1 1 1
FIGURE1.
COXSTANT-PRESSURE DIFFUSION CELL WITH SPECIMEN
G.4SKET A N D
TEST
Diffusion of Water through Insulating Materials Rubber, Synthetic Resins, and Other Organics
Q
A
FIGURE2. WAX DIFFUSIONCELL WITH DRYING AGENTSUPPORTED BY CALIBRATED QUARTZ SPRING
LL organic materials sorb water, and in
this process diffusion of the water into the material plays an important part. The wide use of organic materials as dielectrics and protective coatings in the telephone industry has greatly stimulated the need for practical engineering data and formulas governing the retention and passage of water through such materials. It is customary to evaluate insulating materials by measuring their electrical properties under dry and wet conditions and, in cases where water-resisting characteristics are important, to include measurements of water sorption. Sorption measurements, however, do not always give a complete picture of the water-resisting characteristics of a material since a considerable amount of water may diffuse through it and only a small amount be sorbed. A determination of the rate a t which water diffuses through a material will, consequently, be an important measure of the protection against water which the material affords, and will facilitate a calculation of the amount of material required for this protection under a given set of conditions. The purpose of the present investigation was to obtain data on the rate a t which water passes through several materials on which no data were available, particularly on some of the newer high-polymeric substances such as polyethylene tetrasulfide, polychloroprene, and polyvinyl derivatives. It was also the purpose to establish a simple mathematical basis for the expression of the rate of diffusion and to study the effect of several variables on the diffusion process. Edwards and Pickering (7) found rubber to be many times more permeable to water than to gases. Schumacher and 1255
R. L. TAYLOR, D. B. HERRMANN, AND A. R. KEMP Bell Telephone Laboratories, New York, N. Y.
Data are presented on the rate of water diffusion through various organic materials. A diffusion constant based on Fick’s linear diffusion law is calculated for each material. Several equations are derived from Fick’s law to show how valuable information can be obtained in connect ion with practica 1 problems. The effect of variations in methods and conditions of test is studied. The rate of diffusion through a water-sorbing material such as rubber does not obey Fick’s law when under diffusion conditions favoring high water sorption. Various concepts involving sorption and diffusion processes are discussed as bearing upon the mechanism of the diffusion of water through organic substances.
terinl mewsured. Three tyyim were described in detail by guson (biJuirasrired the pers~ii?~iljility til w t c r of I-lerrmann (rf); ihe essential parts of the description are crrnt coinpiisitions of hard and soft r i h l x ~ riiii(1 ('01 that t,here is no intimate relation betwecu tlie p?rnicai,ility 11s fnllows: rind rriiiior variwt.ious in composition. They nlso foiiiril that P'or rigid and senii-rigid substances a duralumin cell wits used tlle rate of permeation is iuvcrsely 11 i n n-hirli the sample was Ircld in place by a duralumin pressure ring, the seal bcing completed by a suitablc wax-coated gasket. lrlatciy the square of the ure ring was beveled, niaking the thickness at the inner in hardness of the rubber, pdgr #mater 1 han at the outer, to compensate far distortion when the rubber with \I"tcr. cli~iii>ed. The cell was "anodized" to prevent corrosion of the such ns beeswax, shellac diinilumin. ABan addit,ianal protection when salt solut,ionswere ami the like, measuriiig tl used, t,he crl! RSS corttpd on the imide with purified polystyrene. A cell of tliis type is shown in 1. T h e aaseintiled cell was :I pmclrmeiit-like piper plaecd in B desiccator and m d at constant temperature. (;etteus and Bigelow (0) estcuded ilie work i o inaludo LL 'Fhe loss in might, of the CPII y IYRS ta.kcn as the itinaunt vnricty of resins, vmiisiics, plastic?, ~~mscs, a i i d protcativr of water whicli passed tlirouglr htie material. Since the water was rontaiiicd within the cell, wntfr sorbed by tlie material did WM qiings. llcrriiiann (11) corriparcd the ratcs rit which n n t e r not change the tot,al weight. through various organic insislittiug i~i~iteri:iIs silioli FIT Sul,strmees wit.li a tnidrmcs to culd Bow weir iurwortrd b y R w b o n wax, gutta-pcrcha, and polystvrme. ( :lmrcii iml Seroggie (4) studied the permeability of miterids ani1 inoludcd a bibliograjiby. W 1)ubnikow (17) studied the diffusion of w a 1 . i ~tlirini-1, ~~ ricetylR I nitroeelliiloso ~ placing emphasis on tlie : i ~ ! i ~ ~ ~ ~ i i ] ~ : i i ~ y i i i ~ water sorption. < 1
Measurement of Diffusion Rate A simple and direct inetlrod of det.snniiiirig the wte of permeation of water through $1rrlat.erial is to fbst;ildi,dron one side a concentration of water vapor, rnaintairi on the other side a lower concentration, and mcasure the ainouot of water nliich passes through the material in a given tinie. A convenient means is to seal the iriatcrinl across a cup or cell in SOCII a manner that mater passes from the ccll through the s:imple into a drying agent outside. Four typcs of cells were issrxl in t,his work, depending on tire nntiirr of the ina-
rircd n u scaled. Tlre sealing was aeeomplished by rnekinrr to-
thniugli \vt15 collccted by ;drying agent attached to a celihrated qnnrti: spring. The %-axcell and quartz-spring combination is shown in F i ~ u r e2. T h e temprsture was maintained constant by placing the apparatus in e constant-t.empmture room. In t,lie method described. ~resssuresm and ma on tlie high and
on ono &e a capjde containing wat,er is broken, and the water allowed t o diffuse through to build up the pressure on the other side. The change in vapor may be recorded by a manometer, kat,hmmeter, or ol ns for measuring humidity w h i c h will n o t affect the vapor pressure. Figure 3 ~ l m 1 1 stliiv iypc of cell cquippd will, a mercury manometer.
