THE NATURE OF TACK ANDRIES VOETl AND CLAUDE F. GEFFKES J. M . Huber Corp., ,Vew Y o r k , N . Y . applied foice (>A( wcis the ARIOUS conceptions W h e n it became abundantly clear that the older, static cohesive strength of the of tack prevail in difinterpretation of tackiness is inadequate to explain phemalerial (3, 7, S O ) . ferent industries because of nomena observed at high rates of film separation, this Visual examination of ink study was undertaken in order to obtain a closer underthe different conditions under flow on rotating rollers +ov s standing of the dynamics of tackiness of liquids in general which tack is of importance. that film splitting is preceded and of printing inks in particular. I n some industries tack is hv the formation of thin iuk I t was found that rapid film separation does not occur undesirable, while in others, filaments which elongate and by liquid flow as previously thought, but is the result of a such as the adhesive and rubfinal13 break. The higher viscoelastic response of the liquid, which may (more or less) ber industries, tack is usually the rate of film separation, react as a solid toward rapidly applied stresses. Evidence required to provide a perthe shorter are the ink filais not an essential attribute has been found that tackiness manent bond. I n other cases ments at the time of rupture. of every viscous liquid but must be considered as a typical tack is employed to provide The formation andsplitting reaction of a freely moving long-chain molecule to stresses a temporary bond which TT ill of ink filaments on rotating of a short duration. permit separation of the rollers has been elamined The work, more particularly concerned with printing joined surfaces. photographically by Sjodahl inks, results in certain theoretical predictions of ink beThe printing industry is (21). Ph ot o mi cr o g r a ph s havior on a press. In addition, it provides a physical basis particularly concerned with taken with the aid of a for a newer conception of tackiness of liquids and may lead tack ($39,SO) and its effect on microflash at an exposure to a fuller understanding of the phenomena occurring time of 2 X 10” second show distribution and transfer of when films of liquid adhesives are subjected to rapidly that viscous inks a t high ink to various surfaces ( S I ) . changing stresses. speeds produce filaments The influence of the tack of with an elongation of wveral inks is especially - important when ink transfer is effected in a very small fraction of a second. times the original film thickness before breaking occurs. Figure 1, a photomicrograph taken in thc direction of the axis Many attempts have been made t o devise instruments which of the rotating rollers, shows the filamentation a t an enlargement would measure the tack of printing inks. Green (13)described of 6X for a u hite offset ink a t a peripheral ioller speed of 900 feet a n instrument, for measuring the force of separation of two surper minute. faces joined by a liquid, which operates essentially as a parallel It is remarkable that immediately after rupturc hardly any plate viscometer. Reed ($36)measured the resistance offered by broken filaments remain visible. Bt the exceedinglv small extwo inked rollers rotating in contact. Bekk ( 4 ) observed the moposure time, allowing the close examination of phenomma owurtion of a steel ball pulled with a constant force from an ink film. ring in 1 0 - 6 to 10-3 second, the intermediate stage of partly reDeryagin and Poretskaya ( 9 )measured the kinetic energy loss of a ceding filaments 19 viqible for less than 10-5 second on the photocylinder moving at a slow speed on a liquid film. Similar tests micrograph. Thi, indicaates that film separation IS cour1tc.i arted mere made by Bowles ( 6 ) . A general review of adhesion tests b v c.\trr~nit.lvpov, e1 Ful elaytic foic was given by Bikerman (6). 1Iost instruments express results only in arbitrary numbers. Others do not provide for rates of separation sufficiently high for the study of rapid film separation such as encountered in many industrial processes. Xone of the instruments can be used t o determine the tack of an ink between paper and metal surfaces. The present paper deals with a method and apparatus 13-hich will measure tack at high speed and in absolute units in liquid film between surface,Q of a different natuw. Special attention has been given to printing inks. FILM SEF*KATIOh
Upon application of a breaking Ioad, a proper adhcsive joint breaks within the adhesive film. Consequently, film splitting i s an essential part in the process of separating surfaces joined t]? a liquid. \Then subjected to stress, the response of a liquid may he both of a viscous and of an elastic nature. Splitting of films will OWUI by viscous flow when the rate of separation is slow. Upon increasing the rate of film separation, however, the flow response. being proportional to the elapsed time, will become less pronounced, while the elastic response, being of an instantaneous nature, becomes more important. Thus one may expect that at a high rate of film separation the liquid actually has more of the behavior of an elastic solid. Rupture mill then occur when the 1
Present address, J. M. Huber Corp., Borger, Tex.
1614
Figure 1. Photomicrograph of Filamentation for a White Offset Ink at Peripheral Roller Speed of 900 Feet per Miniite ( 6 X )
If an ink filament ifi drawn out slowly, its deformation occurs b j liquid flow. The diameter of a filament is gradually reduced in the middle parts by the process of slow elongation (necking down), causing the originally near-cylindrical form t o change into a shape resembling an hourglass. A break occurs when the thinnest part of the filament gives way. After separation, the
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1951 C
1615
The average free surface energy of inks is about 30 to 50 ergs per sq. cm., while the energy of separation is much greater. This proves that much of the energy required is used in the initial phase of the film separat,ion, the elongation of the ink film into the filaments. EXPERIMENTAL
ROLLINGCYLINDER TACKMETER. The rolling cylinder tackmeter consists essentially of a metal cylinder which i s rolled down an inclined Figure 2. Rolling Cylinder Tackmeter plane on tracks and is then allowed Above. Top view to rise on a second plane. The Below. Side view metal cylinder, A (Figure 2), 10.7 cm. long and 5.25 cm. in diameter, is electromagnetically released at B . The cylinder then rolls down the plane formed by the U-sha ed surface tension causes a retraction of the drawn-out filaments. I n tracks, C, and upwards, after passing the lowest point. $he a viscous ink the retraction by flow may be observed to take greatest height reached is recorded, I n a companion test the several seconds for its completion. experiment is repeated, but a small inked metal plate, D, equal The observation that the retraction of ink filaments separated in length to the cylinder circumference, is now placed in the path of the cylinder. When the cylinder passes, part of the ink is at high speed occurs in probably 1 X to 10 X second transferred from the plate to the cylinder. The kinetic ener y is an indication that film separation in this case does not occur by acquired by the roller is reduced by the energy required for t i e liquid flow, but by rupture of a material with an elastic behavior. transfer. The difference in potential energ of the cylinder a t the The fact that the shape of the filaments remains cylindrical, as end of each of the tests, as indicated by txe difference in height with a rubber test piece being expanded, emphasizes this conclureached, is the energy used for film splitting and may be calculated in absolute units, sion. Plate D may be provided with a film of ink, varnish, or oil or It appears, therefore, that the critical speed, above which film of any other liquid or plastic, of a desired thickness, by means of separation in the inks will occur mainly b y “solid” rupture, is a film applicator. The plate may be lifted from the instrument well within the range of the rate of film separation on a fast and weighed on an analytical balance, making it possible to measure accurately the quantity of ink applied to the plate and printing press. . the quantity transferred to the cylinder. The cylinder may be covered with paper, if desired. TACK ENERGY The surface of the liquid may be placed exactly in the plane of the bars, C, by means of wedges E and F , regulated by a micromA quantity of fundamental importance is the tack energy eter, G, or the surface of the metal plate may be placed even which denotes the total energy necessary t o cause film separawith the plane of the tracks, C , forcing the cylinder to ride the tion. ink film with its full weight. Most of the tests have been carried out in this manner in order to approach the printing pressure. In a process of solid rupture a distinction should be made beTest plates of different surface areas may be used, or a given tween different types of solids. A brittle solid is characterized plate may be partly inked. Rollers of different weights and by pure elasticity, resulting from stress deformation of primary sizes ma be used. Different roller speeds are reached by rebonds and angles as well as