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Kinetics of Droplet Growth in Gelatin/Maltodextrin Mixtures Following Thermal Quenching M. A. K. Williams,*,† D. Fabri,† C. D. Hubbard,† L. Lundin,† T. J. Foster,† A. H. Clark,† I. T. Norton,† N. Lore´n,‡ and A.-M. Hermansson‡ Unilever Research Colworth, Colworth House, Sharnbrook, Bedford MK44 1LQ, U.K., and SIK, The Swedish Institute for Food and Biotechnology, Box 5401, 402 Gothenburg, Sweden Received December 28, 2000. In Final Form: March 12, 2001 Rates of droplet growth, following the thermal quenching of gelatin/maltodextrin mixtures into the incompatible region of the phase diagram, have been obtained from turbidity measurements. The results from experiments carried out at temperatures that prohibit the involvement of biopolymer conformational ordering and gelation are in good agreement with those obtained by similar studies of binary synthetic polymer systems and with theoretical predictions. For mixtures that would phase separate at temperatures above the gelatin ordering temperature (T0) but which are quenched directly to temperatures below this, droplet growth shows modified kinetics owing primarily to restrictions imposed by the viscosifying continuous phase. However, for a mixture that was initially observed to be miscible following quenches to temperatures below T0, it is proposed that biopolymer ordering induces phase separation, which was found to occur after significant delay periods.
Introduction Many mixed biopolymer systems phase separate in aqueous solution. Often, in addition, such systems can be manipulated so that at least one of the components will form a gel. Previous work in this area has clearly demonstrated that the resulting microstructure in mixed biopolymer systems of this type depends crucially on the relative rates of phase separation and gel formation.1-9 Despite this, the complex coupled nature of these phenomena renders true system engineering, in which complete microstructures can be constructed to order, elusive. Ultimately, if the governing physical processes and their inter-relationship can be understood in detail, then such systems offer to provide exquisitely tuneable self-assembling systems with truly designed morphologies and material properties. In the further development of the field, measurements of the rates of structural evolution in mixed biopolymer systems will play a key role. A previous paper1 has considered the role of turbidity measurements in the study of phase-separating biopolymer mixtures and described in detail a method, based on the fitting of turbidity spectra, designed to extract the * To whom correspondence should be sent. † Unilever Research Colworth. ‡ SIK, The Swedish Institute for Food and Biotechnology. (1) Aymard, P.; Williams, M. A. K.; Clark, A. H.; Norton, I. T. Langmuir 2000, 16, 7383-7391. (2) Lundin, L.; Norton, I. T.; Foster, T. J.; Williams, M. A. K.; Hermansson, A.-M.; Bergstro¨m, E. In Gums and Stabilisers for the food industry 10; Williams, P. A., Philips, G. O., Eds.; The Royal Society of Chemistry: Cambridge, U.K., 2000; pp 167-180. (3) Alves, M. M.; Antonov, M. P.; Goncalves, M. P. Int. J. Biol. Macromol. 2000, 27, 41-47. (4) Lore´n, N.; Hermansson, A.-M. Int. J. Biol. Macromol. 2000, 27 (4), 249-262. (5) Tromp, R. H.; Jones, R. A. L. Macromolecules 1996, 29, 81098116. (6) Tromp, R. H.; Rennie, A. R.; Jones, R. A. L. Macromolecules 1995, 28, 4129-4138. (7) Alevisopoulos, S.; Kasapis, S.; Abeysekara, R. Carbohydr. Res. 1996, 293, 79-99. (8) Khomutov, L. I.; Lashek, N. A.; Ptitchkina, N. M.; Morris, E. R. Carbohydr. Polym. 1995, 28, 341-345. (9) Clark, A. H.; Richardson, R. K.; Ross-Murphy, S. B.; Stubbs, J. M. Macromolecules 1983, 26, 1367.
