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Volume 77, 1948-49
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The Adsorption of Water Vapour on Collagen and Elastin.

Summary.

The isopiestic method of Robinson and Sinclair can be used to investigate the adsorption of water vapour on fibrous materials. Adsorption isotherms are described for collagen, elastin, and certain tanned collagen preparations. The approach to equilibrium by adsorption and desorption, the influence of temperature, and the effect of preliminary treatments of the adsorbent are discussed. A comparison is given of several methods for determining the water content of the materials. The experimental results are discussed in the light of the multimolecular adsorption theory of Brunauer, Emmett and Teller, and an attempt is made to interpret them in terms of the molecular structure of the adsorbents.

Introduction.

The interaction of water with collagen and its derivatives is of both theoretical and practical importance in the chemistry of leather and occupies a prominent place in the literature of the subject. In the domain of biochemistry, also, the more general problem of the behaviour of proteins in the presence of water is recognised as fundamental. It is well known that when a protein reacts with liquid water the degree of absorption is governed by a Donnan equilibrium, and the macroscopic or mechanical structure of the absorbent plays a major part. Moreover, the presence of an excess of liquid water of activity approximating to unity proves an embarrassment in the interpretation of results. In spite of these limitations, much valuable information has been obtained from investigations with liquid water or aqueous solutions, but comparatively little consideration has been given to the changes occurring when a protein is permitted to interact with water vapour, whose activity may be fixed at values considerably below unity. Some of the earliest work by leather chemists on this aspect of the problem was done by Veitch, Frey, and Leinbach (1922), and by Wilson and his co-workers (1924, 1926). Although they were more interested in the influence of humidity on the mechanical properties of leather, they did establish that for leather the plot of water adsorbed against humidity is of the sigmoid form typical of so many fibrous and porous adsorbents. That the sigmoid adsorption isotherm is characteristic of most proteins was shown by Bull (1944), who investigated a wide range of purified proteins.

The present paper describes a rather deeper study of the conditions governing the water-vapour adsorption isotherms of two skin proteins, collagen and elastin, and of certain collagen derivatives.

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Experimental. Materials.

It has been shown by the author (1945) that the amount of water-vapour adsorbed by collagen or chrome leather at a given humidity is dependent on the previous treatment that the adsorbent has received. As a standard preliminary treatment, therefore, the following method was adopted. The material after preparation and purification was steeped for at least one hour in each of four portions of acetone. At each change it was filtered and pressed on a Buchner funnel. After the fourth acetone treatment, the material was spread out and exposed to the air of the laboratory overnight. Any remaining traces of acetone were removed by placing in an evacuated desiccator over distilled water for 24 hours, and the substance was finally exposed to the atmosphere again to enable its water content to return to a convenient value.

Collagen. Standard hide powder, according to the specifications of the International Society of Leather Trades' Chemists, was soaked overnight in distilled water and treated as described above.

Denatured or shrunk collagen. Standard hide powder was immersed for five minutes in water at 72°C., which caused it to shrink. It was then filtered on a Buchner funnel and treated with acetone.

Formaldehyde-tanned collagen was prepared from standard hide powder according to the accepted method at pH 8·0. It was washed free from buffer salts and treated with acetone.

Quinone-tanned collagen. Standard hide powder was immersed with occasional shaking in a saturated solution of quinone maintained at pH 8 by a phosphate buffer. After 48 hours it was washed on a Buchner funnel until the wash water gave no reaction with potassium iodide. Even then, acetone removed more quinone, and acetone extraction was prolonged until the washings were colourless.

Chrome-tanned collagen was prepared from standard hide powder and a commercial basic chromic sulphate tanning agent by the usual method at pH 3 3. The chromed material was divided into three parts, the first being washed until free from soluble salts. The other two portions were soaked in distilled water which was changed twice daily for periods of three and six months respectively. All three portions were eventually extracted with acetone as described.

Elastin. This was prepared from the ligamentum nuchae of beef by the method described by McLaughlin and Theis (1945–1). Since this method involves repeated extractions with boiling water, the product will correspond to the substance referred to by Weidinger (1940) as elastoidin II.

The tanned compounds were analysed by the usual methods.

Formaldehyde was determined by the method of Bowes and Pleass (1939), quinone by difference, and the titratable acid in the chromed samples by the method of Riess and Papayannis (1934). The composition of the tanned samples based on the oven-dry weight at 103° C. is shown in Table I.

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Table I.—Composition of Tanned Collagen Samples.
Chrome I. Chrome II. Chrome III. Formaldehyde. Quinone.
Collagen 77.4% 82.2% 86.0% 97.5% 85.6%
Ash 10.44 9.37 8.93 0.1 0.1
Chromic oxide 9.90 8.78 8.48
Acid (as SO1) 8.39 6.40 5.22
Gm. Cr2O3 per 100 gm. collagen 12.8 10.7 9.9
Basicity 46 54 60
Formaldehyde 1.9
Quinone 14.3

Technique of Adsorption Measurements.

In measuring an isotherm for water-vapour adsorption on a protein, the experimental work falls into two parts. First, the adsorbent must be brought as speedily as possible into equilibrium with an atmosphere of known humidity, and then, equilibrium having been reached, the quantity of water held by the adsorbent must be determined.

If many measurements are to be made, a rapid attainment of equilibrium is highly desirable. In earlier work this condition has been lacking. Wilson and his co-workers (1924, 1926) placed their samples in desiccators over sulphuric acid solutions of known aqueous vapour pressure and weighed them at intervals. They found that at least a month was needed before the weight of the samples became constant. Bull (1945), using a similar method but submerging his containers in a constant temperature bath, found periods of the order of six to twelve days to be sufficient. The present author (1945) showed that, by continuously circulating air of constant humidity over hide powder, six samples arranged in series could be brought to constant weight in four days.

