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Ultrasonic studies on aqueous polyethylene oxide in n-alkanols
Journal of Molecular Liquids 126 (2006) 69 – 71 www.elsevier.com/locate/molliq
Ultrasonic studies on aqueous polyethylene oxide in n-alkanols P.S. Ramesh b, D. Geetha a,*, C. Rakkappan b a
Department of Physics, Annamalai University, Annamalainagar, 608 002, Tamil Nadu, India Physics Wing DDE, Annamalai University, Annamalainagar, 608 002, Tamil Nadu, India
b
Received 19 January 2005; accepted 15 September 2005 Available online 27 December 2005
Abstract Ultrasonic velocity, density and viscosity studies were undertaken to study the influence of n-alkanols (butan-1-ol, petan-1-ol and hexan-1-ol) on aqueous PEO (1%) solution at 303 K. From the observed values, the related acoustical parameters are calculated and their variations are discussed in light of molecular interaction of n-alkanols in aqueous polyethylene oxide solution. D 2005 Elsevier B.V. All rights reserved. PACS: 43.35.B34; 43.35.Fj Keywords: Ultrasonic velocity; density; viscosity; n-alkanols
1. Introduction
2. Experimental
Polymers can be classified into (i) natural polymers (ii) semi synthetic polymers and (iii) synthetic polymers. Polyethylene oxide (PEO) is the simple and water soluble synthetic polymer. It has the monomer unit –CH2CH2O– in which oxygens are separated by hydrophobic ethylene unit. Higher molecular weight PEO’s are used as pharmaceutical aids to prepare hydrogels. In general, when two liquids are mixed together, the structure of each of the two liquids will change. Ultrasonic measurements in aqueous solutions of such have been widely reported [1–4]. There is no work done in the addition of n-alkanols in aqueous PEO. In the present investigation, ultrasonic velocity studies were undertaken in the aqueous solutions of PEO 4000 and PEO 6000 (1%) with butan-1-ol, pentan-1-ol and hexan-1-ol with a view to understand the nature of solute–solvent interactions in the aqueous polymer and alcohols at 303 K. The present paper is aimed to investigate the molecular interaction in liquid mixtures from the experimentally measured values of ultrasonic velocity (U), density (q) and viscosity (g s) in different compositions of the mixtures.
The PEO (m.w. 4000 and 6000) samples and alcohols used are of AR grade, purified by standard procedure. The ultrasonic velocities have been measured by employing an ultrasonic interferometer (Mittal Enterprises, New Delhi). The ultrasonic cell has a double-walled jacket and thermostated water is circulated through it from a thermostat with thermal stability of T0.05 -C. The experimental frequency is 3 MHz and the velocity measurements have an accuracy better than T 0.5%. The density and viscosity measurements have been made using a specific gravity bottle and Ostwald viscometer with an accuracy of T 0.1 kg m 3 and T0.2%, respectively. The various physical parameters are calculated from the measured values of density (q), viscosity (g) and ultrasonic velocity (U) using the standard formula. The various physical parameters are calculated from the measured values using the standard formulae, which are presented in a previous paper [5]. 3. Results and discussion In the present work, three alcohols are taken viz.,
* Corresponding author. E-mail address: [email protected] (D. Geetha). 0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2005.09.006
System I: 1% of PEO + butan-1-ol; System II: 1% of PEO + pentan-1-ol; System III: 1% of PEO + hexan-1-ol.
