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Polymer Course

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  • 1. Introduction To The Physical Chemistry Of Polymer
  • 2. Lecture 1
  • 3. Introduction to polymers Poly = many, mer = unit, many units Polymer science is relatively a new branch of science . It deals with chemistry physics and mechanical properties of macromolecule . Macromolecule are involved in all human aspect ; the human body itself is made from proteins a polymer (made of poly amino acid ). Cellulose an Important natural material essential for the existence of man since the down of history, is the complicated polymer structure. Beyond the many natural polymer , the man made polymers ore now for human development . It is impossible to imagine modern life without all the different types of synthetic textile materials (polyester , polyamide………..)
  • 4. In this course we will discuss the following : 1- Types of polymer 2- Step polymerization 3- Addition free radical polymerization 4- Addition ionic polymerization 5- Copolymerization 6- Molecular weights of polymer 7- Elucidation of the structure of polymer
  • 5. Polymer –is a large molecule consisting of a number of repeating units with molecular weight typically several thousand or higher Repeating unit – is the fundamental recurring unit of a polymer Monomer - is the smaller molecule(s) that are used to prepare a polymer Oligomer –is a molecule consisting of reaction of several repeat units of a monomer but not large enough to be consider a polymer (dimer , trimer, tetramer, . . .) Degree of polymerization - number of repeating units Definitions
  • 6.  
  • 7. Nomenclature of polymer 1- Based on monomer source The addition polymer is often named according to the monomer that was used to form it Example : poly( vinyl chloride ) PVC is made from vinyl chloride -CH 2 -CH(Cl)- If “ X “ is a single word the name of polymer is written out directly ex. polystyrene -CH 2 -CH(Ph)- Poly X If “ X “ consists of two or more words parentheses should be used ex , poly (vinyl acetate ) -CH 2 -CH(OCOCH 3 )- 2- Based on polymer structure The most common method for condensation polymers since the polymer contains different functional groups than the monomer
  • 8. Classification schemes Classification by Origin
    • Synthetic organic polymers
    • Biopolymers (proteins, polypeptides, polynucleotide, polysaccharides, natural rubber)
    • Semi-synthetic polymers (chemically modified synthetic polymers)
    • Inorganic polymers (siloxanes, silanes, phosphazenes)
  • 9. Classification by Monomer Composition Homopolymer Copolymer Block Graft Alternating Statistical Homopolymer Consist of only one type of constitutional repeating unit (A) AAAAAAAAAAAAAAA copolymer Consists of two or more constitutional repeating units (A.B )
  • 10.
    • Several classes of copolymer are possible
    • Statistical copolymer (Random)
    • ABAABABBBAABAABB
    • two or more different repeating unit
    • are distributed randomly
    • Alternating copolymer
    • ABABABABABABABAB
    • are made of alternating sequences
    • of the different monomers
    • Block copolymer
    • AAAAAAAAABBBBBBBBB
    • long sequences of a monomer are followed by long sequences of another monomer
    • Graft copolymer
    • AAAAAAAAAAAAAAAAAA
    • B B B
    • B B B
    • Consist of a chain made from one type of monomers with branches of another type
    (d)
  • 11. Classification by Chain structure (molecular architecture)
    • Linear chains :a polymer consisting of a single continuous chain of repeat units
    • Branched chains :a polymer that includes side chains of repeat units connecting onto the main chain of repeat units
    • Hyper branched polymer consist of a constitutional repeating unit including a branching groups
    • Cross linked polymer :a polymer that includes interconnections between chains
    • Net work polymer :a cross linked polymer that includes numerous interconnections between chains
    Linear Branched Cross-linked Network Direction of increasing strength
  • 12. Classification by Chain Configuration and Conformation Configuration or cis-trans isomerism Configuration : Is defined by polymerization method. A change in configuration require the rupture of covalent bonds . Stereoisomerism or tacticity Isotactic Syndiotactic Atactic Conformation : is defined by its sequence of bonds and torsion angles. The change in shape of a given molecule due to torsion about single ( σ ) bonds
  • 13. Geometric Isomerism CH 2 CH CH CH 2
  • 14. isotactic Microstructure - Tacticity atactic syndiotactic Side groups on alternating sides of the backbone Side groups on the same side of the backbone Side groups on random Sides of the backbone
  • 15. Polyolefins with side chains have stereocenters on every other carbon With so many stereocenters, the stereochemistry can be complex. There are three main stereochemical classifications for polymers.
  • 16.
    • Tacticity affects the physical properties
      • Atactic polymers will generally be amorphous, soft, flexible materials
      • Isotactic and syndiotactic polymers will be more crystalline, thus harder and less flexible
    • Polypropylene (PP) is a good example
      • Atactic PP is a low melting, gooey material
      • Isoatactic PP is high melting (176º), crystalline, tough material that is industrially useful
      • Syndiotactic PP has similar properties, but is very clear. It is harder to synthesize
  • 17. Classification by Thermal Behavior Thermoplastics - materials become fluid and processible upon heating, allowing them to be transformed into desired shapes that are stabilized by cooling. Thermosets - initial mixture of reactive, low molar mass compounds reacts upon heating in the mold to form an insoluble, infusible network Classification by Application
    • Plastics
    • Fibers
    • Elastomers
    • Coatings
    • Adhesives
    Classification Based on Kinetics or Mechanism Step-growth Chain-growth
  • 18. 1. A number-average molecular weight M n : divide chains into series of size ranges and then determine the number fraction N i of each size range where M i represents the mean molecular weight of the size range i, and N i is the fraction of total number of chains within the corresponding size range To create a solid with useful mechanical properties the chain must be long !! One may describe chain length in terms of polymer average molecular weight, which can be defined in several ways: Molecular weight averages 2. A weight average molecular weight M w is based on the weight fraction w i within the size ranges: M n = ∑ M i N i / ∑ N i M w = ∑ M i W i / ∑ W i
  • 19. (1)The number-average molecular weight for a discrete distribution of molecular weights is given as     where N is the total number of molecular-weight species in the distribution. (2) The weight-average molecular weight is given as
  • 20. A measure of the molecular-weight distribution is given by the ratios of molecular -weight averages. For this purpose, the most commonly used ratio is Mw/Mn, which is called the polydispersity index or PDI . PDI= M w /M n M w /M n = 1 monodisperse Polymer sample consisting of molecules all of which have the same chain length M w / M n > 1 polydisperse Polymer consisting of molecules with the variety of chain length
  • 21. Description of polymer physical properties 1-Primary bonds : the covalent bonds that connect the atoms of the main chain 2- Secondary bonds : non – covalent bonds that hold one polymer chain to another including hydrogen bond and other dipole –dipole attraction 3-Crystalline polymer : solid polymers with a high degree of structural order and rigidity 4- Amorphous polymers : polymers with a low degree of structural order 5-Semi – crystalline polymer : most polymers actually consist of both crystalline domains and amorphous domains with properties between that expected for a purely crystalline or purely amorphous polymer 6-Glass : the solid form of an amorphous polymer characterized by rigidity and brittleness Amorphous Crystalline
  • 22. 7 – Crystalline melting temperature (T m ) : temperature at which crystalline Polymer converts to a liquid or crystalline domains of a semi crystalline Polymer melt (increased molecular motion ) 8- Glass transition temperature (T g ) : temperature at which an amorphous polymer converts to a liquid or amorphous domains of a semi crystalline polymer melt 9 – Thermoplastics (plastics ( : polymers that undergo thermally reversible Interconversion between the solid state and the liquid state 10- Thermosets : polymers that continue reacted at elevated temperatures generating increasing number of crosslinks such polymers do not exhibit melting or glass transition 11- Liquid – crystalline polymers : polymers with a fluid phase that retains some order 12- Elastomers : rubbery , stretchy polymers the effect is caused by light crosslinking that pulls the chains back to their original state ا
  • 23. Temperature 3 9 6 7 8 4 5 Glass phase (hard plastic) Rubber phase (elastomer) Liquid Leathery phase Log (stiffness) Pa
  • 24. Polymerization mechanisms
    • Chain Growth
    • The only growth reaction is addition of monomer to a growing chain with a reactive monomer
    • The reaction mixture consists of high polymer and unreacted monomers with very few actively growing chain
    • Monomer concentration decreases steadily as reaction time increases
    • Step Growth
    • Reaction can occur independently between any pair of molecular species
    • The reaction mixture consists of oligomers of many sizes in a statically calculable distribution
    • Monomer disappear early in favor of low oligomer
  • 25.
