Neutron Scattering

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Finally, one may test whether only local reptation or also thé creep motion along thé tube is important on this experimental time scale . Local reptation corresponds to Zd = ou and indeed (Fig .15 .19) at low Q a différence between local reptation only and thé global reptation mechanism appears to become distinguishable indicating thé présence of -rd. Here future experimental work will have to set in . As it stands NSE spectroscopy accessing quantitatively thé dynamic structure factor has by now seen clear and unambiguous signature of reptation in a flexible linear polymer chain. The data cover a region ofthé time domain where reptation is in principle applicable . Compared with other phenomenological approaches reptation is by now thé only approach providing a consistent description of all NSE data. It implies that reptation must emerge from any successful microscopie theory of polymer relaxation . 15.5 Summary High resolution neutron spectroscopy permits to access thé molecular motions simultaneously in space and time . Restricting itself to thé dynamics of homopolymers melts this lecture attempted to transmit a flavour of what can be achieved in particular by NSE . Choosing différent time and length scales, we covered thé range of molecular motions, commencing at thé scale ofa few bonds to large scale motions reaching thé scale of thé entire chain. In thé régime of thé `classical relaxations' of polymers neutron spectroscopy informs on thé geometrical evolution ofthé motions in question . We have seen, that thé a-relaxation may be understood as a sublinear diffusion process while thé fi-relaxation is in good agreement with a local jump process of a few angstrom distances. Both processes may be considered with good approximation as statistically independent. At scales where thé detailed chemical structure of thé monomers ceases to be of importance, NSE measurements have by and large confirmed thé prédictions of thé entropy govemed Rouse dynamics both for thé self and thé pair conelation function . Recently, an in depth comparison of specially designed NSE experiments with computer simulation also pointed out thé limits of this approach . The dynamics of polymer melts under thé influence of topological interactions which result from thé mutually interpenetrating chains poses high demands both conceptually and also experimentally . NSE experiments on thé single chain dynamic structure factor of long chain melts, established experimentally thé essential prédiction of local reptation namely thé tube 15- 27
confinement of the relaxation of large scale Rouse modes . Presently there exists no other theory providing a dynamic structure factor, which is in agreement with this data. Referenees A. Review Articles and books M . Doi, S .F . Edwards, The Theory of Polymer (1986) namics, Clarendon Press, Oxford [2] B . Ewen, D . Richter, Advances in Polymer Science 134, Springer, Berlin (1997) [3] D . Richter, Polymer Dynamics by Neutron Spin Echo Spectroscopy in "Scattering in Polymeric and Colloidal Systems" Ed by Wyn Brown and Kell Mortensen, Gordon and Breach, London (2000) [4] D . Richter, Visoelasticity and microscopie motion in dense polymer systems, Review article in Diffusion in Condensed Matter, Eds : J. Kärger, P . Heitjans, R . Haberlandt (Vieweg, Braunschweig (1998)) B. Experimental work [5] A . Arbe, U . Buchenau, L . Willner, D . Richter, Study of the Dynamic Structure Factor in the /Relaxation Regime ofPolybutadiene, Phys . Rev . Lett. 76, 1872 (1996) [6] A . Albe, D . Richter, J. Colmenero, B . Farago, The Merging ofthe a- and P-Relaxations in Polybutadiene ; A Neutron Spin Echo and Dielectric Study, Phys . Rev . E . 54, 3853 (1996) A . Arbe, J . Colmenero, M . Monkenbusch, D . Richter, Dynamics of glass-forming polymers : homogeneous vs. heterogeneous scenario, Phys . Rev . Lett. 81, 590 (1998) [8] D .Richter, M.Monkenbusch, A. Arbe, J.Colmenero, R . Faust, Space Time Obseivation of the a-Process in Polymers by Quasielastic Neutron Scattering, J . Phys . Condens . Matter 11, A297 (1999) A . Arbe, J . Colmenero, B . Frick, M. Monkenbusch, D . Richter, Investigation of the dielectric ß-process in Polyisobutylene by incoherent quasielastic neutron scattering, Macromolecules 29, 4926 (1998) [10] D . Richter, M . Monkenbusch, J . Allgaier, A . Albe, J. Colmenero, B . Farago, Y . Cheol Bac, R . Faust, From Rouse Dynamics to Local Relaxation - A Neutron Spin Echo Study ofPolyisobutylene Melts, J . Chemical Physics 111, 6107 (1999) [11] W. Paul, G.D. Smith, D.Y . Yoon, B . Farago, S . Rathgeber, A. Zirkel, L . Willner, D . Richter, Chain Motion in an Unentangled Polymer Melt : A Critical Test of the Rouse Model by Molecular Dynamics Simulations and Neutron Spin Echo Spectroscopy, Phys . Rev . Lett . 80, 2346 (1998) [12] P . Sehleger, B . Farago, A. Kollmar, C . Lartigue, D . Richter, Clear Evidence of reptation in polyethylene from neutron spin echo Spectroscopy, Phys . Rev . Lett . 81, 124 (1998) [13] H. Montes, M . Monkenbusch, L . Willner, S . Rathgeber, L .J. Fetters, D. Richter, Neutron Spin Echo Investigations of Concentration fluctuations dynamcs in melts of diblockcopolymers, J. Chemical Physics 110, 10188 (1999) 15- 28
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Forschungszentrum Jülich in der He
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Forschungszentrum Jülich GmbH Inst
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Contents . . 1 Neutron Sources H .
