Liquids and Liquid Crystals

Transcription

1 Liquids and Liquid Crystals F.Kremer

2 Content 1. Single molecule versus glassy dynamics. 2. Excursion: Calorimetry and Broadband Dielectric Spectroscopy (BDS) as essential tools to explore the calorimetric and the dynamic glass transition. 3. The calorimetric and the dynamic glass transition. 4. Methods to determine the dynamic properties of glasses. 5. What are Liquid Crystals (LC) 6. Experiment: Phases of thermotropic LC 7. Classification of LC 8. Orientation of LC 9. Structural and optical properties of LC 10. Experiment: How does a LC display work?

3 1. Single molecule versus glassy dynamics.

4 Single-molecule versus glassy dynamics The temperature dependence of the relaxation rate enables one to distinguish between single-molecule and glassy dynamics.

5 Summary concerning single-molecule vs. glassy dynamics 1. The dynamics of single molecules is characterized by an Arrhenius temperature dependence. This follows immediately from Eyrings rate equations. 2. Glassy dynamics follows the empirical Vogel-Fulcher Tammann dependence. The observed temperature dependence of the (apparent) activation energy reflects the fact, that the fluctuating entity changes with temperature. In the high temperature limit one has molecular fluctuating units, towards lower temperatures larger moieties are involved. The question, if a lenthscale has increased or if the density of the moleculas has decresed is open. 3. The dynamic glass transition is by no means a transition, instead it is assigned to a continuous slowing down of fluctuations between structural substates.

6 2. Excursion: Calorimetry and Broadband Dielectric Spectroscopy (BDS) as essential tools to explore the calorimetric and the dynamic glass transition.

7 Calorimetry If you should understand the nature of a substance, but are allowed only one type of measurement to understand it, choose the heat capacity. [Albert Einstein]

8 Basic Equations dq = m c ΔT p d dt dq dt dq dt = m cp = HF = q dt dt dt dt HF = m c q c = p p HF m q In DSC heat flow rate must be calibrated

9 Enthalpy H T T = CpdT Energy U = 0 0 C V dt Entropy S T = 0 C p dt T Gibbs Energy G = H TS Free Energy F = U TS

10 DSC power compensated S S S S dt dt C P φ + = R R R R dt dt C P φ + = dt dt C P P dt dt C dt dt C P P S S R S R R R S S S R S = + = φ φ 0 Symmetrie Heizrate Regelung = = = R R S R S R S C dt dt dt dt T T φ φ

11 10 cm

12 Heat Capacity Measurement - 3 Curves 60 empty 40 HF in mw t in min ϑ in C

13 Heat Capacity Measurement - 3 Curves 60 sapphire empty 40 HF in mw t in min ϑ in C

14 Heat Capacity Measurement - 3 Curves 60 PEEK sapphire empty 40 HF in mw t in min ϑ in C

15 Heat Capacity Measurement - 3 Curves PEEK glass transition, T g melting, T m c p in J g -1 K c p amorphous from ATHAS-DB c p crystalline from ATHAS-DB c p sapphire = cp saphire msample β blue = K( T ) m cold crystallization, T cc β HF HF sample sapphire HF HF empty empty T in C Problem: Base-line reproducebility Yields absolute uncertainty for c p of 2.5% between 0 C and 600 C including 0.5% uncertainty of the sapphire standard itself, S. Sarge PTB 2001, PEI DSC 2.

16 Summary concerning calorimetry 1. Calorimetry enables one to determine basic quantities like U,H,S,G,F. 2. The glass transition, a possible crystallisation and melting shows up as a step or as peaks in the heat capacity versus temperature. 3. From the step height at the glass transition temperature information about the mobile amorphous fraction can be deduced.

