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Spreading of oil drops on highly curved polymer surfaces
Spreading of Oil Drops on Highly Curved Polymer Surfaces Z. RYMUZA Warsaw Technical University, 02-525 Warszawa, Chodkiewicza 8, Poland
Received August 2, 1984;acceptedAugust 21, 1985 The spreading of oil drops on highly curved surfaces of miniature bearing polymer elements was investigated.The experimentalstudy is also followedby theoreticalconsiderationswith the aim to determine relativesurfacefree energiesof polymermaterials used. © 1986AcademicPress,Inc. INTRODUCTION The study of the tribological properties of miniature polymeric elements shows that the friction and wear phenomena are affected by the surface energetics of polymeric microelements (1, 2). The surface energetics of polymeric elements is a function not only of the chemical structure of macromolecules but also of the ultimate physical state of the surface, which is governed by manufacturing conditions (3). The surface free energy of polymeric microelements used in fine mechanisms also significantly affects the spreading dynamics of oil drops used for the lubrication of rubbing microcouple. The migration of oil from the friction area of rubbing polymeric microelements is a severe problem in the tribology of precision engineering. The above two aspects of the tribological problem of polymeric microcouples, i.e., the effect of the surface free energy of a polymeric microelernent especially on its wear rate, and the migration of the oil from the friction region because of high surface energy of microelements and the relatively low surface tension of applied oils (33 m N / m ) have conducted to the reported studies of the spreading of oil drops on the curved, realistic polymeric surfaces. A study of the spreading of oil drops used for lubrication of realistic microelements has
been carried out using instrument oils and microbearing polymeric elements. The methods proposed (4, 5) for determining the surface free energy of polymers by measuring the contact angle were not applicable here because of the strong curvature of the realistic polymeric surfaces. EXPERIMENTAL PROCEDURE For the experimental study of spreading of oil drops, the following instrument oils were used: mineral parafinic oil MWP, siliconemineral oil OKB 122-16, and classic clock XU 430 oil (mixture of mineral and neat's-foot oil). The results of the chromatographic analysis of the oils were as follows: Content (%) of hydrocarbons
Oil MWP OKB 122-16 XU 430
Paraffinicnaphthene Aromatic
Resin content (%)
86.16
10.35
0.30
88.16 72.57
None 12.75
2.44 None
The physical properties of these oils are given in Table I. The oils spread on the bearing surface of the polymer elements as shown in Fig. 1. The polymer microelements selected were as used 221 0021-9797/86 $3.00
Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.
Z. RYMUZA
222
TABLEI InstrumentOilsUsed in Investigationsof Spreading Oil MWP PN-67/C-96069
Properties
Viscosity(mPa/s)
Surfacetension (mN m-l)
OKB 122-16 TY 6-02-897-78
XU 430 TGL 13857/02
20°C
17.8
38.2
416.8
50°C
6.2
16.4
91.7
20°C
28.8
25.7
33.0
50°C
26.2
22.9
29.9
Pour point (°C)
-60
TAN (mg KOH/g)
-70
0.05
0.25
- 15 0.20
in the bearing practice to obtain spreading data and surface free energy information applicable to the realistic tribological systems. The elements were manufactured in a mould at a mould temperature of 80°C. The following polymers were used:
weight in final copolymer). Into the chain of typical POM h (see above formula) are built dioxolane fragments --CHzOH20--. --polyamide 6 (Tarnamid T-27) + 25% glass fibers + 4% graphite (by weight) (Itamid 253, Xenon L6d~, Poland).