Equations for Calculating Diffusion Constant The aasurnptioii of Wroblewski (18) is usually eniployed, ~rarnely,that diffusion within a solid follows Fick's linear diffiision law when water is assumed t o move as vapor. On Fick's law becomes particularly applicable from an engineering stanilpciint since the quantities included arc ciniple arid measurable. If an amount of water, N , diffuses through cross section A ~ h n the g x-axis in timet, the linear equation takes the form:
w t m e I ) = diffusion constant
The iiifksion constant used iir this work expresses tlie nurnber of gritnls of wat,er that will pass in o w direction tlrrough n centimeter cube of the rrrat.wial in unit time under unit pvessure difference. The units are grams per centimeter per Iiour per milliineter of mercury. The reeiprooal, l,'I), would then represent the resistance or impedance of the material to the passage of water; the units are centimeter X hour X iirillheter of mercury per gram. Whrn the diffusion const.ant for a material has been determined, the anrount of water, N , which will pass through the material in a given t i n e under a deinite vapor-pressure difference may be cnlculated by means of this equation. Solving for t would give t h e t i n s requked for a given amount of water to pass through the material, or for z would indicate the thickness nccessary for preventing more than a fixed amount of water from passing in a specified time.
NOVEMBER, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
Equation 1 does not take into account any sorption of water which might take place by the material during the diffusion process, and consequently is only valid as long as the concentration of water in the material a t any point is linearly proportional to the pressure. The equation will apply strictly t o nonsorbing materials and approximately to sorbing materials under equilibrium conditions. “Diffusion of water” is considered here as the movement of water within a material and “permeation of water” as the combined effect of diffusion and sorption. Specific permeability requires correction for sorption t o obtain the diffusion constant. A discussion of these terms is included by Daynes (6). Constant D in Equation 1, when obtained by the methods described, will therefore represent the rate of diffusion for nonsorbing materials but is a measure of permeability in the case of sorbing materials. The permeability constant of sorbing materials is usually smaller than the diffusion constant, owing t o retention of moisture, but approaches the latter under sorption-equilibrium conditions. I n the present work, where the constant was obtained under conditions approaching equilibrium, it is called the “diffusion” constant.
0
o
4
8
12
16 DAYS OVER
20
I
24
2e
1 32
30
1257
FIGERE 5. SECTION OF IXSULATED CABLE
against time t. The slope N / t used in the calculations was taken after the plot had indicated that the sample had reached equilibrium; in most cases a straight line was obtained (Figure 4 ) . Equation 1 is not directly applicable when the lines of flow of water through the material are not parallel or uniformly distributed. Such is the condition in the case of insulation on a cable where the streams of water are not parallel but radial. Based on the above expression, a n equation for this case may be derived as follows: Let L be the length of the cable in centimeters (Figure 5), rl radius of conductor or interior of insulation, r2 outer radius of insulation, N / t the water flowing radially through the insulation in grams per hour, pl the pressure on the outside, and p 2 that on the inside. Neglecting sorption, the magnitude of the stream of water vapor flowing through a n element of area a t a distance x from the center of the cable iq equal to N/ZmLt Hence the pressure gradient a t this point is:
P205
FIQURE4. COMPARISON OF RATE CURVESFOR SORBINQ AND NONSORBIXQ MATERIALS
The precision of the results depends principally upon the effectiveness of the seal. Since the length of seal is determined by the circumference, the larger the diameter of the diffusing area the smaller is the percentage error due to leakage. The quantities used in calculating the diffusion constant were determined with a reliability such that the precision measure of the diffusion constant ranged from 1 to 10 per cent depending on the purpose for which the data were intended. The majority of t,he constants were determined with a precision of at least * 5 per cent Trhich required that the quantities N , t , 2,A , and (pl - p 2 ) each be determined with a precision of *2.2 per cent. The area used was approximately 12.9 sq. cm. The thickness was obtained by averaging ten or more spaced measurements using an Ames micrometer, graduated in 0.0001 cm. The thickness of an average specimen was approximately 0.05 em. The temperature was controlled to =i=O.lO” C. The test cells were weighed once or twice each week on an analytical balance sensitive to *0.0002 gram. For measuring membrane materials from 0.005 to 0.02 em. in thickness, such as coated fabrics, a test procedure requiring a total test time of only 48 hours was employed: The samples were first conditioned in high vacuum for half an hour, clamped in the cells, and placed in teat at the desired temperature. The cells were weighed after 24 hours and again 24 hours later, the time of weighing being recorded t o * 5 minutes. The diffusion area was approximately 20 sq. cm. The amount of water loss, N , mas taken as the difference b e tween successive weighing, the only water which passed through being that of diffusion and leakage. 1%’ was plotted
