Rotational dynamics of small and macromolecules

255 Pages·1987·8.83 MB·English

by  Thomas Dorfmueller, Robert Pecora, Workshop on the Rotational Motion of Small and Macromolecules in Complex Liquids

Lecture Notes
in Physics

Edited by H. Araki, Kyoto, 4 Ehcors, Miinchen, K. Hepp, Zorich
R. Kippenhehn, Machen, H.A, Weidenmiller. Heidelberg
4. Wess, Karoruhe una J, Zittartz, Kale

Managing Editor: W. Beighbick

293

ee

Th. Dortmiiller R. Pecora (Eds.)

Rotational Dynamics of
Small and Macromolecules

Proceedings of a Workshop
Held at the Zentrum fir interdiszipindire Forschung
Universitat Bielefeld, Bielefeld, FRG, April 21-23, 1986.

é

Springer-Verlag

Beriin Heidelberg New York London Paris Tokyo
dors

Th Dothan
“rivers Bielefeld, Fakualfir Chori
Pstiach 8640. 0.4850 Biswtald 1, FRC

R, Pocora
Univers of Stanford, Deparment o: Chest
Stanford. CA 94506, USA

ISBN 3.540-18888.5 Sy-ingerMlrlg Burln Heiulborg NewYork
ISBN DGB. 18683.5 Springer-sereg New York Berlin Heidelberg

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Preface

Under the auspices of the project "Canplex Liquids* of the "Zentrum flr
‘ntordiszinl mire forschung” of the Untyerstty of Btelafeld a workshop an the
"RaLational Hoton of Small and Macromolecules in Complex Liquids" wat held in the
period 3 - 5 ApriT 1986, This volun is based on the lectures held at this workshop.

We usually think of the Tiqutd state as being a cotetend dtsordored. state of
matter displaying 2 tere nobittey a compared La solids. by nobility We aan the
macroscopic fled praperties as well az molecular mability, since both are ta sone
extent interconnected. fny definition of the auld state 1s far from betng
Uunanbiquous even for simple nolecular liquids, and becones even more complicated if He
consider molecules which are highly avisctreptc in shape, for example rod-like
nolecules, or molecules which tateraet via anisotropic Forces, such as the case where
hydregen bonding osewrs, oF Finally, molecules which display high Internat nobiTity
‘ike bulk polymers, Ligunds whose properties are significantly influenced by these
factors are usualy Lermed "complex liquids”

1a complex, as well ag in single Tiquids, # high molecular nobility 1s typteal for
tho Tiquid state, actualy Uhis statement should be made mare specific siuce iw a
ven Tigutd we may have dagrees of retdam shose dyaanic time-vangas differ by
several anders of maghilude, Thus in macromolecular systems some of the intemmoTecular
degrees af freedom may 11a Jn the picosecond to nanosecond tine-range whereas others:
imolving for exanple large-scale cooperative motions, my He in the tine-range of
seconds. Aleg Higuid crystals display rather fast rotational nations around the Tog
relecular axis, While retattons of this axis wT] be cooperative and uch slower,
Rotational motions, which have tine scales uiffering by orders of magnitude, geverally
also have a quite d\ffereot character. In Fact rotations can be classified as
Inertially determined rotations, or a5 ratations whose rate is detemined by random
interactions with the snvironment. The latter case represents a specific type of
vandonly Fluctuating constvainL, controlling the rata of molecular reorientation, end
which can be quantiffed by the Intvaduction of an appropriate Frictien constant this
camecting the micrascopic to the nathenat ically more tractable macroscopic
descriplion. Me also often daseribe rotational apdes on the nolecular level by
Afferent gore spacttic types af constraints, like for exemple entanglenents, or by
the cooperative nation of several qolecules. Th view of this variety af rotational
faodes, the experimental techniques to study then, and the theorétical franes to
describe than also display a large variety. Thus whila inertia controt ed rotation
generally lies in the picosscond and subpicosecond time seale ~ depending on the
molecular nonent oF tsertta ~ viscosily coutrollad rotation may extend fro the
picosecond tine scale dom to racrascoptc times, depending on the molecule, the
articular degree of freedan considered, and the viscasity af the Hquld. In order to
sludy experimentally the whole spectrun of rotation’l motions we mist use several
‘techniques fron those pretently avatlable, Honever, despite the Fact that alnost the
entire tine-range from the fentosscond to the mieroseopte renge are covered hy
aopropriate experinents, Uhe infaraatton given hy all these techniques is usually of 3
different type, and usually precludes simple extrapolation fron one ta another. The
sana situation applies Lo theory, where the Lackniques used in dealing with different
kinds of motion are quite different. Ase eolecular dyuanics cimulation faces sin'Ta™
problens, sinca x similation which is commonly ased in the picosacend tine-range
canct simply be extended to a slover tine scale unless adequate algorithms are
developed to cope with the discrepancy between the different tine seales and the
Finite capacity oF computers.

