A comparison between texture and rheological behaviour of lyotropic liquid crystalline polymers during flow

i3 (1994) l-23

-

A comparison between texture and rheological behaviour of lyotropic liquid crystalline polymers during flow J. Vermant a, P. Moldenaers

a, S.J. Picken b, J. Mewis ‘**

n Department

of Chemical Engineering, K. U. Leuven, de Croylaan 46, B-3001 Heverlee (Belgium) b Akzo Research Laboratories Arnhem, P.O. Box 9600, 6800 SB Arnhem (The Netherlands)

(Received July 13, 1993; in revised form November 29, 1993)

Abstract The flow-induced structures of three types of lyotropic liquid crystals with different degrees of flexibility are investigated during simple shear flow. Both optical microscopy and small angle light scattering are used. Different types of structure appear systematically in shear rate regions that can be associated with specific regions of the rheological curves. Changing concentration and temperature does not affect the correlation between rheological and textural transitions. Stress and texture have also been observed in transient experiments when starting from a monodomain. The types of texture that occur at different shear rates under steady state conditions can also be observed as transient structures at a single shear rate. Keywords:

Monodomain;

Polymeric liquid crystals; Rheology; SALS; Texture

1. Introduction Liquid crystalline polymers (LCPs) constitute an intriguing and interesting class of materials. Their technological importance is the result of a peculiar microstructure, the key aspects of which are a rigid molecular structure and anisotropy. More than with ordinary isotropic polymers, the processing conditions determine the microstructure and the properties of the final product. Therefore the study of their rheological properties has received much attention, the first systematic observations being those by Kiss and Porter [ 1,2]. Various rheo-optical techniques have been * Corresponding author. 0377-0257/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0377-0257(94)01234-9

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used to gain insight into the correlation between the complex molecular superstructure and the rheological behaviour. Based on studies of the intensity of transmitted polarized light, Onogi and coworkers [3,4] proposed three different types of structure to explain the dependence of viscosity on shear rate. At low shear rates a piled polydomain was postulated in which the average orientation is random (region I); it transforms into a structure with disperse polydomains in a nematic sea (region II) at higher shear rates. At even higher shear rates the structure eventually becomes a monodomain (region III). Direct texture observations by Kiss and Porter [5] using a polarizing microscope gave somewhat deviating results. At low shear rates they observed a striated texture, with stripes parallel to the flow direction. At the highest shear rates the image became totally featureless as expected for region III. In the intermediate region, where the first normal stress difference (N,) is negative, the texture exhibited bands perpendicular to the flow direction. The observations of a banded structure during steady state flow could however not be reproduced by other authors [6-lo]. The picture of a polydomain structure during flow was used by Marrucci [ 1l] and by Wissbrum [ 121 to model the viscosity curve. They suggested that an internal “domain” size develops as a result of the balance between the Frank elasticity and hydrodynamic forces. They concluded that domains decrease their size in response to the applied stress. A first indication of texture refinement was reported in the work of Alderman and Mackley [13]. Using optical microscopy on thermotropic LCPs, while applying oscillatory shear, they also observed three types of texture in agreement with the work of Graziano and Mackley [ 141. At low shear rates a line texture exists which turns into worm texture when the shear rate is increased. The distance between individual disclinations decreases progressively. At the highest shear rates the image becomes featureless, indicating a well aligned sample [ 151. Flow does not necessarily align the director. At low shear rates and small strains Srinivasarao and coworkers reported tumbling for solutions of poly-( phenylenebenzobisthiazole) [ 161 and for a thermotropic polymer [ 171. Burghardt and Fuller showed that solutions of poly(y -benzylglutamate) (PBG) also exhibited tumbling. They associated the possibility of director tumbling with texture refinement [ 181. The latter would then be a mechanism for limiting the elastic energy resulting from distortions induced by tumbling. This results in the saturation of the dimensionless groups +z’r/lu, where y is the shear rate, a is a length scale, q a viscosity and K a characteristic elastic constant, as suggested by Marrucci [ 191. Small angle light scattering (SALS) was used to study the effect of flow on texture in PBG and hydroxypropylcellulose solutions by Takebe et al. [20] and by Ernst et al. [8]. Only two types of patterns were reported in these studies, the first one corresponding to a low shear rate regime, with a more or less uniform distribution of defects. The second pattern, observed in the high shear rate regime, is an X-type profile with an equatorial streak perpendicular to the flow direction, for which the authors proposed a qualitative model. The latter assumes a nematic medium with a low concentration of defects, containing domains with a high defect concentration. However, this model does not seem to be in agreement with direct optical observations [5,21].

