Institute of Chemical Technology and Polymer Chemistry
[email protected] http://www.itcp.kit.edu/wilhelm/
Introduction to Polymerscience
Prof. Dr. Manfred Wilhelm
private copy 01/2019
KIT – Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft www.kit.edu Content
1 Introduction 1 1.1 Literature 1 1.2 Definition, materials 3 1.3 Definition, polymers 3 1.4 History and nomenclature 12
2 Polymer chemistry 13 2.1 Molecular architectures 13 2.2 Separation/classification of polymers into classes 16 2.3 Typical monomers, polymers 19 2.4 Synthesis 28 2.5 Carothers equations 30 2.6 Kinetics 31 2.7 Size distribution in linear polymers for step reaction 34 2.8 Chain growth reaction, e.g. radical 38 2.9 The ceiling temperature 42 2.10 Suspension polymerization 43 2.11 Emulsion polymerization 44 2.12 Ionic polymerization 45 2.13 Anionic polymerization 47 2.14 Kinetics and molecular weight distribution of ionic polymerization 49 2.15 Copolymers 54 2.16 Coordinative polymerization 57 2.17 Constitution, conformation and configuration isomers 58
3 Polymer physics, physical chemistry 62 3.1 The lonesome chain 62 3.1.1 End to end distance, contour length 62 3.1.2 Radius of gyration 64 3.1.3 Random-walk and Gaussian chain 65 3.1.4 Entropy-Elasticity, basic idea 68 3.1.5 Deviation from simple-statistics for end to end distance 70 3.1.6 Kuhn segment 72 3.1.7 Persistence length (“how stiff is a polymer”) 73 3.2 Polymer physics of melts 75 3.2.1 The reptation model 75 3.2.2 The amorhous state 79 3.2.3 The crystalline state 88 3.2.4 Kinetics of crystallization 100 3.2.5 How to reach 100% crystallinity in a solid polymer 102
4 Molecules and characterisation 104 4.1 Distribution of molar mass and determination of molar mass of polymers 104 4.2 Experimental determination of molecular weight and distribution 108 4.3 GPC, gel permeation chromatography 110 4.4 Ultracentrifuge 113 4.5 Light scattering of polymer solutions 116 4.6 IR-Spectroscopy 126 4.7 Mass spectroscopy 135 4.8 NMR-spectroscopy 149
5 Engineering properties 160 5.1 Mechanical properties 160 5.2 Dielectric properties 166 5.3 Processing of thermoplast; extrusion, injection molding, calendaring 169
6 Special topics 6.1 Polyelectrolytes 176 6.1.1 Definition, examples 176 6.1.2 Theory: Poisson-Boltzmann, Debeye-Hückel, Skolnick-Fixmann-Odijk 177 6.1.3 Experiments 183 6.1.4 Application: super absorbing polymers (SAP) 184 6.1.5 Application: oil production 187 6.1.6 Conclusion polyelectrolytes 189 6.1.7 Literature, polyelectrolytes 190 6.2 Spatially heterogeneous systems, e.g. blends or blockcopolymers 191 6.2.1 Definition 191 6.2.2 Why does the introduction of heterogeneity make sense? 191 6.2.3 How can heterogeneity be achieved 192 6.2.4 Theory of mixing, Flory-Huggins theory 196
7 Appendix 203 Staudinger - Nobel Lecture, December 11, 1953 Ziegler - Nobel Lecture, December 12, 1963 Natta - Nobel Lecture, December 12, 1963 Flory - Nobel Lecture, December 11, 1974 De Gennes - Nobel Lecture, December 9, 1991
Material classes, development and history of polymers 1
1 Introduction 1.1 Literature: 1) History: - Polymers, The origin and growth of a science, Herbert Morawetz, Dover Pub. 1985 2) Introduction: - Große Moleküle, Hans-Georg Elias, Springer 1985 - Introduction to polymers, R.J. Young, CRC Press 1991 3) Chemistry: - Grundriss der Makromolekularen Chemie, Bruno Vollmert, E. Vollmert- Verlag 1988 - Makromolekulare Chemie, Bernd Tieke, VCH 2005 - Makromolekulare Chemiei, Lechner, Gehrke, Nordmeier, Springer 2003, incl. CD - I.M.G. Cowie, V. Arrighi, Polymers: Chemistry and Physics of modern Materials, CRC Press, 2008 4) Polymer and engineering: - Material science for Polymers for engineers, Oswald/ Menges, Hanser 1995 - Polymermechanik, Schwarzel, Springer 1990 5) Encyclopaedia, dictionary: - Concise, Encyclopaedia of polymer science and engineering, Kroschwitz (editor) Wiley 1990 - I-IV von H.G. Elias, Chemie + Physik + Industrie + Anwendung,Wiley VCH 6-te Edition 1999-2003 6) Physics: - Physik kondensierter Materie, G. Strobl, Springer 2001 - The physics of polymers, 1995, G. Strobl, Springer 1996 - Polymer physics, U.W. Gedde, Chapman & Hall 1996 7) Characterisation: - Principles of instrumental analysis, Skoog, Leavy, Saunders College Publishing 1992 - Polymer Charakterisierung, Arndt/ Müller, Hanser 1996 - Polymer characterisation, B.J. Hunt, M.I. James, Blackie academy 1997 i Title is misleading; covers very detailed all aspects, in German.
Material classes, development and history of polymers 2
- Polymer characterisation- physical techniques, D. Campell, R.A. Pethrick, I.R. White, Staley-Thornes 2000 - Spectroscopy of polymers, J.L. Koenig, Elsevier 1999 8) Polymer technology: - Handbuch der technischen Polymerchemie, A. Echte, VCH 1993 9) Internet: - http://scholar.google.com - www.vke.de (Verband der Kunststofferzeugenden Industrie) - www.pslc.ws/macrorg.htm - web.umr.edu/~mwlf/
Material classes, development and history of polymers 3
1.2 Definition, materials - Materials are synthetically or biologically built chemicals that we generally use due to there physical, dominatingly mechanical and chemical properties, specifically their 2 and 3 dimensional structure. - As a consequence: material science is inherent interdisciplinary: biology, chemistry, physics and mechanical engineering are interacting. - Currently, not only mechanical properties (module, T-stability,) chemical resistance), but also “functional” properties are more and more developed, investigated and applied. For example: magnetic ( storage of data), electric ( computer, CPU), chemical ( medicine) or optical functions are added - Materials can be classified as follows i. Metal (high, low density, conducting, semi-conducting, reactive, …) ii. Glass (organic, inorganic), frozen liquid iii. Ceramics (in general: inorganic, but crystalline) iv. Polymers (organic materials)
1.3 Definition, polymers: Polymers are high molecular weight synthetically or biologically built chemical structures that contain at least one repeat unit that is covalently bound and repeated. The dominant elements are C, H, O, N, Cl, F, S, P, Si,…
How much materials do we need (world wide)?
1990 => 510 9 people 510t9 , if one 1t per person and year
9 t kg Steel: 10year 200 person and year
Polymer: 60 106 t 12 kg year person and year
Al: 15 106 t year 3kg person and year kg Note: Germany 50-70 person and year
Factor 15 steel polymers, but: 78, g , 1 g Fe cm3 Polymer cm3
Material classes, development and history of polymers 4
6 Polymers 2002: 227 10 t year Note: There is an empirical correlation between price and production in general price ~ production-0.4 Factor 10 in production factor 2-3 in price
Material classes, development and history of polymers 5
Source: Schwarzel 1990
Material classes, development and history of polymers 6
Use of polymers in our environment: Nature: construction, storage, clothing, protection Food: carbon hydrates, proteins
Packing: bags, storage tanks (PE for H2, full cell in cars) Traffic: super plastified concrete (1-5% polymers), security glass, belts, airbag, oil additives Clothes: wool, cotton, gore-tex® (teflon), polyester Cosmetics: hairspray Hygiene: super absorber, surfactants Medicine: dialysis, contact lenses, controlled drug release Optics: light conducting fibres, organic LED (O-LED), NLO (non linear optics) Electronics: Photoresists, primer for UV-etching, electrically conducting polymers
What do we want? - mechanical => high E, G module, low compressibility, M - low weight, low density - low price, P (For non functional polymers these properties are very important)
Additionally: - inert - non toxic - temperature stability - dielectric, magnetical, optical properties - easy to form and shape !
If we assume that the importance for a specific applications scales with a scaling exponent (e.g. MPabc,, ) We might generate a “figure of merit” (Kenngröße), F Ma Fabc0 ;,, Pcb If price does not matter (e.g. space application, formula 1, professional sports) Ma F b
Material classes, development and history of polymers 7
Do not take this too literately!
Typical production (source: Nachrichten aus der Chemie 2004, p. 324):
year 2002: 227 106 t , Germany 20 106 t year year
polymer 6 t growth Production 10 y PE 56 (24%) 5,5% PP 32 (14%) 9,1% PET 32 (14%) 8% PVC 20 (12%) 4,7%
€ € In case we have an average price of 1.5 kg PE: 1 kg
Production330 109 € year t€ Assuming a business volume of 200 year and person in a company
16510. 6 people in primary production!
average production per person: 150 t year t Typical factory: 100000 1000000 year PE, PP, worldscale factory about 1000 people per factory
Why investigating materials “Knowledge is power” Francis Bacon (1561-1626)
Two examples: 1) Iron at times of Nebukhadnezar in bible (1125-1104 b.Chr.)
Material classes, development and history of polymers 8
Daniel 2
Material classes, development and history of polymers 9
Material classes, development and history of polymers 10
2) PE in WW II
Source: Morawetz
Material classes, development and history of polymers 11
Read this every year in “Nachrichten aus der Chemie“ or “Macromol. Chem. Phys.“ around Feb. or March
Material classes, development and history of polymers 12
1.4 History and nomenclature: Polymer: greek: poly: many; meros: parts Plastic: Polymer + additives Natural rubber: Kautschuk (German) from Cahuchu = “caa” (wood) and “o-chu” (tears) in the native South American language. The word rubber originates from first use to erase lead pencil marks from paper by rubbing Rubber trees first mentioned 1516
Short history: 5000 b.Chr. cotton (mexico) 3000 b.Chr. silk (china) 2000 b.Chr. bitumen (sealing of boats) 1500 a.Chr. rubber 1832-1838 F. Lüdersdorf + Charles Goodyear => vulcanisation of rubber via sulphur 1870 cellulose nitrate by Isaak Hyatt and John Hyatt films, packing, first thermoplast 1907 Bakelite, Leo Baekeland, phenol-formaldehyde resin, fist synthetic thermo set 1924 Hermann Staudinger (Freiburg, Germany) proposed polymers as linear chains built of covalent bonds; this concept was first heavily criticized by colleagues, Nobel price 1953 1930-1940 Wallace Carothers at Du Pont worked on Polyester and polyamids (Nylon®) 1930-1950 H. Staudinger, Nobel price in 1953 1961, Ziegler Natta, Nobelprice polyolefin catalysis 1974 Nobel price for Paul Flory (chemistry) he worked on physical chemistry 1991 Nobel price for De Gennes, liquid crystals and polymers (reptation theory) 2000 A. Heeger, A.G. Mac Diarmid, H. Shirakawa,, Conducting polymers 2005 Grubbs, Chauvin, Schrock, Metathese
Polymer chemistry 13
2 Polymer chemistry
2.1 Molecular architectures
One monomer: Linear
Comb
Branched
Network
Different topologies (conectivities)
g Typical molecular weight: 50.. 000 500 000 mol , if e.g. made of CH 35. 000 units CH units 500 kg . 2 2 mol “In a plastic bag their wont be two molecules with the same architecture.” CC ;; CC CC i 15A,,, 14A 13A
15A. C 1., 5 A 35 000 units C C contour length 5,. 400nm 5 4 m
i 1A 1010 m
Polymer chemistry 14
Two monomers ( constitutional isomers, see also later)
A: B:
Statistical copolymer:
etc.
Alternating copolymer:
etc. e.g. polyester or polyamid, but normally not called alternating
Tapered copolymer (gradient in the polymer):
P(A) P(B)
x x Gradual change from “A” to “B”
Block copolymers:
Very frequent: phase separation, spatial heterogeneities, morphologies
Grafted copolymer (germ. Pfropfcopolymer):
Polymer chemistry 15
both topology and morphology! Blend:
+
In general, blends are phase separated, typical size is
A B 110m B
Polymer chemistry 16
2.2 Separartion/ classification of polymers into classes
Polymers
Thermoplast rubber Thermoset - Linear or (germ. Duroplast) branched - Can be melted
Semi crystalline Amorphous, non crystalline
Less than 100% Linear and Slightly crosslinked Strongly crosslinked,
crystalline, branched network dense, 3D network typical: 20-50% structures Elastic properties, Rigid, intractable Mostly linear Irregular stereo e.g. can stretch Degrades rather than
topology, low chemistry Very mobile melt amount of Examples: polymer => glass Examples : branching Polystyrene transition Phenol-formaldehyde
Stereo chemistry PMMA Cannot melt resin is regular (Plexiglas®) Examples: Urea-formaldehyde Examples: PC PI (Polyisoprene) resins
Isotactic PP (i-PP) PB (Polybutadiene) Epoxy resins HDPE (high density PE)
Polymer chemistry 17
Remark: Crystalline material is generally more dense than amorphous material (typically 3- 10%), if semicrystalline material is exposed to light, scattering will happen if crystalline size is in dimension of (wavelength of light, ca. 400-800 nm)
material is scattering, white not transparent.
l l : size of crystallite
l
Please note! For Polymers crystallinity does not mean that the crystalline part is not mobile/ moving! Most polymers are packed in Zick-Zack or helix shape. It can be, that the helix jumps up to CH CH O 100001s (e.g. PEO 2 2 ) at room temperature (poly-1-butene
1 ca.11s )! This motion is like a stochastical move of a screw in a threat The motion is not caused by a coherent move of the helix but rather by diffusive motion of a defect along the threat.
Note: about number of different molecules for a statistical polymer Assume: 20 different monomers (e.g. amino-acids in nature) M 100 g With n mol (typical) M 100, 000 g Polymerize to a polymer with n mol n = 1000, No, molecular weight distribution assumed, no polydispersity! Only linear topology! How many molecules are allowed?
1 German: Schraube in Gewinde
Polymer chemistry 18
330 201000 2 1000 10 1000 2 3 10 1000 10 330 10 1000 10 1330 3 210 10 if molecules carry information, basically infinite amount of information can be encoded! Please compare this to other large numbers: e.g. number of water molecules on earth: Earth surface: O4rr610m 26, (6000km)
Assume 1km H2O: h = 1000m
2 V 4 r26331233163 h 4 6 10 10 m 10 36 10 10 m 36 10 m O 10 1m3 50. 000 mol MHO211618: gg 20 since n2 mol mol
23 1mol 6 10 molecules
Therefore
mHO3 2 N 3610 16 510610 4 23 10 46 HOearth2 ,
Polymer chemistry 19
2.3 Typical monomers, polymers
a) Ethylene H H CC HH H2C CH2 Three different ways to show the same. Polyethylene (PE)
H HH H HHH H C CC C CCC H H H H H H H
CH2 CH2 n n : degree of polymerization
CH2 why not 2n ? not the chemical building block Use: Moulded objects, tubing, films, waste bags, electrical insulation, low dielectric loss Several subtypes (no need to memorize): - HDPE (High density PE) - LDPE (Low density PE) - UHMWPE (Ultra high molecular weight PE) - LLDPE (linear low density PE) - M-LLDPE (metalocane, linear low density) € Cheapest polymer, prize 1 kg (year 2005)
b) Propylene H H
CC H H2C CH H C H H CH3 Polypropylene (PP)
Polymer chemistry 20
H H H H H H H H H
CCCCCCCCC
HCH3 H CH3 H CH3 H CH3 H
relative orientation is called "stereochemistry", e.g. atactic (a-PP), isotactic (i-PP), syndiotactic (s-PP)=> later changes drastically e.g. melting point! hinders crystallisation (=> a-PP) => later
Use: similar to PE, lighter, stiffer, very high growth rates in production over last 20 years
(+8 % y !)
c) Tetrafluorethylene F F CC F F Polytetrafluorethylene PTFE F F F F F F F F
CCCCCC CC n F F F F F F or F F Use:
Mouldings or films, high temperature polymerTuse 350 C , excellent electric insulation, low sliding friction, expensive, tradename: Teflon®, also used for Gore- Tex® membranes d) Styrene H H C C H
H2C CH H CC H C C H C C H H
phenylgroup
Polymer chemistry 21
Polystyrene (PS)
CH2 CH CH2 CH CH2 HCHC 2 n
or Question:
Why not? CH2 CHH C CH2
n/2 Head-head polymerisation
Use: Cheap moulded objects, amorph, transparent, copolymerised with butadiene
to make high impact PS (HIPS), expanded with pentane to make foam (styropur® => BASF)
Note: atactic PS is softening at ca. T90Cg (glass-transition temperature Tg), if
stereoselective catalysts are used: Tm 260 C!! T 150 C melt
e) Methyl Methacrylates (Ethyl Methacrylates, Propyl Methacrylates, Methyl Methacrylate) in analogy, less in use
ester acrylic acid COOH are called acrylates, e.g. ethyl acrylate 2
ester methacrylic acid COOH are called methacrylates, e.g. ethyl methacrylate 3
2 E.g. ethyl acrylate (compare: sodiumNa chloridCl ) COOC2H5
3 E.g. ethyl methacrylate COOC2H5
Polymer chemistry 22
CH3
H2C C COO CH2 CH3 poly methyl methacrylate (PMMA) H C 3 CH3
CH2 C CH2 C C O C O O CH O 3
CH3 Question: What is the more rigid structure acrylates or methacrylates, which should
have higher Tg (“Brittle-point“)?
Use: Amorphous, transparent sheets and tubing, more expensive than PS, airplane windows, tradename Plexiglas®, Prespex®, Lucite®, Diakon®
f) Vinyl chloride
H2C CHCl Poly(vinyl chloride) (PVC) H
CH2 C Cl n Use: Records, waste water pipes (very inert), rain coat, bags for blood, floor, toys (=> problem plasticicer e.g. dioctyl phthalate)
C2H5
COO CH2 CH C4H7 Dioctyl phthalate, (DOP)
COO CH2 CH C4H7
H5C2
g) Vinyl acetate
Polymer chemistry 23
vinyl H2C H H2C CH2 C
H3C COOH O CH3 acetic acid C
O Poly (vinyl acetate) (PVA;PVAc)
CH2 CH n OCO CH3 Use:
Chewing gum ( Tg body temperature!), adhesive, coatings, copolymer to make superplastified concrete Remark: If ester is hydrolysed in PVAc the result is poly (vinyl alcohol) why not synthesize via HC C H ? CH2 HC 2 OH n OH , exists also partly hydrolized (“Mowiol®” former Hoechst) Hydrolysis, specifically called saponification in english (“Verseifung”): split of an ester function via the addition of water into an alcohol and carboxylic acid, invers of esterification, e.g.
O O H3C CH2 C + H2O H3C C + H3C CH2 OH OH OCH2 CH3
acetat ethyl acetic acid ethanol exercise: draw PVAc and PMA [poly (methyl acrylate)], look for similarities and differences HH HH
CC CC n n H O O H C C O O
CH3 CH3 PVAc PMA
Polymer chemistry 24
h) Acrylonitril
H2C CH CN
COOH CN
acrylicacid nitril
Polyacrylonitril (PAN) H H H H
CCCC CH2 CH n H C NNH C or CNn Use: textile fiber, Orlon®, Acrylan®, superglue: polycyanacrylate CN
H2C C
C O CH3 O 2-Cyanacrylacidmethylester
i) Ester O
R1 CO R2 e.g. Ethylene glycol:
HCHO 2 CH2 OH Terephthalic acid:
HOOC COOH
Poly (ethylen eterephthalate) (PET) O O
CH2 CH2 OC C O n Draw structure: PBT poly (butylene terephthalate) Polyester in general: O
R1 COR2 n Use: textile fibres (“polyester“ mostly PET), bottles for soft drinks,
Polymer chemistry 25
sympatex® membranes j) Amide General structure: OH
R1 CNR2 Polyamide OH
R1 CNR2 n e.g.
hexamethylendiamine sebacic acid NH2 (CH2)6 NH2 + HOOC (CH2)8 COOH H H OO
N C (CH2)8 C N (CH2)6 + n H2O n Nylon 610. amin carboxylic carbons, carbons incl -COO carbons
Nylon 6: O
C O CH NH 2 NH (CH2)6 C n H2C CH2 CH2 CH2 7-ring (not extra stable) Very common: Nylon 6.6 draw it! Use: textile fibres, industrial fibres: ropes, fishing net, air-bag etc.
k) Polycarbonate (PC) general structure O
OC O carbonate most common: Bisphenol A + Phosgen
Polymer chemistry 26
CH3 O
HCO OH C + Cl Cl CH3
CH3 O
OCO C O n CH3
Amorphous, non crystaline, colourless, high Tg, tough
Use: like PMMA, CD’s are made out of PC.
Polymer chemistry 27
Source: Lechner 2003
Polymer chemistry 28
2.4 Synthesis Two main types: - step growth, polycondensation, e.g. polyester or polyamids, stable intermediates during reaction, elimination of small molecules - chain growth, e.g. olefines ( CC), free radical polymerisation, no elimination of small molecules, reactive intermediate
2.4.1 Polycondensation => step growth Remember basic chemistry,e.g. for ester
H3C COOH + HCHO 2 CH3 H3C COO C2H5 + H2O acetic acid ethanol ethyl - acetat
+ - Na Cl
+ analogy: C2H5 H3C COO- chemically not correct
+ - sodium chloride Na Cl
Note: 1. water is produced => need to remove it, H , solubility, permeability! 2. products are called ester
To get a polymer we need two or more functional sites at each molecule
CH2 OH HOOC COOH + HOOC C O (CH2)2 OH H2O HO CH2 + O
Simplified chemistry: + +
each is a bifunctional monomer => linear polymer: bifunctional monomer needed
During reaction, oligomers (2 + + Polymer chemistry 29 + In case of we need equimolar mixtures! Small access will stop the polymerisation, since all endgroups will either be hydroxy (-OH)- groups or carboxylic (-COOH) acid! Solution to this problem: n x + n x n-1 Chemically: HO CH2 COOH n -hydroxy-carboxylicacid ”end” Reaction: monomer polymer + H2O We need to remove condensate (e.g. water, methanol,…) Ringformation is possible or Note: In early “polymer days“ people assumed that polymers where dominately ring molcules. Polymer chemistry 30 2.5 Carothers equations p : extend of reaction or probability to react number of groups reacted p This can be determined easily, with spectroscopy or titration, number of groups initially therefore important quantity N0: number of groups initially N: number of groups at time t NN0 N p1Np1N0 NN00 N: number of molecules present after a certain extend of reaction 1N number of groups intially 0 X 1 pN Number of groups at time t n Xn : number averaged degree of polymerisation 1 X Carothers equation n 1p e.g. if during a polyester condensation 98% of the groups have reacted (in “normal” chemistry one would say “quantitative”) the degree of polymerisation is Xn = 50 , the product is hardly a polymer! Consequence: e.g. very pure chemicals, very defined and quantitative reaction with no side reactions are needed. Polymer chemistry 31 2.6 Kinetics Definition: Kinetics studies the rate of chemical reaction e.g. RCOOHHOR RCOOR HO2 d R COOH dHO R dR COO R dt dt dt x: concentration of chemical x in mol or mol m3 l The rate of the chemical reaction must be a function of probability ( concentration) of the chemicals that take place in the time determine step (= elementary reaction). Please be aware, that the elementary reaction is frequently not the same as the stoichometric reaction equation! Furthermore, it is often assumed that the reactivity of the reactive groups do not change as the polymer is formed. e.g. elemantary reaction R-COOH+H-O-R + cat. R COO R H O cat. 2 H+ e.g. R-COOH These moleculesls have to meet d R COOH kR COOHR OHcat. dt molecules that have to meet, "educts" the "change" of concentration or rate of reaction k : rate constant for reaction Here reaction is catalysed via H+, protons e.g. coming from R-COOH RCOO- + H+ If no other catalyst is added self-catalyzed dR COOH 2 kR COOH R OH dt If RCOOHR OH is given, same number of functional groups and R COOH c dc kc3 (differential equation) dt dc kdt c3 Integration from t 0 to t t; c c0 to c Polymer chemistry 32 ct1 3 dc k dt c00 c 1 c ckt2 2 c0 11 2 22 2kt c0 cc0 c2 0 12ktc2 c2 0 Using Carothers equations: N1c 00 N1pc 1 2ktc2 1 0 1p 2 plot 1 1p 2 e.g. via titration time If plot gives us a linear relation self catalysed For same reaction a catalyst is added, so [cat.] = const. We have: dc kc' 2 dt [,]cat k `[OH ] [ COOH ] dc kdt c2 ct1 2 dc k dt c00 c c ckt1 c0 11 kt c0 cc0 Polymer chemistry 33 cc1 001ktc cc1p0 1 1ktc 1p 0 Plot: 1 1p 1 time If the plot gives us a linear relation the reaction is not self catalysed. Polymer chemistry 34 2.7 Size distribution in linear polymers for step reaction i H O R COOH H O[] R COOHi1 R COOH For (i-1) ester linkages If “p” is probability that reaction has taken place, then 1- ester bond : p + 2- ester bond : p2 + 3- ester bond : p3 + 4- (i-1)- ester bond next to (i-2) ester bond : pi1 Last bond has not reacted probability: (1-p) i1 Pp1pi If N polymer molecules ( monomers) are present, the number of molecules Ni with length i is given by: i1 NPNNp1pii (A) But N can not be measured, only N0 is known. Carothers (see chapter 2.5): NN1p 0 We can say i1 2 NNp1pi0 (1) There are two different and common ways to quantify the average molecular weight: a) number average Mn b) weight average Mw Mn: we “ask” each polymer molecule: “what is your mass?” and built the average, number average of polymer molecules Mw: we “ask” each monomer: “what is the molecular weight of your polymer” Example: 2 Polymers n4 n1 Polymer chemistry 35 41 M25, n 2 (1st momentum of the distribution) 44441 17 M34, w 55 (related to 2nd momentum of the distribution)4 MMwn , this is a general statement! (memorize!) mass of molecules of length i w , weight probability i total mass of all molecules M0: mass of monomers NiMi0iN i wi (2) NM00 N 0 (1) in (2) i1 2 wip1pi (3) For reaction p=0,99 w 0 xn i 00 3 wxiw 2 1 100 200 300 400 500 600 700 Knowing Ni and wi we can determine Mn and Mw. NMii Mn Ni i1 If the sample contains N-molecules NNi and NNp1pi , see eq. (A) 4 Side comment 22 nn th P(x) Px 1, xxPxdx ; xxPxdx ; xxPxdx , n moment x2 standart deviation 22xx 2; M w x Polymer chemistry 36 M i Npi1 1 p i M MM1pip 0 i1 n0N In mathematical textbooks we find (e.g. Bronstein) 1 ip()i1 if p1 2 i1 ()1p 1M MM1p 0 n0 1p 2 1p M1n xn See Carothers! M1p0 M i MwMiMip1pi1 2 wii0 2 2i1 M1p0 ip We find in math textbooks 2i1 1p ip 3 i1 1p 1p2 1p 1p MM M w01p 3 01p M1pw xw Weight averaged degree of polymerisation M1p0 M Often the ration of w is used to characterize the polydispersity (width of the molecular Mn weight distribution) sometimes called “heterogeneity index”, or PDI, polydispersity index M M0 1p1p 1 w 1p Mn 1p M0 M Memorize: For ideal (full) step reaction p1 w 2 Mn Note: Anionic polymerization M w 103.. 12 Mn Industrial samples up to M w 10 20 (starting from 1.03) Mn Polymer chemistry 37 In case we use functionalities f greater than f2 we can generate branched and networks (networks only if reactants are more than difunctional) structures. Functionality and concentration are the main control parameters, e.g. Monomers Interpenetrating networks (networks which were polymerized in another network), IPN Branched: Only if one reactant is more than difunctional. OH H C OH 2 CH2 HO CH C CH OH HC OH 2 2 CH2 H2C OH OH glycerol pentaerythritol f=3 f=4 Polymer chemistry 38 2.8 Chain growth, e.g. radical Addition reactions are conducted in three steps 1) Initiation via special initiator ( e.g. ester formation) 2) Propagation of reactive species ( e.g. ester formation since there every step leads to stable molecules) 3) Termination, side reaction of reactive species Monomers contain double bonds H R1 reactive species "attack" from this CCneeds space side H R 2 Examples: H2C CH O Ethylene: H C CH 2 2 PE Vinyl acetate: OC PVA CH3 Vinyl chloride: H2C CH Cl PVC H2C CH H C CH 2 Acrylnitril: C N PAN Styrene: PS Cl CH3 Vinylidene chloride: H2C C PVDC CH C O 2 Cl Methyl C PMMA methacrylate: O CH3 The three steps of the addition reaction Initiaton via radicals A radical is a reactive species with an unpaired ( paramagnetic) electron as denoted R . In chemistry a line e.g. CC is a symbol for two electrons CC Initiators form radicals in a controlled way via heat or electromagnetic radiations (e.g. light). Polymer chemistry 39 Examples: Peroxy or azo components peroxy: CO OC instable e.g. O O C O OC Benzoyl peroxide O O O C OOC 2x C O 2x + CO2 conjugated system makes radical more stable Azo: hv R NN NN R R R cis trans Compare NN (very stable) preformed e.g. CH3 CH3 H3C C NNC CH3 C N C N AIBN (2, 2 Azoisobutyronitril) CH CH 3 3 CH T 3 H C C NNC CH 3 3 2x H3C C + N2 C N CN h CN light or very stable heat Polymer chemistry 40 Propagation: After the initiation II 2I active radical IM IM1 If M is R1 H2C C R1 There are two possibilities R1 more probable ICH2 C 1) size R 2 2) radical is stabilized R 1 R I + H2C C 1 H R 1 I C H R2 IM M I M typical time 110ms “turn over rate“. 12 not index degree of polymerisation Again two possibilities for next step R1 R1 I CH2 C CH2 C R1 R1 R2 R2 I CH2 C + H2C C head to tail (more probable) R2 R2 R1 R1 I CH2 C C CH2 R2 R2 head to head Termination: - via combination: R1 CH2 CH + HC CH2 R2 R1 CH2 HCC HCH2 R2 X X X X Head to head Polymer chemistry 41 - via disproportion: can act as macromonomer R1 CH2 CH + HC CH2 R2 R1 CH CH + R2 CH2 CH2 X X X X The kinetic equation of the three different processes (initiation, propagation, termination) can be analysed and lead to the following expression Literature. MMn , the more monomers the longer the polymer 1 Mn 1 the less initiator, the longer the polymer I 2 M Mn 1 I 2 [I] : Initiator concentration, why inverse? [M] : monomer concentration The distribution is M w 1 Mn rate of propagation Where rate of propagation + rate of all other reactions Mw If kkprop rest then 1 and 2 , identical to step growth reaction Mn Auto acceleration If reaction growths/ continuous, polymer gets less mobile, solution becomes more viscous, the active centers do not meet any more rate of termination is reduced. Monomer and initiator still the same mobility. Reaction takes place normally (heat production exothermic!) As consequence: catastrophic failure (e.g. explosion, called Trommsdorf-Norish effect or gel effect) Solve the problem: − Dilute solutions, stop or slow down reaction chemically − Emulsion or suspension polymerisation Inhibitors and retarders: Retarder: slow down reaction e.g. NO2 for Polymer chemistry 42 Inhibitor: Stops reaction after consumption normal rate. Used for storage and transport, removed prior reaction (e.g. via distillation or addition of extra initiator) reaction Normal, ht inhibitor ft ht t retarder ft aht time consumption inhibitor 2.9 The ceiling temperature TC (=> recycling, e.g. PMMA) In case we have reaction kp (1) MMii1 M , for all i kp : Rate of polymerization We can also loose a monomer kdp (2) MMMi1 1 , for all i kdp : Rate of depolymerization For (1) we have the kinetic equation dM kM M dt pi For (2) we have dM kM dt dp i dM If 0 dt kkMdp p The constant kdp and kp are temperature dependant, [M] is assumed to be pure monomer. These conditions define the ceiling temperatuer TC : ceiling temperature Polymer chemistry 43 TC : Maximum temperature where polymer can be formed thermodynamically at dilute solution. Examples TC: Methylacrylate 493 K 120 C (recycle via destillation!), styrene 583K, methylstyrene 334 K 61 °C To reduce the problem of heat transfer two specific ways of radical polymerization are shown. 1) suspension polymerization 2) emulsion polymerization 2.10 Suspension polymerization E.g. styrene, vinyl chloride, methyl methacrylate Monomer droplet: size: 10 m 5mm! Shape: spherical pearl polymerisation Initiator is soluble in monomer droplet H2O Monomer droplet - stabilizer change surface tension and reduce coalescence, e.g. special polymers at interface as surfactants - reaction is “normal” and water cooled, high surface area helps to get rid of heat, no problem if droplets become viscous as long as suspension can be pumped - fire-fighter built in! - in real life discontinuously acting reactors (up to 200 m3 ) Example: Brita Filter®: pearl polymerized + sulfonated polystyrene (sulfonated for ion exchange) + active carbon Polymer chemistry 44 2.11 Emulsion polymerization Monomer droplet with surfactant (rare) I : Initiator, water soluble I : Monomer, partly water I soluble : surfactant (germ. : Tenside) Charged head Empty micell Micell + Micell + monomer polymer Called Latex At the beginning: - monomer droplet, 1m ca. 1010 droplets cm3 - empty micells, built of 100-1000 surfactants ca. 1018 micells monomer droplet, factor 108 cm3 - monomer in water + micells, factor 100 more than pure water - water soluble initiator starts reaction (e.g. K2S2O8) 2 SO28 2SO 4 The addition of monomer reduces solubility enters micelle - In the micell, all the monomer will be polymerized and reaction continues via diffusion of new monomer into micelle (shrinks monomer droplet). Typical size of product 100 300nm - Solid content can be up to 80% (multimodal distribution!) Polymer chemistry 45 2.12 Ionic polymerization Generally subdivided into cationic (positive charged) anionic (negative charged) general scheme: anionic: IMIM 1 anions start reaction, fast IMnn1 M IM growth, n1 Cationic: IMIM 1 cations start reaction, fast IMnn1 M IM growth, n1 Generally: - type of reaction depends on initiator, monomer and solvent. E.g. solvent can stabilize the ions and via dielectric constant, changes energy of the separated ions - often rapid reactions, high degrees of polymerization via low temperatures - control of stereochemistry ( isotactic, syndiotactic, 1.2 addition; 1.4 addition cis or trans) - reactive ends repel each other less side reactions IMnm IM Coulomb! very stable “living” polymerization Example for cationic polymerization H H + - + H ClO H C C H C - 4 + 2 3 C ClO4 perchloric acid, strong acid ion pair In principle three types of initiators exist: a) Proton donating molecules, acid b) Electron accepting molecules, “Lewis-acids” e.g. AlCl3 c) Positive charged carbons, “carbenium” salts Polymer chemistry 46 Technical important system: CH3 H3C AlCl Rubbery material 3 + C CH2 CCH2 trade name: H C n 3 CH ® 3 Oppanol (BASF) iso-butylene polyisobutylene 4xC+1doublebond H3C R1 C H3C R2 e.g. isopropyl alcohol (after shave) H H3C C propanol: H3C CH2 CH2 OH OH H C 3 Polymer chemistry 47 2.13 Anionic polymerization IMIM In case we would allow any HO2 or O2 we would get H2 O IM IM H OH cannot start reaction again OIMIMOO2 cannot start reaction again very, very clean reaction conditions are needed! Initiation scheme: H R1 to attack, we would like to have - I CC not to much electron density in H R the double bond to reduce 2 Coulomb repulsion! Typical monomers: styrene: H2C CH butadiene: CH CH2 H2C CH CH3 isoprene: C CH2 H2C CH Typical initiators: Na, K ( BuNa –Werke Leuna: Butadien + Natrium ) germ. for sodium The product depends a lot on the solvent, example butadiene: 1,4 Counterion Solvent Cis Trans 1,2 Li hexane 0.35 0.58 0.07 unpolar solvent 1,4 Li THF 0.06 0.06 0.88 polar solvent 1,2 Na THF 0.06 0.14 0.80 Polymer chemistry 48 Butadiene: 1,4 cis n n 1,4 trans n n 1,2 n n For rubber tires we need: cis-1,4-polybutadiene Polymer chemistry 49 2.14 Kinetics and molecular weight distribution of ionic polymerisation (copied from lecture Prof. Sillescu) Assume: - no termination reaction - concentration of ions is constant and equal c0 - reaction constant (rate) independent of molecular weight H H H H H - - I CC I C CC H H H k I MM 2 living polymerisation initiator monomer k MM23 M cI c M MMk M 34 k MMnn1 M assume: cccI,23 , ,... c M const . cc20t 30 ... cn1 0 ccIt0 0 cccc023In... c for all t i1 dc I kc c kc dt M II kc M constk. dc 2 kc c kc c pseudo first order, solution: dt M I M2 dc ccekt 2 kc kc I0 dt 2 I for c3 we find: dc 3 kc kc dt 32 In general dc n kc kc in math differential equation set of Kolmogoroff dt nn1 Polymer chemistry 50 Stepwise solution for this set of differential equations, including induction prove dc 2 kc kc c c ekt dt 2I I0 dc 2 kc kc ekt , (I) dt 20 “Ansatz” kt ct2 Ut e to be found dc dU 2 eUkekt kt in (I) dt dt dU ekt kUe kt kc kc e kt 20 dt c2 dU ekceekt kt kt dt 0 dU kc dt 0 Ut kc0 t integration constant In “Ansatz“ kt ct20 kct e ct2 0 0, see assumptions kt kt ct20 kcte c 0 kte dc 3 kc kc dt 32 dc 3 k c kc kt ekt dt 30 kt cUe3 Ansatz kt 2 cc ekt 302! kt 3 cc ekt 403! Assumption: kt n1 cc ekt n0n1 ! Polymer chemistry 51 n kt kt ccn1 0 e, (II) n ! To be put into: dc n1 kc kc, induction prove in maths (III) dt n1 n Derivative of (II): dc nk tn1 n1 ckekckt (product rule) dt0n1 n n 1 ! In (III) nkt n1 ckekckckc kt 0n1n1nnn 1! kt n1 kc ekt kc 0nn1 ! cn The probability of a molecule to have a degree of polymerization “n“ is as follows: ccnn wn c0 cn i1 see "assume" n1 cn kt kt wen cn10 ! Poisson distribution, special case of binomical distribution, only characterized by one parameter (Gauß 2: , ) Average in general: Pxdx 1 xx xPxdx , first moment in math textbooks xxPxdx22 , second moment nn th xxPxdx , n moment n1 n1 ktkt kt kt Pnnn nwn e e n n1 n1n1!! n1 n1 Polymer chemistry 52 23 2kt kt kt Pekt 1 3 4 ... n 1! 2! 3! side calculation: 23 kt kt kt ekt 1 ... 1! 2! 3! 23kt23 kt ktekt kt ... 2! 3! 23 2kt 34kt kt 1 ... 1! 2! 3! kt kt kt kt Pen e kte e Pn n 1 kt kt n 1; here: n n t n1 n1 wex n1 nnn1 ! Number average of molecular weight M nnMP000 Mn M(1 kt ) Note: Mn can be determined via colligative properties (e.g. osmotic pressure), GPC or end-group analysis (titration or NMR). Weight fraction gn of molecules with a degree of polymerization Pn: cn 0 Mn cMnncI WM nn WM nn g n c M cMn M WM n nnc0 n nn n1n1 I n1 112 Pngwn nMW nn nW n MMP MPnnn0n MnMn0 WM2 nn M0 2 MP0w M W Mg nn kt1 kt Mkt1n to be proofed, next page second moment diveded by mean General statement for Mw Specific for anionc M 112 2 kt w MW kt 1 kt 1 M 2 nn 22 n Mn kt 1 kt 1 Polymer chemistry 53 If nkt11 M 1 M w 1 , in reality: w 101.. to 12 M n n Mn Side calculation: Assumption; to be proofed 222 +kt n Wn () kt 1 kt () kt 3kt 1 e kt n1 For Wekt n n1 ! ktn1 kt 0 kt 1 enkt 2 e1 kt 2 2 ... n1 !!! 0 1 4 kt12 9 kt 16 kt 3 1 12!! 3 ! this should be equal to: kt123 kt kt 1ekt 1 ... 123!!! 3kt123 3kt 3kt 3kt ekt ... 112!! 3 2 2 kt kt ekt kt ... 1! 4 kt12 9 kt 16 kt 3 1 ... 12!! 3 ! Note: in textbooks you find: vn Pvn, ev n! vk expection value, Erwartungswert vn1n, mean degree of polymerization since n1 v Polymer chemistry 54 2.15 Copolymers: Remember ( earlier) 1) random copolymers: AABABBAB ... 2) alternating copolymers: ABABAB ... in a strict sense a condensation of e.g. dicarboxylic acid and a diol is an alternating A B copolymer, but generally n is treated as the repeat unit 3) block-copolymers AAAABBBB ... A and B: different monomers, or different tacticity copolymer composition: active end, e.g. radical or charge 4 possibilities for next step (for di block copolymers) k AA * k AB * k BB * k BA * k11 and k22: self-propagation k12 and k21: cross-propagation Assumption: Reactivity depends only on last attached monomer, not on chain length or previous sequence! Consumption of A: dA kA11 A** kA 21 B (I) dt different Mn Consumption of B: dB kB B** kB A (II) dt 22 12 (I) divided by (II) Polymer chemistry 55 A * 1 kk dA A11BB** 21 (III) dB BA * 1 kk12 22 B * B * Assumed steady state: dA * dB * 0 and 0 dt dt New A * are created via cross-propagation from B * dA * kA B* dt 21 Destruction of A * via cross-propagation to B * dA * kB A* dt 12 At steady state, both must be equal kA21 B** kB 12 A kA A * 21 kB12 B* Substituting into (III): k A B kk21 dA A 11kB 21 k 12 21 dB B k A B kk21 12 22 k kB12 21 A kB dA A 11 k 12 dB B B Ak 22 k21 If we define a reactivity ratio: k r 11 1 k 12 k22 r2 k21 Note: r1 and r2 can be determined and found in the literature. Then: Polymer chemistry 56 dA A r A B 1 Copolymer equation! dB B A r2 B Different cases: A) rr112 no preference, random distribution ideal statistic copolymer B) rr012 k11 and k22 are small compared to cross propagation completely alternating copolymer (e.g. polycondensation) C) r11 and r12 lot of A will be incorporated, only rarely B The Q-e-scheme Semi empirical method to predict reactivity ratios for a pair of monomers, specifically for free-radical polymerization. “Q” and ”e” are measured (and tabulated) relative to styrene, where Q10 . and e08 . . The reactivity ratios are given by: Q1 reee1112exp Q2 Q2 reee2221exp Q1 Only estimate of r1 and r2 ! Polymer chemistry 57 Lit.: Tieke Polymer chemistry 58 2.16 Coordinative polymerization (insertion polymerization) Characterized via: 1) monomer is “attached“ (coordinated) to transition metal catalyst (e.g. Cr, Hf, Ti, Zr, …) 2) monomer is added, inserted into the still attached (to the metal) polymer chain examples: - polyethylene German, PE Italy,PP Ziegler - Natta , Nobelprice 1963 via, TiCl3 AlEt3 (typical combination) - polypropylene - polybutadiene The coordinative polymers have often a high degree of stereoregularity. To understand this, we have to distinguish: constitution, configuration and conformation ( next chapter). Basic idea of coordination polymerization: a transition metal can have a “coordinative” chemical bond ( covalent or ionic) Orbitals polymer Monomer is preoriented Cl attached to C vacancy ClTi vacancy C Cl Cl Oktaeder polymer CH2 H2C Cl +CH =CH 4- 2 2 ClTi vacancy Cl Cl This can happen 10 100. 