It has now been found that a still greater reduction in the time for conditioning may be achieved by use of the isopiestic method, originally designed by Robinson and Sinclair (1934) for the study of aqueous solutions. The apparatus consists of flat-bottomed silver or platinum dishes resting on a heavy copper block in a desiccator. One dish contains a saturated salt solution to control the humidity. A second dish (of platinum) contains a weighed quantity of standardised sulphuric acid solution, and the remainder of the dishes hold weighed samples (1–2 gm.) of the adsorbents to be studied. The desiccator is evacuated, submerged in a constant temperature bath, and gently rocked. Equilibrium between the contents of the several dishes is attained by distillation of water from one to another and is much more rapid than in the earlier methods referred to above. This can be attributed to three causes: increased mean free path of the water molecules through evacuation, agitation of the control solutions to ensure that there is no concentration gradient near the surface, and efficient heat transfer through the copper block. The dishes are fitted with hinged lids which are held open during equilibration by wire supports. When equilibrium has been reached the desiccator is opened, the lids are closed, and the change in weight is determined. The relative humidity or water activity (aw) is found from the sulphuric acid concentration by means of the data of Shankman and Gordon (1939).

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Using this method it was found that as many as eight protein samples in one desiccator could be brought to equilibrium at a given humidity in 24 hours. Examples of the rate of equilibration will be given later. The method has the additional advantage that a number of measurements at different humidities can be made on the same sample, so that a complete adsorption isotherm can be obtained on one sample in two to three weeks.

Water Content of Samples.

The method of determining the water content of the conditioned samples must be chosen with care. It is clear that, if the graph of adsorption isotherm is to pass through the origin, the water content must be defined as the greatest weight of water which can be removed at the temperature of the adsorption experiment. As the official method of oven-drying leather might possibly remove more than this amount of water, an examination of different methods of drying was undertaken.

Three samples of collagen were weighed out at the same time and from the same batch. One portion was dried in an air oven at 103° C. and lost weight as shown in Table II.

Table II.—Loss in Weight of Collagen in Oven at 103° C.
Time (hours) 1 12 24 30
Loss % 29.57 20.02 30.10 30.10

Another portion was placed in a weighing bottle in vacuo over phosphorus pentoxide and heated by the vapour of various boiling liquids. These liquids were ether, acetone, ethyl alcohol, and water in order of increasing boiling point. The sample was weighed at one-day intervals until it reached constant weight at each temperature, with the results shown in Table III.

Table III.—Loss in Weight of Collagen in Vacuo over Phosphorus Pentoxide.
Ether Vapour Acetone Vapour. Alcohol Vapour.
35° 56° 78°
27.69% 29.06% 30.05%
28.83 29.70
29.11 29.86 Steam 100°
29.30 29.96 30.11
29.51 29.98 30.10
29.58 29.98
29.58

The third portion was placed in a dish of the isopiestic apparatus together with a platinum dish of concentrated sulphuric acid. The desiccator was opened daily, the dish weighed, and the sulphuric acid renewed. The results are shown in Table IV.

Table IV.—Loss in Weight of Collagen over Conc. Sulphuric Acid.
Time (days) 1 2 3 4
Loss % 29.12 29.30 29.69 29.69

Comparison of the figures in Tables II–IV shows that dehydration at an elevated temperature removes more water than room-temperature dehydration. There is an apparent anomaly in Tables III and IV. Dehydration over sulphuric acid for four days at 25° caused a greater loss than over phosphorus pentoxide at 35°. This can be explained by the state of the drying agents. In the rocking desiccator a new sulphuric acid surface is continually being exposed, but the phosphorus pentoxide in the higher temperature apparatus is undisturbed.

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Even if the latter is renewed frequently it very rapidly acquires a sticky surface of metaphosphoric acid which must greatly reduce its efficiency. In a large number of experiments concentrated sulphuric acid in the rocking desiccator was found to be a better dehydrating agent than phosphorus pentoxide.

Table III shows that raising the temperature under otherwise comparable conditions slightly increases the weight of water driven off, until at 100° the loss is the same as for the air oven at 103°. Bull (1945) dried his protein samples in a vacuum oven at temperatures from 80° to 137° and also found increasing loss with temperature. He arbitrarily defined the moisture content as the loss after 24 hours in vacuo at 105°.

All the materials examined here were dried over sulphuric acid at 25° and in the air oven at 103°, with the results shown in Table V.

Table V.—Water retained on Drying over Conc. H2SO4 at 25°, but eliminated by Oven Drying at 103°.
Gm. H2O per 100 gm. dry material.
Collagen 0.57
Denatured collagen 0.25
Elastin 0.31
Formaldehyde-collagen 0.13
Quinone-collagen 0.44
Chromed collagen I 2.04
Chromed collagen II 1.78
Chromed collagen III 1.14

The importance of a careful choice of method is emphasised by the large difference figures for the chromed samples. It is noteworthy that, of all the tanned collagens, the only one showing great variation from standard collagen is the compound with a tanning agent which is itself hydrated in the free state. It seems probable that the extra water driven off during oven drying is in some way associated with the hydration of the chrome-tanning complex.

In what follows, the term water content is taken to mean that amount of water which can be removed by dehydration at the temperature of the adsorption experiment. It is expressed as gm. water per 100 gm. adsorbent dried at room temperature, except, of course, in the case of oven-dried material. The water content (x) was determined in duplicate, (a) on a sample weighed out at the same time as the samples for adsorption, and (b) on the adsorption sample itself at the conclusion of the experiment.

The Adsorption Isotherms of Collagen.

