JPH01133054A - Manufacture of electrophotographic sensitive body - Google Patents

Abstract

PURPOSE:To manufacture an electrophotographic sensitive body high in sensitivity and low in residual potential at low cost in a manufacturing process for forming an electric charge transfer layer through heating and melt attaching treatment by forming a charge transfer film biaxially stretched in a specified draw ratio. CONSTITUTION:The electrophotographic sensitive body to be formed is functionally separated into a photoconductive layer 3 for generating carriers on light excitement and the charge transfer layer 2 for transferring those carriers and composed essentially of a straight chain polymer having p-phenylene units each substituted by an element of group VIb of the periodic table on the para position. This layer 2 is formed by using the charge transfer film biaxially stretched at least in one axis in a draw ratio of 5-50 and melt attaching this film by heat treatment, thus permitting all the requirements for the electrophotographic process, such as electrostatic charge acceptance, abrasion resistance, environment resistance, high photosensitivity, and low residual potential to be sufficiently satisfied, and a photosensitive body to be produced at low cost.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to an electrophotographic photoreceptor used in electrophotographic copying machines, optical printers, and the like.

2. Description of the Related Art Among electrophotographic photoreceptors, functionally separated electrophotographic photoreceptors are widely used in which a photoconductive layer that generates carriers by photoexcitation and a charge transport layer that transports carriers are made of different materials. By selecting materials according to function in this way, we can not only provide an excellent photoreceptor with highly sensitive electrophotographic properties, but also improve mechanical strength, thermal stability, printing durability,
You can consider the optimal combination from a wide range of materials in terms of environmental resistance, manufacturing cost, and other aspects.

Typical examples of such material combinations include methyl squarate and triarylpyrazoline, Diane blue and oxadiazole, perylene pigment and oxadiazole, and examples of inexpensive electrophotographic photoreceptors using organic materials.
Examples include bisazo pigments and styria anthracene.

In addition, examples of using inorganic materials as the photoconductive layer include Kiyoshi type selenium and polyvinyl carbazole,
No. 45 discloses a functionally separated photoreceptor using an amorphous silicon-based photoconductive layer and an organic semiconductor material as a charge transport layer, and Tokuhan No. 56-24355 discloses a photoreceptor using an inorganic semiconductor material as a charge transport layer. A functionally separated photoreceptor using layers has been proposed.

However, the functionally separated photoreceptor using the above-mentioned organic material,
Although it can be manufactured at low cost, it has poor printing durability and many issues need to be resolved in terms of lifespan and reliability.

In addition, in the latter case, attempts have been made to improve printing durability by using a highly hard photoconductive layer on the surface, but many photoconductive layers with excellent printing durability are difficult to maintain sufficient characteristics. requires substrate heating, or requires a process such as plasma that effectively raises the surface temperature, so conventional organic charge transport layers with poor heat resistance cannot provide photoreceptors with sufficient characteristics. is the current situation.

In such a situation, in Tokusho No. 55-90954 and Toku No. 60-59353, P is used as a charge transport layer.
P5 (poly P-phenylene sulfide) has been proposed as an excellent material that has high carrier mobility or can be manufactured at low cost by being used as a charge transport layer in the form of a film.

Problems to be Solved by the Invention In order to achieve higher sensitivity in a function-separated electrophotographic photoreceptor, a charge transport layer with a smaller dielectric constant, greater mobility and carrier life, and a higher charge generation are required. A combination of capable photoconductive layers is desirable. However, even if the respective required conditions are satisfied, carrier injection between the two must be performed efficiently. It must also fully satisfy the mold surface acceptance ability, abrasion resistance, environmental resistance, etc. required in the electrophotographic process.

In Japanese Patent Publication No. 60-59353, it is stated that PPS is formed as a charge transport layer by thinning it and improving its charge transport ability by vacuum evaporation, but generally in this state the charge transport ability is small and the sensitivity is low. , the residual potential is not sufficient. Furthermore, since a vacuum evaporation method is used, the film forming speed is not sufficient and the photoreceptor is expensive as a photoreceptor using an organic material.

In addition, in Tokuho No. 55-90954, PP
An inexpensive photoreceptor has been proposed by using an S film as a charge transport layer. However, since the charge transport ability is not sufficient, the photosensitivity has not reached the practical level of today's electrophotographic photoreceptors.

