Anchoring strength of a nematic liquid crystal on a ferroelectric crystal interface

Anchoring strength ^{of a nematic} liquid crystal ^{on a} ferroelectric crystal

interface

M. Glogarova (1) and G. Durand (2)

(1) Institute of Physics, Czechoslovak Academy ^of Sciences, ^{Na Slovance} 2, ¹⁸⁰⁴⁰ Prague ^8, Czechoslovakia

(2) Laboratoire de Physique ^{des Solides,} Université de Paris-Sud, ^Bât. 510, 91405 Orsay Cedex, ^France

(Reçu ^{le 30} septembre ^1987, revise le 9 mai, accepté le 16 mai 1988)

Résumé.

En utilisant

montage magnéto-optique,

étudions la biréfringence d’une cellule coin

remplie ^du nématique à l’ambiante MBBA (methoxybenzylidenebutylaniline). La cellule est formée d’une lame clivée de TGS (sulfate ^de triglycine) ^et d’une lame de

Le TGS est traité

silane pour donner

orientation homéotrope. ^{La lame} opposée donne dans

premier temps

orientation planaire, puis homéotrope. ^{Dans les deux} cas, l’ancrage homéotrope ^mesuré

^{le TGS est faible,}

longueur d’extrapolation ^L

^{2.0 ± 0.2} 03BCm. L’ancrage suit la loi simple ^de Rapini-Papoular. Aucun effet polaire n’apparaît, ni d’une éventuelle polarisation ^de surface, ^{ni du} changement d’orientation des domaines

ferroélectriques ^{du TGS.}

Abstract.

Using

magneto-optical set-up,

study ^the birefringence ^of

wedge cell filled with

temperature nematic MBBA (methoxy benzylidene butyl aniline). The cell is constituted by

^TGS (Triglycine sulfate) ^cleaved plate ^and

glass plate. The TGS is silane treated to give

homeotropic orientation. The

antagonistic plate gives initially

planar alignment, ^{and after}

^time

homeotropic

^{In both} cases, the

homeotropic anchoring

TGS is found weak, with

extrapolation length ^L

^{2.0 ± 0.2} 03BCm. The anchoring

follows the simple Rapini-Papoular ^{form. No} polar ^{effect is} found, neither from

possible ^surface polarization,

nor

from the change of orientation of the ferroelectric domains of the TGS plate.

Classification

Physics ^Abstracts

61.30

1. Introduction.

Anchoring properties of nematic liquid crystals ^on

solid surfaces are of great interest, for both funda- mental and applied ^{reasons. A} study ^{of the} anchoring

allows us to understand the nature of interactions which align nematic molecules preferentially along

an easy direction. The mastering of the surface

anchoring also allows specific electrooptic ^{devices to}

be made. Up ^to now, the mostly studied materials

[1] ^were typically amorphous glasses, with various

coatings (indium ^{tin oxide, for} instance), ^{used to}

build up transparent electrodes or to define ^a

preferred ^direction (oblique silicium oxide evapor-

ation, ^or polymer coating). Alignment by crystalline

solids is also interesting, ^{since it} presents orienting properties along ^various crystallographic ^directions [2]. ^In addition, crystals ^can possess ^an intrinsic bulk

polarity, which could enhance the natural polarity ^of

a solid-liquid interface, ^and eventually give ^{rise to}

new polar ^{effects on the} anchoring properties. ^{In this} work, ^we present ^the first determination of the

anchoring strength ^{of a standard room} temperature nematic liquid crystal, ^the methoxybenzylidene butyl ^aniline (MBBA) ^{on the} surface of the fer- roelectric crystal triglycine ^sulfate (TGS)

[(NH2CH2COOH)3 ^x H2SO4 ].

The spontaneous orientation of nematic MBBA

on a cleaved surface of ferroelectric TGS has already

been studied [3]. ^MBBA gives ^a planar alignment (i.e. parallel ^{to the} interface), ^{with an} azimuth which

depends ^on the ferroelectric domain orientation of the bulk substrate. When the spontaneous polariz-

ation Ps is oriented from the surface toward the

crystal, ^{i.e. on} negative domains, the nematic direc- tor is parallel ^{to the} c-crystallographic ^{axis of TGS.}

When Ps ^is opposite (positive domains), ^{it makes an} angle ^{of 58°} with the c-axis. As the c-axis is

approximately ^an axis of the optical indicatrix, ^this

orientational change ^{allows us to} visualize the fer- roelectric domains of TGS by observing ^the sample

between crossed polarizers.

