PROCEEDINGS
`
`OF THE
`
`ROYAL SOCIETY OF LONDON
`
`SERIES A. MATHEMATICAL AND PHYSICAL SCIENCES
`
`VOL 214.
`
`LONDON
`
`Published for the Royal Society by the
`Cambridge University Press
`Bentley House, N.W. I
`
`9 October 1952
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`Analysis of the swimming of long and narrow animals
`
`183
`
`, -13}1a.nks are due to Professor James Gray for permitting the publication of
`S 5, 7 and 12, which have not previously been published, and of figure 11,
`h is taken from a paper to which reference is made in the text. I am also grateful
`. for suggestions made in the course of the work.
`
`REFERENCES
`
`"us H. 1908 Z. f. Math. Phys. 56, 285.
`q, J. 1905 J. Math. Puree eppl. 285.
`dflfiejn, S. 1938 Modem developments in fluid dymzmics, p. 425. Oxford: Clarendon Press.
`’ J, 19390. Proo. Roy. Soc. B, 128, 28.
`J_ 1939!) J. Earp. Biol. 16, 9.
`',. J_ 1946 J. Exp. Biol. 23, 101.
`3’ J, 1949 J. Exp. Biol. 26, 354.
`'5 L, V. 1914. Phil. Trans. A, 214, 373.
`ad, A. R. 1918 Rep. Menwr. Aero. Res. O'omm., Lanai, no. 554.
`]§}_ F. 3; Powell, 0. H. 1917 Rep. Menwr. Acre. Res. 0omm., Lond., no. 307.
`; W. B. 1948 J. Ac-ro. Sci. 15, 49.
`01-, Sir Geoffrey 1952 Proc. Roy. Soc. A, 211, 225.
`m, A. 1928 Rep. Mano:-. Acre. Res. C'omm., Lentil, nos. 1176 and 1194.
`ijtika, S. &. Aoi, T. 1951 Quart. J. Meek. App}. Math. 4, 401.
`' J'.'M. 1949 J. Aero. Sci. 16, 41.
`
`'
`
`I The effect of the temperature of preparation on the
`mechanical properties and structure of gelatin films
`
`BY E. Bsennunv AND C. MARTIN
`The British Cotton Industry Research Association, Shirley Institute,
`Didsbury, Manchester
`
`‘(Communicated by so Eric Rideai, ER..6’.——Receieed 24 October 1951*
`Read 28 _Febmce'y 1952—Reoised 16 April 1952)
`
`[Plate 4]
`
`recedes the formation of a continuous structure, and X—ray and other evidence indicates
`that the molecular chains are in a disordered contracted state not far rernoved from their
`flomiition in the sol. The high—temperature film is characterized by low strength and high
`ooverable extension under conditions of high relative humidity. In the low-temperature
`Preparation the greater degree of crystallization has partially extended the molecular chains,
`(1 the unidirectional contraction of the film on drying has oriented them in the plane of the
`- This filrn exhibits thermal contraction in hot methanol, and is stronger, but at high
`'dity is much less extensible, than the high-temperature preparation.
`
`the adhesives used for sizing rayon textile yarns, gelatin is the most common,
`Probably more is known about its sizing and weaving behaviour than about
`.-Of other adhesives. It is thus a reasonable sta.rting—point in a long-range
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`134.
`
`E. Bradbury and C. ‘Martin
`
`fundamental study, the ultimate aim of which is to relate the physical proper
`of the size film to sizing and weaving behaviour. Although the literature abg '-
`With accounts of work on gelatin in sol11tion and in the gel state, there are fa "
`accounts of work on gelatin films, and none has been found dealing specified‘
`with the eifects of the temperature of preparation on the mechanical propertiaa I
`the films.
`'
`‘
`7‘
`For the experiments described below, a commercial acid-processed skin ge]
`was used. Its isoelectrie point was at pH 6-5, and a 5 ‘7, solution had a 131.16:
`4-2. Films about 0-1 mm thick were prepared by evaporation of water from 5 0
`solutions contained in shallow metal trays, and the conditions in which th-
`evaporation took place were varied as described later. Test-pieces of appmximg
`dimensions 5 cm >2. 6 mm were then cut, and conditioned in atmospheres of cod
`trolled humidity and temperature before being submitted to tensile tests. F01-3119
`tensile tests a rate of loading of about 25 Kg/cmzs was used. At least ten specimmj,
`were tested from each sample, and the load—extension curves, tensile strength am
`extension figures given later are means of these.
