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Mechanism and Kinetics of Phase Separation in a Gelatin/ Maltodextrin Mixture Studied by Small-Angle Light Scattering Michael F. Butler* Unilever Research, Colworth House, Sharnbrook, Bedfordshire, MK44 1LQ, United Kingdom Received January 3, 2002; Revised Manuscript Received April 24, 2002

Phase separation mechanisms and kinetics were studied using small-angle light scattering in a gelatin/ maltodextrin system where phase separation could be studied in both liquid and gelled states. Nucleation and growth or spinodal decomposition occurred, depending on the quench depth. The transition between the two mechanisms occurred relatively sharply. The different mechanisms were distinguishable by the different behavior of the scattering function even though a peak was observed in both cases. Particular differences were the different evolution of the peak intensity and position, the absence of dynamic scaling of the nucleation and growth scattering function, and the final coarsening exponent of 1/3 that was measured when spinodal decomposition occurred but not for nucleation and growth. Gelation severely reduced the coarsening rate and initially placed the phase compositions far from their equilibrium values. Despite the loss of molecular mobility caused by gelation, the gelled systems did continue to evolve, albeit much more slowly than in the liquid case. Multiple coarsening rates were observed for some of the gelled samples, which were ascribed to the gradual movement of these systems toward the equilibrium compositions. Introduction The mixing of different polymers or polymer solutions is often accompanied by the phenomenon of phase separation. This phenomenon has attracted much interest, not least because of its practical implications for the material properties of the resulting two-phase mixture. Knowledge of the factors affecting the mechanical properties, for example, is essential for structural materials made from synthetic polymer mixtures. Likewise, in the food industry, the mechanical properties of biopolymer mixtures can play a significant role in determining the product texture and quality. It is generally accepted that there are two mechanisms of phase separation, depending on where the system is quenched to in the phase diagram, which can result in materials with quite different morphologies.1 Quenches near the binodal, into the metastable region of the phase diagram (see Figure 1, which may be regarded as the relevant cut through the three-dimensional phase diagram for the current system), result in the nucleation and growth (NG) mechanism, characterized by a random array of droplets. Deeper quenches result in a mechanism known as spinodal decomposition (SD), which can possess a bicontinuous or a droplet morphology containing a characteristic length-scale.1 Both mechanisms have been observed in a variety of different binary and ternary polymer systems. There have been very few systematic studies, however, of both mechanisms in one system, at one composition, quenched to different temperatures. In the few examples where the different mechanisms were identified in mixtures of the same materials, changing the composition of the mixture induced them (for example, * E-mail: [email protected]. Tel: +44 (0)1234 22 2958. Fax: +44 (0)1234 22 2757.

Figure 1. Schematic temperature-composition phase diagram for a two-phase system with an upper critical solution temperature, indicating a quench (arrowed) from the one-phase region into the unstable region, where spinodal decomposition is the mechanism of phase separation. Nucleation and growth is the active mechanism for smaller quenches into the metastable region.

by studying a critical mixture to examine SD and a highly off-critical mixture to study NG2,3). When a transition from metastability to instability was measured in a binary oligomer system, however, it was found to be fairly diffuse.4 Nucleation and growth is distinguished from spinodal decomposition by the different development of the concentration fluctuations into the biphasic morphology. Near the binodal, where nucleation and growth occurs, the system is stable to small concentration fluctuations that decay unless they exceed a certain, critical, size. Once a critical nucleus with the final composition is formed, however, it remains stable and begins to coarsen immediately. For deeper quenches, below the spinodal, the free energy of the system is always lowered for a certain range of concentration fluctuation wavelengths. One particular wavelength leads to

10.1021/bm025501m CCC: $22.00 © 2002 American Chemical Society Published on Web 05/18/2002