Therefore
pl
- pz =
lr= L” $ dP = & 2
Thus Solving for r2 makes possible a calculation of the thickness of insulation necessary t o prevent the passage of more than a given amount of water over a specified period. Should p 2 be allowed to vary, which is the condition of the variable pressure method, Fick’s linear diffusion law would not directly apply. S n example would be diffusion through a membrane into an enclosure initially dry, the vapor pressure within the enclosure increasing from zero t o a pressure in equilibrium n-ith that existing outside. For a strict treatment of this case where the material sorbs water, it is necessary to use the more general diffusion equation developed by Peek ( I S , 14). A less complex equation, very useful in practice, which applies in the case of nonsorbing materials and is a close approximation for thin sorbing membranes, can be developed on the assumption that the gradient throughout is linear. Assume water vapor a t a pressure pl t o be diffusing through a membrane into a n enclosure, building up a pressure p 2 . At any instant, p 2 = nM/V
where V M
= volume of enclosure = grams of vr.ater in enclosure n = a constant by which vapor density
in grams per cc. is converted to vapor pressure in mm. Hg (n = 1.03 X lo6 cc. X mm. Hg per gram at 25” C.)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1258
Then p l - p2
nM
Vx d
x dM
= -- = -
Vx
dp,
DA dt nDA dt (7) n m where t = time in hours during which diffusion has taken place By algebraic transformation, since dpz = - 4 p t
- pz)
then Integrating gives
where C = a constant of integration Since p z
=
0 when t
=
C
0,
vx
Variation of Diffusion Rate with Time When permeability is determined by the constant pressure method, the loss in weight of the cell assembly will vary with time a t a rate depending upon the characteristics of the material being measured. I n the case of a material which sorbs very little water, such as purified polystyrene, the loss in weight of the cell assembly will vary linearly with time, but in the case of sorbing materials the variation will depend on the amount of water in the material at the beginning of the test. The data in Figure 4 compare two sorbing materials, phenol fiber and an asphalt sealing compound, with purified polystyrene. The curve for polystyrene is a straight line passing through the origin. The asphalt compound contained an amount of water higher than the equilibrium amount under diffusion conditions. The rate of loss in weight is therefore high at the beginning of the test, decreasing as
= - In p l
nDA
TABLE I. DIFFUSION CONSTANTS OF SELECTED ORQANIC MATERIALS
Combining the two equations containing C gives the expression for the diffusion constant:
Vapor Pressure Diffusion Difference, Constant D PI pz ( X 10-8) G./hr./cm./ 3 . c. CWL. M m . Ho mm. HQ Pure Hydrocarbons 21.1 0.051 18.6-0.0 0.062 21.1 0.054 18,O-0.0 4.33 0.063 1s.0-0,o 3.97 0.106 18.0-O,o 3.88 0.102 18.0-0.0 3.95 18.0-0,O 3.66 0.197 0.209 18.0-0.0 4.12 Average 3 . 9 8 0.054 18.0-6.1 4.05 0.063 18.0-6.1 3.99 0.106 18.0-6.1 4.08 0,102 18.0-6.1 3.79 0.197 18.0-6,l 3.73 0,209 18,0-6.1 4.19 rlverage 3 . 9 7 25.0 0.0367 22.8-0.0 1.81 0.0402 22.8-0.0 1.79 1.66 0.0367 22.8-12.3 0.0402 22.8-12.3 1.70 Rubber and Related Materials 25.0 0,0354 7.66-0.00 6.62 0.0354 12.3-0.0 6.63 17.8-0.0 0.0364 6.66 0.0354 21.5-0.0 6.86 0.0354 22.8-0.0 7.30 0.0354 23.6-0.0 7.70 0.0366 23.6-17.8 7.90
Temp.
(3) Hydrocarbon wax Polystyrene
The vapor pressure within the enclosure is given by t n D_ d -_ p2
VOL. 28, NO. 11
= p l - ple
(4)
vz
The mass of water within the enclosure after diffusion has taken place for a given time n 4 l then be: (5) Balata
The rate at any instant a t which mater is passing into the enclosure after diffusion has taken place for a given time is: Soft vulcanized rubber5
where p z = initial pressure inside enclosure a t time
1 = 0
I
When p z is allowed t o build up under the condition of radial flow of water, such as into an insulated cable, the expression 1 r2 -1n - in Equation 2 is substituted for z,:A in Equation 3 to 2rL r1 give : (7)
Experimental Data Diffusion measurements were made on a variety of materials of different compositions and structures. To facilitate the presentation of data, these materials are broadly classified as pure hydrocarbons (which sorb very little water), rubber and related materials, and miscellaneous substances such as cellulose acetate and phenol fiber. The diffusion constants calculated by means of Equation 1 of a few materials from each of these classes are given in Table I. The application of diffusion data to practical problems is influenced by many factors such as nonlinear vapor-pressure relations, sorption of water, impurities, and temperature. Some of these factors have been investigated and are discussed here.
