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Rheo-optics of colloidal crystals
Studies in Surface Science and Catalysis 132 Y. Iwasawa, N. Oyama and H. Kunieda (Editors) io 2001 Elsevier Science B.V. All rights reserved.
387
Rheo-optics of colloidal crystals T. Okubo, H. Kimura and T. Hatta Department of Applied Chemistry, Gifu University, 1-1 Yanagido, Gifti 501-1193, JAPAN Colloidal crystals, i.e., crystal-like distribution of colloidal particles in suspension, is so soft that the crystal structures are distorted and even broken by the shear stress quite easily. In this study the relationship between rheological (macroscopic) and optical (microscopic) properties have been measured simultaneously for the colloidal crystals of silica spheres in the exhaustively deionized aqueous suspensions. 1. INTRODUCTION Small particles ranging from ca.lO nm to 0.1 mm in diameter are called as colloidal particles. Generally speaking, most colloidal particles in aqueous suspension get the negative charges on their surfaces by two mechanisms; one is the dissociation of ionizable groups and the other is the preferential adsorption of ions from suspension. These ionic groups leave their counterions, and the excess charges accumulate near the surface forming an electrical double layer. The counterions in the diffuse region are distributed according to a balance between the thermal diffusive force and the forces of electrical attraction with colloidal particles. When the suspension is exhaustively deionized with the mixed beds of the ionexchange resins, the electrical double layer expand and the particles arrange regularly [1-9]. In other words, phase of the colloidal suspension changes from "liquid" to "crystal" in the process of the deionization. The elastic modulus of the colloidal crystals is extremely low compared with that of other common crystals such as metals. Thus, the colloidal crystals are distorted quite easily by the external fields such as shearing forces, gravity, electric field, centrifugal force, high pressure, and even suspension temperature and ionic species. Several reports have appeared so far for colloidal crystals in the shearing forces; (i) microscopic change in the lattice constant in a flow cell [10], and (ii) the macroscopic visco-elastic properties [11]. Purpose of this work is to clarify the relationship between the visco-elastic and optical properties from the measurements of the rheological parameters and reflection spectra simultaneously.
388
2. EXPERIMENTAL Aqueous suspensions of colloidal silica spheres (CS-91, 110±4.5 nm in diameter, Catalyst & Chemicals Ind. Co. (Tokyo)) were used. It took more than eight years for the exhaustive deionization with ion-exchange resins (Bio-Rad, Richmond, Calif., USA, AG501-X8(D), 20-50 mesh). Sphere concentration of the stock suspension was 0.13 in volume fraction (0). Four sample suspensions from 0.02 to 0.13 were prepared. Water used for the purification and for suspension preparation was purified by a Milli-Q reagent grade system (Milli-R05 plus and Milli-Q plus, Millipore, Co., Bedford, MA). A coaxial type rheometer (Rheosol-G2000W-GF, UBM Co.(Kyoto)) was used. An outer cup was made of pyrex glass for the simultaneous optical measurements. The shear rates increased linearly up to 0.09 s' in the shear stress-strain measurements. The shear rates changed from 0.001 to 10 s* in the steady shear flow. The reflection spectrum at incident angle of 90' were recorded on a Photonic Multi-channel Analyzer (PMA-50, Hamamatsu Photonics Co.(Tokyo)). The measuring temperature is 25*C 3. RESULTS AND DISCUSSION 3.1. Strain dependence Shear stress, a of colloidal crystals was studied as a function of strain, y increasing up to 5.0 from zero. At 0 of 0.129 CTincreased as 0 increased. Especially, in the case of y< 0.3 c increased linearly with increasing 7, which supports, of course, the elastic nature of colloidal crystals. The elastic modulus estimated from the slope of stress-strain curve was 7.0 Pa. At 7= 0.3, the suspension showed yielding though the graph showing this was omitted. When 7 is larger than 0.3, akept constant at 1.1 Pa irrespective of strain. At low sphere concentrations, the yielding point disappeared since the crystal structures are broken in part by the shearing forces. The reflection spectra were obtained at 0 = 0.043. A single sharp peak was observed. The lattice structure is deduced to