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Langmuir 1996, 12, 2076-2082
Effects of Ionic Strength on the Isotropic-Chiral Nematic Phase Transition of Suspensions of Cellulose Crystallites Xue Min Dong, Tsunehisa Kimura, Jean-Franc¸ ois Revol, and Derek G. Gray* Paprican and Department of Chemistry, McGill University, Pulp and Paper Research Centre, Montreal, Quebec, Canada, H3A 2A7 Received February 21, 1995. In Final Form: August 7, 1995X The formation of ordered phases of acid-hydrolyzed cellulose suspensions was studied as a function of cellulose crystallite concentration and added electrolyte (HCl, NaCl, and KCl) concentrations. A chiral nematic phase formed when the suspension concentration was higher than 5.14 × 10-6 nm-3 in water. For biphasic samples, the cellulose concentrations in both isotropic and anisotropic phases increase with the total suspension concentration and with added electrolyte. The experimental results were compared with the predictions of the theory of Stroobants, Lekkerkerker, and Odijk for the phase separation of charged rods. The suspensions were not stable at electrolyte concentrations sufficiently high to allow complete evaluation of the electrostatic contribution to the interparticle interactions, but the general behavior was in line with theoretical predictions. The chiral nematic pitch of the anisotropic phase decreased with increasing crystallite concentration and with added electrolyte concentration. Apparently, a decrease in double layer thickness increases the chiral interactions between the crystallites.
Introduction Rodlike species can form ordered liquid crystal phases when their concentration reaches a certain critical value. Depending on the properties of the particles and on external conditions, the ordered phase can be nematic, smectic, or chiral nematic. Chiral nematic ordered phases have been observed from some colloidal suspensions such as DNA fragments,1 collagen,2 and chitin.3 Recently, Revol et al. reported that suspensions of acid-hydrolyzed cellulose crystallites can also form an ordered phase displaying chiral nematic orientation.4 The properties of the cellulose suspension depend on the source (which may be wood pulp, cotton, bacterial, or ramie cellulose) and on the hydrolysis conditions.5 These charged suspensions of cellulose would seem to provide a good model system to test recent theories for the phase separation of rodlike polyelectrolytes. In this paper, we will describe the phase separation of cellulose suspensions prepared from cotton filter paper and compare the experimental results with the theoretical predictions. Theoretical Background The phase separation of highly anisometric particles was first considered by Onsager.6 He predicted that, for neutral, perfect rigid rods of length L and diameter D, the critical concentration for ordered phase formation would depend only on the axial ratio of the rod, L/D. However, for charged particles, the electrostatic interaction plays a very important role on the free energy of the system. Even considering this effect up to the second virial term, Onsager’s theory could not predict the phase separation accurately. More recently, theories have been developed for the phase separation of rodlike polyelectrolytes.7-10 Stroobants, Lekkerkerker, and Odijk (SLO) modified Onsager’s theory by introducing two factors, a way to estimate the X
Abstract published in Advance ACS Abstracts, March 15, 1996.
(1) Robinson, C. Tetrahedron 1961, 13, 219. (2) Giraud-Guille, M.-M. Biol. Cell 1981, 67, 97. (3) Revol, J.-F.; Marchessault, R. H. Int. J. Biol. Macromol. 1993, 15, 329-335. (4) Revol, J.-F.; Bradford, H.; Giasson, J.; Marchessault, R. H.; Gray, D. G. Int. J. Biol. Macromol. 1992, 14, 170. (5) Revol, J.-F.; Godbout, L.; Dong, X. M.; Gray, D. G.; Chanzy, H.; Maret, G. Liq. Cryst. 1994, 16, 127. (6) Onsager, L. Ann. N.Y. Acad. Sci. 1949, 51, 627.
