Physicochemical approach to study the solute-solute and solute-solvent interactions of drug Levofloxacin hemihydrate in aqueous sorbitol solutions at different temperatures: Volumetric, acoustic and conductance studies

Accepted Manuscript Physicochemical approach to study the solute-solute and solutesolvent interactions of drug Levofloxacin hemihydrate in aqueous sorbitol solutions at different temperatures: Volumetric, acoustic and conductance studies

Shashi Kant Lomesh, Madhu Bala, Vikas Nathan PII: DOI: Reference:

S0167-7322(18)36612-1 https://doi.org/10.1016/j.molliq.2019.03.055 MOLLIQ 10596

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

15 December 2018 8 March 2019 9 March 2019

Please cite this article as: S.K. Lomesh, M. Bala and V. Nathan, Physicochemical approach to study the solute-solute and solute-solvent interactions of drug Levofloxacin hemihydrate in aqueous sorbitol solutions at different temperatures: Volumetric, acoustic and conductance studies, Journal of Molecular Liquids, https://doi.org/10.1016/ j.molliq.2019.03.055

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ACCEPTED MANUSCRIPT Physicochemical approach to study the solute-solute and solute-solvent interactions of drug Levofloxacin hemihydrate in aqueous sorbitol solutions at different temperatures: volumetric, acoustic and conductance studies

Shashi Kant Lomesh, Madhu Bala,Vikas Nathan Department of Chemistry, Himachal Pradesh University, Shimla-171005, India. E-mail id: [email protected] & [email protected]

𝜕2 Φ𝑜 V 𝜕T2

). From speed of sound data parameters like isentropic compression (βS ),

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constant (

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Abstract The interactions of third generation fluoroquinolone antibiotic drug Levofloxacin Hemihydrate (LFH) with the naturally occurring polyol i.e. sorbitol as a function of temperature have been investigated by volumetric, acoustic and conductance methods. Densities, speeds of sound and conductance values of LFH (0.001-0.01) mol.kg-1 in water and aqueous sorbitol (0.002, 0.004 and 0.006) mol.kg-1 have been measured at different temperatures (300.15, 305.15, 310.15 and 315.15) K. The experimental density data was used to calculate apparent molar volume (ΦV ), limiting apparent molar volume (ΦV𝑜 ), Masson’s coefficient (SV ), partial molar expansibilities (ΦE0 ), transfer volume ΔtrΦV𝑜 and Hepler’s

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intermolecular free length (Lf ), specific acoustic impedance (Z) and molar compressibility (W) were calculated. From conductance data specific conductance (Ҡ), molar conductance (Λm), limiting molar conductance (Λom ), Walden product (Λom ηo), dissociation constant (Kc) and activation energy (Ea) were calculated. The derived data has been discussed in terms of solute-solute and solute-solvent interactions. The positive values of (

𝜕2 Φ0V 𝜕T2

) and positive

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temperature coefficient of Walden product Λom ηo suggests that LFH acts as structure-maker in water and aqueous sorbitol systems. Keywords: Levofloxacin hemihydrate; Transfer properties; Dissociation constant; Activation energy; Molecular interactions.

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1. Introduction Living matter is largely made up of biomolecules consisting of water and complex polymers of amino acids, lipids, nucleotides and carbohydrates. Carbohydrates are the most special among them as they remain associated with other polymers such as amino acid polymers (proteins) forming glycoproteins and with lipids as glycolipids. These are the most abundant biomolecules that belong to the class of organic compounds found in living organisms [1]. The biological breakdown of carbohydrates supplies the principal part of energy that every organism needs for various vital processes. The interactions between drugs and these biologically important macromolecules help us to understand the pharmacodynamics and pharmacokinetics of drugs [2]. The term pharmacodynamics which is often described as the action of drug on the body, involve diverse reactions at receptor sites resulting in antagonistic or synergistic effect while pharmacokinetics refers to the action of body on the drug, involve the absorption, distribution, binding/localization/storage, bio-transformation and excretion of the drug[3]. An abrupt advancement in the field of biochemistry and medicine has created a lot of interest in the 1

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mind of researchers and has attracted them as an augmentation of information from various multidisciplinary sciences [4]. Drugs are the important chemical compounds that have been used from a long time for the detection, mitigation and prediction of diseases in the living systems [5]. It is difficult to understand the interactions between drugs and large bio-molecules like sugars, proteins and carbohydrates due to their complex structure. But with the help of thermodynamic and thermophysical properties, it is possible to understand the solute-solvent interactions that are present in mixed aqueous solutions [6]. Drug molecules are the organic molecules having both hydrophilic as well as hydrophobic groups [7]. Due to presence of these groups, drug molecules exhibit different kinds of molecular interactions in the solution [8]. Various parameters that are obtained from density (𝜌), speed of sound (u) and conductance data are helpful in characterizing structural aspects and properties of solutions [9]. Hence, volumetric and acoustic properties provide helpful information regarding the nature of interactions present between solute and solvent [10]. Antibacterial drugs constitute upto one–fourth part of all the prescriptions and 50% of the drug budget in hospitals [11-13]. Levofloxacin hemihydrate [ (-)-(s)-9 fluoro- 2, 3dihydro-3-methyl-10-(4-methyl-1-piperazinyl)-7-oxo7H-pyrido[1,2,3-de]-1,4 benzox- azine-6-carboxylic acid hemihydrate] is a broad spectrum third generation fluroquinolone antibiotic drug that has been employed for the treatment of infections of bladder, kidney, prostate, sinus and lung [14-15]. It is used alone or together with certain other antibacterial drugs to treat bacterial infections like pneumonia, abdominal and urinary tract infections [16-19]. Sorbitol ((2S, 3R, 4R, 5R)hexane-1, 2, 3, 4, 5, 6-hexol) is a typical polyhydroxy compound and has been widely used in food products and chemical industry due to its low calorific value and little effect on the blood sugar level [20-21]. Many patients are taking food, herbs, supplements together with their prescribed medicines and associated use of these products may lead to food-drug, herb-drug and supplement-drug interactions[22]. These interactions can affect the bioavailability and stability of drug [23]. The action, absorption and transport of drugs across the biological membrane can be well understood with the help of these drug macromolecular interactions which plays a very important role in medicinal and pharmaceutical chemistry [24]. A lot of thermodynamic studies regarding solute-solute and solute-solvent interactions between amino acids and drugs [25-26], thermodynamic studies of LFH with surfactants [27], effect of sorbitol on the pharmacokinetic profile of Lamivudine oral solutions with a varying sorbitol concentration (3.2g-13.4g) [28] have been carried out in past but so far to the best of our knowledge no volumetric, acoustic and conductance studies of the drug LFH in different concentrations of aqueous sorbitol have been reported so far. Thus, it was decided to work on volumetric, acoustic and conductance studies of the drug LFH in different concentrations of aqueous sorbitol (0.002, 0.004 and 0.006) mol.kg-1 at a wide range of temperatures and concentrations for better understanding about the type of interactions present in these systems. The chemical structures of sorbitol and LFH are given below in Table-1. 2. Experimental 2.1 Chemicals For the investigation on the effect of concentration of the drug LFH in different concentrations of aqueous sorbitol solutions at different temperatures, chemicals used along 2

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Sigma Aldrich

>0.99

SD Fine Chem, India

>0.99

used as such

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370.38

2.2 Methods

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182.17

used after recrystallization

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Triply distilled and deionised water having specific conductance of <10-6 S.cm-1 was used for the preparation of solutions. The solutions were prepared on a molality basis. The concentration of LFH was varied from (0.001-0.01) mol.kg-1 while that of sorbitol was (0.002, 0.004 and 0.006) mol.kg-1. The solutions were prepared by weight method with the help of Shimadzu electronic balance (Model No. D432613208, Japan) with an accuracy of 0.1 mg and the conversion of molality into molarity was done by using the standard expression: C= (1000mρ/1000+Mm)