be fee. The peaks became broad as strain increased. It is highly plausible that fee and bcc lattices coexist in shear stress. The peak wavelength, X^ shifted to the longer when 7 increased. Peak intensity, /^ decreased as 7 increased. These observations mean that the lattice constant increases and crystal size decreases as 7increases. Fig. 1 shows that the 7^ values decrease as 0 increases. At low 0, 0.022, \ decreased slightly when 7 increased. When 0 is 0.043, ^ increased especially at high y> 1.0. At high 0 values of 0.086 and 0.129, A^ values were insensitive to 7 smaller than 1.0, while they turned to decrease as 7 increased. The closest intersphere distance / observed [12] and /^ calculated [13] are given, respectively, /= 0.612 Ay« /, = 0.904 c/,0-'^^
(1) (2)
389
where n is the refractive index of the suspension, and taken to be that of water, 1.33 (251C). df^ is the diameter of silica spheres. The / values at 0 = 0.022, 0.043, 0.086 and 0.129 were 364.9, 293.5, 238.7 and 211.7 nm, while theoretical values /, are 354.9, 283.8, 225.3 and 196.8, respectively. The agreement between the observation and the calculation is satisfactory. These changes in ^ under shear are ascribed to the distortion of the electrical double layers by the shearing forces [13]. Decrease in the lattice spacing by the shearing forces is due to 794 the distortion of the shape of the 792
3.2. Shear rate dependence (7 as a function of shear rate, y were examined. At high 0 values of 0.086 and 0.129, crkept constant irrespective of ^. On the other hand, at low 0 values of 0.022 and 0.043, cr increased as y increased. Clearly, phase transition from "crystal" to "liquid" occurred as 0 increased. Fig. 1 Peak wavelength, ^'-z? of colloidal crystals of Optical measurements on /^ and CS-91 spheres as a function of strain, 7 at 25 "C. ?ip were made as a function of y fmax = 0.093 s'K O: 0 = 0.022, X: 0.043, for the sample, 0 = 0.129. / A:0.086, 0:0.129. decreased sharply around 0.1 s' of y, while Xp kept constant. These results support the fact that colloidal crystals melted in part and the crystal size decreased at the shear rates larger than 0.1 s"'. 3.3. Dynamic properties Storage modulus, G' was studied as a function of angular frequency, co. When 0 is high, G'was insensitive to co. At low sphere concentration of 0.022 and 0.043 in volume fraction, the phase transition from "crystal" to "liquid" was observed. At / < 0.2, G' decreased
390 drastically when yincreased, whereas at larger /than 1.0, G'approached to a constant value. The elastic modulus G obtained by stress-strain relationship was 7.0 Pa at 0= 0.129, which is slightly larger than the storage modulus G' = 2 Pa (y = 0.3), observed in the dynamic measurements. This may be due to the contamination of the ionic impurities into the colloidal samples during the measurements. 4. CONCLUSION It is clear that distortion of the electrical double layers play an important role for the micro- and macro- properties of colloidal crystals. At small strains, colloidal crystals are distorted, but its structure does not change so much. On the other hand, at large strains, structural changes such as sliding of the lattice planes, change in shape of the electrical double layers from spherical to flame-like, and also decrease in crystal size occurs. Acknowledgments The rheometer was purchased by the Grants-in-Aid for Scientific Research on Priority Areas (A) (11167241) from Japanese Ministry of Education, Science and Culture, to whom the authors thank deeply. Sample of colloidal silica spheres was a gift from Catalyst & Chemicals Ind. Co. (Tokyo).
REFERENCES 1) Kose, A., M. Ozaki, K.Takano, Y. Kobayashi and S. Hachisu : J. Coloid Interface ScL, 44, 330(1973) 2) Hachisu, S., A. Kose, Y. Kobayashi and K. Takano : J. Coloid Interface ScL, 55, 499 (1976) 3) Lindsay, H. M. and P. M. Chaikin : J. Chem. Phys., 76, 3774 (1982) 4) Pieranski, P.: Contemp. Phys., 24, 25 (1983) 5) Ottewill, R. H.: Ber. Bunsenges. Phys. Chem., 89, 281 (1985) 6) Aastuen, D. J. W., N. A. Clark, L. A. Cotter and B. J. Ackerson : Phys. Rev. Lett., 57, 1733(1986) 7) Okubo, T. :Acc. Chem. Res., 21, 281 (1988) 8) Lowen, H., T. Palberg and R. Simon : Phys. Rev. Lett., 70,1557 (1993) 9) Stevens, M. J., M. L. Falk and M. O. Robbins : J. Chem. Phys., 104, 5209 (1996) 10) Okubo, T.: J. Coloid Interface Sci., 117, 165 (1987) 11) Okubo, T.: Ber. Bunsenges. Phys. Chem., 92, 504 (1988) 12) Okubo, T.: J. Coloid Interface ScL, 135, 259 (1990) 13) Okubo, T.: J. Chem. Soc. Faraday Trans. 1 : 84, 1171 (1988)