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3

In addition to its effect on texture, shear flow also affects the average molecular orientation. To investigate how the overall orientation relates to the rheological behaviour, Hongladarom et al. [22] developed a spectrographic birefringence technique. Using various PBG solutions, they found no evidence for a randomly oriented polydomain structure at low shear rates, as suggested by Onogi and Asada [3]. In the low shear limit the birefringence was about 53-63% of the monodomain value. As the shear rate increased, a transition was observed to a high shear rate regime where the orientation reached a limiting value of about 90% of the monodomain value. The shear rates at which the transition from a low- to a high-oriented state occurs, are related to the changes in sign of N1. Hence, the low shear regime is associated with tumbling and the high shear regime is associated with flow alignment. The average molecular orientation seems to be closely associated with the dynamic moduli [23]. To gain more insight into the different textural transitions, solutions of PBG were recently studied by Larson and Mead [21] and compared with the known behaviour of low molecular weight nematics. These authors state that at low shear rates the Ericksen number determines a sequence of transitions. First the director rotates towards the vorticity direction, followed by the appearance of roll cells. At higher shear rates, a state of director turbulence is achieved. From there on the Deborah number controls the transitions in texture. In the tumbling regime, a speckled, worm texture is observed. In the so called wagging regime for the director, when Ni becomes negative, a striated structure appears. It is associated with a reoccurrence of the roll cell instability. Finally, a uniform monodomain develops at high shear rates. The transient rheological behaviour is known to be characterized by peculiar scaling relations [24-261. Moldenaers et al. [27] used conservative dichroism to study the transient structures during stepwise increase in shear rate or flow reversal. The optical transients compared well with the rheological ones, in that they displayed damped oscillations and obeyed similar strain scaling. This scaling is a consequence of the fact that the material has no internal time scale, as demonstrated by Doi and Otha [28]. It constitutes the basis of the mesoscopic theory proposed by Larson and Doi [ 291. Larson and Mead [ 301 studied the time scale for the texture and orientation development using polarimetry. In agreement with the predictions of the mesoscopic theory, texture and orientation develop on separate time scales. However discrepancies were detected by Hongladarom and Burghardt [31], as birefringence measurements did not confirm the theoretically assumed isotropic situation at rest. No clear picture has yet emerged to correlate the texture with the flow conditions. In this study we first investigate the flow-induced steady state textures as a function of shear rate. Different systems are used to identify general relations between texture and rheological regimes. Techniques include optical microscopy using crossed polarizers and conoscopic SALS (hereafter called CSALS) using a Bertrand lens. The latter provides a two-dimensional Fourier transform of the real image. In this manner we hope to clarify how texture develops in a sheared nematic solution and how it’ affects the rheology. Subsequently the start-up transients from a

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J. Vermant et al. /J. Non-Newtonian Fluid Mech. 53 (1994) l-23

uniformly aligned sample are studied as a function of time. Texture evolution after cessation of flow will be discussed elsewhere.

2. Experimental 2.1 Materials Rheological and rheo-optical experiments were performed on four different solutions of poly-(y -benzylglutamate) (from Sigma) in meta-cresol. Three racemic mixtures contained equal amounts of PBDG with a molecular weight (as indicated by the supplier) of 310 000 and PBLG with a molecular weight of 300 000. The weight concentrations amounted to respectively 25%, 20% and 15%. The fourth sample was a PBDG solution with a molecular weight of 310 000 and a concentration of 15 wt.%. This sample is cholesteric at rest whereas the racemic mixtures form nematic phases. Hence a comparison will provide information on the effect of rest structure on the texture during flow. The aspect ratio of the helical PBG molecules is approximately 140. A considerable amount of data has already been published on these and similar samples [1,2,5,23-25,32-351 thus rendering a comparison with literature data possible. The 25% sample is the same as the one studied by Moldenaers et al. [36]. Measurements were also performed on hydroxypropylcellulose (HPC) in water [37,38]. A solution of 50.1 wt.% with a molecular weight of 100 000 (as indicated by the supplier) was used (KLUCEL@ from Aqualon Co.).. The critical concentration for this system is approximately 41%. Details of the sample preparation are discussed by Grizzuti et al. [39]. Some measurements on a 19.8 wt.% solution of PPTA (poly-phenylene-terephthalamide) with a molecular weight of 30 000 in sulphuric acid are included. The material was supplied by Akzo (Twaronn). The PPTA is well known for its application in high strength fibres. This system has already been studied by Picken and coworkers [9,10,40]. 2.2 Experimental methods The rheological measurements were performed on a Rheometrics Mechanical Spectrometer (RMS) 705F and on an RMS 800. In all experiments cone and plate geometry was used. Temperture was controlled by means of a fluid bath. The optical observations were performed on different set-ups. A first one consisted of a reciprocating sliding plate flow cell mounted on a Leitz Orthoplan polarizing microscope, using a mercury light source. This set-up is described in detail by Picken et al. [lo]. The spacing between the upper and lower plates was 50 pm for the experiments on PBG and HPC, permitting shear rates between 0.25 and 250 s-’ and a maximum strain in one direction of 150 units. The optical experiments on PBG and HPC were performed at room temperature. For PBG additional data were collected at 35°C to evaluate the effect of temperature on texture and its

