Water Absorption of Resins..
.
ERNEST P. IRANY For the quantitative study of water absorption it is necessary to observe the whole course of absorption-time functions under isothermal conditions. Homogeneous resinous substances absorb water by diffusion, in good accord with a theoretically deduced law. The latter specifies two independent material factors, P , the rate of penetration or permeability, and S , the saturation limit under given conditions. Both constants are required for adequate description of the material. In the presence of dispersed granular or fibrous fillers, capillary action predominates. Water-attracting or binding agents -e. g., hydrophylic chemical groups on the resin molecule or impurities such as soluble salts-cause characteristic deviations from the fundamental regimes.
Shawinigan Chemicals Limited, Shawinigan Fails,
Quebec, Canada
the case of diffusion, water and resin are supposed to form homogeneous solutions or mixtures of continuously variable composition; in that of capillary flow, the water is assumed to progress as a separate phase through more or less discrete pores or vacuoles of the resin.
Mathematical Formulation LAWOF DIFFUSION^. The basic postulate of Fourier-Fick
~
(6) expresses the proportionality between the rate of p r o g r e s s and the g r a d i e n t of t h e concentration potential:
(atI w = K dax2 l w (1)
M
OST resinous materials used in the new plastic arts are
This d i f f e r e n t i a l equation, in which w is the water consion. The process of absorption may depend on true but centration a t a dislimited solubility of water in the resinous medium, on chemical tance 2 from the or sorptive phenomena, or on capillary action. From the pracexposed surface a t ........_........._ ._._._________ tical point of view a clear recognition of these principles is desirable, for they control the distribution, accumulation, or time t , can be solved by means of limitation of water absorption and its effects, as well as their a Fourier series. permanency or reversibility. Assuming a planeFunctionally one may distinguish between diffusion and F I Q u R E 1. D I F F u s I o N A w p a r a l l e l body of (EQUATION 3) capillary flow as the two principal forms of penetration. In unlimited area and of thickness d, and penetration from both surfaces toTABLE I. WATERABSORPTION THROUQH DIFFUSION (EQUATION 3) wards the center, the integrated Water Absorption by Polyvinyl Acetala water absorption per unit area W is (Alvar 15-70) Water Absorption by Polyvinyl Acetateb given by Temp. 20OC. 40' C . (Gelva V. 30) water insoluble but are nevertheless capable of absorb-
ing varying amounts of water upon extended immer-
~
S p Time, Days 1 2
3 4 6
8
8.40% 0.0040 sq. om./ day Calcd. Obsvd. Vol. % 2.09: 2.95 3.63C 4.18 5.08 5.79
9
10 11 12 14 16 20 24 Inf.
2.04 2.88 3.56 4.20 5.00 5.75
6:35
6:iS
6:iQ
6:90
7140
7:66
7.78 8.02 8.40
7.85 8.07
..
12.70% 0.0063 sq. cm./ day Calcd. Obsvd. VOl. % 3.43~ 5.22C 8.'86C 8.31 9.41 9.84
10160 10.84 11.29
... ...
1i:io
3.49 5.42
i:iZ 8.67 9.49 9.84 10'63 10.99 11.26
... ... ... ...
Temp.
S P Time, Days 1 4 8 16 30 37 44 51 65 62 70 71
40' C. 42%
P/dn = 0.030
Calcd. Obsvd. VOl. % 8.33 10.28 16.46 22.85 30.48 33.05 35.1
23.20 30.0 32.5 35.8
3j:SO 38.85 39.23
37:Q 38.2 39.6
...
8.10 9.66
17.10
...
4Oo1C. 42% P / d o = 0.0182 Calcd. Obsvd. VOl.
id:i7 12.60 16.60 22.28 24.95 26.70 28.50 29.47 30.96 32164
%
6.35 9.91 12.67 16.92 22.7 25.3 27.2 28.3 29.1 30.8 32.6
...
Acetal derivative of a Dartiallv hvdrolvzed Doluvinul acetate. containing 53.1%- by.weight polyvinyl acetal 41 2% polyvi6yl acetate -and 6 7%-poIyvinyl alcohol. b In order t d prevent deformation: fine &ire screena were molded into iheae samples. For this reason the thickness of the resin body is not well enough defined for purposes of aomputatlon of P from 0
P/d? 0
Corrected according to Equation 2.
