Chapter 12 Light scattering (determination of MW without …12章光散射没有分子的测定…

1、chapter 12. light scattering (determination of mw without calibration)electromagnetic radiation transmissionreflectionabsorptionscatteringincident radiation :1.transmission: transmitted radiation passes through the medium unaltered.2.absorption: energy from the incident beam is taken up, resulting i

2、n: (1)heating, (2) re-emitting at another wavelength (fluorescence, phosphorescence), (3)supporting chemical reactions. * in this discussion, we assume that radiation heating is negligible. other absorption effects are specific to the particular medium, and will also not be considered here.3.scatter

3、ing: scattering is non-specific, meaning the incident radiation is entirely re-emitted in all direction with essentially no change in wavelength. scattering results simply from the optical inhomogeneity of the medium. 4.reflection: scattering at the surface of a matter (not considered here) now we f

4、ocus on the light scattering.application of light scattering for analysis1.classical light scattering (cls) or static light scattering (sls)2.dynamic light scattering (dls, qels, pcs)cls : scattering center = small volumes of material that scatters light. : individual molecule in a gas. consequences

5、 of the interaction of the beam with the scattering center: depends, among other things, on the ratio of the size of the scattering center to the incident wavelength (o). our primary interest is the case where the radius of the scattering center, a, is much smaller than the wavelength of the inciden

6、t light (a 0.05o, less than 5% of o). this condition is satisfied by dissolved polymer coils of moderate molar mass radiated by visible light. when the oscillating electric field of the incident beam interacts with the scattering center, it induces a synchronous oscillating dipole, which re-emits th

7、e electromagnetic energy in all directions. scattering under these circumstances is called rayleigh scattering. the light which is not scattered is transmitted: , where is and it are the intensity of the scattered and transmitted light, respectively.tsoiii io elastic scattering transmission i =is+it

8、 scattering cos1 22riio(2) cos1 22riio constant, k(3) 2 242toaocrtcdcdnnn oscillating electric field of incident beam interacts with scattering center, induces a synchronous oscillating dipole, which re-emits electromagnetic energy in all directions. 1944, debye rearrange:o = , dn/dc = refractive in

9、dex incrementno: refractive index, =, c=g/mlrayleigh scattering : (1+cos2) , scattering center observer (r) .toaoocrtcdcdnnnrii242222cos1 theni is inversely proportional to o. shorter wavelength scatters more than longer wavelengthassume: system is dilute, the net signal at the point of observation

10、is sum of all scattering intensities from individual scatterer - no multiple scattering (scattered light from one center strike another center causing re-scattering, etc.).define “rayleigh ratio” rmeasured toaoocrtcdcdnnnrii242222cos1toaocrtcdcdnnnr2422two ways to access the light scattering informa

11、tion experimentally:1.turbidimeter (or spectrophotometer)2.light scattering1. turbidimeter experiment (transmitted light intensity, it is measured) sample cell monochromatic light source photomultiplier tube measures it = 1 - (it/io) = (16/3) r turbidity, = fraction of incident light which is scatte

12、red out = 1-(it/io) is obtained by integrating i over all angles: r316toavocrtcdcdnnnr242332 : substitute bcmrtc1 substitute: .21332243bcmcdcdnnnoavo camhcdcdnnnhoavo224321 332 :definesolution is dilute, so higher order concentration terms can be ignored.camhccamhc2221 21 procedure: measure at vario

13、us conc. plot hc/t vs. c (straight line) determine m from intercept, 2nd virial coeff., b from slope(5) 12 camrtc(6) 12 camrtct(4) tcrtckr6 4 : (7) 212camrkc* 5% (/20) “rayleigh limit”2. light scattering experiment (measure i at certain and r)the slope of the plot cvsrkc . can be either positive or

14、negative.-condition =0. for polydisperse sample, turbidity ( light scattering) is contributed by molecules of different mw. define: i= mi turbidity iiiibcmhc21iiiiitotaliiiiimchmhcmhccac 02 0 if2(hc)/ vs. c =1/m 0ctotaltotalhciiiiiicmcchmchvmcii substitutetconsviiivmmvmtan mwaverageweightmnmnmnmmnmm

15、miiiiiiiiiiii 2 turbidity light scattering weight-average mw.rayleigh-gans-debye (rgd scattering) : when the scattering centers are larger than rayleigh limit plain polarized light 1 2 a b different part of more extended domain (b) produce scattered light which interferes with that produced by other

16、 part (a) - constructive or destructive(8) )(prrrayleighrgd(9) 5112 qapa =q = scattering vector = (4/)sin(/2)rg (10) : (11) 3521grarandom coil , distribution is symmetrical for small particles (/20). for larger particles, intensity is reduced at all angles except zero.contributions from two scatteri