000 timess ! e.g. 1g cat => 106 g polymer in ppm range metal impurities Polymer chemistry 59 2.17 Constitution, conformation and configuration isomers Constitution: If chemicals (e.g. polymer) exihibit the same sum formula, but different covalent connectivity (“constitution”) the chemicals are constitutional isomers Example: 1) PE PP CHnn22 CH CH CH2 CH2 2 n m CH3 2) Block-copolymers: (55 ; ) 3) Head-tail, head-head polymerization To change the constitutional isomers, we have to break bonds! Configuration: In case the same atoms are connected, but the two molecules can not be put “on top of each other” a configuration isomer is defined Examples: (left hand + right hand !, same connectivity of bones, but can not be on top of each other!) 1) cis 1,4 polyisoprene natural rubber, elastic trans 1,4 polyisoprene Guttapercha, rigid resin Polymer chemistry 60 2) polypropylene (all head-tail !) CH3 CH3 CH3 CH3 CH3 CH3 HH HH H H iso-tactic polypropylene (crystalline) H3C C CH3 zick-zack chain in plane, CH 3 always above (or: always below!) H H3C H3C H H3C H H CH3 H CH3 H CH3 syndio-tactic polypropylene H3C CH3 (crystalline) CH3 is alternating above and below zick-zack plane H C H C H H C H C H 3 3 3 3 a-tactic polypropylene HH H H H C CH3 CH3 3 not crystalline, waxy CH3 CH3 is randomly above and below zick-zack plane Conformation: Single C-C bonds can be rotated with low energy (thermally). Two snap-shots of same polymer are called conformation isomers in case they are non-identical. e.g. 1. rotation (e.g. 1012 in 1 second) to slow down this rotation you need 1-2 Kelvin! H C H -CH3 H 2. H3C CH3 CC H H H H We expect: Max. + min. 180° apart 360° self repeating Every 60° Max MinMax Polymer chemistry 61 RT 2, 4 kJ 300K mol E kJ 15 20 mol -180° -120° -60° 0° 60° 120° 180° 3. different polymer conformations: a) b) c) abc,, : different conformers The conformation determines the shape of the polymer; due to the large amount we can do statistics to evaluate the most probable conformation. Polymer physics, physical chemistry 62 3 Polymer physics, physical chemistry Topics covered: 1. – Polymers in “vacuum” or ideal solution 2. – Polymer dynamic in melt (reptation) 3. – Polymers in crystal, motion, determination of crystallinity 4. – speed of crystallization ( Avrami equation) 3. 1.1 End to end distance, contour length Assumptions: - All lengths between atoms are the same - All angles possible, all have same probability - No own volume of atoms Picture: Contour length: l 3 2 2 Nl , odometer along the polymer chain, total l 1 length, end to end distance if totally stretched N 1 N+1 hl i h i1 N h0 Since vector points with equal probability in all directions h2 ? expectation value NN 2 hll ij i1 j1 For ij : 2 llij l i l j cos l cos 0 all same probability Reason: Polymer physics, physical chemistry 63 2 cos cosd 1 0 0 2 2 -1 1 cos cos1d first moment of cos A Pconst . Normali- zation For ij : IijII ; I 1 NN N 22 hllllNlij iij i1 j1 i1 ij hNl22 hh22: hNl The size h of ideal polymer growths linear with “l“ and as a square roots “N”, e.g. factor 10 in Mn is only factor 3.1 in size. Typical polymers might differ factor 100 in Mn and factor 10 4 6 in size, e.g Mn from 10gmol / to 10gmol / . Polymer physics, physical chemistry 64 3.1.2 Radius of gyration (can be measured, e.g. light scattering) i1 li ri1 S r : center of gravity i S (“Schwerpunkt“) Moment of inertia, see also physics books: IrdmMR 22 Radius of gyration of polymer chain N 221 Rmr ii M i1 N 221 Rmr ii ; mmi for all i, M i1 N 221 Rr i ; MNm N i1 Without any proof (see e.g. Lechner, Gehrke p.42-43) h2 Nl2 R2 66 hlN RRg2 66 The radius of gyration is factor 624 . smaller than end to distance h. Both are second moments with respect to different distribution. Polymer physics, physical chemistry 65 3.1.3 Random-walk and Gaussian chain 2-D picture Let’s assume a lattice with a 3-D grid. We y throw a dice (“Würfel”) if we get 4 2 2 1 move +1 in first dim 1 3 2 move -1 in first dim 0 1 3 move +1 in second dim -1 10 -2 4 move -1 in second dim 5 move +1 in third dim x 0 1 2 3 4 6 move -1 in third dim The shape of this “Monte Carlo”1 simulation should tell us something about the shape of polymers! Poor man’s 1-D version: 1 t0 05. t 1 x 0 1 2 3 At t0 we are at x0 we throw a coin to determine if we move left or right (50:50 probability) by l. binominal distribution NN wpqpp05qKNK N;. nk. KK If pq05. and lim Gaussian distribution (see maths textbooks) N 2 wex2; Nl Where N: number of coins thrown, molecular weight K width of distribution, standard deviation hRg,! length l! Question: In a random walk we move stochastically as a function of time, when we do the analysis of chain conformation we do not need to consider time, so what does time stand for? 1 This type of computer simulation is really named after the gambling place! Polymer physics, physical chemistry 66 Mn !, number of monomers added. In 1-D x2 1 2 wx e 2 2 In 3-D: The probabilities are the same and independent for all three directions xyz222 1 2 wxyz,, wx wy wz e 2 2 xyzr2222 Where 22 Nl Picture: One end is fixed at origin, freely joint chain z r x y To find chain end (“x”) in distance r (at any angle , ) we need to calculate probability to find chain end in shell of thickness dr with volume dV dV 4 r2 dr r2 1 2 wxyz,, e 2 2 r2 1 2 wrdV e2 4rdr 2 2 Polymer physics, physical chemistry 67 e.g. if wxyz,, wr N10l254;.A 100 200 300 rA 100 200 300 rA Question where is wxyz,, 0? for r ! What do we know for rNl(contour length)? wxyz ,, wr 0! Logic? Polymer physics, physical chemistry 68 3.1.4 Entropy- Elasticity, basic idea Let’s assume: x2 2 wx e 2 Gaussian statistics, polymer chain GHTS Boltzmann: w Sk ln w (better: Skln 1 ) w2 We stretch a polymer (e.g. rubber) and see what we would expect for FxT , GHTS 0 2 GTSTkeln x2 Tx kTHook ! dG FTx dx Hook! Polymer “spring“get’s stiffer as temperature increases. Picture: Rubber k band 2 k1 T increase kk21 Hook M M x Mass is lifted! change in temperature moves mass! Compare combustion engine: Polymer physics, physical chemistry 69 T1 < T2 Cool gas Change in prior explosion Hot gas, temperature moves after explosion mass rotation! There must be a set up, where a temperature gradient in combination with rubber strings must create a rotation! Staudinger wheel: motion Cold, zone, soft rubber center of mass Hot, zone rubber is rigid spring Rubber string IR-lamp Centre of rotation below centre of mass rotation to reduce potential energy Polymer physics, physical chemistry 70 3.1.5 Deviation from simple- statistics for end to end distance Remember (3.1, this chapter) - all length between atoms are the same okay - all angles possible, all have same probability not okay better: Since bond angle are generally fixed at 180° (sp), 120° (sp2) and 109.5° (sp3) for ii, 1 for all i i, still same probability li2 P( )=const. i1i2, l i1 ii, 1 ii,1 180 l i sp-orbital: C C i 180 , 0 sp2-orbitals: O C i = 120°, = 60° O sp3-orbitals: C i=109.5°, = 70,5° after longer calculation (see Lechner, Gehrke p. 36-38), Pconst . 1 cos hNl22 where 180 1 cos i modification e.g. i 109.. 5 70 5 hNl222 Polymer physics, physical chemistry 71 if has not same probability ( remember conformation!) the equation is further modified: 2211cos cos hNl 11cos cos Remember: for simple statistics: all segments have no volume. - It is trivial that this can not be correct, but what do we expect if we include chain volume? Simple statistics 4 5 4 5 1 2 3 6 123 6 8 7 This bond had to change direction h h 9 Possible, chain folds 8 7 back on its own 9 If we include chain volume, the chain must try to avoid to overlap with itself “self avoiding walk” this leads generally to larger sizes. 3 1 hN 5instead of 2 - Gaussian statistics must also fail for larger elongations, since 2 wx ex ; wx 0 at xNl (contour length) can’t be Kuhn and Grün 1942: h wh kexp N ln Nl k sinh sinus hyperbolicus lk : Kuhn-segment, see next page -1h -1 LL;: inverse Langevin-function Nl k Polymer physics, physical chemistry 72 Approximation: 24 6 3h 9 h 99h lnwh k N ... 2 Nlkk 20 Nl 350 Nl k Gauss 3.1.6 Kuhn segment: Remember: hNl22 , most simple case 221 cos hNlFor fixed , equal probable 1 cos 2211cos cos hNl 11cos cos We guess that a relation exists: 22 hNl s 15l. ls 3l Typical value for ls The unitless quantity at lim : N l c s l Is a measure of conformative constrains ls : apparent bond length (“s: scheinbar”) For N we assume a Gaussian chain with different length and segment number NN 22 (a) hNls 22* * (b) hNlk ; N : statistical segment number ()b ()a : * 2 Nlk N 1 2 * Nls N 2 Nlk k :* 2 Nls k : ratio between chemical segment number and statistically needed number Polymer physics, physical chemistry 73 22 lklks lk : measure of stiffness 3.1.7 Persistence length (“how stiff is a polymer“) tx1 0 tx 2 Nl If define a tangential unit vector t that moves along the contour from x0 to xNl, what will happen if we correlate two tx 1 and tx 2 vectors with each other? g 0: tx 11 tx 1 for all x1 gtxtx0: 11 for very large, x21 x We expect a strictly monotonic decaying correlation function of the shape: l g1e p lp : persistence length 1 1e 0 lp 1 1 The angular correlation has decayed after l to , or cos polymer has curved by p e ij e typically 68° (memorize: 90°) Polymer physics, physical chemistry 74 Note: A) the persistence length can range from 13nm (polyolefines) to 10nm (polyparaphenylene, PPP) up to 12m for rigid viruses (even with 78nm diameter) ”bamboo” B) correlation functions are frequently used with time as a variable (here: space x for persistence length) general definition gt gt dt g gt2 dt Correlation time: : gd used: e.g. quasielastic light scattering later c 0 C) For special cases we can approximate (see e.g. Lechner p. 40-41) 2l pk l lp : persistence length lk : Kuhn length Polymer physics, physical chemistry 75 3.2. Polymer physics of melts 3.2.1 The reptation model, De Gennes (Nobelprice 1992) Basic idea: one dimensional stochastic process of chain along own contour, restricted by neighbouring chain (reptate: reptile) Simplified s constrain (not moving) Stochastic d motion Tube with diameter d, other chains are static, typical distance s for constrains of other chains s d 30 80 A . If we have a certain position at time t0 , we use one-D Fick equation to describe chain distribution probability pp2 D , 1-D second Fick equation tx1d 2 c [first Fick equation:DJ ] x Solution for Pxt, in case of 1dimensional random walk: 1x 2 Pxt,exp 4D 1d t 4D 1d t x2 Gaussian: e 2 2 22r2nDt with n : Dimensionality Mean square displacement ( second moment) xxPxtdx2Dt22 , 1d Polymer physics, physical chemistry 76 If we assume stochastic friction coefficient , of the polymer where this friction coefficient is proportional to N, therefore M (molar weight) N : friction per monomer unit Using the Einstein relation for 1-d diffusion kT kT DM 1 1d N The time needed to diffuse along L, will allow a fully different conformation, so that all memory of the other constrains is erased 2 r2Dtt 1d ; rLcontour length Nl M1 2 L2D 1d 22 LM 3 1 M 2D1d M M3 The longest relaxation time in a linear, amorphous, monodisperse homopolymer is M 3 . The self-diffusion coefficient Ds is given by the time to move the centre of mass by a typical coil diameter R (3-D problem) 2 r2nDtn3 s ; RM2 DM 2 s 6M 3 RNlM22 2 DMs Assuming a Maxwell model G Pa s GPa G see rheology With: lecture next semester! M3 + chapter 5, this script GM 0 Polymer physics, physical chemistry 77 Molecular weight independent G for rubber plateau, given by temporary entanglements, mesh length Me Me 3 34. polymer M , De Gennes 1971, experiment M For low shear rates! 0 log Slope, typically -0.8-0.9 pivot point 1 log Non entangled polymers: M1 friction of polymer contour log0 M3Mec 3 “3 fingers to hold a stick“ 1 log M M c Rule of thumb for flexible monomers with 2 carbons per backbone (so not true for PPP, polyparaphenylene large persistence length) ne 100 200 monomers (200-400 backbone carbons) - entanglement is rare event - local correlation and parallel orientation (Pechhold, meander 1970 ) - spaghetti picture is misleading, to much free volume (to much space for “sauce”) for melt Polymer physics, physical chemistry 78 examples PE: g 828 mol PDMS: kg 12. 3 mol PMMA: kg 10 mol 1,4PI: kg 54. mol PS: kg 13 mol PIB: kg 73. mol 1,4-PB: kg 18. mol might differ depending on literature source + definition M e typical response for shear module as function of frequency Engineering properties (later), chapter 5 and rheology lecture Polymer physics, physical chemistry 79 3.2.2 The amorphous state Or: When do polymers crystallize? a) X is small : CH2 CH n X stereo regular semi-crystalline example: i-PP not stereo regular amorphous example: a-PP X is very small e.g. X: FOH, b) X is very large and regular: e.g. CH2 CH m C O O CH2 n CH3 n11 side chains will crystallizes, how to suppress crystallisation in side chains? How to prohibit crystallisation? a) for random copolymers; do not crystallize or have reduced crystalline amount, if copolymer is in the range 1-5% b) if cooling rate is sufficient high, the freeze out of motion is faster than the crystallisation kinetics ( see later). The amorphous parts can not rearrange to form crystals, below the “brittle point” (:, Tg glass transition temperature) of the amorphous parts. specific volume v as function of temperature v liquid v If const. T Liquid glass Liquid is 100% crystallized First order phase transition “kinetic“ 2nd order phase transition Problem: amorphous T T T T becomes as dense as P g m crystalline Polymer physics, physical chemistry 80 v T : if const. at T the specific volume v of disordered frozen liquid ( glass) P T p would be below crystal not logic! “something” must happen before! glass transition at Tg , e.g. measured via DSC (heat flux as function of T, differential scanning calorimetry) Typical DSC curve for semicrystalline monopolymer exothermic peak => first order phase transition step Diff. Heat flux step=> second order Endoth. Very small and Integral degree of crystallinity smeared out (be carefull with this analysis) T T T g m Typical heating rates: K 220 min To low takes forever and noisy spectra To high it takes time to crystallize Melting enthalpy for crystals is in the range of 0.1-0.3 kJg determination of crystallinity What influences Tg ? a) Molecule weight 1 If endgroups are “different” the probability to have endgroups in a certain volume , Mn therefore Tg of a finite size polymer needs a correction, since Tg of an infinite Mn system will not be reached A TTgg Mn b) Size of “X” in CH2 CHX n X: inflexible and large Tg Polymer physics, physical chemistry 81 X CH3 CH 3 TCg[] -10 100 115 135 145 a) If “H” is exachenged by CH3 alkyl acrylates alkyl methacrylates H CH3 CH C 2 CH2 C X X CH3 H CH C CH2 C 2 m m C O C O O O CH2 CH2 n-1 n-1 CH3 CH3 Stiffer! Tg The CH3 in main chains 100 increases rigidity, OCH() CH acts as methacrylates 2n1 3 plasticizer for amorphous T100C polymer. Longer side chains can 0 crystallize, e.g. n > 11. -50 acrylates n 1 7 Polymer physics, physical chemistry 82 b) Electric dipol increases Tg Tg [°C] 100 PVC -60 mol% Cl 30 50 in PE Empirical rule; for semi crystalline polymers 2 T g 3Tm Tm in °C or K? we need an energy K Tg of blends and copolymers exo T g1 T g2 Blend size > 1µm, clearly separated T T g2 g1 Copolymer heterogen size 5nm, otherwise “homogenious“on DSC T length scale Generally TT, the rigid polymer 2 is more “plasticized” as mobile polymer 1 is gg21 “rigidified”. Compare: Polymer physics, physical chemistry 83 R11 R2 100 Is R1 more influenced by R2, or R2 more by R1? no symmetry 111 RR R 12 In case only one Tg is detectable ( heterogeneities < 5-10nm) several equations can approximately predict the common glass transition, most known equation is the Fox-equation ( 1950) 1ww12 TTT gg12 g wi :weight fraction of polymers Low molecular weight additions can act as plasticizer ()Tg (opposite effect exists too). PVC is most prominent example Most common plasticizer: DOP (dioctyl phthalate added 0-50% !) O CH3 C O CH3 O CH3 C CH3 O why not n-alkyl?? Daily use example: Extreme dry cellulose (“T-shirt”) has Tg 225 C each 1% of H2O lowers Tg by more than 10°C wet ironing (steam!) afterwards T-shirt is plane and Tg is increased due to dry state. Fox-eq. does not apply since 1 polymer plus one low Mn plasticizer. General considerations for all glass forming materials (polymers, low Mn glass formers, inorganic material) - free volume allows motion (5-10%), T-dependant - similarity with second order phase transition Polymer physics, physical chemistry 84 - non equilibrium, time dependant (e.g. different Tg for different cooling rates) hysteresis - kinetic theories: free volume mobility - thermodynamic theories (Gibbs, Di Marzio 1958) lattice theory with intermolecular contributions - heterogeneity (1-3nm): spatial and dynamic (time and space) solid state NMR, Prof. Spiess WLF-equation Dynamics as a function of temperature for polymer melts William-Landel-Ferry (WLF- equation) Semiempirical: CT1r T log10a T CTT2r aT : shift factor Tr :reference temperature Tgrg T T 100 C TTref aT ref ref T If we chose TTrg C 1 174C516K.; 2 . other Tr (reference temperatures) are possible, but change CC12, 17. 4 T log a T 51. 6K T At T50Csingularity Vogel-Fulcher temperature Polymer physics, physical chemistry 85 log aT Arrhenius Strong changes 0 close to glass transition 1 1 1 1 T T T T m g VF if cryst. TTTmgVF How can we understand the mathematical form of the WLF-equation? Doolittle equation viscosity as function of free volume, f: B A exp f B exp f 11 aBT exp B ffR exp fr If free volume is a linear function of temperature ffgf TT g at Tg f : thermal expansion coefficient (in the following renamed to ) 11 aBexp T fTT f ggg ffgg TT g exp B ff T T gg g 1 B TTg exp f fTT 1 g gg B TT g exp f fg g TTg Polymer physics, physical chemistry 86 C 1 B TTg 2. 303fg log aT fg TTg C2 Combination of linear expansion coefficient for free volume with exponential inverse dependence of dynamics towards free volume makes WLF-equation plausible. CT T log a 1ref: WLF-equation 10 T CTT() shift-factor 2ref B exp with f: free volume f For several techniques e.g. (dielectric spectrometry, rheology, induced aging ...) the change in temperature is used to accelerate in a known plus predictable way ( WLF-eq!) molecular processes, to reduce time of experiments or access, otherwise not easy reachable frequency ranges. This is called time temperature superposition (TTS). Please be aware: If WLF-equation is used, within the temperature range investigated any first order phase transition must be excluded. E.g. melting, smectic- nematic (liquid crystalline phase transition), LCST, UCST (lower/ A B T A+B upper critical solution temperature), TODT (temperature for order- disorder transition) and of course Tm (melting temperature)! Polymer physics, physical chemistry 87 Note on Liquid crystals: director M centre of mass Centre of mass + - - + correlation Director + - + - correlation state: crystalline Liquid/ Liquid crystal Conformation amorphous disordered crystal (condis cryst.) examples: NaCl Water (liquid) Biphenyl Adamantan, Fullerene Polymer physics, physical chemistry 88 3.2.3 The crystalline state Crystals are arrangements of molecules and/or atoms in regular, repeated and three dimensional periodic pattern with translation symmetrie. There are seven crystalline systems abc, 90, 120 c In polymer science: c-axis is polymer axis c c b a Called: Triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, rhombohedral, cubic They exist in 14 space filling lattices (so called “Bravis” lattices) and 230 space groups. Bravis e.g. cubic abc, 90 Cubic (primitiv) Body centred cubic Face centred cubic Only one type of (bcc) (fcc) repeat structure Polymer: crystalline mostly in “all-trans” conformation or in helices. Example for all-trans: PE-orthorhombic abc, 90 Polymer physics, physical chemistry 89 C C C C C 5A C C C C C 75A. Remember: 1A 1010 m 10 A 1nm carbon 154A, 109, 5 x2 cos 90 2x C 109, 5 3 x154A3 , x3 x2 C x125A, 2 2 109, 5 x 1 C25A , 2 Note: PE can incorporate small amounts of CH3 and/or C2H5 branches (<1mol%) but not longer. In unit cell are 2 chains, per chain we need 2 575 . A 20 Minimum space, cross section per polymerchain 2chains chains e.g. surfactant on surface Helical structures Nomenclature: Xy helix, e.g. 31 between A and B. X is the number of monomers (or B carbons) to make y-rotation to achieve translatoric symmetry along c- axis.(“monomer is exactly above monomer”) A c-axis Polymer physics, physical chemistry 90 How can polymers arrange to form crystals (lamella)? a) folded chain crystal Adjacent re-entry (from dilute solution) 10-100 nm Adjacent re-entry with loose folds Random switchboard (Flory 1962) Super folded crystal consistent with SAXS (small angel x-ray scattering) and SANS (small angel neutron scattering) Plane folds on plane Polymer physics, physical chemistry 91 b) fringed micelle (“Fransenmizellen”) generally not correct but historically important In both types of arrangements (a, b) the polymer chains can participate in more than one crystallite. In early polymer days (1920) it was believed that a (unit) cell must have size of a molecule (this is frequently true for low Mn material). 1920 PE: c-axis is 25A. , contour length (106 g/ mol ), 10 µm (factor 40,000) polymers can not exist as long and covalent bond molecules. How can we determine crystalinity? Main examples: - X-Ray, Röntgen - IR regular structure - Dilatometry (density measurement) - NMR mobility - DSC thermodynamic properties Either structural (x-ray, long range spatial correlation, IR: defined energy potential for vibration), dynamic (NMR, contrast in mobility between crystal and amorphous) or thermodynamic properties (dilatometry: density or DSC: heat flux) are used. We can not expect 100% the same values for all techniques using the same sample! But we assume a strong monotonic correlation between the values determined via different techniques. Polymer physics, physical chemistry 92 Basic idea of x-ray (“Röntgen”) (1) Incoming beam (2) Regular array of objects d on a lattice e.g. polymer l1 l2 chains l We find 1 sin d “extra path” for beam (2) 2l1 2d sin To have constructive interference we need n2d sin Bragg-equation ( memorize!) n , e.g. 1,2,3,… for X-ray has dimension of inter-atomic distances and most commonly used sources Cu 1, 54 A (copper anode) Problem: X-Ray source are normally monochromatic but not coherent (similar phase of radiation) but in the derivation we used a coherent X-ray beam, since (1) and (2) were in phase! Explanation: On small size ( 10 50nm ) only coherent contributions need to be considered, since “incoherent rest” kills itself. In case we have only first order peak (n = 1) Cu 1, 54 A and 30 we can use the following simplification: 3 1154A. 2d sinrad 2d ... 3! 154A., 2d rad 2 154A. 2d 360 grad Polymer physics, physical chemistry 93 A 88 2d simplified Wilhelm grad e.g. 220 d44A. ! For ideal crystalline material Real life: semi-crystalline material In“ “ Ac I Sharp peak, I information Bragg about crystal condition thickness! 1 D 0 0 Aa Scherrer equation 30 10 Ac Xc AAca Ac : crystalline peak Aa : amorphous peak (called “amorphous halo”) Please be aware: Crystallinity does not exclude mobility! e.g. PEO up to jumps POM10000 s PE Crystalline area - Small side-chains stops monomer to move outside the crystalline area. stochastic motion - PE under load deforms with time, because the Small branches chains move to avoid load. - Side-chains can force the chains to stay at there place. IR: (Theory later), just basic idea Different resonance (-H vibrations) or deformation for amorphous and crystalline areas C H k m Polymer physics, physical chemistry 94 Typically: N k 500 m for single bond Useful bands: 650 1500cm1 e.g. 1000cm1 n1 absorbance Ic n 1000per 1cm 10m Ia deconvolution V wavenumber 4000 600 cm1 Using Lambert-Beer law of absorbance: cd Icd ,, I0 e dI From IIIecd dx 0 : absorption coefficient c : concentration d : thickness Problem of scattering, light size of crystalls Polymer physics, physical chemistry 95 Dilatometry (density measurements) Typically: a 085.. 095 (at same temperature) c 5-15% more free volume for amorphous material e.g. PE g 1. 000 good packing of chains c cm3 g 0. 853 a cm3 But poly(4-methyl-1pentene) ca ! 2 4 1 3 5 We assume VV ca V volume (what does this imply?!) mm ca m weight m VV V ; cc aa V With VVVac VVVV cc a c VV cc a a V VV acca Vc a c Volume fraction V ca cc Vm c c a Xc mass fraction Vm ca ac, : known, : measured Assumption: Two phase model (crystalline and amorphous phase) In case the density difference is 100 kg and we want to determine X with <1% ca m3 c accuracy. We need to determine relative density differences 103 . ( 1000Kg / m3 ) Technically: Polymer physics, physical chemistry 96 : 1034 2 10 is achieved e.g. use of solvent gradient Solvent l1m density x l1mm Suspended polymer particle location is T control water T1K 10cm T !!! reason Typically: 11 3 10 , thermal expansion coefficient VT K Extension 2 phasemodel: 3 phasemodel c : crystallin c a a : amorphous ao : amorphous oriented ano : amorphous not oriented c ao ano Why not modify “c”? Polymer physics, physical chemistry 97 NMR (theory later) In case we can find a temperature T, where a contrast in bulk mobility is high between crystalline material and amorphous and the mobility ( WLF) is sufficient for the amorphous part to change the NMR resonance, position or shape (but not for the crystalline parts) we can separate the two contributions. Generally TTTgm (close to Tm ) T Tg 40K (TTS) Main reason for line broadening (simplified picture) in solid state NMR (2) B N S Monopol – monopol Fr~ 2 3 r Dipol – monopol Fr~ N Dipol – dipol FrEr~,~43 S (1) 1 Fdx FEr 1 r2 Field of (1) and (2) should be a function of r and . Mathematically similar problem Legendre polynoms 1 31cos2 r3 If we could calculate the pre-factor, we would get (for protons!) 20 30 kHz for rigid solid for r 2 3 Question: how close are protons? H H H H C Polymer physics, physical chemistry 98 If rate of motion2 is large > line broadening mechanism line narrowing, e.g. liquid 1Hz Therefore the extreme cases Rigid material Solution NMR 1 Hz 20 – 30 kHz res res 6 6 res 300 900 10 Hz 300 900 10 Hz Experimental: Tlow Tmed Thigh dynamic contrast everything rigid, amorphous 0 + crystalline Dynamic contrast, integration X . very No dynamic contrast, everything c mobile, no crystals exist anymore TT T simple NMR machines gmmeas. 20 60MHz wide line spectroscopy „minispec“ DSC Already described in chapter 2.2 polymer physics Question: When Xc was determined what was assumed? two phase model Crystalline area, Amorphous everything area, everything same, at least in same, at least in average average homogeneous homogeneous two phase model If we improve, where is further differentiation needed? 2 Mobility effects the line shape, mostly the width, less the location Polymer physics, physical chemistry 99 disordered amorphous ordered amorphous crystalline 3 phase model with 2 amorphous and 1crystalline would be appropriate extension (Maximum speed of crystallization halfway between Tg and Tm ) C a C a0 aa 3 phase model Polymer physics, physical chemistry 100 3.2.4 Kinetics of crystallization ( Avrami equation) Growth of spherulites P P P L t0 start all nucleation takes place time at t0 , athermal Probability that number of spheroids “C“ be at point “P” until time t? Poisson distribution (1837), E=E(t) C 0 Pt() C 0 Averrage EEC exp value of PC C 0 EP C! crystalline fronts not to be a crystal ( amorphous); C=0 passing P PE(0) exp( ) t All nuclei grow at t0 number does not change = athermal nucleation growth rate rconst . radius rt r t volume occupied by crystal = probability of crystals to hit “P” 4 Et rtg3 3 g : concentration of nuclei 4 33 P0 1 Vc exp rtg 3 General Avrami equation n 1Vc exp kt kn, they are typical constants depending on type of nucleation (athermal or thermal) and growth mechanism, e.g. line, circular, fibrillar, sheaf3 3 Bündel, Garbe Polymer physics, physical chemistry 101 experimental determination of “n” hint about local mechanism Typically: 13n46; n dimensionality of the problem typical At early times, Taylor expansion of Avrami n Vktc Göler equation Polymer physics, physical chemistry 102 3.2.5 How to reach 100% crystallinity in a solid polymer Start from melt ? Topological constrains impossible to reach 100% Idea: Single crystal of monomers + thermal or ionizing radiation (1970, Prof. Wegner) source: Young C C R C C R C C R C C R topochemical reaction polymer Polymer physics, physical chemistry 103 Unusual optical, electronical and mechanical properties, e.g. anisotropic, defect free, conjugated. Molecules and characterisation 104 4 Molecules and characterisation 4.1 Distribution of molar mass and determination of molar mass of polymers In general we have a discrete distribution, but approximate it with a continuous distribution. Probability Pn n With Pdn 1 n 0 The distribution does not need to be symmetric Probability Pn Gauß n Or have a single maximum Probability Pn n Number average (number of polymers number of monomers !) MMPndn1 (first moment) n0n Molecules and characterisation 105 Weight average: g :weight n MPndnPnMnMdnM22 gndn 0n n 0 0 0 n Mw MPndn MPndn M Pndn 0n 0n 0 n second moment M first moment 0 z- average: (Centrifuge average) PnMdn 33 n0 third moment MMz0 PnMdn 22 second moment n0 If we would know all moments, we would have the full information about the distribution (functional analysis, maths), but most experimental techniques give “only” MMMMnwz,,, . average: viscosity average, measured via viscosity a Pndnn M Pndn a1 n a1519.., close to Mw a , no necessary 1, 2, 3,… Mp ; peak molecular weight: The most probable molecular weight is called Mp In general: MMMMnwz Probability Mp Pn Width of distribution M n Mn Mw Mz To describe the “width” of the distribution we can use the standard deviation : 22xx2 where xPxxdx22 and xPxxdx mathematical definition Molecules and characterisation 106 Using 2 MMwn x second moment of Pn Mxn first moment of Pn 22 MMnw M n MM nw M n (I) Most commonly in polymer science the width of the distribution is described via the polydispersity (PDI, polydispersity index): M w , always 1 Mn In German literature often the term “Uneinheitlichkeit” is used to describe the width of the distribution Mw 2 U : 1Mn Mn 22 2 UMnnwnnwn M M M M M M ()I 22 UMn MUn Three examples of molecular weight distribution wi : weight distribution ( mass) M104 g 50 M5105 g 40 M2107 g 1 mol 2 mol 3 mol (1) 0.1 0.9 0 (2) 0 0.9 0.1 (3) 0.05 0.9 0.05 MM,, M 105 g nw z in mol , U Mn Mw Mz U (1) 0.85 4.51 4.99 4.3 (2) 5.54 24.5 164.18 3.4 (3) 1.47 14.5 139.48 8.9 Factor 200, even if M09 .! 2 Molecules and characterisation 107 Small amounts of low Mn , do not change much MMwzand , but Mn . Small amounts of high Mn , changes drastically MMwzand . Molecules and characterisation 108 4.2 Experimental determination of molecular weight and distribution, most common examples absolute: Method Determined quantity g Optimum case: range mol 46 Osmotic pressure Mn 10 10 Colligative properties 4 Vapour pressure osmosis Mn 210 1 4 Cryoscopy, ebulloscopy Mn 510 2 Ultra centrifuge MMMnwz,, 10 3 Light scattering (static) Mw 510 3 X-ray Mw 510 3 Dynamic light scattering Mw 510 5 NMR (endgroups) Mn 210 4 Titration Mn 510 6 Mass spectrometry MMMnwz,, 10 relative: 2 Viscosity MMnw 10 4 GPC MMMnwz,, 210 Several of these methods will be presented. Please note, that frequently even the full information about Pn is not sufficient, if topology is not known, or chemistry e.g. block-copolymers is not clear! 1 “Siedepunkt“ Molecules and characterisation 109 Example of colligative properties: osmotic pressure Scheme: h solvent Solvent + polymer Membrane: solvent can cross membrane. Polymer can not cross through membrane. - similar chemical potential of solvent left and right of membrane - additional pressure is generated since solvent concentration at the right is lower and polymer is restricted to right side (“entropy”!) gh : density g : gravity h : height If polymer would behave as a gas, ideal gas-law ( p ) for polymer pV nRT n RT V c cRT Range: 20 1035gg M 2 10 moln mol Lower limit: Polymer is so small, can diffuse across membrane holes Upper limit: is to small to be detected Molecules and characterisation 110 4.3 GPC, gel permeation chromatography also called size exclusion chromatography (SEC) Basic principle: Flowing solvent Low Mn polymer through porous solution media, large High M polymer surface area+ n solution holes in nm range Detectors: what would you want to detect? Who comes out first? high Mn fraction, since it can not enter all the holes and interact with all surface area, low Mn fraction more trapped. Note: Size entropy PM n Low Mn Low Mn High Mn Concentration transform High Mn polymer Elution volume M 0 n Compare: HPLC (high pressure liquid chromatography) and GPC Principle Related effect HPLC Energetic interaction Specific adsorption GPC Entropic interaction Size exclusion Molecules and characterisation 111 Detection Information UV, IR Chemical constitution + concentration Viscosity Mn (via calibration), detection of pressure loss, Hagen- Poisseuille n (refractive index) Concentration, RI-detector (refractive index) Light scattering MMnw,, special set-up called MALLS (multi-angle laser light scattering) LASER Several detectors, simultaneous detection sample To correlate detected concentration with Mn , frequently viscosity is used: Newton: F (shear stress) A For solution we expect: cM, n Concentration + molecular weight solvent specific To “take out solvent”, no units! solvent Normalize to concentration specific , reduce viscosity, unit of inverse concentration red c To take away polymer- polymer interaction: limred : , intrinsic viscosity, unit of inverse concentration, “Staudinger index” c0 What can we guess for: Mn ? Einstein (1906+1911) solvent125.. specific 25 :volume fraction rigid If molecules would collapse to spheres with same density where solvent can not enter fM n ! Molecules and characterisation 112 If Gaussian chain would immobilize solvent: Immobilized sphere, volume V h, end to end vector hNl22 1 hNlNlNl3153. 2 2Volume of spheres mass polymer 1 322 specificVhNlNl olume sphere , Einstein! mass 11 specific NM22 c 1 information about shape?! M 2 Kuhn-Mark-Houwink-equation, also called Staudinger-Mark-Houwink kM a good solvent theta solvent ka,: empirical constants 05. a 1 , typically in tables for different polymer- solvent combination: 5 m3 k10 kg M : molecular weight (monodisperse) Molecules and characterisation 113 4.4 Ultracentrifuge Principle Liquid gravity medium Particles sink down, sedimentation + diffusion due to Brownian motion Particles or molecules feel gravity. Shape, size, density difference and gravitational forces determine sedimentation velocity. To increase speed of this process ultracentrifuge Pioneering work: T. Svedberg (from Sweden) (since 1923, Nobel price 1927) Method to proof hypothesis of Staudinger that high molecular weight polymers exist (but: Staudinger had no money to buy it, so he developed viscosity measurements…) 37g Range: 10 10 mol Determination: MMMnwz,, Disadvantage: long measurement times (h to days), expensive equipment Force towards molecule under rotation: costt cos 2 xr, xr x sintt sin 2 Fmxm r acceleration m is effective mass: Mp m1V p NL NL : Avogadro number : density solvent Molecules and characterisation 114 3 V : specific volume cm polymer p g Mp : molar mass polymer This centrifuge force is balanced by friction proportional to sedimentation velocity. dr Ff dt f : friction coefficient M dr 2 r1Vfp p centrifugal NdtL acceleration velocity dr fNLLdt s fN Mp 2 1Vp r1V p :S Svedberg How can we determine “f” ?! kT f B Einstein relation D D : diffusion constant sRT Mp Svedberg equation D 1V p D light scattering or via Stokes-Einstein: kT D 6r Apparatus (“Beckmann”) Typically: 105 rpm optics, triggered: UV, absorption filter refractive index 106 g (earth acceleration) sample + solvent detectors rotor axis Solvent can be with density gradient Applications: - particle size of polymer emulsions in water or organic solvent Molecules and characterisation 115 - absolute Mn for extreme high Mn where GPC and light scattering is problematic (e.g. 6 g 10 mol ) - molecular weight distribution for polymers that interact with GPC column - determination of chemical heterogeneity using density gradients; seperation of polymer mixtures and copolymers Molecules and characterisation 116 4.5 Light scattering of polymer solutions Two types: - coherent, elastic scattering, frequency is not affected - incoherent, inelastic scattering, frequency is modulated via polymer motion (Doppler shift) (also called: inelastic, quasi-elastic, dynamic light scattering) general set-up: transmitted IIe cd incident beam beam 0 I0, Scattered light 4 frequently Laser 10 I0 Sample-cell polymer solution detector note: for special cases, e.g. crystallisation or phase separartion the transmitted light Itis measured, making use of the “Tyndall” effect. Basic equations: EE0 cos t electric field of light beam pE 0 cos t polarisation of molecule via light 2 2 dp 2 Is 2 scattered light (change in dipole) , dt Two types of polarisation p a) for unpolar molecules+ polar molecules shift of centre of mass of electron cloud relative to protons, fast process shift polarisation b) polar molecules only: if a permanent dipole exists, it can be oriented. Orientation of molecule results in total polarisation, can be calculated using Boltzmann distribution dipole of molecule field p2 Langevin equation with final result pE but this process is for light 0 3kT 1 scattering to slow! v10 14 light s Molecules and characterisation 117 orientation polarisation, detected via dielectric spectroscopy (not covered in this chapter, see chapter 5) How to vibrate electrons? All interactions are summed up, Taylor + stop after quadratic term + - k proton electron mpe 2000 m mmep No need to use reduced mass me mmep k 2 No external force: 0 , resonance frequency km 0e me With electric field EE 0 sin t dx2 mmxeEt 2 sin ee00dt2 e : charge Solution: eE0 xt22 sin t 0em In phase, even if not at resonance. Typical resonance frequency for vibration of atoms is in IR region 11415 ( 3000cm,, 10 Hz0 10 ) k 500 N m for single bond We guess: factor 2000 in mass electron proton proton proton Changes into k N 30 0 , with k 500 m and m10kge m Molecules and characterisation 118 for electrons : 16 0 210 light 0xRay For light scattering: eE0 0 xt 2 sin t 0em For X-ray: eE0 0 xt 2 sin t me Dipole moment is: pt e xt 2 2p Is 2 t 2 22 eE0 light scattering: Its 2 sin 0em 2 2 eE0 X-ray scattering: Its sin me 4 Is for light scattering! Blue sky, Rayleigh scattering (1871) Ifs X-ray! 1 3 Is 2 if number of electrons is proportional to r (size of scattering particle) me 2 1 6 Irs large particles scatter much more m number of e electrons Scattering of light is dependant an orientation of dipole and polarisation of light Molecules and characterisation 119 z y y Incomming light x-y plane I sin2 s x x No scattering along dipol axis Dipole vibrates along y-axis Incomming light z y x-z plane y x x Isotropic in x-y plane Dipole vibrates along z-axis non-polarized : 1 cos2 For a certain volume we find: 2 2 p 2 2 2 2 I2s0 0 0 three sources of scattering intensity t impotant term 0 : mean : fluctuation Idea of Einstein 1910: 2 II20s0 s 0 Reason: In scattering volume v we will find a lot of electric dipoles. Always a pair is found that will cancel each other. Therefore only the quadratic fluctuation leads to scattering intensity ( Doppler effect, frequency shift) n Molecules and characterisation 120 2 2 22nn 2 2 2 nnc00B cB density fluctuation polymer concentration fluctuation, polymer + solvent 0 important contribution n : refraction index :density 2 222ncB Ins0 c B; c B RTc B thermo- cB T dynamic To compare scattering intensities we define Ir 2 R IV00 V0 : scattering volume I0 : incident beam intensity Reduced scattering intensity or Rayleigh ratio R . To get scattering intensity from polymer RR solution R solvent : R cB RkcRT B T : Osmotic pressure 2 22 4n 0 n k 4 , k :optical constant NcL0 B no increment, no scattering isorefractive solvent, index match kcB 1 RRTc B T M light scattering can measure polymer weight M! For polymers we find for osmotic pressure : c RTB A22 c A 33 c ... M BB (*) Molecules and characterisation 121 (*) second virial coefficient, may differ from osmotic second virial coefficient kc B 1 2AcB for non-monodisperse solutions, fundamental scattering equation RM W Holds, if R , e.g. M10 5 g g 20 mol In case R : Debye scattering, includes intra- and intermolecular scattering g 20 kc B 1 2A2B c (I) RMP w I P , form factor, scattering factor. I0 Debye 1915: 1 sin qr ij P 2 Nqrij ij 4 q .sin (II) 2 rij :distance scattering centre i from j 3 1 sin and rr22 3! 