    • Chain growth
    • High polymer appears immediately , average molecular weight does not change much as reaction proceeds
    • Increased reaction time increases overall product yield , but does not affect polymer average molecular weight
    • Step Growth
    • Oligomers steadily increases in size, polymer average molecular weight increases as reaction proceeds
    • Long reaction time are essential to produce polymer with height average molecular weight
    Polymerization mechanisms
  • 26. Lecture 2 Polymerization mechanisms
  • 27. Polymerization mechanisms - Step-growth polymerization
  • 28. Stepwise (Condensation) polymerization Reaction Requirements for Step-Growth Polymerization • High monomer conversion • High monomer purity • High reaction yield • Stoichiometric equivalence of functional groups The characteristic features of this type of polymerization process as follow . 1-Growth occurs throughout the matrix 2-There is the rapid loss of the monomer species 3-The molecular weight slowly increases throughout the reaction 4- The same mechanism operate throughout the reaction 5-The polymerization rate decreases as the number of functional group decreases 6-No initiator is required to start the reaction
  • 29. Step-Growth Polymerization
  • 30. Example formation of polyester nHO-R-OH + nHOOC-Rˉ-COOH H-(O-R-OOC-Rˉ-CO-) n OH+(2n-1)H 2 O Kinetics of condensation (step – Growth ) polymerization Consider the synthesis of polyester from a diol and a diacid. The first step is the reaction of the diol and the diacid monomers to form dimer , HO-R-OH + HOOC-R"-COOH--> HO-R-OCO-R'-COOH + H 2 O The dimer then forms trimer by the reaction with diol monomer , HO-R-OCO-R'-COOH + HO-R-OH--> HO-R-OCO-R'-COO-R-OH +H 2 O and also with diacid monomer , HO-R-OCO-R'-COOH + HOOC-R'-COOH--> HOOC-R'-COO-R-OCO-R'-COOH + H 2 O
  • 31. Kinetics of Condensation (Step-Growth) Polymerization
    • Step-Growth polymerization occurs by consecutive reactions in which the degree of polymerization and average molecular weight of the polymer increase as the reaction proceeds. Usually (although not always), the reactions involve the elimination of a small molecule (e.g., water). Condensation polymerization may be represented by the following reactions:
    • Monomer + Monomer Dimer + H 2 O
    • Monomer + Dimer Trimer + H 2 O
    • Monomer + Trimer Tetramer + H 2 O
    • Dimer + Dimer Tetramer + H 2 O
    • Dimer + Trimer Pentamer + H 2 O
    • Trimer + Trimer Hexamer + H 2 O
    • Generally, the reactions are reversible, thus the eliminated water must be removed if a high molecular weight polymer is to be formed.
    • Based on the assumption that the polymerization kinetics are independent of molecular size, the condensation reactions may all be simplified to:
    • ~~~~COOH + HO~~~~  ~~~~COO~~~~ + H 2 O
  • 32. Kinetic analysis ~~~~COOH + HO~~~~  ~~~~COO~~~~ + H 2 O Most step polymerization involve bimolecular reaction that are often catalyzed ~~~~A + B~~~~ + catalyst  ~~~~AB~~~~ + catalyst The rate is accelerated according to -d [A] By integration dt = k [A][B] [catalyst] -d [A] dt = k ' [A][B] -d [A] dt = k ' [A]2 1 [M] - 1 = k 't [M]o Or Where k ‘ = k [catalyst] I f [A] = [B] ** By use the extent of the reaction P (fraction of A or B functional groups that has reacted at time t ) P = extent of the reaction = the fraction of conversion
  • 33. The concentration at any time given by [M] [M] = [M]o - [M]o P = [M]o (1- P ) By substitution in (** ) = k ' [A]o t + 1
      • Note that experimental data are usually linear only beyond ca. 80% conversion.
    1 (1-p)
  • 34. Polyesterification Without Acidic Catalyst dt = k [A] 2 [B] -d [A] dt = k [A] 3 Or I f [A] = [B] 1 [M] 2 - 1 = 2k t [M]o 2 ** The rate equation is given by - d[A] By integration [M] = [M]o - [M]o P = [M]o (1- P ) By substitution in (** ) 1 (1-p) 2 =2 k [A] 2 ot + 1
  • 35. Uncatalyzed Polyesterification
    • Note that experimental data for esterification reactions show that plots of 1/(1-p) 2 vs. time are linear only after ca. 80% conversion .
  • 36.
      • This behavior has been attributed to the reaction medium changing from one of pure reactants to one in which the ester product is the solvent.
      • Thus, the true rate constants for condensation polymerizations should only be obtained from the linear portions of the plots (i.e., the latter stages of polymerization).
    • For example, the kinetic plots for the polymerization of adipic acid and 1,10-decamethylene glycol show that at 202 o C, the third-order rate constant for the uncatalyzed polyesterification is k = 1.75 x 10-2 (kg/equiv) 2 min -1 .
    Polyesterification Without Acidic Catalyst (continued)
  • 37. The Number Average Molecular Weight in Polycondensation . The number-average degree of polymerization X n is given as the total number of monomer molecules initially present divided by the total number of molecules present at time t, X n = N o / N = [ M ] o / [ M ] [ M ] = [ M ] o ( 1 – P ) X n = 1 / 1 - P
    • This relationship is the Carother's Equation .
    • Example
    • If monomer conversion is 99% what is X n ?
    • X n = 1 / 1 – P = 1 / 1 - 0.99 = 100
    • If P =99.5 % X n = 1 / 1 - 0.995 = 200
    • If P =99.6 % X n = 1 / 1 - 0.996 = 250
  • 38. The number-average molecular weight M n , defined as M n = M o X n + M eg = M o / 1 – P + M eg where M o is the mean of the molecular weights of the structural units, and M eg is the molecular weight of the end groups. The latter becomes negligible at even moderate molecular weight M n = M o X n + M eg = M o / 1 – P = k ' [A] o t + 1 X n = k ' [A] o t + 1 X 2 n =2 k [A] 2 o t + 1 H-(O-R-OOC-Rˉ-CO-) n OH 1 (1-p)
  • 39. M n as a Function of Conversion
  • 40. Molecular Weight Control in Linear Polymerization In the synthesis of polymers one is usually interested in obtaining a product of very specific molecular weight since its properties are highly dependent on its molecular weight. The desired molecular weight can be obtained by 1-Quenching the reaction (e.g., by cooling) at the appropriate time. However, the polymer obtained in this case is unstable, since it can undergo further polymerization if it is heated. This is because the end groups on the polymer chains are still active and they can react with each other. 2-By increasing one reactant over the other. In this way the monomer in excess will block any further increase in the polymer chains. Excess H 2 N-R-NH 2 + HOOC-R'-COOH ---> H-(-NH-R-NHCO-R'-CO-) n -NH-R-NH 2 The use of excess diacid accomplishes the same result; the polyamide in this case has carboxyl end groups ExcessHOOC-R'-COOH+H 2 N-R-NH 2 --->HO-(-CO-R'-CONH-R-NH-) n -CO-R'-COOH
  • 41. 3- Another method of controlling the molecular weight is by adding small amounts of monofunctional monomer. (Acetic acid ) Type (2) For the polymerization of bifunctional monomers A-A and B-B where B-B is present in excess, the numbers of A and B F.gs. are given by N A and N B . Notice that N A and N B are equal to twice the number of A-A and B-B molecules, respectively. The stoichiometric imbalance r of the two f.gs. is given by r = N A /N B . ≤ 1 The total number of monomer molecules is given by (N A +N B )/2 or N A (1+1/r)/2. , the total number of polymer molecules is one half the total number of chain ends or [N A (1-p)+N B (1-rp]/2. The number-average DP( X n )is the total number of A-A and B-B molecules initially present divided by the total number of polymer molecules: X n = N A (1+1/r)/2. [N A (1-p)+N B (1-rp]/2.