A preliminary experiment was made to determine the time required for the samples to reach equilibrium at a given humidity. Two portions of the sample of collagen were equilibrated in the isopiestic apparatus to a relative humidity (aw) of about 0 29, using saturated calcium chloride as the control solution and standardised sulphuric acid solution to indicate the exact value of the humidity. The calcium chloride was then replaced by saturated potassium iodide solution, (aw=0·6813.) and the samples were weighed, at intervals. After equilibrium had been reached, the humidity was again raised by means of saturated sodium sulphate solution (aw =0·9391). After a suitable period, the potassium iodide solution

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was put back in the desiccator and more readings were taken. In this way the approach to equilibrium at aw = 0·6813 was observed from both lower and higher humidity, i.e., by adsorption and desorption. The results are given in Table VI and Fig. 1.

It will be noticed that the approach to equilibrium is much more rapid in adsorption than in desorption. It was found that, except at high humidities or where the change in aw was unusually large, adsorption was complete in 24 hours. All adsorptions were carried out in duplicate and doubtful cases were weighed after one and two days. In studying an adsorption isotherm, it was usual to begin at a fairly low aw and increase the aw in small steps until the whole range had been covered. Table VI shows very clearly that the water content at equilibrium depends on whether the point is approached from lower or higher humidity, that is, the isotherm exhibits hysteresis.

Table VI—Water Content in Approach to Equilibrium at aw = 0.6813.
Time (hrs.). Adsorption. Desorption.
0 13.79% 44.81%
1 16.32 37.53
2 21.50 32.69
3 23.74 29.70
4 24.75 28.43
6 25.90 27.99
10 26.51 28.03
23 26.70 27.70
56 26.72 27.50
72 27.31
96 26.60 27.28
168 27.15
245 27.18
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Fig. 1.—Adsorption and desorption curves as a Function of the Time.

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As preliminary work had indicated that excessive dehydration also influenced the adsorption, an experiment was made to examine the extent of this effect. Samples of collagen were conditioned over laturated lithium bromide (aw = 0 0676) and then allowed to adsorb water over saturated magnesium chloride solution (aw = 0 3229). They were then placed over 73% sulphuric acid solution, which had a lower aw than lithium bromide, and again brought up to the magnesium chloride point. The experiment was repeated using more concentrated acid as the conditioning agent and then returning to the magnesium chloride point. The series was completed using concentrated sulphuric acid, and lastly the samples were oven-dried and again allowed to adsorb water from saturated magnesium chloride. Table VII shows the results obtained.

Table VII.—Effect of Initial Water Content on Adsorption.
Conditioning Agent. Water Content.
Over Conditioning Over Sat. MgCl2
Agent. aw = 0.3229.
Saturated LiBr soln. 6.64% 13.24%
73% sulphuric acid 4.27 13.30
77% sulphuric acid 2.41 12.94
Conc, sulphuric acid 0 12.51
Oven-drying at 103° —0.57* 9.95*

It was evident, then, that dehydration of collagen to a water content of less than about 4% produced a change in the adsorbent which influenced the subsequent course of the isotherm. The greater the dehydration beyond this point, the more pronounced was the change, which reached a maximum with oven drying.

To investigate this effect more fully, complete adsorption isotherms were measured for collagen treated in the following different ways:

A.

Dried in air oven at 103°.

B.

Dehydrated over phosphorus pentoxide at 25°.

C.

Conditioned over 77% sulphuric acid solution (water content of sample = 2 41%).

D.

Conditioned over 73% sulphuric acid solution (water content of sample = 4·27%).

E.

Conditioned over water at 50° and then over 73% sulphuric acid solution.

F.

Denatured and conditioned over 73% sulphuric acid.

G.

Denatured and dried in oven at 103°.

For lack of a better term, samples like D, which were neither excessively dehydrated nor conditioned at high temperature, will be referred to here as “standard” samples.

The experimental results for standard collagen are given in full in Table VIII, but, as each series was measured at a different set of aw values, the remainder of the results have been interpolated to round, values of aw and, to save space, are given in that form in Table IX. For comparison, the figures for standard collagen are included in this table also. The experimental points for samples A, B, D, F, G are shown in the isotherms plotted in Figs. 2 and 3. It will be noticed that the isotherms for samples D and F have not been

[Footnote] * The figures for oven-dried collagen are shown here as gm. water per 100gm. P2O5-dry collagen. Calculated to an oven-dry basis, the first column is zero and the second is 10.58%.

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Fig. 2.—Adsorption isotherms of standard collagen ▽, P2O dried collagen □, oven dried collagen ▵, standard elastin X, oven dried elastin ⊙.

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drawn back to the origin of co-ordinates, since no adsorption curve for standard collagen exists at very low values of aw. We have seen that the collagen undergoes a change as soon as this low humidity region is entered and ceases for the time being to behave as standard collagen. It will also be noticed that, although the isotherms for partially or completely dehydrated collagen are lower than the standard isotherm, they gradually merge into it at high humidities. This reversion is a function of the humidity only and not of the time taken in traversing the curve from point to point, as was shown by taking a second P2O3-dried sample direct to aw = 0·92 when the water content became 45·30%, coinciding with the value shown in Table IX.

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Fig. 3.—Adsorption Isotherms of Standard Collagen ⊙, Denatured Collagen Δ, and Denatured Collagen, Oven-dried □.