17、ng centers can be summed to give the net scattering intensity. the result is a net reduction of the scattered intensityp = shape factor or form factor)(8 211bcmprkcalways p 1, function of size and shape of scattering volume. now we start seeing the angle dependence of the scattered light ! p() decre

18、ases with . p() decreases more for higher mw.effect of mw and chain conformation on p, and on measured mw at 90o.conformationrandom coilpolystyrenepolystyrene( condition)pmmapolyisoprene(70% cis)sphericalbovine serum albuminbushy stunt virusrod shapedpoly- -benzyl-l-glutamatemyosindnamw (g/mol)51k42

19、0k680k940k66k10700k130k493k4000krg (nm)81936483122647117p(90o)0.980.950.700.561.000.980.910.740.35mw(90o)51k400k480k530k66k10500k118k365k1400kcase 2 c0:camrkc221 : plot kc/r vs. c: y-=1/m, =2a2 2sin316112222grmmrkcplot kc/r vs. sin2(/2): y-=1/m, = (162/3m2) rg2three information!case 1 0:(11) 3521gra

20、random coil , (12) 2sin31612122222grcamrkc(11) (9) (7) : final rayleigh equation for random coil polymer (1) r. (2) kc/r vs. c, kc/r vs. sin2( /2) plot . (3) =0 c =0 extrapolate.kc/r vs. sin2( /2)kc/r vs. czimm plot: : . : extrapolated pointscases1. small polymers: . (horizontal line)- .- mw a2 - .z

21、imm plot for pmma in butanoneo=546 nm, 25, no 1.348, dn/dc = 0.112 cm3/g(kc/r) vs. c-calculated values : mw = 66,000 g/mol a2 = 0 mol cm3/g2- kc/r at small angles fall mostly below the horizontal line plotted through the points from medium and large angles.2. small polymers in -solvent: .zimm plot o

22、f poly(2-hydroxyethyl methacrylate) in isopropanolo=436 nm, 25, no 1.391, dn/dc = 0.125 cm3/g-solvent : a2=0 , -, - , .3. larger polymers in good solvent: .zimm plot of polystyrene in tolueneo=546 nm, 25, no 1.498, dn/dc = 0.110 cm3/g4. polymers in poor solvent: a2 ( . )zimm plot of polybutadiene in

23、 dioxaneo=546 nm, 25, no 1.422, dn/dc = 0.110 cm3/g- (nonlinear).- : microgel, , aggregate .- curve-fitting . . - good solvent .- 2x105 , kc/r (a2=) . - athermal condition - no effect of temperature on polymer structure stand-alone mode: ls instrument is used itself. zimm plot m, a2, r ls instrument

24、 is used as a detector for a separator. c=0 . slice kc/r vs. sin2(/2) , y- (m), rg . y-=1/m, = (162/3m2) rg2 slice monodisperse . ( ).average molecular weights1.no-average: mn=(ci)/(ci/mi)2.wt-average: mw=(ci mi)/ (ci)3.z-average: mz= (ci mi2)/(ci/mi)average sizes (mean square radii)1.no-average: n=

25、 (ci/mi)i/(ci/mi)2.wt-average: w= (cii)/ci3.z-average: z=(cimii)/(cimi)stand-alone vs. on-line malslight scattering instrumentsmalls (multi angle laser light scattering) : i is measured at 15 angles(1) stand-alone mode: measure scattered light at different angles for different concentrations make a

26、zimm plot determine m, b, rg(2) on-line mode: assume c=0, plot 2sin . 2vsrkcfor each slice. determine m from intercept (intercept = 1/m), rg from slope (slope = )222316grmassuming each slice is narrow distribution, mw miaverage m can be calculated. it is therefore very important to have a good resol

27、ution.talls (triple angle): i is measured at 45o, 90o, and 135o not useful when the plot of 2sin . 2vsrkc deviates from linearity angular dependence of kc / r ( = high molecular weight dna)effect of particles/gels on light scattering measurementnote the delicacy of extrapolation to zero angle from l

28、arger distances.dalls (dual angle): i is measured at 15o and 90olalls (low angle): i is measured at one low angle (assume: = 0)(1) static mode: measure ls at a few c plot kc/r vs. c determine m and b from intercept and slope.(2) on-line mode: determine kc/r for each slice ( calculate m). considering

29、 each slice is narrow distribution, let mw ( mi, from which average mws can be calculated (as learned in chapter 1). it is therefore again very important to have a good resolution.ralls (right angle) i is measured at 90o. simple design higher s/n ratio, application is limited to cases where p is clo

