Polymer Physics

Introduction &Ideal Chain in Solution

A.Higuchi

NCU

Polymer Physics (2013)

1. History of Polymer Physics April 17,182. Ideal chains April 24,253. Real chains May 1,24. Polymer Solution May 8,9• Polymer Characterization (MW measurement) Part 1 May 15,16• Mid-term Exam May15,16• Polymer Characterization (MW measurement) Part 2 May 22,231. Polymer Solid May 22,232. Rheology May 29, 3010. Crystalline and glassy polymer June 5,611. Final exam June 12

Histroy of Polymer Science (Physics)

Much of human history has been influenced by the availability of materials!History is divided into eras named after the primary materials used:The Stone Age, the Bronze Age, the Iron Age (& Ceramics, Semiconductor, Polymer & Composite Age?).

Chemists started polymerizing synthetic macromolecules in the middle of the nineteenth century, but they did not believe that they were creating very large molecules! The beginning of the twentieth century was that these materials (natural rubber) were believed as colloids-physically associated clusters of small molecules.Why?Many scientists actually measured high molar masses for these materials (of order 104g/mol or even 105g/mol), but rejected their own measurements because the values changed systematically with concentration.

Loed Ernest Rutherford said:“Science is divided into two categories, physics and stamp-collecting.”

The wisdom of Werner Heisenberg:“Science progresses not only because it helps to explain newly discovered facts, but also because it teaches us over and over again what the word understanding may mean”

In 1920, Staudinger (1953 Nobel prize winner) proposed the macromolecular hypothesis: Polymers are molecules made of covalently bonded elementary units, called monomers.By 1929, Carothers had synthesized a variety of polymers with well-defined structures, and the Polymer Age was born.During the following 30 years (1930-1960), the main concepts of polymer science were established.The work of Kuhn on macromolecular sizes (Chp. 2), the work of swelling a single chain in a good solvent (Chp.3), the work of Huggins and Flory (Nobel Prizer (Chemistry), 1974) on thermodynamics (Chp. 4), the work of Flory and Stockmayer on gelation (Chp. 6).

Textbook:

Flory, P.J. Principle of Polymer Chemistry (Cornell University Press, Ithaca, New York 1953, Nobel Prizer (Chemistry))De Gennes (Nobel Prizer (Physics), 1991), P.-G., Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, New York 1979) Michael Rubinstein, Ralph H. Colby, Polymer Physics, Oxford University Press, 2003

1883 ： gasoline 自動車発明、 1895 ：空気入り自転車用 tire 発明、 1905 ：加硫 rubber 、 carbon black 補強、 rubber 工業の基礎確立

自動車用 tire の発明

Wilhelm II 皇帝

1859-1941

合成 rubber tire

1912 年

Polyethylene

Polyethylene or polythe (IUPAC name polyethene or poly(methylene)) is the most widely used plastic, with an annual production of approximately 80 million metric tons.[1] Its primary use is within packaging (plastic bag, plastic films, geomembranes, etc.).

Bio-derived polyethylene

Braskem and Toyota Tsusho Corporation started Joint marketing activities for producing polyethylene from sugar cane. Braskem will build a new facility at their existing industrial unit in Triunfo, RS, Brazil with an annual production capacity of 200,000 short tons (180,000,000 kg), and will produce high-density polyethylene (HDPE) and low-density polyethylene (LDPE) from bioethanol derived from sugarcane. Polyethylene can also be made from other feedstocks, including wheat grain and sugar beet.

The Texture of Polyethylene C.W. Bunn and T.C. Alcock

Trans. Farady Soc., 41, 317 (1945)

Thin Film of PE between corssed Nicols ; x 500

Electron Microscope of Thin Film of PE ; x 10,000 Mechanism of Cold-drawing

Fringed Micelle

Polyethylene Fine Strucutre W.M.D. Bryant

J. Polym. Sci., 2, 547 (1947)

PE and Paraffin 単結晶

PE 　　　　　　 　　　Paraffin

A Note on Single Crystals in Polymers :

Evidence for a Folded Chain Configuration A. Keller

Phil. Mag. Ser. 8, Vol-2, 1171 (1957)

Flat Single Crystals. The molecules must bend sharply back on themselves forming a regular folded configuration.

