1954
SSKFORD
H. EHRLICH AND
FREDERICK
h.BETTELHEIM
Vol. 67
IXFRARED SPECTROSCOPY OF THE WATER VAPOR SORPTIOS PROCESS OF &IUCOPOLYSACCHARIDES1 BY SANFORD H. EHRLICH~ AKD FREDERICK A. BETTELHEIM Chemistry Department, Adelphi College, Garden Czty, IT.Y . Received March do, 196.3 Infrared spectra of isomeric chondroitin sulfates and heparin were obtained during the different stages of the water and deuterated water sorption process. On the basis of the change in the integrated intensities of the different absorption bands, the role of the different polar groups in the water sorption process was investigated. The deuterium exchange was interpreted on the basis of accessibility of the hydroxyl groups toward water vapor st difierent vapor pressures. I t was found that the different polar groups of the polymers bind water vapor simultaneously according to their steric accessibilities
In view of the fact that mucopolysaccharides have a large number of water binding sites with different degrees of polarity, the question arises as to what extent the different groups participate in water vapor sorption. The interpretation of the thermodynamic functions of the sorption process led to a stepwise mechanism.3 Therefore, it is important to investigate whether the sorption occurs first on a single energetically favorable site and proceeds to energetically less favorable atomic groups, or whether all polar groups sorb water simultaneously according to their accessibilities, and the stepmise mechanism refers to the swelling process. To answer these questions infrared spectroscopic studies were performed on the water sorption process of these polyelectrolytes. Many infrared studies of dehydration processes reported in the literature, mainly on inorganic polymer^^-^ indicate that this approach is successful. Experimental 1, Sample Preparation .-Thin films of mucopolysaccharides8 were prepared by solvent casting on ferro-chrome alloy plates. Concentrated aqueous solutions of the polymers were evaporated a t 35' and 25 mm. to produce thin films in which the strongest infrared absorption bands allowed 5-10% transmitted radiation. 2 . Infrared Apparatus and Procedure.-A vacuum Pyrex cell was constructed. Each arm of the cell is basically a IO-cm. gas cell equipped v i t h two vacuum ground 29/42 glass joints having a common Pyrex tube. Single crystal silver chloride windows supplied by Harshaw Chemical Company, Cleveland, Ohio, having the dimensions of 4-cm. diameter and 2.1-mm. thickness were used. An adapter 29/42 t o 10/30 vacuum ground tapered joint which accommodated a calibrated thermometer (0-50") divided into 0.1' increments was inserted into the sample arm of the cell. An aluminum jig containing the sample film was clamped in a vertical position immediately above the bulb of the thermometer. The sorbates, degassed water, and deuterated water, were stored in flasks isolated from the spectral cell by means of stopcocks. A heating element was wound around the outside of the cell, around the water flasks, onto the manometer and inserted into a relay. The cell then was insulated with asbestos tape which covered a thermoregulator held against the sample arm. A dynamic vacuum of approximately 10-6 mm. was attained (1) Supported in part by Grant C-03984 BBC of the National Cancer Institute, Public Health Service. (2) Based in part on a thesis submitted by S. H. Ehrlich to the Graduate School of Adelphi College for the partial fulfillment of the Ph.D. requirements. (3) F. A. Bettelheim and S. H. Ehrlich. J. Phy. Chem., 67, 1948 (1963). (4) M. Folman and D. J. C. Yates, Trans. Faraday Soe., 54, Part 11, 1684 (1958). ( 5 ) A. V. Kiselw and V. I. Lygin. Proc. Second Intern Cowr. Surface Actzvzty, 2, 204 (1957). (6) L. H. Little and M. V. Mathiew, dctes Congr. Intern. Catalyse 9.Paris, 1, n l (1960). (7) J. J . Fripiat, J. Chaussidon, and R. Touillaux, J . Phys. Chem., 64, 1234 (1960). (8) Th. H. Elmer, I. D. Chapman, and h1. E. Nordberg, zbzd., 66, 1517 (1962).