17 Broadband Dielectric Spectroscopy (BDS) BDS- measures complex dielectric function in a wide temperature and frequency range. E P P S P electric field E 0 polarization P Orientational polarization Induced polarization 0 complex dielectric function t t ε S ε Debye relaxation ε' ε'' ' ε ε ' = = ε * ( ω) = ε '( ω) iε ''( ω) ε S ε Δ = ε'' max ε ε εs ε * = ε + ε s ε (1 + iω τ ) 0.2 ωmax ε ( ω ) = ε + ω [rad s -1 ] 1 + ε s ε ε ( ω ) = ω τ 1 + ε s ( ω τ) 2 1 τ = ω ε ( ω τ ) 2 max

18 Information content of dielectric spectra K 220 K 10 4 propylene glycol ε Data fitted with empirical Havriliak-Negami function ε K 190 K frequency [Hz] Δε σ ε ( ω, T) = Im[ ε + ] + ε ω '' 0 HN γ 0 β ( 1+ ( iωτ HN ) ) frequency [Hz] Relaxation time Dielectric strength τ = 1 ω max n Δε = 3ε 0 kt Fg < μ2 > Conductivity Relaxation time distribution σ ' (ω) = ωε 0 ε '' (ω) σ '' (ω) = ωε 0 ε ' (ω) ε, β, γ, τ H N C. Gutsche, F. Kremer, M. Krüger, M. Rauscher, R. Weeber, J. Harting, submitted to J. Chem. Phys. (2008) Δ

19 Basic relations between the complex dielectric function ε* and the complex conductivity σ* The linear interaction of electromagnetic fields with matter is described by Maxwell s equations D 0 D curl H = j + t = ε ε E j = σ E (Ohm s law) (Current-density and the time derivative of D are equivalent) = ( ) = + i ε ω ε ε ( ) i σ ω σ σ σ = iωε ε 0

20 The dynamic glass transition (α-relaxation) of glycerol The dynamic glass transition is traced over more than 12 decades

21

22 Analysis of dielectric data log 10 (1/τ max [Hz]) experimental data: propylene glycol bulk VFT-fit: 1/τ=A exp(dt 0 /(T-T 0 )) /T [K -1 ]

23 Brief summary concerning Broadband Dielectric Spectroscopy (BDS) 1. The spectral range of BDS ranges from 10-6 Hz to Hz. 2. Orientational polarisation of polar moieties and charge transport are equivalent and both are observed. 3. The main information content of dielectric spectra comprises for fluctuations of polar moieties the relaxation - rate, the type of its thermal activation, the relaxational strength and the relaxationtime distribution function. 4.For charge transport the characteristic diffusion rate, the d.c.conductivity and their type of thermal activation can be deduced.

24 3. The calorimetric and the dynamic glass transition.

25 The calorimetric glass transition temperature 10 8 Differential scanning calorimetry log (1/τ)[1/s] T g =232K heat capacity C T g /T [1/K] Temperature /K Dynamic glass transition: a gradual decrease of dynamics over many orders of magnitude upon cooling. Measured quantity: Heat capacity

26 The dynamic glass transition as measured by AC-calorimetry log (1/τ [1/s]) /T [1/K] Tg =253K C'(ω) [a.u.] T [K] C (ω) [a.u.] Dynamic glass transition : a gradual decrease of dynamics over many orders of magnitude upon cooling.

27 log (1/τ)[1/s] The dynamic glass transition Calorimetric /T [1/K] Dynamic glass transition: a gradual decrease of dynamics over many orders of magnitude upon cooling. T g n (λ=540nm) n', n'' [a.u.] Ellipsometry Tg 2 ( n) 2 T Temperature /K ( n) T Measured quantities: n and d

28 The dynamic glass transition Broadband Dielectric Spectroscopy log(1/τ [1/s])] Tg = 206 K ε'' K 235 K 230 K 225 K 220 K 215 K /T [1/K] f [Hz] Dynamic glass transition: a gradual decrease of dynamics over many orders of magnitude upon cooling. Measured quantity: Molecular dynamics

29 Summary concerning methods to measure the dynamic glass transition 1. Glasses are amorphous materials the dynamics of which is characterized by the dynamic glass transtion. 2. The dynamic glass transition is a relaxation process, which covers the spectral range from THz to mhz and below. The temperature at a relaxation rate of.01 Hz typically coincides with the calorimetric glass transition temperature. 3. The dynamic glass transition temperature can be determined by various experimental techniques, e.g. BDS, Photon Correlation Spectroscopy (PCS), Nuclear Magnetic Resonance (NMR), Mechanical Spectroscopy, Calorimetry.

