Article Cite This: Langmuir XXXX, XXX, XXX−XXX
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Phase Separation and Stack Alignment in Aqueous Cellulose Nanocrystal Suspension under Weak Magnetic Field Yimin Mao,*,†,‡ Markus Bleuel,†,‡ Yadong Lyu,§ Xin Zhang,† Doug Henderson,† Howard Wang,† and Robert M. Briber† †
Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, United States NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States § Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States Downloaded via TUFTS UNIV on June 30, 2018 at 23:52:03 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
‡
S Supporting Information *
ABSTRACT: Isotropic−nematic (I−N) transitions in cellulose nanocrystal (CNC) suspension and self-assembled structures in the isotropic and nematic phases were investigated using scattering and microscopy methods. A CNC suspension with a mass fraction of 7.4% spontaneously phase separated into an isotropic phase of 6.9% in the top layer and a nematic phase of 7.9% in the bottom layer. In both the phases, the CNC particles formed stacks with an interparticle distance being of ≈37 nm. One-dimensional small-angle neutron scattering (SANS) profiles due to both phases could be fitted using a stacking model considering finite particle sizes. SANS and atomic force microscopy studies indicate that the nematic phase in the bottom layer contains more populations of larger particles. A weak magnetic field of ≈0.5 T was able to induce a preferred orientation of CNC stacks in the nematic phase, with the stack normals being aligned with the field (perpendicular to the long axis of CNC particles). The Hermans orientation parameter, ⟨P2⟩, was ≈0.5 for the nematic phase; it remained unchanged during the relaxation process of ≈10 h. The fraction of oriented CNC populations decreased during the relaxation; dramatic decrease occurred in the first 3 h. The top layer remained isotropic in the weak field. Polarized microscopy studies revealed that the nematic phase was chiral. Adjacent particles in a stack form a twisting angle of ≈0.6 °, resulting in a helix pitch distance of ≈22 μm.
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INTRODUCTION Cellulose is a type of polysaccharide, with 6-membered pyranose rings being connected by 1,4 β-linkages. The molecular chain is rigid, possessing a near-planar conformation in a crystal. It is produced in cell walls of high plants, algae, fungi, bacteria, and so on. Because of the rich number of interchain hydrogen bonds, cellulose molecules crystallize during the biosynthesis process, forming microfibrils with a high degree of crystallinity. These microfibrils are associated into macrofibrillar bundles and further into fiber networks, serving as a scaffold providing mechanical strength for cell walls.1−5 The structural hierarchy of cellulose has been attracting attention from material scientists for a long time. In the last two decades, owing to the development of techniques to subtract nanosized crystals from biomass, intensive efforts have been taken to produce functional materials using cellulose nanocrystals/nanofibers (CNCs/CNFs) as building blocks.6,7 In general, CNC/CNF subtraction methods fall into one of the two major categories. Acid hydrolysis is a conventional method. Defects and amorphous regions in cellulose fibers are readily attacked by acid molecules; high crystalline regions © XXXX American Chemical Society
are more resistant. Therefore, by choosing appropriate reaction conditions (pH value, temperature, etc.), nanosized crystals can be produced.8,9 CNCs due to acid hydrolysis are approximately 100 to 200 nm long with characteristic sizes of the cross section being of few tens of nanometers, depending on the hydrolysis condition.10,11 In the late 90s, another effective method using 2,2,6,6-tetramethylpiperidine1-oxyl (TEMPO)-mediated oxidation was developed. In this approach, the oxidation reaction takes place in a relatively mild condition, so that very thin (nominal cross-sectional size being of few nanometers) and long (in a micrometer scale) fibrils can be disintegrated and separated from macrofibers.12−16 Both CNCs and CNFs have important applications in materials science. The enormous aspect ratio of CNFs makes them suitable to produce fibers (hybridize with polymer), films, hydrogels, and so on.17−22 CNCs, on the other hand, show more complex colloidal properties in aqueous suspensions. It has been found that an isotropic−nematic Received: May 3, 2018 Revised: June 12, 2018
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DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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out. The suspension was then dialyzed against deionized water for 1 week, with the bath being changed twice a day. The final product had a mass fraction of 2.4% and a pH value of ≈3. The dialyzed CNC suspension was ultrasonicated to produce a stable colloidal suspension. Typically, a probe with a diameter of 6 mm was used for a 10 mL suspension; the power was maintained at 375 W for 10 min. To prepare samples for SANS measurements, the suspension was blown dry using nitrogen and was redispersed in D2O for the desired concentrations. In this paper, a 7.4% CNC suspension was used, the sample was kept static for 1 day allowing for phase separation. The phase-separated suspension consisted of two layers; they were loaded into titanium sample cells separately for the SANS study. SANS Experiment. SANS experiments were carried out at the beamline NGB 30m SANS in the NIST Center for Neutron Research (NCNR), National Institute for Standards and Technology (NIST).44 Neutron wavelength was set as 6 Å, with a wavelength spread of ≈12%. Three instrumental configurations with sample-to-detector distances of 1, 4, and 13 m were used to cover a q-range of ≈0.003 to ≈0.5 Å−1 (q is the absolute value of the scattering vector; q = (4π/λ) sin θ, with λ and θ being the neutron wavelength and half of the scattering angle, respectively). Titanium cells with two quartz windows were used as sample holders for the SANS experiment. The cell thickness was 1 mm, and the aperture size was 19 mm in diameter. The neutron beam size was 12.7 mm in diameter. In the magnetic alignment study, the orientation of the sample cell, magnetic field, and neutron beam is schematically shown in Figure 1. The neutron beam is perpendicular