70
P.S. Ramesh et al. / Journal of Molecular Liquids 126 (2006) 69 – 71
Table 1 Ultrasonic velocity and related parameters of butanol, pentanol and hexanol in the solution of 1% PEO (4000) + water at 303 K Samples PEO + water + butanol
PEO + water + pentanol
PEO + water + hexanol
Conc. of electrolytes %
U (m s
0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10
1486 1489 1492 1496 1499 1504 1509 1512 1516 1521 1546 1549 1553 1558 1563
1
)
q (kg m
3
)
978 979 980 984 985 996 1001 1007 1013 1027 1039 1045 1052 1061 1074
g 103 (N s m 2)
b 1010 (N 1 m2)
˚) L f (A
V f 10
1.0004 1.0106 1.0307 1.0600 1.0798 1.0019 1.0225 1.0437 1.0624 1.0846 1.0162 1.0351 1.0566 1.0714 1.0956
4.6305 4.6071 4.5839 4.5409 4.5181 4.4386 4.3872 4.3438 4.2953 4.2089 4.0269 3.9882 3.9677 3.8828 3.8113
0.4295 0.4284 0.4273 0.4253 0.4243 0.4205 0.4181 0.4160 0.4137 0.4095 0.4005 0.3986 0.3962 0.3933 0.3898
4.0377 3.9847 3.8765 3.7269 3.6302 4.0819 3.9723 3.8595 3.7680 3.6650 4.1097 4.0054 3.8938 3.8257 3.7115
4
p i 10 P
6
871 875 883 897 905 876 886 898 909 925 892 903 915 925 942
R
Z 106
2170 2169 2168 2162 2161 2142 2134 2123 2112 2086 2073 2063 2051 2035 2013
1453 1457 1462 1472 1476 1497 1510 1522 1535 1562 1606 1618 1633 1653 1678
U — Ultrasonic velocity; V f — Free volume; q — Density; p i — Internal pressure; g — Viscosity; R — Rao’s constant; b — Adiabatic compound; Z — Acoustic impedance; L f — Free length.
The ultrasonic velocity, density and viscosity measurements are carried out in 1% aqueous solutions of PEO with addition of n-alkanols of different concentrations at 303 K. The ultrasonic velocity in 1% PEO aqueous solutions with butanol, pentanol and hexanol is found to increase with alcohol concentration (Table 1). The increment in molecular weight of PEO (6000) increases the velocity (Table 2). Adiabatic compressibility decreases with increase of concentration of PEO (1%) in alcohols. Intermolecular free length also behaves in similar manner as that of adiabatic compressibility. Rao’s constant (R) decreases with increase of alcohol concentration and also with the increase of molecular weight of PEO. The acoustic impedance (Z) increases with increase of alcohol concentration and when the molecular weight increases, Z increases further. In all the three systems studied, the variation in ultrasonic velocity is not much appreciable at higher concentration when
compared to lower concentrations. This behaviour may be explained as follows, the molecules of synthetic polymers are randomly coiled in solution and the chains have no overall tendency to adopt any particular conformation. In general the polymer molecules are linear, consisting of a sufficient number of chain linkages, which is an essential prerequisite of chain, result from the interactions of chain segments with its environments. These interactions involved the segments of the same as well as the other chain in addition to the solvent. In a good solvent, each chain segment will prefer to contact with solvent molecules rather than with the segments of its own or those of neighbouring chains. Because of this, the chain will be extended. In a poor solvent, if the polymer – polymer and solvent –solvent contacts are favoured, the chain will have a contracted form [6]. Dissolved macromolecules frequently form molecular association complexes either with species of low molecular
Table 2 Ultrasonic velocity and related parameters of butanol, pentanol and hexanol in the solution of 1% PEO (6000) + water at 303 K Samples PEO + water + butanol
PEO + water + pentanol
PEO + water + hexanol
Conc. of electrolytes %
U (m s
0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10
1519 1523 1527 1532 1536 1525 1531 1536 1541 1546 1529 1533 1539 1544 1549
1
)
q (kg m 1036 1070 1089 1096 1103 1087 1093 1104 1112 1126 1089 1100 1106 1116 1127
3
)
g 103 (N s m 2)
b 1010 (N 1 m2)
˚) L f (A
V f 10
1.0152 1.0410 1.0498 1.0621 1.0798 1.0496 1.0619 1.0798 1.0886 1.0924 1.0527 1.0628 1.0813 1.0891 1.0975
4.0733 4.0292 3.9382 3.8875 3.8427 3.9558 3.9033 3.8393 3.780 3.7157 3.9279 3.8683 3.8174 3.7587 3.6981
0.4028 0.4007 0.3961 0.3935 0.3913 0.3970 0.3943 0.3911 0.3884 0.3848 0.3956 0.3926 0.3900 0.3870 0.3838
3.2111 3.1006 3.0697 3.0264 2.9600 3.0692 3.0279 2.9626 2.9362 2.9304 3.0728 3.0370 2.9710 2.9486 2.9243
4
p i 10 P 690 713 724 730 738 722 728 737 743 749 723 730 738 744 750
6
R
Z 106
2596 2516 2475 2461 2448 2481 2470 2448 2433 2406 2480 2457 2447 2428 2406
1573 1629 1662 1679 1694 1657 1673 1695 1713 1740 1665 1686 1702 1723 1745
U — Ultrasonic velocity; V f — Free volume; q — Density; p i — Internal pressure; g — Viscosity; R — Rao’s constant; b — Adiabatic compound; Z — Acoustic impedance; L f — Free length.
