This document summarizes a study on the structure and thermodynamics of colloid solutions interacting through Yukawa or Lu-Marlow potentials. The researchers used an expression described by Lu and Marlow that accounts for finite particle size. They calculated structure factors using a variational method based on the Gibbs-Bogoliubov inequality. The theoretical structure factors obtained were found to be in good agreement with experimental data, justifying the interest in the Lu-Marlow potential. They also used a reference system of hard spheres and the variational method to estimate thermodynamic properties of the colloid solutions.
This document discusses computer simulations of the structure and thermodynamics of colloidal solutions interacting through Yukawa or Lu-Marlow potentials. It presents:
1) A new attractive potential proposed by Lu and Marlow that takes into account particle size and is proportional to the inverse sixth power of distance for large separations.
2) Use of this potential and a repulsive electrostatic potential in a variational method to calculate theoretical structure factors, finding good agreement with experimental data.
3) Choice of hard spheres as a reference system and use of the Gibbs-Bogoliubov inequality to obtain an upper bound for the free energy of the colloidal system.
This document summarizes a study of the phase diagram of colloids immersed in a binary liquid mixture near the mixture's consolute point. The study uses the random phase approximation with hard spheres as a reference system to model the interactions. It finds that the phase diagram is governed by three parameters: the colloid packing fraction, the temperature shift from the consolute point, and the attraction energy between colloids. Key results include determining the critical point coordinates analytically, finding that the spinodal curve is universal, and deriving parametric equations for the coexistence curve to obtain the complete phase diagram.
This document summarizes a numerical study of the structure and thermodynamics of colloidal suspensions using the variational method and integral equation theory. The interactions between colloid particles are modeled using either a Yukawa or Sogami potential. Results from the integral equation theory using a Sogami potential are found to be in good agreement with Monte Carlo simulation results and experimental data. The variational method and integral equation theory are used to calculate structural properties like the pair correlation function and thermodynamic properties.
This document describes a study using integral equation theory and Monte Carlo simulation to determine the structure and thermodynamics of a colloidal solution where particles interact via Yukawa or Sogami potentials. The authors use the hybridized mean spherical approximation within the integral equation theory to calculate properties like the pair correlation function, structure factor, internal energy and pressure. They find good quantitative agreement between results from integral equation theory using a Sogami potential and results from Monte Carlo simulation. The theoretical results are also compared to experimental data and show agreement when using a Sogami potential.
This document summarizes a study analyzing the lateral phase separation between phospholipids and adhesion macromolecules on two adhering membranes. The key findings are:
1) Adhesion macromolecules are modeled as long, flexible polymer chains anchored by their ends to anchors on the inner monolayers of two adjacent plasma membranes.
2) A field theory is developed to derive an expression for the mixing free energy of the phospholipid-anchor mixture on the membranes.
3) The phase diagram in the composition-temperature plane is extracted from the free energy expression. The phase separation is influenced by polymer chain length, solvent quality, and undulations between the coupled membranes.
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.
This document discusses two parallel biomembranes connected by long-polymer chains. Each chain is anchored to the biomembranes by amphiphile molecules at both ends. As temperature or other parameters change, the anchors undergo a phase transition from dispersed to condensed. The goal is to determine the phase diagram in the temperature-composition plane by computing the free energy of the anchors and deducing critical phase behavior. The role of excluded volume, thermal fluctuations, and interactions between membranes is also examined.
This document summarizes a study on the phase separation between phospholipids and grafted polymer chains on a biomembrane. The researchers developed a theoretical model to determine the mixing free energy expression and extract the phase diagram in the composition-temperature plane. They found that the condensation of polymer chains is very sensitive to solvent quality and the polydispersity of the anchored chains. The structure factor was also computed, showing behavior at small distances and defining the correlation length. Future work could extend this study to charged systems and membranes with dynamics and multiple layers.
This document summarizes two workshops on soft condensed matter physics and biological systems held from April 28-30, 2010 in Fez, Morocco. It discusses polymeric fractals confined within tubular vesicles and between two parallel membranes. For polymers within tubular vesicles, the standard Flory theory is extended to relate the polymer's parallel extension to characteristics of the polymer and vesicle. For polymers between membranes, the behavior combines critical phenomena of polymer mass limit and membrane unbinding transition, with the parallel radius decreasing as unbinding occurs. The aim is to study conformations of arbitrarily topologically polymers under these two confinement conditions.
