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Lecture8 Notes - Lecture 8 Solution Characterization of...

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Unformatted text preview: Lecture 8 Solution Characterization of Polymers 2 ANNOUNCEMENT: Review Session will be Tuesday during normal lecture time. Practice exam is posted; equation sheet coming soon Exam will cover lectures 1-9 1 Monday, October 18, 2010 Characterizing Macromolecules with EM 2 Monday, October 18, 2010 Today’s Topic: • • • Light Scattering – Static Light Scattering – Dynamic Light Scattering SANS SAXS 3 Monday, October 18, 2010 Interactions between light and matter • Reflection – specular reflection: when a light beam is reflection in a very definite direction by a flat surface such as a mirror – diffuse reflection: when light is reflected in various directions from an irregular surface such as a piece of white paper • Refraction: the light ray is deviated or bent from its original direction • Diffraction: the light ray is deviated slight from its original path upon interaction with matter; may also be considered a spatial redistribution of waves • Absorption: a process that removes energy from the incident light beam by converting it to another form 4 Monday, October 18, 2010 Light Scattering • Interactions between light and matter may produce different effects, depending on the wavelength of light and the characteristics of the material. • Light scattering is the alteration of the direction and intensity of a light beam that strikes an object. This is due to the combined effects of reflection, refraction and diffraction • Scattering occurs when the electron cloud of the scatterer removes energy from the light beam (photon by photon) and then re-emits this energy (photon by photon) without otherwise altering it Scattering = Reflection + Refraction + Diffraction 5 Monday, October 18, 2010 What’s so great about light scattering? • non-invasive and non-destructive • small sample volumes • size range: 2 nm to 10 um! • Mw 1K to 10 million! • Wide range of acceptable concentrations • can detect aggregation, can be used for complex samples • Static Light Scattering: can get Mw, Rg, and A2 – looks at the intensity of scattered light at different concentrations and different angles • Dynamic Light Scattering (also referred to as Quasi-Elastic Light Scattering, or QELS): can get Rh and D – looks at fluctuations in scattered light intensity due to Brownian motion at a single angle 6 Monday, October 18, 2010 Light Scattering • • • E = E 0 cosωt Light is an electromagnetic field The electric field of light drives oscillatory motions of the electrons in a molecule (induced dipole) The magnitude of the dipole moment is: p = αE = αE 0 cos 2πc st λ 7 Monday, October 18, 2010 Light scattering 8 Monday, October 18, 2010 Light Scattering • • The oscillating dipole scatters the light The intensity of the scattered light is given by: 8π 4 I ' = I0α 2 4 (1 + cos2 θ ) rλ 2 9 Monday, October 18, 2010 8π 4 I ' = I0α 2 4 (1 + cos2 θ ) rλ 2 • Light Scattering We can normalize this scattering to the number of molecules per unit volume: 1 dn M α= 2π dc N Av Characteristics of incident light ( 2 4 ⎡ n ⎤ ⎡ I 0 8π ⎤ 2 ⎡ 1 + cos θ Iθ = ⎢ ⎥ ⎢ 4 ⎥ ⎡α ⎤ ⎢ ⎣⎦ r2 ⎣V ⎦ ⎣ λ ⎦ ⎢ ⎣ )⎤ ⎥ ⎥ ⎦ Angle of observation and distance from the scattering object Polarizability of the molecule Number of molecules per unit volume 10 Monday, October 18, 2010 Scattering and Size: Intensity is Proportional to Molar Mass • If you have two separate particles in solution,they undergo brownian motion; this imparts a randomness to the phase of the scattered light, such that the light from the two separate monomers is incoherent; it adds as classically expected (1+1=2) • Once the monomers are attached together to form a dimer, the scattered light from one monomer has a phase relationship with the other (coherent scattering). Scattered light from the dimer is twice as intense as for two separated monomers! • Doubling the mass while keeping the concentration the same doubles the intensity of scattered light. 