As described above, it has been difficult to manufacture an electrophotographic photoreceptor with high surface hardness, long life, high sensitivity, and low residual potential at a low cost.

Means for Solving the Problems In a method for manufacturing a functionally separated electrophotographic photoreceptor having a photoconductive layer that generates carriers by photoexcitation and a charge transport layer that transfers the carriers, a photoreceptor containing P-phenylene at the para position is used. When forming the charge transport layer mainly composed of a linear compound polymer layer containing a VTB group element, there is a step of fusing and forming the film forming the charge transport layer by heat treatment, and the stretching ratio is At least one axis of
The charge transport layer film formed by biaxial stretching 50 times is used.

As a result of various studies to overcome the shortcomings of PPS films such as low carrier mobility and carrier life, we found that a linear film containing P-phenylene and a chalcogen element at the para position, represented by PPS, was developed. A film containing a compound polymer layer as a main component is treated in an atmosphere containing oxygen atoms at a temperature of 260 to 320°C for 0.2 to 50 hours, preferably at 260 to 290°C for 1 to 12 hours. We found that by doing this, the charge transport ability can be dramatically improved.

It was confirmed that the above polymer film contained oxygen atoms of 1 to 35 atmz, preferably 1 to 20 atmX.

In a polymer with a structure such as PPS that has P-phenylene in the main chain direction and a chalcogen element in the para position, the charge transport ability is significantly improved by heat treatment in an oxygen-containing atmosphere. This has not been sufficiently analyzed at present. However, at this point, we can think of the following.

Generally, carrier movement in polymers occurs through hopping conduction between electron orbits along the main chain direction of the polymer, but the carrier mobility increases as the overlap between adjacent orbitals increases. ,To increase. When the chalcogen element at the para position of P-phenylene is in a neutral state, the π electron orbits of adjacent P-phenylenes are in a spatially orthogonal coordination state, and the mobility is small. However, when the chalcogen element is positively charged and ionized by the added O atoms, the spatial twist of P-phenylene is resolved and the π electron orbitals are arranged in the same plane, resulting in an increase in hopping probability and an improvement in mobility. It is thought that this will be achieved.

Further, the polymer film is hardened due to the heat treatment. In fact, the hardness of PPS formed into a film by biaxial stretching with at least one stretching ratio of 5 to 50 times is so soft that it cannot be accurately measured with a micro-Vickers hardness meter in the untreated state.

On the other hand, the Vickers hardness of the film subjected to the above treatment increased to 10 to 80, indicating that oxygen atoms that improve charge transport ability were stably incorporated into the film, or that the spatial twist of P-phenylene was resolved. It is considered that the electrophotographic photoreceptor is stabilized, is stable to substrate heating during the formation of a photoconductive layer, or is stable to a film forming process using plasma, and has high sensitivity and low residual potential.

On the other hand, a film formed on a support by directly heating and melting unstretched PPS powder does not show any significant improvement in charge transport ability even after heat treatment in oxygen. From this, when the spatial twist of P-phenylene in PPS is somewhat relaxed by stretching, by heat treatment in an oxygen-containing atmosphere, the chalcogen element is positively charged by the added 0 atoms, and easily The spatial twist of P-phenylene is resolved,
It is thought that mobility is improved.

Here, as mentioned above, charge acceptance ability, abrasion resistance, environmental resistance, high photosensitivity, and
It is necessary to satisfy the requirements such as low residual potential.

In addition, since polymer films typified by PPS can be formed by directly heating and fusing onto a conductive support of an electrophotographic photoreceptor, an inexpensive photoreceptor can be manufactured.

In addition, hardness increases through hardening, making it more resistant.

Rigidity is also improved.

The embodiment diagram schematically shows a cross section of one embodiment of the most basic electrophotographic photoreceptor of the present invention.

The electrophotographic photoreceptor shown in the figure includes a polymer layer having a structure having P-phenylene at least in the main chain direction and a chalcogen element at the para position on a support l as an electrophotographic photoreceptor, and a polymer layer containing oxygen. It has a charge transport layer N2 and a photoconductor N3 consisting of a polymer layer heat-treated in an atmosphere, the photoconductor layer 3 having a free surface 4 on the one hand.

