Sept., 1960
COMPLEX COACERVATES OF GELATIK
1203
PHASE SEPARATION IN POLYELECTROLYTE SYSTEMS. I. COMPLEX COACERVATES OF GELATIN BY ARTHURVEIS AND CATHERINE ARANYI Arniour and Company, Research Division, Central Research Laboratories, Chicago, Illinois Received M a r c h 7,1960
The complex coacervation of mixtures of gelatins of different isoionic pH (PI = 5.0, 9.0) was studied in a test of the applicability of the Voorn-Overbeek thermodynamic analysis of the coacervation process. The compositions of the coexisting phases a t equilibrium and the total amounts of gelatin in each phase were determined as functions of the equilibration temperature and initial mixing concentration, CT. Concentrations ranged from 0 to 1% gelatin and temperatures from 10 to 50”. A parameter, 0, was defined to describe the intensity of the coacervation. In general it was found that 0 increased aa the temperature was decreased. In isotherms above the gelation temperature ( t 40”) e decreased as the total gelatin concentration increased. A t t < 40’ plots of e us. CT showed a minimum which shifted to lower values of CT as t was decreased until, a t loo, the minimum disappeared and e increased with increasing CT. These data could not be fitted in with requirements and assumptions of the Voorn-Overbeek theory. A change in the modeloof the reacting system has been suggested in which electrostatic aggregates are formed in the initial mixture even a t t > 40 . The coacervation equilibrium is supposed to exist between dilute solutions of large, nearly neutral polyion aggregates and the concentrated phase of intertwined but not specifically aggregated random coils. Coacervation in the region where gelation is significant ( t < 40”) is more complicated and must be treated separately.
h binary liquid mixture mill form a stable, homogeneous solution if the condition
O(
v
is satisfied for all values of the mole fraction N z of component 2. When this inequality fails, then spontaneous demixing or phase separation occurs. Overbeek and TToornland VoornZb3 have taken this fundamental thermodynamic approach to the problems involved in “complex coacervation,” the spontaneous liquid-liquid phase separation that frequently occurs when solutions of oppositely charged polymeric polyelectrolytes are mixed in the same solvent. They reasoned that the critical conditions for phase separation could be determined from analytical expressions for the free energy of mixing of the polyelectrolytes and solvent. When the polyion concentration was greater than the critical demixing concentration, the equilibrium concentrations also could be determined by equating the chemical potentials, derived from F , in both liquid phases. The crux of the problem became that of formulating F in simple enough terms so that the subsequent calculations could be carried out and still retain the significant experimental parameters. Overbeek and T’oorn set Ft”t,l (1) = F n i i x l n g (H)
+
Feleotrostatlo (-2)
(2)
and then substituted the Flory-Huggins approximation for FM. F , was calculated by treating the polyions as the sum of single charges and approximating the total electrical interaction free energy by the Debye-Huckcl theory. Their final result was
iii
which .Vr
total no. of lattice sites in the, system = no. of sites occupied by particle i = charge density of particle i =
(1) J. Th. G. Overbeek and X. J. Voorn, J . Cellular Cornparatwe Physiol., 49, Sugpl. 1, 7 (1957). (2) hI. J. Voorn, Rec. trau. china., 75, 317, 405, 427, 925, 1021 (1956). (3) SI. J. Voorn, Portschr. Hochpolym., Forsoh Bd 1, SI92 (1959).
