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INDUSTRIAL AND ENGINEERING CHEMISTRY
cases where the raw sugar contained large amounts of impurities; when mixed with the asbestos, these impurities were likely to give trouble in the multistage centrifugal pumps used in feeding the filter presses. A whiter and more sparkling sugar could be produced by using more than 0.3y0 asbestos, but as little as 0.157, often made it possible to obtain a product good enough for the local market. The asbestos was always added to the sirup in a small mixing tank between the melting tanks and centrifugal pumps; the amount was divided so that the first batch or first h o batches of sirup got most of the total amount' of asbestos used, in order to produce an effect similar to precoating. K i t h raw sugar containing large percentages of solid impurities, high flow rate and pumping efficiency could be attained by using a precoating of asbestos in aqueous suspension, although clarification and decolorizing were usually more effective when the asbestos was thoroughly mixed with all of the hot sirup before filtration. The asbest'os in the filter cake could be recovered and re-used several times. It was most economically revivified by washing the filter cake, cither manually or mechanically, with four times its weight of warm water, then x i t h four times its weight of warm soap solution, and repeatedly with similar quantities of water
Vol. 38, No. 5
until they were clear and the asbestos free from sugar and colloidal matter. The first washing, xhich extracted over 85% of t,he sugap left in the cake, was used, together with final molasses, for the manufacture of power alcohol in the distillery attached to the refinery. ACKNOWLEDGMENT
The author wishes to express his gratitude to C. ?;. Shen, @. \Vu, and C. H. Huang, of China United Sugar Refining Company, for their kindness in placing all available facilities a t his disposal during the investigation. Thanks are also due to C. C. Chien, T . F. Wu, and S. C. Liu for their enthusiastic assistance in carry' ing out the experimental routine. James R. Withrow, of Ohio State University, very kindly handled the manuscript and checked proof, to save t,he long delay in transit to China. LITERATURE CITED
(1) Balch, R. T., IND.ENG.CHEM.,A N ~ LED., . 3, 124 (1931). (2) Kopke, E. W., Facts A b o u t Sugar, 23, 177 (1925). (3) Peters, H. H., and Phelps, E'. P., Bur. S t a n d a r d s , Tech. Papers, 338, 261-7 (1927). IND.ENG.CHEM.,ANAL.ED., 6, 178 (1934); 7. (4) Zerban, F. W., 157 (1935) ; 8, lG8 (1936).
Moisture Adsorption of Textile Yarns at Low Temperatures ROBERT C. DARLING' AND HARWOOD S. BELDING Fatigue Laboratory, Harcard University, Soldiers Field, Boston, iMass.
T
H E fact that textiles between air and material a t T h e moisture adsorption of wool, cotton, cellulose acetake up and lose moise q u i l i b r i u m . Since all tate, and viscose rayon yarns was measured at +40", Oo, ture in rclation to the temworkers agree that the equiand -20' F. and at several relative humidities above 50%. perature and humidity of the librium points for adsorption The equilibrium values obtained, together with similar air has interested many and desorption are different, values at higher temperatures in the literature, indicate workers, not only because of the latter technique is subthat at constant relative humidity there is a high point the practical influence on ject t o the criticism that between 0' and 40' F., and that less water is bound at weight and insulation, but there was undoubtedly adlower as well as higher temperatures. The significance of also because of the light this sorption of excess on some% this finding in terms of possible changes of heat of adsorpproperty throws on the physifibers followed by partial drytion is discussed. Curves of the rate of w-ater adsorption cal chemistry of the maing of these fibers and transof the yarns are also presented, from which the over-all terials. The most complete fer to others. temperature coefficient of the process is derived. investigation of a variety of Wiegerinckestablished that, yarns was that of Wiegerinck up t o 212" F. a t constant relative humidity, there was a linear relation betwcen log moisture ( 1 2 ) . However, his emphasis was on high temperatures, the lomest temperature tested being 96' F. (35.6" C.). Speakman and content a t equilibrium and the reciprocal of absolute temperature Cooper (9), hovxver, carried the measurements on wool down to ( l / T ) . He presented this as anempirical relation, but others have 25' C. (77" F.), and Grquhart and Williams (11)on cotton down given their data theoretical significance by graphing them. Babbitt (2) reviewed and extended the theoretical treatment of the to 20" C. (68" F,). Several other workers, according to Babbitt ( 2 ) ,have studied purified and crude cellulose from cotton or wood data of others on cellulosc. He utilized the method employed by sources, but not below 20" C. Likewise the measurements of Bull Stamm and Loughborough (10) for calculating heat of adsorption (5) on a variety of proteins included those on wool a t 2.5' and from a graph of log pHpO against 1 / T and compared the values 40" C. (104' F.). The results of various workers are in fairly obtained with the direct measurements of Kata ( 5 ) and Argue and good agreement although the techniques differed somewhat. Maass (1). Bull (S),on wool and other proteins, calculated the Wiegerinck obtained true adsorptive values by a theoretically free energy change in full saturation adsorption as the area under better technique than that of Speakman and Cooper or Urquhart a curve of a/x against 2, where a represents grams of water adand Williams; he exposed the materials to a rapidly moving sorbed per 100 grams protein, and x is relative vapor pressure. stream of air of controlled temperature and humidity, whereas the From the free energy change a t two temperatures he calculated other workers exposed them in a chamber of still air with a known the heat of adsorption. I n these calculations either the variaamount of water vapor and measured the distribution of water tions in heat of adsorption with temperature are not discussed, or it appears that the heat of adsorption is essentially un1 Present address, College of Physicians and Surgeons, Columbia Unichanged over the temperature range studied. versity, N e i r York 32, N. Y.
