Journal of Electrostatics, 4 (!978) 267--282 267 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

ANTISTATIC FIBRES IN FABRICS AND CARPETS

J. LOWELL

UMIST, Sackville Street, Manchester, M60 1QD (Gt. Britain)

and

J.E. McINTYRE

ICI Fibres, Hookstone Road, Harrogate, Yorkshire, HG2 8QN (Gt. Britain)

(Received March 18, 1977; in revised form October 24, 1977)

Summary

The build-up of large electrostatic charges on carpets and textiles can be prevented by incorporating conducting fibres in them. How the fibres act has not, however, been clear. This work is an investigation of the mechanism by which the conducting fibres prevent charging.

Conducting staple fibres in fabrics minimise the effect of static electricity by, in ef- fect, distributing it uniformly across the fabric. If the fibres are .conducting on the out- side (epitropic fibres) they can actually prevent transfer of charge to the fabric if the material rubbing the fabric is moderately conducting.

In carpets, conducting filaments act in a quite different way. They limit the body potential of a person walking on the carpet by limiting the electric field which can exist between his shoe soles and the ground -- the conducting fibre promotes air breakdown by enhancing the field locally.

1. Introduction

Most materials can acquire electrical charge by contact or friction with other materials. At high humidities, particularly with textiles of high mois- ture regain such as wool and cotton, this charge rapidly flows away and is not noticed. At intermediate humidities, synthetic materials of low regain, and at low humidities all materials, have so high a resistivity that the charge does not readily leak away. A number of undesirable effects may result from the presence of static charge. For example, static electricity in textiles may cause an explosion; it can cause rapid soiling and it can cause "cling" between gar- ments. The charge generated when a person walks on a nylon carpet can cause a painful shock when he touches a metal object, especially in the very dry environments caused by central heating.

A wide variety of methods (recently reviewed by McIntyre [1] ) have been used to alleviate these problems. Many of these rely on chemical t reatment to promote adsorption of water and so increase the electrical conductivity

268

of the material. These methods tend to be inefficient in very dry conditions and lose their effectiveness as the humectant is removed by wear and cleaning. A more durable effect can be obtained by including a polymeric humectant in the fibre during manufacture, preferably as a dispersed fibrillar phase. This method, too, is less efficient under very dry conditions. A still more permanent remedy is the incorporation of a proportion of highly-conducting filaments in the cloth or carpet; successful filaments include stainless steel wires [2, 3] and polymer fibres loaded with carbon either on the surface [4,5] (epitropics) or internally as a "core" [6]. It seems clear that the effi- cacy of conducting fibres is not merely a result of their increasing the effec- tive conductivity of the fabric or carpet, for they work perfectly well at very low concentrations -- less than 0.1% of conducting fibres in a carpet can entirely eliminate shocks from charge generation. Although a number of alternative mechanisms have been proposed [1], none of them has been satis- factorily verified by experiment. The investigation reported here was carried out in order to clarify the mechanisms responsible for the absence of "s ta t ic" effects in textiles and carpets which contain conducting fibres.

2. Charging of textiles: effect of conducting fibres

We describe experiments to determine the effect of carbon-coated epi- tropic and conducting-core fibres on the charging of woven and knit ted Terylene staple fabrics.

In the first kind of experiment, we use a proof plane to investigate the spreading of charge which is initially deposited along a line across the fabric. The fabric (about 15 cm square) is held tautly in an insulating frame; a proof-plane (about 6 mm in diameter) connected to an electrometer is moved across the fabric at a uniform velocity of about 3 cm s -1 and the charge on the part of the fabric below the proof-plane is displayed on an xy-recorder as a function of the position of the proof-plane. Charge is depo- sited initially along a line perpendicular to the direction of motion of the proof-plane by drawing a metal rod across the fabric. By traversing the probe at different times after depositing charge, we can observe how the charge spreads. Figure l(a) shows how the charge spreads over a sample of Tery- lene fabric; the asymmetry for t ~ 0 is due to the fact that for small t the charge spreads rapidly in comparison with the speed of the proof-plane.