from displacement of particles leasing txe rollers at different heights, or b modifying the angle of inclination of the plane. The model useJhad a constant angle against van der Waals’ forces. The maximum energy necessary of inclination of 16’. Released a t the top at a height of 21.9 cm., to cause rupture of such materials is equal to the energy required a cylinder of 411 grams was found to have reached the inked to form the new surface, although the presence of structural flaws plate placed at a height of 10.5 cm. with a peripheral speed of usually reduces this quantity materially. The free surface en235 em. per second, corresponding to 470 feet per minute, which is in the range of medium high-speed printing. ergy has a value of not more than a few hundred ergs per square Inks were thoroughly worked before being applied to the test centimeter for most solids. The maximum rupture stress may be plate. About 2 minutes generally elapsed between the application indicated by dividing the free surface energy by the distance of the film and the passing of the roller for weighed test plates. over which the attractive forces operate. Experiments with films applied with a film applicator have been carried out within 2 seconds after film application, without showI n s y s t e m consisting of large, highly elongated molecules more out any noticeable difference in tack energy with f i l m subjected complicated reactions to mechanical stress may occur. Such to a longer period of rest. responses reveal the characteristics of the individual long chain The ressure employed in actual printing operations is considmolecules as well as the interactions with neighboring chains. erably Righer than the pressure of a cylinder riding the ink film. The load may be applied by either a static or an impact method. The use of lead-filled cylinders, while markedly increasing the pressure, greatly reduces the accuracy of the measurements, Static loads are applied slowly and are increased t o a maximum, since the tack energy is then only a minor portion of the total which is followed by failure of the material. The stress necessary energy involved. Even the lead-filled steel cylinders, however, to cause failure is the tensile strength of the material. Impact did not ield a pressure of over 20% of the average printing presloads are applied suddenly, or with shock. They induce vibrasure. J n c e the most important effect of the printing pressure is to regulate the transfer of ink, the differences between roller and tions ( I d ) , by which stresses and strains may be propagated as printing may not be very significant. At very high pressures, shock waves a t very high rates of deformation. The essential however a saturation effect is found in ink transfer. A quantitaultimate property in an impact test is not the maximum stress s u p tive prediction of ink behavior in the saturation range cannot be ported by the sample, but rather the energy necessary to cause carried out satisfactorily on the basis of roller experiments. Another possible point of difference is the fact that whjle the failure. printing process itself allows a period of time between the inking The deformation of an ink film in high speed printing is very of the form arid the actual impression, this period is admittedly abrupt. Thus, in newspaper printing a halftone dot is separated much longer in the tackmeter than on the press, especially when in about 2 X 10-6 second. Therefore, it is necessary to consider the test plate is weighed. Consequently, the ink has more o p the energy of separation instead of the maximum stress required portunity to rebuild a destroyed structure on the tackmeter than on the press. This objection, however, appears not to be very to cause film break.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1616
Vol. 43, No. 7
not believed to differ markedly froni the precision of the expe1,iments. C.4LCcLATION O F ENERGYUSED I S FILM TRANSFER. If :I roller of a mass &I loses Ah centimeters in height while passing over an inked plate of an area, 0, equal t o the contacted cylinder area, t’he energy, E;, used for film trnnsfer per square centimeter a t speed V is:
2
= .
X
i
fI 2.0
r
.
E;.
=
J i g Ah 0
where g is the acceleration of gravity. This energy, howeve!,, must be corrected for frictional losses, which may be calculated from the difference in descendiiig and ascending distances covered by a cylinder in the absence of the inked plat,e. If the frictional loss factor is I , the total energy needed for film transfer a t speed V is
w
2i1.0 2
The factor I is relatively small. arid h i the authors’ instrument amounted in general to less than 4yo of the total energy involved.
w
U Y
5 RESULTS 20
0
FILM
Figure 3.
40 60 THICKNESS, M I C R O N S
80
Influence of Film Thickness on Tack Energy
P’ A:
Publication green Rotary blue hlagaaine black 0 . Mineral oil
3hovr.n (30, 35) that much more than a fen seconds aie iequiied t o iebuild a destroyed structure in suitable inks. Only in ex-
treniely “short” and “buttery” pigment dispersions, Trhich cannot be used on a press, does a rapid rebuilding of structure OCCUI. Thus, it has been found experimentally that the data obtained on the tackmeter after 2 seconds are hardly different from data measured 1 minute after the application of a thoroughly worked ink film. 3.0 0
r
X
i U
2.0
$ 2 \
UI LU
7‘.
g 1.0 Y Y
Y
U
4
c 0
2.0 4.0 6.0 8.0 10.0 THICKNESS OF TRANSFERRED FILM, M I C R O N S
Figure 4.
Tack Energy z’s. Thiclciiess of Part of Film Transferred t o Paper
P: A.
Publication green Rotary blue Alagaaine black 0 . Ninernl oil
The instrument iras not provided with temperature control. It was used in a room of a reasonably uniform temperature, recorded during each experiment. By placing the plate on a hollow box. through which water of a constant temperature is circulated, it would be possible to provide temperaturecontrol. The precision of the tack energy data was found to be *3y0 for average and high tack values, but decreabes considerably for smaller values. The accuracy of the data in absolute values is
TACKENERGY,FILMTHICKNESS, A Z D FILMTRANSFER. A series of experiments were carried out ivith a variety of inks on different surfaces, a t a peripheral speed of 235 em. per second. Figure 3 shows the influence of the film thickness on the tac-k energy. The tack energy has been plotted against the film thickness for t’hree different inks on news stock. While it appears that the tack energy increases with increased film thickness, the curves obtained show an irregular character, making any simple relat’ionshipillusory. Similar irregular curves are obtained by plotting tack energy against film thicknesfi for inks on different surfaces. Figure 4 shows the identical tack energy values as given in Figure 3, but now plotted against the thickness of the part of the film transferred to the paper, determined by weighing the plate before and after film transfer. A linear relationship exists, indicating that the tack energy is directly proportional t o the thickness of the transferred part of the film. The data for the tack energy on bond stock for the samc inks have also been obtained. Thesevalues appear to follow a similar relationship as found on news stock. Figure 5 indicates the relationship between tack enei and transferred film thickness for a magazine black on a variety of printing surfaces, including paper and met:il foils. The direct proportionality between tack enerKy and transferred film thickness is again clearly indicated and the same proportionalit,y factor exists, independent of the type of surface. Only coated stock s h o w a slight positive deviation, perhaps caused by the presence of an adhesive in the stock. From t.he general validity of the direct proportionality of tack energy per square centimeter and thickness of transferred ink film, one may arrive a t the tack energy per unit volume of transferred ink, under the conditions of the experiment. This quantity may be found as the slope (tangent) of the line denoting the tack energy-transferred film thickness relationship with the ordinate. The tack energy per unit of volume of transferred ink, of a dimension ml-It-2, vi11 henceforth be indicated as “tack energy density,” DV,at the speed V. The tack cnergy density of an ink appears to be independent of the pyinting surface, contrary to the tack energy itself, which is greatly dependent upon the type of surface used. Table I indicates the tack energy densities for a number of inks a t different temperatures, a t a peripheral roller speed of 235 em. per second. The viscosity data are also included: they are discusded below.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
July 1951
1617
INFLUENCE OF VISCOSITY. Figure 6 shows the tack energy TABLE I. TACKENERGY DENSITIES FOR INKSOF DIFFERENT densities] D235, for different inks plotted against the viscosities VISCOSITIES measured at the temperature for which the tack energies had been (Peripheral roller speed, 235 cm./second) Tack Energy (Plastic) Density, Dass, Viscosity, Ergs per ,Cc. Poises ' x 10-7
Ink News red Magazine red Mineral oil varnish Publication green Rotary blue Magazine black Mineral oil Mineral oil Rotary red Rotary blue
25
400 220
210 192 77 80 56 45 45
0.37 30.0 13.0 10.7 10.2 2.4 2.5 1.4 1.1 1.1
Temp.,
c.