May, 1946
INDUSTRIAL AND ENGINEERING CHEMISTRY
As far as could be discovered, no actual measurements of moisture adsorption of any textile material below 20' C. have been made. Fourt ( 4 ) utilized the empirical relation proposed by Wiegerinck t o extrapolate equilibrium values down to -30" C., but recognized the dangers of extrapolation and the need for direct measurements. Measurements at low temperatures should be useful in evaluating the possible caloric gain of moisture adsorption t o wearers of clothing in the cold and also in extending the theoretical thermodynamic treatment mentioned above. Furthermore, since the speed of adsorption should be slow a t the low vapor pressures encountered in the cold, it should be possible to plot accurately the time course of adsorption a t the lower temperatures and develop a quantitative relation between rate and temperature. Although cellulose and protein fibers vary in the absolute amount of water adsorbed, the shape of the isothermal curves and presumably the mechanisms of adsorption are, to a large extent, similar and independent of the nature of the reactive groups on the surface, to which the water is thought t o be bound. The amount of water adsorbed is probably determined chiefly by the effective surface; this has been used to explain the greater adsorption of wood over cotton and of mercerized cotton over untreated cotton. As long as we do not speculate on the reactive chemical groups, it seems profitable to discuss the various textile materials together. A word of caution should be given. Since the phenomenon of marked hysteresis (i.e., unequal adsorption and desorption equilibria) is a regular one in adsorption of water on both cellulose and protein fibers, it is not possible to discuss reversible reactions in the strict sense. Therefore i t should not be permissible to apply rigorously thermodynamic laws involving reversible equilibria. If this limitation is kept in mind, however, it is probably valid to indicate the ofder of magnitude and the trend of changes in values calculated accprding to theoretical laws. DRYING AND ADSORPTION
Wool, cotton, acetate rayon, and viscose rayon were kindly furnished by the National Bureau of Standards and were from the same lots as those tested by Wiegerinck'. An additional sample of wool, already purified was supplied through the courtesy of Lyman Fourt. Twenty-eve t o fifty grams of each sample were made into a skein and fastened on a m a l l wire hanger, and the samples were subjected t o the purification methods used by Wiegerinck: ( a ) for raw cotton, thorough washing with water; ( b ) for "purified" cotton, successive extractions with alcohol, ether, and 1% sodium hydroxide, followed by a rinse in 5% acetic acid and then water; ( c ) for the viscose rayon and cellulose acetate yarns, washing in warm 1% ammonia and rinsing in warm water; and ( d ) for the clothing wool yarn, extraction with alcohol and ether and a rinse in warm water. The 'yarns were &st dried under a bell jar over magnesium perchlorate for 4 t o 6 weeks, until a constant weight was obtained on two successive weighings a week apart. No procedure was devised for weighing in the dry environment, but advantage was taken of the fact t h a t the uptake is very slow at cold temperatures so the weighings were carried out in a cold room (usually a t 0" F.). Any standard of dryness for proteins and cellulose may be considered arbitrary, but this method is readily reproduced and was found by Wiegerinck t o be more satisfactory than oven drying. A student type analytic balance, capable of weighing to 1 m was used throughout the study, but for the sake of rapidity tki weighings were carried out only to 10 mg.; this was within about 0.03% of the dry weight of the yarns. Three measurements of the moisture uptake of the yarns were made a t 0" F. (55%, 70%, and 84% relative humidity), two a t $40" F. (50% and 90% relative humidity), and one a t -20" F. (69% relative humidity). All humidities are expressed as relative to saturation over water, even though the temperatures were mostly below freezing. The apparatus consisted of an airtight copper box about 24 X 15 x 15 inches, with a tubing joint at each end, baffle plates inside each opening, and a tight-fitting door on the side for access to the samples which hung on hooks from the roof. Tubing a t the inlet ezld was connected t o the humidifyin or dehumidifying apparatus t o be described; the outlet end lecfvia a small glasswool filter through rubber tubing out of the cold room to a small