Hard rubber (68R-325) Paragutta insulationb
25.0 25.0
Gutta-percha insulation
25.0
Vulcanized chloroprene polymer Polyethylene tetrasulfide Phenol fiber
25.0
Molded Bakelite Cellulose acetate Plasticized cellulose acetate Waterproof cellulose film Benzyl cellulose Plasticized rubber hydrochloride Asphalt sealing compound Flasticized vinyl chloride
Thickness
-
21.1
0.0485 0.0469 0.0449 0.0467 0 0449 0.0324 0 0324 0.0324 0 0324 0,0865
22.8-0.0 22.8-0 0 22.8-0 0 22.8-12.3 22.8-12.3 22.8-0.0 22.8-0.0 22.8-12.3 22. 8-12,3 18.0-0.0
1.51 1.92 1.86 1.79 1.72 1.47 1.49 1.44 1.45 2.63
21.1
0.0763
18.0-0.0
0.22
Miscellaneous >laterials 0.0780 22.8-0.0 22.8-0,O 0,0788 25.0 0.0627 22.8-0.0 0,0585 22.8-0,O 25.0 0.0163 22.8-0.0 0 0156 22.8-0.0 25,O 0.00246 22.8-0.0
25.0
O.OS20
22.8-0 0 22.8-0.0 22.8-0.0 18.0-0.0 18.0-0.0 22.8-0.0
21.1
0.0481 0.0460
18.0-0.0 18.0-0.0
25.0 23.9 21.1
0.00432 0.00447 0.0686 0.0029 0.0029
4.88 5.21 4.66 4.94 156
162 1.18 81.4 81.5 10.6 53.9 51.4 1.15 3.79
3.91
Composition of rubber: Crepe 90, sulfur 1.5, zinc oxide 2.5, mineral rubber 3.0, paraffin 1.5, stearic acid 0.5, Tuads 0.5. Neozone 1.0. Vulcanized in a mold 20 minutes a t 126' C. b Submarine cable insulation [Kemp., J. Franklin Inst., 211, 37 (19301. a
NOVEMBER, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
equilibrium conditions are established. The curve for phenol fiber is concave upwards because of sorption of water before equilibrium was established. It is consequently important that such materials be conditioned before test or that the test be prolonged until equilibrium is reached. The time required t o establish diffusion equilibrium varies with sample thickness and with the vapor pressure a t which the test is made. Thick samples require the longer time. Typical rate curves for a sample of soft vulcanized rubber witfh different vapor pressures on the high-pressure side are shown in Figure 6. These curves were obtained by varying pl, the vapor pressure on the wet side, and maintaining p 2 , the pressure on the dry side, constant a t 0.00 mm. mercury. The same sample was used in obtaining each curve. It was thoroughly dried before beginning the test a t 0.33 relative vapor pressure, and the gradient was allowed to build up through each successive relative pressure. .4t the higher relative pressures, sorption decreases the permeability until the concentration gradient is established. Since the rate of diffusion through a material is dependent upon the vapor pressure in contact with'the surface, a more reliable diffusion constant will be obtained if air of fixed humidity is passed over each surface of the test specimen. This constant is generally higher than that obtained in still air. Wosnessensky and Dubnikow (17') found that in their apparatus 50 cc. of air per minute sufficed to maintain a partial pressure equal to zero. Still air was used in the work reported here, since this condition more closely simulated practice. The rate of diffusion is appreciably higher for some materials when water rather than water vapor is in contact with the surface. The data reported here are for vapor in contact with the surface. The distance of the sample from the drying agent, the area of the drying agent, and the rate a t which water is passing into it are important considerations when still air is used, When Pz05 was employed as the desiccating agent, it was renewed after 0.005 gram of water per square centimeter rough surface had been taken up, since linearity does not prevail beyond that amount of water.
Variation of Diffusion Constant with Vapor Pressure If a material does not sorb water, there is no apparent reason to expect a variation of the diffusion constant with vapor pressure. That such is the case is indicated by the data on polystyrene in Table I, where p?, the pressure on the low side, was varied. Thus the pressure drop from 18.0 to 0.0 mm. mercury gave an average diffusion constant of 3.98 X l O - X , and the drop from 18.0 to 6.1 gave 3.97 X The rate of permeation through sorbing materials varies with the relative vapor pressure in contact with the surface of the material in the manner shown in Figure 6. The curves show that the rate through rubber is proportional t o the vapor-pressure drop across the sample a t low relative pressure but increases with relative vapor pressure. This is more clearly illustrated in Figure 7 where diffusion constant D is plotted against pressure p l at 25' C. The abscissa is given in terms of the corresponding relative vapor pressureP for clarity. The diffusion constants were calculated after the permeability-the curves in Figure 6 had reached equilibrium. Although a t equilibrium these rate curves were straight lines, water was still being sorbed at the higher relative pressures but at a much slower rate. The type of curve obtained in Figure 7 would also be obtained a t other temperatures. The shape of the curve may be explained as follows: At low relative vapor pressures the concentration of water in the rubber follows Henry's law, being linearly proportional to the vapor pressure. Such linearity prevails a t vapor pressures below that of a saturated
1259
VAPOR PRESSURE p( IN M M . H e
a20
0.40 060 RELATIVE VAPOR PRESSURE
as0
ID0
FIGURE 6 ( T o p ) . VARIATION OF RATE OF PERMEATION OF SOFT VULCANIZED RUBBERWITH VAPOR PRESSURE FIQURE 7 (Bottom). V.4RIATION O F DIFFUSIONCONSTArCT OF SOFT VULCANIZED RUBBERWITH VAPORPRESSURE
solution of the water-soluble materials in rubber, as shown by the work of Lowry and Kohman ( I d ) . Fick's linear diffusion law will therefore be obeyed in this region. Above this region the concentration of water fails t o follow Henry's law, increasing rapidly Tvith vapor pressure. The high concentration of water on the wet side resulted in a higher diffusion constant. This was the only acceptable experimental evidence obtained demonstrating that diffusion is more rapid through rubber saturated with water. It is difficult t o measure saturated rubber a t high values of p 2 and interpret the results, since the diffusion constant cannot be readily distinguished from the permeability constant. It is likewise difficult to interpret results when measuring saturated rubber with the variable pressure method, because a t pressures below that of a saturated solution of the water-soluble constituents, diffusion from the rubber accelerates the increase in pz; a t pressures above that oE the water-soluble constituents, the increase in p , is accelerated by the water which dry rubber would have sorbed. The permeability is consequently greater with saturated rubber by virtue of the experimental conditions. JThen p 2 is raised above zero, the amount of water taken up by the sample increases. This effects a decrease in permeability until equilibrium is approached, after which the permeability increases t o the value obtained mhen p2 = 0.0 in the pressure range where the gradient is linear, but increases above the value for pz = 0.0 in the range above the linear gradient. In the softer compounds the increase is retarded somewhat by continued sorption, particularly for thick samples. A consideration of the distribution of water nithin the rubber under diffusion conditions will assist in explaining the variation of the diffusion rate with vapor pressure.
