Rheology and Structure of Suspensions in Liquid Crystalline

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Rheology and Structure of Suspensions in Liquid Crystalline Hydroxypropylcellulose Solutions H. Hoekstra, J. Vermant,* and J. Mewis Department of Chemical Engineering, de Croylaan 46, B-3001 Leuven, K.U. Leuven, Belgium

T. Narayanan European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, Cedex, France Received January 29, 2002. In Final Form: April 29, 2002 The rheology and flow-induced microstructure of filled liquid crystalline polymers (LCPs) are studied. The matrix consists of hydroxypropylcellulose in water. The particle diameters are 28 and 3000 nm, i.e., ranging from the textural length scale to 100 times smaller. Contrary to earlier results in the literature, small amounts of the smallest particles did not induce a drop in viscosity. Even very small amounts of particles of either size eliminate or drastically shift the shear rate region where the first normal stress differences are negative. This is associated with a reduction in flow-induced ordering as detected with X-ray scattering. Different methods to deduce ordering from the SAXS data are compared. Using light scattering a substantial change in texture, due to the presence of the fillers, can be detected. Transient experiments indicate that texture still governs the rheology of filled LCPs. The characteristic time scales of the transients are reduced by the presence of fillers, which is consistent with a reduction in textural length scale. The latter causes an additional increase in viscosity when adding particles. This is not the case for N1, which is more affected by global orientation than by texture as such. The structure factor of the particles has been measured, using SAXS, in a suspension with a volume fraction of 0.1. The particle structure remains essentially liquidlike and is not affected by shear in the range of shear rates covered here. The ordering effects that can be observed in low molecular weight LCs do not appear in the LCPs studied here.

1. Introduction Liquid crystalline polymers display a complex rheological behavior owing to the interplay between flow, molecular anisotropy, and texture. Locally the polymer molecules are typically organized in a nematic structure with a narrow orientation distribution around an average direction (the director). When subjected to a weak shear flow, the local orientation distribution function will not change but instead a tumbling of the director is induced. A coordinated director tumbling on a large scale would, however, be difficult, and hence, variations of local director orientation are introduced along with the formation of defects. The characteristic length scales associated with the orientation variations and the defect spacing are typically up to a few micrometers.1,2 Together these two features constitute the “texture”, which evolves in a complex fashion as a function of the flow conditions.2-5 Director tumbling and the presence of a “polydomain” texture will lead to some very characteristic rheological features. These include stress transients which show a damped oscillatory behavior scaling with strain,6 large values for strain recovery,7 and a relaxation behavior upon cessation of flow that can be scaled with the preceding shear rate rather than with time.8 Most of these phe* Corresponding author. E-mail: [email protected]. (1) Kiss, G.; Porter, R. S. Mol. Cryst. Liq. Cryst. 1980, 60, 267-280. (2) Vermant, J.; Moldenaers, P.; Picken, S. J.; Mewis, J. J. NonNewtonian Fluid Mech. 1994, 53, 1-23. (3) Onogi, S.; Asada, T. In Rheology Vol. 1, Proceedings of the 8th International Congress on Rheology; Astarita, G., Marruci, G., Nicolais L., Eds.; Plenum Press: New York, 1980. (4) Larson, R. G.; Mead, D. W. Liq. Cryst. 1993, 15, 151-169. (5) Muller, J. A.; Stein, R. S.; Winter, H. H. Rheol. Acta 1996, 35, 160-167. (6) Moldenaers, P.; Mewis, J. J. Rheol. 1986, 30, 567-584. (7) Larson, R. G.; Mead, D. W. J. Rheol. 1989, 33, 1254-1281.

nomena are captured, at least qualitatively, by the Larson-Doi polydomain model.9 An additional complication in the rheological behavior of LCPs stems from their ability to switch from tumbling to flow-aligning behavior under strong flow conditions. A typical rheological signature of that transition is the occurrence of negative first normal stress differences,10 as predicted by the molecular Doi model.11,12 When particles are added to a liquid crystalline matrix, their presence may alter both the orientation distribution and the textural organization. For low molecular weight liquid crystals, interesting particulate structures and defect arrangements can be observed under static conditions depending on the anchoring conditions.13,14 These can give rise to rheological features such as a yield stress.15 For filled polymeric liquid crystals, no structural information is available, either at equilibrium or during flow. The rheological properties of filled LCPs have received more attention. In such systems, no yield stresses are observed, but the steady-state viscosity increases substantially with particle volume fraction, similar to suspensions in isotropic systems.16-19 The viscosity curves at (8) Moldenaers, P.; Mewis, J. J. Non-Newtonian Fluid. Mech. 1990, 34, 359-374. (9) Larson, R. G.; Doi, M. J. Rheol. 1991, 35, 539-563. (10) Kiss, G.; Porter, R. S. J. Polym. Sci., Polym. Symp. 1978, 65, 361. (11) Marrucci, G.; Maffettone, P. L. Macromolecules 1989, 22, 40764082. (12) Marrucci, G.; Greco, F. Adv. Chem. Phys. 1993, 86, 331-401. (13) Poulin, P.; Stark, H.; Lubensky, T. C.; Weitz, D. A. Science 1997, 275, 1770-1773. (14) Poulin, P. Curr. Opin. Colloid Interface Sci. 1999, 4, 66-71. (15) Sequeira, V.; Hill, D. A. J. Rheol. 1998, 42 (1), 203-213. (16) Kulichikin, V. G.; Shumskii, V. F.; Semakov, A. V. In Rheology and processing of liquid crystal polymers; Acierno, D., Collyer, A. A., Eds.; Chapman & Hall: New York, 1996.