`-
`
`
`
`JFFECT ON THE TENSILE PROPERTIES 0]!‘ THE TEMPERATURE OF PREPARATION H"
`AND OF THE HUMIDITY DURING TESTING
`
`Films were prepared by drying in atmospheres diflering in temperature 1;‘
`having the same relative humidity as follows:
`(ca) 20° C, 70 0/0 r.h.
`._
`((9) 60° C, 70 3/0 r.h.
`The film (ca) too}; about four days to become sufficiently dry for removal fro"
`the tray, whereas the film (.-5) reached this condition in about six hours.
`In
`early stages of the drying of (6) the temperature in the drying film fell to 56°
`owing to the rapid rate of evaporation. Thus a range of temperatures (56 to 60”
`was covered during the drying, and this also applies, but over a wider range, 2
`films dried at still h.igher temperatures described later.
`
`
`
`TABLE 1. FILM PREPARATION TEMPERATURE AND THE AMBIENT HUMIDITY '-
`DURING TESTING-J EFFECT ON TENSILE PROPERTIES
`
`film
`preparation
`teInpe1'a.ture
`(° C)
`20
`56 to 60
`20
`56 to 60
`20
`55 to 60
`20
`56 to 60
`20
`56 to 60
`
`i
`
`testing
`1-.h. (0/0)
`45
`45
`55
`55
`65
`35
`75
`75
`85
`85
`
`'
`
`tcnpgile strength
`,_.i...§.iEfl1..}_.._
`mean
`s.d.
`910
`48
`854
`31
`832
`52
`585
`3-3
`646
`59
`350
`22
`418
`29
`172
`36
`1'70
`38
`81
`11
`
`[s.d. = standard deviation.)
`
`BX‘lJBI'lSl.0I;. at break
`../9 __..
`s.d.
`0-2
`[}*1
`0-3
`0-1
`0-7
`0-2
`1'7
`5-5
`3'3
`20
`
`mean
`1-9
`1'1
`2-2
`1-5
`3-7
`1-7
`10-2
`46-1
`238
`129
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`Mechaniwl properties and structure of‘ gelatin films
`
`185
`
`-11 types of film were conditioned and ‘subsequently tested under dflferent
`"
`conditions covering a range from 45 to 85 % r.h. The mean figures for
`fin;-ength and percentage extension at break are given in table 1, and the
`xfiension curves in figures 1 and_ 2.
`
`'
`
`_ 1200
`
`900
`
`600
`
`300
`
`
`
`load(K.g}sq.eIn)
`
`
`0
`1-0
`2-0
`3-0
`4-0
`
`'
`
`extension {%)
`
`_ Goa: l. Load-extension curves at relative htirnidities of 45 to 65 %, indicated
`' on the curves. 0, Film. (:5) dried at 20° C; -, film (D) dried at 56 to 60° C.
`
`
`
`75
`
`75
`
`.---"""".--D
`.,o""""'§E
`
`'
`
`.
`
`_
`.__________.._n_._.—-—-—--""""-"'-_—-.
`20
`40
`60
`
` .___a35
`
`30
`
`100
`
`I20
`
`140
`
`extension %
`
`"FIGURE 2. Load-extension curves at relative humidities of 75 and 85 %.
`'
`Oendoasonfigure 1.
`-
`
`seen flom the table that increasing the drying temperature from 20° C to
`0° 0 -had a. profound eifeet on the tensile properties. At all humidities the
`perature preparation (ca) was much stronger than the preparation (b), and
`
`
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`186 '
`
`E. Bradbury and C. Martin
`
`up to 65 9/0 r.h. had also a greater extension at break. At 75 and 85 ‘yo r_h_
`extension of the film (b) was much greater than that of the film (ti).
`Up to 65 %T.h. (figure 1) the load-extension curves show no obvious yi ‘
`point, and the extension at break was Very low for both types of film.
`At '75 and 85 % r.h. (figure 2) the curves show an apparent yield point, be
`which the extension per unit load is greater than in the initial part of the g
`This extension is of a different order of magnitude from that obtained up __
`65 % r.h., and increases rapidly with increasing humidity. An important paint"?