0743-7463/96/2412-2076$12.00/0
increased effective diameter and a twisting factor due to electrostatic repulsion.8 They demonstrated that for a system with excess added monovalent electrolyte, the effects of electrostatic interactions on phase separation were 2-fold. First, the effect on the free energy could be presented by an increased effective diameter (Deff). Second, electrostatic repulsion favored a perpendicular orientation of particles which could be viewed as a twisting action between rods, whose magnitude was characterized by a twisting factor (h). The SLO theory of phase equilibrium of charged rods may be rewritten in the following form, where the coexisting concentrations Ci and Ca of the isotropic phase and the anisotropic phase are given by11
Ci ) 3.290[(1 - 0.675h)b]-1
(1)
Ca ) 4.191[(1 - 0.730h)b]-1 where the concentrations are expressed as the number density of rods, b is the second virial coefficient of the system, and b and h are given by
π 2 L Deff 4
(2)
h ) (κDeff)-1
(3)
b)
Here, Deff is defined as
Deff ) D + κ-1(ln A′ + 0.7704)
(4)
A′ ) 2πνeff2Qκ-1 exp(-κD)
(5)
where
In these equations, Q ) e2/kBT is the Bjerrum length (7.14 Å for this aqueous system at 25 °C), kB is the (7) Stroobants, A.; Lekkerkerker, H. N. W.; Odijk, T. Macromolecules 1986, 19, 2232. (8) Sato, T.; Teramoto, A. Physica A 1991, 176, 72-86. (9) Semenov, A. N.; Kokhlov, A. R. Sov. Phys. Usp. 1988, 31, 988. (10) Lee, S. D. J. Chem. Phys. 1987, 87, 4972. (11) Odijk, T. Macromolecules 1986, 19, 2313.
© 1996 American Chemical Society
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Boltzmann constant, is the electrical permittivity of the medium, T is the temperature, νeff is the effective linear charge density, and κ-1 denotes the Debye radius. In the case of thin molecules, the effective linear charge density νeff is the density of charge per unit length actually calculable along the molecular axis. However, for thick molecules with surface charge density σ, the value of νeff is a hypothetical linear charge located on the molecular axis so as to produce, in the outer region of the molecule, the electrostatic potential similar to that realized by the actual surface charge. The following equation relates σ to νeff12
νeff )
2πσ κK1(κD/2)
(6)
where K1 denotes the first order Bessel function. The Debye radius, κ-1, is one of the dominant factors in the phase separation of rodlike polyelectrolytes and can be calculated from the ionic strength of the system. In the original SLO theory, κ is given by
κ2 ) 8πQns
(7)
where ns is the concentration of added monovalent salt. In this case an excess of 1-1 electrolyte is assumed. This assumption, however, does not hold for systems with no added electrolytes or with a high concentration of highly charged (νQ > 1)7 rods. In these cases, eq 7 requires modification. For pure polyelectrolyte solutions, Manning demonstrated that the Debye radius depends only on the counterion concentration nc and the valence of the counterion zc.13 Therefore κ is expressed as
κ2 ) 4πQnczc2
(8)
On the other hand, for a system with rather high polyelectrolyte concentration, where the contribution of polyelectrolyte to the ionic strength of the system is not negligible, eq 7 is modified following Teramoto8 to give
κ2 ) 8πQ(ns + Γzpnp)
(9)
where zp is the univalent charge of a polyion and np is the polyion concentration. Γ denotes the Donnan salt exclusion coefficient, which is given by14
Γ ) (4Q/β)-1
(10)
with β being the distance between two charges. This equation holds for Q/β > 1, which is satisfied in our cellulose crystallite sample with β ) 2.23 Å. Experimental Section The suspensions were prepared by acid catalyzed hydrolysis of natural cellulose fibers as described previously.5 In this case, Whatman No. 1 filter paper was ground to smaller than 20 mesh powder in a Wiley mill. The ground paper (20 g) was mixed with sulfuric acid (175 mL, 64%) and stirred at 45 °C for 1 h. The acid was removed by centrifugation and prolonged dialysis with pure water. The suspension was then treated by placing it in contact with a mixed-bed ion exchange resin [Rexyn I-300 (H-OH) from Fisher Scientific, Inc., or an equivalent capacity mixture of Amberlite IR-120 and Amberlite IRA-400 (OH)]. Finally it was purified by filtration and centrifugation to get rid of the resin. This procedure ensured that all ionic materials were removed (12) Brenner, S. L.; Parsegian, V. A. Biophys. J. 1974, 14, 327. (13) Manning, G.; Zimm, B. H. J. Chem. Phys. 1965, 43, 4250. (14) Manning, G. J. Chem. Phys. 1969, 51, 924.
