184
JOHN D. FERRY .iND JOHN E. ELDRIDGE
STUDIES OF THE CROSS-LINUXG PROCESS IN GELATIN GELS. I' JOHN D. FERRY
.%SI) JOHN
E. E:T,DRIDGE?
I h p a r l r r i c)i t o f Ch eviinlyi/ T .nielersify o,f Il'iscon,.~; ) I , J l n d i s o t L , Il'iacons i t , I?cceioccl
:Lirgitst
19, t9@
The gelation of gelatin solutions may be attributed to linkage of elongated molecules by secondary forces of attraction t o form a three-dimensional network; a variety of evidence supports this interpretation (9, 12, 15, 16). Little is known concerning the nature of the linking process, however. One potential source of a better understanding of gelation is the well-k\nown phenomenon of a change in opt'ical rotatory power which always accompanies the development of rigidity in gelatin solutions (4, 16, 19, 22). While numerous studies of optical activitJy have been reported in t'he literature (reviewed elsewhere (9)), in very few cases have any other physical measurements on the same gelatin samples been given. The comhinat#ion of different, data on identical samples can 'greatly facilit,ate interpretation. I n the present study, the availability of a series of degraded gelatins of known average molecular iveight and molecular weight distribution (10, 21) has made such comparisons possible, and has permitted invest'igation for t'he first time of the effect of molecular weight on optical activity and other properties. I n this paper, measurements of optical actirit'y and rigidity are reported. M.\TERI.%LS .%ND .MF>THODS
Five samples of the series of degraded ossein gelatins described by Scatchard, Oncley, Williams, and Bro\vn (21) were e r n p l ~ y e d . ~The statistical theory of degradation (21), which is supported by measurements of osmotic pressure, sediment,ation, and viscosity, specifies a wide distribution of molecular weights in each sample, and permits calculation of the weight-average molecular weight (M,) when t'he numher-average molecular weight (Mn) has been determined experimentally. The values of these averages (20) are given in table 1. The samples had been stored, since preparat'ion (between April and October, 1943 (23)), as sterile solutions a t a concentration of about GO g.11. in 0.15 ill sodium chloride a t pH 7 ; they were kept a t 0°C. except for occasional brief Tvarming to 37°C. t.o withdraw samples (with sterile precautions). From studies of the rate of degradation (20, 21), no perceptible change in molecular weight \vould be expected for several years under these conditions. In support of this conclusion, the rigidit,y nieasui-ementmsdescribed here, made after about five 1 Preseiited a t the Tweiity-sCeotid Kational Colloid Symposiuiii, which was held under t,hc auspices of tlir Divisioii of Colloid Chemistry of the Ainrricaii C'hcinical Society a t Cambridge, hIassachusctts, June 23-25, 1948. 2 Presetit address: E. I. tln Pont de Semoui.s and Compniiy. Plastics Departnient, Arlington, Ncw .Jerscy. 3 The authors are indebted t o Prolessors George Scatchard atid John L. Oncley for these iuatterials, originally furnislicd through the kindness of Dr. D. Tourtellotte of Knos Gelatin? Prot,cin Products, IUC.
CROSS-LINKING PROCESS I N GKL.4'l'IK
GELS
1 s5
years' storage, fit very well with previous tneasurenients on similar samples (10) made after less than two years' storage (figure 7), even though the rigidity i s quite sensitive to molecular weight. The concentrations of the stock solutions I\ ere determined t)y dry w i g h t :it 110"C., correcting for the sodiiim chloride content. Refore use, the stock solutions were \\armed at 37°C'. ~ ' ( J I *1 111.. to elimiiiate ]~re\-iousthermal history, and dilnted with 0.1.5 .lI sodiuiii chht-ide l o the desired concentrrltions. Tlie final sohitions were timsfeiared to the appi*opihtevessels (rectangular glass cells for rigidity measurements 0 1 ' polarimeter t i i t m for optical actilrity), rapidly chilled to O"C., and maintained a t that tempei*atiircfor 24 hr. IIeawiwncnts \\.ere then made as described hcltr\v.
Optical crctiitity
tri cos ti remeti is
The specific rotation \ \ a s cleterminetl \\ ith ii Schmidt-Ilaenscli polarimeter, liking. 1 - h i . tiihes with \\ ater jackets throiigh \I hich water from a thcrmostnt was
Sr\UPLI' .~
P6-00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1'6-20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L3-SO . . . . . . . . . . . . . . . . . . . . . . . . . . . . L1-120.. . . . . . . . . . . . . . . . . . . . . . . . . . . PG-180. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~
~
-
~~~~
circiil:itecl. l'he green line (5461 .I.) of the mercury arc \\.as cmpluj.etl. 'I'hc precision was at)out 0.5" under the most favomble conditions (solutions above tbeir melting points) and about) 10" iincler the least' fai~ornhle. Since most> pre1,ious \\.ark has been tione ivith the sodiiini D line, our numericttl values of [a]are not, directly comparalde \\.it'll others ; ho\vever, the re1atiT.e dependence of specific rotat,ion on temperatiire 2nd concentration, \\it11 \vhich \\'e are primarily concerned, shoiild be \.eiy similar at, different>\\.aye lengths, as sho\vn hy t8he ini,est>igat,ionsof rotatory dispersion tnatle hy Carpenter ( 3 , 5 ) .