Phase Separation Mechanisms and Kinetics

the greatest decrease in free energy and therefore grows fastest, leading to the expression of a characteristic lengthscale in the structure. During the early stages of spinodal decomposition the difference in composition between the two phase separated regions continues to grow and the interface between the phases sharpens, but the size of the regions remains the same. This early stage does not last for very long, however, and the structure can begin to coarsen before the phases have reached their equilibrium concentrations. In the liquid state, coarsening of the structures formed via NG and SD can occur via interfacial and bulk diffusion of the components, droplet coalescence due to Brownian motion, and, in some cases, surface-tension-driven hydrodynamic flow. For the diffusive mechanism, various theoretical5,6 and numerical7-14 calculations predict an eventual coarsening exponent of R ) 1/3 in the power law R(t) ∼ tR that describes the growth of the characteristic length-scale, R(t), with time. Smaller coarsening exponents, most commonly taking the value of 1/4, have been predicted in a preasymptotic regime8,11-13,16 and in the case where the interfacial width is so large that the interface introduces an extra length-scale into the system.8,11,14,16,17 When the droplet size is approximately equal to the droplet separation, a coarsening exponent of 1/3 is predicted for the droplet coalescence mechanism.18 When the separation is larger than the droplet size, however, the exponent becomes lower because of the lower collision frequency.4,18,19 An exponent of 1 is predicted for the hydrodynamic coarsening mechanism20 where convective flow is coupled with droplet motion to accelarate the rate of coarsening. Experimentally, 1/3 and 1 are the most commonly observed values in SD systems. The lowest values (∼1/10) in liquid systems, however, have been observed in NG systems where the droplets are widely spaced and collisions are rare.4 When gelation of one or both of the components occurs, the phase separation kinetics are complicated by those of gelation, which make the effective quench depth a function of time as well as temperature.2 As well as introducing an elastic energy term into the free energy of the system, gelation is also associated with changes in molecular weight and molecular weight distribution (hence entropy of mixing). In addition, gelation of gelatin is accompanied by a coilhelix conformational change that alters the interaction parameter, which has been shown to enhance the phase separation kinetics in gelatin/maltodextrin systems.21,22 Gelation of the continuous phase prevents droplet coalescence and hydrodynamic coarsening and hinders diffusion by reducing the mobility of the components. As predicted by theories that account for the kinetics of cross-link formation21-26,30-32 in the free energy of mixing, and shown by experiments in systems containing gelatin2,26-29 and other polymers,33 gelation severely reduces coarsening of the microstructure. The coarsening exponent is much lower than the values predicted and observed in liquid systems. Under certain conditions, complete cessation of coarsening (“pinning”) has been predicted23,24,32 and experimentally observed in the gelatin/methanol system.26 The aim of the work presented in this paper was to probe the phase separation mechanism and kinetics in a ternary

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polymer system in a systematic manner by quenching the mixture to temperatures in both the metastable and unstable region of the phase diagram. It was of particular interest to compare the scattering function that was obtained via the NG and SD mechanisms and to compare the width of the transition from metastability to instability with results obtained in a binary oligomer system.4 Because the binodal temperature was above the gelation temperature of the gelatin component, the coarsening kinetics of gelled mixtures could be compared with those of liquid ones. Experimental Technique Materials and Sample Preparation. The gelatin was a limetreated gelatin (LH1e) supplied by SKW. Using size-exclusion chromatography (SEC) coupled with light scattering the weight and number average molecular weights were found to be Mw 146000 and Mn 83300. The maltodextrin was a DE2 grade (SA2) supplied by Avebe. SEC measurements revealed a broad molecular weight distribution, although the DE value allows an estimate of 9000 g‚mol-1 to be made for the value of Mn. Moisture contents of 12.4% and 10.0% for gelatin and maltodextrin respectively were taken into account when making solutions. To prevent biological degradation, all solutions were used only on the day that they were made. Care was taken throughout sample preparation to prevent dehydration. Solutions were prepared as follows: Maltodextrin powder was first dispersed in cold water and then mildly stirred at 95 °C for 30 min to form a solution. Gelatin solutions were prepared similarly, but were not heated above 60 °C to prevent any thermal degradation. Before heating, sodium chloride was added to the gelatin solution to increase the total ionic strength of the final mixed solution to 0.1 M (this figure includes the ionic contributions from the maltodextrin and the gelatin). After 30 min at 95 °C the maltodextrin was cooled to 60 °C for 5 min and then mixed with the gelatin solution, to form a final mixture containing 4.5 wt % gelatin and 2.25 wt % maltodextrin. The mix was then kept at 60 °C and stirred continuously. Small-Angle Light Scattering. Samples for study by small-angle light scattering (SALS) were made by placing a drop of the mixed solution onto a glass coverslip (thickness 0.17 mm, diameter 22 mm) in the center of a 100 µm stainless steel spacer which was heated to 65 °C on a Linkam THMS600 microscope stage. Another, identical, glass coverslip was placed on top of the sample to ensure that it was a constant thickness of 100 µm. The details of the SALS apparatus and data acquisition system have been reported previously.34 Scattering patterns were obtained every 30 s to investigate the mechanism and kinetics of phase separation. Data collection began at the start of the temperature profile, beginning with an isotherm at 65 °C for 5 min followed by a rapid quench, at 60 °C/min to the quench temperature. Quench temperatures were chosen in 2 °C steps from 12 to 48 °C. The sample was maintained at the quench temperature for 95 min. The scattering patterns collected during the first 5 min at 65 °C were averaged, and this average was subtracted from the subsequently collected scattering patterns. The two-dimensional scattering patterns were radially averaged to produce plots of intensity (I) versus scattering vector (q ) 4π/λ sin(θ/2), where λ is the wavelength of the incident light and θ is the scattering angle), known as the scattering function. Calibration of the scattering vector was performed using the scattering pattern (Airy function) from a 25 µm diameter pinhole. Analysis of the Scattering Function. The shape of the scattering function was used to qualitatively determine the phase separation

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mechanism. When a peak was present in the scattering function, the time dependence of the peak height, Im(t), and peak position, qm(t), was analyzed. The peak position was fitted with a function of the form qm(t) ∝ t-R to obtain the coarsening exponent, R, which was compared with theoretical values. Since it is predicted that the late stages of growth will be characterized by self-similarity of the structure (dynamic scaling),35,36 the scaled structure function was constructed from the measured scattering functions. The scaled structure function, F(q/qm,t), is given by

F(q/qm,t) ∝ qm3I(q/qm,t) where I(q,t) is the measured scattering function. From this relation, it follows that the quantity Imqm3/S2(t), where S2(t) ) ∫∞0 I(q,t)q2 dq, should be constant when dynamic scaling is operative. Testing for the constancy of this quantity can therefore be used to assess whether dynamic scaling is operative.

Results Scattering Function. A peak was observed in the scattering function at a nonzero scattering vector (qm) in all of the samples at some time during phase separation with the exception of the sample quenched to 46 °C, for which the scattered intensity was a monotonically decreasing function of the scattering vector. Below 38 °C, shown in parts a and b of Figure 2 for samples quenched to 16 °C (gel) and 36 °C (liquid), respectively, the peak moved toward lower scattering vectors from the onset of phase separation. Above 38 °C, shown in Figure 2c for the sample quenched to 42 °C as an example, the scattered intensity was initially a monotonically decreasing function of the scattering vector (inset graph), but as the overall scattered intensity increased, a peak developed at a nonzero scattering vector. The position of this maximum initially moved to higher scattering vector before moving back toward lower ones. At 44 °C, the scattered intensity was a monotonically decreasing function of the scattering vector at all times. The scattering vector at which the peak was initially located moved toward lower values as the quench depth was increased. The breadth of the peak, however, increased as the quench depth increased. The inset curves in parts a and b of Figure 2 show the scattering function plotted against double logarithmic axes (known as Porod plots) at selected times, as examples for a gelled and a liquid system. The amplitude of the scattering function was proportional to q2 in the low q limit (q , qm) and proportional to q-4 in the high q limit (q . qm) from the start of phase separation for the liquid samples and at later times for the gelled samples. In the earlier stages of coarsening of the gelled samples there were small, but significant, deviations from the theoretical asymptotic gradients. In all cases the intercept of the slope with the ordinate made by the q-4 limiting curve increased during coarsening. Peak Height. Figure 3a shows the evolution of the peak maximum for the samples in which the gelatin gelled. A rapid increase in peak height was followed by a gradual decay, the degree of which became more extensive with increasing quench depth. The time taken to reach the maximum value of the peak height decreased with increasing quench depth. Figure 3b shows the evolution of the peak maximum for the

Figure 2. Scattering functions for quenches to different temperatures: (a) 16 °C (gel); (b) 36 °C (liquid); (c) 42 °C (liquid). The inset curves in (a) and (b) are Porod plots, with the asymptotic gradients of 2 and -4 expected from a system containing sharp interfaces superimposed for comparison with the data. The inset curve in (c) shows the scattering function in the early stages of coarsening before the peak appeared.

samples in which the system remained liquid during phase separation. At temperatures below 38 °C a behavior similar to that observed in the gelled samples was seen, although any decrease in value with time after the initial rapid rise was much less marked. Above 38 °C, however, the plot exhibited a sigmoidal profile, with the bend in the curve systematically moving to shorter times as the quench depth increased. Peak Position. The coarsening kinetics were monitored by plotting the time evolution of the scattering function peak position (qm) and were highly dependent upon the quench temperature. Power law coarsening kinetics were observed in all samples, although the number of power laws that were observed over the time range studied varied systematically with quench depth. The variation of qm with time is shown in Figure 4a for the gelled samples and in Figure 4b for the samples that remained liquid. The different coarsening exponents that were measured in the various regimes are shown in Figure 5. Quenches to temperatures between 12 and 20 °C obeyed single power law behavior (shown in Figure 4a for quenches to 16 and 20 °C as examples). The coarsening exponent decreased with increasing quench depth. At 22 °C two power laws were observed, and between 24



Figure 3. Evolution of the peak height with time for (a) gelled samples, (b) liquid samples, showing a transition in behavior between 36 and 38 °C.

and 30 °C four power laws were observed over the time range studied (shown in Figure 4a for quenches to 24 and 30 °C as examples). There was an initial, fast, coarsening regime (marked I in Figure 4a) that gave way to a slower period of coarsening (marked II in Figure 4a) after about 100 s. However, for quenches between 24 and 30 °C, after approximately 500 s the coarsening rate became faster again (marked III in Figure 4a) before a final, slow, coarsening regime (marked IV in Figure 4a) was reached. Regime IV was reached at earlier times and possessed a smaller coarsening exponent, for deeper quenches. Between 30 and 38 °C two power laws were observed (shown in Figure 4b for quenches to 32 and 36 °C). The first regime was the slowest. The second coarsening regime was reached after about 3000 s and possessed a coarsening exponent of 1/3. Between 38 and 44 °C qm initially moved to high scattering vectors before coarsening of the microstructure commenced (shown in Figure 4b for quenches to 38 and 42 °C). The duration of the initial shift of qm to higher values became shorter and the power law exponent measured in the coarsening stage decreased as the quench depth increased. The rate of coarsening was lower for quenches above 38 °C than for quenches in the liquid state below 38 °C. No coarsening was observed at all for the sample quenched to 44 °C. Dynamic Scaling. Parts a-d of Figure 6 show the scaled scattering function at different times in the late stages of coarsening for quenches to 16 °C (gel, single coarsening exponent), 24 °C (gel, multiple coarsening exponents), 36 °C (liquid), and 42 °C (liquid), respectively. The parameter Imqm3/S(t), which should be constant if dynamic scaling is obeyed, is plotted in Figure 7. Dynamic scaling did not occur

Figure 4. Evolution of the peak position with time for (a) gelled samples, showing multiple coarsening regimes for quenches to temperatures between 24 and 30 °C and (b) liquid samples, showing a transition in behavior between 36 and 38 °C.