2N2 ij 1 P1qr 22 Guinier 1939 3 General, independent of shape 11 1qr22 (III) P3 Putting (I), (II) and (III) together 2 kc 1 16 B 1r22 sin 2Ac 2 z 2B Rc , Bw M 3 2 if polydispersity included Molecules and characterisation 122 Analysis via Zimm-plot variation extrapolate 0 kc R extrapolate slope A2 to c0 r2 Mw z 2 qkc1 free parameter Form factor P contains information about shape of molecule, e.g. sphere, stick, Gaussian shape… Incoherent, inelastic, quasi-elastic or dynamic light scattering Idea: velocity I00, particl 310Hz14 0 It, intensity modulation and frequency shift (Doppler-shift) frequency distribution „in“ 14 broadened 0 310Hz 6 110Hz 0 frequency distribution „out“, but 108 can not easy be measured in frequency space Molecules and characterisation 123 Solution to this problem: Wiener-Khintschin theorem (1930+1934) “The spectral density (=spectrum) is the Fourier-transform of the autocorrelation function” 1 Sgtedt it 2 gt S eit d What is the time autocorrelation function? It It It dt g It2 dt t t t 1 2 3 4 Large particle Small particle I I I I c c t t slow fluctuations fast fluctuations c typical time need to be again at mean value or cross this value I . Note: I is function of t due to concentration fluctuation general form of autocorrelation functions t GA1B exp , calculated by “autocorrelator” c Molecules and characterisation 124 gt gt 1e t log t c c c should depend on? 4 1 - Scattering angle, q sin , unit: 2 length area - Diffusion coefficient, unit: time - Size of spherical particle - Viscosity of media Stokes- Einstein: kT D 6r r : size of particle, hydrodynamic radius : medium, e.g. H2O, 1mPas 1 For large D small ? ccD Autocorrelation for monodisperse spheres At low concentration: t 2 gt ec eDq t 1 c Dq2 Generally: no single exponential function Analysis: It gt Dr Pr intensity auto- distribution of size fluctuation correlation diffusion distribution coefficient The step from autocorrelation to the distribution of diffusion coefficient is not easy (mathematically), via e.g.: - cumulated method - non-negative least square (NNLS) - Contin algorithm Molecules and characterisation 125 Experimentally conducted via two techniques: scattered light Photo Auto- data Homodyne multiplier correlator (simpler, mostly in commercial application) non-scattered light, Photo Auto- data heterodyne multiplier correlator scatterd light Application of dynamic light scattering - polymers in solution - suspension - emulsion Typical: r: 10 1000 nm m2 D10: 12 10 14 s Be aware of the following relation: number volume scattering intensity 1 : 1 1 : 1000 1 : 1000000 10 100 r 10 100 r 10 100 r nm nm nm Molecules and characterisation 126 4.6 IR-Spectroscopy Spectral regions 1 m cm Hz Near 0.78-2.5 12800-4000 38.. 1014 12 10 14 most Middle 2.5-50 4000-200 12. 1014 6 10 12 important Far 50-1000 200-10 61012 310 11 Remember: 1eV 9000 cm1 kT 200 cm1 1 wavenumber energy E=h hc 1 : how many waves per 1 cm, e.g. 4000cm,., 2 5 m since 25. 10632 4 10 10 m 1cm Important since: - analysis + characterization - isotope selective - not selective towards optical isomers (chiral) - combination, gas chromatography, GPC - FT resulted in factor 100-1000 increase in sensitivity per time, e.g. monomolecular layers detectable via IR IR: vibrations between nuclei in molecules can be excited in case electrical dipole is present vibration Raman: polarizibility, CO2! Electric + - dipol A B l Ql Vibration frequency: Newton: Fmamx kx (Hook) Molecules and characterisation 127 “Ansatz”: xt Ae it mAe2it kAe it k 2 m k m 1k 2m k :force constant via chemical bond, electrons m : nucleus mass, sensitive to isotope! Potential: harmonic, if force is linear in x Fkx 1 1 VFdxkx2 2 Ex E A A vibrational levels A A Quantum mechanics 2 x How many degrees of freedom for vibrations if N-atoms in molecule are present? f3N6 xyz,, Translation or rotation of whole molecule does not lead to vibration f3N5 for linear molecule e.g. H2O: f3 these vibrations are separated in: - stretch + bending vibrations distance angle, torsion Molecules and characterisation 128 stretch symmetric asymmetric In plane rocking In plane scissoring bending + + + - wagging twisting - in principle we should be able to detect all degrees of freedom in spectrum, via anharmonic potential even more but: 1) symmetry, ( degeneration) reduces number of resonances (also called bands or vibration modes) 2) often the energy differences between different resonances are small (especially for bending) 3) resonances are forbidden (e.g. no dipole moment) very low intensity 4) resonances are outside investigated spectral region treatment of harmonic potential in quantum mechanics leads to: 1h k Reduced mass En mm 22 12 mm12 Zero point energy (Heisenberg), particle cannot stand still typically 001A. for vibrations n n012 ,,,... 2 He x ; H: Hermite polynoms Molecules and characterisation 129 Selection rule: Golden rule (Fermi), perturbation theory 2 ˆ Absorbance f1iH ˆ HE1 ˆ electric field ˆ : dipole moment ˆ xQˆ charge space operator 1 xIIˆ ˆˆ ladder operator ˆˆIxiyIxiy ˆˆ; ˆˆ 2 2 ˆˆ fiII if,: set of orthogonal functions n1 Selection rule for IR but: spin- orbit coupling, heavy atom effect, Born-Oppenheimer… Typical force constants N k510 2 single bond m N 110 3 double bond m N 15. 103 triple bond m vk H e.g. 1 molecule H2O should be stretched by 1A, how many molecules H2O O are needed to generate this force simply by weight? H F k x 500 1010 N 5 10 8 N 18gH O 0. 18N 6 1023 molecules 2 -8 5 10Nx molecules H O 82316 2 510 610 310 x1510. 17 !!! 018.. 018 the spring is very, very rigid ! Molecules and characterisation 130 Hardware: IR-light sources: - blackbody radiation at 1500 2200K (sun: 6000K visible) hot iron red - Nernst glower (rare earth oxide, electrically heated) - Globar source (SiC) - Mercury arc (high pressure to widen the resonance lines) 1 - Tunable CO2- laser (900 1100cm ) high intensity, not vissible Detectors: 6 V - thermal ( T of10 K detectable, 68 W ) - photo conducting detectors, e.g. Hg Cd Te, PbS IR-instruments: 1) dispersive instruments 1 2 Generally double beam 3 prism 2) FT-IR (see later) 3) Non- dispersive at fixed frequency ( atmosphere measurements) 4) Reflective instruments, e.g. in emission, for example to detect chemicals via large distance FT-instruments - multiplex instruments ( information theory) more than a single information is simultaneous transmitted via a single channel I 1 1 I 2 2 Not multiplex I 3 3 prism compare telephone wire: several conversations simultaneous via one wire Molecules and characterisation 131 FT-advantages 1) flux- or Jaquinot advantage, less optical elements (e.g. collimation, slits etc.) lead to higher signal, factor: 10 100 2) higher precision averaging of spectra easier possible, Sn , n:scans 3) multiplex or Fellgett advantage all vibrations are simultaneous excited, factor: 10 100 FT conducted via Michelson interferometer; A.A. Michelson (first built 1891, Nobel prize 1907) fixed mirror moving mirror lamp x Semi-transperent 1 0 1 (reflectant) mirror, 2 2 e.g. Ag ca. 100 A sample detector Pt 1 0 1 2 2 No sample Intensity varies as a function of absorption (reduction) Molecules and characterisation 132 Setup at “0” constructive interference, “maximum” Interference pattern xDWSW e.g. 4000cm1 Pxt 1 DW 1.( 25 m SW ) 2DW mechanically demanding 0 x [cm] Amplitude of mirror motion xAQ spectral resolution e.g. 10cm 0. 1cm1 Source: Skoog Molecules and characterisation 133 12-25: methylacetophenon O C CH3 CH3 12-26: acrolein H2C CH CHO + H2O 12-27: propannitril CH3 CH2 CN Molecules and characterisation 134 IR-spectroscopy for polymers, applications: - chemical composition and additives - kinetics (IR is very fast) of polymerization - analysis of sequences in copolymers, changes of resonance - detection of small amount of branches, e.g. in PE (dimension 1 per 1000 CH2) cd - semi quantitative using Lambert-Beer IIe0 ( c : concentration, : extinction coefficient) - stereo regularity (e.g. a-PP, i-PP) - blend composition - orientation via rotation of sample along IP 2 second Legendre polynom - detection and quantification of crystallinity - characterisation of polymer surfaces Note: Raman spectroscopy and SERS (surface enhanced Raman spectroscopy) is getting more and more applications due to high intense Laser light sources. Molecules and characterisation 135 4.7 Mass spectrometry How to measure the weight of a molecule??? In general no spectroscopy since non coherent and non resonant Definition of atomic mass: 1amu 1Dalton 2(unit Dalton frequently used in Biology) 12 12g C 1 mol 12 23 6. 0221 10 atoms mol 1. 66054 1024 g atom12C Question: 35 3 Why is 17 Cl 34. 9688 Dalton 0. 0312 Dalton energy to bind nuclear particles together Emc 2 - atoms of same element can be in different isotopes e.g. 123H 99.%, 985 H 0 .%, 015 H 0 % AAp ii isotopes A : mean atomic mass Ai : mass of isotope “i” pi : relative probability of isotope “i” Mass spectrometer: - measures amount and mass of charged atoms, molecules and molecular fragments m - relative precision: 105 m - absolute price: 1056 10 € 2 amu (atomic mass unit) 3 Explanation protons + neutrons protons X , X: element abbreviation Molecules and characterisation 136 - set up, each part in more detail afterwards sample Inlet Ion Mass detector system source analyser separation Signal Vacuum system processor 58 10 10 Torr, 760 Torr 1 bar Why? mean free path length of ions Read out inlet system: - ng might be enough - different for liquid or gas phase samples coupling to gas- chromatography or TGA (for polymers) - samples should be in gaseous phase so that they can be ionized Detectors: Most ions are cations (ca ions, positive charged) - dynode amplifier photomultiplier - Faraday cup, continuous decrease in electric potential along electric resistance, U decreasing distance E , electric field d Molecules and characterisation 137 About 20 times, each factor 2-3 2.! 520 10 7 10 8 Why?! Source: Skoog Mass resolution - e.g. to determine sum formula - purine C6H5N4 m 120. 044 N N N N H - benzamidine C7H8N2 m 120. 069 H N C NH2 - acetopheone C8H8O m 120. 058 O C CH3 Molecules and characterisation 138 001. Needed resolution: 80ppm , commercial:1 to 1ppm 120 IM 1 Information also from isotope distribution 12CCNN,,,... 13 14 15 IM 1 H 1:. 0 015 % 2 H 14 N 1034:. % 15 N 28 Si 151:.% 29 Si 12 C 111:.% 13 C 35 Cl 1325:.% 37 Cl 16 O 1004:. % 17 O CHNO6424: 13 C61166:.%.% 2 H:.%.% 4 0015 006 15 N2037074:.%.% 17 O4004016:.%.% 756.% CH12 24 : 13 C1211132:.%.% ! 2 H:.%.% 24 0 015 0 36 13.% 56 Mass analyser - separation of mass with respect to different acceleration (at similar force) in B-/ or E- fields, magnetic or electric 1) acceleration in electric field 1 2 zeV 2 mv (1) 2) force in B-field (Lorentz-force) FzevB with vB FzevB (2) Molecules and characterisation 139 3) Centrifugal force cost rt r at 2 r 0 sin t v r vv22 Fmam2 rm rm (3) rr2 From (2) = (3) v2 Bezv m r Bezr v m In (1) Bezr2222 zeV 1 m 2 m2 B22 ezr m B 22 er V 1 2 mz2V Variation of BrV,, Molecules and characterisation 140 4-10mm ca.15 cm Faraday cup Source: Skoog Molecules and characterisation 141 Quadrupole mass filter Monopole: Dipole: Quadrupole: The electric potential at the poles contain a time dependant oscillatory and constant dc-offset. m The trajectory for the ions is different for different and v (when entering the quadrupole). z The quadrupole acts simultaneous as filter for low and high masses. TOF: time of flight Scheme: No electric field, ions fly All ions generated simultaneous ( 025. s) Detector 34 10 10 Volt Time of flight:130s repetition rate Further: - FT-transform - Combination of B and E-fields Ion sources - depending on ion source, the molecules will experience different degrees of fragmentation hard and soft sources common ways to produce ions: - electron impact - chemical ionisation Molecules and characterisation 142 - field ionisation - field desorption M106 g - Maldi- TOF, very important for polymers ( n mol ) matrix assisted laser desorption of ions, + time of flight detection Electron impact (hard) gas M M Anode Acceleration voltage: 70V binding energy 34eV strong fragmentation Fragmentation ( mass spectrometry books), e.g. Norrish I: X scission Norrish II: X scission - CO2, H2O elimination Molecules and characterisation 143 -H2O 18 45 -COOH 63 Electron impact (hard) Field ionisation Field desorption (soft) Source: Skoog Advantage - via fragmentation chemicals have unique decomposition Disadvantage: - very complex spectra - sample must be in gas phase Molecules and characterisation 144 Chemical ionisation (soft) Idea: CH44 CH CH 53 CH e CH4 reactive, will transfer proton with charge Field ionisation (middle) Needles, ca. 1m thick Very high E-field at tip ionisation! kathode, 10 m 10-20kV Trungsten anode Desorption methods ( m 10000 amu, soft) - field desorption, sample on Tungsten anode, similar to field ionisation - fast atom bombardment: Xe, Ar Glycol + sample Matrix 1000 : 1 Maldi-TOF Laser ions COOH Sample + + Salt (e.g. silver) Very low amount, e.g. polymer Molecules and characterisation 145 Further important for MS (mass spectrometry): - combination with GC, gas chromatography - Tandem MS, also called MS/MS, (e.g. QQQ: 3quadrupole) First: soft ionisation, only molecular ions Second: selection of specific mass, e.g. via quadrupole Third: hard fragmentation via ions (e.g. He) in quadrupole Forth: analysis of fragmentation fingerprint Advantage: very fast (compared to GC/MS), ms versus min! - Detection of elements via extreme hard sources (plasma) 01. 10ppb detection limit - SIMS (secondary ion, mass spectrometry) + + + Ar , Cs , N2 MS + O2 Sample t = 0 Sample t = later Depth resolution: 100 A Sensitivity: 1015 g m2 - Laser microprobe mass spectrometry Sensitivity: 1020 g ! Molecules and characterisation 146 1000 gmol M n 5.000 g mol 1.000 g mol Mun u 0.2 u 0.04 M W 1,04 (monodisperse) M n Molecules and characterisation 147 Source: J. Räder, MPI-P Molecules and characterisation 148 MS- application to polymers (examples) - identification of polymeric systems - identification of additives (e.g. combination with TGA, thermo gravimetry) - molecular weight and molecular weight distribution (but: ionisation probability is function of Mn separation via GPC, quantification via MS) calibration of GPC - end group analysis - characterisation of copolymers (distribution of each component) - oligomer characterisation Molecules and characterisation 149 4.8 NMR- spectroscopy -Very versatile spectroscopy of the nucleus with respect to chemical structure, dynamics and orientation. This spectroscopy is mostly used for solutions but can also investigate bulk material. Large dynamic range (1095 s 10 s ) and spatial range (1012 m l 10 0 m NMR imaging). NMR- spectroscopy is isotope (not element!) sensitive. Most important isotopes to be investigated: 1H, 2H, 13C, 14N, 19F, 29Si, 31P… Principle ( QM): The nuclear spin is related to a quantified, absolute angular momentum, eigenvalue of the ˆI2 operator ( QM) ˆ2 III1 ; 1 I : nuclear spin quantum number, e.g.: 01,2 , ,... 1 1 13 15 19 29 31 Spin 2 : H, C, N, F, Si, P The z-component of the angular momentum is given by ˆ ImzI ; mII1II : , ,... magnetic quantum number 1 1 1 For spin 2 only two possible states: 2 and 2 exist. The total magnetic moment is given by Iz; : gyromagnetic ratio, isotope specific Since the energy for a classical magnetic moment is given by: EBIBmB zI Molecules and characterisation 150 We expect: - energy gap linear in B-field m 1 E 2 Transition possible! Eh 1 m 2 B-field 1 1 Transition between two states 2 and 2 can happen if electromagnetic wave has energy that “fits” the difference 11 EB Bh L B 22 Larmor frequency 42MHz ,. B 1 5 22 H T Tesla : resonance frequency: range: 60 900 MHz for protons 15 225 MHz for 13 C Spectroscopically used, only population difference (Boltzmann) 34 6 23 N12 E h NL 6 10 300 10 6 10 exp exp exp NkTRT1 8 300 2 300MHz exp 61055 1 610 Very, very small!! 1 Picture for magnetisation (spin 2 ) QM: Spin components with respect to absolute value and z-component spin classical magnetisation M Molecules and characterisation 151 z M B 0 y y x applied B1-field for some time so that tBt90 1 or 180° e.g. If B1 is switched off after 90 , magnetisation is in xy-plane, rotating with Lamor precision MM() 0Lsin t around B1-field. Since: ddM UMt cos , we expect periodic signal for induced voltage in a coil. dt dt L0 L B1 Exponential envelope 1 Free induction decay = FID T 1 e 2 FT T2 t 0 1 Bt 90 T T t520s 50ms-1s The exponential decay is given, since magnetisation wants to go back to equilibrium (along z- axis). Any vector M can be separated into two vector components: along z-axis (B0-field) and perpendicular z-axis. Both components have individual relaxation constants. Mz Along z: M T1, spin-lattice, longitudinal relaxation time z : T2, spin-spin, transversal relaxation time Mx,y Molecules and characterisation 152 Who will relax magnetisation back to equilibrium? fluctuation of local magnetic field, analogue light scattering or dielectric spectroscopy, spectral density I Along z: T1, energy is changed, spins “look” for fluctuations. at Larmor frequency range e.g. 100MHz to make transition information about fast motions, I L z : T2, energy is not changed, magnetisation “fans” out I 0 information about slow motion Question: Why the hell would we do NMR if we would see only 1 peak? chemical shift! Simple picture: B0 Bohr orbit nucleus B Lenz Electrons on orbit (moving charge) will counteract applied B0-field and generate a Lenz-field BLenz. Nucleus “feels” sum of both. Lenz-field is function of local electron density (order number z), anisotropy ( solid state NMR), hybridisation (e.g. sp3, sp2, sp)… We expect small changes. Since we have no “naked” 1H or 13C we detect relative differences. CH Si 1 13 29 Chemical standard is TMS (3 4 H: = 0 ppm, C: = 0 ppm, Si: = 0 ppm) Isotropic chemical shift sample TMS TMS Molecules and characterisation 153 Range: 010ppmH 1 0 200 ppm13 C Note : 1 Since 42 MHz and H 4 a 1ppm changes means 300 Hz at 7 Tesla for IH Tesla 13 C protons and 75 Hz for 13C, current limit: 1Hz ! ( up to 109 )4 ”theoretically” 3000 resonances in 1H and 15,000 resonances in 13C can be separated 13C better resolution power (selectivity). The isotropic chemical shift (“chemical shift”) is very sensitive to chemical environment, up to 4-6 bonds away influence vanishes. Samples: 110wt % solution in 5-10 mm test tube (1-100 mg), typically Temperature: -150°C up to 200°C typically Spectrum can be integrated to achieve relative distribution of 1H (13C more complicated), up to 1 relative accuracy 4 Record Mösbauer: 1014 ! Molecules and characterisation 154 Source: Skoog Molecules and characterisation 155 For solution NMR, two more interactions are important called I -coupling and NOE-effect. I-coupling, dimension: 1-200Hz, information about spin state transferred along the covalent bonds, via s-electrons Idea: H s-electrons “dive” B into nucleus along H O A C H the bond C H H B H Proton HA “sees” proton HB having the following magnetic quantum states: or 1: or 2: 1: spectra HA: I Intensity 1 2 1 Pascale triangle “triplet” (others: singulet, doublet, quartet…) NOE-effect: (2) B0 N Spin 1 systems can simplified be viewed as stick magnets. 2 S 1 Depending on orientation and distance r ( 6 ) they r r N interact. It is possible to use this information to detect spatial S proximity ( 5A) (1) Molecules and characterisation 156 Decoupling: The magnetic moments of e.g. 1H affect the 13C spectra. To switch off this influence one can irradiate at 1H while detecting 13C, 2D-NMR: The basic idea is to correlate resonances of different isotopes (e.g. 1H. 13C) and/or different interactions (e.g. with or without decoupling, along the bond using J-coupling, through space using NOE) in analogy to a joint probabilityP12 . This joint probability is displayed like a chess board. The correlation is generated via complicated pulse-sequences that switch on and off specific interactions. 2D-NMR answers questions like: 1 “Proton with 1 has covalent H neighbours with 2 ” COSY “Proton with 1 has spatial neighbours with 2 ” NOSY 13 “Carbon with 1 has covalent C with 2 ” inadequate (NMR abbreviation) Currently perhaps 100-300 NMR selection methods “pulse sequences” are known! Experimental realisation (idea), assuming T1 Pulse generates Magnetisation magnet. along z In x-y plane assumption 1 2 3 1 A is correlated B 3 To B via pulse 1 1 sequence t 2 B A Direct detection 2 types of resonance, A+B t22 t11 Molecules and characterisation 157 Spectra: 2 projections A 12 0 B 0 1 The information for resonance A during t1 is “transported” to t2 via the amplitude at 1 . Variation of distance between the first two pulses transfers the whole information as amplitude modulation to t2 (Ernst, Nobel prize 1991 idea: Jeener 1971). Applications to polymers: - Mode of addition (head to head, head to tail etc.) - Stereo chemistry, tacticity - Isomers of dien polymers (1,4 or 1,2 addition, cis-, trans-,…) - Chain branching - End groups - Copolymer composition - Sequences of monomers copolymerization constant rr12, - Coupling to GPC Solid-state NMR: Solid state NMR allows to study bulk properties (e.g. orientation, dynamics and chemical structure) of polymers. Lines are generally broader due to non-averaged motion and dipolar interaction, e.g. 1H-liquid-resonance: 1-100 Hz 1H-rigid-solid-resonance: 10-20 kHz, Gaussian shape To achieve better resolution and sensitivity several hardware and HF-techniques might be applied: - CP, cross polarisation, transfer of e.g. 1H magnetisation to 13C using Hartmann-Hahn condition Molecules and characterisation 158 - DD, dipolar decoupling, high intensity irradiation to reduce 1H 13C dipolar coupling - MAS, fast rotation of sample (e.g. 7 mm rotor, 200 mg) along “most trivial” orientation (1,1,1)54, 7 relative to z-axis ”magic angle”. If rotation frequency is fast, interaction is detected only as averaged quantity. rotor : 3 35kHz mechanical 2 motion! MAS: magic angle spinning - Solid-state NMR can (as liquid NMR) be performed in 1D, 2D, 3D and 4D! 4D: 4 frequency axis + 1 intensity axis Solid state NMR application on polymers: - quantification of crystallinity - determination of orientation distribution e.g. fibres and films - chemical assignment of insoluble or cross linked material - dynamics in bulk material, e.g. spatial and dynamic heterogeneity for glasses 1 1000 - motion in polymer crystals (helix jumps 10 sec to sec ) - spatial proximity in H-bond systems, DNA, bio polymers, fuel cell membranes… Molecules and characterisation 159 Source: Diploma thesis Wilhelm, 1992 Engineering properties 160 5 Engineering properties Polymeric materials are mostly used (and have to be processed) due to optical, mechanical and electrical properties. 5.1 Mechanical properties For melts, typically three measurements Fv . Newton Ad A) shear rate dependant viscosity log v 0 1 d Bending point n log linear homo polymer 1 : unit of inverse time s : unit of pressure time Pas 3 0 : plateau viscosity, relaxation time nM0n; , reptation model : bending point “knee”, if applied shear rate exceeds inverse of longest relaxation time n : scaling exponent, polymer is frequently shear thinning n0709 .. Fit of shear rate dependant viscosity via 2-6 parameter models, e.g. 0 n 1 Engineering properties 161 B) step experiment Torque (time) t 0 t e.g. e c 0 t 0 t Fast step, 0 G Hook in shear 3 c : correlation time, Mn , if network : no decay to t0 Very slow processes can be seen, since t can be measured for minutes to hours, 1 related frequency range 1024 to10 Hz c C) oscillatory measurements (small amplitudes, GG,, G 00 G ) xt sample 1 idea: apply: xt xsin t 0 d tt0 sin What happens for: spring, elasticity (memory, storage) Gt Hook (1634-1703) Gt0 sin in phase t ; 0 , amplitude t t t t - perfect viscosity, dash pot, viscosity (no memory, loss) Newton (1642-1727): ; : constant 0 sin t 0 cos t Engineering properties 162 tt0 cos , 90° out of phase In “real” live superposition of spring and dash pot e.g. Maxwell or Kelvin-Voigt in series SDP SDP SDP SDP Many more combinations exist! Separation of response in “in-phase” (=elasticity) and “out of phase” (=viscosity) contributions phase lag sin t 0 G tGsin tG cos t tan 00 G G : storage modulus, shear t G : loss modulus, shear t t ()t Typical shape of GG , for monodisperse linear polymer melt IV Polymer log G I II III GPa Glass 109 Gp analog Rubber plateau 6 G 10 p 1 TTS 2 flow 1 tan Temp. log length scales Rg 10-50nm ; Re 2-3nm Large frequency range available via TTS, e.g. 10 decades Engineering properties 163 Zone I: G 2 analog Maxwell-model G 1 GG viscosity dominated at low frequency length scale probed: Rg Longest relaxation time: 1, for tan 1 Zone II: GG elasticity dominated, physical networks of entanglements, maximum relative elacticity at tan : minimum Entanglement molecular weight via RT kg M , typical values: 1000 3 , e G m T 450K,. R 8 3J , M 10 kg molKe mol 5-10nm G1010Pa 56 ! memorize, rubber plateau 3 Plateau length in is strong function of Mn since M e.g. M12 10M Zone II 3 decades larger Zone III: Transition zone towards polymer glass Zone IV: G10Pa 9 , length scale probed 23nm , polymer glass In solids, polymer materials are tested in elongation using test bones ll 0 Force Elongation 1 , zero for no change l0 l Deformation ratio: , one for no change l0 l0 For small elongations: E In shear: G-modulus, in elongation: E-modulus, Young’s modulus For simple elongation the following types of response can be identified in a stress-strain curve: Engineering properties 164 Maximum: yield S Brittle and hard Tough and hard point rupture Tough and soft Limit of linearity soft y s Yield point with y , yield stress and y yield elongation Van-der-Waals bounds are destroyed, necking happens S :: S maximum tensile stress, tensile strength S : elongation at break Young’s E-modulus are also determined under oscillatory conditions (DMTA: dynamic mechanical thermo analyser), 1 frequency, T-variation, simple apparatus E (storage) and E (loss) xx10 z yy20 F z0 F y x y0 Uni-axial: y=z zz20 x0 Simplify: xyz1000 Volume conservation, incompressibility: xyz000 x 010202 y z 2 1 12 1 2 ; 1 : 1 1 2 (cross section area) 2 For Gaussian chain 222 22 22 22 xyz000 xy00202 z Pxyz1000,, e and Pxyz2 ,, e P S ln 1 Boltzmann 1896 P2 Engineering properties 165 222 222211 Sxyzxyz000 0 0 0 22 211 2 x1y1z1000 xyz1000 22211 2 2 111 33 S 2 1 1, H0 force 21 2 2 2 2, GTSW Fd force 1 1 stress E area 2 2 Young' s modulus Careful: for experimental reasons, the non-stretched area is used ( zy00 ) For simple model (incompressible, small, isotropic) it can be shown that E 3G E, more general: G ; 005 . 21 : Poisson number Engineering properties 166 5.2 Dielectric properties Since polymers are frequently used for electrical insulation the interaction of electric fields as a function of frequency is practically importanti. From a spectroscopic point one can learn something about molecular motions as function of frequency and temperature. Principle (macroscopic): it UUe 0 applied voltage it IIe0 electric current U E electric field d Dielectric displacement, D As DE8910* ,. 12 00 Vm Complex dielectric function (dielectric permittivity) * i Polarization: * 1 PDD00i 1 E p V pi : individual dipole molecular quantity pQli , charge times distance In contrast to pi is P a macroscopic quantity. The individual dipole moments result from: , p fast in time large: 1. electronic polarization, shift of electronic orbits 2. atomic polarization, shift of relative position of nucleus studied, molecular motion, : 3. dipole polarization as result of orientation of permanent dipoles under influence of electric field the dielectric spectrum is an analogy to quasi-elastic light scattering (see there) and use of the Wiener-Khinchine theorem the Fourier transform of the dipole autocorrelation function i E.g. radar technology in WWII, superior dielectric properties of polyethylene Engineering properties 167 * gte it dt 0 FT PP0 t Autocorrelation function: gt e.g. exp called Debye relaxation P2 For Debye relaxation: t t 1 it -(i + ) t * eedteit dt e dt 1 00 0 t 1 1 i 11it e 111 iii t0 complex conjugated 1 i 2 112 22 22 i 2 1 2 1 ,real part ,imaginary part For dielectric spectroscopy a Debye relaxation is described by 1 2 1 2 : relaxation strength To describe non-(single)-exponential relaxation, the most common equation used is the Havriliak-Negami function (1966). HN 1i HN : symmetric broadening of : asymmetric broadening of HN MAX !! but close The local arrangement of dipoles in macromolecules was classified by Stockmeyer (1967): Engineering properties 168 Type “A” e.g. 1,4 cis Polyisoprene end-to-end vector! Normal mode! Type “B” e.g. PVC Type “C”e.g. PMMA Typical spectrum amorphous polymer: type A: Normal ´´ ,T ! mode segmental local Conductivity glass 1 log -3 12 10 e.g. Li+ from anionic polymerisation Experimentally: 15 decades! Normal mode: end-to-end vector only for type “A” M3 , strong molecular weight dependence. Segmental: Glass transition, cooperative, non single Debye, T-dependant, apparent activation energy called relaxation (,, : increasing frequency), several monomers ( x 13nm), main chain involved, determination of Tg. Local: Single exponential, Debye, Arrhenius type (Ea) -relaxation, frequently side chain motion. Be careful, for semi crystalline polymers: : crystalline motion, : segmental, : local Engineering properties 169 5.3 processing of thermoplast; extrusion, injection molding, calendaring For practical applications rarely pure polymer systems are used. Most of the time polymers are combined with other polymers to form a blend (e.g. PS + Polybutadiene called HIPS, high impact polystyrene), plasticizer, flame retardants, antistatic agents, fillers, blowing agents, processing agents or pigments. Plasticizer: Reduce crystallinity, modulus (up to 103), viscosity, easier processable, similar effect as raising temperature (but without degradation), example: DOP (dioctyl phthalate), low Mn polyester, chlorinated polyester,… Flame retardants: Flammability serious problem, parameter used, e.g. limiting oxygen index (LOI) or critical oxygen index (COI). Recommended: LOI > 0.27 (27% O2 in N2 per volume), e.g. PE: 0.18; PTFE: 0.95; PC: 0.27; PEO: 0.15 Halogens (Cl, Br) or phosphorous, trap radical production during burning. Antistatic agent: For specific use, static charging can not be tolerated, e.g. when dust ( explosions) is present or sensitive parts ( microcomputers) are involved agents. Carbon black, carbon nanotubes (why?) and conducting surfaces (H2O, PVA) are used. Fillers: Two main groups: o to improve mechanical strength composites, e.g. glass fibres in epoxy resin, o to reduce the amount of polymers needed (called: extender) e.g. CaCO3, SiO2, € clay, wood, etc., must be cheap < 1 kg Blowing agents: Production of open or closed cellular structure, expand plastics ( 2 1000 kg ), e.g. EP m3 o thermal decomposition NCO22, o heat + low boiling liquid (CH512614, CH ), e.g. styropor o chemical reaction, e.g. NCOHO222 NHCO o gas expansion, foams can be very heterogeneous xyz,, ! Engineering properties 170 Processing agents: To improve processing ability, e.g. salts of fatty acids, fluorinated alkanes, mineral oils,… Stabilizer: Combination of heat + oxygen affects final properties (strength, colour yellow), antioxidants or peroxide decomposers, PVC is thermally most problematic since HCl acts as autocatalyst, example: sterically hindered phenols Pigments: To colour the material To get a homogenious distribution, mixing is needed Two main types: - distributive mixing, number of particles constant, shape changes (surface area) shear or or elongation 2 1 important is viscosity ration 2 and surface tension between two liquids 1 - dispersive mixing: break up of agglomerates and/or particles (e.g. carbon black for rubbers) shear or or elongation shear or or Breakup of (satellites, misting) elongation droplets balance between shear forces and surface tension is described by the “capillary number” F FrAr 22 ; , surface shearA shear sh Engineering properties 171 r : size F Fr surface tension l surface tesion ST 2 shrr sh Ca capillary number ST r ST Often elongation is more effective compared to shear for mixing In processing, mixing is achieved via static or dynamic mixing mostly via extruders. Extruders are snail pumps (analogue Archimedes screw). They are single or double crew type. The double screw can be intermeshing or non intermeshing and co-rotating or counter rotating. Depending on friction of screw and wall the extruder is solely a pump or locally rotating the melt. For optimum mixing the shaft should have low friction (polished) and the wall should have high friction. Generally an extruder transports the solid, melts it and pumps the material e.g. for injection moulding. To intensity mixing process special sections are included along the extruder, e.g. pinmixing, pinbarrel extruder (QSM: Quer-Strom-Mischer) pineapple mixer, cavity transfer mixer, cok- neader, shear torpedo, Maddock-Le Roy-mixer, congestion ring, kneading block, etc. … After exiting the extruder a dye is responsible for the shape of the continuous extrudate. This can be hollow or filled, spherical, quadratic, rectangular shape, covering of wires etc. Since polymer melts exhibit a shape memory the dye shape and dimension is not necessarily the product shape and dimension (dye swell, first normal stress coefficient rheology, Weissenberg effect). 08. Energy consumption of extruder is highly reduced if processing is fast since , upper limit are shear instabilities called shark skin, stick-slip and melt fracture. The polymer exiting the dye are either cooled (air, water) and cut into pieces (granulate) or directly put into shape via injection molding. Note: The outer screw diameter might vary between 16 and 900 mm, the output between kg kg 5 t 0.5 h and 50,000 h 510 y! (PE, PP, world scale). The mechanics of the extruder is designed to last 100,000h (12y) with only 10% failure probability, for production purpose. Engineering properties 172 Source: Menges Engineering properties 173 Engineering properties 174 Calendering: Two or more polished cylinders (heated) that have a defined slit between them transport material due to counterrotating motion. Typically: 4 or 5 cylinders with diameter 400-900 mm are used, width of 1-3m, 10-50rpm. Mostly used for PVC, shape e.g. “F” form or “L”-form. F-form L-form Engineering properties 175 Special topics 176 6.1 Polyelectrolytes 6.1.1 Definition, examples Polyelectrolytes are covalent bound macromolecules which could carry charges (electric monopoles). These charges are compensated via low molecular counterions. Question: -[O-CH2-CH2]n- polyelectrolyte? -[O-CH2]n- Examples: CH 2 CH CH2 CH CH2 CH n n n - COO Na+ poly(acrylicacid)poly(acrylacid) N+ + Br- Na CH2 SO - 3 poly(styrolsulfonicacid) poly(styrolsulfonacid) poly(vinyl-pyridinium-bromide) CH H 3 H2 2 C C CH2 C n n + COO- Na poly(diallyldimethyl-ammoniumchloride) poly(DADMAC) poly(methacrylicacid)poly(methacrylacid) N+ Cl- H3C CH3 poly(vinylpyrrolidon): CH2 CH n N O C Special topics 177 Typical chemical groups: - - - - 2- -COO , -CSS , -O-SO3 , -SO3 , -O-PO3 + + + + -NH3 , -NRH2 ,-NR2H , -NR3 R Subgroup of polyelektrolytes: ionene (CH2)m N+ n R Polyelectrolytes with quaternary ammoniumgroups in the main chain: "ionic amines", via "m" adjustment of charge density 6.1.2 Theory: Poisson-Boltzmann, Debye-Hückel, Skolnick-Fixman and Odijk… simplified: polyelectrolyte = polymer + charges + - - - + - + + + + ++- - - - + + - - + - + + + - - - + + - - - + + - + + + - + - - - Special topics 178 r 2 W (x, y, z) Ae 2nl 2 1 / 2 r2 n l r2 S k lnW c k n = 24 2nl 2 fdr dG; T, P const dG dH TdS 0 dS n = 1 f T Tr dr l n = 24 Entropy via conformational degrees of freedom Coulomb-law: Q Q + F 1 2 - 4 r2 + + 0 r ++- - - Mean value for the maximum distance between + - + + neighbouring ions and simple cubic lattice. - - + - 1:1 electrolyte: + + - 3 3 - l 2cN L 0,001 m 0,94 1 l nm nm 3 c 3 c c in mol/l e.g.: 10-3 M: 10 nm 1 M: 1 nm l Special topics 179 Maxwell-equation (1865): + - The source of the electric field are charges E ; : charge density 0 r E ; : electric potential 2 Poisson - equation 0 r 2 : in spherical coordinates : 1d 2 1 2 r rdr 0 r Approximation of via Boltzmann-distribution, has the form of a screened Coulomb potential Q(r) Q(r) (r) exp( ) (1 ) 0 kT 0 kT homo Q(r) (r) eff 0 kT 1d 2 r 2 Eigen - value equation rdr 2 first Maxwell equation, Debye - Hückel - differential equation q (r) exp(r); 4 0 r r (0) e 2 (r) - exp(r) 4r 1/ rD ; rD : Debye - length, compare: 1S - orbital, H - atom, Bohr - radius r , (0,5Å) B Laguerre - polynome for radial despence of electronic wave function for 1:1 electrolyte : 0,304 rD 1 nm c c 0.01 M, rD 3 nm Special topics 180 Bjerrum-length lb: At what length do we gain kT per molecule if we bring a charge from infinity close to another charge? The medium is assumed to have a dielectric constant r. electrostatic interaction l + b H + O H medium Problems: macroscopic dielectric constant r: scalar? polarization? tensorial property? as simple as possible W fdr lb ee kT dr 2 4 0 r r RT = 2,4 kJ/mol r = 80 lb = 7 Å Bjerrum-length in water for distance < lb: Manning condensation: reduction of the efficient charges density please be aware: Manning condensation Mannich reaction (organic chemistry) Special topics 181 Extended theory Skolnick-Fixman-Odijk (1977): Additional stiffness via charges in the polymer backbone uncharged: charged: + + + d l0 + + + + + + l = l0 + le L: contour length l: persistenz length l = l0 + le d: distance between charges cs: salt concentration for large L/rD (high cs, large polymer chains), incl. Manning condensation: 2 lrbD 1 lldeb22; large distance between charges, low charge density along chain 4ddcS r 2 1 lldD ; high charge density along polymer chain eb4lc bS cs high pure polymer behaviour, no “charge” contribution Special topics 182 Slow mode (Exp.): Dynamic light scattering on poly(vinylpyridin), g(t)= A exp (-q2Dt) Aggregation? Cluster? Cooperativeness? Large domains? 