Bio-Molecular Interaction Studies in the Systemof Pectin + α-amylase at 298.15 K

Subramanian Nithiyanantham

Published online: 14 August 2013# Springer Science+Business Media New York 2013

List of Symbols

kT Temperature Dependent Constantk Temperature Independent ConstantMeff, M Effective Molecular Weight,x Mole Fractioni Component% Percentagem Molecular Weightβ Adiabatic CompressibilityLf Free LengthVf Free Volumeπi Internal PressureT TemperatureR Universal Gas Constantb Atomic Scaling Factorα Molecular Interaction Parameter∑ Summatione Percentage Deviation

of free length theory [9], Danusso model [10], Junjie’s method[11], and Rao formalism [12] interpreted in the results in termsofmolecular interactions. There has been increasing interest inthe study of intermolecular interactions in several years andnumbers of experimental techniques have been used to inves-tigate the interactions between the binary and ternary mixturescomponents. Ultrasonic studies of liquid mixtures, due to thenondestructive nature, have been extensively carried out indifferent branches of science (physical, chemical, biological)to measure the thermodynamic properties to predict the natureof molecular interactions between the molecules in a medium.The ultrasonic sound velocity, and the thermodynamic param-eters derived from it have been widely used to interpret theinteractions between unlike molecules in the binary and ter-nary mixtures. In the present study, an attempt has been madeto study the intermolecular interaction in the binary mixture ofpectin with α-amylase solution by measuring the ultrasonicvelocity, density, and viscosity of the mixtures at 298.15 K[13]. Various theories and relations suggested by Danusso(1951), Jacobson (1952), Junjie (1984), and Gokalae (1989)are used to calculate the ultrasonic velocity [9–12].

2 Sample Preparation

All the solutions are prepared by using AR-grade chemicals,which are further purified by standard methods [14]. Howev-er, the preparation of 7.0 % amylase solution did not showthorough mixing, and hence, the 6.0 % amylase solution isused throughout the entire work. The pectin solutions areprepared for various percentages (%) from 0.2 to 1.0 in stepsof 0.2 % [gram of substance dissolve in water to make100 ml]. The aqueous mixtures of amylase with pectin were

S. Nithiyanantham (*)School of Physical Sciences and Femtotechnology(Ultrasonics/Bio-Physics Division), SRM University,Kattankulathur, Kanchipuram, District, Tamil Nadu, India 603 203e-mail: bknithu@gmail.com

BioNanoSci. (2013) 3:451–455DOI 10.1007/s12668-013-0104-7

1 Introduction

In recent years, measurement of ultrasonic investigationsfound extensive applications in determining the physicochem-ical behavior of liquid mixtures [1–5]. Several researchers[6–8] carried out ultrasonic velocity with theoretical relation

made in three different proportions as 90:10, 50:50, and 10:90by weight, and were left for 2 h to attain complete stability[15].

3 Experimental Techniques

The ultrasonic velocity in the mixtures is measured using avariable path-fixed frequency Ultrasonic interferometer work-ing at 2 MHz frequency (Mittal type, New Delhi, India) at298.15 K. The accuracy of sound velocity is ±0.1 ms−1

(0.01 %). The density and viscosity of the mixture are mea-sured using a specific gravity bottle (5 ml) and an Ostwald’sviscometer (10 ml), respectively. The accuracy in densitymeasurement is ±0.1 kgm−3 (0.053 %) and that in viscositymeasurement is ±0.001 m Nsm−2 (0.09 %) [16].

4 Theory and Calculation

Comparison of theoretical values of ultrasonic velocities withthose obtained experimentally in the present binary liquidmixtures is expected to reveal the nature of interaction be-tween component molecules in the mixture. Such theoreticalstudy is useful in finding the comprehensive theoretical modelfor the liquid medium.

The ultrasonic velocity in binary mixtures can be evaluatedtheoretically using the following theories and empiricalrelations.

4.1 Danusso Model

The velocity of ultrasonic wave of given establishedempirical formula suggested by Danusso (1951) in bi-nary liquid mixtures on the linear dependence molarvolume as [10]

UDM ¼ 1

ρmix

1

Meff

x1M 1

ρ21u21

þ x2M 2

ρ22u22

� �� �1=3

ð1Þ

4.2 Free Length Theory

Jacobson (1952) derived an empirical relation for the evalua-tion of ultrasonic velocities in pure liquids from the free lengthdata between the molecules [9].

Lf ¼ K

U expρ1=2exp

ð2Þ

Where, Lf is the free length, Uexp is the experimentalultrasonic velocity in liquid, and ρexp is the experimental

density of the liquid. K is the temperature dependent constant[197.7×10−8 (MKS)].