J. Vermant et al. 1 J. Non-Newtonian

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5

transitions. For the measurements on PPTA (80 and 90°C) a spacing of 25 pm was used enabling shear rates between 0.5 and 500 s-l and a maximum strain of 300 units. In all experiments the observations were performed in the plane formed by the flow and the vorticity direction. The images were recorded with a Panasonic WVP-FlOE video camera and a video recorder. Both the real images and CSALS patterns were studied. The disadvantage of the sliding plate set-up is that only a limited deformation can be applied to the sample. This limitation can be overcome by mounting the optical set-up on a rotational rheometer. For that purpose the RMS 705F was equipped with parallel glass plates. Experiments have only been performed at room temperature with this set-up. The gap was varied between 200 and 400 pm. Parallel plates have the disadvantage that the shear rate changes along the radial direction. This is however no major drawback for optical observations as only a limited area of the sample is under observation. The real images were recorded using an Ikegami 825P CCD-camera, and a video recorder mounted onto a Wild Ml0 microscope equipped with crossed polarizers oriented at 0” and 90” to the flow direction.

3. Results 3.1 Steady state Jtow 3.1.1 Poly(y -benzylglutamate): rheological results The vicosity and first normal stress difference for respectively the 15%, 20% and 25% PBG solutions are shown in Figs. l-3. The curves display the typical behaviour for PBGs [ 1,241. For the viscosity a Newtonian and a shear-thinning region are recorded. No region I behaviour was observed in the shear rate range under consideration. For the first normal stress difference positive values are measured at the lowest shear rates and negative ones at higher shear rates. JVi is known to become positive again at still higher shear rates [ 11. Changing the concentration affects both the plateau viscosity and the critical shear rates that bound the region where N, is negative [ 11. The plateau viscosity in solutions of rod-like molecules increases sharply with the concentration towards the isotropic-nematic transition. Beyond the critical concentration the viscosity rapidly decreases. At the highest concentrations, it increases again. For the system used here, the plateau viscosity exhibits a minimum around 20%. The concentration also has an effect on the nonlinear rheological behaviour. At higher concentrations the interaction potential between the molecules increases, thus requiring a larger viscous stress to overcome the elastic interactions [41]. As a result the region with negative N1 shifts to higher shear rates. The critical shear rates for the different solutions are listed in the three first columns of Table 1. As noted by Moldenaers et al. [36] the critical shear rates for a transition from positive to negative ZV1values are sensitive to the cone angle for these solutions. All experiments reported here are performed with a cone angle of 0.0197 radians and a radius of 12.5 mm thus rendering a comparison between the three solutions possible.

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shear

rate

(s-l)

Fig. 1. Steady state viscosity (0) and first normal stress difference (A; open, positive; filled, negative) as a function of shear rate for the 15% PBG solution in m-cresol at 20°C.

Table 1 Critical shear rates (SK’) of rheological and optical phenomena for the steady state rheology of the various PBG and HPC samples Sample cont.

N 1,max

NI = 0

Nl,min

Speckled-striated

Striated-uniform

PBG ( 15%) PBDG (15%) PBG (20%) PBG (25%) PBG (25%) 35°C HPC (50%)

2 2 3 5 20 2

4 4 1 15 50 9

>30 >30 >40 150

1.25-2s 1.25-2.5 2.5 2.5-5 5-10 0.1

25-50 25-50 50- 100 loo-250 > 250 25

-40

3.1.2 Poly (y -benzylglutamate): structural results Depending on the shear rate, different structures can be distinguished. The structures are similar for the three PBG solutions. In the following sections the structures will be discussed in order of increasing shear rate. The structures reported here are the steady state structures. In the parallel plate flow cell the maximum strain that can be applied would be adequate to reach steady state conditions for both shear and normal stresses [36]. Reaching a steady state texture might take

J. Vermant et al. 1 J. Non-Newtonian Fluid Mech. 53 (1994) l-23

[_

I

[a-

N, positive (Pa) N, negative (Pa) 7) 111 Pa s ; 0 L.. _..-. _ ._.._.__.__ ___._____..

