489 research outputs found
Partition function, metastability, and kinetics of the escape transition for an ideal chain
No full textThe exact partition of the gaussian chain squeezed between two cylinders for a phase transition in a single macromolecule is analyzed. The polymer chain is squeezed between two pistons which results in abrupt transition from a confined coil state to an inhomogeneous conformation. The landau free energy is used in a one dimensional fokker-plank equation to predict the life-time of the metastable states. The analysis shows that the mean first passage time is estimated on the basis of the fokker-planck formalism.Baumgartner W, 2000, P NATL ACAD SCI USA, V97, P4005, DOI 10.1073-pnas.070052697; Carslaw H, 1947, CONDUCTION HEAT SOLI; Chaikin P.M., 2000, PRINCIPLES CONDENSED; De Gennes PG, 1979, SCALING CONCEPTS POL; de Gennes P.-G., 1993, PHYS LIQUID CRYSTALS; DESCLOIZEAUX G, 1990, POLYM SOLUTION THEIR; Doi M, 1986, THEORY POLYM DYNAMIC; EISENRIEGLER E, 1982, J CHEM PHYS, V77, P6296, DOI 10.1063-1.443835; Eisenriegler E., 1998, LECT NOTES PHYS, V508; Ennis J, 1999, PHYS REV E, V60, P6906, DOI 10.1103-PhysRevE.60.6906; Fleer G. J., 1993, POLYM INTERFACES; Flory PJ, 1953, PRINCIPLES POLYM CHE; Grosberg AY, 1994, STAT PHYS MACROMOLEC; GUFFOND MC, 1997, LANGMUIR, V13, P1591; Haupt BJ, 1999, LANGMUIR, V15, P3886, DOI 10.1021-la981112v; Hugel T, 2001, MACROMOLECULES, V34, P1039, DOI 10.1021-ma0009404; Hugel T, 2001, MACROMOL RAPID COMM, V22, P989, DOI 10.1002-1521-3927(20010901)22:13989::AID-MARC9893.0.CO;2-D; Jimenez J, 1998, LANGMUIR, V14, P2598, DOI 10.1021-la971233f; Klushin LI, 2002, PHYS REV E, V66, DOI 10.1103-PhysRevE.66.036114; Landau L. D., 1976, STAT PHYS; Leermakers FAM, 2002, MACROMOLECULES, V35, P8640, DOI 10.1021-ma020718u; Milchev A, 1999, PHYS CHEM CHEM PHYS, V1, P2083, DOI 10.1039-a809795j; Milchev A, 1999, EUROPHYS LETT, V47, P675, DOI 10.1209-epl-i1999-00442-2; Muthukumar M, 2001, PHYS REV LETT, V86, P3188, DOI 10.1103-PhysRevLett.86.3188; Senden TJ, 2001, CURR OPIN COLLOID IN, V6, P95, DOI 10.1016-S1359-0294(01)00067-X; Sevick EM, 1999, MACROMOLECULES, V32, P6841, DOI 10.1021-ma990589q; Skvortsov AM, 2001, J CHEM PHYS, V115, P1586, DOI 10.1063-1.1374210; Skvortsov AM, 2000, J CHEM PHYS, V112, P7238, DOI 10.1063-1.481313; Skvortsov AM, 2001, PHYSICA A, V290, P445, DOI 10.1016-S0378-4371(00)00402-7; Skvortsov AM, 2002, EUROPHYS LETT, V58, P292, DOI 10.1209-epl-i2002-00636-0; Steels BM, 2000, J CHROMATOGR B, V743, P31, DOI 10.1016-S0378-4347(00)00199-7; Subramanian G, 1996, MACROMOLECULES, V29, P4045, DOI 10.1021-ma946439r; SUBRAMANIAN G, 1995, EUROPHYS LETT, V29, P285, DOI 10.1209-0295-5075-29-4-003; WILLIAMS DRM, 1995, J PHYS II, V9, P1417; Zhang WK, 2000, J PHYS CHEM B, V104, P10258, DOI 10.1021-jp000459f17191
Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain
No full textAn end-tethered polymer chain compressed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flowerlike conformation partially escaped from the gap. This phase transition is first order in the thermodynamic limit of infinitely long chains. A rigorous analytical theory is presented for a Gaussian chain in two ensembles: (a) the H -ensemble, in which the distance H between the pistons plays the role of the independent control parameter, and (b) the conjugate f -ensemble, in which the external compression force f is the independent parameter. Details about the metastable chain configurations are analyzed by introducing the Landau free energy as a function of the chain stretching order parameter. The binodal and spinodal lines, as well as the barrier heights between the stable and metastable states in the free energy landscape, are presented in both ensembles. In the loop region for the average force with dependence on the distance H (i.e., in the H -ensemble) a negative compressibility exists, whereas in the f -ensemble the average distance as a function of the force is strictly monotonic. The average fraction of imprisoned segments and the lateral force, taken as functions of the distance H or the average H, respectively, have different behaviors in the two ensembles. These results demonstrate a clear counterexample of