- The document discusses the confinement of polymeric fractals between two parallel fluid membranes. It presents the theoretical framework, including Flory theory and Helfrich theory, for describing the interaction and conformations of polymers and membranes.
- The key results are expressions showing that a polymer can only be confined when its size is much larger than the membrane separation, and that the polymer conformation depends critically on temperature as the membranes approach their unbinding transition.
- The polymer parallel extension is found to combine aspects of fractal polymer scaling and membrane critical behavior, becoming smaller as the membranes separate at the phase transition.
This document summarizes a study examining the Casimir force between two parallel plates confining a biomembrane. The researchers first develop a field theory model to describe the interactions of the confined biomembrane, which depends on the bending rigidity of the membrane and an elastic constant related to the plate separation. They then use this model to calculate the static and dynamic Casimir forces. They find that the static force decays with plate separation as D-3 and is significant for membranes with low bending rigidity. The dynamic force and membrane roughness are also calculated, finding both increase as power laws of time until equilibrium is reached. Hydrodynamic interactions are shown to increase the growth rates.
This document summarizes a study on the structure and thermodynamics of colloid solutions interacting through Yukawa or Lu-Marlow potentials. The researchers used an expression described by Lu and Marlow that accounts for finite particle size. They calculated structure factors using a variational method based on the Gibbs-Bogoliubov inequality. The theoretical structure factors obtained were found to be in good agreement with experimental data, justifying the interest in the Lu-Marlow potential. They also used a reference system of hard spheres and the variational method to estimate thermodynamic properties of the colloid solutions.
This document discusses computer simulations of the structure and thermodynamics of colloidal solutions interacting through Yukawa or Lu-Marlow potentials. It presents:
1) A new attractive potential proposed by Lu and Marlow that takes into account particle size and is proportional to the inverse sixth power of distance for large separations.
2) Use of this potential and a repulsive electrostatic potential in a variational method to calculate theoretical structure factors, finding good agreement with experimental data.
3) Choice of hard spheres as a reference system and use of the Gibbs-Bogoliubov inequality to obtain an upper bound for the free energy of the colloidal system.
This document summarizes a study of the phase diagram of colloids immersed in a binary liquid mixture near the mixture's consolute point. The study uses the random phase approximation with hard spheres as a reference system to model the interactions. It finds that the phase diagram is governed by three parameters: the colloid packing fraction, the temperature shift from the consolute point, and the attraction energy between colloids. Key results include determining the critical point coordinates analytically, finding that the spinodal curve is universal, and deriving parametric equations for the coexistence curve to obtain the complete phase diagram.
This document summarizes a numerical study of the structure and thermodynamics of colloidal suspensions using the variational method and integral equation theory. The interactions between colloid particles are modeled using either a Yukawa or Sogami potential. Results from the integral equation theory using a Sogami potential are found to be in good agreement with Monte Carlo simulation results and experimental data. The variational method and integral equation theory are used to calculate structural properties like the pair correlation function and thermodynamic properties.
This document describes a study using integral equation theory and Monte Carlo simulation to determine the structure and thermodynamics of a colloidal solution where particles interact via Yukawa or Sogami potentials. The authors use the hybridized mean spherical approximation within the integral equation theory to calculate properties like the pair correlation function, structure factor, internal energy and pressure. They find good quantitative agreement between results from integral equation theory using a Sogami potential and results from Monte Carlo simulation. The theoretical results are also compared to experimental data and show agreement when using a Sogami potential.
This document summarizes a study analyzing the lateral phase separation between phospholipids and adhesion macromolecules on two adhering membranes. The key findings are:
1) Adhesion macromolecules are modeled as long, flexible polymer chains anchored by their ends to anchors on the inner monolayers of two adjacent plasma membranes.
2) A field theory is developed to derive an expression for the mixing free energy of the phospholipid-anchor mixture on the membranes.
3) The phase diagram in the composition-temperature plane is extracted from the free energy expression. The phase separation is influenced by polymer chain length, solvent quality, and undulations between the coupled membranes.
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.
This document discusses two parallel biomembranes connected by long-polymer chains. Each chain is anchored to the biomembranes by amphiphile molecules at both ends. As temperature or other parameters change, the anchors undergo a phase transition from dispersed to condensed. The goal is to determine the phase diagram in the temperature-composition plane by computing the free energy of the anchors and deducing critical phase behavior. The role of excluded volume, thermal fluctuations, and interactions between membranes is also examined.