-20
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TEMPERATURE "F. 20 40 60
I
I
I
80
I
I
100 120 140 160 I
I
I
1
25-
0
a
20-
5: 0
15-
P
5w do
? B P
'2109-
b 15-
I
-0I X ,0640
.0&8
,0636 0034 I/T 'ABSOLUTE
,0632
,0630
Figure 1. Relation between Log of E q u i l i b r i u m Rloisture Adsorbed and Reciprocal of Absolute Temperature at
0
-
Various Relative Humidities f o r Wool and Purified Cotton *
- -
Speakman and Cooper our datai X Wiegerinak'lr data; data on wool; 0 Urquhart and &liam# data on aotton
motor blower, which sucked a constant stream of air (20-25 liters per minute) through the entire system. The system up t o the pump was repeatedly tested and found leak-free. Periodically the outlet of the pump was connected to a weighed phosphorus pentoxide adsorption tube and thence t o a gas meter for measuring gravimetrically the humidity of the air. While humidity measurements were not in progress the air pumped through the sistem was allowed t o escape into the laboratory. Satisfactory phosphorus pentoxide tubes t o handle the rapid flow of the pump were found, after several trials, in the form of sintered glass filters (Corning 39580); into them was introduced a mixture of phosphorus pentoxide and an inert material to increase porosity. The most satisfactory inert material used was carefully dried Decalso, a commercial mixture of hydrated aluminum silicates generally used as an adsorbing agent. The sintered glass filter was.found necessary t o prevent dry phosphorus pentoxide from being blown out of the tubes. Two absorbing tubes were regularly used in tandem, the second serving largely as a check on completeness of absorption in the first. Sufficient air was run through the tubes in each measurement t o absorb 0.3 to 0.5 gram of water. The mechanism for achievin constant humidity of the incoming air was simple and crufe. I t s success was due largely to certain features of the cold room. Repeated gravimetric measurements in the cold room air have shown t h a t after several days a t a given temperature the relative humidity varies less than 2% over periods up t o 2 months. This constancy is nearly independent of the number of people entering or working in the room and is probably due t o the fact that the air circulator in the room blows a large volume of air over cooling coils at essentially constant temperature. This fact gave one sample of air a t constant humidity a t each of the three temperatures. I n one experiment a t a humidity higher than that in the room a box (2 X 1 X I foot) filled with snow was connected in the inlet t o the copper box and was found t o yield air of constant high humidity (within 1% of a mean value). For humidities lower than that of the room (one point each at 0" and 40" F.) the stream of air was directed over concentrated sulfuric acid before entering the box. It was empirically shown that the humidity of the air thus obtained was a function largely of the speed of air flow (which was nearly constant in these experiments) and was independent, within a wide
INDUSTRIAL AND ENGINEERING CHEMISTRY -20
0
r
TEMPERATURE OF. 20 40 60
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100 120 140 160 I
l
l
1
' \
\ .0030
,0039
,0034
,0036
I/T 'ABSOLUTE
0038
,0040
.0042
Figure 3 . Data on Purified Cotton Replotted from Figure 1 (Including Further Data of Urquhart and Williams a t Loiter Humidities)
.0040
.0038
I
,
,
,0036
,0034
,0039
I/T 'ABSOLUTE
,0030
Figure 2. Relation between Log of Equilibrium AIoisture Adsorbed and Reciprocal of Absolute Temperature a t Various Relative Humidities for Raw Cotton, Viscose Rayon, and Cellulose Acetate 0
-
our data: X
-
Wiegerinck's data
range, of sulfuric acid concentration. Since the absolute amount of moisture removed was small and, therefore, diluted the acid only slowly, such an absorber provided air of constant humidity (within 1% of the mean) for 4 t o 6 weeks a t 0' F. and for 2 weeks at 40". The sulfuric acid vessel was a commercial 12-inch glass brick into whichbt w o holes had been bored a t opposite corners. In each hole a tube, as long as the inside of the chamber, was inserted parallel t o one side wall; each tube had openings in a line along it and an airtight ground-glass joint at its base. When the tubes were inserted, the stream of air was thus blown from one side across the entire surface of the acid to the other side of the square. At the