P.S. Ramesh et al. / Journal of Molecular Liquids 126 (2006) 69 – 71
weight solvent or with other macromolecules. In the case of PEO with alcohols, the variation of velocity indicates that there is a strong interaction between solvent and solute molecules. It may be due to the higher number of available solvated molecules for the interaction at lower concentration than at the higher concentration. Initially adding water to pure polymer, a number of H2O molecules are bonded by H-bonds with the oxygens of the oxirane groups, until there are two water molecules for each oxygen. Furthermore because of the hydroxyl end group a larger number of water molecules can be allocated in the first hydration shell of the polymer [7]. After adding the alcohols to the aqueous PEO solutions, the variation in velocity may be due to the addition of alcohols. Such an effect has been reported in other case of polymer solutions by Sundarasan [8]. The rapid decrease of adiabatic compressibility with increase of concentration in alcohol systems clearly indicates the formation of a large number of tightly bound systems. Since the velocity increases with concentration and the density does so, the compressibility must decrease with increase in concentration. This could be caused by a more rigid liquid structure associated with hydrogen bonding of PEO with alcohols. Such reduction in compressibilities has been found in the solution due to solvent molecules [9]. At lower concentration of PEO in alcohols the molecules are not closer and thus intermolecular length (L f) is high. In the more concentrated solution the molecules come closer and segment – segment interaction will exist, thereby decreasing the intermolecular free length and hence internal pressure increases. From the experimental analysis, it is observed that the number of solvent molecules solvated per polymer unit is observed to decrease with increase in the polymer concentration. This is due to the cohesion among the polymer chains and reduction in the hydrodynamic volume. Similar observation is made by Rajagopalan and Sharma [10]. If the variation of Rao’s constant with concentrations of one of the components is non-linear, it generally indicates a strong
71
association between molecules. As Rao’s constant varies nonlinearly with concentration it may be concluded that there is an association between PEO and alcohol molecules. The increase of acoustic impedance with increasing concentration in alcohol systems predicts a strong polymer –solvent interaction [11]. Hence it may be concluded that there exists polymer – solvent interaction through hydrogen bonding. The increase in velocity with butanol, pentanol and hexanol systems may be due to less hydrogen bonds formed at lower concentrations and at higher concentrations the hydrogen bonds formed may be more due to segment –segment interaction. When the molecular weight of PEO increases, the molecular effect is high when compared to lower molecular weight PEO. Further ultrasonic absorption work will throw more light on the structural aspects and relaxational behaviour of the three systems. Acknowledgement The authors are thankful to Dr. AN. Kannappan, Professor and Dr. R. Sabesan, UGC Professor, for encouraging them to take up these studies. References [1] A.M. Northy, R.A. Pethrick, B.T. Poh, Adv. Mol. Relax. Process. 19 (1981) 209. [2] R.A. Pethrick, B.T. Poh, Br. Polym. J. 15 (1983) 149. [3] P. Spickler, F. Ibrahim, S. Fast, D. Tannenbaum, S. Yun, F.B. Stumpf, J. Acoust. Soc. Am. 83 (1988) 1388. [4] R. Feng, Z. Chen, Acta Acust, (China) 7 (1982) 263. [5] D. Geetha, C. Rakkappan, Ind. J. Phys. 77B (5) (2003) 525. [6] W. Brown, Cellulose and Cellulose Derivatives IV, Inter. Sci. Publi. Inc., New York, 1965. [7] M.P. Jannelli, S. Magazu, G. Maisano, D. Majolino, P. Migliando, J. Mol. Struct. 322 (1994) 337. [8] B. Sundarasan, Polym. Int. 33 (1994) 425. [9] W.R. Moore, J. Polym. Sci. 16 (1967) 571. [10] S. Rajagopalan, S.J. Sharma, J. Pure Appl. Ultrason. 24 (2002) 1. [11] P.Z. Debye, Electrochemistry 45 (1939) 174.