10.1021/la020097y CCC: $22.00 © 2002 American Chemical Society Published on Web 06/19/2002

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different volume fractions can, however, only be superposed by shifting data at constant shear rate17 rather than at constant shear stress as is the case of normal polymer solutions.21 A second intriguing result has been reported by Nuell and Denn,20 suggesting a minimum in the viscosity/volume fraction relation at low volume fractions, when submicrometer particles are used. A more pronounced and characteristic effect has been reported for the steady-state first normal stress difference. When 3.0 µm polystyrene spheres are added to a matrix of hydroxypropylcellulose (HPC) in water, the region of negative normal stresses disappears or at least shifts to higher shear rates at volume fractions as low as 0.001.18 In transient experiments the texture scaling of time with shear rate is preserved. When particles are added, the absolute values of the time scales have been found to be reduced considerably;18 this also holds for recoil and relaxation. The available data are too fragmentary to draw any conclusions about the general nature of possible data reduction schemes or to allow a structural interpretation. Considering the results of Nuell and Denn20 the question arises whether particle size is an important factor here. In earlier systematic experiments17,18 the particle diameter (3 µm) was of the same order of magnitude as the domain size of the LCP solution used. Here, much smaller particles will be incorporated rendering it possible to study the effect of particles on the molecular ordering in the liquid crystalline structure. Effects of flow on molecular orientation and the organization of the particles in the matrix, as well as changes in the polydomain structure, will be investigated using light and X-ray scattering on flowing systems. 2. Materials and Methods For all samples studied the matrix phase consisted of hydroxypropylcellulose (HPC, Klucel LF from Aqualon) in twice distilled water at a concentration of 55 wt %. Using optical microscopy it was confirmed that the matrix phase was fully liquid crystalline. Two types of particles were used. Monodisperse polystyrene particles of 3.0 ( 0.1 µm were synthesized by a dispersion polymerization method.22 Silica particles (Ludox TM50 from DuPont), with an average diameter of 28 nm as determined by SAXS measurements, constituted the smaller particles. Samples were prepared by slowly adding the required amount of HPC powder to a suspension of the particles in water. The HPC powder was previously dried overnight in a vacuum oven at 80 °C. Using this procedure, samples with particle volume fractions of up to 0.1 were prepared. All samples were stored in a refrigerator for at least 1 month prior to the measurements. Air bubbles were eliminated by centrifugation. As the medium in which the particles are dispersed is fairly viscous, homogeneous and at least kinetically stable dispersions could be obtained by the simple mixing procedure used. With the larger spheres, the homogeneous dispersion of the particles in the samples could be easily verified with an optical microscope. For the rheological experiments an RMS800 rheometer (Rheometric Scientific) was used. This rotational device was equipped with a 2000 g/(g cm) force and torque rebalanced transducer. The recoil experiments were performed on a dynamic stress rheometer (Rheometric Scientific). All experiments were conducted at 25.0 °C, using a cone and plate geometry with a (17) Moldenaers, P.; Vermant, J.; Heinrich, E.; Mewis, J. Rheol. Acta 1998, 37, 463-469. (18) Hartmann, V.; Vermant, J.; Heinrich, E.; Mewis, J.; Moldenaers, P. J. Rheol. 2000, 44, 1417-1432. (19) Araki, K.; Kitano, T.; Hausernova, B. Appl. Rheol. 2001, 11, 188-196. (20) Nuel, L.; Denn, M. M. Rheol. Acta 1991, 30, 65-70. (21) Ohl, N.; Gleissle, W. J. Rheol. 1993, 37, 381-406. (22) Almog, Y.; Reich, S.; Levy, M. Br. Polym. J. 1982, 131-136.

Hoekstra et al. cone angle of 0.1 rad and a diameter of 25 mm. A mercury seal prevented evaporation of water from the systems and delayed the onset of shear fracture.23 Both X-ray scattering and birefringence are suitable methods for measuring the mesoscopic order in flowing LCPs, as recently reviewed by Burghardt.24 In the case of filled LCPs, birefringence cannot be applied as the particles and the presence of the LC texture cause too much depolarization in the scattering. Instead, X-ray scattering measurements will be used. Care must be taken, however, to avoid interference between the scattering of the particles and that of the macromolecules in the LC phase. The size of the particles was chosen sufficiently large for their X-ray scattering to be well into the Porod regime at the scattering angles where the diffuse scattering lobes of the liquid crystalline matrix are measured. The requirement that the structural organization of the particles could be investigated by small-angle scattering set an upper limit to the particle size. From the X-ray scattering patterns the mesoscopic orientation parameter during flow can be determined quantitatively. The calculation of the orientation parameter is however not straightforward given the strong background scattering from the particles. The X-ray scattering experiments were performed at the high brilliance beamline (ID-2) of the European Synchrotron Radiation Facility in Grenoble, France. The samples were subjected to flow by means of a Couette cell. X-ray scattering patterns were recorded using an image-intensified CCD detector; the entire scattered beam flight path is in a vacuum. The incident X-ray wavelength was 0.099 nm, and the beam size was 0.3 mm × 0.3 mm. The sample to detector distance was varied from 1 to 10 m covering a q-range of 0.02-6 nm-1. The standard procedure for data acquisition and treatment is described elsewhere.25,26 Due to the wide q-range available, both the diffuse scattering profiles of the liquid crystalline matrix and the structure factor of filler silica particles could be measured in a single experiment by changing the sample to detector distance from 1 to 10 m. The polydomain texture manifests itself here at length scales that are typically on the order of a few micrometers. This is outside the range of the X-ray experiments. Small-angle light scattering (SALS), using polarized light, is then a more suitable method.2,27,28 The scattering from the particles is essentially constant in the range of scattering vectors where the polydomain texture is probed, and therefore, interference could be avoided. The SALS experiments were performed during flow to evaluate the textural length scale of the filled LCP under shear. The setup consisted of a Linkam CSS450 flow cell equipped with a parallelplate geometry, a He-Ne laser, a Glan-Thompson polarizer oriented at 0° with respect to the flow direction, and a dichroic sheet analyzer at 90° orientation (Hv mode). The SALS pattern was collected on a semitransparent screen and recorded using a 10-bit high-resolution digital camera (TM-1300 from PULNIX), connected to a digital frame grabber (TCi-Digital SE from Coreco). The images were analyzed with in-house-developed software.