(I−N) transition can take place in CNC suspensions when a critical concentration is reached.23,24 This phenomenon is wellknown for rodlike colloidal systems;25−27 the theoretical treatment was first given by Onsager, who used it to explain the I−N transition observed in aqueous tobacco mosaic virus (TMV) suspensions.28 Gray studied CNC phase separation for suspensions with different ionic strengths, and the results were qualitatively consistent with the theory for charged rodlike particles.24 The nematic phase due to I−N transition in CNC suspension is chiral.23,29,30 The pitch distance of a helix is in macroscopic length scale, readily to be observed using polarized optical microscopy (POM). Moreover, CNC particles can be aligned by a magnetic field because of their diamagnetic anisotropy, which originates from the permanent magnetic susceptibility of the pyranose ring and chemical bonds with specific orientation.31,32 This behavior has also been found in many other systems such as rigid synthetic polymers, polypeptides, globule proteins, viruses, and biomacromolecular filaments.33−39 The overall magnetic susceptibility is the sum of that from each individual functional group in a particle; it can be positive or negative. CNC particles are negatively anisotropic, which means that when applying a magnetic field, the long axis of the particle aligns perpendicularly to the field direction.40 Efforts have been made to utilize the diamagnetic anisotropic property of cellulose, either to achieve crystal alignment for structural studies or to produce materials showing directional properties. However, the susceptibility in a CNC particle is weak; and a strong magnetic field (typically >10 T) is needed to achieve particle alignment,31,32,41,42 which makes this method practically less useful. More recently, it has been reported that a weak field of ≈1 T can also achieve a certain degree of CNC alignment in relatively concentrated suspensions; and a cooperative motion of CNC particles was found during the aligning process.43 The author rationalized that the reason for achieving alignment by such a weak magnetic field was because particle relaxation in concentrated solution was slow, while in dilute solution the weak magnetic force could not compete with particle Brownian motion. In this paper, we revisit the I−N transition in aqueous CNC suspension beyond the critical concentration by carefully examining the structures in both isotropic and nematic phases. Structural details about self-assembled CNC stacks are quantitatively analyzed using small-angle neutron scattering (SANS). We also show that CNCs in the nematic phase can be aligned by applying a fairly weak magnetic field of ≈0.5 T. In situ SANS experiment revealed details about the stack relaxation from the aligned state. Combined with atomic force microscopy (AFM) and POM studies, CNC morphologies as well as the chiral nematic structures are examined.
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Figure 1. Relative orientations of the sample cell, magnetic field, and neutron beam in the SANS experiment. to the magnetic field direction. In the center of the sample cell, the field strength is ≈0.5 T. Because of practical considerations, the in situ relaxation process (rather than alignment process) was monitored using SANS. The CNC suspensions were first loaded into the cells, sandwiched between two magnets, and allowed to stand for 12 h. Then, the cells were taken out of the magnetic field and mounted at the beamline. SANS data were collected approximately every 1 h to trace the relaxation process. SANS data reduction was carried out using an IGOR-based macro developed at NCNR.45 The reduction considered various corrections including contributions from the empty sample cell, sample transmission, detector noise from environmental backgrounds, and so on. Multiple scattering effects were negligible for all samples. Wide-Angle X-ray Scattering. Wide-angle X-ray scattering (WAXS) experiments were conducted at the A1 undulator station of Cornell High Energy Synchrotron Source. A short X-ray wavelength of 0.642 Å was used to mitigate water absorption. 2D scattering patterns were recorded using a large-field-of-view detector (ADSC, Quantum-210) placed at a distance of 504.7 mm from the sample. The X-ray beam was attenuated to maximize utilization of the
EXPERIMENTAL SECTION
Materials. Colloidal CNC suspensions were prepared using the sulfuric acid hydrolysis method, following a well-documented protocol.11,24 Briefly, 5 g of no. 1 Whatman filter paper was mixed with 60 mL of 64% (mass fraction is used as the unit for concentration throughout this paper) sulfuric acid. The mixture was maintained at 45 °C and kept stirred for 1 h. To terminate the reaction, the mixture was quenched by adding 60 mL of ice cold deionized water. The mixture was immediately centrifuged for 15 min with a relative centrifugal force of 3220g, and the supernatant was discarded. The washing step was repeated for five times, until a turbid suspension was formed, and no further centrifugation could be carried B
DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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Langmuir detector’s dynamic range. Preliminary data processing for quick presentation during the experiment (setup calibration, centering, and azimuthal integration) was performed using BioXTAS RAW software.46 Liquid sample was sealed in a Kapton tube with an inner diameter of 1 mm. The typical exposure time was 90 s. Atomic Force Microscopy. CNC morphology studies were carried out using AFM (Dimension Icon, Bruker), operating in tapping-mode. An antimony-doped silicon probe (TESPA-V2) was used for all measurements. The samples from the top and bottom layers were diluted by 1000 and 2000 folds, respectively, for AFM study. Data analysis was performed using the Nanoscope image processing package. Polarized Optical Microscopy. Polarized optical microscopic characterization was carried out using an Olympus BX60 microscope. Samples were loaded and sealed using epoxy in a rectangular capillary (100 μm thick and 2 mm wide). The optical path and the applied magnetic field were perpendicular.