with the aid of an oil diffusion pump. A Beckman IR-7 double beam prism grating spectrophotometer was used with sodium chloride optics. The dual cell was placed in supporting cell holders mounted to the sample compartment floor. A mobile vacuum apparatus was then glass blown onto the manifold adjacent to the sorbate flasks. The adapter, thermometer, and jig were inserted into the sample cell while the cell was in position on the spectrophotometer and all joints then were vacuum sealed by applying Apiezon wax "W." After the evacuation process a t 40" for 18 hr., the sample cell temperature was decreased to the desired experimental temperature. The spectrum of the film a t zero relative vapor pressure then was recorded using the double beam technique. Water vapor was introduced onto the desorbed film while the temperature m-as maintained constant to less than f 0.1". Spectra were recorded immediately on introduction of the vapor into the cell, and a t 2-hr. intervals until equilibrium was established. The deuteration equilibrium was assumed when the spectroscopic reproduction of the integrated intensity of the 0-D stretching mode a t 2,560 cm.-l was noted. Approximately eight spectra were recorded from the initial pressure to 0.7 relative vapor pressure under equilibrium conditions.
Results and Discussion In the water sorption of mucopolysaccharides the polar sites of the polymers have the capability to hydrogen-bond the sorbate. This interaction has sufficiently pronounced effects in the infrared spectra to allow characterization. Among these observable effects the shift in the frequency of the stretching modes toward iower wave numbers, the production of new bands, an enhanced integrated intensity, and band broadenings are the most important. The shift to lower frequencies reflects the lengthening of the bond in the RO-H and RN-H groups due to hydrogen bonding to another electronegative atom such as the oxygen of the ~ a t e r . ~ - ' ~ In the spectra of complex molecules such as mucopolysaccharides these shifts are observable but the accuracy of determination is low due to the overlap of many absorption bands and also due to the broadening of the bands. The increase in the integrated band intensitiesll could be used with greater accuracy to provide a parameter for the hydrogen bonding of the sorbate on specific polar sites. Expecially for the more pronounced bands of the -OH stretching modes in interand intramolecular hydrogen bonding at 3350 cm.-', the ionic -COO- antisymmetric stretching mode a t 1635 cm.-l, the amide I1 band at 1555 cm.-l and the -S=O stretching mode of vibration a t 1247 cm.-l were useful in tracing the mater vapor sorption. The peak heights were taken as a parameter for the integrated band intensities. Although this method provides only a semi(9) G. Sutherland, Trans. Faraday Soe., 36,889 (1940). (10) R. Rundle, J . A m . Chem. Sac., 77, 6480 (1955). (11) G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond," lVq H. Freeman and Co., San Franclsco, Calif., 1960, p. 96.
SPECTRA OF WATERVAPORSORPTIOX PROCESS OF MUCOPOLYSACCHARIDES
Oct., 1963 1.175
I
I
1
I
I
I
I
1
1 - 1
1.15C
1.125
>-' 0 2
a
m
2m
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a a W
3
1.075
-1
a
E
0
z
1.05C
1.025
I
ooc 0
0.2
0.4
06
0.8
1.0
PP". Fig. 1.-Normalized absorbancies of the -OH, -COO-, -NH, and S=O bands of calcium chondroitin sulfate A as a function of the relative vapor pressure of water at 32.5'.
Fig. 2.-Normaliaed absorbancies of the -OH, -COO-, -KH, and S=O bands of calcium chondroitin sulfate B as a function of relative vapor pressure of water a t 32.2".