3. Rheological Behavior 3.1. Steady-State Shear Flow. First, the effect of the small silica particles on the steady-state rheological properties will be studied. The results will be compared with published data on larger particles to evaluate the effect of particle size. Readings of the steady-state viscosity were taken after shearing for at least 600 strain units. The viscosity curves for particle volume fractions up to 0.1 are presented in Figure 1a.When the matrix is an ordinary, isotropic, polymer system, the concept of an internal shear rate can be used to superpose viscosity (23) Grizutti, N.; Moldenaers, P.; Mortier, M.; Mewis, J. Rheol. Acta 1995, 34, 218-226. (24) Burghardt, W. R. Macromol. Chem. Phys. 1998, 199, 471-488. (25) Narayanan, T.; Diat, O.; Boesecke, P. Nucl. Instrum. Methods Phys. Res., Sect. A 2001, 467, 1005-1009. (26) Hammersley, A. P.; Svensson, S. O.; Thompson, A.; Graafsma, H.; Kvick, Å.; Moy, J. P. Rev. Sci. Instrum. 1995, 66, 2729-2733. (27) Walker, L. M.; Wagner, N. J. Macromolecules 1996, 29, 22982301. (28) Riti, J. B.; Cidade, M. T.; Godinho, M. H.; Martins, A. F.; Navard, P. J. Rheol. 1997, 41, 1247-1260.

Liquid Crystalline Hydroxypropylcellulose Solutions

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Figure 2. Dependence of the shift factor on particle volume fraction and particle size: 28 nm silica particles (O); 3 µm polystyrene particles (0). Data for the 3 µm size particles were taken from refs 17 and 18. (Lines are to guide the eye.)

Figure 1. (a) Flow curves for liquid crystalline HPC solutions with silica particles at 25.0 °C. Volume fractions are 0 (O), 0.011 (0), 0.031 (4), 0.056 (]), and 0.10 (3). (b) Rescaled flow curves using the shift factor defined by eq 1.

curves for suspensions with different volume fractions.21 This concept does not lead to a satisfactory superposition with the present data, consistent with earlier results for suspensions of larger particles in liquid crystalline HPC solutions.17,18 A good superposition of the viscosity curves could be achieved when using a shift factor C at constant shear rate rather than at constant stress.17 Hence, the shift factor reduces to the relative viscosity at constant shear rate:

Figure 3. Steady-state values of the first normal stress difference at 25.0 °C for different volume fractions of silica particles: 0 (O, positive values); 0 (b, negative values); 0.011 (0); 0.031 (4); 0.056 (]); 0.10 (3).

Figure 1b shows the flow curves superimposed by means of the factor C. The value of C was determined using a least-squares method (linear). It can be concluded that this data reduction scheme also applies to the present data. The values of C are, however, considerably larger than those reported earlier for 3 µm particles.18 The results for the two types of particles are compared in Figure 2. Values of the shift factor C smaller than 1, as reported by Nuell and Denn,20 were not observed for the systems under investigation. It can be concluded that small particles do not necessarily cause a viscosity drop in LCPs. Moreover, as they cause a stronger increase in viscosity than larger particles, they provide a more critical test for possible scalings of the rheological transients. The first normal stress difference (N1) shows a different behavior (Figure 3). The unfilled system displays a region of negative N1 at intermediate shear rates which is characteristic for HPC solutions23 and lyotropic main chain LCPs in general.29 The lower limit is not as sensitive to

the particle concentration as the viscosity. This is again in contrast with suspensions in isotropic polymer systems. The region of negative N1, however, disappears even for the lowest volume fractions probed in the present experiments. 3.2. Transient Behavior. 3.2.1. Flow Reversal. In flow reversal experiments, the sample is sheared until the steady state is reached. Subsequently the flow direction is suddenly reversed; this instant is referred to as time zero. For the unfilled system the reduced shear stress (σ/σSS, where the subscript SS refers to the steady state), as well as the reduced first normal stress difference (N1/ N1,SS), exhibits damped oscillatory patterns before the new steady state is reached again. When flow reversal experiments at different shear rates are compared, the positions of the maxima and minima scale with strain.6,30 This behavior is characteristic for LCPs and can be explained on the basis of director tumbling.12 The effect of systematically varying the volume fraction of the silica particles is shown in Figure 4a for the rescaled shear stress and in Figure 4b for the rescaled first normal stress difference. In these experiments the shear rate is kept constant (0.6 s-1). The superposition of the positions of the first maximum of the shear stress and the minima of the first normal stress difference is quite good when C is used as a scaling factor for the strain. 3.2.2. Recoil and Stress Relaxation. In recoil experiments, a constant stress is applied and suddenly removed

(29) Mewis, J.; Moldenaers, P. Curr. Opin. Colloid Interface Sci. 1996, 1, 466-471.