a main principle of statistical mechanics, stating that all ensembles are equivalent in the thermodynamic limit. The authors show that the negative compressibility in the escape transition is a purely equilibrium result and analyze in detail the origin of the nonequivalence of the ensembles. It is argued that it should be possible to employ the escape transition and its anomalous behavior in macroscopically homogeneous, but microscopically inhomogeneous, materials. © 2007 American Institute of Physics.Balescu R., 1975, EQUILIBRIUM NONEQUIL; Baughman RH, 2003, NATURE, V425, P667, DOI 10.1038-425667a; Baughman RH, 1998, SCIENCE, V279, P1522, DOI 10.1126-science.279.5356.1522; BINNIG G, 1986, PHYS REV LETT, V56, P930, DOI 10.1103-PhysRevLett.56.930; BRAGANZA LF, 1986, BIOCHEMISTRY-US, V25, P7484, DOI 10.1021-bi00371a034; DAMMER U, 1995, SCIENCE, V267, P1173, DOI 10.1126-science.7855599; Ennis J, 1999, PHYS REV E, V60, P6906, DOI 10.1103-PhysRevE.60.6906; Ennis J, 2001, MACROMOLECULES, V34, P1908; Fisher M., 1965, NATURE CRITICAL POIN; Florin EL, 1997, J STRUCT BIOL, V119, P202, DOI 10.1006-jsbi.1997.3880; Gaub H. E., 1998, ADV MATER, V3, P316; GauthierManuel B, 1997, REV SCI INSTRUM, V68, P2486, DOI 10.1063-1.1148146; Guffond MC, 1997, LANGMUIR, V13, P5691, DOI 10.1021-la970377r; Hugel T, 2001, MACROMOLECULES, V34, P1039, DOI 10.1021-ma0009404; Hugel T, 2001, MACROMOL RAPID COMM, V22, P989, DOI 10.1002-1521-3927(20010901)22:13989::AID-MARC9893.0.CO;2-D; ISRAELACHVILI JN, 1978, J CHEM SOC FARAD T 1, V74, P975, DOI 10.1039-f19787400975; Jimenez J, 1998, LANGMUIR, V14, P2598, DOI 10.1021-la971233f; Klushin LI, 2004, PHYS REV E, V69, DOI 10.1103-PhysRevE.69.061101; Leermakers FAM, 2004, J STAT MECH-THEORY E, DOI 10.1088-1742-5468-2004-10-P10001; Leermakers FAM, 2002, MACROMOLECULES, V35, P8640, DOI 10.1021-ma020718u; Lubensky DK, 2000, PHYS REV LETT, V85, P1572, DOI 10.1103-PhysRevLett.85.1572; Maaloum M, 1999, MACROMOLECULES, V32, P4989, DOI 10.1021-ma981023p; Matsuoka H, 2001, MACROMOL RAPID COMM, V22, P51, DOI 10.1002-1521-3927(20010201)22:251::AID-MARC513.0.CO;2-5; Milchev A, 1999, PHYS CHEM CHEM PHYS, V1, P2083, DOI 10.1039-a809795j; Ortiz C, 1999, MACROMOLECULES, V32, P780, DOI 10.1021-ma981245n; Rief M, 1997, SCIENCE, V275, P1295, DOI 10.1126-science.275.5304.1295; Sevick EM, 2000, MACROMOLECULES, V33, P5743, DOI 10.1021-ma991348l; Sevick EM, 1999, MACROMOLECULES, V32, P6841, DOI 10.1021-ma990589q; Skvortsov AM, 2000, J CHEM PHYS, V112, P7238, DOI 10.1063-1.481313; Skvortsov AM, 2002, EUROPHYS LETT, V58, P292, DOI 10.1209-epl-i2002-00636-0; Steels BM, 2000, J CHROMATOGR B, V743, P31, DOI 10.1016-S0378-4347(00)00199-7; Subramanian G, 1996, MACROMOLECULES, V29, P4045, DOI 10.1021-ma946439r; Vakarin EV, 2006, J CHEM PHYS, V124, DOI 10.1063-1.2191054; Wang MD, 1998, SCIENCE, V282, P902, DOI 10.1126-science.282.5390.902; WILLIAMS DRM, 1995, J PHYS II, V9, P1417; Zhang WK, 2000, J PHYS CHEM B, V104, P10258, DOI 10.1021-jp000459f10111
On the escape transition of a tethered Gaussian chain; exact results in two conjugate ensembles
No full textUpon compression between two pistons an end-tethered polymer chain undergoes an abrupt transition from a confined coil state to an inhomogeneous flower-like conformation that is partially escaped from the gap. In the thermodynamic limit the system demonstrates a first-order phase transition. A rigorous analytical theory of this phenomenon for a Gaussian chain is presented in two ensembles: a) the H-ensemble, in which the distance H between pistons plays the role of the control parameter, and b) the conjugate f-ensemble in which the external compression force f is the independent parameter. A loop region for (f(H)) with negative compressibility exists in the H-ensemble, while in the f-ensemble (H(f)) is strictly monotonic. The average lateral forces taken as functions of H (or (H), respectively) have distinctly different behavior in the two ensembles. This result is a clear counterexample of the main principles of statistical mechanics stating that all ensembles are equivalent in the thermodynamic limit. Another theorem states that the thermodynamic potential as a function of volume must be concave