--polyamide 6 (PA 6) (Tarnamid T-27 manufactured by Zaktady Azotowe Tarn6w, Poland)
The roughness of the bearing surfaces &the polymer microelements was measured using microinterferometer M II-4 (USRR). The determined roughness height parameter Rz (see ISO/DIS 428711 and 468 standards) was ca. 0.3 #m, i.e., profile mean arithmetic deviation Ra ~ 0.06 txm. The spreading of oil drops on the bearing surface of the polymer microelement was recorded with a 16-mm cine camera (using ORWO UP 32, 21 DIN film, 32 frames/s). The apparatus is shown in Fig. 2. The drop volume was 0.02 ml. The ambient temperature was kept at ca. 22°C. The film was analyzed step by step after a 15-fold enlargement. The accuracy of the determination of the polymer/oil phase boundary (length of the drop) was about 0.01 mm. The maximum drop length (Fig. 3) measured along the beating hole axis was assumed to be the drop dimension. The mass of drops was small (less than 2 mg). The drop spreading was evaluated as the relative drop dimension increment given by
[--NH--(CH2)5--CO--]n --polyoxymethylene homopolymer (POM h) (Delrin 500 NC 10, Du Pont de Nemours) (--CHz--O--)n
--polyoxymethylene copolymer (POM c) Tarnoform 300, Zaktady Azotowe Tarn6w, Poland): Manufactured by the copolymerization of trioxane with 1,3-dioxolane (6% by
BeQrin~ surface
FIGURE 1 Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
223
SPREADING OF OIL DROPS
FIGURE 2
x = l, - lo/lo
[1]
where 10 is the initial drop dimension and/,the drop dimension of the ith image. EXPERIMENTAL RESULTS AND DISCUSSION
The results were analyzed using a computer. The curves characterizing the spreading were plotted at the defined "smoothing." The relative smoothing SF was calculated using the formula m
SF = ~ (xj - &)2/(m -
i)o7
j=l
(where m = number of variables (number of measurements), xj = value of the ordinate of regression function for j t h point, :~ = mean empirical value for the j t h point, and £
= mean value of regression function). The average relative smoothing of the characteristic curves of spreading presented below was for all polymers as follows: MWP, OKB, and X U oils 3.9, 3.8, and 7.9%, respectively. The average relative smoothing of the characteristic curves for polymers was ca. 7.1 (highest value) for POM c and 4% for PA 6 + G F as lowest value. The MWP oil spreads very fast on all the investigated polymer surfaces (Fig. 4). The spreading speed d X / d t (spreading time = 0 was highest for MWP oil spreading on PA 6 + G F and lowest on POM c surfaces, respectively. The highest, relative to the other oils, relative increment of the drop length observed (after ca. 0.8 s of spreading) at MWP oil spreading was accompanied with "microteeth" (microoutflows) occurring at the oil/polymer phase boundary during spreading. These advance microoutflows of oil had lengths less than 0.03 m m on POM c, POM h, and PA 6 elements but were 0.05- to 0.15-mm long on a PA 6 + G F element. It is possible to assume that these effects were the results of capillary flows of oil because of the anisotropy of polymer surfaces as the result of the presence on the surface glass fibers with high surface free energy in the case of PA 6 + G F material.
1.5
i.o
- t - - .
-----i-
-----
.5
"~
0,0
i
0,0
i
,5
I
1,0
601
FIGURE
3
r
1,5 t
t
2,0
2.5
(s) MWP
FIGURE 4 Journal of Colloid and Interface Science,
Vol. 112, No. 1, J u l y 1986
224
z. RYMUZA
The spreading of X U oil on the polymers POM c and POM h was accompanied (at the end phase of spreading, when spreading speed was low) by "microjumps" of oil at the boundary of the polymer/oil system. The microwithdrawals (ca. 0.05 mm) were also observed. The spreading dynamics of X U oil on the POM c and POM h polymer surfaces compared with spreading speeds of MWP and OKB oils drops is presented in Figs. 5 and 6. The spreading speeds of X U oil on POM surfaces were relatively low as compared to the other two oils. The highest spreading speeds were observed for oils spreading on PA 6 and particularly on PA 6 + GF surfaces (Figs. 7 and 8). The average spreading speeds of oils on polymer surfaces investigated are given in Table II. The significant differences in the spreading speeds for the polymer surfaces studied can be seen. The spreading speeds for POM c and POM h are similar. The regression functions describing the spreading of oils on polymer microelements used are listed in Table III. It is seen that the spreading of the instrument oils investigated on the surface of the bearing hole of the polymeric microbushes can be represented by a power function k = a t b where a > 0 and 0.3
,7! ! ,61
i ,5[
t
i
2
1
i
I
3
I
4
5
I
6
t (s) 607
DELRIN
FIGURE 6
< b < 0.6. The character of the spreading curves k =fit) is similar to the spreading characteristics of PDMS liquids on a horizontal PTFE surface (6) and also as on a silicon metal surface (7). The motion of oil dynamically wetting of polymer surface can occur only if oil flow arises near the contact line (8) and the following inequality is fulfilled
[2]
> '~pl + 7 I v COS O
7pv
.5 1,{
\
\\ -,0 O,O 609
I
I
.5
I
1,0
I
1,5 2.0 t (s)
I
I
2,5
0,I
I
3.0
3.5
TARNOFORM
FIGURE 5 Journal of Colloid and Interface Science. Vol. 112, No. 1, July 1986
I
I
0.0
,5
i
1,0
)
1.5
t (s) 611
TARNAMID
FIGURE 7
l
2,0
2.5
225
SPREADING OF OIL DROPS1,5
TABLE III Regression Functions for Spreading of Oil Drops on Polymeric Highly Curved Surfaces Parameters
1,0 Polymer
.5
\
o.o 0
, l
2
Oil
a
b
POM c
MWP OKB XU
0.943 0.513 0.420
0.32 0.49 0.43
POM h
MWP OKB XU
0.762 0.6•4 0.481
0.45 0.51 0.41
PA 6
MWP OKB XU
1.329 0.767 0.577
0.36 0.43 0.40
PA 6 + GF
MWP OKB XU
1.183 0.748 0.667
0.48 0.58 0.47
i 3
4
5
6
7
t (s)
623 ITAMID25G FIGURE
8
where 3' is specific surface free energy of the corresponding phase boundary and 0 is contact angle at time t. It was demonstrated (9, 10) that gravity does not affect the spreading speed of drops with mass up to 20 rag. The mass of the oil drop used was ca. 2 mg. It is known (11) that the spreading speed of a drop on a solid surface depends mainly on the surface free energy of the solid and the surface tension, viscosity, and mass of the liquid drop and to a lesser extent on the surface roughness and the environmental conditions. Theoretical considerations (12) carried out
for undirectional (inside a "through") viscous spreading of a liquid on a solid surface have shown that the spreading can be described with the formula x =
1 3Fm~l/3(t.)l/3
Average (for 3 Oils Used) Spreading Speed dX/dt on the Polymer Surfaces Investigated
Polymer
0.3 s°
1.0 s"
2.0 sa
POM c POM h PA 6 PA 6 + GF
0.45 0.54 0.72 0.80
0.24 0.29 0.34 0.44
0.16 0.20 0.23 0.31
[4]
For high molecular weight liquid/polymer systems it may be assumed that 3/ol "~ Tpv + Tlv -- 2(TpvTlv) 1/2.