dimensional (1D) profiles are shown in Figure 3. A strong interference peak (first-order) was found in the scattering data
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RESULTS AND DISCUSSION The as-prepared, homogeneous 7.4% CNC suspension became biphasic after standing for 24 h, as shown in Figure 2. A clear
Figure 3. 2D SANS patterns of the top and bottom layer (a,b); corresponding 1D curves reduced from the 2D patterns (c). Solid lines are fitted results (see details in the text). Curves are shifted to facilitate visualization. Figure 2. CNC suspension of 7.4% (a) as-prepared suspension and (b) biphasic suspension after standing for 24 h.
of both top and bottom layers. The scattering pattern for the top layer was isotropic, which is due to random orientation of CNC particles. The anisotropic scattering pattern for the bottom layer suggested a preferred orientation of CNC particles. The scattering pattern is due to interference of waves scattered by all particles exposed in the neutron beam; the local orientational order must be averaged out in the large scattering volume (defined by the neutron beam size and sample thickness). Therefore, the preferred orientation is mainly due to the alignment effect caused by gravity during the phase separation process. A minor reason would be the shear effect during the sample loading (using a syringe and hypodermic needle). In the 1D SANS profiles (Figure 3c), the position of the first-order interference peak occurs at q ≈ 0.017 Å−1 (for both phases), corresponding to an interparticle distance of ≈37 nm. A shoulder of the second-order interference peak is also visible; the ratio of the two peak positions is about 1:2. It turns out that both curves can be fitted using a stacking model considering finite particle sizes. Details of model fitting are given in the Appendix. The method is briefly introduced here. An individual CNC particle is modeled as a parallelepiped with a length L, width b, and thickness a (see Figure 10 in the Appendix). The rectangular shaped cross section is due to the unit cell dimensions of cellulose crystals.40,48−50 In the stacking model, CNC particles are stacked in one direction (z-axis in
boundary between the two phases can be seen. The top layer is visually more transparent. Systematic studies on the phase diagram of aqueous CNC suspensions have been reported.24,29 Spontaneous phase transition occurs in a concentration range between ≈5 and ≈13%. The volume fraction of the two phases depends on the initial concentration. In our experiment, the 7.4% CNC suspension phase separated into two phases with a volume ratio of approximately 1:1, and the concentrations of the top and bottom layer are 6.9 and 7.9%, respectively, which is consistent with the reported phase diagram. The biphasic suspension is due to the I−N transition in lyotropic liquid crystal systems. Onsager first treated this problem by using a hard-core potential for rodlike particles.25,26,28,47 The free energy of a hard rod fluid was calculated using the virial expansion approach, truncating to the second term. The theory shows that the origin of the I−N transition is purely entropic. Particles adopt a parallel packing in the nematic phase to increase translational entropy, sacrificing for the orientational freedom. In the isotropic phase (top layer), the particles remain randomly oriented. We collected samples from the top and bottom layers in the biphasic suspension and examined them separately using SANS. The 2D scattering patterns and the reduced oneC
DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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Langmuir Figure 10). d is the distance between the surfaces of two adjacent particles. Interparticle distance is hence d + a; the position of the first interference peak stems from the averaged value of this distance. Stacking of parallelepipeds follows 1D paracrystal statistics. The model was originally developed by Zernike and Prins, to treat 1D fluid containing atoms with a fixed diameter.51 Ruland introduced a mathematically neat form, which could treat general cases when both particle size and interparticle distance have polydispersity.52 This has been successfully applied to layered structures with lateral sizes much larger than characteristic lengths in the packing direction.53,54 In our case, particle length L can be considered “infinitely large”, as it in general exceeds ≈150 nm; this produces ∼q−1 asymptote in the 1D scattering profile due to particle’s form factor in lowq.50 b and a are fitting parameters in the stacking model; they can also be obtained by fitting the 1D scattering curves from dilute CNC suspensions. The methodology has been reported elsewhere.50 Details about deriving b and a using 1D SANS profiles for dilute suspensions are given in the Supporting Information. Particles in the top and bottom layers have different sizes, as will be discussed later. The stacking model allows continuous length distributions for the intervals between the particles, d, and the particle thickness, a. We select a Γ-distribution which rejects all negative values. The broadness of the distributions is characterized by the standard deviations, σd and σa. The model does not consider twisting angles between particles. It will be shown later that CNC particles can form chiral nematic liquid crystal phase. The pitch distance, however, is in the microscopic scale. Thus, it can be safely ignored in SANS data fitting. Fitting results of 1D SANS profiles in Figure 3 are given in Table 1. Interparticle distance, a̅ + d̅, for stacks in both top and
Figure 4. AFM images of CNC particles in the bottom (a,b) and top layers (c,d). (a,c) are height images; (b,d) are amplitude error images.