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Table VIII.—Adsorption of Water Vapour on Standard Collagen.
aw Water Content. aw Water Content.
0.0681 5.82% 0.4324 15.96%
0.1130 7.33 0.5239 19.02
0.1633 8.63 0.5818 20.91
0.1977 9.52 0.6811 24.75
0.2719 11.71 0.7494 28.23
0.3236 13.24 0.8400 33.48
0.3860 14.68 0.9305 45.52
Table IX.—Adsorption of Water Vapour on Collagen.
aw Water Content.
A* B* C* D* E* F* G*
0.05 2.52% 3.73% 1.95%
0.08 6.20% 7.55% 7.58%
0.10 4.22 5.53 6.24 6.88 8.05 7.96 3.71
0.20 7.18 8.82 9.55 9.85 10.49 9.88 6.42
0.30 9.98 11.87 12.37 12.50 13.03 11.95 8.77
0.40 12.78 14.50 14.86 15.14 15.80 14.37 10.87
0.50 15.69 17.42 17.82 18.10 18.84 17.01
0.60 19.00 21.20 21.38 21.59 22.15 19.82
0.70 23.00 25.50 25.60 25.69 26.13 22.95
0.80 28.43 30.88 30.95 30.88 27.58
0.90 39.22 40.20 40.25 38.70
0.92 45.15 45.25 45.25

The question arises whether the coincidence of the several collagen isotherms at high humidity is confined to that region or whether it is an indication that the samples have returned to the standard state. This question was answered by the following experiment. Three collagen samples—one standard, one dried over phosphorus pentoxide, and one oven-dried—were allowed to adsorb water from saturated calcium chloride solution at aw = 0·2960. They were next placed in a desiccator over water for two days, then for three days over saturated lithium bromide at aw = 0·0785. Finally, the samples were again allowed to adsorb water from saturated calcium chloride solution at the same humidity as at first.

As a standard for comparison, all the water contents were calculated on the P2O5-dry basis. The results, which are given in Table X, show that placing the sample in a saturated atmosphere does indeed restore the P2O5-dried material to the standard state. This is in agreement with the results obtained by Speakman and Stott (1936) for wool. The reversion of the oven-dried sample to the standard state is almost, but not quite, accomplished by two days over water. Therefore the samples were again conditioned over water, this time for seven days, then over lithium bromide for two days, and lastly allowed to reach equilibrium with saturated calcium chloride at aw = 0·2960. The result of this adsorption appears in the last line of Table × and demonstrates that, while P2O5-dried collagen can be restored to the standard state by exposure to saturated water-vapour, the effect of oven-drying cannot be entirely reversed by this means.

[Footnote] * A—Oven-dried; B—P2O5-dried; C—Dehydrated to 2.41% water over 77% H2SO4; D—Standard collagen; E—Conditioned over water at 50° then over 73% H2SO4; F—Denatured, standard; G—Denatured and oven-dried.

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Table X.—Effect of Conditioning Dried Collagen over Water.
Gm. H2O per 100 gm. dry collagen.
Standard. P2O5-dried. Oven-dried.
First adsorption at aw = 0.2960 12.81 12.27 9.85
Conditioned over water 71.3 73.1 70.7
Desorption at aw = 0.0785 7.63 7.46 7.13
Second adsorption at aw = 0.2960 12.85 12.80 12.24
Third adsorption at aw = 0.2960
after 7 days over water 12.83 12.87 12.31

A similar experiment to the above was carried out with denatured collagen and elastin, as shown in Table XI.

Table XI.—Effect of Conditioning Dried Samples over Water.
Gm. H2O per 100 gm. dry adsorbent.
Denatured Collagen. Denatured Collagen, Oven-dried. Standard Elastin. Elastin, Oven-dried.
First adsorption at aw = 0.2960 11.91 8.71 7.75 4.54
Conditioned over water two days 79.4 76.0 44.4 42.6
Second adsorption at aw = 0.2960 12.01 11.65 7.80 7.46

It appears from these experiments that oven-drying has a strong reducing effect on the adsorptive power of the proteins studied. Exposure to saturated water-vapour causes a partial reversal of this effect, but the oven-dried materials never return entirely to the standard state. It may be significant that for each of the proteins examined this difference in water content from the standard condition is approximately equal to the extra water driven off by oven-drying as shown in Table V. Apparently there is a small amount of very firmly held water which can be removed only by oven-drying and whose loss produces an irreversible change in the protein.

Adsorption Isotherms of Collagen Derivatives.

Adsorption on the several tanned collagen samples was studied in a similar way, care being taken to avoid too great dehydration at the beginning of each experiment. The interpolated results are shown in Table XII and the experimental points are plotted in Fig. 4.

Adsorption Isotherms of Elastin.

Table XIII and Fig. 2 show the results obtained for water adsorption on elastin. The complete isotherm was determined for a sample which had never been dried below 5·2% water and which should therefore be analogous to the standard state of collagen. A few points for oven-dried elastin are also included.

Table XII.—Adsorption of Water Vapour on Collagen Derivatives.
aw Formaldehyde. Quinone. Chrome I Chrome II. Chrome III.
0.08 7.68% 6.27% 8.20% 8.16% 8.15%
0.10 8.38 6.90 8.82 8.72 8.75
0.20 11.33 9.37 11.09 11.03 11.19
0.30 13.97 11.30 12.78 12.98 13.19
0.40 17.06 13.55 14.83 15.33 15.43
0.50 20.42 15.98 17.25 18.02 18.14
0.60 24.07 18.80 19.86 21.10 21.32
0.70 27.57 21.90 23.30 24.87 25.08
0.80 34.16 26.52 28.40 30.16 30.45
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Fig. 4.—Adsorption Isotherms of Collagen Deprivatives. Quinone Tanned ⊙, Chrome Tanned II ▵, Formaldehyde Tanned X.

Table XIII.—Adsorption of Water Vapour on Elastin.
aw Water Content. aw Water Content.
Standard. Oven-dried. Standard.
0.08 4.98% 1.52% 0.50 10.93%
0.10 5.24 1.87 0.60 13.00
0.20 6.45 3.52 0.70 15.28
0.30 7.70 5.03 0.80 17.80
0.40 9.13 6.43

Hysteresis.