sizes of demixed inclusions. This study extends the work by applying temperature quenches to gelatin/maltodextrin systems, in contrast to decreasing the temperature at 1 °C min-1, as was carried out previously. The measurement of the isothermal rate of droplet growth following the initiation of demixing promises to be a simpler theoretical situation, facilitating useful comparisons with the large body of work on binary mixtures of liquids and polymers as well as with theoretical treatments. The work is primarily carried out by employing analysis of turbidity spectra, and details regarding the method itself are as described previously.1 In particular, the results obtained from systems quenched to above the ordering temperature of gelatin (30 °C), where ordering and network formation are not important (designated quench route i), are contrasted with two further scenarios. The first of these involves mixtures that would phase separate upon holding at temperatures above 30 °C but which instead are quenched directly to temperatures where ordering and ultimately network formation are involved (quench route ii). The second is a system that does not exhibit phase separation until 20 °C, when cooled at 1 °C min-1, is quenched to 25 and 30 °C and the turbidity of the system is observed as a function of time. These temperatures are greater than the intrinsic phase separation temperature for the initial unordered system but below the ordering temperature of gelatin (quench route iii). These different quench routes are shown schematically in Figure 1, along with data reproduced from the previous study (obtained at 1 °C min-1), which serve as a guide to phase behavior in different regions of the temperature/composition diagram (although they are underestimates of the true phase separation temperatures owing to the kinetic nature of the experiment). Experimental Section Sample Preparation. The gelatin sample was a LH limetreated gelatin supplied by SKW. Using size-exclusion chromatography coupled with light scattering, values of Mn ) 83 300 and Mw ) 146 000 g mol-1 were determined. The maltodextrin was a DE 2 grade supplied by Avebe (SA2). From the DE value, Mn can be estimated to be about 9000 g mol-1. The moisture
10.1021/la001811j CCC: $20.00 © 2001 American Chemical Society Published on Web 04/24/2001
Droplet Growth in Gelatin/Maltodextrin Mixtures
Figure 1. Estimates of the phase separation temperature obtained from turbidity increases observed during cooling from 60 to 10 °C at 1 °C min-1 as a function of SA2 concentration, for 4.5% LH in 0.1 M salt. Also shown are three distinct quench routes and the gelatin ordering temperature (30 °C). The other dotted lines are an approximate phase boundary between the miscible (at higher temperatures) and demixed regions.
Figure 2. Temperature quenches (from 60 to 10 °C) obtained with the custom-built cell holder. Two data sets are shown. content (10% for maltodextrin and 12.4% for gelatin) was taken into account for preparation of the solutions. Biopolymer solutions were prepared as follows: SA2 powder was first dispersed in cold water and then stirred at 95 °C for 30 min. Gelatin was prepared similarly, but not heated above 60 °C to prevent any thermal degradation, and was stirred for 20 min. Sodium azide (500 ppm) and sodium chloride were added, the latter in an amount such that the total ionic strength of the solution (including the contribution from the biopolymers) was 0.1 M. SA2 solutions were cooled to 60 °C for 5 min and then mixed with the gelatin solution at 60 °C, to achieve the required weight percent of the components. Mixtures were stirred for 5-10 min more before the introduction of the sample into the appropriate instrument of study. Turbidity Measurements and Spectral Analysis. All measurements were carried out using a Perkin-Elmer Lambda 40 spectrophotometer. The apparent acceptance angle of the experimental setup was measured using a method described previously1 and was found to be approximately 3°. A custom temperature-controlled cell holder was constructed in order to perform thermal quenching, which consisted of a copper cell holder, the temperature of which could be controlled by Peltier devices. Further details are given elsewhere.10 Typical quench profiles obtained from the custom setup are shown in Figure 2. Confocal Laser Scanning Microscopy. The CLSM system used was a Leica TCS 4D confocal laser ccanning microscope (10) Williams, M. A. K.; Fabri, D.; Halstead, T. K.; Hubbard, C. D. Instrum. Sci. Technol. 2001, submitted for publication.