An interesting feature of these charge decay curves is the persistence of a small amount of charge (apparent in the curve for 6 min in Fig. l(a) which spreads much more slowly than the remainder of the charge. It is a feature of all the samples studied, but is too small to be of practical significance.

If the same measurements are performed on a sample of Terylene fabric containing 2% epitropic staple fibre uniformly blended into the Terylene yarn (Fig.l(b)) there is no detectable charge, apart from a small persistent charge similar to that commented on above. Figure l(c) shows the effect of con- ducting polyester staple fibres of the conducting-core (cc) type (provided by

269

D.D. Dunbur of ICI Fibres) also uniformly blended into the Terylene yarn. Charge is deposited at the position marked B at the instant when the tra- versing proof-plane is at the position marked A. The step at A in Fig.l(c) shows clearly that a large part of the localised charge deposited at B spreads very rapidly across the fabric. A small amount of charge remains localised at B, as in the 100% Terylene and the Terylene containing epitropic fibre (Figs.l(a), l(b)).

In the experiment with the epitropic fibres (Fig.l(b)) no step is found such as that occurring at A in Fig.l(c). We conclude that the action of the two kinds of fibres is quite different; epitropic fibres appear to prevent the deposition of charge on the fabric altogether, whereas conducting-core fibres do not prevent charge being deposited -- they merely cause it to spread very quickly across the fabric.

To investigate the difference in behaviour of the two types of fibre, we performed experiments to measure the total charge transferred to the fabric.

Charge / ~t~O sec

t PW 70 / / ;

l ,, ,oo sm,o • i !

B t |

It)

f

~Cff~.

Fig.1. Charge density as a function of position on a fabric sample at various times after depositing a line of charge. (a) 100% Terylene staple fibre; (b) Terylene staple fibre con- taining 2% conducting epitropic staple fibre; (c) Terylene staple fibre containing 5% conducting-core staple fibre.

2 7 0

A square of fabric about 15 cm X 15 cm is held tautly in an insulating frame; about 1 cm below the fabric is a metal sheet (much larger than the fabric) which is connected to an electrometer -- any charge deposited on the cloth induced an equal and opposite charge on the metal plate which, in turn, gives rise to an electrometer deflection proportional to the charge on the cloth.

Figure 2 shows the charge transferred to Terylene by rubbing with a brass rod. It is apparent that epitropic fibres almost entirely prevent the transfer of charge whereas conducting-core fibres have little influence on the charge transferred.

Table 1 summarises the results of several experiments of this type, using other materials as well as brass to rub the fabric. When the fabric is rubbed with a brass rod, the presence of epitropic fibres reduces the charging by about two orders of magnitude. Epitropic fibres are almost as effective when rubbed with a glass rod (which has a fairly good conducting surface under

A

Charge

h NO ANT ISTAT FIBRES

Z~

2% EPlTROPlCo(X IoO ) 0 o o o

O O O O no. of rubs

0 o

' " O O NO ANTISTAT FIBRES o -k

0 ×

+,¢ o ~ \ s ~

O I-%.1 ¢ C C -+. x-I- %

i i

t x X

Fig.2 . Charge on Terylene as a func t ion o f the number o f rubs with a brass rod. (a) (Woven fabrics o f corresponding weights ) 100% Terylene , Tery lene + 2% ep i trop ic fibre (X 10) ; (b ) (Kni t t ed fabrics o f corresponding we ights ) 100% Terylene , Tery lene + 1% cc fibre, Terylene + 5% cc fibre.

271

normal atmospheric conditions, due to a film of moisture on its surface), but they are much less effective when the cloth is rubbed with PTFE; the charge in that case is reduced only by a factor of two.

We conclude that epitropic fibres are very effective in preventing net charge transfer when Terylene is rubbed by conducting materials bu t com- paratively ineffective in preventing charge transfer from highly-insulating materials. We think that the lack of charge is due to back-transfer [10] be- tween the fabric and the rubbing material, as discussed below.