To measure the anchoring strength ^{of a} given surface, ^{one must} determine the surface orientation

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019880049090157500

in the presence of ^a destabilizing ^surface torque which will change the surface director ^n. This

destabilizing torque ^can originate ^{from a curvature} imposed by ^an antagonistic boundary, ^{as in a} hybrid

cell [4], ^{or from a} magnetic ^field [5], for instance.

The surface orientation can be deduced from the

change ^of birefringence of the nematic slab, ^under

the effect of the surface torque. Because TGS is

already ^a birefringent material, ^it is very complicated

to measure the anchoring strength ^{of a} planar alignment ^{for a} twist distortion. We must specialize

on planar distortions, where the director remains in the plane ^{normal to the} interface, which contains the c-axis of the TGS substrate. We have first tried to build a hybrid cell, using the c-axis planar ^oriented

TGS and a silane coated homeotropic (normal orientation) glass plate. ^{In fact, this} hybrid alignment

is not stable, ^and gives ^{rise to a uniform} homeotropic

orientation. We have measured the anchoring strength of this stable homeotropic anchoring ^of

MBBA on TGS, using ^{an external} magnetic ^{field to}

create the destabilizing ^surface torque.

2. Model of a distorted interface.

We are just interested in the optical behaviour of ^a nematic cell under the action of a large magnetic

field. We assume a planar anchoring ^{or a} very weak

homeotropic anchoring ^{on one} plate, ^{so that the} change ⁱⁿ birefringence ^{is dominated} by ^{the be-}

haviour of the other interface under study, ^{here the}

TGS homeotropic interface. The director distri- bution n(z) (n2 = 1) is characterized by ^its angle

0 (z ) with the easy direction

(z2 = 1 ) ^{normal to the}

TGS interface (see Fig. 1). ^A magnetic ^{field H is}

Fig. ^1.

^Cell geometry. ^The

^field alignment

^the

lower TGS plate ^is homeotropic (n//z ).

aligned parallel ^to the c-axis of the TGS substrate, ⁱⁿ

the direction x. At the TGS surface, ^for large fields,

0 goes ^to 7r/2. ^{We call u}

11’ /2 - (J ^{the small} angle

of ⁿ compared ^{to the} plate. ^{We use the} one-constant curvature K approximation. ^{From a} standard calcu- lation [6], ^{we can write for u the} expression :

where 6 is the coherence length associated with the

applied magnetic ^{field :}

X a is the diamagnetic anisotropy of the material. The surface angle us is determined from the equilibrium

between the curvature elastic torque ^K de

I z ^and

dz 1,=o the anchoring torque ^at the interface. To define the surface anchoring strength, we assume a Rapini- Papoular (R.P.) ^form

for the surface potential, where L is the usual [6]

extrapolation length (0.1 ^{tim L 10} jim ) ^{to be}

determined. The surface torques equilibrium ^can

then be written as :

Expanding (4) for small us, ^we obtain :

The director becomes planar (us

0) ^{for a critical}

field HL corresponding to ç(HL)

L, ^{i.e. to a} field :

Below and close to HL, ^{one can} compute ^the change

in birefringence ^induced by ^the mangetic field. For H = HL, the whole texture is planar ( 9

’IT /2),

with the birefringence ^An = ne - n,. (ne and n. ^are the extraordinary ^and ordinary refractive indices.) An (H) ^{is a} function of ^u. Writing ^{as usual}

n2 _ n2

R = n; - 2’ n; ^{one can} express the apparent ^extraor- ne

dinary ^{index n, for a} light ^wave propagating along ^z

as :

for small u(z). Integrating ^{over the} profile u(z) given by (1), ^{one obtains, for the} optical path

difference dr

FL - r (H) between the planar

texture (r L) ^{and the} weakly ^{distorted one} (F(H)),

the expression :

Air can be expressed ^versus H, ^{as :}

which is linear in H- 1. _However, because, ^{of the}

small u approximation, âT is also linear in H - HL

for H close to HL.

