Self‐avoiding walks in 2‐d and 3‐d lattices are implemented as models of polymer propagation in confined media like vesicle bilayers and micelles. Simulations conducted on such microreactors of various sizes (total number of monomers Ntot between 80 and 106) and shapes show that the propagation rate essentially depends on the ratio of the degree of polymerization (D.P.) and Ntot. A scaling function is proposed giving excellent agreement with the simulations: it features a decrease of the rate of propagation arising from a direct boundary effect, related to the contact between the radical and the impermeable boundaries of the lattice, and from an exponential factor, accounting for the confinement effect. Taking into account this rate dependence on the D.P., length and mass distributions are shown to be increasing functions of the D.P. when the rate of termination (by transfer) is small enough. In this limit, these distributions present a sharp increase in the vicinity of a D.P. about Ntot. This accumulation of polymers at a D.P. close to Ntot entails a significant decrease of the polydispersity.

1.
H.
Bader
,
K.
Dorn
,
B.
Hupfer
, and
H.
Ringsdorf
,
Adv. Polym. Sci.
64
,
1
(
1985
).
2.
H.
Ringsdorf
,
B.
Schlarb
, and
J.
Venzmer
,
Angew. Chem.
27
,
113
(
1988
).
3.
A. Malliaris and C. M. Paleos, Surfactants in Solution, Symposium Series, Vol. 9, edited by K. L. Mittal (Plenum, New York, 1989), pp. 119–132.
4.
W.
Reed
,
L.
Guterman
,
P.
Tundo
, and
J. H.
Fendler
,
J. Am. Chem. Soc.
106
,
1897
(
1984
);
J.
Serrano
,
S.
Mucino
,
S.
Millan
,
R.
Reynoso
,
L. A.
Fucugauchi
,
W.
Reed
,
F.
Nome
,
P.
Tundo
, and
J. H.
Fendler
,
Macromolecules
18
,
1999
(
1985
).
5.
S. I.
Stupp
,
S.
Son
,
H. C.
Lin
, and
L. S.
Li
,
Science
259
,
59
(
1993
).
6.
A.
Provata
,
J. W.
Turner
, and
G.
Nicolis
,
J. Stat. Phys.
70
,
1195
(
1993
).
7.
P. G. de Gennes, Scaling Concept in Polymer Physics (Cornell University, Ithaca 1979).
8.
J. Descloizeaux and G. Jannink, Polymers in Solution, their Modelling & Structures (Clarendon, Oxford, 1990).
9.
D. S.
MacKenzie
,
Phys. Rep.
27c
,
36
(
1976
).
10.
B.
Duplantier
and
F.
Douis
,
J. Stat. Phys.
51
,
327
(
1988
).
11.
S.
Bluestone
and
M. J.
Vold
,
J. Chem. Phys.
42
,
4175
(
1965
).
12.
W. F.
Reed
,
Macromolecules
18
,
2402
(
1985
).
13.
S. Windwer, Markov Chain & Monte Carlo Calculations in Polymer Science, Monograph in Macromol. Chem., edited by G. G. Lowry (Dekker, New York, 1970), pp. 125–152;
J. M.
Hammersley
and
K. W.
Morton
,
J. R. Stat. Soc. B
16
,
23
(
1954
).
14.
E.
Tsuchida
,
E.
Hasegawa
,
N.
Kimura
,
M.
Hatashita
, and
C.
Makino
,
Macromolecules
25
,
207
(
1992
).
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