Figure 5. Coarsening exponents measured for all of the samples. The horizontal solid line indicates the theoretical value of 1/3, expected from droplet coalescence and diffusion of the components. In the samples where more than one coarsening exponent was measured, the different exponents are labeled regime I to IV, in the order in which they appeared.

for any of the samples in the early stages of coarsening, since the scaled structure functions did not form a master curve and the parameter Imqm3/S(t) did not reach a constant value and was not attained at any stage of coarsening for any of the samples that remained liquid. For the gelled samples, however, dynamic scaling did occur in the late stages of coarsening. In the samples that exhibited four coarsening

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Figure 7. Plot of the scaled maximum intensity to test for the occurrence of dynamic scaling for samples quenched to a range of temperatures.

Figure 6. Scaled structure functions for quenches to different temperatures: (a) 16 °C (gel, one coarsening regime); (b) 24 °C (gel, four coarsening regimes); (c) 36 °C (liquid); (d) 42 °C (liquid).

regimes (i.e., quenches between 24 and 30 °C), dynamic scaling occurred in the final slowest regime. Discussion Phase Separation Mechanism. The spinodal mechanism is expected to give a peak in the scattering function at

nonzero scattering vectors that initially remains at a constant position and then moves toward lower scattering vectors as the structure coarsens.1,37-40 As this behavior was observed for all quenches below 38 °C, it is concluded that spinodal decomposition was the phase separation mechanism in this temperature range. Above 38 °C, up to the binodal temperature, the initial monotonic decrease in intensity of the scattering function with scattering vector, which is expected from a low volume fraction of spatially uncorrelated polydisperse spheres,41 shows that nucleation and growth was the phase separation mechanism in that temperature range. That a peak developed at a nonzero scattering vector in the latter case supports previous numerical and experimental findings of a peak in the scattering function caused by the NG mechanism.3,4,42-47 However, the present results show that the NG peak can be distinguished from the SD peak by its different behavior. The three main differences are the different profile of the evolution of the peak height with time, the initial movement of the NG peak to higher scattering vectors, and the lower coarsening exponents from the NG peak. The presence of a peak in NG colloidal and polymer systems above a certain droplet volume fraction has been explained by the presence of a depletion layer around the droplets3,41-46 that causes further nucleation to occur in preferred regions. When the droplet volume fraction is high enough, this effect leads to a correlated morphology.4,41-43,47 The development of a correlated morphology in the NG samples once a certain droplet volume fraction has been attained accounts for the experimental observation of the development of the peak in the scattering pattern at some time after the first droplets have nucleated. The scattered intensity is proportional to the size and number of the scattering objects and the density difference between them and the surrounding medium. Since the composition of the phases is fixed at the time of nucleation, the gradual increase of the scattered intensity for the NG samples results from the increasing number of scattering objects in the system as nucleation continues. The decreasing spacing between the increasing number of droplets therefore accounts for the initial movement of the peak in the scattering function to higher scattering vectors.41-43 In contrast, the peak height evolves differently for the SD samples because in this case the number of scattering objects is fixed at the start of phase separation but the phase compositions rapidly change,


although the absence of dynamic scaling in the system precludes a straightforward analysis of the values. Moreover, because the SD structure can only coarsen, the peak in the SD samples can only move toward lower scattering vectors, as observed. The width of the transition from metastability to instability was significantly sharper than the transition observed in the binary oligomer system previously reported.4 In that system, the transition occurred over a range of about 20 °C and was attributed to the expected behavior of a short-range force system. In a mean-field system, however, a sharp transition is predicted.4 The sharp transition that was observed in the gelatin/maltodextrin system therefore indicates that this system is described more accurately by mean-field critical behavior, as expected from a concentrated polymer solution. Scattering Function. The scattering functions for the SD samples possessed the form predicted by Furukawa35,36 for a droplet structure with a negligible interfacial width formed from an off-critical quench I(q) ∼