This calculation has been made with the Rapini- Papoular ^form K cos2 us for the surface potential

2L

Ws. ^{The more} general ^{form for} Ws ^{with a maximum}

at us

0 and the n - - n symmetry would have been written for small us ^{as :}

which would have given for us the value

Imposing ^{the same curvature as the R.P. form, we}

d2Ws

must write

2

K/L. ^{For the R.P. form,} dus us = 0

d4Ws d2Ws ^{4 K}

---l- dus o = - 4 ----;.. = L’ ^{which results in}

- -

4

dus ^{o L} which results ^m

equation (5). ^{For an} arbitrary potential, ^{we can}

define a dimensionless number a by :

i.e.

In principle, the observation of HL gives ^{the curva-}

d2Ws

ture dus 2

us -

of the surface potential, ^i.e. gives ^L dus Us = 0

with the reduced units of surface energy K/L. ^The

measurement of AF(H) ^{for H} HL gives ^{the fourth}

derivative

dus 4 us - 0

i.e.

A significative ^devi- d s us

⁰

ation from

= 1 would invalidate the R.P. form.

3. Experimental ^results.

A TGS single crystal is cleaved to result in ^a 8 x 5 x 1 mm 3 plate, with the main plane ^{normal to}

the Ps direction. A layer ^{of MBBA on the main}

surface revealed the positive ^and negative ^domains

of the ferroelectric TGS, ^as bright ^{and dark areas,} respectively ^when observing ^the sample ^{under a} polarizing microscope [3]. ^{We then put on the}

MBBA layer ^a coverglass coated with DMOAP silane [8]. ^{Within a few} seconds, ^{the contrast is lost} and the cell constituted by ^{the TGS, the MBBA}

layer and silane plate becomes dark at the optical

extinction orientation of the TGS substrate. We have measured independently ^the optical path ^differ-

ence of the TGS plate ^alone, and of the total cell, using ^an optical compensator. ^{Within our} exper- imental accuracy, they ^are equal, ^{for the same}

observation point. ^{This means} that the MBBA is

aligned along the normal z to the plate, ^{i.e. is} homeotropically oriented. This orientation is found stable. It is the strength ^{of this} homeotropic align-

ment which has been measured at room temperature

(T

²⁰ °C ), using ^the following set-up : ^we replace

the silane coated upper plane by ^{a SiO} oblique evaporated ^cover plate which is known to provide ^a planar anchoring ^{on MBBA} [1]. The direction x of this planar anchoring ^{is oriented} parallel ^{to the c-axis}

of the TGS substrate. The cell is wedge-shaped, ^with

a variable thickness d from 0 to 50 _03BCm. This shape ^is produced by using ^a single wire spacer ^{on one} side

(see Fig. 2a). ^{In fact,} the TGS cleaved surface contains many cleavage steps, ^of depth up ^to several 03BCm. This makes an absolute determination of the cell thickness impossible, and then of r (H). ^We apply ^the magnetic ^{field H,} up ^to 14 kG, along ^{x, to} keep the distortion in the (x, z) plane (see Fig. 1).

To measure AF, ^we illuminate the sample ^with

monochromatic light ^{of wave} length ^A

^{0.546 )JLm}

under crossed polarizers. ^{We count} the number of

fringes (and fraction of fringes) which pass when

increasing ^H through ^a particular point ^{of the TGS} surface, for the twelve positions ^{of the} wedge ^cell,

shown in figure ^2b.

Fig. ^2.

a) ^The wedge geometry. ^The angle is exagger- ated. b) Location of the observed points inside the cell,

along

In principle, ^{for a} planar-homeotropic (hybrid)

cell with weak anchoring, ^we expect ^a rapid ^increase

of T (H) for low field (g ’" d), in the kG range,

corresponding ^{to the texture} change, ^{and a slower}

linear increase close to r L, in the 10 kG range,

(6 - L) corresponding ^to the saturation of the surface anchoring. ^We do find such ^a behaviour for

some points of the cell as shown in figure ^{3 which} represents ^r (H) - ^r (0) ^for position ⁴ (d - ³⁵ 03BCm).

A saturation FL ^is observed above HL ^{= 11 kG.}

Note that the initial increase of r (H) ^{shows no}

apparent threshold, ^as expected ^{for the} already

distorded hybrid cell. For some other points ^{of the}

Fig. ^3.