quantitative treatment, the alternative way to try to resolve the individual peaks either analytically, assuming gaussian distribution, or visually, carries with it
195;
almost as much inaccuracy as taking peak heights for the intensities. The water vapor sorption isotherms showed an increasing absorbance with increase in vapor pressure in all the bands. These increases were specific to each absorption band and much larger in magnitude than can be accounted for by the increase in the thickness of the film due t o swelling. The increase in absorbancy due to swelling was taken into account in the spectra a t each vapor pressure by establishing the base line from the flat portion of the spectra from 1900-2500cm.-1. This base line was slightly rising in absorbance going from lower to higher wave numbers as was expected on the basis of Rayleigh scattering, which is greater a t shorter wave lengths. One could observe that with increasing vapor pressure the amount of light scattering decreases since the refractive index fluctuation within the polymer film decreases when water fills up voids previously occupied by air. The polyelectrolytes in this investigation have refractive indices in the neighborhood of 1.50, hence the change of the embedding medium from air to water reduces the refractive index difference from 0.50 to 0.17.12 Therefore, the establishment of a base line for each spectrum and the measurements of the peaks from these base lines eliminate the effects caused by swelling and light scattering. In order to compare the relative importance of each polar group on a single polyelectrolyte in the water vapor sorption process, the normalized absorbancies were plotted vs. relative vapor pressures (Fig. 1-4). The absorbancies were normalized by arbitrarily selecting the absorbance a t zero relative vapor pressure as one. (We are aware of the semantic difficulties in nomenclature : normalization in most cases means setting the maximal rather than the minimal function equal to one. According to this a relative absorbancy term would have been more proper. On the other hand, the terminology "relative vapor pressure" in which the maximum is set to one is so well established that keeping within the logic of our two variables the selection of the normalized absorbancy terms seems less contradicting.) Figure 1 indicates that the most important sorbing group on the calcium chondroitin sulfate A is the hydroxyl group, while the -NH group has the second largest increase a t low vapor pressures. At the same time, however, all the other polar groups participate in water vapor binding, although to a lesser extent. This is a general phenomenon observable also in the other mucopolysaccharides and probably the most important single result of our infrared spectroscopic measurements. This indicates that the different polar sites do not possess large enough differences from the point of view of the energetics of the sorption. Therefore, a t a certain vapor pressure there is no preferential sorption on one site to the exclusion of other sites. It is the availability of a site which gorerns which specific atomic groups participate in the sorption process. It is interesting to note that the calcium chondroitin sulfate A, which showed the smallest vapor sorption capacity among the mucopolysaccharides, exhibited a decrease in the -OH and -NH absorbancies a t medium vapor pressures, This occurs while there is a continuous increase in the absorbancies of the sulfate and carboxyl (12) E. Macchia, M.S. Thesis, Adelphi College, Garden City, N. Y . . 1962.
1956
SANFORD H. EHRLICH AND FREDERICK A. BETTELHEIN
groups. We may interpret this as the transfer of the partially localized water vapor on -OH and -KH sites onto -COO- and -SO?- sites probably made available by partial swelling. This type of mechaiiistic interpretation is in agreement with our previous conclusions on calcium chondroitin sulfate A, namely, that this polyiner swells with the greatest difficulty among our samples and, therefore, has the tightest matrix in the solid state. This restrictive swelling demonstrates itself in the observation that transfer from one sorption site to another occurs instead of continuous sorption oii all sites which mould be the case in free swelling. I n Fig. 2 the normalized absorbancies of calcium chondroitin sulfate B are presented as a function of relative vapor pressure. Compared to Fig. 1 the first striking difference is the greater magnitude of the increases in the absorbancies with vapor pressure. Sorption isotherms of chondroitin sulfate B showed also a greater sorptive capacity than A. One can also observe that the carboxyl group plays a relatively prominent role in water vapor sorption especially a t low vapor pressures. Since the only difference between choiidroitin sulfate h and B is the steric position of the carboxyl group the indication is that in the L-iduronic acid moiety this group is niore accessible than in the Dglucuronic acid part. Similar conclusions were reached on the basis of sorptive capacity and thermodynamic functions in the previous a r t i ~ l e . ~The hydroxyl groups become the most dominant sorptive sites a t higher vapor pressures while the sulfate group plays a relatively minor part in water sorption up to 0.4 relative vapor pressure. This can be interpreted as follows. The sulfate group provides most of the iiiterchain linkage in the solid state for chondroitin sulfate B and, therefore, it participates in water binding to a greater extent only after swelling. Chondroitin sulfate C represents an interesting case as shown in Fig. 3. Here a t low vapor pressures all the measured polar groups participate about equally in water binding. At higher mpor pressures the numerically large number of hydroxyl groups dominate the scene while the -SH, -COO-, and -SO,-groups which have equal molar concentrations within the polymer show equal participatioii in water binding. This would indicate equal ayailability of the polar groups in chondroitin sulfate C which is tantaniouiit to free swelling. Similar conclusions were reached on the basis of the hysteresis loop, sorptive capacity and thermodynamic functions in the previous article. Also, the magnitude of the increases in absorbancies is in agreement with the sorption isotherm which showed the greatest sorptive capacity by chondroitin sulfate C. I n Fig. 4 the normalized absorbancy of hepariii films is shown as a function of relative vapor pressure. The inagiiitude of the normalized absorbancies are about the same or somewhat less than those of calcium chondroitin sulfate C, in agreement with sorption isotherms. The numerically more important groups -OH and -SOahare the greatest absorbancy increases. Howerer, there is indication that in heparin not all the sulfate groups are readily accessible. A comparison of the -KS and -SO bond absorbancies would indicate that a t lorn vapor pressures only the sulfainic acid group is available for vapor sorption while the sulfate groups
J.01. 67
PIP*. Fig. 3.-Sorrnalized absorbancies of the -OH, -COO-, -SH, and ;S=O bands of calcium chondroitin sulfate C as a function of relative vapor pressure of water a t 34'.