everywhere. We demonstrated that the exact free energy in the H-ensemble contradicts this statement. Inapplicability of these fundamental theorems to a macromolecule undergoing the escape transition is clearly related to the fact that phase coexistence in the present system is strictly impossible. This is a direct consequence of the tethering and the absence of global translational degrees of freedom of the polymer chain. © 2006 WILEY-VCH Verlag GmbH and Co. KGaA.Balescu R., 1975, EQUILIBRIUM NONEQUIL; BINNIG G, 1986, PHYS REV LETT, V56, P930, DOI 10.1103-PhysRevLett.56.930; De Gennes PG, 1979, SCALING CONCEPTS POL; EISENRIEGLER E, 1998, LECT NOTE PHYS, P508; Ennis J, 1999, PHYS REV E, V60, P6906, DOI 10.1103-PhysRevE.60.6906; Fisher M., 1965, NATURE CRITICAL POIN; Florin EL, 1997, J STRUCT BIOL, V119, P202, DOI 10.1006-jsbi.1997.3880; Flory PJ, 1953, PRINCIPLES POLYM CHE; GauthierManuel B, 1997, REV SCI INSTRUM, V68, P2486, DOI 10.1063-1.1148146; GROSBERG AY, 1996, STAT PHYS MACROMOLEC; Guffond MC, 1997, LANGMUIR, V13, P5691, DOI 10.1021-la970377r; Hugel T, 2001, MACROMOL RAPID COMM, V22, P989, DOI 10.1002-1521-3927(20010901)22:13989::AID-MARC9893.0.CO;2-D; ISRAELACHVILI JN, 1978, J CHEM SOC FARAD T 1, V74, P975, DOI 10.1039-f19787400975; Jimenez J, 1998, LANGMUIR, V14, P2598, DOI 10.1021-la971233f; Klushin LI, 2004, PHYS REV E, V69, DOI 10.1103-PhysRevE.69.061101; Klushin LI, 2002, PHYS REV E, V66, DOI 10.1103-PhysRevE.66.036114; Klushin LI, 1997, PHYS REV E, V56, P1511, DOI 10.1103-PhysRevE.56.1511; Matsuoka H, 2001, MACROMOL RAPID COMM, V22, P51, DOI 10.1002-1521-3927(20010201)22:251::AID-MARC513.0.CO;2-5; Milchev A, 1999, PHYS CHEM CHEM PHYS, V1, P2083, DOI 10.1039-a809795j; Skvortsov AM, 2002, EUROPHYS LETT, V58, P292, DOI 10.1209-epl-i2002-00636-0; Subramanian G, 1996, MACROMOLECULES, V29, P4045, DOI 10.1021-ma946439r; WILLIAMS DRM, 1995, J PHYS II, V9, P14179101
The polymer brush model of neurofilament projections: Effect of protein composition
No full textApplying self-consistent field theory, we consider a coarse-grained model for the polymerlike projections of neurofilament (NF) proteins that form a brush structure around neurofilaments. We focus on effects of molecular composition, which is the relative occurrence of NF-H, NF-M, and NF-L proteins, on the organization of NF projection domains. We consider NF brushes with selectively truncated projections, and with a varied ratio L:H:M of constituent tails. Our conclusion is that the NF brush structure is remarkably tolerant with respect to the variation in M and H chains. Results compare favorably with experimental data on model animals, provided that due attention is paid on the level of phosphorylation of the KSP repeat
How the projection domains of NF-L and alpha-internexin determine the conformations of NF-M and NF-H in neurofilaments
No full textMaking use of a numerical self-consistent field method and polymer brush concepts, we model the solvated corona of neurofilaments (NF) composed of projection domains (unstructured tails) of constituent proteins. Projections are modeled with amino acid resolution. We focus on the importance of the two shortest ones (alpha-internexin and NF-L) in regulating the conformations of the two longer ones (NF-M and NF-H) in an isolated NF. We take the wild-type NF with no alpha-internexin as the reference, for which the phosphorylation-induced translocation of M- and H-tails has been examined previously. We demonstrate that a subbrush of L-tails creates an electrostatic potential profile with an approximately parabolic shape. An experimentally relevant (2:1) ratio of L- to alpha-projections reduces the charge density of the L subbrush and shifts the translocation transition of the H-tails to slightly higher degrees of phosphorylation. Replacing all L-tails by alpha-projections destroys the substructure of the NF corona and this alters the NF response to the phosphorylation of long tail
Negative compressibility for a polymer chain squeezed between two pistons going through the escape transition