rates of flow necessary, a bubbler system was considered to have too much resistance and t o introduce too much hazard of spattering through the system. Fully dried yarns were used a t three starting points during the series and served t o check the maintenance of constant dry weight. At two points (going from lower to higher humidity a t the.same temperature) no intermediate drying was carried out, and a t one point there was only partial drying. In each run the following steps were carried out: A current of air was blown through the box and system for 2 t o 4 days or until repeated measurements of humidity were constant and satisfactory. The yarns were taken into the cold room in the desiccator and allowed to reach temperature equilibrium. They were weighed rapidly, hung in the box, and at appropriate times removed from the box and weighed rapidly. The times were chosen, frequent a t the start (every 2 to 4 hours) and less frequent toward the end (every 1 t o 5 days), so that the curve of uptake against time could be fully established. All weighings during runs a t other than room humidity were carried out with the air flow temporarily shut off to minimize contact with room air. The humidity of the air pulled through the box was measured a t least once a day. Each run was continued until there was less than 0.1% change in weight of any yarn sample over the course of several days (1 to 2 days a t 40' F., 3 to 4 days at 0", 5 t o 7 days a t -20"). This study cannot be considered a complete mapping of the moisture absorbing properties of yarnq at low temperatures,
comparable to that of Kiegerinck a i high temperatures. Such a study at, low temperatures would require several years since approximately 200 hours are required for equilibrium at each point a t 40" F., 600 to 800 hours a t O " , and 1200 hours a t -20". However, the points established here seem to give a fair picture of t,he direction of the changes with t,emperature and humidity ovcr a fairly wide range, and t o add experimental evidence for logical extrapolation into unverified ranges. EQUILIBRIUM ADSORPTION VALUES
Table I lists results a t the six equilibrium points, together with notes on the starting condition of the yarns. The t'hree points a t 0" F. established the shaps of curves of moisture uptake against relative humidity a t the same temperature; they were nearly straight lines within the range studied. Draiving lines a t the other two temperatures through established points parallel t.o those of the same yarn a t 0" F. gave fuller equilibrium data. Presumably such values are accurate t o 0.5%. Table I1 gives these data, together with values extrapolated for wool and cotton from the literature (9, f f) a t higher temperatures, according to the linear relat'ion proposed by Wiegerinck. It is apparent from Table I1 that: (a) Values a t 40" and 0" F. are very close in most instances but valucs at -20" are lower in all cases. ( b ) With wool the values a t all temperatures were lower than expected by extrapolation from higher temperatures; this discrepancy is highest a t the lowest temperature. ( c ) With cotton a t 40" F. the measured values are equal to or higher than the extrapolated ones, but a t the two loiver temperatures t,he observed valucs arc again significantly below the predicted ones. These conclusions from Table I1 suggest strongly that ,the empirical linear relation proposed by Wiegerinck between t,he log equilibrium moisture content and the reciprocal of the absolute temperature does not hold over the temperature range studied here. Figures 1 and 2 are graphs of 112' against, equilibrium moisture content. The curves a t lower temperat,ures are far from straight lines; in fact t,hey flatten and e m n r e w s c their slope. I t should be mentioned again that, relative humidity is expressed throughout, even below freezing, as the actual vapor pressure relat,iveto that of liquid water. If it had been exprcswd relative to the vapor pressure of ice, the deflection in thc ciirvcs would have been even more abrupt.
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1946
pectation, and variations in heat of adsorption of water on the yarn with temperature and with extent of adsorption can be predicted from the curves. Such reasoning should be useful for comparison with heat of hydration measured or calculated by other methods. The steps in the proof are presented in detail for the benefit of readers unacquainted with the mathematics.