1 A

100

10

:

.-

A A A 1 : A

011

0.01

5

C”,,”

I

0.1

1

shear

10

rate

I

J

100

1000

(s-l)

Fig. 2. Steady state viscosity ( 0) and first norrnal stress difference (A; open, positive; filled, negative) as a function of shear rate for the 20% PBG solution in m-cresol at 20°C.

longer but 150 deformation units seem sufficient. This was confirmed by the fact that observations after larger deformations in the optical set-up on the RMS 705F are identical to those in the parallel plate flow cell. At the lowest shear rates a speckled, grainy structure is observed between crossed polarizers oriented at 0 and 90” to the flow direction (Hv position). Alderman and Mackley called this a worm texture because the overall view resembles “ a vat of teeming worms” [ 131. A typical example of such a texture is shown in Fig. 4(a). At first sight, the image reflects a poorly oriented state. However, when the sample is observed under polarizers crossed at 45/135”, the colour is uniformly yellow; inserting a quarter wave plate shows that most of the material is aligned in the flow direction. In addition the substantial birefringence at low shear rates [22], indicates a significant degree of orientation. A similar conclusion was reached by Picken et al. [lo] who studied the orientation in solutions of PPTA. The speckled texture consists of a defect network that can be clearly observed by using only a polarizer but no analyzer. A second feature of these images is the presence of spots of variable, fluctuating intensity which apparently move at a velocity different from that of the defect network. The corresponding CSALS images show an almost elliptical pattern with a weak streak perpendicular to the flow direction, indicating the presence of anisotropic

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J. Vermant et al. 1J. Non-Newtonian Fluid Mech. 53 (1994) l-23

A 1

0.1

A A

E

-.--.

0.01

L .-L-L

L1

Iu.L-_L-l--LL~LL____J

0.1

_..L_L-LLULl._

1

10

.A.

..L..L_LLUd-~_.l.I 100

1000

Fig. 3. Steady state viscosity (0) and first normal stress difference (A; open, positive; filled, negative) as a function of shear rate for the 25% PBG solution in m-cresol at 20°C.

scattering elements oriented in the flow direction. The intensity of this streak increases with shear rate. The CSALS results are similar to the SALS obtained by Takebe et al. [20] and Ernst et al. [8], though we did not observe a clear single elliptical pattern without a streak, which might however occur at even lower shear rates. As the shear rate is increased a striated structure gradually develops (Figs. 4(b) and 5(a)), with stripes running parallel to the flow direction. First it appears only as a transient phenomenon but as the shear rate is increased further- a striated texture remains present under steady state conditions. The shear rate ranges in which this transition occurs are listed in Table 1 for the different samples. A typical example of a well-developed texture of this nature is shown in Fig. 4(c). The CSALS patterns now show a clear and distinct streak perpendicular to the flow direction (Fig. 5(b)). It seems logical that the streak in the CSALS patterns is related to the striations. At relatively low shear rates the density of the striations is not constant throughout the sample. In regions with a high concentration of striations the spacing between them tends however to a constant value (approximately 10 pm). In the CSALS images the distribution of length scales causes the equatorial streak to be smeared out; however if one calculates the average length scale from the CSALS it is comparable to the one measured from the real image. As the shear rate is increased additional striations appear. The distance between striations is similar for the three PBG concentrations under investigation.

J. Vermant et al. 1 J. Non-Newtonian Fluid Mech. 53 (1994) l-23

(4

(b)

Fig. 4. Typical textures observed during steady state flow of a 15% PBG solution (A, analyser, P, polarizer; area shown, 0.64 mm by 0.42 mm). (a) Worm texture; (b) texture at the transition from a worm texture to a striated texture (if = 2.5 SC’); (c) striated texture (1’= 10 SC’).