nh preparing this volume fer publication we wish to express aur gratitude to the 7°F
of the University of Bielefeld far providing the (Inaacial support for the prodect
“Conplax Liquids". We are grateful to the staff af the ZiF, in partieular to Hs.
Hoffnann vho expertly handled the organization of the mesting. Ue are also very
pleased 10 achowledge the expert assistance of Wrs..L. Jagerlaaer in the preparation
Of this voluna, and Tor her excellent typing of Uke menuseript. Oue of us (RAP) wishes
to acknowledge the “Alexander von Huybold-Stiftung” for a "Senlar U.S. Scientist
ura

Biclereld, October 1957 ‘Thomas Dordt er
Robart Pecore
Cconcenes

2. Kiyvelaon
VUTATTONAL COSBLATION TIMES FOR SHALE MOLECHLAS AN LuguHES, 1

(601, Lefekaum, ¥, Gaiamint and M. Agusde Gore
STATISTICAL STUDY OF FREELY ROTATING ASF TRIC TOP NOLECELES. CASE OF
PLANAR TOPS. sree cso ceeritiontsssissnnetsantstensavescesselS

J. Mevonnedt
TRELIGATION OF RIGID AND (OR-RICID MOLECULES 1M CIOCNS

4.0, teres
UE PEON OP ANNORAL, TTION OF MOLEGULES OTHE LIQUID as S220 FR NM
RELAXATION STCDTER : : : a

COMPARATIVE STCUL OF MET ECULAR ROTATEON AS STUDIED BY TRUM LICHT
SCATTERING, FLUDIDSCENCE ATTSOTROPY DECAY ASD RAMAN BAIDWIDE ANALYSIS... 67

1.0. Freed
WOLEGILAK ROTATIONAL TENANTS AN ISOTOPIC AID ORLERD FLULER SACIAD BY HR. 89

1D. Frankel
‘GHEVTER SDELLATION OF FRETRANGITIONAL PARANA Iv AAED CORE MOTELS FOR
Tract CHYSTAS. Sete hisestaneess eA

K. muller and 6. rathe
MOLECULAR GHEE AND ITMAKICS OF LYOUID CHYSTAL TOLMGRS SICWTED BY MCLTIPULSE,
Hea He TRS m

‘7a ELASTLC TRIMEBELL TEL FUR DURANCE OF STIFF CATES. 192

Kc. Spears
AOFSTIOM OF LANGE ROLLIMLAR 1048 AND TRANSIENT DIELECTRIC RELAXATION EFFEC. 208

Rod Leta aod Peene
DRRATCS CE SOFTRTGKD KACAWMOLCUES LA DILATE SOLUTION: STUDLES OF DA
RESTRICTION FRAGIENTS. : co

%. Spices
SLOW AND UL7HASLON ROCANTONAL NOTING OF MACOWLETIIS IN THE VICKIITY
OF THE GLASS TRAYSITTON AO TH DTQUIL QASIALLDNE POLLTERS a8 REVEN ED
FY PUTA DEUTER EO ann at
ROTH-LOVAL CORRELITIOS TIMES #95 SHRLL FOLECULES 15 LIQU=OS