Jacobson (1952) also formulated the free length in terms ofavailable volume Va and surface area of the molecule Y [17].The expression for Lf is given by

Lf ¼ 2Va

Yð3Þ

where

Va ¼ VT−Vo ð4Þ

VT is the molar volume of the liquid at the tempera-ture of measurement (T) Vo=molar volume of the liquidat absolute zero temperature. Vo is calculated from theequation,

Vo ¼ VT 1−T

Tc

� �0:3

ð5Þ

Where, T=absolute temperature of measurement, andTc=critical temperature in K. If Tc is not available forany liquid, another formula may be used to calculate thevalue of Va for liquids whose density is greater andvelocity is less than U∞ (1,600 ms−1) [18] and is givenby

Va ¼ VT 1−U exp

U∞

� �ð6Þ

Where Uexp is the experimental velocity of liquid. Now, Vocan be evaluated from

Vo ¼ VT−Va ð7Þ

The surface area is also calculated from the given relation

Y ¼ 36πNV 2o

� �1=3 ð8Þ

On using Eqs. 2–7, ultrasonic velocity in pure liquids canbe calculated. The same theorymay also be extended to binarymixtures by the relation

Lmix ¼2hVTM− XAVoA þ XBVoBð Þ

XAYA þ XBYBð9Þ

where XA and XB are the mole fractions of components Aand B, respectively. VoA and VoB are volumes at absolutezero and YA and YB are surface areas per mole of thecomponents A and B, respectively. VMT is the molar

452 BioNanoSci. (2013) 3:451–455

volume of the mixture and is obtained by the relationgiven below:

VMT ¼ XAMA þ XBMBð Þ=ρmix ð10Þ

Where MA and MB are the molecular weight of the respec-tive components,The theoretical ultrasonic velocity in themixture Umix can be obtained by using the relation

Umix ¼ K

Lmix ρ1=2mix

ð11Þ

In terms of adiabatic compressibility, βad equationmay alsobe written as

Lf exp ¼ K βadð Þ1=2 ð12Þ

where,

βad ¼1

U2exp ρexp

ð13Þ

The calculated free length from the experimental velocity iscalled experimental free length Lf exp .

4.3 Junjie’s Relation

The ultrasonic velocity by Junjie (1984) relation is given bythe expression (14) [11],

UJR ¼X 1M 1

ρ1þ X 2M 2

ρ2

� �

X 1M 1 þ X 2M 2ð Þ X 1M1

V 21 ρ1

þ X 2M2

V 22 ρ2

� �1=2 ð14Þ

4.4 Rao’s Specific Velocity

According to Gokhale [1994] and his units, the velocity ofsound in binary mixture is [11] deduced from Rao [17]

UR ¼X

xiriρið Þ3 ð15Þ

Rao’s specific sound velocity = ¼ U 1=3i

ρið16Þ

4.4.1 Percentage of Deviation

The percentage of deviation is deviation in sound velocitybetween the experimental and computed values and they are

calculated as [19]

ΔU

U

� �% ¼ U expt−Uthe

U expt

� �100% ð17Þ

4.4.2 Molecular Interaction Parameter

The degree of molecular interaction [20]

α ¼ U2exp

U2IMR

!−1 ð18Þ

5 Results and Discussions

The experimentally measured ultrasonic velocity values andthe estimated/computed ultrasonic velocity obtained from thevarious theoretical models, and their percentage of deviationin velocity and molecular interaction parameter for the binarymixtures are given in Table 1.

The perusal of Table 1 reveals that good and fair agreementbetween the experimental and the calculated sound velocitiesand their deviation owing to the many assumptions and ap-proximations are made in the respective theories. Further-more, it is interesting to note that the prediction based onpercentage deviation (ΔU/U) is similar.

The percentage deviations between the observed and cal-culated sound velocities may be attributed to the molecularinteractions [7] between the components of liquid mixture.Such types of interactions have not been taken into consider-ation in the formalism of respective theories. Furthermore,they are inadequate to account comprehensively for the ex-perimental manifestation of molecular interaction in variousultrasonic processes. The extent of deviation in velocities maybe attributed to the presumption made in the theories for thenon polar–non polar and non polar–polar interaction betweenthe molecules.

Among the various theories taken into consideration,Danusso Model (DM) is found to give an excellent predictionof sound velocity for this binary system. The prediction givenby DM method closely resembles that of experimental valuesfor most of the percentage at all percentage of compositions(Table 1). However, better coincidence can be found for manypercentages in Rao’s formalism (RF). However, the percent-age of deviation is positive, negative, and close to zero for DMand RF. Moreover, this trend confirms that both the DM andRF approach yields best predictions of the happenings in thebinary system of aqueous amylase–pectin system [4, 12].