except the H+ counterions associated with the sulfate groups on the surface of the crystallites. The crystallites were dispersed by a brief ultrasonic treatment with a sonifier cell disrupter 350 (Branson Sonic Power Co.). The suspension was fractionated by means of the observed phase separation.15 By continuous evaporation of an isotropic sample, the first anisotropic phase to separate was discarded, and the final isotropic phase was also discarded. The intermediate anisotropic sample (∼60% of the starting suspension) was kept as a stock suspension for the experimental work. Although the preparation conditions were kept as constant as possible, small differences were observed for different batches of the suspension. For three different batches, the measured dimensions agreed within (10%. Measurements of the isotropic/liquid crystal phase equilibrium were made at room temperature (20 ( 2 °C). The stock suspension was diluted with deionized water to obtain a series of concentrations. These samples were then sealed in glass tubes and kept standing vertically for 2-3 days until equilibrium was attained. The volume fraction of anisotropic phase in the total suspension was obtained by measuring the heights of mesophase/isotropic interface and the total amount of suspension in the tubes. The concentrations of both isotropic phase and anisotropic phase in each sample were also measured by weighing suspensions and the corresponding dried samples. In order to compare with theoretical predictions, the number density concentration C was calculated from measured weight percentage concentration (w) using eq 11. The particles were taken to be square rods, and the density of cellulose in water (F) was assumed to be 1.6 g/cm3 for all samples.
C)
w [w + (100 - w)F]LD2
(11)
To investigate the effects of adding small electrolytes, a stock suspension with a higher concentration was diluted with different concentrations of salt or acid to a final fixed suspension concentration (9.2 × 10-6 nm-3). The electrolyte concentration was calculated from the amount added and the final suspension volume. For the acidic suspensions in water, the effective counterion concentration was measured using an Accumet 50 pH meter (Fisher Scientific Inc.). The texture of the liquid crystal phase was observed using a cross polarized optical microscope (Wild Stereo microscope) and the chiral nematic pitch was determined by optical microscopy from the spacing of lines in the fingerprint texture. Dynamic light scattering measurements were made at 25.0 ( 0.1 °C and at scattering angle of 45° with a BI-2030-AT digital correlator (Brookhaven Instruments Corp.). The suspension sample was prepared in 0.01 M NaCl solution with a concentration of 0.25%. The autocorrelation functions were analyzed using the cumulant method. The particle length was calculated from the measured translational diffusion coefficient and a fixed particle width of 7 nm using eqs II.1-II.4 in ref 16.
Results and Discussion Characterization of Crystallites. A transmission electron microscope (Philips EM 400T) was used to image the cellulose crystallites. The individual crystallites, prepared by drying a drop of a dilute suspension (∼0.1% (w/w)) on a carbon-coated microscope grid, were rodlike in appearance, 70-170 nm long, and ∼7 nm wide (Figure 1). The average particle length determined by image analysis was 115 ( 10 nm. Dynamic light scattering16,17 gave an average width of 15.5 nm, taking 115 nm as the particle length. The apparent difference in length may arise from particle swelling, polydispersity in particle length, coagulation of particles, or the effect of the electrical double layer on the light scattering measurements. For all the calculations in this paper, the particle size (15) Sato, T.; Kakihara, T.; Teramoto, A. Polymer 1990, 31, 824. (16) Zero, K. M.; Pecora, R. Macromolecules 1982, 15, 87. (17) Schumacher, G. A.; Ven, T. G. M. v. d. J. Chem. Soc. Faraday Trans. 1991, 87, 971.