(1 + γ/2)q2 γ/2 + qγ

where γ ) d + 1, with d being the dimensionality of the system (3 in the present case because the droplet size was much smaller than the sample dimensions). The interface between the phases was sharp, as shown by the gradients of +2 and -4 in the Porod plots for the low- and high-scattering vector asymptotes, respectively,35,36 for the liquid samples, and in the later stages of coarsening of the gelled samples. The deviations from the predicted asymptotic gradients in the earlier stages of coarsening of the gelled samples were probably because the interfacial width was not negligibly small compared to the droplet size in those samples. It is expected that the retardation of the phase separation kinetics caused by gelation will prevent the initially diffuse interface that is always formed in the early stages of spinodal decomposition from becoming sharp as rapidly as in the liquid systems. The significance of the gradual decrease in the intercept of the high-scattering vector asymptotic gradient with the ordinate in the Porod plots is shown by the equation that predicts the form of the scattering function at large scattering vectors (q . qm) ln(Iasympt(q,t)) ∼ ln

( )

A(t) - 4 ln(q) V

where A(t) is the surface area of the interfacial region in the volume, V, of the region that is irradiated by the incident beam. A decreasing intercept therefore indicates a decreasing interfacial area, as expected from a mechanism of droplet coarsening via coalescence or diffusion of the components. The occurrence of dynamic scaling of the scattering function in the final stage of coarsening in the gelled SD samples agrees with numerical simulations of phase separation that show dynamic scaling in the asymptotic coarsening regime in systems that coarsen by the diffusive mechanism,11 where the structure evolution can be described by a simple scaling law R(t) ∼ tR. The absence of dynamic scaling in the early stages can be explained by the finite time taken


for the phases to reach their equilibrium compositions, which is expected to prevent scaling even when the interfaces are sharp,18 as well as the presence of a second length-scale caused by sufficiently diffuse interfaces in the gelled samples. Evidence that a gradual movement toward the equilibrium compositions occurred was provided by the tendency of the peak height (which is directly related to the composition difference between the phases for the SD samples) toward a constant value at the late stages of the current experiments. The reason for the absence of dynamic scaling in the final coarsening regime for the liquid samples, where it has been observed in similar systems,2,34 is uncertain. Convective effects, which can occur in liquid but not gelled samples, lead to departures from scaling.2,34 Although convection was not seen to significantly affect the coarsening kinetics over the time period studied, possibly a small amount occurred that was sufficient to prevent the structure from evolving in a self-similar manner. Another possibility may be that the sample was simply left for an insufficient time to reach the asymptotic scaling regime. The absence of dynamic scaling in the liquid NG samples is unsurprising. Scaling of the scattering function in the NG samples did not occur because the nucleation of new droplets caused continuous changes in the length-scale of the morphology, and the system did not obey the R(t) ∼ tR scaling relationship. Coarsening Kinetics of the Liquid Systems. Previous work on the gelatin/maltodextrin system21,22,34 has shown that droplet coalescence is the dominant coarsening mechanism when the system remains liquid. This mechanism explains the slow initial coarsening rates that reach an asymptotic value of -1/3 in the SD samples. Initially the droplet separation was sufficiently larger than the droplet size for droplet collisions to be relatively infrequent, and therefore coarsening rates to be fairly low.4 This idea is supported by the observation of higher initial coarsening rates and a more rapid transition to the final coarsening exponent of -1/3 in the samples with a smaller initial droplet separation (i.e., those quenched to lower temperatures in the liquid region). Later, once the droplets had grown so that their size and separation were approximately equal, the conditions were met for the coarsening exponent of -1/3 to be seen. It should be noted that a phenomenon termed the moving droplet phase,18 in which droplets collide but do not coalesce, could also explain low coarsening exponents. However, since it is believed that the continuous phase must be a simple fluid for this phenomenon to occur, it can probably be discounted in the current study. The coalescence mechanism combined with the occurrence of nucleation can account for the lower coarsening exponents observed in the NG samples. Since the droplets in the NG samples were spaced further apart than in the SD samples (shown by the initial position of the peak in the scattering vector being at lower scattering angles for the NG samples) the coalescence rates will be correspondingly lower. Continued nucleation, which moves the peak to higher scattering vectors, at the same time as coalescence would also give a smaller apparent coarsening exponent in the NG samples. Coarsening Kinetics of the Gelled Systems. Coarsening in the gelled sample is believed to occur via a diffusive