`that, even when the film (b) had been extended to 130 % of its length, it rel;
`in time to within a small percentage of its original length on removal of the 10
`It is evident that, with the fairly high rate of loading used, there was little plug
`'
`flow during the extension of the film.
`The magnitude of the effect of humidity on the tensile properties is of ggnf
`significance and deserves comment. The greater effect was shown by the '
`E‘
`temperature preparation. For an increase in relative humidity from 45 to 85$;
`it suffered a fall in strength to approximately one-eighth of its initial value, W;
`the extension at break was increased a hundred—fold.
`'
`
`EFFECTS ON THE '1‘ENS.TLE PROPERTIES OF THE RATE AND DEGREE OF DRYINQ
`In the previous experiment the results show that films (a)_ and (b) djjf'
`considerably in mechanical properties. The cause was assumed to be the diff:
`in preparation temperature, although related diflerences occurred in two ct
`factors. These were the rate of drying, and the moisture content of the film w_'
`equilibrium was attained with the moist atmosphere, which may be called
`degree of drying. The possible independent contributions of these factors ‘tot
`diflerence in mechanical properties could not be ignored. The experimen
`
`
`
`TABLE 2. THE RATE or DRYING or THE rrciu, an-n THE AMBIENT HUMIDITY
`nunmc nnrme: EFFECT on rnusitn PROPERTIES AT 65 '37, B..H’..
`
`-
`
`faclior
`_
`investigated
`rate of drying
`
`ambient
`humidity of '
`preparation
`
`ambient conditions
`during film prep.
`temp. (°C} %r.li.
`‘___.__-._.....__‘
`20
`70
`20
`4-0
`60
`70
`60
`'70
`20
`70
`20
`--40
`60
`70
`60
`2e
`
`'
`
`-
`
`-
`
`,
`*‘*PP"°"_““‘““’
`d‘ry_mg
`period
`4- days
`6 ll
`24 h
`6 h
`—
`—
`—
`—
`
`tensile strength
`{Kg,u"sq.ern}
`mean
`sd.
`r__.._‘
`647
`59
`G42
`42
`348
`23
`350
`22
`647
`59
`650
`35
`350
`22
`352
`19
`
`extension
`at break {%)
`mean
`ad.
`,___»_,
`3'7
`0'7
`3'6
`0'4
`2-0
`0-3
`1-’?
`0'2
`3-7
`0-1’
`3-9
`0'5
`1-7
`0-2
`2-1
`0-3
`
`-
`
`described below were carried out to provide a rough estimate of the magnitude
`the effects of these complicating factors.
`In each experiment the films =
`preparation were conditioned and tested at 65 % r.h.
`The effect of rate of drying was investigated at both temperature levels (20 -'
`60° C) by varying either the degree of ventilation or the atmospheric humi
`
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`
`Mechanical properties and structure of gelatin films
`
`18_7
`
`drying or both. The results are given in table 2 and show that the differences
`by djlferences in the rate of drying are-insignificant in magnitude compared
`-etgmperature effect.
`effect of degree of drying was investigated by varying the atmospheric
`W during drying. As in the foregoing experiment, it was impossible com~
`to isolate" the effect of the rate, from that of the degree, of drying, since
`1- humidity results both in more rapid drying of the film and in film of
`final moisture content. However, the results in table 2 again indicate
`insignificant by comparison with the temperature effect.
`concluded therefore that, over the range of conditions investigated, neither
`be nor the degree of drying has more than a small effect on the tensile
`'es of the film.
`
`FURTHER EXPERHEIENTS ON FILM I’H.EI’AItA'1‘ION TEl\‘IPERA'1'U'.B.E
`
`.- jments were carried out to find the effect on’ the tensile properties of
`ation temperatures higher than the range 56 to 60° 0 previously used. The
`were prepared by drying over an electric hot-plate in the uncontrolled
`phere of the laboratory. The ranges of temperature in the drying films were
`'-'90 and 80 to 100° C respectively. If the tray was left on the hot plate for
`" r the film had obviously formed, the film cracked into small pieces. For
`an the tray was removed from the hot—plate as soon as the film had
`,'but before all the water was driven off, and since this was a matter of
`113.1 judgement, the film preparation conditions were to this extent not
`defined.
`:-films were conditioned and the tensile properties determined at 65 % r.h.