P/PO
Fig. 4.--Normalized
4
absorbancies of the -OH, -COO-,
S=Q, and -X'S band of calcium salt of heparin as a functiim of relative vapor pressure of water a t 33.6".
participate in iiiterchaiii hydrogen boiidiiig. Oiily upon swelling mill these additional sulfate groups participate in water binding.
SPECTRA OF WATERVAPORSORPTION PROCESS OF ~ ~ U C O P O L Y S A C C H B R I D E S
Oct., 1963
7-7-Ii
1957
.
>.
V
2
a a m
t.10
5: m Q
0
w
N /
1.05
I '
2
a
II
----'
0
z
I N-H 1555cm-' 1
UNIT
2
3
2
I
3
I
Fig. 5-6.--Sormalized absorbancies of the -OH and COObands of the different mucopolysaccharides as a function of water - -_ , calcium chondroitin sulfate A; -, vapor coverage: calcium chondroitin sulfate B; - - - -, calcium chondroitin sulfate C; - -,heparin.
-
---
Another way of comparing the relative role of a polar group in the different polymers is to plot the normalized absorbancies IZS a function of molar coverages of the different polymers. Our absorbancy data were obtained on films, measuring equilibrium pressures. On the other hand, our molar coverage was obtained from isotherms on powder sample^.^ The only condition under which a plot of absorbancies us. coverage can be calculated is i,he assumption that the powder and the film sample sorb equal amounts of sorbate under identical temperature and pressure conditions. For most of the water soluble polymers this condition is fulfilled in water vapor sorption.13e14 I n examining Fig. 5-8 one has to bear in mind that the comparison between the cliff erent polymers is a t equal coverages irrespective of the history, i.e., a t what vapor pressures the different polymers achieved their coverages. Figure 5 shows that the hydroxyl group role a t lower coverages is the most important in chondroitin sulfate A and the least important in heparin. At higher coverages, however, more hydroxyl group binds water in C than in the rest and the decreasing order is heparin > B and A, the same as the sorptive capacity order. The role of carboxyl group in water binding is the most important in chondroitin sulfate B a t lower cover(13) s. W. Benson, D. A. Ellis, and R. W. Zwanzig, J. A m . Chem. Soc., '22, 2102 (1950). (14)
F. A. Bettelheim, C. Sterling, and D. H. Volman, J. Polymer Sci..
22, 303 (195G).
4
5
6
MOLES HzO/MOLE REPEATING UNIT. 4
5
I
I
I
I
6
HEPARIN 33.6'
C
,
Fig. 7-8.-Normalized absorbancies of the -NH and S=O bands of the different mucopolysaccharides as a function of water vapor coverage: - -, calcium chondroitin sulfate A; -, calcium chondroitin sulfate B; - -, calcium chondroitin sulfate C; - - - -, heparin.