  • 42. If r = 1 X n = 1 / 1-p If p = 1 X n = 1 + r / 1 - r Example What is X n when P = 1 but use 0. 9800 moles of A-A and 1. 0100 moles of B – B r = N A / N B = 0.98 x 2 / 1.01 x 2 = 0.97 X n = 1 + r / 1 – r = 1.97 / 0.03 = 66 X n = 1 + r 1 + r – 2rP
  • 43. Type (3) the molecular weight can also be controlled by adding small amounts of monofunctional monomer. Moles of A-A = N A / 2 Moles of B-B = N B / 2 Moles of mono functional B = N B ˉ r = ½ N A / ½ N B + N B ˉ = N A / N B + 2 N B ˉ Example Find X n for 1 mole of A-A ,1mole of B-B and 0.01 mole of RBˉ when P = 1 r = 1/ 1 + 2x 0.01 = 0.99 X n 1 + r / 1 – r = 1 + 0.99 / 1 – 0.99 = 199 The poly dispersity index X w / X n = 1 + P X n = 1 /1-P X w = 1 + p / 1 - P
  • 44. Summary = k ' [A]o t + 1 1 (1-p) 2 =2 k [A] 2 ot + 1 X n = N o / N = [ M ] o / [ M] X n = 1 / 1 - P M n = M o X n + M eg = M o / 1 – P X n = k ' [A] o t + 1 X 2 n =2 k [A] 2 o t + 1 r = N A /N B . ≤ 1 If r = 1 X n = 1 / 1-p If p = 1 X n = 1 + r / 1 - r r = ½ N A / ½ N B + N B ˉ = N A / N B + 2 N B ˉ The poly dispersity index X w / X n = 1 + P X n = 1 /1-P X w = 1 + p / 1 - P 1 (1-p) X n = 1 + r 1 + r – 2rP
  • 45. Lecture 3 Polymerization mechanisms
  • 46. Polymerization mechanisms - Chain-growth polymerization
  • 47. Chain polymerization The characteristic of chain polymerization are as follow : 1- Growth is by the addition of the monomer at the end of the chain 2-Even at long reaction time some monomer are remain in the reaction mixture 3-The molecular weight of the polymer are increase rapidly 4-Different mechanisms operates at different stages of the reaction 5-The polymerization rate initially increases and then become constant 6-An initiator is required to start the reaction Chain polymerization reaction consists of three stages 1- Initiation 2- Propagation 3-Termination
  • 48. Polymerization depend on thermodynamic Polymerization is possible only if the free energy difference between monomer and polymer is negative  G =  H - T  S  0 Must be -ve for Polymerization to work In chain polymerization are exothermic Always +ve Always –ve in chain polymerization
  • 49. Chain polymerization Radical polym. The C=C is prefer the Polym. by R.P. and also can be used in the steric hindrance of the substituent Ionic polym . Anionic polym. Cationic polym. Electron with drawing substituent decreasing the electron density on the double bond and facilitate the attack of anionic species such as cyano and carbonyl δ+ δ- CH 2 =CH Y Electron donating substituent increasing the electron density on the double bond and facilitate the attack of cationic species such as alkoxy, alkyl, alkenyl, and phenyl δ- δ+ CH 2 =CH Y
  • 50. The only exceptions to the unreactivity of tri- and tetra-substituted vinyl monomers are those with fluorine, like tetrafluoroethylene (CF 2 =CF 2 ). The main cause of this reactivity pattern is the steric size of the substituents. Vinyl monomers for addition polymerizations Tetrasubstituted Almost never works. Trisubstituted Almost never works. 1,2-Disubstituted Seldom works. 1,1-Disubstituted Usually works. Monosubstituted Works fine. Unsubstituted (ethylene) Works fine.
  • 51. Free Radical Vinyl Chain Polymerization Rate of Radical Chain Polymerization Radical polymerization consists of three steps-initiation, propagation, and termination. The initiation step consists of two reactions. 1-The production of the free radical k d I ------> 2R˙ 2- Addition of this radical to a monomer molecule to produce the chain initiating species M 1 k i R˙ + M 1 -----> M 1 ˙ The propagation consists of the growth of M 1 k p M n + M 1 ˙ ------> M n+1 ˙ (Rapid reaction )
  • 52. . Termination with the annihilation of the radical centers occurs by bimolecular reaction between radicals either by combination or,, by disproportionation k tc M n ˙ + M m ˙ -----> M n+m k td M n ˙ + M m ˙ -----> M n + M m The termination step can be represented by k t M n ˙ + M m ˙ ----> dead polymer
  • 53. Kinetic Rate Expression The rate of monomer disappearance, = the rate of polymerization, is given by Since for the production of high molar mass material R p » R i this equation can be re-written as:
    • From the beginning of the polymerization:
    • increasing number of radicals due to decomposition of the initiator
    • increasing termination due to increasing radical concentration (R t  [M·] 2 )
    • eventually a steady state in radical concentration:
    **
  • 54. This is equivalent to stating that the rate of initiation R i equals the rate of termination R t R p =k p [M] ( R i /2k t ) ½ R i = 2k t [M . ] 2 [ M˙ ] = ( R i /2k t ) ½ and substitution in Eq.* * yields for the rate of polymerization.
  • 55. Initiation free radical polymerization
    • Thermal initiators
    • Photochemical
    • Redox initiators
    • Ionizing radiation
  • 56.
    • Thermal initiators:
      • Most common kind of FR initiator.
      • Unimolecular decomposition.
      • First order kinetics.
      • Most common examples: peroxides (benzoyl peroxide)or azo compounds(azo isobuteronitrile).
    Peroxides Azo compaunds (I  2R •) (Temperatures are for 10 hour half-lives.)
  • 57. The thermal, homolytic dissociation of initiators is the most widely used method for generating radicals to initiate polymerization. The compounds used as initiators are those with bond dissociation energies in the range 100-170 kJ/mole. The rate of producing primary radicals by thermal homolysis of an initiator R d is given by R d = 2fk d [I] where [I] is the concentration of the initiator and f is the initiator efficiency. and the rate of initiation is given by R i =2fk d [I] By substitute in R p =k p [M] ( R i /2k t ) ½ R p =k p [M] (fk d [I] /k t ) ½
  • 58.
    • Photochemical initiators :
      • One or two component.
      • Used for thin films.
    Peroxides Azo compaunds Disulfides Ketones
    • Redox initiators :
      • Usually 2 component.
