ied interestingly because of their potential applica- tions such as light-emitting diodes, batteries, electro- magnetic shielding, gas sensors, antistatic and anticor-.
Indian Journal of Chemical Technology Vol. 9, March 2002, pp. 134-136
Estimation of dielectric constants of some polyamides by group additive methods Muneera Begum", A Varada Rajulub & Siddaramaiaha* "Department of Chemistry and Department of Polymer Science & Technology, S 1 College of Engineering, Mysore 570 006, India bDepartment of Polymer Science and Technology, S K University, Ananthapur 515 003, India
Received 22 April 2001; revised 22 No vember 2001; accepted 28 December 2001 The dielectric constants (£) of some polyamides (nylons) have been estimated by employing five different equations based on the group additive principle. The estimated values have been compared with the experimental values. The suitability of individual equations is discussed.
In recent years, conducting polymers have been studied interestingly because of their potential applications such as light-emitting diodes, batteries, electromagnetic shielding, gas sensors, antistatic and anticorrosion agents and field effect transistors 1· 6 • Much research has been carried out on the thermal stability of engineering polymers. The glass transition temperature (Tg) is a unique feature of macromolecules and is very important in polymer characterization since the processing temperature of end used temperature of a polymeric material are highly dependent on its Tg. The authors have estimated the thermal parameters by group additive methods for some polyamides (nylons)7. A knowledge of the dielectric constant (£) values of the polyamides helps one to choose the materials as a right dielectric. In the present paper, the authors have estimated dielectric constant values of twelve polyamides employing five semi-empirical equations based on the 8 group additive principle proposed by Askadskii , 9 10 II · Darby , Scott and Vankrevelen . The est1mated values have been compared with the experimental ones.
Here, n can be estimated using the Eq . (2) :
R= nz -1 x N A :L~V; 2
n +2
.. . (2)
Kav
where, N A is the Avogadro number, 2:~ V; is the van der Waals volume of the repeating unit of the polymer, R is the molar refraction of the repeating unit and Kav is the packing factor whose value is 0.681 for amorphous polymers in bulk 8 . The dielectric constant is related to the molar polarization (PLL) in terms of molar volume (V) as: E -I
PLL
=--
£+2
v
£is also related to Pv - the molar polarization in terms of molecular weight M of the repeating unit as: .. . (4) 9
Theory The dielectric constant (£) of a polymer may be expressed in terms of the refractive index (n) by the Maxwell's relationship: . .. (I)
*For correspondence (Fax : +91-0821-515770; E-mai l : siddaramaiah @yahoo.com)
Darby et a/. suggested a correlation between the Hildebrand parameter (8) and the dielectric constant as: .. . (5) The 8 can be estimated using the Hildebrand and 10 Scott relation as:
8= p:LE M
... (6)
BEGUM eta/.: ESTIMATION OF DIELECTRIC CONSTANTS OF SOME POLY AM IDES
135
Table !--Estimated and experimental values of dielectric constant (E) of pol yam ides along with % deviation Polymer
Nylon 6 Nylon 7 Nylon 8 Nylon 9 Nylon 10 Nylon II Nylon 12 Nylon 6,6 Nylon 6,10 Nylon 4,6 Nylon 4,10 Nylon 10, 10 Average
Exptl. Values
Eq. (I)
% Deviation
Eq. (3)
% Deviation
Eq. (4)
% Deviation
Eq. (6)
4.2
2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.31 2.31 2.31
44.7
4.14 3.80 3.56 3.39 3.25 3.15 3.06 4. 14 3.56 4.67 3.80 3.25
1.4
4.06 3.84 3.64 3.49 3.37 3.27 3.18 4.07 3.64 4.40 3.83 3.37
3.2
3. 14 3.06 3.01 2.96 2.92 2.89 2.86 3. 14 3.01 3.09 3.06
3.2 4.0 3.5
3.4
27.5 42 .0 33.7
32.0 35.9 (% )
4.4 3.5 1.7
4.4 3.08 (%)
where, p is the density of the polymer and I.E is the sum of the molar attractive constants of all chemical groups in the repeating unit. 8 can also be estimated with the help of Askadskii 8 as:
8 2 = I.l'iE; N;I.I'i V;
". (7)
where, 2.11.£; is the cohesion energy of individual atoms in the repeating unit.
