slimmc

A Monte Carlo simulation program of radical polymerization kinetics

slimmc — model file syntax

slimmc runs a kinetic Monte Carlo (kMC) simulation of free‑radical polymerization. It reads a plain‑text model file that defines the kinetic parameters and initial concentrations, and schedules breakpoints — points in simulated time at which commands run (write output, change a concentration, print a message).

A model file is just a sequence of lines. Every non‑blank, non‑comment line is one of three things: a parameter assignment, a list directive, or a breakpoint. Lines are processed independently, so their order is free — with one requirement: at least one breakpoint must be defined, otherwise slimmc aborts.

---

Lexical rules

• Comment — a line whose first character is #. It must be in column 0; an indented # is not treated as a comment.
• Blank lines are ignored.
• Numbers are floating point; scientific notation is accepted (1e-4, 5.0e-15, -2.1, 3500).
• Time is in seconds; concentrations in mol/L.

---

The implemented kinetic model

The parameters below describe this reaction scheme:

I            ->  2 R•        kd , efficiency f      (initiator decomposition)
R• +  M      ->    P•        ki                     (initiation)
P• +  M      ->    P•        kp                     (propagation)
P•           ->    P• + M    kdp                    (depropagation)
P• +  P•     ->    D         ktc                    (termination by combination)
P• +  P•     ->    D + D     ktd                    (termination by disproportionation)

Species symbols used throughout (parameters, dc, output files):

symbol	meaning
I	initiator
Rx	primary radical (R•)
M	monomer

---

Parameters

Syntax: name = value (whitespace around = optional). Unknown names abort with an error. Any parameter left out keeps its default.

name	meaning	unit	default
kd	initiator decomposition rate constant	1/s	0.0
f	initiator efficiency	—	0.0
ki	initiation rate constant	L/(mol·s)	0.0
kp	propagation rate constant	L/(mol·s)	0.0
kdp	depropagation rate constant	L/(mol·s)	0.0
ktc	termination by combination	L/(mol·s)	0.0
ktd	termination by disproportionation	L/(mol·s)	0.0
cI0	initial initiator concentration	mol/L	0.0
cM0	initial monomer concentration	mol/L	0.0
cRx0	initial primary‑radical concentration	mol/L	0.0
cPx0	initial macroradical concentration	mol/L	0.0
cD0	initial dead‑chain concentration	mol/L	0.0
MwM	monomer molar mass	g/mol	0.0
V_MC	simulation control volume	L	1.0e-17
seed	PRNG seed (0 → seeded from clock)	uint32	0

V_MC sets the number of molecules in the box: n = c · V_MC · N_A. It is chosen so the box holds a workable number of radicals (≈10 at a steady‑state radical concentration of ~1e‑7 mol/L corresponds to V_MC ≈ 1.7e-16 L).

---

list directives

Print diagnostic information. One directive per line:

line	effect
list parameters	print the parsed parameter set
list breakpoints	print the expanded breakpoint schedule
list initialstate	print initial molecule counts (nI, nRx, nM, nPx, nD, total N)

---

Breakpoints

A breakpoint binds a simulated time to a comma‑separated list of commands.

Single breakpoint

<time> : <commands>

Loop (a series of breakpoints)

<t0> : <dt> : <N> : <commands>

generates N + 1 breakpoints at t0 + i·dt for i = 0, 1, … , N, each carrying the same command list. Example: 0:100:10:conc produces breakpoints at 0, 100, 200, … , 1000 (eleven points).

If two breakpoints land on the same time, their command lists are merged.

Commands are separated by commas. A comma inside a single‑quoted print string is literal, not a separator:

3000000:print 'final dump, including a comma', conc, poly

---

Commands

command	action
conc	write current concentrations of all species to files (see below)
poly	compute and write the chain‑length / molecular‑weight distributions
dc <S> <v>	change (inc/dec) concentration of species S (I/M/Rx) by v mol/L (v may be negative); used for semi‑batch feeding
print	print a progress line: t=… (step/total) elapsed‑seconds
print progress	same as bare print
print '<text>'	print the literal single‑quoted text

---

Output files

conc appends one row per breakpoint to five files — one per species — cI.txt, cRx.txt, cM.txt, cPx.txt, cD.txt. Each row is tab‑separated:

step    time(s)    concentration(mol/L)    molecule_count

poly overwrites four files per call, with the breakpoint time encoded in the filename (P = living chains, D = dead chains):

• P.<time>.cld.txt, D.<time>.cld.txt — chain‑length distribution; a #nChains: <count> header line, then DP <tab> count for each populated degree of polymerization.
• P.<time>.HlogM.txt, D.<time>.HlogM.txt — the GPC‑style w(log M) trace; log10(M) <tab> dw, where dw ∝ n · M² (here n · DP² · MwM²) and M = DP · MwM.

---

Complete example

plp.model:

# A description of a PLP experiment simulation.
# For comparison see: M. Buback, M. Busch, R. A. L¨ammel,
# Modeling of molecular weight distribution in pulsed laser free-radical homopolymerizations,
# Macromol. Theory Simulations 1996, 5, 845 Fig. 1.


# Initiation, propagation, termination rate coefficients
ki   = 4800
kp   = 480
ktc  = 1.25e7
ktd  = 1.25e7

# Initial monomer conc
cM0  = 9.4
# Mol weight of the monomer
MwM  = 100.12

# Total volume of the simulated system
V_MC = 5.0e-12

list parameters
list initialstate
list breakpoints


# PLP
0.0:0.1:10:dc Rx 5e-7, conc, print '...*'
1.1:dc Rx 5e-7, poly, conc

# Progress info
0:0.01:100:print

Run it with:

slimmc plp.model

To see the resulting MWD:

gnuplot -e "set xrange [3.5:6]; plot 'D.1.100000000000e+00.HlogM.txt' u 1:2 w l; pause -1"