-
-
--
ages. At moderate and high coverage chondroitin sulfate C makes equal or greater use of the carboxyl groups in water binding compared to B. The least important carboxyl groups from the point of water binding are in heparin. At equal coverages more water is bound by the NH groups in chondroitin sulfate A than in B which in turn has more KH participation in water binding than C and heparin. Finally a t low coverages the importance of the sulfate group in water binding is exhibited in the following order: C > A > heparin > B while a t higher coverages after swelling the order is heparin > C > A > B. The normalized absorbancy us. coverage curves indicate the role that the individual atomic groups play in binding a certain number of moles of water per repeating unit, and hence are related to the water retentive power of the different mucopolysaccharides. On the other hand, the normalized absorbancy us. relative vapor pressure diagrams provide a bridge between the sorption isotherms and infrared spectroscopic data as they are related to the stepwise swelling mechanism of the polymer during sorption process. The same curves also give an understanding about the availability of polar groups for water binding a t the different stages of swelling. Hence they are related to the sorptive capacity of the polymers. Another way of measuring the availability of a site to water vapor is to investigate the deuterium-protium exchange effect. Mann and h!Iarrinan15 performed
SAXFORD H . EHRLICH AKD FREDERICK A. BETTELHEIM
1958
deuteration experiment on cellulose, and on the assuniption that only the amorphous part of the cellulose can be deuterated they estimated the extinction coefficient (absorptivity) ratio of koD/kOH=- 1.11. This ratio was obtained by measuring the absorbancies of the OD band a t 2560 cm.-l and of the OH at 3360 cni.-’, and from the equation
- \r
I
I
I
/OW
they evaluated the mean value of koDIkoH. In the above equation the left-hand side is that absorbancy ratio while Con and Coa are mole fraction concentrations and 1 is the path length. Similar experiments performed on the mucopolysaccharides can be interpreted in terms of the accessibility of the OH group to deuterium exchange, hence to heavy water vapor. Using the Mann and Marrinan coefficient ratio for OD/OH exchange we defined our accessibility as the mole fraction of OD. These accessibilities are plotted against relative vapor pressure in Fig. 9. The diagram indicates that in chondroitin sulfate C the OH group is most accessible: 40% a t the lowest vapor pressure and increasing somewhat further with increasing pressure. The initial large accessibility of the OH groups again prows that chondroitin sulfate C chains are loosely bound to each other in the solid state and relatively free swelling occurs on water vapor sorption. At very low vapor pressures the order of the accessibilities of OH groups is the same as the sorptive capacities of the polymers which is again indicative that the more numerous OH groups play a large role in the sorption processes. Beyond the initial accessibilities in heparin and chondroitin sulfate B there is very little increase with vapor pressure up to relatively high vapor pressures. Since sorptive capacity, thermodynamic analysis of the isotherms, and the infrared absorbancy data indicated that both heparin and chondroitin sulfate B swell, the flat portions of the accessibility curves indicate that during this part of the swelling mostly the other polar groups open up and become available for sorption. Similarly the initial small accessibility of chondroitin sulfate A and the relatively large increases in accessibility indicate that chondroitin sulfate A is a tightly bound matrix in the solid state and a large amount of swelling is needed to accommodate more water molecules, a conclusion supported by previous considerations. Conclusions Infrared spectroscopy of the water and deuterated water sorption process prored that many polar groups participate simultaneously in the sorbate binding. This indicates that the different polarities do not introduce large energetic differences to the effect that sorption may occur on a single energetically favorable site only, Our picture of the mechanism of sorption emphasizes the availability or accessibilities of the different sites in the polynier chain. It is envisaged that (15) J. Rlann and H. J. Marrinan, Trans. Faraday Soc., 52, 481, 491 (19561.
T-ol. 67
20
I
30
40
P/p
.