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Figure 3. Size evolution of included phase growth following the quenching of a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 32 °C. Results are obtained from fitting turbidity spectra. (Heidelberg, Germany), equipped with a Linkam TMS 92 heating and cooling table. The emission maximum at 488 nm of an argonkrypton laser was used as the light source. Based on the size of the dispersed phase, the microscope objectives having a magnification of 63 times and a computer zooming of 3.97× were used. The signal from the sample was collected, and eight scans were averaged during the creation of an image. Because, for the concentrations studied here, phase separation yields maltodextrin-rich inclusions in a continuous gelatin-rich matrix, it was found to be advantageous to stain the discontinuous maltodextrin phase. A method to covalently label maltodextrin with RITC (Rhodamine B isothiocyanate) has been developed by Garnier et al.,11 based on the procedure of De Belder and Granath,12 and this has been used here. Mixed solutions of gelatin/ labeled maltodextrin were transferred to a preheated metallic cup in the CLSM at 60 °C. This had an inner diameter of 14.2 mm and a depth of 1.8 mm, giving a sample volume of 0.29 mL. (It is noteworthy that preliminary experiments were carried out using turbidity measurements in order to assess the effect of the labeling of the maltodextrin component on the phase behavior, and no differences between labeled and unlabeled material were found in this respect.) To prevent cooling-induced phase separation close to the surface, an 80 °C preheated cover glass was used. The sample was stabilized for a few minutes at 60 °C and then cooled from 60 °C to the required quench temperature at a rate of approximately 30 °C min-1.
Results and Discussion Kinetics. (i) Systems That Phase Separate at Temperatures above T0. Figure 3 shows results obtained from quenching a 4.5% LH1/2.25% SA2/0.1 M salt system from 60 to 32 °C. For all work presented, t ) 0 corresponds to the beginning of the quench (to within 15 s). The size extraction from turbidity measurements was carried out by analyzing spectra obtained between 600 and 800 nm assuming spherical scatterers, as described previously.1 It should be noted that the decrease in the droplet growth rate observed in one of the turbidity runs in Figure 3 (b) is taken to arise from sedimentation of larger droplets. This reduction is mirrored by a decrease in the magnitude of the turbidity value (which is discussed in due course and shown in Figure 12). This value continues to fall over a further 20 h, and manual inspection of the cuvette, after this time, reveals a bulk phase-separated system. The measurement of the respective volumes of the bulk phaseseparated layers gave an included phase volume ratio of (11) Garnier, C.; Bourriot, S.; Doublier, J.-L. In Gums and Stabilisers for the Food Industry 9; Phillips, G. O., Wedlock, D. J.; Williams, P. A., Eds.; IRL Press: Oxford, 1998; pp 247-256. (12) De Belder, A. N.; Granath, K. Carbohydr. Res. 1973, 30, 375.
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around 0.1, in reasonable agreement with the phase diagram previously reported.1 This is, in turn, supportive of the use of solely a spherical form factor (and neglect of interparticle interactions) in the analysis of the turbidity spectra, as has been carried out here. There is, however, some spread in the magnitudes of the extracted sizes, which is evident between repeat runs. The data within an individual run do not seem particularly noisy as the consistency of time evolution shows, and the temperature quenches are reproducible as described. It is suggested then that the difficulty encountered in reproducing the exact magnitude of the result is primarily a consequence of the sensitivity of the mixture to minor changes in the preparation method and to sample heterogeneity. It is interesting to consider the predicted form of a plot such as Figure 3. During off-critical quenches, the initial stages of phase separation are expected to involve diffusion-limited growth of isolated particles, with the average size of particles expected to follow a power law with an exponent of 1/2.5 This growth is then expected to slow with predicted power law exponents of between 1/6 and 1/3 (depending on the details of the model). The morphology will then begin to coarsen, and there is general agreement that the average size of particles in the longer time regime should evolve with a power law with an exponent of 1/3. Guidelines indicating exponents of 1/2 and 1/3 are included in Figure 3. It is possible to argue that the data show a region of initial phase separation with the average inclusion diameter growing with a t0.5 dependence between 5 and 10 min and that the system coarsens with a power law exponent of 1/3. Furthermore, this result compares favorably with work carried out on phase-separating binary synthetic polymer systems such as polystyrene/ polybutadiene, polystyrene/polyisoprene, and polystyrene/ styrene-butadiene block copolymer, where gradients extracted from plots analogous to Figure 3 were reported as 0.32 ( 0.05, 0.26 ( 0.03, and 0.26 ( 0.03, respectively.13 These were considered to be in reasonable agreement with