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Colloidal patchy particles with divalent attractive interaction canself-assemble into linear polymer chains. Their equilibrium properties in 2Dand 3D are well described by Wertheim's thermodynamic perturbation theory whichpredicts a well-defined exponentially decaying equilibrium chain lengthdistribution. In experimental realizations, due to gravity, particles sedimentto the bottom of the suspension forming a monolayer of particles with agravitational height smaller than the particle diameter. In accordance withexperiments, an anomalously high monomer concentration is observed insimulations which is not well understood. To account for this observation, weinterpret the polymerization as taking place in a highly confined quasi-2Dplane and extend the Wertheim thermodynamic perturbation theory by definingaddition reactions constants as functions of the chain length. We derive thetheory, test it on simple square well potentials, and apply it to theexperimental case of synthetic colloidal patchy particles immersed in a binaryliquid mixture that are described by an accurate effective critical Casimirpatchy particle potential. The important interaction parameters entering thetheory are explicitly computed using the integral method in combination withMonte Carlo sampling. Without any adjustable parameter, the predictions of thechain length distribution are in excellent agreement with explicit simulationsof self-assembling particles. We discuss generality of the approach, and itsapplication range.

Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement