APPLICATION OF PHOTON CORRELATION SPECTROSCOPY IN SOFT MATTER RESEARCH Irena Drevenšek-Olenik Faculty of Mathematics and Physics, University of Ljubljana and J. Stefan Institute, Ljubljana, Slovenia
LIGHT SCATTERING WITH COHERENT SOURCE Random diffraction pattern (speckle pattern ) random refractive index variation n(r) Coherent radiation (e.g. laser) To observe speckle pattern, coherent illumination of the scattering medium is needed. All radiation is at least partially coherent. • Longitudinal (temporal) coherence • Transverse (spatial) coherence Longitudinal coherence length Transverse coherence length
LIGHT SCATTERING WITH PARTIALLY COHERENT SOURCE • Inside the coherence volume radiation can be described as a monochromatic plane wave. • Field amplitudes and phases in different coherence volumes are uncorrelated !!! To observe scattering in the form of speckle pattern, the scattering volume of the sample must lie within one coherence volume of the illumination source.
EXPERIMENTAL RESTRICTIONS speckles =scattering angle To see speckle at 0 < < 2, requires To see speckle at 0 < < m (SAXS,...), requires 2 m T m
DYNAMIC LIGHT SCATTERING (DLS) Incident wave r= r2 -r1 r(t+)- r(t) (/sin( /2)) relative phase coherence is lost r1(t) r1(t+) r2(t+) r2 (t) Scattered waves detector (specle size!!!) moving scattering objects produce temporal variations of local refractive index n=n(r,t). Consequently, intensity of specles fluctuates with time. Count rate (kHz) Example: t(ms) Brownian motionof macromolecules in solution
PHOTON CORRELATION SPECTROSCOPY small size Tc Autocorrelation function of scattered light intensity I at selected scattering angle (scattering wave vector q) is measured. G(2)()= Operation is repeated for many different values of in the range 10-9 s < < 103 s(typical autocorrelator gives results for 256 values of).
CORRELATION FUNCTIONS Intensity correlation functionG(2)() Usually normalised function is measured. example of measured g(2) (t).
FIELD CORRELATION FUNCTION detector at distance R from sample n = refractive index contrast n G(1)()= Field correlation function:
RELATION BETWEEN g(1) and g(2) For scattered field Es(q,t), which can be described as 2D random walk (Gaussian field), the following relation is valid: Siegert relation In practice we measure: The value of depends on the details of the detection system.
WHAT CAN BE INVESTIGATED by DLS? DLS detects fluctuations of refractive index of the medium: n(r,t)=n(q,t)eiqr q Maximum cross section for n(q=qs) . sample Laser H H V Detector (I(t)|Es(t) |2) measurement g(2)(t)=<I(t’)I(t’+t)>/<I>2=1+ (g(1)(t))2 l Information on dynamic modes related to n(q,t) on the time scale 10-9 –103 s .
FLUCTUATIONS OF REFRACTIVE INDEX n(r,t)=n(q,t)eiqr The main challenge of DLS investigations is to deduce the origin of refractive index fluctuations n(r,t) and to gain understanding on dynamic processes associated with them. • Some phenomena, which can cause refractive index changes: • thermaly induced density fluctuations of the medium • translational and rotational motion of the “scatterers” • mechanical stress/strain • birefringence fluctuations • ...
DLS INVESTIGATION of SELF-ASSEMBLY OF BIOLOGICAL MOLECULES IN SOLUTION In aqueous solutions (physiological conditions) biological molecules often exhibit tendency to self-organize into highly ordered supramolecular structures (secondary, tertiary structure, ...) Example of a 3D protein structure Aggregation into 1D structures: Technologial challenges of 1D self-aggregation: Columnar aggregates exhibit strongly anisotropic electronic transport properties – prospective for applications assupramolecular nanowires, photoconductive switches, for polarized O-LEDs, ....
SPECIFICITY OF THE 1D AGGREGATION N 1D: N0,N =-(N-1)kT N 2D: N0,N =-(N-N1/2)kT nD: N0,N =-(N-Np)kT, p<1 1= 0,1+kTlnX1 N= N0,N +kTlnXN Aggregate endeffects G=-(N 1)+N=0 condition of coexistence Critical aggregate (micellar) concentration CMC e- for p<1, transition from monomers to N aggregates for p=1, transition from monomers to finite size linear aggregates with size distribution: XN=N(X1e)Ne-, 1D aggregates are modeled as rod-shaped objects.