No full textThe analysis of the exact partition function of an end-fixed Gaussian chain compressed between two pistons reveals a loop-like curve of the average pressure as a function of the inter-piston volume. In the thermodynamic limit the system undergoes a first-order phase transition from a compressed coil to a partially escaped flower conformation. In the transition region the fixed volume ensemble is not equivalent to the fixed pressure ensemble, and for finite chains there appears a region with a negative compressibility. There is no conflict with the general notion that the pressure for a thermodynamic system should be a non-increasing function of the volume because the negative compressibility disappears in the thermodynamic limit. Our results are also expected to hold for self-avoiding chains and are experimentally accessible for real chains. © 2004 IOP Publishing Ltd.Balescu R., 1975, EQUILIBRIUM NONEQUIL; De Gennes PG, 1979, SCALING CONCEPTS POL; EISENRIEGLER E, 1998, SPRINGER LECT NOTES, V508; Ennis J, 1999, PHYS REV E, V60, P6906, DOI 10.1103-PhysRevE.60.6906; Fisher M., 1965, NATURE CRITICAL POIN; Flory PJ, 1953, PRINCIPLES POLYM CHE; GROSBERG AY, 1979, STAT PHYS MACROMOLEC; Hugel T, 2001, MACROMOL RAPID COMM, V22, P989, DOI 10.1002-1521-3927(20010901)22:13989::AID-MARC9893.0.CO;2-D; Klushin LI, 2002, PHYS REV E, V66, DOI 10.1103-PhysRevE.66.036114; KLUSHIN LI, 2004, IN PRESS PHYS REV E; Klushin LI, 1997, PHYS REV E, V56, P1511, DOI 10.1103-PhysRevE.56.1511; Leger JF, 1999, PHYS REV LETT, V83, P1066, DOI 10.1103-PhysRevLett.83.1066; Lubensky DK, 2002, PHYS REV E, V65, DOI 10.1103-PhysRevE.65.031917; Lubensky DK, 2000, PHYS REV LETT, V85, P1572, DOI 10.1103-PhysRevLett.85.1572; Milchev A, 1999, PHYS CHEM CHEM PHYS, V1, P2083, DOI 10.1039-a809795j; Sevick EM, 1999, MACROMOLECULES, V32, P6841, DOI 10.1021-ma990589q; Skvortsov AM, 2002, EUROPHYS LETT, V58, P292, DOI 10.1209-epl-i2002-00636-0; SUBRAMANIAN G, 1995, EUROPHYS LETT, V29, P285, DOI 10.1209-0295-5075-29-4-0036
Self-organization of polymers in bulk and at interfaces
No full textFully atomistic analysis of polymeric systems is computationally very demanding because the time and length scales involved span over several orders of magnitude. At the same time many properties of polymers are universal in the sense that they do not depend on the chemical nature of the comprising monomers. This makes coarse-grained methods, such as self-consistent field (SCF) modeling, an ideal tool for studying them. In this thesis we employ SCF modeling to study intra- and intermolecular self-organization organization of polymers and ordering of polymers near interfaces. Where possible, the results are compared to experiments and predictions of analytical theories
The lipid bilayer membrane and its interactions with additives
No full textThe aim of this study was to make accurate predictions on the interaction of biologically relevant molecules with lipid bilayer membranes. We emphasised on the partitioning of these molecules between the membrane phase, and the aqueous phase quantified by the partition coefficient. To make detailed predictions a theory had to be set up along the lines of the self-consistent-field theory developed by Scheutjens and Fleer and extended by Evers, Leermakers, Van Lent, Böhmer, Barneveld, Israëls, Wijmans, Van der Linden, and others for (chain) molecules in inhomogeneous systems.As a first step towards this goal we have investigated bare membranes in chapter 1. A membrane of dimyristoylphosphatidylcholine (DMPC) has been used as a model for biological membranes, existing in plant and animals, in which this molecule is a major component. For comparison, membranes consisting of the anionic dimyristoylphosphatidylserine (DMPS) were also modelled. It was found that the zwitterionic phosphatidylcholine (PC) head group was laying on average flat on the membrane surface. This result is in line with experiments and in accordance with other theoretical calculations. At high salt concentrations however, two preferred conformations had to be distinguished, both about equally populated, one with the choline moiety closer to the water phase than the phosphate moiety and one the other way around. Due to the out of plane tilting of the head group, an electrostatic potential profile develops. The