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Figure 1. Transmission electron micrograph of a dried suspension of cellulose crystallites prepared by sulfuric acid hydrolysis of cotton filter paper.
determined by image analysis will be used, that is L ) 115 nm and D ) 7 nm. The electrophoretic mobility of cellulose crystallites prepared by sulfuric acid hydrolysis showed that the particles were negatively charged, in accord with previous observations.18,19 The surface charge on the particles, due to the presence of acid sulfate groups, was determined by conductivity titration with base.20 The surface charge density was 0.155 e/nm2, where e is the elemental charge. Phase Diagram of Acidic Suspensions. Above the critical concentration, suspensions of cellulose crystallite separate into two phases with very clear phase boundaries (Figure 2a). The lower anisotropic phase shows optical properties characteristic of chiral nematic liquid crystals. The microscopic texture under crossed polars is shown in Figure 2b. The phase transition diagram of a pure cellulose suspension in deionized water is given in Figure 3. When the total cellulose crystallite concentration was below 5.14 × 10-6 nm-3 (corresponding to a weight concentration of 4.55%), the suspension displayed a single isotropic phase. As the total concentration rose above this critical point, a second phase appeared, to give an upper isotropic phase and a lower anisotropic phase. The volume of the lower anisotropic phase increased with the total suspension concentration until, at a concentration of 15.3 × 10-6 nm-3 (corresponding to a weight concentration of 13.13%), the isotropic phase disappeared completely and the whole suspension was anisotropic. In the biphasic region, as the total concentration of suspension, Ct, is increased, the volume fraction, φ, of anisotropic phase with a concentration Ca increases, while the volume fraction of isotropic phase (1 - φ) of concentration Ci decreases. The change in φ with total concentration, dφ/dCt, is more rapid at lower concentrations. The suspension concentrations measured in both phases are shown in Figure 4. The concentrations in the isotropic and anisotropic phases do not remain constant in the biphasic region as expected for the neutral rods but increase with increasing total suspension concentration. (18) Marchessault, R. H.; Morehead, F. F.; Koch, M. J. J. Colloid Sci. 1961, 16, 327. (19) Ranby, B. G. Discuss. Faraday Soc. 1951, 158. (20) Katz, S.; Beatson, R. P.; Scallan, A. M. Sven. Papperstidn. 1984, 87, R48.
Figure 2. (a) (top) Phase separation of cellulose suspension in pure water at different crystallite concentrations. From left to right, the sample concentrations are 8.78, 7.75, 6.85, and 5.78 wt %, respectively. (b) (bottom) Chiral nematic texture of the anisotropic phase of a cellulose suspension.
Figure 3. Phase transition diagram for a cellulose crystallite suspension in pure water.
The anisotropic volume fraction φ may be expressed as
φ ) (Ct - Ci)/(Ca - Ci)
(12)
Equation 12 implies that if Ci and Ca are constant in the biphasic region, φ will depend linearly on Ct and give a straight line in the phase diagram. However, the cellulose crystallites are charged; Ci and Ca are functions of Ct as demonstrated in Figure 4. Accordingly, φ does not show a linear dependence on total suspension concentration.
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Langmuir, Vol. 12, No. 8, 1996 2079
Figure 4. Cellulose concentration in the isotropic phase (Ci) and in the anisotropic phase (Ca) plotted against total suspension concentration (Ct).
Figure 5. Phase diagram of cellulose suspension at a constant pH (pH ) 1.61). The straight line was obtained from the linear fitting of the experimental data.