determined in a noninvasive manner by examining dilute suspensions using scattering methods. Length and width as determined using SANS are 24.1 and 5.4 nm for particles in the bottom layer and were 19.4 and 4.7 nm for that in the top layer (details are given in the Supporting Information). There are theories concerning the influence of the size polydispersity on the I−N transition in lyotropic liquid crystal systems. Lekkerkerker tested a binary system containing two populations of rods with different lengths.55 It turned out that the bottom layer consisted of a significantly higher number of longer particles. Vroege considered a more general case where the rodlike particles have a continuous length distribution.56 It has been shown that polydispersity can broaden the concentration window for I−N transition to occur and the bottom layer contains populations of longer particles. These results have been observed for other rodlike systems such as clay and virus.57−60 The similarity between the 1D SANS profiles of the samples from the top and bottom layers should be considered carefully. In the nematic phase, high-order interference peaks are often observed in small-angle scattering experiments. For example, Caspar et al. studied nematic TMV using small-angle X-ray scattering (SAXS); two interference peaks were observed.61 The first peak was due to particle interaction, and it varied with concentration. The position of the second peak, however, was independent of concentration; it was interpreted as due to the particle form factor. Scattering data interpretation for the isotropic phase has been focused mostly on the first-order interference peak. This peak shows up in both dilute (well below the overlap concentration, c*, which scales as ∼L3, with L being the rod length) and semidilute suspensions. In the dilute regime, the peak position scaled as c1/3 (c is the suspension concentration); while in semidilute suspensions, it scaled as c1/2. Its origin was interpreted as caused by liquidlike interactions because of nearest neighbor particles.62,63 A ratio of the two interference peak positions of 1:2 is a signature of lamellar periodic structures. Moreover, a layered structure with infinite lateral width produces a ∼q−4 asymptote which can be understood from the interface distribution function.53,54,64 Considering the finite lateral extension, 1D scattering curves show a ∼q−3 asymptote (see the Appendix for detail). The low-q data shows a ∼q−1 asymptote, which is due
Table 1. Particle Dimensions and Interparticle Distance in a CNC Stack. a and b Are the Particle Cross-Sectional Thickness and Width, Respectively; d is the Distance between Two Adjacent Particles in a CNC Stack; They Are Determined Through Model Fitting of SANS Dataa
top bottom
a̅ (nm)
σa (nm)
d̅ (nm)
σd (nm)
b̅ (nm)
L̅ (nm)
σL (nm)
3.2 3.7
2.0 2.3
33.6 33.0
10.1 8.3
15.5 22.5
202.7 129.1
33.3 25.5
a
L is the particle length, determined by AFM. See details in the text.