(1)

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Sorbitol

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Levofloxacin Hemihydrate

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with molar mass, provenance, mass fraction purity and purification method are presented in Table-1. The LFH (mass fraction purity >0.99) was purchased from Sigma Aldrich and used as such and sorbitol (mass fraction purity >0.99) was purchased from SD Fine Chem, India and was used after recrystallization from ethanol[29] to attain maximum purity. TABLE-1: Provenance and purity of chemical samples studied: Chemical Name Molar mass Provenance Mass fraction Purification Structure (g.mol-1) purity method

The uncertainties in the molality of solutions are within ±1x10-3mol.kg-1. In expression (1) ρ and m stand for density and molality of solution respectively and M is the molecular mass of LFH. Densities and speed of sound measurements of solutions of different concentrations were carried out by using automated vibrating tube densimeter (DSA 5000, Anton Paar, Austria) at T=(300.15-315.15) K with 5 K intervals. The DSA calibrations were done using triply distilled and de-ionized water as directed in user manual. Conductance measurements were done using a Digital Conductivity Meter (ELICO CM 183EC-TDS ANALYSER) at 50 Hz which was calibrated using aqueous KCl solution. Before taking reading the conductivity cell was washed thoroughly with distilled water and then rinsed with the sample solution under study. Viscosity measurements were carried out with a jacketed Ubbelohde type viscometer or suspended-level viscometer connected to a water thermostat which uses a capillary based method of measuring viscosity. The viscometer was positioned exactly vertically with the help of a clamp and temperature was kept constant with the help of 3

ACCEPTED MANUSCRIPT electric water thermostat within the variation limit ±0.05 K. Before use, the viscometer was thoroughly cleaned with chromic acid and then washed with water and acetone and dried with vacuum pump. While taking measurements, the solution in the viscometer was allowed to attain the temperature of the water thermostat for 10-15 min. The efflux time of solutions were recorded three times with digital stop watch with an accuracy of ±0.01s. The average of three sets of flow time recorded for each solution was considered as the final efflux time for each sample which was used for the calculation of viscosity. The viscosity of (0.002, 0.004 and 0.006) mol.kg-1 aqueous solution of sorbitol was determined by using the following equation [30]:

η/η0 = ρt/ρ0t0

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(2)

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Where η, ρ, t and η0, ρ0, t0 are the viscosity, density and flow time of solution and solvent respectively. The viscosity values of water at experimental temperatures were obtained from literature [31].

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3. Results and discussion 3.1. Volumetric properties

(3)

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ΦV = (M/ρ0)+(1000(ρ0-ρ)/mρρ0)

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3.1.1 Limiting apparent molar volume The experimental densities of LFH (0.001-0.01) mol.kg-1 in water and aqueous sorbitol solutions at different temperatures (300.15, 305.15, 310.15 and 315.15) K are recorded in Table-2. Various parameters like apparent molar volume, limiting apparent molar volume, Masson’s coefficient, partial molar expansibility and Hepler’s constant are calculated from the measured density data. The apparent molar volume (ΦV ) of LFH in water and different concentrations of aqueous sorbitol was obtained by using experimental data according to the equation (3)

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Where m is the molality (mol.kg-1) of LFH in water and aqueous sorbitol solutions, M is the molar mass of LFH, ρ(kg.m-3) and ρ0(kg.m-3) are the densities of the solution and solvent respectively. Apparent molar volumes are generally larger than molecular volumes and a real measurement of the molecular size of the hydrated molecules in solution. This is because of creation of gap by solute molecules between itself and neighbouring solvent molecules. The water molecules are not in direct contact with the solute but are held to it by H-bonds. Apparent molar volumes are the contribution from the intrinsic volume of the solute, the volume due to solute-solute interactions and that contributed by solute-solvent interactions [32-33]. The calculated apparent molar volumes (ΦV ) are also included in Table-2. It shows that apparent molar volume of LFH increases with temperature and also with concentration of sorbitol in water-sorbitol system. Partial molar volumes are known to be the structural volume of solute in solvent and change in volume of solvent upon shell formation [34]. Partial molar volume of the solute in the solution is the apparent molar volume occupied by one mole of the solute at infinite dilution [35-36] and which can be calculated by the least square fitting of ΦV vs m by [37]Masson’s equation (4)

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ACCEPTED MANUSCRIPT ΦV =ΦV𝑜 +SV m

(4)

From this equation we obtain intercept ΦV𝑜 and slope SV which signifies solute-solvent and solute-solute interactions respectively and m stands for the molality of LFH in water and different water- sorbitol systems [38-39]. TABLE-2: Values of density ρ and apparent molar volume 𝚽𝐕 of LFH in water and different concentrations of aqueous sorbitol at T=(300.15K-315.15K) and atmospheric pressure. ρx10-3

.

-1

.

(mol kg )

𝚽𝐕 x106

PT

m

-3

(m3.mol-1)

(kg m ) 300.15(K)

305.15(K)

310.15(K)

315.15(K)

300.15(K)

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

0.9968 0.9969 0.9970 0.9972 0.9973 0.9974 0.9975 0.9976 0.9978 0.9979 0.9980

0.9952 0.9953 0.9954 0.9956 0.9957 0.9958 0.9959 0.9960 0.9962 0.9963 0.9964

0.9953 0.9946 0.9954 0.9947 248.77 0.9955 0.9948 248.53 0.9956 0.9949 248.34 0.9958 0.9951 248.17 0.9959 0.9952 247.84 0.9960 0.9953 247.61 0.9961 0.9954 247.44 0.9963 0.9955 247.17 0.9964 0.9957 246.96 0.9965 0.9958 246.68 LFH in 0.002mol.kg-1 aqueous sorbitol

249.36 249.18 248.96 248.77 248.53 248.37 248.24 248.01 247.83 247.67

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0.9960 0.9961 0.9962 0.9963 0.9965 0.9966 0.9967 0.9968 0.9970 0.9971 0.9972

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0.9967 0.9968 0.9969 0.9970 0.9972 0.9973 0.9974 0.9975 0.9977 0.9978 0.9979

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0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

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LFH in water

305.15(K)

310.15(K)

315.15(K)