Concentration Gradient during Diffusion For nonsorbing materials the concentration of water a t any point in the material cannot be greater than in saturated vapor but will be less, for the material occupies a definite
INDUSTRIAL AND ENGINEERING CHEMISTRY
1260 ,028
I
..
I
I
, a .020
,/
, I
DOTTED LINES REPRESENT U W R S IN TnE EXPERIMENTAL SAMPLE
!--THESE
I
I
+
2 ,024
,
,,
i
l
,
'
I
I
l
l
l
I
I
I
I
l
l
140
160
I
u1 4 2 0 ,016
z
ic 8
,012
L ,008
K
I ,004 C>
0
I 8
23.6
20
1 22
t WET SIDE
8
40
I ' 1 20 18
60
'
80 100 120 THICKNESS IN MILS
1 1 1 ' 1 , I ' I I 16 14 19 IO 8 VAPOR PRESSURE IN MM.Hg
l 6
f
I a 4
180
I , I 0
2
t
DRY SIDE OF SAMPLE
OF SAMPLE
FIQURE8. CONCENTRATION GRADIEXT OF SOFT VULCANIZED RUBBERUNDER DIFFUSIOX EQUILIBRIUM
space. Since a t 25" C. saturated air contains 2.28 X gram of water per cc., the greatest concentration of water during diffusion within the material will therefore be less than this amount, and the concentration will he linearly proportional to the pressure, Doubling the thickness halves the gradient and vice versa, but doubles the area under the concentration-thickness curve and vice versa. The area represents in grams the total amount of water in the sample. I n a sorbing material the concentration will likewise be proportional to the pressure, but the gradient will deviate markedly from a straight line since the rate of sorption is not linearly related to the vapor pressure. To determine the actual distribution of water in rubber under diffusion conditions, the following experiment was carried out: Thin sheets of the rubber compound described in Table I were clamped together t o form a single laminated thickness across which diffusion equilibrium was established. The water content of each sheet was then determined. Plotting the water content against thickness gave the distribution across the total thickness. Figure 8 shows the data obtained. The gradient is extremely steep near the wet side. If the water content in equilibrium with a given vapor pressure is known, it should be possible to calculate the concentration gradient for rubber. Such concentration os. pressure data were presented by Lowry and Kohman ( 1 2 ) . Their data for a washed smoked sheet vulcanized with 5 per cent sulfur are shown by the broken line in Figure 8. This line was obtained by first assuming a constant-pressure YI I 6
w
5E
2
14
12
t E
10
L
? e
3 L
2
m
drop from the wet to the dry side, and by plotting the water content in equilibrium with the pressure. The two curves show a remarkable similarity. Of striking interest is the fact that the lower parts of both curves are straight lines. Lowry and Kohman point out that the sorption of water by rubber obeys Henry's law up to the vapor pressure of a saturated solution of the water-soluble impurities. As stated, the steep concentration gradient on the highpressure side is believed to account for the increase in diffusion constant with relative vapor pressure, the constant apparently being greater for the thin layer of material on the wet side. Saturation of the wet edge is equivalent to a reduction in thickness. Schumacher and Ferguson (15) suggested that a loosening in structure of saturated rubber might effect an increase in permeability. If an increase in permeability results from a change in structure, the rate of diffusion through a dry rubber sample previously saturated may possibly be greater than the rate through a dry sample not previously saturated. An attempt was made to detect such a change in structure by measuring the permeability of two dry and two wet samples of rubber. The data for two different thicknesses are plotted in Figure 9. The curves show that water diffused through the two dry samples a t a constant rate, giving for D a value of 6.95 x 10-8 for a thickness of 0.159 cm. and of 6.85 X 10-8 for 0.0912 em. The slopes of the curves for the Ret samples show that they have a high initial rate of diffusion due to loss of water during the establishing of the concentration gradient. This high rate constantly decreased and gradually approached that of the dry samples. At the end of 18 days the water content, c, of both dry and wet thin samples was approximately the same; yet the diffusion constant of the wet sample was 11per cent higher than that of the dry. This same process was occurring in the case of the thick samples but required more time to attain equilibrium. ~
~~
~
TABLE 11. EFFECTOF SORBED WATERON DIFFUSIONCONSTANT OF VARNISHED SILK Treatment
Water before Test
?6 1. New material, dried over PzOr 12 days 2. Dried for 13 d a w after test 1 3. New material, after 1 2 days in lab., relative humidity 30 to 60% 4. -
5.
6.
Dried ~. for 13 days after test 3 New material, immersed 12 days in distd. water at 21' C. Dried for 13 days after test 5
Diffusion Constant a t 35' C. ( X 10-8) G /cm./hr./
mm. Hu
0.0 0 0
1.15 1.16
1.5 0.0
2.08 1.85
8 5
3.51
0.0
2.36
The 18-day test did not indicate any marked change in the rate of diffusion due t o alteration of structure. Evidence that a change in structure of a material affects the diffusion rate was, however, obtained from measurements on varnished silk, which was permanently altered by the sorption of water. These results are given in Table I1 and indicate that the rate of diffusion increased after soaking the varnished silk in water and drying. The diffusion constant was calculated after equilibrium was established. Each value is the average of two specimens. ,411 specimens, a total of six, were taken from the same piece of silk.