11 Monday, October 18, 2010 Rayleigh Ratio • A reduced intensity from the previous equation: ( 2 ⎡ I 0 8π 4 ⎤ 2 ⎡ 1 + cos θ ⎡n⎤ Iθ = ⎢ ⎥ ⎢ 4 ⎥ ⎡α ⎤ ⎢ ⎣⎦ r2 ⎣V ⎦ ⎣ λ ⎦ ⎢ ⎣ )⎤ ⎥ Characteristics of incident light ⎥ ⎦ Iθ r 2 ⎡ n ⎤ ⎡ 8π 4 ⎤ 2 Rθ = = ⎢ ⎥ ⎢ 4 ⎥ ⎡α ⎤ ⎡ 1 + cos 2 θ ⎤ ⎣ ⎦⎣ ⎦ I0 ⎣V ⎦ ⎣ λ ⎦ ( ) Angle of observation from the scattering object Polarizability of the molecule Number of molecules per unit volume 12 Monday, October 18, 2010 Rayleigh Scattering Iθ r 2 ⎡ n ⎤ ⎡ 8π 4 ⎤ 2 Rθ = = ⎢ ⎥ ⎢ 4 ⎥ ⎡α ⎤ ⎡ 1 + cos 2 θ ⎤ ⎦ I0 V ⎦⎣ λ ⎦⎣ ⎦⎣ ⎣ ( ) 13 Monday, October 18, 2010 Polarizability • • • • • The more polarizable the (macro)molecule, the larger the induced dipole The larger the induced dipole, the greater the intensity of scattered light In order to characterize scattering from a solution of (macro)molecules, we need to know their polarizability The polarizability is related to the refractive index increment of the analyte in the solution: 1 dn M α= 2π dc N Av We can substitute this into the Rayleigh ratio equation: ⎡ n ⎤ ⎡ 2π ⎤ ⎛ dn ⎞ ⎡ M ⎤ Rθ = ⎢ ⎥ ⎢ 4 ⎥ ⎜ ⎟ ⎢ ⎥ V ⎦ ⎣ λ ⎦ ⎝ dc ⎠ ⎣ N Av ⎦ ⎣ 2 2 2 14 Monday, October 18, 2010 Specific refractive index increment ⎛ Δn ⎞ dn = lim⎜ ⎟ dc c = 0 ⎝ c ⎠ λ,T •The bigger the better •Depends on: •solvent •temperature •light wavelength Δn = n - no If polymer solvent combination is isorefractive, no scattering will be observed 15 Monday, October 18, 2010 Light Scattering • • • We are interested in light scattering from dilute solutions Local fluctuations in concentration and density give rise to light scattering How do we quantify the concentration fluctuations? Iθ r 2 ⎡ n ⎤ ⎡ 8π 4 ⎤ 2 Rθ = = ⎢ ⎥ ⎢ 4 ⎥ ⎡α ⎤ ⎡ 1 + cos 2 θ ⎤ ⎣ ⎦⎣ ⎦ I0 ⎣V ⎦ ⎣ λ ⎦ ( ) 2 ⎡ n ⎤ ⎡ 2π ⎤ ⎛ dn ⎞ ⎡ M ⎤ Rθ = ⎢ ⎥ ⎢ 4 ⎥ ⎜ ⎟ ⎢ ⎥ ⎣ V ⎦ ⎣ λ ⎦ ⎝ dc ⎠ ⎣ N Av ⎦ 2 2 2 n 0 ⎡ dn ⎤ 2 Δα = Δc ⎣⎦ 4 π 2 ⎢ dc ⎥ kT Δc 2 = 2 ∂ G / ∂c 2 2 16 Monday, October 18, 2010 Light Scattering • This (concentration fluctuation) is equivalent to the first derivative of the chemical potential or osmotic pressure: ⎡ ⎤ ⎡ M 2 n ⎤ ⎢ RTVs ⎥ Rθ = K (1 + cos 2 θ ) ⎢ ⎥ ⎣ N AvV ⎦ ⎢ ∂µ s ⎥ ⎢ ∂c ⎥ ⎣ ⎦ 2 2π 2 n0 K= N Av λ 4 • • ⎡ dn ⎤ ⎢ dc ⎥ ⎣⎦ 2 Parameters that are known or easily measured are lumped into the optical constant, K This approach also brings in a virial equation: ∂µ s ∂π RT = Vs = + 2 Bc + 3Cc 2 + … ∂c ∂c M RT = [1 + Γ2c + Γ3c 2 + …] M 17 Monday, October 18, 2010 Light Scattering • This expression only allows for a discrete molecular weight – how do we bring in the distribution normally exhibited by polymeric samples? ⎡ ⎤ ⎡ M 2 n ⎤ ⎢ RTVs ⎥ Rθ = K 1 + cos 2 θ ⎢ ⎥ ⎣ N AvV ⎦ ⎢ ∂µ s ⎥ ⎢ ∂c ⎥ ⎣ ⎦ ( ) 2 2π 2 n0 ⎡ dn ⎤ K= N Av λ 4 ⎢ dc ⎥ ⎣⎦ Go back to a definition for concentration that accounts for multiple species: 2 Get virial terms from here ∑N M = M ∑N M ∑N M c= 2 i i w i i i i VN Av Plug it into our Rayleigh Ratio equation: Rearrange: ⎡ ⎤ M wc Rθ0 = K (1 + cos2 θ )⎢ ⎥ 2 ⎣1 + Γ2c + Γ3c + …⎦ K (1 + cos2 θ )c 0 θ R = 1 [1 + Γ2c + Γ3c 2 + …] Mw 18 Monday, October 18, 2010 Debye Plot consider a polymer solution - measure scattered light at several different concentrations and a fixed angle, θ Kc 1 = + 2 A2 c Rθ M w this works well if polymers act as point scatterers. What happens as the size of the polymer approaches the wavelength of light? 