bottom layer are about the same, namely, ≈37 nm. Stacks in the bottom layer, however, seems to have more ordered packing, as the distance deviation from d̅ is smaller. Moreover, CNC particles in the top layer seem to have smaller sizes; particularly, the particle width, b̅, in the top layer is ≈7 nm smaller, as compared with that of particles in the bottom layer. In our previous studies, we have discussed that the lengths of CNC particles are too long to be confidently derived from SANS data.50 AFM provides a direct measure; this is shown in Figure 4. The average length (L̅ ) of the CNC particles in the bottom layer is 202.7 nm and that in the top layer is 129.1 nm (with standard deviations, σL, being of 33.3 and 25.5 nm, respectively): compared with particles in the top layer, particles in the bottom layer are more than 50% longer. It turned out that aggregation during the drying process of AFM sample preparation made it difficult to determine the width and thickness of individual CNC particle. These sizes can be D
DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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Langmuir to the form factor for long rodlike particles. These features have been observed in 1D scattering profiles of our CNC suspensions, in both top and bottom layers (see Figure 3). They suggest that CNC particles in the isotropic phase are not homogenously dispersed but can form stacks. There are existing reports suggesting that CNC aggregation can occur at fairly low concentrations.29 A weak magnetic field of ≈0.5 T was applied to both isotropic and nematic phases for 12 h. The weak field could not cause particle alignment in the isotropic phase. However, a considerable degree of preferred orientation was observed in the nematic phase in the bottom layer. 2D SANS and WAXS patterns of magnetically aligned nematic CNC are shown in Figure 5; the magnetic field is in the s3 direction. In
Figure 6. Hierarchical structures of a CNC stack. Each individual CNC particle is represented by a parallelepiped. When a magnetic field is applied, the z-axis is aligned with the field direction. Cellulose chains extend along the long-axis of a CNC particle. Pyranose rings of cellulose molecules are in the xy-plane.
magnetic force needs to overweigh particle relaxation. However, as predicted in liquid crystal theory, a much smaller field is needed to achieve particle alignment in the nematic phase.34,39 Effect of both viscosity and particle stacking play a role; the former damps the particle relaxation, while the latter might cause a synergic effect due to the addition of diamagnetic susceptibility of particles in a stack. We need to point out that there have been efforts trying to investigate the preferred orientation of CNC particles in the isotropic and nematic phases separately, though cutting from different perspectives. Tatsumi et al. prepared polymer composites using in situ polymerization of CNC/2-hydroxyethyl methacrylate aqueous suspension with a magnetic field applied.69 The author also observed that alignment could only be achieved when the nematic phase CNC was used. The authors used an 8 T magnetic field; this is perhaps because that polymerization suspension had a much higher viscosity. The relaxation process of the nematic phase CNC suspension after taken out of the magnetic field (after being aligned for 12 h) was studied in situ using SANS. Scattering intensity distribution along the polar angle in reciprocal space is related to an orientation distribution function of rodlike particles in the real space. In the 1949s paper, Onsager crafted a trial function with the following form to calculate free energy of a hard-rod fluid28
Figure 5. 2D SANS and WAXS patterns of nematic CNC suspension aligned by ≈0.5 T magnetic field for 12 h. The s3-axis as shown in the scattering patterns indicates the magnetic field direction.
comparison to the SANS pattern shown in Figure 3b for the as-prepared nematic phase, the SANS pattern in Figure 5a clearly indicates that CNC stacks are preferably oriented with their normals in parallel to the magnetic field direction. In the WAXS pattern (Figure 5b), the strongest peak at q = 1.61 Å−1 is more concentrated on the s3-axis. Cellulose samples with plant origin often show crystals of a mixture of two modifications, namely, Iα and Iβ forms.65,66 The former has a P1 space group and the latter P21.67,68 Though Iβ has a higher degree of symmetry, from the crystallographic point of view, the difference in diffraction peaks of these two crystal forms can only be told by comparing high quality fiber diffraction data. In the powder form, most Bragg peaks from these two crystal forms overlap. The strongest peak for the Iα form is indexed as (1 1 0), and it is (2 0 0) for the Iβ form. They both appear at the same position.66 The (1 1 0) plane in the Iα form and the (2 0 0) plane in the Iβ form are all due to the planes containing pyranose rings of cellulose molecules (crystallographic details of these two crystal forms have been well-documented in Langan’s pioneering work.67,68 Molecular packing in these two forms is given in the Supporting Information). Combining small- and wideangle scattering data, the hierarchical structures of CNC stack are schematically shown in Figure 6. Here, CNC particles were modeled as parallelepipeds, pyranose rings of cellulose molecules are in the xy-plane, and the cellulose chains extend along the long-axis. The magnetic field affected the orientation of the entire stack. Though most existing studies on aligning CNC suspension taking advantage of diamagnetic susceptibility of CNC particles employ strong magnetic fields, it is not surprising that the nematic phase could be aligned by a weak field. Orienting an individual particle is indeed challenging, as the
g (β) = p csch(p) cosh(p cos β)
(1)
where p is a parameter defining the distribution width and β is the angle characterizing the orientation of the particle with respect to a reference axis. In seeking for analytical solutions to the integration kernel, Burger independently worked out a neat expression for the polar angle intensity distribution70−72 F(ϕ , ϕ′) = p csch(p) cosh(px) I0(py)
(2)