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8 W=S--(S-Wo) ?y2
exp
1 + 112
z ( 2 n n=O
[- ~?r2(2n+
1)2$]
(2)
1 The author expresses his reoognition of the paper by Andrew8 and Johnston (9) on the rate of absorption of water by rubber, which has come t o hie attention since the present article was submitted for Dubhation. The aDDroaoh to the problem ot'diffusion is essentiailv the same' and the confirmatory' Exsot solutions for bodies of various shapes (slab, square bar, cube, cylinder, sphere) were given by Williamson and Adams (7) in their analogous treatment of heat absorption by solids.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1552
Vol. 33, No. 12
Experimental Most of the materials studied in the present survey were polyvinyl acetate and acetate-acetal-alcohol resins which contain, 30 in variable but exactly c o n t r olla b l e amounts, groups with different behavior towards water. The 20 pure ester and the pure acetal are insoluble in water, but the alcohol is soluble; it 10 is possible, therefore, to produce materials of varying water absorption characterisI I 1 tics by a suitable 10 20 Days 10 20 30 40 50 60 Days combination of these constituent groupings FIGURE 2. WATERABSORPTIONTHROUQH DIFFUSION a. Polyvinylrosin (Alvar 15-70) a t 20' C.; curve A , sample thickness d = 0.037om.;curve B , d = 0.182 om. Curve B in the macromolecule. calculated (Equation 3), points observed (Table I). The resins are perb. Polyvinyl acetates at 40' C. Curves calculated (Equation 3), points observed (Table I). m a n e n t ly thermop l a s t i c a n d allow of further modificawhere W Ois the initial water content and S its maximum, the tion through admixture of plasticizers or fillers. saturation limit for infinite exposure (Figure 1). Barring The measurements must be carried out under carefully conthe initial stages of absorption which, in any case, are of trolled isothermal conditions. Test pieces of standard shape and limited interest and assuming W O= 0, the rigorous solution area (4 X 1 inch) are molded or cut from a plate of convenient (Equation 2) can be simplified into: thickness, and their edges are sealed with beeswax. They are weighed on an analytical balance, and their volumes are computed by means of their density. They are then immersed in distilled water kept in a thermostat, care being taken t o support (3) them so that the surfaces remain fully accessible. Each series should include a t least one standard sample of known absorption This equation contains two material constants, P , the rate of rate. At chosen time intervals the samples are taken out of the bath one by one, the adhering water is quickly removed by filter penetration or permeability, and S,the saturation limit of paper, and the test piece is wrapped into a weighed sheath of the material under experimental conditions of temperature and pressure. Equation 3 is accurately obeyed by many homogeneous materials, as exemplified in Figure 2 and Table I. It requires that the time for the absorption of a given amount of water be inversely proportional to the square of the thickness of the body; this relation was confirmed by experiments on two test pieces of different thickness (Table 11). 40
TABLE11. WATERABSORPTIONW (dl
-
PIECE
AND
-
THICKNESS d OF TEST
0.182 om., ds = 0.0345 om.: Equation 3 for equal W, t l / h (di/dd2 27.6)
w,% 2.20 3.10
4.50 7.30
fl,
Hr.
28 56 106 335
f2,
Hr. 1
2 33/4 13
=
tl/t2
28 28 28 26
LAW OF CArILLARrTY. Purely capillary penetration of water follows a parabolic function of time derived from Poiseuille's law of flow through tubes of small diameter ($) : W=cdt
(4)
where c is a material factor. Observed and calculated absorption data are compared in Figure 3, Table 111.
FIGURE3.
WATER ABSORPTIONTHROUGH CAPILLARITY
Curve A , Bakelite laminated a t 20° C.; curves B and C, filled polyvinyl resin a t 40° C. Curvee caloulated (Equation 4 ) , points observed (Table 111).
December, 1941
INDUSTRIAL A N D ENGINEERING C'HEMISTRY
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THROUQN CAPILLARITY TABLE111. WATERABSORPTION
Laminated BakeKte (Fig. 3, Curve A ) : Equation 4, E 1.15 (20' C.) i Water ~ Absorption, ~ , Wt. % ~ i Water ~ Absorption, ~ , Wt. % ~ Days Calcd. Obsvd. Days Crtlcd. Obsvd. 1.11 1.61 2.00 2.33 2.82 3.03 3.25 3.48
1.15 1.62 1.99 2.32 2.82 3.04 3.25 3.45
3.64 3.82 4.22 4.36 4.50 5.22 6.08
3.64 3.81 4.14 4.30 4.45 5.27 6.08
10
11
13 14 15 21 28
Filled Polyvinyl Resin (Fig. 3, Curves B and C)
-R
CIlrVe
(Alvar 15-70), vol. yo Slate powder, vol. % Equation 4
c
-80 20 e = 1.16
67.5 32.5 c = 1.55
A -
% ' Water Absorption,
Days 21/,
4 71/¶ 9
11 127/~
Calcd.