electrostatic potential is positive in the membrane centre and on the membrane surface, but negative in the middle of the head group region at the average position of the phosphate groups.The ionic head groups of DMPS are found tilted towards the aqueous solution. Counterions interpenetrate the head group region and compensate the charge to a large extent even at low ionic strength. At high salt concentrations ions are depleted from the head group space but, due to asymmetric depletion of anions and cations, charge compensation is still achieved.The variability of the PC head group orientation was investigated theoretically by attaching a hydrophilic chain to the choline moiety of DMPC. Varying the chain length had two effects: First, due to the interchain steric repulsion the head group area increased and therefore the dimension of the hydrophobic core decreased which eventually destabilised the membranes. Second, the head group orientation changed non-monotonously. Short chains attached to the choline moiety 'drag' it towards the water phase, while longer chains attached to it do not affect the average orientation of the dipole, which is parallel to the membrane surface. This is caused by the fact that, for longer hydrophilic chains, the most bulky part of the head group is located further from the hydrophobic core in the centre of the polymeric coil. This relaxes the packing constraints at the position of the choline. Hence the phosphate moieties and the electrostatics forces, that favour a flat conformation, meet less opposition.In the second chapter we concentrate on the interplay of the electrostatic potential profile across the membrane and the valence of the ions present in solution. From the calculations it can be concluded that the electrostatic interactions can explain the accumulation of charges in the head group area without introduction of specific chemical interactions between e.g. a divalent ion like calcium and the phosphate group.An important issue in the modelling of non-interacting, free-standing membranes is the proof that the modelled bilayers are thermodynamically the most stable structures. From thermodynamic arguments, it can be shown that the surface tension of these layers should vanish. This is a necessary, but not sufficient condition. For isolated, free-standing bilayers to be stable, the membranes should be mutually repulsive. The interaction between bilayers is the topic of chapter 3. In this chapter a thermodynamic derivation is presented of the various ways the interaction curve can be calculated from the self-consistent-anisotropic-field (SCAF) theory. The results show that three force-distance regimes can be distinguished for a DMPC bilayer in a moderate salt concentration: two repulsive regimes, one of electrostatic and one of steric origin flank an attractive one that was shown to be of entropic origin. The entropic attraction is caused by an increase in the number of head group conformations. At large separation the head groups are oriented mostly parallel to the membrane surface. Upon closer approach of two bilayers the head group conformation is allowed to change. The head group can now cross the gap between the bilayers without an electrostatic penalty. As a function of the screening of the electrostatic interactions we observe various changes in the interaction curves. At high salt concentration both the electrostatic repulsion and the entropic attraction become negligible. At low salt concentration the entropic attraction increases whereas, at the same time, the electrostatic repulsion vanishes. This last effect is caused by the perfect alignment of the head group parallel to the membrane surface so that virtually no charge separation occurs.Stretching the membranes increases the entropic attraction but decreases the electrostatic repulsion. We did not incorporate undulations in our theory so the decrease of undulations was not the phenomenon that caused the stress-induced tendency to adhere. In our model stretched membranes have a larger head group area which relaxes the head group packing constraints. This allows these groups to assume a position more parallel to the bilayer surface, leading