10-7 log D cm 2 / s 10-9 slow mode 0,1 1 log cp/cs Pearl-necklace (Sim.): - - - - counterions ------ polymer with charges generation of local temporary aggregates along the polyelectrolyte chain electrostatic energy hydrophobic energy Special topics 183 6.1.3 Experiments 1 g super absorber, polyelectrolyte, sap (super absorbing polymer) 1. + 150 ml dest. H2O ( beaker), approximately 2 min. stir, 2 min. wait 2. add salt (NaCl) Remark: - Isotonic NaCl solution; c = 9 g NaCl/l; 0,15 M, posmose = 7,5 bar; rD = 8 Å ( Bjerrum- length) - Ocean water: c = 30 g NaCl/l; 0,5 M; rD = 4 Å!! - Experiments of Stanley Miller and Harald Urey, 1952 (Science 117 528 (1953), but: Loeb 1913! „Ursuppe“ made of H2O, H2, NH3, CH4 plus electric charges aminoacids; no salts! Special topics 184 6.1.4 Application - baby diapers - packing (food) - sealant - agriculture: but: 1 mm thickness 10.000 kg SAP/ha!! grain, sereals (e.s. rye, corn): 1 t = 100 EURO harvest: ~ 7 t/ha Superabsorber Swelling is influenced via physical or chemical influenced: pH, ions, temperature… Intelligent gels Swell up to 1000 – times of the own-weight R=1 R=10 compare: Hobermann sphere as mechanical model Special topics 185 Chemistry super absorbing polymers ( SAP) afterwards: cut, dry, grind particle size distribution: 150 - 850 µm LD50/oral/rat: > 2g/kg! polymer network (mesh) with carboxylate groups: poly(acrylacid - co -acrylacidsalt) further types: - crosslinked poly(acrylate) or poly(acrylamide) - cellulose- oder starck-acrylnitril-graft-copolymers - crosslinked maleic acid anhydrid-copolymers difunctional crosslinker: alkylene-bisacrylamid Special topics 186 trifunctional crosslinker: tetrafunctional crosslinker: triallylamin tetraallyloxyethan Strukture: SAP 1. generation 2. generation 3. generation optimization of water optimization of water combination of both absorption uptake under load advantages via cove- shell systems small crosslink density, max high crosslink density highly crosslinked shell and swelling appropriate absorption under weakly crosslinked cove load (AUL) high amount of extractable high capacity polymer high gel strength good mechanical strength small gel strength ( G’) small capacity high AUL 4-generation? Including ionexchange $$$ + Euros: SAP assume: 8 x 109 people (average: 20 years old) 0 – 3 years kids have diapers 5 diapers per day 10 g sap per diaper, 1 kg sap ≈ 2 € Special topics 187 6.1.5 Application: oil production constraints: oilreserves, definition: via drilling known, and currently useful with profit: 141 x 109 t (1998) consumption: 3,35 x 109 t/year factor 42 but: 1% higher yield compensates 1 - 2 years world consumption! drill fluids: per 1000 m increase: P = 100 bar, T = 30 K in 5000 m: - 500 bar pressure - 400 - 450 K - high shear rates - variable pH - high salt concentration approx. 1 - 3 % addition of polyelectrolytes O -OOC HO Na+ CH2 CH CH2 CH HO n m O O O HOOC CONH2 O Na+ O polyacrylamide, partly hydrolysed HO OH -OOC OH carboxymethylcellulose CH2 CH CH2 CH CH2 CH n m m HOOC CONH2 CO acrylamido-2-methylpropan-sulfonacid NH H3C C CH3 CH2 SO3H Special topics 188 Scale-inhibitors about 10 ppm, e.g. CH CH CH CH 2 2 CH2 CH n m n COOH SO3H HOOC polyacrylat-polyvinylsulfonat polyacrylicacid copolymer polyacrylacid O O CH CH HO P H2C NCH2 P OH n HOOC HOOC OH CH2 OH O P OH polymaleinacid OH amino-tri-methylenphosphonacid demulgator: H OCH2 CH2 O C CH2 O n m CH3 Ethylenoxid-Propylenoxid-Blockcopolymere, "Pluronics" ethylenoxid-propylenoxid-blockcopolymer, „pluronics“ OCH2 CH2 O H n alkylphenol-formaldehydresinAlklyphenol-Formaldehydharze m 2 4 Mn: 5 x 10 - 10 g/mol poly(diallyldimethyl- Poly(diallyldimethyl- H ammoniumchlorid) H2 2 poly(DADMAC)ammoiumchlorid) C C Poly(DADMAC) n CH2 CH n + N+ Cl- R3NOC H C CH quart.quart. polyacrylamide Polyacrylamide 3 3 4 7 Mn: 10 - 10 g/mol Special topics 189 6.1.6 Conclusion polyelectrolytes - polyelektrolytes are more complex as polymers or electrolytes - structure can partly be explained via superposition of Coulomb and entropic effects Several reasons for complex behaviour: - many particle interaction - long distance electrostatic interaction - no separation of involved time scales - dielectric constant - ions have volume application polyelectrolytes: - flocculation additives - extraction of metal, oil - adjustment of rheological properties - storage of water - reduction of energy needed for transportation (pumping-systems) - blood plasma expander - contolled drug release Special topics 190 6.1.7 Literature review: 1) Polelectrolytes in Solution; S. Förster, M. Schmidt; Advances in Polymer Science; 1995, 120, 51 2) Polyelectrolytes, Hanser Publisher München (1994); H. Dautzenberg, W. Jaeger, J. Kötz, B. Philipp, Ch. Seidel, D. Stscherbina; Advances in Chemical Physics, 1996, 94, 1; J.-L. Barrat, J.-F. Joanny; Theory of Polyelectrolyte Solutions; T. Radeva (Ed.); 3) Physical Chemistry of Polyelectrolytes; Surfactant Science Series; M. Dekker Inc.; Vol. 99; 2001 4) Enzyclopedia of Polymers Science and Engineering; Wiley 1990, 788; Concise 5) Intermolecular & Surface Forces; Academic Press; 1992; J. Israelachvili 6) Macroions in Solution and Colloidal Suspensions; VCH (1994); K.S. Schmitz layer formation of polyelectrolytes: 1) G. Decher; Science 1997, 277, 1232 2) Ölindustrie: W. Gulden; Kein Erdöl ohne die Chemie; Chemie in unserer Zeit; 2001, 35, 82 3) J. P. Gerling, F.W. Wellmer; Wie lange gibt es noch Erdöl und Erdgas; Chemie in unserer Zeit; 2005, 39, 236 superabsorbing polymers: 1) www.gia.com/~cricher/history.htm 2) www.basf.de/de/corporate/innovationen/erklaert/baby Special topics 191 6.2 Spatially heterogeneous systems, e.g. blends or blockcopolymers 6.2.1 Definition In case two or more polymers are blended or covalently bound, e.g. blockcopolymers, they can be homogeneous or heterogeneous with respect to their properties (e.g. mechanical, chemical). please distinguish: homogeneous heterogeneous - spatially dependant scalar property and isotropic non isotropic - orientation dependant vectorial (or tensorial) property Question: can a homopolymer be heterogeneous? can a homopolymer be nonisotropic? Obviously the term homogeneous must depend on the observed length scale, e.g. everything is heterogeneous on a length scale of 1-5 Å. Consequently this term becomes only meaningful for length scales > 1nm. In case of a homogeneous blend, crystallisation is often not possible and the common glass transition temperature is influenced by both compounds (see chapter 3.2, Fox-equation). 6.2.2 Why does the introduction of heterogeneity make sense? homogeneous polymer crack or if force is applied craze propagates high local stress (force per area) crack easy to propagate catastrophic failure Special topics 192 heterogeneous system soft segment if force is applied (low Tg) hard segment (high Tg) crack low local stress, since critical stress σc force needed to surface area soft segment propagate 6.2.3 How can heterogeneity be achieved: - blending needs high shear rates to achieve domains in the dimension of μm. In most cases different polymers will phase separate. 1-5 μm - copolymerization, e.g. polystyrene and polybutadiene to form “HIPS” (high impact polystyrene) example: HIPS: ca. 90% PS and 10% PB radical droplets, rich in polymerization t2 > t1 PB t1 droplets rich in styrene and PS matrix, rich in butadiene as matrix, rich in PS monomers PB phase inversion! Special topics 193 at the end “salami” morphology PS covered with PB additionally: grafting of PS on PB during polymerization gives optimized PS mechanical properties 1μm Example: ABS – polymers Acrylonitrile-butadiene-styrene polymer H H H2 homopolymer CC head-tail + mostly isotactic H2CC n CN CN rigid: acrylonitrile + styrene flexible: butadiene ˆ rubber part ( 1,2 and 1,4 cis + trans) very variable due to: three component system, Mn, grafting, rubber particle size and morphology, further monomers synthesis: free radical polymerization of styrene and acrylonitril in presence of polybutadiene (or PB-copolymer) Special topics 194 - block-copolymerization [A]n - [B]m e.g. PS - PI diblock high Tg – low Tg PS – PB – PS triblock high Tg – low Tg – high Tg Mostly via anionic synthesis From a mechanical point of view PB – PS – PB does not make sense, why? phase separation should be on B the order of Rg f (Mn) A RgA RgB Type of micro phase separation depends on volume fraction of the components, minimum interface ? ? fA fB fA » fB fA › fB fA ≈ fB fB › fA fB » fA sometimes gyroide spheres columns lamellar Via Mn, the spacing can be adjusted typically in the range of 5 – 100 nm Special topics 195 z long periode please distinguish lamellae thickness If we go along z-axis several “types” of phase-separation are possible __ A 1- no phase separation A = 0,5 0,5- weak phase separation (weak segregation) strong phase separation (strong segregation) 0- z long periode For a symmetric 50:50 (in volume) lamellar diblock the following scattering is expected (FT of electron density in x space) I I weak strong | | | q q q 3q q 0 0 0 Macroscopically the systems are frequently isotropic even though they are microscopically very anisotropic Special topics 196 orientation via - B-field - E-field - shear (elongation) same long period! In case shear is applied there are three possibilities: or or parallel perpendicular transversal 6.2.4 Theory of mixing, Flory-Huggins theory In case we mix polymers, two types of curvature are in principal possible: Δ G d 2 G mix 0 d 2 stable against demixing | | | α β A volume fraction, A Special topics 197 Δ G d 2 G mix 0 d 2 unstable against demixing | | | α β A volume fraction, A generally: one phase two phases stable one phase metastable metastable Δ Gmix unstable stable metastable metastable binodal spinodal A volume fraction, A as function of temperature: T LCST, lower critical solution temp. mixed single UCST, upper critical solution temp. phase phase sep. binodal volume fraction, A spinodal A metastable LCST: highest temp. where no phase separation takes place UCST: lowest temp. where no phase separation takes place, sometimes kinetically hindered, since Tg of one polymer makes structure to rigid Special topics 198 In most cases polymer blends tend to phase separate due to conformation entropy: Nevertheless several systems exist that do no phase separate, e.g. H3C - PS/PXE PXE: polyphenyleneoxide O n H3C CH2 CH - PS/PVME PVME: poly(vinylmethylether) n OCH3 - PMMA/PVF2 PVF2: polyvinylidenfluoride H2 F2 C C n - PMMA/PC To understand why phase separation occurs, thermodynamic of solutions has to be considered - ideal solution of polymer in solvent ΔGM = G1,2 – (G1 + G2) G1,2: free enthalpy of solution G1, G2: free enthalpy of solvent respective polymer additionally we have: ΔGM = ΔHM - TΔSM ΔSM: always positive ΔHM: for ideal solutions: ΔHM=0 Special topics 199 ΔSM is calculated via a lattice model (monomer in solution) 1 2 3 4 5 6 7 8 9 here: 1 81 lattice position 2 Ο 3 5 monomers N2 4 Ο N1+N2=N 5 76 solvent molecules N1 6 Ο Ο 7 8 Ο 9 possibilities: N N ! N! 1 2 N1!N 2 ! N1!N 2 ! using: S M k ln N N ! 1 2 S M k ln N1!N 2! using the Stirling approximation: lnNN ! ln NN proof: ln N! ln(1 2 3... N ) ln1 ln 2 ln 3 ln... ln N N N N lnx lnxdx x ln x x x1 1 1 dxln x x 1 since: x lnxx 1 ln dx x ln N! N N ln N N 1ln1 1 x ln x x 1 0 N ln N N 1 N ln N N q.e.d further: N1 n1 number of moles of “1” N A N 2 n2 NA: Avogardo number, number of moles of ”2” N A n1 n2 x1 analog x2 , molefraction n1 n2 n1 n2 Special topics 200 N N ! ln 1 2 lnN1 N 2 ! ln N1! ln N 2 ! N1!N 2! N 1 N 2 lnN 1 N 2 N 1 N 2 N 1 ln N 1 N 1 N 2 ln N 2 N 2 N ln N N 1 ln N 1 N 2 ln N 2 N 1 N 2 ln N N 1 ln N 1 N 2 ln N 2 N 1 ln N ln N 1 N 2 ln N ln N 2 N1 N 2 N1 ln N 2 ln N N N N N N 1 1 2 2 N A ln ln N A N N A N N A n1 ln x1 n2 ln x2 S M Rn1 ln x1 n2 ln x2 (1) S M kN11ln x N 2 ln x 2 (2) for ideal case we assume H M 0 , therefore GM HTSM M GM RTn(ln1122 x n ln) x for polymers this formula is not sufficient, due to: − polymer molecules are much larger than solvent molecules − H M often 0 − monomers in a polymer are covalent-bounded, can not move fully free, joint probability Px(|)12 x Special topics 201 Flory-Huggins-Theory theory for non-ideal polymer-solutions GM HTSM M a) SM : N1: number of solvent molecules N2: number of polymer molecules n: number of segments (?monomers?) in a single polymer n·N2: volume occupied by N2 polymer chains using (2) NnN12 SM kN12ln N ln NnN12 NnN 12 number volume fraction using the volume fraction i N1 nN2 11N 1 2 NnN12 NnN12 22nN note: nN21 N 12 (3) and NA we receive SM Rn1122ln n ln b) H M : we have the following interaction energies − solvent - polymer: 12 − solvent – solvent: 11 − polymer – polymer: 22 If we start to dissolve a polymer, one polymer – polymer contact, one solvent – solvent contact is broken, but two solvent – polymer contacts are generated. 1 122 11 22 Please note: to have 0 (to be ideal) it is not needed to have 12 = 11 = 22 ! 212 = 11 + 22 is already sufficient. The total number of polymer – solvent contacts “p” for a rather concentrated, non- ideal solution is p nN21 z nN2: total number of segments Special topics 202 z: co-ordination number 1: probability of having a lattice cell occupied by a solvent molecule (= volume fraction) using eq. (3) nN21 N 12 we receive pzN12 therefore HpM zN12 z if we define , knowing Nk nR kT 11 HNM 12 kT HnM 12 RT to be put into GHTSM MM GRTnM 112ln n ln 2 n 12 (4) The Flory-Huggins theory describes GM for non-ideal, but not for dilute solutions. Eq. (4) becomes ideal again, if =0 and n=1 (n = number of segments in polymer) GRTnxnxM 1122ln ln is called Flory-Huggins parameter and is the normalized (to RT) local change in energy if a polymer is dissolved. If two polymers of the same degree of polymerization (n) are mixed, phase separation can occure if n >2 0 ·n>2 ! G/RT ·n=2 ·n<2 0 0,5 1 A HERMANN STAUDINGER Macromolecular chemistry Nobel Lecture, December 11, 1953 Macromolecular chemistry is the youngest branch of organic chemistry and as such has experienced the honour of the award of the Nobel Prize for Chemistry. I sincerely hope that this great distinction will be the means whereby macromolecular chemistry will undergo further fruiful devel- opment. Some few months after I had the opportunity of speaking in this audito- rium on the development of macromolecular chemistry into a new branch of organic chemistry at the International Congress for Pure and Applied Chemistry 1, it is today my duty to describe to you the characteristic features of macromolecular chemistry and demonstrate the new features which it introduces into organic chemistry. The macromolecular compounds include the most important substances occurring in nature such as proteins, enzymes, the nucleic acids, besides the polysaccharides such as cellulose, starch and pectins, as well as rubber, and lastly the large number of new, fully synthetic plastics and artificial fibres. Macromolecular chemistry is very important both for technology and for biology. In common with all organic compounds, the structure of the organic macromolecular compounds (inorganic macromolecular compounds are not discussed in the following) involves in addition to carbon atoms, chiefly hydrogen, oxygen, and nitrogen atoms which in accordance with the laws of Kekulé’s structural theory are bound by chief valences2. The only dif- ference between macromolecules and the small molecules of low molecular substances is one of structural size. If it is desired to lay down a boundary between macromolecular and low molecular compounds - there are of course transitions linking the two groups - the substances with a molecular weight greater than ten thousand, i.e. the molecules of which consist of one thousand and more atoms, may be classified as macromolecular. Beyond roughly this size, characteristic macromolecular properties occur. So far no upper limits can be given for the size of the macromolecules. Macromolec- ular compounds with a molecular weight of several millions are known, 398 1953 H.STAUDINGER i.e. compounds in which one million and more atoms form the macro- molecules in the manner prescribed by Kekulé’s structural theory. In recent decennia the field of macromolecular chemistry has been the scene of very intensive scientific and technical activity. I personally have been concerned3 with macromolecular chemistry since 1920 initially at the Federal Institute of Technology in Zurich. Since my move to the chemical laboratory in Freiburg University I have devoted myself entirely to extend- ing this field which, since my retirement, has been further studied in a special research institute in Freiburg. In this work I have been assisted by a number of first-class colleagues who have published valuable research on this field. Here I should like to mention the oldest of them, Signer4, now in Bern, whose support during the discus- sions on the structure of these compounds in the 1920’s was very valuable and who introduced the flow birefringence method for studying the particle shape of macromolecular substances. In addition Schulz, now in Mainz, extended the physico-chemical studies in the last two decennia, especially the molecular weight determination of macromolecular substancess. He also worked on the kinetics involved in the formation of macromolecular sub- 6 7 stances . Kern , now in Mainz, studied the behaviour of polyelectrolytes. Husemann 8, Freiburg i. Br., studied polysaccharides, i.e. starch, wood poly- saccharides and, in conjunction with Schulz, the fine structure of cellulose9. Kohlschütter 10,now in Darmstadt, investigated topochemical reactions using polyoxymethylenes. Batzer 11 has in recent years successfully continued Carothers’ work on polyesters. Hengstenberg18, Sauter13 and Plötzer14 car- ried out X-ray studies at different periods. Staudinger (M.)15 conducted morphological studies of macromolecular substances, and introduced light, ultraviolet and electron microscopy - and for some time now, phase contrast microscopy as well - into macromolecular chemistry. In addition, over the last 25 years in which almost 400 publications have appeared, she has collab- orated in these and a series of books. She is the originator in particular of new considerations in respect of the relations between macromolecular chemistry and biology16. Icannot mention here the names of all the individual assistants and grad- uate students but today I remember with gratitude the assistance of all those colleagues who have participated in expanding this field. Since, as I explained, macromolecular compounds are built up according to the laws of Kekulé’s structural theory in exactly the same manner as the low-molecular organic compounds, i.e. they are genuine organic com- MACROMOLECULAR CHEMISTRY 399 pounds but with particularly large molecules, the question arises whether there is any need at all to classify macromolecular chemistry as a new field of organic chemistry. It has been found, however, that owing to the size of the macromolecules, a whole series of new problems do actually arise here so that in many respects macromolecular chemistry differs substantially from low molecular chemistry. Even the classification of the macromolecular compounds is based on other criteria than in low molecular chemistry: the naturally occurring macromolecular substances are conveniently treated separately from the fully synthetic compounds (Table 1). Table I. Classification of macromolecular substances. I. Substances occurring in nature 1. Hydrocarbons - rubber, guttapercha, balata. 2. Polysaccharides - celluloses, starches, glycogens, mannans, pectins, polyuronic acids, chitines. 3. Polynucleotides (nucleic acids). 4. Proteins and enzymes. 5. Lignins and tans (transition from low- to macromolecular substances). II. Cowersion products of natural substances Vulcanized rubber, rayon, cellophane, cellulose nitrate, leather, lanital, galalith, etc. III. Synthetic materials Plastics (polyplastics) formed by polymerization - buna, polystyrene, poiymethacrylic ester. polycondensation - bakelite, nylon, Perlon, Terylene. polyaddition - polyurethane. For the low molecular compounds such a division is unnecessary and irrel- evant; the low molecular substances occurring in nature can largely be manufactured synthetically and these synthetic compounds are indistin- guishable from the natural products. The situation is otherwise for the ma- cromolecular compounds. It has so far proved impossible to build a macro- molecular natural substance by a clear, stepwise synthesis from low molecular compounds. Thus synthetic polyisoprene is not identical with, say, natural rubber but has an essentially different constitution and hence other physical properties as well. In deriving macromolecular natural substances from veg- etable and animal material the original macromolecules are in many cases modified to a greater or lesser extent by isolation and purification, and thus 400 1953 H.STAUDINGER the macromolecules examined are not the same as those formed by Nature. Problems of this type prevail for instance in the production of cellulose, starch, and many proteins. Low molecular products on the contrary can be isolated from natural products without modification. It is furthermore pos- sible that Nature creates macromolecules of uniform size but positive proof of this fact has so far been found only in a few cases. In 1926 for example Svedberg I7 made the astounding discovery that a number of respiratory proteins are monodisperse, i.e. that they are composed of uniformly large macromolecules. Recently a whole series of enzymes and hormone proteins have been crystallized so that here too the occurrence of natural products with uniformly large macromolecules is very probable18. Against that the technically manufactured transformation products of nat- ural macromolecular substances which can be termed semi-synthetic prod- ucts are invariably polymolecular mixtures since the original macromol- ecules are broken down to a greater or lesser extent during processing. In all fully synthetic products, i.e. in plastics and fibres, there are also insep- arable mixtures of polymer homologues. It is thus impossible to prepare completely uniform products by synthesis as was formerly considered nec- essary by the organic chemist to elucidate the constitution of organic com- pounds. Macromolecular products are created in various ways. The first to deserve mention is polymerization, constituting a particular chain reaction such as is unknown in low molecular chemistry19 (Formula 1). Owing to the Formula I. Polymerization of styrene. MACROMOLECULAR CHEMISTRY 401 technical importance of the polymerisates, e.g. polystyrenes, polymetha- crylic esters and polyvinyl chlorides, this reaction has been studied very thoroughly with reference to the kinetics and the influence of catalysts on the course of the polymerization20. In addition, macromolecular substances can be produced by polyconden- sation, a process which has long been known to technology and the one whereby Baekeland secured the phenoplasts which are of unusual technical importance. This field was then further studied by Carothers21 and led to such technically valuable products as nylon (Formula 2). Formula 2. Polyamides. A further technique to produce macromolecular compounds evolved by O. Bayer is polyaddition with diisocyanates (Formula 3). Formula 3. Polyurethanes. In the most favourable case therefore, in the manufacture of fully synthetic products, uniform polymeric compounds are formed, i.e. mixtures of fil- amentary molecules of equal constitution but different length. Very recently, research conducted by Melville23 and others showed that polymerization processes are frequently more complex than had formerly been assumed so that the resultant products are mixtures of polymer isomers. Since most natural macromolecular substances as studied are polymolec- ular mixtures in common with all synthetic macromolecular substances, a 402 1953 H.STAUDINGER macromolecular substance must be identified by different criteria than a pure low molecular substance. Ostwald (Wi.)24, in his Analytical Chemistry, has pointed out that the task of the analytical chemist is facilitated by the fact that the agreement of just a few properties of two substances is sufficient for regarding them as identical. This principle applies only for low molecular compounds in which, owing to the small size of the molecules or ions, relatively large differences in the properties occur, i.e. they differ abruptly from one compound to another. The situation is different for macromo- lecular compounds; a plastic such as, say, a polystyrene can be consistent with another polystyrene in a number of essential properties and still differ in composition. It is moreover also impossible to characterize and identify macromolecular substances by the melting point and by the mixed melting- point test, a technique which has contributed greatly to the rapid successes in the identification of natural substances in low molecular chemistry. Initially identifying the constitution of macromolecular compounds seem- ed to be further complicated by the fact that they do not yield normal mono- disperse solutions but that - if they dissolve at all - they mostly form poly- disperse, colloidal solutions. The procedure for elucidating the constitution of organic compounds can again be referred to here: It consists in dissolving the particular compound after elementary analysis and then determining the size and finally the intrinsic structure of the dissolved particles by further studies. With completely insoluble substances occurring as a single aggregate only25, details of the type of bond in the smaller groups in their molecules can in many cases be disclosed by decomposition; but the molecular weight of such a substance is indeterminable. Against that, however, it may not be inferred from the insolubility of a substance alone that it has a particularly Table 2. New classification of disperse systems by the number of atoms. Increasing degree of dispersion. 9 Coarse dispersions The particles are composed of more than 10 atoms, do not pass through filter paper and can be made visible microscopically. They are poly- disperse. Colloids The particles are composed of 103 to 109 atoms, pass through filter paper, cannot be resolved microscopically and cannot be dialysed. They are polydisperse or monodisperse. Low molecular dispersions The particles are composed of 2 to 103 atoms, cannot be resolved microscopically, diffuse and dialyse readily. The molecules or ions of uniform substances are identical in structure and size. MACROMOLECULAR CHEMISTRY 403 high molecular weight, a fact which emerged during studies on amino- plasts26 in the laboratory at Freiburg. When considering the various modes of dispersion of organic substances in a liquid, it is expedient to indicate the size of the dispersed particles by the number of atoms they contain, the convention27 adopted in Table 2. The particles of the low molecular organic compounds thus contain up to a maximum of 103 atoms and as a rule are identical with the molecules. The molecule concept is defined here in the same way as in low molecular chem- istry: a molecule is the smallest particle in which all the atoms are linked by chief valences 2.I. t can readily be ascertained whether such particles con- tain not molecules but associations or double molecules, as applies with e.g. solutions of fatty acids in benzene. The particles of colloidal size which are composed of 103 to 109 atoms can have a much more varied structure than the particles made up of fewer atoms (Table 3). It follows from Table 3 that for one thing lyophobic colloids can occur which formerly roused special interest when Ostwald (Wo.)29 drew atten- tion to the "field of neglected dimensions" and pointed out that every sub- stance can be broken down into particles of colloid size by appropriate Table 3. Classification of colloidal solutions of organic substances. 404 1953 H.STAUDINGER dispersion. A further group of colloids are the lyophilic colloids to which belong on the one hand the micellar colloids and on the other the solutions of macromolecular substances. Since macromolecules are the size of colloid particles they can dissolve in no other way than colloidally, even if the sol- vent is changed, whereas with micellar colloids, e.g. the soaps, low molec- ular disperse solutions are also possible in certain solvents. The solutions of macromolecular substances may hence also be termed molecular colloids30. Surprisingly, one group of macromolecular compounds, the linear macro- molecular substances, exhibit in many respects properties like those of typ- ical micellar colloids. In particular there is great similarity here to the soaps, the colloidal nature of which was recognized at the beginning of the century through the work of Krafft31, Zsigmondy32, McBain33, and others. Since the solutions of linear macromolecular substances, however, differ substan- tially from the solutions of low molecular substances, it can be understood why, a few decennia ago, the colloid particles in these solutions of macro- molecular substances were assumed to have a micellar structure similar to those in aqueous soap solutions (Table 4). Table 4. Properties of various substances. Initially therefore, the efforts of the workers studying rubber, cellulose, starch, and proteins were aimed at determining the size of the molecules making up these micells. A number of workers such as Karrer 34, Bergmann35, Pummerer 36 and Hess37 assumed them to be small molecules whereas Meyer and Mark38 held that these micells consisted of rather long chief valence chains. MACROMOLECULAR CHEMISTRY 405 Notwithstanding this similarity in the behaviour of micellar colloids and linear molecular colloids which derives from the elongated shape of the colloid particles in both cases, there is a profound difference between the two groups: the particles of the micellar colloids are loose aggregates of small molecules, in the case of the molecular colloids they are the macro- molecules themselves. The proof was obtained by the conventional methods of organic chem- istry, i.e. by determination of the "macroradicals". In this context the word "radical" is used in the meaning given to it by Liebig in his studies of the benzoyl radical. In many instances a polymeric compound can be trans- formed into derivatives of a different type without any change in the degree of polymerization of the compound in exactly the same way as small mol- ecules can be transformed. A polymer compound can hence be transformed into polymer analogous derivatives, the transformation proving that all the basic molecules contained in the colloid particles of these polymeric com- pounds are linked together by chief valences, in other words the colloid par- ticles are macromolecules. This proof becomes especially clear because out of a series ofpolymer homologues various ones can be transformed into polymer analogous derivatives. Anexplanation can be given with reference to cellulose. The bond of the glucose radical in cellulose was established by the studies of Haworth39 and Freudenberg40; furthermore Sponsler and Dore 4I demonstrated that the results of X-ray studies are consistent with the chain structure of cellulose. Subsequent studies then clarified the question whether the colloid particles in the solutions of celluloses and their deriv- atives have a macromolecular or micellar structure42. Table 5. Comparison of the molecular weights of decomposed cellulose triacetates as determined by the osmotic and end-groups methods, and the Km-constants of these compounds. 406 1953 H.STAUDINGER In a polymer homologous series of decomposed low polymeric cellulose acetates, the molecular weight determined by the end groups agrees with that determined by the osmotic method, proof that unbranched filamentary molecules are present. The viscosity number of these compounds is proportional to the degree of polymerization as shown in Table 5. The end-group molecular weight of higher polymer cellulose acetates can not be determined. The relations between the degree of polymerization determined by the osmotic method and the viscosity number are the same, however, as in the low molecular compounds appearing in Table 5, testifying that these high polymer cellulose acetates are dissolved in the ma- cromolecular form and their chains are unbranched (Table 6). Table 6. Determination of Km- constants of higher polymeric cellulose triacetates in m- cresol. With care, these cellulose acetates can be saponified to polymer analogous celluloses, so proving that both the cellulose acetates and the celluloses are present in solution in the macromolecular state43 (Table 7). Finally, with care being exercised, polymer homologous celluloses can be nitrated to polymer analogous cellulose nitrates with a mixture of nitric acid and phosphoric acid, so demonstrating the macromolecular structure of the cellulose nitrates44 (Table 8). The studies conducted at the Freiburg laboratory have frequently been con- cerned with determining macromolecular structure by polymer analogous transformations of this type. By that means it has been proved for further polysaccharides, i.e. starch’s, glycogen46, mannan47, and for a number of plastics that the colloid particles in their solutions are identical with the ma- MACROMOLECULAR CHEMISTRY 407 Table 7. Transformation of cellulose triacetates to polymer-analogous celluloses. cromolecules. It is surprising that with these molecules, some of which are very large and complex, reactions can be conducted which are customary with molecules of lower molecular compounds. Such polymer analogous transformations hence provide an impressive instance of the stability of the macroradicals which is also of significance for the substances of living cells. The question now arises of the origin of the frequent instability and changeability in the viscosity of macromolecular substances in solution. These "aging phenomena" arise because even slight amounts of low molec- ular substances are suffficient, chiefly in the presence of atmospheric oxygen, Table 8. Transformation of celluloses into polymer-analogous cellulose nitrates. 408 1953 H.STAUDINGER to decompose the linear macromolecules, leading to a profound change in the solution viscosity. This is shown in Table 9. Table g. Initially, as was the case for instance with rubber, these aging phenomena were particularly obscure because under certain conditions oxygen decom- poses the filamentary molecules but can also link them together, this be- coming apparent in an increase of viscosity and, should the linking of the filamentary molecules proceed further, it causes the soluble rubber to change into insoluble rubber. For this reason even polymer analogous transforma- tions involving macromolecular substances are mostly to be conducted only under special experimental conditions since atmospheric oxygen for in- stance must be completely excluded. The tests are also complicated by the fact that the transformation products cannot be purified since all substances are polymolecular and reprecipitation together with purification would lead to a change in the composition of the polymolecular mixture. These com- plications do not exist where low molecular substances are involved. With the most important group of macromolecular compounds, the pro- teins and nucleic acids, scarcely any polymer analogous transformations have so far been performed; here too it is difficult to produce polymer homol- ogous series. The size and structure of the macromolecules have to be deter- mined by different methods from those applied with the polysaccharides, rubber, and the plastics. The molecule concept as formulated for homopolar organic compounds is not applicable here without limitation since besides chief valences, very powerful secondary valences also participate in the struc- ture of the particles. The proof for the macromolecular structure of colloid particles is of fundamental importance since it signifies that these colloids cannot be con- sidered in terms of the colloid doctrine as variable associations of small mol- ecules but rather as macromolecules which must be treated by the methods of organic chemistry in common with molecules of low molecular substances48. MACROMOLECULAR CHEMISTRY 409 There are still further profound differences between macromolecular and low molecular compounds: these are based primarily on the fact that the shape of the macromolecules affects the physical and chemical properties of the substances considerably more strongly than is the case with the low mo- lecular compounds. Whereas, for example, normal nonane with elongated molecules, and tetraethylmethane with spherical molecules, both hydro- carbons having the composition C9H20, scarcely differ in terms of their prop- erties, a glycogen in which 5,000 glucose radicals are linked to form a sphere has properties differing fundamentally from those of a cellulose in which the same number of glucose radicals are arranged in a long chain. This state of affairs led to the macromolecular substances being classified into two large groups, spheromacromolecular substances, i.e. substances with spherical molecules, and linear macromolecular substances with filamentary molecules. These two classes are, of course, bridged by transitions: a large number of natural and synthetic substances have heavily branched macro- molecules, e.g. starch45.Table 10 indicates the significant bearing of the shape on the physical properties of natural macromolecular substances49. Table 10. Spherical and filamentary polysaccharides and proteins. 