TEXTURE DEVELOPMENT IN THE SHEAR FLOW OF NEMATIC SOLUTIONS OF RODLIKE POLYMERS. Guy C. Berry

Transcription

1 TEXTURE DEVELOPMENT IN THE SHEAR FLOW OF NEMATIC SOLUTIONS OF RODLIKE POLYMERS Guy C. Berry Department of Chemistry Carnegie Mellon University Zhanjie Tan Sudha Vijaykumar 1 Beibei Diao 2 Present address : 1. Ethicon Endo-Surgery, Inc., Cincinnati, OH 2. du Pont Co., Inc., Buffalo, NY Mohan Srinivasaro 3 Kiyofumi Matsuoka 4 3. Georgia Tech. 4. Showa Denko KK, Oita, Japan Acknowledgments: Support from the National Science Foundation is acknowledged.

2 Questions on the flow of nematic solutions of rodlike chains in shear flow What is the nature of the Director Field? Do Line Defects (disclinations) play a role? Does the persistence length in dilute solution play a role? Do the Frank curvature elasticities and Leslie viscosities play a role? Do universal scaling laws for the stress exist? Carnegie Mellon 1

3 N S S N PBZT n O C N H O C N H PPTA n Birefringence: Magnetic Susceptibility Anisotropy n = ( n/c) o c S ( n/c) o = 1.0, PBZT ( n/c) o = 0.6, PPTA χ = ( χ/c) o c S χ n Persistence Length in Dilute Solution PBZT PPTA â/nm > Carnegie Mellon 2

4 Typical Steady-State Behavior Anomalous Slow Flow Region I η ss J R γ 1 η ss Log "Shear Viscosity" Slow Flow Region II Fast Flow Region III Log Recoverable Compliance Slow Flow Region II JR Fast Flow Region III η ss Slow Flow Region II Fast Flow Region III Log "Normal Viscosity" + + Log Shear Rate Carnegie Mellon 3

5 "Polydomain" Representation Quiescent Fluid Slow Flow Fast Flow Carnegie Mellon 4

6 Late stages of texture coarsening under the influence of confining surfaces Lines formed in the wake of a rising air bubble (bubble moving to left) Loop Defects relax and disappear very slowly Carnegie Mellon 5

7 0 hr 30 hr 48 hr 54 hr 72 hr 83 hr Collapse of a loop defect Carnegie Mellon 6

8 Nematic PBZT Solutions do not align in slow shearing flows Drive Glass Sample Drive Glass Lens Initial flow of a well aligned nematic solution (PBZT) 10 d = 125 µm (Filled) d = 250 µm (Unfilled) ϕ, deg γ app = v t/d o Carnegie Mellon 7

9 Filling tube Radial flow Upper Surface Lower Surface Following Fast Flow Tangential flow Sample Optical Measurements (Incident light along shear gradient): Carnegie Mellon 8

10 nm) Intensity of transmitted light (laser, 633 nm) Scattered light intensity distribution (laser, 633 Creep γ(t) Recovery Strain σt/η γr(t) Time Linear Viscoelasticity: Creep: γ(t) = σ J(t) = σ {R(t) + t/η} Recovery on cessation of steady flow: γ R (t) = σ R(t) γ R (t) = γ R ( )R(t)/R( ) Mesoscopic Theory: R( ) = J s Steady slow flow: γ(t) = γ ss t Recovery on cessation of steady slow flow: γ R (t) = γ R ( )H( γ ss t) Carnegie Mellon 9

11 Texture via CD-camera ( 5 µm resolution, white light) Clear r = R radius Vorticity P Turbid Flow r =0 Photo of turbid-clear transition. Torque = 100,250 dyn cm; Shear rate calculated at transition: 1.64 s -1 Carnegie Mellon 10

12 Near Edge Near Middle Near Center Flow direction from left to right. Width 1.5 mm; 9.74%, 500µm;. Steady-state behavior. Carnegie Mellon 11

13 4.0 Log t/j(t) (cgs) Log Transmission Log Time/sec 0 Log Transmission Log Strain 12.0%/500µm Carnegie Mellon 12