30、se to 1 (e.g., less than 200k of linear random polymer) ralls combined with differential viscometer (commercially available from viscotek, trisec)assume p = 1 and a2 = 0. determine mest. kcrmestbcmprkc211 fromrg can be obtained using the flory-fox equation: 3161mrg is determined by differential visc

31、ometer, and m determined in step 2.calculate new mw by 90 pmmestestgo to step 2. repeat until mest does not change.sin4 x where,12212gooxrnxexpcalculate p(=90). 2sin3161212222grbcmrkc k b parameter . 2432dcdnnnkoavo .1.n: refractive index2.dn/dc : specific refractive index increment3.b: 2nd virial c

32、oefficient (static mode b static mode ).1. refractive index ri . (r )solventrir x 106 cm-1carbon disulfide1.620757.5a-chloronaphthalene (140 oc)1.532352.81,2,4-trichlorobenzene (135 oc)1.50235.7chlorobenzene1.518718.6o-xylene (35 oc)1.5015.5toluene1.4914.1benzene1.5012.6chloroform1.4446.9methylene c

33、hloride1.42236.3carbon tetrachloride1.466.2dimethyl formamide1.43 (589 nm)5.6cyclohexane1.4255.1cyclohexanone1.44664.7methyl ethyl ketone1.384.5ethyle acetate1.374.4thf1.414.4acetone1.364.3dimethyl sulfoxide1.478 (589 nm)4.1methanol1.332.9water1.331.2 except where otherwise noted, all measurements m

34、ade at = 632.8 nm and t=23 oc. ri at 632.8 nm calculated by extrapolation from values measured at other wavelengths. extrapolation reference: johnson, b. l.; smith, j. light scattering from polymer solutions huglin, m. b. ed., academic press, new york, 1972, pp 272. specific refractive index, dn/dc

35、(polymer handbook, huglin, ed., light scattering from polymer solutions, academic press, 1972) conventional method dri (n2-n1) (recommended conc. = 2, 3, 4, 5 x 10-3 g/ml) (n2-n1)/c2 vs. vs. c2 plot zero concentration extrapolate dn/dc intercept .0212ccnndcdnfor concentration ranges generally used,

36、the refractive index difference, n2-n1, is a linear function of concentration. in other words, (n2-n1)/c2 is constant. (n2-n1)/c2 vs. c2 =0. this means that (n2-n1) needs to be measured for only one or two different concentrations. if (n2-n1)/c2 shows no significant dependence on c, then dn/dc can b

37、e obtained by averaging (n2-n1)/c2 values sec/ri iricdcdnkrri = detector signal at the slice ikr = ri constci = conc. (g/ml) of the slice i) dn/dc kr : stdstdstdrcdcdnareak , dn/dc : ckareadcdnr estimate .extrapolate to desired wavelength: kkdcdn 2) polymer refractive index estimate: 122nndcdn n2 po

38、lymer partial specific volume ml/g. n2 1. dn/dc light scattering . dn/dc . dn/dc . dn/dc . .3. virial coefficient, b or a2 (: polymer handbook). (stand-alone light scattering) 2nd virial coefficient solute-solvent interaction .+: polymer-solvent interaction, good solvent (the higher, the better solv

39、ent).0: unperturbed system-: polymer-polymer interaction, poor solvent. a2 : a2 = b m-a log a2 vs. log m . , . dn/dc a2 : s. lee, o.-s. kwon, determination of molecular weight and size of ultrahigh molecular weight pmma using thermal field-flow fractionation/light scattering in chromatographic chara

40、cterization of polymers. hyphenated and multidimensional techniques, provder, t., barth, h. g., and urban, m. w. ed.; advances in chemistry ser. no. 247; acs: washington, d. c., 1995; pp93.light scattering (concerns) dn/dc, ri constant, a2 . as dn/dc increases, calculated mw decrease, calculated mas

41、s decrease, and no effect on calculated rg. as ri constant increases, calculated mw decreases, calculated mass increases, and no effect on rg . as a2 increases, calculated mw increases, no effect on calculated mass, rg slightly increases.refractive index detector calibration ri calibration constant:

42、 inversely proportional to the detector sensitivity. sensitivity of most ri detector is solvent-dependent. a calibration constant measured in a solvent may not be accurate for other solvents. it is recommended to use a solvent that will be used most often (e.g., thf or toluene). for ri calibration,

43、only the ri signal is used. light scattering instrument calibration is not needed. concentration of standards should be such that the output of ri detector varies between about 0.1 - 1.0 v and should correspond to normal peak heights of samples (for a waters 410 ri at sensitivity setting of 64, this