410 1953 H.STAUDINGER In appearance, solubility, and in their further behaviour, macromolecular substances with spherocolloid molecules scarcely differ from low molecular substances; only the determination of the molecular weight proves that macromolecules are involved. The striking properties of macromolecular substances which, as listed in Table 4, caused a different type of micellar struc- ture to be assigned to these compounds, occur only with the linear macro- molecules; these include the natural and fully synthetic fibres, the rubber- elastic substances and many of the most important plastics. Linear macro- molecular substances with long filamentary molecules behave in a manner alien to low molecular substances: inclusion and swelling phenomena, high solution viscosity, abnormal flow behaviour, etc. Since the constitution of these substances is known, their striking behaviour can be ascribed to the length of the filamentary molecules. A comparison of various examples of a polymer homologous series shows that as the filamentary molecules be- come longer, their properties change so profoundly that the earlier concepts which led to the conclusion that the units at the beginning and at the end had a completely dissimilar structure (Table11) can be appreciated. Table II. Relation between physical properties and mean degree of polymerization (DP) of polymer homologous celluloses. MACROMOLECULAR CHEMISTRY 411 It was therefore particularly difficult to study these linear macromolecular substances. Even to determine the molecular weight, for example, it was not possible to apply the customary physical techniques such as the osmotic, diffusion, or Svedberg ultracentrifuge methods until the abnormal behaviour of the solutions of these substances could be clarified50. The viscosity behaviour of the linear macromolecular substances is partic- ularly striking. Whereas Einstein’s law applies to the spheromacromolecular substances such as ovalbumin or glycogen, in the case of solutions of sub- stances with filamentary molecules, the viscosity of solutions of equal con- centration increases with the chain length, and with some of these substances, especially polysaccharides, there is a proportionality between the viscosity number Zh, and the chain length n or the degree of polymerization P of fil- amentary molecules. This viscosity number is the specific viscosity of a solution, i.e. the increase in viscosity caused by 1 g in one litre, or else its limit value. Since viscosity measurements are simple to perform, this method has been extensively adopted in technology to determine e.g. the degree of polymerization of celluloses and cellulose derivatives, as this parameter has a considerable bearing on the fibre properties as shown in Table 11. With other linear macromolecular substances such as e.g. the polyesters11 and many polyvinyl derivatives, the relation between viscosity number Zh and degree of polymerization is not as simple as with the polysaccharides, al- though there is a functional relation corresponding to an equation formulated by Kuhn51 (Table 12). Table 12. Viscosity relations. The reasons. are as follows: the filamentary molecules of a linear macro- molecular substance are usually elongated in the solid crystalline state. The length of the elementary units and hence the length of the filamentary mol- 412 1953 H.STAUDINGER ecules can be determined by X-ray examination, e.g. in the case of cellulose. On dissolution, owing to vibrations and intramolecular forces of attraction between the individual groups of the filamentary molecule, the latter be- comes convolute to a greater or lesser extent depending on the temperature and also on the type of solvent. Thus the filamentary molecules in good solvents are more elongated than in poor solvents; in the former the viscos- ity number of a substance is higher than in a poor solvent. Kuhn 52 states that the entanglement of a filamentary molecule can be so pronounced in a poor solvent that the molecule assumes an almost spherical configuration such as has been experimentally determined with the polyisobutylenes53. A filamentary molecule would adopt that configuration in the gaseous state although in practice this state is unattainable, since the boiling point of all macromolecular substances lies far beyond the point at which they decom- pose. Besides these reversible changes in shape which are governed by the na- ture of the filamentary molecule and the type of the solvent, chemical action also brings about irreversible changes in shape which permanently affect the physical properties of a linear-macromolecular substance. Thus it is common knowledge that owing to its long, filamentary molecules, rubber yields highly viscous solutions with swelling. Against this, the solutions of chlo- rinated rubber, which is used as a paint, are of relatively low viscosity and therefore it was originally assumed that in the transformation from rubber to chlorinated rubber the long filamentary molecules were decomposed. Such is not the case as the degree of polymerization of chlorinated rubber is approximately the same as that of rubber54. Thus, when rubber is con- verted into chlorinated rubber, no decomposition takes place but rather a strong, chief valence cyclization which induces a permanent convolution of the filamentary molecules (Table 13). Table 13. Polymer-analogous transformation of rubber and balata to chlorination products. MACROMOLECULAR CHEMISTRY 413 Fig. I. Swelling of a piece of polystyrene with divinyl bonds. Before swelling (left). After swelling in benzene (right). It is - as already mentioned - characteristic of the chemistry of macromo- lecular materials that the smallest amounts of substances are capable of modifying profoundly their physical properties. Hence a 0.0025% addition of divinyl benzene to styrene is sufficient during polymerization to link the chains of the polystyrene by divinyl benzene bonds55. Soluble poly- styrene with its unlimited swelling capacity is thus transformed into a va- riety with limited swelling capacity which absorbs solvents by solvation and so swells without altering its shape (Fig. I) and without being able to dissolve. The replacement of a hydroxyl group in low molecular compounds by a methoxyl group alters the physical and, above all, the chemical behaviour of the compound considerably. The same applies also to macromolecular substances except that the percentage proportion of a methoxyl end group in the macromolecule can be so small that it readily escapes detection. Auerbach and Barschall56 described two polyoxymethylenes: one is sol- uble in sodium hydroxide, the other insoluble, yet they are identical in appearance. The product soluble in sodium hydroxide is a polyoxymethyl- ene dihydrate, the insoluble product a polyoxymethylene dimethylether57 (Formula 4). The slight percentage methoxyl end-group content thus blocks the de- composition of the chains by sodium hydroxide. This reagent can only at- 414 1953 H.STAUDINGER tack hydroxyl groups and so dissolve polyo-xymethylene dihydrate. In bio- logical processes as well, a slight percentage change in a macromolecule can bring about profound changes in the chemical and physiological behav- iour of the macromolecular substance. Possibly the most important distinction between low molecular and ma- cromolecular compounds is that the latter can exhibit properties which cannot be predicted even by a thorough study of the low molecular sub- stances. This may be illustrated by comparing the organic molecules with buildings in which the bricks must be joined together systematically. With a few bricks it is impossible to erect a great variety of buildings; nevertheless, provided that 10,000 or 100,000 bricks are available it is quite possible to construct the most diverse buildings, viz. houses, halls, etc., the special con- struction of which cannot simply be predicted from the buildings com- prising few bricks. One such new type of behaviour of macromolecular substances are, for example, the swelling phenomena of the linear macromolecular substances caused by the solvation of the long filamentary molecules on the addition of solvent without immediately being able to go into solution. These swel- ling phenomena are complicated, as has been described, in that linking of the filamentary molecules induces a substance with unlimited swelling capac- ity to change into a substance of restricted swelling capacity55, this also being a very potent factor with proteins. A further instance here are inclusion phenomena. Inclusion is an indirect swelling of linear macromolecular sub- stances with liquids that are not solvents. They have mainly been studied in the case of cellulose, between the filamentary molecules of which inert liquids such as benzene, carbon tetrachloride, and others can be embedded. It is noteworthy that these liquids cannot be altogether eliminated from the linear macromolecular substance even under a high vacuum; they are held mechanically between the filamentary molecules of the substances. As a MACROMOLECULAR CHEMISTRY 415 Table 14. Amount of solvent included in mercerized cotton (DP 1,600) after drying for two days under high vacuum at 100°C. result of this inclusion, however, the reactivity of cellulose is appreciably raised58 (Table 14). A particularly significant phenomenon with linear macromolecular sub- stances is a characteristic state of dissolution which is impossible with sphero- macromolecular and low molecular substances: the state in which the fil- amentary molecules are completely solvated, i.e. essentially dissolved, but owing to their large bulk, their range of action, they have no free mobility. The term "gel solution" has been proposed for this characteristic state of dissolution which is intermediate between the normal state of dissolution and that of swelling 59.The solutions of cellulose, cellulose derivatives and plastics as used technically are gel solutions. It will be the task of macromolecular chemistry to examine further these new, characteristic properties which are governed by the size and configura- tion of the macromolecules since it will thus be possible to gain fresh insight into biological processes as well. The existence of macromolecules and the steadily deepening knowledge of their properties have revealed the nature of the building units which the living cell requires to creatematter 16.The existence of macromolecules makes possible the vastly wide variation of the substances required; thus, for example, the very number of the isomers in protein molecules is prac- tically infinite. Assuming a protein of molecular weight 100,000 and com- 416 1953 H.STAUDINGER posed of 20 different amino acids, the number of its isomers is 10 1270. The size of this number becomes clear when compared with the number of mol- ecules of water present in the seas of the earth - a mere 10 46 (Table 15). Table 15. Number of isomers of a protein having a molecular weight 105; the protein molecule composed of 50 molecules of each of 20 different amino acids. Number of isomers: 101270. For comparison the number of molecules of water in the seas of the earth: Volume of the seas is about 1.3 x 1024 cm3; 18g water contain 6 x 1023 molecules. The seas thus contain about 4 x 1046 molecules. It is thus possible by isomerism alone to create an infinite number of sub- stances. This number is increased still further by variation in the configura- tion of the macromolecules while they are being built, or else by the influence of their environment. So, each living organism can create its own nucleic acids, protein molecules, etc. This conclusion is necessary since every organism, and every human being too, differs chemically from another. Associated with this boundless profusion of matter in the macromolecular sphere, in contrast, is a remarkable stability of the macromolecules, a stabil- ity which is governed by their structure as organic compounds in compliance with the laws of Kekulé’s structural theory. That alone is capable of satisfying the "inconceivably strict demands on the integrity of the germ plasm" which are applied to the normal process of development of an organism 60. This stability of the macromolecules, associated with their reactivity, sup- plies the living substance with the necessary basis for so specific a process as that of heredity. The known facts of macromolecular chemistry show further that an individual macromolecule is still not "living", however large it is and how- ever complex its structure. On the contrary, the term is relevant to a certain amount of substance comprising numerous macromolecules with the con- stituent small molecules combined together in strictly prescribed order, an "atomos" of living matter16 which is indivisible without losing its "living- ness". Living nature supplies the answer to the question how large such an "atomos" has to be in the form of the various germ cells, for nothing can be removed from such a cell, whether a spore or a fertilized ovum, otherwise no normal organism can be formed from it. One of the smallest units capable of se&propagation is, for example, a bacterial spore. The following estimate MACROMOLECULAR CHEMISTRY 417 Table 16. A bacterial spore of 0.124p diameter weighs 10-15g (sp.gr. = I) and after removal of 50% water content comprises 5·107 atoms. may afford an idea of what numbers of macromolecules and molecules are the necessary minimum for "livingness" here (Table 16). In contrast to former opinions one of the smallest living units thus requires a quantity of substance. In this way macromolecular chemistry appears today to fit between low molecular organic chemistry and cytology. It is the connecting link between them, growing systematically out of low molecular chemistry but, with the incomparably larger wealth of its chemical scope, forming living matter. In addition, over and above the quantitative laws of pure chemistry, macro- molecular chemistry makes use of a number of qualitative correlations: those of shape and of the associated configurational scope, up to the level of the "atomos" of living substance, on which the game of Life ensues. In the light of this new knowledge of macromolecular chemistry, the wonder of Life in its chemical aspect is revealed in the astounding abundance and masterly macromolecular architecture of living matter. 1. H. Staudinger, Chem. Ztg., 77 (1953) 679. 2. H. Staudinger, Die Chemie der organischen hochmolekularen Stoffe im Sinne der Kekuléschen Strukturlehre, (Vortrag auf der Versammlung Deutscher Natur- forscher und in Dusseldorf), Ber. Deut. Chem. Ges., 59 (1926) 3019. 3. H. Staudinger, Ber. Deut. Chem. Ges., 53 (1920) 1073. H. Staudinger and J. Fritschi, Helv. Chem. Acta, 5 (1922) 785. 4. R. Signer, Z. Physik. Chem., A 150 (1930) 257, and subsequent papers. 5. G. V. Schulz, Z. Physik. Chem., B 30 (1935) 379; B 32 (1936) 27; A 176( 1936) 317, and subsequent papers. 6. Cf. G. V. Schulz in Röhrs-Staudinger-Vieweg, Fortschritte der Chemie, Physik und Technik der makromolekularen Stoffe, Vol. 1, Verlag Lehmann, München, 1939, p. 28. 418 1953 H.STAUDINGER 7. W. Kern, Z. Physik. Chem., A 181 (1938) 249, 283; A 184 (1939) 197, 302, and subsequent papers. 8. E. Husemann, J. Prakt. Chem., 155 (1940) 13,241, and subsequent papers. 9. G. V. Schulz and E. Husemann, Z. Physik. Chem., B 52 (1942) 23, and subsequent papers. 10. H. W. Kohlschütter, Liebigs Ann. Chem., 482 (1930) 75; 484 (1930) 155, and subsequent papers. 11. H. Batzer, Makromol. Chem., 5 (1950) 5, and subsequent papers. 12. J. Hengstenberg, Arm. Physik, 84 (1927) 245 ; H. Staudinger, H. Johner and R. Signer, G. Mie, and J. Hengstenberg, Z. Physik. Chem., 126 (1927) 425, and sub- sequent papers. 13. E. Sauter, Z. Physik. Chem., B 18 (1932) 417, and subsequent papers. 14. E. Plötze and H. Person, Z. Physik. Chem., B 45 (1940) 193. 15. M. Staudinger, Chem. Ztg., 67 (1943) 316, and other papers. 16. M. Staudinger, Makromolekulare Chemie und Biologie, Verlag Wepf & Co. Basel, 1947. 17. The Svedberg, Z. Physik. Chem., 121 (1926) 65; The Svedberg and K. 0. Pedersen, Die Ultrazentrifuge, Verlag Steinkopff, Dresden, 1940. 18. J. H. Northrop, Crystalline Enzymes, New York, 1939. 19. H. Staudinger and W. Frost, Ber. Dart. Chem. Ges., 68 ( 1935) 2351; G. V. Schulz and E. Husemann, Z. Physik. Chem., B 34 (1936) 187, and subsequent papers. 20. L. Küchler, Polymerisationskinetik, Springer Verlag, Berlin, 1951. 21. W. H. Carothers, Collected Papers, New York, 1940. 22. O. Bayer et al., Angew. Chem., 62 (1950) 57. 23. J. C. Bevington, G. M. Guzman, and H. W. Melville, Nature, 170 (1952) 1026. 24. Wi. Ostwald, Die wissenschaftichen Grundlagen der analytischen Chemie, 2nd ed., Leipzig, 1897, p. 3. 25. H. Staudinger et al., Liebigs Ann. Chem., 474 (1929) 168. 26. H. Staudinger and K. Wagner, Makromol. Chem., 11 (1953) 79. 27.H. Staudinger, Organische Kolloidchemie, Verlag Vieweg, Brunswick, 1950, 3rd ed.; French edition, Dunod, Paris, 1953. 28. H. Staudinger, Zur Nomenklatur auf dem Gebiete der Makromoleküle, Makromol. Chem., 9 (1953) 221. 29. Wo. Ostwald, Die Welt der vernachlässigten Dimensionen, 1st ed., Verlag Steinkopff, Dresden, 1914. 30. H. Staudinger, Ber. Deut. Chem. Ges., 62 (1929) 2893. 31. F. Krafft and A. Stem, Ber. Deut. Chem. Ges., 27 (1894) 1747 et seq. 32. R. Zsigmondy and W. Bachman, Kolloid-Z., II (1912) 145. 33. J. W. McBain, Advan. Colloid Chem., 5 (1944) 102. 34. P. Karrer, Helv. Chem. Acta, 3 (1920) 620; P. Karrer et al., Helv. Chem. Acta, 4 (1921) 185, 263 ; P. Karrer, Einführung in die Chemie der polymeren Koklenkydrate, Leipzig, 1925, pp. 4 and 8. 35. M. Bergmann, Angew. Chem., 38 (1925) 1141; Naturwiss., 14 (1926) 1224; Ber. Dart. Chem. Ges., 59 (1926) 2973. 36. R. Pummererer, Ber. Deut. Chem. Ges., 60 (1927) 2167. MACROMOLECULAR CHEMISTRY 419 37. K. Hess, Chemie der Cellulose, Leipzig, 1928, p. 590, 38. K. H. Meyer and H. Mark, Ber. Deut. Chem. Ges., 61 (1928) 593, 1939. 39. W. N. Haworth, The Constitution of Sugars, London, 1929. 40. K. Freudenberg, Tannin, Cellulose, Lignin, Berlin, 1933. 41. 0. L. Sponsler and W. H. Dore, Colloid Symposium Monograph, 126 (1926) 174. 42. H. Staudinger, Svensk Kem. Tidskr., 49 (1937) 3 ; Suomen Kemistilehti, A 24 (1951) III. 43. H. Staudinger and G. Daumiller, Liebigs Ann. Chem., 529 (1937) 219. 44. H. Staudinger and R. Mohr, Ber. Deut. Chem. Ges., 70 (1937) 2302. 45. H. Staudinger and E. Husemann, Liebigs Ann. Chem., 527 (1937) 195. 46. H. Staudinger and E. Husemann, Liebigs Ann. Chem., 530 (1937) I. 47. E. Husemann, J. Prakt. Chem., 155 (1940) 241. 48. H. Staudinger, Die hochmolekularen organischen Verbindungen, Kautschuk und Cel- lulose, Springer Verlag, Berlin, 1932. 49. H. Staudinger, Ber. Deut. Chem. Ges., 68 (1935) 1682. 50. H. A. Stuart, Die Physik der Hochpolymeren, Vol. 2: Dar Makromolekül in Lösungen, Springer Verlag, Berlin, 1953. 51. W. Kuhn, Angew. Chem., 49 (1936) 858; W. Kuhn and H. Kuhn, Helv. Chem. Acta, 26(1943) 1394;28 (1945) 1533. 52. W. Kuhn, Helv. Chem. Acta, 32 (1949) 735. 53. H. Staudinger and H. Hellfritz, Makromol. Chem., 7 (1952) 274. 54. H. Staudinger and Hj. Staudinger, J. Prakt. Chem., 162 (1943) 148. 55. H. Staudinger and W. Heuer, Ber. Deut. Chem. Ges., 67 (1934) 1164. 56. F. Auerback and H. Barschall, Arb. Kaiserl. Gesundh. Amt, 27 (1907) 183. 57. H. Staudinger and M. Lüthy, Helv. Chem. Acta, 8 (1925) 65 ; H. Staudinger, R. Signer et al., Liebigs Ann. Chem., 474 (1929) 145. 58. H. Staudinger and W. Döhle, J. Prakt. Chem., 161 (1942) 219; H. Staudinger, K. H. In Den Sir-ken and M. Staudinger, Makromol. Chem., 9 (1953) 148. 59. H. Staudinger, Z. Physik. Chem., A 153 (1931) 391. 60. E. Hadorn, VersammIung der Gesellschaft deutscher Naturforscher und Springer Verlag, 1953, p. 39. K ARL ZIEGLER Consequences and development of an invention* Nobel Lecture, December 12, 1963 The awarding of the Nobel Prize for Chemistry for the year 1963 is related to the precipitous expansion of macromolecular chemistry and its industrial ap- plications, which began precisely ten years ago at my Max-Planck-Institute for Coal Research, in Mülheim/Ruhr. The suddenness with which this began, and the rapidity with which it was propagated are comparable to an explosion. The energy carriers in this case were the ingenuity, activity, creative imagina- tion and bold concepts of the many unnamed chemists, designers and entre- preneurs in the world who have fashioned great industries from our humble beginnings. If today I stand with my colleague Natta, who has been particularly effective in promoting this explosive wave, in the limelight of distinction, and do wish to manifest, with this address, my appreciation for the honor bestowed upon me, I must begin by thanking these many anonymous persons. They, too, deserve this distinction. The extent of this "explosion" may be illustrated by two charts1, in which the location of newly-established plants is indicated. The places marked by black circles refer to the production of high molecular weight materials, the crosses to new production facilities which, though concerned with low mo- lecular weight materials, nevertheless also have some connection with the ad- dress I am delivering today (Figs. 1 and 2). The new development had its inception near the end of 1953, when I, to- gether with Holzkamp, Breil and Martina, observed-during only a few days of an almost dramatic course of events-that ethylene gas will polymerize very rapidly with certain catalysts that are extremely easy to prepare, at 100, 20 and 5 atmospheres and, finally, even at normal pressure, to a high molecular weight plastic. I would like to first describe our normal-pressure polymerization experi- ment, which actually takes about an hour but which has been condensed in the films to a few minutes (not shown here). *This translation of Prof. Ziegler’s Nobel Lecture is reproduced with some modifica- tions, by permission of the publishers, from Rubber Chem. Technol., 38 (1965) xxii. CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 7 Fig. 1. Location of industrial applications of the Mülheim processes in Europe (as of 1963). On the figure: ˜ H"igh molecular weight materials; x , Aluminium alkyls and low mo- lecular weight materials; Under construction or planned. Fig. 2. Location of industrial applications of the Mülheim processes in the world (as of 1963). Symbols as in Fig. 1. Numbers indicate the number of factories. 8 1963 KARL ZIEGLER The catalyst is prepared simply by simultaneously pouring, with exclusion of air, two liquid materials into about two liters of a gasoline-like hydro- carbon, after which ethylene is introduced, while stirring. The gas is absorbed quickly;. within an hour one can easily introduce 300-400 liters of ethylene into the two liters of liquid. At the same time, a solid substance precipitates, in such a way that after approximately one hour the material becomes doughy and can scarcely be stirred any more. If the brown catalyst is then destroyed, by the addition of some alcohol and by the introduction of air, the precipitate becomes scow- white and can be filtered off. In its final state it will accumulate, in amounts of 300-500g, as a dry, white powder. The results of this experiment greatly surprised us, and, later on, many others, since up to that time ethylene had been considered extremely difficult to polymerize. The "polythene" of the Imperial Chemical Industries, a prod- uct which had been known for some seventeen years, was being prepared under pressures of 1000-2000 atmospheres, and at a temperature of 200ºC. Our experiment thus destroyed a dogma. It led, in addition, to a polyethylene which differed quite markedly from the high-pressure product. Low-pres- sure polyethylene not only has a better resistance to elevated temperatures and a higher density, but is also more rigid. This is easily demonstrated by holding in one hand two similar objects made of the two materials, and press- Fig. 3. Comparison between the rigidity of two beakers, one of low-pressure, one of high-pressure polyethylene. CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 9 ing them together (Fig. 3). Low-pressure polyethylene can be drawn without difficulty to form fibers or ribbons of high tensile strength. This cannot be done at all with high-pressure polyethylene, or at best only an indication of drawing is obtained. We established these facts immediately after our dis- covery, with test specimens which were still quite primitive1. The differences can be attributed to the fact that in our process molecules of ethylene are joined together linearly, without interruption, whereas in the high-pressure process chain growth is disturbed, so that a strongly branched molecule results (Fig. 4). Fig. 4. High-pressure polyethylene, structural principle. The low-pressure process found immediate acceptance in industry. By 1955, 200 metric tons of this new type of plastic had been produced; in 1958 it was 17000 tons, and in 1962 some 120000 tons. The much higher figures occasionally cited for this and other plastics have resulted from the confusion of available, but unused, capacities with actual production. The increase in dimensions can be indicated by comparison of our first test specimens, pre- pared ten years ago with rather primitive means, with containers that are twenty cubic meters in capacity, the largest now being made from polyethyl- ene. A subsequent figure shows the lightness of the material, since a very large container can easily be carried by only a few men. The catalyst employed in the experiment described was prepared by mixing aluminium triethyl, or diethyl aluminium chloride, with titanium tetrachlo- ride. However, this is only one example, taken from the countless series of "organometallic mixed catalysts". Most generally they will form, as we found, whenever standard organometallic compounds, preferably those of alumin- ium, but also many of other metals, are brought into contact with com- pounds of certain heavy metals. Those of titanium, zirconium, vanadium, chromium, molybdenum, cobalt and the like are especially effective. Since 10 1963 KARL ZIEGLER there are many different metal alkyls and many different heavy metal com- pounds, and since, furthermore, components can be mixed together in varying proportions, and by different methods, and because all this can have an effect, often a truly decisive effect, on the nature of the catalytic activity, it is easy to understand why this field has grown to practically limitless proportions. In place of the metal alkyls, one can also use metal hydrides, or the metals themselves, whereas metal alkyls probably will still form during the catalyzed processes. Our catalysts then became known, at the turn of the year 1953/4, to our friends in industry and to their foreign colleagues, in Frankfurt, the Ruhr, Manchester, and-last but not least-Milan. Shortly thereafter this knowledge jumped over to the U. S. A. as well, and ultimately our findings became avail- able to all. The consequences have been characterized, elsewhere, by the state- ment that revelation of the Mülheim catalysts had the same effect as the starting gun of a race in which the laboratories of the interested industries had been entered4. However, representatives of purely scientific chemistry also partici- pated. Because of the magnitude of the new field, arrival at further stages, or the order of such arrivals, was necessarily dependent upon contingencies. Indeed, many important observations were made within short spaces of time, inde- pendently of one another, and at different places. Let me illustrate this with two examples: It was pure chance that in November of 1953 the first of the catalysts in which our invention was clearly recognizable happened to be a relatively weak-acting combination of an aluminium alkyl with a zirconium compound, by which ethylene could be polymerized only under a few atmo- spheres pressure, and with which propylene, already tested the day after our critical experiment with ethylene, would not polymerize at all. Then, for a number of weeks, we were absorbed in experimenting with normal-pressure polymerizations of ethylene by means of titanium- containing catalysts. Early in 1954 we recognized the possibility ofcopolymerizing ethylene and propyl- ene, after which we succeeded, at Mülheim, in polymerizing propylene with more effective catalysts, but - and this we did not know at the time - a short while after my colleague Natta of Milan had already observed this. In a first substantiation of his observation, and in an act of fairness, Natta had referred to the catalyst used as a "Ziegler catalyst", and that is how this expression found 5 its way into the literature . It is surely understandable that I myself prefer to speak of them as "Mülheim catalysts". The second example: Near the close of 1955 work was being done in many CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 11 places on the polymerization of butadiene with our catalysts. But no one had observed that in addition to the desired high polymers, a very interesting trimer of butadiene, namely 1,5,9-cyclododecatriene, was being produced. Günther Wilke, of my institute, became aware of this, and showed how one can guide the reaction entirely in this new direction. While endeavouring to explain the formation mechanism of cyclododecatriene, Wilke discovered a way to redirect this reaction at will, either toward a dimerization to an eight- membered ring, or - by a co-reaction with ethylene - toward a co-oligomeri- 6 zation to a ten-membered ring . The result was that the Mülheim catalysts also achieved importance for polycondensation plastics such as Nylons 8, 10 and 12, into which the ring compounds can be transformed. These cyclizations constituted the third surprising development afforded the scientific community by the organometallic mixed catalysts, if I assign number one to the new polyethylene process. I saved the second surprise for Fig. 5. Portions of the chains of (a) polyethylene, (b) atactic, (c) isotactic and (d) syndio- tactic polypropylene. The methyls in the polypropylene are striped, and are actually much larger than shown. 12 1963 KARL ZIEGLER later, and I must go into that now. From the middle of 1954 on, it began to be obvious that the Mülheim catalysts were capable of polymerizing in a struc- turally specific, as well as a stereo-specific manner. This realization is an es- sential contribution of my colleague Natta. He had often pondered over the mechanism of the polymerization, and very successfully strove to "train" the catalysts in such a way that they would possess extremely high specificity. Without wishing to anticipate Natta7 in any way, I nevertheless feel obliged, for the sake of completeness, to explain briefly what this is all about. The chain of linear polyethylene in the model, at an enlargement of fifty million, has approximately the following shape: (Fig. 5a). If a substituted ethylene, for example propylene, is polymerized, only the two doubly-bound carbon atoms of the olefin molecule will participate in the chain formation. The substituents, as side chains, will remain on the outside. If they combine in a purely random fashion the resultant product will show an entirely arbitrary distribution of the substituents along the two sides. Previously it had been believed that only those polymers could be formed which Natta - so far as I know at the suggestion of his wife - later called "atactic" (Fig. 5b). In stereo- specific polymerizations, polymers with highly regular structure are pro- duced, with all the substituents on one side - isotactic (Fig. 5c) according to Natta - or with the substituents in a regular right-left sequence - syndiotactic (Fig. 5d) according to Natta. Both these terms were again inspired by Mrs. Natta. The particularly favorable properties of the products correspond to the regularity of the structure. Analogous phenomena were encountered when our catalysts were used for polymerization of butadiene. In this instance, either only one of the two double bonds present can take part in the polymerization process. The result is a con- figuration comparable to that of polypropylene and containing, instead of methyl groups, only the unsaturated residues of ethylene, the so-called vinyl groupsC2H3,in which case it can still be isotactic, atactic, or syndiotactic. This is a so-called 1,2-polymer of butadiene (Fig. 6, upper). Or, all four of the C-atoms can enter into the long chain of the polymer, in 1,4-polymeri- zations, so that in the middle of each individual C4structure unit a new double bond is formed, which was not present previously at that particular site (Fig. 6, lower). In addition, because of the double bonds, and from their aspect, the va- lences of the two adjacent carbon atoms point either both toward one side, or to opposite sides. The first is the cis configuration, and the other is the trans (Fig.7). CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 13 Fig.6. "1,2-"(upper) and "1,4-"(lower) polymerizations of butadiene. Hydrogenatoms are not shown. Natural rubber is a cis-1,4-polybutadiene, in which, are very disable bond, the hydrogen atom has been replaced by a methyl group. Another important natural substance, guttapercha, corresponds to the trans-1,4-polymer( Fig. 7). The difficulty with all earlier attempts to synthesize rubber or rubberlike materials was that it was not possible to steer the polymerization of the basic materials - butadiene, isoprene - uniformly into the one or the other configu- ration. For this reason synthetic products contained a chaotic array of 1,4-cis, 1,4-trans and 1,2 structural units, even in the individual molecules. Although they resembled the natural product to some extent, none of them ever cor- responded to it completely. With the aid of the easily prepared Mülheim catalysts it is now possible to synthesize all these types uniformly, as desired, in a structure-specific or stereospecific manner. For example, 1,2-polybutadiene is formed by using a Fig. 7. Structural principle of natural rubber (cis) and guttapercha (tram). White circles: methyl groups. Hydrogen atoms are not shown. 14 1963 KARL ZIEGLER catalyst made from titanium acid ester and 3 aluminium triethyl. With the catalysts obtained from TiCl4 + 0.5 Al(C2H 5)2 2C1, trans-1,4-polybutadiene can be produced, and with those derived from 1 Til4+ 1 Al(C2H5)3or 1 CoCl2 + 1 Al(C2 H 5 ) 2 Cl, cis-1,4-polybutadiene will be formed, Finally, I would like to add that an increase of the Al : Ti ratio in the catalyst, to 5 : 1, will lead to cyclododecatriene. A group from the B. F. Goodrich Research Center in the U. S. A. first made these observations with cis-1,4-polyisoprene, the synthetic "natural rubber", a few week; after their company had learned about the essential features of our cataiysts 8. Actually, this represented only the final, closing stages of a So-year effort to synthesize "genuine" rubber. Corresponding polymers of buta- diene itself were then intensely studied, in a number of places, and cis-1,4- polybutadiene is today considered to be of great technological importance. I will close this short survey with a discussion of recent developments per- taining to the rubber-like copolymers of ethylene and propylene, particularly those obtained with vanadium-containing organometallic mixed catalysts, and to the so-called terpolymers, into whose molecules certain diolefins - (dicyclopentadiene, or, again as discovered by Natta and coworkers 9, our cyclooctadiene-1,5) - have been incorporated. Large quantities of all these new synthetic materials, discovered in con- nection with low-pressure polyethylene, are already being produced throughout the world, and production is sure to continue rising at a sub- stantial rate. With this I have shown, in broad outline, what has resulted in the course of ten years from our early experiments with organometallic mixed catalysts. In order to make the sequence of events which led to such a fruitful invention more understandable, I shall have to go back exactly forty years. Shortly after my graduation, having been a student of Karl von Auwers at the University of Marburg/Lahn, I began my independent scientific work with experiments for testing the theory of so-called free radicals. I incidentally found, in 1923, a new method for the formation of organic compounds of the alkali metals potassium and sodium10, which brought my attention to the metal alkyls as an interesting, highly diversified field, that has continued to fascinate me, over and over again, up to the present. The new catalysts grew out of this, as a side sprout, in 1953. Permit me now to pursue the unbroken chain of causal rela- tionships that links Then and Now by using special block schemes (Fig. 8, 1, Figs.9-12). 11-13 A few years later, in 1927, Bähr and I made the discovery - important CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 15 for the further development - that alkali alkyls can be added with ease to butadiene or styrene, at room temperature (Fig. 8,2). Repetition of the process leads first to oligomers, in a "stepwise organometallic synthesis", and finally to polymers and high polymer reaction products (Fig. 8,4). This first contact of mine with "macromolecular chemistry" later gave impe- tus to many investigations by third parties, and recently butyl lithium has also been suggested for industrial polymerizations of isoprene. At first, however, another, indirect result of our work was of more importance. Secondary ob- servations suggested the conclusion that metallic lithium should be amenable to a reaction analogous to the one by which Grignard compounds are formed from magnesium: Fig. 8. Preliminary work (Marburg/Lahn, Heidelberg, Halle/Saale) 1931-1939. First results in Mülheim/Ruhr. 16 1963 KARL ZIEGLER With Colonius14, I was able to confirm this in 1930, and that is how the organolithium compounds became easily accessible (Fig. 8,3). In Mülheim/Ruhr, where I have been working since 1943, Gellert and I succeeded in transferring the technique of a "stepwise organometallic syn- thesis" from butadiene to ethylene 15.In this instance the reaction leads from lithium alkyl directly to the higher straight-chain lithium alkyls, and hence also to alcohols, carboxylic acids, and the like (Fig. 8,5). growth which a chain can undergo, since, for ethylene addition, the tempera- tures required are such that the lithium alkyls will readily decompose to lithium hydride + olefin. This certainly seemed to justify the following con- clusion: If, in such decompositions, it is a question of a reversible reaction, as we had reason to believe, then lithium hydride and lithium alkyls should, under proper conditions, function as catalysts for the polymerization, or rather, oligomerization, of ethylene to the higher -olefins (Fig. 8, 6). We did find such a reaction in principle, but it was so complicated by sec- ondary and subsequent reactions that we could do nothing with it. Then when I had already decided to give up these efforts, my coworker, H. G. Gellert, conducted one more experiment-and the last, he was convinced-with the just recently discovered lithium aluminium hydride. This led immediately to the desired higher (Fig. 8, 7). As the decisive turning point, this resulted in the realization that the alkali metal was not the crucial issue at all, and that everything we already knew about the lithium alkyls, and all that we had anticipated besides, with respect to the chemistry of the olefinic hydro- carbons, could be achieved with a great deal more ease through use of organo- aluminium compounds16. That is: (1) There are genuine equilibria aluminium alkyle aluminium hydride + olefin lying, as a rule, entirely to the left, so that, in reverse of the situation with lithium, it is possible to synthesize the aluminium alkyls from hydride + olefin (Fig. 8, 8,9). (2) In the case of aluminium, too - and this came as a real surprise - at mod- erately high temperatures a stepwise organometallic synthesis, or as we now CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 17 call it, a "growth" or propagation reaction takes place, leading to the higher aluminium alkyls; thus, a synthesis of the higher straight-chain primary monofunctional aliphatic compounds, particularly the fatty alcohols (Fig. 9, 10,11), became possible. (3) Furthermore, we have, from about 150º on, a catalytic oligomerization of the ethylene to higher - olefins (Fig. 9, 21). Here the organometallic synthesis appears as the partial reaction of a com- pletely understood, homogeneous intermediate reaction catalysis: After a certain number of addition steps the intermediate product decomposes to a hydride and an olefin whereupon, after the addition of ethylene to the hydride, the cycle is repeated. Such a reaction was encountered in its most primitive form with propylene, for which the homogeneous catalysis leads, without supplementary chain growth, almost exclusively to a well-defined dimer17 (Fig.9, 19): Recently this reaction has achieved significance for high molecular weight chemistry as well, since the cracking of isohexene, following the shifting of the double bond, produces isoprene, in addition to methane18 (Fig.9, 20). 