We now propose a model for the absence of localised charge in fabric containing conducting-core fibres, and for the almost complete absence of charge in fabrics containing epitropic fibres. It is difficult to believe that deposited charge simply flows away along the conducting fibres, for this charge should take an appreciable time to flow from the ordinary to the conducting fibres; but our experiments show that the spreading of charge is virtually instantaneous. We believe instead that the important mechanism is local charge cancellation; ordinary charged fibres induce charge of oppo- site sign on nearby conducting fibres, leaving charge of the original sign on remote portions of the conducting fibres (Fig.3). The net effect is to distri- bute the .:~eposited charge over the whole of the cloth; in addition to this distributed charge there is a localised "dipole" formed by the original charge deposited by rubbing together with the compensating charge on nearby conducting filaments. This dipole charge has little external effect since its field falls off very rapidly with distance. We have carried out a model ex- periment to verify the validity of this model. We used a sheet of PTFE in- stead of the cloth (charge remains localised almost indefinitely on the sur- face of PTFE). Thin copper wires were laid down on top of the PTFE to the line of charge and about 1/2 mm apart. Then, a line of charge was deposited perpendicular to the wires. Scanning the proof-plane across the line of charge, we found that conducting wires masked the charge on the PTFE almost com- pletely (Fig.4). The wires were then removed one pair at a time; the charge

T A B L E 1

C h a r g e ( in u n i t s o f 10 -11 C) o n c l o t h w i t h o r w i t h o u t e p i t r o p i c f i b r e s a f t e r 10 r u b s w i t h v a r i o u s m a t e r i a l s . E a c h v a l u e r e p r e s e n t s t h e m e a n o f f o u r t r ia ls , a n d t h e e r r o r q u o t e d r ep re - s e n t s t h e s p r e a d in t h e s e f o u r tr ials .

C l o t h r u b b e d Brass P T F E Glass w i t h ( e a r t h e d ) ( i n s u l a t e d )

c l o t h

T e r y l e n e - - 2 2 +- 5 +15 +- 3 - - 3 3 +- 12 T e r y l e n e + 2% e p i t r o p i c f ib re - - 0 . 3 + - 0 .4 + 8 -+ 1 - - 0 . 8 +- 0 .3

272

Conduct ing

J ~ Deposited Chorge

Fig. 3. Charge distribution on staple fibres after charge is deposited locally.

on the PTFE did not become apparent until the gap between the wires was comparable to the height of the proof-plane above the PTFE.

The model pictured in Figure 3 also accounts for the difference in the be- haviour of fabrics with epitropic and with carbon-core fibres. When, say, a metal rod is rubbed across the fabric the rod loses, say, q coulombs of charge; the cloth acquires a net charge q, which is distributed over the net- work of conduct ing fibres, and also a local "dipole" which, of course, con- tains no net charge. If the filaments are epitropic (conducting on the out-

L- . . . . . . t . . . . . . . - . . . .

Fig.4. Cancel lat ion of field o f loeal ised charge by nearby conductors . The curves on tbe left s h o w the signal on a proo f plane scanned across a l ine o f charge w h e n wires are ar- ranged in various ways across the charge.

273

side) contacts between the rod and the conducting fibres enable the charge - q on the rod to cancel the charge +q on the conducting fibres, leaving only the dipole. If, on the other hand, the conducting fibres are of the conducting- core type there cannot be any contact between the rod and the conducting fibres so that charge cancellation cannot occur and the fabric retains a net charge.

The difference in behaviour between samples with epitropic and con- ducting-core fibres suggests that the two kinds of fibre may differ in their efficiency as antistatic agents. In particular, if a fabric containing conducting- core fibres is rubbed, the conducting fibres may acquire sufficient mobile charge to produce strong electric fields if the cloth is brought close to a metal object. It may be, then, that conducting-core fibres are not as reliable as antistatic agents in such applications as clothing used in explosive atmospheres. To test this possibility, we carried out experiments to detect sparks while rubbing fabrics; we used an aerial feeding into a broad-band amplifier con- nected to a storage oscilloscope with a slow free-running time base to detect sparks by the radiation they emit. Figure 5 shows oscilloscope traces ob- tained when Terylene is rubbed with a glass rod; evidently, epitropic fibres are much more efficient than conducting-core fibres in suppressing sparks. Similar results were obtained when the fabric was rubbed with an earthed brass rod.