dX/dt (s-')
r3)
where x is half drop length (it is 0 at zero absolute spreading time t*); F---spreading force, m - - d r o p mass; 7, p--viscosity and density of liquid, respectively, and k--drop breadth. The spreading force is given by F = (%v - %0 - 3qv.
TABLE II
a Spreading time.
Note. Base formula 2, = at b (X--see formula [1]. t - spreading time in s).
[5]
Therefore, the spreading force in the oil/polymer system can be expressed by F ~ 23,~/2 + @{2 - 3,t~=.
[6]
The relative increment of drop length, taking into consideration Eqs. [1] and [3], can be calculated using the formula Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
226
z. RYMUZA (---~k t*~1/3
X=
~01
Because t*
- 1.
= to + t,
[71
surfaces are approximately the same). Since F is given by formula [6] the ratio or the spreading speeds for the drops of the same oil spreading on two different polymer surfaces is
[8]
(dX/dt)x ltmV (dX/dt)-------~2~ I,~v/2~ 3,~v/2] " _
the approximate description of spreading of oil drops on highly curved polymer surfaces can be formulated as
X =-[-~ (1 +~0)] 3- 1. Since at t* = to x =
lo/2,
[9]
therefore from Eq.
[3] to :
Fm
[10]
The spreading speed of the oil drop on the polymer surfaces investigated may be expressed as
¥ = 3 ,gl U + D
to
_
[16]
The results of the spreading speeds were utilized for approximative determination of the ratios of specific surface free energies of polymers used as bearing materials in tribological studies of the polymeric miniature bearings. The results of the calculations are listed in Table IV. The values of the specific surface free energies of polymers are related to the specific surface free energy of polyamide 6 (Tarnamid T-27) since the surface free energy of polymer was determined earlier (14) to be 53.5 m J / m 2 using a polymer plate (moulded under similar
[11]
J
TABLE IV or Approximate Values of Ratios of Surface Free Energies of Polymer Microelements Examined
[121 Since for the oils used
3Fm
---t~> 8ko
,
1
[141
The ratio of the spreading speeds at the same time t using the same oil on two different polymer surfaces is given by
(dX/dt), (F,~ ',3 (dMdt)--~2~ \-ff~2]
[151
when we assume with very good agreement with the realistic effects, that ml ~ m2; kl k2, and 101 ~ /02 (i.e., mass, breadth, and length of the drops on two different polymer Journal of Colloid and Interface Science, Vol. 112, No, 1, July 1986
Ratio of sr~citic surface free energies
POM c POM h
MWP OKB XU
0.85 0.71 0.94
POM c PA 6
MWP OKB XU
0.64 0.68 0.79
POM c PA 6 + GF
MWP OKB XU
0.34 0,27 0,40
POM h PA 6
MWP OKB XU
0.75 0.96 0.84
POM h PA 6 + GF
MWP OKB XU
0.40 0.38 0.43
PA 6 PA 6 + GF
MWP OKB XU
0.53 0.40 0.51
[13]
therefore
dX 1 ( Fm] 1/3 --~ ~ To &-~pl t-2/3"
Oil
Polymers
227
SPREADING OF OIL DROPS
conditions as our bearing bushes) and applying the Owens and Wendt (4) method. The ratios of the specific surface free energies differ considerably with the choice of oil in the cases of polymers having relatively low specific surface free energy, i.e., POM c and POM h. Seeing that the differences are considerable in the case of OKB and XU oils (i.e., the oils with the lowest and highest surface tensions; see Table I) it can be assumed that the theoretical description (theoretical model) of the phenomena studied is probably too approximative. The effects of the surface tension and surface free energy of polymers and also viscosity and mass of the oil drop are so complex that a theoretical model, special for the investigated highly curved polymer surfaces, is needed for the eventual determination of a surface free energy of polymers. The chemical structure of the oils investigated can also have an influence on the spreading dynamics of the investigated oils on the polymer materials. The average values of the specific surface free energies of POM c, POM h, and PA 6 + GF calculated, based on the aforementioned specific surface free energy ofPA 6 (Tarnamid T-27), were 37.6, 45.5, and 111.5 mJ/m 2, respectively. The results of the latest (15) measurements (using Owens and Wendt method (4)) of a specific surface free energy of polymers (fiat plates manufactured in the similar conditions of the above described polymer microelements used in this study) show that the specific surface free energy of POM c (but U1traform N 2200 produced by BASF in the Federal Republic of Germany instead of our Tarnoform 300) is ca. 42.1 mJ/m 2. The result of the same studies of the determination of a specific surface free energy for PA 6 (Ultramid, BASF, F.R.G.) was 47.5 mJ/m 2, i.e., 1.13 of the specific surface free energy of POM c (UItraform). In our studies this ratio of the specific surface free energies ofPA 6 (Tarnamid T-27) and POM c (Tarnoform 300) polymers was 1.42 (average value). The specific surface free energy ofPOM h is not clearly given; the values are for, generally, polyoxymethylene (ca.