250.36 250.18 249.99 249.86 249.63 249.47 249.34 249.11 248.93 248.77

251.77 251.53 251.40 251.22 251.06 250.91 250.73 250.59 250.37 250.18

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0.9945 0.9938 0.9946 0.9939 250.46 251.78 252.68 254.09 0.9947 0.9940 250.23 251.60 252.55 253.96 0.9949 0.9942 250.00 251.42 252.35 253.79 0.9950 0.9943 249.82 251.26 252.24 253.64 0.9951 0.9944 249.64 251.05 252.07 253.46 0.9952 0.9945 249.44 250.82 251.92 253.37 0.9953 0.9946 249.29 250.65 251.75 253.14 0.9955 0.9948 249.04 250.51 251.61 252.97 0.9956 0.9949 248.73 250.39 251.38 252.82 0.9957 0.9950 248.58 250.19 251.19 252.70 LFH in 0.004mol.kg-1 aqueous sorbitol 0.000 0.9968 0.9954 0.9948 0.9941 0.001 0.9970 0.9955 0.9949 0.9942 252.47 253.88 255.88 257.80 0.002 0.9971 0.9956 0.9950 0.9943 252.24 253.70 255.75 257.62 0.003 0.9972 0.9957 0.9951 0.9944 252.04 253.51 255.62 257.47 0.004 0.9973 0.9958 0.9952 0.9945 251.85 253.38 255.44 257.36 0.005 0.9974 0.9960 0.9953 0.9946 251.64 253.25 255.36 257.22 0.006 0.9976 0.9961 0.9955 0.9948 251.45 253.05 255.09 257.05 0.007 0.9977 0.9962 0.9956 0.9949 251.30 252.93 255.04 256.87 0.008 0.9978 0.9963 0.9957 0.9950 251.05 252.76 254.86 256.73 0.009 0.9979 0.9964 0.9958 0.9951 250.85 252.62 254.72 256.62 0.010 0.9980 0.9966 0.9959 0.9952 250.69 252.39 254.60 256.52 . -1 LFH in 0.006mol kg aqueous sorbitol 0.000 0.9970 0.9956 0.9950 0.9942 0.001 0.9971 0.9957 0.9951 0.9943 254.46 256.87 257.97 259.09 0.002 0.9972 0.9958 0.9952 0.9944 254.23 256.69 257.79 258.96 0.003 0.9973 0.9959 0.9953 0.9946 254.04 256.58 257.68 258.80 0.004 0.9974 0.9961 0.9954 0.9947 253.87 256.38 257.48 258.65 0.005 0.9976 0.9962 0.9956 0.9948 253.64 256.25 257.35 258.51 0.006 0.9977 0.9963 0.9957 0.9949 253.46 256.09 257.25 258.37 0.007 0.9978 0.9964 0.9958 0.9951 253.29 255.93 257.13 258.30 0.008 0.9979 0.9965 0.9959 0.9951 253.18 255.76 256.98 258.11 0.009 0.9980 0.9966 0.9960 0.9952 252.96 255.62 256.83 258.06 0.010 0.9982 0.9967 0.9961 0.9953 252.79 255.50 256.69 257.92 Standard uncertainty in u(m) molality are ±1x10 -3mol.kg-1. Standard uncertainity in u(ρ) density are ±3.2x10-3 kg.m-3. Standard uncertainty in u(T) temperature are 0.05K and that in case of pressure u(P) are 0.1MPa.

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ACCEPTED MANUSCRIPT The variation of apparent molar volume ΦV with m for LFH in distilled water, (0.002, 0.004 and 0.006) mol.kg-1 aqueous Sorbitol at different temperatures is shown in fig-1(a-d):

252.0

300.15K 305.15K 310.15K 315.15K

251.5 251.0

253.5

252.0

-1

VX10 (m .mol )

252.5

249.5

251.5

6

3

249.0

251.0

6

248.5

250.0

247.5

249.5

247.0

249.0 248.5

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0.004

0.006

0.008

0.010

0.000

-1

m(mol.kg )

0.010

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0.006

0.008

300.15K 305.15K 310.15K 315.15K

257.5 257.0 -1

-1

0.008

-1

258.0

256.5

3

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254

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3

255

0.004

0.006

m(mol.kg )

258.5

256.0

6

256

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0.004

259.0

VX10 (m .mol )

257

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300.15K 305.15K 310.15K 315.15K

258

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(b) LFH in 0.002 mol.kg-1 sorbitol

(a) LFH in water

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246.5 0.000

VX10 (m .mol )

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253.0

250.0

3

-1

VX10 (m .mol )

250.5

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300.15K 305.15K 310.15K 315.15K

254.0

255.5 255.0 254.5 254.0 253.5 253.0 252.5 0.000

0.010

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m(mol.kg )

0.002

0.004

0.006

0.008

0.010

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m(mol.kg )

(d) LFH in 0.006 mol.kg-1 sorbitol

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(c) LFH in 0.004 mol.kg-1 sorbitol

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Fig-1(a-d): Sample plots for the Variation of apparent molar volume (ΦV) with concentration (m) for LFH in water, (0.002, 0.004 and 0.006) mol.kg-1 aqueous sorbitol solutions at different temperatures. The values of ΦV𝑜 and SV for LFH in water and different aqueous sorbitol solutions are recorded in Table-3.The values of ΦV𝑜 for LFH in water and aqueous sorbitol solutions are positive implying the existence of strong solute-solvent interactions. The ΦV𝑜 values for LFH in water sorbitol system are greater as compared to those for LFH in water. The increase in values of ΦV𝑜 for LFH from water to aqueous sorbitol solutions indicate that the extent of molecular interactions such as ion-hydrophilic and hydrophilic-hydrophilic is increasing with increase in concentration of sorbitol. Further, higher ΦV𝑜 values for greater concentration of sorbitol signify the dominance of ion-hydrophilic or hydrophilic-hydrophilic interactions over hydrophobic-hydrophobic interactions. With increase in concentration of sorbitol, the 6

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interactions between positively polarised hydrogen or negatively polarised oxygen of sorbitol with polarised groups present in LFH is increasing. The value of ΦV𝑜 for LFH in water and aqueous sorbitol (0.002, 0.004 and 0.006) mol.kg-1 also increases with rise in temperature. This may be due to decrement of electrostriction and liberation of some solvent molecules from the loose hydration layers of solute in solution [40]. The above results are also explained in terms of geometrical fit of the drug molecule in an ordered solvent. At lower temperature, it is difficult to indulge the structured solute in an ordered solvent environment like water but as the temperature rises, the cavity size gets enlarged resulting in a better fit of the bioactive solute. Also, as the temperature rises, the contribution from the (drug+solvent) binding is lowered and consequently the limiting apparent molar volume (ΦV𝑜 ) of drug molecule increases with temperature [41].

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The values of SV are negative for LFH in water and aqueous sorbitol solutions which indicate very weak or negligible solute-solute interactions [42]. The order of increasing LFHsorbitol interactions with temperature and sorbitol concentration is shown in Fig-2.

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TABLE-3: Limiting apparent molar volume (𝚽𝐕𝒐 ) and Experimental slope (𝐒𝐕 ) values for LFH in water and aqueous sorbitol system.

3.

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𝚽𝐕𝒐 x106

Solvent

-1

(m mol ) 305.15(K) 310.15(K)

300.15(K)

𝐒𝐕 x106 3.

315.15(K)

300.15(K)

(m mol-3/2.l1/2) 305.15(K) 310.15(K)

315.15(K)

249.5

250.5

251.9

-231.1

-188.6

-176.9

-170.4

250.6

251.9

252.8

254.2

-206.2

-177.7

-162.7

-158.3

0.004 mol.kg-1

252.6

254.0

257.9

-197.1

-158.8

-145.1

-144.3

259.2

-183.1

-154.7

-138.4

-130.6

.

0.002 mol kg

sorbitol 0.006 mol.kg-1

256.0

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sorbitol

D

249.0 -1

Water

254.6

257.0

0.002mol.kg-1 Aq.Sorbitol

300.15K

0.004 mol.kg-1 Aq.Sorbitol

305.15K

In

At

Solvents -1

0.006 mol.kg Aq.Sorbitol

Temp. Levofloxacin Hemihydrate(0.001-0.01)mol.kg-1

310.15K

315.15K

Fig-2: Increasing trend of drug-solvent interactions with temperature and solvent concentration. 7

Drug-solvent interactions increases

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Drug-solvent interactions increases

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sorbitol

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ACCEPTED MANUSCRIPT 3.1.2 Temperature dependence of volumetric properties The volumetric properties are susceptible [43-44] to temperature and the dependence of ΦV𝑜 on temperature is given by the following equation (5): ΦV𝑜 = a+bT+cT2

(5)

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Where T is the temperature expressed in Kelvin and the coefficients a, b, c are calculated by the method of elimination by using equation (5) and whose values are given in Table 4.