      • Rarely used.
    • Ionizing radiation :
      • X-ray, gamma-ray.
      • Random destruction leads to radical formation.
      • Used only in very special cases .
    Fentons reagent
  • 59. Experimental Determination of R p R p can be experimentally determined by measuring the change in any property that differs for the monomer(s) and polymer, for example, solubility, density, refractive index, and spectral absorption The polymerization can also be followed by separation and isolation of the reaction products. Chemical analysis of the unreacted monomers as a function time is also used. The disappearance of monomers or the appearance of polymer can be followed spectroscopically, i.r. or uv spectroscopy Dilatometry Dilatometry is the volume changes that occurs upon polymerization to follow the conversion. It is the most accurate method for chain polymerization because of the large difference in density between monomer and polymer
  • 60.  
  • 61. Kinetic chain length  By substitute R i =2f k d [I] R p =k p [M] (f k d [I] /k i ) ½ ν =R p /R i =R p /R t = k p [M] / 2 (f k d k t [I] ) 1/2 Kinetic chain length v is defined as the average number of monomer molecules polymerized per each radical, which initiate a polymer chain. In other words, v is the ratio between the propagation rate to that of initiation, or termination.
  • 62. The number average degree of polymerization X n of chains formed at a certain moment is dependent on the termination mechanism: * combination: X n = 2  * disproportionation: X n =  chemistry:
  • 63. Lecture 4 Polymerization mechanisms Polymerization Monomer Polymer
  • 64. Chain Transfer Chain transfer is a chain breaking reaction; it is a premature termination of polymer growing radical by the transfer of hydrogen or other atom or species to it from some compound present in the system . This leads to a decrease in the molecular weight than expected. M n ˙ + XY M n -X +Y . where XY may be monomer, solvent, initiator, or other molecule and X is the atom or species transferred. The rate of chain transfer reaction is given by R tr = K tr [M . ][XY] where K tr is the chain transfer rate constant. Chain transfer results in the production of a new radical Y ˙ which could induce polymerization. The effect of chain transfer on the polymerization rate depends on whether the rate of reinitiation is comparable to the original rate of initiation k tr
  • 65. Effect of Chain Transfer on R p and X n In case (1) ν ( chain length ) is not changed X n (number average degree of polymerization ) is altered Large decrease Large decrease Degradative chain transfer K p <<k tr k a <K p 4 Decrease Decrease Retardation K p >>k tr k a <K p 3 Large decrease None Telomerization K p <<k tr k a ~K p 2 Decrease None Normal chain transfer K p >>k tr k a ~K p 1 Effect on X n Effect on R p Type of effect Relative rate constants for Transfer, Propagation, and Reinitiation Case
  • 66.
    • The degree of polymerization now should be redefined as the polymerization rate divided by the sum of all the chain breaking reactions:
    • X n = R p
    • (R t /2) + K trM [M˙][M] + K trs [M˙][S] + K trI [M˙][I]
    • C=chain transfer constant = K tr / K p
    • C M =K trM /K p C S =K trS /K p C I =K trI /K p R p =K p [M][M˙]
    • 1/X n =R t /2R p + K trM [M˙][M]/R p + K trs [M˙][S]/R p +K trI [M˙][I]/R p
    • Substitute by the value of R p
    • 1/X n =R t / 2R p +K trM / K p + K trs [S] / K p [M] +K trI [I] / K p [M]
    • Substitute by the value of C
    • 1/X n =R t / 2R p +C M +C S [S] / [M] +C I [I] / [M] Mayo – walling equation
      • 1/X n = 1/(X n ) o +C M +C S [S] / [M]+C I [I] / [M]
  • 67. Generic Mayo plot For a given amount of initiator [I] and monomer [M] and In the presence of chain transfer agent 1/X n = 1/(X n ) o +C S [S] / [M ]
  • 68. Energetic Characteristics Activation Energy and Frequency Factor . Increasing the temperaure usually increase the rate and decrease the molecular weight. The rate constants of initiation, propagation, and termination can be expressed by an Arrhenius-type relationship k = A e – E / RT or lnk = lnA – E / RT where A is the collision frequency factor, and E the Arrhenius activation energy. A plot of ln k vs 1/T allows the determination of both values.
  • 69. Rate of Polymerization For a polymerization initiated by the thermal decomposition of an initiator the polymerization rate depends on three rate constants K p ( k d / k t ) 1/2 The composite or overall activation energy for the rate of polymerization E R is [E p + (E d /2)-(E t/ 2)]. can be written as R p =k p [M] (fk d [I] /k t ) ½ ً Where
  • 70.  G =  H - T  S  0 Thermodynamics of Polymerization Polymerization of 1,2-Disubstituted Ethylenes 1,2-Disubstituted ethylenes exhibit very little or no tendency to undergo polymerization. Steric inhibition is the cause of this behavior R R substituted Must be -ve for Polymerization to work In chain polymerization are exothermic Always +ve Always –ve in chain polymerization
  • 71. Polymerization-Depolymerization Equilibria Ceiling Temperature For most chain polymerization there is some temperature at which the reaction becomes a reversible one, that is, the propagation step should be written as an equilibrium reaction where k dp is rate constant for the reverse reaction-termed depolymerization or depropagation The reaction isotherm ∆ G = ∆G o + RT lnK . For an equilibrium situation  G=0 by  G o =  H o - T  S o = - RT ln K equilibrium constant is defined by K p /k dp or by
  • 72. Ionic chain polymerization The characteristic of ionic chain polymerization are as follow 1-Ionic polymerization is limited because the ions are usually unstable and require stabilization by solvation and lower temperature for polymerization to proceed 2- The ionic polymerization proceeds with very high rates and is very sensitive to the presence of small amounts of impurities 3-Cationic and anionic polymerizations have very similar characteristics. both depend on the formation and propagation of ionic species 4-solvents of high polarity cannot be used. The highly polar hydroxylic solvents (water, alcohol) react and destroy most ionic initiators. Other polar solvents such as ketones form highly stable complexes with the initiators preventing thus the polymerization. Ionic polymerization,thus require solvent of low or moderate polarity such as CH 3 Cl,CH 2 Cl 2 , and pentane . 5-Ionic polymerizations are characterized by a wide variety of modes of initiation and termination.
  • 73. CATIONIC POLYMERIZATION Initiation a-Protonic Acids Protonic acids can be used to some extent but the anion of the acid should not be highly nucleophilic Halogen acids are not used because of the highly nucleophilic character of the halide ion Other strong acids such as perchloric, sulfuric, phosphoric, chlorosulfonic, methansulfonic,etc, used for cationic polymerization. mineral acids ( initiators ) : H 2 SO 4 , H 3 PO 4 (  provide H+) The molecular weight obtained is low (few thousand).