40 mJ/m 2 (16)). The value of a specific surface free energy ofPA 6 + GF was not, up to now, estimated. The difference between the specific surface free energy of POM c given in (14) and obtained in our studies can be effected by the differences in the copolymerization (copolymerized substances) processing and manufacturing conditions of the samples (different morphology, crystallinity, etc. of the samples). The study of the realistic samples for the determination of a specific surface free energy of the analyzed polymeric materials (elements) is, therefore, very important. CONCLUSIONS
The spreading of instrument oil drops on the miniature polymer elements with strongly curved bearing surfaces was studied using a cine camera. The spreading speed depends on the combination of oil/polymer and is determined mainly by the surface tension, viscosity of the oil, and by surface free energy of the polymer material. The maximum spreading speed dk/dt was observed for the spreading of mineral oil MWP on PA 6 + GF (glass fibers) + graphite surfaces. The spreading speeds observed for classic clock oil XU 430 spreading on POM c surfaces were lowest. The aforementioned "microteeth" (microoutflows of oil) effects at low spreading speed range at spreading of MWP oil on POM c, POM h, PA 6 and, in particular, PA 6 + GF polymer surfaces have been observed. The hysteresis effects at spreading of oil XU 430 on POM surfaces were characteristic. The spreading of oil drops on strongly curved polymer surfaces can be described with power function k = at+ where a > 0 and 0.3 < b < 0.6. The determination of the spreading speed d~/dt enables estimation of the surface free energy of polymers but an adequate theoretical model of spreading is needed. REFERENCES 1. Rymuza, Z., W e a r 58, 97 (1980). 2. Rymuza, Z., in "Physicochemical Aspects of Polymer Journal of ColloM and Interface Science, Vol. 112,No. 1, July 1986
228
3. 4. 5. 6. 7.
8. 9.
Z. RYMUZA
Surfaces" (K. L. Mittal, Ed.). Plenum Vol. 1. p. 451. New York/London, 1983. Schonhorn, H., Frisch, H. L., and Gaines, G. L., Polym. Eng. Sci. 17,440 (1977). Owens, D. K., and Wendt, R. C., J. Appl. Polym. Sci. 13, 1741 (1969). Neumann, A. W., Good, R. J., Hope, C. J., and Sejpal, M., J. Colloid Interface Sci. 49, 291 (1974). Ogarev, V. A., Timonina, T. N., Arslanov, V. V., and Trapeznikov, A. A., J. Adhesion 6, 337 (1974). Sawicki, G. G., in "Wetting, Spreading and Adhesion" (J. F. Padday, Ed.), p. 361, Academic Press, New York/London, 1978. Miller, C. A., and Ruckenstein, E., J. Colloid Interface Sci. 48, 368 (1974). Schonhom, H., Frisch, H. L., and Kwei, T.~K., J. AppL Phys. 37, 4967 (1966).
Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
10. Kwei, T. K., Schonhorn, H., and Frisch, H. L., J. Colloid Interface Sci. 28, 543 f1968). 11. Summ, B. D., and Goryunov, V. C., "Physical-chemical Principles of Wetting and Spreading." Khimya, Moscow, 1977, in Russian. 12. Raud, E. A., Summ, B. D., and Shchukin, E. D., Dokl. Akad. Nauk SSSR 205, 1134 (1972), in Russian. 13. Girifalco, L. A., and Good, R. J., J. Phys. Chem. 64, 561 (1960). 14. Kosicki, J. E., and Nadolny, K., in "Proceedings, 3rd International Tribology Congress Eurotrib 81 in Warsaw," Vol. II/A, p. 101. Technical UniversityRadom, 1981. 15. Erhard, G., Zum Reibungs- und Verschleissverhalten von Polymerwerkstoffen, Dissertation, Universitat Karlsruhe, Fed. Rep. Germany, 1980.