Ultrasonic studies on aqueous polyethylene oxide in n-alkanols P.S. Ramesh b, D. Geetha a,*, C. Rakkappan b a
Department of Physics, Annamalai University, Annamalainagar, 608 002, Tamil Nadu, India Physics Wing DDE, Annamalai University, Annamalainagar, 608 002, Tamil Nadu, India
b
Received 19 January 2005; accepted 15 September 2005 Available online 27 December 2005
Abstract Ultrasonic velocity, density and viscosity studies were undertaken to study the influence of n-alkanols (butan-1-ol, petan-1-ol and hexan-1-ol) on aqueous PEO (1%) solution at 303 K. From the observed values, the related acoustical parameters are calculated and their variations are discussed in light of molecular interaction of n-alkanols in aqueous polyethylene oxide solution. D 2005 Elsevier B.V. All rights reserved. PACS: 43.35.B34; 43.35.Fj Keywords: Ultrasonic velocity; density; viscosity; n-alkanols
1. Introduction
2. Experimental
Polymers can be classified into (i) natural polymers (ii) semi synthetic polymers and (iii) synthetic polymers. Polyethylene oxide (PEO) is the simple and water soluble synthetic polymer. It has the monomer unit –CH2CH2O– in which oxygens are separated by hydrophobic ethylene unit. Higher molecular weight PEO’s are used as pharmaceutical aids to prepare hydrogels. In general, when two liquids are mixed together, the structure of each of the two liquids will change. Ultrasonic measurements in aqueous solutions of such have been widely reported [1–4]. There is no work done in the addition of n-alkanols in aqueous PEO. In the present investigation, ultrasonic velocity studies were undertaken in the aqueous solutions of PEO 4000 and PEO 6000 (1%) with butan-1-ol, pentan-1-ol and hexan-1-ol with a view to understand the nature of solute–solvent interactions in the aqueous polymer and alcohols at 303 K. The present paper is aimed to investigate the molecular interaction in liquid mixtures from the experimentally measured values of ultrasonic velocity (U), density (q) and viscosity (g s) in different compositions of the mixtures.
The PEO (m.w. 4000 and 6000) samples and alcohols used are of AR grade, purified by standard procedure. The ultrasonic velocities have been measured by employing an ultrasonic interferometer (Mittal Enterprises, New Delhi). The ultrasonic cell has a double-walled jacket and thermostated water is circulated through it from a thermostat with thermal stability of T0.05 -C. The experimental frequency is 3 MHz and the velocity measurements have an accuracy better than T 0.5%. The density and viscosity measurements have been made using a specific gravity bottle and Ostwald viscometer with an accuracy of T 0.1 kg m 3 and T0.2%, respectively. The various physical parameters are calculated from the measured values of density (q), viscosity (g) and ultrasonic velocity (U) using the standard formula. The various physical parameters are calculated from the measured values using the standard formulae, which are presented in a previous paper [5]. 3. Results and discussion In the present work, three alcohols are taken viz.,
* Corresponding author. E-mail address: [email protected] (D. Geetha). 0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2005.09.006
System I: 1% of PEO + butan-1-ol; System II: 1% of PEO + pentan-1-ol; System III: 1% of PEO + hexan-1-ol.