3. Antistatic fibres in carpets

It is known that conducting fibres of both the epitropic and conducting- core kinds are effective in preventing a person walking on a nylon carpet acquiring a sufficiently large charge to give a shock when he touches a metal object. We shall show that the mechanism by which conducting fibres pre- vent electric shocks from carpets is quite different from the mechanism by which they prevent charging of fabrics. Conducting-core fibres do not pre- vent charge transfer at all, and epitropic fibres only prevent charge transfer if the rubbing material is fairly conducting -- and shoe-soles are often high- ly insulating. We shall suggest below that conducting fibres in carpets exert their influence by promoting air breakdown. But we shall first develop a simple model to describe the build-up of the body potential of a person walking across a carpet, and then describe experiments on the effect of con- ducting fibres on body potential.

4. A model for the body voltage

In walking on a carpet, the charge transferred between carpet and shoe will generally depend on the charge already on the shoe -- presumably, the charge on the shoe will eventually saturate, so that no more may be added. However, if a single step results in the transfer of only a very small part of this saturation charge, and if, moreover, considerable loss of charge occurs by

274

Fig. 5. Oscilloscope traces showing sparks occurring when Terylene is rubbed with a glass rod. (a) 100% Terylene staple fibre; (b) Terylene staple fibre containing 2% conducting epitropic staple fibre; (c) Terylene staple fibre containing 5% conducting-core staple fibre

275

leakage, then this saturation charge is never approached. In that case, it is reasonable to suppose that the charge transferred is the same at every step. This appears to be so in our experiments, and we shall make it a basic assump- tion of the model.

We therefore assume that at each Step a fixed amount of charge transfer takes place, sufficient to increase the body voltage by v0.

We know from experiment that charge leaks away by conduction at an ap- preciable rate. We shall show below that when a person stands still on the car- pet his body potential falls according to an exponential law

V = constant exp(-t/r) (1)

at least for values of t much smaller than the time constant r. The time to during which one foot is in contact with the carpet while taking one step is much smaller than r, so we may assume that the fall in body potential due to this leakage is

a V= Vto/r (2)

per step. We add to this loss of potential the gain v0 per step mentioned above; if one walks across the carpet at a rate of N steps per second, the rate of change of body potential is therefore

dV/dt = Nvo-NVto/r so that

v= V°r [1--exp (--Nt°t --7-- (3)

The body voltage V rises with time constant r/Nto towards an asymptotic value Vo r/to.

In our experiments on the effect of conducting fibres in carpets, we used a modified version of the customary "stroll test" [8]. The person walking along the carpet kept his hand in light contact with a wire stretched between insulated supports. The wire was connected to an electrometer whose output was fed to a chart recorder. The carpet was laid on a wooden floor of fairly high conductivity; we found that metal foil placed below the carpet made no difference to the results, even if the metal was earthed.

Different samples of carpet of the same construction, and even different areas of the same carpet roll, can exhibit significantly different charging rates in the stroll test. In order to eliminate such differences, we always used the same piece of carpet. Continuous conducting filaments (metal wires, epitropic nylon monofilament, or conducting-core 24 dtex 3-filament nylon yarn) were introduced by laying them across the carpet in parallel lines, per- pendicular to the direction of walking. A single length was used in each case and laid back and forth in parallel lines about 2" apart. We made stroll tests after removing the wires as well as before laying them down; agreement be- tween these two tests confirmed that changes observed when conducting

276

fibres were present were really caused by the conducting fibres and not by changes in the carpet itself.

Figure 6 shows the results of stroll tests on the carpet at several different times during the course of our experiments (body potential is measured with both feet down on the carpet). The line is a plot of the relation

Y = 5.8(1--exp (--t/11.2)) (4)

and shows that the experimental data are adequately represented by eqn. (3). (The parameters in (4) were chosen by trial and error.) As an additional check, we have measured the decay in body potential of a person standing still on the carpet. For large values of the time the decay is non-exponential, but for the times of interest (~-1 s, the time during which one foot is in contact with the carpet) the decay can be represented, within experimental error, by an exponential of time constant 11.2 s as required by eq. (4).