Daniel ined son

evtment of Cheniscrys ariversity of California
os tegeles, UF S0Nz8 7 ISA

lig article 4s a summary of ay late g'¥en at the conferences *t ineTudes things T
said, things { wanted co sey, Un'eys thel I stuuls have sais, and ourhaps sore ratngs
tha: L swuld ao: havo cad, Ibe presoncation 1a5 been mol’Tied as a result c# <Is-
cusstons a% the eonfercree, partailarly tr racpanse tn comments by 4. Fixnan

3. Freed, K. Speers ate Th, Jorbulller

wT] feces on the votetional mavten oF oma¥] molecules. in Higuids. Tris 7
conpare: to all other relevent molecular wet uns, ution iy equi

tion iy efton "slo
talent t sayiag that rotaciont are arkovlen or Aiffustonal, Ie thie case tae cove
lation fenettoe few a earmal zed sakerical Raraoric, Yyy

with a decay tne tq, (7 broed seme 4 Con idertity tie classes of exponevitel vasa
tticral relanation in licuids: ane wife 19 doi“zstonsl 10 that ‘he antion takes lace
via sual] vandom angaler Jos, ane the other #1 wich the wolacule rezates quite
rapidly but not frequcatly eceuse tost of the tine 12 is held in an ctexTacery wel]
watch itself Teosens sp only tnfrequentty “11. This Tattar wobion cnevesponds <2 van
um Terge angular Jums; alttough for this ution tye sav decay acde does ivectl ep
paar ta se eupmential, the Mbratisnal mdes are irpartant and give cise to an zp
peceiable Ugh “requuney rutssional speckran, Zt is Tialy Ul the Vege angular Jumps
boucone ineracs ingly imertant at high viscos’ty. iether or rot che Lior 13 exis
noasial, we can aluays cefine a conrelabior tae (21

cord), relases enyzrentially

seo Faery a

dere + repregarte an couiTitrium average, The stray u* the furetTonol Surm a”
the relastticn proccss smi its descripston tm terrs of dymarical pracesses is an in-

torestieg one, but one which we stall consider anty serfuncterily.

fren che mast atviking features of qolecular rotations ir Viquics 18 the fact
shat tye rutationsT correlation Line obeys a fon o” halden's rule, te. 1% is Wear
In (nil), wore n 16 the coefficient of shear v'ccssity and T te texperatere [2]-
+ fs net hare to firs deviations from this vesult, aut s2 much sueeces hos been

raild by proCltgato te ecard “t as re of

sehretes otc U's relabionsh’p thak 1

Suppor led in pats sy the Sational Science Fusieat on chreuyh grart Wo. CHE-o-C1UI4,
tre undorptonings of 2 sheo~y af walecular ratacions #1 Tqutae, Hore aroctsely, one
finds that [3]

seats? 2)

inure A ane of ane nelet!vely indeperdent

# Leaperatare, and prssibly af aressure
(See Fig. 2.) There is still considable uncerte“nty about ste -wleeuler uria a of
this relav’on [4], end ¢ shel] say a ine words abuut tis. There eve als cascs where
line Joviet' ons fro1 this axpross an are considerable, “ou gueat ta se "ennved. and it
5S Mese cases witch, 1 zoliews, are parltesTarly "interesting

Kg

Gyr) 10%epe

2) SubsTip (C0215) at,
STip>(CDEN) 2 HSC goa
2

es. (VT). Lires thrcugh wer‘sunzal guise, uecrapslaled 0 20°09
oy! $00'Eq, (2). Plots of expovimortal scints can bo found Ah Reference [7]
in exetRereveneas ven Unie {Hy} Delon.

ney. Sieetia. (i)

3 ieailanzig stip 2+ smnernis teulvatert to CULL y. Ox

2 aacusted as ie (a).3

ig? she) aay
fe) CHS €EME(C NgTg. e . (1
3 eat. {very T). Boo. Yewer Here, J. chem. Phys. 60, 1865 (2978)

Hy Meat! Nooy TH TE! tw, thy Gattaglia and Bei, Haddor, Hol, Phye, 35, 2578
(1g93" alse RI. Wold, Sa ports and aby 7014, &y Agar Rosen, S497 (1976).