30 4. Concepts to describe the dynamic glass transition.

31 Glassy dynamics

32 Types of thermal activation: Vogel-Fulcher-Tammann (VFT)-equation: 1 ν() T v exp DT 0 = = 2 πτ( T) T T0 ( 1/ ) 2 T0 1 log dlogν = ( DT0 ) d T T e v ( 2πτ ) 1 = D is a constant and T0 denotes the Vogel temperature Arrhenius-type temperature dependence: EA ν ( T ) = ν exp kt Mode-Coupling-Theory (MCT): d logν E d(1 / T) k A = log e τα ~ η ~ Tc T T c γ d log v γ log e = d T T T T 2 (1 / ) c / 1 /

33 Mode-Coupling-Theory (MCT) hydrodynamic approach being based on a generalised non-linear oscillator equation () 2 t d Φq t d Φ 2 q t d Φ 2 q +ΩΦ 2 q() + +Ω q( ) dt dt d 0 where the normalised density correlation function Φ(t)q is defined as Δρq(t): density fluctuations at a wavevector q; Ω: is a microscopic oscillator frequency; z: frictional coefficient; memory function: mq(t-τ). ( ) ( τ) t ζ m t τ dτ τ () t Φ = Δρ q ( t) Δρ ( 0) q 2 Δρq q

34 Some Predictions of Mode-Coupling-Theory for T > Tc the relaxation time τα of the α-relaxation scales according to γ T c τα ~ η ~ T Tc where γ is a constant. the relaxation function of the α-relaxation can be described by t Φ q ( t ) exp τ α β KWW with (0 < βkww < 1), where Φq is the amplitude of the α-relaxation. For T > Tc the relaxation-time distribution should be temperature independent, i.e. time-temperature-superposition should hold.

35 Activation- and derivative-plot for relaxation-processes having different types of thermal activation

36 Activation- and derivative-plot for glycerol

37 Activation- and derivative-plot for propyleneglycol and poly(propylene glycol)

38 Activation- and derivative-plot for salol

39 Activation- and derivative-plot for ortho-terphenyl The dynamic glass transition is an ubiquitous phenomenon which can be measured by means of several spectroscopies

40 Does time-temperature superposition holds in general? No!

41 Does time-temperature superposition holds in general? No! Tc: MCT Tc

42 Is there a characteristic change in glassy dynamics? Yes! Between about.1 GHz - 1 GHz the temperature dependence of glassy dynamics changes

43 Summary concerning concepts to describe the dynamic glass transition. 1.: The dynamic glass transition is not at all a transition. 2.: The dynamic glass transition scales usually with the calorimetric glass transion Tg. 3.: Time-temperature superposition does not hold in general. 4.: Neither the Vogel-Fulcher-Tammann - nor the Arrheniusequation describe correctly the observed findings. The predictions of Mode-Coupling Theory are not fullfilled in as well. 5.: At about 1 GHz a change in the temperature dependence of glassy dynamics takes place.

44 Final summary for soft glasses 1. Soft glasses are amorphous materials which are characterized by a (typically by calorimetry determined) glass transition temperature and the dynamic glass transition. 2. The dynamic glass transition is by no means a transition in the meaning of a phase transition in physics. It corresponds to a continuous slowing down of fluctuations between structural substates. This slowing down is not stopped at the glass transition temperature and is continuated also below Tg. It ends at the hypothetical Vogel-temperature T0, which is not accessible in a dynamic experiment. 3. The temperature dependence of the dynamic glass transition temperature can be described by the empirical Vogel-Fulcher Tammann (VFT) equation.