  • 74. b-Lewis Acids Lewis acids used to initiate cationic polymerization at low temperatures, may yield high molecular weight polymers Lewis acids ( co-initiators ) : AlCl 3 , BF 3 , TiCl 4 , SnCl 4 (often require other proton or cation source)  Forming ( co-initiator / initiator ) system Very active Lewis acids  can undergo auto-ionization The initiation process can be generalized as I + ZY k Y + ( I Z ) -
  • 75. Propagation: depending on the association degree between ions The initiator ion pair (the carbonium ion and its counter ion) produced in the initiation step proceeds to grow by the successive addition of monomer molecules This addition can be occuring by insertion of ( M ) between the carbonium ion and its counter ion HM n + (IZ) - + M HM n M + (IZ) -
  • 76. 1-Chain Transfer to Monomer . This involves transfer of a proton to a monomer molecule with the formation of terminal unsaturation in the polymer molecule HM n M + (IZ) - + M M n+1 + HM + (IZ) - 2-Spontaneous Termination Spontaneous termination involves regeneration of the initiator-coinitiator complex by expulsion from the propagating ion pair with the polymer molecule left with terminal unsaturation. HM n M + (IZ) - M n+1 + H + (IZ) - 3-Combination with counter ion Termination by combination of the propagating carbonium ion with its counter ion occurs HM n M + (IZ) - HM n MIZ Termination
  • 77. Kinetics Under steady state conditions (R i =R t ) follows in a manner similar to that for radical polymerization. The rates of initiation, propagation, and termination are given by R i = Kk i [I][ZY][M] R p = K p [YM + (IZ) - ][M] R t = k t [YM + (IZ) - ] Where [YM + (IZ) - ] is the total concentration of all sized propagation centers The number-average degree of polymerization is obtained as the propagation rate over the termination rate
  • 78. When chain breaking involves chain transfer to monomer and/or termination in addition to combination with gegenion, the degree of polymerization is The rate of chain transfer to monomer is given by R tr,M = k tr,M [YM + (IZ - )][M] Then Or where C M is the chain transfer constant for monomer.
  • 79. Effect of Reaction Medium Solvent Effects Large increase in the rate and degree of polymerization are observed if one increases the solvating power of the solvent. . The free ion concentration increases with increased solvating power, this leads to an increase in R p as the free ions propagate faster than the ion pair. Effect of Gegenion The larger and less tightly bound the gegenion, the greater should be the reactivity of the ion pair toward propagation
  • 80. Energetics Cationic polymerization is also exothermic, since the reaction involves the conversion of π-bond into σ-bond. the activation energies for the rate and degree of polymerization are obtained as E R = E i +E p -E t
  • 81.  
  • 82. Trommsdorff effect In radical polymerization we speak about: 1) low conversion, i.e. polymer chains are in dilute solution (no contact among chains) 2) “intermediate” conversion, i.e. the area in between low and high conversion 3) high conversion, i.e. chains are getting highly entangled; k p decreases. Somewhere in the “intermediate” conversion regime: * polymer chains loose mobility. * Termination rate decreases * Radical concentration increases * Rate of polymerization increases * Molar mass increases This effect is called: gel effect, Trommsdorff effect,or auto-acceleration In the polymerization of MMA this occurs at relatively low conversion.
  • 83. Molar mass If termination takes place by combination) If termination by takes place disproportionation) However, a growing chain may transfer its activity to a new chain: This reaction is then followed by re- initiation, the start of a new chain: in the ideal case:
  • 84. Kinetics of free-radical chain polymerization considering chain transfer reactions RM n • + S-H  RM n -H + S • R tr = k tr [M•][Transfer agent]
  • 85.
    • Chain transfer
    • chain transfer to:
    • monomer
    • initiator
    • solvent or chain transfer agent
    • polymer
    • allylic transfer
    • monomer, initiator and chain transfer agent are mathematically treated identically:
    As derived before this leads to:
  • 86. The rate of “polymer formation” is now defined as: The rate of polymerization as derived before: From the definition of number average degree of polymerization it follows: thus:
  • 87.  
  • 88.
    • Chain transfer to polymer
    • Intermolecular chain transfer
    • Intramolecular chain transfer
    Traditional approach: intermolecular, strong increase in branching density towards high conversion. Recent results:
    • Hardly conversion dependent
    • Dilution results in higher degree of grafting
  • 89. Summary Chain-length Rate of polymerization Initiator decomposition is the reaction step most strongly influenced by temperature. Time of chain-growth
  • 90.  
  • 91. E a = 1/2E d +(E p -1/2E t ) Overall activation energy of polymerization: E d  125 – 170 kJ mol -1 (E p -1/2E t )  20 – 30 kJ mol -1 Thus, initiation is the rate determining step Polymeriszation rate  exp(-E a /RT) Thus, it will increase as the temperature is raised Thermodynamics of radical polymerisation
  • 92.  G =  H - T  S  0  G will increase if T is raised Increasing the temperature  G eventually becomes 0 and the polymerization stops. This occurs because the loss in entropy arising from joining many molecules into one starts to outweigh the energetic benefit of converting double bonds to single bonds. T he temperature above which a monomer cannot be converted to long chain polymer is known as the ceiling temperatute T c . RM n • + M  RM n+1 •  k p k dp R p = k p [M•][M] - k dp [M•] = 0 [ M•](k p [M] – k dp ) = 0 or k p [M] = k dp if [M•]  const K = (k p / k dp ) = 1/ [M e ]  G = -RT c lnK = RT c ln [M e ] =  H - T c  S RT c ln[M e ] + T c  S =  H T c =  H/(  S + Rln[M e ]) Thermodynamics of radical polymerisation
  • 93. k 11 k 12 k 21 k 22 Copolymerization — M 1 • + M 1  —M 1 • — M 1 • + M 2  —M 2 • — M 2 • + M 1  —M 1 • — M 2 • + M 2  —M 2 • } }
  • 94. Copolymerization f i : fraction of monomer i in reaction mixture f 1 = [M 1 ] / ([M 1 ] + [M 2 ]) F i : fraction of monomer i built into polymer F 1 = d[M 1 ] / (d[M 1 ] + d[M 2 ]) Long chain assumption ( k i , k d ignored; k p , k t not ~ chain length) Reactivity ratios independent of environmental factors Average copolymerisation rate:
  • 95. Ideal copolymerisation Composition drift If f 1 ≠ F 1 -> f 1 changes -> F 1 changes What does composition drift mean for the polymer that is formed?
  • 96. Polymerization techniques
    • Kinetic / mechanistic factors related to chain length, chain composition
    • Technological factors e.g. heat removal, reaction rate, viscosity of the reaction mixture, morphology of the product
    • Economic factors; production costs, enviromental aspects, purification steps etc.
    Sometimes for one monomer several techniques of polymerizing are available. Choice of a specific technique depends on a number of factors:
  • 97.
    • Homogeneous systems
    • Bulk polymerization
    • Solution polymerization
    • Heterogeneous systems
    • Suspension polymerization
    • Emulsion polymerization
    • Precipitation polymerization
    • Polymerization in solid state
    • Polymerization in the gas phase
    Polymerization techniques
  • 98. Bulk polymerization Advantages: Disadvantages:
    • Simple, only the monomer and initiator are present in the reaction mixture
    • High molecular weight
    Exotherm of the reaction might be hard to control- molecular weights very disperse The polymer is soluble in the monomer: The polymer is not soluble in the monomer: Viscosity of the reaction increases markedly (gel effect) Polymer precipitates out without increase in solution viscosity R p
  • 99. Solution polymerization Monomer dissolved in solvent, formed polymer stays dissolved. Depending on concentration of monomer the solution does not increase in viscosity. Advantages Disadvantages * Product sometimes * Contamination with directly usable solvent * Controlled heat * Chain transfer to release solvent * Recycling solvent Applications Acrylic coating, fibrespinning, film casting
  • 100.  
  • 101. Suspension polymerization
    • Water insoluble monomers are dispersed in water.
    • Initiator dissolved in monomer.
    • Stabilization of droplets/polymer particles with non-micelle forming emulsifiers like polyvinylalcohol or Na-carboxymethylcellulose.
    • Equivalent to bulk polymerization,
    • small droplets dispersed in water.
    • Product can easily be separated,
    • particles 0.01-1mm.
    • Pore sizes can be controlled by adding a combination of solvent (swelling agent) and non-solvent.
    • Viscosity does not change much.