Magnetic ^field dependence ^{of the} optical path

difference r (H) - r(0) ^for point 4. The dotted line is the calculated dependence ^{close to} HL, assuming

Rapini- Papoular model. The H

0 texture is hybrid.

cell, ^like position ¹⁰ (d - ¹⁵ )JLm), ^we have found a more complicated ^behaviour (Fig. 4) : r (H) ^first

shows a rapid ^{increase with an} apparent threshold, Hc ^{and then two linear} regions ^{close to} the maximum value T L. The threshold appears for 1.7 kG. This compares well with the estimated value

K 1/2 1

Hc = ( K ) 1 = 1.6 kG ^{for a} homeotropic

Xa d

sample of thickness 15 _03BCm, using ^{the value}

( - 1/2 ^{= 2.4 cgs [9]. We guess that, at such a}

Xa

point ^{of the} cell, ^{the two} boundaries must give ^a homeotropic alignment. This could also explain ^the

two linear regions ^{close to} saturation observed on

r(H): we measure simultaneously ^{two different} anchoring strengths, ^{one for each} homeotropic boundary.

Fig. ^4.

^Same

figure ^{3, for} point ^{10. The H}

⁰

texture is homeotropic. He is the threshold field. The two linear regimes ^must be associated with weak anchoring

the ^two TGS and glass plates. HLl corresponds ^to TGS,

HL2 ^{to the glass.}

To check this interpretation, ^we have measured the maximum increase observed of optical path

difference r(HL) - r(0)

T L, for the various ob-

served points ^{of our} wedge cell. The results are

plotted ⁱⁿ figure 5. The solid lines represent ^the calculated values of r L (d) ^{for a} hybrid cell which becomes planar (curve A) ^{and for a} homeotropic ^cell

which becomes planar (curve B). ^The birefringence

of MBBA is taken as [10] : ^{An= 0.225, with}

R

0.239. The birefringence ^{of the} hybrid ^{cell with} 0s

0 is calculated according ^{to reference} [4] ^as

0.104. TL ^{for the} hybrid ^cell (A) ^is obviously ^weaker

than the full birefringence d(ne - no) of ^{curve B. We}

do observe a separation ^{of the data in two} groups,

one around the line A (data 2-5), the other around the line B (data 6-13). ^{From this} correlation, ^{we can}

conclude that for data 2-5, ^the starting alignment (for ^H

0) ^was hybrid, although for data 6-13 it was

homeotropic. This classification is trivial when ob-

serving ^a nematic slab between two amorphous glass plates. ^{It is more delicate in our case, where we}

observe the nematic texture behind the optically anisotropic ^TGS crystal.

Fig. ^5.

Saturated value TL=T(HL)-T(O) ^{of the} optical path difference magnetically induced in the cell,

versus

the thickness d, for the 12 observed points. ^{Line A}

is calculated for the H

0 hybrid texture, B for the H

0 homeotropic ^texture.

As expected, data 2-5 for the initial hybrid ^orien-

tation only ^{show one linear} region ^for T (H) ^{close to} large H, ^{as in} figure ^{3. This} dependence ^{can then be} safely attributed to the TGS homeotropic anchoring potential, ^{close to} 0 s

7T /2. ^{Note that, on the}

average, T L is smaller than the one calculated on curve A. This can be attributed to the large ^thickness uncertainty, ^{related to the} cleavage steps ^{on the} TGS surface. Anyway ^the possibility remains that the H

0 alignment ^{on TGS is not} exactly ^homeo- tropic. ^{We do not} believe this to be the _case, since when preparing ^the sample, ^{we have} definitely

observed the full planar ^to homeotropic change ^of

orientation on the TGS surface. Anyway, ^the starting

orientation is not important ^{for the} anchoring energy determination.

Data 6-13 are also a bit scattered around the line B, probably ^{for the same} large absolute thickness

uncertainty. They ^{do show two linear} parts ^{in the}

T (H) ^{curve for} large ^{H, as in} figure ^{4. This means}

that, for these data corresponding ^{to an initial}

homeotropic orientation, ^we do observe two weak

homeotropic anchorings, ^{one as} expected ^{on TGS at}

H

HL1’ ^{and the other on the glass, for H}

HL2. ^It

is interesting ^{to note that data 6-13} have been taken 2 hours after the 2-5 data collection. One can

presume that the homeotropic anchoring ^{of the} planar glass plate ^{has been induced} by ^{some silane}

molecules dissolved in the nematic material.