= electrical interaction constant,
= =
site volume volume fraction (or site fraction) of particles of type i
The critical conditions for coacervation were derived from equation 3 for the symmetrical twocomponent case in which each polyion was of the same size (rz = r3 = T , subscripts 2 and 3 refer to the polyions, 1 to the solvent) and charge density (uZ = u3 = U) and both were present in equal initial concentration (42 = 43 = 4 ) . For the solvent rl = 1, u1 = 0. The result, equation 4 u3r =
64 9a2
[(1 - +)Yl l + +I l
(4)
showed that coacervation would take place at ordinary temperatures in water only when u3r 2 0.4 since 4 lo3) 411 was nearly inI1
+++-)
= ff2d
(5)
dependent of r and depended only on the charge density and, through CY, on the temperature and solvent. From equation 5 , however, one can see that small changes in u are reflected by large variations in 411. The polymer size, at large T , is important in regulating 41 and &I only when u is close to its critical value. Complex coacervation is of special interest because it may be involved in many natural biological phenomena that appear to be influenced by interactions of oppositely charged macromolecules. It seemed appropriate t o us to explore the applicability of the thermodynamic analysis described above to biological macromolecules and to proteins in particular. The model and approximations used in the Voorn-Overbeek treatment place definite limitations on the choice of experimental systems. The major assumptions are: (1) that the heat of mixing
of polyion and solvent be zero; (2) that the charge densities are sufficiently low so that P, can be given by a Debye-Huckel work term; and (3) that Fhf can be expressed in terms of the Flory-Huggins lattice solution theory. These assumptions require: (1) that the polyions have the unperturbed random coil configuration; (2) that the charges be distributed throughout the solution without regard to the fact that they reside on the polymer chains; (3) that there are no specific intermolecular associations between polyions; and (4) that, a t the least, the solvent-solute interactions be the same for each partner in the coacervation process. Gelatin is one of the few proteins that have the random coil configuration, and it is well known that gelatins of different isoionic points can be prepared by proper choice of preconditioning of the gelatin stock. Furthermore, experiments on gelatin mixtures, made for other reasons14had resulted in the formation of two phase coacervate systems. When isoionic solutions of gelatins of different pI are mixed, they titrate each other to equal charge. From titration c u r ~ e sthe , ~ net charge on each gelatin (PI = 5 and 9) is -15 ionized groups per 105 grams in the absence of added salt a t pH 6.5. Thus the net charge density is relatively low. In view of the similarity in structure and chemical constitution one might also expect that non-electrostatic interactions between gelatin molecules and between gelatin and water would be nearly independent of the gelatin source. Finally, according to the theory given above, once the critical molecular size is exceeded, the actual magnitude of the molecular size does not greatly influence +I1. Thus, one would not expect the molecular-weight heterogeneity of the gelatins to be a severe handicap. For all these reasons, we chose to investigate the gelatingelatin complex coacervation system in detail. Experimental Procedure The basic data required to establish the coacervation phase relationships are simply the compositions of the coexisting phases a t equilibrium, the total amounts in each phase, and the equilibrium temperature. Such data were obtained from essentially straightforward measurements but we found that many extreme precautions were required to achieve reproducible behavior. Therefore, these direct experiments must be described in some detail. I. The Gelatins. Characterization and Analysis.All measurments were made with two commercial gelatins: gelatin A, an acid-precursor pig-skin gelatin from the Grayslake Gelatin Company, and an alkali-precursor calf-skin gelatin, B, from the Peter Cooper Corp. These gelatins were selected because their light-scattering weightaverage molecular weights appeared to be identical.'j Their sedimentation coefficients were also identical although their intrinsic viscosities were not.6 The characterization data are given in Table I. The sedimentation velocity measurements, though yielding the same average apparent Sovalues, showed some differences in boundary spreading indicating that the molecular weight and/or shape distributions were not identical, in accord with the viscosity data. The PI'S were determined by the ion-eschange method of Janus, Kenc~hington and Ward.' Larger batches of each (4) A. Veis, J. Anesey and .T. Cohen. "Reccnt .4dvances in Gelatine and Glue Research," Peiganion Press, 1957, p. 155. ( 5 ) A. W. Kenehinyton a n d A. G . Ward, Bzochem. J., 58, 202 (1954). (6) A. Veis a n d J. Cohcn, J . Polvmcr Scz., 26, 113 (1957). ( 7 ) J R'. Janus, A. W. Kenchington and A. G. Ward. Research, 4, 247 (1951).