387
Rheo-optics of colloidal crystals T. Okubo, H. Kimura and T. Hatta Department of Applied Chemistry, Gifu University, 1-1 Yanagido, Gifti 501-1193, JAPAN Colloidal crystals, i.e., crystal-like distribution of colloidal particles in suspension, is so soft that the crystal structures are distorted and even broken by the shear stress quite easily. In this study the relationship between rheological (macroscopic) and optical (microscopic) properties have been measured simultaneously for the colloidal crystals of silica spheres in the exhaustively deionized aqueous suspensions. 1. INTRODUCTION Small particles ranging from ca.lO nm to 0.1 mm in diameter are called as colloidal particles. Generally speaking, most colloidal particles in aqueous suspension get the negative charges on their surfaces by two mechanisms; one is the dissociation of ionizable groups and the other is the preferential adsorption of ions from suspension. These ionic groups leave their counterions, and the excess charges accumulate near the surface forming an electrical double layer. The counterions in the diffuse region are distributed according to a balance between the thermal diffusive force and the forces of electrical attraction with colloidal particles. When the suspension is exhaustively deionized with the mixed beds of the ionexchange resins, the electrical double layer expand and the particles arrange regularly [1-9]. In other words, phase of the colloidal suspension changes from "liquid" to "crystal" in the process of the deionization. The elastic modulus of the colloidal crystals is extremely low compared with that of other common crystals such as metals. Thus, the colloidal crystals are distorted quite easily by the external fields such as shearing forces, gravity, electric field, centrifugal force, high pressure, and even suspension temperature and ionic species. Several reports have appeared so far for colloidal crystals in the shearing forces; (i) microscopic change in the lattice constant in a flow cell [10], and (ii) the macroscopic visco-elastic properties [11]. Purpose of this work is to clarify the relationship between the visco-elastic and optical properties from the measurements of the rheological parameters and reflection spectra simultaneously.
388
2. EXPERIMENTAL Aqueous suspensions of colloidal silica spheres (CS-91, 110±4.5 nm in diameter, Catalyst & Chemicals Ind. Co. (Tokyo)) were used. It took more than eight years for the exhaustive deionization with ion-exchange resins (Bio-Rad, Richmond, Calif., USA, AG501-X8(D), 20-50 mesh). Sphere concentration of the stock suspension was 0.13 in volume fraction (0). Four sample suspensions from 0.02 to 0.13 were prepared. Water used for the purification and for suspension preparation was purified by a Milli-Q reagent grade system (Milli-R05 plus and Milli-Q plus, Millipore, Co., Bedford, MA). A coaxial type rheometer (Rheosol-G2000W-GF, UBM Co.(Kyoto)) was used. An outer cup was made of pyrex glass for the simultaneous optical measurements. The shear rates increased linearly up to 0.09 s' in the shear stress-strain measurements. The shear rates changed from 0.001 to 10 s* in the steady shear flow. The reflection spectrum at incident angle of 90' were recorded on a Photonic Multi-channel Analyzer (PMA-50, Hamamatsu Photonics Co.(Tokyo)). The measuring temperature is 25*C 3. RESULTS AND DISCUSSION 3.1. Strain dependence Shear stress, a of colloidal crystals was studied as a function of strain, y increasing up to 5.0 from zero. At 0 of 0.129 CTincreased as 0 increased. Especially, in the case of y< 0.3 c increased linearly with increasing 7, which supports, of course, the elastic nature of colloidal crystals. The elastic modulus estimated from the slope of stress-strain curve was 7.0 Pa. At 7= 0.3, the suspension showed yielding though the graph showing this was omitted. When 7 is larger than 0.3, akept constant at 1.1 Pa irrespective of strain. At low sphere concentrations, the yielding point disappeared since the crystal structures are broken in part by the shearing forces. The reflection spectra were obtained at 0 = 0.043. A single sharp peak was observed. The lattice structure is deduced to be fee. The peaks became broad as strain increased. It is highly plausible that fee and bcc lattices coexist in shear stress. The peak wavelength, X^ shifted to the longer when 7 increased. Peak intensity, /^ decreased as 7 increased. These observations mean that the lattice constant increases and crystal size decreases as 7increases. Fig. 1 shows that the 7^ values decrease as 0 increases. At low 0, 0.022, \ decreased slightly when 7 increased. When 0 is 0.043, ^ increased especially at high y> 1.0. At high 0 values of 0.086 and 0.129, A^ values were insensitive to 7 smaller than 1.0, while they turned to decrease as 7 increased. The closest intersphere distance / observed [12] and /^ calculated [13] are given, respectively, /= 0.612 Ay« /, = 0.904 c/,0-'^^
