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Real Space Structure of Opaque Gel Yukiko Doi and Masayuki Tokita* Department of Physics, Faculty of Science, Kyushu University, 4-2-1 Ropponmatsu, Fukuoka 810-8560, Japan Received February 21, 2005. In Final Form: April 6, 2005 The structure of the opaque poly(acrylamide) gels is studied by using a confocal laser scanning microscope. The polymer network of the gel consists of the fractal aggregate of the colloidal particles in the higher concentration region of the cross-linker. The diameter of the colloidal particle, which formed in the gel, increases from 180 to 420 nm with an increase of the concentration of cross-linker. On the other hand, the fractal dimensions of the aggregate remain constant, ranging from 1.5 to 1.7. The densities of the particle are calculated to be 0.7 and 1.2 × 103 kg/m3, which are >10 times larger than the average density of the polymer network of the gel. The results indicate that the monomer and the cross-linker are densely cross-linked into the particles.
Introduction Gel is a soft solid that consists of the three-dimensional polymer network and a large amount of solvent. Gels are used in a wide variety of chemical and biological systems because of their unique structure. When a gel is prepared under well-defined conditions, the gel becomes transparent and highly elastic. However, the opacity of the gel is known to increase with an increase of the cross-linker concentration.1,2 The increase of the opaqueness in the gel strongly suggests changes of the structure of the polymer network in the gel with the concentration of the cross-linker. The friction between the polymer network of the gel and the solvent, for instance, decreases with the opaqueness of the gel.3 In addition, we recently found that the friction of poly(acrylamide) gel decreases >4 orders of magnitude when the mole fraction of the cross-linker is >0.2. In this concentration region of the cross-linker, the gels become totally opaque. Such a drastic decrease of the friction may suggest the structural transition of the polymer network of the gel. The structural study of the opaque gel in the higher concentration region of the cross-linker is, hence, required for the understanding of the structural transition in the gel. Although many studies are made, quantitative studies on the structure of opaque gels have yet to be made.4,5 The structure of the polymer network of gels has been studied thus far by using scattering techniques such as small-angle X-ray scattering and light scattering. The increase in the opacity of the gel, however, strongly suggests that the characteristic scale of the length of the structure, which is created in the opaque gel, is of the same order of magnitude as that of the wavelength of light. The network structure of the opaque gel is, hence, quite heterogeneous. In such a gel, light scattering studies are not appropriate because of the multiple scattering effects. Besides, the effects of the spatial fluctuation of the refractive index within the gel are also taken into account in the analysis of the scattering data. The smallangle X-ray scattering method, on the other hand, may * Corresponding author (e-mail
[email protected]). (1) Bansil, R.; Gupta, M. K. Ferroelectrics 1980, 30, 63. (2) Richards, E. G.; Temple, C. J. Nature (Phys. Sci.) 1971, 230, 92. (3) Tokita, M.; Tanaka, T. J. Chem. Phys. 1991, 95, 4613. (4) Weiss, N.; Silberberg, A. J. Polym. Sci., Polym. Phys. Ed. 1975, 17, 2229. (5) Hsu, T. P.; Ma, D. S.; Cohen, C. Polymer 1983, 24, 1273.
be better if the fine structures of the opaque gel, for instance, a few nanometers in length, are discussed. In these methods, hence, careful experiments and complex analysis of the scattering data should be made. On the other hand, it has been shown that the structure of the gel can be determined by using the confocal laser scanning microscope (CLSM).6 There are many advantages of using the CLSM to determine the structure of the polymer network of the gel. Because the optical cross section of the sample is observed in the case of the CLSM, the structure of the bulk gel can be determined noninvasively. The image thus obtained by using the CLSM represents the structure of the gel in the real space. Hence, it may be more intuitive than the scattering results. Besides, the analysis of the structure is simple, and it can be done on a small microcomputer. The purpose of present work is to describe the details of the structural study of the opaque poly(acrylamide) gel. The gels are prepared at various conditions of composition and reaction temperature. The structure of the opaque gels is determined by the CLSM. The images gained by the CLSM are analyzed using the image analysis software. Then the results are discussed in terms of the fractals. Experimental Section The sample gel studied here was a poly(acrylamide) gel. Both acrylamide (main-chain constituent, electrophoresis grade) and N,N′-methylenebis(acrylamide) (cross-linker, electrophoresis grade) were purchased from Bio-Rad Laboratories, Co., and used without further purification. The gel was prepared according to a photopolymerization method. The photoinitiator used in this study was 2,2′-azobis[2-methylene-N-(2-hydroxyethyl)propionamide] that was kindly supplied from Wako Chemical Co. Predetermined amounts of acrylamide, N,N′-methylenebis(acrylamide), and photoinitiator were dissolved into distilled and deionized water. The pre-gel solution was then degassed for 30 min and transferred into the reaction cell. The solution was irradiated by UV light at a wavelength of 360 nm for 20 min. The gel thus obtained was washed in distilled and deionized water to remove unreacted substances. Then the gel was labeled by fluorescein isothiocyanate (Isomer I, Sigma Chemical Co.) using a standard method.7 Finally, the gel labeled by fluorescence dye (6) Hirokawa, Y.; Jinnai, H.; Nishikawa, Y.; Okamoto, T.; Hashimoto, T. Macromolecules 1999, 32, 7093. (7) Hermanson, T. G. Bioconjugate Techniques; Academic Press: San Diego, CA, 1996.
