Lecture7 Notes

Lecture7 Notes - Lecture 7 Solution Characterization of...

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Unformatted text preview: Lecture 7 Solution Characterization of Polymers 1 Wednesday, October 13, 2010 Osmotic pressure (Π) Π RT ( )c= 0 = + A2c + A3c 2 c Mn 2 Wednesday, October 13, 2010 Membrane Osmometry • • Colligative property (depending on the collection) Useful in the range of Mn ≈ 50,000 – 2,000,000 • Tends to overestimate Mn (why???) • • Static equilibrium – measure the hydrostatic head (Δh) after it equilibrates Dynamic equilibrium method – measure the counter pressure needed to maintain equal liquid levels 3 Wednesday, October 13, 2010 So far… • We’ve talked about polymer size and shape in solution, but how do we actually measure it? • What things do we consistently need to know? 4 Wednesday, October 13, 2010 Small molecules vs macromolecules It’s relatively easy to determine the molecular weight of a small molecule via mass spec, freezing point depression, boiling point elevation, titration For polymers, it is a little bit more difficult – can use osmometry (Mn), light scattering (Mw), viscosity (Mv), End-group analysis (Mn), ultracentrifugation (Mw, Mz)… EASY TOUGH 5 Wednesday, October 13, 2010 Population of macromolecules •Typical synthetic organic molecules in a pure sample are all the same molar mass •Typical synthetic polymer molecules in a pure sample may differ not only in molar mass but also in molecular shape Ordinary small molecule sample Ordinary synthetic polymer sample 6 Wednesday, October 13, 2010 Intrinsic Viscosity 7 Wednesday, October 13, 2010 What is intrinsic viscosity of a polymer • The limiting value of the reduced viscosity or the inherent viscosity, at infinite dilution of the polymer m [η ] = lci→ 0 () ηi m c = li→ 0 ηinh c • This term is also known as the Staudinger index • The unit must be specified, typically dL/g (inverse concentration) • This quantity is neither a viscosity nor a pure number. The term is to be looked on as a traditional name • Describes a solute’s contribution to the viscosity of a solution 8 Wednesday, October 13, 2010 Viscosity A fluid continues to deform under the action of shear stress, dissipating the energy as flow The top surface moves a distance δ in t sec: τ= Fs A0 . θ . δv γ= = 0 zz δ z dv d ⎛ dx ⎞ γ xy = =⎜⎟ dz dt ⎝ dz ⎠ . 9 Wednesday, October 13, 2010 Viscosity Viscosity: resistance of a fluid to deformation under shear stress stress (τ) : applied force per unit area . Strain rate (γ) : change in strain over time Newtonian fluid: linear response to stress non-Newtonian fluid: non-linear response to stress . τ = ηγ n n < 1 pseudoplastic (shear thinning) n = 1 Newtonian n > 1 dilatent (shear thickening) pseudoplastic newtonian fluid ! η G dilatent ." the main point (for now)? viscosity is the slope of the stress-strain RATE curve; rate indicates time dependence to strain - so the viscosity of a solution is proportional to the time it takes to deform it to a given strain, given a fixed 10 stress. Wednesday, October 13, 2010 Viscosity • We can measure the rate of flow of a polymer solution through a capillary (pipe) • Measure how long it takes a solution to travel a certain distance (pass a certain mark on the viscometer) Measure the relative viscosity • π rc4 ΔP η= = Aρt 8V f L 11 Wednesday, October 13, 2010 Relative Viscosity • • The relative viscosity is easily measured; simply measure the time it takes a solution to