4. Anchoring strength analysis.

From the data, ^{we can} essentially ^{draw two} indepen-

dent experimental parameters : ^the saturation field

HL ^{and the} slope ^{of the} F (H) ^curve in the linear

regime ^{close to} HL. Concerning HL, ^{we must first}

decide for the double saturation field data 6-13 which one to choose. Comparing with the 2-5 data,

the one which _compares better is the largest HL

HL1 ^{which we attribute to the TGS anchoring.}

Using ^the magnetic data of reference [9], ^{we have}

calculated the values of the surface extrapolation length L for all the observed positions ^{of the} homeotropic anchoring ^{on TGS. The detailed data}

are listed in table I. On the average ^we find L

2.0 _{um ±} 0.2 _jim, which corresponds ^{to a rela-} tively ^weak anchoring.

We have analysed ^the slopes of the linear depen-

dence of r (H) ^{close to} HL, ^{to derive a. The data for}

«

are plotted ^{in table} I, for all the observed positions.

On the average, ^we find a

0.86 ± 0.24. Within

our experimental accuracy and because of the

simplicity ^{of our model} (the ^one constant K approxi- mation), ^{we can} say that the R.P. form describes

reasonably ^{well the} saturation behaviour of the

homeotropic ^surface potential ^{close to} 0s

7r/2.

One of our motivations, ^{to measure} the surface

anchoring ^{of TGS, was to look for} possible polar

effects from the ferroelectric nature of this material,

and from the solid-liquid ^interface symmetry ⁱⁿ general. ^{In absence of bulk} ferroelectricity, ^the polar symmetry of the interface alone allows for the existence of one (or ^a few) nematic molecules ferroelectric layer ^{at the TGS} nematic interface.

Some consequences of this surface polarity ^have already been discussed [11]. One of these conse-

quences ^{is the} existence of a polar ^term [12]

~

cos 8s in Ws. ^This polar ^term prevents ^the planar

orientation from being ^an equilibrium orientation at the surface, ^{so that one does not} expect any finite saturation field HL. ^{As we} did observe a finite saturation field, ^{we can} say that, ^{if such a ferroelec-} tric layer ^{exists at the TGS} surface, ^{it does not}

contribute to the anchoring strength ^{for MBBA.}

Recently, ^a ferroelectric ordering ^has been observed

[13] ^from cyanobiphenyl compounds ^{at a solid}

interface. These compounds present ^a large longitu-

dinal electric dipole, ^much stronger ^{than that of} MBBA. We have reproduced ^our experiment ^with

the room temperature pentyl cyanobiphenyl (5 CB).

We again ^{observe a finite} saturation field HL, ^which

seems to indicate that the first ferroelectric layer orientation, ^{if it} exists, ^{is too} tightly ^{bound to}

contribute to the anchoring strength. ^Note finally

that the surface polarization ^{we have} just ^discussed

is induced by ^some direct local interaction, ^which

does not imply any nematic ordering. ^{It is also} possible ^{to create a surface} polarization by destroy- ing the inversion symmetry ^{of the nematic} phase

with some surface field. In this _case, because the nematic properties remain invariant in the n - - n

symmetry, the induced surface polarization ^{will not} give any polar contribution to the surface anchoring.

For instance, ^a gradient ^{of nematic order VS//z}

normal to, say, ^a rough ^solid amorphous surface,

will induce an order electric polarization [14]

Po . Po ^is proportional ^{to VS.} (nn - I /z ). ^{In the}

presence of ^a surface field Es//z, ^{it will} give ^an angular contribution to the surface energy which goes like :

and not cos 9S ^as expected ^from the ferroelectric surface layer. ^{The same} argument is valid for the flexoelectric polarization [6].

The second possible polar ^{effect comes from the}

bulk ferroelectricity. ^{Let us} discuss for instance the

case of a flexoelectric polarization. ^{The same} argu- ment can be developed ^{for a} possible ordoelectric

polarization. ^{The curvature} distortion of the quasi-

Table I.