[99 CH1e an atiares. foanes 1). glia. ane Pd. Madden, "oi Flys. 35,
ea. (197

Ho) CiLisé in isluene, ces Ph FB.
2903 2980)

orving end P.S. PaiTTips, J. Chom, 7hys.
before proceeding, “t seems nerthoht le to respond ts a question posed by Har
shel] Fhenars why does ene care ruet abnu uslceWer votactone? There is, of course,
ntarest i mlccular rolaLivis #6 4 phonuweron i its om rght, but aerhaps tt *6
true tha it hos boon aver-exantned and that tre ron insights develope: over she gaat
‘years have been rather meager, Hnwees. 1 xeTiove that a coud uacers:ard™ng 0” wlu-
cular rutazfone, end ir porsicver of tw relatlorshia 4 Ey. (2), con be use“el “n

fdert!fyirg ocher ralecutar processes tr Viquics. Waleesla> wotatns oan ceres as a
rather serstLire pmbe af ablyorlar ijamtes avd waleevlar structure, swe wee 50 Uhm
Learslaticral mtion. ‘mu cany Unersforc, teke Une punt of view He: behavior suet as
‘that predicted by Z9, (2} is an seme vespects “universal* end, “f 2 may visk 3 controw
Versial statenert, “un'nteresting", but that cev-ations tvom Eq. (Zi een yleld “tae
esting® spoe'Tig Information about the sysvem usr study. Wta chic as mstivac‘an,

it is useful so understend Eq. {2} 2s thoroughly as pusetble, to anderstead sore of
sae general ortectples hich underlie 1s and sour of the geaeral pronoena “hat a1
Tend te deviat‘onss ane can tier subtract ost tre “uninteresting universal asaacts
of the prohen, and if tacre is en *abprectezle* remainder we can associaze “t with
specific “intgrestirg" prsrovona such a5 solvation, HyWoger-bondlag, aygrogalive a
ther motnesla~ resrvangemen:, I s1al say more abact this Tater.

The Saramter fin fg. 12

In hewednm’e Uvorivs uf molecular vulat’ons, the -? term ir Ey. (2) °s missing
The Stokes-Einsceic-Debye theory [£ vwdels a rotat'ng molecule as a rolat‘ng sphere
tna conttascus, acmgencotls “Ids i135 @ tednodymarie Ciwuey ard i: yields

Ne ataiedig!!, where y 1s tre molecular volme, ky, the Bsltriage conctart,
and the ohder of the rotational function being studied, Parric 161 extended the

hovey Uy ullipsotdal budiess tie Factor & i Uy theury i auguenter ey yecwelel-

col faccor wriet is ane far a sprers and ‘nereasus with increasing aspherieity (7
Tose theories ansame stick buuteaey cand vices at Ute suetace uf the “tacaed” par
ticles cvis mars taat the “rst layer of Fluic sticks te tre surface, bu: cHs is rot
ouivaloat Le bene fide solvaLior becayse tao Mutd molecules are taf" tostnal in
size. (See Fig, 2] Ho and Zoan2ig [8] extender the teary te sIip boundary conditions;
for & spncre Ubsre fy then 2 Fneraclige between Uw tagged parstele ard the “Tu'A ¢
chat 5, =, but rotating non-sptorieal particles tazereet by oushing [utd astde.
(Seo 1°9. S) Gee con convev‘ent ly express Aas [5,6]

fs ets 5)

ere fig a supe factor arsociater witn etek zaundary conditions, and © fe 4
factor depardny spon atape 212 bounsery eced'tiow, “21, ev 3g tec.