R1:giditg ))msiwemetifs Rigidity \ \ a s ctet.erniined from the ve1ocit)y of propagatioii of t rnnrjverse ivaves as described previoiisly (1, 8, 10). The "\vave rigidit,y", c, is given 1)y V % , where V is the velocity of propagation and p the density of the gel; since the clamping is small, it' differs only slighttlyfrom G', the dynaniic rigidity (1I ) . For each gel at' each temperature, mea.surements of T v \\.ere m~itleat t\vo 01'three different frequencies, covering a range of about, t\vofokl. The, gel tlensi ty was cdculatmedfrom the tlensi ty of t,lie salt soli~t~ioii n.nd w n assiinietl - \ d i i e of 0.iO for the part'ial specific volume of gelatin. There \vas no evidence of dispersion of bhe rigiditmy,except IJossihI; just helow t)he melting point. The rigidity
180
JOHK D. FERRY AND JOHN E. ELDRIDGE
values \yere therefore averaged regardless of frequency, and the probable error of the mean ranged from about 1 per cent for the st,rongest gels t,o about 3 per cent for the \yealiest gels. In a fen- cases the damping \vas measured from displacements of the quartz \vedge lines in the wave pattern (8), using an enlarged t,racing of a photograph rather than direct, micrometer measurements as previoiisly described. If 4 is the relative retardation (phase difference) measured on the Bahinet, then a plot of In tan 4 (tan A being nearly proportional to 6 , the relative retardation in t'he gel) against x,the distance from the source, gives a straight line whose reciprocal slope is GI, the critical damping distance. The severity of damping is measured by the ratio X:l.co, where X is the wave length (11). RESULTS O F 0PTIC.iL ACTIVITY MEbSUREMENTS
-4ft'er chilling each gel a t 0°C. for 24 hr. and measuring its specific rotation at that temperature, the temperature was raised a few degrees and maintained constant until the specific rotation attained a constant I*alue. The time reqiiiineclwas about 1&hr. This sequence was repeated until the optical rotation no longer changed with increasing temperature. Thus, all temperatures except the lowest, near O"C., were approached from below. The advantages of this proceclure are discussed elsewhere (9, 10).
Dcpetacleticci
O I L concenfrafiona
d tcmpcra/we
The specific rotation, [ a ] ,is plott,ed against temperature in figure 1 for geIs of PG-20 a t four different concentrations. The point's all fall close t o the same curve, showing that the optical rot,ation is proportional to the first power of the concentration. The cun-e shows the well-known transition observed by many preIrious inveutigat,ors. Al)ove 35°C. the numerical value of the specific rotation, - [ a ] , appears to be approaching a constant, in agreement Ivith the result8sof previous investigat,ors; the limiting value (lG5") is a lit'tle smaller than the value interpolated from data of Carpenter and Lovelace (5) at this wave length ( a h l t 175"). With respect to behavior a t lower t,emperatures, previous reports are conflicting. Smith ( 2 2 ) found that - [a]increased with decreasing temperature from 35" t o 15"C., but \vas constant below 15°C. a t a maximum numerical vaIue (for the sodium D line) of 313"; whereas Braemer and Fanselow (lo), who cont,rolled the pH carefully, found that - [a]increased with decreasing temperature over the entire range experimentally accessible. Our results confirm the latter report. Our experiments further agree ivith those of Kraemer and FanseIow, and are at variance with those of Smith, in sho\\-ing - [ a ] to be independent of concentration at pH 7 over t,he entire temperature range. These result's are important in i n t e r p r e h g the significance of the optical activity change, since they rule out Smith's concept, of a bimolecular reaction and other discussions based on this assumption (17). Depcridence
0th
aiwage molecular weight
In figure 2 - [a]is plotted against temperature for solutions of the five samples, high t'emperatures, the specific each at a concentratmionof about, 40 g.,'l.
CROSS-LINKIiYG PROCESS I N GELSTIN GELS
18'7
rotation appears to be independent of both temperature and molecular weight). A t lower temperatures, - [a]decreases marlcedly v,iLli decreasing molecular
cr)
W
L1
a
8
-
nwo n
& I
200
20 30 TEMPERATURE,"^.
0
10
40
FIG. 1. Specific rotatioil plul tetl ngniiist temperaturc for sample P6-20 at four different ccmrent r~ t i O W .