(30) Moldenaers, P.; Mortier, M.; Mewis, J. Chem. Eng. Sci. 1994, 49, 699-707.

C)

|

η(φ) η(0)

γ˘ )const

(1)

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This also applies to stress relaxation upon cessation of flow (not shown). Hence, these processes are accelerated by the presence of particles, even though adding particles increases the viscosity. 4. Structure during Flow

Figure 4. Reduced stresses after flow reversal in HPC solutions with silica particles (γ3 ) 0.6 s-1, T ) 25.0 °C). Volume fractions: 0 (O); 0.031 (4); 0.056 (]). The strain axis has been rescaled using the factor C (eq 1).

Figure 5. Scaled recoil of HPC solutions with silica particles (previous shear rate 0.6 s-1, T ) 25.0 °C). Volume fractions: 0 (O); 0.031 (4); 0.056 (]). The time has been multiplied by the previously applied shear rate and by the shift factor C.

once steady-state conditions have been reached. The resulting strain recovery is monitored as a function of time. LCP solutions are known to exhibit a large recoil, i.e., of the order of a few strain units. This large recoil reflects the elastic energy stored in the texture.7 The time evolution of the recoil process scales with the steady-state shear rate to which the sample has been subjected prior to the removal of the stress. To render a direct comparison of the time scales in all transient experiments possible, the reported recoil data have been obtained at stress levels that correspond to previous shear rates, identical to those in Figure 4. Results of recoil experiments on silica filled LCP solutions are shown in Figure 5 for a previous shear rate of 0.6 s-1. The normal LCP scaling has been used, except that the time axis has been multiplied by the factor C of eq 1. In this manner the various curves can be superposed.

4.1. Length Scales and Scattering Techniques. Investigating the structure of filled LCPs requires probing at three different length scales. A suitable model system was selected to be able to cover the molecular, particle, and domain length scales. To obtain information about the molecular order in the matrix phase, the range of scattering vectors (q) should encompass the region corresponding to the lateral nematic stacking of the molecules. For the densely packed 55% HPC solution the intermolecular distance is about 1.3 nm, meaning a q-value of 4.9 nm-1, which is accessible in the X-ray scattering experiments. Both the silica particles and the PS spheres were sufficiently large for the particle scattering to be well into their Porod regime. Hence, they did not cause interference with the typical features of the scattering from the nematic phase. To obtain information about the organization of the particles in the matrix one has to probe the particulate structure factor. The size and volume fraction of the silica particles were chosen for the scattering vectors associated with peaks in the structure and form factor (q ∼ 0.280.41 nm-1) to be between those of the molecules and those of the LC texture. Hence the structure factor of these colloidal particles could also be probed in SAXS experiments. Due to their large size this was not possible for the 3 µm PS suspensions. The texture length scale is situated in the micrometer size range; hence, small-angle light scattering (SALS) is required. Again the silica particles are suitable for this purpose because the scattering from these small particles is constant in the relevant q-range (q ∼ 1.0 × 10-4-1.5 × 10-3 nm-1). In the frequency range of visible light the difference in refractive index difference between the PS spheres and the matrix is large. This renders these particles unsuitable for the SALS experiments due to multiple scattering effects. 4.2. Molecular Orientation in the Matrix Phase. At a sample-to-detector distance of 1 m, lobes are observed in the X-ray scattering pattern that can be attributed to the interference of scattering from the densely packed molecules. Examples of the scattering patterns during flow are shown in Figure 6, for both an unfilled and a filled LCP. The HPC molecules are expected to be oriented on average in the flow direction when the flow vorticity plane is considered. Due to the presence of an orientation distribution, the packing of the rods shows up as two diffuse lobes rather than two sharp peaks. Flow-induced alignment in the matrix phase causes the scattered radiation to concentrate more toward the vorticity direction when the shear rate is increased. Several procedures have been used to derive a measure of the overall orientation from LCP scattering data, and the three most commonly used methods will be discussed here. To our knowledge, the different methods for determining the orientation parameter in LCPs have not yet been compared against a single set of experimental data. 4.2.1. Method of Mitchell and Windle. Mitchell and Windle31 proposed a description based on the scattering of individual rods, distributed uniaxially around a director. Interference between the different scatterers was not (31) Mitchell, G. R.; Windle, A. H. In Developments in crystalline polymers-2; Basset, D. C., Ed.; Elsevier: London, 1988.