TABLE I. MEASURED EQUILIBRIUM POINTS FOR ADSORPTION OF WATERON YARNSAT LOW
Expt. No. 1 2
3 4 5 6 0
Temp., F. f40 +40 0 0 0
TEMPERATURES
Equilibrium Moisture Content, % of Dry Wt. Wool 1 EquilibStarting (Bur.of Puririum Stateof Stand- Wool fied Raw Viscose Acetate Time, Yarn ards) 2 cotton cotton cotton rayon Hr. Dry I1 5 5.9 11.7 5.7 10.4 5.0 287 23 0 23.2 12.9 From1 12.9 24.0 12.7 191 13.2 12.8 6.6 Nearly 6.8 11.9 6.5 406 dry Dry 18 4 18.6 9.8 96 17.4 9.7 576 21 0 21.7 11.8 From4 11.6 21.4 12.3 879 Dry 16 8 16 9 8 4 8.4 15.1 7.7 1200 per cent referred to liquid water.
?.,
R. % 50 90 55 70
84
69 -20 Relative humidity in
527
QUANTITATIVE ANALYSIS OF DATA
The slope of Figure 3 can be expressed a t any point on one of the curves as The practical significance of these findings is apparent. The capacity of textile yarns to adsorb moisture from the environment a t constant relative humidity reaches a high point somewhere between 0" and 40' F. and decreases both above and below this range. The extremely high potentials for moisture adsorption a t subzero temperatures envisaged from extrapolation do not exist.
x = d (log relative humidity)
(1)
d(l/T)
Relative humidity = ( P l / P z )x 100 where PI = vapor tension of HZOin air P2 = vapor tension of liquid water at same temperature According to laws of differentiation,
ADSORPTION CAPACITY AT LOW TEMPERATURE
Why does adsorption capacity diminish below about 20' F.? It has been postulated in the review by Babbitt (8) that, as the water vapor pressure is increased, adsorption on cellulose and protein proceeds first in a single layer of water molecules, then predominately in multiple layers, and finally as capillary adsorption. Is it possible that a t temperatures below freezing the last form of adsorption, involving as it does grosser aggregates of water, is restricted when the water is in the form of ice crystals? If the theoretical treatment to be presented is correct, this is unlikely because the heat of capillary adsorption is smaller than the other forms yet the calculated heat of adsorption actually falls with a drop in temperature. Another possible but unlikely cause of this drop in adsorption at low temperatures might be a marked accentuation of hysteresis in this range. To prove this it would be necessary to measure desorption equilibrium, which was not done. A more likely explanation lies in variations in heat of adsorption with temperature. If, in spite of hysteresis, we assume that an approximately reversible equilibrium exists, i t is possible to treat the data of Figures 1 and 2 so that the slope of the curves will be related t o the heats of adsorption. The treatment is similar to that of the workers noted above except that log relative humidity rather than log pHs0 is plotted against 1/T a t various levels of percentage adsorbed water. The data on purified cotton are presented in Figure 3 as a n example; the form of the curves was similar for all the yarns. Although the curves of Figures 1 and 2 do not have exactly the same shape, they are similar in being nearly straight lines a t the higher temperatures, and in becoming flat and reversing the sign of their slope between 40° and 0" F. The discussion Till show that the slope of the curves in Figure 3 is a measure of the difference between the heat of adsorption of the yarn from water vapor and. the heat of condensation of water. Further, the nonlinear shape is a logical ex-
d ( l / T ) = -(dT/Tz) Rearranging and substituting in Equation 1,
According to the widely used thermodynamic equation, which may be considered a general form of the Clausius-Clapeyron equation, LS -d l=n K - , (3) dT RTZ where K p = equilibrium constant of a reaction a t constant pressure aH = heat of reaction at constant pressure R = gas constant Rearranging Equation 3 and changing to log
AH =
2.303RT2 d(log K P ) dT
(4)
Let us consider the reaction of the adsorption on cotton, written in simplified form:
HzO (gas)
+ cotton t;HPO.cotton .