1945 57

1. Electron Diffraction pattern of thin polymer films

2. Polymer single crystal

3. Lamellar morphology in spherulite

4. Small angle diffraction pattern (Long spacing)

5. Crystal facets and scetorization

6. No molecular weight change during crystallization

Lots of Evidences of chain folding

No other possibility but the chains fold up at regular intervals

If the contribution of Storks sets the birth data of chain folding,

Keller’s major merit has been to popularize and, more importantly,

to transfer the concept of chain folding to bulk materials, thus

opening the way to the “ modern analysis of the polymer

crystalline state.

Polymer Single Crystals: What About the Impact of the Folds?

B.A. Lotz

Polym. Mater.Sci. & Eng. 97, 66 (2007)

50 Years after the Discovery of Polymer Single Crystals, ACS Meeting at Boston

高分子、 52 、 90 、（ 2003 ）

回顧録　 Chain folding at Dupoint in the mid-50’s. 　

P.H.Geil: J. Polym. Sci., Phys. 　 34, 1165 (1957)

Wallace Carothers (left), inventor of nylon--now used to produce monofilament fishing line and other modern conveniences-and Carl Marvel, another pioneer in the field of polymer chemistry, fishing at Squaw Lake,W7isconsin, ca. 1935. Photo from the Carl Marvel Archives, CHE

Wallace Carothers

ナイロン靴下の宣伝（ 1939 ）

Nylon

Nylon is a thermoplastic silky material, first used commercially in a nylon-bristled toothbrush (1938), followed more famously by women's “nylons” stockings (1940). It is made of repeating units linked by peptide bonds (another name for amide bonds) and is frequently referred to as polyamide (PA). Nylon was the first commercially successful polymer and the first synthetic fiber to be made entirely from coal, water and air.

Nylon 6,6Pleats and creases can be heat-set at higher temperatures Difficult to dye Nylon 6Better dye Affinity Softer Hand Greater elasticity and elastic recovery Better weathering properties; better sunlight resistance

Bill Pittendreigh, DuPont, and other individuals and corporations worked diligently during the first few months of World War II to find a way to replace Asian silk with nylon in parachutes. It was also used to make tires, tents, ropes, ponchos, and other military supplies. It was even used in the production of a high-grade paper for U.S. currency.(----- History of Asahi Chemical Co. Toray Co. and Kuraray Co.---)

Polycarbonate (PC) -> ABS -> High molecular weight polystyrene

The characteristics of polycarbonate are quite like those of polymethyl methacrylate (PMMA, acrylic), but polycarbonate is stronger, usable in a wider temperature range but more expensive. This polymer is highly transparent to visible light and has better light transmission characteristics than many kinds of glass.

IR transmittance of polycarbonate. Also, polycarbonate is almost completely transparent throughout the entire visible region until 400 nm, blocking UV light.

Polycarbonate (PC)

Kevlar (Aramid fiber)[-CO-C6H4-CO-NH-C6H4-NH-]n

high strength material was first commercially used in the early 1970s as a replacement for steel in racing tires. Typically it is spun into ropes or fabric sheets that can be used as such or as an ingredient in composite material components.

Currently, Kevlar has many applications, ranging from bicycle tires and racing sails to body armor ( 防護具) because of its high tensile strength-to-weight ratio; by this measure it is 5 times stronger than steel on an equal weight basis.[2] When used as a woven material, it is suitable for mooring lines and other underwater applications.

Acrylonitrile butadiene styrene (ABS)

Monomer in ABS polymer

It is a copolymer made by polymerizing styrene and acrylonitrile in the presence of polybutadiene. The proportions can vary from 15 to 35% acrylonitrile, 5 to 30% butadiene and 40 to 60% styrene. The result is a long chain of polybutadiene criss-crossed with shorter chains of poly(styrene-co-acrylonitrile). The nitrile groups from neighboring chains, being polar, attract each other and bind the chains together, making ABS stronger than pure polystyrene.

Biodegradable polymer

While aromatic polyesters are almost totally resistant to microbial attack, most aliphatic polyesters are biodegradable due to their potentially hydrolysable ester bonds:

Naturally Produced: Polyhydroxyalkanoates (PHAs) like the poly-3-hydroxybutyrate (PHB), polyhydroxyvalerate (PHV) and polyhydroxyhexanoate (PHH);Renewable Resource: Polylactic acid (PLA);Synthetic: Polybutylene succinate (PBS), polycaprolactone (PCL)...

PolyanhydridesPolyvinyl alcoholMost of the starch derivativesCellulose esters like cellulose acetate and nitrocellulose and their derivatives (celluloid).

PLA

PLGA (poly(lactic-co-glycolic acid)

PLA PGA

Biodegradable polymer

Poly(ε-caprolactone)

Polyhydroxyalkanoates

ICI had developed the material to pilot plant stage in the 1980s, but interest faded when it became clear that the cost of material was too high, and its properties could not match those of polypropylene.