flow a specific distance versus pure solvent The relative viscosity is simply the ratio of the solution viscosity to the solvent viscosity; units cancel out η tρ t ηrel = = ≈ η0 t 0 ρ 0 t 0 • If the relative viscosity has a simple dependence on the frictional forces between polymer and solvent, then a plot of ηrel versus c would be linear This calls for H.O.T.!!! 12 Wednesday, October 13, 2010 Different Measures of Solution Viscosity • • • • Relative Viscosity Specific Viscosity Inherent Viscosity Intrinsic Viscosity η ηrel = η0 η − η0 ηsp = = ηrel − 1 η0 ln ηrel ηi = c m [η ] = lci→ 0 ηsp ηc incremental viscosity per unit concentration of polymer capacity of a polymer to cause the viscosity of the solution to increase 13 Wednesday, October 13, 2010 Higher Order Terms in Viscosity • When we start to see a concentration dependence, we can use a power series ηrel = • η = 1 + [η]c + kc 2 + … Intrinsic viscosity: [η] η0 Truncate our power series to ignore H.O.T.; rearrange: ηrel − 1 1 ⎛ η − η0 ⎞ =⎜ ⎟ = [η] + kc c c ⎝ η0 ⎠ • The specific viscosity is simply ηrel-1 • The intrinsic viscosity should then be the value of intercept of a plot of ηsp/c versus c as c 0 (Problem – the slope of the plot should be k, but it varies with [η]2! (Huggins)) ηsp 2 = [η] + k ' [η] c c 14 Wednesday, October 13, 2010 Inherent viscosity • Kraemer defines the intrinsic viscosity differently: ηinh = • ln ηrel 2 = [η] + k" [η] c c Both this equation and the Huggins equation lead to the same extrapolated value of [η] ⎛ ηsp ⎞ [η] = ⎜ ⎟ = (ηinh ) c = 0 ⎝ c ⎠c= 0 capacity of a polymer to cause the viscosity of the solution to increase 15 Wednesday, October 13, 2010 Intrinsic Viscosity Plots are not always pretty • Solutions of ionic polymers or polyelectrolytes cause severe deviation from linear behavior ⎛ ηsp ⎞ [η] = ⎜ ⎟ = (ηinh ) c = 0 ⎝ c ⎠c= 0 16 Wednesday, October 13, 2010 So how do we relate [η] to polymer size? 17 Wednesday, October 13, 2010 Polymers in solution • • • • Models of frictional properties of polymers in solution can be used to derive the relationship between viscosity and molecular weight In the freely draining model, the velocity of the solvent is essentially unperturbed by the polymer; the polymer is treated as a string of beads through which the solvent freely drains The force on each bead is described by Stokes law In the other extreme (equivalent hydrodynamic sphere), we can assume the polymer perturbs the solvent so much that the solvent at the center of the coil moves with the polymer (the polymer and all of the solvent molecules in its pervaded volume move together) Experimental results lean toward this model 18 Wednesday, October 13, 2010 Equivalent Hydrodynamic Sphere • Can use the Einstein relationship for the viscosity of a dilute solution of particles (hard spheres): η ηrel = = 1 + γφ η0 • ηrel = 1 + 2.5φ Combine with the definition of a volume fractions, φ: n⎛ M ⎞ c= ⎜ ⎟ V ⎝ NA ⎠ nVh φ= V ⎛ NA ⎞ φ = Vh ⎜ ⎟c ⎝M⎠ n: number of chains (mol) M: molar mass of each chain Vh: volume of each chain c: mass concentration ⎛ NA ⎞ ηrel − 1 = ηsp = 2.5φ = 2.5Vh ⎜ ⎟c ⎝M⎠ Now we’ve related a viscosity to a size - the hydrodynamic radius of the polymer Wednesday, October 13, 2010 19 Chain expansion factor • Flory found an expression for a chain expansion factor that minimizes free energy, which is expressed in terms of a series in volume fraction of the polymer: ⎡1 ⎤φ α 5 ~ N 0.5 ⎢ − χ⎥ + + … ⎣2 ⎦3 R2 • 0.5 ~ αN 0.5 ~ N 0.6 Here, at