In the present invention, the photoconductive layer is an amorphous layer containing silicon such as a-5i (:tl:X),
a-5it-vc,, (:Il”,X) (0<ycl)
, a-5it-VlOv(:1IX)(Oy<l),
a-5i+-vNy(:tl:X)(0<ykut)
, a-5i+-zGez(:H:X)(0<z<1)
, a-(Si+-zGez)+-vN, (:H:X)
(0<y, z<I), a-(Sit-zGez)+-
Jy (:H:XXO<y, z<1), or a-(Si
t −zGez)+−vc, (:n:x)(o<y,
A single layer with z<1) or a stack of these layers can be used. It can also be used when y is changed continuously.

As a photoconductive layer containing a chalcogen element, AS2Se3
．． An amorphous layer such as 5e (containing Te) or GeSe may also be used. In addition to this, CdS, CdSe,
A layer may be formed by binding CdTe crystal powder with a resin.

At this time, the thickness of the charge transport layer is 5 to 50 μm, preferably 1 μm.
0~257zm, and the film thickness of the photoconductive layer is 0.1~10μ
m is preferably 0.2 to 511 m.

In the present invention, in order to further improve the electrophotographic properties, a barrier layer is provided between the support l and the charge transport N2 in order to effectively prevent carriers from being injected from the support 1 into the charge transport N2. It may be provided.

Materials for forming the barrier layer include A I 203, Ba
O1Ba02, Be01 B12(h, CaO
1CeO2, Ce2O3, Shia203, Dy2O3,
LLJ203, Cr2(13, CuO1CU20, Fe
05pbo, MgO1SrO, Ta2O3, Th02,
z"02, HfO2, TiO2, Ti01Si02, G
Metal oxides such as eO2, 5iO1GeO or TiN,
AIN, SnN, NbN, TaN, GaN
Metal nitrides such as SiC, SiN, GeC, GeN, etc., or metal carbides such as SnC, TiC1, etc., 8
Insulators such as C and ON, and organic compounds such as polyethylene, polycarbonate, polyurethane, and polyparaxylene are used.

Furthermore, in order to improve cleaning properties, abrasion resistance, or corona resistance, a surface coating layer is formed on the free surface 4 in the figure. Suitable materials for the surface coating layer include S1, OI, and S! xc+-*, 5ixNI-
xx GexO+-xs (+exC+-x-Gex
N+-x, BtN+-r, 88C! -1, AlxN+-
X (O < Examples include synthetic resins such as ethylene fluoride, polyvinylidene fluoride, and polyurethane.

Furthermore, in the present invention, the above a-5i(:I:X)
, a-5i+ −, C, (2H:XXO<y<1),
a-5it-JyCH: XXOku/<l), a-5i+
-vNv(2H:X) (0<y<1), or by adding impurities to these Ge-added films, conductivity can be controlled and desired electrophotographic properties can be obtained. . Examples of n-type impurities that provide p-type conductivity include B, ALGa, and Tn, which belong to Group Ⅰ of the periodic table. B and ALGa are preferably used;
Type impurities include N, which belongs to Group II of the periodic table;
There are P, As, Sb, etc., and P and As are preferably used.

In addition, as a method of adding these impurities, in the case of n-type impurities, 82116, BaH+e, B5H9, BsH
++, 861112, 86HI4, BF3
, BC13, BBr2, AlCl3, (
CH3)3A1, (C2)15)3A1, (ic4H9
)3AI, (CH3)3Ga, (C2)15)3G
a, I nCI3, (C2tls)31 n, in the case of n-type impurity, N2, NHi, N01N20, NO2,
PH3, P2H4, PHal, PFt, PFs, PCl
3, PCl5, PBr3. PBrs, PI3, ASH3
, ASF3, AsC13, AsBr3.5b) I3, S
In the plasma CVD method, gases such as bF3.5BFs, 5bCI3.5bCI5, or these gases diluted with H2, )Ie, and Ar are used as raw materials such as the above-mentioned Si atoms when forming each film. It can be used by mixing it with gas. Alternatively, in the reactive sputtering method, it is used in combination with a sputtering gas such as Ar.