This document summarizes a study on the phase separation between phospholipids and grafted polymer chains on a biomembrane. The researchers developed a theoretical model to determine the mixing free energy expression and extract the phase diagram in the composition-temperature plane. They found that the condensation of polymer chains is very sensitive to solvent quality and the polydispersity of the anchored chains. The structure factor was also computed, showing behavior at small distances and defining the correlation length. Future work could extend this study to charged systems and membranes with dynamics and multiple layers.
This document summarizes two workshops on soft condensed matter physics and biological systems held from April 28-30, 2010 in Fez, Morocco. It discusses polymeric fractals confined within tubular vesicles and between two parallel membranes. For polymers within tubular vesicles, the standard Flory theory is extended to relate the polymer's parallel extension to characteristics of the polymer and vesicle. For polymers between membranes, the behavior combines critical phenomena of polymer mass limit and membrane unbinding transition, with the parallel radius decreasing as unbinding occurs. The aim is to study conformations of arbitrarily topologically polymers under these two confinement conditions.
- The document discusses the confinement of polymeric fractals between two parallel fluid membranes. It presents the theoretical framework, including Flory theory and Helfrich theory, for describing the interaction and conformations of polymers and membranes.
- The key results are expressions showing that a polymer can only be confined when its size is much larger than the membrane separation, and that the polymer conformation depends critically on temperature as the membranes approach their unbinding transition.
- The polymer parallel extension is found to combine aspects of fractal polymer scaling and membrane critical behavior, becoming smaller as the membranes separate at the phase transition.
This document summarizes a study examining the Casimir force between two parallel plates confining a biomembrane. The researchers first develop a field theory model to describe the interactions of the confined biomembrane, which depends on the bending rigidity of the membrane and an elastic constant related to the plate separation. They then use this model to calculate the static and dynamic Casimir forces. They find that the static force decays with plate separation as D-3 and is significant for membranes with low bending rigidity. The dynamic force and membrane roughness are also calculated, finding both increase as power laws of time until equilibrium is reached. Hydrodynamic interactions are shown to increase the growth rates.
1. UNIVERSITE HASSAN-II MOHAMMEDIAUNIVERSITE HASSAN-II MOHAMMEDIA
--
FACULTE DES SCIENCES BEN M’SIKFACULTE DES SCIENCES BEN M’SIK
--
CASABLANCACASABLANCA
Laboratoire de Physique des Polymères et Phénomènes CritiquesLaboratoire de Physique des Polymères et Phénomènes Critiques
Présentée par EL HASNAOUI KHALIDPrésentée par EL HASNAOUI KHALID
Encadrée par les Professeurs: M. BENHAMOU et M. CHAHIDEncadrée par les Professeurs: M. BENHAMOU et M. CHAHID
2. Introduction
Structure et composition de la membrane plasmique
Les rôles principaux de la membrane
Mobilité des phospholipides dans les Membranes
Etude de toutes les propriétés analytique du potentiel
Conclusions
3. Dans ce travaille nous avons cherché à étudier des propriétés statistique
des membranes biologiques , au contact d’une paroi solide plane pour cette
Raison nous étudions Les propriétés analytiques un potentiel extérieur à un corps
nous choisissons comme potentiel , celui d’Helfrich-Van der Waals , qui est la somme
d’un potentiel répulsif et d’un potentiel attractif ( de type de Van der Waals)
Les Membranes constituent pour les biophysiciens l’élément de base de la paroi
cellulaire qui ont des propriétés physique spéciales comme la souplesse et une gamme
d’échelle spatiales très large
Les fluctuations des membranes sont généralement gouvernées par plusieurs
paramètres , comme le module de courbure intrinsèque de la membrane
qui stabilise les fluctuations à des petites distances et la tension de surface
4. La celluleest la plus petite unité du vivant séparée du milieu
extérieur par une membrane perméable
7. La membrane plasmique c’est une couche à la surface de cellule qui mesure 7,5nm
d’épaisseur .
49 %
Lipides
45,5 %
Protéines
1,6 %
Glucides
Membrane plasmique
100%
8. On observe dans la
membrane :
_ _ _
phospholipides
cholestérol
55 %
25 %
18 %
2%
acides gras
glycolipides
11. Mobilité des phospholipides dans les
Membranes
Facteurs d’influence :
_ Une température élevée augmente la fluidité.
_ La saturation des chaînes carbonées rend la membrane plus rigide.
_ Le cholestérol augmente la fluidité et diminue la congélation.