TABLE I CHARACTERIZATION OF A GPlatin
Type
A
Acidprecursor Alkaliprecursor
13
MwX
AND
B GELATINS
&o in 0.1 [q]40 in 0.2 2 1 1 KCl M KCI
10-5
PI
3.3 =k 0 . 3
5.0
0.42
8.95
0.3
5.0
0.58
5.00
3.3
gelatin were deionized by this same technique. Complete desalting was essential. All coacervation experiments were carried out with deionized gelatins. Since the deionized gelatin solutions %*ere free of any other components, refractive index measurements were convenient for concentration determinations. The biuret method8 was also used. Calibration curves of refractive index us. concentration, and biuret complex optical density vs. concentration were identical for both A and B and mixtures of A and B. In practice, refractive index measurements were used to establish most carefully the concentrations of the stock gelatin solutions. The more rapid but less precise biuret method was used to analyze the coaeervation mixtures. The basic calibrations were established with gelatin whose moisture was determined by drying a t 110" to constant weight. 11. The Coacervation Equilibrium System.-This study has been restricted to the simplest case, that of "symmetrical" mixtures of equal amounts of each gelatin. The total amount of gelat,in was varied, however. Each system was set up essentially as follows. Stock solutions of each deionized gelatin were made up in doubly distilled water. The concentrations of these solutions were determined interferometrically a t 40". Individual solutions of appropriate amount and concentration were then prepared, a t 40°,and equal amounts of solutions of A and B a t identical concentrations were mixed in an appropriat? sized centrifuge tube. The mixing also took place a t 40 . The mixtures wcre then transferred to a bath a t the appropriate temperature and were equilibrated a t that temperature for 30 f 1 minutes. The centrifuge tubes were transferred to a Serval1 centrifuge and spun for 5 minutes a t 26,000 X g. As soon as the centrifuge stopped. t,he tubes were transferred hack to the temperature equilibration bath and allowed to stand for about 15 minutes. By this time, the coacervate had formcd a liquid layer a t the bottom of the tube and a very sharp boundary separated the phases. An aliquot was pipet'ted from the dilute equilibrium liquid for concentration analysis. The centrifuge tubes were next placed in a Beckmtln tube slicer and were cut just above the phase boundary. The remainder of the equilibrium liquid was discarded, and the coacervate layer was allowed to gel. The small amount of equilibrium liquid could then be washed off with cold distilled water. At this point, either the Coacervate Concentration w'as determined or the total amount of gelatin in the coacervate was measured. Duplicate experiments were analyzed in these alternat'e ways so that the coacervate volumes could be calculated. When the coacervate volumes were large, they were measured directly in a special device built for this purpose. The material balance for earh coacervation system is given by equation 6 in which VTCT = BcCc FLCL (6) V and C refer to volume and conrentration, respectively, and the subscripts T , C and L refer, rrspectively, to the total system, the coacervate phase, and the equilibrium liquid phase. Of these, CL and CcVc can be determined most accurately. However, Cc could also be det.erminet1 satisfactorily in large scale espclriments. An analysis was nccept,ed only when all valucs rheclicd the. ovcr-all material balance. The complications in this simplc procctlure are the result of the aggregation and gelat,ion of gelat#ina t temperatures lower than 40". We found that,, t,o achieve reproducible results, the time and temperature schedules had to be adhered to strictly. I t was particularly important that t,he thermal history of each gelatin solution was identical and that the A and B solutions be mixed a t 40" and then cooled
+
(8) A. G. Gornall, C. 3 . Bardaaill a n d hl. M David. J . B i d . Chem., lT7,751 (1949).
Sept., 1960
C ' o a n ~ ~ rCO.ICEIWATES x OF C~E.I..LTIS
1205
first layer and washing the gelled coacervate only served to tear off the surface of the original coacervate. Thus, for measurements above room temperature, it was importaut to work swiftly after centrifugation and to maiiitain each system a t its equilibrium temperature. The tube-slicing separation of the equilibrium liquid from the coacervate layer reduced this source of error and provided sharply bountlcd coacervate layers.