It has already been mentioned that adsorption and desorption give different values for the water content. The extent of this hysteresis

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phenomenon for collagen was investigated at four different humidities. Precautions were taken to avoid excessive dehydration which would effect the adsorption value and give a fictitiously high figure for the hysteresis. Adsorption and desorption points are reliable only if they are unchanged when approached from several different humidities at a reasonable distance along the curve. By definition, hysteresis is zero at each end of the isotherm and, by virtue of the dehydration effect, it is somewhat indeterminate below about aw = 0·07. The difference between adsorption and desorption was found to be greatest for collagen near aw = 0 50. Because of the long time needed to reach equilibrium by desorption, hysteresis for chromed collagen was measured at three points and for the other materials at one humidity only, namely, aw = 0·5280, using saturated magnesium nitrate solution as a control. The differences found, expressed as gm. water per 100 gm. adsorbent, are shown in Table XIV. The table shows clearly how important it is to specify whether a given water content is approached by adsorption or by desorption.

Table XIV.—Hysteresis.
Adsorbent. aw Hysteresis.
Collagen (standard) 0.1120 0.15
0.2907 1.25
0.5721 1.36
0.7519 0.53
Collagen (denatured) 0.5280 3.18
Elastin 0.5280 2.73
Chromed collagen II 0.3259 1.84
0.5280 4.62
0.7520 1.73
Formaldehyde-collagen 0.5280 3.36
Quinone-collagen 0.5280 3.44

Effect of Temperature on Adsorption.

To obtain some information concerning the effect of temperature on adsorption, isotherms up to aw = 0 40 were measured for collagen (sample E) and for standard elastin at both 20° and 30°. To facilitate calculation of heats of adsorption, the experimental results were interpolated for integral values of the water adsorbed and are shown in that form in Tables XV and XVI.

Table XV.—Effect of Temperature on Adsorption by Collagen (Sample E).
Gm. water per aw
100 gm. collagen. 20° 30°
8 0.1014 0.1168
9 0.1330 0.1514
10 0.1699 0.1906
11 0.2105 0.2324
12 0.2523 0.2744
13 0.2933 0.3151
14 0.3324 0.3532
15 0.3687 0.3886
16 0.4022 0.4211
Table XVI.—Effect of Temperature on Adsorption by Standard Elastin.
Gm. water per aw
100 gm. elastin. 20° 30°
5 0.0867 0.1095
6 0.1504 0.1739
7 0.2296 0.2485
8 0.3069 0.3208
9 0.3744 0.3845
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Discussion.

Two properties of an adsorbent suggest themselves as probably determining the course of the isotherm; the surface area available or the number of active points capable of holding adsorbate molecules, and the affinity of the adsorbent for the adsorbate, measured by the heat of adsorption. This view was taken by Brunauer, Emmett and Teller (1938) in developing their theory of multimolecular adsorption. Although the originators of the theory were concerned principally with the adsorption of non-polar molecules, such as nitrogen, on such substances as ferric oxide or activated carbon, we shall attempt to apply their equations to water-vapour adsorption on proteins. In both cases the general shape of the adsorption isotherm is sigmoid, to account for which Brunauer, Emmett and Teller extended the Langmuir theory and postulated that the molecules of the adsorbate form a number of layers built up on the surface of adsorbent. They then deduced the following general equation:

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

x =vmCa/1 — a · 1 — (n+1) an + nan+1/1 + (C—1)a — Can+1 (1)

where

x = gm. adsorbate per 100 gm. adsorbent

a = relative pressure of adsorbate

= relative humidity, aw, in this case

vm = gm. adsorbate required to fill the first layer, i.e., to cover completely the surface of 100 gm. of the adsorbent

C = exp. E1/RT where E1 = excess of heat of adsorption of first layer over the latent heat of condensation.

n = maximum number of layers of adsorbate which can be built up

When there is no restriction on the number of layers, i.e., when n = ∞, equation (1) reduces to

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

x = VmCa/(1 — a) 1 + (C — 1) a}…(2)

which may be put in the form

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

a/x (1 — a) = 1/vmC + C — 1/VmC a…(3)

When n is 5 or greater, equation (1) also approximates closely to equation (2) and (3) if a has a small value. Consequently, a plot of a/x (1 — a) against a is a straight line from which vm and C may easily be found.

In the present work, the best straight line for each adsorbent was calculated from the experimental values of a and a/x (1–a) in the humidity range 0 05 to 0·40 by applying the method of least squares. Fig. 5 shows plots of this kind for several of the adsorbents.

By substituting the values obtained for vm and C in equation (1), we can find by trial a value of n which fits the experimental data in the higher humidity range. A graph of equation (1) with these values inserted should then fall on the experimental curve. Table XVII shows the B.E.T. constants calculated for all the adsorbents studied

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Fig. 5.—Plots of the B.E.T. Function. aw/x (1—aw) against aw. Standard Collagen ⊙, Formaldahyde Collagen □, Quinone Collagen X.

here. The constants for standard collagen were substituted in equation (1) to calculate values of × for varying aw with the results shown in Table XVIII and Fig. 6. It will be observed that the most general form of the B.E.T. equation can be made to fit the experimental points

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up to a humidity of 0·7 or more. At higher humidities the experimental curve is steeper than the calculated one, and it is generally supposed that in this region the adsorbate is suffering condensation in the capillaries of the adsorbent.

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Fig. 6.—Application of the Extended B.E.T. Equation to Collagen. Middle Curve: Experimental Upper Curve: Theoretical, n = 7. Lower Curve: Theoretical, n = 6.