Received August 2, 1984;acceptedAugust 21, 1985 The spreading of oil drops on highly curved surfaces of miniature bearing polymer elements was investigated.The experimentalstudy is also followedby theoreticalconsiderationswith the aim to determine relativesurfacefree energiesof polymermaterials used. © 1986AcademicPress,Inc. INTRODUCTION The study of the tribological properties of miniature polymeric elements shows that the friction and wear phenomena are affected by the surface energetics of polymeric microelements (1, 2). The surface energetics of polymeric elements is a function not only of the chemical structure of macromolecules but also of the ultimate physical state of the surface, which is governed by manufacturing conditions (3). The surface free energy of polymeric microelements used in fine mechanisms also significantly affects the spreading dynamics of oil drops used for the lubrication of rubbing microcouple. The migration of oil from the friction area of rubbing polymeric microelements is a severe problem in the tribology of precision engineering. The above two aspects of the tribological problem of polymeric microcouples, i.e., the effect of the surface free energy of a polymeric microelernent especially on its wear rate, and the migration of the oil from the friction region because of high surface energy of microelements and the relatively low surface tension of applied oils (33 m N / m ) have conducted to the reported studies of the spreading of oil drops on the curved, realistic polymeric surfaces. A study of the spreading of oil drops used for lubrication of realistic microelements has
been carried out using instrument oils and microbearing polymeric elements. The methods proposed (4, 5) for determining the surface free energy of polymers by measuring the contact angle were not applicable here because of the strong curvature of the realistic polymeric surfaces. EXPERIMENTAL PROCEDURE For the experimental study of spreading of oil drops, the following instrument oils were used: mineral parafinic oil MWP, siliconemineral oil OKB 122-16, and classic clock XU 430 oil (mixture of mineral and neat's-foot oil). The results of the chromatographic analysis of the oils were as follows: Content (%) of hydrocarbons
Oil MWP OKB 122-16 XU 430
Paraffinicnaphthene Aromatic
Resin content (%)
86.16
10.35
0.30
88.16 72.57
None 12.75
2.44 None
The physical properties of these oils are given in Table I. The oils spread on the bearing surface of the polymer elements as shown in Fig. 1. The polymer microelements selected were as used 221 0021-9797/86 $3.00
Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.
Z. RYMUZA
222
TABLEI InstrumentOilsUsed in Investigationsof Spreading Oil MWP PN-67/C-96069
Properties
Viscosity(mPa/s)
Surfacetension (mN m-l)
OKB 122-16 TY 6-02-897-78
XU 430 TGL 13857/02
20°C
17.8
38.2
416.8
50°C
6.2
16.4
91.7
20°C
28.8
25.7
33.0
50°C
26.2
22.9
29.9
Pour point (°C)
-60
TAN (mg KOH/g)
-70
0.05
0.25
- 15 0.20
in the bearing practice to obtain spreading data and surface free energy information applicable to the realistic tribological systems. The elements were manufactured in a mould at a mould temperature of 80°C. The following polymers were used:
weight in final copolymer). Into the chain of typical POM h (see above formula) are built dioxolane fragments --CHzOH20--. --polyamide 6 (Tarnamid T-27) + 25% glass fibers + 4% graphite (by weight) (Itamid 253, Xenon L6d~, Poland).
--polyamide 6 (PA 6) (Tarnamid T-27 manufactured by Zaktady Azotowe Tarn6w, Poland)
The roughness of the bearing surfaces &the polymer microelements was measured using microinterferometer M II-4 (USRR). The determined roughness height parameter Rz (see ISO/DIS 428711 and 468 standards) was ca. 0.3 #m, i.e., profile mean arithmetic deviation Ra ~ 0.06 txm. The spreading of oil drops on the bearing surface of the polymer microelement was recorded with a 16-mm cine camera (using ORWO UP 32, 21 DIN film, 32 frames/s). The apparatus is shown in Fig. 2. The drop volume was 0.02 ml. The ambient temperature was kept at ca. 22°C. The film was analyzed step by step after a 15-fold enlargement. The accuracy of the determination of the polymer/oil phase boundary (length of the drop) was about 0.01 mm. The maximum drop length (Fig. 3) measured along the beating hole axis was assumed to be the drop dimension. The mass of drops was small (less than 2 mg). The drop spreading was evaluated as the relative drop dimension increment given by
[--NH--(CH2)5--CO--]n --polyoxymethylene homopolymer (POM h) (Delrin 500 NC 10, Du Pont de Nemours) (--CHz--O--)n
--polyoxymethylene copolymer (POM c) Tarnoform 300, Zaktady Azotowe Tarn6w, Poland): Manufactured by the copolymerization of trioxane with 1,3-dioxolane (6% by
BeQrin~ surface
FIGURE 1 Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
223
SPREADING OF OIL DROPS
FIGURE 2
x = l, - lo/lo
[1]
where 10 is the initial drop dimension and/,the drop dimension of the ith image. EXPERIMENTAL RESULTS AND DISCUSSION
