This document studies the effects of polydispersity and solvent quality on the phase separation between phospholipids and anchored polymer chains in a biomembrane. A theoretical model is developed to determine the mixing free energy expression and extract the phase diagram shape in the composition-temperature plane. It is found that the polymer chains condensation is very sensitive to the solvent quality and polydispersity of the anchored chains. The study aims to quantify how these factors influence the segregation phenomenon.

1. I. Joudar, K. El Hasnaoui, H. Kaïdi
H. Ridouane , H. Qamar, M. Benhamou
We reexamine here the study of the phase separation between phospholipids and anchored polymer chains onto a fluid membrane,under a change
of some suitable parameter (temperature). The purpose is to quantify the important e ects of the solvent quality and the polydispersity of theff
grafted chains on the segregation phenomenon. First, we elaborate a theoretical model that allows us the determination of the mixing free energy
expression. From the latter, we extract the phase diagram shape in the composition temperature plane. Second, we compute the structure factor
and discuss the role of the strong fluctuations of composition near the consolute point. The main conclusion is that, the polymer chains
condensation is very sensitive to the solvent quality and polydispersity of the anchored chains.
The aim is the study of the effects of polydispersity and solvent
quality on the phase separation between phospholipids and
anchored polymer chains by more than one points.
Objective
Perspectives
Extension of the study to charged systemsExtension of the study to charged systems
.
Abstract
Biomembrane with anchored polymer chains
Studied system
Notation
:: volume fraction of anchors ;volume fraction of anchors ; :: That of phospholipid moleculesThat of phospholipid molecules..
TT : Absolute temperatureAbsolute temperature..
aa :: area of the phospholipids polar-heads ;area of the phospholipids polar-heads ; AA : that of anchorsthat of anchors..
: Areas ratio;Areas ratio;
Good solvents :Good solvents : Theta solvents :Theta solvents :
Segregation parameter :Segregation parameter :
Free energy
Coefficients a and b :Coefficients a and b : They depend on the chemical details and membraneThey depend on the chemical details and membrane
characteristiccharacteristic
Phase diagram
Spinodal curve :
0,0 0,2 0,4 0,6 0,8 1,0
0
10
20
30
40
Theta solvents
Φ
χ c
.
0,0 0,2 0,4 0,6 0,8 1,0
0
10
20
30
40
Good solvents
Φ
χ c
Second International Workshop On Soft Condensed Matter Physics and Biological Systems 28 – 30 April 2010, nationalSecond International Workshop On Soft Condensed Matter Physics and Biological Systems 28 – 30 April 2010, national
Fez, MoroccoFez, Morocco
Laboratoire de Physique des Polymères et Phénomènes Critiques
Faculté des Sciences Ben M’sik, P.O. Box 7955, Casablanca, Morocco
Dynamic studyDynamic study
Extension to more than membraneExtension to more than membrane
Structure factor
Definition :Definition :
Small distances behavior :Small distances behavior :
Correlation length :Correlation length :Integration constant :Integration constant :
Partenariats
( ) 





Φ−+
Φ−
+
Φ
=Φ −2
)()1(
1
11
2
1 β
ββχ qu
q
c
β
χ Φ+Φ−Φ+Φ−Φ−+Φ
Φ
= )()1()1ln()1(ln qu
qTk
F
B
)()0()()0()(;)()( 2
rrrGerGrdqS iqr
ϕϕϕϕ −== ∫
tq
q
E
q
E
qS ξη
<<=≈ −
−
1
4/72
;)(
Φ−1Φ
q
Aq =
T
b
a +=χ
6
11=β 2=β
E Tξ
02
2
=
Φ∂
∂ F