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On the basis of above equation (5), the values of Partial molar expansibility, (ΦE0 ) for LFH in water and water sorbitol system can be calculated by using b and c in the equation (6) (6)

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ΦE0 = (𝜕ΦV𝑜/𝜕T) = b+2cT

∂Φ0E ∂T

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The partial molar expansibility, ΦE0 of solute can provide valuable information regarding solute–solvent interactions existing in the solution and the size of the solute and its hydrophobicity [45]. The variation of ΦE0 with temperature for LFH in water and different aqueous sorbitol solutions are shown in Fig-3. It is observed from Table-4 that the value of ΦE0 are positive for and increases with rise in temperature for LFH in water and different aqueous sorbitol solutions. The partial molar expansibility is the sum of contributions from two terms i.e. ΦEO (Elect) which is expansivity due to electrostriction changes (contribution of hydration around the solute) and ΦE0 (Str.) which is the expansivity due to changes in the structure of the solvent [46]. The structural component ΦE0 (Str.) is the predominant factor at low temperature whereas Electrostriction component, ΦE0 (Elect), is the predominant factor at high temperature. Thus, it is concluded from Table-4 that temperature affect the outer hydrated water molecules resulting in increase in the value of ΦE0 with rise in temperature. A thermodynamic term has been given by Hepler (which is second derivative of limiting apparent molar volume with respect to temperature), which gives information regarding structure maker (Kosmotropic) or structure breaker (Chaotropic) ability of solute when dissolved in solvent. The thermodynamic term given by Hepler used is as follows [47]: 𝜕2 Φ𝑜 V

=(

𝜕T2

) = 2𝑐

(7)

𝑃

As stated by Hepler, the structure making solutes should have positive value of (𝜕2Φv0/𝜕T2)P and for structure breaking solutes, it should be negative. The values of (𝜕2Φv0/𝜕T2)P for LFH in water and aqueous sorbitol solutions at different temperatures are recorded in Table-4. These values are positive for LFH in water and aqueous sorbitol solutions suggesting that LFH acts as structure maker in water as well as in aqueous solutions of sorbitol. The isobaric thermal expansion coefficient (αo) of LFH has been computed by using the following relation: 1

αo = Φ𝑜 [ V

𝜕Φ𝑜 V 𝜕𝑇

]

(8) 𝑃

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ACCEPTED MANUSCRIPT According to Cabani et al. [48], the coefficient of thermal expansion (αo ) can be used to interpret the solute- solvent interactions. The values of coefficient of thermal expansion at all the experimental temperatures are listed in Table-4. The values of αo are increasing with rise in temperature for LFH in water and aqueous sorbitol system indicating that the LFH-water binding is weakened which give rise to higher value of expansivity [49]. The values of ΦE0 and αo shows irregular trend with increase in concentration of sorbitol.

ΦE0x106 3.

-1.

𝜶𝒐 -1

(K-1)

(m mol K ) 300.15 (K)

305.15 (K)

310.15 (K)

315.15 (K)

300.15 (K)

305.15 (K)

310.15 (K)

315.15 (K)

a (m3mol-1)

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Table-4: Partial molar expansibility (𝚽𝐄𝟎 ), Isobaric thermal expansion coefficient (𝜶𝒐 ), a, b, c and Hepler’s constant values for LFH in water and aqueous sorbitol systems. b (m3mol-1K-1)

c (m3mol-1K-2)

(𝝏2Φv0/𝝏T2)P = 2c

2.65

2.74

2.84

0.01026

0.01060

0.01092

0.01122

292.5667

-2.8465

0.009

0.018

0.26

0.27

0.28

0.29

0.00101

0.00105

0.00108

0.00112

264.1517

-0.3453

0.001

0.002

0.004 mol.kg-1

0.26

0.31

0.36

0.41

0.00100

0.00120

0.00138

0.00157

626.5118

-2.7465

0.005

0.010

0.14

0.18

0.22

0.26

0.00054

0.00070

572.9390

-2.2612

0.004

0.008

.

0.002 mol kg sorbitol

0.00100

MA

sorbitol

0.00085

2.85

0.42

2.80

LFH in 0.002m Sorbitol LFH in 0.004m Sorbitol LFH in 0.006m Sorbitol

0.40

LFH in distilled water

0.38 0.36 0.34

0

2.65

2.60

298

300

302

304

CE

2.55 306

308

310

312

314

0.30 0.28

3

-1 -1

0.32

0.26

6

6

3

PT E

2.70

0

D

-1

-1

E X10 (m mol k )

2.75

E X10 (m mol k )

0.006 mol.kg-1

NU

sorbitol

SC

2.56 -1

Water

0.24 0.22 0.20 0.18 0.16 0.14

316

298

T(K)

300

302

304

306

308

310

312

314

316

T(K)

(b) LFH in (0.002, 0.004 and 0.006) mol.kg-1 Sorbitol

AC

(a) LFH in water

Fig-3: Plots showing the variation of 𝚽𝐄𝟎 with temperature for LFH in water, (0.002, 0.004 and 0.006) mol.kg-1 aqueous sorbitol.

3.1.3 Limiting apparent molar volumes of transfer Transfer properties give information regarding solute-solvent interactions and do not take into account solute-solute interactions [50].Transfer volume of the drug LFH from water to aqueous sorbitol solutions at infinite dilution were calculated by using the equation: ΔtrΦV𝑜 = ΦV𝑜 (sorbitol+water) - ΦV𝑜 (water)

(9)

9

ACCEPTED MANUSCRIPT

PT

Equation (8) indicates that the values of partial molar volumes of transfer ΔtrΦV𝑜 are unaffected by solute- solute interactions but provide useful information regarding solutesolvent interactions. The calculated values of partial molar volumes of transfer ΔtrΦV𝑜 are given in Table-5 and are all positive. The positive values of partial molar volumes of transfer ΔtrΦV𝑜 indicates the structure promoter nature of drug LFH which may be due to its solvophobic solvation as well as structural interaction for two co-spheres according to cosphere overlap model [51-52]. According to this model, an overlap of co-spheres of two ionic species results in an increase in volume whereas the overlap of hydrophobic-hydrophobic and ion-hydrophobic groups results to decrease in the volume. The various interactions that occur between LFH and aqueous sorbitol are given in fig-4 and can be categorized as:

SC

RI

a) Ion-hydrophilic interactions between the anionic COO- / cationic NH+ group of LFH and –OH groups of sorbitol. b) H-bonding between –F, ≡N and =O groups of LFH and –OH groups of sorbitol. c) Hydrophobic- hydrophobic interactions between the alkyl and aryl groups present in LFH and alkyl groups in sorbitol.

AC

CE

PT E

D

MA

NU

Ion-hydrophilic interactions and H-bonding interactions contribute positively to ΔtrΦV𝑜 values whereas hydrophobic-hydrophobic interactions contribute negatively. The positive values of ΔtrΦV𝑜 indicate that ion-hydrophilic and H-bonding interactions dominate over hydrophobichydrophobic interactions. The values of ΔtrΦV𝑜 increase with increase in the molality of sorbitol in sorbitol-water system. The explanation for this behaviour may be due to the increase in ion-hydrophilic interactions between ionized carboxylic group of LFH and –OH groups of sorbitol as well as as well as due to H-bonding interactions between the polar groups of LFH and sorbitol.

10

ACCEPTED MANUSCRIPT OH

H-O

OH HO O-H

HO

OH

HO H

HO

CH3

HO

ng

O-H

OH N

H-O

OH HO

RI

O O -

OOC

N

SC

HO

PT

Hy

dr

e og

di on nb

N+

F

O-H

OH

OH

HO

HO

CH3

NU

O-H HO

Hydrophobic-hydrophobic interactions

Ion-hydrophilic interactions

MA

OH

Fig-4: Various possible interactions between LFH and aqueous sorbitol solutions.