low concentrations in a good solvent, the amount the chain expands varies as N0.1, which leads to the good solvent prediction for R. Wednesday, October 13, 2010 Equivalent Hydrodynamic Sphere • If we divide both sides by c: ⎛ ηsp ⎞ ⎛ NA ⎞ = [η] = 2.5Vh ⎜ ⎟ ⎜⎟ ⎝M⎠ ⎝ c ⎠ c →0 • If we assume the the volume occupied by a polymer coil is equal to a sphere with a radius of the root mean square end to end distance ⎛ 2 1 ⎞3 4 V '= π⎜ R 2 ⎟ 3⎝ ⎠ • Vh ~ R 3 We know <R2>1/2 is related to M0.5α, where α is the chain expansion factor; if we assume that V’ is proportional to Vh, the intrinsic viscosity should be related to the molecular weight: [η] = K ' M 0.5α 3 = KM a 21 Wednesday, October 13, 2010 Intrinisic Viscosity is related to Molecular Weight • First established empirically • This led to the Mark-Houwink-Sakurada equation: [η] = KM a • • K and a are constants for a particular polymer in a particular solvent at a particular temperature Which molecular weight is this? 22 Wednesday, October 13, 2010 Intrinisic Viscosity is related to Molecular Weight • This is a new average – called the viscosity average molecular weight [η] = KM v • a If we assume that the specific viscosity of a dilute solution is the sum of the contributions from all the chains present, we arrive at the following: ⎡∑ N M i ⎢ Mv = ⎢ ∑ Ni Mi ⎣ a +1 i • ⎤ ⎥ ⎥ ⎦ 1/ a This is in between the weight average molecular weight and the number average molecular weight 23 Wednesday, October 13, 2010 Polymer Conformation and Scaling <Rg2>1/2 ~ Mν ν = 0.5 theta ν < 0.5 poor solvent ν > 0.5 good solvent ν = 1 rod-like ν = 0.588 Good solvent Mark-Houwink: [η] = KMa a = 0.5 theta a < 0.5 poor solvent a > 0.5 good solvent a = 2 rod-like a = 0.764 Good solvent ν = 0.5 theta solvent a = 0.5 theta solvent ν= 0.33 hard sphere limit a = 0 hard sphere limit 1/ν: fractal dimensionality a = 3ν−1 24 Wednesday, October 13, 2010 a = 2 rod-like a = 0.764 Good solvent a = 0.5 theta solvent a = 0 hard sphere limit 25 Wednesday, October 13, 2010 Size Exclusion Chromatography 26 Wednesday, October 13, 2010 Equivalent Techniques SEC-Size Exclusion Chromatography • Includes rigid stationary phases GPC-Gel Permeation Chromatography • “Soft” gel stationary phases GFC-Gel Filtration Chromatography • Separation of biological molecules (nature’s polymers) in an aqueous environment • used principally for natural polymers (in H2O) • • with hydrophilic gels (crosslinked dextran or polyacrylamide) separated by molecular sieving, adsorption, ion exchange, and ion exclusion 27 Wednesday, October 13, 2010 GPC Mechanism 28 Wednesday, October 13, 2010 GPC • • • • • • sample injection port GPC columns high-pressure pumping system UV detector refractive index detector fraction collector? Wednesday, October 13, 2010 GPC column • semirigid beads of polystyrene (crosslinked with divinyl benzene, and swollen with solvent) • or rigid porous beads of glass or silica 29 GPC Chromatogram ●plots detector response vs. elution volume (Vr) ● compares with a reference chromatogram (a calibration curve) ● height ∝ NiMi ● polystyrene standards (with a polydispersity index close to 1) are used for obtaining calibration curve ● relative MW is obtained Wednesday, October 13, 2010 30 Polymer standards--Column Calibration Rtn Vol Peak Mw 15.739 7500000 15.728 7500000 16.878 2560000 16.879 2560000 17.92 841700 17.935 841700 18.95 320000 18.953 320000 19.605 148000 19.62 148000 20.387 59500 20.386 59500 20.581 50000 20.583 