45 5. What are Liquid Crystals (LC) A typical LC molecule: aliphatic tail rigid core, mesogen the core alone has a strong tendency to crystallize, but this is counterbalanced by the tendency of the aliphatic tails to form a glass.

46 Thermotropic LC The botanist Reinitzer observed 2 melting points in cholesteryl benzoate ( 1888) solid hazy liquid clear liquid Temperature Liquid crystals are an intermediate state between ordered three-dimensional crystalline arrays and isotropic disorder.

47 (Monatshefte für Chemie 9:421 41)

48 Summary concerning the question, what are LC? 1. LC molecules are allways characterized by a rigid core (mesogen) and a typically aliphatic tail. 2. The mesogen may have very different shapes. 3. The structure of the LC molecule causes mesophases between the crystalline and the liquid state.

49 6. Classification of liquid crystals Thermotropic LCs - obtained by heating up the crystalline solid or cooling the isotropic liquid Lyotropic LCs - obtained by dissolving the LC in an appropriate solvent under given concentration and temperature conditions

50 Lyotropic liquid crystal isolated molecules spherical micelles, rod-like micelles packed in a hexagonal arrangement, a lamellar phase.

51 Shape of LC molecules calamitic (rod-like molecules) discotic (disc-like) banana-shaped liquid crystal

52 Calamitic liquid crystals Nematic Cholesteric phase (chiral nematic) Smectic pitch d n -director

53 Mesophase polymorphism

54 temperature Phase type Isotropic N SmA SmC SmB SmI SmF SmJ Molecular orientation orthogonal tilted orthogonal Tilt to apex of hexagon Tilt to side of hexagon Tilt to apex of hexagon Molecular packing random random hexagonal pseudo hexagonal Orientational ordering Short range long range Positional ordering Short range SmG SmE SmK SmH Solid crystal Tilt to side of hexagon orthogonal Tilted to side a Tilted to side b orthorombic monoclinic monoclinic long range

55 Structures of discotic LC phases

56 Blue phases special types of liquid crystal phases that appear in the temperature range between a chiral nematic phase and an isotropic liquid phase have a regular three-dimensional cubic structure of defects with lattice periods of several hundred nanometers exhibit selective Bragg reflections in the wavelength range of light Molecules twisting out from the centre to form helical structure Double twist cylinder Director Molecules

57 Typical DSC curve of LCs

58 DSC curve of enantiotropic and monotropic liquid crystalline phases

59 Pressure-temperature phase diagram H. Uehara et al. J. Phys. Soc. Jpn.,. 71, 2002 Liquid crystalline phase can be induced by pressure.

60 The odd-even effect The LC properties (e.g., the phase transition temperature, the order parameter, the transition entropy show a pronounced alternation as the end-chain increases Isotropic The addition of an even-numbered carbon atome is along the major molecular axis. Nematic When the chains become longer their flexibility increases and the odd-even effect becomes less pronounced.

61 Summary concerning the classification of LC 1. One separates between thermotropic and lyotropic LC 2. LC phases show a pronounced polymorphism 3. Besides temperature and concentration also pressure determines the phase sequence 4. The phase sequence depends in a subtle manner on the molecular structure, e.g. the even-odd effect

62 7. Orientation of LC 1. LC can be oriented by magnetic fields if the mesogen has a strong magnetic moment. 2. LC can be easily oriented by an external electric field if the mesogen has an electric dipolemoment 3. LC can be easily oriented due to surface interactions

63 Why can we order LC molecules by the external magnetic field? Most liquid crystals are diamagnetic and their magnetic anisotropy arises from the electronic structure of the mesogens (delocalisation of electronic charge enhances the diamagnetic susceptibility). Since the component of the diamagnetic susceptibility perpendicular to a benzene ring is greater than the in plane component, calamitic mesogens have a positive diamagnetic anisotropy. The molecules align along the direction of an external magnetic field.