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Figure 6. 2-D images of the scattering pattern in the flow-vorticity plane at 7 s-1. The graph shows the azimuthal intensity profile for the unfilled sample (O) and the sample with 3.1% particles (0). The lines are fitted to the experimental data using eq 6.

taken into account. This orientation parameter has been employed very often to characterize order in low to moderately concentrated PBG solutions, where most of the assumptions seem to be valid (see e.g. Hongladarom et al.32). Keates et al.33 have applied this method also to HPC solutions, despite the fact that these more concentrated solutions cause strong interference due to their densely packed nature. The orientation parameter is calculated as

2 SM ) N

∫0π/2 I(q*, φ)P2(cos φ) sin φ dφ

4.2.2. Method of Deutsch. The second method uses the same type of azimuthal integration with a different geometrical function to account for intermolecular interference.34 This method has been employed by Berret and co-workers36 in the analysis of the scattering from densely packed micellar surfactant nematics. The orientation parameter is now calculated using

SD ) 1 -

∫0π/2I(q*, φ) ×

1 3 N2

(2)

[sin φ + sin φ cos φ ln 1 +cossinφ φ] dφ (3)

where SM is the orientation parameter, I(q*, φ) is the azimuthal intensity profile, φ is the azimuthal angle (φ ) 0 corresponds to the flow direction), q* is the q-value corresponding to the maximum intensity in the lobes, and P2(cos φ) is the second-order Legendre polynomial of cos φ: P2(cos φ) ) (1/2)(3 cos2 φ - 1). N is a normalization factor and is given by N ) ∫π/2 0 I(q*, φ) sin φ dφ. Although the patterns have been corrected for scattering by the flow cell, solvent, and air, some residual isotropic background always remains present in the intensity profiles. For the particle filled systems under consideration, the particles will cause an isotropic contribution. Such contributions have to be subtracted from the scattering of the anisotropic liquid crystalline phase. The isotropic contribution is usually derived from the pattern at high shear rates.24 It is assumed that shear flow can align the molecules sufficiently to concentrate the scattering from the oriented rodlike molecules near the vorticity direction. The remaining intensity scattered in the flow direction is then assumed to reflect the isotropic contribution and is subtracted from all measured azimuthal intensity profiles. Small changes in the values used for the correction of this background scattering can strongly affect the calculated values for the orientation parameter.35

with N a normalization factor being given by N ) ∫π/2 0 I(q*, φ) dφ. The isotropic background contribution is determined using the same protocol as in the method of Mitchell and Windle. The value of the background correction affects both the numerator and the normalization factor of eq 3. Small changes in the value used will again substantially affect the values of SD. 4.2.3. Method According to Picken. In the previous two methods no assumption about the actual shape of the orientation distribution function was made, except that it had to be uniaxial. The value of S could be obtained by direct integration of the azimuthal intensity profile. Picken et al.37 assumed a Maier-Saupe type of orientation distribution function; they found that in that case the scattering from the liquid crystalline phase I(q*, φ) is generally well described by

(32) Hongladarom, K.; Ugaz, V. M.; Cinader, D. K.; Burghardt, W. R.; Quintana, J. P.; Hsiao, B. S.; Dadmun, M. D.; Hamilton, W. A.; Butler, P. D. Macromolecules 1996, 29, 5346-5355.

2

2

I(q*, φ) ) I0 exp[R(P2(sin φ) - 1)]

(4)

The parameter R characterizes the width of the intensity (33) Keates, P. A.; Mitchell, G. R.; Peuvrel-Disdier, E.; Navard, P. Polymer 1996, 37, 893-901. (34) Deutsch, M. Phys. Rev. A 1991, 44, 8264-8270. (35) Cinader, D. K., Jr.; Burghardt, W. R. Polymer 1999, 40, 41694180. (36) Berret, J. F.; Roux, D. C.; Lindner, P. Eur. Phys. J., B 1998, 5, 67-77.

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Figure 7. Comparison of the orientation parameter calculated according to the procedures by Mitchell and Windle (0), Deutsch (4), and Picken (O) for an unfilled system of 55% HPC in water as a function of the imposed shear rate.

Figure 8. Effect of volume fraction of silica particles on the orientation parameter for the filled HPC solutions. Volume fractions: 0 (O); 0.031 (4); 0.10 (3).

profile. The value R can be derived from the width of the peak at half-maximum of the azimuthal intensity profile. The orientation parameter can then be most easily calculated using

polydomain material under consideration. Yet at high shear rates the orientation parameter does at least approach the value of 0.792, which is the minimal value for the molecular order parameter in quiescent liquid crystalline polymer as calculated from the Doi theory using an Onsager potential.38 The method of Picken gives a smoother evolution of the orientation parameter, because it is the most robust method with respect to the background correction. Hence, this method is selected for the analysis of the filled materials. For the filled materials the background correction is even more important due to the presence of isotropic scattering from the particles. In addition, for these systems at high shear rates, one cannot assume a priori that the molecules align sufficiently in the flow direction for the scattering to be concentrated only near the vorticity direction. Hence, unlike the unfilled systems, it is not possible to identify the background contribution as the remaining intensity in the flow direction. The method of Picken suffers less from this drawback, provided that the scattered intensity in the vorticity direction is sufficiently larger than in the flow direction and a good fit of the intensity profile can be achieved with eq 4. This is the case in all the present experiments. The effect of adding particles on the overall orientation at a given shear rate is relatively small for volume fractions below 0.03, as the orientation parameters do not differ significantly from those for the unfilled material (Figure 8). At higher volume fractions a clear reduction in orientation is observed. The effect of particle size is shown in Figure 9. The small silica particles are somewhat more effective at reducing the overall order than the 3 µm PS particles. On the average, data for the larger particles are about 25% higher than those for the silica particles at the same volume fraction. 4.3. Organization of the Particles. Poulin et al.13 demonstrated that a nematic suspending medium can induce certain anisotropic or additional colloidal interactions, which could lead to unexpected colloidal organizations and consequently affect the rheological behavior. To determine the particulate structure factor a sample with 10% silica particles was investigated by moving the detector to a distance of 10 m from the sample in the X-ray experiments. This sample has a high enough volume fraction to detect the particulate structure factor (S(q)). The scattered intensity is given by