18 1963 KARL ZIEGLER The transition of all these reactions into industrial applications was finally accomplished by the so-called "direct synthesis" of aluminium alkyls from aluminium, hydrogen and olefins, discovered by us at approximately the same time as the new polyethylene process. Aluminium hydride, from which the aluminium trialkyls are quite easy to obtain through the addition of olefins, cannot be prepared directly from the metal and hydrogen. However, in already-prepared aluminium trialkyls, aluminium will dissociate with hy- drogen to dialkyl aluminium hydrides which, with ethylene, will give 1.5 times the original amount of aluminium triethyl, so that any amount of aluminium trialkyl can be prepared without difficulty 19 (Fig.10, 12,14). In the charts shown at the beginning of this address, the location of the in - dustries engaged in the production of aluminium alkyls and their low molec- ular weight applications were included. This area of the industrial develop- ment initiated by Mülheim is likewise in a state of continuous evolution, though it has been less rapid than that of the high molecular weight phase. CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 19 Fig. 10. Course of the Mülheim Experiments, Part II. Up to the year 1952 we had frequently conducted "growth" reactions based on aluminium triethyl, and thought we were thoroughly acquainted with such reactions. But when, together with E. Holzkamp20, I attempted to apply this type of reaction to aluminium tripropyl the formation of chains, to our great surprise, did not materialize at all. On the contrary, we obtained propyl- ene-from the propyl aluminium - in addition to aluminium triethyl and butylene. Even starting from aluminium triethyl our reaction now yielded nothing but butylene and the unchanged aluminium compound. The explanation was obvious: A catalyst in trace amounts must have gotten into this series of experiments, leading to an uncommonly rapid acceleration of the displacement reactions: and mediately after the first propagation step, as butylene. It is now generally 20 1963 KARL ZIEGLER known that we detected a tiny trace of metallic nickel as the disturbing ele- ment2(Fig.9, 22). Thus our attention was again directed to the problem to polymerize also ethylene just as, years ago, we had been able to do with butadiene and styrene, to produce a genuine macromolecule with the aid of metal alkyls, in this case aluminium alkyls in particular. Our growth reaction must lead to a genuine polyethylene, if we succeeded in adding about 1000 ethylene units to the aluminium triethyl. For this, with our reaction, only about 100-200 atmospheres pressure, instead of the 1000- 2000 atmospheres used heretofore, would be required. Nevertheless, in prop- erly performed experiments we had obtained only waxy products, because the chain at the aluminium was prematurely split off-apparently by a dis- placement reaction-as an olefin, with there-formation of ethyl at the alumin - ium, an occurrence known to chemists working in the high molecular weight field as a "chain transfer reaction": To the extent that catalyst traces, as we now might well suspect, had been involved here also in effecting the displacement, there existed the prospect that completely "aseptic" procedures could eventually lead to a true poly- ethylene. In order to provide the essentials for the "asepsis", we began, in the middle of 1953, to systematically investigate substances which have effects somewhat similar to those of nickel. We found, instead, the polymerization- promoting organometallic mixed catalysts, and, in particular, we achieved a low-pressure polymerization of ethylene, and with this I have again arrived at my starting point (Fig. 9, 23). Fig. II, which follows, once again shows, in schematic form, all that has resulted from the discovery of organometallic mixed catalysts. In this con- nection, isoprene is doubly concerned in our work: because of the aforemen- tioned synthesis, and for polymerization purposes. Finally, I would like to present the following scheme (Fig. 12), in order to show the entire development. The areas in two types of hatching indicate the important transitions (from Li to Al, from the Al-alkyls to the mixed cata- lysts), and also a third transition to an electrochemical side branch, which I cannot go into at this time ( cf: Fig. 10, 15 18). The important consequences of the discovery of organometallic mixed catalysts, evident even to the lay- man, have led many to regard me, nowadays, as a "macromolecular chemist", and, in fact, even as a plastics expert. I have intentionally set my work in this field within a much broader framework, to show you that I am a "macro- CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 21 Fig. II. Course of the Mülheim Experiments, Part III. Fig.12. The Mülheim experiments (1948-1963), overall aspect. Numbers are as in Figs.8-II. 12 1963 KARL ZIEGLER molecular chemist" only peripherally, and that I am not at all a plastics expert. Rather, I have always looked upon myself as a pure chemist. Perhaps that is also why the impact of the invention has been so enduring. The new knowl- edge has, after all, not come from macromolecular chemistry. It is the metal alkyls that have insinuated themselves into the chemistry of macromolecules to effectively fertilize this field. Typical of the course I have followed from those early beginnings of forty years ago until today, is the fact that I have never started with anything like a formally presented problem. The whole effort developed quite spontaneously, from a beginning which was actually irrational in nature, through an unbroken causal series of observations, inter- pretations of findings, rechecking of the interpretations by new experiments, new observations, etc. My method resembled a meandering through a new land, during which interesting prospects kept opening up, during which one could frequently view part of the road to be traveled, but such that one never quite knew where this trip was actually leading. For decades I never had the slightest notion that successful technological and industrial applications were also to be encountered during the journey. Twice this path seemed seriously blocked. The first time was before the transition from lithium hydride to lithium aluminium hydride and from the lithium to the aluminium compounds had been accomplished. The second was when our growth reaction suddenly, in a truly mysterious way, refused to go any more. In both cases, a capitulation in the face of these difficulties would undoubtedly have broken the red thread of continuity, which can now be followed clearly. But a much more formidable impediment might have presented itself In order to illustrate this, I must elaborate on the paradox that the critical con- cluding stages of the investigations I have reported took place in an institute for "coal research". When I was called to the Institut für Kohlenforschung in 1943, I was dis- turbed by the objectives implied in its name: I was afraid I would have to switch over to the consideration of assigned problems in applied chemistry. Since ethylene was available in the Ruhr from coke manufacture, the search for a new polyethylene process, for example, could certainly have represented such a problem. Today I know for certain, however, and I suspected at the time, that any attempt to strive for a set goal at the very beginning, in Mül- heim, would have completely dried up the springs of my creative activity. As a matter of fact: Giving up my preoccupation with organometallic com- pounds in favor of the other, "bread-and-butter" problems of coal chemis- CONSEQUENCES AND DEVELOPMENT OF AN INVENTION 23 try - many of my colleagues were of the opinion, at the time, that this would be the natural consequence of my removal to Mülheim - would have cut the leads which I already held invisibly in my hand, and which were to lead me safely to the results that proved of such importance also for the Ruhr industry. As a condition of my transfer to Mülheim I stipulated that I was to have complete freedom of action in the entire field of the chemistry of carbon compounds, without regard to whether any direct relation to coal research was or was not recognizable. The acquiescence of my stipulation was in accord with the principles of the then Kaiser-Wilhelm, and now Max-Planck Society, of which my institute is a part. As far as the German coal mining in- dustry which supported my institute is concerned, this was an act of great foresight on their part which did in fact provide the conditions for everything that occurred, particularly the present circumstance that my institute, and I with it, have now received this very great distinction. The institute, however, - what is it, in its distinctive spritual and intellec- tual substance, other than the totality of its active people. I began this address with an expression of gratitude to the many people in the world whom I know only slightly, or not at all, and who have developed great industries from our beginnings. I will end the address by expressing my heartfelt thanks to the many, very well known members of my institute who have stood by me faithfully throughout all these years, and who share with me the prize for which I have been singled out. 1.Figs. I-II are taken from K. Ziegler, Arbeitsgemeinsch. Forch. des Landes Nordrhein - Westfalen, 128 (1964) 33. 2. K. Ziegler, E. Holzkamp, H. Breil and H. Martin, Angew. Chem., 67 (1955) 541. 3.The experiment corresponding to ref. I, Fig. I was shown as a movie in Stockholm. 4. Hercules Chemist, 46 (1963) 7. 5.K. Ziegler, E. Holzkamp, H. Breil and H. Martin, Angew. Chem., 67 (1955) 426. 6.G. Wilke, Angew. Chem., 75 (1963) 10; Angew. Chem., Intern. Ed., 2 (1663) 105. 7. G. Natta, following lecture; also Angew. Chem., 76 (1964) 553. 8.S. E. Honer et al., Ind. Eng. Chem., 48 (1956) 754. 9. G. Natta et al., Chimie Ind. (Milan), 45 (1963) 651. 10. K. Ziegler and F. Thielmann, Ber., 56 (1923) 1740. 11. K. Ziegler and K. Bähr, Ber., 61 (1928) 253. 12. K. Ziegler and H. Kleiner, Ann. Chem., 473 (1929) 57. 13. K. Ziegler, F. Dersch and H. Wollthan, Ann. Chem., 511 (1934) 13. 14.K. Ziegler and H. Colonius, Ann. Chem., 479 (1930) 135. 15. K. Ziegler and H.-G. Gellert, Ann. Chem., 567 (1950) 195. 24 1963 KARL ZIEGLER 16.K. Ziegler, Angew. Chem., 68 (1956) 721, 724. 17.K. Ziegler, Angew. Chem., 64 (1952) 323, 326. 18.V.F. Anhom et al., Chem. Eng. Prog., 57 (1964) 43. 19.K. Ziegler et al., Ann. Chem., 629 (1960) 1. 20.K. Ziegler et al., Ann. Chem., 629 (1960) 121, 135. G IULIO N ATTA From the stereospecific polymerization to the asymmetric autocatalytic synthesis of macromolecules Nobel Lecture, December 12, 1963 Introduction Macromolecular chemistry is a relatively young science. Though natural and synthetic macromolecular substances had long been known, it was only between 1920 and 1930 that Hermann Staudinger placed our knowledge of the chemical structure of several macromolecular substances on a scientific basis1. In the wake of Staudinger’s discoveries and hypotheses, macromolecu- lar chemistry has made considerable progress. Very many synthetic macromolecular substances were prepared both by polymerization and by polycondensation; methods were found for the regu- lation of the value and distribution of molecular weights; attempts were made to clarify the relationships existing among structure, chemical regularity, molecular weight, and physical and technological properties of the macro- molecular substances. It was far more difficult to obtain synthetic macromole- cules having a regular structure from both the chemical and steric points of view. An early result in this field, which aroused a certain interest in relation to elastomers, was the preparation of a polybutadiene having a very high content of trans-1,4 monomeric units, in the presence of heterogeneous catalysts2. A wider development of this field was made possible by the recent discovery of stereospecific polymerization. This led to the synthesis of sterically regular polymers as well as to that of new classes of crystalline polymers. Before referring to the stereospecific polymerizations and to their subse- quent developments, I wish to make a short report on the particular conditions that enabled my School to rapidly achieve conclusive results on the genesis and structure of new classes of macromolecules. I also wish to describe the main stages of the synthesis and characterization of the first stereoregular polymers of - olefins. 28 1963 GIULIO NATTA The achievement of these results has also been helped by the research I did in 1924 when I was a trainee student under the guidance of Professor Bruni. At that time I began to apply X-ray study of the structures of crystals to the reso - lution of chemical and structural problems3. At first, investigations were mainly directed to the study of low-molecular- weight inorganic substances and of isomorphism phenomena; but, after I had the luck to meet Professor Staudinger in Freiburg in 1932, I was attracted by the study of linear high polymers and tried to determine their lattice structures. To this end I also employed the electron-diffraction methods which I had learned from Dr. Seemann in Freiburg and which appeared particularly suit- able for the examination of thin-oriented films4. I applied both X-ray and electron-diffraction methods also to the study of the structure of the hetero- geneous catalysts used for certain important organic industrial syntheses, and thus had the possibility of studying in the laboratory the processes for the syn- thesis of methanols and the higher alcohols6, and also of following their in- dustrial development in Italy and abroad. In view of the experienceIhad acquired in the field of chemical industry, certain Italian Government and industrial bodies entrusted me in 1938 with the task of instituting research and development studies on the production of synthetic rubber in Italy. Thus the first industrial production of butadiene-styrene copolymers was realized in Italy at the Ferrara plants, where a purely physical process of frac- tionated absorption was applied for the first time to the separation of buta- diene from 1-butene7. At that time I also began to be interested in the possible chemical applica- tions of petroleum derivatives, and particularly in the use of olefins and di- olefins as raw materials for chemical syntheses such as oxosynthesis8 and polymerization9. The knowledge acquired in the field of the polymerizations of olefins en- abled me to appreciate the singularity of the methods for the dimerization of a-olefins that Karl Ziegler described10 in a lecture delivered in Frankfurt in 1952; I was struck by the fact that in the presence of organometallic catalysts it was possible to obtain only one dimer from each a-olefin, while I knew that the ordinary, cationic catalysts previously used yielded complex mixtures of isomers with different structures. At this time I also became acquainted with Ziegler’s results on the produc- tion of strictly linear ethylene oligomers, obtained in the presence of homo- geneous catalysts. My interest was aroused, and in order to understand better STEREOSPECIFIC POLYMERIZATION 0F MACROMOLECULES 29 the reaction mechanism11, concerning which very little was known, I started the kinetic study of such polymerizations. In the meantime Ziegler discovered the process for the low-pressure polymerization of ethylene12. I then decided to focus attention on the polymerization of monomers other than ethylene; in particular I studied the a -olefins, which were readily available at low cost in the petroleum industry. At the beginning of 1954 we succeded in polymerizing propylene, other a-olefins, and styrene; thus we obtained polymers having very different properties from those shown by the previously known polymers obtained from these monomers13. I soon observed that the first crude polymers ofa- olefins and of styrene, initially obtained in the presence of certain Ziegler catalysts (TiCl4 + aluminium alkyls), were not homogeneous, but consisted of a mixture of different products, some amorphous and non-crystallizable, others more or less crystalline or crystallizable. Accordingly, I studied the separation of the different types of polymer by solvent extraction and the structures of the single separated products. Even if the more soluble polymers were amorphous and had a molecular weight lower than that of the crystal- line, but far less soluble, polymers deriving from the same crude product, I observed that some little-soluble crystalline fractions had a molecular weight only a little higher than that of other amorphous fractions. Therefore, con- vinced of the well-known saying natura non facit saltus, I did not attribute crys- tallinity to a higher molecular weight, but to a different steric structure of the macromolecules present in the different fractions14. In fact all vinyl polymers may be regarded as built from monomeric units containing a tertiary carbon atom. Thus in a polymer of finite length, such a carbon atom can be considered asymmetric, and hence two types of mono- meric units may exist, which are enantiomorphous13,15 . Since all the polymers of vinyl hydrocarbons previously known, even those recognized as having a head-to-tail enchainment like polystyrene, were amorphous, we examined the possibility that the crystallinity we observed was due to a chemically regular (head-to-tail) structure, accompanied by regular succession of steric configurations of the single monomeric units. In- deed, X-ray analysis permitted us to determine the lattice constants of crys- talline polypropylene16 and polystyrene17. The identity period along the chain axis in the fiber spectra was of about 6.5 Å and might be attributed to a chain segment containing three monomeric units18. This led us to exclude the idea that the crystallinity was due to a regular alternation of monomeric units having opposite steric configuration. Thus it could be foreseen, as was in fact 30 1963 GIULIO NATTA later proved by more accurate calculations of the structure factors, that the polymeric chains consisted of regular successions of monomeric units, all having the same steric configuration14. In the-subsequent study of the butadiene polymers, prepared by us in the presence of organometallic catalysts (for example, catalysts containing chro- mium19) that have 1,2-enchainment, two different types of crystalline poly- mers were isolated and purified. The X-ray and electron-diffraction analyses of these products enabled us to establish that the structure of one of them is analogous to the structures of olefins20-that is, characterized by the repetition of monomeric units having the same configuration. We also established that the other crystalline product is characterized by a succession of monomeric units, which are chemi- cally equivalent but have alternately opposite steric configuration21, as con- firmed by a thorough X-ray analysis of the structure. In order to distinguish these different structures I proposed the adoption of terms coined from the a b Fig. I. Models of chains of head-to-tail vinyl polymers supposed arbitrarily stretched on a plane, having, respectively, isotactic (a), syndiotactic (b), and atactic (c) successions of the monomeric units. STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 31 ancient Greek, and these are now generally used22; that is, isotactic 14 and syn- diotacti21. Fig.Ishows the first device we used for an easy distinction of the different types of stereoisomerism of vinyl polymers; the main chains have been sup- posed arbitrarily stretched on a plane. By accurate examination of the structure of isotactic polymers on fiber spectra, we could establish that all crystalline isotactic polymers have a helical structure, analogous to that found by Pauling and Corey23 for a-keratin (Fig. 2); in fact only the helix allows a regular repetition of the monomeric units containing asymmetric carbon atoms, as was foreseen by Bunn24. Fig.2. Model of chain of according to Pauling and Corey. Soon after the first polymerizations of a -olefins we realized the importance and vastness of the fields that were opened to research, from both the theoret- ical and the practical points of view. Our efforts were then directed to three main fields of research: (1) To in- vestigate the structures of the new polymers in order-to establish the relation- ships existing between chemical structure, configuration, and conformation of the macromolecules in the crystalline state. (2) To find the conditions that allowed the synthesis of olefinic polyhydrocarbons having a determined type of steric structure, with high yields and high degree of steric regularity 25, as well as to study the reaction mechanism, and regulation of the molecular weight. (3) To attempt the synthesis, possibly in the presence of nonorgano- metallic catalysts, of stereoregular polymers corresponding to other classes of monomers having a chemical nature different from that of a-olefins. 32 1963 GIULIO NATTA I. Crystalline Structure of High Stereoregular Polymers 1. Homopolymers The synthesis of new classes of crystalline macromolecules and the X-ray analysis of their structures led to the formulation of some general rules which determine the structure of linear macromolecules26. Table 1 summarizes some data concerning the structure of isotactic polymers; the data indicate that four-fold or higher order helices exist besides the three-fold ones already mentioned. Table 1 X-Ray data on some typical isotactic polymers with different chain conformations. The conformation assumed by the single macromolecules in the lattice al- ways corresponds to the conformation, or to one of the conformations, of the isolated molecule that shows the lowest internal energy content, the intra- molecular Van der Waals forces being taken into account. The mode of pack- STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 33 ing of the polymer chains in a crystalline lattice takes place, as in the case of molecular crystals of low-molecular-weight substances, so as to fill the space in the best possible way. If the polymer chain assumes a helicoidal conformation in the crystalline state, and if it does not contain asymmetric carbon atoms, it can be expected that either helices of the same sense, or, in equal ratio, helices of opposite sense are represented in the lattice. Analogous to the case of nonenantiomorphous low-molecular-weight crystalline substances, so also in polymers that do not contain asymmetric carbon atoms, right- and left-handed helices are usually represented in the lattice in equal amount. On the other hand, in the case of isotactic polymers containing asymmetric carbon atoms, the space group will not contain symmetry elements involving inversion, as, for instance, centers of symmetry or mirror or glide planes. A racemic mixture of antipode macromolecules can be an exception. Fur- thermore, it is interesting to note that the chain symmetry is often maintained in the space group to which the unit cell of the polymer belongs. With regard to the occurrence of enantiomorphous space groups, typical examples are represented by some isotactic poly-1-alkylbutadienes, in the Fig. 3. Model of packing of isotactic trans-1,4-poly-I-ethylbutadiene in the crystalline state, projected on the (001) plane (space group 34 1963 GIULIO NATTA crystalline lattice of which macromolecules with helices of exclusively one sense, right or left, exist for each crystal27 (Fig. 3). Also in the case of isotactic poly-tert.-butylacrylate, the helices in the lattice seem to be all of the same sense28. If the chain symmetry is maintained in the crystal lattice, the possible occur- rence of different space groups is considerably restricted. Where equal amounts of enantiomorphous macromolecules are contained in the lattice, we must dis- tinguish two cases concerning the relative orientation of side groups of enan- tiomorphous macromolecules facing one another, which can be either iso- clined or anticlined. In the first case, possible symmetry operators for the covering of near macromolecules are either a mirror plane or a glide plane, parallel to the chain axis. It is, however, known that good packing is generally obtained more easily with a glide plane than with a mirror plane, especially in the case of bodies having periodical recesses and prominences, as in the case of spiralized polymer chains. In the case of a three-fold helix, each right-handed helix will be sur- rounded, because of the existence of the glide plane, by three isoclined left- handed helices, and vice versa; the space group will be R3c (Fig.4). This lattice is shown, for example, by isotactic polystyrene29, by polybutene30, by 1,2- 32 polybutadiene31, and by poly- o -fluorostyrene ; on the other hand it is not shown by isotactic polypropylene, because it would give rise to an insuffi- ciently compact lattice, if Van der Waals contact distances, between carbon atoms of near chains, must be maintained3 around 4.2 Å. In the second case previously considered, in which the relative orientation of the side groups of enantiomorphous macromolecules facing one another is anticlined, the only symmetry operator relating neighboring macromolecules is a symmetry center. And again, if the helix is threefold, each right-handed helix will be sur- rounded, by the action of three symmetry centers at 120°C, by three left- handed helices, and vice versa; the macromolecules are oriented so as to mini- mize the length of the unit cell axes perpendicular to the three-fold axis, with the best possible Van der Waals distances: the space group, which probably is the one presented, for instance, by polyvinylmethyl ether33 and by poly-n- 34 butylvinyl ether , will be R3 (Fig. 5). STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 35 36 1963 GIULIO NATTA 2. Copolymers The "random" introduction of different monomeric units in a crystalline polymer by copolymerization generally causes a decrease in crystallinity and melting point when their content is lower than 20 to 25 percent, but at higher content values the copolymer is generally amorphous. As we shall remark in the section dealing with the stereoregular polymers of hydrocarbon monomers containing an internal double bond, it is sometimes possible to obtain chemically and sterically regular alternating copolymers of these monomers with ethylene, which are also crystalline. This is the case, for instance, for the alternating ethylene-cis-2-butene35, ethylene-cyclopen- tene36, and ethylene-cycloheptene37 copolymers. In these cases, reaction conditions were used in which one of the monomers is unable to homopolymerize, but can copolymerize to alternating polymers in the presence of a large excess of the first monomer. Moreover, in the case of other nonhydrocarbon monomers, crystalline alternating copolymers have been obtained38 from two different monomers that are both very reactive in the presence of stereospecific catalysts (for example, in the copolymerization of dimethylketene with higher aldehydes39), when the values of the relative copolymerization rates are much higher than those of homopolymerization. In the cases mentioned above, the repeating structural unit has the structure of a polyester obtained by treating a dimethylketene molecule with one mole- cule of the carbonyl monomer considered. Our researches also enabled us to find particular crystalline copolymers, though with a "random" distribution, when the different monomeric units in the polymeric chain showed considerable analogies both in chemical nature and size. This phenomenon was defined by us as isomorphism of monomeric units, even if, in contrast to the isomorphism phenomena of low-molecular-weight sub- stances, the crystals do not consist of physical mixtures of isomorphous mole- cules, but of macromolecules in which monomeric units of different type can substitute each with the other. In this case, copolymers show physical prop- erties (density, melting temperature, and so on) which vary continuously with the composition, and which are intermediate between those of the pure homo- polymers. This phenomenon was observed in the copolymerization of styrene with monofluorostyrenes40 and also in the copolymerization of butadiene with 1,3-pentadiene to trans-1,4 polymer41. Crystalline copolymers of a completely different type are obtained by suc- STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 37 cessive polymerization of different monomers in the presence of catalysts able to homopolymerize both of them. These are linear copolymers constituted by successive blocks, each consisting of a chemically and sterically regular suc- cession of units of the same type. In some of these cases X-ray analysis reveals both the crystallinities corre- sponding to the single homopolymers42. The importance of the stereospecific polymerization - from the standpoint of both theory and practical applications - is due to the fact that in most cases (even if not always) the stereoregularity of linear polymers determines crys- tallinity. When the glass transition temperature and the melting temperature are very different, the physical and especially the mechanical properties are very different from those of the corresponding stereoirregular polymers. Due to such properties, these materials have very interesting practical applications, either as plastics and textiles when the melting point is high or as elastomers when the melting point does not considerably exceed the temperature of use. The knowledge acquired in these last10years in the field of the stereospeci- ficity of the polymerization processes shows that stereoregular and, in partic- ular, isotactic polymers can be obtained in the presence of suitable catalysts acting through an ionic (both anionic and cationic) coordinated mechanism; however, they cannot generally be obtained by processes characterized by radical mechanism. The catalysts having a higher degree of stereospecificity are characterized by the presence of metal atoms able to coordinate the monomer molecules in a stage immediately preceding that of insertion of the monomeric unit between the end of the growing chain and the catalyst 43-45 . In fact, a stereospecific action is shown either by the catalysts containing metal atoms, the coordinating properties of which are due to their charge and to their small ionic radius aluminium, beryllium, lithium)44, or by com- pounds of the transition metals46,47 . Some authors48 were led to believe that the steric structure of the last monomeric unit, or units, of the growing chain played an important role in the steric regulation of the polymerization processes. However, the low de- gree of stereospecificity observed in the radical processes shows that this factor alone cannot exert a determining action. In any case stereoregularity in these 38 1963 GIULIO NATTA last processes is of the syndiotactic type and may be attributed also to thermo- dynamic factors, according to the strong increase in stereospecificity with de- crease in temperature. The first highly stereoregular isotactic polymers were obtained in the pres- ence of heterogeneous catalysts; however, it soon became clear that the heter- ogeneity of the catalytic system is an essential factor for the polymerization of aliphatic olefins to isotactic polymers, but not for the polymerization of other types of monomers. In fact it was found that aliphatic aldehydes and certain monomers containing two electron-donor functional groups able to be co- ordinated (for example, conjugated diolefins, vinyl ethers, alkenyl ethers, acrylic monomers, styrenes that are substituted differently in the benzene ring, vinyl pyridine, and so on) can be polymerized in the stereospecific way also in the presence of soluble catalysts. It must be borne in mind that, even if the most typical highly stereospecific catalysts for the polymerization of a-olefins contain organometallic com- pounds, some classes of monomers (for example, vinyl ethers) can be poly- merized to isotactic polymers in the presence of cationic catalysts without the presence of organometallic compounds49. The stereospecificity of the polymerization processes not only depends on the catalytic system but is a property of each monomer-catalyst system. This is particularly evident in the case of the polymerization of some conjugated homologs of diolefins, in which the variation of the monomer changes both the degree of stereospecificity of the process and, in some cases, the type of stereoregularity of the polymer obtained50. Therefore, in order to attain a general view of the present state of the stereo- specific polymerization, it is helpful to examine the most important results obtained in each class of monomers. This is the most studied branch of stereospecific polymerization. As already mentioned, isotactic polymers of a-olefins have been obtained so far only with the use of heterogeneous catalysts. High stereospecificity is observed only when one employs organometallic catalysts containing a particular crystalline substrate, such as that deriving from the violet a, (ref. 51), and (ref. 52) modifications of TiCl3, having a 42,53,54 layer lattice . The use of the modification of TiCl3 (ref.55), which does not correspond to layer lattices, or of other heterogeneous catalysts (for STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 39 example, catalysts containing a substrate formed by metal oxides) which also yield linear polymers of ethylene, leads to the formation of catalysts having little stereospecificity in the polymerization of a-olefins 53,56 . The study of the catalysts prepared from organometallic compounds con- taining aromatic groups56 or labeled carbon enabled us to determine the ionic coordinated mechanism of such polymerization and the number of active centers on the surface of the heterogeneous catalysts57. Chemical and kinetic studies led to the conclusion that the stereospecific polymerization of propylene is a polyaddition reaction (stepwise addition),in which each monomeric unit, on its addition, is inserted on the bond between an electropositive metal and the electronegative terminal carbon atom of the growing polymeric chain. This study revealed also that some organometallic catalysts, which contain only titanium as metal atoms, could be stereospecific (ref. 58). The first reaction step corresponds to a coordination of the monomer molecule to the transition metal belonging to the active center43,45. The reaction chain generally does not show a kinetic termination59, the length of the single macromolecules being determined by the rate of the pro- cesses of chain transfer either with the monomer60 or with the alkyls of the 61 organometallic compounds present ; these transfer processes allow, after the formation of a macromolecule, the start of another macromolecule on the same active center56,62 . The single-rate constants of the different concurrent processes of chain growth and termination have been determined for some typical catalysts63. Later on, the study of homogeneous catalysts based on vanadium compounds and on alkyl aluminium monochloride permitted us to synthesize crystalline polypropylenes with a nonisotactic structure. The detailed development of this study led to the preparation of catalysts, obtained by treating hydro- carbon-soluble vanadium compounds (acetylacetonates or vanadium tetra- chloride) with dialkyl aluminium monochloride. These catalysts yield, at low temperature, more or less crystalline polymers, free, however, from iso- tactic crystallizable macromolecules64. X-Ray analysis, applied to the fiber spectra, permitted us to establish that this is a syndiotactic polymer; its lattice structure has an identity period of 7.4 Å, corresponding to four monomeric units65. The comparison between isotactic and syndiotactic polypropelene structures is shown in Fig. 6. The same type of homogeneous catalyst, which at low temperature homo- polymerizes propylene to syndiotactic polymer, was used at higher tempera- tures (for example, 0°C) for the production of copolymers having a random 40 1963 GIULIO NATTA Fig. 6. Comparison between the side and end views of the chain structure of isotactic (a) and syndiotactic (b) polypropylenes (stable modifications) in the crystalline state. 66 distribution of propylene withethylene .These polymers, which are linear, are completely amorphous when the ethylene content decreases below 75 percent. They have a very flexible chain, due to the frequent CH2-CH2 bonds, while the relatively small number of CH-CH3 groups is enough to hinder crystallization of the polymethylenic chain segments. These copoly- mers can be easily vulcanized through the use of peroxides; on the other hand the terpolymers, which contain not only ethylene and propylene but also small amounts (from 2 to 3 percent, by weight) of monomeric units, origi- nated from the random copolymerizations of suitable diolefins67 (or of cyclic compounds, such as cyclooctadiene, which can be prepared easily by dimeri- zation of butadiene, following the method proposed by Wilke), can be vul- canized easily by the conventional methods used for the vulcanization of low- STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 41 unsaturation rubber. They yield elastomers that are very interesting also from the practical point of view, because they can be obtained from low-priced materials and also because of their physical properties and resistance to aging. Polymers of 1-methyl-2-deuteroethylene. The study on the polymerization of differently deuterated propylenes, undertaken by us in order to arrive at more certain and univocal attributions of certain bands to the infrared spectrum of isotactic polypropylene, led us to the discovery of new interesting types of stereoisomerism in polymers of 1-methyl- 2-deutero-ethylene, and general- ly in the case of polymers of 1,2-disubstituted ethylenes68. In fact, propylenes deuterated in the methylenic group can lead to monomer units having different steric structure depending on the relative orientation of the CH3 and D substituents. Starting from these deuterated monomers show- ing phenomena of geometric isomerism, two types of polymers were ob- a b Fig.7. Models of the chains of head-to-tail ditactic polymers supposed arbitrarily stretched on a plane, having, respectively, threo-diisotactic (a), erythro-diisotactic (b), and disyndiotactic (c) succession of the monomeric units. 