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1 . Neutron Sources Harald Conrad 1
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d) f, = v a, , q - ti = P a, - 0 .3
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Period Example Flux (D [1013 1950-6
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In stage 1 the primary proton knock
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get as heat, the rest is transporte
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down power and stronger absorption
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Appendix Neutron Sources - an overv
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led remotely. It is rauch more conv
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2 . Properties of the neutron, elem
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In the 60's the ferst high flux rea
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Hot neutrons in reactors are obtain
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elated values for the FRJ-2 reactor
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2 .5 Scattering amplitude and cross
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(A+k2 ) yr = u(Z:) yr V( u~r)= z "
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_du _ mn \2 A2-~2z r2~ I(k' IVI k)I
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E ô ô x z w 0 z _w U N Figure 2 .
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scattering is observed with the ave
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For a spherical electron distributi
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A more thorough introduction to neu
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3 . Elastie Seattering from Many-Bo
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Q = Q = k2 + k2 - 2kk' cos2B (3 .3)
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3 .2 Fundamental Scattering Theory
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The meaning of (3 .l4) is immediate
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1 . e. in the second approximation,
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The saure problem will bc dealt wit
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ALQ) = Y-bfe'Q'-rB(r-(n .a+m .b+p»
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du LQ) = ALQJ2 = e'Q .A' . * -i e-
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Tab . 3.1 : The scattering lengths
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We note immediately that we should
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These magnetic structures can be un
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M1LQ)=Q-MQ)xQ M(Q)= IM (r)e i Q " d
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Orbital magnetic spin angular ,,- m
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aQ . r 3 àQ . N . QR . aQ .t k _ML
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Schweika Analysis Polarization W .
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ducing a complex component and were
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ir v s ftft 3956 2 s 2 0.81[X] 80 c
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Some polarizers using Bragg reflect
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Different to the coherent nuclear s
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where QBG denotes the background .
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4 .4 Applications We now consider e
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Fig. 4 .3 .4 probably represents th
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. occur only in the non-spin flip c
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The results for the magnetization d
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a large solid angle with polarizers
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scattering to spin-flip scattering
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An experimental verification of thi
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Correlation Functions Measured by S
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In real liquids however usually an
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The term in big parentheses of equa
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4 0 -5 0 5 10 15 20 ho) [meV] Figur
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Figure 5 .5 : The pair correlation
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Figure 5 .6 : Partial differential
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Then equation (5 .21) can be conver
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The route from expression (5 .27) t
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In addition it is often useful to d
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2 . The pair correlation function h
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G(r, t) G(r, t) i(Q, t) r Q i(Q, t)
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Insertion of this result into (5 .6
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With this example we can also demon
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6. Continuum description : Grazing
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Starting point is the exact atomic
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For specular reflectivity measureme
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v v z l 2r V(z) = 2 -2erfC~ with er
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F{dV(z)/dz ) to calculate the refle
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Equation (6 .13) also shows that th
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ut is completely reflected . The cr
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0.4° . The full dynamical theory c
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1) If no magnetic induction B (whic
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Diffractometer Gernot Heger
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select a special wavelengths band (
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" The direction of the reciprocal l
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Bragg-intensities of single crystal
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monochromator, on the mosaic spread
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complex sample environments, such a
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the diffraction plane) two further
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Small-angle Scattering and Reflecto
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L= (1) ( k ) a e -(k/k T ) 2 Ak (8
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possible neutron wave lengths betwe
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figure and with neutrons of about 1
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1 .0 Danvinkurve 0 .8 0 .6 0 .4 0 .
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tails. This reflection curve leads
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For the Nickel film one gets a thic
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I The rotor of a velocity selector
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multiplier are arranged in a quadra
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9 . Crystal spectrometer : triple-a
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machine which will be followed by a
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10 .3 Beaur shaping Due to the fact
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G.k=zGz . (11) This case is fulfill
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tribution of bisecting planes (ntos
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directions which is exploited for t
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Fig . 14) Dispersion surfaces for B
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whereby E and v,, denote energy and
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[1] B . N. Brockhouse, in Inelastic
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10 . Time-of-flight spectrometers M
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Tnloderator /K V7 2/m/s A/nm Aiw/eV
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10.2 .1 Interpretation of spectra A
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----~ Probe ' (Chopper 2) Zeit I Ch
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the similar intensity distribution
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is performed without Jacobian due t
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10.2 .6 Crystal monochromators The
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larger energy transfers . However i
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10.3 Inverted TOF-spectrometer In t
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constant offset to the TOF . To be
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sample size of cm and a detection p
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Contents 10 .1 Introduction . . . .