DIFFUSION CONSTANTS OF THE ROD-SHAPED SCATTERERS Diluted solution: g(1)( ) Polarized light scattering (VV): g(1)( ) Depolarized light scattering (VH): Translational diffusion Rotational diffusion j j Model of Tirado and Garcia de la Torre (2<(p=L/d)<30)
SELF-ASSEMBLING OF GUANOSINE DERIVATIVES cell ageing, telomers, quadruplexes, G-quartets..... Chromosome ends are made of G-rich sequences, which form quadruplex structures. Self-assembly of guanosine monophosphate (GMP) in aqueous solutions.
ISOTROPIC COLUMNAR PHASE Phase diagram for dGMP (ammonium salt) T=23oC c=4 wt % Studied by PCS in: Concentration region: 0.1 wt% < c < 33 wt% Temperature region: 290 K < T < 340 K. c=12 wt% Spherulite of the Ch phase (Optical polarization microscopy)
DLS RESULTS– concentration dependence In this system 2 dispersive modes are observed in polarized (VV) scattering and 1 nondispersive mode is detected in depolarized (VH) scattering (in case of excess of salt) Results for polarized scattering (VV): 1 wt% < c<12.5 wt% fast VV mode = translational motion of G4 stacks slow VV mode =translational motion of globules??? T = 298 K EM, bar= 0.1 m c= 3.5 wt% = CMC Length of stacks: L=368 nm (approx. of dilute solution) D=1/(q2)
DLS RESULTS – added salt dependence Results for polarized scattering (VV): added salt was KCl K fast VV mode = translational motion of G4 stacks Polyelectrolyte behaviour = electrostatic interactions play a vital role. Length of stacks: L=345 nm (approx. of complete polyion screening) Translational diffusion of charged rods (macroions) in the solution of small ions. Theory of coupled dynamic modes Approximate analytical solution: Lin-Lee-Schur Electrostatic term Standard diffusion term Poisson-Boltzmann equation
31P NMR study – added salt dependence added salt was KCl At cKCl=0.1 maximum possible aggregation level of 75% is reached!
DLS RESULTS – added salt dependence Results for depolarized scattering (VH): added salt was KCl VH mode = orientational fluctuations of G4 stacks (very nonexponential mode, gel-like structure) Critical slowing-down due to approaching of the CI-Ch transition.
MELTING OF THE AGGREGATES VV fast mode: Temperature dependence Why does DLS “see” longer aggregates than other techniques? DLS AFM dGMP (Na) ? T<Tm (Rh~3Rg) T>Tm (Rh~Rg) ~10 nm SAXS
Discrepancy SAXS/DLS - search for explanation Problem = Motion of columnar aggregates in a dense solution of non aggregated species? In GMP solutions the concentration region of the CI phase is quite narrow: c*~10 wt%, cCI-Ch ~ 25 wt% (Motion in a dense “soup”) !! Effective viscosity of the “soup” = 3H2O ?? • I. Drevenšek-Olenik, L. Spindler, M. Čopič, H. Sawade, D. Kruerke, G. Heppke:Phys. Rev. E, 65, 011705-1-9 (2001). • L. Spindler, I. Drevenšek-Olenik, M. Čopič, J. Cerar, J. Škerjanc, R. Romih, P. Mariani:Eur. Phys. J. E, 7, 95-102. (2002). • L. Spindler, I. Drevenšek-Olenik, M. Čopič, J. Cerar, J. Škerjanc, R. Romih, P. Mariani:Eur. Phys. J. E, 13, 27-33 (2004).
ORIENTATIONAL FLUCTUATIONS IN LIQUID CRYSTALS
LIQUID CRYSTALS (LC) heating Liquid phase Solid phase (crystal) cooling Liquid crystal phase n(r) Optical polarization microscopy LC orientational order is described by nematic director field n(r) and scalar order parameter S=<(3(cos2)-1)>/2.
OPTICAL BIREFRINGENCE OF LIQUID CRYSTALS (LCs) n(r) Liquid crystals (LC): usually commercial mixtures, characterized by strong optical birefringence. typical LC molecule: (pentyl-cianobiphenyl) Nematic director field n(r)can be strongly modified by low external voltages. Variation of n(r)causes large modification of optical properties. This specific property of LCs represents a basic principle of operation of LCD devices.
