated the data of water activity by applying hydrophobic interaction as well as hydrophobic the model developed by Flory-Huggins for polymer hydration processes are operative. In infinitely dilute solutions?9 According to this model, one can write solution hydrophobic hydration and at finite concentrations of ~-CD, the additional hydrophobic interactions determine the overall thermodynamic properties of solutions. References where aw and ifJw is the activity and volume fraction of I Reid D S, Biochemical Thermodynamics; Chapter V water and r2 is the number of segments of (Elsevier Scientific Publishing Company, New York) 1979, macromolecule defined as the molar volume of 168. macromolecule divided by molar volume of water. X 2 Tanford, C. Physical Chemistry of Macromolecules (Wiley, 12 New York) 1961. is the interaction parameter of the system. Figure 5 3 (a) Franks F, Hydrogen Bonded Solvent Systems (Covin gton shows the variation of (In a 11 .-ln ifJ.,.)/(1-ifJw) as a A K & Jones P eds., Taylor and Francis, London) 1968: (b) function of solute volume fraction (1-ifJw) for ~-CD in Patil K J, Sargar A M & Dagade D H, Indian J Chem A, 41 aqueous soluti ons at 298. 15 K. (2002) 1804; (c) Patil K J & Dagade D H, J Chem Thennodyn, 36 (2004) 677. The value for interaction parameter X is found to 12 4 Special Secti on on Supramo lecular Chemi stry and Self be 0.193 and that of segmental sites is 39.7. The x12 Assembly, Science, 295 (2002) 2395. value is less than 0.5 and the total numbers of polar 5 Joli coeur C, Meth Biochem Anal, 27 ( 19 8 1) 171. groups including etheric oxygen are 35. Therefore, the 6 Wood D J, Hruska F E & Saenger W, J Am Chem Soc. 99 weak hydration of ~-CD through incorporation of ( 1977) 1735. water molecules in ~-CD cavities is a r.easonabl e 7 Saenger W, Beyer K & Manor P C, Acta Crystallogr. B. 32 interpretation for the observed properties. This also ( 1976) 120. 8 Franks F, Cryobiology, 20 (1983) 335. can be supported by the structure of 13-CD in solid 9 Taylor J B & Row Iinson J S, Trans Faraday Soc. 51 ( 1955) state where undried crystallized sample contain s - 7 1183. water molecul es. I 0 Stokes R H & Robinson R A, J Phys Chem, 70 ( 1966) 2 126. T hus, our analysis of the applications of the lattice I I Frank s F, Ravenhill J R & Reid D S, J Soln Chem. I theory of Flory-Huggins as well as McMillan-Mayer ( 1972) 3. 2080 INDIAN J CHEM, SEC A, OCTOBER 2004 12 Saenger W, Angew ChemIn/ Ed Engl. 19 ( 1980) 344. 21 (a) Kozak J J, Knight W S & Kauzmann W, J Chem Phys. 48 13 Kolhapurkar R R, Deshpande R K, Dagade D H & Patil K J, ( 1968) 675; (b) Pitzer K S & Brewer L. Thermodynamics Unpublished Observations. (Revision of Lewis and Randall) (McGraw Hill Book Co. 14 McMillan W & Mayer J, J Chem Phys, 13 ( 1945) 276. 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Systems, Vol. IV (lnterscience, New York) 1960,302. 20 Pati l K J, Pawar R B & Dagade D H, J Phys Chem A, 106 29 Molyneux P, Water: A Comprehensive Treaties, edited by (2002) 9606. Franks F, Vol. IV (Pl enum Press, New York ) 1974,569.