where x = cos ϕ cos ϕ′ and y = sin ϕ sin ϕ′; I0 is the modified Bessel function of the first kind of order zero. F(ϕ,ϕ′) is the kernel proportional to the scattering intensity; ϕ′ is the position where distribution is peaked. In our case, ϕ′ = 0, as indicated in Figure 5a. Furthermore, the Hermans orientation function, ⟨P2⟩, also known as the order parameter for the nematic liquid crystal, is given as ⟨P2⟩ = 1 − 3[coth(p) − 1/p] /p E
(3) DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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Langmuir In Figure 7a, the I(ϕ) versus ϕ plots at different relaxation times are shown (the starting and end points of polar angle, ϕ,
magnetic field, the fraction of oriented CNC population keeps decreasing, with the most dramatic decrease occurring in the first 3 h. The curve of relaxation kinetics can be fitted using a unimodal exponential decay, as shown in Figure 7b. The degree of orientation of the oriented populations, however, remains unchanged. In Onsager’s theory, the I−N transition produced the nematic phase with a large order parameter (>0.8). This has been experimentally observed for monodispersed systems, essentially biological particles. For CNC systems, it has been shown that the transition is only qualitatively in agreement with the theory. Elaborated theories considering size polydispersity show a broad concentration window for I−N transitions and a lower degree of orientation in the nematic phase.56 It is of interest to examine the influence of magnetic field on the packing of CNC particles by comparing the 1D SANS profiles of the nematic phase at different stages of relaxation. Figure 8 shows the SANS profiles of a sample before
Figure 7. Polar angle dependence of scattering intensities (a) and the change of oriented fraction of CNC and Hermans orientation parameter (⟨P2⟩) during the relaxation process of the nematic phase (b). I(ϕ) vs ϕ plots were produced using data from the first-order peak in the 1D SANS profiles, within the range 0.01 Å−1 < q < 0.025 Å−1. The decrease of oriented fraction of CNC in (b) can be fitted using an exponential decay (solid line).
Figure 8. 1D SANS profiles of the nematic CNC sample having different history of magnetic alignment. See the text for details.
alignment, the same sample being magnetically aligned for 12 h and relaxed for 10 h. All curves are normalized according to their transmission coefficients. It can be seen that magnetic field indeed caused the profile of the aligned sample to produce slightly stronger intensity maxima. However, the differences between the three curves are rather minor, as compared to significant difference in the polar angle dependence of the intensity (Figure 7a). The characteristic features of the curves, the two interference maxima due to CNC stacking, are the same; and the peak positions remain unchanged during the relaxation. This suggests that the weak magnetic field plays only a role in rotating the stacks according to the field direction and does not induce a different packing. The nematic phase of CNC suspension due to I−N transition is chiral in a macroscopic scale, which is evident under polarized microscopy, as shown in Figure 9. Isotropic phase in the top layer does not show birefringence, and it becomes dark under cross-polarized mode (by decreasing angle between the polarizer and the analyzer, a bright, homogeneous field can be seen, as shown in Figure 9b). In contrast, the nematic phase is birefringent, but as the asprepared sample has a poor preferred orientation, no optical fringes can be observed. After aligning the nematic phase for 12 h, fringes perpendicular to the magnetic field direction are clearly visible (Figure 9c). The fringes are highly periodic; by Fourier transforming the POM image, oscillatory interference patterns can be produced. The peak positions of the intensity
is defined in Figure 5a). The profiles are fitted using eq 2. With careful data calibration and background subtraction, the scattering intensity shown in Figure 7a is in the absolute scale. This allows us to examine not only the width of the distribution function but also the background level because of unoriented populations of CNC particles. From Figure 7a, it seems that the intensity distribution becomes “broader” as time elapses. Intuitively, a broad intensity distribution corresponds to a lower degree of preferred orientation of particles. However, careful fitting of the profiles using eq 2 considering the background level variations indicates that the degree of orientation, namely, ⟨P2⟩, keeps unchanged during the relaxation process. The fraction of the orientated particles, which is derived by taking the ratio between the area of bellshaped distribution and the overall area including the contribution due to a constant background within [−π/2, π/ 2], however, decreases with time. These results are quantitatively shown in Figure 7b. Cranston et al. studied CNC orientation induced by magnetic field in situ using SAXS.43 They observed a twostage orientation kinetics, with the first stage being fast, taking place in 2 h, followed by a much slower process. Our kinetic study for the reverse process shows that, aligned by the weak F
DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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nematic phase is chiral, and the pitch distance is about 22 μm, which is due to a ≈0.6° twisting angle between two adjacent particles. Our quantitative study of the biphasic CNC suspension reveals its complex nature to be further understood. The structure and phase behavior are influenced by multiple factors such as surface charge, particle shape (rectangular cross section), size polydispersity, and so on. The effective alignment archived using weak magnetic field sheds new light on structure manipulation, which is potentially useful for producing functional materials with tuned optical properties. Also, it has been demonstrated that SANS is a unique probe to investigate biopolymers in aqueous suspensions. The kinetic process can be examined without concerning the sample damage, which usually poses a serious limitation to the use of X-ray scattering. SANS can also provide more structural details when applied to multicomponent systems, such as CNCpolymer composites, using the contrast-matching technique.