64 Orientation due to surface interactions Homeotropic orientation Planar orientation The polymer solution is spin coated on the surface

65 Summary concerning the Orientation of LC 1. LC can easily oriented by different means 2. Orientation on macroscopic scales (~100cm) was for a long time not possible, but is no problem in modern technology

66 8. Structural and optical properties of LC

67 Structural studies of LCs Peaks arise from the average end-to-end and side-to- side separations of the close-packed molecules. The peaks are diffuse because positional correlations only extend over short distances, typically, a few molecular diameters. The widths of the diffuse maxima are inversely proportional to these correlation lengths.

68 Structural studies of LCs d

69 Structural studies of LCs Intensity/ a.u (001) 3BT 60 o C (110) (111) (002) (003) (200) (210) θ/deg c 3BT 60 C a = 8.00 ± 0,02 Å b = 5.35 ± 0,02 Å c = 17/36 ± 0,05Å a distance between two molecules b diameter of the molecules c layer thickness BBOA a = 5.02±0.2 A, c = ± 0.05

70 Optical properties of LCs Birefringence (double refraction) - the decomposition of a light beam into two rays (the ordinary and the extraordinary rays) when it passes through materials. Velocities of both components, are different and vary with the propagation direction through the specim and the waves get out of phase. ordinary ray Unpolarized light extraordinary ray

71 Twisted nematic liquid crystal display

72 First LCD 1969 George Heilmeier, RCA David Sarnoff Research Center, first liquid crystalline display (125 o C,) DSM (dynamic scattering method) :an electrical charge is applied which rearranges the molecules so that they scatter light) The picture above shows George Heilmeier with the first dynamic scattering method-based liquid crystal display

73 Summary concerning the structural and optical properties of LC 1. The structural properties of LC are explored by X-ray and ν - diffraction 2. The pronounced optical bifringence is the basis for applications in displays

74 10. Textures of LC

75 polarization colors result from the interference of the two components of light split by the anisotropic specimen and may be regarded as white light minus those colors that are interfering destructively

76 Schlieren Defect Texture (Nematic) Distribution of directors in the neighborhood of 4 brushed defects dark brush Crossed polarizers Distribution of directors in the neighborhood of 2 brushed defects dark brush

77 Fan shape focal-conic smectic A

78 Schlieren Defects in Antiferroelectric LCs

79 Textures Textures - delocalized topological defects As the number defects increases the entropy (S) gets larger and free energy (G) decreases G = E - TS internal energy

80 Mosaic textures Mosaic texture (smectic B) Mosaic texture (smectic G)

81 Summary concerning the textures of LC 1. The textures of LC are a world for itself. 2. Under normal conditions a manifold of defects of different topology can be observed

82 Final Summary for LC 1. LC form a special class of materials between the solid and the liquid state 2. LC show a manifold of mesophases which is determined by ist chemical structure 3. LC gained tremendous technological impact within the last 2 decades 4. LC can be incorporated into polymeric and elastomeric systems; by that novel materials are designed, e.g. artificial muscles or soft organic lasers

83 Final summary for soft glasses 1. Soft glasses are amorphous materials which are characterized by a (typically by calorimetry determined) glass transition temperature and the dynamic glass transition. 2. The dynamic glass transition is by no means a transition in the meaning of a phase transition in physics. It corresponds to a continuous slowing down of fluctuations between structural substates. This slowing down is not stopped at the glass transition temperature and is continuated also below Tg. It ends at the hypothetical Vogel-temperature T0, which is not accessible in a dynamic experiment. 3. The temperature dependence of the dynamic glass transition temperature can be described by the empirical Vogel-Fulcher Tammann (VFT) equation.