  • 102. Advantages Disadvantages * Heat control simple * Contamination with * Product directly stabilizing agent usable * Coagulation possible * Easy handling Applications Ion-exchange resins, polystyrene foam, PVC Suspension Polymerization
  • 103.  
  • 104. Emulsion Polymerization
    • A micelle forming emulsifier is used.
    • Initiator is water soluble.
    • The formed latex particles are much smaller
    • than suspension particles (0.05-2 µm).
    • Kinetics differ considerable from other techniques.
    • Polymer is formed within the micelles
    • and not in the monomer droplets.
  • 105. Emulsion Polymerization Advantages Disadvantages * Low viscosity even * Contamination of at high solid contents products with additives * Independent control * More complicated of rate and in case of water molecular-weight soluble monomers * Direct application of complete reactor contents
  • 106. • Ionic polymerizations are more selective than radical processes due to strict requirements for stabilization of ionic propagating species. Cationic: limited to monomers with electrondonating groups Overview of Ionic Polymerization: Selectivity Anionic: limited to monomers with electron withdrawing groups
  • 107. • A counterion is present in both anionic and cationic polymerizations, yielding ion pairs, not free ions. Cationic: ~~~C+(X-) Anionic: ~~~C-(M+) • There will be similar effects of counterion and solvent on the rate, stereochemistry, and copolymerization for both cationic and anionic polymerization. • Formation of relatively stable ions is necessary in order to have reasonable lifetimes for propagation. This is accomplished by using low temperatures (-100 to 50 °C) to suppress termination and transfer and mildly polar solvents (pentane, methyl chloride, ethylene dichloride). Overview of Ionic Chain Polymerization: Counterions
  • 108. There are four states of ion-pair binding: (I) ~~~BA ~~~B+A - (II) covalent bond tight or contact ion pair, intimate ion pair (III) ~~~B+||A - ~~~B+ + A - (IV) solvent-separated, Free ion, very reactive loose ion pair but low concentration Most ionic polymerizations have equilibrium between ion pairs (II or III, depending upon solvent) and free ion (IV). Overview of Ionic Polymerization Ion-pair Binding
  • 109. • Reactions are fast but are extremely sensitive to small amounts of impurities. Highly polar solvents (water, alcohols, ketones) will react with and destroy or inactivate the initiator. Moreover, heterogeneous initiators are used making the nature of the reaction medium unclear and determination of the mechanism difficult. • Termination by neutralization of the carbo-cation (carbonium ion, carbenium ion) occurs by several processes for cationic polymerization, but termination is absent for anionic polymerization. Overview of Ionic Chain Polymerization: Mechanistic Analysis
  • 110. Initiation of Cationic Chain Polymerization: Protonic Acids HBr, HI HA + (CH 3 ) 2 C=CH 2 -> (CH 3 ) 3 C + (A - ) Lewis Acids AlCl 3 , BF 3 , SnCl 4 A co-initiator (water, protonic acids, alkyl halides) is needed to activate the Lewis acid. BF 3 + H 2 O -> BF 3 -OH 2 BF 3 -OH 2 + (CH 3 ) 2 =CH 2 -> (CH 3 ) 2 C + (BF 3 OH ) -
  • 111. Cationic Chain Propagation: Monomer Structure Substituents must be able to stabilize a formal positive charge. For olefins, tertiary > secondary > primary due to inductive effect. For styrenic monomers: CH2=CH R Monomer kp, liter/mole sec R = Cl 0.0012 R = H 0.0037 R = CH3 0.095 R = OCH3 6 Steric effects dominate for ortho substitution in styrene, and all substituents reduce kp irrespective of inductive effects. Substituents must be able to stabilize a formal positive charge. For olefins, tertiary > secondary > primary due to inductive effect. For styrenic monomers: Monomer kp, liter/mole sec R = Cl 0.0012 R = H 0.0037 R = CH3 0.095 R = OCH3 6 Steric effects dominate for ortho substitution in styrene, and all substituents reduce kp irrespective of inductive effects. Cationic Chain Propagation: Monomer Structure
  • 112. Cationic initiators: Proton acids with unreactive counterions Lewis acid + other reactive compound With Lewis acid initiator one must need a co-initiator, a protogen: a cationogen: or
  • 113. Common steps of cationic polymerization: (i, ii) initiation, propagation The mechanism of cationic polymerization is a kind of repetitive alkylation reaction. Electron donating groups are needed as the R groups because these can stabilize the propagating species by resonance. Examples: Propagation is usually very fast. Therefore, cationic vinyl polymerizations must often be run at low temperatures. Unfortunately, cooling large reactors is difficult and expensive. Also, the reaction can be inhibited by water if present in more than trace amounts, so careful drying of ingredients is necessary (another expense ).
  • 114. Lewis acids form active catalyst-co-catalyst complexes with proton donors
  • 115. Regiochemistry of propagation Markownikov addition – form the most stable carbocation: Electron-donating groups R stabilize a cation and affect regiochemistry by directing the incoming group E to an opposite side to the donating group. R = Alkyl, Aryl, Halide, OR
  • 116. Common steps of cationic polymerization: (iii) termination by unimolecular rearrangment of the ion pair A B
  • 117. Common steps of cationic polymerization: (iv) chain transfer to monomer Cationic vinyl polymerization can be stopped also by numerous side reactions, most of which lead to chain transfer. It is difficult to achieve high MW because each initiator can give rise to many separate chains because of chain transfer. These side reactions can be minimized but not eliminated by running the reaction at low temperature .
  • 118. Common steps of cationic polymerization: (iv) chain transfer to polymer backbiting: hydraide transfer:
  • 119. • Initiation • Propagation • Termination  i = k i c [ M ] I + A ─ + M  IM + A ─ IM 1 + A ─ + M  IM 2 + A ─ … IM n + A ─  IM n + H + A ─  t = k t [ M + ] General kinetic scheme for cationic polymerisation IM n + A ─ + M  IM n+1 + A ─  p = k p [ M + ][ M ]
  • 120. General kinetic scheme for cationic polymerisation (continuation ) Steady-state approximation:  i =  t k i c [ M ] = k t [ M + ] [ M + ] = k i c [ M ]/ k t  p = k p [ M + ][ M ] = ( k p k i / k t ) c [ M ] 2 X n = v p / v t = ( k p / k t ) [ M ]
  • 121. Common steps of anionic polymerization: (i, ii) initiation, propagation The mechanism of anionic polymerization is a kind of repetitive conjugate addition reaction (the &quot;Michael reaction&quot; in organic chemistry). Electron withdrawing groups (ester, cyano) or groups with double bonds (phenyl, vinyl) are needed as the R groups because these can stabilize the propagating species by resonance. Examples:
  • 122. Anionic initiators: For initiation to be successful, the free energy of the initiation step must be favorable. Therefore, it is necessary to match the monomer with the appropriate strength of initiator so that the first addition is &quot;downhill.&quot; If the propagating anion is not very strongly stabilized, a powerful nucleophile is required as initiator. On the other hand, if the propagating anion is strongly stabilized, a rather weak nucleophile will be successful as initiator. (Of course, more powerful ones would work, too, in the latter case.) But two EWGs are so effective in stabilizing anions that even water can initiate cyanoacrylate (&quot;Super Glue&quot;). Weak bases (such as those on the proteins in skin) work even better.