24.6 23.3 23.6 23.9 23.9 22.0 23.3 23.4 23.3 23.3
determined. The viscosities were measured by means of a precision high-shear rotational viscometer. For Newtonian liquids the viscosities are indicated. For non-Newtonian liquids the plastic viscosities, obtained from the rheograms as the slope of the straight part of the equilibrium torque-revolutions per minute relationship, are given. The relationship shown in Figure 5 has a general parabolic character. Figure 7 shows the identical data as given in Figure 6 , but now p!otted in a logarithmic scale. The logarithmic relationship is linear, indicating the validity of the relationship
Dm
E! 3.0
X O'
(3)
where D23.5 is the tack energy density a t a speed of 235 cm. per second; V I the viscosity; K2t6and c , constants of a value of 3.35 X lo4 and 1.52, respectively. INFLUENCE OF TEMPERATURE. Because the various data obtained at different temperatures fulfill the identical relationship, it must be concluded that the tack energy density varies with the temperature in the same way as the viscosity raised to the power 1.5. The viscosity of a liquid is generally found to vary with the temperature according to the following relationship:
*
X
d sl. 2.0
= K235
-
d
x
where A is a general constant; e , the base of the natural logarithms; R, the gas constant; T,the absolute temperature; and e,, the activation energy for viscous flow. Hence, 0
9.0 4.0 6.0 9.0 THICKNESS O F TRANSFERRED FILM, M I C R O N S
10.0
Figure 5. Relationship between Tack Energy and Transferred Film Thickness for Magazine Black on Various Printing Surfaces
where A' is a constant. Plots of In 9 against the reciprocal absolute temperature are generally straight lines, though only over a fairly limited range ( 8 ) . Thus, plots of the logarithm of the tack energy density against the reciprocal absolute temperature are also expected to he straight lines, with a slope 1.5 times the slope of the corre-
3.0
u'
Y
P Y
>*2.0
c v)
tCI
G5 1.0 t
U Y
6
VISCOSITY, POISES
Figure 6. Tack Energy Densities vs. Viscosities for Different Inks on Various Printing Surfaces Viscosities measured at temperature for which tack energies had been determined Bond 0. News A. Metal foils
+.
i XiD 1
Figure 7.
10 VISCOSITY, POISES
100
1000
Logarithmic Plot of Data Given in Figure 6
+. Bond 0. News
A. Metal foils
INDUSTRIAL AND ENGINEERING CHEMISTRY
1618
sponding viscosity plot. The range of validity of Equation 5 is wide enough to cover industrially all used printing temperatures. Figure 8 demonstrates the experimental proof of the predicted temperature dependency of Dzas for different inks, showing a linear relationship between D235 and 1/T. INFLUENCE OF THE RATE OF FILMSEPARATION. Figure 9 shows the tack energy densities a t different speeds, measured for two inks on news stock, plotted against the peripheral cylinder speeds. The speed variations were obtained by releasing the cylinder from different heights. A linear relationship exists between tack energy density and peripheral roller speed. Dv=bXV
(6)
where b is a constant. j 18.5 U
\ VL
w
f’f 18.0 W
n
6
‘
5 Y
17.5
Y I-
I
I t
2 11.0 0
9 4
25
23 16.5 z 3.9
3.4
1/r
Figure 8.
3.6
x
3.8
4.0
10s
Experimental Proof of Dependency of Tack Energy on Temperature 0 . Publication green
Equation 5 indicates the relationship which exists between tack energy density and viscosity a t a peripheral cylinder speed of 235 em. per second. Therefore, it appears that the tack energy density is proportional to the peripheral cylinder speed as well as proportional to the viscosity raised to the power 1.5 This may be expressed as follows: =
12 X V X q 3 ”
(7)
The constant, k , is thus expected to be independent of the speed. This relationship was confirmed experimentally, as may be seen from Table I1 where the constant, k , has been calculated from the data of Figure 9. The average value of the constant k is found to be 142, and Equation 7 may be written as Dv = 142V X q 3 ’ 2
From these data it may be concluded that the film separation energy is directly proportional to the area of film separated. Therefore, a value for the tack energy per unit area can be obtained by dividing the total tack energy measured by the total urea of film separated. INFLUENCE OF PRESSURE. Experiments were carried out in which the tack energy density, D235, was determined with rollers of different weights, but of the same dimensions (Table ISr). Table IV shows that the tack energy density is independent of the roller weight and thus independent of the pressure, although the quantities of ink transferred as well as the tack energies involved markedly increase with increased roller weight, as a result of the increased “printing” pressure. Tack energy densities have been determined without exerting any pressure a t all on the film, beyond a mere “touch” of the surface. This may be done, as previously outlined, by placing the top surface of the inked plate in the same plane as the tracks on which the cylinder moves. While the quantity of ink transferred is markedly decreased, the tack energy density remains unchanged in this test arrangement. Experiments were made with a roller having a radius of 8.35cm., instead of the usual roller of 5.25-em. diameter. Tack energy measurements were carried out for a heavy mineral oil, with both rollers, under identical conditions. The results show that the tack energy values are consistently smaller, in average about lo%, for the roller with the larger diameter In addition, however, the quantity of ink transferred appears to be about 10% smaller for the larger diameter roller. Consequently, the tack energy density remains unchanged. Generalizing this conclusion, it is apparent that while the tack energy is dependent upon the curvature of the surface, the tack energy density is independent of surface curvatures. Consequently, the geometry of the system may influence tack energy, but the tack energy density, the tack energy per unit of volume of transferred ink, remains unchanged, regardless of the curvature of the surface. INFLUENCE OF SURFACE ENERGY.The magnitude of the energy of separation, 3000 to 100,000ergs per sq. om., indicates that the energy necessary to create and eliminate the various inter-
TABLE 11. RELATIONSHIP O F TACKEKERGY DENSITY, PERIPHERAL CYLIXDER SPEED,AND VISCOSITY
H. Magazine black
Dv
Vol. 43, No. 2:
(74
This equation is of general importance. It allows the calculation of the tack energy density from the plastic viscosity for any given ink a t any desired peripheral roller speed, corresponding to any desired web speed in the printing process. Experiments were carried IA-FLUENCE OF AREA OF CONTACT. out in which the film separation energy was measured under the identical conditions r i t h the same ink on paper, but for different areas of contact. The results are shown in Table 111.
Peripheral Cylinder Speed Crn./&c.
