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Fakrach B.,Moulay Ismaï University | Rahmani A.,Moulay Ismaï University | Chadli H.,Moulay Ismaï University | Sbai K.,Moulay Ismaï University | And 5 more authors.
Journal of Physics Condensed Matter | Year: 2012

In this work, the infrared active modes are computed for homogeneous bundles of single-walled boron nitride nanotubes (BBNNTs), using the so-called spectral moments method. The dependence of the wavenumber on these modes in terms of diameters, lengths, and numbers of tubes, is investigated. To this end, use is made of a Lennard-Jones potential for describing the van der Waals interactions between tubes in a bundle. We find that, for a finite homogeneous bundle, additional modes appear as a specific signature. Finally, these results are useful for the interpretation of the experimental infrared spectra of BBNNTs. © 2012 IOP Publishing Ltd.


El Fassi S.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Benhamou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Boughou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Kaidi H.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | And 2 more authors.
Acta Physica Polonica A | Year: 2010

We consider a crosslinked polymer blend made of two polymers of different chemical nature. We suppose that such a system incorporates small colloidal particles, which prefer to be attracted by one polymer, close to the spinodal temperature. This is the so-called critical adsorption. As assumption, the particle diameter, d0, is considered to be small enough in comparison with the size of microdomains (mesh size) ξ ~ an 1' 2, with a - the monomer size and n - the number of monomers between consecutive crosslinks. The critical fluctuations of the crosslinked polymer mixture induce a pair-potential between particles located in the non-preferred phase. The purpose is the determination of the Casimir pair-potential, U 2(r), as a function of the interparticle distance r. To achieve calculations, use is made of an extended de Gennes field theory that takes into account the colloid-polymer interactions. Within the framework of this theory, we first show that the pair-particle is attractive. Second, we find for this potential the exact form: U 2(r)/k BT = -A H(d 0/r) 2 exp(-r/ξ) - B H(d0/r) 4 exp(-2r/ξ), with the known universal amplitudes A H > 0 and B H > 0 (the Hamaker constants). This expression clearly shows that the pair-potential differs from its homologue with no crosslinks only by the two exponential factors exp(-r/ξ) and exp(-2r/ξ ). The main conclusion is that the presence of reticulations reduces substantially the Casimir effect in crosslinked polymer blends.


Benhamou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Elhasnaoui K.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Kaidi H.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Chahid M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
Physica A: Statistical Mechanics and its Applications | Year: 2010

We consider a bilayer membrane surrounded by small impurities, assumed to be attractive or repulsive. The purpose is a quantitative study of the effects of these impurities on the statistical properties of the supported membrane. Using the replica trick combined with a variational method, we compute the membrane mean-roughness and the height correlation function for almost-flat membranes, as functions of the primitive elastic constants of the membrane and some parameter that is proportional to the volume fraction of impurities and their interaction strength. As results, the attractive impurities increase the shape fluctuations due to the membrane undulations, while repulsive ones suppress these fluctuations. Second, we compute the equilibrium diameter of (spherical) vesicles surrounded by small random particles starting from the curvature equation. Third, the study is extended to a lamellar phase composed of two parallel fluid membranes, which are separated by a finite distance. This lamellar phase undergoes an unbinding transition. We demonstrate that the attractive impurities increase the unbinding critical temperature, while repulsive ones decrease this temperature. Finally, we say that the presence of small impurities in an aqueous medium may be a mechanism to suppress or to produce an unbinding transition, even the temperature and polarizability of the aqueous medium are fixed, in lamellar phases formed by parallel lipid bilayers. © 2010 Elsevier B.V. All rights reserved.