The results were analyzed using a computer. The curves characterizing the spreading were plotted at the defined "smoothing." The relative smoothing SF was calculated using the formula m
SF = ~ (xj - &)2/(m -
i)o7
j=l
(where m = number of variables (number of measurements), xj = value of the ordinate of regression function for j t h point, :~ = mean empirical value for the j t h point, and £
= mean value of regression function). The average relative smoothing of the characteristic curves of spreading presented below was for all polymers as follows: MWP, OKB, and X U oils 3.9, 3.8, and 7.9%, respectively. The average relative smoothing of the characteristic curves for polymers was ca. 7.1 (highest value) for POM c and 4% for PA 6 + G F as lowest value. The MWP oil spreads very fast on all the investigated polymer surfaces (Fig. 4). The spreading speed d X / d t (spreading time = 0 was highest for MWP oil spreading on PA 6 + G F and lowest on POM c surfaces, respectively. The highest, relative to the other oils, relative increment of the drop length observed (after ca. 0.8 s of spreading) at MWP oil spreading was accompanied with "microteeth" (microoutflows) occurring at the oil/polymer phase boundary during spreading. These advance microoutflows of oil had lengths less than 0.03 m m on POM c, POM h, and PA 6 elements but were 0.05- to 0.15-mm long on a PA 6 + G F element. It is possible to assume that these effects were the results of capillary flows of oil because of the anisotropy of polymer surfaces as the result of the presence on the surface glass fibers with high surface free energy in the case of PA 6 + G F material.
1.5
i.o
- t - - .
-----i-
-----
.5
"~
0,0
i
0,0
i
,5
I
1,0
601
FIGURE
3
r
1,5 t
t
2,0
2.5
(s) MWP
FIGURE 4 Journal of Colloid and Interface Science,
Vol. 112, No. 1, J u l y 1986
224
z. RYMUZA
The spreading of X U oil on the polymers POM c and POM h was accompanied (at the end phase of spreading, when spreading speed was low) by "microjumps" of oil at the boundary of the polymer/oil system. The microwithdrawals (ca. 0.05 mm) were also observed. The spreading dynamics of X U oil on the POM c and POM h polymer surfaces compared with spreading speeds of MWP and OKB oils drops is presented in Figs. 5 and 6. The spreading speeds of X U oil on POM surfaces were relatively low as compared to the other two oils. The highest spreading speeds were observed for oils spreading on PA 6 and particularly on PA 6 + GF surfaces (Figs. 7 and 8). The average spreading speeds of oils on polymer surfaces investigated are given in Table II. The significant differences in the spreading speeds for the polymer surfaces studied can be seen. The spreading speeds for POM c and POM h are similar. The regression functions describing the spreading of oils on polymer microelements used are listed in Table III. It is seen that the spreading of the instrument oils investigated on the surface of the bearing hole of the polymeric microbushes can be represented by a power function k = a t b where a > 0 and 0.3
,7! ! ,61
i ,5[
t
i
2
1
i
I
3
I
4
5
I
6
t (s) 607
DELRIN
FIGURE 6
< b < 0.6. The character of the spreading curves k =fit) is similar to the spreading characteristics of PDMS liquids on a horizontal PTFE surface (6) and also as on a silicon metal surface (7). The motion of oil dynamically wetting of polymer surface can occur only if oil flow arises near the contact line (8) and the following inequality is fulfilled
[2]
> '~pl + 7 I v COS O
7pv
.5 1,{
\
\\ -,0 O,O 609
I
I
.5
I
1,0
I
1,5 2.0 t (s)
I
I
2,5
0,I
I
3.0
3.5
TARNOFORM
FIGURE 5 Journal of Colloid and Interface Science. Vol. 112, No. 1, July 1986
I
I
0.0
,5
i
1,0
)
1.5
t (s) 611
TARNAMID
FIGURE 7
l
2,0
2.5
225
SPREADING OF OIL DROPS1,5
TABLE III Regression Functions for Spreading of Oil Drops on Polymeric Highly Curved Surfaces Parameters
1,0 Polymer
.5
\
o.o 0
, l
2
Oil
a
b
POM c
MWP OKB XU
0.943 0.513 0.420
0.32 0.49 0.43
POM h
MWP OKB XU
0.762 0.6•4 0.481
0.45 0.51 0.41
PA 6
MWP OKB XU
1.329 0.767 0.577
0.36 0.43 0.40
PA 6 + GF
MWP OKB XU
1.183 0.748 0.667
0.48 0.58 0.47
i 3
4
5
6
7
t (s)
623 ITAMID25G FIGURE
8
where 3' is specific surface free energy of the corresponding phase boundary and 0 is contact angle at time t. It was demonstrated (9, 10) that gravity does not affect the spreading speed of drops with mass up to 20 rag. The mass of the oil drop used was ca. 2 mg. It is known (11) that the spreading speed of a drop on a solid surface depends mainly on the surface free energy of the solid and the surface tension, viscosity, and mass of the liquid drop and to a lesser extent on the surface roughness and the environmental conditions. Theoretical considerations (12) carried out
for undirectional (inside a "through") viscous spreading of a liquid on a solid surface have shown that the spreading can be described with the formula x =
1 3Fm~l/3(t.)l/3
Average (for 3 Oils Used) Spreading Speed dX/dt on the Polymer Surfaces Investigated
Polymer
0.3 s°
1.0 s"
2.0 sa
POM c POM h PA 6 PA 6 + GF
0.45 0.54 0.72 0.80
0.24 0.29 0.34 0.44
0.16 0.20 0.23 0.31
[4]
For high molecular weight liquid/polymer systems it may be assumed that 3/ol "~ Tpv + Tlv -- 2(TpvTlv) 1/2.