19 Monday, October 18, 2010 Light Scattering • • • We’ve been assuming that polymers act as point scatterers Beyond a certain size (~λ/20), a polymer can no longer be considered a point scatterer, and instead there is an angular dependence to scattered light The scattering envelope is asymmetric, and we must add in a term for this angular dependence K (1 + cos2 θ )c Rθ0 ⎡ ⎤ 1 1 2 2 2⎛ θ ⎞ = [1 + Γ2c + Γ3c + …] = M [1 + Γ2c + Γ3c + …] × ⎢1 + S sin ⎜ 2 ⎟⎥ ⎝ ⎠⎦ M w P (θ ) ⎣ w 20 Monday, October 18, 2010 Zimm Plots K (1 + cos2 θ )c Rθ0 = ⎡ ⎛ θ ⎞⎤ 1 1 + Γ2c + Γ3c 2 + …] × ⎢1 + S sin 2 ⎜ ⎟⎥ [ ⎝ 2 ⎠⎦ Mw ⎣ 21 Monday, October 18, 2010 Commonly found equations for light scattering 2 ⎛ Kc ⎞ ⎤ 1 ⎡ 16π 2 n 0 2 2⎛ θ ⎞ = Rg sin ⎜ ⎟ + ...⎥ ⎜⎟ ⎢1 + 2 ⎝ 2⎠ 3λ ⎦ ⎝ Rθ ⎠ c →0 M w ⎣ 2 ⎛θ ⎞ 16π 2 n 0 2 P (θ ) = 1 − Rg sin 2 ⎜ ⎟ + ... ⎝ 2⎠ 3λ2 ⎛ dn ⎞ 2 4π ⎜ ⎟ n 0 ⎝ dc ⎠ K= 4 N Av I0 2 2 22 Monday, October 18, 2010 Different LS techniques – MALLS gives molecular architecture information without assumptions IF there is a measurable angular dependence on the scattered light intensity – RALLS (sin(90)=1) is more forgiving of dusty samples and returns essentially the same information as LALLS IF the polymer is small compared to λο – LALLS is more sensitive, requires no correction over a huge range of molar mass 23 Monday, October 18, 2010 SEC/MALLS MALLS DRI DRI degas pump injector 24 Monday, October 18, 2010 Angular dependence of scattering intensity 3D Plot - PBLG Scattered intensity Ve 16 15 14 13 12 11 10 9 8 7 6 5 ga in 4 gle n ter at Sc 25 Monday, October 18, 2010 Angular Dependence of Scattering Intensity 140000 InterceptMolecular weight 120000 R/Kc 100000 80000 SlopeSize 60000 c = 0.044 mg/mL M = 130000 g/mol 40000 No A2! 20000 0 0.0 0.2 0.4 0.6 0.8 1.0 2 sin (! /2) 26 Monday, October 18, 2010 But I thought LS gave Mw, not Mn • Simple assumption….monodisperse fractions from the GPC columns. Therefore, Mw,i = Mi • This assumption may lead to an over-estimation of Mn 27 Monday, October 18, 2010 SEC/RALS/VIS ΔP η viscometer LS90o DRI degas pump injector 28 Monday, October 18, 2010 Dynamic Light Scattering 29 Monday, October 18, 2010 Dynamic Light Scattering • • • • Macromolecules in solution have random (Brownian motion) – think of the polymer as a particle of a particular size This motion is random, and there is no correlation between one particle and the next As light scatters from the polymers, this motion imparts a randomness to the phase of the scattered light; the scattered light from two or more particles, when added, will have a changing destructive or constructive interference This leads to time-dependent fluctuations in the intensity of scattered light 30 Monday, October 18, 2010 Dynamic Light Scattering • • • Time-dependent fluctuations in scattered light are directly related to the rate of diffusion of a molecule through solvent The fluctuations can be analyzed to determine a hydrodynamic radius for the sample The fluctuations are quantified via a second order correlation function: g (τ ) = 2 • I( t ) I( t + τ ) I( t ) 2 The correlation function depends on the delay, tau 31 Monday, October 18, 2010 Dynamic Light Scattering • The correlation function for a monodisperse sample can be analyzed from the following equation: g( 2) (τ ) = B + β exp(−2Γτ ) • The function decay rate can be used to obtain the diffusion coefficient, which can be used to find the hydrodynamic radius D= Γ q2 4 πn 0 ⎛ θ ⎞ q= sin⎜ ⎟ ⎝2⎠ λ0 Rh = kT 6πη0 D 32 Monday, October 18, 2010 Comparison SLS and DLS • Static LS – fast and accurate determination of Mw – easy to do (especially with modern equipment) – applicable to a wide range of polymers (natural and synthetic – good at detecting aggregates – highly reproducible – caution: sensitive to dust, need accurate value of dn/dc • Dynamic LS – aggregation kinetics – particle size 33 Monday, October 18, 2010 Other Scattering Polymer conformations are studied by