the expected value of 0.33. It has become customary in investigations of the present kind to display data on a log-log plot and obtain power law exponents from the gradient or simply to compare data with inserted lines of a defined gradient as has been done thus far.5,6,13-15 However, it has recently been suggested that, at least while the system is coarsening, the data should be more accurately described by D3 ) D03 + K(t - t0), where D0 is the length scale at the end of the early stage time period, t0, and K is the volume growth rate.16 Initially, D versus t data obtained from turbidity-derived results over 10-60 min [shown in Figure 3 (b)] were fitted directly to D ) (Kt)b. The fit quality was reasonable (r2 ) 0.996), and the values of 1.66 ( 0.13 µm3 min-1 and 0.313 ( 0.06 were obtained for K and b, respectively. The closeness of the exponent to 1/3 is in clear agreement with the results shown Figure 3. However, if the same data are now fitted to the form discussed above, D ) [A + K(t t0)]b, the result obtained is quite different. The fit is slightly better (r2 ) 0.999), although the values of A and t0 cannot be extracted by the fitting to any degree of certainty owing to severe cross correlation in the model. Despite this, (13) Cavanaugh, T. J.; Nauman, B. E. J Polym. Sci., Polym. Phys. 1998, 36, 2191-2196. (14) Tran-Cong, Q.; Kawai, J.; Endoh, K. Chaos 1999, 9 (2), 298307. (15) Takeno, H.; Nakamura, E.; Hashimoto, T. J. Chem. Phys. 1999, 110 (7), 3612-3619. (16) Graham, P. D.; Barton, B. F.; McHugh, A. J. J. Polym. Sci., Polym. Phys. 1999, 37, 1461-1467.
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values of K and b are extracted with reasonable 95% confidence limits and are significantly different from those extracted from the previous fit, being 3.5 ( 0.5 µm3 min-1 and 0.271 ( 0.06, respectively. Attempts to fix either A or t0 allowed a reasonably ranged estimate of the other to be obtained, but in all cases the value of the exponent was essentially unchanged. Therefore, it can be seen that it is important when comparing analyzed data with models (which may be distinguished by slightly different values of the power law exponent) to bear in mind that using log-log plots to obtain gradients directly can give rise to different power laws compared with a direct analysis assuming a preliminary phase of separation. However, it is still clear that the results obtained by the turbidity method are in reasonable agreement with those obtained by similar studies of binary synthetic polymer systems, and with theoretical predictions. The two main mechanisms by which late time structural coarsening proceeds are coalescence and Ostwald ripening, both of which yield a power law growth with a predicted exponent of 1/3. Previously, attempts have been made to distinguish between these two mechanisms on the grounds of (i) predicted size distribution13 and (ii) rate.17 The former is a considerably more complex processing task and, hence, an attempt to apply the second method is used here. For a coalescence model, it is possible to obtain D3 ) (8kTν/ πµ)t, where ν is the volume fraction of droplets and µ is the system viscosity, while an Ostwald ripening mechanism should be described by D3 ) (64σDmcVm/9RT)t, where σ is the interfacial tension, Dm is the diffusion coefficient, in the continuous phase, of the biopolymer component that is rich in the included phase, c is the molar fraction of this biopolymer in the continuous phase, and Vm is the molar volume of the included phase. Although some of these parameters are difficult to obtain in practice and the equations are strictly derived for binary mixtures, the outcomes of these two scenarios can at least be estimated for the case reported here. A viscosity of approximately 0.02 kg m-1 s-1 has been obtained at 32 °C from a measurement carried out on the mixed system during cooling. (The measurement was carried out using parallel-plate geometry at a constant stress of 0.1 Pa.) Taking this value as an estimate of the continuous-phase viscosity and a phase volume ratio of 0.1, as previously discussed, the predicted growth rate according to a coalescence mechanism is about 3 µm3 min-1. The estimate based on an Ostwald ripening mechanism, on the other hand, is found to be at least 6 orders of magnitude lower than this. The experimental value obtained from a linear regression analysis of D3 as a function of t is, in fact, 1.21 ( 0.02 µm3 min-1. It can also be noted from the above that the simplistic and more involved nonlinear regression analyses carried out with the power law exponent as a fitting parameter yielded 1.66 ( 0.13 and 3.5 ( 0.5 µm3 min-1, respectively, although it must be remembered that, strictly, these data analyses do not adhere to the form of the rate predicting equations because an exponent of 1/3 is not extracted. It is, in any case, clear from the magnitude of the estimates presented that microstructural coarsening of these systems is dominated by coalescence. Figure 4 shows further results obtained from turbidity experiments carried out on the same system but quenched to a temperature of 35 °C. In general, the same power law type behavior is observed, as expected. (17) Matsuyama, H.; Teramoto, M.; Uesaka, T.; Goto, M.; Nakashio, F. J. Membr. Sci. 1999, 152, 227-234.