Constant K 1 =
[HzO.cotton] PI [cotton]
Since [HzO.cotton] and [cotton] are both concentrations of solid substances, they may be considered constants. Let a
=
[HzO.cotton] [cotton]
Then K I = a/P1
MOISTURE CONTENT (ADSORPTION) OF YARNS TO SATURATION OVER WATER, INTERPOLATED FROY TABLE I TABLE 11. EQUILIBRIUM Purified Cotton, % ' of Dry Wt.'" Av. of 2 Wools, % of Dry WLa -20' F. 40' F. O°F. -20OF. R. H., % 4OOF. 0' F. 50 ll.e(l3.4) 11.5 16.2) ll.l(l7.9) 5.9 6 0) 6.0 7.0) 4.9 7 5) 14.4(15.7) 14.7$19.2 14.1 21.3) 7.8{7:0) 7.9{8:1{ 6.7{8:6) 60 70 17.8(18.2) 18.5(22.1{ 17.0b.4) 9.7( 8.3) 9.8 9 6 8.6(20.4) 80 20.4(20.4) 20.6(24.2 11.4 10 3 11 a(11 6) l2.S[14:1] ' ,* ' 90 23.1 (24.8) Figurea in parenthesis were obtained by extrapolation from literature values a t higher b Points above 100% humidity relative to saturation over ice.
Raw Cotton. % ' of Dry Wt.
Viscose Rayon, % of Dry Wt.
F. F. F. F. 5.7 5.7 4.9 10.4 7.4 7.5 . 6 . 7 13.7 9.4 9.6 8.5 17.1 11.0 10.9 b 20.6 12,g 24,0
temperatures.
F. 10.3 13.7
F. 9.0 12.3
17.4
16.6
20.2
b b
Acetate Rayon, % of Dry Wt. F. F. 5.0 5.7 6.9 7.6 9.0 9.7 10.9 11.5 12.7 b
F. 4.0 5.9 7i9 b
INDUSTRIAL AND ENGINEERING CHEMISTRY
/ 0 -
.-
'EQUILIBRIUM REACHED BETWffN IO00 AND 1200 HRS.
i !
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Figure 8 .
150 200 250 300 350 HOURS EXPOSURE OF WOOL YARN
100
460
560
In words this means that the equilibrium is determined by
not radically changed with temperature. Until more is known about this, the assumption is reasonable for the purpose of discussion. HzO (liquid), Similarly in the reaction, HzO (gas)
where PZ = saturation vapor pressure of water Letting b = [HzO ( L ) ]
Applying Equation 4 to these two reactions, 2.303RT2 d log
2 P I
dT
Substitut,ingin Equation 2,
Thus in words, the slope of any of the curves a t any point is equal to a constant times the difference in the heats of the two reactions. It is important to recall the convention that AH has R negative value when heat is evolved and a positive one when heat is
absorbed. Both AH, and AH1are known to be large negative quantities in this case. Therefore, when the slope is negative as it is over most of the curves, theexpression ( AH1 - AH,) is negative and AH2 (the heat of condensation of water) is smaller (a smaller negative quantity) than AHl (the heat of adsorption on cotton) Conversely, when the curves are flat, the two heats are equal, and when the slope is positive, the heat of adsorption on cotton must be smaller than the heat of condensation of water. The variability of AHz with temperature i c established a t least above freezing temperatures; its absolute value decreases with a risc in temperature or rises with a rise in 112'. In order for any of the curves on Figure 3 to be straight lines, AH1 would have to vary with temperature in the same direction as A H , in such a way that the difference between the two heats was constant. In view of these rigid and unusual conditions, it is not surprising
that the curves are not linear. Since actually from the curves the sloDe. and therefore the expression ( A H 1 - AH,), becomes less negative (or more positive) with a fall in temperature (rise in l/T), it follows that AHI must increase less rapidly in absolute value than A H , and finally come to fall below it somewhere near 20' F. ( l / T = 0.0038). So far we have considered t.he changes with temperature a t any one of several constant degrees of hydration of the cotton. Further conclusions may be drawn considering the slopes of the various curves a t the same temperature, best demonstrated at the higher temperatures (e.g., 1/T = 0.0030). It is apparent in this region that the slope becomes less negative as the cotton becomes more hydrated. Since the value of AH2 is merely a function of temperature unrelated to the yarn, it follom that A H , must decrease in absolute amount as the cotton becomes more hydrated. This finding is identical t o the result calculat,eri by Katz (5) and Babbitt ( 2 ) by differentiating the integral hcat of wetting of cellulose and similar t o that observed in t'he adsorp tion of gases on charcoal, so it may be considered reasonable. The actual changes in the differences in heats of adsorption and condensation discussed above are probably of greater theoretical than practical importance. From the data a t hand it would not be worth while to indicate more than their order of magnitude. Rouqh calculation from Figure 3 shows that the value of ( A H 1 - AH,) a t l / T = 0.0030 ($140' F.) would be 1550 calories/mole H20 (85 calories/gram) at 4% adsorpt,ion. and 420 calories/mole H,O (23 calones/gram) a t 1070 adsorption. .The figures obtained above are differential heats of adsorption; t,herefore it should not be expected that t,hey ncccssarjly agree with actual calorimetric values which are integral hcats. Lauer and co-wqrkers (6) recently reported a value of 3.4 kg.cal./mole of water for the hcat of hydration from liquid water of various forms of cellulose, By the law of conservation of energy the heat of hydration from liquid water plus the heat of condensation of water equals our value AHi, which represents the heat of hydration from water vapor. I n other words, their value corresponds t o our ( A H , - 'AH,). The reaction t'hey measured included the attachment of the first molecules of water to dry cellulose which would correspond t o a curve below the lowest (4y0,) on Figure &--one with a higher slope and a larger A H I . Neale and Stringfellow ( 7 ) actually measured the heat of adsnrption of the first few tenths pcr cent of adsorbed water and found a value of 15.7 kg.-cal./mole; Babbitt stated that this value agrees with extrapolation of his calculation back t o zero vapor
Comparison of Rates of Moisture Adsorption of Wool Yarn at 40°, O o , and -20' F.