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mechanism, since gelation of the continuous phase prevents motion of the droplets so that they cannot coalesce. The much lower coarsening exponents that were measured than were expected from a freely diffusing system (1/3 for bulk diffusion) were due to the continuing increase in molecular weight of the gelatin component during gelation which severely hindered bulk diffusion.2,23-32 The low coarsening exponents that were measured can be qualitatively explained by a model in which surface tension (which drives coarsening in the liquid samples) is canceled out by the elastic force due to gelation.25 This model predicts very low coarsening exponents that are related to the crosslink density in the gel by an equation of the form R ) 1/3 Aν, where A is a numerical constant and ν is the cross-link density. Higher cross-link densities, formed by deeper quenches, cause lower coarsening exponents, as observed, since they hinder diffusion to a greater extent. The competition between gelation and phase separation is revealed by the greater number of coarsening regimes in the samples quenched to temperatures between 22 and 30 °C. Below 22 °C the gelation kinetics are so rapid that the coarsening rate is very low from the start of the experiment. Above this temperature, however, the gelation kinetics are sufficiently slow that a period of more rapid coarsening can occur before the cross-link density becomes sufficiently high to dramatically slow the coarsening rate. Complete pinning of the microstructure, as predicted under certain conditions by another model23-26 and observed in the gelling gelatin/ methanol and hydroxypropylmethylcellulose systems, was most probably not obtained either because the mathematical conditions for pinning to occur were not met or because of the high polydispersity of the current system. Low molecular weight material that was unaffected by the gelation process can still diffuse and enables coarsening to continue. Indeed, transmission electron microscopy has provided evidence that smaller maltodextrin inclusions are able to diffuse through a gelatin matrix even when gelation has occurred.28 The presence of a period of slow coarsening followed by a regime of faster coarsening, as observed for the shallower quenches in the gelled samples, has been observed in numerical simulations of phase separation in gelled systems for shallower quenches and after long times.24,30 This behavior was termed a “depinning” transition and was explained to be a consequence of the gradual movement of the system toward its equilibrium state, which was not attained in the early stages of phase separation, by redidual diffusion. As discussed earlier, the experimental evidence showed that the gelled systems did not reach their equilibrium compositions rapidly and did continue to coarsen, implying that there was some residual diffusion in these systems. The transition to the final, slower, regime probably occurred once gelation had reduced the mobility to such an extent that the faster coarsening could no longer be sustained. Conclusions Phase separation was observed in the metastable and unstable regions of the phase diagram by systematically quenching the gelatin/maltodextrin system, at a fixed com-