∫-11exp[RP2(sin φ)]P2(sin φ) d sin φ SP ) ∫-11 exp[RP2(sin φ)] d sin φ

(5)

This procedure yields results that are similar to those of the method by Mittchell and Windle, when a Maier-Saupe distribution function is inserted in eq 2.37 A correction for background scattering still needs to be applied, but in this case it can be obtained by directly fitting a distribution function to the measured intensity. In this work, the parameter R was not calculated from the width at half-maximum; instead the data were directly fitted to eq 6, with Ic an isotropic contribution to the azimuthal profile. The correlations obtained in the fitting procedure were very good. Once R is known, eq 5 can be integrated numerically. The baseline correction has a smaller effect on the value of Sp than in the other methods, because it does not affect the value of R as long as the peak intensity is sufficiently large in comparison with the value of Ic.

I(q*, φ) ) I0 exp[R(P2(sin φ) - 1)] + Ic

(6)

4.2.4. Orientation Parameter. Figure 7 compares the values of the orientation parameter obtained by the different methods on an unfilled system of 55% HPC. For the method of Mitchell and Windle and that of Deutsch, the baseline for the unfilled systems was determined using the procedure outlined by Cinader et al.35 For the method of Picken the baseline correction was a parameter in the fitting procedure, and its value differed somewhat from one image to another. The different methods in Figure 7 exhibit the same overall trends. The absolute values of the orientation parameter, however, differ substantially. This reflects the difference in physical background of the methods and their sensitivity to the baseline correction. Especially, the analyses of Mitchell and Windle and that of Deutsch are compromised by uncertainties in determining the background intensity in the present case. It can be concluded that the numerical value of the orientation parameter should be interpreted with caution. Strictly speaking, none of the three methods is valid for the (37) Picken, S. J.; Aerts, J.; Visser, R.; Northolt, M. G. Macromolecules 1990, 23, 3849-3854.

I(q) ∝ P(q) S(q) (38) Larson, R. G. Macromolecules 1990, 23, 3983-3992.

(7)


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Figure 9. Effect of particle size on the orientation parameter for the filled HPC solutions with a volume fraction of 0.10 particles: 28 nm silica particles (O); 3 µm polystyrene particles (0).

Figure 11. Alignment factor for the sample with a volume fraction of 0.10 silica particles. Shear rates: 1 s-1 (O); 10 s-1 (0); 100 s-1 (4).

Figure 10. Particulate structure factor during flow for the sample with a volume fraction of 0.1 silica particles. Shear rates: 1 s-1 (O); 10 s-1 (0); 100 s-1 (4).

with P(q) the form factor of the particles which arises from interference of scattered radiation from different elements within a single particle. The structure factor S(q) is the result of interparticle interference. The form factor of the particles was determined by measuring the scattered intensity for a 0.1% suspension of silica particles in water. To determine the structure factor of the filled HPC solutions the scattering intensities were divided by the recorded form factor. S(q) was subsequently determined by azimuthal averaging. The structure factor as a function of the magnitude of the scattering vector is displayed in Figure 10. The structure factor reflects liquidlike behavior; the first maximum occurs at q ≈ 0.275 nm-1 and is independent of the shear rate. This value is somewhat larger than the value for a 10% suspension of Brownian hard spheres in the Percus-Yevick approximation39 (q ≈ 0.21 nm-1 for 28 nm particles). This discrepancy can be attributed to the polydispersity of the silicas and some small deviations in the form factor of the suspended particles.40 All directional information is lost when applying an azimuthal averaging procedure. To quantify the degree of anisotropy in the scattering pattern an alignment factor can be introduced. Here a factor Af(q) is used, as defined by Walker et al.27 to analyze their anisotropic neutron scattering data of liquid crystalline materials. Combined with eq 7 their expression becomes

∫02πS(q, φ) cos(2φ) dφ Af(q) ) ∫02πS(q, φ) dφ

(8)

Figure 12. Contour plots of Hv SALS patterns in the flowvorticity plane for HPC solutions during flow (0.6 s-1) at different volume fractions of silica particles.

Figure 11 shows the calculated values of Af as a function of q. The alignment factor is found to be independent of shear rate, its magnitude being indicative of an isotropic pattern over the accessible range of shear rates and scattering vectors. The small decrease at low q can be explained by the reduced angular resolution close to the beam-stop. 4.4. Evolution of the Texture. SALS has proven to be a useful tool to investigate the evolution of texture in LCPs.2,27,28,41,44 The detailed SALS patterns are, however, more complex than the X-ray scattering patterns. Figure 12 shows the depolarized light scattering for samples with different volume fractions of silica particles. The scattering patterns were obtained in the so-called Hv mode, with the polarizer parallel and the analyzer perpendicular to the (39) Hunter, R. J. Foundation of colloid science; Clarendon Press: Oxford, U.K., 1989; Vol. 2. (40) Ballauff, M. Curr. Opin. Colloid Interface Sci. 2001, 6, 132139. (41) Walker, L. M.; Kernick, W. A.; Wagner, N. J. Macromolecules 1997, 30, 508-514. (42) Kapsabelis, S.; Prestidge, C. A. J. Colloid Interface Sci. 2000, 228, 297-305. (43) Walker, L. M.; Wagner, N. J. J. Rheol. 1997, 38, 1525-1547. (44) Ernst, B.; Navard, P.; Hashimoto, T.; Takebe, T. Macromolecules 1989, 23, 1370-1374.