PT E

D

TABLE-5: Values of partial molar volumes of transfer Δtr𝚽𝐕𝒐 for LFH in aqueous sorbitol solutions at temperatures (300.15K, 305.15K, 310.15K, 315.15K)

Transfer volumes/ ΔtrΦvo x106 (m3.mol-1)

Temperature

0.004 mol.kg-1 sorbitol

0.006 mol.kg-1 sorbitol

1.6

3.6

5.6

305.15K

2.4

4.5

7.5

310.15K

2.3

5.5

7.5

315.15K

2.3

6.0

7.3

CE

0.002 mol.kg-1 Sorbitol

AC

300.15K

3.2 Acoustic Studies: From the ultrasonic velocity (u) data various parameters such as isentropic compression (βS ), intermolecular free length (Lf), specific acoustic impedance (Z) and molar compressibility (W) for LFH in water and aqueous sorbitol solutions have been calculated and recorded in Table-6. The isentropic compression (βS ) was obtained by applying Newton- Laplace equation (10) [53], 11

ACCEPTED MANUSCRIPT 1

∂V

βS = (− V) (∂P) . S

NU

SC

RI

PT

Or βS = 1/u2ρ (10) Where u represents the speed of sound and ρ is the density of solution. V, P and S represent the volume, pressure and entropy of the system. u increases steadily with increase in concentration and temperature, which suggests that ion–solvent interactions increase with increase in concentration and temperature. The compressibility of a solution is mainly due to free solvent molecules around solute molecules [54]. From Table-6, the values of isentropic compression (βS ) decreases with increase in concentration of LFH in water and water-sorbitol system which can be due to the fact that the solute molecules occupy the interstitial spaces of water, making the medium less compressible (electostriction). Further, the decrease in isentropic compression (βS ) with increase in sorbitol content in water may be due to filling of interstitial spaces of water by cosolute, sorbitol molecules thereby making tight structure [55-56]. Therefore, the tight solvation layer formed around solute LFH causes a decrease in the value of isentropic compression (βS ). The decrease in the value of isentropic compression (βS ) with rise in temperature may be attributed to the fact that as the temperature increases, the attractive forces among the molecules decreases thereby causing a decrease in isentropic compression (βS ).

-1

(mol.kg )

𝛃𝐒 (10-10Pa-1)

Speed of sound (u)(m.s-1)

Lf (10-11m)

Z (106kg.m-2.s-1)

W (10-4m3mol-1Pa1/7)

4.4450 4.3522 4.4433 4.3513 4.4417 4.3506 4.4402 4.3498 4.4385 4.3490 4.4372 4.3484 4.4356 4.3476 4.4340 4.3468 4.4323 4.3460 4.4307 4.3452 LFH in 0.002 mol.kg-1 aqueous Sorbitol at 300.15K

1.4974 1.4978 1.4982 1.4985 1.4989 1.4992 1.4996 1.4999 1.5003 1.5007

1.4597 1.4601 1.4605 1.4609 1.4613 1.4617 1.4621 1.4625 1.4629 1.4633

4.4023 4.3312 4.4002 4.3302 4.3983 4.3293 4.3965 4.3284 4.3945 4.3274 4.3927 4.3265 4.3907 4.3255 4.3886 4.3245 4.3867 4.3236 4.3847 4.3226 LFH in 0.004 mol.kg-1 aqueous Sorbitol at 300.15K

1.5048 1.5052 1.5056 1.5061 1.5065 1.5069 1.5073 1.5078 1.5082 1.5086

1.4620 1.4619 1.4623 1.4627 1.4632 1.4636 1.4640 1.4644 1.4649 1.4653

1.5147 1.5152 1.5156 1.5160

1.4651 1.4645 1.4649 1.4654

PT E

m

D

MA

TABLE-6: Ultrasonic velocity (𝐮), Isentropic compression (𝛃𝐒 ), Intermolecular free length (Lf), Specific acoustic impedance (Z) and molar compressibility (W) values for LFH in water and water-sorbitol systems at different temperatures and atmospheric pressure.

LFH in water at 300.15K

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.000 0.001 0.002 0.003 0.004

CE

1502.01 1502.31 1502.51 1502.69 1502.85 1503.03 1503.17 1503.35 1503.52 1503.72 1503.89

AC

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1509.21 1509.49 1509.75 1509.98 1510.21 1510.46 1510.68 1510.92 1511.19 1511.43 1511.68 1519.03 1519.39 1519.65 1519.89 1520.13

4.3449 4.3429 4.3410 4.3391

4.3394 4.3384 4.3374 4.3365

12

ACCEPTED MANUSCRIPT

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1526.75 1527.11 1527.34 1527.59 1527.86 1528.09 1528.31 1528.57 1528.81 1529.04 1529.29

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007

AC

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

4.3797 4.3594 4.3784 4.3587 4.3770 4.3580 4.3757 4.3573 4.3743 4.3566 4.3728 4.3559 4.3714 4.3552 4.3700 4.3545 4.3686 4.3538 4.3672 4.3531 LFH in 0.002 mol.kg-1 aqueous Sorbitol at 305.15K

1.5080 1.5084 1.5087 1.5090 1.5094 1.5097 1.5100 1.5104 1.5107 1.5110

1.4638 1.4642 1.4646 1.4650 1.4654 1.4658 1.4662 1.4666 1.4670 1.4674

4.3256 4.3323 4.3234 4.3312 4.3213 4.3302 4.3191 4.3291 4.3169 4.3280 4.3148 4.3269 4.3127 4.3259 4.3106 4.3248 4.3083 4.3237 4.3063 4.3226 LFH in 0.004 mol.kg-1 aqueous Sorbitol at 305.15K

1.5169 1.5173 1.5178 1.5183 1.5187 1.5192 1.5197 1.5201 1.5206 1.5211

1.4680 1.4679 1.4683 1.4688 1.4692 1.4697 1.4701 1.4706 1.4710 1.4714

4.3074 4.3621 4.3056 4.3612 4.3037 4.3603 4.3016 4.3592 4.2998 4.3583 4.2981 4.3574 4.2961 4.3564 4.2943 4.3555 4.2925 4.3546 4.2905 4.3536 LFH in 0.006 mol.kg-1 aqueous Sorbitol at 305.15K

1.5202 1.5206 1.5210 1.5215 1.5219 1.5223 1.5227 1.5231 1.5235 1.5240

1.4691 1.4685 1.4689 1.4694 1.4698 1.4702 1.4706 1.4711 1.4715 1.4719

1532.98 1533.67 1533.89 1534.08 1534.31 1534.52 1534.73 1534.95 1535.16 1535.29 1535.47

4.2697 4.3430 4.2680 4.3421 4.2664 4.3413 4.2647 4.3404 4.2630 4.3396 4.2614 4.3388 4.2596 4.3379 4.2580 4.3370 4.2568 4.3364 4.2553 4.3357 LFH in water at 310.15K

1.5270 1.5274 1.5278 1.5282 1.5286 1.5290 1.5294 1.5298 1.5301 1.5304

1.4711 1.4699 1.4704 1.4708 1.4712 1.4717 1.4721 1.4725 1.4729 1.4733

1523.72 1523.97 1524.11 1524.26 1524.45 1524.59 1524.73 1524.89

4.3256 4.3242 4.3229 4.3213 4.3199 4.3186 4.3172

1.5169 1.5172 1.5176 1.5180 1.5183 1.5186 1.5189

1.4674 1.4678 1.4682 1.4686 1.4690 1.4694 1.4698

PT

1523.91 1524.03 1524.32 1524.59 1524.89 1525.19 1525.47 1525.75 1526.03 1526.34 1526.61

1.4670 1.4659 1.4663 1.4667 1.4672 1.4676 1.4680 1.4685 1.4689 1.4693

RI

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1.5206 1.5211 1.5215 1.5219 1.5223 1.5227 1.5231 1.5235 1.5239 1.5243

SC

1513.68 1513.99 1514.13 1514.27 1514.41 1514.56 1514.71 1514.87 1515.02 1515.17 1515.31