In addition, the following organic semiconductors can be used as the leading ftrM, (1) phthalocyanine pigments (referred to as PC), such as metal-free Pc, XPc (X = Cu, N
i, Co, T io, Mg, S 1 (OH le,
etc.), AlClPcC1, Ti0CIPcCI, InC
lPcC1, InClPc, InBrPcBr, etc. Furthermore, (2) azo dyes such as monoazo dyes and disazo dyes, (3) penylene pigments such as penylene acid anhydride and benylene imide, (4) indigoid dyes, (5) quinacridone pigments, (6) anthraquinones, pyrenequinones, etc. Polycyclic quinones (7) Cyanine dyes (8)
Examples include xanthine dyes (9) charge transfer complexes such as PVK/TNF, (10) eutectic complexes formed from biryllium salt dyes and polycarbonate resins, and (11) azulenium salt compounds.

A vacuum evaporation method, a deep coating method, an ion cluster beam method, an electrodeposition method, etc. are used to form films of these organic semiconductors.

The polymer layer, which is the charge transport layer, uses a film oriented by biaxial stretching, and as described below, it is heated in an oxygen-containing atmosphere on a quartz glass substrate or on a conductive support of an electrophotographic photoreceptor. They were fused and formed, and further heat-treated in oxygen if necessary.

On the other hand, in order to monitor the progress of the heat treatment, the hardness of the polymer layer was determined after film formation. For this reason, a quartz glass substrate was used, and a film having a thickness of 10 μrn or more was formed on the substrate and evaluated.

The hardness was measured using a micro Vickers hardness meter, and the load of the diamond indenter was set to lOg.

Furthermore, a film with low hardness such as an untreated PPS film is so soft that it is difficult to measure the hardness with a micro-Vickers hardness meter.

Examples will be described below.

Example 1 PPS films with a film thickness of 16 μm with varying stretching ratios were layered on a quartz glass substrate, and in order to further improve uniformity, a stainless steel substrate coated with Teflon as a mold release agent was applied as a load. Stacked and placed in oxygen for 280''
A CI time treatment was performed to fuse the PPS. When the hardness of this film was measured using a micro Vickers hardness meter, the hardness of the film at a stretching ratio of 30 to 50 was 35 ± 5.5 ~
The value was 15±5.2 for the 10x film and 7±2 for the 5x film.

Under these conditions, PPS was also fused to the aluminum substrate to form a charge transport layer. Next, Se was formed as a photoconductive layer to a thickness of about 0 to 8 μm by vacuum evaporation to obtain an electrophotographic photoreceptor.

At this time, an electrophotographic photoreceptor with a PPS charge transport layer of a film with a stretching ratio of 30 to 50 was charged to a surface potential of +600 V, and exposed to 500 nm light. It showed a very high sensitivity of 1.31 ux-sec. Further, the residual potential was 60 V or less, which showed excellent characteristics.

Furthermore, when an electrophotographic photoreceptor with a charge transport layer made of PPS with a stretching ratio of 5 to 10 times was evaluated under the same conditions as above, the half-potential exposure amount was as high as 1.51 ux"Sec. The residual potential was 120V, which was a little high.

However, an electrophotographic photoreceptor using a PPS film with a stretching ratio of 2 to 5 times has an extremely high residual potential of 300 to 350 V or more, and has not reached a practical level.

Example 2 Next, a film obtained by setting the stretching ratio to 2 times in one axis direction and 30 times in the other axis was placed on an aluminum substrate at 285
Heat fusion treatment was performed in air at 280°C, and further treatment was performed in oxygen at 280°C for 9 hours.

On the other hand, a film with a stretching ratio of 2 in both axes was fused onto an aluminum substrate in the same manner as above, and then heated at 280° C. in oxygen.
A leap treatment was performed at 9°C.

When the surfaces of both electrophotographic photoreceptors were charged and exposed to white light, the former had a residual potential of 80V.
The sensitivity was as low as 0.71 ux-sec, and the sensitivity was very high. The latter had a low charging potential of 250 V and a residual potential of 160 V or more, so it was not put into practical use.

Example 3 Next, in the same manner as in Example 2, a PPS film obtained with a stretching ratio of 60 times in the l-axis direction and 20 times in the other axis was fused onto an aluminum substrate, and further stretched in oxygen. 280℃
The treatment was carried out for 122 hours. On the other hand, a film with a stretching ratio of 60 times in both axes was fused in the same manner as above, and 28
The treatment was carried out at 0°C for 122 hours.