Viscosity, Poises 260 260 260
235 175 125 235 175 125
DV
90 90 90
x 10-7 14.0 10.4 7.4 2.80 2.15 1.50
k 143 142 142 140 144 141
OF AREAOF CONTACT ON F r r z TABLE111. INFLUENCE SEPARATIOX EKERGY
Area,
Sq. Cm.
37.6 74.6
Film Separation Energy ( V = 235) per Cm. of Transferred Film Thickness (in Ergs) for Total Area 4 . 6 4 x 109 9 . 2 6 x 109
Dzas X 10-8, Ergs per Cc. 1.23 1.24
Temp.,
C.
22.2 22.2
OF TACKENERGY DENSITY WITH TABLEIV. DETERMINATIOK ROLLERS O F DIFFERENT WEIGHTS BUT O F SaME DrnrENsIoNs
Roller Weight, Grams 2560 412 170
x lo-’, Er s per 1.30 1.28 1.29
D 2 3 6
E,.
Temp.,
c.
24.5 24.5 24.5
July 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
1619
9.0
For a given small initial film thickness the stress, F , may, therefore, be considered constant in the experiments and the energy of separation may then be represented by
E, = F(h/
- ho)
(10)
Substituting Equation 9 in 10, 0
Figure 9.
I00 150 VELOCITY, CM./SECOND
50
Tack Energy Densities at Different Speeds Peripheral Cylinder Speeds
US.
0 . Publication green (21.0' C.) W,
a2 1 E, = 3 7 - -
¶SO
900
XIagaaine black (21.Io C.)
faces involved (below 100 ergs per sq. cm.) is exceedingly small compared with the actual separation energy. This fact could be established independently by the following experiment. The energy of film separation was determined on the rolling rylinder apparatus for a mineral oil on news stock. I n a subsequent test the experiment was repeated but a quantity of O.O40J, of a silicone oil (DC 200, of Dow-borning Corp., Midland, Mich.) was added to the oil. This did not measurably influence the viscosity of the oil, but reduced the value of the static surface tension by about 25%, as found by measurements with the aid of a du Nouy tensiometer, and presumably also reduced the dynamic surface tension. The result of these tests did not indicate any difference in tack energy densities for the oils with equal viscosity but different surface tension, although the energy required for the creation and abolition of the surface areas involved differs materially in both cases. This result, however, can be easily explained. The mechanical work absorbed by the system is considerably larger than the energy necessary to create the new surfat-es, even taking into account the energy required for the additional surface area created in the process of filamentation. The accuracy of the experiments, +=3y0, is simply not high enough to register the relativcly srnitll differenres in surface energy involved. HYDRODYNAMICS OF FILM SEPARATION BY FLOW
It is now possible to check experimentally the validity of the hitherto often accepted hypothesis of film separation by liquid flow (IS). The energy of film separation is directly proportional to the transferred film thickness and also proportional to the viscosity raised to the power 1.5. The tack energy is, furthermore, directly proportional to the rate of separation. Since the rate of separation is inversely proportional to the contact time, the tack energy is also inversely proportional to the time of contact. The actual energy of separation for a Newtonian mineral oil of a viscosity of 56 poises a t 23.4" C., in a film thickness of 10 microns, was found to be 3.0 X lo3 ergs per sq. cm. a t a rate of separation of 235 cm. per second on a metal surface. The hydrodynamics of flow of a Newtonian liquid between parallel plates has been carried out by Stefan (28). The stress, F , necessary to se arate two parallel circular plates of radius a in time 1 was foun: to be
where h, and h/ are the initial and final distances between the plates, and 7 the viscosity of the Newtonian liquid which separates the plates. To find the energy of separation, no integration is necessary or even possible, since Stefan's equation is derived for the horizontal liquid flow which occurs when the values of ho and hf are only small fractions of radius a. This condition is fulfilled in the present experiments, where the film thickness is much smaller than the dimensions of the contact area. A break was found to occur for h, = 5h,, by direct microscopic examination of an ink film between rotating rollers. This value may be considered an average value. Since in this case l/h' is negligible compared with lih.2, Equation 8 reduced t o
t ho
(11)
The above relationship indicat,es that the energy of separation must be directly proportional to the viscosity of the liquid and inversely proportional to the film thickness, in comdete contradiction to the observed facts. For a quantitative evaluation it is necessary to estimate the expansion time during which the ink film is subjected to the stress acting to cause separation. The total contact time between roller and plate may be divided into two essentially equal periods-namely, the compression and the expansion period. The contact time may be roughly estimated from a measurement of the width of a roller impression of the oil deposited on the plate a t rest. For the oil of a viscosity of 56 poises a t 23.4' C., a t a film thickness of 10 microns, this value was found to be 0.15 om. The contact time may now be found by calculating the ratio of the impression width to the total length contacted per second. Thus, for a speed of 235 cm. per second, the contact time t236 was found to be I
/2ja
=
0.15 235
- = G.0 X
second
(12)
Therefore, the expansion time is estimated at 3.0 X 10-4 second. A more accurate method for the determination of the expansion time is by means of high s eed photomicrography. From Sjodahl's photomicrographs, t a i e n a t an ex osure time of 2 X lo-' second (27), the time elapsed between tEe beginning of the film elongation and the moment of final rupture may be determined. In the exam le of a viscous offset ink, a t a speed of 450 cm. per second, an eyongating stress duration of 3.4 X 10-4 second was found. For less viscous inks, smaller values are expected. Thus, in general, in high s eed printing, expansion contact times of the order of 10-4 seconcfare expected. It must be remarked that these values have been determined for heavy, continuous ink films. For lighter films, and especially for discontinuous films such as are applied in halftone printing, even smaller values for the expansion stress duration period are expected, leading to probable values of an order as small as 10-6 second a t high printing speeds. Substituting the value found from Equation 12 into the relationship expressed by Equation 11, the energy of separation for unit area, by liquid flow, of the mineral oil with a viscosity of 56 poises and an initial film thickness of 10 microns is found to be
E, = 5.6 X
lo6ergs per sq. cm.