4.3117 4.3228 4.3098 4.3218 4.3077 4.3208 4.3059 4.3199 4.3041 4.3190 4.3023 4.3181 4.3006 4.3172 4.2989 4.3164 4.2971 4.3155 4.2954 4.3146 LFH in water at 305.15K

NU

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1.4658 1.4662 1.4667 1.4671 1.4675 1.4680

MA

1524.69 1525.13 1525.38 1525.65 1525.88 1526.11 1526.34 1526.55 1526.77 1526.99 1527.21

1.5165 1.5168 1.5173 1.5177 1.5182 1.5186

D

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

4.3371 4.3355 4.3354 4.3346 4.3333 4.3336 4.3314 4.3327 4.3294 4.3316 4.3273 4.3306 . -1 LFH in 0.006 mol kg aqueous Sorbitol at 300.15K

PT E

1520.39 1520.60 1520.87 1521.11 1521.37 1521.65

CE

0.005 0.006 0.007 0.008 0.009 0.010

4.3713 4.3707 4.3700 4.3691 4.3685 4.3678 4.3671

13

ACCEPTED MANUSCRIPT

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1532.16 1532.47 1532.61 1532.78 1532.91 1533.06 1533.21 1533.37 1533.51 1533.68 1533.83

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1538.83 1539.31 1539.57 1539.85 1540.14 1540.38 1540.61 1540.85 1541.08 1541.31 1541.56

AC

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

PT

1542.66 1543.16 1543.38 1543.59 1543.82 1544.03 1544.26 1544.47 1544.67 1544.89 1545.11

1.4712 1.4711 1.4716 1.4720 1.4724 1.4729 1.4733 1.4738 1.4742 1.4746

4.2484 4.3734 4.2465 4.3724 4.2446 4.3714 4.2430 4.3706 4.2413 4.3697 4.2395 4.3688 4.2378 4.3679 4.2361 4.3670 4.2344 4.3662 4.2328 4.3654 LFH in 0.006 mol.kg-1 aqueous Sorbitol at 310.15K

1.5302 1.5307 1.5311 1.5315 1.5319 1.5323 1.5327 1.5331 1.5335 1.5338

1.4729 1.4723 1.4727 1.4732 1.4736 1.4740 1.4745 1.4749 1.4753 1.4757

1.5355 1.5359 1.5363 1.5367 1.5371 1.5375 1.5379 1.5383 1.5387 1.5391

1.4745 1.4733 1.4738 1.4742 1.4746 1.4751 1.4755 1.4759 1.4763 1.4768

4.2808 4.3874 4.2795 4.3868 4.2780 4.3860 4.2768 4.3854 4.2754 4.3847 4.2741 4.3840 4.2727 4.3833 4.2714 4.3826 4.2699 4.3818 4.2685 4.3811 LFH in 0.002 mol.kg-1 aqueous Sorbitol at 315.15K

1.5243 1.5246 1.5250 1.5253 1.5256 1.5259 1.5263 1.5266 1.5270 1.5273

1.4706 1.4710 1.4715 1.4719 1.4723 1.4727 1.4731 1.4735 1.4739 1.4743

4.2461 4.3696 4.2441 4.3686 4.2421 4.3676 4.2400 4.3665 4.2382 4.3655 4.2364 4.3646 4.2346 4.3637 4.2328 4.3628 4.2310 4.3619 4.2292 4.3609 LFH in 0.004 mol.kg-1 aqueous Sorbitol at 315.15K

1.5299 1.5304 1.5308 1.5313 1.5317 1.5321 1.5325 1.5330 1.5334 1.5338

1.4740 1.4739 1.4743 1.4748 1.4752 1.4756 1.4761 1.4765 1.4769 1.4774

1.5350 1.5354 1.5358 1.5362 1.5366 1.5370 1.5374 1.5378 1.5382 1.5386

1.4754 1.4748 1.4752 1.4757 1.4761 1.4765 1.4770 1.4774 1.4778 1.4783

RI

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1.5242 1.5247 1.5251 1.5256 1.5261 1.5260 1.5270 1.5274 1.5279 1.5283

SC

1537.73 1538.16 1538.41 1538.66 1538.87 1539.09 1539.31 1539.54 1539.76 1539.97 1540.17

4.2811 4.3488 4.2789 4.3477 4.2769 4.3467 4.2748 4.3456 4.2726 4.3445 4.2706 4.3435 4.2685 4.3424 4.2667 4.3415 4.2646 4.3404 4.2626 4.3394 LFH in 0.004 mol.kg-1 aqueous Sorbitol at 310.15K

NU

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

1.4702 1.4706 1.4710

4.2200 4.3587 4.2183 4.3578 4.2166 4.3570 4.2149 4.3561 4.213 4.3553 4.2115 4.3544 4.2099 4.3535 4.2083 4.3527 4.2067 4.3518 4.2050 4.3510 LFH in water at 315.15K

MA

1531.72 1532.47 1532.76 1533.03 1533.32 1533.62 1533.88 1534.17 1534.41 1534.69 1534.96

1.5193 1.5196 1.5200

D

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

4.3159 4.3664 4.3144 4.3657 4.3129 4.3649 . -1 LFH in 0.002 mol kg aqueous Sorbitol at 310.15K

PT E

1525.02 1525.19 1525.37

CE

0.008 0.009 0.010

1543.67 1544.02 1544.27 1544.49 1544.73 1544.97 1545.19 1545.42 1545.63 1545.85 1546.07

4.1915 4.1898 4.1882 4.1865 4.1849 4.1834 4.1815 4.1801 4.1783 4.1767

4.3557 4.3548 4.3539 4.3530 4.3521 4.3512 4.3503 4.3494 4.3486 4.3477

14

ACCEPTED MANUSCRIPT

PT

LFH in 0.006 mol.kg-1 aqueous Sorbitol at 315.15K 0.000 1548.19 0.001 1548.99 4.1915 4.3414 1.5402 1.4771 0.002 1549.21 4.1898 4.3406 1.5405 1.4759 0.003 1549.43 4.1882 4.3397 1.5409 1.4763 0.004 1549.64 4.1865 4.3389 1.5413 1.4768 0.005 1549.85 4.1849 4.3380 1.5417 1.4772 0.006 1550.04 4.1834 4.3373 1.5421 1.4776 0.007 1550.26 4.1815 4.3363 1.5426 1.4780 0.008 1550.48 4.1801 4.3355 1.5429 1.4785 0.009 1550.72 4.1783 4.3346 1.5433 1.4789 0.010 1550.94 4.1767 4.3338 1.5437 1.4794  Standard uncertainties in u(m) molality are ±1x10 -3mol.kg-1. Standard uncertainties in u(u) speed of sound measurements are ±0.5m.s-1. Standard uncertainties in u (T) temperatures are 0.05K. Standard uncertainties in u (P) pressures are 0.1MPa.

𝐿𝑓 = 𝑈

𝐾

𝑒𝑥𝑝 √𝜌𝑒𝑥𝑝

= 𝐾√βs

SC

RI

The intermolecular free length (Lf) depends on the intermolecular interaction involved among different species and is the distance between the surfaces of neighbouring molecules. The experimental values of isentropic compression (βS ) were further utilized to calculate the intermolecular free length (Lf) by using the equation (11): (11)

PT E

D

MA

NU

Where 𝐾 is the temperature dependent constant (= (93.875 + 0.375T) × 10-8) [57]. As from equation (11), Lf depends on isentropic compression and it shows the behaviour similar to isentropic compression. Table-6 shows that Lf values increase with rise in temperature for LFH in water and water-sorbitol system which implies that the mean distance between the molecules for the studied systems increase, thereby decresing the potential energy of interaction between them. The decrease in Lf values with increase in concentration of LFH in water and water-sorbitol system is an indication of decrease in distance between the molecules and an increase in potential energy of interaction between them [58]. The sample plots for the variation of βs and W as a function of m for LFH in 0.002 mol.kg-1 aqueous sorbitol at the experimental temperatures are as shown in Fig-5:

CE

300.15K 305.15K 310.15K 315.15K

4.40

4.30

1.474 1/7 -1

4.32

300.15K 305.15K 310.15K 315.15K

1.472 1.470

3

(10

-10

-1

Pa )

4.34

1.476

W(10 m mol Pa )

4.36

1.478

AC

4.38

-4

4.28 4.26

1.466 1.464

4.24 4.22 0.000

1.468

1.462

0.002

0.004

0.006

0.008

0.010

0.000

-1

m(mol.Kg )

0.002

0.004

0.006

0.008

0.010

-1

m(mol.Kg )

(a) β Vs m for LFH in 0.002 mol.kg-1 Sorbitol

(b) W Vs m for LFH in 0.002 mol.kg-1 Sorbitol

15

ACCEPTED MANUSCRIPT Fig-5: Plots showing the variation of βs and W with m for LFH in 0.002 mol.kg-1 aqueous sorbitol at different temperatures.