The results in Figures 3 and 4 resemble theoretical curves for the effect of polydispersity on the phase separation of neutral particle systems.21 However, the polydispersity effect alone could not cause the large difference in the coexisting concentrations (see Figure 6 below). The increase of Ci and Ca with suspension concentration (Figure 4) is mainly ascribed to the change of ionic strength in the aqueous medium as the concentration of charged crystallites increases. In a pure polyelectrolyte solution with univalent counterions and univalent charged polyions, the counterion concentration, nc, is given by14
nc ) γnp
(13)
with γ being the number of charged sites on each polyion. As polyion concentration increases, the resultant counterions increase the ionic strength, which in turn will tend to decrease the effective diameter of rods and increase the coexisting concentrations, as discussed below. Ideally, if the ionic strength can be held constant while changing the suspension concentrations, the effects of electrostatic interaction on phase separation will also remain constant. Thus, Deff and the twisting factor h in eqs 1-5 would not change with the polyelectrolyte concentration, and constant values of Ci and Ca will be expected across the biphasic region for a monodisperse system. However, for highly charged polyelectrolyte systems, such as our cellulose crystallite suspension, it is not easy to keep a constant ionic strength with variable polyelectrolyte concentrations, especially when the polyelectrolyte concentration is high. The added salt concentration required to swamp the changes in counterion concentration may be so large that it causes coagulation of the suspension. In order to prepare suspensions with a relatively constant ionic strength, a sample of the cellulose suspension was dialyzed exhaustively against 0.01 M HCl solution and a concentrated suspension was obtained with a measured pH of 1.61. A range of concentrations was then prepared by diluting this concentrated suspension with HCl solution to get a final pH of 1.61 for all the samples. The phase separation was examined for this series of solutions with constant hydrogen ion concentration, and the phase diagram is given in Figure 5. Relatively good linearity is obtained for the plot of φ against (21) Buining, P. A.; Lekkerkerker, H. N. W. J. Phys. Chem. 1993, 97, 11510.
Figure 6. Cellulose concentration in the isotropic phase (Ci) and in the anisotropic phase (Ca) plotted against total suspension concentration at a constant pH ) 1.61. The two lines were obtained from the linear fitting of the experimental points.
total concentration. A higher suspension concentration is required to form an ordered phase in these solutions than in water. The extrapolations of φ to 0 and 1 give the critical concentrations for phase transition. From isotropic to biphasic, the critical value is 12.4 × 10-6 nm-3, and from biphasic to anisotropic, it is 18.6 × 10-6 nm-3. These correspond to critical weight concentrations of 10.7% and 15.8%, respectively. The coexisting concentrations were also measured for the controlled pH system. Results are plotted in Figure 6. The values for Ci and Ca both increase slightly with the total concentration, but the slopes of these two lines are much smaller than those for the pure suspension system (Figure 4). This indicates that at constant pH, the coexisting concentrations are much less sensitive to the suspension concentration. There is only a slight increase in Ci and Ca, and, more significantly, the concentration difference between isotropic and anisotropic phase (shown in Figure 6) is much larger than in the case where only counterions are present. Effect of Added Electrolyte on Phase Separation. The effect of added electrolyte HCl, NaCl, and KCl, at concentrations from 0 to 2.5 mM, on the phase separation of cellulose suspensions is given in Figure 7. In order to demonstrate clearly the effect of added electrolyte, the total suspension concentration was fixed at 9.2 × 10-6 nm-3 for all the samples. The phase equilibrium is very sensitive to added electrolyte. The volume fraction of
2080 Langmuir, Vol. 12, No. 8, 1996
Figure 7. Effect of added electrolyte concentration on volume fraction of anisotropic phase in biphasic samples at a fixed total concentration of cellulose (9.2 × 10-6 nm-3).
Figure 8. Effect of added electrolyte concentration (NaCl and KCl) on cellulose concentration in both phases of samples with a fixed total concentration of cellulose (9.2 × 10-6 nm-3). The solid squares and circles present measured Ci and Ca. The dotted lines correspond to Cic and Cac calculated from SLO theory.