2J 300 C
-? II
I5
' 2co 0
1
0
2
0
3
0
~
TEMPERATURE,"^. Frc.. 2. Specific rotatioil plotted against temperature for five sainples of different itveragc molecular weights. ~ appear to be a simple function of either AIIluor weight. It does not, 1 1 0 eirer, ill, at constant temperature.
S p c c i j c rotatiori itL a mistum of sairiplcs ?'wo samples of Ividely different nivernge molecular weight, PG-00 and PG-180, were combined in eqiinl proportions by weight, yielding a. mixture vith AI,&
188
JOHN D. FERRY AND JOHN E. ELDRIDGE
= 25,000 and 64, = 53,000, with an abnormal size distribution. Its specific rotation is compared with those of the original samples, all a t a concentration of about 40 g./l., in figure 3. The rotations of L1-120, which has almost the same Mn,and L3-80, which has the same M,, are included for comparison, together with the arithmetic mean of the rotations of the two individual samples. The specific rotation of the mixture corresponds closely to the mean, and not t o the normal sample with the same Mn nor that with the same M,. This contrasts markedly with the case for rigidity, which in a n abnormal mixture is determined by AI,,,, (10).
TEMPERATURE,"C. 3. Specific rotatiuu plotted against temperature for a mixture of samples P6-00 arid P6-180, equal parts by weight. Points, experimental values; dashed curve, arithmetic mean of values for individual samples. M,: curve for natural sample (L3-80) with same M, as mixture. M,, : curve for natural sample (LI-120) with 4 per cent higher M, than t h a t of mixture. VI(;.
E.ffect of ann.ealiny and rswarminy In t,\\.o experiment,s wit8hPG-20, a t concentrations of 20.3 and 59.2 g./l., specific rot ntions were measured with the usual sequence of increasing temperatures up to 35°C.; then the procedure was reversed, cooling a few degrees and holding the temperature constant for several hours, measuring the rotation, and repeating the process unt.il a temperature of 16°C. was reached. Finally the sequence of measurements with increasing temperature was repeated from 16" to 35OC. In the cooling sequence, the optical rotations did not quite become constant within several hours; in the second warming sequence, constancy was achie7-ed after about 3 hr. a t each temperature. The specific rotat,ion is plotted against temperature in figiue 4 fur the three sequences (concentration 59.2 g./l.). :It intermediate temperatures, each step
in the cycle results in an incrensc jn - [ a ] . a,t the lower concent8rntioii.
\'ei*y similar rcxiilts \\-ere obtained
Irat,ionof useful cross-links in the system (as would be expected if the rigidit,y is due to rubberlike elast8icitjy)antl that the concent'rat'ion of useful cross-links is proportional to the square of the total concentration (which would follow from a binary association if the proportion of cross-linlting loci combined is always small). It is necessary to assume that the ratio of useless cross-links (10, 13) to total cross-links is eit,her small 01' constant. The change in optical activity is always closely associated with the deITelopment of rigidity. For example, the temperature dependences of the two phenomena are superficially similar (figures 2 and G ) , although for each sample the drop in specific rotat'ion takes place in a temperature range a felv degrees higher than the corresponding drop in rigidit'y. Also, earlier reports in the literature sho\v that, the effects of neutral salt's and other added sihstances in lowering - [ a ] , the rigidity, and the melting point run parallel (9). It has heen natural t,o assume that the change in optical activity results from the cross-linking process; n restriction of mobility accompanying the formation of secondary Iionds could cause a large increase in specific rotation, as in the case of ring formation in compounds of lo\\. molecular weight or crystallization of a liquid (2, 18). Xevertheless, the fact t'hat [a]is independent of concenti'ation sho\rs t,hat the number of units responsihle for the change in optical activity is proport,ional to the first power of the concentration rat>herthan the square, and so the relation between the two phenomena cannot he a simple one. This conclusion is supported by other evidence from our experiments: ( a ) in a mixture of samples, the specific rotation is determined by the mean of the values for the components (figure 3), while the rigidity depends on the weight-average molecular \\eight ; ( b ) after annealing, the entire specific rotation-temperature curve is shifted upwards (figure 4) while that of rigidity is unaffected (figure 9) ; (c) after an increase in temperature less time is required for the specific rotation to become constant than for the rigidity. The different) behavior of optical actii7it)y ancl rigidity can be interpreted I)y either of two alternative hypot,heses: ( a ) The change in optical act'ivity reflects the formation of cross-links, but most, of the links are intramolccdar; the typical bond is fornietl betn,een two loci on the same molecule. A relat,ively small number of the links are intermolecular, ho\\ever, and these are responsible for gelation. There must al\vnys lie enough free loci so that the two types of links do not compete; the necessary inequalities are : intermolecular cross-links