Droplet Growth in Gelatin/Maltodextrin Mixtures
Figure 4. Size evolution of included phase growth obtained by fitting turbidity spectra following the quenching of a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 35 °C.
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Figure 6. Size evolution of included phase growth obtained by fitting turbidity spectra following the quenching of a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 20 °C.
Figure 5. Size evolution of included phase growth obtained by fitting turbidity spectra following the quenching of a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 25 °C.
(ii) Systems That Would Phase Separate above T0 Quenched Directly to Temperatures below. Figure 5 shows results obtained from quenching a 4.5% LH1/2.25% SA2/ 0.1 M salt system from 60 to 25 °C. It is clear that the size evolution now shows some distinctly different features from that determined in quench route i, in particular the eventual cessation of growth. It seems clear that, as has been reported before,5,6 quenches of this type show modified kinetics, owing primarily to growth restrictions imposed by the viscosifying continuous phase. In cases such as these, the constantly evolving character of the ordering gelatin component continually shifts the thermodynamic goalposts. Under conditions of time-dependent free energy minima, it is difficult to perform any sort of analysis as was pursued in i. Indeed, it is not trivial even to divide the evolution into periods in which phase separation or coarsening processes dominate. We concentrate instead on comparing inclusion sizes obtained via turbidity measurements with microscopy, discussing the implications of the continued applicability of the turbidity method, and commenting on the effect of the varying quench temperature. Figure 6 shows results obtained from quenching a 4.5% LH1/2.25% SA2/0.1 M salt system from 60 to 20 °C. In this case a confocal micrograph was obtained 30 min after the quench for comparison with the size estimate extracted from the turbidity method. The micrograph is shown in Figure 7, and it can clearly be seen that 5 µm is indeed
Figure 7. Confocal micrograph obtained 30 min after quenching a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 20 °C. The scale-bar represents 10 µm.
a very reasonable estimate for the size of the included regions. This point is of particular interest because it is also clear that although the included phase volume has increased slightly compared to the same system at 32 °C (and with it the likelihood of interparticle correlation being important) the fitting routine derived from the simple scattering form for isolated spheres still gives good size estimates. Often in turbid systems multiple scattering can occur and bedevil the useful analysis of light scattering data. Although, in principle, such multiple scattering does not affect the total amount scattered over all angles, it should be noted that the existence of a finite acceptance angle in a turbidity measuring instrument means that the possible consequences of multiple scattering should not be dismissed out of hand. It is worth reiterating then that the agreement of the experimental droplet growth kinetics with expected power law exponents, together with the reasonable agreement of extracted sizes with microscopy, is strong evidence for the usefulness of the turbidity technique and suggests that, at least for the systems
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Figure 8. Size evolution of included phase growth obtained by fitting turbidity spectra following the quenching of a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 10 °C.