Distribution of ^values of ^the surface extrapolation length ^{L and} of ^the coefficient

characterizing

the departure of ^the surface potential from ^the Rapini-Papoular form ( « = 1), for different points of ^the

wedgeshape cell. The first ^row denotes the position, ^{d is} the thickness at the corresponding point.

planar ^{texture close to} us

0 creates a bulk flexoelectric polarization Pf ~ n eus

^where

6

e - 10-3 cgs is the flexoelectric coefficient. Pfcouples

with the electric field EF created in the nematic by

the ferroelectric TGS. This results ^{on a} surface term

-

EF eus. Although ^{this term is} non-polar ^with respect ^{to the n = - n} symmetry, ^it depends ^{on the} sign ^of EF. ^In principle, the saturation field should

depend ^on the orientation of the TGS ferroelectric domains. We have not observed such an effect. In fact the observed interference fringes ^are perfectly

continuous across the TGS domain boundaries. Our

simplest explanation ^{of this} negative result is that

EF ^{must be} screened, probably by ^{the ions} present ⁱⁿ the nematic material.

Finally, ^{in a} pure dielectric material, ^{one also} expects ^a dielectric self energy from the flexoelectric

(or ordoelectric) polarization. This energy Ws ^inte- grated in the volume close to the surface, ^{is of the}

order of g . Pfz Ef, ^where Ef ^{is now} the field created from the flexoelectric charges. Writing Dz

⁰

EEf ^{+ 4} 7rP, (e ^mean dielectric constant),

one finds :

Ws compares with Ws, ^{because e 2 - K and 4}

Its effect is to modify the bulk distortion below

HL. ^If neglected, ^{this term leads to an} apparent surface energy which does ^not obey the R.P. form

[15]. ^{In our case, the R.P. form is found to be}

correct, ^{which means that the} flexocontribution

must be weak. This can also be attributed to an ionic

screening of the flexoelectric charges, ^{with a} Debye screening length much smaller than L

2 _jim.

5. Conclusion.

We have studied the anchoring strength ^{of a cleaved}

surface of ferroelectric TGS, ^{on the room} _tempera-

ture nematic liquid crystal MBBA. The normal orientation of MBBA on TGS is planar. ^When making ^a nematic cell with a silane coated glass

plate, the stable nematic orientation of MBBA on

TGS becomes homeotropic. Analogous spontaneous changes of orientation to homeotropic alignment

have already been described [1], ^for Schiff base nematics. In our case, ^we believe that this reorien- tation is due to the adsorption ^{on the TGS surface of}

silane molecules dissolved in the nematic liquid crystal. ^{We do not} know whether the surface elec-

tric,field ^{of TGS} plays ^a role in this adsorption.

To measure the strength ^{of this stable} homeotropic

orientation of MBBA on TGS, ^we have used a

magneto-optical experiment. We have measured the

change ⁱⁿ birefringence ^of hybrid ^and homeotropic

textures, ^when forcing ^a planar orientation, parallel

to the TGS plate, ^{with an external} magnetic ^field.

The homeotropic anchoring strength ^{is found to be} weak, ^{with an} extrapolation length ^{L - 2 um. Within}

our experimental accuracy, the saturated surface

potential, ^{close to the} planar orientation, obeys ^the simple Rapini-Papoular form. In all _cases, the obser- vation of a finite saturation magnetic field eliminates the possibility ^{of an} anchoring polar contribution from a surface oriented ferroelectric nematic layer.

The same non-polar behaviour has been observed on

the room temperature ^nematic 5CB, which is known to induce such a ferroelectric layer ^{on a solid}

interface. We could also expect ^{another kind of} polar effect, ^{from the} change ^of sign ^{of the} coupling

between the flexoelectric, ^or ordoelectric, ^nematic polarization ^{with the} opposite electric fields created

by ^the opposite polarization ferroelectric domains of the bulk TGS. We have not observed such an effect,

nor any flexo ^or ordoelectric self energy. It ^seems that electric field effects are screened in the bulk, probably by ^available ions, ^{so that the} homeotropic anchoring is dominated by the silane coating. ^It

would be interesting ^to check if this simple ^behaviour persists ^{for the} spontaneous planar orientation of MBBA on TGS observed in absence of silane

coating.

Aknowledgment.

We acknowledge discussions with G. Barbero.

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