I
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I 50
60
70
J
80
Fig. g.-Accessibility of the OH groups of the different mucopolysaccharides for deuterium exchanges a3 a function of relative vapor pressure of deuterated water: - - - , calcium chon, calcium chondroitin sulfate B; - - - -, droitin sulfate A; calcium chondroitin sulfate C; - - - - -, heparin. ~
tightly bound (hydrogen or ionic bond) polar sites exist in the solid polyelectrolytes. These tightly bound sites are less available for water sorption than the non-hydrogen bonded polar groups on the L‘surfaces.’’ Hence the primary sorption will occur on these free polar sites and subsequent swelling will open up previously bonded, hence, inaccessible sites. This way the mater sorption process in swelling polymers has a zipper mechanism, that is, water molecules will penetrate into the whole matrix by occupying the free sites causing partial swelling, next breaking existing hydrogen bonds between polymer chains and establishing new ones with the sorbate. Similarly, the desorption process will first break hydrogen bonds between water and polar groups of the polymer and establish new ones between the polymer chains. On the basis of increase in the intensities of the absorption bands of different polar groups in the different polymers and on the basis of the accessibility of OH groups for deuterium exchange, we can conclude the following. (a) Chondroitin sulfate A has the most tightly bound polymeric matrix in the solid state; about 8% of the hydroxyl groups are available for deuterium exchange ; upon sorption swelling occurs which primarily opens up the -OH and - S H groups first, hence the increase in accessibility for deuteration up to 5001,. The carboxyl and sulfate groups become increasingly important in the sorption process only a t the medium vapor pressures. (b) Chondroitin sulfate B has about 24y0 accessible -OH groups a t very low pressures. This accessibility, however, does not demonstrate itself in the water sorptive capacities at the low vapor pressure because the dominant sorbing groups in chondroitin sulfate B are the carboxyl and -3H groups. (c) Chondroitin sulfate C demonstrated its free swelling and large sorptive capacities in both the normalized absorbancy curves and in the accessibilities. Especially interesting was the observation that the numerically predominant -OH groups play the more important part in water sorption while the equimolar carboxyl, sulfate, and amide groups play an equal part. (d) The results with heparin showed that in spite of its large number of polar groups, the reason for the equal to less sorptive capacity for water compared to chon-
Oct., 1963
S P E C T R A O F W A T E R V A P O R S O R P T I O N P R O C E S S O F h!!UCOPOLYS.4CCH.4RIDES
droitin sulfate C is due to the fact that most of the sulfate and carboxyl groups participate in the interchain binding in the solid state and, therefore, heparin has mechanical constraints opposing swelling. Comparing all the data from infrared spectroscopy, one comes to the conclusion that what one measures by accessibility for deuterium exchange and participation in water bincling is not the same quantity. This may be due to the fact that an -OH group may hydrogen bond to a water molecule and to a lesser degree to a deuterated water molecule without exchanging adjacent hydrogen to deuterium. For that reason, in all of our curves the OH participation in water vapor binding was greater than their capacity for deuterium exchange. However, in their own way both methods measure the availability of polar sites and the spectroscopic findings reinforce the conclusions based on the analysis of sorption isotherms.
.DISCUSSIOS A. W. ADAMSON (University of Southern California).-I wonder if you would comment on the precise significance of thermodynamic quantities calculated from adsoxption data showing hysteresis. It would seem to me that in such a circumstance one cannot absolutely afFirrn that the data pertain to a reversible equilibrium situation and that calculated AS, etc., quantities may therefore have no definite meaning. F. A. BETTELHE1M.---The significance of the thermodynamic functions in such cases will depend on the model one advances for the hysteresis phenomenon [see D. F. Everett and W.I. Whitton, Trans. Faraday Xoc., 48, 749 (1952), and J. 31.Sechof, et al., J . Am. Chem. Soc., 75,2427 (1953)l. I n our case we agree with Cassie’s model in emphasizing the mechanical constraints developing in the polymer network upon swelling. However, irrespectiyely of a particular model we used these calculated A S and AH values for comparative purposes among the polymeric systems investigated and therefore we attached only a relative merit to these calculations. L. H. REYERSON (University of Minnesota).-Was D 2 0 vapor sorbed on a fully deuterated sample of the mucopolysaccharides or on the original hydrogen compounds? Deuteration probably takes place during adsorption-desorption of D20 on the hydrogen material. Desorption values should be off by the amount of exchange which increases the weight of the sample. F. A. BETTEL.HEI>I.--’The DzO vapor was sorbed on the hydrogen compound and, as our accessibility data indicate, hydrogendeuterium exchange did occur (see Fig. 9 of the second paper). However, judging from the infrared data, this exchange was small, 3 p.p.t., so that the increase in the weight of sample fell within the limits of error of our gravimetric measurements. J. W.WHALEN(Socony Rfobil Oil (30.)-You utilize maxima in the diffe-entia1 entropy function in arriving a t conclusions regarding monolayer completion. Entropic maxima are related to monolayer oompletim for integ-al-not difte-ential-quantities. The entropic maximum in the differential curve will lead that in the integral curve by a n amount dependent on the abruptness of monolayer completion. Would shifts of $ 5 to $10 mg. of adsorbate per gram of adsorbent in your monolayer values influence your general conclusions? F. A. BETTBLHEIM --.This difference between the differential and integral entropy curves was also pointed out by Hill, et aE. [T. Hill, P. Emmett, and C. Joyner, J . Am. Chem. SOC.,73, 5102 (!951)]. Since we took only the approximate positions of the differential entropy maxima, an excess of 10 mg. of water per gram of polymer in the will not affect our conclusions. V. K. LA MER (Columbia University) (communicated).The objections of Drs. Adamon, Reyerson, Goddard, and several others to the authors’ calculation of enthalpies and entropies using a Clapeyron-Clausius operation upon data admittedly obtained for dynamic systems exhibiting hysteresis on adsorption and desorption raise important questions that merit attenlion.