10.1021/la050453n CCC: $30.25 © 2005 American Chemical Society Published on Web 05/11/2005
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was extensively washed in distilled and deionized water to remove unreacted fluorescence dye. The typical thickness of the sample gel prepared here was 0.2. It was also found that the opacity of the gel increases when the reaction temperature is lowered. Hence, two series of sample gels were prepared to clarify the effects of the concentration of cross-linker and that of the reaction temperature on the opaque phenomenon of the gels. In the first series, the concentration of cross-linker was changed from 140 to 350 mM at a constant total concentration of 700 mM. This corresponds to the mole fraction of the crosslinker, φc, from 0.2 to 0.5. The reaction temperature was fixed at 20 °C. In the second series, the reaction temperature was lowered to 10 and 0 °C at a constant composition of the gel. In this case, the mole fraction of the cross-linker was fixed at φc ) 0.2 at a total concentration of 700 mM. In all cases, the reaction temperature was controlled within an accuracy of better than (0.2 °C. The CLSM used in this study was constructed by an inverted microscope (Axiovert S100, Carl Zeiss), a confocal unit (CSU 10, Yokogawa), and an Ar-ion laser (type 532-50BS/170, Omnichrome). The objective lens used here was a Plan-APOCHROMAT (Carl Zeiss; magnification, 100×; N.A., 1.4). Under these conditions, the thickness of the focal plane was 1 µm. The confocal images of gels were gained using an image processor (cooled CCD camera C5985H and ARGUS-20, Hamamatsu). The CLSM system was controlled by a microcomputer (Power Macintosh 7600/200, Apple) that was equipped with an image graver system (LG3, Scion Co.) and image analysis software (IPLab Spectrum, Scanalytics, Inc.). In the present CLSM system, the laser light at a wavelength of 488 nm exited the fluorescence dye. Then the image of emitted fluorescence at a wavelength of 525 nm was obtained. The resolution of the present fluorescence CLSM system was determined by the magnification of the objective lens and the size of the pixel of the CCD camera. Calibration of the total CLSM system yields that the resolution limit of the present system was 100 nm. When sample was observed by the CLSM, p-phenylenediamine solution, which is a fade prevention substance of the fluorescence dye, was added in the surrounding water. The concentration of the fade prevention substance was fixed at 0.1 g/100 mL.
Results Equilibrium Swelling Ratio of the Gels. It is wellknown that poly(acrylamide) gels swell in water.8 The swelling of the gel may change the structure of the polymer network of the gel. The swelling ratio of the gels, hence, should be determined prior to the detailed study of the structure of the gel. In Figure 1, the equilibrium swelling ratio of the gel in water, d/d0, is plotted as a function of the cross-linker concentration and the reaction temperature. Here, d is the diameter of the rod-shaped gel at the equilibrium state in water, and d0 is that at preparation. The swelling ratio of the gel is determined under microscope because the value of d0 is 141 µm. The results given in Figure 1 show that the swelling ratio of the gels is independent of the conditions of the preparation. Furthermore, the values of the swelling ratio of these gels are almost equal to unity. These results indicate that the opaque poly(acrylamide) gels studied here do not swell in water. The structure of the polymer network of opaque gel immediately after gelation is, hence, not affected by the swelling of the gel. Cross-Linker Concentration Dependence of the Structure. In Figure 2, the CLSM images of opaque poly(8) Tanaka, T. Sci. Am. 1981, 244, 124.