Figure 9. Confocal micrograph obtained 15 min after quenching a 4.5% LH/2.25% SA2/0.1 M salt system from 60 to 10 °C. The scale-bar represents 10 µm.
discussed thus far, the complication of multiple scattering is unimportant. Figure 8 shows results obtained from quenching a 4.5% LH1/2.25% SA2/0.1 M salt system from 60 to 10 °C. A confocal micrograph was also obtained for comparison with the size estimate extracted from the turbidity method, this time 15 min after the quench. As can be seen from the figure, the average size of the included phase regions is predicted from the turbidity method to be about 3.5 µm after 15 min. (The slight apparent decrease in size that is observed with time is consistent with data obtained in temperature-ramped studies and is discussed further in the following section.) The appropriate micrograph is shown in Figure 9, and it can be seen that once again the value derived from the turbidity spectra is in good agreement with the CLSM data. This is of particular significance with respect to the continued applicability of the turbidity method. It is clear here that the included phase volume ratio has increased significantly compared to the previous examples. Following a cursory glance at Figure 9, it is not immediately obvious that the calculation
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Figure 10. Comparison of included phase growth, obtained by fitting turbidity spectra, following quenches of a 4.5% LH/ 2.25% SA2/0.1 M salt system from 60 °C to T (indicated in the figure).
of the wavelength dependence of the turbidity of such a sample can be adequately carried out by considering the scattering from isolated spheres. Nevertheless, the fitting routine used here appears to work reasonably well and is based on just such an assumption. In this context it is interesting to consider how the total scattering function appropriate for a system of this kind is comprised from form and structure factors relating to intra- and interparticle correlations, respectively. Scattering profiles have recently been simulated for model systems with similar morphologies to those of interest here.18 When a simulation is selected from ref 18 that looks somewhat like the micrograph presented in Figure 9, the calculated scattering profile for a system with two phases of uniform refractive index (that is, a sharp boundary) shows that for all q values greater than about 1 µm-1 scattering is still dominated by that from single spheres. This q vector corresponds (at 700 nm) to a scattering angle of approximately 7°, and because the turbidity method described here takes no account of light scattered by less than 3° (owing to the spectrophotometer acceptance angle), this perhaps offers some form of explanation of the method still remaining useful in such cases. Further work involving the direct measurement of SALS profiles is currently being carried out in order to test this hypothesis and explain the apparent continued applicability of the turbidity method. Figure 10 shows a comparison of the kinetics results obtained from the 4.5% LH1/2.25% SA2/0.1M salt system following quenches to end temperatures of 35, 32, 25, 20, and 10 °C and forms a summary of the results presented thus far. The quenches to 35 and 32 °C do not involve gelatin ordering, or network formation, and proceed largely with a power law dependence, characteristic of coalescence. The quench to 25 °C shows accelerated initial kinetics, likely owing to both temperature and ordering effects, followed by a gradual restriction of the growth caused by the viscosifying of the continuous phase. In a similar vein the kinetics of separation following the quench to 20 °C also show accelerated kinetics of initial growth but now coupled with subsequent fast kinetic trapping of the structure, owing to rapid network formation. The quench to 10 °C again results in fast demixing, but the network formation now starts to dominate and traps the structure at an earlier stage, producing smaller inclusions. (18) Elicabe, G. E.; Larrondo, H. A.; Williams, R. J. J. Macromolecules 1998, 31, 8173-8182.
Droplet Growth in Gelatin/Maltodextrin Mixtures
Figure 11. Size evolution of included phase growth obtained by fitting turbidity spectra following the quenching of a 4.5% LH/0.5% SA2/0.1 M salt system from 60 to 25 and 30 °C.
