Exploiting Nonlinear Chemical Kinetics in Polymer Systems: a review

Steve Scott School of Chemistry University of Leeds

• Feedback • Consequences of feedback: clocks and oscillations waves and patterns • Feedback in polymer systems • Polymerisation linked to oscillatory systems • Polymerisation as origin of feedback • Frontal polymerisation

Feedback in Chemical Kinetics

• Even for complex reactions can generally measure the concentration

c

of some reactant (or final product) as function of time.

• Define: and

extent of reaction, rate, r

=

d



/dt

 =

c

0 

c

• Construct a

rate vs extent

plot

r

Deceleratory reactions

n = 1 

r

Acceleratory reactions

 Indicative of intermediate species that influence the rate of their own production: cycles in chemical mechanism

Characteristic features of reactions with feedback: 1. Well-stirred reactors • Clock reactions • Oscillations

• Complex oscillations • Chaos

Characteristic features: 2. Waves and patterns

• Reaction + diffusion: • Clocks  wave fronts / flames • Oscillatory systems  wave pulses

spirals Important in biology

Turing Patterns

• Alan Turing, 1952 • “diffusion-driven instability” • Feedback kinetics + reduced diffusivity for feedback species: can cause an initially spatially-uniform state to spontaneously develop to give spatial patterns

Gel disk reactor Ouyang and Swinney 1991,

Chaos

,

1

, 411.

• Importance of gel – prevent convection but also immobilises large molecules • Used to induce “transverse instabilities” in propagating pH fronts • Assumed to be an “inert support” • But …… MBO oscillator: developing interest in intrinsic instabilities in gelling

Patterns from feedback reaction + convection

• differential-flow induced chemical instability DIFICI • requires selective diffusivity but can be

any

species • immobilise one species • flow remaining reactants down tube • above a “critical” flow velocity, distinct “stripes” of oxidation (blue) appear and travel through tube pressure regulator reservoir ion exchange column loaded with ferroin

Experiment



c

f

=

2.1 cm = 0.138 cm s  1

f =

2.8 s frame  1 [BrO 3  ] = 0.8 M [BrMA] = 0.4 M [H 2 SO 4 ] = 0.6 M Rita Toth, Attila Papp (Debrecen), Annette Taylor (Leeds)

Flow Distributed Oscillations (FDO) •patterns without differential diffusion or flow •Very simple reactor configuration: plug-flow tubular reactor fed from CSTR •reaction run under conditions so it is oscillatory in batch, but steady-state in CSTR

Nonlinear Dynamics in Polymer Systems

Pojman (Macromol. Symp. 160, 207, 2000) identifies three strategies for exploiting nonlinear kinetics in polymeric systems • 1. Couple polymeris n to reaction exhibiting oscillations or pattern formation • 2. Exploit intrinsic nonlinearities and feedback in polymer chemistry themselves • 3. Exploit effect of physical changes arising from polymeris n on instabilities –

e.g.

effects of polydispersity

1. Polymerisation coupled to oscillations/pattern formation

• Yoshida

et al.

,

Macromol. Rapd. Comm

.,

16

, 305 (1995) – coupled pH-oscillator to pH-sensitive gels • Yoshida

et al.

,

J. Phys. Chem. A

,

103

, 8573 (1999) – used BZ reaction with redox catalyst incorporated into gel sensitive to its oxidation state

BZ + acrylonitrile

• Vàradi and Beck,

Chem. Comm.

, 30, (1973) showed that acrylonitrile inhibits BZ oscillations.

• Pojman

et al.

(

JACS

,

114

, 8298) showed polymeris n occurs periodically in this system in phase with oscillations due to periodic termination through BrO 2 (Washington et al. 121 , 7373, 1999) • “interesting”, but useful?