Obsvd
8.39 11.40 15.61 17.10 18.90 20.45
8.45 11.28 15.7 17.1 18.7 20.8
% Water Absorption, Calcd.
Obavd.
11.18 15.20 20.81 22.80 25.20 27.76
10.9 14.7 21.1 23.3 25.6
1553
single measurement of water absorption can adequately define the process or its physical effects. Figure 4 shows several curves representing different combinations of X and P; it is evident that no comparison is possible unless the absorption curve or its elements S and P are fully determined. If these two constants are well enough known, conclusions of practical concern may be drawn. A high saturation limit, S , indicates a high water concentration in the exposed surface and, eventually, deleterious effects in such applications which depend mostly on the permanence of the surface (for example, in protective coatings). On the other hand, a high rate of penetration, P , would not necessarily affect the surface, but would favor the rapid admission of water to the interior of more bulky objects and cause changes in shape, dimensions, strength, dielectric, or other vital properties. Practical experience is mostly in accord with these conclusions. Numerical values of S and P for several materials are shown in Table V.
..
metal foil. So rotected, it can be manipulated and weighed without apprecisle evaporation loss; it can be immersed again for continued absorption. The results are preferably expressed in volume per cent. The mechanism of absorption is deduced from the course of the curve obtained by plotting the quantity of absorbed water against the time of immersion, and comparing the experimental results with Equations 3 and 4. The most important criterion is the appearance of a definite saturation limit on prolonged exposure, which would point to diffusion as the governing principle of absorption. For this purpose it is advisable to use a very thin test piece and to expose it until the repeated weighings are constant. The quantitative progress of absorption is then recorded by means of a specimen of greater thickness (Figure 2a). I n most cases of practical interest the rate of penetration is slow, and most of the water remains near the surface unless the exposure be carried t o adequate length. Experimental specifications based on relatively short periods of immersion, such as that accepted by the A. S. T. M. ( 1 ) for the testing of insulating materials (24 hours a t 25" C., thickness of specimen inch), yield comparative rate values but no information on absorption capacity. Table IV shows that the absolute quantities of water taken up by test pieces of greatly varying thickness are the same for a considerable period of immersion; i. e., the interior of the bodies is not reached. Under these conditions absorption stated in weight or volume per cent has no meaning. TABLEIV. SUPERFICIAL ABAORPTION (SHORTEXPOSURE) Grams Water Absorbed after: 12 hr. 24 hr.
Thickness d , Cm.
8 hr.
0.055 0.195 0.384 0.704 1.424
0.2752 0.3077 0.2869 0.2974 0.3116
0.3388 0.3875 0.3546 0.3687 0.3810
0.5488 0.5648 0.6026 0.6293 0,6510
Discussion I n general it is not difficult to distinguish between the two basic regimes of diffusion and capillarity, as illustrated in Figures 2 and 3. Most homogeneous resinous materials absorb water by diffusion; capillarity is probably always connected with some form of structural discontinuity. As indicated in Equation 3, pure diffusion depends on two independent material constants, 8 and P. For this reasodno
/ / / /
Time
-
-
FIGURE4. DIFFUSION CURVES(EQUATION 3)
S
saturation limit, P
rate of penetration (permeability).
TABLE V. . COXSTANTS S AND P (EQUATION 3) Material Polyvinyl acetal resin Alyar 15-70) Polyvinyl butyral resin Po$xin4 acetate (Gelva M&hTmethacr late resin Phenol-formaldei de, oast Rubber compoundl
Temp.. O
C. 20 40 25 40 25 25 20
S Vol %
Sa. Cm./ Day
8.40 12.70 10.3 42.0
0.0040 0.0053 0.0003 0.0005
1.50 8.6 1.23
0.0023
Source of Data Table I Table I T&Ie I
0.00020
0.0007
(8)
Capillary progress is clearly indicated in inhomogeneous materials such as plastics containing powdery or fibrous fillers. The example in Figure 3 represents a highly impervious type of resin, cured Bakelite (6),combined with an impregnated fabric (Bakelite Laminated) which apparently conducts the water as a distinct phase. The same holds true where a more permeable resin-. g., an alcohol-acetate-acetal polyvinyl type is tilled with nonabsorbent silica, slate, or burnt clay powder. Absorption follows the capillarity law (4) with great accuracy and its initial rate is proportional to the amount of filler, again indicating that the water penetrates along the filler-resin interfaces. If adsorptive or ionizable substances are present in the resinous medium, the osmotic pressure of the absorbed water and, consequently, its diffusion potential may be altered to such an extent that the basic law of diffusion may become unrecognizable. Chemical fixation through hydrate formation has similar effects. These conditions tend to impose an ab-
1554
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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35, NO. 15:
50
40
30
20
IO
IO
FIGURE 5. ABNORMAL DIFFUSION Polyvinyl resin (Alvar 7-70) a t 40’ C. A , normal (5.7 per cent polyvinyl alcohol, 0.02 per cent salts); B , high salt content (6.5 per cent polyvinyl alcohol, 0.5 Per cent salts): C , high polyvinyl alcohol content (10.8% 0.01% salts).