Table XVII.—B.E.T. Constants for Water Vapour on Various Adsorbents.
Adsorbent. vm C n
Collagen
Oven-dried 9.4 6.3 6—7
P2O5-dried 10.0 9.5 6—7
Standard 10.1 14.3 6—7
Conditioned over water at 50° 10.1 21.0 6—7
Denatured 8.9 35.0 6—7
Denatured and oven-dried 8.2 6.6
Collagen derivatives
Formaldehyde 10.9 21.2 6—7
Quinone 8.7 22.6 6
Chrome I 9.2 64.0 6—7
Chrome II 9.5 44.5 6—7
Chrome III 10.3 22.7 5—6
Elastin standard 5.9 30.6 6—7
Oven-dried 5.4 4.1
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Table XVIII.—Isotherms Calculated for Standard Collagen from B.E.T. Equation.
gm. H2O per 100 gm. collagen.
aw n = 6 Observed. n = 7
0.1 6.89 6.88 6.89
0.2 9.87 9.85 9.87
0.3 12.36 12.50 12.39
0.4 15.00 15.14 15.13
0.5 17.97 18.10 18.35
0.6 21.24 21.59 22.16
0.7 24.76 25.69 26.47
0.8 28.28 30.88 31.01

If we consider the values of vm and C obtained for the various modifications of collagen, we see that vm is much less sensitive than C to pre-treatment of the collagen. In the B.E.T. interpretation, vm is proportional to the surface area of the collagen available to water molecules. It remains virtually unchanged for all pre-treatments at moderate temperature, but is diminished by oven-drying. Denatured or shrunk collagen has an even lower vm which becomes less still on oven-drying. Evidently heat treatment either in the oven or in water has the effect of inactivating some of the adsorbent groups of the protein so that there is a reduction in the number of points on the surface available for adsorption.

The constant C, whose logarithm is proportional to the heat of adsorption of the first layer, varies in a different way. Any dehydration of the collagen below about 4% water causes a decrease in C which is more marked with more severe dehydration. On the other hand, treatment with warm water, either above or below the shrinkage temperature, gives higher values of C. The heat of adsorption calculated from C for denatured collagen is approximately double that for the oven-dried material.

The number of adsorbent points in elastin is proportionately much less, since vm is less than 60% of the figure for collagen. Here also vm and C are reduced by oven-drying. For the standard elastin preparation, C is rather large, but this is not surprising when it is remembered that one feature of its preparation is repeated extraction with boiling water.

It will be noticed that for all the adsorbents studied, n, the number of B.E.T. layers, lies between 6 and 7 with the exception of the most basic chromed sample where it is certain that n is not less than 5. This coincidence may not be as striking as it at first appears. If we calculate isotherms for hypothetical values of vm, C, and n, we find that for the range of C shown in Table XVIII values of n less than 4 produce curves which lack that upward sweep typical of the adsorbents we are studying. In fact, the curve for n = 5 is the first to exhibit any appreciable increase of slope at higher humidities. For values of n greater than 7, on the other hand, the isotherms are closely packed so that the curve for n = 10 is almost indistinguishable from that for n = ∞. It follows, then, that almost any S-shaped isotherm can be fitted to a value of n between 5 and 8.

For a fuller understanding of the B.E.T. constants, we must study the mathematical derivation of the equations. We find, first of all, that the theory is developed from a postulate of layers of

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molecules superimposed one on another. That is, the layers are primarily layers of position and not merely different energy levels. The constant vm represents the amount of adsorbate required to fill up the first layer, or to cover the whole area of the adsorbent with one layer of adsorbate molecules. It would appear, then, that all molecules not included in vm must be adsorbed by adherence to molecules already adsorbed and not by direct attachment to the adsorbent itself. Consequently, if we are to use the B.E.T. theory at all, we must regard vm as representing the sum of all the points on the adsorbent capable of holding an adsorbate molecule even at high humidity. Any attempt, therefore, to interpret the B.E.T. constants in terms of the structure of the protein molecule must relate vm to the total number of polar groups, whether in the side-chains or in the polypeptide backbone, which can adsorb water.

In a recent paper, Pauling (1945) uses Bull's values of vm for a number of proteins and traces a connection between vm and the number of polar side-chains (arginine, glutamic acid, lysine, etc.) in the protein. He expresses the opinion that most of the carbonyl and imino groups of the polypeptide backbone are linked by hydrogen bonds and adsorb only weakly if at all. However, where the protein contains proline or hydroxyproline residues, tertiary nitrogen atoms, having no power to form hydrogen bonds with carbonyl groups, appear in the polypeptide chain. Pauling therefore assumes that a certain number of carbonyl groups, determined by the number of tertiary nitrogen atoms, are free to co-ordinate water, and he includes these in his calculation of the number of polar groups. In Table XIX we have applied Pauling's method to collagen and elastin, using the analyses quoted by McLaughlin and Theis (1945—2). It will be seen that the method gives good agreement for collagen, but none at all for elastin, which possesses singularly few polar side-chains. It seems, then, that we must credit the polypeptide backbone with more power to co-ordinate water molecules than Pauling would allot to it.

Table XIX.—Comparison of vm with number of Polar Groups (after Pauling).
vm moles, water Polar groups. Total reported amino-acids.
per 105 gm. moles./105 gm.
Collagen 561 567 103 4%
Elastin 328 168 94.4%

To account for the changes in the B.E.T. constants for collagen shown in Table XVII, we suggest that the first layer, denoted by vm is made up partly of molecules adsorbed on polar side-chains and partly of molecules adsorbed directly on the polypeptide chains. We further suggest that the latter molecules are the more firmly held, probably being linked to two neighbouring backbones by hydrogen bonds. It has been shown that dehydration of collagen to less than about 4% water diminishes its adsorptive power. This figure of 4 gm. water per 100 gm. collagen is very nearly equal to the difference between the observed value of vm and the quantity of water which would be adsorbed by the polar side-chains calculated on the basis of one molecule of water per polar group. That is, it corresponds to water in the first layer attached directly to the backbone. We may suppose that removal of each of these water molecules permits the

– 42 –

formation of one or even two hydrogen bonds between adjacent carbonyl and imino groups. Consequently, a P2O5-dried sample of collagen will contain more cross links than the standard preparation. When it is allowed to adsorb water again some of the original adsorbent sites will not be so easily available and a higher aw will be needed to fill them.