70
P.S. Ramesh et al. / Journal of Molecular Liquids 126 (2006) 69 – 71
Table 1 Ultrasonic velocity and related parameters of butanol, pentanol and hexanol in the solution of 1% PEO (4000) + water at 303 K Samples PEO + water + butanol
PEO + water + pentanol
PEO + water + hexanol
Conc. of electrolytes %
U (m s
0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10
1486 1489 1492 1496 1499 1504 1509 1512 1516 1521 1546 1549 1553 1558 1563
1
)
q (kg m
3
)
978 979 980 984 985 996 1001 1007 1013 1027 1039 1045 1052 1061 1074
g 103 (N s m 2)
b 1010 (N 1 m2)
˚) L f (A
V f 10
1.0004 1.0106 1.0307 1.0600 1.0798 1.0019 1.0225 1.0437 1.0624 1.0846 1.0162 1.0351 1.0566 1.0714 1.0956
4.6305 4.6071 4.5839 4.5409 4.5181 4.4386 4.3872 4.3438 4.2953 4.2089 4.0269 3.9882 3.9677 3.8828 3.8113
0.4295 0.4284 0.4273 0.4253 0.4243 0.4205 0.4181 0.4160 0.4137 0.4095 0.4005 0.3986 0.3962 0.3933 0.3898
4.0377 3.9847 3.8765 3.7269 3.6302 4.0819 3.9723 3.8595 3.7680 3.6650 4.1097 4.0054 3.8938 3.8257 3.7115
4
p i 10 P
6
871 875 883 897 905 876 886 898 909 925 892 903 915 925 942
R
Z 106
2170 2169 2168 2162 2161 2142 2134 2123 2112 2086 2073 2063 2051 2035 2013
1453 1457 1462 1472 1476 1497 1510 1522 1535 1562 1606 1618 1633 1653 1678
U — Ultrasonic velocity; V f — Free volume; q — Density; p i — Internal pressure; g — Viscosity; R — Rao’s constant; b — Adiabatic compound; Z — Acoustic impedance; L f — Free length.
The ultrasonic velocity, density and viscosity measurements are carried out in 1% aqueous solutions of PEO with addition of n-alkanols of different concentrations at 303 K. The ultrasonic velocity in 1% PEO aqueous solutions with butanol, pentanol and hexanol is found to increase with alcohol concentration (Table 1). The increment in molecular weight of PEO (6000) increases the velocity (Table 2). Adiabatic compressibility decreases with increase of concentration of PEO (1%) in alcohols. Intermolecular free length also behaves in similar manner as that of adiabatic compressibility. Rao’s constant (R) decreases with increase of alcohol concentration and also with the increase of molecular weight of PEO. The acoustic impedance (Z) increases with increase of alcohol concentration and when the molecular weight increases, Z increases further. In all the three systems studied, the variation in ultrasonic velocity is not much appreciable at higher concentration when
compared to lower concentrations. This behaviour may be explained as follows, the molecules of synthetic polymers are randomly coiled in solution and the chains have no overall tendency to adopt any particular conformation. In general the polymer molecules are linear, consisting of a sufficient number of chain linkages, which is an essential prerequisite of chain, result from the interactions of chain segments with its environments. These interactions involved the segments of the same as well as the other chain in addition to the solvent. In a good solvent, each chain segment will prefer to contact with solvent molecules rather than with the segments of its own or those of neighbouring chains. Because of this, the chain will be extended. In a poor solvent, if the polymer – polymer and solvent –solvent contacts are favoured, the chain will have a contracted form [6]. Dissolved macromolecules frequently form molecular association complexes either with species of low molecular
Table 2 Ultrasonic velocity and related parameters of butanol, pentanol and hexanol in the solution of 1% PEO (6000) + water at 303 K Samples PEO + water + butanol
PEO + water + pentanol
PEO + water + hexanol
Conc. of electrolytes %
U (m s
0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10 0.02 0.04 0.06 0.08 0.10
1519 1523 1527 1532 1536 1525 1531 1536 1541 1546 1529 1533 1539 1544 1549
1
)
q (kg m 1036 1070 1089 1096 1103 1087 1093 1104 1112 1126 1089 1100 1106 1116 1127
3
)
g 103 (N s m 2)
b 1010 (N 1 m2)
˚) L f (A
V f 10
1.0152 1.0410 1.0498 1.0621 1.0798 1.0496 1.0619 1.0798 1.0886 1.0924 1.0527 1.0628 1.0813 1.0891 1.0975
4.0733 4.0292 3.9382 3.8875 3.8427 3.9558 3.9033 3.8393 3.780 3.7157 3.9279 3.8683 3.8174 3.7587 3.6981
0.4028 0.4007 0.3961 0.3935 0.3913 0.3970 0.3943 0.3911 0.3884 0.3848 0.3956 0.3926 0.3900 0.3870 0.3838
3.2111 3.1006 3.0697 3.0264 2.9600 3.0692 3.0279 2.9626 2.9362 2.9304 3.0728 3.0370 2.9710 2.9486 2.9243
4
p i 10 P 690 713 724 730 738 722 728 737 743 749 723 730 738 744 750
6
R
Z 106
2596 2516 2475 2461 2448 2481 2470 2448 2433 2406 2480 2457 2447 2428 2406
1573 1629 1662 1679 1694 1657 1673 1695 1713 1740 1665 1686 1702 1723 1745
U — Ultrasonic velocity; V f — Free volume; q — Density; p i — Internal pressure; g — Viscosity; R — Rao’s constant; b — Adiabatic compound; Z — Acoustic impedance; L f — Free length.