1959
I confess surpriee and amazement a t the apologies and justifications that were offered by certain distinguished investigators of adsorption phenomena in support of the procedure. They seemed to be based more upon pragmatism than upon thermodynamics. I have been taught by such masters as Bronsted, Debye, G. pu’. Lewis, and P. S. Epstein that thermodynamic calculations have physical meaning only when the procees involves a reversible path. This means that the states employed in the calculation must be attainable from both directions to qualify as equilibrium states. A system exhibiting hysteresis violates this requirement. “An equilibrium state cannot be assumed just because cyclic repetition can be reproduced.” Instead, hysteresis requires treatment from the standpoint of so-called irreversible ther modynamics, the time rate of entropy production, steady-state processes, and particularly metastable and partial or frozen equilibria which are foreign to classical thermodynamic calculations. A perfectly reversible path is, of course, a figment of the imagination, but it is attained frequently within such narrow limits of expe imental perccption that no sensible error is incurred. The data under question exhibit a hysteresis far exc-eding the expeiimental limits of pe-ception. It would seem, a t least, that a more acceptable treatment would be to calculate the enthalpies and entropies from both the upper and lower curves of the hysteresis loop, thus offering a measure of upper and lower bounds of reliability. My questions to the speaker and those who support such calculations are these. How does one know, a priori, which branch of the hysteresis loop is the correct and proper one to use? Also, can they cite any thermodynamic authority which grants to colloid chemistry and particularly to adsorption phenomena a special dispensation to treat such data contrary to the preccpts of thermodynamics? F. A. BETTELHEIM.-TOthe first question my reply is that the use of the adsorption branch of the hysteresis loop is the proper one. The reason is that in this case the reference state, Le., the dry polymer network, is always the sime. On the other hand, the desorption path depends on the previously attained swelling of the polymer network; hence, we do not have a single reference state. With respect of the use of thermodynamics in metastable systems, I have t o agree with Dr. La Mer-one has no theo-etical justification. I may add that the entropy production ineide a system which measures the irreversibility of a process has been shown by Prigogine to be a minimum property in stationary nonequilibrium states. My contention is that since the sorption values obtained a t each relative vapor p.essure were limiting values with respect to time, one deals he e with stationary nonequilibrium states. The eforc, the claseical Clausius-Clapeyron equation may be used as a first approximation and the values obtained will have a minimal deviation from those for true equilibrium processes. I would like to emphasize that we never claimed that the enthalpy and entropy values obtained have any absolute meaning. As a matter of fact we pointed out that both functions contain contributions from the polymer networks as well as from the sorbate water and we cannot separate theee contributions. We discussed only the magnitude of these values and their relationship in the diffe-ent polymeric systems. The whole purpose of the articles is to show that by diffe-ent arguments, Le., sorptive capacity, hysteresis, thermodynamic functions, “monolayer” coverage, infrared absorbancy of different polar groups, and accessibility, one comes to a single conclusion with respect to the functional structures of the different mucopolysaccharides. A. W. ADAMSOK.--I would like to underscore Professor La Mer’s point that second-law calculations, such as those giving isosteric heats, imply the presence of a reversible path. This is demonstrably not present when the state cannot be approached from both sides of equilibrium. It seems to me that there are two types of circumstances where this dictum may be softened, although with some peril. The first is the obvious one where irreversibility is small, and its manifestations, such as hysteresis, seem to be within experimental error. One may then assume, faute de mieux, that uncertainties in the meaning of derived thermodynamic quantities will likewiEe be small. The second type of situation is that in which a particular model is proposed, on the basis of which thermodynamic calculations are interpreted, such as, in the case of adsorption, a par-