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Figure 1. Equilibrium swelling ratio of opaque poly(acrylamide) gels: (a) dependence on the mole fraction of cross-linker φc; (b) dependence on the reaction temperature.
(acrylamide) gels prepared by changing the concentration of cross-linker are shown. In this study, the fluorescence dye is chemically labeled to the polymer network of the gel. The brighter region of the image, hence, is the region where the density of the polymer network is higher. On the other hand, the density of the polymer network is much lower in the darker region of the image. These images show that the colloidal particles are aggregated to form the network of the gel. The colloidal particles can be clearly seen in the images where the mole fraction of the cross-linker is >0.3. It is also shown that the spatial distribution of the particles in these gels is quite heterogeneous. In contrast, the distribution of the brighter region within the image is rather uniform when the mole fraction of the cross-linker is lowered to 0.2. These results indicate that the structure of the gel is characterized by two parameters. One is the diameter of the spherical particle, and the other is the spatial distribution of them. The diameter of particles observed in the image is directly measured. More than 100 particles are randomly chosen from the image. Then the diameter of each particle is measured on the computer. The average values of the diameter of particle thus obtained are given in Table 1. The diameter of particles is found to increase from 180 to 420 nm with the concentration of the cross-linker. The resolution of the present CLSM system is not enough to determine the exact diameter of particles in Figure 2a. The diameter of the particles is, hence, measured at the mole fraction of cross-linker >0.3. All of the structures shown in Figure 2 exhibit a very ramified structure, suggesting that the analysis should be in terms of fractals.9 However, the images shown in Figure 2 are, of course, two-dimensional. These images, hence, represent a projection of the three-dimensional network as it exists in the gel. Therefore, all of the analyses of the CLSM images are made in terms of a twodimensional projection of the three-dimensional object. The relationship between the radius of the sampling circle, r, and the total mass of the particle, M, in the sampling circle is expressed as follows:
M ∼ rD
(1)
Here, D is the fractal dimension. The total mass of the particle in the sampling circle is proportional to the number of particles in it. Then the number of particles in the sampling circle is proportional to the area that is (9) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: New York, 1983.
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Figure 2. Confocal laser scanning micrographs of opaque poly(acrylamide) gels. The total concentration of the pre-gel solution is 700 mM. The mole fractions of the cross-linker are (a) 0.2, (b) 0.3, (c) 0.4, and (d) 0.5. The reaction temperature is fixed at 20 °C. Both sides of the images are 28 µm. Table 1. Cross-Linker Concentration Dependence of the Structural Parameters φc 0.2 diameter (nm) fractal dimension Φ F (×103 kg/m3)
2.0
0.3
0.4
0.5
180 1.6 0.44 1.27
300 1.6 0.33 1.15
420 1.5 0.23 1.22
occupied by the particles, that is, the area of brighter region. Hence, the area of the bright region in the sampling circle, S, is measured as a function of the radius of the concentric sampling circles, which are drawn at the center of the image, systematically. A logarithmic plot of the radius of the concentric sampling circle and the occupied area is shown in Figure 3. The results shown in Figure 3 exhibit the linear behavior expected of fractals. The solid lines in this figure are the least-squares fit to the results. From the slopes of these lines, as well as those of many data sets, the fractal dimensions of the gels are determined. The average values of the fractal dimension thus obtained are also summarized in Table 1. The spatial distribution of the particle is a fractal of D ∼ 1.6 when the mole fraction of cross-linker is >0.3. On the other hand, the fractal dimension of D ) 2.0 is obtained at the mole fraction of cross-linker of 0.2. It is indicative of the uniform spatial distribution of the mass in the area of the image. In addition to these analyses, the fraction of the total brighter
Figure 3. Typical results of fractal analysis of the images. The occupied area of the brighter region, S, in the sampling circle is plotted as a function of the radius of the sampling circle, r, in the double-logarithmic manner. The mole fractions of the cross-linker are (9) 0.2, (O) 0.3, (0) 0.4, and (b) 0.5. In the case of the concentration region of the cross-linker from 0.2 to 0.4, only one-third of the total data points are shown in this figure for the sake of simplicity. The straight lines in this figure are the results of the least-squares analysis. The slopes of these straight lines are, 2.0, 1.8, 1.8, and 1.9 from top to bottom.
region in the image, Φ, is also measured, and the values are given in Table 1. Temperature Dependence of the Structure. In Figure 4, the CLSM images of poly(acrylamide) gels that prepared at temperatures of 10 and 0 °C are shown. The composition of the gel is the same as that of Figure 2a.
