Exploiting Nonlinear Chemical Kinetics in Polymer Systems:

a review

Steve Scott

School of Chemistry

University of Leeds

• Feedback• Consequences of

feedback:clocks and oscillationswaves 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: extent of reaction, = c0 cand rate, r = d /dt

• Construct a rate vs extent plot

Deceleratory reactions

n = 1

r

Acceleratory reactions

r

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

p re ssu rereg u la to r

rese rv o ir

io n -ex ch an g eco lu m nlo a d edw ithfe rro in

Experiment

= 2.1 cm

cf = 0.138 cm s1

f = 2.8 s frame1

[BrO3] = 0.8 M

[BrMA] = 0.4 M

[H2SO4] = 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 Dynamicsin

Polymer Systems

Pojman (Macromol. Symp. 160, 207, 2000) identifies three strategies for exploiting nonlinear kinetics in polymeric systems

• 1. Couple polymerisn 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 polymerisn 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 polymerisn occurs periodically in this system in phase with oscillations due to periodic termination through BrO2 (Washington et al. 121, 7373, 1999)

• “interesting”, but useful?

Coupling to chemical waves

• Failure to use BZ waves to drive polymn 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 polymn – viscosity increases with increasing extend of reaction, decreasing termination rates

• Copolymerisation with O2 and an inhibitor leading to production of HO2 radicals which can cleave and initiate new chains:e.g. oscillations in styrene polymn with O2 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 copolymn (Keane 1972, T & R, Chem. Eng. Sci., 47, 4133, 1992)

• Emulsion polymerisationoscillations observed in MMA polymn 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-resinsbinary 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.