anisotropic phase, φ, in the biphasic samples decreased dramatically with increasing electrolyte concentration, from 0.56 to 0.05 as the electrolyte increased from 0 to 2.4 mM, while Ci and Ca are not as sensitive to the added electrolyte. The measured concentrations in both phases are presented in Figure 8. Ci and Ca both increased slightly with the amount of electrolyte. For a given total suspension concentration, an increase in both Ci and Ca can only occur if the relative proportion of each phase changes. As shown in Figure 7, the portion of ansiotropic phase, with a higher concentration, decreased significantly with the added electrolyte. Thus, an increase in suspension concentration was observed in both phases. It should also be noticed that the acidic electrolyte HCl and the neutral electrolytes NaCl and KCl have exactly the same effect on suppressing anisotropic phase formation. The phase diagrams of cellulose suspensions at fixed added NaCl concentrations are shown in Figure 9. The counterions on the cellulose crystallites were exchanged to Na+ from H+ so that all the cations in the suspension were Na+ for these results. Five NaCl concentrations, 0.13 mM, 0.31 mM, 0.62 mM, 0.99 mM, and 1.95 mM were used. As shown in the figure, the plot of φ versus suspension concentration gives a straight line at all salt concentrations in the experimental range. The critical concentration for the isotropic to biphasic phase transition
Dong et al.
Figure 9. Anisotropic phase volume fraction plotted against total concentration of cellulose crystallites, measured at the NaCl concentrations indicated on the figure.
Figure 10. Critical concentrations for the phase transition from isotropic to biphasic suspensions, plotted against added salt concentration.
was obtained by extrapolating these lines to φ ) 0. The results are plotted in Figure 10. The critical concentration increases with the added salt concentration. The apparent contradiction between values for the critical concentrations shown in Figure 8 and Figure 10 is due to the fact that in Figure 8, the data are measured at a constant total suspension concentration (9.2 × 10-6 nm-3). Hence the cellulose crystallites make a constant contribution to the total ionic strength. This is not the case in Figure 10, where the ordinate is the total concentration at which the ordered phase starts to separate. In this case the phase separation appears more sensitive to added salt. Cellulose is optically active, and thus a chiral contribution to interparticle interaction is expected. The ordered phase of the system does display the optical characteristics of helicoidally oriented chiral nematic liquid crystalline phases.4,5 The intensity of the chiral interaction between particles is characterized by the chiral nematic pitch P. The smaller the pitch, the stronger the interaction. As is usually the case for lyotropic chiral nematics such as cellulose derivatives,22-24 the pitch decreases with increasing concentration, changing from ∼80 to ∼10 µm as (22) Guo, J. X.; Gray, D. G. Cellulosic Polymers, Blends and Composites; Gilbert, R. D., Ed.; Hanser: New York, 1994; pp 25-45. (23) Werbowyj, R. S.; Gray, D. G. Mol. Cryst. Liq. Cryst. 1976, 34, 97. (24) Gibson, H. W. Liquid Crystals the Fourth State Matter; Marcel Dekker, Inc.: New York, 1979.
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Table 1. Comparison of Theory and Experiment for Pure Cellulose Suspensionsa pH
Ct × (nm-3)
κ-1 (nm)
νeff (e/nm)
h
Deff (nm)
b × 105 (nm3)
Cic × 10-6 (nm-3)
Cac × 10-6 (nm-3)
2.02 2.11 2.17 2.19 2.27 2.33 2.41
15.31 12.15 10.68 10.06 8.37 7.34 6.10
4.40 4.88 5.23 5.35 5.87 6.29 6.90
4.93 4.69 4.55 4.51 4.35 4.26 4.14
0.144 0.144 0.144 0.144 0.143 0.143 0.142
30.58 33.94 36.41 37.27 40.99 44.08 48.60
3.18 3.53 3.78 3.87 4.26 4.58 5.05
11.47 10.34 9.64 9.41 8.55 7.95 7.21
14.75 13.28 12.38 12.09 10.99 10.22 9.26
10-6
a
Ci × 10-6 (nm-3) N.A. 9.70 8.85 8.62 7.49 6.74 5.77
Ca × 10-6 (nm-3) 15.31 12.54 11.12 10.68 9.40 8.30 7.26
Cic and Cac are calculated concentrations from SLO theory. Ct, Ci, and Ca are measured concentrations.
Figure 11. Effect of electrolyte concentration on chiral nematic pitch of the anisotropic phase in biphasic suspensions The total cellulose content was fixed at 9.2 × 10-6 nm-3.