Results I. Coacervation in the Non-gelling Region,-.it 40°, intermolecular interactions that lead to galationg do not occur and the thermal history of a gelatin solution is effectively erased. It was, therefore, most important to study the coacervation process at this temperature. A sharply bounded two phase system formed a t all concentrations from 0 -*+-e , , t--7-CT = 2 x to 1 x g./cc. The Cc data 0 2 4 F 8 10 are shown in Fig. 1. The amounts of coacervate, CT x 103, ~ . / c c . as the fraction of total protein in the coacervate Fig. 1.-The concentration of the coacervate phase a t phase, CCV~/CTVT = p , are shown in Fig. 2. 40' as a function of the initial concentration of gelatin. As set up, these symmetrical deionized systems The smooth curve was calculated from the equation: contain only two components, the polymer 'kalt" Cc = 0.1055 - 13.74C~- 1.229 X 1 0 3 C ~ 2 4.992 X 1 0 5 C ~-~ 3.137 X 10'C,p4 P+Q- and HzO. Therefore, in the range where con-hich was computed using all of the experimental points acervation occurs, one would expect two phases to and the least squares method I.B.M. 650 routines No. form with compositions Cc and CL and that these concentrations mould be invariant. Only p should 6.006 and 6.010. The standard deviation u was 5.67 X 10-3. change, in a linear fashion, as CT is varied. In other words, the system represents a single isotherm on a composition-temperature phase diagram and i 0.15 -1 I ideally could be represented as a straight line with two points marking Cc and CL. Inspection of Figs. 1 and 2 shows that these simple phase relationships do not hold and that CC and p depend on CT. Neither CC nor p expresses adequately the in2 . & '-- i- t- t --t- tensity of the coacervation since p may increase 0 2 4 6 8 lo when CC decreases. On empirical grounds it CT x 103, g./cc. seemed more appropriate to express the coacervaFig. 2.-The fraction of gelatin in the coacervate phase above tion data in terms of some combination of these efthe gelation temperature: 0, 40'; X, 50". fects. The two most characteristic parameters are p, which describes the fraction of polymer isolated P in the concentrated phase, and an enrichment factor, E, the ratio of the coacervate and equilibrium liquid polyion concentrations (e = CC/CL). Theoretically, e can be calculated through the thermodynamic formulation described in the Introduction. The intensity of coacervation, 6, is then defined as 0 2 4 6 8 10 e = ep. A plot of 6 vs. CT, Fig. 3, shows that the cTx 103, g./Cc. Fig. 3.-The intensity of coacervation as a function of coacervation intensity decreases as CT increases the initial concentration a t temperatures above the gelation over the concentration range examined. There is temperature. The poinis were calculated from the smooth an abrupt drop in 0 a t CT = 7 X g./cc. These curve values of CC, CL and p: 0, 40"; X, 50'. observations will be discussed in detail later. The data obtained a t 50' were similar in all to the equilibrium temperature. As an example, for experiments a t lo', each 1 .O% gelatin solution would have been respects to the 40' data except that p m s smaller. gelled, yet when t,he gelatins were mixed a t 40" and then 6 is plotted in Fig. 3. equilibrated a t 10 , the system separated into two layers. The coacervates a t 40 and 50' were very turbid Each layer was viscous a t loo, but was liquid in character. On the other hand, a mixture of A and B with salt present but the equilibrium liquid was clear. The coacerto prevent coacervation, also would have set to a solid gel. vate layer appeared to be uniform over the conAlthough the systems studied are thermodynamically centration range examined. reversible, the dense viscous coacervate droplets form more 11. Coacervation in the Gelation Region.readily than they disperse nithout agitation. Thus, it was extremely important to maintain the systems a t their chosen When the experiments were carried out a t temperaequilibrium temperature up to the time of centrifugation. tures below 40°, the equilibration mixtures did After centrifugation, if the coacervated system were allowed not set to gels during the 30-minute equilibration to cool below the equilibration temperature, the supernatant equilibrium liquid became turbid and fresh coacervate period. However, aggregation obviously began began to settle out. As long as a dense coherent second immediately. The mixtures became turbid and coacervate layer did not form, the low temperature coacer- viscous as they cooled. Centrifugation, however, vate could be redispersed by heating it to the original still separated the system into sharply bounded equilibrium temperature. If a coherent second layer (usuf
--*---
+
3r--
"\
ally of high turbidity) did form, it adhered firmly to the
(9) H. Boedtker and P. Doty, THIB JOURNAL, 58, 968 (1954).