Figure 7(a) shows the body potential as a function of time when uninsu- lated 26 s.w.g, copper wires, are laid across the carpet at 2 " intervals as de- scribed above. The dot ted curve is a reproduction of the line drawn in Fig.6 and represents the body potential in the absence of the wires; in addition we have shown portions of this curve displaced along the time axis. It can be seen that the body potential initially follows the same curve as for the carpet wi thout wires; when the body potential reaches a value of about 2.4 kV it drops suddenly and then begins to rise again in the same way as it did initially. Similar behaviour is apparent in later parts of the stroll test, interspaced with regions in which the potential varies erratically. This test is typical of several made with bare copper wires.

Body Potential kV

• ~.~%~o-~ o~z-** ~ -~, o • x x • oo.~ oo ~x ~xxx x~

• ~ Z a . . . . . x

. 4

20 40 60 t seC I I I _ ~ -

Fig.6. Body potential versus t ime in three different stroll tests. The solid line is a plot of eqn. (4).

277

The fact that the initial rise of the body potential is unaffected by the presence of conducting wires shows that the wires do not exert their influ- ence by enhancing the conductivity of the carpet or by changing the capaci- tance between subject and ground, for either of these mechanisms would change the form of the curve (eqn. (4)). On the other hand, the very sharp drops in body potential which occur when the potential reaches 2--3 kV strongly suggests that the body potential is limited by air breakdown, pre- sumably aided by the presence of the conducting wires.

Figure 7(b) shows a stroll test conducted on a carpet with epitropic fibres arranged in the same way as the copper wires in the experiment described above. The dot ted curve again shows the results obtained with the carpet alone (solid line in Fig.6). As in the experiment with copper wires, the initial rise in body potential closely follows the curve found for the carpet alone, and we again find sharp drops in the body potential which we attribute to air breakdown.

Figure 8 shows the effect of using conductors with an insulating coating; enamelled copper wire (Fig.8(a)) and conducting-core fibres (Fig.8(b)) give rise to very similar behaviour in stroll tests. We again note that the initial

6 Body Potent ia l ~ . - - - " -

kV ~ - " /

t I /

- 4 " / ' j / / s S

, , ' . . . - g. , , o r . ; . .4 .

k , " , t " " .7 " /t "

i f: J tirne

r 20 40 69

kV

i /

"211

(b/

I

r z ~ l ~ . 2 0 4 0 sec I ~ •

Fig.7. (a) Stroll test on a carpet with 26 s.w.g, bare copper wires laid in parallel lines at 2 " intervals perpendicular to the direct ion of walking. The do t t ed lines are the curve o f Fig.6 and por t ions of it displaced along the t ime axis. (b) Similar test with conduct ing epi t ropic monof i l ament .

278

rise in body potential is the same as it is when no conducting filaments are present. Discontinuous drops in potential are not evident in these cases; in- stead, the potential tends to flatten off at about 3 kV. We suppose that this levelling-off is again due to air breakdown but that the insulating coating of the wires limits the extent of the discharge, so that numerous feeble sparks occur rather than a few powerful ones. As might be expected, these insu- lated filaments are somewhat less efficient than metallic wires or epitropic fibres.

We have shown that the initial rise in body voltage during a stroll test is not affected by the presence of conducting fibres. This result shows that the action of conducting fibres in reducing the m a x i m u m body potential cannot be attributed merely to an increase in the effective conductivity of the car- pet, i.e. to a smaller value of T in eqn. (3). Nor can it be a~ributed to an in- crease in capacitance which, for a given charge transfer, would result in a smaller v0. Either of these mechanisms would give a form of potential rise quite different from that observed.

It is, in addition, clear from the experiments that the conducting fibres do not significantly influence the effective conductivity of the carpet. We have measured the fall of body potential as a function of time while standing

Body Potential kV /

, 4 / /

/ S..

, ' . ,~ , 2 1 "

,S i

i •

(al

t~V " ~ /

/ /

/ /

,,

r (b? i •

f 20 40 s¢c

Fig.8. Strol l tes ts in the presence of (a) 40 s.w.g, enamel l ed c o p p e r wires and (b) con- duct ing-core f i l amen t yarn. The d o t t e d l ines r ep roduce the solid l ine of Fig.6.