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Figure 4. Confocal laser scanning micrographs of opaque poly(acrylamide) gels. The reaction temperatures are (left) 0 °C and (right) 10 °C. The composition of the gel is the same as that shown in Figure 2a, φc ) 0.2. Both sides of the images are 28 µm. Table 2. Reaction Temperature Dependence of the Structural Parameters reaction temperature diameter (nm) fractal dimension Φ F (×103 kg/m3)
0 °C
10 °C
240 1.7 0.58 0.66
160 1.7 0.84 0.69
When the gel is prepared at lower temperatures, the structure of the gel becomes heterogeneous, as shown in Figure 4. These images are analyzed in the same manner as described in the previous section. The results are summarized in Table 2. The results show that the diameter of particles that formed in the gel increases as the reaction temperature is lowered. On the other hand, the reaction temperature does not affect the distribution of particles in the aggregate. Discussion The CLSM image is the two-dimensional projection of the thin observation volume to the focal plane. The observation volume of the image is known because both the thickness of the focal plane and the sides of the image are known. The total mass in the observation volume is conserved before and after gelation because the opaque gels studied here do not swell in water. The total mass of the particles, hence, can be calculated from the composition of the pre-gel solution. On the other hand, the total number of particles in the observation volume can be also calculated from two parameters of the image: the average diameter of the particles and the area of the total brighter region in the image. The average mass of a particle and, hence, the average density of the particle can be determined from these parameters. The average densities of the particle, F, thus obtained are given in Tables 1 and 2. The density of the particle is almost constant in the two series of samples. The density of the particle is 1.2 × 103 kg/m3 in the case of the first series, which is given in Table 1, and is 0.7 × 103 kg/m3 in the case of the second series, which is given in Table 2. The average density of the particle in the first series is almost twice as large as that of second series. It is, however, found that the transition from the transparent gel, which is the uniform network gel, to the opaque gel, which is the colloidal gel, occurs when the mole fraction of the cross-linker is ∼0.2. The structural transition of the gel is also confirmed by
the recent measurements of the friction of the opaque gels. Thus, the structure of the gels in the second series is that at the transition point. Although the gel does not swell in water, the gel prepared at this mole fraction of the cross-linker, hence, may contain many dangling chains. The optical microscope, even the CLSM, cannot reveal the existence of such chains of molecular size due to the Brownian movement of the chains. These movable chains, hence, do not contribute to the density of the particle. The densities of the particle in the second series become, hence, smaller than that of first series. These values are, however, still >10 times larger than the average density of only the polymer network of the gel, 0.06 × 103 kg/m3, which can be calculated from the mass in feed. Furthermore, the density of the particle obtained in the first series is close to the density of the main-chain constituent and the crosslinker in the solid state. Both the main-chain constituent and the cross-linker are, hence, densely cross-linked in the spherical particles. It is, however, worth noting here that this calculation will be possible if there is not too much overlap of the particles, which makes the resultant density larger. The densities listed in the tables should be regarded as maximum values of the density of the particles observed in the present CLSM images. The aggregation of small clusters to form a large aggregate is a universal phenomenon, which occurs in a diverse length of scale. The studies so far made strongly suggest that the irreversible aggregation of single particles may result in aggregates that are well described as fractals. The Housdorff dimension or fractal dimension of the aggregate depends on the Euclidean dimension of the space. It has been shown by many computer simulations that the aggregation of the clusters also yields the fractal aggregates.10-13 In this case, the fractal dimension of the aggregate is 1.75 in the three-dimensional space. It should be noted that the projection of the three-dimensional fractal with the fractal dimension D < 3 remains in the fractal, with the same D, provided D < 2.9 The fractal dimension of the polymer network obtained here is, hence, close to the one that is expected for the cluster-cluster aggregation process. In our system, the fraction of the cross-linker is much higher than that in the usual composition for which (10) Witten, T. A.; Sander, L. M. Phys. Rev. Lett. 1981, 47, 1400. (11) Witten. T. A.; Sander, L. M. Phys. Rev. 1983, B27, 5686. (12) Meakin, P. Phys. Rev. Lett. 1983, 51, 1119. (13) Kolb, M.; Botet, R.; Jullien, R. Phys. Rev. Lett. 1983, 51, 1123.