The resultant interaction in a liquid mixture is not fullydependent on the molecular strength of component liquids. It

BioNanoSci. (2013) 3:451–455 453

is measured that all the molecules are spherical in shape,which is not true every time (amylase (chain)) on mixingtwo liquids because of presence of various type of forces suchas dispersion forces, dipole–dipole interaction, dipole-induceddipole interaction, H bonding charge transfer interaction, orcomplex formation. In the observed as well as predicted (DMand RF) sound velocity values, there is no sudden variationand hence, the chances for complex formations or chargetransfer are overruled. As there is no evident or hidden freepolar groups in the component molecules, either the dipole–dipole or dipole-induced dipole interaction is not possible.Hence, it leads to the existence of dispersion forces. Thissuggestion seems to be good as amylase is a larger molecule,having lengthy chain arrangements that can easily be hydro-lyzed by the components of the system. Any dispersive type ismore likely between unlike components and hence this leadsto solute–solvent or solute–solute type, as concluded inNithiyanantham et al. [8, 21, 22]. Thus, the observed deviationof theoretical values of velocity from the experimental valuesshows that the molecular interaction is taking place betweenthe unlike molecules in the liquid mixtures. Here, Rao’sspecific velocity method provides the result better than othermodels in all proportions

The interaction parameters characterizing a system varieswith temperature, molar mass, percentage of mass (larger size-

poly molecule), and temperature. It is employed to account forthe contribution of non-combinational entropy of mixing andthe enthalpy of mixing to the Gibb’s energy of mixing. Whenthe values of interaction parameters show a positive sign, itrepresents strong interaction between the mixing molecules.In the system studied, we observed that the interaction param-eter are negative for all given mixtures indicating weakerinteraction, this may be due to the existence of interactionthrough hydrogen bonds.

Furthermore, the values of molecular interaction parameter(α) as obtained from the IMR values listed in Table 1, indicatesthat α is negative for almost all percentage at all combinationtaken up. The negative α values suggest the possibility offormation of intra molecular hydrogen bonds and it clearlyindicated the existence of weak dipolar and dispersive interac-tions [7]. Furthermore, the maximum α value obtained is−0.0275 for 1.0 % in (90:10) and minimum α is −0.0001 for0.8 % in (50:50) and 0.0001 for 1.0 % of pectin. This confirmsthat pectin exhibits poor interaction with enzyme amylase. Thismodel is reported earlier by Nithiyanantham (2006) [7, 16].

The net interactions in a liquid mixture are the result ofmany factors. However, as amylase is the largest molecule inthe present system, its contribution is largely considerable. Anymolecule that’s large in size will definitely offer dispersive typeof intra molecular interactions. Furthermore, the chances for

Table 1 The measured and calculated values of ultrasonic velocity (U), their percentage deviation, and molecular interaction parameter (α) for variouspercentages (%) of pectin in aqueous 6 % of amylase solution at 298.15 K