`' ults are given in table 3, together with those obtained earlier from the
`56 to 60° C preparations.
`
`TABLE 3; EFFECT or PREPARATION TEMPERATURE oN_'rENs1Ln
`
`PROPERTIES (rmms ‘TESTED AT 65 % 11.11.)
`tensile strength
`extension at
`(Kg,isq.cm)
`break (%)
`,_m_A__.—.-_.., mm‘
`mean
`s.d.
`mean
`sd.
`647
`59
`3-7
`0-‘?
`350
`22
`1-7
`0-2
`312
`33
`1-8
`0-2 '
`314
`18
`1-8
`0-2
`
`_
`.
`I preparation
`rature {"0}
`
`.
`
`-_56 to 60
`'
`to 90
`0 to 100
`
`-\(lJ'fl"ered only slightly from those of the film prepared at 56 to 60° C. It seems
`onclude, therefore, that two types of film can be produced by varying
`; temperature. For ease of reference these two types have been called
`d’ and the ‘hot’. The transition region occurs somewhere between the
`Matures of 20 and 60° C; at temperatures below this the strong ‘cold’ film
`'1l106d, and at temperatures above, the weaker ‘hot’ film. Further work
`_ out to elucidate the phenomenon is described later in the paper.
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`I88
`
`'
`
`E. Bradbury and 0. Martin
`
`THE REV]'JRSIBI[.rI'I‘Y OF THE DRYING TEMPERATURE EFFECT
`
`The fact that an increase in the preparation temperature beyond 60° 0 pmdlul
`little change in film properties would seem to rule out chemical degradation
`gelatin at the higher temperatures as a possible cause of the difference in"
`perties of the ‘hot’ and ‘cold " films. It was, nevertheless, of interest to'di_=mD
`Whether the gelatin had suffered any permanent change in its film-forming
`perties during the preparation of the film at the higher temperature. To ljhjg
`films of the ‘hot ’ type were dissolved in water-and films re—made from the sole
`at 20° C. All films -were conditioned and tested at 65 % r.h. The re-made films
`the same properties as films of the ‘cold’ type prepared at 20° 0 (table
`demonstrating that there was no permanent degradation of the gelatin d
`the preparation of the ‘hot’ film. This suggests that the difference between
`two films is one of structure.
`'
`
`TABLE 4. THE REVERSIBILPTY or THE DRYING TEMPERATURE nrrscr
`
`(mmrs TESTED AT 65 “/0 ZB..H.)
`
`tensile strength
`(Kg,I'sq.cm)
`r—'*'—’mw
`
`extension at
`break (0/0)
`r-m"‘-—--—.,
`
`
`
`film preparation
`_
`film prepared at 56 to 60° C
`fihn prepared at 56 to 60° 0, dissolved
`and re-made at 20° 0
`
`film prepared at 65 to 90° 0, dissolved
`and re-made at 20° C
`
`film prepared at 20° C
`
`mean
`350
`631
`
`669
`
`647
`
`s.d.
`22
`42
`
`37
`
`59
`
`mean
`1-7
`4-2
`
`3-7
`_
`
`3-7
`
`X-BAY EXAMINATION or THE ‘HOT’ AND ‘GOLD ’ FLLMS
`
`ad
`0.2
`0-5
`
`0-3
`
`0-
`
`X—ray diifraction photographs using filtered GL1 Kat. radiation were taken iii
`the gelatin film arranged vertically and the X—ray beam directed either par__
`to, or perpendicular to, the plane of the film. The two photographs of the ‘co
`film are reproduced as figures 3 and 4, plate 4. The photograph of the ‘li
`film with the beam parallel to the film surface is reproduced in figure 6;_
`corresponding photograph with the beam perpendicular to the film surface '5
`identical in appearance and is not shown.
`I
`'
`The original photographs show some features that are not easily seen in".
`reproductions. They all show the three spacings (labelled R1, R2, R3 in
`of about 2-85, 4-5 and 11 A that are characteristic of previously published phO._.
`graphs of gelatin and collagen (e.g. Hermann, Gerngross 8:’. Abitz 1930;
`'_
`85 Derksen 1932; Astbury 194.0). Thus the same kind of crystalline structure
`present in the ‘cold’ and ‘hot’ films. However, in the ‘hot’ films the main c_
`spacing of 2-851$ is much weaker, and the side spacing of about 11 A both was
`and more diffuse, than in the ‘cold’ film, indicating that the crystallites
`smaller in the former than in the latter. The ‘cold’ film with the X-ray ha:
`
`* Some additional rings are due to wator—so1uble inorganic impurities.