(1) (2)
389
where n is the refractive index of the suspension, and taken to be that of water, 1.33 (251C). df^ is the diameter of silica spheres. The / values at 0 = 0.022, 0.043, 0.086 and 0.129 were 364.9, 293.5, 238.7 and 211.7 nm, while theoretical values /, are 354.9, 283.8, 225.3 and 196.8, respectively. The agreement between the observation and the calculation is satisfactory. These changes in ^ under shear are ascribed to the distortion of the electrical double layers by the shearing forces [13]. Decrease in the lattice spacing by the shearing forces is due to 794 the distortion of the shape of the 792
3.2. Shear rate dependence (7 as a function of shear rate, y were examined. At high 0 values of 0.086 and 0.129, crkept constant irrespective of ^. On the other hand, at low 0 values of 0.022 and 0.043, cr increased as y increased. Clearly, phase transition from "crystal" to "liquid" occurred as 0 increased. Fig. 1 Peak wavelength, ^'-z? of colloidal crystals of Optical measurements on /^ and CS-91 spheres as a function of strain, 7 at 25 "C. ?ip were made as a function of y fmax = 0.093 s'K O: 0 = 0.022, X: 0.043, for the sample, 0 = 0.129. / A:0.086, 0:0.129. decreased sharply around 0.1 s' of y, while Xp kept constant. These results support the fact that colloidal crystals melted in part and the crystal size decreased at the shear rates larger than 0.1 s"'. 3.3. Dynamic properties Storage modulus, G' was studied as a function of angular frequency, co. When 0 is high, G'was insensitive to co. At low sphere concentration of 0.022 and 0.043 in volume fraction, the phase transition from "crystal" to "liquid" was observed. At / < 0.2, G' decreased
390 drastically when yincreased, whereas at larger /than 1.0, G'approached to a constant value. The elastic modulus G obtained by stress-strain relationship was 7.0 Pa at 0= 0.129, which is slightly larger than the storage modulus G' = 2 Pa (y = 0.3), observed in the dynamic measurements. This may be due to the contamination of the ionic impurities into the colloidal samples during the measurements. 4. CONCLUSION It is clear that distortion of the electrical double layers play an important role for the micro- and macro- properties of colloidal crystals. At small strains, colloidal crystals are distorted, but its structure does not change so much. On the other hand, at large strains, structural changes such as sliding of the lattice planes, change in shape of the electrical double layers from spherical to flame-like, and also decrease in crystal size occurs. Acknowledgments The rheometer was purchased by the Grants-in-Aid for Scientific Research on Priority Areas (A) (11167241) from Japanese Ministry of Education, Science and Culture, to whom the authors thank deeply. Sample of colloidal silica spheres was a gift from Catalyst & Chemicals Ind. Co. (Tokyo).
REFERENCES 1) Kose, A., M. Ozaki, K.Takano, Y. Kobayashi and S. Hachisu : J. Coloid Interface ScL, 44, 330(1973) 2) Hachisu, S., A. Kose, Y. Kobayashi and K. Takano : J. Coloid Interface ScL, 55, 499 (1976) 3) Lindsay, H. M. and P. M. Chaikin : J. Chem. Phys., 76, 3774 (1982) 4) Pieranski, P.: Contemp. Phys., 24, 25 (1983) 5) Ottewill, R. H.: Ber. Bunsenges. Phys. Chem., 89, 281 (1985) 6) Aastuen, D. J. W., N. A. Clark, L. A. Cotter and B. J. Ackerson : Phys. Rev. Lett., 57, 1733(1986) 7) Okubo, T. :Acc. Chem. Res., 21, 281 (1988) 8) Lowen, H., T. Palberg and R. Simon : Phys. Rev. Lett., 70,1557 (1993) 9) Stevens, M. J., M. L. Falk and M. O. Robbins : J. Chem. Phys., 104, 5209 (1996) 10) Okubo, T.: J. Coloid Interface Sci., 117, 165 (1987) 11) Okubo, T.: Ber. Bunsenges. Phys. Chem., 92, 504 (1988) 12) Okubo, T.: J. Coloid Interface ScL, 135, 259 (1990) 13) Okubo, T.: J. Chem. Soc. Faraday Trans. 1 : 84, 1171 (1988)