dX/dt (s-')
r3)
where x is half drop length (it is 0 at zero absolute spreading time t*); F---spreading force, m - - d r o p mass; 7, p--viscosity and density of liquid, respectively, and k--drop breadth. The spreading force is given by F = (%v - %0 - 3qv.
TABLE II
a Spreading time.
Note. Base formula 2, = at b (X--see formula [1]. t - spreading time in s).
[5]
Therefore, the spreading force in the oil/polymer system can be expressed by F ~ 23,~/2 + @{2 - 3,t~=.
[6]
The relative increment of drop length, taking into consideration Eqs. [1] and [3], can be calculated using the formula Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
226
z. RYMUZA (---~k t*~1/3
X=
~01
Because t*
- 1.
= to + t,
[71
surfaces are approximately the same). Since F is given by formula [6] the ratio or the spreading speeds for the drops of the same oil spreading on two different polymer surfaces is
[8]
(dX/dt)x ltmV (dX/dt)-------~2~ I,~v/2~ 3,~v/2] " _
the approximate description of spreading of oil drops on highly curved polymer surfaces can be formulated as
X =-[-~ (1 +~0)] 3- 1. Since at t* = to x =
lo/2,
[9]
therefore from Eq.
[3] to :
Fm
[10]
The spreading speed of the oil drop on the polymer surfaces investigated may be expressed as
¥ = 3 ,gl U + D
to
_
[16]
The results of the spreading speeds were utilized for approximative determination of the ratios of specific surface free energies of polymers used as bearing materials in tribological studies of the polymeric miniature bearings. The results of the calculations are listed in Table IV. The values of the specific surface free energies of polymers are related to the specific surface free energy of polyamide 6 (Tarnamid T-27) since the surface free energy of polymer was determined earlier (14) to be 53.5 m J / m 2 using a polymer plate (moulded under similar
[11]
J
TABLE IV or Approximate Values of Ratios of Surface Free Energies of Polymer Microelements Examined
[121 Since for the oils used
3Fm
---t~> 8ko
,
1
[141
The ratio of the spreading speeds at the same time t using the same oil on two different polymer surfaces is given by
(dX/dt), (F,~ ',3 (dMdt)--~2~ \-ff~2]
[151
when we assume with very good agreement with the realistic effects, that ml ~ m2; kl k2, and 101 ~ /02 (i.e., mass, breadth, and length of the drops on two different polymer Journal of Colloid and Interface Science, Vol. 112, No, 1, July 1986
Ratio of sr~citic surface free energies
POM c POM h
MWP OKB XU
0.85 0.71 0.94
POM c PA 6
MWP OKB XU
0.64 0.68 0.79
POM c PA 6 + GF
MWP OKB XU
0.34 0,27 0,40
POM h PA 6
MWP OKB XU
0.75 0.96 0.84
POM h PA 6 + GF
MWP OKB XU
0.40 0.38 0.43
PA 6 PA 6 + GF
MWP OKB XU
0.53 0.40 0.51
[13]
therefore
dX 1 ( Fm] 1/3 --~ ~ To &-~pl t-2/3"
Oil
Polymers
227
SPREADING OF OIL DROPS
conditions as our bearing bushes) and applying the Owens and Wendt (4) method. The ratios of the specific surface free energies differ considerably with the choice of oil in the cases of polymers having relatively low specific surface free energy, i.e., POM c and POM h. Seeing that the differences are considerable in the case of OKB and XU oils (i.e., the oils with the lowest and highest surface tensions; see Table I) it can be assumed that the theoretical description (theoretical model) of the phenomena studied is probably too approximative. The effects of the surface tension and surface free energy of polymers and also viscosity and mass of the oil drop are so complex that a theoretical model, special for the investigated highly curved polymer surfaces, is needed for the eventual determination of a surface free energy of polymers. The chemical structure of the oils investigated can also have an influence on the spreading dynamics of the investigated oils on the polymer materials. The average values of the specific surface free energies of POM c, POM h, and PA 6 + GF calculated, based on the aforementioned specific surface free energy ofPA 6 (Tarnamid T-27), were 37.6, 45.5, and 111.5 mJ/m 2, respectively. The results of the latest (15) measurements (using Owens and Wendt method (4)) of a specific surface free energy of polymers (fiat plates manufactured in the similar conditions of the above described polymer microelements used in this study) show that the specific surface free energy of POM c (but U1traform N 2200 produced by BASF in the Federal Republic of Germany instead of our Tarnoform 300) is ca. 42.1 mJ/m 2. The result of the same studies of the determination of a specific surface free energy for PA 6 (Ultramid, BASF, F.R.G.) was 47.5 mJ/m 2, i.e., 1.13 of the specific surface free energy of POM c (UItraform). In our studies this ratio of the specific surface free energies ofPA 6 (Tarnamid T-27) and POM c (Tarnoform 300) polymers was 1.42 (average value). The specific surface free energy ofPOM h is not clearly given; the values are for, generally, polyoxymethylene (ca.