scattering, including LS, SANS and SAXS These techniques require some sort of contrast between the polymer and the background solution As we know, LS contrast is the difference in refractive index between polymer and solution In X-ray scattering, contrast is difference in electron density between sample and environment In neutron scattering, contrast is usually deuterated material versus nondeuterated Deuteration does not affect conformation, but can affect miscibility? X-rays interact with electron cloud, neutrons interact with nucleus 34 Monday, October 18, 2010 Small Angle Neutron Scattering • • • • • The technique of small-angle neutron scattering (SANS) is used for studying the structure of a material on length scale of 10 to 1000 Å using scattering of a monochromatic beam of neutrons from the sample and measuring the scattered neutron intensity as a function of the scattering angle(~ 0.5–10°) Deuterium can be used as contrast probes structures on the scale of d=ʎ/θ Neutrons can penetrate a sample far better than other scattering techniques There are some 37 neutron sources in 21 countries and of these 23 are in Europe, 10 in North America (including Canada), 2 in Japan and 1 in each of Australia & India. 35 Monday, October 18, 2010 SANS Applications • Conformation of polymers in solution and in melt • structure of microphase segregated block copolymers • blend miscibility • Organization of biomolecular complexes in solution • Conformational changes of proteins, enzymes, DNA/protein complexes, membranes • mechanisms and pathways for protein folding and DNA supercoiling 36 Monday, October 18, 2010 Disadvantages of SANS • SANS is a routine technique available at neutron-scattering facilities associated with research nuclear reactors (have to book beam time, no source at your research facility, typically) • Neutron sources are very expensive to build and to maintain - millions of dollars annually to operate a nuclear research reactor and a ton in electrical bills alone to run a pulsed neutron source. • Neutron flux is very low. Presently, the neutron flux available at these reactors is equivalent to the X-ray flux available in the 1940s. This makes for long measurement times and increased demand from researchers to use the facilities. • Interaction of neutrons with matter is weak. Therefore, large samples are required. Although small angle scattering techniques provide beneficial data, these limitations exclude their use 37 Monday, October 18, 2010 Small Angle X-ray Scattering • Elastic scattering of xrays used to look at inhomogeneities in the nm range (electron density contrast) • typically represented as scattered intensity as a function of scattering vector, q: 4π n ⎛ θ ⎞ q≡ λ sin ⎜ ⎟ ⎝ 2⎠ • SAXS patterns contain data concerning correlations on an inter-molecular level (macromolecular or aggregate order) • SAXS is a unique method for studying low resolution structure and structural transitions of individual proteins and large macromolecular complexes in solution 38 Monday, October 18, 2010 Summary • Scattering techniques are powerful tools for polymer characterization • SLS gives Mw, Rg and A2, under appropriate experimental conditions • DLS gives D and Rh • SANS and SAXS are scattering techniques to probe smaller size scales; much less common • SANS is limited by source • SAXS limited by size scale? 39 Monday, October 18, 2010 Next time... • more solution techniques for biomacromolecules • applying characterization methods to research problems 40 Monday, October 18, 2010 ...
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This note was uploaded on 11/29/2010 for the course BME 104 taught by Professor Kasko during the Fall '10 term at UCLA.

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