to a reduced electrostatic repulsion and a stronger entropic attraction.Addition of non-ionic surfactants (dodecanol) to DMPC bilayers caused the membranes to grow thicker without changing the interaction curve. Ionic surfactants (e.g. dodecylammonium and dodecylsulphide) did not change the overall membrane thickness but made, due to a modification of the electrostatic interactions, the interaction profile completely repulsive. Cationic surfactants had a more pronounced effect than anionics. Cationics push the choline moieties outwards while the anionics pull these more inwards towards the membrane centre.Finally in chapter 4 the SCAF theory for molecules containing rigid structures is given. The coupling of the segment potential {u(z)} to the volume fraction profile {(p(z)} is in principle accomplished according to the following simple, basic method. First, all conformations of the molecules are generated and then the statistical weights of these conformations in the potential field are added and normalised. For flexible molecules, that can assume very many conformations, an efficient technique exists that is just doing this in one single operation, it generate the conformations, calculate the statistical weight, and add the results to obtain the densities (the propagator method). For rigid structures, that can assume relatively few conformations, the basic methods is already effective. A hybrid scheme was developed for partly rigid molecules, where the basic method for the rigid parts was combined with the propagator method for the flexible parts.Partition coefficients calculated for a number of linear and branched alcohols as well as for phenols were compared with measurements. Good quantitative comparison was found for these molecules. Trends known from literature, like the exponential dependence of the partition coefficient on the chain length in homologue series, were reproduced.To illustrate the possibilities of the theory some results were presented of calculations on three groups of molecules having the same zwitterionic isomer (C 22N+S -, containing a benzene-like structure). The calculations showed that in DMPC membranes the partition coefficient can change by a factor of ten depending on the molecular architecture. The positional and orientational data revealed that negatively charged units partition much more readily into the membrane core than positively charged segments do. This can be rationalised by the electrostatic potential profile which, as told above, is positive both in the centre and on the outskirts of the membrane while being negative at the average position of the phosphate segments.Calculations on a number of substituted tetrahydroxynaphthalenes showed that, with only small changes in the partition coefficient, large orientational and positional variations can be realised, changing from spanning the membrane for 2,3,6,7- tetrahydroxy naphthalene to parallel to the membrane surface positioned at the head group-hydrophobic core interface for 1,3,5,7-tetrahydroxy naphthalene. This kind of large orientational changes, while keeping the partition coefficient virtually constant, can be of great importance in the development and the improvement of new drugs, or in elucidating the working mechanism of existing ones.Our model has provided a detailed insight into the nature of model lipid membranes and will hopefully advance the development of products and contribute to the optimisation and interpretation of experiments in which lipid bilayers play a role. At present reasonable (semi) quantitative agreement with many experimental results have already been achieved. There are however cases where the present theory does not yet give good enough predictions. For this it is good to know that the theory can be readily extended to incorporate more details in the calculations
A one-parameter model for microemulsions