Variation of Diffusion Constant with Thickness
2
5
a o &
VOL. 28, NO. 11
TIME IN HOURS
FIQURE 9. COMPARISON OF PERMEABILITIES OF DRY RUBBERAND OF RUBBERPREVIOUSLY SATURATED WITH
WATER
Fick's linear diffusion law states that the rate of diffusion is inversely proportional to the first power of the thickness. The concentration gradient varies in a like manner. Fick's law will therefore apply t o purified polystyrene which sorbs practically no water. The data for polystyrene in Table I
NOVEMBER, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
show that three thicknesses ranging from 0.05 to 0.21 cm. deviate less than =t4 per cent from the mean. Soft vulcanized rubber behaves somewhat differently as regards variation with thickness. At low relative vapor pressures the concentration gradient is practically linear, and no variation of the diffusion constant with thickness occurs. Figure 10 presents data on four thicknesses for the pressure drop from 7.66 to 0.00 mm. mercury a t 25" C. This relation holds throughout the region where Henry's law is obeyed. At higher relative pressures the Concentration gradient departs from linearity and the diffusion constant increases with thickness as shown by the upper curve in Figure 10. The rate of permeation varies inversely as the 0.95 power of the thickness. Several experiments were carried out to indicate the nature of the variation with thickness a t high relative pressures. Under ordinary water-sorpt ion conditions, the time required to reach a given degree of saturation appears to be approximately proportional to the square of the thickness of the sheet, as pointed out by Andrews arid Johnston ( 2 ) . I t follows that the thin sheets sorb less water per sheet and therefore less water per unit area exposed, but more water per cubic centimeter or per unit thickness of material, than do the thick sheets during a given time of immersion. Since equilibrium is seldom reached when soft vulcanized rubber is immersed in distilled water, the above sorption relations indicate that the higher water content of the thin sheets should be reflected in a correspondingly higher diffusion constant. During the first part of the test the thin sheets did have the higher constant, for they reached their steady state while water was still being taken up by the thick sheets; but as sorption neared completion, the constant for the thick surpassed that for the thin sheets. Further investigation showed that under diffusion conditions the sorption-thickness relation is the reverse of that for ordinary sorption, and the percentage water retained increases rather than decreases with thickness. Data demonstrating this relation after diffusion had taken place for 51 days are given in the following table. The values are to be considered approximate, as the test mas carried out a t room temperature. The effective area of each sample was 12.9 sq. cm.: Thiokness 07%
0.0615 0.0925 0.168 0.246
Water Content in Diffusion Area G./sample Q./ec. 0.0024 0.0030 0.0066 0.0055 0.016 0.0074 0.021 0.0066
The higher percentage of water in the thick samples indicated that the concentration gradient varied with thickness. The concentration gradient was, therefore, again determined on laminated samples of two different thicknesses but a t a temperature of 35" C. in order to hasten equilibrium. These data (Figure 11) show that the thick samples had a higher water content, particularly over the low relative-pressure area, and a correspondingly higher diffusion constant. The fact that the curves cross near the high-pressure side may not be significant. Variation of the permeability constant with thickness is rather great for rubber compounds which sorb comparatively large quantities of water. The following table indicates the magnitude of this variation obtained on three laminated thicknesses of dental dam after diffusion had taken place for 60 days a t 21 O C. : Thickness, Cm. 0.0896 0.179 0.265
Permeability Constant D ( X 10-8) 9.5 15.9
20.7
'024 ,022
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a THICKNESS IN CENTIMETERS TOTAL THICKNESS
-
- - a301 CM
p , = 4 1 8 M M H9 P 2 = 0 0 HM Hg
---
TOTAL THICKNESS 0 47 C M DIFFUSION CONSTANT 7a x1o-8 p 1 ' 4 1 8 M M Hg
I
8
8
7
6
5
4
3
2
,I
0
R E L A T I V E VAPOR PRESSURE
FIQURE
10 ( T o p ) . VARIATIOVOF DIFFWIOX CONST~Y OFT SOFT
VIJLC~NIZED RUBBER WITH THICKNESS FIQIJRE 11 (Bottom). CONCENTRATION GRADIENT OF VULCANIZED
RUBBERIJXDER APPROXIMATE
EQUILIBRIU\.f CONDITIOUS
The variation with thickness and the shape of the concentration gradient curves for dental dam suggest a surface effect which, however, was not investigated. The high permeability may indicate that diffusion through this material is due largely to migration of water over adsorbed water particles in the interior. Although variation of the rate of diffusion with thickness has been a subject of controversy for some time, the lack of agreement among observers appears more a matter of interpretation of experimental data than of differences in findings. Data obtained by the constant-pressure method show that the permeability of rubber varies inversely as the first power of the thickness; data obtained by the variable-pressure method indicate that the permeability varies inversely as approximately the second power. Sorption is the complicating factor, particularly in the variable pressure method, since the constant measured is the permeability constant and not the diffusion constant; the latter under fixed conditions should be the same irrespective of the method of measurement. With low sorbing materials, such as waxes and purified polystyrene, the two methods (Equations 1and 3) gave almost identical diffusion constants. But when rubber was measured by the variable-pressure method, the value of D was found to be dependent upon the test technic and the slope of the pressure-time curve a t which D was calculated. The curves in Figure 12, taken on the same piece of rubber, illustrate differences in technic and the manner in which D decreases with time due to sorption of water by the rubber. Curve 1 was obtained using dry rubber and gives a low value of D, since water passed into the sample rather than through it to build up p ~ .Curve 2 gives data obtained after first establishing the concentration gradient. The gradient was established by evacuating the low-pressure side for 16 hours after the completion of curve 1. Sorption took place principally on the low-pressure side. Curve 3 was obtained by evacuating the low-pressure side for 5 minutes following the completion of