MA

NU

SC

RI

PT

Specific acoustic impedance (Z) assesses the absorption of sound waves in a medium and determines the elastic behaviour of the medium. The values of Z for LFH in water and different water-sorbitol systems are reported in Table-6 which is calculated by using equation (12). Z= u ρ (12) Where u and ρ are the speed of sound and density of solutions respectively. The increase in values of Z with increasing concentration of LFH in water and watersorbitol system indicates associative molecular interactions between molecules[59]. The increase in the value of Z with increasing sorbitol concentration can be explained on the basis of greater degree of H-bonding or electrostatic interaction in solutions. Molar compressibility (W) was also obtained for LFH in water and aqueous sorbitol solutions using equation (13): Where M represents the apparent molecular weight of the solution and was calculated as: −1/7 W = (𝑀⁄𝜌)𝛽 (13) 𝑀 = 𝑀1 W1 + 𝑀2 W2 , where W1 and W2 are weight fractions and 𝑀1 and 𝑀2 are molecular weights of solvent and solute respectively. The increasing values of W with increase in concentration of LFH in different aqueous sorbitol solutions indicate the presence of strong interactions between LFH and aqueous sorbitol solutions [58,60]. 3.3. Conductance studies:

AC

CE

PT E

D

The specific conductance (𝜅) data is obtained from conductance study. The specific conductance (𝜅) values for LFH in water and aqueous sorbitol system increase with increase in concentration and temperature. With increase in concentration of LFH (0.001-0.01) mol.kg1 in water and aqueous sorbitol system number of ions per cm3 of solvent increases due to which specific conductance increases and with rise in temperature speed of ions increases which is the main cause for the increase of specific conductance. The specific conductance data is used for the calculation of molar conductance which is further utilized to calculate the Walden product.

3.3.1. Molar Conductance The molar conductance Λm is calculated by using equation (14) for LFH (0.001-0.01) mol kg in water and aqueous sorbitol solutions at different temperatures are recorded in Table-7. .

Λm =

-1

𝜅×1000

(14)

𝐶

Here 𝜅 is specific conductance and 𝐶 is molar concentration. The nature of solute-solvent interactions, degree of dissociation, dissociation constant and the structure making/breaking tendency of solute in a given solvent can be understood with the help of electrical 16

ACCEPTED MANUSCRIPT conductance. From Table-7 it is observed that the values of Λm for LFH in water and aqueous sorbitol system increases with rise in temperature. This may be due to (i) increase in number of ions (ii) due to high mobility of ions at higher temperature. The values of Λm also decreases with increase in concentration of sorbitol in water-sorbitol systems which may be due to increase in solute-cosolute interactions [61-63]. The plots for the variation of molar conductance for LFH in water and aqueous sorbitol solutions are shown in Fig-6.

PT

TABLE-7: Molar Conductance (𝚲m) of LFH in water and in aqueous sorbitol solutions at different temperatures: Λm (300. 15K)

Λm (305.15K)

Λm (310.15K)

Λm (315.15K)

(mol1/2l-1/2)

Ohm-1cm2mol-1

Ohm-1cm2mol-1

Ohm-1cm2mol-1

Ohm-1cm2mol-1

149.33 131.45 128.42 125.75 123.38 121.31 119.72 118.17 116.65 115.25

173.21 156.45 153.58 150.62 147.86 145.56 143.25 141.12 139.06 137.25

136.13 121.32 120.01 118.72 117.52 116.38 115.34 114.27 113.32 112.46

151.19 139.85 137.97 136.25 134.85 133.42 132.23 131.08 130.12 129.14

125.24 114.95 113.65 112.37 111.41 110.37 109.45 108.34 107.36 106.24

140.25 131.02 130.31 129.58 128.85 128.02 127.14 126.34 125.63 124.89

114.26 103.77 101.99 100.44 99.39 98.15 97.29 96.33 95.37 94.41

128.78 118.29 116.45 114.92 113.55 112.25 111.09 110.13 109.23 108.47

0.315 0.446 0.546 0.631 0.705 0.773 0.835 0.892 0.946 0.997

118.42 125.03 108.26 112.47 106.16 111.07 104.12 109.57 102.47 108.15 100.86 106.76 99.18 105.32 97.69 103.96 96.36 102.65 95.19 101.43 LFH in 0.004 mol.kg-1 aqueous sorbitol



MA

D

PT E

CE AC

0.315 0.446 0.546 0.631 0.705 0.773 0.835 0.892 0.946 0.997

NU

122.51 133.85 109.02 121.72 106.95 118.86 104.99 116.16 102.98 113.83 101.19 111.74 99.54 109.91 98.11 107.987 96.71 106.39 95.25 104.93 LFH in 0.002 mol.kg-1 aqueous sorbitol

SC

LFH in water 0.315 0.446 0.546 0.631 0.705 0.773 0.835 0.892 0.946 0.997

RI

Concentration

109.51 116.67 98.56 105.59 97.45 104.12 96.36 103.05 95.45 102.05 94.52 101.05 93.55 100.04 92.64 99.04 91.73 98.17 90.89 97.45 LFH in 0.006 mol.kg-1 aqueous sorbitol

0.315 100.25 105.55 0.446 89.36 95.65 0.546 88.26 93.87 0.631 87.04 92.09 0.705 85.73 90.72 0.773 84.42 89.52 0.835 83.05 88.56 0.892 81.69 87.49 0.946 80.47 86.48 0.997 79.14 85.54 Standard uncertainty u(κ) in the value of specific conductance is ±4.2x10 -3S.cm-1.

17

ACCEPTED MANUSCRIPT

175

300.15K 305.15K 310.15K 315.15K

170 165 160 155 145

2

140 135

-1

-1

m(ohm cm mol )

150

130 125 120 115 110 105 100 95 0.4

0.5

0.6

0.7

0.8

1/2

0.9

1.0

1.1

PT

0.3

1/2 -1/2

(Cx100) (mol l )

RI

155

305.15K 305.15K 310.15K 315.15K

150 145 140

SC

115

NU

110 105 100 95 0.3

0.4

0.5

0.6

0.7 1/2

0.8

0.9

1.0

1.1

1/2 -1/2

MA

(Cx100) (mol l )

(a) LFH in water

135

-1 2 -1

120 115 110 105

CE

100 95 90 0.3

0.4

0.5

0.6

0.7

1/2

0.8

0.9

300.15K 305.15K 310.15K 315.15K

125 120 115

m(ohm cm mol )

125 m(ohm cm mol )

130

PT E

130

D

300.15K 305.15K 310.15K 315.15K

140

(b) LFH in 0.002mol.kg-1 sorbitol

-1

120

110

2

2

125

105

-1

-1

130

-1

m(ohm cm mol )