50000 20.583 50000 21.073 28500 21.087 28500 22.008 10850 22.005 10850 23.359 2930 23.378 2930 24.832 580 24.838 580 31 Wednesday, October 13, 2010 Column selection 32 Wednesday, October 13, 2010 SEC is a relative technique Problems •Polymer chains are not created equal Ma = Mb = Mc Va > Vb < Vc Solutions •Absolute molecular weight detectors (light scattering, viscometry) •Universal calibration 33 Wednesday, October 13, 2010 SEC is a relative technique 34 Wednesday, October 13, 2010 Universal Calibration: whatever comes out at a particular volume has the same product , [η]M. • [η]M is independent of polymer type (assumes all are hydrodynamic spheres) • log ([η]M) is a constant for all polymers for a given column, temperature, and elution volume [η] M = 2.5Vh N A 35 Wednesday, October 13, 2010 Universal Calibration: whatever comes out at a particular volume has the same product , [η]M. [η] M = 2.5Vh N A Let’s say a sample has the same hydrodynamic volume as a standard: Universal Calibration A = analyte; S = standard [η]A⋅MA = [η]S⋅MS= f (Ve) (fixed Ve) We know that the product of their intrinsic viscosity and molar mass will be equal. We know the intrinsic viscosity of the standard, and its molar mass Measure the viscosity of the outcoming sample, calculate intrinsic viscosity (need to know concentration, can calculate molar mass. Alternatively, if you know K and a for a sample, you can use this relationship to determine molar mass a [η] = KM a [η ] M = KM M a a a +1 K1M1 1 M1 = K 2 M 2 2 M 2 → K1M1 1 = K 2M 2 a 2 +1 (at fixed Ve) log K1 + (a1 + 1) log M1 = log K 2 + (a 2 + 1) log M 2 log M 2 = [log K 1 − log K 2 + (a1 + 1) log M 1 ] a2 + 1 Wednesday, October 13, 2010 ⎛1 =⎜ ⎜1+ a 2 ⎝ ⎞ K (1 + a1 ) ⎟ log 1 + log M 1 ⎟ K 2 (1 + a 2 ) ⎠ 36 HPLC 37 Wednesday, October 13, 2010 TLC vs. HPLC Type of Analysis qualitative quantitative Stationary Phase 2D, thin layer plate 3D column Instrumentation none Pump, columns, injector, etc Sample application spot inject Mobile Phase Movement Capillary action High pressure Visualization of Results UV, iodine UV, RI Results Retention times, peaks Retention factors 38 Wednesday, October 13, 2010 HPLC Chromatograms Approximation of peak area by Absorbance → triangulation 0 Peak A Peak B height 1 2 3 4 5 6 Time (minutes) Rt = 3.0 min. faster moving less retained Rt = 5.2 min. slower moving more retained 7 base Area = base x height 2 39 Wednesday, October 13, 2010 Chromatography Stationary Phases C18 Silica Gel Silica Gel OH HO Si O O HO Si O O OH Si O O Si O O OH Si O O Si O O OH Si OH O Si OH O Bulk (SiO2)x relatively polar surface “normal phase” OR RO S i O O RO S i O O OR Si O O Si O O OR Si O O Si O O OR Si OR O Si OR O Bulk (SiO2)x R=C18H37 octadecyl silyl derivative=C18 relatively nonpolar surface “reversed phase” 40 Wednesday, October 13, 2010 Normal vs. Reversed Phase Chromatography Normal Reversed Phase Stationary Phase Polar (silica) Non-polar (C18) Mobile Phase Non-polar (organic solvents) Polar (aq. or organic) Sample Movement Non-polar fastest Polar fastest Separation Based On Different polarities (functionality) Different hydrocarbon content (non-polarity) 41 Wednesday, October 13, 2010 Mass Spectrometry 42 Wednesday, October 13, 2010 Mass Spectrometry MALDI-MS (MALDI-TOF) MALDI-MS (matrix-assisted laser desorption ionization mass spectrometry) (TOF − time-of-flight) • Embeds polymer in a matrix of low MW organic compound • Irradiates the matrix with UV laser • Matrix transfers