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silica volume fraction. For volume fractions of 0, 0.001, 0.01, and 0.10 the correlation lengths are 1.47, 1.29, 1.23, and 0.97 µm, respectively. The results are in good agreement with correlation lengths previously reported for 60% HPC solutions in water.41 5. Discussion

Figure 13. Modified Debye-Bueche plots for the HPC solutions (γ _) 0.6 s-1). Volume fractions of silica particles: unfilled (O); 0.001 (0); 0.01 (4); 0.1 (]).

flow direction. In this scattering mode an orientation correlation length in the matrix material can be extracted from the scattering patterns.45 The pattern for the unfilled systems shows the typical behavior observed for a sheared LCP in region II, displaying 4 lobes and a streak. The streak is believed to arise from stretched defect lines.2,28 When particles are added, the typical features of the scattering patterns first remain present but they become less pronounced. Small volume fractions suffice to induce a measurable change in texture. When particles are added, first the streak disappears and subsequently the pattern becomes more isotropic. Increasing the volume fraction of the particles has a similar effect as reducing the shear rate in an unfilled system (see e.g. Walker et al.41). The detailed nature of the SALS pattern is still poorly understood. A complex polydomain structure and a complex scattering mechanism (depolarization) make the treatment of the ill-posed inverse problem very difficult. Following Walker and Wagner,41 we use a modified Debye-Bueche model46 to extract a characteristic length scale from the data:

IHv(q) )

I′ac3 (1 + (qac)2)2

(9)

Here I′ combines the effects of material and instrument. The correlation length ac can be obtained from plots of IHv-1/2 versus q2. It has been suggested that the correlation length can be identified with the texture length scale ac.41 The data represent however a projection of the structure in the flow-vorticity plane. As textural characteristics are not necessarily isotropic in all three dimensions, no absolute value for the textural length scale can be obtained. Therefore, the discussion will be limited to a correlation length, regardless of its exact relation to the texture size. To obtain a statistically relevant scattering pattern associated with steady-state flow, a linear average of three consecutive patterns, each with an exposure time of 1/25 s was made. The analysis was performed by azimuthal averaging of the patterns over the two-dimensional image. As the streak in the patterns at low volume fraction is due to the defect lines, it was removed from the scattering patterns prior to the correlation length analysis. The results of the analysis are shown in Figure 13, where Debye-Bueche plots are given for systems with different volume fractions. The correlation lengths obtained from the graphs of Figure 13 indeed decrease with increasing (45) Stein, R. S. In Polymer Blends; Paul, D. R., Newman, S., Eds.; Academic Press: San Diego, CA, 1978; Vol. 1. (46) Debye, P.; Bueche, A. M. J. Appl. Phys. 1949, 20, 518.

Adding particles to a lyotropic LCP causes a viscosity increase for all investigated volume fractions of both submicrometer silica and 3 µm PS particles. The increase is stronger than expected for hard spheres in Newtonian or even isotropic viscoelastic matrixes. This increase cannot be caused by particle aggregation as direct microscopic observation for the PS particles and SAXS measurements for the silica particles do not indicate any. Particle repulsion cannot explain the viscosity increase either as at low particle volume fractions the electroviscous effects have a much smaller effect on viscosity than what is observed for the filled LCPs. The viscosity increase is also observed when salt is added to these suspensions. Adsorption of HPC onto the particle surfaces and depletion of HPC from the bulk cannot explain the observed effects either. On the basis of adsorption data of cellulose to silica surfaces by Kapsabelis and Prestidge,42 the maximum change in concentration of the matrix, by depletion of the polymer, is on the order of 0.5%. Given the relative independence of the rheological properties for concentrations around 55%,43 this can be neglected. The possible changes in the effective volume of the particles are too small to explain the observed changes in the steady and transient rheology. If the curves in Figure 2 are fitted with the Krieger-Dougherty equation, unrealistically low values for the maximum packing volume fraction are obtained even when a reasonable layer thickness of adsorbed polymer is assumed. This indicates that steric effects due to polymer adsorption cannot explain the viscosity rise either. Actually, polymer adsorption would, at low shear rates, have approximately the same effect on the viscosity as on the first normal stress difference. The increase in N1 at these shear rates is however far less pronounced than the increase of the viscosity. Hence, the rise of the viscosity with the addition of particles is a texture effect because it is mainly texture determined whereas for N1 orientation effects are more important. This is confirmed by the SALS measurements (Figure 12). The characteristic length scale derived from the Debye-Bueche model decreases as the particle concentration increases. Smaller length scales entail a higher viscosity, according to the Ericksen balance.12 The detailed mechanism by which the particles affect the texture is not yet clear, especially for the small silica particles where the interparticle spacing is at least 1 order of magnitude smaller than the textural length scale. Possibly the particles interact with some of the defects present in the virgin LCP or help in creating new ones. The X-ray scattering data indicate that addition of particles reduces the overall orientational order. The orientation parameter shows a substantial decrease when particles are added to a volume fraction of 0.10; flowinduced ordering is clearly hindered by the presence of the particles. The measured orientation parameter is the mesoscopic one, which is affected by the local orientation distribution function as well as by the distribution of directors over the various domains. A measurable reduction of S only occurs at sufficiently high particle concentrations that correspond to a clear change in the shape of the SALS pattern (Figure 12). Hence the decrease of the overall orientation parameter is mostly determined by changes in texture, i.e., the distribution of director