Figure 12. Plot of the coexisting concentrations against the total concentration of cellulose crystallites, where only the H+ counterions of surface sulfate groups are present. The dotted lines are calculated from SLO theory.
the suspension concentration increases across the biphasic region. There has however been very little data published on the effect of ionic strength on chiral nematic pitch. When the suspension concentration was fixed at 9.2 × 10-6 nm-3, the pitch changes dramatically with added electrolyte concentration (Figure 11). No obvious difference was found for the three different added electrolytes HCl, NaCl, and KCl. The chiral nematic pitch decreases with increasing the electrolyte concentration, and the chiral twist power, defined as 1/P, doubles in value indicating that a stronger chiral interaction is present at higher ionic strengths. It seems unlikely that the slight increase in crystallite concentration, as shown in Figure 8, is responsible for this effect. It may be that the chiral interaction is screened by the electrical double layer. As the electrical double layer is suppressed at higher ionic strengths, the chiral interaction become stronger. Comparison with Theory. The phase separation of cellulose suspensions is obviously strongly dependent on the suspension concentration and ionic strength of the system. The experimental results may be compared with the theoretical predictions of SLO theory. Two series of experimental data, one for the pure suspension system and one for a system with added electrolyte, will be used. The calculations of the Debye radius κ-1 differ from those of the original SLO theory for the reasons mentioned in the theoretical background. For the pure cellulose suspensions dispersed in water, eq 8 was used to calculate κ-1. Since these cellulose suspensions had only H+ counterions associated with the sulfate groups on the cellulose, the effective counterion concentration can be determined directly from the pH of the suspensions. The parameters h, Deff, and νeff were then calculated from the measured counterion concentrations using eqs 3, 4, and 6, respectively. The results are listed in Table 1. The coexisting concentrations Cic and Cac of the isotropic and anisotropic phase, calculated from
eq 1, are also given in Table 1 and compared with the experimental data in Figure 12. As shown in Figure 12, a relatively good agreement between theoretical prediction and experimental measurement was obtained. With the increase of suspension concentration, both theoretical and experimental coexisting concentrations increase, and the difference between Ci and Ca or Cic and Cac is enlarged. However, the theoretical results are slightly higher than the measured values. At higher concentrations the difference is about 5%, and at lower concentrations the difference is about 20%. For suspensions with added electrolyte, the double layer thickness is estimated from eq 9. The equilibrium salt concentration ns was approximated by the concentration of added salt. Γ was computed from the linear charge density with eq 10. The calculated results are listed in Table 2, and the coexisting concentrations are compared with the experimental data in Figure 8. The agreement is satisfactory at high salt contents, but the SLO theory predicts a decrease in the coexisting concentrations with added electrolyte concentration, while the experimental measurements only show a small variation. The calculated Cac and Cic values are clearly too low at low ionic strength for the system with a fixed total suspension concentration. There are several possible reasons for the discrepancy between theory and experiment. First, it may be attributed to polydispersity in particle size. For all the theoretical results, the particles were assumed to be monodisperse, with a particle length of 115 nm and width of 7 nm. However the particle length measured by image analysis varies from 70 to 170 nm, and image analysis gives no information on any coagulated flocs that may be present in the suspension. Although the suspension was treated with ultrasound in order to break up the flocs,
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Table 2. Comparison of Theory and Experiment for Suspensions with Added Electrolyte ns (mM)
(nm)
νeff (e/nm)
h
Deff (nm)
b × 105 (nm3)
Cic × 10-6 (nm-3)
Cac × 10-6 (nm-3)
Ci × 10-6 (nm-3)
Ca × 10-6 (nm-3)
0 0.43 0.53 0.83 1.05 1.38 1.65 1.98 2.37
11.76 9.17 8.77 7.87 7.35 6.71 6.32 5.92 5.55
3.72 3.87 3.99 4.00 4.07 4.17 4.25 4.34 4.46
0.136 0.139 0.140 0.141 0.141 0.142 0.143 0.143 0.143
86.6 66.0 62.8 56.0 52.0 47.2 44.4 41.3 38.5
143.9 109.7 104.3 93.1 86.4 78.4 73.8 68.6 64.0
4.02 5.30 5.56 6.25 6.73 7.42 7.90 8.48 9.10
5.17 6.80 7.15 8.03 8.65 9.54 10.15 10.90 11.70
8.29 8.31 8.27 8.48 8.54 8.77 8.77 9.03 9.03
10.06 10.10 9.92 10.20 10.03 10.31 10.31 N.A. N.A.