Butler

position, to different temperatures. Nucleation and growth occurred in the metastable region. The scattering function from this mechanism was identified by an initial monotonic decrease in intensity with scattering vector that subsequently developed a peak that moved to higher scattering vectors with time. Because of the gradual nucleation of new droplets, self-similarity of nucleation and growth structures with time was not observed. Spinodal decomposition occurred in the unstable region and was identified by a scattering function that possessed a peak that always moved to lower scattering vectors with time. The transition from metastability to instability was relatively sharp, as expected from a system displaying mean-field critical behavior. Self-similarity of spinodal structures was observed in the late stages of coarsening of the gelled samples but not in the liquid samples. This difference was possibly due to the different coarsening mechanisms in the gelled and liquid states (bulk diffusion of the components in the former case and droplet coalescence in the latter). In all cases, dynamic scaling did not occur in the early stages of coarsening because the phases had not attained their equilibrium compositions, shown by a gradual change in the peak height toward an asymptotic limit. In the early stages of coarsening of the gelled samples, the interface was sufficiently diffuse to cause deviations from Porods law. In the later stages for the gelled samples, and all times for the liquid samples, the interfacial width was negligible compared to the wavelength of the light used to probe the structure. Coarsening laws of the form R(t) ∼ tR were obeyed in the spinodal samples. Coarsening exponents with values between 1/10 and 1/5, including in some cases a transition to a temporary faster coarsening regime, were measured in the gelled samples. The low coarsening exponents were a consequence of the loss of mobility of the gelatin component caused by gelation and the presence of multiple coarsening regimes was explained as being a nonequilibrium effect resulting from the gradual movement of the system toward the equilibrium compositions. At earlier times for the spinodal liquid samples and at all times for the nucleation and growth samples, the coarsening exponent was lower than 1/3 because coarsening occurred via droplet coalescence and the droplet size was significantly smaller than the droplet separation. A coarsening exponent of 1/3 was measured in the final stage of coarsening in the liquid samples once the droplet size was believed to be similar to the droplet separation. Acknowledgment. Helpful discussions with Ian Norton, Allan Clark, and Bill Williams, of Unilever Research, Colworth, are gratefully acknowledged. References and Notes (1) Strobl, G. The Phyics of Polymers; Springer-Verlag: Berlin, 1996. (2) Tromp, R. H.; Rennie, A. R.; Jones, R. A. L. Macromolecules 1995, 28, 4129. (3) Tromp, R. H.; Jones, R. A. L. Macromolecules 1996, 29, 8109. (4) Tanaka, H.; Yokokawa, T.; Abe, H.; Hayashi, T.; Nishi, T. Phys. ReV. Lett. 1990, 65, 3136. (5) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (6) Tokuyama, M.; Kawasaki, K. Physica A 1984, 123, 386. (7) Mazenko, G. F. Phys. ReV. B 1991, 43, 8204. (8) Mazenko, G. F. Phys. ReV. Lett. 1989, 63, 1605.

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Biomacromolecules, Vol. 3, No. 4, 2002 683 (27) Loreń, N.; Hermansson, A.-M. Int. J. Biol. Macromol. 2000, 27, 249. (28) Loreń, N.; Altska¨r, A.; Hermansson, A.-M. Macromolecules 2001, 34, 8117. (29) Anderson, V. J.; Jones, R. A. L. Polymer 2001, 42, 9601. (30) Castellano, C.; Corberi, F. Phys. ReV. E 1998, 57, 672. (31) Castellano, C.; Corberi, F. Phys. ReV. E 2000, 61, 3252. (32) Chen, W.-J.; Chen, S.-H. Phys. ReV. E 1995, 52, 5696. (33) Kita, R.; Kaku, T.; Kubota, K.; Dobashi, T. Phys. Lett. A 1999, 259, 302. (34) Heppenstall-Butler, M.; Butler, M. F. Biomacromolecules 2001, 2, 812. (35) Furukawa, H. AdV. Phys. 1985, 34, 703. (36) Furukawa, H. J. Appl. Crystallogr. 1988, 21, 805. (37) Cahn, J. W.; Hilliard, J. E. J. Chem. Phys. 1958, 92, 258. (38) Cahn, J. W. J. Chem. Phys. 1965, 42, 93. (39) Nose, T. Phase Transitions 1987, 8, 245. (40) Hashimoto, T. Phase Transitions 1988, 12, 47. (41) Eliç abe, G. E.; Larrondo, H. A.; Williams, R. J. J. Macromolecules 1997, 30, 6550. (42) Eliç abe, G. E.; Larrondo, H. A.; Williams, R. J. J. Macromolecules 1998, 31, 8173. (43) Eliç abe, G. E. Macromol. Theory Simul. 1999, 8, 375. (44) Rikvold, P. A.; Gunton, J. D. Phys. ReV. Lett. 1982, 49, 286. (45) Carpineti, M.; Giglio, M.; Degiorgio, V. Phys. ReV. E 1995, 51, 590. (46) Banfi, G.; Degiorgio, V.; Rennie, A. R.; Barker, G. Phys. ReV. Lett. 1992, 69, 3401. (47) Maugey, J.; Van Nuland, T.; Navard, P. Polymer 2001, 42, 4353.

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