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J. Vermant et al. 1 J. Non-Newtonian Fluid Mech. 53 (1994) l-23 A

FLOW

P

b

+

FLOW

b

N.A. = 0.2

I

(4

Fig. 5. CSALS during flow as a function of shear rate for the typical textures. (a) Texture at the transition from a worm texture to a striated texture (it = 2.5 s-l); (b) striated texture (v = 10 s-l); (c) aligned texture (f = 100 s-l). The line coresponds to a numerical aperture (N.A.) of 0.2

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11

The nature of the striations is not yet clear. The CSALS images show that scattering objects are present which are oriented in the flow direction. The insertion of a quarter wave plate at 45” shows alternating blue and pink colours in between neighbouring striations, indicating that there is a periodic misalignment. One of the interesting features of the striations is that they remain present after stopping the flow [30]. Yet, the bands that form perpendicular to the flow direction are not hindered by their presence. Notwithstanding the formation of the bands a residual image of the striations remains both in the microscopic and CSALS images. The latter is more pronounced when the concentration is lowered. When the shear rate is still increased further the texture refines, the striations gradually fade away and the picture becomes progressively black. The latter corresponds to an almost uniformly aligned texture. The CSALS image no longer shows an equatorial streak (see Fig. 5(c)), but only a very small diffuse lobe of a periodic structure perpendicular to the flow direction, which is initially also seen in the microscopic images. This might be related to the observations by Kiss and Porter[5]. After the striated regime the latter authors reported what they called a “row-nucleated” texture. This regime was observed by neither Takebe et al. [20] nor by Ernst et al. [ 81,probably because these authors did not reach such high shear rates. The shear rate ranges in which the texture changes are given in Table 1 for three concentrations of PBG. In addition to the influence of concentration the effect of rest structure and temperature on the transitions was also investigated. The types of texture and the shear rate at which the changes occur are identical for the 15% cholesteric PBDG sample and the 15% nematic mixture. This independence is not surprising as the cholesteric structure changes to a nematic one during flow and both display identical steady state rheological behaviour. Changing the temperature for the 25% PBG solution from ambient temperature to 35°C shifts the transition shear rates for the optical and rheological phenomena as indicated in Table 1. This shift can be rationalized when compared with low molecular weight liquid crystals. For these systems it is known [42] that

where y, is the rotational viscosity, S is the order parameter. The Frank elastic constant K (one-constant approach) and the order parameter are related by KwS’. Hence we expect for L (length scale) Lhffhi ’ and thus we find for it,,+, S

Ycritz L2 exp(E/kT) * From our measurements and the data of Mewis and Moldenaers [43] it is concluded that the viscosity changes by a decade over a temperature range of approximately

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35 K, while the critical shear rates change slightly less. In this range the textural length scales seem hardly affected at all by temperature. These results are compatible with the given equation. 3.1.3 HPC and PPTA The rheological steady state properties of the HPC solution have been studied by Grizzuti et al. [39]. This sample clearly displays a three region flow curve, and an intermediate region with negative normal stresses. The critical shear rates associated with the transitions in the first normal stress difference are listed in Table 1. The textural length scales in HPC are roughly five times smaller than those observed in PBG solutions. The structures in HPC are therefore more difficult to observe and are at the limit of the optical resolution of the microscope. The sequence of the textures observed in the parallel plate flow cell is shown in Fig. 6. The textures are quite similar to those encountered in PBG samples. However striations persist until the lowest shear rates that could be achieved in the parallel plate flow cell (0.25 s-l). Observations in the rotational device indicate that a worm texture exists below approximately 0.1 s-l. The shear rate ranges for the textural transitions are also listed in Table 1. The PPTA solution has also been studied in the parallel plate flow cell [lo]. In the shear rate range under observation, essentially a single type of texture can be observed. It is a speckled, grainy texture. The length scale of the structure is comparable to the one observed in HPC and again the texture is refined with increasing shear rate. The PPTA molecules are known to be more flexible than PBG and less flexible than HPC [44]. No reliable N, data are available for this material to locate the critical shear rates. Preliminary measurements indicate that around 1 s-’ N, is positive. 3.2 Transient behaviour

In order to elucidate further the relation between the rheological and the textural characteristics of our samples some transient experiments were performed. In the present work start-up experiments from a uniformly aligned sample are used to illustrate the correlation. The initial alignment in the flow direction can be generated in two ways. A first possibility is to shear the sample at sufhciently high shear rates [30], i.e. in the flow aligning regime. This flow alignment persists for a long time after the flow is stopped. A second possibility is to shear the sample at a somewhat lower shear rate. When the flow is stopped after reaching a stationary regime, a banded texture perpendicular to the flow direction is formed. This banded structure will relax to a well-aligned condition given a sufficiently long rest period [7,31,45]. Rheological start-up experiments were performed on the 15% PBG. In Fig. 7 the stress growth curve for a shear rate of 2.5 s-’ is shown. After 1 strain unit the slope of the stress curve suddenly changes. The shear stress rises to a first maximum at 13 strain units, followed by a minimum at 18 strain units. A second maximum and minimum are reached after respectively approximately 35 and 75 strain units.

J. Vermant et al. / J. Non-Newtonian Fluid Mech. 53 (1994) 1-23

13

FLOW .

