Rheology Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering 中央大學化材系講稿 10/28/2011 什 麼 是 流 變 (Rheology)? Rheology is the science of fluids. More specifically, the study of Non-Newtonian Fluids Y 流體 牛頓流體 - 水、有機小分子溶劑等 黏度η為定值 非牛頓流體 - 高分子溶液、膠體等 Small molecule Macromolecule V ● V Newton’s law of viscosity V yx V Y Deformable 黏度不為定值 (尤其在快速流場下) 非牛頓流體的三大特徵 特徵時間與無因次群分析 非牛頓流體的特徵 非牛頓黏度 (Non-Newtonian Viscosity) - Shear Thinning p Flow curve for non-Newtonian Fluids 牛頓流體 (甘油加水) 非牛頓流體 (高分子溶液) 正向應力差值的效應 (Normal Stress Differences) - Rod-Climbing 牛頓流體 (水) 非牛頓流體 (稀薄高分子溶液) 記憶效應 (Memory effects) - Elastic Recoil - Open Syphon Flow Time-dependent effects (搖變性) Thixotropy behavior Anti-thixotropy behavior A decrease (thixotropy) and increase (anti-thixotropy) of the apparent viscosity with time at a constant rate of shear, followed by a gradual recovery when the motion is stopped The distinction between a thixotropic fluid and a shear thinning fluid: A thixotropic fluid displays a decrease in viscosity over time at a constant shear rate. A shear thinning fluid displays decreasing viscosity with increasing shear rate. 非 牛 頓 流 體 的 不 穏 定 性: 黏 彈 性 效 應 “The mountains flowed before the Lord” [From Deborah’s Song, Biblical Book of Judges, verse 5:5], quoted by Markus Reiner at the Fourth International Congress on Rheology in 1963 De Elastic force tflow Viscous force or We = (Re 103 for all cases) - 描述非牛頓流體行為之程度 : 流體的特徵或 “鬆弛” 時間 tflow : 流動系統的特徵時間 : 剪切速率 De 0 0.2 牛頓流體 (葡萄糖漿) 3 1 收 縮 流 道 非牛頓流體 (0.057% 聚丙烯醯胺/葡萄糖 溶液) 8 典型製程之流場強度範圍 Lubrication High-speed coating Rolling Spraying Injection molding Pipe flow Chewing Extrusion Sedimentation 105 103 101 101 (s-1 ) 103 105 107 Typical viscosity curve of a polyolefin- PP homopolymer, melt flow rate (230 C/2.16 Kg) of 8 g/10 minat 230 C with indication of the shear rate regions of different conversion techniques. [Reproduced from M. Gahleitner, “Melt rheology of polyolefins”, Prog. Polym. Sci., 26, 895 (2001).] 小振幅反覆式剪切流: 黏性與彈性檢定 Exp b: Small-Amplitude Oscillatory Shear Flow The shear stress oscillates with frequency , but is not in phase with either the shear strain or shear rate Shear Stress : yx A() 0 sin(t ) Shear rate: yx (t ) 0 cos t Shear strain: yx (t ) 0 sin t Oscillatory shear strain, shear rate, shear stress, and first normal stress difference in small-amplitude oscillatory shear flow It is customary to rewrite the above equations to display the in-phase and out-of-phase parts of the shear stress Storage modulus yx G() 0 sin t G() 0 cos t Loss modulus Storage and loss moduli, G’ and G”, as functions of frequency ω at a reference temperature of T0=423 K for the low-density polyethylene melt shown in Fig. 3.3-1. The solid curves are calculated from the generalized Maxwell model, Eqs. 5.2-13 through 15 解決流變問題的途徑為何? 傳統 vs. 現代(未來) 流體加工性質 macrorheology 基本流變性質 the De, Wi numbers 機械量測 microrheology microscopy/spectroscopy birefringence/dichroism light/ neutron scatterings particle tracking 光學量測 0 N G molecular orientation / alignment particle size distribution/ diffusivity micro/mesoscopic structures 本質方程式 分子動力理論 flow pattern 模流分析 Traditional route Modern (predictive) route monomer mobility, elastic modulus etc. 量子、原子、多尺度計算 物質特性 (化學合成) Polarizer Analyzer PMT VV and VH polarizations; θ = 30° to 150° Multi-angle dynamic/static light scattering Morphologies of MEH-PPV Solutions The DLS autocorrelation function at any angles can be expressed as translational internal ìï P ( x) ü ¥ N é ù ïï P ( x ) 2 2 ïí 0 0 é ù ê ú c j e xp( Dq t ) + 1 exp ( Dq + 2 t ) t dRh å i i c ê ú ò ë ûý ê ú 0 ï ï P ( x ) P ( x ) i ë û ï îï þ g (1) (q, t ) = ¥ N ò å cij i dRh Intensity Distribution 0 Mixed Dynamics 1.0 i where ìï (qRg ) 2 = (1.505qRh ) 2 coil P( x) = (2 x ) [exp(- x) - 1 + x ], x = ïí ïï (0.775qR ) 2 sphere h î 2 P0 ( x) = (p x ) exp(- x 6 ) éëêerf( x1/ 2 2)ù ú û ïìï (1.505 Rh ) 2 ( kBT 6phs Rh ) coil 2 t c = Rg D = í ïï (0.775 Rh ) 2 ( kBT 6phs Rh ) sphere î 2 q / q kBT 0.2 0.02 0.5 1.5 2.0 q<Rg> 2.5 3.0 102 103 Rh (nm) 0.8 0.6 0.4 0.2 100 101 102 103 Rh (nm) 0.04 3.5 0.5 Initial decay rate: G(0) q = 1.0 1.5 2.0 q<Rg> 2.5 3.0 104 0.0 0.06 0.02 1.0 101 1 mg/mL MEH-PPV/chloroform 3 0.04 (0) (0) 3 q / q kBT 0.3 mg/mL 1 mg/mL 3 mg/mL Intensity Distribution Rh asymptote of the Zimm model 0.1 mg/mL 0.3 mg/mL 1 mg/mL 3 mg/mL Internal motion 0.4 1.0 MEH-PPV/chloroform 0.06 Center-of-mass diffusion & Internal motion 0.6 100 0.08 MEH-PPV/toluene 0.8 0.0 Suppressed Internal Motions of MEH-PPV Aggregates 0.08 1 mg/mL MEH-PPV/toluene 3.5 ¶ ln g (1) (q, t ) ¶t t= 0 104 Flow Birefringence Measuring System 高分子溶液於流場下,會因流場大小的不同,造成高分子鏈被拉伸、旋轉與變形的程度不同,因 此我們可以藉由流變儀搭配光學雙折射系統,量測高分子鏈於不同流場下的變化情形。 y 0 y y small l arg e x x x 何謂雙折射: 當光經過非均向介質,會分解為兩道不同路徑的折射光,其一恆遵守 折射率定律的正常光 (ordinary ray, o-ray ) ,其光的偏振方向,即電場振 動方向是垂直於光軸,另一道即是違反折射率定律的光為異常光 (extraordinary ray, e-ray ) ,其光的偏振方向是平行於光軸。當光於雙折射 材料中傳播時,因其具有兩個不同方向的主軸,光在兩軸中前進時的速度 分別為C1、C2,且C1>C2,因此我們將軸向1稱為快軸 (fast axis),軸向2 稱為慢軸 (slow axis)。所以光在兩分量間會有相位延遲現象產生,稱為 光波相位差,我們即可從相位差中推得折射率差。 2 D 2 d (n1 n2) 雙折射現象 d 為樣品厚度, 為光的波長。 流變雙折射: 高分子溶液的流動光學雙折射 (flow birefringnece) 有兩個來源:本 質的雙折射 (intrinsic birefringence) 和形狀的雙折射 (form birefringence) 。前者與高分子片段的非均向性極化有關,當鏈的構形發生改變時,鏈局 部的非均向性會變成巨觀的非均向性,因而造成本質的雙折射。後者與高 分子片段密度的非均向性相關,在稀薄溶液系統中較為重要。 光波之相位延遲 Phase modulated flow birefringence (PMFB) 分析與量測: 本實驗的光學雙折射主要基於Frattini和Fuller的相位調變系統來作量測 [Frattini and Fuller J.Rheol. 28,61(1984);Fuller et al (1985)]。假設δ和χ分別代表樣品的相位延遲量和方位角,I 為接收器量測到的光強,Io為光彈調變器上的入射光強;δm代表光彈調變器的相位延遲量 ,δm = A sin ωt,其中A為相對相位振福,ω為光彈調變器的共振頻率。 我們即可從探測器上得到光強 I I0 1 cos 2 sin 2 1 cos cos cos 2 sin sin m m 2 推算出: cos 2 sin 1 sin 4(1 cos ) 2 212 22 1 2 cos 4 tan 2 1/ 2 2 14 22 1 進而利用應力-光學定律進行檢測 C n tan 2 2 2 sin2 2 sin 4 2 n 2 d 應力-光學定律目的主要為了將光學特性轉換成流變特性。高分子流體於流場下,因 流場產生的應力場使其具光學的非均向性,其主應力差值的張量與折射率差值的張量成一 比例關係,其比例即為應力-光學常數 C 。因此,我們可利用此比例關係來進行檢驗。 