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`
`
`
`
`
`
`
`
`3
`
`4
`
`5
`
`
`
`
`
`‘Cold.’ film: liemn parallel to film.
`FIGURE 3.
`‘Cold’ film: beam perpendic11.lar to film.
`EEGUBE 4.
`FIGURE 5. ‘Hot’ film: beam parallel to film.
`
`
`
`(Pacino 13. 133)
`
`
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`Mechanical gmcperties and structure of gelatin films
`
`189
`
`31 to the film surfacelfigure 3) shows evidence of orientation, while that of
`.
`' hot’ film does not. This evidence is most marked in the side spacing R3. There
`1,0 5V‘id.Bl.'lC-B of orientation in the photographs of either type of film with the
`e
`]'_'p6I1Cl.'lGl.l.la:I' to the surface.
`examination thus confirms the suspicion that the films differ in structure,
`I is consistent with the following picture. In the ‘cold’ film the chain molecules
`"associated into crystallites, which are large by comparison with those in the
`1.’; mm, and are randomly arranged with their long axes roughly parallel with
`gfijm surface.
`In the ‘hot’ film the crystallites are much smaller and are
`-gomly arranged in three dimensions.
`
`THERMAL conrnaorron
`
`
`
`The molecular chains in the gelatin crystallite are generally considered to be in
`extended state as they are in the collagen crystallite. By analogy with
`agen it would therefore be expected that an oriented gelatin film would exhibit
`phenomenon of thermal contraction, provided means could be found of freeing
`1;" molecules sufficiently to allow them to collapse to the contracted state,
`thout complete solution taking place. It was found that immersion of the film
`La. short time in boiling methanol produced the desired result. The ‘cold’ film
`ntracted both in length and width to about two-thirds of the original dimension
`’ "increased in thickness. The ‘hot’ film did not change its dimensions under the
`the treatment.
`If the boiling methanol treatment was prolonged, both films
`to elongate slowly under the influence of their own weight, but with the
`1d’ film this only took place after the initial contraction. X-ray photographs
`the thermally contracted ‘cold’ film, with the X-ray beam either parallel or
`endicular to the film surface, were almost identical with that of the ‘hot’
`
`" (figure 5, plate 4).
`The occurrence and nature of the thermal contraction in the ‘cold’ film, and
`3' bsence in the ‘hot’, are consistent with the structural pictures deduced from
`X~ra.y results.
`
`DISCUSSION
`
`Our conclusions that the two types of film dit't'er in degree of crystallinity is in
`essential agreement with the earlier work of Katz and his collaborators (Katz,
`_'k'sen & Bon 1931; Katz 65 Derksen 1932), who reported that the ‘cold’ film
`vs a crystalline X—ray diagram while the ‘hot’ film gave an amorphous one.
`I
`in accord with this conclusion was the observation of Pinoir & Pouradier
`9.48) that thin ‘hot’ films were soluble in water at room temperature.
`In
`trast to Katz’s findings, however, the hot films prepared by us show some
`Virience of crystallinity and, as will be seen from the later argument, this may
`fa consequence of the fact that none of our films were evaporated to complete
`' ass before cooling.
`From our own thermal contraction evidence on gelatin, and also from a com
`deration of the thermal contraction of collagen, it follows that the molecules in
`9 gelatin sol are in the contracted state. Moreover, the magnitude of the
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`190
`
`E. Bradbury and C. Martin
`
`
`
`contraction in the more crystalline and more oriented collagen strum,
`namely, to less than one—quarter of the original length (Astbury 194.0), indica
`a considerable change in length of the molecule from its extended condi .
`in the crystallite. Robinson 8:: Bott (1951) have suggested that the free 33],,
`polypeptide chains in the sol are folded in the intramolecular bonded 9,.