Poly-3-hydroxybutyrate (P3HB)

polyhydroxyvalerate (PHV)

In 1996 Monsanto (who sold PHB as a copolymer with PHV under the trade name Biopol) bought all patents for making the polymer from ICI/Zeneca.

Monsanto's fermenters producing PHB from bacteria were closed down at the start of 2004. Monsanto began to focus on producing PHB from plants instead of bacteria.

Excise 1

1. Write chemical scheme of Nylon, polycarbonate, and Kevlar. What are application usage of these polymers?

2. Iist up biodegradable polymers and their chemical scheme.What are application usage of these polymers?

Example of Polymers

FibersClothesTentRopeBulletproof vestPlastics (paper, board, cup, plate, bottle)Polarized FilterPlastic glassContact lensAdhesion agentFRP (tennis racket)Tissue culture flaskCatheterDialysis membranes （透析膜）RO membranesUF, MF membranesPiezo unit 　（圧電素子）Conductive polymer

Example of Polymers (Chemical structure)

Synthetic polymer Polyethylene, PEPolypropylenePolyvinylchloride, PVCPolyvinyldenechloridePolyvinyldenefluoride, PVDFNylonPolyurethanePolyethylenephtalate, PETPolyvinylalcoholPolystyrenePolymethylmethacrylate, PMMAPolyacrylic resinPolyacrylonitrilePolysulfonePolyimideTeflonPolylactic acidPolyhydroxyethylmethacrylate, HEMASilicone rubberNatural rubberSilk

M = NxMmonomer

Fig. 1.2 The two sequence isomers of polypropylene

Fig. 1.3 The three structual isomers of polybutadiene.

Fig. 1.4 Tacticities of vinyl polymers, illustrated with all backbone carbons in the plane of the page and with H and R groups pointing either into or out from the page.

Linear ring star H

Fig. 1.5 Examples of polymer architectures.

Comb ladder dendrimer randomly branched

Fig. 1.6 Schematic architecture of a polymer network, with the dots indicating crosslinks

Excise 2

1. Write the chemical structure of Nylon 6 and PET (polyethylene

terephtalate)

2. Please explain the chemical structure of (a) isotactic polymer,

(b) syndiotactic polymer, and (c) atactic polymer

3. Please explain alternating copolymer, random copolymer,

fdiblock copolymer, triblock copolymer, graft copolymer, and

random copolymer.

A polymer’s conformation is dictated by its interactions, here illustrated using a chain with 1010 monomers (one of the largest DNA molecules) of size 1 cm (magnify by the factor 108 (l = 1 cm).

Strong attraction between monomersV=nl3=1010cm3=104m3

No interaction between Monomer, random walk R=n1/2l=1 km

Excluded volume repulsions (short-range repulsion)R=n3/5l=10 km

Long-range repulsions (such as electrostatic), R=nl=105 km

Most of polymer conformation are self-similar (fractal)

Fig. 1.14 Fractal structure of an ideal chain with fractal dimension D = 2Obtained by computer simulation.

What is “fractal”?≈ ~

V = (4π/3) R3 ≈ 4.2R3 ~ mass (m) (1.2)

m ~ r3 fractal dimension D =3

Two-dimensional object is a sheet of paper with uniform thickness and density. The mass m of the circle cut out of the piece of paper is proportional to the square of the radius r of this circle:

m ~ r2 fractal dimension D = 2

m ~ rD fractal dimension D =3

What is “fractal”?

Fig. 1.11 Mass m of the part of the wire inside a sphere of radius r. Both axes have logarithmic scales.

Excise 3 Explain this figure.

Fig. 1.12 Construction of a triadic Koch curve.

Divide a straight line into three equal subsections. On the top of the middle subsection we draw an equlateral triangle and erase its bottom side. Repeat these procedures. In order to calculate the dependence of the mass of the triadic Koch curve on the length scale, let us draw circles of diameter 2r equal to the lengths of the segments of two consecutive generations.

The radius of the circles changes by the

factor of 3 (r1=3r2), while the mass m of

the section of the curve inside these circles

changes by the factor of 4 (m1=4m2)

m1=Ar1D=A(3r2)D

m2=4m2 = 4Ar2D

Then, (3r2)D = 4r2D -> 3D=4

D = log4/log3 = 1.26

m ~ rD fractal dimension D =3

Excise 4 Consider Sierpinki gasket and find fractal number D

There are two types of polymer liquids; polymer melts and polymer solutionPolymer solutions can be obtained by dissolving a polymer in a solvent.