  • 123. Anionic initiators (continuation): There is one other category of initiator, known as electron transfer , that works best with styrene and related monomers. The actual initiating species is derived from an alkalai metal like sodium. An aromatic compound is required to catalyze the process by accepting an electron from sodium to form a radical anion salt with Na + counterion. A polar solvent is required to stabilize this complex salt. The electron is subsequently transferred to the monomer to create a new radical anion which quickly dimerizes by free radical combination (similar to the termination reaction in free radical polymerization). The eventual result is a dianion , with reactive groups at either end. Propagation then occurs from the middle outwards. This system is especially useful for producing ABA block copolymers, which have important technological uses as thermoplastic elastomers.
  • 124. Common steps of anionic polymerization: (iii) chain transfer Acrylates have problems in anionic propagation because of chain transfer to polymer. The hydrogen atoms adjacent to the ester groups are slightly acidic, and can be pulled off by the propagating anion. The new anion thus created can reinitiate, leading to branched polymers. This side reaction is difficult to suppress.
  • 125. Common steps of anionic polymerization: (iv) termination (continuation) When carried out under the appropriate conditions, termination reactions do not occur in anionic polymerization . One usually adds purposefully a compound such as water or alcohol to terminate the process. The new anionic species is too weak to reinitiate. The &quot;Dark Side:&quot; Compounds such as water, alcohols, molecular oxygen, carbon dioxide, etc. react very quickly with the carbanions at the chain ends, terminating the propagation. Therefore, one must scrupulously dry and deaerate the polymerization ingredients to be able to get a truly living system. This is not easy to do, and adds to the potential costs of the process.
  • 126. Functionalization of the chain ends in anionic polymerization The beauty of anionic polymerization lies in the lack of termination reactions when carried out under the appropriate conditions ( living polymerization ). This means that the propagating species remains unchanged at the chain end when the monomer is consumed, so subsequent chemical reactions can be carried out. (The chain end is a carbanion, and the organic chemistry of carbanions is diverse.) Here are a few examples among many possible: Carboxylation of end groups: Alcohol end groups via ethylene oxide: Coupling agents:
  • 127. Living anionic polymerization
    • Chains are initiated all at once (fast initiation)
    • Little or no termination (except purposeful).
    • Little or no depolymerization.
    • All chains grow under identical conditions.
    The usual circumstances: The result is that the monomers get divided evenly among chains.
    • Narrow MW distribution (PD approaches 1.0, typically 1.05 - 1.2).
    • The MW is predictable (unlike other polymerizations).
    For monofunctional initiators, the chain length is simply x = [monomer] / [initiator]. For difunctional initiators (electron transfer), the chain length is twice as large.
  • 128. B: + CH 2 =CHR -> BCH 2 C: - HR carbanion • The strength of the base depends upon monomer reactivity. • Monomers with strongly electron-withdrawing substituents require relatively weak bases (low pKa). • Ability of substituents to stabilize carbanions decreases as: -NO 2 > -C=O > -SO 2 > -CO 2 ~ -CN > -SO > Ph ~ -CH=CH 2 >>> -CH 3 Anionic Initiation: Direct Attack by Base
  • 129. Types of Base Initiators: • Base Initiators are often organometallic compounds or salt of a strong base, such as an alkali metal alkoxide. Examples: • Potassium with liquid ammonia. • Stable alkali metal complexes may be formed with aromatic compounds (e.g. Na/naphthalene) in ether. • Sodium metal in tetrahydrofuran.
  • 130. M• + CH 2 =CHR -> [CH 2 =/•CHR] - M + monomer radical anion 2[CH 2 =/•CHR] - M + -> M +- RHCCH 2 CH 2 CHR -+ M dianion The dianion allows propagation from both ends of the initiator. Highly reactive radical anions usually dimerize . Anionic Initiation: Direct Electron Transfer from Alkali Metal
  • 131. M• + A: -> A:• -M+ A:•-M+ + CH 2 =CHR -> [CH 2 =/•CHR] - M + + A: Monomer radical anion • Stable alkali metal complexes may be formed with aromatic compounds (e.g. Na/naphthalene) in ether. • Rapid dimerization often occurs due to high free radical concentration: 2[CH 2 =/•CHR] - Na + -> Na +- RHCCH2CH2CHR -+ Na Propagation from both ends! dianion Anionic Initiation: Transfer of an Electron to an Intermediate
  • 132.
    • For R i >> R p , all chains start at almost the same time.
    • If there is no chain transfer and no termination, chains will have equal lifetimes and grow to about the same size.
    • [M] = monomer concentration
    • [C] = aromatic complex concentration
    • To obtain instantaneous initiation, the electron affinity of the monomer must be much greater than that of the aromatic compound.
    Anionic Initiation: Transfer of an Electron to an Intermediate
  • 133. Initiation could be instantaneous, of comparable rate, or much slower than propagation. If termination is absent, Termination By impurities and transfer agents: • Oxygen and carbon dioxide can react with propagating anions, and water will terminate the chain by proton transfer. Thus, the reactions must be carried out under high vacuum or in an inert atmosphere. By nucleophilic attack of initiator on polar monomer • Polar monomers such as methyl methacrylate, methyl vinyl ketone, and acrylonitrile have substituents that will react with nucleophiles. These side reactions broaden the molecular weight distribution. To minimize the effect, use a less nucleophilic initiator, lower reaction temperatures, and more polar solvents. Mechanism of Base Initiation: Relative Initiator Activity
  • 134. Solvent Dielectric Constant k p (liter/mole sec) Benzene 2.2 2 Dioxane 2.2 5 Tetrahydrofuran 7.6 550 1,2-Dimethoxyethane 5.5 3,800 • As the dielectric constant increases, the solvating power of the reaction medium increases and there is an increased fraction of free ions (which are highly reactive). Effect of Reaction Medium: Solvent
  • 135. The separation between the counterion and the carbanion end group on the polymer is the major factor determining the rate, equilibrium, and stereochemistry. Counterion k p , liter/mole sec in tetrahydrofuran in dioxane Cation size Li+ 160 0.94 Na+ 80 3.4 K+ 60-80 19.8 Rb+ 50-80 21.5 Cs+ 22 24.5 Free anion 65,000! Tetrahydrofuran is a good solvating solvent (ε = 7.4) Dioxane is a poor solvating solvent (ε = 2.2) Effect of Reaction Medium: Counterion
  • 136. Reaction Set Initiation: GA -> G + + A - G + + A - + M -> G + + AM - Note that the nature of the solvent will determine whether the propagating anion behaves as a free ion, AM-, as a loose or tight ion pair, AM - G + , or both. We will assume free ions for this treatment. Propagation: AM - + M -> AMM - AMM - + M -> AM 2 M - AM n-1 M - + M -> AM n M - Termination: There is no termination step in the absence of impurities. Kinetics of Anionic Polymerization :
  • 137. [A-] = total concentration of anions of all lengths =[GA]o = concentration of initiator before dissociation Integrate to obtain: Rate of Polymerization
  • 138. Solid-State Properties
  • 139. POLYMERS IN THE SOLID STATE Semi-crystalline Amorphous Glassy Rubbery Questions: Relationship to microstructure Relationship of structure to properties
  • 140.
    • The glass transition, Tg, is temp. below which a polymer OR glass is brittle or glass-like; above that temperature the material is more plastic.
    • The Tg to a first approximation is a measure of the strength of the secondary bonds between chains in a polymer; the stronger the secondary bonds; the higher the glass transition temperature.
    • Polyethylene Tg = 0°C; Polystyrene = 97 °C
    • PMMA (plexiglass) = 105 °C.
    • Since room temp. is < Tg for PMMA, it is brittle at room temp.
    • For rubber bands; Tg = - 73°C…. So to make rubber brittle
    • you need to cool it. Had the Challenger taken off on a warm day the disaster may never have happened!