`figuration, Whilst those in the crystal lite are in the ‘collagen fold’ of A1115,
`85 Elliott (I951). Whether or not this is so in fact, the difference in length oft
`polypeptide chain in the two types of fold is not able to account- for the thenm
`contraction of collagen, and the explanation must lie elsewhere. According
`current views, the gelatin molecule i11 very dilute solution is coiled or foldai
`such a way that its overall shape is very much elongated in one direction. Abri},
`Pouradier 8:. Venet (1949) have deduced from intrinsic viscosity measurema
`that the state of contraction is influenced by the charges on the acidic and b
`groups in the side chains, and is greatest at the isoelectric point. It seems proha E,
`that, in highly concentrated sols, some departure from the accepted shape in dim;
`solution will occur, owing to interference from neighbouring molecules, and itig
`assumed that some degree of irregular or random crumpling of the molecuté
`takes place.
`"
`In the preparation of the ‘hot’ film the gelatin solution remains fluid untfll
`becomes highly concentrated, and .under our conditions of incomplete drying iii,
`probable that the final film structure is formed only on cooling. Thus it seems that
`the formation of a continuous structure is delayed until the contracted molecule;
`are in a disordered, entangled and closely packed condition, and the low degrees
`crystallinity is probably a consequence of this. According to the theory originally
`advanced by Hermann & Gerngross (1932), a single molecule can become bonded
`to a number of different molecules at intervals along its length. If the molecules
`are in a closely packed condition at the time that intermolecular bonding takm
`place (as in the ‘hot ’ film), there should be many positions along the length of an
`one molecule at which bonding occurs. In these circumstances, the further growt
`in size of these bonded regions should be very limited; the system should quickl
`reach the state of lowest potential energy and the molecules become locked in
`a more or less randomly contracted state.
`In the ‘cold’ film, the continuous structure is formed when the original 5 ‘7
`solution forms a gel, i.e. in circumstances in which the‘ molecules are much more
`widely separated that at the corresponding stage in the ‘hot’ film.
`In furthe
`contrast to the conditions for the ‘hot’ film, the development of the structure 0
`the ‘cold’ film can be regarded as a two—stage process. The first stage is the formatic
`of the gel, i.e. the initial structure, and the second is the modification of this
`caused by contraction on drying. The development of the continuous structure '
`the hot film is in this sense a one-stage process; there is no appreciable contraeti
`after the film is formed.
`In the preparation of the ‘cold’ film the initial gel would be expected to consis
`of a random continuous network of molecules bonded at relatively i.n.‘Ereqll6'flt
`intervals to other molecules by regions of bonding that are longer than these '
`the ‘hot’ film. When the gel dries during film preparation, it suffers a twenty—f01 _:
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`DL 214- A.
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`1 3
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`Mechanical j99°opcmIes and structme of gelatin fihns
`191
`motion in a direction perpendicular to the supporting base, and this uni-
`‘ -lonal contraction accounts for the orientation found hi the final film. The
`‘d re ‘one should tend to Inaintain their identity during this collapse and to
`3 01-ie1_1ted in the plane of the film. They may, of course, grow in length and
`te more molecules as the network becomes condensed. The
`"e-1y to incorpora
`olecular chain connecting the original unbonded regions
`3 forced into new confi.gurations by the collapse, and might be expected to
`new but smaller bonded regions with other free parts of molecules with which
`
`G01-dlng to this reasoning the bonded regions in a molecule in the ‘cold’ film
`(}{)nSldBI"él.-bly in length, and the longer ones (formed in the initial gel) tend to
`he plane of the film. The bonded regions in the molecule in the ‘hot’ film
`hort, more uniform in size than those in the ‘cold’ film, and randomly
`in three dimensions. In the ‘hot’ film the molecule as a whole is not
`dition in the concentrated so]; in the cold
`
`ego suggested structural pictures account in a qualitative manner for the
`anical properties of the two types of film as is shown below.
`ia ‘cold’ film is stronger than the ‘hot ’, and it would be expected to be so both
`f the greater degree of orientation of the
`
`an adequately cross-bonded network of molecules, and
`h films consist of
`i.e. under conditions
`Eaccounts for their low extension at the lower humidities,
`ch the great majority of the bonded regions are strong enough to avoid
`‘plate failure before the film breaks at some weak spot or position of abnormal
`
`tthe higher humidities, when the intermolecular bonds have been sufficiently
`sued by the absorbed water, a low tension is sufficient to rupture a large
`her of the bonded regions, the load-extension curves show a yield point,
`id which the partially freed molecules can be pulled out to their extended
`ntractcd molecules in the ‘hot’ film are able to
`-a much greater extension than the already partially extended and oriented
`ules in the ‘cold’ film.
