Introduction to Dielectric Properties and Magnetism

Transcription

1 Intoduction to Dielectic opeties and Magnetism At the end of the last lectue we looked at some of the electical popeties of matte and intoduces the notions of electic field and electical conductivity. We shall now look at the inteaction of field with matte. l V- voltage diffeence κ lectic field in vacuum between two plates V V/l /( ), whee 8.85* - F/m dielectic pemittivity of fee space What is potential? otential diffeence is l/( ) and the capacity defined as: chage potential l l C

2 Dielectic popeties Lets now see what will happen if we fill the space between the plates with a dielectic (non-conducting mateial, we know what will happen if we fill it with conducting mateial). We will find that capacity o elative pemittivity inceased by a facto of dielectic constant of the mateial. ince in ou simple consideation is unchanged, then potential diffeence must change and not due to as that is the same too. Hence we conclude that oveall potential has changed by and theefoe the electic field is changed: V This eduction in field is due to polaisation of the mateial. The applied electic field distots atoms and molecules and oients existing dipoles in such a way as to ceate a field opposing to the applied field (it is as if mateial is tying to minimise the effect of the extenal field). Thus the esultant field is educed.

3 We now define polaisation as the electostatic moment (l) pe unit volume induced in dielectic. We can ewite as follows: Dielectic popeties cntd ( ) We can now see that is euivalent to chage pe unit aea and hence the effective chage on the plates is /- and V V V l l V l I I

4 olaisation of gases Gases: molecules (atoms) too fa apat4inteactionmatte. Thus each gas molecule sees and that affects them as follows: (i) By distoting the electonic cloud aound the nucleus of each molecule; we call the polaisation of this type e (ii) By stetching o bending bonds of pola molecules; a ~. e (iii) By oienting existing molecula dipoles: d Lets stat fom (i). As a esult of application of electic field to initially neutal molecule (atom) it will acuie dipole moment pα, whee α is the molecula (atomic) polaizabilty. Thus fo n molecules pe m we will obtain e npnα.

5 olaisation of gases: the case of neutal monoatomic molecules -Ze -Ze(x/) Ze -Ze Ze Ze x (positive chage) (negative chage) F Ze Ze 4πx this balanced by distotion foce F Ze euating we get Zex 4π p α α 4π e nα n4π 4nπ, but Zex p hence p 4π ( ) x 4π x Z e x 4π Thus, by measuing some macoscopic electical popeties (such as ) we can get info on micoscopic ones (such as ).

6 olaisation of gases: the case pola molecules Apat fom polaization pola molecules will show (ii) stetching o bending bonds of pola molecules (e. g. if field is applied at an angle to the intilial dipole moment) but a ~. e, so we shall neglect it and conside (iii) Oientation of existing molecula dipoles: d -e e p chage*sepaation.6* -9 C* - m.6* -9 Cm Å No field, no net momentum due to andomization. witch on field and all dipoles ae aligned, then d np, and fo a gas at T n * 5 m -, hence d 5* -4 C/m, and the field poduced is d d / 6* 7 V/m This would be moe then enough to ionize most gases, but expeiments show that this is not possible. Can you suggest why? The answe is tempeatue. Themal motion distots alignment of dipoles educing the net dipole moment and hence the electic field. Ou ough estimate will not be even achieved at absolute zeo due to uantum effect of zeo point motion. Can one suggest how the T dependence of net dipole moment would look like?

7 olaisation of gases: effect of feuency Lets also analyse the effect of alteing on electonic polaisation e. Assume mass m, chage e and an electon bound to nucleus by a foce with constant k (F-kx). Thanks to Isaac Newton, we have:.. F ma kx mx && kx o x ω x, wheeω k / m - natual vib. feuency Now, if we apply a sinusoidal electic field sinωt we will get: && x ω x x F / m e / m e sinωt m ω ω e sinωt p ex and we have a esonance effect just like on a swing m ω ω e np and we have a esonance effect fo too : e np sinωt fo which a steady state solution is

8 Dielectic popeties of liuid and solids (i) Weak inteaction (non-pola molecules) p 4π whee is atomic adius. Fo cubic stuctue in D n π np, but ( ) ( ) π This is the case fo many solids/liuids: -. We should point out that in a cystal which has a well defined stuctual anisotopy will depend on cystal diection.

9 Dielectic popeties of liuid and solids, cntd. (ii) tong inteaction. If we conside the case of inteacting dipoles the pictue becomes a little moe complicated. Not only thee will be a net polaisation due to applied electic field, but each dipole with p4π will poduce field p/4π at a distance. This field is compaable to the applied field itself and inceases polaisation effect. α π α fo weak inteaction nα now we will have o, α now depends on and so does polaisation which can now be anything fom the case of weak inteaction (if -) to lage dipole inteaction if 7. Few wods on feuency dependence of in solids. It has somewhat simila effect in liuids to that of gases, but moe sluggish due to stonge inteaction. Conseuently, has vitually no effect in solids as it is difficult o impossible to otate a bound pola molecule.

10 ummay olaisation due to electic field occus in the following ways: a. Distotion of electon cloud; all atoms (molecules) show this effect b. With pola molecules stetching o bending of bonds can poduce a small contibution to the polaisation c. With pola molecules oientation of the molecule may poduce vey lage polaisation, but the field has to compete with andomisation effect of T. T has no effect on (a) since this involves electonic popeties and electon enegies much highe then themal enegy (ev K). T esists incease of polaisation in (b) and (c), still polaisation can not incease indefinitely as we lowe T as mateials tuns into solid and it may become impossible to otate molecula dipoles. Feuency has maked effect on all types of polaisation. Oientation of whole dipoles becomes impossible at about Hz. tetching/bending becomes unable to follow field at 4 Hz. Only electonic polaisation emains up to 5-6 Hz. This is optical ange and theefoe the only pat of dielectic mechanism that plays pat in efactive index of the mateial. In the solid state the pictue is futhe complicated by stong inteatomic inteactions which can geatly incease polaisation effect in the mateial.