實驗裝置: 實際實驗裝置 聚苯乙烯溶液的雙折射量測結果: 示意圖 以分子量200萬之聚苯乙烯溶於 DOP 下,配置10wt% 的溶液進行量測,利用應 力-光學定律進行檢測。 實驗結果: 固態材料 (四分之一波片) 量測結果: 2M PS/DOP 10wt% 45 Experimental value Theoretical value 40 100 80 60 1e-6 35 30 1e-7 25 20 1e-8 C Orientation angle ( Retardation Angle 120 Theoretical value Experimental value 15 1e-9 10 5 10 15 20 25 30 35 40 45 Quartar Wave Angle 5 5 10 15 20 25 30 35 40 45 1e-10 Angle (degree) 相位延遲量之理論與實驗值比較 方位角之理論與實驗值比較 Experimental C 5.9*10-9 4.5*10-9 1e-11 0 5 10 Shear Rate ( 1/s ) 15 20 25 Small-Angle Light Scattering (SALS) 原理: 利用同調入射光於撞擊粒子後產生之散射光,其光程差於接收器產生的干涉 原理,經由適當的分析可推知溶質在溶液中的結構與動態情形。 裝置實體與示意圖: 實驗校正: 1 Measured diffraction pattern Airy function I() / I(0) 0.1 0.01 0.001 0.0001 0 2 4 6 8 10 k a sin Fig.1 Comparison of the predicted scattering pattern (the airy function) of a 50 μm pinhole with the experimentally measured one. Fig. 2. Comparison of the form factor predicted by the Mie theory with the experimentally measured one. 應用: SALS之量測角度範圍一般為1°≦θ≦10°,多半作為較大尺度結構解析之用途。其應用範圍可為 高分子材料之混合 (mixing)、分層(demixing)、相變化 (phase changes)、結構破壞 (structure break-up)、與結構整合(structure build-up) 等相關研究。 Flow Wide-Angle Light Scattering 簡介 流動光散射與一般光散射最大不同,在於流場下可同時觀測流體的機械性質及 微觀結構變化,以更直接掌握高分子於加工過程中其微結構與分子型態的變化。 此外本系統亦可搭配光纖,利用其體積小、可彎曲的特點而有效增加量測系統的 靈活度。 原理 當所施加的剪切速率(shear rate)足夠壓制高分子鏈本身的轉動擴散 (rotational diffusion)運動,此時高分子鏈的構形將偏離其於靜止狀態下的特性, 並逐漸朝流動方向伸展與排向,同時造成高分子鏈大小與形狀(orientation)不同 程度的改變(deformation)。藉由測量方向角(orientation angle,χ)以及使用 Zimm-plot分析其迴旋半徑 Rg,可得知流場下高分子鏈的拉伸與排向的程度。 高分子在靜止狀態為捲曲體, 可視為球狀體,在施加流場後 高分子鏈開始變形,由球狀轉 為橢圓狀,並隨流動方向排向 與拉伸;藉由此系統可即時量測 高分子的排向情形與拉伸變形 的程度。左圖中 G為梯度方向 (gradient direction),V為流 體方(flow direction),χ 為方 向角(orientation angle)。 原理與實驗分析 如圖示:方向角χ為長軸與速度梯度 的夾角;θ為入射光與偵測器的夾角; ψ’為速度梯度與散射向量的夾角。 [Ellen C. Lee, Macromolecules 1997, 30, 7313-7321] 如圖:最高點為 可得知 χ [Lee et al., Macromolecules 1997, 30, 7313-7321] ' max ,利用 90 ' max 實驗裝置 本系統需依照流變儀之立體條件所設計,包含光學夾具、折射率匹配槽, 雙圓心旋轉桌板等皆需自行設計。 實驗校正 本系統需確定散射光強與散射體積之比例關係,因此選用甲苯做靜態光 散射校正。此外與一般光散射校正不同處為,需對自製桌板做校正及注意光纖光 強之接收。 toluene 40 intensity(kcounts/sec) 35 實驗裝置簡圖 30 25 20 15 10 20 40 60 80 100 degree 雙圓心旋轉台之操作原理為,選定入射光及偵測器 夾角θ後,即固定散射向量 q 的大小。此時轉動桌 板後散射向量 q 與梯度方向 G 的夾角ψ’即可任 意改變。 120 140 即時光學—流變系統 示意圖與功能 I. Particle Interactions II. Microstructures III. Molecular Anisotropy Quartz couette cell (Rheology) 2-D detection (θ and φ dirs.) (Flow Light Scattering) Phase-modulated light (Flow Birefringence/Dichroism) CCD camera (Flow SALS) in situ rheo-optical measuring system 實體圖 多尺度分子計算 (Multiscale Computations) 無可調參數 AND 絕對預測能力? Parameter-Free Multiscale Simulations (5) Dumbbell model & BD simulation (4) Bead-chain model & BD simulation (2) Monomer model & CGMD/LD simulation (3) Ellipsoid-chain model & MC simulation Shie, S. C.; Hua, C. C.; Chen, S. A., Macromol. Theor. Simul. 2007, 16, 111. Shie, S. C.; Lee, C. K.; Hua, C. C.; Chen, S. A., Macromol. Theor. Simul. 