Benhamou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | El Fazni A.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Bettachy A.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Derouiche A.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
European Physical Journal E | Year: 2010

The aim of this work is a theoretical study of the effects of the solvent quality on the microphase separation in crosslinked polymer blends, from a static and kinetics point of view. More precisely, we assume that the crosslinked mixture is trapped in a θ -solvent. The static microphase properties are studied through the static structure factor. The latter is computed using an extended blob model, where the crosslinked unlike chains can be viewed as sequences of blobs. We demonstrate that the presence of the θ -solvent simply leads to a multiplicative renormalization of these properties, and the renormalization factors are powers of the overall monomer volume fraction. Second, we investigate the early kinetics of the microphase separation, via the relaxation rate, τ q, which is a function of the wave number q (at fixed temperature and monomer volume fraction). We first show that the kinetics is entirely controlled by local motions of Rouse type, since the slow motions are frozen out by the presence of crosslinks. Using the blob model, we find an explicit form for the growth rate Ω (q) = τ q -1, which depends, in addition to the wave number q, on the overall monomer volume fraction, Φ . Also, we discuss the effect of initial entanglements that are trapped when the system is crosslinked. In fact, these play the role of true reticulation points, and then, they quantitatively contribute to the microseparation phenomenon. Finally, the results are compared to their homologous relatively to the molten state and to the good solvent case. The main conclusion is that the quality of the solvent induces drastic changes of the microphase properties. © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.


Benhamou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
The European physical journal. E, Soft matter | Year: 2011

We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties.


Benhamou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Derouiche A.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Bettachy A.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Elhajjaji F.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
European Physical Journal E | Year: 2011

We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.


Benhamou M.,Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques | Benhamou M.,Moulay Ismaï University
European Physical Journal E | Year: 2011

Consider a fluid membrane decorated by moving hard or soft inclusions. The aim of this work is a quantitative study of the influence of thermal fluctuations on the three-dimensional primitive forces between these inclusions. Integrating over all membrane fluctuations, we obtain a general form giving the modified primitive interactions upon the transverse distance. The established formalism enables us to obtain the modified expression of some standard interaction potentials. In particular, for power-like potentials, we found a modified expression featuring the Whittaker function. The present formalism may be extended to other primitive interaction potentials. Finally, the main conclusion is that, decorated fluid membranes may be regarded as effective two-dimensional colloidal solutions where inclusions interact via the computed effective interactions. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.


PubMed | Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
Type: Journal Article | Journal: The European physical journal. E, Soft matter | Year: 2011

Consider a fluid membrane decorated by moving hard or soft inclusions. The aim of this work is a quantitative study of the influence of thermal fluctuations on the three-dimensional primitive forces between these inclusions. Integrating over all membrane fluctuations, we obtain a general form giving the modified primitive interactions upon the transverse distance. The established formalism enables us to obtain the modified expression of some standard interaction potentials. In particular, for power-like potentials, we found a modified expression featuring the Whittaker function. The present formalism may be extended to other primitive interaction potentials. Finally, the main conclusion is that, decorated fluid membranes may be regarded as effective two-dimensional colloidal solutions where inclusions interact via the computed effective interactions.


PubMed | Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
Type: Journal Article | Journal: The European physical journal. E, Soft matter | Year: 2011

We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties.


PubMed | Laboratoire Of Physique Des Polymeres Et Phenomenes Critiques
Type: Journal Article | Journal: The European physical journal. E, Soft matter | Year: 2010

The aim of this work is a theoretical study of the effects of the solvent quality on the microphase separation in crosslinked polymer blends, from a static and kinetics point of view. More precisely, we assume that the crosslinked mixture is trapped in a -solvent. The static microphase properties are studied through the static structure factor. The latter is computed using an extended blob model, where the crosslinked unlike chains can be viewed as sequences of blobs. We demonstrate that the presence of the -solvent simply leads to a multiplicative renormalization of these properties, and the renormalization factors are powers of the overall monomer volume fraction. Second, we investigate the early kinetics of the microphase separation, via the relaxation rate, (q), which is a function of the wave number q (at fixed temperature and monomer volume fraction). We first show that the kinetics is entirely controlled by local motions of Rouse type, since the slow motions are frozen out by the presence of crosslinks. Using the blob model, we find an explicit form for the growth rate (q) = (q), which depends, in addition to the wave number q , on the overall monomer volume fraction, . Also, we discuss the effect of initial entanglements that are trapped when the system is crosslinked. In fact, these play the role of true reticulation points, and then, they quantitatively contribute to the microseparation phenomenon. Finally, the results are compared to their homologous relatively to the molten state and to the good solvent case. The main conclusion is that the quality of the solvent induces drastic changes of the microphase properties.

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