40 mJ/m 2 (16)). The value of a specific surface free energy ofPA 6 + GF was not, up to now, estimated. The difference between the specific surface free energy of POM c given in (14) and obtained in our studies can be effected by the differences in the copolymerization (copolymerized substances) processing and manufacturing conditions of the samples (different morphology, crystallinity, etc. of the samples). The study of the realistic samples for the determination of a specific surface free energy of the analyzed polymeric materials (elements) is, therefore, very important. CONCLUSIONS
The spreading of instrument oil drops on the miniature polymer elements with strongly curved bearing surfaces was studied using a cine camera. The spreading speed depends on the combination of oil/polymer and is determined mainly by the surface tension, viscosity of the oil, and by surface free energy of the polymer material. The maximum spreading speed dk/dt was observed for the spreading of mineral oil MWP on PA 6 + GF (glass fibers) + graphite surfaces. The spreading speeds observed for classic clock oil XU 430 spreading on POM c surfaces were lowest. The aforementioned "microteeth" (microoutflows of oil) effects at low spreading speed range at spreading of MWP oil on POM c, POM h, PA 6 and, in particular, PA 6 + GF polymer surfaces have been observed. The hysteresis effects at spreading of oil XU 430 on POM surfaces were characteristic. The spreading of oil drops on strongly curved polymer surfaces can be described with power function k = at+ where a > 0 and 0.3 < b < 0.6. The determination of the spreading speed d~/dt enables estimation of the surface free energy of polymers but an adequate theoretical model of spreading is needed. REFERENCES 1. Rymuza, Z., W e a r 58, 97 (1980). 2. Rymuza, Z., in "Physicochemical Aspects of Polymer Journal of ColloM and Interface Science, Vol. 112,No. 1, July 1986
228
3. 4. 5. 6. 7.
8. 9.
Z. RYMUZA
Surfaces" (K. L. Mittal, Ed.). Plenum Vol. 1. p. 451. New York/London, 1983. Schonhorn, H., Frisch, H. L., and Gaines, G. L., Polym. Eng. Sci. 17,440 (1977). Owens, D. K., and Wendt, R. C., J. Appl. Polym. Sci. 13, 1741 (1969). Neumann, A. W., Good, R. J., Hope, C. J., and Sejpal, M., J. Colloid Interface Sci. 49, 291 (1974). Ogarev, V. A., Timonina, T. N., Arslanov, V. V., and Trapeznikov, A. A., J. Adhesion 6, 337 (1974). Sawicki, G. G., in "Wetting, Spreading and Adhesion" (J. F. Padday, Ed.), p. 361, Academic Press, New York/London, 1978. Miller, C. A., and Ruckenstein, E., J. Colloid Interface Sci. 48, 368 (1974). Schonhom, H., Frisch, H. L., and Kwei, T.~K., J. AppL Phys. 37, 4967 (1966).
Journal of Colloid and Interface Science, Vol. 112, No. 1, July 1986
10. Kwei, T. K., Schonhorn, H., and Frisch, H. L., J. Colloid Interface Sci. 28, 543 f1968). 11. Summ, B. D., and Goryunov, V. C., "Physical-chemical Principles of Wetting and Spreading." Khimya, Moscow, 1977, in Russian. 12. Raud, E. A., Summ, B. D., and Shchukin, E. D., Dokl. Akad. Nauk SSSR 205, 1134 (1972), in Russian. 13. Girifalco, L. A., and Good, R. J., J. Phys. Chem. 64, 561 (1960). 14. Kosicki, J. E., and Nadolny, K., in "Proceedings, 3rd International Tribology Congress Eurotrib 81 in Warsaw," Vol. II/A, p. 101. Technical UniversityRadom, 1981. 15. Erhard, G., Zum Reibungs- und Verschleissverhalten von Polymerwerkstoffen, Dissertation, Universitat Karlsruhe, Fed. Rep. Germany, 1980.