As a result, although vm will remain unchanged, the energy of adsorption, represented by C, will be less. Oven drying may be supposed to promote the formation of still more cross-links, some of which are broken only at very high humidities, while some appear to be permanent. Since measurements of vm are made below aw = 0·40 and since many of the cross-links formed during oven-drying are stable above that humidity, the value of vm will be diminished by this treatment. At the same time C will fall, since the sites with the highest energy of adsorption have been blocked. Our view that these changes in vm and C are associated with backbone adsorption is supported by the fact that decreases of the same magnitude were observed on oven-drying elastin, which has very few polar side-chains.

It is not easy to explain the reduction of vm when the collagen is denatured in hot water. It may be that when the polypeptide chains fold back on themselves during shrinkage some of the adsorptive points mutually saturate one another or are blocked by steric effects. It is interesting to note that oven drying the denatured collagen causes the same changes in the B.E.T. constants as we have already discussed for standard collagen and elastin.

We have said that C is related to E1, the heat of adsorption of the first layer. For collagen, sample E, we find

E1 = 1,800 cal. per mole and for standard elastin

E1 = 2,020 cal. per mole.

These values may be compared with the heat of adsorption L calculated from the data in Tables XV and XVI by means of the Clausius-Clapeyron equation

We may mention here that, as well as providing a means of evaluating vm and C, the simple B.E.T. equation (2) can be conveniently used as an interpolation formula for smoothing experimental data. The values of aw in Tables XV and XVI were smoothed by making use of the inverse form of equation (2).

It must be remembered that, whereas E1 represents the mean heat of adsorption of the first layer, L is the differential heat of adsorption, varying continuously over the whole range of humidity. Differential heats of adsorption may be calculated in two ways depending on whether aw or × is held constant. The most useful method is that used here where × is constant, yielding the isosteric heat of adsorption.

Babbitt (1942), in his discussion of adsorption on cellulose, points out that, before E1 and L can be compared, a correcting term must be applied to the latter. We must subtract from L the quantity

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RT log Po/P or —RT log aw

where

P = vapour pressure of adsorbate

Po = saturation vapour pressure.

This quantity is the free energy of expansion of a gas from saturation pressure to the pressure of the experiment, and when subtracted from L leaves, us with Q, the change in internal energy of the water vapour during the transition from the adsorbed to the free state. Tables XX and XXI show the results of these calculations for collagen, sample E, and elastin. The quantity —RT log aw is calculated from Tables IX and XIII for 25° since this is the mean of the experimental temperatures employed.

Table XX.—Isosteric Heat of Adsorption of Water Vapour on Collagen (Sample E).
E1 = 1800 cal./mole.
x a30/a20 L —RT log aw Q=L+RT log aw
8 1.152 2500 600 1900
9 1.138 2280 510 1770
10 1.122 2030 440 1590
11 1.104 1740 390 1350
12 1.088 1490 350 1140
13 1.074 1260 310 950
14 1.063 1080 280 800
15 1.054 930 250 680
16 1.047 810 230 580
Table XXI.—Isosteric Heat of Adsorption of Water Vapour on Elastin.
E1 = 2020 cal./mole.
x a30/a20 L —RT log aw Q=L+RT log aw
5 1.263 4120 640 3480
6 1.156 2560 470 2090
7 1.082 1390 360 1030
8 1.045 780 290 490
9 1.027 470 240 230

The tables show that the heat of adsorption diminishes as × increases, which was to be expected, as the more active adsorbent sites would be the first filled. The two energies of adsorption agree closely enough to provide qualitative support of the B.E.T. theory.

Returning to the mathematical derivation of the B.E.T. equations, we find that the second and higher molecular layers begin to fill up well before the first layer is completed. Moreover, a simplifying assumption is made that the energy of adsorption of these higher layers is equal to the latent heat of vaporisation of water, or in other words that E2 = E3 = … = O. If this assumption is true, the higher layers can make no contribution to Q. Each value of Q found here represents the heat of adsorption of 1 mole of water distributed over several layers. For collagen at × = 9, say, the first layer is more than half full and an appreciable amount of adsorbate is in the second layer. Consequently, we should expect Q at this point to be considerably less than E1, the mean heat of adsorption of the first layer. However, the table shows that at this point Q is equal to E1. It would appear from this, then, that the heats of adsorption of the second and probably higher layers are in reality greater than the latent heat of vaporisation of water.

– 44 –

Modification of the B.E.T. theory to provide for different values of E for the several layers causes the mathematics to become very cumbersome, but it seems possible that such a treatment might produce an equation which would satisfy the experimental conditions for a lower and physically more significant value of n.

Turning to the collagen derivatives, we find that the high value of vm for formaldehyde-tanned collagen can be explained by the same hypothesis that we used above to account for the changes with dehydration. According to McLaughlin and Theis (1945—3), it is generally accepted that when formaldehyde reacts with collagen some of the molecules combine with the terminal amino groups of the lysine side chains, while others form covalent bridges by condensation with two imino groups in adjacent polypeptide chains.

This latter reaction probably accounts for the high thermal stability imparted by formaldehyde tanning. Now, in native collagen the imino groups which have reacted with formaldehyde were probably linked to neighbouring carbonyl groups by co-ordinate hydrogen bonds which would have to be broken before water molecules could be adsorbed. After formaldehyde tanning the carbonyl groups are no longer co-ordinated and are in a favourable position to donate a pair of electrons to the hydrogen of a water molecule. In other words, formaldehyde tanning has made available more active points for water adsorption to the extent, in the most favourable case, of two water molecules to every formaldehyde molecule combined. The preparation investigated here contained 0·063 moles formaldehyde per 100 gm. collagen and the increase in vm noted corresponded to 0·044 moles water per 100 gm. collagen. Remembering the complexity of the system and the fact that not all the formaldehyde is combined with imino groups, we consider that these figures give further qualitative support to our interpretation of the meaning of vm.