    Glass Transition Temperature
  • 141.
    • Determination of the glass transition temperature:
    • Dynamic Mechanical tests: E', E&quot;, Tan 
    • Torsion pendulum
    • Tensile or flexural vibration vs T,
    • Torsional braid
    • Dilatometry,
    • DSC,
    • Dielectric loss,
    • Bouncing ball
    •  
  • 142. Glass Transition Temp.
    • Breakdown of Van Der Waals Forces
    • Onset of large scale molecular motions
    • Polymer goes from Glassy/Rigid to rubbery behavior
    • Upper service temperature in amorphous polymers
    Molecular Factors and Tg
    • Free Volume
    • Backbone Stiffness
    • Steric effects (side groups)
    • Network structure (thermosets)
    • Anything which makes movement more difficult will increase Tg
  • 143.  
  • 144.  
  • 145.  
  • 146.  
  • 147.  
  • 148.  
  • 149.
    • Crystallization in linear polymers involves the folding back and forth
    • of the long chains upon themselves to achieve a very regular arrangement
    • of the mers
    • Crystalline polymers 
    • stereoregular/ linear/ strong dipole-dipole interaction
    • Crystallites 
    • Crystalline and ordered microdomains ; fringed micelle
    • Induction of crystallinity
    • cooling of molten polymer
    • evaporation of polymer solution
    • annealing  heating of polymer at a specific temperature
    • drawing  stretching at a temperature above T g
    Crystallinity
  • 150.
    • Crystalline regions
    • a plateletlike
    • structure (~ 100 Å thick)
    • folded-chain
    • lamella model
    • Extended-chain crystals
    • less common; and often take a needle form
    • usually formed with low MW polymer by slow crystallization or
    • under pressure
    • Nucleation  onset of crystallinity
    • homogeneous nucleation  occur randomly throughout the
    • matrix
    • heterogeneous nucleation  occur at the interface of a foreign
    • impurity (e.g. a finely divided silica)
  • 151. Crystalline morphologies Spherulite  aggregates of small fibrils in a radial pattern ( crystallization under no stress ) Drawn fibrillar  obtained by drawing the spherulitic fibrils Epitaxial  one crystallite grown on another; lamella growth on long fibrils; the so-called shish-kebab morphology ( crystallization under stirring )
  • 152.
    • Crystalline polymers (vs amorphous polymers)
    • tougher, stiffer (due to stronger interactions)
    • higher density, higher solvent resistance (due to closely packing
    • morphology)
    • more opaque (due to light scattering by crystallites)
    • Detection of crystallinity degree 
    • insoluble fraction / density / XRD / thermal analysis / (IR)
  • 153. Factors Influencing Crystallinity
    • Backbone stiffness
    • Backbone symmetry
    • Absence or presence of branches
    • Pendant group size
    • Pendant group polarity
    • Pendant group regularity
    • A number of factors determine the capacity and/or tendency of a polymer
    • to form crystalline regions within the material.
      • As a general rule, only linear polymers can form crystals
      • Stereoregularity of the molecule is critical
      • Copolymers, due to their molecular irregularity, rarely form crystals
      • Slower cooling promotes crystal formation and growth
  • 154. Effect of Crystallization
    • Increased Density
    • Increases Stiffness (modulus)
    • Reduces permeability
    • Increases chemical resistance
    • Reduces toughness
  • 155. Thermal & Mechanical Properties
  • 156. Thermodynamics of T m and T g dG = - SdT + Vdp V T First-order Transition C p T Second order Transition
  • 157. Crystalline vs. Amorphous Phase transitions for long-chain polymers. =>
  • 158. Detect the occurrence of glass transition dilatometry  measure volume increase calorimetry  measure the enthalpy change mechanical measurements  modulus and stiffness
  • 159. Semi-crystalline Amorphous V or H T m V T g
  • 160. Modulus & Temperature
  • 161. Rheology
  • 162.
    • Rheology  the science of deformation and flow
    • To cause a polymer to deform or flow 
    • need a force
    • (a) if the force is withdrawn quickly)
    •  polymer will rebound (a relaxation process)
    • (b) if the force is applied consistently
    •  polymer will flow irreversibly
    • the flowing polymer liquid will be very viscous
    • due to chain entanglement and frictional effects
    • amorphous polymers are viscoelastic materials
    •  combination of elasticity and viscous flow
  • 163. Shear (tangential stress)  the most concerned force type Shear stress (dyne/cm 2 ; newton/m 2 ) F: force (dynes; newtons) A: surface area (cm 2 ; m 2 ) Shear modulus (Resistance to shear) (  : shear strain) (  = G  ) (s -1 ) Shear strain (amount of deformation of one plane with respect to another) Shear rate (velocity gradient)
  • 164. An ideal (or Newtonian) liquid follows Newton’s law of viscosity (i.e. shear stress increases linearly with shear rate)  : viscosity (a measure of resistance to flow) poises (dyne s/cm 2 ) SI system: Pascal-seconds (Pa s = newton s/m 2 ) Viscosity: air (10 -5 Pa s), H 2 O (10 -3 Pa s), glycerin (1 Pa s), molten polymer (10 2 - 10 6 Pa s) Viscosity can be related to temperature by an Arrhenius-type equation A: related to molecular motion E a : activation energy for forming viscous flow
  • 165.
    • E a
    • determined mainly by local chain segmental motion
    • relatively insensitive to MW
    • highly depending on chain structure and branching
    • bulkier chain branch or substituent  higher E a
    • bulkier group  makes viscosity more sensitive to
    • temperature
    • Bingham Newtonian fluid (Eugene Cook Bingham)
     c : critical shear stress; threshold stress
    • Probably caused by some special type of structural arrangement ,
    • arising from conformational and secondary bonding forces
  • 166. Non-Newtonian  shear stress is not linearly proportional to shear rate shear thinning (pseudoplastic)  more common shear thickening (dilatant)  less common shear viscosity at a specified shear rate  (i.e., the slope of a secant drawn from the origin)
  • 167. Increasing shear rate make disentangling faster than reentangling
    • thixotropic liquid 
    • has gel-like properties or a high viscosity under low stress, but
    • thin out on stirring
    • depending on shear time , but not shear rate (different from shear
    • thinning)
    • commercial paints are typical examples
    General expression 
    • for a Newtonian fluid  B = 1 and A =  (  =
    )
    • plot log  vs log
     slope = B; intercept = log A
  • 168. General expression 
    • for a Newtonian fluid  B = 1 and A =  (  =
    )
    • plot log  vs log
     slope = B; intercept = log A
  • 169. MW effect
    •  critical molecular weight for entanglement to begin
    • typical range  4,000 to 15,000
    • typical chain length
     about 600
  • 170. MW distribution effect
    • Chain branching effect
    • lower hydrodynamic volume and lower entanglement
    •  lower viscosity at a given shear rate and MW
    • weaker secondary bonding forces  poorer mechanical properties
    • Polymer conformation (or shape) effect
    • a  0.5 for a random coil ; a  1 for a more rodlike extended shape
    • more rigid polymers are significantly more viscous
  • 171. Determine viscosity of a polymer melt
    • using a cone-plate rotational viscometer
    • shear stress 
    • M: torque; dynes/cm (CGS) or newtons/m (SI)
    • R: cone radius; cm or m
    shear rate  : angular velocity; degrees/s (CGS) or radians/s (SI)  : cone angle; degrees or radians viscosity  (k is a constant defined by viscometer design)
  • 172.
    • Other types of viscometers
    • rotating cylinders immersed in the viscous fluid
    • steel capillaries through which the molten polymer is forced at
    • constant pressure or constant flow