Hon should che formula asove 2= used? Ono car medel 216 wolecclar stapo and
‘ae ap accurstely 49 poss" ple, and ore edn then epleulate 8 for sath etek and stip
€ Hydrodynamic flint 1 Hydrodynamic Istick)

dl Actual slip with

€) Sovation [superstick) protubewrees
tick

Ligure 2+ Boundary cond” ers (Brownian particie)

ie
3
a} Slip-Nonspherical

b) Subslip- Nonspherical
covsinvous mesiuay hysredynamic #143
marly fee potet!on

1 solvent aolecte

Ligure 5: a} §

1 Leege solve me

ules

souncary condtions (78). Unual’y une 16 Tess anbitioss and replaces she eset: shape
Site an equivalent sphere & for ahisn Acar veedily he obsatred “rom Uw Perr'n fare
rmulaa for stick and freq the i and Zeenzig Laz'es for siz bouiory eanditins. O°
fenirse, for a spherical tzp malecule 2 for relabiuns uicer sTip boundary condi tons
thou: Coy Hkis, LM abpruaeh is irva' “4, and ove must irelede she “knoD3" 6° prs-

tuberarcas tha: Jut a2. theresy desbroy'ny tho cyTinirigal symetey. (See Fig. 4.)
Furmlas unis: whch enable ws to obtain vasslts easily fur w weciu'y of hign symmetry
steps [7,9]. Sut iL is rol ccwersting merely to state that the hovecéey condiziore
are slips a2ick ot inbetwean. We senc a hatter pict re.

alEquivolent Sphervid
(continuous solvent]

Na slip resistance

bj Protuberances
(continuous solvent)
Slip resistance

<] Protuberances
(maleculae solvent]
Liltle resistance

C

Figure 4: Yodels for barzene, £1ip boundary conditions

‘2 fons that on mest coves, for aml] mv ecules & is conciderab’y tess
tran cgneted “rom stice boundary conc-t-ans;and eather Close to that expected From
S¥ip boundary concitans, (See “ig. 1.) Tor large arovnien particles, howyer, stick
hncery cond iow seam Wu hols. One cen rationelize thece results by acsum'ng s1°p
boundary cord tions and focusing oh “Ae “lative sige of tre tagged mo" ecule to the
so'wurLmulecu es a5 9 sigrificant factor: calyent acleceles “Towing over sacth sum
faces behave Vike a ‘9° ipping® (Ividhhue f Une surface tas cracks and protuzerances,
and i the selvont wo" vcules ave sufficiently maT, cher taey Mey make much better
cortoc: wits che surtace than atzected

jv sphere «ay appear vey rough lo stall sslvenL mulewules, and thougy sI-p azundcey
conf tions may be appracr‘ate, they are sliz beundary canditisns “or 9 rowsh. rather
‘tar far a saat sphere, 2 ecedisier wnica is equivalent to tick boundary conditions
fur a sincth shire. {See Tig. 2.) Tkes i one ignores the details af molervar sapes
uw vould expect s1¢p boundery condi tiens to pa'd uteneyer co" vent acleculas ave com
povar"e to or Targer Unen the ‘agged cart cle or the protuberarcus cr the tasaed par~
ticles, sve one wau'd expect scick cord-tions "f tie reverse weve cro. [IMs picture

a kmoth Surtaee. Ierefune, & Tarde Brow

ig comrect. we vosTdy in or mcisle yet gers ible rosulls by colzeTaLing corpelat‘on Lime
itr sp courdaxy conditiers avd realist shaves. In seme cazes, however, one vight

et coore™ results qth rea'fstic that wilt amvclhw! surfaces. secon se the hydracynamic
sears assume “ninites imal satvart walaciTes thet can flaw i976 any wo ecular crack,