1206
ARANYI
- 4 R T H U R VEIS AND CATHERINE
liquid phases. I n every case, even a t temperatures as low as 4', the equilibrium layers were liquid. Once phase separation had taken place, two different kinds of behavior could be noted on further cooling. Rapid cooling set the entire system to a turbid gel. Slow cooling gelled the coacervate and caused the precipitation of a new coacervate phase from the equilibrium liquid. Heating a coacervated system to 40°, if carried out without agitation, reduced the turbidity of the layers without causing them to disperse. Indeed, the low-temperature coacervates frequently were water clear at 40'. In such rewarming experiments it became apparent immediately that the coacervates were not of uniform composition but, depending on the temperature a t which they were formed, consisted of two or more layers. The initial concentration of the system also affected the number of coacervate layers and their relative amounts. In general, when several coacervate layers were present, they did not have the same turbidity. These qualitative remarks point out the complexity of the system when gelation and aggregation phenomena accompany the coacervation process. These complications will be dealt with in more detail in later papers in this series. For the present, however, we will focus our attention on C ~ , e , p and e where these refer to the average or total values for all of the coacervate layers considered as one phase. Figures 4, 5 and 6 show plots of Cc,p and e isotherms, respectively, a t 35, 30, 25.5, 19, 15 and 10'. In the 6 isotherms one can see the progressive increase in the intensity of coacervation as T decreases and a decided change in the character of the 6-c~relationship. The latter change coincides with the presence of multi-layer coacervates in the higher CT region. For example, the 35' coacervate consists of two layers. The higher density layer is turbid, the lower density layer clear a t 40'. The turbid layer increases in volume, just as the 40' coacervate does, until CT m 6-7 X g./cc. and then decreases sharply as CT is increased further. The clear layer becomes visible at CT s 5 X l o w 3g./cc. and increases in volume as CT is increased. Discussion I. The Applicability of the Voorn-Overbeek Model for Coacervation.-The Voorn-Overbeek treatment of the complex coacervation phase equilibria predicts, through equation 5 (and eq. 42 ref. 2b), the equilibrium concentrations of the supernatant and coacervate layers in terms of the parameters u and r which represent the charge density and polyion size. For any given T and CT, above the critical value for CT, the mixture of oppositely charged polyions should separate spontaneously into two layers of fixed composition, CL and CC, and only the amounts of the two phases should vary as the total concentration progresses from CL to CC. It is obvious from the data presented in the preceding section that these direct requirements of the phase rule are not satisfied although the systems come reproducibly to an apparent equilibrium. At every temperkture, the equilibrium concentrations depend on the total
64
x' s 0 0 G
2
cTx
4
6 103, g./cc.
8
10
,
0 i 0
-
r
-
r
-
t
6 8 10 x 103, g./cc. Fig. 4a and b.-Coacervate concentration as a function of initial concentration a t temperatures below the critical gelation temperature: (A) A, 35"; 0,30"; (B) 10"; x, 15", the smooth curve represents the data a t 25.5 computed from the equation Cc = 0.07283 - 11.52C~ 1.978 X 1 0 3 C ~* 1.185 X 105C~3 The standard deviation u was 4.49 x 10-3. The equation was computed by the same techniques given in the legend of Fig. 2.
2
4
cT
9,
+
polyion concentration a t the initial mixing. This behavior can be explained in terms of the existence jn the real case of more than the two components of the idealized model. A. The Effect of Molecular Weight Heterogeneity.-Since gelatins are known to be heterogeneous with respect to molecular weight, it is pertinent to consider first the effect of this type of heterogeneity on the phase diagrams, assuming that the Voorn-Overbeek model applies to each of the homologous series of polyions. Consider a system composed of polycations PI+, P2+,P3+ and a single polyanion Q- in equivalent amount. Further, let the ratios of amounts of Pl+, P2+and P3+ be some fixed values (a constant mixture of P's) and assume that the critical concentrations of P's for coacervation with Q are CI', C2'and C3'such that C1' < C2' < C3'. As CT is increased from zero, a coacervate PI&will begin to form when C1 > C1' in an amount proportional to (C, - C,'). Only PIQ will form a separate layer until Cz exceeds CZ' when a new coacervate P2Q will form along with P1Q in an amount proportional to (C2 - Cz'). Similarly, coacervate P3Q will only form after C3 > C3'. A plot of p 0 s . C ~for this case, e.g., Fig. 7, would consist, starting from the critical value of CI', of three linear segments of increasing slope. On the other hand, a plot of the average CC VS.CTwould show a negative slope since the Voorn-Orerbeek treatment predicts that the