No full textOil and water do not mix. Oil molecules like each other and so does water molecules. Oil molecules however do not like water molecules as much as their own. Thus, there exists a effective repulsive force between oil and water molecules. Imagine pouring a glass of water into a container that has oil. Eventually, the oil will phase separate and reach the top of the container. This happens as a result of the repulsive force often referred to as the hydrophobic nature of oil. Indeed gravity dictates their position, but, interaction drives the separation. As a thought experiment, imagine oil likes water. Do you think that if we repeat the same experiment in the presence of gravity, will oil come to the top of the container? I will leave this as an open question. When oil separates from water, an interface will form between the oil-rich and water-rich regions. However, there are enormous scenarios where we would like the oil to mix completely with water. It would be extremely beneficial if we can achieve this without providing mechanical work. Such stable mixtures of oil and water can be achieved by adding a surfactant. These surfactants have both oil-loving and water-loving parts and hence assemble at the interface between oil and water. Such assembly promotes thermodynamically stable mixtures (no mechanical work required) with an enormous interfacial area. Such thermodynamically stable mixtures of oil, water and surfactant are defined as microemulsions.To understand microemulsions. This is all this thesis is about. Our target is to generate a generic yet simplistic model to the whole class of microemulsions with accuracy at the molecular level. Firstly, we will provide a brief review of microemulsions. Later, we will present various applications of microemulsions in different fields. Finally, we will discuss existing models and conclude with an outline of the thesis
Adsorption of charged diblock copolymers : effect on colloidal stability
No full textIn this thesis we present Scheutjens-Fleer (SF) calculations on the adsorption of diblock copolymers. More specifically, we restrict ourselves to adsorption at uncharged surfaces, while the specific type of block copolymers we consider have one uncharged adsorbing "anchor" block and one non-adsorbing charged "buoy" block. We compare these systems with a more simple one, that of the charged brushes. A polymer brush is the structure that is formed when polymer molecules are attached by one end to a surface, with a density high enough so that the chains are obliged to stretch away from the interface. Complementary to the numerical computations, the scaling behaviour of these systems is discussed. We study the structure of the adsorbed layer, and try to answer ultimately the question what the effect of the adsorption is on colloidal stability.In the introductory Chapter 1 we explain the most important terms and discuss the relevance of this study. Furthermore, we introduce the SF model and compare it to two other approaches: Monte Carlo and Scaling. Finally, we briefly present the available information on the two systems under consideration, and compare them to a number of related systems.The body of this work is divided in two parts. In Chapters 2 and 3 we discuss charged brushes, systems that are simpler than diblock copolymer adsorption, but still exhibit similar characteristics. In the subsequent two chapters we then proceed to the adsorption of diblock copolymers (Chapter 4) and its effect on colloidal stability (Chapter 5).In Chapter 2 we present numerical results from the SF model for the structure and sealing behaviour of charged brushes and compare these with predictions of an analytical model on the same system. The relevant parameters are the chain length N , the average anchoring density σ, the average segmental charge αon the chains, and the salt concentration φ S .At high anchoring densities, three regimes of brush behaviour may be distinguished. In the salt-free case, the behaviour of the brush is dominated by electrostatic interactions if the charges are high (the so-called Osmotic Brush) or by non-electrostatic excluded volume interactions if the charges are low (the quasi-Neutral Brush regime). Upon adding salt a third regime can be found: the Salted Brush. The behaviour in this regime, although resulting from electrostatic interactions, is very similar to that in a neutral brush and can effectively be described using an electrostatic excluded volume parameter