κ-1
doublets or triplets may still exist in the highly concentrated suspension. Light scattering measurements did indeed indicate a larger average particle size. Large particles in the suspension will reduce the measured coexisting concentrations below the theoretical values, as observed in Figure 12. On the other hand, polydispersity in particles size will also introduce a complicated discrepancy from theory. On the basis of a lattice theory for phase separation of rodlike species, Moscicki and Williams showed that increasing the width of the distribution of rod lengths caused a curvature in the relationship between total concentration of rods and volume fraction of the anisotropic phase25 (as observed in Figure 3) and an increase in Ci and Ca with increasing total concentration. The second effect can be clearly seen from the results in Figure 12. As the pH of the suspension decreases (the total suspension concentration increases), the increase in Ci and Ca is more rapid than the increase in Cic and Cac. As a second source of discrepancy, the theories for calculating νeff and phase separation concentrations were derived for a system with excess added monovalent salt, where the electrostatic interaction between polyions could be neglected. For a salt-free polyelectrolyte system, the electrostatic interaction between polyions cannot be ignored. Even for the system with added electrolyte, the simple salt concentrations are far less than the equivalent polyelectrolyte concentration. This does not satisfy the conditions for using SLO theory. A much bigger difference between theory and experiment in the systems with added electrolyte system (Figure 8) may arise from errors in estimating the ionic strength. Although the contribution of the polyion to ionic strength was considered in eq 10, it was underestimated compared to the real system. Since the added electrolyte concentration is much lower than the equivalent concentration of the polyelectrolyte, in the outer region of the polyelectrolyte, the counterions still play a major role on the total ionic strength. (25) Moscicki, J. K.; Williams, G. Polymer 1982, 23, 559.
The application of SLO theory to other highly charged colloidal suspensions, such as TMV26 and DNA27 systems, also showed some discrepancies from the experimental data. Although the flexibility of the suspended species may contribute to the discrepancy in some systems, it is unlikely to be a factor for the cellulose crystallites. Conclusions The phase separation of suspensions of cellulose crystallites resembles those observed for stiff-chain polypeptide28 and polysaccharide29,30 macromolecules. The critical concentrations for a sample exhaustively dialyzed against water were determined as, from isotropic to biphasic, C ) 5.14 × 10-6 nm-3, and from biphasic to anisotropic, C ) 15.3 × 10-6 nm-3. Particle geometry and ionic strength are the most important factors governing phase separation. With increasing total suspension concentration or increasing ionic strength, coexisting concentrations in both isotropic and anisotropic phases increase, but the chiral nematic pitch of the anisotropic phase decreases. For a biphasic sample at a fixed total concentration of crystallites, increasing the amount of added electrolyte decreases anisotropic phase formation, but the coexisting concentrations in both phases are only increased slightly. A relatively good agreement between theoretical predictions and experimental results is obtained for the pure suspension. Acknowledgment. We thank L. Godbout for useful discussions, and the Pall Corporation for a scholarship (X.M.D.). LA950133B (26) Fraden, S.; Maret, G.; Casper, D. L. D.; Meyer, R. B. Phys. Rev. Lett. 1989, 63, 2068. (27) Strzelecka, T. E.; Rill, R. L. Macromolecules 1991, 24, 5124. (28) Robinson, C. Faraday Soc. Trans. 1956, 52, 571. (29) Maret, G.; Milas, M.; Rinaudo, M. Polym. Bull. 1981, 4, 291. (30) Van, K.; Teramoto, A. Polym. J. 1982, 14, 999.