44、 corresponds roughly to concentrations of 0.1 - 1.0 mg/ml. ri output can be usually monitored by light scattering instrument (e.g., channel 26 of dawn). use nacl in water as a standard for aqueous system. the ri calibration constant will change if you change the sensitivity setting of the detector:

45、so it is important to use the same sensitivity setting of ri detector as that used when the detector was calibrated.ri calibration preparation: one manual injector with at least 2 ml loop, five or more known concentrations (0.1 - 1 mg/ml) of about 200 k polystyrene in thf.ri calibration procedure1.r

46、emove columns. place manual injector with loop.2.pump thf through a ri detector at normal flow rate (about 1 ml/min). purge both reference and sample cells of detector until baseline becomes flat & stable.3.stop purging and wait till baseline becomes stable. 4.set up the light scattering data co

47、llection software (enter filename, dn/dc, etc.) enter 1 x 10-4 for ri constant (light scattering instrument usually requires the ri constants to be entered). set about 60 ml for duration of collect . 5.begin collecting data with astra.6.inject pure solvent first followed by stds from low to high con

48、c, and finish with pure solvent. 7.repeat the measurements if you want.8.data analysis: (1)set baseline using signals from pure solvent at the beginning and the end (2)calculate each concentration as a separate peak by marking exactly 1 ml as peak width (or 30 slices at 1 ml/min, 2 seconds of collec

49、tion interval).(3)calculate the mass of the peak (4)plot the injected mass (y-axis) vs. calculated mass (x-axis) (5)do linear regression on data by forcing the intercept be zero (6)calculate ri constant using ri constant = slope x 1x10-4 chemical heterogeneity within each slice leads to non-defined

50、dn/dc quantitation of chemical heterogeneous samples is very difficult. limited sensitivity to low mw components. mn(exp)mn(true). the same concern with differential viscometer experiments.limited sensitivity of light scattering and ri detector g values may be in error if each peak slice contains bo

51、th linear and branched polymer or different types of long-chain branching: g will be overestimated. quality of data is highly affected by the presence of particles. lower limit of rg with mals 10 nm (about 100k mw) inter-detector volume must be known accurately.comparison of online ls vs. viscometer

52、lsviscometermwdabsoluterelativeneed precise n and dn/dcuniversal calibration must be valid or need m-h coefficientindependent of separation mechanismindependent of separation mechanism if m-h coefficients are used. dependent on separation mechanism if universal calibration is used. distributionindir

53、ect from universal calibrationdirect, independent of separation mechanismrgdirect from mals (limited to 10 nm)indirect from universal cal. and flory-fox eqn. applicable to linear molecules onlychain conformation malls: rg vs. m plot vs. m plot (m-h coefficients can be obtained) rg vs. m plot.branchi

54、ngg obtained directly from mals, indirectly from lalls & universal calibrationg obtained directlyheterogeneous sampleslimited because of dn/dc uncertaintydirectly applicable with univ. calib., but the change in dn/dc will affect dri responseslower mw detectability2k. depends on dn/dc and polydis

55、persityas low as 300-400 has been reportedresponse to particle contaminationlalls: highly sensitive, malls: less sensitiveinsensitiveinformation contentprimarysecondarylallsmmallsmrgpcsdrh, mviscometer m, rgprimary information: high precision and accuracy, insensitive to sec variables, requires no s

56、ec column calibration.features: mwd measured by ls ivd measured by viscometer both viscometer and ls are insensitive to experimental conditions and separation mechanism no band broadening corrections are needed for mw, , a, k, and g precise and accurate calculation of hydrodynamic radius distributio

57、n, m-h constants, and branching distributiondynamic light scattering (dls, qels, pcs) classical light scattering: time-averaged scattering intensity scattering center (algebraic summation). algebraic summation random array, phase relationship scattering volume dimension interference effect average-o

58、ut . scattering volume dimension , scattering center interfere (constructive or destructive) . brownian motion (diffusion) . fluctuate. fluctuate diffusion rate (diffusion rate fluctuate). nanometer micron viscosity viscosity media disperse , (fluctuation) microsecond millisecond. a vertically polar

59、ized laser beam is scattered from a colloidal dispersion. the photomultiplier detects single photons scattered in the horizontal plane at an angle from the incident beam, and the technique is referred to as photon correlation spectroscopy (pcs)“ because the particles are undergoing brownian motion,

60、there is a time fluctuation of the scattered light intensity, as seen by the detector. the particles are continually diffusing about their equilibrium positions. analyzing the intensity fluctuations with a correlator yields the effect diffusivity of the particles. measured intensity, i = vector sum of scatt