ORIENTATIONAL FLUCTUATIONS and LIGHT SCATTERING Thermaly induced orientational fluctuations in a planarly aligned LC layer (D>>): n(r)=n0(r)+n(r) n(r)=n(q)eiqr D are related to increase of the elastic deformation energy of the LC director field n(r): 2 2 Wd=(V/2)n1(q)(K1q2+K3q2)+n2(q)(K2q2+K3q2) q kT kT Ki 10-11 N Relaxation of the fluctuations : n0 dWd/dni=-ini/t, i=1,2 1 q 2 n(q,t)=n(q,0)e-t/ Relaxation rate: (1/)(K/)q2 10-5cm2/s 10-6 –1 s
CONFINED LIQUID CRYSTALS POLYMER DISPERSED LIQUID CRYSTALS (PDLCs) light beam (UV) Photopolymerization of the prepolymer/LC mixture induces phase separation of the constituents. This process results in formation of liquid crystal droplets, embedded in a polymer matrix. PDLC HOLOGRAPHIC POLYMER DISPERSED LIQUID CRYSTALS (HPDLCs) Planes with LC droplets separated by planes of more or less pure polymer SEM image inhomogeneous phase separation
SWITCHABLE DIFFRACTION IN HPDLCs Image of diffraction pattern observed on a far field screen: a) E=0, b) E=100 V/mm. Polymer matrix: SEM-image a) b) HPDLC quasicrystal structure with 10-fold symmetry. (20 mm HPDLC layer between ITO coated glass plates) Standard open problem = size and structure of LC domains.
EFFECT OF CONFINEMENT ON FLUCTUATIONS • Spherical droplets ofradius R • qmin/R, (1/)min(K/)R-2 qmin/D, (1/)min(K/)D-2 B) Thin planar layer of thickness D ? s For ellipsoidal droplets one expects a situation intermediate between A) and B)
TYPICAL EXAMPLE OF g(1)(t)FOR H-PDLC slow process : 10-103ms S: 0.1-0.2 fast process : 0.1-1 ms S > 0.75 Fit: g(1)(t)=A+Bexp((-t/t)S)+Bslowexp( (-t/tslow)Sslow) Two different orientational relaxation processes are detected
SLOW RELAXATION – DIFFUSION OFTHE AVERAGE LC DROPLET ORIENTATION <n(r)>. - Sensitive to“imperfections” of the LC-polymer interface and to interpore orientational coupling. (Quasi)periodic network results in band structure of the modes. M. Avsec, I. Drevensek-Olenik, A. Mertelj, S. Gorkhali, G. P. Crawford, M. Copic:Phys. Rev. Lett. 98, 173901-1-4 (2007).
FAST RELAXATION– decay of the normal modes of nematic director field n(q,t). - Signal from“intrapore” orientational fluctuations. -Dispersion is observed at large scattering angles – relaxation time decreases with increasing scattering angle .
DISPERSION OF THE FAST MODE (sample =0.8 m) y z dz250 nm 1 mm dy600 nm SEM qi,min (/ di) Analysis of dispersion data reveals size and shape of the LC domains. 1) I. Drevensek-Olenik, M. E. Sousa, A. K. Fontecchio, G. P. Crawford, M. Copic: Phys. Rev. E, 69, 051703-1-9 (2004). 2) “Dynamic processes in confined liquid crystals”, M. Vilfan, I. Drevenšek Olenik, M. Čopič:in "Time-resolved Spectroscopy in Complex Liquids - An Experimental Perspective", edited by R. Torre, p. 185-216 (Springer 2008). s
CONCLUSIONS • Photon correlation spectroscopy is a very convenient tool to probe refractive index fluctuations in different materials in the time range from nanoseconds to hundreds of seconds. • It requires illumination of the sample by coherent radiation and detection of the scattered light within the region smaller from a speckle size (photomultipliers, avalanche photodiodes, ...) • It is one of the standard techniques used to deduce the shape and size (size distribution) of submicrometer particles in solutions (studies of polymers, proteins, nanotubes, ...) • It is a convenient probe of liquid crystal orientational and viscoelastic properties in all kinds of mesophases and structures. • In astronomy PCS can be used to investigate...........?