(4

(4 Fig. 6. Typical textures observed during steady state flow of a 50% HPC solution (A, analyzer, P, polarizer; area shown, 0.305 mm by 0.20mm). (a) Weakly striated (3 =0.25 s-l); (b) striated texture (y = 1.25 SK’); (c) flow aligning texture (y = 25 s-l).

J. Vermant et al. 1 J. Non-Newtonian Fluid Mech. 53 (1994) l-23

d

e

1

f

- - -__ _

b

I

@@--------

E

6

a

I --

-_.----

45 s-‘, rest 45 se*, rest 45 s-*, rest

time time time

300 300 500

s s s

/

10

u’,“‘,‘.,‘l’,,“,,“,,,“,‘,“,‘,

0

10

20

30

40 applied

50

60

~‘~~*~‘~‘a~‘~~“’ 70 80 90

100

strain

Fig. 7. Shear stress upon start-up from a well-aligned 15% PBG sample (i = 2.5 SC’). The sample was presheared at 45s~’ and allowed to rest for 300-500 s.

The first normal stress difference (not shown here), first rises to a maximum after l-2 strain units, followed by a minimum at approximately 10 strain units. The textural evolution is also observed during start-up of flow at a shear rate of 2.5 s-l for the uniformly aligned sample. The results are shown in Fig. 8. The arrows in Fig. 7 indicate the moments at which the pictures were taken. Upon inception of flow, the image remains featureless for less than 1 strain unit. Then a transient banded texture develops perpendicular to the flow direction. This pattern is initially regular, the bands displaying a rolling motion (Figs. 8(I.a) and 8(II.a)). After approximately 5 strain units defects are generated and the bands are broken up into smaller units (Figs. 8(I.b) and 8QI.b)). After approximately 15 strain units the defects are elongated in the fiow direction. The remainder of the transient bands disappears (see Figs. 8(I.c) and 8(II.c) for respectively the microscopic and CSALS observations). From the elongated defect network striations are formed after approximately 25 strain units. At lirst, the striations are very regular (up to x 50 strain units-see Figs. 8(I.d.) and 8(II.d.)), subsequently they lose their regularity, the striated texture becomes less pronounced The decrease in regularity can be clearly observed in Fig. 8(e) for a shear rate of 2.5 s-l in both the microscopic and the CSALS pictures. The steady state texture is only weakly striated (see Fig. 4(b) for the real image, Fig. 5(a) for the CSALS image). A shear rate of 2.5 s-l was chosen because it shows all possible textures consecutively. At 0.25 s-’ where the worm texture is the steady state texture, the initial textural evolution is similar to the one described above but no striations are formed after a substantial deformation has been applied to the sample. At 0.5 and

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1.25 s-’ a striated texture appears only as a transient phenomenon. For example at 1.25 s-’ it is clearly developed after 40 s and disappears again after 100 s. At shear rates higher than 2.5 s-l, the sequence again deviates. At 25 s-l, the initial banded

P

-+ FLOW .

Fig. 8. (a), (b). Continued over next two pages.

16

II(c)

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II(d)

169

II(e) Fig. 8. Texture evolution upon start-up from a uniformly aligned 15% PBG solution at a shear rate of 2.5 s-’ after: (a) 2 s; (b) 4 s; (c) 8 s; (d) 16 s; (e) 30 s. I. microscopic observations; II corresponding CSALS patterns; area shown, 0.64 mm by 0.425 mm.

structure is less regular than that at lower shear rates. At even higher shear rates, no transient banded texture could be detected with our techniques. Above 100 s-* the image remains featureless during and upon cessation of flow. The same tendencies as observed during start-up from a monodomain are present when the flow is started from a banded texture or from a coarse texture. The evolution of the texture upon inception of flow in HPC is qualitatively similar to the one in PBG. A uniformly aligned state could however not be achieved for HPC

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at the highest shear rate attainable (250 s-l). For PPTA the situation is clearly different. No transient banded structure is observed and no uniform aligned monodomain could be achieved, not even after prehearing at 500 s-l. It should be noted that although the grainy texture remains visible during flow, even at high shear rates, the overall degree of orientation in PPTA solutions appears to be very high [40] over a wide range of shear rates. After preshearing at high shear rates, and allowing the sample to relax for a few minutes, the texture contains a limited number of clearly visible defects. When flow is started these defects are deformed. After 20 strain units there is a massive multiplication of defects [IO]. The multiplication is not homogeneous throughout the sample.