In contrast to this small change in vm for water adsorption caused by formaldehyde tanning, it is interesting to note the results of Zettlemoyer, Schweitzer, and Walker (1946) for nitrogen adsorption on collagen. Working at the temperature of liquid nitrogen they found that formaldehyde tanning caused vm for nitrogen adsorption to be reduced to one-sixth of its original value. Moreover, they found vm even for collagen to be only about one-tenth of the values recorded here. It is clear that this adsorption must have an entirely different mechanism from that involving water molecules.

The other tanned collagens are more complex and their structure is less fully understood. We may point out, however, that the ratio of vm for the quinone derivative to vm for standard collagen is equal to the proportion of collagen in the former.

The adsorption for chrome-tanned collagen is the resultant of two different effects—adsorption on collagen and hydration of the

– 45 –

chromium co-ordination complex—and it is impossible in the present state of our knowledge to differentiate between them or to say how they react on each other. The author (1945) has already pointed out that the water content of some basic sulphates of chromium is a continuous function of the humidity which diminishes with increasing basicity. We notice that increase in basicity of the chromium complex in tanned collagen causes vm to increase and C to decrease. That is, more water is held in the first layer, but held less strongly. How this water is distributed between collagen and chromium is a subject for further investigation.

No satisfactory theory is available to interpret all the facts of adsorption hysteresis. For example, the wide difference in hysteresis on standard and denatured collagen is difficult to explain in terms of what is known about their molecular structure. Barkas (1942), from thermodynamic considerations of swelling and adsorption, formed the opinion that one cause of hysteresis can arise from the presence of shear stresses which originate from swelling of a nonisotropic adsorbent. This mechanical effect may account for some of the figures shown in Table XIV. When collagen is heat denatured it obviously becomes more compact, and it seems reasonable that this change should be accompanied by greater resistance to swelling and hence greater stresses when swelling does occur. The same argument may be applied to the tanned materials, which gain rigidity from the molecular cross-links introduced by the tanning agent. The greater the rigidity, the greater will be the shear stresses during swelling, and, according to Barkas, the greater the hysteresis.

Conclusion.

The isopiestic method affords a rapid means of measuring adsorption isotherms of water vapour on fibrous materials. It has been used to study adsorption on collagen and elastin and on collagen tanned with formaldehyde, quinone, and a basic chromic sulphate.

Equilibrium is attained much more rapidly by adsorption than by desorption, and the isotherm exhibits hysteresis. The hysteresis effect is greatest in the tanned samples.

The affinity of the adsorbent for water vapour is diminished by preliminary dehydration even at room temperature. Oven-drying has an even stronger influence. Exposure of the dehydrated samples to saturated water vapour restores them to the original condition, except in the case of the oven-dried material, where part of the change is irreversible.

Oven-drying liberates more water from the samples than does dehydration at the temperature of the adsorption experiment, and the latter method was adopted in this work.

Analysis of the experimental data by means of the equations of Brunauer, Emmett and Teller shows that both the surface area of the adsorbent and the energy of adsorption are influenced by the previous history of the sample.

Heats of adsorption calculated from the B.E.T. and the Clausius-Clapeyron equations, when reduced to a common basis, are of the same order of magnitude.

– 46 –

A connection is traced between the quantity vm and the structure of the adsorbent molecule. It is suggested that first-layer adsorption occurs partly on the ends of the polar side-chains and partly on carbonyl groups in the polypeptide molecular backbone. Water molecules attached directly to the backbone appear to be the most firmly held.

A possible explanation of the different hysteresis effects may be the varying degrees of mechanical rigidity of the adsorbents.

Acknowledgment.

The author wishes to express his indebtedness to Professor R. A. Robinson for his practical interest and encouragement, and to the Chemical Society for a grant from their Research Fund.

References.

Babbitt, J. D., 1942. Can. J. Research, 20A, 143.

Barkas, W. W., 1942. Trans. Faraday Soc., 38, 194.

Bowes, J. H., and Pleass, W. B., 1939. J. Intern. Soc. Leather Trades Chem., 23, 365.

Brunauer, S., Emmett, P. H., and Teller, E., 1938. J. Amer. Chem. Soc., 60, 309.

Bull, H. B., 1944, Ibid., 66, 1499.

Green, R. W., 1945, J. Amer. Leather. Chem. Assoc., 40, 378.

McLaughlin, G. D., and Theis, E. R., 1945. The Chemistry of Leather Manufacture, Reinhold Publishing Corp., New York, (1), p. 43; (2), p. 32; (3), p. 386.

Pauling, L., 1945. J. Amer. Chem. Soc., 67, 555.

Riess, C., and Papayannis, A, 1934. Collegium, 769, 226.

Robinson, R. A., and Sinclair, D. A., 1934. J. Amer. Chem. Soc., 56, 1830.

Shankman, S., and Gordon, A. R., 1939, Ibid., 61, 2370.

Speakman, J. B., and Stott, E., 1936. J. Textile Inst., 27, 186T.

Veitch, F. P., Frey, R. W., and Leinbach, L. R., 1922. J. Amer. Leather Chem. Assoc., 17, 492.

Weidinger, A., 1940. Collegium, 837, 1.

Wilson, J. A., and Gallun, A. F., 1924. Ind. Eng. Chem., 16, 268.

Wilson, J. A., and Kern, E. J., 1926. J. Amer. Leather Chem. Assoc., 21, 351.

Zettlemoyer, A. C., Schweitzer, E. D., and Walker, W. C., 1946. Ibid, 41, 253.