Results and Discussion The diel ectric constant va lu es of all the polyamides have been estimated using Eqs (!), (3), (4) and (5). While employing Eq. (I) the refractive index has been estimated using Eq . (2). The required R and 11. V; val8 ues have been taken from the literature . Whiie employmg Eqs (3, 4) the required values of PLL and P v 11 have been taken from the literature • In order to estimate £ using ' Hildebrand parameter Eqs (6) and (7) have been employed. The required values of I.E, p and 2.11.£; have been taken from the appropriate sources 12' 13 ' 8.
0.6 1.7 4.0
%
Deviation
25.2
10.6 21.5 14.3
Eq. (7)
4.89 4.68 4.5 1 4.37 4.25 4. 16 4.07 4.89 4.5 5.16 4.68
%
Deviation
16.4
27 .2 22.3 28.6
0.9 2.10
17.9
23.6
(% )
(%)
(% )
may be due to the fact that £ is generally measured at 2 9 relatively low frequencies (10 to 10 Hz) where, n is 14 measured in the range of visible light (5 to 7x l0 Hz) while employing Eqs (3) and (4). For the estimation of£ from 8 values, when Eq . (6) has been employed an average deviation of 17.9% has been observed whereas the deviation is higher (23 .6) when Eq. (7) has been employed . Though both these equations appear to be similar, the lower accuracy of Eq . (7) is due to the consideration of van der Waal s volume and cohesive energy of individual atom s rather than the groups 10 in the repeating unit. Thus, the dielectric constants of polymers can be estimated accurately using Eqs (3), (4) and (6).
Conclusions The dielectric constants estimated using molar polarization and Hildebrand parameters [using Eq. (6)] are found to be nearer to the experimental values whereas, large deviation between the estimated and experimental values is found when refraction and so lubility parameter are used ru si ng Eq . (7)].
Acknowledgement The estimated values of£ using Eqs (!), (3), (4) and (5) together with Eqs (2), (6) and (7) have been presented in Table I along with the experimental values 13 . The percent deviation in each case is also presented in the same table. An average deviation of 35.9% is observed, when Eq. (I) invo lvin g the refractive index has been employed. The large deviation
One of the authors (SR) thanks Department of Science and Technology , New Delhi for SERC- visiting Fellowship.
References I 2
P·arker T D, J Appl Phys , 75 ( 1994) 1656. Matsunaga T, Daifuka H, Nakajima T & Kawagoe T, Polvm Adi' Tech , I ( 1990) 33.
136 3 4 5 6 7 8
INDIAN J. CHEM. TECHNOL., MARCH 2002
Bigg D M, Adv Polym Tech, 4 ( 1984) 255. Sotomayor M P T , M-A , De Paoli & Oliveira W A, Anal Chem Acta, 353 ( 1997) 275. Jeeva nanda T, Palaniappan S & Siddaramaiah, J Appl Polym Sci, 74 (1999) 3507. Sumura AT, Fuchigami H & Koezuka H, Synth Met, 1181 ( 1991) 41. Muneera Begum, Varadarjulu A & Siddaramaiah, J Polym Marl, 17 (3) (2000) 329. Askadskii A A, in Polymer Year Book 4, edited by Pethrick R A (Hardwood Academic Publishers, London), 1987.
9
Darby J R, Touchette N W & Sears K, Polym Eng Sci, 7 ( 1967) 295.
10
Hildebrand J H & Scott R L, Solubility of non-Electrolytes (Reinhold Publishers, New York) 1970.
II
Vankrevelen D W, Properties of Polyme rs (Elsevier Science Publishers, Amsterdam) 1990.
12
Billmeyer F W, Text Book of Polymer Science, (John Wiley and Sons, New York), 1984.
13
Bandrup J & Immergu E H (Eds), Polymer Hand Book, 3'd Edn (Wiley-lnterscience, New York ), 1989.