(%) Ultrasonic velocity (ms−1) Percentage deviation α

UExp UDM UFLT URF UJUN DM FLT RF JUN

(Amylase: pectin) 90; 10

0.2 1,515.6 1,496.0 1,513.9 1,528.3 1,413.6 1.2954 0.1107 −0.8350 6.7331 −0.0175

0.4 1,518.0 1,499.5 1,514.7 1,528.5 1,416.5 1.2203 0.2276 −0.6814 6.6874 −0.0148

0.6 1,519.8 1,503.7 1,516.1 1,528.7 1,418.2 1.0622 0.2443 −0.5889 6.6845 −0.0127

0.8 1,521.6 1,505.5 1,516.7 1,529.0 1,420.1 1.0559 0.3443 −0.4639 6.6685 −0.0106

1.0 1,522.5 1,513.6 1,515.7 1,488.3 1,421.0 0.5839 0.4441 2.2476 6.6644 −0.0275

(Amylase: pectin) 50:50

0.2 1,519.7 1,539.9 1,507.4 1,519.6 1,224.2 −1.3292 0.8083 0.0026 19.447 −0.0030

0.4 1,521.2 1,538.1 1,504.9 1,520.5 1,226.6 −1.1085 1.0715 0.0492 19.369 −0.0031

0.6 1,523.7 1,541.1 1,508.6 1,521.7 1,228.3 −1.1428 0.9893 0.1280 19.386 −0.0009

0.8 1,525.3 1,541.2 1,509.2 1,522.6 1,230.2 −1.0456 1.0546 0.1776 19.345 −0.0001

1.0 1,526.8 1,541.1 1,509.4 1,523.4 1,232.1 −0.9367 1.1370 0.2244 19.305 0.0010

(Amylase: pectin) 10:90

0.2 1524.2 1,584.8 1499.5 1,514.2 1,093.9 −3.9780 1.5774 0.6109 28.232 0.0105

0.4 1,525.7 1,583.2 1,499.9 1,515.3 1,094.9 −3.7709 1.6261 0.6177 28.239 0.0091

0.6 1,527.0 1,581.5 1,500.4 1,516.5 1,095.7 −3.5716 1.6748 0.6253 28.246 0.0091

0.8 1,528.0 1,580.0 1,502.3 1,518.6 1,096.6 −3.4017 1.7071 0.6402 28.236 0.0084

1.0 1,529.1 1,581.6 1,503.4 1,501.8 1,096.3 −3.4313 1.7396 1.8436 28.302 0.0001

454 BioNanoSci. (2013) 3:451–455

weak dipolar type interactions are favored as the carbohydratemolecules are having their own active group [23].

6 Conclusions

(1) From the four theories/model taken up for the prediction ofsound velocity, DM and RF are found to be best suited forthe systems studied.

(2) The existence of weak dispersive type interaction be-tween the components of the mixture is evident.

(3) The magnitude with their type of interactions is con-firmed as obtained in the respective binary systems.

(4) It approaches ideality as their percentages are increasedin the mixtures under investigation.

Acknowledgments The author express his thanks to Prof. Dr. K.Ganesan(Retd), Head, Dept. of Physics, T.B.M.L. College, Porayar, India, And Prof.L. Palaniappan, Dept. of Physics, Annamalai University, Annamalai nagar,Chidambaram, Tamil Nadu, India for inspiring this work.

References

1. Hilderbrand, J. H. (1971). Science, 174, 490.2. Nikam, P. S., Jagdale, B. S., Sawart, A. B., Hasan, M. (2000). Journal of

Pure and Applied Ultrasoc, 22, 115.3. Pandey, J. D., Singh, A. K., Dey, R. (2005). Pramana, Journal of

Physics, 64(1), 135.4. Rama Rao, G. V., Viswanatha Sarma, A., Sivarama Krishnan, J.,

Ramababu, C. (2005). Indian Journal of Pure & Applied Physics, 43,345.

5. Ali, A., Pandey, J. D., Soni, N. K., Nain, A. K., Lal, B., Chand.(2005). Chinese Journal of Solution Chemistry, 23(4), 377.

6. Pandey, J. D., Dey, R., Duri vedi, D. K. (1999). Pramana, Journal ofPhysics, 52(2), 187.

7. Nithiyanantham, S., Palaniappan L., Jeyalaxmi, R. (2012). Journal ofComputational and Theoretical Nano Science, 9(8), 1115.

8. Nithiyanantham, S., & Palaniappan L. (2012). Journal of BiomedicalNano Science, 7, 1–4.

9. Eyring, H., & John, M. S. (1969). Significance of Liquid Structures.New York: Wiley Eastern.

10. Jacobson, B. (1952). Acta Scandinavica, 6, 1482.11. Danusso, F. (1951). Alti Delta Academica nazimade, di linies, 10,

235.12. Junzie, Z. (1984). Journal of University of Science and Technology,

14, 298.13. Nithiyanantham, S., Phd. (2006). Thesis, Submitted to Annamalai

University, Annamalai Nagar, Chidambaram, Tamil Nadu, India.14. Gokhale, V. D., & Bhagavat, N. N. (1994). Indian Journal of Pure &

Applied Ultra, 11, 21.15. Riddick, J. A., Burger, W. B., Sokano, T. K. (1994). Tech-

niques in chemistry, Vol.2, Organic solvent (4th ed.). NewYork: John Willey.

16. Vogel, A. (1989). A text book of practical organic chemistry (5th ed.).New York: John Willey.

17. Jacobson, B. (1952). Journal of Chemical Physics, 20, 927.18. Schaaff, W., & Molekularkustik. (1963). (Springer-Verlag Berlin

Chaps 11 and 12).19. Pearson, K. (1978). Fundamental of mathematical statistics (p. 903).

New Delhi: S. Chand & Company.20. Van Deal, W., & Vangeal, E. (1969). Proceedings of the first inter-

national conference on colorimetry and thermodynamics. Warsaw,556.

21. Fakrudhin, S. K. (2011). Journal of Environmental, Computer Engi-neering & Technology, 1(3), 295.

22. Subhashini, E., & Kavitha, P. (2011). Indian Journal of ChemicalEngineering Pharmaceutical Research, 2(2-3), 92.

23. Nithiyanantham, S., & Palaniappan, L. (2013). Journal of BiomedicalNano Science. [accepted].

BioNanoSci. (2013) 3:451–455 455