A simple calculation of dielectric loss from dielectric dispersion for polar polymers

Abstract

For polar polymers undergoing orientation polarization it is possible to calcula te diel ectric losses from dielectric constant data by use of a single approximation already familiar from its application to m echanical properties, if t h is approximation is applied to t he real part of t he dielectric constant only and if data over a suffi ciently wide freq uency range are available. Data obtained at frequen cies from 102 to 108 cycles per second for Butvar and for a copol ymer of styrene and methyl methacrylate are a nalyzed and it is fou nd that obse rved and calculated values of t he dielectric losses agree wi thi n 10 per cent or better .Equations r elating the real and the imaginary parts of the dielectric constant have been given , but are not in general use b ecause the equations involved are cumbersome [1 , 2, 3).1 ",;Yorker s mter ested in the mechanical behavior of high polymers h ave shown ho v the real and th e imaginary part of th e modulus of rigidity are r elated through a distribu tion function [4] and how this function can b e obtained by anapproximation m ethod from the r eal par t of th e modulu [5,6] and from both r eal and imaginary parts [7]. I t will be shown how the dielectric loss can b e calculated from dielectric con tant data by an analogous approximation m ethod.The D ebye equations [8], generaliz ed fo r a distribution of capacitance elem en ts wi th r esistance elements in parallel [9], each with its characteristic relaxation time, ma thematically equivalen t to a m echanical retardation time, are where e', e" are the r eal and th e imaginary part of the dielectric constant, withe angular frequen cy, r is the relaxation t ime and y (r) i the distribution of relaxation times. For mathematical convenience, we define y (r) dr = Y(ln r )d In r. The cut-off approximation [5,6,7] assuming the integrands in (la), (lb) to vanish for (tJr> 1 and to reduce to their numerators by difl"crentiaLion of (2a) wi th respect Lo the upper limi t and carry out this operation graphically. The exact eq (1 b ) is th en used to obtain e"2 by a graphical in tegration for each valu e of w. The integration i done o-raphically, beca use even th e most widely applicabl e equations that have been suggested for y (r) on semi empirical grounds [2,10] and that migh t have been expected to r epresent th e results cited do no t fi t th e data over th e en tire frequency range and because, if th e curve for Y(ln T) is approximated in sections by simple analytical expressions, in tegration often b ecom es impossible. Data are presented over a wide frequency rano·e, including ei ther side of the absorption maximum, for Butvar (polyvinylbutyral) [11], a m aterial which, for an unplastieiz ed polymer, has a fairly sh arp dispersion and for SM-2, a copolymer with a broad dispersion made from 49-mole-percent styr ene and 51-mole-percent m ethyl methacrylate ; bo th polymers h aving n egligible d-c conductivi ty (tables 1 and 2).In each case th e calculated valu es of e", which can be obtained for points at least one dec...

Dielectric properties of teflon from room temperature to 314-degrees-C and from frequencies of 10_2 to 10_5 c/s

“…Such a variation would not be expected in view of the very low values of the dissipation factor. The frequency dependence of the dielectric constant can be predicted from the observed values of the loss factor by extending [3] a procedure already described [4] …”

Dielectric relaxation in a styrene-acrylonitrile copolymer during and after its polymerization

“…e., the two fun ctions are simply related through a constant over their entire spectrum, and by (6), (ll), and (15) Y(lnr)=-1/2.303 dfoe~j= -2/7r e' dd~~;'j1. (16) The appearan ce of the fa ctor 2/7r immediately explains the discr epan cy between the ob erved and calculated values of e" noted previously [15], since the use of approximation (9) …”

“…The ame treatment applied to the electrical case would result in Y(lnl / w)=-e" dlog(e"/w). dlogw (7) A ha b een pointed out [15], the use of th e approximation resulting in (7), when used in the calculation of e" from e' , leads to values that are 30 to 40 percent too small. The reason for this discrepancy is that, wh ereas the approximation made in the calculation of (6), namely, (8) is excellent, the approximation which results in (7), namely, …”

“…Equation (17) provides a very convenient first approximation conn ecting dielectric dispereion and loss. Table 8 gives a comparison of values of the loss factor as observed and as calculated by the procedure previously described [15], i. e., through use of eq (6), followed by (5). It also presents values of Y(ln r ) calculated fr.om r eal and imaginary parts of the dielectric constant through the use of eq (16).…”

“…The systems investigated there~ fore show the high values of both heat and entropy of activation commonly observed for dipolar relaxa~ tion in high polymers [11]. It has been shown that distributions of r elaxation times can be calculated from dielectric dispersion [9, 15,16] and that dielectric losses can be calculated from dielectric-constant data without introducing any assumptions concerning the form of the distribution function [15]. We have for a linear dielectric of very small d-c conductivity:…”