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Figure 9. Polarized optical micrographs of nematic CNC suspension before alignment (a); top layer (b) and bottom layer (c) being aligned for 12 h; and the bottom layer relaxed for 1 day after a 12 h alignment (d). A schematic of chiral nematic stack is shown in (e). lp refers to the pitch distance; z-axis is preferably aligned with the magnetic field direction.
APPENDIX
Scattering from a CNC Stack
This appendix concerns scattering from a stack consisting of parallelepipeds with a length L, width b, and thickness a, as schematically shown in Figure 10. Parallelepipeds are packed in
maxima in the interference pattern give a statistical measure of the interfringe distance, which is ≈22 μm (details of image processing using FFT are given in the Supporting Information). Misorientation of CNC stacks is evident in the micrograph of the sample relaxed for 1 day (Figure 9d). A 22 μm pitch distance indicates that there are ≈600 CNC particles in one pitch (interparticle distance is ≈37 nm, see Table 1). Therefore, the adjacent particles possess a twisting angle of ≈0.6°. A chiral nematic CNC stack is schematically shown in Figure 9e. The mechanism for CNC particles to form a chiral nematic phase is not fully understood. Two factors might play an important role. At the molecular level, cellulose molecules are chiral, and they are packed in a crystal with fixed orientation, preserving the chiral interaction for nanocrystals.23 For charged rodlike particles, the surface charges can cause a twisting force, which might also be associated with the helical nature of CNC stacks.73
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CONCLUSIONS We investigated self-assembled structures in the isotropic and nematic phases of CNC suspension due to I−N transitions. Spontaneous phase transition occurred in a 7.4% CNC suspension. SANS data indicated that CNC stacks existed in both isotropic and nematic phases, though the former has a lower concentration. Interparticle distances in both phases are ≈37 nm, derived by fitting the 1D curve using a stacking model. CNC particles are polydisperse in size, particularly for their lengths. Both SANS fitting results and AFM micrographs indicated that the nematic phase contained more populations of larger particles. The nematic phase was able to be aligned by applying a weak magnetic field of ≈0.5 T, while the isotropic phase cannot. After being subjected to the magnetic field for 12 h, CNC stacks in the nematic phase are preferably aligned along the magnetic field. The Hermans orientation parameter, ⟨P2⟩, was ≈0.5, and it kept unchanged during the process of relaxation for 10 h. The fraction of aligned CNC particles decreased in the relaxation process; dramatic decrease occurred in the first 3 h. POM studies indicate that the
Figure 10. Stack consisting of parallelepipeds with length L, width b, and thickness a. In real space, Cartesian coordinates with basis vectors x, y, and z are used to define a stack; packing direction is along the zaxis. In reciprocal space, three orthogonal basis vectors s1, s2, and s3 are employed. Spherical coordinate using radius s, polar angle ϕ, and azimuthal angle ψ can also be used, depending on convenience.
an ordered manner only in one direction. In Figure 10, two sets of orthogonal coordinates with a common origin (O) are used to define such a stack in real space (with three basis vectors being x, y, and z), and reciprocal space (with basis vectors being s1, s2, and s3). The stacking direction is along the z-axis in real space. Figure 10 shows the condition when L ≫ b ≫ a, which is relevant for the CNC system as discussed in the text. Several approximations are made when deriving the relationship between scattering intensity due to such a stack G
DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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where t = πbs/β. I0[...] in eq 8 is the modified Bessel function of the first kind of order zero. β takes a numerical value of 1.61, which enables that the area under sinc2(x) and exp(−x2/β2) are the same within [−π, π]. Equation 8 is used to fit circularaveraged SANS data, where I1(s) is given by eq 5. Note that the combination of eqs 5 and 6 produces an asymptote of I ∼ s−3. The stacking model for a lamellar structure with an infinitely large lateral size produces an asymptote of ∼s−4, as the intensity is localized along layers’ normal (s3 direction in Figure 10). Because of a finite width of a parallelepiped, b, scattering intensity is localized in a plane (s2s3) rather than along an axis, producing an overall asymptote of ∼s−3. Γ-distribution [denoted as hΓ(x)] is a useful choice of length distribution for d and a
as a function of absolute value of scattering vector s, where s = 2 sin θ/λ. s is equivalent to the q-notation, with q = 2πs. First of all, it is assumed that L ≫ a, b, which is usually an excellent approximation for CNCs or CNFs. In this case, scattering intensity (not angular averaged) must be largely localized in the s2s3-plane in the reciprocal space, that is I(s1 , s2 , s3) = b2 sinc 2(πbs2) ·δ(s1) ·I1(s3)
(4)
In eq 4, sinc(x) = sin(x)/x. The δ-function, δ(s1), simply states that scattering intensity can only be observed when s1 = 0. I1(s3) is the scattering intensity along s3. The distance between two parallelepipeds along the z-axis is allowed to vary. The “density” profile along the z-axis of a stack is schematically shown in Figure 11. Δρ in Figure 11 refers to the scattering length density difference between a particle and its surroundings.