4. Discussion 4.1 Steady state results As can be seen from Table 1, concentration and temperature cause the rheological and textural transitions to shift in a similar fashion along the shear rate axis. The high shear transition to a featureless structure occurs near the position of the extremum of the negative N,. Theoretical work suggests that this corresponds to the onset of flow alignment [41]. Under such conditions no substantial amount of elastic energy is stored in the material. Consequently the texture hardly changes after stopping the flow. The low shear transition from a speckled to a striated texture is a very gradual one. It takes place around shear rates which are one to two decades below the transition to the featureless structure. For PBG solutions striations become visible around the position of maximum positive Ni. For HPC this happend earlier. Larson and Mead [21] associated the striated regime with the occurrence of a flow instability which coincides with the change from director tumbling to wagging. The latter happens at the transition from positive to negative Ni [46]. The present data do not support this relation with the rheological behaviour. This is especially clear for HPC. In the data for PBG the gap dependence of this transition observed by Moldenaers et al. [36] could cause some interference. The nature of the three observed textures is not fully understood. At low shear rates, where a speckled structure is observed, the CSALS displays an almost elliptical pattern, indicating a slight deformation of the disclination distribution [20]. But even at the lowest shear rates observed, the patterns also exhibit an equatorial streak, indicating the existence of a limited number of scattering elements elongated in the flow direction. This small streak is present in the CSALS before a striated structure becomes visible in the microscope. The effect of concentration and temperature on the length scales of texture seems to be marginal. In the worm texture the magnitude of the speckles is typically of the order of magnitude of 10 pm for PBG and of a few micrometers for HPC and PPTA. The length scales obtained are possibly determined more by the persistence length of the molecules than by the concentration, in agreement with Dannels et al. [47]. It should be noted

J. Vermant et al. 1 J. Non-Newtonian Fluid Mech. 53 (1994) 1-23

19

that the size of the initial striation spacing is similar to the initial band width upon cessation of flow for the various PBG solutions. The same holds for HPC but apparently not for PPTA. For none of these three materials could pronounced texture refinement be observed in the shear rate region where the speckled texture appears, although rheo-optical measurements seem to suggest it, at least for PBG

v71. As the shear rate is increased, there is a gradual transition to a striated structure. The CSALS patterns clearly exhibit an equatorial streak, when the striations are visible in the microscopic images. To explain the patterns in this region, Takebe et al. [20] and Ernst et al. [8] assume regions with high and low defect density. The vertical streak in the CSALS patterns can also be explained by the periodicity associated with the striations. These striations might be caused by elongated defects either accompanying a roll-cell instability [21] or by the presence of defects elongated by the flow field itself. Marrucci and Maffetone [48] studied theoretically the dynamics of defects in LCPs in the presence of a flow field. They calculated that disclinations are stretched by the flow field, provided both the disclination size and the shear rate exceed a critical value. Their conclusion is in agreement with the observations by De’Neve et al. [49] on a thermotropic polymer. This could also explain the nature of the striated texture observed here. The fact that a residual image of the striations remains present upon cessation of flow remains unexplained. If the striations consist of stretched disclination loops, one would rather expect them to collapse, unless they are being trapped, e.g. if the existence of the banded structure would impose limitations on the mobility of the disclinations. According to Marrucci [ 191and Marrucci and Greco [50] the texture should refine proportionally to i, -5 in the regime with stretched disclination loops. The microscopic observations show an exponent of -0.34 in the shear rate range where distinct striations appear in the microscopic images. This value was obtained by measuring the average spacing between striations from the microscopic images for the various samples. At high shear rates the sample is uniformly aligned. In the CSALS patterns the equatorial streak disappears and the lobes come closer and closer to the central beam from which they cannot be distinguished any more with the present equipment. This structure is most easily understood as being a uniformly aligned sample. It must be noted that the behaviour of the PPTA solution seems quite different. No striated regime is found. Also the evolution to the steady state texture is different. Whereas in HPC and PBG the texture gradually refines, there is a critical strain in the PPTA solution at which the disclinations rapidly multiply. Probably higher shear rates are needed to achieve a striated or flow aligned texture; alternatively the alignment might just seem worse because of the higher birefringence. 4.2 Transient Jrow The transition in start-up flow from a uniformly aligned monodomain to its steady state texture is characterized by a number of typical steps. The details of the evolution depend on the applied shear rate. For shear rates below the flow aligning