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INDUSTRIAL AND ENGINEERING CHEMISTRY
curve 2. Water already in the rubber passed into the measuring chamber, building up the pressure a t a rate faster than the rate corresponding to the actual passage of water through this thickness; for when measured using t,he constant pressure method, a diffusion constant of 7.7 X 10-8 was obtained. This value lies between those calculated from curves 2 and 3. It is therefore apparent that evaporation of sorbed water from the rubber, rather than saturation of the rubber, causes the high measured permeability. By working a t lower relative pressures, some of the difficulties due to sorption may be averted. Since the amount of water sorbed during the measurement of permeability by the variable-pressure method increases with thickness, the constant obtained will decrease with thickness owing t o this sorption. Figure 13 gives data obtained on three different thicknesses of the rubber compound described in Table I. Curves 1 to 3 are rate curves on dry rubber for the thicknesses 0.142, 0.0731, and 0.0418 cm., respectively. Curves 19 to 3 8 are the corresponding curves obtained after establishing the concentration gradient as already described. For nonsorbing material, the slopes would be sfraight lines and vary inversely with thickness. The general shape of the curves in Figure 13 shows strong sorption of water when pz reaches the region where the sorption isotherm deviates from Henry's law, and during the establishing of the gradient at the beginning of the test on dry rubber. The rate of permeation is consequently an inverse function of the rate of sorption and will therefore vary inversely with
a power of the thickness greater than one. At test periods proportioned as the square of the thickness, the slopes of curves 1A,2A, and 3A are, respectively, 0.037,0.174, 0:488 a t 5.0, 1.3, and 0.44 hours. The rate of permeation therefore varies inversely as approximately the square of the thickness. After 5 hours, sorption has lowered the slopes of curves 2A and 3A sufficiently to produce a variation inverse as approximately the first power of the thickness. The values of D calculated from these slopes are given in Figure 13. Sorption of water is obviously the explanation for the different permeabilities obtained by the two methods of measurement.
Effect of Water-Soluble Constituents in Rubber Different types of water-soluble substances which reach saturation a t different vapor pressures are present in most rubber compositions. At relative vapor pressures below that of a saturated solution of water-soluble materials, the permeability will be only slightly affected; but at relative pressures above this point the permeability will maintain a comparatively low value during saturation of the solubles, gradually increasing after each has reached saturation and until dilution has established a peak in the concentration gradient on the wet side. TABLE111. EFFECTOF WATER-SOLUBLE CONSTITUENTS ON PERMEABILITY OF RUBBER AT 25" C. Vapor Pressure of Satd. Soln.
Salt Added
Mm. Hg ....
None MgClz NaCl KZS04
7.7 17.9 22.8 22.8
KzSOi
Thickness Cm. 0.0620 0.0580 0.0587 0.0618 0.0593
Vapor Pressure Difference
Permeability Constant D ( X 10-8)
Mm. Hg 22.8-0.0 22.8-0.0 22.8-0.0 12.2-0.0 22.8-0.0
6.80
5.07 5.66 4.73 4.75
The effect of adding water-soluble material is to prolong the reaching of equilibrium, as is illustrated by the data in Table 111. The vapor pressure internal t o the rubber was altered by the addition of 0.5 per cent powdered salt t o the rubber compound described in Table I. The test was run for only one month, during which time the permeability remained practically constant at the low values. A longer test period would be necessary t o show an increase in the permeability. The added salts act as desiccating agents. Since magnesium chloride is a stronger desiccant than sodium chloride, it produced a lower permeability. I n the test with potassium sulfate the same vapor pressure existed both external and internal t o the rubber, resulting in a still lower constant. It is believed that under these conditions the salt not only acts as an impurity but produces an effect similar to raising the vapor pressure internal t o the rubber.
Variation of Diffusion Constant with Temperature 0
1
2
3
4 5 TIME IN HOURS
0
7
a
OF RUBBER MEMFIQURE12 ( T o p ) . PERMEABILITY BRANE BY VARIABLE-PRESSURE METHOD
It is important that the diffusion constant be determined at the temperature at which the material is to be used, since the constant varies with temperature. This variation is illustrated by the data in Figure 14 and the following table:
1 dry rubber: 2, gradient established by rekvacuating lowGessure side for 16 hours; 3, after evacuating low-pressure side again for 5 minutes
FIGURE13 (Boftom). VARIATION OF PERMEABILITY RUBBER WITH THICKNESS BY VARIABLE-PRESSURE METHOD
OF
Solid curves for dry rubber; broken curves with gradient established
Temp. 0
c.
Polystyrene
21.1
Varnished silk
30.0
35.0 35.0
Diffusion Constant D ( X 10-8)
Temp. O
4.0 4.5 3.4 4.7
Vulcanized rubber
c.
0.0
21.0 26.0 35.0
Diffusion Constant D ( X 10-8) 5.0
6.9
7.3
8.5
NOVEMBER, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
The increase in diffusion with temperature is probably associated with changes in structure of the material and with changes in the concentration gradient due to increased sorption of water. The value a t 0" C. for rubber may be low, since equilibrium is reached slowly a t that temperature.
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the surface increases and the work required to remove an adatom decreases with surface concentration, thus increasing evaporation and decreasing the heat of adsorption for the atoms. Such a n effect would be expected to accompany diffusion through cellulosic materials.