The hardness of the PPS film under the former condition was 75±5. However, cracks occurred in some parts of the latter film.

The former substrate was placed on the anode side of a parallel plate capacitively coupled plasma CVD apparatus having a 6-inch discharge electrode, and after the reaction vessel was evacuated to 5X 1O-6 Torr or less, the substrate was heated to 150 to 200°C. Heated. 5iHn to 1
0 to 40 sec, 1 Oppa+ of B2H6 was introduced, and the pressure was 0.2 to 1.

a-5i:8 at 0 Torr, high frequency power 20-100W
The layer was formed as a photoconductive layer with a thickness of 0.2 to 1 μm. Furthermore, 5
iH<10~30sccm, C214m 20~4
0sccn + introduced, pressure 0-2 to 1.0 Torr, high frequency power 50 to 150W, 5l-tcx: H (0<
x<l) was formed as a front WJ coating layer with a thickness of 0.08 to 0.3 μm to prepare an electrophotographic photoreceptor.

The former sample also has improved resistance to plasma, and when exposed to white light after being charged to a surface potential of 500 V, it showed a high sensitivity of 0.71 ux-sec and a residual potential of 1.
00V, a photoreceptor with a practical level was obtained.

On the other hand, in the latter sample, cracks further increased and some film peeling occurred.

Example 4 Cylindrical P with a film thickness of 15 μm was formed by the inflation method.
Create PS film. At this time, the stretching magnification is 20 to 30 times on the cylinder axis, and 10 times in the direction perpendicular to the cylinder axis.
~15 times. The diameter of the cylindrical film was 92φ.

A mirror-polished aluminum drum of 88φ was inserted into the above cylindrical PPS film, heated to 200° C., and PPS was laminated on the aluminum drum-F by thermal shrinkage.

On the other hand, a sample fused onto a quartz substrate for hardness measurement was placed in a heat treatment device in oxygen at the same time as the drum above.
The treatment was carried out at ℃ for 6 hours.

When Vickers hardness was measured using a sample for hardness measurement, it showed a hardness of 55±4.

Further, the drum was placed in a cylindrical rotary type vacuum evaporation apparatus, and after the inside of the apparatus was evacuated to 5X 1O-6 Torr or less, the substrate was heated to 25 to 40° C. as a photoconductive layer, and metal-free Pc was applied at 0.05 to 100° C.
The film was deposited to a thickness of 2 to 0.371 m. Before vapor deposition, the metal-free Pc was washed twice with hot water and washed once with a tetrahydrotrope, and after making M, it was vapor-deposited.

The photosensitive drum thus obtained had a surface potential of 600 V.
When the photosensitive drum was exposed to white light after being charged, the half potential exposure amount was 1.31 ux-sec, which showed high sensitivity, and the residual potential was 60 V or less, which was a sufficiently small photosensitive drum.

Example 5 Similarly to Example 4, when laminating a PPS film as a charge transport layer on an aluminum drum substrate by heat shrinkage, T CN Q (
The heat treatment was performed in an atmosphere to which 7,7,8,8,-tetracyanoquinodimethane) was added.

Furthermore, it was placed in a heat treatment apparatus in oxygen and was treated at 265° C. for 6 hours.

Similarly, a film was treated as a sample for hardness measurement, and the hardness was measured by adhering it to a quartz substrate.

The film hardness at this time was 25±4.

In addition, the drum was immersed in a solution containing 100:20 parts by weight of CdS photoconductive powder and a binder resin (the binder resin is a polyurethane resin), dried at 170°C for 30 minutes, and exposed to 5 μm light. A conductive layer was formed.

The photosensitive drum thus obtained had a surface potential of 600
After carrying out the charging treatment in step (2), exposure to white light was performed, and a photosensitive drum was obtained that exhibited high sensitivity with a half-potential exposure amount of 2.31 ux-sec and a sufficiently small residual potential of 90 V or less. .

Here, TCNQ was used as an electron acceptor, but SO
3. The same applies if A s F s etc. are used.

In addition, although a film containing PPS as the main component was used as the charge transport layer, similar effects can be obtained with polymers having a structure that has P-phenylene in the main chain direction and other chalcogen elements in the para position. It will be done.

Example 6 Contrary to the drawings, an example in which a photoconductive layer is disposed on a substrate will be described.