hΓ(x) = Γ(ν)−1α −νx ν − 1exp( −ν /α) with x ̅ = αν, and σ = α ν
(9)
where x̅ is the mean value of the distance x and σ is the standard deviation of the distribution. The Fourier transform of hΓ(x) is a complex function and is written as54 HΓ(s) = (1 − 2πiαs)−ν Figure 11. Density profile along the z-axis of a stack.
Simulated 1D SANS profiles due to stacking models discussed above with two different size distributions are shown in Figure 12. Size polydispersity broadens the
Structures possessing such a density profile are categorized as 1D paracrystals. Zernike and Prins first developed a model to treat scattering from a 1D fluid.51 The original treatment used a fixed “atomic” diameter and an exponential decay of probability function for the interparticle distance distribution. A neat mathematical form of I1 considering an arbitrary distribution of particle thickness, a, and the internal between two adjacent particles, d, has been given by Ruland,52 as shown in eq 5. ÄÅ ÉÑ 1 ÅÅÅ (1 − Hd)(1 − Ha) ÑÑÑ ÑÑ I1 ∝ 2 ReÅÅÅ ÑÑ ÅÅÇ 1 − HdHa s ÑÖ (5) In eq 5, Re[...] stands for the real part of a complex function. Hd and Ha are Fourier transforms of length distribution of d and a. Note that the 1/s2 asymptote stems from the operation of taking second derivative of the Heaviside’s function (Figure 11) when deriving interface distribution function.64 eq 5 is sometimes referred to as the stacking model. It is convenient to employ a spherical coordinate system defined by (s, ϕ, ψ), as shown in Figure 10.
Figure 12. Examples of simulated 1D scattering profile due to a CNC stack illustrated in Figure 10, with different length distribution of thickness, a, and interval between two parallelepipeds, d. The mean values of a and d are 4 and 33 nm, respectively.
s = s12 + s22 + s32 ; ϕ and ψ are the polar and azimuthal angle, respectively. Accordingly, s3 = s cos ϕ and s2 = s sin ϕ. The scattering intensity after angular averaging is written as I (s ) =
a 2 b2 2πs
∫0
2π
sinc 2[πbs sin ϕ]·I1(s cos ϕ)dϕ
interference peaks but does not change their positions. Peak positions follow a ratio of sp1/sp2 = 1:2... Position of the firstorder interference peak, sp1, corresponds to the interparticle distance, namely, a̅ + d̅ = 1/sp1.
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(6)
Under the condition that b ≫ a, I1 does not varies much from the value when ϕ = 0, so that eq 6 can be approximated as follows a 2 b2 I (s ) ≈ I1(s) 2πs
∫0
π
sinc 2[πbs sin ϕ]dϕ 2
2
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b01452.
(7)
SANS data and model fitting of dilute CNC suspensions; 1D WAXS profile of nematic CNC suspension; molecular packing of Iα and Iβ form cellulose crystals; and image analysis for POM data using FFT (PDF)
2
If we approximate sinc x as exp(−x /β ); the integrand in eq 7 can be worked out, so that I (s ) ≈
a 2 b2 I1(s) ·exp[−t 2/2]·I0[t 2/2] s3
ASSOCIATED CONTENT
(8) H
DOI: 10.1021/acs.langmuir.8b01452 Langmuir XXXX, XXX, XXX−XXX
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Yimin Mao: 0000-0002-6240-3791 Notes
The authors declare no competing financial interest. Disclaimer. The identification of any commercial product or trade name does not imply endorsement or recommendation by the National Institute of Standards and Technology.
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ACKNOWLEDGMENTS We acknowledge support under award 70NANB12H238 from the National Institute of Standards Center for Neutron Research. Access to NGB 30m SANS beamline at the NIST Center for Neutron Research was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under Agreement No. DMR1508249; we are grateful to the help from Dr. Cedric Gagnon. Dr. Stanislav Stoupin’s assistance for synchrotron WAXS experiment at A1 beamline of CHESS was greatly appreciated. CHESS is supported by the NSF award DMR-1332208.
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