the absorbed energy to polymer and vaporize the polymer • Peak height/integration should reflect concentration of that chain in the sample • Mn, Mw can be calculated • At higher MWs, lose peak separation Soft ionization methods (doesn’t fragment the molecule) • field desorption (FD-MS) • laser desorption (LD-MS) • electrospray ionization (ESI-MS) 43 Wednesday, October 13, 2010 OTHER METHODS 44 Wednesday, October 13, 2010 End-group analysis Titration polyester (-COOH, -OH), polyamide (-C(O)NH-), polyurethanes (isocyanate), epoxy polymer (epoxide), acetyl-terminated polyamide (acetyl) Elemental analysis Radioactive labeling UV / NMR / (IR) Upper limit M. W. ≈ 50,000 (due to the low concentration of end groups) preferred range: 5,000-10,000 Not applicable to branched polymers (unless well-defined) Analysis is meaningful only when the mechanisms of initiation and termination are well understood 45 Wednesday, October 13, 2010 Fractional Solution With solvent extraction • use a Soxhlet-type extraction apparatus • dissolve into fractions of increasing MW with time With chromatographic column • coat polymer (on fine sand or glass beads) • pack column • elute the coated polymer → first use a pure nonsolvent, then increase the solvent fraction with time • low MW polymer dissolved and eluted first • equivalent to reverse GPC Fractional Precipitation Reverse of fractional solution • Prepare polymer solution (dilute solution) • Precipitate HMW polymer by adding small amount of nonsolvent • Collect HMW polymer • Add more nonsolvent to precipitate LMW polymer Turbidimetry • addition of nonsolvent to a polymer solution • turbidity is recorded as scattered light and then correlated to MW 46 Wednesday, October 13, 2010 Ultracentrifugation • expensive equipment • Extensively used with proteins • Determining Mw Mz • Sedimentation rate is proportional to molecular mass • Distributed according to size along the perpendicular direction • Concentration gradients within the polymer solution are observed by refractive index measurements and interferometry 47 Wednesday, October 13, 2010 Cryoscopy and Ebulliometry Thermodynamic relationships ⎛ ΔT f ⎜ ⎜C ⎝ ⎞ RT 2 ⎟ = + A2C ⎟ ⎠C = 0 ρΔH f M n RT 2 ⎛ ΔTb ⎞ = + A2 C ⎜ ⎟ ⎝ C ⎠ C =0 ρΔH v M n for freezing-point depression for boiling-point elevation T: ΔH f : ΔHv: A2 : ρ: freezing point or boiling point (solvent) latent heat of fusion (per gram) latent heat of vaporization (per gram) second virial coefficient solvent density • Limited by the sensitivity of measuring ΔTf, ΔTb • As MW increases ΔTf, ΔTb decrease • Upper limit - Mn = 40,000 • Preferred - Mn < 20,000 48 Wednesday, October 13, 2010 Vapor Pressure Osmometry • For Mn < 25,000 • No membrane needed • Thermodynamic principle similar to membrane osmometry • There are two insulated chambers – one for solvent and one for polymer solution • Each solution is placed in an insulted chamber (at saturated solvent vapor) and allowed to reach vapor equilibrium • Compared to pure solvent, if a polymer solution is placed in a saturated vapor chamber, some of that vapor will condense into the solution; this releases heat, and the change in temperature is measured For dilute solutions RT 2 ⎛ c 2 ⎞ M sol ΔT = ⎜ ⎟ ΔH v ⎝ M n ⎠ 1000 c2: polymer concentration, g/kg Msol: molar mass of solvent The vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution (Raoult’s law) 49 Wednesday, October 13, 2010 ...
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