P I ( =pHzO) a t any temperature. I n considering [H20 . cotton] a constant a t all temperatures along one of the curves, it is assumed that the mode of attachment of a given weight of water is
AH1 =
450
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pressure. Similarly, the value calculated by Bull (3) for adsorption on wool from water vapor (1950 calories/gram H20) is much higher than our apparent value. (A plot of our data on wool as in Figure 3 indicates a heat of hydration from water vapor of about 650 calories/gram HgO). In this case the difference between our highest calculated differential heat of adsorption and his integral heat is considerably greater than in the case of the cotton discussed above; however, he claims only a low order of accuracy in his method of calculating the integral heat of adsorption. RATES OF MOISTURE UPTAKE
'
Some idea of the rates of uptake in the experiments a t lower temperatures may be gained from the figures for the duration of our experiments (Table I). I n contrast, Wiegerinck remarked that his experiments required up t o 24 hours or more. However, it is probable that the rates of air flow in our experiments were lower than his, since 25 liters per minute in our box represented a Linear velocity of only 20 cm. per minute. Analysis of our curves reveals that uptake is not far from a simple exponential function, but on more careful analysis we were able to show that each followed roughly the sum of two exponential functions, analogous in many ways to a previous formulation of the conditions for diffusion into a cylinder. Utilizing the formula of Roughton (8) for diffusion into a cylinder, it was possible to show that the rate of possible diffusion into a cylinder of the size of our skein of yarn was about twice that actually observed. Also it was shown that the maximum possible rate of diffusion across the film of "dead air" on the surface of the skein was about twice that actually observed. Thus these two factors were about equally limiting in effect. In addition, a t the start of a run, the available moisture in the air was a serious limiting factor, as shown by the fact that over half the moisture in the air was adsorbed during the first few hours of each experiment. Therefore the curves obviously are no measure of the speed of chemical reaction but are chiefly a function of the gradient of vapor pressure existing, There were differences in the relative rate of adsorption on the different yarns, but these were due a t least in part to differences in weight of the skeins. The cotton samples were lightest and reached equilibrium first. The wool samples were next heavier and reached equilibrium next; the viscose rayon and cellulose acetate were heaviest (but not, greatest in volume) and required considerably longer to come t o constant weight. Although it cannot be proved, i t seems likely that the slowness of the last two yarns mentioned was in part a function of the yarn and not of the size of the skein. The data op relative rates of adsorption on the same material a t different temperatures are more reliable and give some values of possible practical interest; the heat from the moisture taken up by dry garments contributes in part to the heat balance of the wearer but becomes insignificant if spread over too long a period of time. Figure 4 shows the relative rates of uptake of wool (as an example) a t the three temperatures, plotted on the same graph using percentage of equilibrium value rather than absolute amount of uptake so that the curves can be more easily compared. Because of the slow air flow in our apparatus and the bulky shape of our samples, it is probable that practical conditions would shorten the uptake times rather than lengthen them. The curves show that a t 0" it took five to seven times as long to reach a given percentage of the equilibrium as a t 40" F.; at -20" F. it took two and a half to three times as long as a t 0". From these figures it may be concluded roughly that in this range the reaction velocity is increased 1.5 to 1.7 times for every 10' F. rise in temperature or 2.1 to 2.6 times per 10" C. The latter figure is analogous to the Qlo of chemical reactions. Therefore it can be calculated that a t 96" F. (the lowest temperature used by Wiegerinck) a time of the order of 7 hours should be required
