chemart / mechanical-self-assembly

hub:
  repo_type: generator
  builtin: mechanical-self-assembly
  tags:
  - banzhaf-yamamoto
chemistries:
- id: mechanical-self-assembly
  name: Mechanical self-assembly (Hosokawa)
  intuition: 'Proof that chemical kinetics does not need chemicals. Plastic triangles with magnets in
    two faces are shaken in a dish; they stick into dimers, trimers and larger assemblies, and the yields
    over time fit an ordinary mass-action reaction network. The instructive detail is where the rate constant
    comes from: it factorises into how often two pieces collide and the probability they are correctly
    oriented when they do - an encounter term times a geometric term.

    '
  origin: Hosokawa, Shimoyama & Miura, 1994
  book: '20.1'
  refs:
  - '[404]'
  - '[352]'
  - '[918]'
  - '[919]'
  - '[69]'
  family: non-chemical
  kind: generator
  constructive: false
  S:
    repr: triangular plastic bodies with permanent magnets in two of three faces; x = monomer, x2..x6
      = assemblies
    definition: explicit
  R:
    definition: explicit
    arity: 2
    scheme: 'x+x -> x2 ; x+x2 -> x3 ; x+x3 -> x4 ; x+x4 -> x5 ; x+x5 -> x6 ; x2+x2 -> x4 ; x2+x3 -> x5
      ; x2+x4 -> x6 ; x3+x3 -> x6

      '
  A:
    reactor: ode
    dilution: none
    notes: x(t+1) = x(t) + F(x(t)); F factorises into a collision probability P_c (mass-action-like, from
      concentration) and a bonding probability P_b (from the GEOMETRY of the encounter)
  params:
  - name: n_monomers
    type: int
    default: 100
    min: 1
    role: population
    meaning: initial number of monomers x (book figure 20.3a)
  - name: agitation_rate
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: collision frequency; rate = agitation_rate * P_b
  - name: P_b
    type: dict
    default: {}
    role: kinetic
    meaning: bonding probability per pair, keyed 'x+x2' etc.; pairs not listed use 1.0
  provides:
  - topology
  - stoichiometry
  - rate-constants
  - mass-conservation
  - initial-state
  fidelity: book+decisions
  decisions:
  - The book gives no numerical bonding probabilities ('under reasonable assumptions'); every P_b defaults
    to 1 and can be overridden per pair.
  - The book's discrete-time update is represented by mass-action rates k = agitation_rate * P_b. extras.conservation
    records the monomer count (x=1 ... x6=6).
  phenomena:
  - simulated from 100 monomers, the intermediates x4 and x5 stabilise together with the final product
    x6 (book fig. 20.3a)
  - model and experiment agree roughly in the x3-x6 plane; the book notes the statistics did not allow
    a more accurate comparison (fig. 20.3b)
  notes: 'Proof that chemical kinetics is substrate-independent, and the cleanest example of a rate coefficient
    that FACTORISES into an encounter term and a geometric orientation term.

    '