Sept ., 1960
COMPLEX COACERVATES OF GELATIS
0.8
0.6
< 0.4
0.2
7 /-*-
A
0
I
1
I
I
I
I
-a=, I
I
I
,\& I
I
t
6 8 10 cTx 103, g./cc. Fig. 5.-The fraction of gelatin in the coacervate phase as a function of initial concentration a t temperatures below the critical gelation temperature: A, 35"; 0 , 30'; 0, 25.5'; e, 190; x, 150; 0,ioo. 2
4
lower the critical concentration for coacervation, the higher the coacervate concentration will be. The best data against which to test these considerations are those of Figs. 1 and 2, representing the coacervation a t 40°, in the non-gelation region. The p u8.C~plot is exactly the opposite of that described above and, although Cc decreases with increasing CT,the slope of the CC us. CT plot is not monotonically negative. At lower temperatures (25 to 10') where gelation-type aggregation does occur, the p-CT plots begin to approximate the shape of the curve for the heterodisperse system but the CC-CT curves are still different in character (Figs. 4b and 5 ) . Thus, heterodispersity in molecular weight cannot give rise to the observed behavior, within the framework of the Voorn-Overbeek treatment. B. Self-suppression of Coacervation.-The shapes of the p-CT and CC-CT plots are similar to the three-component case of self-suppression of coacervation noted in mixtures of polymer salts P+A-, B+Q- where the diffusible microions B+ and A- increase the ionic strength as the total
1207
polyion concentration is increased. In this case, however, the critical requirement is that the microions must be distributed in nearly equal concentration in both phases. In our system of isoionic polyampholytes, the only microions are H + and OH- and H+ is at a concentration less than 10-6 eq./l. in each phase. It is possible to cons der the excess balanced, fixed charge on each polyampholyte as contributing to the total ionic strength but these charges cannot be distributed over the entire solution and hence cannot be used to explain the concentration dependence of Cc and CL. We are, therefore, obliged to consider other sources for the apparent deviation of the coacervation of polyampholytes from the phase rule and from the Voorn-Overbeek model. C. The Behavior of Isoionic Gelatin Solutions.-The behavior of salt-free isoionic solutions of randomly coiled polyampholytes has been described by Ehrlich and Doty'O and applied to gelatin solutions by Boedtker and Dotyg and by Veis and C0hen.j iiccording to these works two effects are evident. First, because of the attraction of oppositely charged segments of the fame molecule the extension of that molecule in space is decreased from that of the unperturbed random coil configuration. Second, because of the intermolecular attractive force resulting from charge fluctuations" large intermolecular aggregates may be formed under conditions where gelation-aggregation phenomena are absent. The electrostatic aggregates in isoionic solutions may be quite large. Thus, even at 40" the behavior of the isoionic gelatin solutions before mixing cannot be represented in terms of non-interacting random coils as required by the Voorn-Overbeek treatment. Furthermore, the electrical charge cannot be considered as being uniformly distributed throughout the solution. When mixtures of isoionic gelatins of different pI are made, a net charge is induced on each type of molecule and strong intermolecular electrostatic interactions cause new aggregates to form. These aggregates are governed in size by the initial concentration of the mixture but, once formed, are stable and can be diluted (at zero ionic strength) without dissociation. According to Boedtker and Dotyg the electrostatic aggregates are more dense, compact structures than the gel-type gelatin aggregates. Clearly, it should not be assumed that the component polyions of any mixture of oppositely charged polyions a t low ionic strength can ever exist as independent molecules. Thus, the coacervation equilibrium must be established between dilute solutions of aggregates, of near zero net charge, and the concentrated coacervate phase. Since reaching this conclusion, we have begun a series of experiments on the state of aggregation in the equilibrium phase. These studies are not ready to be described in detail but the preliminary results confirm that aggregates are present in the dilute equilibrium phase. For example, a mixture of gelatins h and B a t 40' and a t CT = 7 X J. A m . Chem. Soc., 7 6 , 3704 (1954). (11) J. G. Kirkuood and J. B Shumaker, Proc Vutl. Acad Scz., 98, (10) G. Ehrlich and P. Doty, 863 (1952).