normally high saturation limit or to remove it altogether, and the process of absorption becomes almost linear. Figure 5 illustrates the effects of two typical impurities. Curve A represents a polyvinyl acetal-acetate-alcohol resin of moderate alcohol percentage, freed from the salts (mostly sodium acetate) present during the last stage of the production process. Although not reaching an absolute saturation limit, water absorption increases only slowly after about 10-day exposure. A portion of the same batch of resin was finished without washing, and its salt content remained high, causing an excessive rate of penetration as shown in curve B. Another sample, free from salts but high in hydrophylic alcohol groups, gave curve C. Experiments on thin test pieces ascertained a high but definite saturation value (above 90 per cent water) in the case of B, but C continued to absorb water until it reached almost complete disintegration. These observations indicate that salts form solutions with the absorbed water which always remain dispersed as a separate phase and which eventually reach an osmotic equilibrium. If, however, the water enters into progressive solvation with constituents of the resin molecule-e. g., with the polyvinyl alcohol groups-it is able to distend and finally to destroy the original resin structure. The above tests were carried out a t 40” C., and the continued exposure of some of the samples reached 3 months. These conditions are far more severe than those under normal use, but practical trials showed that the conclusions are significant. For example, resin B, applied as a varnish, gave distinctly better results than C on intermittent exposure to water, due to the existence of a saturation limit. Molded into flat disks, however, B failed more severely than C because of its faster rate of penetration. The occurrence of the typical tangential deviation into almost straight lines is frequent and easily reproducible. In these cases it may be assumed that the function represents a form of diffusion in which the saturation limit is not k e d but increases at a rate of its own due to some irreversible process of hydration or solvation. If, for example, the saturation limit increases steadily with time,
20
30
40
50
60
Days
FIGURB 6. EFFBCT OF WATERPROOFING AGENT Polyvinyl resin (Alvar 15-70) containing salts, A ; mixed with 6 per cent of a fusible cresol-acetaldehyde resin, B I ; with 10 per cent, Bz; with 20 per cent, B8. C shows water absorption of same resin after purification.
s = so + at
(5)
the function of water absorption would, for high values of t, approach an asymptote
where 6 represents the rate of abnormal increase of the saturation value due to a gradual change of the substance and an irreversible straining of its physical structure. Graphically this rate appears as the gradient of the asymptotic part of the absorption curve. Figure 6 shows a series of salt-containing polyvinyl acetalacetate-alcohol resins in which this effect of superimposition of normal diffusion and abnormal saturation variance is clearly discernible. It is interesting to note that the admixture of increasing amounts of a waterproofing agent (a permanently fusible cresol-acetaldehyde resin) suppresses specifically the abnormal water-fixing tendency, as expressed by a lowering of the gradient 6. The asymptotic deviations seem to be turned around a pivotal point, SO,on the t = 0 axis which marks the saturation limit of the pure resin. It is possible, therefore, t o evaluate the true saturation limit even in such cases where the complete elimination of the causes of abnormal absorption is difficult or impossible.
Literature Cited (1) Am. Soo. for Testing Materials, Standards, Designations D4833 (1933) and D570-40T (1940). and Johnston, J., J . Am. Chem. Soc., 46, 640-50 (2) Andrews, D. H., (1924). (3) Bell, J. M., and Cameron, F. K., J . Phys. Chem., 10, 858-72 (1906). (4) Kline, G.M., Martin, A. R., and Crouse, W. A., Proe. Am. Soc. Testing Materials, 40, 1273-82 (1940). (5) . , LeoDold. H. G.. and Johnston, J., J . Phus. Chem., 32, 876-8 (i928j. (6) Mellor, J. W., “Higher Mathematics”, 2nd ed., p. 483, London, Longmans, Green & Co., 19lG. (7) .Williamson, E. D.,and Adams, L. H., Phys. Rev., 14, 99-114 (1919).