A mirror-polished 15 cm square aluminum substrate was placed in a parallel plate type capacitively coupled plasma CVD device with a 6 inch discharge electrode, and the interior of the reaction vessel was 5X 1O-6T.
After evacuation to below orr, the substrate was heated to 250°C or higher, preferably 280 to 320°C. Next, add SiH4 to 10~
40sccn+ was introduced, and C2H2 was mixed as a carbon source so that C atoms were mixed with Si atoms at 1 to 25 atmX.The total gas was diluted to 5% or less with hydrogen gas, and the gas was heated at a pressure of 0.2 to 1.0 Torr. , high frequency power 20~10
a-5it-, (,: 14 layers as photoconductive layer at 0W
．． 5 to 57 tm was formed.

Furthermore, a biaxially stretched PPS polymer film of 25 μm with a stretching ratio of 20 to 30 times for the l axis and 30 to 45 times for the other axes was brought into close contact with the end portions, and the film was stretched in air for 28 hours.
An electrophotographic photoreceptor was prepared by heating and fusing the mixture at a temperature of 0 to 290° C. in an oxygen atmosphere for a time period of 1 to 5 hours to form a charge transfer layer.

The hardness of PPS at this time was 60±4.

When this photoreceptor was charged to -500V and exposed to white light, the half-potential exposure amount was 1. oIux-sec
The sensitivity was very good. Also, the residual potential is 18
It was possible to obtain excellent characteristics of 0V or less.

Also, at this time a-5it-xcy:N! and the board,
Block charge injection! As layer E, a-5i+-x of 0.1 layer m
When one layer of Nx was inserted, the charge retention ability was improved and an image with high contrast was obtained.

Effects of the Invention According to the present invention, the charge transport layer contains P-phenylene,
In a method for producing an electrophotographic photoreceptor, the main component is a linear compound polymer layer having a group VIb element at the para position, and the method includes a step of fusing and forming the charge transport layer film by heat treatment, wherein the stretching ratio is at least 1 axis is 5 to 50 times 2
By using the charge transport layer film formed by axial stretching, an electrophotographic photoreceptor with high sensitivity and low residual potential can be manufactured at low cost.

In addition, the hardness of the charge transport layer formed by heat treatment increases to Vickers hardness 1O ~ 80, which significantly improves printing durability. At the same time, resistance to plasma is also improved, and plasma resistance of amorphous silicon, etc. Light guide used - fi P
In the process of forming the film, it is now possible to deposit a film without any damage caused by plasma. These have made it possible to extend the lifespan.

[Brief explanation of the drawing]

The figure is a sectional view of an electrophotographic photoreceptor in an example of the present invention. 1... Support, 2... Charge transport layer, 3... Photoconductive layer, 4... Free surface.

Claims (7)

[Claims] (1) A photoconductive layer that generates carriers by photoexcitation;
In the method for manufacturing a functionally separated electrophotographic photoreceptor having a charge transport layer for transferring carriers, the charge transport layer mainly comprises a linear compound polymer layer containing P-phenylene and a Group VIb element at the para position. When forming the transport layer, there is a step of fusing and forming the film forming the charge transport layer by heat treatment, and the charge transport layer formed by biaxial stretching at least one axis of the stretching ratio is 5 to 50 times. A method for producing an electrophotographic photoreceptor, the method comprising using a transport layer film. The method for manufacturing an electrophotographic photoreceptor according to claim 1, which comprises the step of (2) shrinking and bringing the cylindrical film into close contact with each other by heating. (3) The method for manufacturing an electrophotographic photoreceptor according to claim 1, which comprises the step of heating the film in an oxygen-containing atmosphere during or after fusing. (4) The method for producing an electrophotographic photoreceptor according to claim 1, which includes the step of adding an electron acceptor to the polymer layer that is the charge transfer layer. (5) The method for manufacturing an electrophotographic photoreceptor according to claim 1, which comprises the step of forming an amorphous layer in which the photoconductive layer contains a modifier that reduces electron spin density. (6) The method for manufacturing an electrophotographic photoreceptor according to claim 6, wherein the photoconductive layer contains at least either hydrogen or a halogen element. (7) The method for manufacturing an electrophotographic photoreceptor according to claim 1, which comprises the step of forming a surface coating layer on the free surface.