P.S. Ramesh et al. / Journal of Molecular Liquids 126 (2006) 69 – 71
weight solvent or with other macromolecules. In the case of PEO with alcohols, the variation of velocity indicates that there is a strong interaction between solvent and solute molecules. It may be due to the higher number of available solvated molecules for the interaction at lower concentration than at the higher concentration. Initially adding water to pure polymer, a number of H2O molecules are bonded by H-bonds with the oxygens of the oxirane groups, until there are two water molecules for each oxygen. Furthermore because of the hydroxyl end group a larger number of water molecules can be allocated in the first hydration shell of the polymer [7]. After adding the alcohols to the aqueous PEO solutions, the variation in velocity may be due to the addition of alcohols. Such an effect has been reported in other case of polymer solutions by Sundarasan [8]. The rapid decrease of adiabatic compressibility with increase of concentration in alcohol systems clearly indicates the formation of a large number of tightly bound systems. Since the velocity increases with concentration and the density does so, the compressibility must decrease with increase in concentration. This could be caused by a more rigid liquid structure associated with hydrogen bonding of PEO with alcohols. Such reduction in compressibilities has been found in the solution due to solvent molecules [9]. At lower concentration of PEO in alcohols the molecules are not closer and thus intermolecular length (L f) is high. In the more concentrated solution the molecules come closer and segment – segment interaction will exist, thereby decreasing the intermolecular free length and hence internal pressure increases. From the experimental analysis, it is observed that the number of solvent molecules solvated per polymer unit is observed to decrease with increase in the polymer concentration. This is due to the cohesion among the polymer chains and reduction in the hydrodynamic volume. Similar observation is made by Rajagopalan and Sharma [10]. If the variation of Rao’s constant with concentrations of one of the components is non-linear, it generally indicates a strong
71
association between molecules. As Rao’s constant varies nonlinearly with concentration it may be concluded that there is an association between PEO and alcohol molecules. The increase of acoustic impedance with increasing concentration in alcohol systems predicts a strong polymer –solvent interaction [11]. Hence it may be concluded that there exists polymer – solvent interaction through hydrogen bonding. The increase in velocity with butanol, pentanol and hexanol systems may be due to less hydrogen bonds formed at lower concentrations and at higher concentrations the hydrogen bonds formed may be more due to segment –segment interaction. When the molecular weight of PEO increases, the molecular effect is high when compared to lower molecular weight PEO. Further ultrasonic absorption work will throw more light on the structural aspects and relaxational behaviour of the three systems. Acknowledgement The authors are thankful to Dr. AN. Kannappan, Professor and Dr. R. Sabesan, UGC Professor, for encouraging them to take up these studies. References [1] A.M. Northy, R.A. Pethrick, B.T. Poh, Adv. Mol. Relax. Process. 19 (1981) 209. [2] R.A. Pethrick, B.T. Poh, Br. Polym. J. 15 (1983) 149. [3] P. Spickler, F. Ibrahim, S. Fast, D. Tannenbaum, S. Yun, F.B. Stumpf, J. Acoust. Soc. Am. 83 (1988) 1388. [4] R. Feng, Z. Chen, Acta Acust, (China) 7 (1982) 263. [5] D. Geetha, C. Rakkappan, Ind. J. Phys. 77B (5) (2003) 525. [6] W. Brown, Cellulose and Cellulose Derivatives IV, Inter. Sci. Publi. Inc., New York, 1965. [7] M.P. Jannelli, S. Magazu, G. Maisano, D. Majolino, P. Migliando, J. Mol. Struct. 322 (1994) 337. [8] B. Sundarasan, Polym. Int. 33 (1994) 425. [9] W.R. Moore, J. Polym. Sci. 16 (1967) 571. [10] S. Rajagopalan, S.J. Sharma, J. Pure Appl. Ultrason. 24 (2002) 1. [11] P.Z. Debye, Electrochemistry 45 (1939) 174.