14 100,000 γ R (γ) η/poise 10,000 1, /2 9.74/ / /200 1 J (γ)/dyn/cm 2. s / Transmission γ /s -1 Carnegie Mellon 13

15 I I P(π/4) P(0) II P(π/2) I I a b c P(π/4) P(π/4) P(π/4) ~1s ~3s ~5s d e f Vorticity Flow Refraction effects observed immediately on start up of moderate flow. All with no analyzer: a-c show the pattern within 2 s for various polarizations of the incident light; d-f show the patterns at the indicated times after onset of flow Carnegie Mellon 14

16 Transient scattering in a slow flow; 9.74% 500 µm Top: Before flow, Bottom: About 10 m into flow finally went to weak diffuse scattering in steady state flow Carnegie Mellon 15

17 P(π/4) Flow I II Vorticity P(π/2) P(0) I II Transient scattering streak observed after 30 min creep in a moderate flow. Disappeared in steady state moderate flow Carnegie Mellon 16

18 Example scattering patterns in steady-state flow, increasing in shear rate from top-left to bottom-right 9.74%; 500µm Carnegie Mellon 17

19 Flow P(0) P(π/2) P(π/4) A(3π/4) Vorticity P(π/4) A(0) P(π/4) A(π/2) Scattering in fast flow. Torque =98,000 dyn cm I II I Scattering at the entry to the fast flow regime Carnegie Mellon 18

20 Tendency for lower range of L and c/cni Stationary Flow Plate Separation Diffuse scatter Slow Flow Fast Flow No Texture Scattering along Vorticity Stria along Flow Velocity Tendency for higher range of L and c/cni Stationary Flow Plate Separation Diffuse scatter Slow Flow Fast Flow No Texture Scattering along Vorticity Stria along Flow Velocity Carnegie Mellon 19

21 0 2-1 log(r(t)/pa ) log(transmission) log(t/sec) log(γ t) 12%/200µm ss The recoil and transmission on cessation of steady-state flow: 12.0%, 200µm Carnegie Mellon 20

22 Relation between recoverable strain and optical transmission Relaxed prior to successive creep (Lw = 155 nm; c/cνι = 1.71) Transmission High shear rate flow prior to successive creep (Lw = 155 nm; c/cνι = 1.61) γ (t) R Transmission of light during recovery for samples with different deformation histories Carnegie Mellon 21

23 P(0) Visual Image P(π/2) Vorticity Flow Scattering pattern after 8 hr relaxation from moderate flow: Torque in flow = 4,430 dyn cm; 9.74%-500µm Carnegie Mellon 22

24 Band 0.5mm time time P Vorticity Flow Scattering pattern observed early in the relaxation from a fast flow with a clear texture. The total elapsed time is about 15 min. The insert at the bottom-right shows the striations and band structure during the stage of well-developed scattering along the flow axis. Torque in flow: 210,700; 9.74%, 500 µm. Carnegie Mellon 23

25 P(π/4) P(0) P(π/2) P(π/4) A(3π/4) P(π/4) A(0) P(π/4) A(π/2) Flow Vorticity Refraction effects seen in the 16 hr after cessation of a fast flow. Torque in flow: 100,250 dyn cm; 9.74%, 500µm. Carnegie Mellon 24

26 Phase-grating immediately on cessation of Flow with Striations Vorticity loop observed as phase-grating relaxes Carnegie Mellon 25

27 Transient structure in Creep-Recovery: Phase-grating pattern A F Flow band; ~800sec. Vorticity band, ~12hrs P Concentration 12%; Shear rate Interpretation: There is considerable preferential alignment in flow along the flow direction, but an alternating twist of the director out of the shear plane, and in planes parallel to the surfaces, is imposed on that general alignment; The rheological behavior in flow in creep reveals the preferential alignment through an increase in the creep rate (creep acceleration); Carnegie Mellon 26

28 Idealized "Chevron" pattern of director field with no out-of-plane distortion The flow induced alignment is not stable, owing to the twist distortions pervading the sample; an "immediate" elastic retraction along the flow direction produces a phase grating that evolves to defect loops along the vorticity; The tendency for striation development may be related to the weaker anchoring for twist distortions as compared with splay distortions. Carnegie Mellon 27