135

100 95 90 85 80 75

1.0

1.1

0.3

1/2 -1/2

0.4

0.5

0.6

0.7 1/2

0.8

0.9

1.0

1.1

1/2 -1/2

(Cx100) (mol l )

AC

(Cx100) (mol l )

(c) LFH in 0.004 mol.kg-1 sorbitol

(d) LFH in 0.006 mol.kg-1 sorbitol

Fig-6: Plots showing the variation of Λm with (Cx100)1/2 for LFH in water, (0.002, 0.004 and 0.006) mol.kg-1 aqueous Sorbitol at different temperatures. The limiting molar conductance i,e, molar conductance at infinite dilution is evaluated by applying the least squares fit to the experimental values of 1/Λm Vs ΛmC by using Kraus – Bray conductivity equation which is another form of Ostwald’s dilution law: [64] 1 Λm

1

= Λ0 + m

Λm C 𝐾𝑐 Λ0m

(12)

2

18

ACCEPTED MANUSCRIPT Here Λ0m is the limiting molar conductance, Kc is dissociation constant and 𝐶 is molar concentration. The sample plot for the variation of 1/Λm Vs ΛmC for LFH in 0.002m sorbitol at 305.15K is shown in Fig-7. 0.0100

305.15K

0.0096

PT

-2

1/m(ohm.cm .mol)

0.0098

0.0094

RI

0.0092

0.0088 0.2

0.4

0.6 -1

SC

0.0090

0.8

2 -1

NU

mc(ohm cm l )

1.0

MA

Fig-7: Plot for the variation of 1/Λm Vs ΛmC for LFH in 0.002mol.kg-1 sorbitol at 305.15K

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The intercept and slope of plot gives the value of Λ0m and Kc respectively. The value of Λ0m is higher for water and then decreases with the increase in the concentration of sorbirtol in water. This may be due to the formation of H-bond between sorbitol and water molecules which reduces the ionic mobility and decreases the value of Λ0m . The increase in values of Λ0m with increase in temperature for LFH in water and water-sorbitol system may be due to the fact that increase in thermal energy breaks more number of hydrogen bonds thereby increasing the mobility of ionic species [65]. Kc increases with temperature for LFH in aqueous sorbitol solutions and its variation with temperature indicates the exothermic nature of system [66]. The activation energy (Ea ) of conducting process can be obtained from Arrhenius equation, Λ0m =A𝑒 −Ea ⁄𝑅𝑇 A is the frequency factor, R is gas constant and T is temperature. The activation energy of −E

a rate process can be calculated from the slope of linear plot of logΛ0m vs 1/T (slope=2.303R )

.The values of limiting molar conductance (Λ0m ), dissociation constant (Kc) and activation energy (Ea ) are listed in Table-8. TABLE-8: Limiting molar conductance at different temperature for LFH in water and aqueous sorbitol solutions:

Solvent

𝚲𝟎𝐦 (Ohm-1cm2mol-1) 300.15K

𝚲𝟎𝐦 (Ohm1cm2mol-1) 305.15K

𝚲𝟎𝐦 (Ohm1cm2mol-1) 310.15K

𝚲𝟎𝐦 (Ohm-1cm2mol-1) 315.15K

19

Kc (mol.l-1) 300.15K

Kc (mol.l-1) 305.15K

Kc (mol.l-1) 310.15K

Kc (mol.l-1) 315.15K

𝐄𝐚 (KJ. mol-1)

ACCEPTED MANUSCRIPT Distilled Water

114.03

127.55

136.24

163.13

0.0423

0.0375

0.0449

0.0442

17.90

112.74

116.41

123.92

142.65

0.0449

0.0615

0.0868

0.0847

12.03

100.91

107.87

117.51

132.98

0.0818

0.0826

0.0862

0.1488

14.34

93.55

98.52

106.16

120.77

0.0478

0.0559

0.0704

0.0753

13.19

0.002 mol.kg-1 Sorbitol 0.004 mol.kg-1 Sorbitol 0.006 mol.kg-1 Sorbitol

PT

From Table-8, it can be seen that the value of activation energy (Ea) are all positive indicating that the solubilisation is favourable [67].

RI

3.3.2. Walden product (𝚲𝟎𝐦 ηo)

D

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SC

Solute can be classified as structure maker/breaker on the basis of Walden product i.e. product of limiting molar conductance (Λ0m ) and viscosity (η0 ) of solvent and its temperature dependence. The negative temperature coefficient of Walden product indicates that the solute acts as structure breaker and positive temperature coefficient indicates that the solute acts as structure maker. The experimentally measured values of viscosity for solvent decreases with rise in temperature which means that higher is the mobility of ions and higher is the conductance of ions. The values of Walden product for LFH in water and aqueous sorbitol solutions at 300.15K, 305.15 K, 310.15 K and 315.15 K temperatures are recorded in Table9. The positive temperature coefficient in the plot of Walden product Vs temperature suggests that LFH behaves as a structure maker in water and aqueous sorbitol solutions [68-69]. The plot showing the variation of Walden product Vs temperature is shown in Fig-8.

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TABLE-9:

Λ0m (ohm-1cm2mol-1) LFH in distilled water

Solvent

305.15K 310.15K

AC

315.15K

CE

300.15K

ηox103 (Pa.s)

Λmoηox105 (ohm-1cm2mol-1Pa.s)

114.03

0.8211

0.9363

127.55

0.7792

0.9939

136.24

0.7459

1.0162

163.13

0.6513

1.0625

LFH in 0.002 mol.kg-1 sorbitol

300.15K

112.74

0.8265

0.9317

305.15K

116.41

0.8093

0.9421

310.15K

123.92

0.7699

0.9541

315.15K

142.65

0.6983

0.9961

LFH in 0.004 mol.kg-1 sorbitol 300.15K

100.91

0.8792

0.8872

305.15K

107.87

0.8255

0.8904

310.15K

117.51

0.7711

0.9061

315.15K

132.98

0.7162

0.9524

20

ACCEPTED MANUSCRIPT LFH in 0.006 mol.kg-1 sorbitol 93.55

0.8856

0.8284

305.15K

98.52

0.8434

0.8309

310.15K

106.16

0.7995

0.8487

315.15K

120.77

0.7322

0.8843

LFH in water LFH in 0.002m sorbitol LFH in 0.004m sorbitol LFH in 0.006m sorbitol

1.08 1.06

1.00

0.94

SC

2

0.98

-1

-1

1.02

0.96

5

RI

1.04

oox10 (ohm cm mol Pa.s)

PT

Standard uncertainty u(η) in viscosity measurements is ±3.2x10 -1 Pa.s and that in case of temperature u(T) is 0.05K.

0.92 0.90 0.88 0.86 0.84 0.82 300.15K

305.15K

310.15K

315.15K

MA

T(K)

NU



300.15K

D

Fig-8: Plot showing the variation of 𝚲𝟎𝐦 𝛈𝟎 𝐰𝐢𝐭𝐡 Temperature for LFH in water and aqueous sorbitol solutions at different temperatures.

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4. CONCLUSION:

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The various parameters that are calculated from experimental density, ultrasonic speed and conductance data indicate the presence of strong solute-solvent interactions between LFH in water and aqueous sorbitol solutions. The solute-solvent interactions increase with increase in concenteration of solute and also with rise in temperature. The increase in ΦE0 with increase in temperature suggests that there is presence of caging effect. The variation of Kc with temperature indicates the exothermic nature of system. The results of Hepler’s constant and Walden product show that LFH acts as structure maker in water and aqueous sorbitol solutions. References:

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Highlights  Different possible interactions between LFH in water and aqueous sorbitol systems are studied.  The various possible interactions are interpreted using Volumetric, acoustic and conductance studies.  Solute-Solvent interactions predominate over solute-solute interactions  All these studies confirmed the structure maker behaviour of LFH in water and watersorbitol system

25