`‘-8 suddenness of the change in extension properties of the ‘hot’ film between
`id 75 ‘V0 r.h. suggests the almost simultaneous failure of a large number of
`ended regions at a particular level of moisture regain in the film, and is
`tent with the suggested tendency to unformity in size of the bonded regions.
`change in extension of the ‘cold’ film with increasing humidity is more
`11&1. The sudden change in the hot film occurs in the neighbourhood of 20 %
`_, and this is of interest, since this level of moisture regain is considered by
`"investigators (Braybrooks, McCandlish db Atkin 1939; Bull 1944) to mark the
`letion of a stage in the absorption of water by the polypeptide chains. At
`15051113 the chains can be said to be saturated in the sense that all the sites
`1l_a»ble for the binding of water molecules have been occupied.
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`.192
`
`E. Bradbury and C. Martin
`
`I+‘ina.lly, it should be pointed out that all the experiments described in thja
`have been carried out with a particular grade of gelatin which was neither «
`nor of high quality. It is nevertheless considered that the results obtained an
`deductions made are of such a nature as would apply, though possibly to 3, ,,
`or less degree, to other grades of gelatin.
`'
`
`The authors are indebted to the Director ofthe British Cotton Industry R_ _
`Association for permission to publish this account, and to Dr J. O. Warwic];
`taking the X-ray diffraction photographs and for help in their interpretati
`
`REFERENCES
`
`Abribat, M., Pouradier, J. & Vcnot, A. M. 194.9 J. Poiymsr Sci. 4-, 523.
`Ambrose, E. J‘. 85 Elliott, A. 1951 Proc. Roy. Soc. A, 205, 47.
`Astbury, W. T. 194.0 J. Int. Soc. Leather. Chem. 24, 69.
`Braybrooks, W. E., McCendIish, D. 3.: Atkin, W. It. 1939 J. Int. Soc. Leather. 053%
`111.
`
`'
`
`Bull, H. B. 1944 J. Amer. Chem. Soc. 66, 1499.
`Hermann, K. «St Gerngross, 0.
`I932. Kautschuk, 8, 181.
`Hermann, K., Gerngross, O. & Abitz, W. 1930 Z. Phys. Chem. B 10, 371.
`Katz, J. R. &. Derksen, J. C. 1932 Rec. Tme claim. Pays-Bus, 51, 513.
`Katz, J. R., Derkson, J. C. & Bon, W. F. 1931 Bee. Tran. chi-m. Pays-Baa, 50, 725.
`Pinoir, R. &. Pouradior, J. 1948 0.12. Acad. Sci., Paris, 227, 190.
`Robinson, C.
`35 Bott, M. J. 1951 Nature, Lomi, 168, 325.
`
`
`
`The theory of regular solutions
`
`Br J. S. ROWLINSON
`
`Department of Chemistry, University of llfaackester
`
`(Communicated by M. G. Evans, 1F.R.S.—Receised 12 February 1952-_
`Revised 23 May 1952)
`
`The usual theory of regular solutions, which is based on the assumption that all molecules
`are on the sites of a. lattice, is modified. Each molecule is supposed to move near its site
`in a potential cleterminedby the field of its nearest neighbours. The number of neighbours c
`each component is fixed by the quasi-chemical approximation. Four zuuodifications are
`considered, which differ only in the way in which the freedrolume of any molecule is sup-
`posed to depend on the nature of its neighbours. The first of these :I:uodi_fica.tions gives th
`usual theory. The second and third are cases which have been considered by One and by"
`Prigogine do!» Gm-i.kian respectively. The fourth is new, and is probably the most exact. It is
`shown that, for all modifications, the usual theory is unchanged, to a first approximatiml, if
`A = 1, where
`
`
`
`
`and E is the energy of interaction of an isolated pair of molecules. If A =f= 1, then an importan
`correction term is needed. The application of the most exact of these modified theories 130 .
`the critical solution temperature is discussed.
`It is shown that, for molecules with similar energies of interaction, this theory gives thfl
`same relations between the properties of the solution and those of the components, as (1083
`the theory of conformal solutions, derived by Lenguot-Higgins.
`
`'
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