Mechanism of Water Diffusion Water passes through organic materials but not through metals, The difference may be due to the greater intermolecular spacings of the organic materials. A rough calculation of the average center-to-center distances between molecules of a metal such as aluminum shows the spacing t o be too small to allow the passage of water. A similar calculation for a hydrocarbon wax indicates the center-to-center distance to be about three times the diameter of the water molecule. Materials with free spaces greater than the diameter of the water molecule are more likely to be permeable t o water. The experimental data have shown that nonsorbing materials offer a uniform resistance to the passage of water and obey Fick's linear diffusion law. This process suggests the action of a molecular sieve; the water simply filters through. Diffusion through nonpolar materials, which as a class sorb but little water, probably takes place in this manner. I n the case of polar materials the process of diffusion is usually complicated by sorption of water. I n the discussion of nonsorbing materials it was assumed that water will not pass through a material whose intermolecular spacings are smaller than the diameter of the water molecule. However, particles ionized through adsorption do not possess the properties of the unadsorbed particles, since some of their electrons become associated with the surface atoms. It is possible that an adsorbed particle, if it shares an electron with the surface, may pass through a smaller space than if undistorted. I n some instances adsorption may be so pronounced as to bring about chemical reaction. Hanawalt (IO), for example, suggests from x-ray studies of palladium and hydrogen that P d H molecules are formed on adsorption. I n this connection Alty (1) suggests and cites experimental evidence to show that the passage of inert gases through fused silica is due to the diffusion of adsorbed particles along the narrow cracks of silica, the atoms entering the cracks directly from the gas phase rather than from the layer of gas adsorbed on the surface. Diffusion may also be facilitated by the migration of adsorbed particles over the surface under the influence of strong spreading forces. The tendency of adsorbed particles to migrate in this manner has been shown by Becker (3) for cesium, barium, and oxygen on tungsten, by Cockcroft ( 5 ) for cadmium on copper, and by Volmer and Estermann (16) on the rate of crystal growth. This process of migration may explain why the rate of diffusion increases as concentration of water within the material is increased (Figures 7 and 11). Another way in which adsorption may influence diffusion results from differences in heats of adsorption a t various vapor pressures. During the diffusion process, water is condensed on the wet side a t a high vapor pressure with low heat of condensation; it evaporates from the dry side a t a lower vapor pressure accompanied by a high heat of vaporization. A considerable amount of energy concentrated on the dry side will be necessary for vaporization, but since the sample is held at a constant temperature, vaporization will be retarded. If the vapor pressure on the low-pressure side is increased to a point where the heat of adsorption is negligible, the heat required will decrease and vaporization will take place with greater ease. This conclusion is supported by analogous experimental evidence on the adsorption of cesium and oxygen on tungsten. Becker (3) finds that the ratio of adions t o adatoms decreases as the surface concentration increases; but the work required to remove a n adion from
. .
TEMPERATURE IN DEGREES C.
FIQURE 14. VARIATIONOF DIFFUSIONCONSTANT OF SOFT VULCANIZED RUBBERWITH TEMPERATURE AT THE RELATIVE VAPORPRESSURE DIFFERENCE p , - p , = 0.97 - 0.00
A suggested concept of the probable mechanism of diffusion may be formulated as follows: If a vapor diffuses through a material, it is assumed that a concentration gradient has been established. The vapor, by virtue of molecular motion, may simply filter through the large spaces between the molecules of material without sorption taking place. Sorption may enter as an additional factor. Where sorption is strong, vapor will be adsorbed on the surface of the material, the first layer being strongly polarized and possibly ionized. The percentage of the adsorbed molecules ionized will decrease with the vapor pressure which, in general, means an increase in diffusion because of the lower heat of vaporization. Other layers of molecules polarized to a lesser degree will be built upon the first layer, should the cohesion force of the liquid be sufficiently high. By virtue of the concentration gradient, the large spreading force associated with the adsorbed particles will cause them to migrate through the material to the other side and evaporate to neutralize the lower equilibrium vapor pressure existing on that side. Should the forces of adsorption be extremely strong, the particles may not evaporate from the low-pressure side, the result being sorption but not diffusion. This effect should be proportional to the heat of adsorption which is in turn more pronounced a t lower relative pressures, provided that the heat of vaporization of the first adsorbed layer is greater than that for the second or third layers.
Literature Cited Alty, T., Phil. Mag., 15, 1035 (1933). Andrews, D. H., and Johnston, J., J . Am. Chem. Soc., 46, 640 (1924). Becker, J. A., Trans. Am. Electrochem. Soc., 55, 153 (1929). Charch, W. H., and Scroggie, A. G.. Paper Trade J., 101, 201 (1935). Cockcroft, J. D., Proc. Roy. SOC.(London), A119, 293 (1928). Daynes, H. A., Inst. Rubber Ind. Trans., 3, 428 (1927-28). Edwards, J. D., and Pickering, S. F., Chem. & Met. Eng., 23, 17 (1920). Gettens, R. J., Tech. Studiss Field Fine Arts, 1, 63 (1932). Gettens, R. J., and Bigelow, E., Ibid., 2, 15 (1933). Hanawalt, J. D., Phys. Rev., 33, 444 (1929). Herrmann, D. B., Bell Lab. Record, 13, 45 (1934). Lowry, H. H., and Kohman, G. T., J . Phys. Chem., 31, 23 (1927). Peek, R. L., Ann. Math., 30, 265 (1928-29). Peek, R. L., Phys. Rev., 35, 554 (1930). Schumacher, E. E., and F e r g u s o n , L., IKD. EKG.CHEM.,21, 158 (1929). Volmer, M., and Esterrnann, I., Z. Physik, 7, 13 (1921). Wosnessensky, S., and Dubnikow, L. hl., Kolloid-Z., 74, 183 (1936). Wroblewski, S.,Wied. Ann. Phys. Chem., 8 , 29 (1879). RECEIVED October 14,1935. Presented before the meeting of the Division of Rubber Chemistry of the Ameriaan Chemical Society, Akron, Ohio, September 30 and October, 1, 1935.