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to reach within O.l%,equilibrium. Since he reports a time of 24 hours or longer, it is possible that the acceleration per 10" F. is somewhat less at higher temperatures. CONCLUSIONS
By comparing the data obtained here with those of other workers a t higher temperatures, particularly with respect to the relation between log equilibrium moisture content and the reciprocal of absolute temperature, the following conclusions are drawn: (a) At constant humidity relative to saturation over water, the equilibrium moisture content is nearly the same a t 40" and 0" F. but somewhat lower a t -20" F. ( b ) The curve of log equilibrium moisture content against 1/T is not linear over the entire range of temperature -20 O to 160' F. but rather is flat between 0" and 40" F., and has a negative slope a t higher tem eratures and a positive slope a t lower temperatures. TEe sha e of the detailed curve for cotton (Figure 3) can b e interpretecf in relation to the heat of adsorption, and the following conclusions are drawn from the analysis: ( c ) These curve5 have a similar (but inverted) shape to those described under conclusion b. ( d ) The slope of any point on these curves is equal to a constant times the difference between the heat of adsorption of the yarn and the heat of condensation of water a t that point; linearity of the curve would require this difference to be constant a t all temperatures, a condition unlikely to be fulfilled. ( e ) From the actual curves the heat of adsorption on the yarn a t a constant moisture content falls as the temperature falls, somewhat more rapidly than does the heat of condensation of water, until it equals or falls below the latter a t about 40' F. (f) At a constant temperature the heat of adsorption on t h e yarn falls as the amount of adsorbed water increases. The ratios of velocity of moisture adsorption of the yarns a t -20", O", and 40" F. is approximately 1:3:18, which means a D acceleration of about 1.6 fold per 10" F. or 2.3 fold per 10" C. The absolute times for half e uilibrium of wool a t these three temperatures are 96, 33, and 5%ours, respectively, and the times necessary for full equilibrium (within 0.1%) are 1200, 430, and 90 hours. The absolute times are somewhat longer than would probably exist under practical conditions involving woven textiles in more rapid air movement. The chief factor controlling the rates of adsorption is the diffusion pressure of water vapor existing at the different temperatures.
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ACKNOWLEDGMENT
We are indebted to the Climatic Research Laboratory, Lawrence, Mass., for assigning a group of enlisted men for work a t this laboratory. Of this group, M. Castiglione carried out many of the routine measurements, and J. Poulin and A. Razoyk constructed a portion bf the apparatus. The mathematical treatment was started along lines suggested by F. J. W. Roughton who assisted in the analysis of some of the earlier experiments, but was not present at the final write-up and so shares none of the responsibilities for possible error in this report. The work reported here was carried on as a side issue of a n extensive program on moisture in clothing undertaken for the Military Planning Division, Office of the Quartermaster General; it was done under a contract, recommended by the Committee on Medical Research, between the Office of Scientific Research and Development and the President and Fellows of Harvard College. LITERATURE CITED
(1) Argue, G. H.,and Maass, O., Can. J . Research, 12, 564-74 (1935). (2) Babbitt, J. D., Ibid., 20A, 143-72 (1942). (3) Bull, H.B., J . Am. Chem. Soc., 66,1499-1507 (1944). (4) Fourt, Lyman, personal communication. (5) Katz, J. R.,KoZZoidchem. Beihefte, 9,1-182 (1917). Doderlein,R., Jjckel, C., and Wilde, O., J . makromol. (6) Lauer, K., Chem., 1, 76-96 (1943). (7) Neale, S. M.,and Stringfellow, W. A., Trans. Faraday SOC., 37, 525-32 (1941). (8) Roughton, F. J. W., Proc. Roy. SOC.(London), B111, 1-36 (1932). (9) Speakman, T.B., and Cooper, C. A., J . TeatiZeInst., 27,T191-6 (1936). (10) Stamm, A. J., and Loughborough, W. K., J . Phys. Chem., 39, 121-32 (1935). (11) Urquhart, A. R., and Williams, A. M., 'J. Textile Inst., 15, T559-72 (1924). (12) Wiegerinck, J. G.,J . Research Natl. Bur. Standards, 24, 645-64 (1940).