(iii) Systems That Only Phase Separate at Temperatures below T0. Figure 11 shows results obtained from quenching a 4.5% LH1/0.5% SA2/0.1 M salt system from 60 to 30 and 25 °C. (The initial size of around 400 nm is typical of that found from a similar treatment of the spectra obtained from SA2 solutions and forms a natural baseline. This size value, however, should not be taken as a measurement of the true size of the scattering entities because they are unlikely to display a spherical form factor.) In stark contrast to previous results reported herein, it can clearly be seen that a phase separation event is observed to occur after holding the sample isothermally in the one-phase region for a significant amount of time. It is proposed that this event is triggered by the ordering of gelatin modifying the system thermodynamics in such a way as to induce incompatibility. In keeping with this hypothesis, that such separation events are driven by ordering of the gelatin component, it is clear that the system held at 30 °C shows a significantly longer time delay than that at 25 °C resulting from slower ordering kinetics at elevated temperatures. Further investigation of this hypothesis is reported in a further paper.19 It is interesting to see that once the phase separation event is initiated in this system the kinetics of included phase growth appear to follow a power law with an exponent of close to 1/3. Fitting the data in a fashion similar to that described previously but taking t ) 0 to be the initiation of the phase separation event (and ignoring the initial decrease that is at present unexplained in detail but is thought to relate to the modification of the baseline scattering form by the initial phase separation) gives the following results: a linear regression analysis of D3 vs t data obtained at 30 and 25 °C gives growth rates of 0.085 ( 0.002 µm3 min-1 (r2 ) 0.989) and 0.091 ( 0.003 µm3 min-1 (r2 ) 0.993), respectively. The fact that this rate is some 15 times slower than that at temperatures just above ordering (32 °C) is not surprising owing to the substantially higher viscosity of the continuous phase at temperatures below T0. However, in light of the difficulties inherent in the analysis of such continually evolving systems, it is perhaps puzzling to observe the same power law dependence over a substantial period. The gelatin ordering does not stop simply because phase separation is invoked, and indeed it may be expected to speed up if phase concentration occurs. (19) Lore´n, N.; Hermansson, A. M.; Williams, M. A. K.; Lundin, L.; Foster, T. J.; Hubbard, C. D.; Clark, A. H.; Norton, I. T.; Bergstrom, E. T.; Goodall, D. M. Macromolecules 2001, 34, 289-297.
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Figure 12. Turbidity values measured at 800 nm following quenches of the 4.5% LH/2.25% SA2/0.1 M salt system from 60 °C to T (indicated in the figure).
In any case, systems that exhibit delayed phase separation can be seen to offer an unparalleled opportunity for the study of phase-separating biopolymer mixtures without any problems associated with finite temperature quench effects. Further work, in addition to that already described, will involve CLSM and SALS studies in order to elucidate the initial mechanism of delayed phase separation. Magnitude of Turbidity. Figure 12 shows the magnitudes of the turbidity measured at 800 nm for the 4.5% LH/2.25% SA2/0.1 M salt systems described previously (the corresponding spectra were fitted to produce the kinetic data). The data resulting from a quench to 32 °C show a slow decrease with time that is consistent with sedimentation and the observation of the eventual formation of two bulk phase-separated macroscopic layers. However, it can clearly be seen that following the quenches to 20 and 10 °C the turbidity shows distinctly different substantial decreases with time. This is consistent with the reductions obtained in thermal ramping experiments.1 There is also an apparent simultaneous reduction of size, and again this behavior has also been observed in the reported temperature ramping study of this system. At present, the best explanation of this phenomenon is as described previously.1 That is, the gelatin gelation alters the thermodynamics of the system in such a way that the “current tie-line” applicable to the unordered system is rotated so as to reduce the refractive index contrast and hence the turbidity. The apparent decreases in the droplet diameter are most likely explained by the continued growth of new particles owing to a constantly evolving miscibility criteria, which in turn leads to a reduction in the weighted average size. The two events appear heavily correlated, because both are dependent upon the ordering process of gelatin. Conclusions Results obtained regarding the rates of droplet growth for systems that phase separate without the involvement of ordering are in good agreement with those obtained by similar studies in binary synthetic polymer systems and with theoretical predictions. Coalescence is the major mechanism of structural coarsening. For systems that are capable of phase separation above T0 but that are quenched directly to temperatures below this value, phase separation shows modified kinetics owing primarily to growth restrictions imposed by the viscosifying continuous phase. It is also likely that the ordering provides an additional driving force for demixing.
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For a more intrinsically compatible system that only phase separates below T0, significant delay periods have been observed before the initiation of demixing. It is suggested that these delays are required for the development of a certain degree of gelatin order, which drives immiscibility. Acknowledgment. This study has been carried out with financial support from the Commission of the
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European Communities, Agriculture and Fisheries (FAIR) specific RTD program, CT 96 1015, “Mixed Biopolymerss Mechanism and Application of Phase Separation”. It does not necessarily reflect its views and in no way anticipates the Commission’s future policy in the area. The authors thank P. Aymard for performing the viscosity measurement. LA001811J