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transparent gel is obtained. In such a system the reactions between the cross-linker molecules, which have four reaction sites, are dominant. The clusters of the crosslinker are, hence, formed much more easily than the long flexible chains in this system. The opaque gels studied here do not contain a loose polymer network. This is confirmed by the facts that these opaque gels do not swell in water. The loose polymer network can swell under water because it consists of the long flexible chains. The results of the swelling experiments are, hence, the direct evidence of the absence of the loose polymer network in the opaque gels studied here. The presence of such clusters of the cross-linker in the opaque gel is also confirmed by Raman spectroscopy.1 The CLSM images obtained here suggest that the clusters, which formed by the reaction between the cross-linkers, aggregate to form colloidal particles. Such particles aggregate by Brownian movement to form the polymer network of the opaque gel. The network structure of the opaque gel, therefore, consists of the fractal aggregate of the colloidal particles. The fractal dimension of the network structure of the opaque gel is, hence, similar to that of the aggregate that formed by the cluster-cluster aggregation model. A similar study has been made on the transmitting electron micrographs of the aggregates of colloidal gold.14 The results are quite similar to those with the present system. The structure of the gel also depends on the reaction temperature as shown in Figure 4. There may be many effects that should be taken into account to discuss the results. The gelation in the present system occurs with the formation of the colloidal particles and subsequent aggregation of them. Hence, the time interval before aggregation is one of the important parameters that should be taken into account first. The aggregation process of the colloidal particles has been studied often in terms of the Smoluchowski theory. One of the important results of the theory is the explanation of the half-life time of the aggregation process, τ.15
τ ) 1/8πD0RN ∼ η/T
(2)
Here, R, D0 ) kT/6πηR, and N are the radius of the particle, the diffusion coefficient of the particle, and the number of particles. The half-life time is, hence, proportional to the ratio of the viscosity of the fluid in which the particles are suspended, η, and the temperature, T. The half-life time at 0 °C, which is calculated from the viscosity of water, is almost twice as large as that at 20 °C. Hence, the particles grow larger during the half-life time at lower temperatures. Besides, the solubility of the cross-linker may also affect the structure of the aggregate. The cross(14) Weitz, D. A.; Huang, J. S. In Kinetics of Aggregation and Gelation; Family, F., Landau, D. P., Eds.; North-Holland: Amsterdam, The Netherlands, 1984; p 19. (15) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, U.K., 1989, and references cited therein.
linker is not very soluble in water and, hence, it tends to segregate from the solution when polymerized. The segregation of the polymer depends strongly on the temperature and the molecular weight of the polymer. The detailed and quantitative studies are, hence, still required for the full understanding of the temperature dependence of the network structure of the opaque gel. It is of importance to study the frictional property and the structure of opaque gels to understand the relationship between them. Such a study was recently made where the structural transition from the uniform network gel to the colloidal gel was found. It would be also of interest to study the gelation process by CLSM as well as by the small-angle X-ray scattering method, by which the fine structure of the colloidal particle can be revealed. Recently, the diffraction pattern due to the fine structure of the particle has indeed been observed in the small-angle X-ray scattering. These studies are now underway and will be reported elsewhere. Conclusion The structure of the polymer network of opaque poly(acrylamide) gel is studied by using CLSM. Because CLSM is an optical microscope, the structure of the polymer network is analyzed on the basis of the real space images of the gel. The results obtained in this study indicate that the opaque poly(acrylamide) gel consists of the fractal aggregate of the colloidal particles. The diameter of the particle is of the same order of magnitude as that of the wavelength of light. The density of the particle can be calculated from the structural parameters of the polymer network. The density of the particle thus obtained is >10 times larger than that of the average density of the polymer network. The results indicate that acrylamide and N,N′-methylenebis(acrylamide) are densely polymerized into the particles. Finally, the CLSM method works quite well to study the structure of the opaque poly(acrylamide) gels. The opaque phenomena of the gels can be seen in many systems such as the thermosensitive gels and the polysaccharide gels. The method can be applied to these gel systems in which the large-scale heterogeneous structures are frozen. In some cases, the time evolution of the structure can be determined. Such studies of the gel will open a new insight into the science and technology of the heterogeneous gels. Acknowledgment. We thank Professor Y. Kimura of Kyushu University for a critical reading of the manuscript. We also thank Professor M. Sugiyama of Kyoto University and Professor M. Mtsushita of Chuo University for fruitful discussions on the small-angle X-ray scattering experiments and the fractal analysis of the CLSM images. This work was partly supported by the Ministry of Education, Science, Sports, and Culture of Japan (Grants-in-Aid for Scientific Research 08640504 and 09440153). LA050453N