orientations. This does not imply, however, that the local orientation distribution function is not affected. Here the effects are more subtle. A sensitive measure of the changes in the local orientation distribution function is the transition from positive to negative N1.12 For this to occur, the director has to be oriented everywhere quite close to the flow direction, so the flow can widen the local orientational distribution function and tilt the director to negative angles. Judging from the disappearance of the region of negative N1 at volume fractions as low as 0.001,18 very small amounts of particles interfere with these phenomena. Probably the complex and variable velocity profile around and between particles prevents such an alignment. The transient response is characterized by a reduction of the characteristic time scales with increasing filler concentration. The filled samples show the same type of oscillating stress transients after flow reversal as the unfilled material. Oscillating stress transients in LCPs are associated with director tumbling. The fact that these oscillating stress transients persist in the filled systems suggests that director tumbling is not suppressed by the presence of particles. When the data obtained on the HPC solutions filled with the 28 nm particles in Figure 4 are compared with those on their 3 µm counterparts,18 the same qualitative trends are observed. The oscillatory nature of the stresses is conserved, but the oscillations become more damped as the volume fraction of the particles is increased. When the measurements at the same volume fraction are compared, the damping is more pronounced for the smaller particles. The scaling of the time constant for recoil with shear rate and the large values of the final recoil indicate that the LCP texture is still the driving force in determining the transient rheological response in the filled systems. In all transient experiments performed (flow reversal, recoil, and stress relaxation) increasing the particle concentration and reducing the particle size results in faster transients. The shift of the data with particle concentration is not in agreement with a mere increase of the internal shear rate, as this would imply a shift of the data with a shift factor B, based on the relative viscosity at constant stress levels.17 Using the latter shift factor neither the steady nor the transient data superpose well. The reduction in time scale seems to be related to the increase of the viscosity, as the factor C enables a reduction of the different flow curves (Figure 4). Assuming equal Frank elastic constants for the unfilled and filled materials, the Ericksen balance (η ∝ K/(γ3 a2)) suggests that the applicability of the factor C is a result of the change in the characteristic length scale. The SAXS measurements with the detector at 10 m show that the particles are dispersed in a very random manner in the liquid crystalline matrix and remain liquidlike during flow. In the polymeric matrix used in this work, little or no effect of the matrix on the particulate structure was observed during flow. Flow did not induce any pronounced anisotropy in the particulate structure, as was demonstrated by the analysis of the anisotropy

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factor (Figure 11). Aggregation could not be observed within the scattering experiments or the optical microscopy of the PS samples. The isotropic particulate structure prevails for the small as well as the large particles, the PS particles having an apolar surface22 whereas the silica particles carry silanol groups on the surface. The absence of interaction with very different types of particles indicates that the coupling between the particles and the LCP is quite weak. It could be caused by the relative weakness of the nematic interaction in HPC and the high viscosity of the matrix phase. As the ratio between Frank elastic constants and viscosity is quite similar for most polymeric liquid crystals, this could be a general conclusion for LCPs. 6. Conclusions A combination of rheological and scattering techniques has been used to quantify the effect of particles on the various levels of structure in filled liquid crystalline polymers. The radius of the particles used ranged from 3 µm down to 28 nm. Contrary to earlier results in the literature, small amounts of the smallest particles did not induce a drop in viscosity. On the contrary, even a stronger increase in viscosity is observed than in the case of isotropic polymers. Very small amounts of particles were observed to either eliminate or drastically shift the shear rate region where the first normal stress differences (N1) are negative. This is associated with a reduction in flowinduced ordering, as detected with X-ray scattering. Light scattering shows a substantial change in texture when fillers are added to LCPs. The damped oscillatory response of the flow reversal experiments, the substantial recoil, and the strain scaling indicate that texture still governs the rheology of filled LCPs. The characteristic time scales of the transients are reduced by the presence of fillers, which is consistent with a reduction in textural length scale, a phenomenon that is confirmed by the SALS data. It is the reduction in textural length scale that causes an additional increase in viscosity when adding particles. This is not the case for N1, which is more affected by global orientation than by texture as such. In the range of shear rates covered, the structure factor of the particles remains essentially liquidlike for volume fractions of 0.1. The ordering effects that can be observed in low molecular weight LCs do not appear in LCPs. Acknowledgment. We acknowledge support of the European Synchrotron Radiation Facility (ESRF) in providing the facilities and financial support for the X-ray scattering experiments (Experiment SC-617). Some of the authors acknowledge funding from the Fund for Scientific Research-Flanders (FWO-Vlaanderen, Belgium), Project FWO-G.0208.00.NLOT (J.M. and J.V.) and KAN99 1.5.109.99 (J.V.). Financial support for this work has also been provided by the European Union in the framework of the TMR network on “Rheology of Liquid Crystalline Materials” (No. ERBFMRXCT96-0003). LA020097Y

Rheology and Structure of Suspensions in Liquid Crystalline

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