vel ≈ φ S-1α2. We find excellent agreement regarding structure as well as scaling relations between the two theories in these three (high anchoring density ) regimes. At extremely low anchoring densities, the agreement with the analytical theory is less good. This is due to the breakdown at low densities of the mean-field approximationpresently used in the numerical model.In between, at intermediate anchoring densities, the analytical theory predicts a very peculiar regime, where the thickness H scales as H ≈N3σ-1α2. This so-called " Pincus Brush ", named after the author who originally described it, is not recovered with the numerical theory. For the wide range of parameters used, we find the Pincus regime is too small to be detected. This is probably true for any reasonable set of parameters.In Chapter 3 we consider the acid-base equilibrium of the charged brush segments, so that grafted weak polyacids may be studied. For these systems the charge of a brush segment depends on its local environment and on the pH in the solution. The scaling dependence of the thickness H on the salt concentration φ S for such a brush is very different from that for a conventional charged brush with constant charge density.In Chapter 4 we proceed to the adsorption of ionic diblock copolymers. One block, the "anchor", consists of N A uncharged adsorbing A segments, whereas the "buoy" block has N B segments which carry a fixed charge and are non-adsorbing. Upon adsorption these sorbed amount and layer thickness as a function of the block lengths N A and N B , the charge αe on the B segments, and the salt concentration φ S in each of the four regimes. The scaling relations axe checked using SF calculations.The existence of two regimes for uncharged diblock copolymer adsorption has been reported previously. We argue that those HU and LU regimes are closely related to the two regimes HC and LC we find for charged molecules. Scaling relations can be translated from the uncharged to the corresponding charged regimes by replacing the excluded volume parameter v of the buoy segments by an effective electrostatic excluded volume parameter ve = α 2/φ S .In the LC regime the chain density σscales as σ α( N A /N B ) 3/2ve-1and the layer thickness H as H α ( N A /N B ) 1/2. The latter scaling is independent of ve . Using the SF model, these relations axe found to be valid for an adsorbed amount of A segments below 10% of monolayer coverage.In the HC regime the adsorption is dominated by the anchoring block and the scaling relation σ α1/ N A for the chain density is identical to that for uncharged molecules. The SF calculations show that this regime will not be reached in practical situations.Finally, we address in Chapter 5 the effect of the adsorption of charged diblock copolymers on colloidal stability. Using again a scaling as well as the SF approach, we focus on the LC regime and find that the adsorbed layer may cause a significant repulsive interaction between two surfaces, despite the very low adsorbed amounts. The magnitude of this repulsion is well within the range that could be mea, sured using a surface force apparatus. Moreover, we estimate that the repulsive interaction may be strong enough to induce kinetic stability, provided the particle radius is large enough. Upon lowering the salt concentration, however, a critical concentration φ S * is reached eventually, below which the repulsion is no longer strong enough to effect colloidal stability. The scaling analysis predicts that this critical concentration scales as:φ S * ≈ N Bα2/ RN A3where R is the radius of the particles and the other parameters have been defined above. Thus the repulsive interaction decreases when the relative importance of charge effects increases, i.e., with decreasing salt concentration, and increasing buoy block length or buoy block charge. This counterintuitive behaviour can be explained from the effect that electrostatic interactions have on the adsorbed amount: stronger interactions lead to a lower adsorbed amount, which, in turn, leads to a weaker repulsion. The SF calculations confirm these scaling predictions
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