12. 1-Déterminer la taille et la forme de la cellule
2-Maintenir les différences indispensables entre l’intérieur
de la molécule et le milieu extracellulaire .(filtre sélective)
(régulateur des échanges de matière )
3- Facilite la communication entre les cellule
13.
14.
15.
16. On peut décrire la forme de la surface dans la Présentation du Monge ou la position
d’un point de la membrane est repéré par sa hauteur à un plan
de référence parallèle à la position moyenne de la membrane
Quasi-plane
y)u(x,)ru( =
z0
z0
17. la constante de rigidité
de courbure
le coefficient de tension
interfaciale
Potentiel d’interaction
L’énergie libre décrivant la mécanique Statistique de la Membrane fluctuante
19. 0)( =zW
0
0*
'
'
1
z
A
C
z
z >
−
=
0)(' =zW
Un zéro acceptable
0
3
1
0
)
'
'
(1
z
A
C
z
zm >
−
=
Un seul extremum
La condition :
'' AC <
Pour chercher les zéros:
Pour chercher les extrémums:
23. Perspective : même démarche pourrait être étendue à d’autre formes
du potentiel d’interaction
24. les fluctuations de la membrane sont influencées par des facteurs physique-chimique
comme la température , la pression , l’environnement membranaire
La membrane joue un rôle très important dans la vie de la cellule ,on peut l’appeler
Soit par le filtre sélective ou le régulateur des échanges de matière
de la température => la fluidité => favorise une transition de phase (gel –fluide )
25. UNIVERSITE HASSAN-II MOHAMMEDIAUNIVERSITE HASSAN-II MOHAMMEDIA
--
FACULTE DES SCIENCES BEN M’SIKFACULTE DES SCIENCES BEN M’SIK
--
CASABLANCACASABLANCA
Laboratoire de physique des polymères et phénomènes critiquesLaboratoire de physique des polymères et phénomènes critiques
Fin de l’exposéFin de l’exposé
Merci de votre attentionMerci de votre attention
26.
27.
28.
29.
30.
31.
32.
33.
34. )()()( zUzUzU répatttot +=
)()()( zUzUzU VdWnhydratatiotot +=
δ
Z est la distance entre films de lipides ~7,5 nm
]
)²2(
1
)²(
2
²
1
[
12
)(
δδπ +
+
−
−−=
ZZZ
A
ZUVdW
)exp()(
0Z
Z
AZU hnhydratatio −=
hhlP
PaPh
98
1010 −≈ nmlh 3,02,0 −≈
²
1
')2exp(')(
0 Z
A
Z
Z
CZU −=
²
1
12
)2exp()(
0 Z
A
Z
Z
AzU htot
π
−−=
L’épaisseur d’un film lipidique
Décrit la répulsion des têtes lipidiques
Pour les membranes lipidiques
JA 2120
1010 −−
−≈
43. La hauteur de la barrière :
)1()( 0
2
−==
MM
m
Z
Z
Z
A
zUh
MM ZZsiZU >> 00)( )1()( 0
2
−==
MM
M
Z
Z
Z
A
zUH
mm ZZsiZU << 00)(
La profondeur :
44. 06/14/14
CETTE BICOUCHE LIPIDIQUE CONSTITUE UNE BARRIÈRE DE DIFFUSION AUX IONS ET
AUX MOLÉCULES POLAIRES, LES PROTÉINES SONT RESPONSABLES DES FONCTIONS
DE LA MEMBRANE
Les ions inorganiques (Na+
, K+
, Cl-
, Ca2+
) peuvent traverser la membrane (on dit qu'elle leur est
perméable) tandis que les ions organiques (P-
) ne le peuvent pas (on dit qu'elle leur est imperméable).
Du fait de sa partie centrale hydrophobe, la
bicouche lipidique a une faible
perméabilité aux ions, ainsi qu’aux
protéines polaires, hydrophiles. Leurs
mouvements passifs ne se font qu'au
niveau de protéines transmembranaires
spécialisées, les protéines-canaux.
Les mouvements passifs d'ions à travers la
membrane entraîneraient des changements
dans la composition des milieux intra et
extracellulaires, si des protéines ne
rétablissaient continuellement, par
transport actif, l'inégalité de répartition des
ions entre les deux milieux. Ces protéines
sont des pompes ou des transporteurs.
Ainsi, la membrane plasmique assure
continuellement grâce à ses protéines
une régulation stricte du passage des
ions et des molécules entre les deux
milieux (fonctions dynamiques).