20 40 t s~c

279

still on the carpet, and we find that the presence of conducting fibres does not influence the decay significantly.

The experiments with metal wires (Fig.7(a) strongly suggest that the con- ducting filaments prevent the development of high body potentials by pro- moting air breakdown, as has been suggested previously [2, 7]. The con- ducting fibres "concent ra te" the electric field lines, so that air breakdown oc- curs near them. The experiments indicate that conducting fibres have a rather less pronounced effect on the body potential if they are surrounded by an insulating sheath. It is plausible that the insulating layer, by obstructing the discharge of ions, causes a space charge to build up so that discharge soon quenches. Each discharge reduces the body potential by a rather small amount -- but because the body potential remains fairly high, the discharges occur rather more frequently; the body potential does not fluctuate as much as it does in the case of filaments which have no insulation.

To at tempt a more detailed analysis, we shall consider a uniformly-charged shoe sole parallel to a conducting plane, and a conducting fibre between the shoe sole and the plane with its axis parallel to both (Fig.9). We ignore charge on the carpet in the vicinity of the conducting fibre, since it will be small com- pared to the charge on the shoe sole after just a few steps.

If the conducting fibre is short (i.e. shorter than the width of the shoe) the electrostatic field is easily calculated provided that the distance of the fibre from the shoe sole and conducting plane is large compared to its radius.

[ < W (a)

I

l + + + -~ + + ~ ÷ (3

, =+ + 1 ~ + +

_L_

(D)

Fig.9. (a) Field d i s t r i bu t ion for a sho r t and a long wire b e t w e e n a charged shoe hole and g round (view f rom side o f shoe) . (b) Charge d i s t r i bu t ion on a wire o f l eng th l u n d e r a show sole of w id th w which is u n i f o r m l y charged (view f ron t o f shoe) .

280

The fibre increases the field locally by a factor [12] whose maximum value is 2 -- perhaps a little more if the ends of the fibre are taken into account.

It follows that if the charging between shoe sole and carpet is limited by air breakdown, the presence of short fibres can reduce the charge density on the shoe sole, but only by a factor ~ 2. If, as in our experiments, the electric field due to the charge on the shoe sole is not sufficient to produce air break- down, then the presence of short conducting fibres cannot even reduce the charge density by 2. Indeed, if the charge on the shoe sole is less than half the critical charge at which air breakdown occurs, adding short conducting fibres to the carpet will achieve nothing.

The situation is quite different if long conducting fibres are incorporated in the carpet, i.e. if the length I of the fibres is much larger than the width w of the shoe sole. Charge from distant portions of the wire flows into the portion immediately below the shoe sole, attracted by the charge on the sole. The charge (per unit length) on the part of the fibre under the shoe sole may be quite large, and so, therefore, may be the electric field in the vicinity of this portion of the wire. So it is to be expected that when long conducting fibres are present the charge on the shoe sole is limited to quite low values. For a quantitative estimate, we must calculate the electric field in the immediate vicinity of the conducting fibre in terms of the charge on the shoe sole or, what is the same thing, the electric field in the absence of conducting fibres.

Suppose that a long wire runs below the shoe sole (Fig.9) and that the capacitance per unit length between the wire and the ground plane is C. The total capacitance of the wire can then be regarded as a capacitance Cw be- longing to the portion of the wire beneath the shoe sole and a capacitance C(l--w} ~ Cl belonging to the rest of the wire, these capacitances being in parallel. If l > > w, as we have assumed, then the potential of the wire is close to zero, so the charge Q on the portion of the wire underneath the shoe sole is given by (Fig.9)

Q/ Cw = --E ( b--a )

where E is the (uniform) electric field between the shoe sole and ground in the absence of the wire, - -E(b- -a) is the potential at the position of the wire in the wire's absence, and Q is the induced charge necessary to nullify this potential.

The local field, due to this charge, at a distance R from the axis of the wire is

Q/W --Ec(b--a) Elo c - - (assuming R < < a, b).

2~ eoR 2~eoR

Putting [12] C = 2~eo / ln [2 (b - -a ) r ] , we have

E loc b--a 1

E R ln[2(b--a)/r]

281

So the field is enhanced by an amount whose maximum value (R = r) is

Eloe /E = a b / r

where c~ = ( b - - a ) / b In [2 (b - -a ) / r ] is a constant which is close to uni ty pro- vided that the wire is not too close to the ground plane or shoe sole (a~--l/2b).

In the absence of the wire, the field below the shoe sole is V / b where V is the body potential. So, when the wire is present, the maximum local field is approximately V / b × ~ V/r , and if air breakdown occurs at a field E b (-~ 30 kV/cm), the body potential will be limited to V ~- rEb /a . If we consider the 26 s.w.g. (r ~ 0.2 mm) wires of Fig.4 and assume a--~l/2b --~ 2 mm then a ~ 1/6, and, if E b = 30 kV/cm, then V -~ 3.6 kV in reasonable agreement with the observations.

Reducing the wire radius will result in a smaller body potential. The re- duction in V will not, however, be in the same proportion as the reduction in r since the breakdown field tends to increase as r is reduced. But it seems quite reasonable to suppose that values of V ~ 1 kV may readily be obtained.

Air breakdown necessarily requires an initiating ion; it is easy to show that the usual ion concentration of 10 ions cm -3 is sufficient, thanks to the high mobility of ions in air (-~ 10 m/s per kV/cm) and the relatively long time (-~ 1 s) available for breakdown to occur.

It is rather difficult to estimate the area of shoe sole discharged at each breakdown event. This is unfortunate, since it is presumably this factor which determines the concentration of conducting filament necessary for effective antistatic action.

5. Conclusions

There are several distinct ways in which conducting fibres reduce "s ta t ic" effects in textiles and carpets. In textiles, epitropic fibres prevent any net charge being transferred to the cloth by rubbing, except when the surface of the rubbing object is a very good insulator. Conducting-core fibres do not prevent charge being transferred to the fabric but do allow the charge ef- fectively to distribute itself across the fabric and so minimise its effect. One important consequence of this difference between conducting-core and epi- tropic fibres is that conducting-core fibres are less efficient than epitropic fibres in preventing sparks when the fabric is rubbed.

In carpets, conducting filaments act in quite a different way. They limit the body potential of a person walking on the carpet by locally enhancing the electric field between his shoe soles and the ground, so that discharge occurs before a high potential is built up. Short conducting staple fibres blended into staple carpets have not yet been tested by these techniques, and the mechanism of their action may not be the same.

282

Acknowledgements

We are grateful to A.C. Rose-Innes and C.G. Cannon for valuable sugges- tions and for useful criticism. Mr P. Mossack gave us considerable help with the experimental work. Messrs D.D. Dunbar, M.A. Hems and M. Woods provided samples for evaluation and gave us valued advice.

References

1 J.E. McIntyre, Rep. Prog. Appl. Chem., 59 (1974) 99--108. 2 Unitika Ltd., ELESAFE antistatic working uniform, Jpn. Text. News, (Oct. 1974)

63--65. 3 G.F. Barry, Carpet static control with stainless steel fibres, Mod. Text. Mag., 50

(1969) 64--67. 4 Imperial Chemical Industries Ltd., U.K. Patents 1,391,262 (priority 22 June 1971);

1,417,394 (priority 18 Oct. 1971); 1,468,010 (priority 12 March 1973). 5 V.S. Ellis, Epitropics- third generation conductive fibres, Text. Manuf., 101 (1974)

19--23. 6 E.I. Du Pont de Nemours and Co., Inc., U.K. Patent 1,393,234 (priority U.S.A. 21

July 1972). 7 K.K. Teijin, U.K. Patent 1,242,686 (priority Japan, 18 Nov. 1967). 8 American Association of Textile Chemists and Colorists, Text Method 134 (1969).

Electrostatic propensity of carpets. 9 J.E. Blakemore, Text. Res.J., 44 (1974) 459--463.

10 J.A. Medley, J. Text.Inst., 45 (1954) T123; ibid., 48 (1957) 112. 11 H.R. Harper, Proc. R. Soc. London, Ser.A 205 (1951) 83. 12 B.I. Bleaney and B. Bleaney, Electricity and Magnetism, Oxford Univ. Press, 1965,

Chap. 2.