2010, 19, 179. Lee, C. K.; Hua, C. C.; Chen, S. A., J. Chem. Phys. 2010, 133, 064902. Lee, C. K.; Hua, C. C., J. Chem. Phys. 2010, 132, 224904. Lee, C. K.; Hua, C. C.; Chen, S. A., J. Phys. Chem. B 2009, 113, 15937. (1) Atomistic model & MD simulation Lee, C. K.; Hua, C. C.; Chen, S. A., J. Phys. Chem. B 2008, 112, 11479. Hua, C. C.; Chen, C. L.; Chang, C. W.; Lee, C. K.; Chen, S. A., J. Rheol. 2005, 49, 641. Lee, C. K.; Hua, C. C.; Chen, S. A., Macromolecules, 2011, 44, 320–324 Lee, C. K.; Hua, C. C, Optoelectronics / Book 1,( InTech, ISBN 978-953-307-276-0) Lee, C. K.; Hua, C. C.; Chen, S. A., (to be submitted). Quantum chemistry calculation A Software Package under Development for Multiscale simulations Analysis tools Main program Dumbbell model & BD simulation RDF Bead-chain model & BD simulation Structure factor Ellipsoid-chain model & MC simulation Intensity Monomer model & CGMD/LD simulation Atomistic model & MD simulation Back-Mapping techniques The mutiscale simulation package developed at Complex Fluids & Molecular Rheology Laboratory by C. K. Lee, S. C. Shie, and C. C. Hua, in the Department of Chemical Engineering, National Chung Cheng University, Taiwan, R.O.C Single-Chain Conformations of Conducting Conjugated Polymers from Solution to the Quenching State: A Multiscale Simulation PANI-EB MEH-PPV 60 CF / T CF / CB Vacuum (V) Rg (Angstrom) 55 Toluene (T) Chloroform (CF) 50 45 40 35 30 CF 100% CF 75 % CF 66 % CF 50 % CF 33 % CF 25 % CF 0 % Number Ratio Chlorobenzene (CB) Mixed CF and T Mixed CF and CB 11 6 3:1 2:1 1:1 1:2 1:3 Mixed CF and T 10 V CF T CB CF+T CF+CB 9 1.5 8 7 1.0 RDFs vdw only 5 4 3 2 1 6 0 5 3.0 3.5 4.0 4.5 5.0 4 0.5 5 10 15 20 25 30 3 Angstrom 2 2.0 Local Ratio (CF : CB) / Bulk Ratio vdw + HB + π-π Local Ratio (CF : T) / Bulk Ratio 2.0 1 3:1 2:1 1:1 1:2 1:3 Mixed CF and CB 0 0 1.5 1 2 3 4 5 6 7 8 9 distance (Angstrom) 1.0 0.5 5 10 15 20 Angstrom 25 30 10 11 12 13 14 Morphologies and Pair Interactions in Fullerene-Conjugated Oligomer Hybrids Investigated by Atomistic Molecular Dynamics Links between Molecular dynamics and Quantum chemical calculations Force-field validation: PPV backbone, dihedral angle Energy level diagram for a donor–acceptor heterojunction: Structures refined by semi-empirical (SE) and density functional theory (DFT) 16 MP2_6-31G MD(original) MD (fit) 14 Energy, kJ/mol 12 10 8 6 4 Compound 2 (eV) 0 -2 0 20 40 60 80 100 120 140 160 MEH-PPV 180 Angle, deg C60 30 Energy, kJ/mol 25 PCBM 20 15 LUMO HOMO LUMO HOMO LUMO HOMO SE(PM3) DFT(B3LYP/3-21G*) -0.754 -1.211 -8.549 -5.204 -2.886 -3.769 -9.480 -6.364 -2.807 -3.386 -9.165 -6.115 Excitation energies of a single chain MEH-PPV, calculated by ZINDO/S method 10 MP2_6-31G MD(original) MD (fit) 5 0 0 5 10 15 20 25 30 Angle, deg 60 Energy, kJ/mol Chlorobenzene (CB) MP2_6-31G MD(original) MD (fit) 50 40 30 20 10 Mixed Nonane and CB (1:1) 0 -25 -20 -15 -10 Angle, deg -5 0 Quantum calculations were carried out using Gaussian 09 software package as provided by the NCHC 誰把流變做大了?