or about 2000 times the actual value. This result emphasizes the complete failure of attempts to explain the observed phenomena by liquid flow. Equation 8 was derived for a separation of the plates by a motion perpendicular to the plane of the plates in the presence of an unlimited amount of liquid. Actually a circular motion is carried out by the roller peri hery, while only a limited quantity of liquid is present between tEe cylinder and the plate. Thus, the geometry of the system differs from the system visualized by Stefan (68). The rather complicated hydrodynamics of such a system has been investigated by Reynolds ( 2 6 ) in a study of lubrication problems. Re nolds carried out a very general theoretical investigation of t t e frictional forces in rotating journals on cylindrical as well as on flat surfaces, in the presence of a limited as well as an unlimited supply of a Newtonian lubricant. For a case of a cylinder rotating on a flat surface in the presence of a limited sup ly of a Newtonian lubricant (Reynolds' case KO. 7 ) , the hYBrodynamical approach leads to the conclusion that the frictional resistance is directly ro ortional to the viscosity of the lubricant and increases as t l e $stance between the surfaces decreases. For a limited supply of lubricant the frictional resistance increases with peripheral cylinder velocity, but less than direct proportionality. At a very limited su ply of lubricant the ftictional resistance may even be indepedent of the cylinder speed.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1620
For an unlimited supply of lubricant, howcver, the frictional resistance is directly proportional to the peripheral cylinder speed. Since the energy dissipated is proportional to the frictional resistance (15) Reynolds findings may be summarized in the following equation :
where E , is the hydrodynamically calculated separation energy; h, the film thickness; p , a constant; 7, t,he viscosity of the liquid; and Ti, the peripheral roller speed. The exponent n varies in value from n = 0 for very small quantities of liquid to n = 1 for an unlimited supply of liquid, while the exponent m has a positive value, generally not greatly different from 1. The present experiments have shown the actual energy of film
separation a t speed V to be represented by:
Ev
= 142 X q 3 I 2X ht X
V
(14)
where ht is the transferred film thickness, a type of relationship already indicated in Equation 7a. While the transferred film thickness is not directly proportional to the actual film thickness, the value of hr always increases with increasing h. Proportionality is generally reached for large values of h ( 2 2 ) . Therefore, it appears that even a more precise hgdrodynamical treatment of the energy dissipated in the rolling cylinder tackmeter, calculated on the basis of the flow of a Newtonian li uid, leads to a result utterly incompatible with the experiment3 tests. The conclusion must be reached that in rapid film separation the film does not split by simple liquid flow. VISCOELASTIC FILM BEHAVIOR
ELASTIC RESPOSSES TO STRESS IS LIQUIDS. In the process of film separation the ink filaments are elongated and finally rupture. I n rapid separation the elongation of the filaments is not solely caused by liquid flow, but by a viscoelastic response of the liquid to the applied stress. The energy necessary for rupture of the film is a negligible part of the total energy required for film separation and the bulk of the energy is used up in the process of film elongation. The concept that any liquid may react elastically to shearing stresses, if applied sufficiently rapidly, was suggested by Poisson ( 2 3 ) as early as 1831. Direct experimental proof was given by Raman et al. (24)who showed that a simple liquid such as glycerol can be made to support transverse vibrations, provided the frequency is high enough. Instantaneous elasticit,y in brittle solids gives rise to a modulus of elasticity of the order of 10'2 dynes per sq. em., only slightly affected by temperature changes. Elastic responses to stress of a different nature may occur in materials consisting essent,ially of large, highly elongated molecules. Such a behavior is especially pronounced in rubbery materials and generally connected with a modulus of elast,icity of the order of 106 dynes per sq. cm., which increases proportionally t o the absolute temperature. This mechanism, known as configurational elasticity, is a process connected with the orientation, alignment, and elongation by uncurling of large chain molecules. Configurational elasticity gives rise to a retarded elastic effect, since the stress relaxation occurs by a time-consuming diffusion process of the individual segments of the chain molecules into unstrained positions (1). Liquids consisting of medium and longer chain molecules subjected to shearing stresses of brief impulsive or rapidly oscillating character exhibit another type of shear elasticity, identified by Mason (18) as a Maxwell type of viscoelastic behavior (81). This elasticity is characterized by a modulus of t'he order of 5 X 1 0 6 to 5 X 108 dynes per sq. em. a t ordinary room temperatures, for frequencies of the order of 10 to 100 kilocycles per second, cbrresponding to impulsive stress of a duration of to 3.0-5 second. The logarithm of this modulus is inversely proportional to the absolute temperature. Measurements in polystyrenes and polyisobutylenes have shown that this rigidity occurs in both polymer solutions as well as in liquid polymers, alt,hough the modulus in solutions decreases markedly with decreasing polymer concentration (10).
Vol. 43, No. 7
The mechanism of this response to stress appears to be connected with a composite motion of the molecular chains, which includes hindered rotations within chains as well as interaction of small segments between chains. This type of elasticity is not an equilibrium condition, since, for the short impulses considered, equilibrium is not established and the reaction depends on the nearest neighbors. If sufficient time is given, however, the normal configurational type of eIasticity will prevail (16, 19). At frequencies higher than 100 kilocycles per second, corresponding to stress impulses of a duration below 1 0 - 6 second, the indicated motions cannot take place and the rigidity approaches the value for an elastic solid (go). The modulus connected with the nonequilibrium shear stiffness shows a remarkable analogy with viscosity, in that its magnitude as well as its temperature dependency is closely related to those of viscosity. The stress relaxation of this mechanism, according t o Ferry ( I O ) , involves most likely a kind of molecular motion similar to the motion responsible for viscous deformation. SHEAU MODULUS OF INK FILMS.I n order to identify the mechanism of film elongation in the process of film separation, it is important to estimate the order of magnitude of the ehear modulus of the ink film subjected to brief impulsive stresses. It is possible to arrive a t an approximated value of the shear modulus from the experimentally determined tack energy density values, on the basis of direct calculations. Assuming, for thiE calculation, that the duration of the stress impulse is so short that the flow response of the ink film is negligible, the material then behaves as an elastic solid. Assume a linear force-deformation curve for the ink (Hooke body), in which the slope is represented by a Young's modulus, S. Let the original film thickness be indicated by h,, and let the film thickness be h upon Eubjugation to a stress, F . The elongation, A, a dimensionless quantity, is defined by A=--
h
- h, ho
The maximum filii1 thickness, h M , corresponding to a maximum elongation, AX, is obtained at the maximum stress, F M , just prior to rupture. The separation energy a t the peripheral cylinder speed, V , is then given by the equation
SAh,dA =
1 - hoSA% (16) 2
and thus
Identifying for this rather crude approach the transferred film thickness with the actual film thickness, a procedure allowable where only the order of magnitude is of interest, one finds
Since the film is considered incompressible, the shear modulus is given as follows:
G = -S 3
and
Equation 20 relates the shear modulus directly t o the tack energy density, for the restrictions set forth previously.
July 1951
INDUSTRIAL A N D ENGINEERING CHEMISTRY
For a numerical evaluation of Equation 20 it is necessary to obtain the value of the maximum elongation prior to film rupture. This value may be directly determined from Sjodahl’s experiments for a viscous offset ink (27). At a speed of 235 cm. per second, the maximum length of the ink filaments is about 25 times the original film thickness, as found by interpolation from data at other speeds. One must consider, however, that the film does not elongate homogeneously, but in filaments. The total cross-sectional area of the filaments may be estimated at less than one fourth of the original film area. The ink in the filaments originates, therefore, from a film thickness of a t least four times the original film thickness. The maximum elongation of the film is estimated a t only about 6. I n view of the doublesided filament expansion in the latter case, compared to the singlesided expansion of the filaments on the flat plate, the maximum elongation on the tackmeter is smaller. I n general, the maximum elongation at a speed of 235 cm. per second may be estimated at between 3 and 10 for conventional inks, in which the vehicle itself is not of a rubbery nature. The tack energy density varies for most printing inks at the indicated speed between IO7 and 109 ergs per cc. From Equation 20 the shear modulus for most commercial inks has a value estimated to be of the order of 106 to 108 dynes per sq. cm. The relation of the shear modulus to a viscosity is indicated by Equations 20 and 7. The logarithm of the modulus is expected to be inversely proportional to the absolute temperature, under certain conditions with respect to the maximum elongation, more fully discussed afterwards. The maximum stress necessary to cause rupture may now be calculated.