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regime, the texture first remains uniform and subsequently a texture with bands perpendicular to the flow direction is formed. These bands were observed by Larson and Mead for both an homeotropic and a flow oriented sample in a limited region of shear rates [30]. The bands show what can be described as a rolling motion. The bands are possibly related to two phenomena. It has been shown experimentally that lyotropic solutions of liquid crystals, including PBG, can exhibit tumbling [ 15,181. Secondly, in analogy with band patterns that form in magnetically induced reorientations [ 511, a periodic secondary flow might be present [21]. If tumbling is present, it will create locally large distortions. Due to the spatial gradients, defects are created [ 501. These defects are refined and can be elongated in the flow direction at high enough shear rates. It appears that these elongated defects give rise to the striated structure [48]. It is not obvious yet why the striated structure appears only as a transient phenomenon at shear rates close to the critical point where the striated structure is the steady state structure. The closer to the transition the longer the striated structure remains present. The evolution of shear stress during start-up of shear flow can be compared with the textural observations. The kink in the shear stress curve after one strain unit seems to be linked to the breaking up of the monodomain. The maximum in the shear stress occurs at approximately 13 strain units, where defects have already been created and the defect network becomes deformed in the flow direction. The first minimum in the shear stress occurs at the point were the remainder of the banded structure perpendicular to the flow direction disappears and the striations start to appear. There are indications that the complex texture is not directly responsible for the stress transients. Indeed, some monodomain models seem to be able to describe qualitatively most features of the rheological behaviour [50]. This is experimentally confirmed by transient measurements of the overall molecular orientations, from birefringence, which seem to follow closely the patterns of the stress transients [52]. A similar conclusion was derived from the measurement of parallel superposition moduli [23]. Hence an averaging procedure over the domains seems adequate to describe the instantaneous stress level. However, the time evolution of the domain orientation and consequently the stress evolution will be mainly determined by the elastic forces caused by spatial director gradients. Hence the detailed microstructure will interfere here. Evidence for this is provided by the strong similarities between some stress transients and transients of conservative dichroism. The following picture seems to describe qualitatively the various observations. Application of a shear rate below the flow alignment transition causes massive director tumbling after strains of the order unity. The tumbling results in periodic fluctuations in molecular orientation and stress. However the rotation causes director winding, increased director gradients and elastic stresses, until these balance the viscous stresses. This results in defect generation. A polydomain structure develops with or without striations. The formation mechanism of the latter is not uniquely defined at this moment. The domain structure makes massive oscillations impossible and damps out local fluctuations. The larger scale structures which are observed in the microscope have less effect on the rheology than small scale structures.

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5. Conclusions

Rheological and textural characteristics of liquid crystalline solutions of PBG and HPC have been compared. In regions II and III of the viscosity curves three types of texture can be distinguished. At low shear rates a speckled polydomain structure exists. Upon increasing the shear rate, first striations running in the flow direction appear. They gradually become clearer and denser, fading away when the shear rate is further increased. Finally a nearly featureless monodomain structure develops. The striations become visible in the microscope before the first normal stress becomes negative. For the HPC solution distinct stripes are even present before the positive N, reaches its maximum. Consequently striations do not seem to be caused by director wagging which starts at the onset of negative N,. In the CSALS patterns the structures in the flow direction are visible before they appear in the microscopic images. The CSALS results also suggest a domain refinement which cannot be detected in the microscope. The distance between striations is found to change with 3 -“.34, while theoretical calculations of the defect density predict a change with i, -O.‘. The transition to a monodomain occurs around the negative extremum in Ni. It thus seems to be associated with the onset of flow alignment. For a solution of an aromatic polyamide (PPTA) only the speckled texture could be generated in the available range of shear rates. It is not known whether striations could appear at still higher shear rates or whether this material behaves differently. Changing the concentration or the temperature shifts both the rheological and the textural transitions in a similar fashion, providing further evidence for their interrelationship. For poly-benzylglutamates the rest structure can be cholesteric (for single enantiomer systems) or nematic (for racemic mixtures). If the other parameters are kept constant, the nature of the rest structure does not alter the transition shear rates. The types of texture that are obtained by varying the shear rate can also be generated during transients at a single shear rate. A start-up experiment from a monodomain results consecutively in transverse bands and striations before reaching the steady state structure. Texture, rheo-optical and rheological transients have been compared. This suggests that instantaneous stress levels are determined by the average molecular arrangement.

Acknowledgments

The work was made possible by the financial support of Akzo International Research, Arnhem (The Netherlands), N.F.W.O. (Nationaal Fonds voor Wetenschappelijk Onderzoek, Belgium) and I.W.O.N.L. (Instituut tot Aanmoediging van het Wetenschappelijk Onderzoek in Nijverheid en Landbouw, Belgium). We thank Dr. M. Srinivasarao for stimulating discussions.

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