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11 . Neutron spin-echo spectrometer
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2 0 L Tr -0 L 2 ArDet Figure 11 .1
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initial velocity-reassemble at the
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distribution (current sheets) that
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esults, where il is an irrelevant c
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10000 - 8000 - co 6000 - C ô 4000-
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e0 oX n .5 1 .0 1 .5 so 0 .0 0 .0 1
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nel" coils) the required homogeneit
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Figure 11 .9 : S(Q, t)IS(Q) of a 2
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Contents 11 .1 Introduction . . . .
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12 . Structure determination G . He
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Important: Thc measured Bragg inten
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determination of accurate atomic pa
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The knowledge of the overall occupa
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(even anharmonic) effects. This com
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Fig . 4 . Coordination ofthe D20 mo
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fenoelectric phase of orthorhombic
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(c) and (d) calculated densities at
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13 Inelastic Neutron Scattering Pho
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Figurel Schematical drawing of a ge
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equilibrium position the atom is in
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s - ' f N .mwn .I )oo K L .~um..un
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esults from the quantum mechanics o
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y absorption . 13 .1 .3 Magnetic in
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Figure 7 The plane in reciprocal sp
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5 100s1 [OSl ] IOSSI [SSS y i 4 0 r
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dynamics of ionic compounds with th
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16 14 12 F.. . 10 ô 8 q 6 cr 4 G.
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21 [ooç 1 " - 19 18 17 16 "" 298 K
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n = v - cap[i(pga . - wt)] (13 .22)
Page 299 and 300: Y c 3 c Cc E Figure 16 Magnon dispe
Page 301 and 302: . . 2 H . Bilz and W . Kress, Phono
Page 304 and 305: 14 . Soft Matter : Structure Dietma
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Page 308 and 309: 2 P(Q) = 1 ~exp(-Ii - j'6 Q2 ) (14
Page 310 and 311: fraction. In the region of large Q
Page 312 and 313: with the partial structure factor S
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Page 316 and 317: For the intramolecular and intermol
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Page 320 and 321: scaling behavior of the susceptibil
Page 322: 15 Polymer Dynamics Dieter Richter
Page 325 and 326: constraints due to the mutual inter
Page 327 and 328: (15 .3) T ß ( E)=T ô exp E k,T -
Page 329 and 330: This incoherent approximation does
Page 331 and 332: 10 an 0 2 0 Figure 15.4 : Relaxatio
Page 333 and 334: In order to test Eq .[15 .9] the re
Page 335 and 336: Arrhenius temperature dependence wi
Page 337 and 338: 1 3kBT ~ z 2 72 2 p2 a = f2 N2 P =W
Page 339 and 340: S (Q,t) = 12 fdu exp ~ -u_ (S2Rt) v
Page 341 and 342: We now use these data, in order to
Page 343 and 344: c 0 .8 0 .6 00 .055 x 0 .1 110 .14
Page 345 and 346: small but systematic deviations fro
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Page 349: only one single parameter, the tube
Page 354: 16 Magnetism Thomas Brückel
Page 357 and 358: the ground state of metallic magnet
Page 359 and 360: c~ ~ o 0 `,~i) g',, b o 0 Q! b o 0
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Page 365 and 366: Fie. 16.4: Scattering geometry for
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Page 369 and 370: Here, J;j denotes the exchange cons
Page 371 and 372: Fig. 16.8 : Contour plot of the mag
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Page 376: 17 Translation and Rotation M . Pra
Page 379 and 380: 17.1 Introduction Atomic and molecu
Page 381 and 382: 17 .2.2 Diffusion, microscopic appr
Page 383 and 384: 0.6 H20 2 x2tÄ z ) Figure 17 .2 :
Page 385 and 386: The scattering function of a polycr
Page 387 and 388: e (2) 1 (j 1, 0 > - 0,1 >), respect
Page 389 and 390: leads to the eigenvalue problem ~q
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Page 393 and 394: m Eu W Figure 17 .7 : Eigenenergies
Page 395 and 396: -so o so Energy transfer (NeV) Ener
Page 397 and 398: Bibliography [1] T. Springer, Quasi
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18 . Texture in Materials and Earth
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Further important structure related
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The axes of the cartesian Kp coordi
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4.0 Experimental Texture Analysis T
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Fig. 18.14: Variation of reflection
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measurements can be performed in tr
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Apart from the global description o
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In the following, two experimental
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The neutron diffraction pole figure
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dependent pole densities, and (4) g
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Schriften des Forschungszentrums J
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Forschungszentrum Jülich in der He
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Neutron Scattering

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