1. Aggregation of long-polymer chains
connecting two parallel
biomembranes
I. Joudar, K. El Hasnaoui, H. Kaïdi
M.Chahid , A. Cherkaoui, M. Benhamou
In this work, we consider two parallel biomembranes connected together by long-polymer chains. Each is
anchored to the membranes by two extremities that are big amphiphile molecules (anchors).
For simplicity, we assume that all connected chains have the same polymerization degree. Under a variation of
some suitable parameter, such as temperature, lateral pressure of ionic forces, the anchors undergo a phase
transition from a dispersed phase (gaz) to a densed one (liquid).The purpose is to determine the phase diagram
architecture, in the temperature-composition plane. To this end, we first compute the free energy of anchors,
from which we deduce the critical phase behavior. Also, we show the role of the excluded volume, the thermal
fluctuations, and all interactions between the two membranes..
The aim is the study of the aggregation of anchors, under a
change of a suitable parameter, such as temperature, lateral
pressure or ionic forces.
;ˆ 0 eχχχχ ++=
6/11
)1()1ln()1(ln Φ+Φ−Φ+Φ−Φ−+Φ
Φ
= C
qTk
F
B
χ
:0χ
:eχ
rdrUtot

∫≈ )(ˆχ
:)(rUtot

Phase diagram
Studied system
Objective
Notation
Perspectives
- Extension of the study to theta solvent- Extension of the study to theta solvent..
- Impurities effets- Impurities effets..
( ) 





Φ−
+
Φ
+Φ++=Φ −
∗
1
11
36
55
2
1 6/1
qq
N
emc χχχ
0,0 0,2 0,4 0,6 0,8 1,0
0
10
20
30
40
Good solvents
Φ
χc