F M = AM = 3 G h ~
(21)
Substitution in Equation 20 yields
FM = -.2Dv x.w
The value of the maximum stress may now be calculated from Equation 22. For most commercial inks the maximum stress appears to have a n order of magnitude of lo7 to IO@ dynes per sq. cm. These data indicate that the maximum shearing stress to which an ink is subjected on a press is exceedingly high. It occurs, however, only for an extremely short period of time, just prior to filament rupture. STRESSRELAXATION MECHANISM 09 FILM SEPARATION. From the foregoing it must be concluded that the viscoelastic response to stress found to exist in the liquid films can neither be of the simple elastic solid, nor of the configurational elastic type. For the elastic solid type the modulus would be much higher than actually found and hardly affected by temperature. For configurational elasticity the modulus would increase with increased temperature, instead of showing a pronounced decrease. It is not difficult to identify the elastic response to stress of the ink film with the nonequilibrium elasticity, characterized by chain rotation and interaction of neighboring chain segments, as previously discussed. The duration of the stress impulse, 10-4 to 10-6 second, is of the correct order of magnitude for this type of stress relaxation, and the modulus is of the same order of magnitude as found by Mason ( 18)by direct measurement by means of transverse vibrations induced by piezoelectric crystals in long chain molecules. A direct experimental proof of the existence of such a stress relaxation in printing ink vehicles was obtained by Mason ( 1 7 ) , who investigated printing ink vehicles with the aid of vibrating crystals. Even a vehicle as simple as a mineral oil showed pronounced elastic reactions to stress at the measuring frequency of 19.7 kilocycles per second, corresponding to a stress duration of 5 X 10-6 second. A linseed oil vehicle showej even stronger elastic reaction. Therefore, it is rather obvious that all printing inks,
1621
which usually have vehicles of a more complicated structure and of a larger molecular size, will show pronounced elastic reactions to stress at printing speeds. Table V shows the observed values of the shear modulus as well as the values calculated from the measured tack energy density b y means of Equation 20, taking into account a maximum elongation of between 3 and 5.
TABLE V.
OBSERVED VALUESOF SHEARMODULIA N D VALUES CALCULATED FROM MEASURED TACK ENERGY DENSITY
Viscosity, poises at 25’ C. Tack ener y density ergs/oo. X 10-7 Calcd. rno%ulua, dyn’es/sq. om. X 10-8 Obsvd. modulus, dynes/sq. om. X (17)
Mineral Oil 63 1.67 4 to 16 7.85
Bodied Linseed Oil 65 1.75 5 to 18
15.8
In view of the character of the approximation, meant only to indicate the order of magnitude of the modulus, the result must be considered satisfactory. The logarithms of the nonequilibrium moduli are inversely proportional to the absolute temperature, exactly as had been found by the authors for the tack energy density (Figure 7 ) . Consequently, the viscoelastic theory of film separation provides the quantitative prediction of the order of magnitude of the energy of film separation, in contradiction to the flow theory of film separation where the calculated values in a test case differed by a factor of 2000 from the experimental energy data. The proposed mechanism for film separation is thus of the Maxwell type and, therefore, may be schematically represented by a spring in series with a dashpot. The spring symbolizes the instantaneous reversible elasticity with the shear modulus, G, and the dashpot , the time-dependent irreversible liquid flow with a viscosity q. The shear elasticity of a Maxwell element can be relaxed in the relaxation time, T , which may be determined from the relationship:
Since the average order of magnitude of the shear modulus is estimated at 106 to lo7 dynes per sq. cm. for printing inks which have a viscosity between 10 and 500 poises, the relaxation time of inks is of the order of second. The relaxation frequency, the reciprocal of the relaxation time, is, therefore, of the order of lo4 cycles per second. The stress duration in the present experiments is of the order of lo-’ to 10-6 second, corresponding to a frequency of 104 to lo5 cycles per second and hence of a somewhat smaller order of magnitude than the relaxation time. At high speed printing the stress duration is much smaller than the relaxation time and elastic effects completely overshadow viscous effects a t these speeds. The modulus is indicative of the rigidity a t a frequency which is high compared t o the relaxation frequency. From Maxwell’s theoretical views it has been derived that for frequencies oomparable t o the relaxation frequency the rigidity decreases slightly with decreasing frequency (8). Thus, a t a frequency equal to the relaxation frequency, the rigidity is only 0.83 times its value a t infinite frequency. A slight increase in the modulus with frequency (or with roller speed) a t the slower speeds must be expected, because in this range the stress duration for most inks is of the same order of magnitude as the relaxation time of the Maxwell element responsible for film separation. This effect, known as the dispersion of rigidity, has been established experimentally in polymers and polymer solutions subject to stresses of a frequency comparable to the relaxation frequency (11). The modulus, G , is actually an adiabatic modulus, since the
1622
INDUSTRIAL A N D ENGINEERING CHEMISTRY
duration of the streas is too short to allou temperature exchange with the environment. Adiabatic extensions, however, are followed by adiabatic returns in extremely short periods of time and in the absence of hysteresis no temperature changes are expected. Thus the shear modulus may not, be different from an isothermal modulus (1). The mechanical work of separation, however, is not actually taken up reversibly by the system and cannot, therefore, be completely identified with the free energy of film separation. The stress relaxation mechanism outlined above now provides the explanation of the experimentally derived Equation 14, expressing the direct proportionality of the energy of film separation to the rate of film splitting as well as to the transferred film thickness, I n addition, it must indicate the established relatiomhip between tack energy and plastic ink viscosity. FILXTHICKNESS AND IXKTRANSFER. The proposed mechanism for the film separation is the key to the influence of the film thickness. The energy required for the composite chain motion must be proportional to the number of molecules subjected to stress and thus to the volume energetically involved. Per unit area this energy will be directlyproportional to that part of the film which reacts to the mechanical stress. The question of whether the entire film or only part of tile film is energetically involved in the film separation needs further elucidation. I n a solid film showing instantaneous elasticity the entire material is obviously strained by a stress. This type of elasticity, however, is not of any significance in the ink film. Partial involvement of the film, on the other hand, may be expected in the stress relaxation mechanism previously indicated for film separation. I n the rolling cylinder apparatus the stress exerted on the film must be considered an impact load, which necessarily creates a vibration. This vibration starts as an impulse and may be propagated as a shear wave of a frequency at least of the order of 104 cycles per second, in view of the stress duration period. Such shear waves are rapidly damped; their critical damping distance is of the order of one wave length (11). Experiments indicate that a complete saturation of the damping of such waves may even occur within a few microns (16). The present test produces low pressure and thus the amplitude of the vibration is rather low. Under these conditions the saturation of the damping of the oscillation in the filaments takes place at a short distance from the impacting roller, at a fraction of the total film thickness. Rupture will occur at the maximum elongation, causing separation and transfer of the vibrating part of the filaments. At higher printing pressures, resulting in an increased amplitude, effective damping is materially reduced, which in turn leads to an increased film transfer. The mechanical work taken up by the ink resides in the transferred layer. The tack energy density is, therefore, proportional to the transferred film thickness. This proportionality is a direct consequence of the mechanism of film separation. INFLUENCE OF RATEOF FILMSEPARATION.It was found experimentally, as expressed in Equation 7, that the tack energy density is proportional to the roller speed. This proportionality is also directly connected with the mechanism of film separation. Equation 17 expresses the proportionality between the tack energy and Young's modulus. This equation may be written, in view of Equation 19, as
A series of experiments have been carried out in which the volume fraction of the ink film transferred to the paper, fv, was determined as a function of the roller speed, for different film thicknesses. The results indicate that for each film thickness fv is proportional to the contact time, or inversely proportional t o the roller speed.
f1-
where d is a coustant.
Vol. 43, No. 7
=
This relationship leads to
Substituting t,his relation into Equation 24 gives the expression
and
Hence, the tack energy density is directly proportional to the roller speed and thus to the rate of separation, as found experimentally. As had been previously indicated, the modulus is not entirely independent of the speed, but will increase slightly with roller speed in the critical frequency range, where the relaxation time is of the same order of magnitude as the stress duration. In addition, the maximum elongation is reduced slightly with increased speed. These effects, however, are only secondary. Equation 25, obviously, is valid only in the range of limited transfer covered by these experinients. It cannot hold in the saturation range, at much higher pressures, where a neai complete film tranefer occurs. INFLUENCE OF VISCOSITY.Equation 7 indicates that the tack energy density is proportional to the viscosity raised t o the power 1.5. From the theoretical approximation, Equation 20, it appears that 2
Dv = 3- GXtf
(29)
The shear modulus of the nonequilibrium stress relaxation mechanism has been determined for a number of medium and longer chain organic materials and its dependency upon the viscosity has been established. The modulus is approximately proportional to the square root of the viscosity in the frequency rmge of lo4 to lo6 cycles per second (16, 18). The relationship between the maximum elongation of the ink filaments and the ink viscosity is not known at present, although it has been found that the maximum elongation is larger for more viscous inks. From an examination of the theoretical Equation 29 and the experimental relationship expressed in Equation 7 it is concluded that Equation 7 may be reconciled with Equation 29 by the hypothesis that the maximum elongation, AM, is proportional to the square root of the viscosity, for comparable liquids. This hypothesis does not appear to be contradictory to any experimental or theoretical conclusion. The complete theoretical derivation of Equation 7 is possible only when the relationship betn e m the maximum filament elongation and the ink viscosity has been uncovered. One of the interesting conclusions of the experimental part is that the tack energy density depends on the plastic viscosity and not on the apparent viscosity. I n attempting to explain this fact, two different effects of high speeds in printing must be distinguished. I n the first place, a t high speeds the ink is subjected to high shearing stresses, causing the more or less complete breakdown of the loosely connected particle arrangement known as structure. I n the second place, a t high speeds the rate of film separation is high, resulting in a more pronounced elastic response of the ink film to stress. Press speed, therefore, determines the character of the film separation. Both phenomena are not necessarily tied together, since it is possible, in principle, t o print a t any desired rate of film separation with an ink in any state of structural breakdown, by operating the ink distribution merhanism of a press independently from the printing mechanism,
July 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
As previously indicated, commercial inks do not show a very rapid rebuilding of a broken-down structure and inks subjected to high shearing stresses will generally remain in a structure-free state for a period of time long enough t o operate the rolling cylinder tackmeter (3%’). Another important consideration is that one of the results of the structural build-up in inks i s that an applied stress is partly used to break up the existing structures. The plastic viscosity is the resistance to viscous deformation a t higher shearing stress, in the absence of structures, while the apparent viscosity a t lower shearing stresses results from a mixed response t o stress, partly the breaking up of structures, partly viscous flow. It now becomes apparent that the ink cannot respond to a brief impulsive stress of the order of 1 0 - 4 second by the destruction of the structures. The time scale of the action is too rapid for a viscous ap well as for an equilibrium configurational elastic response and evokes only local chain motions. Such rapid impulses do not, therefore, cause a breaking of the structures in non-Newtonian dispersions, the relaxation time of which is generally much larger than second. Thus, it may be concluded that the structural build-up in inks a t rest is entirely without significance for the tack energy and only the plastic viscosity is relevant. While basically the mechanism of stress response in the ink film has been ascribed in this investigation to the reaction of longer chain organic compounds, the presence of pigments and other ink constituents will affect the magnitude of the stress response. The stress relaxation mechanism involves the same type of molecular motion as the viscous deformation (IO). Therefore, it is understandable that the presence of pigments and other ink constituents will influence the activation energy of the composite chain motion responsible for the stress relaxation, by modification of attractive forces, by steric hindrance, or by other mechanisms, in the same manner as the activation energy of the viscosity i@modified. Consequently, while the response t o strew is basically a reaction t o stress of the longer chain vehicle constituents, the influence of other materials present may be very pronounced. A similar effect is observed in rubber, where the mechanism of response to stress is basically a reaction of the long chain hydrocarbon molecules, but which may be modified markedly by other constituents, such as carbon black and like materials. It is possible t o prepare viscous liquids which cannot react elastically to stresses of a duration of 10-4 t o 10-6 second. Such systems may be made by incorporating pigments, such as clay, carbon black, etc., in liquids such as water, ethyl alcohol, or similar materials consisting of small molecules. The resultant dispersions show a pronounced resistance to flow; yet they are devoid of all tack. This agrees with the results of the present investigation, indicating that not the visrous flow, but a viscoelastic mechanism is responsible for tackiness. The observation that all adhesives are of a high molecular nature emphasizes this conclusion. It wm found that while the tack energy density increases with the viscosity of the liquid, all liquids investigated were of a high molecular nature and consisted of molecules with long carbon chains. In all these cases both the stress relaxation by viscous flow and by the described viscoelastic mechanism depend on the same molecular motion (IO). Thus, the coefficient of viscosity in all experiments described affords simply a convenient measure for the resistance t o stress relaxation by the viscoelastic mechanism. This explains the paradox that while the stress relaxation occurs by a viscoelastic effect, the coefficient of viscosity seems to be a determining factor in the tack energy. An intereRting observation is that tackiness seems to be accompanied by “stringiness.” Viscous aqueous pigment dispersions are not only nontacky, but they cannot be drawn into strings. It does not seem improbable that both tackiness and stringiness of liquids are the result of similar viscoelastic reactions of longer chain molecules.