ARTHURVEIS AND CATHERIXE ARAXYI
1208
T-OL
64
g./cc. was made in an analytical ultracentrifuge cell. The cell was spun a t 20,000 X g for a few minutes to bring down the coacervate phase, The cell speed then was increased and the sedimentation of the equilibrium liquid observed. The S40 -t value computed from these observations was 71.3 S and this should be compared with the S40 values of 5.0 for each gelatin alone, shown in Table I. Light scattering measurements4 also indicated the presence of aggregates in the equilibrium liquid. D. Gelatin and the Critical Conditions for Coacervation.-Returning to the Voorn-Overbeek model, equation 4 places a minimum value of about 0.4 for the critical product u3r. For either gelatin (from titration curves and the data of Table I) considered as independent molecules, T is approximately lo4 sites and unet at pH 6.5 is -3 X charges/site so that u3r becomes -0.3 X This is far below the critical value for coacervation. If, alternatively, one uses the total charge on a gelatin molecule at pH 6.5 as Overbeek' 0 2 4 6 8 suggests, UTotal M 4 x lo-' and UTota13T M 0.6. cT x 103, g./cc. This latter value probably is appropriate for use Fig. 6.-The intensity of coacervation as a function of when discussing the freely distributable charge in initial concentration a t various temperatures: a, 35"; the concentrated coacervate phase but certainly 0, 30"; A, 25.5'; 0, 19'; x, 15'; 0 , 10'. cannot apply to the dilute equilibrium phase nor to the initial gelatin mixtures at low CT. Thus, independent gelatin molecules of the size I studied and a t the pH of our experiments, should not have formed coacervates. Assuming that u is relatively independent of the environment, r would have to be on the order of lo7 to surpass the critical value. From this point of view we are again led to conclude that the independent molecule-uniform charge distribution model cannot lic valid for the dilute phase. E. The Temperature Dependence of the Coacervation Process.-From equation 3 and the 0 2 4 6 approximation of equation 5 , it would appear that Total concn. CC should depend on the temperature only through Fig. 7.-An pxample of the expected effect of molecular the electrostatic interaction coefficient CY in the heterogeneity on the fraction of gelatin in the conon-gelation range. In turn, CY is a function of weight acervate hase. If the system contains four components (DT)-'/z. It is difficult to evaluate the dielectric whose refative amounts and critical concentrations for constant exactly for both phases and for such com- coacervation for each of these components are fixed values plicated solutes but it seems reasonable to take the as given below, the fraction of material in the coacervate will follow the course shown in the diagram. The change in D with T to he the same as that of water. phase numbers in the various parts of the diagram represent the Values of D,(DT)"z, cy and cy2 are listed in Table component species that make up the coacervate phase a t each stage of the process. See the text for the detailed 11.
t
rI
explanation.
TABLE I1 THEVARIATIONOF THE ELECTROSTATIC INTERACTION CoEFFICIENT WITH TEMPERATURE D 1. 'C.
10 20 30 40 50
(pure water)
(DT)*P X 10-6
a
a2
84.11 80.36 76.75 73.78 69.04
3.67 3.61 3.55 3.48 3.40
4.007 4,073 4.148 4.236 4.334
16.05 16.59 17.78 17.94 18.78
Accordingly, equation 5 predicts that CC should increase about 4y0for each 10' rise in the temperature. A change in CC of that order of magnitude is within the range of the experimental error a t 40 and 50' and the CC data cannot verify this difference. However, p decreases significantly between 40 and 50'. Because of the relatively large
1 2 3 4
Relative amt. of each cornponent.
%
Critical concn. for coacervation for each component
Total concn. a t which t h e components reach tlieir critical concn.
Concn. of each component when coacervation can occur
0.25 0.25 0.25 0.25
C1' = 0.25 Cz' = 1.00 Cs' = 1 . 2 5 C,' = 1.50
CT,= 1.00
Cl 2 0.25 C p 2 1.00 Cs >= 1.25 C, 2 1.50
C T ~= 4.00 CT' = 5.00 CT* = G . 0 0
volume of equilibrium liquid p is most sensitive to rhanges in CL and indicates that, a t constant CT, CL should increase with increasing temperature. This is verified by the direct CL measurements. A plot of CCand CL as a function of temperature a t constant CT (CT chosen close to the inflection point of each CC vs. CT isotherm), Fig. 8, shows t,hat the coacervation process clearly follows two different mechanisms. The discontinuity in Cc
Sept. , 1960
I
COMPJXX CO.4CERV.%TIgionsM hrw t h r coacervation intensity is greatest.