Coupling to chemical waves

• Failure to use BZ waves to drive polym n of acrylonitrile • Also, failure to use pH waves • Perhaps, could use enzyme chemistry – suggestion due to Noszticzius (Budapest) to exploit urease: acid-to-alkali front • Can we couple to

patterns

2. Intrinsic nonlinearities

• Isothermal autocatalysis • Thermal feedback • Hysteresis in swelling • Temperature-dependent immiscibility

Isothermal autocatalysis

• “ gel effect ” (Norrish 1942, Trommsdorff, 1948): free radical polym n – viscosity increases with increasing extend of reaction, decreasing termination rates • Copolymerisation with O 2 and an inhibitor leading to production of HO 2 radicals which can cleave and initiate new chains:

e.g.

oscillations in styrene polym n with O 2 and phenols (Kurbatov

et al.

,

Dokl. Akad. Nauk SSSR

,

264

, 1428, 1982).

• Amine-cured epoxy systems : autocatalysis through OH – rate increases with extent (Mijovic & Wijaya,

Macromol.

,

27

, 7589, 1994; Eloundou

et al.

,

Ang. Makrom. Chem.

,

230

, 13, 1995) • RNA replication – can occur as a travelling wave front (Bauer

et al

.,

PNAS

,

86

, 7937 1989; McCaskill and Bauer,

PNAS

,

90

, 4191, 1993: “

images of evolution

”).

Thermal feedback

• Widely studied as classic area in reactor engineering (Harmon Ray) – temperature-dependent viscosity and viscosity-dependent rate coefficient for exothermic reactions.

• Vinyl acetate in lab CSTR (Teymour and Ray,

Chem. Eng. Sci.

,

47

, 4121, 1992) • Industrial-scale copolym n (Keane 1972, T & R,

Chem. Eng. Sci.

,

47

, 4133, 1992)

• Emulsion polymerisation oscillations observed in MMA polym n in a CSTR (Schork and Ray,

J. App. Poly. Sci. (Chem.)

,

34

, 1259, 1987) • Frontal polymerisation (Pojman)

Frontal Polymerisation

• Conversion of monomer to polymer in a localised reaction zone that propagates through reactant solution.

• Typically driven by exothermic reaction coupled to Arrhenius temperature dependence

• Discovered by Chechilo

et al.

(

Dokl. Akad. Nauk SSSR

,

204

, 1180, 1972).

• Review up to 1984 by Davtyan

et al.

(

Russ. Chem. Rev.

,

53

, 150) • Major research effort due to Pojman group (see, for example,

J. Chem. Soc. Faraday Trans.

,

92

, 2825, 1996) who propose this as basis for synthesis of novel materials or materials with novel properties.

Frontal Polymerisation

• Observed in:

neat liquid monomers

(e.g. styrene, TGDMA);

solid monomers with m.p. < “flame” temp.

(e.g. acrylamide)

solvent-based systems

(e.g. acrylamide)

epoxy-resins binary systems

to produce simultaneous interpenetrating polymer networks (SINs)

Advantages

Advantages include: • solvent-free, • shorter reaction times due to high temps evolved, • no external heating required, • can synthesise products that would phase separate under normal conditions

“Problems”

• Bubble formation affects front propagation • Convection naturally arises: leads to many instabilities also seen in pyrotechnic combustion – spinning heads – can also lead to quenching • But …. Instabilities allow “tailored” material properties – gradients in physical properties

Hysteresis in swelling

• Some polymer gels swell significantly as conditions are changed and exhibit hysteresis in permeability if conditions are cycled: (Baker and Siegel,

Macromol. Rapid Comm.

,

17

, 409 (1995).

• Exploited with glucose-driven pH oscillator for periodic drug delivery (Leroux & Siegel,

Chaos

,

9

, 267, 1999).

Temperature-dependent immiscibility

• Tran-Cong & Harada,

Phys. Rev. Lett.

,

76

, 1162, 1996.

3. Effects of Polydispersity

• Diffusion coefficients dependent on polymer chain length.

• Theoretical studies suggest that this may couple with reaction and lead to spatial patterning.