1623
PRACTICAL APPLICATIONS
An extensive study has been made of the phenomena of picking and trapping, the results of which will be reported more extensively elsewhere. It can be said, however, that picking, the rupture of a paper surface by inks, depends solely on the tack energy density of the ink. On the basis of the experimentally determined paper strength it is possible t o predict the behavior of the paper on the press, by applying the relationship expressed by Equation 7. Similarly, trapping, the proper printing of one film upon the next, depends entirely upon the tack energy density of the ink. Proper predictions of ink behavior in trapping can be made on the ha& of Equation 7. CONCLUSION
Tack in liquid films is related to a response to stress mechanism found in long chain molecules, characterized by a modulus of 106 to lo8 dynes per sq. cm., and a relaxation time of the order of 10-4 second. This is not in disagreement with the general predictions of Josefowitz and Mark ( 1 4 ) on the physical conditions governing the phenomenon of‘ tack, correlating stickiness (tack) with a response-to-stress mechanism of longer chain molecules with easy movable chain segments or chain links, of an average length of about a hundred links. The fact that very short periods of stress duration are included in the present investigation explains that the viscosity range has been extended toward fower viscosities w d includes somewhat shorter chains. ACKNOWLEDGMENT
The authors wish to express their thanks to W. P. Mason, of the Bell Telephone Go., Murray Hill, K. J., for his most valuable cooperation in investigating the viscoelastic properties of some of the printing ink vehicles with the aid of vibrating crystals, and to the J. M. Huber Corp., for their permission t o publish this work. NOMENCLATURE = radius of circular plate A , = constant A = constant
a
b
c
= constant = constant
= constant Dv = tack energy’density a t speed V , ergs per cubic centimeter e = base of natural logarithms E; = energy of film separation corrected for frictional losses Ev’= energy of film separation not corrected for frictional losses E, = energy of film separation by viscous flow F = stress f v = volume fraction of film transferred a t speed V g = acceleration of gravity G = shear modulus of elasticity h = film thickness ho = initial film thickness hf = final film thickness h, = maximum film thicknem hr = transferred film thickness Ah = difference in height K V = constant IC = constant 2 = frictional loss factor M = mass of cylinder m = exponent n = exponent 0 = area of cylinder p = constant R = gas constant S = Young’s modulus of elasticity .T = absolute temperature t = time t v = contact time a t speed V = activation energy of viscous flow so = coefficient of viscosity A = elongation A M = maximum elongation 7 = relaxation time
d
INDUSTRIAL AND ENGINEERING CHEMISTRY
1624
LITERATURE CITED (1)
(2) (3) (4) (5) (6) (7) (8) (9)
(10) (11) (12) (13) (14)
Alfrey, T., "Mechanical Behavior of High Polymers," S e w York, Interscience Publishers, Inc., 1948. Andrade, E. N. da C . , Phil. M a g . , 17, 497, 698 (1934). Askew, F. A , , Paint Technol., 9, S o . 106, 217 (1944). Bekk, J., Deut. Drucker, 44, No. 256, 450 (1938). Bikerman, J. J., Palra Packaging Bzdl. 2 (1945). Bowles, R. F., P a i n t Technol., 9 , Yo. 106, 213 (1944). De Bruyne, S . X.. Ibz'd., 9 , S o . 106, 211 (1944). Derjaguine, B., Beitr. ongew. Geophys., 4, 452 (1934). Deryagin, B. W,,and Poretskaya, A. P., "The PhysicalChemical Fundamentals of the Printing Process," Moscow, The Graphic Institute, 1937 (in Russian). Ferry, J. D., Ann. AT.1'. Acad. Sci., 44,313 (1943). Ferry, J. D., J . Am. Chem. Soc., 64, 1323 (1942). Gilkey, H. J., et al., "Materials Testing," New York, 5IcGran-Hill Publishing Co., 1941. Green, H., IND.ENG.CHEM.,AS.IL. ED., 13, 632 (1941). Josefowitz, D., and Mark, H., I t i d i u Rubbw W o l l d , 106, 33 (1942).
Vol. 43, No. 7
Lamb. H., "Hydrodynamics," 6th ed., p. 588, CambIidge, England, The University Press, 1932. Mason, W. P., J . Colloid Sei., 3, 147 (1948). Mason, W.P., private communication. Mason, W.P., T m n s . A m . Soc. Mech. Engrs., 69, 359 (1947) Mason, W.P., et al., J . -4pplied Phys., 73, 1074 (1948). (22) (23) (24) (25) (26) (27) (28)
(29) (30) (31) (32) (33)
Ibid., 75, 936 (1949). Maxwell, J. C., Phil. Tians. Royal SOC.,157, 49 (1867). Mill, C. C., et al., Patra J., 3, 215 (1940). Poisson, S. D., J . dcole polytech., 20, 139 (1831). Ramati, C. V., et aZ., h i a t w e , 143, 198 (1939). Reed, R . F., Am. Ink Maker, 17, No. 12, 27 (1939). Reynolds, O., Trans. Royal Soc. London, 177, 190 [1886). Sjodahl, L. H., Modern Lithography, 17, 8 5 (1949). Stefan, J., Sitz. her. A k a d . Wiss.Wien, Math. naturw. Klasss, 69, 713 118741. Toe:; i., Am.Ink Maker, 18, S o . 3, 27 (1940). Ibid., 23, No. 10, 65 (1945). Ibid., 27, No. 2, 27 (1949). Ibid., S o . 6, p. 31. Voet, A, J . Phys. &: Colloid G h m . , 51, 1037 (1947).
RECEIYED March 2 , 1960,
Vapor-Liquid Equilibrium of Antimony Pentafluoride-Hydrogen Fluoride PROPERTIES OF ANTIMONY PENTAFLUORIDE ROBERT C. SHAIR' .4ND W. FRED SCHURIG Polytechnic I n s t i t u t e of Brooklyn, Brooklyn 2, hi. Y . Antimony pentafluoride is used as a fluorinating agent. The process for its manufacture consists of interacting antimony pentachloride with hydrogen fluoride to form the pentafluoride. A necessary step in the purification of the product is separation of the excess hydrogen fluoride by distillation. For design of a suitable distilling column, vapor-liquid equilibrium data on the binary system and information on some of the physical properties of the compounds are necessary. Vapor-liquid equilibrium data for the binary system, antimony pentafluoride-hydrogen fluoride, are reported at 1 atmosphere pressure. The system is very far from ideal.
The vapor pressure of antiinony pentafluoride is reported from 50" C. to its normal boiling point, which was determined to be 142.7" C. The specific gravity is 3.145 at 15.5"/15.5' C.; its latent heat of vaporization is estimated I O be 10,370 calories per gram-mole at the normal boiling point. The results add to the Itnowledge of the physical properties of antimony pentafluoride and are of significance in process equipment design. The work further develops the techniques of the use of an Othmer-type recirculation still for vapor-liquid equilibrium, specifically a metal modification where internal visual observations are limited.
&-TIMONY pentafluoride is used as a fluorinating agent, and is especially applicable in many instances because it is a liquid. In the manufacture of antimony pentafluoride, antimony pentachloride is treated with hydrogen fluoride in excess to interact the halogens. A necessary step in the preparation is separation of the excess hydrogen fluoride from the antimony pentafluoride by distillation. It was desired to determine the vaporliquid equilibrium data requiied for designing the distillation equipment.
impurities \vere found, the antimony pentafluoride was concluded to be 100% pure. The hydrogen fluoride used was a commercial grade of 99.8% purity.
PREPARATION OF MATERIALS
Hydrogen fluoride mas bubbled into antimony pentachloride in excess to form antimony pentafluoride (7). The crude antimony pentafluoride was distilled and the middle fraction collected and redistilled. The middle cut of this second distillation was collected and analyzed for all possible impurities, since the only analytical method available for antimony pentafluoride was not found reliable. The only possible impurities in the antimony pentafluoride were aluminum fluoride, antimony pentachloride, antimony trifluoride, water, and hydrogen fluoride. \Then no 1
Present address, Stauffer Chemical Co., New Y o l k 17 N. Y .
ANALYTICAL METHOD
Antimony pentafluoride has a specific gravity of about 3. Hydrogen fluoride has a specific gravity of about 1. This difference enables an accurate analysis of mixtures of the two compounds by density. With ordinary care, using a calibrated pycnometer, specific gravity could be determined to t0.002. For a spread in specific gravity from 3.000 to 1,000, which rppresented 100 weight yo in composition, a determination of *0.002 was equivalent to an analysis precise to *O.l weight %. It is probable that for solutions containing low hydrogen fluoride percentages, the precision was reduced to +0.5 weight yo. Two pycnometers similar in principle to the specific gravity bottle were specially made of aluminum and calibrated. Mixtures of known composition of hydrogen 5uoride and antimony pentafluoride were carefully made up and their specific gravities measured to give the specific gravity-composition relationship ehown in Table I and Figure I .