42 1963 GIULIO NATTA tained. They exhibited the same X-ray spectra but different infrared spectra@. This means that such polymers possess the same helix structure as normal isotactic polypropylene, but that the relative orientation of D and CH 3 groups can lead to a new type of stereoisomerism. In general, starting from a mono- mer of the CHA=CHB type, three types of stereoregular isomers can be expected (see Fig. 7). The type of stereoisomer obtainable by stereoregular polymerization de- pends on the mode of presentation and type of opening of the double bond of each monomer molecule on entering the growing chain (Fig. 8). Fig. 8. Scheme of presentation and opening of the double bond ofmonomeric units when entering the growing chain. Subsequently, diisotactic polymers were obtained with the aid of cationic catalysts, starting from monomers of the CHA = CHB type, wherein A desig- nates an OR group and B, chlorine 70 or an alkyl group71 (Fig. 7). Stereoregular homopolymers of hydrocarbons having an internal double bond. First of all, I wish to report on the results we have obtained in the polymerization of cyclobutene, which is of particular interest as it yields several crystalline poly- mers having different chemical or steric structure, depending on the catalyst used72 (Fig. 9). The different stereoregular polymers we have obtained and a number of their properties are shown in Table 2, from which it may be seen that the polymerization can take place by opening of the double bond to form cyclic monomer units containing two sites of optical type stereoisomerism, so that crystalline polymers are of ditactic type. In view of the fact that under suitable conditions it is possible to obtain two crystalline polymers containing enchained rings that show different physical STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 43 Fig.9. Types of polymerization of cyclobutene: 1, cyclobutylenamer; 2, cis-1,4-poly- butadiene; 3, trans-1,4-polybutadiene. properties, we have ascribed the differences in their properties to the different steric structure and have attributed an erythro-diisotactic structure to one of them and an erythro -disyndiotactic structure to the other73 (Fig. 10). In the presence of other catalysts the ring opens to form unsaturated mono- mer units, which may show isomerism of geometric type. In this case, too, 44 1963 GIULIO NATTA two different products are obtained (depending on the catalyst used), the properties of which correspond to those, respectively, of cis-1,4 - and trans- 1,4-polybutadiene72 (Fig. 9). Fig. 10. Schematic drawing of the structures of erythro-diisotactic (a) and erythro-disyn- diotactic (b)cyclobutylenamer. Ditactic polymers are also obtained from certain monomers containing in- ternal unsaturation, which are unable to homopolymerize but, as mentioned above, can copolymerize with ethylene, yielding crystalline, alternating co- polymers of erythro-diisotactic structure. Among these monomers are cis-2- butene35, cyclopentene36, and cycloheptene37; trans-2-butene and cyclo- hexene behave in a different way and do not give crystalline copolymers. Unlike the ditactic polymers of deuterated propylene, the ditactic polymers obtained by alternate copolymerization can exist in two disyndiotactic forms. It is to be noted that the copolymerization of cis-2-butene is stereospecific only in the presence of heterogeneous catalysts of the type used in polymeriz- ing a-olefins to isotactic polymers, while the copolymerization of cyclo- pentene and cycloheptene is also stereospecific when homogeneous catalysts are used. We have recently74 proposed an interpretation of these facts based essentially on steric criteria. Stereoisomerism phenomena in the field of diolefins, and in particular of con- jugated diolefins, are more complex than phenomena occurring in the case of monoolefinic monomers. In fact, besides the stereoisomerism phenomena ob- STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 45 served in these last (isomerism due to asymmetric carbon atoms), isomerism phenomena of geometric type may also be present, depending on the cis- or trans-configuration of the residual double bonds present in the monomeric units. Butadienepolymers. The simplest conjugated diolefin, 1,3-butadiene, can in fact yield two types of polymers, according to whether the polymerization takes place by opening of the vinyl bond (to form 1,2-enchained polymers) or by opening of both conjugated double bonds (to form 1,4-enchained poly- mers) In the first case, the same stereoisomerism phenomena observed in other vinyl polymers (for example, isotactic, syndiotactic, and atactic polymers) can be expected. In the second case, each monomeric unit still contains a double bond in the 2-3 position, which can assume cis- or trans-configuration. Thus, four types of stereoregular polymers could be foreseen "a priori" and precisely: trans- 1,4-, cis -1,4-,isotactic-1,2-, and syndiotactic-1,2-polybutadienes. All four these stereoisomers were prepared at my Institute with the aid of different stereospecific catalysts75,76 with a high degree of steric purity (up to above 98 percent), as shown by infrared analysis”. X-Ray examination had made it possible for us not only to establish the steric structure of the different polymers but also to determine the confor- mation of the chains in the crystals and, for three of them, also adetailed lattice structurear21,78 . Fig. 11 shows the conformations of the chains of the various stereoisomers, while in Table 3 a number of physical characteristics of the single polymers are reported. As mentioned above, stereoregularity in the field of butadiene polymers is not necessarily connected with the use of heterogeneous catalysts, and, in fact, all four regular stereoisomers can be obtained with the aid of homogeneous catalysts. In the case of cis-1,4-polybutadiene, the highest steric purity is obtained by 76 the use of homogeneous catalysts . Of the four polybutadiene stereoisomers, 46 1963 GIULIO NATTA Fig. 11. Side and end views of the chain conformations of the four stereoisomers of poly- butadiene: (a) trans-1,4; (b) cis-1,4; (c) syndiotactic-1,2; (d) isotactic-1.2. a trans-1,4-Polybutadiene exists in two crystalline modifications: one (mod. I) is stable below 75ºC, the other (mod. II) is stable between about 75ºC and the melting point of the polymer. STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 47 the cis-1,4 stereoisomer is of particular interest also from a practical view- point. Its preparation and properties have been investigated by a large number of workers79. Isoprene polymers. The two polyisoprene geometrical isomers were already known in nature: natural rubber (cis-1,4 polymer) and gutta-percha and balata (trans-1,4 polymers). Both were obtained by synthesis through stereo- specific polymerization. The cis-1,4 polymer was obtained for the first time in the United States by Goodrich’s workers80, while the trans-1,4 polymer was prepared by us81 at the beginning of 1955. The other stereoisomers, having 1,2- or 3,4-enchainment, have not been prepared as yet in such a degree of steric purity as to yield crystalline products. In fact, the only known polymer having 3,4-enchainment, obtained in the presence of the same catalysts yielding syndiotactic 1,2-polybutadiene, is amorphous. 1,3-Pentudiene polymers. Unlike butadiene polymers, the stereoregular poly- mers of 1,3 -pentadiene obtained so far contain at least one asymmetric carbon atom in the monomer unit. Furthermore, for some of them it is possible to expect geometric isomers, due to the presence of internal double bonds which may have cis- or trans-configuration, so that all the polymers will show two centers of steric isomerism. And in fact polymers having 3,4-enchainment, containing two asymmetric carbon atoms, show two sites of optical isomer- ism; all the others exhibit one site of optical isomerism and one of geometric isomerism (1,2 and 1,4 units). On the assumption that only polymers showing stereoregularity in both possible sites (ditactic polymers) will be crystalline, 11 crystalline pentadiene polymers can be expected: (1) Polymers having 3,4-enchainment (Fig. 12a): (i) erythro-diisotactic polymer, (ii) threo-diisotactic polymer, (iii) Syndiotactic polymer. (2) Polymers having 1,2-enchainment (Fig. 12b): (iv,v) Isotactic poly- mers containing, respectively, one cis- or trans-double bond in the side-chain, (vi,vii) Syndiotactic polymers containing, respectively, one cis- or trans- double bond in the side-chain. (3) Polymers having 1,4-enchainment (Fig. 12c): (viii,ix) cis-1,4-isotactic and syndiotactic polymers, respectively, (x,xi) trans-1,4-isotactic and syn- diotactic polymers, respectively. Of these stereoisomers the only three so far known were prepared in my 83 Institute: trans-1,4-isotactic 82, cis-1,4-isotactic , and cis-1,4-syndiotactic 48 1963 GIULIO NATTA Fig. 13. Side and end views of the macromolecule of isotactic trans-poly(I-methylbuta- 1,3-diene) (that is, trans-1,4-polypentadiene) in the crystalline state. STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 49 Table 4 polymer84. In Table 4a number of physical properties characteristic of these isomers are reported; Figs. 13 and 14 show the conformation of the chains in the crystals. As could be expected, the best elastic properties in vulcanized polymers are observed for cis-1,4-polymers, owing to their melting point, which is slightly below the melting point of natural rubber. -- -- Fig. 14. Side and end views of the macromolecule of isotactic cis-1,4-polypentadiene (a) and syndiotactic cis-1,4-polypentadiene (b). 50 1963 GIULIO NATTA Unlike the polymerization of unsatured hydrocarbons, and particularly - olefins, the polymerization of monomers containing functional groups, in the presence of catalysts based on organometallic compounds, has not been investigated until recently. This is due to the fact that the functional groups contained in such monomers can react with organometallic catalysts through reactions that are well known in the field of classical organic chemistry, such as Grignard reactions, Michael’s reaction, or splitting of an ether bond. Initially it was feared that these reactions might involve both deactivation of the catalytic agent and total or partial alteration of the said monomers. In 1956 we demonstrated for the first time in the case of acrylonitrile85 and its homologs that, by suitably selecting the transition metal compounds and organometallic compounds forming the catalytic complex, it is possible to bring about stereospecific, anionic coordinated polymerization of these monomers while impeding or delaying the above-mentioned side reactions between monomer and catalyst. Therefore, it has been demonstrated that stereospecific polymerization of nonhydrocarbon monomers can also be carried out with the use of pure organometallic compounds other than those of the Ziegler type, or even with the aid of catalytic compounds that do not contain metal-to-carbon bonds. The research work on these monomers has taken two separate but parallel paths; that is, on the one hand it was directed to stereospecific cationic co- ordinated polymerization and, on the other, to stereospecific anionic poly- merization (see Tables 5 and 6). The cationic coordinated polymerizations carried out by us in the presence of catalysts of the type of Lewis acids (based on organometallic compounds or Friedel-Craft catalysts) were chiefly directed to the following classes of mo- nomers: vinyl alkyl ethers86,87 , alkenyl alkyl ethers70, alkoxy-styrenes88, vi- nylcarbazole 89, and - chlorovinyl ethers71. The polymerization of isobutyl vinyl ethers to crystalline polymers had al- ready been carried out by Schildknecht49 in 1949. As a result of our further research work it was possible to attribute their crystallinity to an isotactic structure 86. Stereospecific anionic coordinated polymerization, which is in general car- ried out in the presence of basic-type catalysts (organometallic or metal amid- ic compounds, alcoholates) was chiefly investigated in connection with the following classes of monomers: higher homologs of acrylonitrile90, vinyl- STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 51 Table 5 Unlike the a-olefin polymerization, which requires the presence of a cata- lyst containing a crystalline substrate in order that it may proceed in a stereo- specific isotactic manner, the polymerization of nonhydrocarbon monomers containing functional groups or atoms haying free electron pairs (such as, for example, ethereal, carbonylic, or carboxylic oxygen; aminic, amidic, or ni- trilic nitrogen) can proceed in a stereospecific way also in the absence of a solid substrate - that is, in a homogeneous phase. Here the stereospecificity - which in this case is also connected with a constant orientation and constant mode of presentation, on polymerizing, of the monomer units with respect to the growing chain and to the catalytic agent - is due to the coordination of an 52 1963 GIULIO NATTA electron pair in the monomer with the metal of the catalytic agent by means of a dative bond47,95. As the olefinic double bond too is necessarily bound to the active center, such monomers appear to be doubly linked to the complex formed by the catalytic agent and the terminal group of the growing chain. A predetermined steric orientation is thus made possible. Likewise, both the diolefins containing two olefin groups bound to the catalyst complex and certain aromatic a-olefins, wherein the second an- choring point is provided by the aromatic group -linked to a catalyst con- taining a highly electropositive atom with a very small radius (lithium) 96, can be polymerized stereospecifically even in the homogeneous phase. The coordination of the monomer with the catalytic agent, which is the indispensable step preceding any stereospecific polymerization both in the homogeneous and in the heterogeneous phase, has been particularly well esemplified by the stereospecific polymerization of 2-vinylpyridine in the presence of organometallic compounds of magnesium97. In fact, the presence of Lewis bases in the polymerization of this monomer exerts a determining influence on its behavior in the polymerizations. Com- pounds having a higher degree of basicity than vinylpyridine itself (for ex- ample, pyridine) form stable coordination compounds with the catalyst, thus impeding the coordination of the monomer; in this way, not only does the catalytic activity appear very much reduced, but also the stereospecificity disappears and the polymer obtained is atactic. Compounds having a lower degree of basicity than the monomer (aliphatic ethers) compete with the mo- nomer only in so far as the association with the catalyst is concerned. Accord- ingly this does not result in the disappearance of the catalyst reactivity, but only in its reduction along with the degree of stereospecificity of the reaction. The asymmetric synthesis of optically active high polymers, starting from monomers showing no centers of optical-type asymmetry, constituted a par- ticular, more advanced case of isotactic stereospecific polymerization. In fact, whereas in the normal stereospecific polymerization to isotactic poly- mers a succession of monomer units with a given configuration takes place in each single macromolecule so that enantiomorphous macromolecules in equal amounts are present in crude polymers, in the case ofasymmetric synthesis one STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 53 of the two enantiomorphous isomers of the monomer unit is contained in higher amounts. It should be noted that isotactic high polymers or of other sim- ple vinyl monomers cannot show detectable optical activity, since an ideal isotactic polymer of infinite length does not contain asymmetric carbon atoms, and in isotactic polymers having finite length98 the optical activity, due to a difference in the terminal groups, can be detected only in oligomers and de- creases with increase in the molecular weight. This is due to the fact that the asymmetry of each asymmetric carbon atom is to be ascribed not to the chemi- cal difference of contiguous groups linked to the said carbon atom but to a difference in length of the chain segments linked to it99. In fact, in the case of optically active polymers were ob- tained by polymerization only from monomers having an asymmetric carbon atom100 . On the basis of our investigations it has been possible to obtain optically active polymers from monomers containing no centers of optical asymmetry only when, during the polymerization, monomer units are incorporated so as to develop new asymmetric centers. The asymmetry of the new centers arises from a difference in the chemical constitution of the groups contiguous to the carbon atoms themselves101-104 . Such a result was obtained by means of stereospecific polymerization pro- cesses, operating under conditions that allow asymmetric induction to favor the formation of one of the two enantiomorphous structures of the monomer unit. The methods that have led us to the asymmetric synthesis of polymers of substituted diolefins and of certain heterocyclic, unsaturated compounds are of two types. (1) The first is the use of normal stereospecific catalysts wherein at least one group bound to the organometallic compound used in the catalyst prepara- tion, which will be the terminal group of the macromolecules, is optically ac- tive101. In this case the asymmetric induction is probably due to the particular configuration of the terminal group of the growing chain bound to the catalyst. (2) A second method is based on the use of conventional stereospecific cata- lysts prepared without using optically active alkyls, provided they are com- plexed with optically active Lewis bases, such as b-phenylalanine 102, or with the use of an optically active transition metal compound104 (Table 7). In the first case, as the polymerization proceeds, the optical activity de- 54 1963 GIULIO NATTA creases, as could be expected in view of the fact that any accidental inversion of configuration exerts an action not confined to one monomer unit only, but tending to extend to subsequent units. In the second case, on the other hand, the induction is due to the asymmetry 105 of the optically active counterion ,which maintains its steric structure also in the case where the asymmetric polymerization gives low optical yields. These results can be extended to the interpretation of stereospecific catalysis of vinyl monomers. They suggest that a higher stereospecificity can be expec- ted when using catalysts, the active centers of which are per se asymmetric, than when symmetric catalysts are used, in which the stereospecificity derives from asymmetric induction brought about by the configuration assumed by the last polymerized unit. Even before the discovery of the asymmetric synthesis of high polymers, we attributed 106 the stereospecificity of certain heterogeneous catalysts, prepared by reaction of solid titanium halides, to the fact that the active centers contain surface atoms of a transition metal having coordination number 6. In fact it is known that, in such a case, when at least two of the coordinated groups show a different chemical nature with respect to the others, enantiomorphous struc- tures of the surface complexes can exist. The high stereospecificity of such catalysts is probably due to the fact that the initial complex maintains its asymmetry even when linked to the growing chain. An interesting aspect of the asymmetric polymerization of benzofuran STEREOSPECIFIC POLYMERIZATION OF MAROCMOLECULES 55 consists in an autocatalytic effect observed in the first reaction period. In fact it was noticed that the optical activity of the polymers increases as the poly- merization proceeds107 (Table 8). To clarify this phenomenon further, polymerization runs have been per- formed in the presence of optically active polybenzofuran previously ob- tained. Although the sign of the optical activity always corresponds to that of the - phenylalanine complexed with the counter ion, nevertheless the presence of preformed polymer, obtained in the same polymerization or added to the catalytic system at the beginning of the polymerization, causes an increase in the optical activity of the polymer newly formed. 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Rubber Technol.Conf, 4th, London, 1962; G. Crespi and E.di Giuho, Rev. Gen. Caoutchouc, 40 (1963) 99 ; G.Natta, G. Crespi, G.Mazzanti, A. Valvassori and G. Sartori, Chim. Ind. (Milan), 45(1963)651. 68. G.Natta, M.Farina and M.Peraldo, Atti Accad.Nazl.Lincei, Rend., [8]25(1958) 424. 69. M.Peraldo and M.Farina, Chim. Ind. (Milan), 42(1960)1349. STEREOSPECIFIC POLYMERIZATION OF MACROMOLECULES 59 70. G.Natta, M.Peraldo, M.Farina and G.Bressan, Makromol.Chem., 55(1962)139. 71. G.Natta, M.Farina, M.Peraldo, P. Corradini, G.Bressan and P. Ganis, Atti Accad. Nazl.Lincei, Rend., [8]28(1960)442. 72. G.Dall’Asta, G.Mazzanti, G.Natta and L.Porri, Makromol.Chem., 56(1962)224. 73. G. Natta, G.Dall’Asta, G. Mazzanti and G. Motroni, Makromol.Chem., 69(1963) 163. 74. G.Dall'Asta and G.Mazzanti, Makromol.Chem., 61(1963)178. 75. G. Natta, L.Porri, P. Corradini and D.Morero, Chim.Ind. (Milan), 40 (1958) 362; G.Natta,L.PorriandA.Mazzei, ibid.,41 (1959) 116; G.Natta,L.Porri and A.Car- bonaro, Atti Accad. Nazl.Lincei, Rend., [8]31(1961)I89; G. Natta, L. Porri and L.Fiore, Gazz.Chim. Ital., 89(1959) 761; G.Natta, L.Porri, G.Zanini and L.Fiore, Chim. Ind. (Milan), 41 (1959) 526; G.Natta, L.Porri, G.Zanini and A.Palvarini, ibid.,41(1959)1163. 76. G.Natta, L.Porri, A.Mazzei and D.Morero, Chim. Ind. (Milan), 41 (1959) 398; G.Natta, Rubber Plastics Age, 38(1957)495; G.Natta, Chim.Ind. (Milan), 39 (1957)653; G.Natta, Rev. Gen.Caoutchouc, 40(1963)785. 77. D.Morero, A. Santambrogio, L.Porri and F. Ciampelli, Chim. Indf (Milan), 41 (1959)758. 78. G.Natta, P.Corradini and L.Porri, Atti Accad.Nazl.Lincei, Rend., [8] 20 (1956) 728; G.Natta and P.Corradini, Angew.Chem., 68 (1956) 615; G.Natta, P.Corra- dini and I. W. Bassi, Atti Accad. Nazl. Lincei, Rend., [8]23(1957)363; G. Natta and P.Corradini, Nuovo Cimento, Suppl., [10]15(1960)122. 79. See, for example, Belgian Pat. 551, 851 (1956), Phillips Company U.S.; Belgian Pat.573.680 (1958) and 575, 507 (1959), Montecatini, Milan, Italy; see G.Natta, G. Crespi, G. Guzzetta, S. Leghissa and F. Sabbioni, Rubber Plastics Age, 42(1961) 402; G.Crespi and U.Flisi, Makromol.Chem., 60(1963)191. 80. S.E.Home et al., Ind.Eng.Chem., 48(1956)784. 81. G.Natta, L.Porri and G.Mazzanti, Belgian Pat., 545,952(Italian priority, March 1955). 82. G. Natta, L. Porri, P. Corradini, G. Zanini and F. Ciampelli, Atti Accad. Nazl.Lincei, Rend., [8]29(1960)257; J.Polymer Sci., 51(1961) 463. 83.G.Natta, L.Porri, G. Stoppa, G.Allegra and F. Ciampelli, J.Polymer Sci., IB (1963) 67 84.G. Natta, L. Porri, A. Carbonaro, F. Ciampelli and G. Allegra, Makromol.Chem., 51 (1962)229. 85. G.Natta and G.Dall'Asta, Italian Pat., 570,434(1956). 86. G.Natta, I. W.Bassi and P.Corradini, Makromol.Chem., 18-19(1955)455. 87. G. Natta, G. Dall’Asta, G. Mazzanti, U. Giannini and S. Cesca, Angew.Chem., 71 (1959) 205. 88. G.Natta, G.Dall’Asta, G.Marzanti and A. CasaIe, Makromol.Chem., 58(1962)217. 89. G. Natta, G. Mazzanti, G.Dall’Asta and A. Cassale, Italian Pat., 652,763(1960). 90. G.Natta, G.Mazzanti and G.Dall’Asta, Italian Pat., 643, 282 (1960) ; G. Natta, G.Dall‘Asta and G.Mazzanti, Italian Put. 648,564(1961). 91. G.Natta, G. Mazzanti, G.Dall’Asta and P.Longi, Makromol.Chem., 37(1960)160. 60 1963 GIULIO NATTA 92. G. Natta, M. Farina, P. Corradini, M.Peraldo, M.Donati and P. Ganis, Chim.Ind. (Milan), 42(1960) 1360. 93. G.Natta, G.Mazzanti, P.Longi and F.Bernardini, Chim.Ind. (Milan), 42(1960) 457. 94. G.Natta, G.Mazzanti and P.Corradini, Atti Accad. Nazl.Lincei, Rend., [8] 28 (1960) 8; G.Natta, P.Corradini and I.W.Bassi, ibid., [8] 28(1960)284; G.Natta, G.Mazzanti, P.Corradini and I.W.Bassi, Makromol.Chem., 37(1960)156; G.Nat- ta, P.Corradiniand I.W.Bassi, J.Polymer Sci., 51(1961)505. 95. I.W.Bassi, G.Dall’Asta, U.Campigli and E.Strepparola, Makromol.Chem., 60 (1963)202. 96. D.Braun, W.Betz and W.Kern, Makromol.Chem., 28(1958) 66. 97. G.Natta, G.Mazzanti, P.Longi, G.Dall’Asta and F.Bernardini, J.Polynrer Sci., 51 (1961)487. 98.Actually an isotactic chain of finite length does include asymmetric carbon atoms, but each one is neutralized by another at an equal distance from the center of the main chain: Hence the fully isotactic polypropylene is a particular case of a meso-configuration and must be optically inactive. 99. G.Natta, P.Pino and G.Mazzanti, Gazz.Chim. Ital., 87(1957) 528. 100. P.Pino, G.P.Lorenzi and L.Lardicci, Chim.Ind. (Milan), 43(1960) 711; P.Pino and G.P.Lorenzi, Soc., 82 (1960) 4745 ; W. J.Baileg and E.T.Yates, J.Org.Chem., 25(1960)1800. 101. G.Natta,M.Farina,M.Pera.ldo andM.Donati, Chim.Ind.(Milan), 42(1960)1363; G.Natta, M.Farina and M.Donati, Makromol.Chem., 43(1961)251. 102. G.Natta, M.Farina, M.Peraldo and G.Bressan, Chim. Ind. (Milan), 43(1961)161; Makromol. Chem., 43(1961)68. 103. G.Natta, L.Poni, A.Carbonaro and G.Lugli, Chim.Ind. (Milan), 43(1961)529. 104.G.Natta, L.Porri and S.Valante, Makromol.Chem., 67(1963)225. 105. M.Farina and G.Bressan, Makromol.Chem., 61(1963)79. 106. G.Natta, Ric. Sci., Suppl., 28 (1958) 1. 107. G.Natta, G.Bresan and M.Farina, Atti Accad. Nazl.Lincei, Rend., [8]34(1963)475; M.Farina, G.Natta and G.Bressan, Symp. Macromolecelar Chemistry I.U.P.A.C., Paris, 1963; J.Polymer Sci., C4,(1964) 141. SPATIAL CONFIGURATION OF MACROMOLE- CULAR CHAINS Nobel Lecture, December 11, 1974 by PAUL J. FLORY Department of Chemistry Stanford University, Stanford, California The science of macromolecules has developed from primitive beginnings to a flourishing field of investigative activities within the comparatively brief span of some forty years. A wealth of knowledge has been acquired and new points of view have illumined various branches of the subject. These advances are the fruits of efforts of many dedicated investigators working in laboratories spread around the world. In a very real sense, I am before you on this occasion as their representative. In these circumstances, the presentation of a lecture of a scope commensurate with the supreme honor the Royal Swedish Academy of Sciences has bestowed in granting me the Nobel Prize for Chemistry is an insuperable task. Rather than attempt to cover the field comprehensively in keeping with the generous citation by the Royal Academy of Sciences, I have chosen to dwell on a single theme. This theme is central to the growth of ideas and concepts concerning macromolecules and their properties.Implemented by methods that have emerged in recent years, researches along lines I shall attempt to highlight in this lecture give promise of far-reaching advances in our understanding of macromolecular substances - materials that are invaluable to mankind. These polymeric substances are distinguished at the molecular level from other materials by the concatenation of atoms or groups to form chains, often of great length. That chemical structures of this design should occur is implicit in the multivalency manifested by certain atoms, notably carbon, silicon, oxygen, nitrogen, sulfur and phosphorus, and in the capacity of these atoms to enter into sequential combinations. The concept of a chain molecule consisting of atoms covalently linked is as old as modern chemistry. It dates from the origins of the graphic formula introduced by Couper in 1858 and advanced by Kekult, Loschmidt and others shortly thereafter. Nothing in chemical theory, either then apparent or later revealed, sets a limit on the number of atoms that may be thus joined together. The rules of chemical valency, even in their most primitive form, anticipate the occurrence of macromolecular structures. The importance of macromolecular substances, or polymers, is matched by their ubiquity. Examples too numerous to mention abound in biological systems. They comprise the structural materials of both plants and animals. Macromolecules elaborated through processes of evolution perform intricate regulatory and reproductive functions in living cells. Synthetic polymers in P.J. Flory 157 great variety are familiar in articles of commerce. The prevailing structural motif is the linear chain of serially connected atoms, groups or structural units. Departures from strict linearity may sometimes occur through the agency of occasional branched units that impart a ramified pattern to the over-all structure.Linearity is predominant in most macromolecular substances, however. It is noteworthy that the chemical bonds in macromolecules differ in no discernible respect from those in “monomeric” compounds of low molecular weight. The same rules of valency apply; the lengths of the bonds, e.g., C-C, C-H, C-O, etc., are the same as the corresponding bonds in monomeric molecules within limits of experimental measurement. This seemingly trivial observation has two important implications: first, the chemistry of macro- molecules is coextensive with that of low molecular substances; second, the chemical basis for the special properties of polymers that equip them for so many applications and functions, both in nature and in the artifacts of man, is not therefore to be sought in peculiarities of chemical bonding but rather in their macromolecular constitution, specifically, in the attributes of long molecular chains. Comprehension of the spatial relationships between the atoms of a molecule is a universal prerequisite for bridging the connection between the graphic formula and the properties of the substance so constituted. Structural chemistry has provided a wealth of information on bond lengths and bond angles. By means of this information the graphic formula, primarily a topological device, has been superseded by the structural formula and by the space model that affords a quantitative representation of the molecule in three dimensions. The stage was thus set for the consideration of rotations about chemical bonds, i.e., for conformational analysis of conventional organic compounds, especially cyclic ones. A proper account of bond rotations obviously is essential for a definitive analysis of the spatial geometry of a molecule whose structure permits such rotations. The configuration of a linear macromolecule in space involves circum- stances of much greater complexity. A portion of such a molecule is shown schematically in Figure 1. Consecutive bonds comprising the chain skeleton are joined at angles q fixed within narrow limits. Rotations may occur about these skeletal bonds. Each such rotation is subject, however, to a potential determined by the character of the bond itself and by hindrances imposed by steric interactions between pendant atoms and groups. The number and variety of configurations (or conformations in the language of organic chemistry) that may be generated by execution of rotations about each of the skeletal bonds of a long chain, comprising thousands of bonds in a typical polymer, is prodigiousbeyond comprehension. When the macromolecule is free of constraints, e.g., when in dilutesolution, all of these configurations are accessible. Analysis of the manner in which such a molecule may arrange itself in space finds close analogies elsewhere in science, e.g., in the familiar problem of random walk, in diffusion, in the mathematical treatment of systems in one dimension, and in the behavior of real gases. ïëè Chemistry 1974 Ú·¹ò ïò λ°®»•»²¬¿¬·±² ±º ¬¸» •µ»´»¬¿´ ¾±²¼• ±º ¿ •»½¬·±² ±º ¿ ½¸¿·² ³±´»½«´» •¸±©·²¹ •«°°´»³»²¬• ¯ ±º ¾±²¼ ¿²¹´»•ô ¿²¼ ¬±®•·±²¿´ ®±¬¿¬·±²• º±® ¾±²¼• ·ô · õ ïô »¬½ò Inquiry into the spatial configuration of these long-chain molecules, fascinat- ing in itself, derives compelling motivation from its close relevancy to the properties imparted by such molecules to the materials comprising them. Indeed, most of the properties that distinguish polymers from other substances are intimately related to the spatial configurations of their molecules, these configurations being available in profusion as noted. The phenomenon of rubber-like elasticity, the hydrodynamic and thermodynamic properties of polymer solutions, and various optical properties are but a few that reflect the spatial character of the random macromolecule. The subject is the nexus between chemical constitution and physical and chemical properties of poly- meric substances, both biological and synthetic. The importance of gaining a grasp of the spatial character of polymeric chains became evident immediately upon the establishment, ca. 1930, of the hypothesis that they are covalently linked molecules rather than aggregates of smaller molecules, an achievement due in large measure to the compelling evidence adduced and forcefully presented by H. Staudinger, Nobelist for 1953. In 1932 K. H. Meyer1 adumbrated the theory of rubber-like elasticity by calling attention to the capacity of randomly coiled polymer chains to accommodate large deformations owing to the variety of configurations acces- sible to them. W. Kuhn2 and E. Guth and H. Mark3 made the first attempts at mathe- matical description of the spatial configurations of random chains. The com- plexities of bond geometry and of bond rotations, poorly understood at the time, were circumvented by taking refuge in the analogy to unrestricted random flights, the theory of which had been fully developed by Lord Rayleigh. The skeletal bonds of the molecular chain were thus likened to the steps in a random walk in three dimensions, the steps being uncorrelated one to another. Restrictions imposed by bond angles and hindrances to rotation were dismissed on the grounds that they should not affect the form of the results. For a random flight chain consisting of n bonds each of length l, the mean- square of the distance r between the ends of the chain is given by the familiar relation The angle brackets denote the average taken over all configurations. Kuhn4 P. J Flory 159 argued that the consequences of fixed bond angles and hindrances to rotation could be accommodated by letting several bonds of the chain molecule be represented by one longer “equivalent” bond, or step, of the random flight. This would require n to be diminished and l to be increased in Eq. 1. Equiv- alently, one may preserve the identification of n and l with the actual molec- ular quantities and replace Eq. (1) with (2) where C is a constant for polymers of a given homologous series, i.e., for polymers differing in length but composed of identical monomeric units. The proportionality between Ú·¹ò îò ̸» »ºº»½¬ ±º »¨½´«¼»¼ ª±´«³»ò̸» ½±²º·¹«®¿¬·±² ±² ¬¸» ´»º¬ ®»°®»•»²¬• ¬¸» ®¿²¼±³ ½±·´ ·² ¿¾•»²½» ±º ª±´«³» »¨½´«•·±²ô ¬¸» ½¸¿·² ¾»·²¹ »¯«·ª¿´»²¬ ¬± ¿ ´·²» ·² •°¿½»ò ײ ¬¸» •µ»¬½¸ ±² ¬¸» ®·¹¸¬ô ¬¸» «²·¬• ±º ¬¸» ½¸¿·² ±½½«°§ º·²·¬» ¼±³¿·²• º®±³ ©¸·½¸ ±¬¸»® «²·¬• ¿®» »¨½´«¼»¼ô ©·¬¸ ¬¸» ®»•«´¬ ¬¸¿¬ ¬¸» ¿ª»®¿¹» •·¦» ±º ¬¸» ½±²º·¹«®¿ó ¬·±² ·• ·²½®»¿•»¼ò the analogy between the trajectory of a particle executing a random flight and the molecular chain, a material body. The particle may cross its own path at will, but self intersections of the polymer chain are forbidden. The effect of excluded volume must be dealt with regardless of the model chosen for representation of the chain. In practice, elimination of the effect of volume exclusion is a prerequisite to the analysis of experimental results, as I will explain in more detail later. The closely related problems of random flights with disallowance of self intersections and of volume exclusion within long-chain molecules have attracted the attention of many theorists. A variety of mathematical techniques have been applied to the treatment of these problems, and a profusion of theories have been put forward, some with a high order of sophistication. Extensive numerical computations of random walks on lattices of various sorts also have been carried out. Convergence of results obtained by the many investigators captivated by the subject over the past quarter century seems at last to be discernible. I shall confine myself to a brief sketch of an early, comparatively simple approach to the solution of this problem.5 The results it yields contrast with its simplicity. Returning to the analogy of the trajectory traced by a particle undergoing a sequence of finite displacements, we consider only those trajectories that are free of intersections as being acceptable for the chain molecule. Directions of successive steps may or may not be correlated, i.e., restrictions on bond angles and rotational hindrances may or may not be operative; this is im- material with respect to the matter immediately at hand. Obviously, the set of eligible configurations will occupy a larger domain, on the average, than those having one or more self intersections. Hence, volume exclusion must cause where A is a numerical factor expected to be of the order of magnitude of unity. It is necessary to digress at this point for the purpose of drawing a distinction between (4) Equation (2), having been derived without regard for excluded volume interactions, should be replaced by (2') where C reaches a constant value with increase in n for any series of finitely flexible chains. The smoothed density within the domain of a linear macromolecule having a molecular weight of 100,000 or greater (i.e., n > 1000) is low, only on the order of one percent or less of the space being occupied by chain segments. For a random dispersion of the segments over the volume V, encounters in which segments overlap are rare in the sense that few of them are thus in- volved. However, the expectation that such a dispersion is entirely free of overlaps between any pair of segments is very small for a long chain. The attrition of configurations due to excluded volume is therefore severe. In light of the low segment density, it suffices to consider only binary encounters. Hence, if b is the volume excluded by a segment, the probability that an arbitrary distribution of their centers within the volume V is free of conflicts between any pair of segments is P. J. Flory 163 sums are executed over all configurations of the chain. The squared radius of gyration s2, i.e.,the mean-square of the distances of the segments from their center of gravity, is preferable to r2as a parameter with which to characterize the spatial distribution.’ Treatments carried out with these refinements affirm the essential validity of the result expressed by Eq. (12) or (12’). They show conclusively 7,8 that the form of the result should hold in the limit of large values of i.e.,for large excluded volume and/or high chain length, and hence for > > 1. In this limit, /z = 1.67 according to H. Fujita and T. Norisuye.8 For a <~ 1.4, however, this ratio decreases, reaching a value of 1.276 at = 1 .8,9 The general utility of the foregoing result derived from the most elementary considerations is thus substantiated by elaboration and refinement of the analysis, the quantitative inaccuracy of Eqs. (12) and (12’) in the range 1.0 < a 1.4 notwithstanding. The relationship between a and the parameter z prescribed by these equations, especially as refined by Fujita and Norisuye,8 appears to be well supported by experiment.10,11 The principal conclusions to be drawn from the foregoing results are the following: the expansion of the configuration due to volume exclusion increases with chain length without limit for b > 0; for very large values of relative to it should increase as the l/10 power of the chain length. The sustained increase of the perturbation with chain length reflects the fact that interactions between segments that are remote in sequence along the chain are dominant in affecting the dimensions of the chain. It is on this account that the excluded volume effect is often referred to as a long-range inter- action.9-12 The problem has been treated by a variety of other procedures.9-12 Notable amongst these treatments is the self-consistent field theory of S. F. Edwards.12 The asymptotic dependence of a on the one-tenth power of the chain length, and hence the dependence of the concentration c being expressed in weight per unit volume. The increment in viscosity due to a polymer molecule. is proportional to its hydrodynamic volume, which in turn should be proportional to chain. Hence, should be proportional to the product of molecular weight, provided of course that the molecular weight, and hence the chain length, is sufficiently large. If the excluded volume effect could be ignored, the intrinsic viscosity should vary proportionally toM1/2.Since, however, a increases with M, a stronger dependence on M generally is observed. Often the dependence of on molecular weight can be represented in satisfactory approximation by the empirical relation Measurement of light scattering as a function of angle, a method introduced by the late P. Debye, affords a convenient means for determining the mean- square radius of gyration. Small-angle scattering of x-rays (and lately of neutrons) offers an alternative for securing the same information. From the radius of gyration one may obtain the parameter Ú·¹ò íò ײ¬®·²•·½ ª·•½±•·¬·»• ±º °±´§•¬§®»²» º®¿½¬·±²• °´±¬¬»¼ ¿¹¿·²•¬ ¬¸»·® ³±´»½«´¿® ©»·¹¸¬• ±² ´±¹¿®·¬¸³·½ •½¿´»• ·² ¿½½±®¼¿²½» ©·¬¸ Û¯ò øïì÷ò ̸» «°°»® •»¬ ±º ¼¿¬¿ ©¿• ¼»¬»®³·²»¼ ·² ¾»²¦»²»ô ¿ ¹±±¼ •±´ª»²¬ º±® ¬¸·• °±´§³»®ò ̸» ´±©»® •»¬ ±º ¼¿¬¿ ©¿• ¼»¬»®³·²»¼ ·² ½§½´±¸»¨¿²» ¿¬ ¬¸» ̸»¬¿ °±·²¬ò ̸» •´±°»• ±º ¬¸» ´·²»• ¿®» a ã ðòéë ¿²¼ ðòëðô ®»•°»½¬·ª»´§ò Ú®±³ ¬¸» ®»•«´¬• ±º ß´¬¿®»•ô ɧ³¿² ¿²¼ ß´´»²òïì attention to the role of short range features: structural geometry, bond rotation potentials, and steric interactions between near-neighboring groups. It is here that the influences of chemical architecture are laid bare. If the marked differences in properties that distinguish the great variety of polymeric substances, both natural and synthetic,are to be rationally understood in fundamental, molecular terms, this must be the focus of future research. Rigorous theoretical methods have recently become available for dealing realistically with short-range features peculiar to a given structure. Most of the remainder of this lecture is devoted to a brief overview of these methods. Although the field is comparatively new and its exploration has only begun, space will not permit a digest of the results already obtained. The broad objective of the methods to which we now turn attention is to treat the structure and conformations accessible to the chain molecule in such a manner as will enable one to calculate configuration-dependent quantities and to average them over all conformations, or spatial configurations, of the unperturbed chain. The properties under consideration are constitutive; they P. J. Flory 167 × × × × × I I ïòð ðòè ð Ú·¹ò ìò ײ¬®·²•·½ ª·•½±•·¬·»• ±º º®¿½¬·±²• ±º °±´§ø³»¬¸§´ ³»¬¸¿½®§´¿¬»÷ ¿½½±®¼·²¹ ¬± ݸ·²¿· ¿²¼ Í¿³«»´•ïë °´±¬¬»¼ ¿• ·² Ú·¹ò íò ̸» «°°»® •»¬ ±º °±·²¬• ©¿• ³»¿•«®»¼ ·² ³»¬¸§´ »¬¸§´ µ»¬±²»ô ¿ ¹±±¼ •±´ª»²¬ò ̸» ´±©»® •»¬ ©¿• ¼»¬»®³·²»¼ ·² ¿ ³·¨¬«®» ±º ³»¬¸§´ ethyl ketone and isopropanol ¿¬ ¬¸» ̸»¬¿ °±·²¬ò Í´±°»• ¿®» ¿ ã ðòéç ¿²¼ ðòëðô ®»•°»½ó ¬·ª»´§ò represent sums of contributions from the individual units, or chemical 2 2 groupings, comprising the chain. In addition to Ú·¹ò ëò Ì©± ±º ¬¸» •¬¿¹¹»®»¼ ½±²º±®³¿¬·±²• º±® ²ó¾«¬¿²»æ ¬®¿²• ±² ¬¸» ´»º¬ ¿²¼ ¹¿«½¸»ó ³·²«• ±² ¬¸» ®·¹¸¬ò the eclipsed forms. The t and g- conformations of n-butane are shown in Fig. 5. The energies of the eclipsed conformations separating t from g+ and t from g- are about 3.5 kcal. mol-1 above the energy of the trans conformation. Hence, in good approximation, it is justified to consider each bond to occur in one of three ®±¬¿¬·±²¿´ ·•±³»®·½ •¬¿¬»• centered near (but not necessarily precisely at) the energy minima associated with the three staggered conformations.20-24 The gauche minima lie at an energy of about 500 cal. mol-1 above trans. Each of the former is therefore disfavored compared to the latter by a “sta- tistical weight” factor we choose to call s » exp( -Eg/RT), where Egis about 500 cal. mol-1; thus, (s » 0.5 at T = 400 K. A complication arises from the fact that the potentials affecting bond rotations usually are neighbor dependent; i.e.,the potential affecting depends on the rotations and Bond rotations cannot, therefore, be treated indepen- dently.20,21,24,25 The source of this interdependence in the case of an n-alkane chain is illustrated in Fig. 6 showing a pair of consecutive bonds in three of their nine conformations. In the conformations tt, tg+, g+t, tg- and g-t, the two methylene groups pendant to this pair of bonds are well separated. For gauche rotations g+g+ and g-g- of the same hand (Fig. 6b), these groups are proximate but not appreciably overlapped. Semi-empirical calculations21,24,26, 27 show the intramolecular energy for these two equivalent conformations to be very nearly equal to the sum (cu. 1000 cal. mol-1) for two well-separated gauche bonds; i.e., the interdependence of the pair of rotations is negligible. In the remaining conformations, g+g-and g-g+,the steric overlap is severe (Fig. 6c). It may be alleviated somewhat by compromising rotations, but the excess energy associated therewith is nevertheless about 2.0 kcal. mol-1. Hence, a statistical weight factor w » exp (-2000/RT) is required for each such pair. 24,26,28 Inspection of models in detail shows that interactions dependent upon rotations about three, four of five consecutive bonds are disallowed by interferences of shorter range and hence may be ignored.24 It suffices there- fore to consider first neighbors only. The occurrence of interactions that depend on pairs of skeletal bonds is the rule in chain molecules. In some of them, notably in vinyl polymers, such interactions may affect most of the conformations. Hence, interdependence of rotations usually plays a major role in determining the spatial configuration P. J Flory 169 HH H H H H of the chain. The rotational isometric state approximation, whereby the continuous variation of each j is replaced by discrete states, provides the key to mathematical solution of the problem posed by rotational interde- pendence.20,21,24,25 It is necessary therefore to consider the bonds pairwise consecutively, and to formulate a set of statistical weights for bond i that take account of the state of bond i-l. These statistical weights are conveniently presented in the form of an array, or matrix, as follows: where the rows are indexed in the order t, g+, g-to the state of bond i- 1, and the columns are indexed to the state of bond i in the same order. According to the analysis of the alkane chain conformations presented briefly 24,26,28 above, Uitakes the form 170 Chemistry 1974 A conformation of the chain is specified in the rotational isometric state approximation by stipulation of the states for all internal bonds 2 to n-l inclusive; e.g., by g+ttg-g-, etc. Owing to the three-fold symmetry of the terminal methyl groups of the alkane chain, rotations about the terminal bonds are inconsequential and hence are ignored. The statistical weight for the specified conformation of the chain is obtained by selecting the appropriate factor for each bond from the array (15) according to the state of this bond and of its predecessor, and taking the product of such factors for all bonds 2 to n - 1. In the example above this product is , etc. It will be obvious that the first superscripted index in one of the factors u must repeat the second index of its predecessor since these indices refer to the same bond. The configuration partition function,representing the sum of all such factors, one for each conformation of the chain as represented by the scheme of rotational isomeric states, is where the subscripts are serial indexes. Each uimust be assigned as specified above. The sum, which extends over all ordered combinations of rotational states, may be generated identically as the product of the arrays Uitreated as matrices. That is, according to the rules of matrix multiplication whereU1= row (1, 0, 0) and Un= column (1, 1, 1). Matrix multiplication generates products precisely of the character to which attention is directed at the close of the preceding paragraph. Serial multiplication of the statistical weight matrices generates this product for each and every conformation of the chain, and Eq. (18) with the operators U1and Unappended gives their sum. The foregoing procedure for evaluation of Z is a minor variant of the method of H. A. Kramers and G. H. Wannier 29 for treating a hypothetical one- dimensional ferromagnet or lattice. A number of interesting characteristics of the chain molecule can be deduced from the partition function by application of familiar techniques of statistical mechanics. I shall resist the temptation to elaborate these beyond mentioning two properties of the molecule that may be derived directly from the partition function, namely, the incidences of the various rotational states and combinations thereof, and the equilibrium con- stants between isomeric structures of the chain in the presence of catalysts effectuating their inter-conversion. Vinyl polymers having the structure depicted in Fig. 7 with R’ ¹ R afford examples wherein the study of equilibria ¾»¬©»»² various diastereomeric forms arising from the local chirality of individual skeletal bonds has been especially fruitful.30 Consider the evaluation of a configuration-dependent property for a given configuration, or conformation, of the chain. Since the configuration is seldom “given”, the problem as stated is artificial. Its solution, however, is a necessary precursor to the ultimate goal, which is to obtain the average of the property over all configurations. A property or characteristic of the chain that will serve for illustration is the end-to-end vector r. Suppose we wish to express this ª»½¬±® ©·¬¸ ®»º»®»²½» ¬± ¬¸» º·®•¬ ¬©± ¾±²¼• ±º ¬¸» ½¸¿·²ò For ¼»º·²·¬»²»••ô ´»¬ ¿ Cartesian coordinate system be affixed to these two bonds with its X,-axis along the º·®•¬ ¾±²¼ ¿²¼ ·¬• Çï󿨷• ·² ¬¸» °´¿²» ±º ¾±²¼• ï ¿²¼ îô ¿• •¸±©² ·² Ú·¹ò èò ·² ¬¸·• ®»º»®»²½» º®¿³»ò In order to facilitate the task of transforming every bond vector to the reference frame affiliated with the first bond, it is helpful to define a reference frame for each skeletal bond of the chain. For example, one may place the axis Xialong bond i, the Yi-axis in the plane of bonds i - l and i, and choose the Zi-axis to complete a right-handed Cartesian system. Let Tisymbolize the transformation that, by premultiplication, converts the representation of a vector in reference frame i+l to its representation in the preceding reference frame i. Then bond i referred to the initial reference frame is given by where liis presented in reference frame i. The required sum is just (19) This sum of products can be generated according to a simple algorithm. 31,32 We first define a “generator” matrix ß· as follows ïéî Chemistry 1974 Ú·¹ò èò Í°»½·º·½¿¬·±² ±º ¬¸» ½±±®¼·²¿¬» ¿¨»• ¿ºº·¨»¼ ¬± »¿½¸ ±º ¬¸» º·®•¬ ¬©± ¾±²¼• ±º ¬¸» ½¸¿·²æ ÈïÇﺱ® ¾±²¼ ï ¿²¼ ÈîÇ® ¾±²¼ îò together with the two terminal matrices (21) (22) In these equations Tiis the matrix representation of the transformation speci- fied above and 0 is the null matrix of order 1 x 3. The desired vector r is generated identically by taking the serial product of the A’s; i.e., as may easily be verified from the elementary rules of matrix multiplication. Each generator matrix Aidepends on the length of bond i and, through Ti, on both the angle between bonds i and i+l and on the angle of rotation about bond i (see Fig. 1). In order to obtain the average of r over all configurations of the chain, it is necessary to evaluate the sum over all products of the kind given in Eq. (23) with each of them multiplied by the appropriate statistical weight for the specified configuration of the chain; see Eq. (17). That is, P. J Flory 173 Then31 The matrix aicomprises the elements of Ui(see Eq. (15)) joined with the A matrix for the rotational state of bond i as prescribed by the column index. It will be apparent that serial multiplication of the aiaccording to Eq. (28) generates the statistical weight factor u2u3. ..un-1 for every configuration of the chain in the same way that these factors are generated by serial multiplication of the statistical weight matrices Uiin Eq. (18). Simultaneously, Eq. (28) generates the product of A’s (see Eq. (23)) that produces the vector ® for each configuration thus weighted. The resulting products of statistical weights and of A’s are precisely the terms required by Eq. (24). The terminal factors in Eq. (28) yield their sum. With greater mathematical concision31,32 If each bond vector liis expressed in its own reference frame i, then (34) ïéì Chemistry 1974 ð îð 40 60 80 ïðð ÒËÓÞÛÎ ÑÚ ÞÑÒÜÍô ² Ú·¹ò çò ݸ¿®¿½¬»®·•¬·½ ®¿¬·±• ä®îâ °´±¬¬»¼ ¿¹¿·²•¬ ¬¸» ²«³¾»® ±º ¾±²¼• ² ·² ¬¸» ½¸¿·² º±® °±´§³»¬¸§´»²»ô ¿²¼ º±® ·•±¬¿½¬·½ ¿²¼ •§²¼·±¬¿½¬·½ °±´§ ø³»¬¸§´ ³»¬¿½®§´¿¬»÷ ••ò Ú®±³ ¬¸» ½¿´½«´¿¬·±²• ±º ß¾»ô Ö»®²·¹¿² ¿²¼ Ú´±®§îê ¿²¼ ±º DZ±²òíì That is, (35) where G1has the form of the first row, and Gnthat of final column of Eq. (34). 2 32,33 Evaluation of •«ºº·½·»²¬´§ ¹®»¿¬ ¬± ¹«¿®¿²¬»» ²«³»®±«• ½±³¾·²¿¬·±²• ±º ¿®®¿²¹»³»²¬• ·² which the condition of mutual exclusion of space is met throughout the sys- tem as a whole. Moreover, the task of packing chain molecules is not made easier by partial ordering of the chains or by segregating them.6,37 Any state of organization short of complete abandonment of disorder in favor of creation of a crystalline phase offers no advantage, in a statistical-thermodynamic sense. Theoretical arguments aside, experimental evidence is compelling in showing the chains to occur in random configurations in amorphous polymers, and further that these configurations correspond quantitatively with those of the unperturbed state discussed above. 38 The evidence comes from a variety of sources: from investigations on rubber elasticity, chemical cyclization equi- libria, thermodynamics of solutions, and, most recently, from neutron scatter- ing studies on protonated polymers in deuterated hosts (or vice versa).39 The investigations last mentioned go further. They confirm the prediction made ¬©»²¬§óº·ª» years ago that the excluded volume perturbation should be annulled in the bulk amorphous state. 5 The excluded volume effect is therefore an aberration of the dilute solution, which, unfortunately, is the medium preferred for physicochemical characterization of macromolecules. Knowledge gained through investigations, theoretical and experimental, on the spatial configuration and associated properties of random macro- molecular chains acquires added significance and importance from its direct, quantitative applicability to the amorphous state. In a somewhat less quanti- tative sense, this knowledge applies to the intercrystalline regions of semi- crystalline polymers as well. It is the special properties of polymeric materials in amorphous phases that render them uniquely suited to many of the functions they perform both in biological systems and in technological applications. These properties are intimately related to the nature of the spatial configura- tions of the constituent molecules. Investigation of the conformations and spatial configurations of macro- molecular chains is motivated therefore by considerations that go much beyond ·¬• ¿°°»¿´ ¿• ¿ •¬·³«´¿¬·²¹ ·²¬»´´»½¬«¿´ »¨»®½·•»ò ß½¯«·•·¬·±² ±º ¿ ¬¸±®±«¹¸ «²¼»®•¬¿²¼·²¹ ±º ¬¸» •«¾¶»½¬ ³«•¬ ¾» ®»¹¿®¼»¼ ¿• ·²¼·•°»²•¿¾´» ¬± ¬¸» ½±³ó °®»¸»²•·±² ±º ®¿¬·±²¿´ ½±²²»½¬·±²• ¾»¬©»»² ½¸»³·½¿´ ½±²•¬·¬«¬·±² ¿²¼ ¬¸±•» °®±°»®¬·»• ¬¸¿¬ ®»²¼»® °±´§³»®• »••»²¬·¿´ ¬± ´·ª·²¹ ±®¹¿²·•³• ¿²¼ ¬± ¬¸» ²»»¼• of man. 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J., ¿²¼ Ú±¨ô Ìò Ùòô Ö®òô Öò б´§³»® ͽ·òô ëô éìë øïçëð÷ å Öò ß³»®ò ݸ»³ò ͱ½òô éíô ïçðì øïçëï÷ò ïìò ß´¬¿®»•ô Ìòô ɧ³¿²ô Üò Ðò ¿²¼ ß´´»²ô Êò Îòô Öò б´§³»® ͽ·òô ßô îô ìëíí øïçêì÷ò ïëò ݸ·²¿·ô Íò Òòô ¿²¼ Í¿³«»´•ô Îò Öòô Öò б´§³»® ͽ·òô ïçô ìêí øïçëê÷ò ïêò Ó¿²¼»´µ»®²ô Ôòô ¿²¼ Ú´±®§ô Ðò Öòô Öò ݸ»³ò 觕òô îðô îïî øïçëî÷ô Ó¿²¼»´µ»®²ô Ôòô Õ®·¹¾¿«³ô Éò Îò ¿²¼ Ú´±®§ô Ðò Öòô ·¾·¼òô îðô ïíçî øïçëî÷ò ïéò Ú±¨ô Ìò Ùòô Ö®òô ¿²¼ Ú´±®§ô Ðò Öòô Öò ß³»®ò ݸ»³ò ͱ½òô éíô ïçðçô ïçïë øïçëï÷ò ïèò Õ®·¹¾¿«³ô Éò Îòô Ó¿²¼»´µ»®²ô Ôòô ¿²¼ Ú´±®§ô Ðò Öòô Öò б´§³»® ͽ·òô çô íèï øïçëî÷ò Õ®·¹¾¿«³ô Éò Îò ¿²¼ Ú´±®§ô Ðò Öòô ·¾·¼ô ïïô íé øïçëí÷ô ïçò Û·•»²¾»®¹ô Øòô ¿²¼ Ú»´•»²º»´¼ô Ùòô Öò Ó±´ò Þ·±´òô íðô ïé øïçêé÷ò ײ²»®•ô Ôò Üòô ¿²¼ Ú»´•»²º»´¼ô Ùòô ·¾·¼òô ëðô íéí øïçéð÷ò îðò ʱ´µ»²•¬»·²ô Óò Êòô Configurational Statistics of Polymeric Chains, ¬®¿²•´¿¬»¼ º®±³ ¬¸» Ϋ••·¿² »¼òô ïçëçô ¾§ Íò Òò ¿²¼ Óò Öò Ì·³¿•¸»ººôײ¬»®•½·»²½»ô Ò»© DZ®µô ïçêíò îïò Þ·®•¸¬»·²ô Ìò Óò ¿²¼ Ь·¬•§²ô Ñò Þòô Conformations of Macromolecules, ¬®¿²•´¿¬»¼ º®±³ ¬¸» Ϋ••·¿² »¼òô ïçêìô ¾§ Íò Òò ¿²¼ Óò Öò Ì·³¿•¸»ººô ײ¬»®•½·»²½»ô Ò»© DZ®µô ïçêêò îîò 符»®ô Õò Íòô Ü·•½«••·±²• Ú¿®¿¼¿§ ͱ½òô ïðô êê øïçëï÷ò îíò Ó·¦«•¸·³¿ô Íòô ͬ®«½¬«®» ±º Ó±´»½«´»• ¿²¼ ײ¬»®²¿´ ન¬·±²ô ß½¿¼»³·½ Ю»••ô Ò»© DZ®µô ïçëìò îìò Ú´±®§ô Ðò Öòô Statistical MechanicsofChain Molecules, ײ¬»®•½·»²½» Ы¾´·•¸»®•ô Ò»© DZ®µô ïçêçò îëò Ù±¬´·¾ô Ç«ò Ç¿òô Ƹò Ú·¦ Ì»µ¸²ô îçô ëîí øïçëç÷ò Þ·®•¸¬»·²ô Ìò Óòô ¿²¼ Ь·¬•§²ô Ñò Þòô ·¾·¼òô îçô ïðìè øïçëç÷ò Ô·¬•±²ô Íòô Öò ݸ»³ò 觕òô íðô çêì øïçëç÷ò Ò¿¹¿·ô Õòô ·¾·¼òô íïô ïïêç øïçëç÷ô ر»ª»ô Ýò ßò Öòô ·¾·¼òô íîô èèè øïçêð÷ò îêò ß¾»ô ßòô Ö»®²·¹¿²ô Îò Ôòô ¿²¼ Ú´±®§ô Ðò Öòô Öò ß³»®ò ݸ»³ò ͱ½òô èèô êí ï ø ïçêê÷ò îéò ͽ±¬¬ô Îò ßòô ¿²¼ ͽ¸»®¿¹¿ô Øò ßòô Öò ݸ»³ò 觕òô ììô íðëì øïçêê÷ò îèò ر»ª»ô Ýò ßò Öòô Öò ݸ»³ò 觕òô íëô ïîêê øïçêï÷ò îçò Õ®¿³»®•ô Øò ßòô ¿²¼ É¿²²·»®ô Ùò Øòô 觕ò λªòô êðô îëî øïçìï÷ò íðò É·´´·¿³•ô ßò Üòô ¿²¼ Ú´±®§ô Ðò Öòô Öò ß³»®ò ݸ»³ò ͱ½òô çïô íïïïô íïïè øïçêç÷ò Ú´±®§ô Ðò Öòô ¿²¼ з½µ´»•ô Ýò Öòô Öò ݸ»³ò ͱ½òô Ú¿®¿¼¿§ Ì®¿²•ò ××ô êçô êíî ø ïçéí÷ò Í«¬»®ô Ëò Éòô Ы½½·ô Íòô ¿²¼ з²±ô Ðòô Öò ß³»®ò ݸ»³ò ͱ½òô çé ïðïè øïçéë÷ò íïò Ú´±®§ô Ðò Öòô Ю±½ò Ò¿¬ò ß½¿¼ò ͽ·òô éðô ïèïç øïçéí÷ò íîò Ú´±®§ô Ðò Öòô Ó¿½®±³±´»½«´»•ô éô íèï øïçéì÷ò ííò Ú´±®§ô Ðò Öòô ¿²¼ ß¾»ô Çòô Öò ݸ»³ò 觕ò ëìô ïíëï øïçéï÷ò íìò DZ±²ô Üò Çòô «²°«¾´·•¸»¼ ®»•«´¬•ô Ô¿¾±®¿¬±®§ ±º Ó¿½®±³±´»½«´¿® ݸ»³·•¬®§ô ͬ¿²ó º±®¼ ˲·ª»®•·¬§ò íëò Í«²¼¿®¿®¿¶¿²ô Ðò Îòô ¿²¼ Ú´±®§ô Ðò Öòô Öò ß³»®ò ݸ»³ò ͱ½òô çêô ëðîë øïçéì÷ò íêò Õ·®•¬»ô Îò Ùòô ¿²¼ Õ®¿¬µ§ô Ñòô Æò 觕·µô ݸ»³ò Ò»«» Ú±´¹»ô íïô íêí øïçêî÷ò Õ·®•¬»ô Îò Ùòô Ó¿µ®±³±´ò ݸ»³òô ïðïô çï øïçêé÷ò Õ·®•¬»ô Îò Ùòô Õ®«•»ô Éò ßòô ¿²¼ ×¾»´ô Õòô б´§³»®ô ïêô ïîð øïçéë÷ò íéò Ú´±®§ô Ðò Öòô Ю±½ò α§¿´ ͱ½òô ßô îíìô êð øïçëê÷ò Ú´±®§ô Ðò Öòô Öò б´§³ò ͽ·òô ìçô ïðë øïçêï÷ò íèò Ú´±®§ô Ðò Öòô Ы®» ú ß°°´ò ݸ»³òô Ó¿½®±³±´»½«´¿® ݸ»³òô èô ´óïë øïçéî÷ò íçò Õ·®•¬»ô Îò Ùòô Õ®«•»ô Éò ßòô ¿²¼ ͽ¸»´¬»²ô Öòô Ó¿µ®±³±´ò ݸ»³òô ïêîô îçç øïçéî÷ò Þ»²±·¬ô Øòô Ü»½µ»®ô Üòô Ø·¹¹·²•ô Öò Íòô з½±¬ô Ýòô ݱ¬¬±²ô Öò Ðòô Ú¿®²±«¨ô Þòô Ö¿²ó ²·²µô Ùòô ¿²¼ Ѿ»®ô Îòô Ò¿¬«®»ô 觕·½¿´ ͽ·»²½»•ô îìëô ïí øïçéí÷ò Þ¿´´¿®¼ô Üò Ùò Øòô É·¹²¿´´ô Ùò Üòô ¿²¼ ͽ¸»´¬»²ô Öòô Û«®ò б´§³»® Öòô çô çêë øïçéí÷å ·¾·¼ô îðô èêï øïçéì÷ò Ú·•½¸»®ô Ûò Éòô Ô»·•»®ô Ùòô ¿²¼ ×¾»´ô Õò б´§³»® Ô»¬¬»®•ô ïíô íç øïçéë÷ò ÍÑÚÌ ÓßÌÌÛÎ Nobel Lecture, December 9, 1991 ¾§ PIERRE- GILLESDE GENNES College de France, Paris, France What do we mean by soft matter? Americans prefer to call it “complex fluids”. This is a rather ugly name, which tends to discourage the young students. But it does indeed bring in two of the major features: ×÷ ݱ³°´»¨·¬§ò We may, in a certain primitive sense, say that modern biology has proceeded from studies on simple model systems (bacterias) to complex multicellular organisms (plants, invertebrates, vertebrates...). Simi- larly, from the explosion of atomic physics in the first half of this century, one of the outgrowths is soft matter, based on polymers, surfactants, liquid crystals, and also on colloidal grains. î÷ Ú´»¨·¾·´·¬§ò I like to explain this through one early polymer experiment, which has been initiated by the Indians of the Amazon basin: they collected the sap from the hevea tree, put it on their foot, let it “dry” for a short time. And, behold, they have a ¾±±¬ò From a microscopic point of view, the starting point is a set of independent, flexible polymer chains. The oxygen from the air builds in a few bridges between the chains, and this brings in a spectacu- lar change: we shift from a liquid to a network structure which can resist tension - what we now call a ®«¾¾»® (in French: caoutchouc, a direct transcription of the Indian word). What is striking in this experiment, is the fact that a very mild chemical action has induced a drastic change in mechanical properties: a typical feature of soft matter. Of course, with some other polymer systems, we tend to build more rigid structures. An important example is an enzyme. This is a long sequence of aminoacids, which folds up into a compact globule. A few of these amino- acids play a critical role: they build up the “active site” which is built to perform a specific form of catalysis (or recognition). An interesting ques- tion, raised long ago by Jacques Monod, is the following: we have a choice of twenty aminoacids at each point in the sequence, and we want to build a receptor site where the active units are positioned in space in some strict way. We cannot just put in these active units, because, if linked directly, they would not realise the correct orientations and positions. So, in between two active units, we need a “spacer”, a sequence of aminoacids which has enough variability to allow a good relative positioning of the active sites at both ends of the spacer. Monod’s question was; what is the minimum length of spacers? It turns out that the answer is rather sharply defined(l). The magic number is around 13-14. Below 14 units, you will not usually succeed in getting the desired conformation. Above 14, you will have many sequences Pierre Gilles de Gennes 9 which can make it. The argument is primitive; it takes into account excluded volume effects, but it does not recognise another need for a stable enzyme - namely that the interior should be built preferably with hydrophobic units, while the outer surface must be hydrophilic. My guess is that this cannot change the magic number by much more than one unit. Indeed, when we look at the spacer sizes in a simple globular protein like myosin, we see that they are not far from the magic number. Let me return now to flexible polymers in solution, and sketch some of their strange mechanical properties. One beautiful example is the four roller experiment set up by Andrew Keller and his coworkers(2). Here, a dilute solution of coils is subjected to a purely longitudinal shear. If the exit trajectory is well chosen (in the symmetry plane of the exit channel), the molecules are stressed over long times. What is found is that, if the shear rate exceeds a certain threshold value an abrupt transition takes place, and the medium becomes birefringent. This is what I had called a “coil- stretch transition”(3). When the shear begins to open the coil, it offers more grip to the flow, and opens even more... leading to a sharp transition. Here, we see another fascinating aspect of soft matter - the amazing coupling between mechanics and conformations. Indeed, Keller showed that rather soon (at shear rates > the chains break), and they do so very near to their midpoint - a spectacular result. Another interesting feature of dilute coils is their ability to reduce the losses in turbulent flows. This is currently called the Toms effect. But in actual fact it was found, even before Toms, by Karol Mysels(4). He is here today, to my great pleasure. Together with M. Tabor, we tried to work out a scaling model of coils in a turbulent cascade(5), but our friends in mechan- ics think that it is not realistic, the future will tell what the correct answer is. I have talked a lot about polymers. It would be logical to do the same with colloids, or - as I like to call it - “ultra divided matter”. But since I just gave another talk with this title at the Nobel symposium in Göteborg, I will omit the subject, in spite of its enormous practical importance. Let me rather switch to surfactants, molecules with two parts: a polar head which likes water, and an aliphatic tail which hates water. Benjamin Franklin performed a beautiful experiment using surfactants; on a pond at Clapham Common, he poured a small amount of oleic acid, a natural surfactant which tends to form a dense film at the water-air interface. He measured the volume required to cover all the pond. Knowing the area, he then knew the height of the film, something like three nanometers in our current units. This was to my knowledge the first measurement of the size of molecules. In our days, when we are spoilt with exceedingly complex toys, such as nuclear reactors or synchrotron sources, I particularly like to describe experiments of this Franklin style to my students. Surfactants allow us to protect a water surface, and to generate these beautiful soap bubbles, which are the delight of our children. Most of our understanding of these soap bubbles is due to a remarkable team, Mysels, Shinoda and Frankel, who wrote the book on this subject(6). Unfortunately, 10 Physics 1991 this book is now very hard to find, I very much hope that it will be reprinted. Long ago Françoise Brochard, Jean-François Lennon and I(7) became interested in some bilayer systems, where we have two sheets of surfactant, each pointing towards the neighbouring water. A related (although more complex) system of this type is a red blood cell. For many years it had been known that, when observed under phase contrast, these cells flicker. - It was sometimes believed that this flicker reflected an instability of a living system under non-equilibrium conditions. Ultimately, the thing is simpler. The essential property of insoluble bilayers is that they optimise their area at fixed surfactant number. Thus, the energy is stationary with respect to area: the surface tension vanishes. This means that the fluctuations in shape of these deflated cells, or “vesicles”, are huge: the flicker is just an example of Brownian motion for a very flexible object. What Jean-François had done was to measure space time correlations for the flicker. Françoise then showed that they could be understood from a model containing no surface tensions, but only curvature energies plus viscous forces - another good example of soft matter. This was, in fact, one of the starting points for many studies on surfactant bilayers, pioneered by W. Helfrich and, on a more formal side, on random surfaces especially with D. Nelson. One of the great successes in this field has been the invention of the “sponge phase” of microemulsions(8,9). But, more generally, it is amusing to learn from these people that there is some overlap in thought between the highbrow string theories and the descrip- tions of soaps! Let me now move to another corner in our garden - liquid crystals. Here, I must pay tribute first to two great pioneers: i) Georges Friedel, who was the first to understand exactly what is a liquid crystal, and what are the main types; ii) Charles Frank, who (after some early work of Oseen) constructed the elastic theory of nematics, and described also a number of their topological defects (“disclinations”). I will talk here only about the smectics. Observing certain defects (“focal conics”) in smectics, Friedel was able to prove that their structure must be a set of liquid, equidistant, deformable layers(l0). By observations at the one hundred micron scale, he was thus able to infer the correct stucture at the ten Å scale - an amazing achievement. Smectics bring me naturally to another important feature of complex fluids - namely that, in our days, it is sometimes possible ¬± ½®»¿¬» ²»© º±®³• ±º ³¿¬¬»®ò The sponge phase quoted above was an example. Another striking case was the invention of ferroelectric smectics by R.B. Meyer, in Orsay, circa 1975. He thought about a certain molecular arrangement, with chiral molecules, which should automatically generate a phase (the “C* phase”) carrying a non-zero electric dipole. Within a few months, our local chemists had produced the right molecule, and the first liquid ferroelectric was born!(ll). In our days, these materials may become very important for display purposes, they commute l03 times faster than the nematics in our wrist-watches. Pierre-Gilles de Gennes 11 Another case of far smaller importance, but amusing, is the •º»®®±•³»½¬·½Œ constructed by M. Veyssié and P. Fabre. The starting point is a water based ferrofluid; a suspension of very fine magnetic particles. (Ferrofluids were invented long ago by R. Rosensweig, and have many amazing properties). Here, what is done, is to prepare a “club sandwich” . . . A system like this, subjected to a magnetic field H, is happier when H is parallel to the layers. It is then interesting to observe the sandwich, with a polarizing microscope, in the frustrated situation where is normal to the layers. At very small H, nothing is seen. But beyond a certain weak threshold Hc, figures like flowers grow in the field(l2). We understand this as a two step process a) just above threshold there is a chemical undulation instability b) later, focal conics appear, with a basic size imposed by the original undulation, but also with smaller conics (which are required to fill space correctly). This “club sandwich” is ultimately detecting rather weak magnetic fields 30 gauss). Let me quote still another new animal: the Janus ¹®¿·²•ô first made by C. Casagrande and M. Veyssié. The god Janus had two faces. The grains have two sides: one apolar, and the other polar. Thus, they have certain features in common with surfactants. But there is an interesting difference if we consider the films which they make, for instance at a water air interface. A dense film of a conventional surfactant is quite impermeable. On the other hand, a dense film of Janus grains always has some interstices between the grains, and allows for chemical exchange between the two sides; “the skin can breathe”. This may possibly be of some practical interest. The first technique used to make the Janus grains was based on spherical particles, half embedded in a plastic and silanated on the accessible side( 13). This produces only microquantities of material. But a group at Gold- schmidt(l4) research invented a much more clever pathway. The starting point is a collection of ¸±´´±© glass particles, which are available commercial- ly. There the outer surface is hydrophobized, and finally the particles are crushed. The resulting platelets have one side hydrophilic and one side hydrophobic. They are irregular, but they can be produced in tons. I would like now to spend a few minutes thinking about the style of soft matter research. One first, major, feature, is the possibility of very simple experiments-in the spirit of Benjamin Franklin. Let me quote two examples. The first concerns the ©»¬¬·²¹ ±º º·¾»®•ò Usually a fiber, after being dipped in a liquid, shows a string of droplets, and thus, for some time, people thought that most common fibers were non-wettable. F. Brochard analysed theoretically the equilibria on curved surfaces, and suggested that in many cases we should have a wetting film on the fiber, in between the droplets. J.M. di Meglio and D. Queré established the existence, and the thickness, of the film, in a very elegant way(l5). They created a pair of neighbouring droplets, one small and one large, and showed that the small one emptied slowly into the big one (as capillarity wants it to go). Measuring the speed of the process, they could go back to the thickness of the film 12 Physics 1991 which lies on the fiber and connects the two droplets: the Poiseuille flow rates in the film are very sensitive to thickness. Another elegant experiment in wetting concerns the ½±´´»½¬·ª» ³±¼»• ±º ¿ ½±²¬¿½¬ ´·²»å the edge of a drop standing on a solid. If one distorts the line by some external means, it returns to its equilibrium shape with a relaxation rate dependent upon the wavelength of the distortion, which we wanted to study. But how could we distort the line? I thought of very complex tricks, using electric fields from an evaporated metal comb, or other, even worse, procedures. But Thierry Ondarcuhu came up with a simple method. 1) He first prepared the unperturbed contact line L by putting a large droplet on a solid. 2) He then dipped a fiber in the same liquid, pulled it out, and obtained, from the Rayleigh instability, a very periodic string of drops. 3) He laid the fiber on the solid, parallel to L, and generated a line of droplets on the solid. 4) He pushed the line L (by tilting the solid), up to the moment where L touched the droplets; then coalescence took place, and he had a single, wavy line on which he could measure relaxation rates(16). I have emphasized experiments more than theory. Of course we need some theory when thinking of soft matter. And in fact some amusing theoretical analogies sometimes show up between soft matter and other fields. One major example is due to S.F. Edwards(l7). Edwards showed a beautiful correspondence between the conformations of a flexible chain and the trajectories of a non relativistic particle; the statistical weight of the chain corresponding to the propagator of the particle. In the presence of external potentials, both systems are ruled by exactly the same Schrödinger equation! This observation has been the key to all later developments in polymer statistics. Another amusing analogy relates the smectics A to superconductors. It was discovered simultaneously by the late W. McMillan (a great scientist, who we all miss) and by us. Later, it has been exploited artistically by T. Lubensky and his colleagues(l8). Here again, we see a new form of matter being invented. We knew that type II superconductors let in the magnetic field in the form of quantized vortices. The analog here is a smectic A inside which we add chiral solutes, which play the role of the field. In some favorable cases, as predicted in 1988 by Lubensky, this may generate a smectic phase drilled by screw dislocations - the so called A* phase. This was discovered experimentally only one year later by Pindak and cowork- ers(19), a beautiful feat. Let me now end up this sentimental journey into soft matter, with a brief mention of my companions. Some were met during the way, like Jean Jacques, a great inventor of liquid crystals, or Karol Mysels, the undisputed master of surfactant science. Some others were with me all along the way; Henri Benoit and Sam Edwards, who taught me polymer science; Jacques des Cloizeaux and Gerard Jannink, who have produced a deep theoretical book on this subject. Finally, an inner core of fellow travelers, over all forms Pierre-Gilles de Gennes 13 of land and sea: Phil Pincus, Shlomo Alexander, Etienne Guyon, Madeleine Veyssié; and last but not least, Françoise Brochard - sans laquelle les chases ne seraient que ce qu’elles sont. The final lines are not mine: they come from an experiment on soft matter, after Boudin, which is shown on the following figure. 14 Physics 1991 An English translation might run like this: “Have fun on sea and land Unhappy it is to become famous Riches, honors, false glitters of this world All is but soap bubbles” No conclusion could be more appropriate today. REFERENCES: 1. P G de Gennes, in Pvor. 2nd Conf. “Physique théorique et Biologie”. Editions CNRS 1969 (15 Quai A. France 75007 Paris, France). 2. J.A. Odell, A. Keller, in Polymer-flow Interactions (ed. I. Rabin), AIP, New York 1985 ; Av. Keller, J. Odell, Coll. Polym. Sci., 263, 181 (1985). 3. P.G. de Gennes, J. Chem. Phys., 60, 5030 (1974). 4. For a historical review see K. Mysels, Chem. Eng. Prog., Symposium series, 67, 45, (1971). 5. M. Tabor, P.G. de Gennes, Europhys. Lett., 2, 519 (1986) P.G. de Gennes, Physica, 140 A, 9 (1986). 6. K. Mysels, K. Shinoda, S. Frankel, SoapFilms , Pergamon, London (1959). 7. F. Brochard, J.F. Lennon, J. Physique (Paris), 36, 1035 (1976). 8. G. Porte, J. Marignan, P. Bassereau, R. May, J. Physique (Paris), 49, 511 (1988). 9. D. Roux, M.E. Cates, Proceedings of the 4th Nishinomya-Yukawa Symposium, Springer (to be published). 10. G. Friedel, Annales de Physique, 18, 273 (1922). 11. R.B. Meyer, L. Liebert, L. Strzelecki, P. Keller, J. Physique L. 69 (1975). 12. P. Fabre, C. Casagrande, M. Veyssié, V. Cabuil, R. Massart, “Ferrosmectics : A new Magnetic and Mesomorphic Phase”, Phys. Rev. Lett., 64, 539 (1990). 13. C. Casagrande, M. Veyssié, C.R. Acad. Sci. (Paris), 306 II, 1423 (1988). C. Casagrande, P. Fabre, M. Veyssié, E. Raphael, Europhys. Lett., 9, 251 (1989). 14. B. Grüining, U. Holtschmidt, G. Koerner, G. Rössmy US Patent no 4, 715, 986 (Dec 1987). 15. J.M. di Meglio, CR. Acad. Sci. (Paris), 303 II, 437 (1986). 16. T. Ondarcuhu, M. Veyssié, Nature, 352, 418 (1991). 17. S.F. Edwards, Proc. Phys. Sot. (London), 85, 613 (1965). 18. S.R. Renn, T. Lubensky, Phys. Rev., A 38, 2132 (1988). 19. J.W. Goodby, M.A. Waugh, S.M. Stein, E. Chin, R. Pindak, J.S. Patel, J. Am. Chem. Soc., 111, 8119 (1989).0 that characterize the macromolecule itself and are generally quite independent of the solvent. Evaluation of a according to Eq. (11) and (12) would require the excluded volume b. This parameter depends on the solvent in a manner P. J. Flory 165 that eludes prediction. Fairly extensive experimental measurements are required for its estimation, or for otherwise making correction for the ex- pansion a. All these difficulties are circumvented if measurements on the polymer solution are conducted under conditions such that the effects of excluded volume are suppressed. The resistance of atoms to superposition cannot, of course, be set aside. But the consequences thereof can be neutralized. We have only to recall that the effects of excluded volume in a gas comprising real molecules of finite size are exactly compensated by intermolecular attractions at the Boyle temperature (up to moderately high gas densities). At this temperature the real gas masquerades as an ideal one. For the macromolecule in solution, realization of the analogous condition requires a relatively poor solvent in which the polymer segments prefer self- contacts over contacts with the solvent. The incidence of self-contacts may then be adjusted by manipulating the temperature and/or the solvent com- position until the required balance is established. Carrying the analogy to a real gas a step further, we require the excluded volume integral for the inter- action between a pair of segments to vanish; that is, we require that b=0. This is the necessary and sufficient condition. 5,6,13 As already noted, estimation of the value of b is difficult; the prediction of conditions under which b shall precisely vanish would be even more precarious. However, the “Theta point,” so-called, at which this condition is met is readily identified with high accuracy by any of several experimental procedures. An excluded volume of zero connotes a second virial coefficient of zero, and hence conformance of the osmotic pressure to the celebrated law of J. H. van’t Hoff. The Theta point may be located directly from osmotic pressure determinations, from light scattering measured as a function of concentration, or from determination of the precipitation point as a function of molecular weight.6,13 The efficacy of this procedure, validated a number of years ago with the collaboration of T. G. Fox, W. R. Krigbaum, and others,13,17,18 is illustrated in Figs. 3 and 4 by the lower plots of data representing intrinsic viscosities measured under ideal, or Theta conditions.6 The slopes of the lines drawn through the lower sets of points are exactly 1/2, as required by Eq. (13’) when b = 0 and hence a = 1. The excellent agreement here illustrated has been abundantly confirmed for linear macromolecules of the widest variety, ranging from polyisobutylene and polyethylene to polyribonucleotides.19 At the Theta 2 point the mean-square chain vector 0 invariably are found to be proportional to chain length. A highly effective strategy for characterization of macromolecules emerges from these findings. By conducting experiments at the Theta point, the disconcerting (albeit interesting!) effects of excluded volume on experimentally 2 2 measured quantities may be eliminated. Parameters (e.g., 0) are thus obtained that are characteristic of the molecular chain. They are found to be virtually independent of the nature of the “Theta solvent” selected. Having eliminated the effects of long range interactions, one may turn ïêê Chemistry 19740, they include: mean-square dipole moments;the optical anisotropies underlying strain birefringence, depolarized light scattering and electric birefringence; di- chroism; and the higher moments, both scalar and tensor, of the chainvector r. Classical statistical mechanics provides the basis for evaluating the con- figurational averages of these quantities. Since bond lengths and bond angles ordinarily may be regarded as fixed, the bond rotations ¶ are the variables over which averaging must be carried out. The procedure rests on the rota- ¬·±²¿´ ·•±³»®·½ •¬¿¬» •½¸»³»ô the foundations for which were set forth in large measure by M. V. Volkenstein20 and his colleagues21 in Leningrad in the late 1950’s and early 1960’s. It is best explained by examples. Consider rotation about an internal bond of an n-alkane chain. As is now well established,22,23 the three staggered conformations, trans(t), gauche- plus(g+) and its mirror image, gauche-minus(g-), are of lower energy than ïêè Chemistry 19740 = (n+ 1) the optical polarizability and its invariants that govern the ij optical anistropy as manifested in depolarized light scattering, in strain bire- P. J. Flory 175 fringence and in electric birefringence; x-ray scattering at small angles; and NMR chemical shifts. 2 2 For illustration, characteristic ratios