Polymer solutions are classfied as dilute or semidilute depending on the polymer mass concentration c.

Ф(volume fraction) = c/ρ = c x vmonomerNAV/Mmonomer

The pervaded volume V is the volume of solution spanned by the polymer chain

V ≈ R3

Fig. 1.15 Solution regimes of flexible polymers.

The fractal nature of polymers (N ~ RD) with typical fractal dimension D < 3, means most of the pervaded volume is filled with solvent or other chains.

The volume fraction of a single molecule inside its pervaded volume is called the overlap volume fraction Ф* or the corresponding overlap concentration c*

Ф* = N x vmonomer / V

c* = ρ x N x vmonomer/V = M / V x NAV

Fig. 1.15 Solution regimes of flexible polymers.

Polymer Physics

Ideal Chain in Solution

A.Higuchi

NCU

What we learn & why we learn?

• Ideal chains and real chains• Θ-temperature & Θ-solvent• End-to-end distance• Ideal chain models• Freely jointed chain model• Flory’s characteristic ratio, Cn

• Kuhn length• Hindered rotation model (HR)• Rotational isomeric state model (RIS)

Ideal Chains and Real Chains

We consider the conformations of chains with no interactions between monomers that are far apart along the chain, even if they approach each other in space. Such chains are called “ideal chains”. This situation is never completely realized for real chains, but they are several types of polymeric systems with nearly ideal chains. Real chains interact with both their solvent and themselves. The relative strength of these interactions determined whether the monomers effectively attract or repel one another.

　　 Real chains in a solvent at low temperatures can be found in a collapsed conformation due to a dominance of attractive over repulsive interactions between monomers. At high temperatures, chains swell due to dominance of repulsive interactions. At a special intermediate temperature, called theta-temperature, chains are in nearly ideal conformations because the attractive and repulsive parts of monomer-monomer interactions cancel each other.

The conformation of an ideal chain, with no interactions between monomers, is the essential starting point of most models in polymer physics.

Ideal Chains and Real Chains

Θ-temperature is a special intermediate temperature where chains are in nearly ideal conformations because attractive and repulsive parts of monomer-monomer interactions cancel each other.

Θ-solvent

Flexibility Mechanism

l=1.54A, θ=68 degree

The main source of polymer flexibility is the variation of torsion angles.Consider a plane defined by three neighbouring carbon atoms C i-2, Ci-1, Ci.

Trans Gauche+ Gauche-

Any section of the chain with consecutive trans states of torsion angles is in a rod-like zig-zag conformation. If all torsion angles of the whole chain are in the trans state, the chain has the largest possible value of its end-to-end distance Rmax.

Rmax = n l cos (θ/2) (2.1)

Fig. 2.2 All-trans (zig-zag) conformation of a short polymer with n=10 main-chain bonds.

Conformations of an ideal chain

Fig. 2.3 One conformation of a flexible polymer

The end-to-end vector is the sum of all n bond vectors in the chain:

The average end-to –end vector of an isotropic collection of chains of n backbone atoms is zero:

The simplest non-zero average is the mean-square end-to-end distance:

In a typical polymer chain, there are correlations between bond vectors and <cos θ ij> is not zero.

Excise 5

Calculate the Kuhn length b of a polyethylene chain with C∞ =7.4, main-chain length l = 1.54A, and bond angle θ=68 degree.

The values of the Kuhn length b and corresponding molar mass of a Kuhn monomer Mo

Hindered rotation model (HR)

The hindered rotation model assumes bond lengths and bond angles are constant and torsion angles are taken to be hindered by a potential U(φ). The probability of any value of the torsion angle φ is taken to be proportional to the Boltzmann factor exp[-U(φ)/kT].

Hindered rotation model (HR)

Rotational Isomeric State Model (RIS)

Rotational Isomeric State Model (RIS)

Fig. One conformation of a randomly branched polymer and its centre of mass, denoted by cm.

Fig. One conformation of a randomly branched polymer and its centre of mass, denoted by cm.

Radius of gyration

Radius of gyration of an ideal linear chain

Classic Debye result!

Radius of gyration

Excise 6

Calculate the mean-square end-to-end distance of atactic polystyrene with degree of polymerization 100 assuming that it is an ideal chain with characteristic ratio C∞=9.5(Note that the characteristic ratio is defined in terms of the main-chain bonds length l=1.54 A rather than monomers.)