Topological Changes in Telechelic Micelles: Flowers versus StarsClick to copy article linkArticle link copied!
- Vladimir A. Baulin*Vladimir A. Baulin*Email: [email protected]Departament Química Física i Inorgànica, Universitat Rovira i Virgili, Marcel.lí Domingo s/n, 43007 Tarragona, SpainMore by Vladimir A. Baulin
Abstract
The micellization and morphology of spherical telechelic micelles formed by triblock copolymers with short solvophobic end blocks at low concentrations are discussed within scaling arguments and Single Chain Mean Field Theory (SCMFT). In an ultradilute regime, individual telechelic polymer chains can exist in solution in two distinct states: an open linear chain conformation with two free ends and a closed loop conformation in which two ends are connected by the effective attraction between two solvophobic ends. At concentrations below the gelation point, closed loops tend to form micelles comprised mostly of loops in flower-like micelles, while linear polymers in open conformations tend to form star-shaped aggregates with one hydrophobic dangling end. The resulting two kinds of micelles have remarkably different topologies and dimensions, while the transition between them can be driven by the entropy, namely conformation changes between domination of the looped and linear conformations. The transition between two types of micelles lies in a narrow interaction parameters range. Thus, these topological micelles are very sensitive to the changes in the external environment, and they can serve as very sensitive stimuli responsive smart materials.
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Introduction
Telechelic Micelle Morphologies: Scaling Arguments
Figure 1
Figure 1. Two distinct conformations of telechelic unimers: (a) hydrophobic blocks (red) are separated and (b) hydrophobic blocks are reversibly connected, and the hydrophilic block (blue) forms a loop.
Figure 2
Figure 2. Possible structures of individual triblock copolymer micelles: all loops are closed (flower-like or “camomile” micelle), a mixture of loops and free ends (mixed micelle), and all loops are opened (a star-like or “aster” micelle).



















Figure 3
Figure 3. Aggregation of triblock copolymers into micelles. (A) Variation of Ω with the aggregation number p and (B) the corresponding size distributions for γ = 0.57. The length of a hydrophilic block N = 500, and the length of the hydrophobic block Lc = 50.
Interaction-Driven Transitions: Single Chain Mean Field Theory













Figure 4
Figure 4. SCMF theory of telechelic micelles. (A) Chemical potential difference Δμ between monomers in the micelles and in the solution as a function of the aggregation number p for strong attraction, εTT = −3.8, flower-like micelle, green curve, open squares, and weak attraction, εTT = −1.9, star-like micelle, orange curve, closed squares. Minimum volume fractions of hydrophobic blocks (red), hydrophilic blocks (blue), and the sum (gray) as a function of the distance from the center in the (B) flower-like micelle, p = 14 and (C) star-like micelle, p = 19.
Conclusion
Acknowledgments
This publication is a part of the project I+D+i: PID2020-114347RB-C33, financed by MCIN/AEI 10.13039/501100011033.
References
This article references 24 other publications.
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- 20Gezae Daful, A.; Baulin, V. A.; Bonet Avalos, J.; Mackie, A. D. Accurate Critical Micelle Concentrations from a Microscopic Surfactant Model. J. Phys. Chem. B 2011, 115, 3434– 3443, DOI: 10.1021/jp1102302Google Scholar20Accurate critical micelle concentrations from a microscopic surfactant modelGezae Daful Asfaw; Baulin Vladimir A; Bonet Avalos Josep; Mackie Allan DThe journal of physical chemistry. B (2011), 115 (13), 3434-43 ISSN:.A single chain mean field theory is used to quantitatively describe the micellization process of the nonionic polyethylene oxide alkyl ether, C(n)E(m) class of surfactants at 25 °C. An explicit but simple microscopic model with only three interaction parameters is shown to be able to reproduce with high accuracy the critical micelle concentrations of a wide range of head and tail surfactant lengths. In addition, the aggregation number of the micelles is studied, the effect of the number of the hydrophobic and hydrophilic segments on CMC and aggregation number of the micelles are discussed and volume fraction profiles are given.
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- 22Pogodin, S.; Baulin, V. A. Coarse-Grained Models of Phospholipid Membranes within the Single Chain Mean Field Theory. Soft Matter 2010, 6, 2216– 2226, DOI: 10.1039/b927437eGoogle Scholar22Coarse-grained models of phospholipid membranes within the single chain mean field theoryPogodin, Sergey; Baulin, Vladimir A.Soft Matter (2010), 6 (10), 2216-2226CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)The single chain mean field theory is used to simulate the equil. structure of phospholipid membranes at the mol. level. Three levels of coarse-graining of DMPC phospholipid surfactants are present: The detailed 44-beads double tails model, the 10-beads double tails model and the minimal 3-beads model. The authors show that all 3 models are able to reproduce the essential equil. properties of the phospholipid bilayer, while the simplest 3-beads model is the fastest model which can describe adequately the thickness of the layer, the area per lipid and the rigidity of the membrane. The accuracy of the method in description of equil. structures of membranes compete with Monte Carlo simulations while the speed of computation and the mean field nature of the approach allows for straightforward applications to systems with great complexity.
- 23Guo, Y.; Pogodin, S.; Baulin, V. A. General model of phospholipid bilayers in fluid phase within the single chain mean field theory. J. Chem. Phys. 2014, 140, 174903, DOI: 10.1063/1.4873586Google Scholar23General model of phospholipid bilayers in fluid phase within the single chain mean field theoryGuo, Yachong; Pogodin, Sergey; Baulin, Vladimir A.Journal of Chemical Physics (2014), 140 (17), 174903/1-174903/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Coarse-grained model for satd. phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsatd. phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equil. and mech. properties of a range of satd. lipid mols. that differ only in length of their hydrophobic tails and unsatd. (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as satd. lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equil. area per lipid correspond to exptl. measured values for each lipid, changing linearly with the length of the tail. The model for unsatd. phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estn. of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable ests. for free energies. The proposed model may further be used for studies of mixts. of lipids, small mol. inclusions, interactions of bilayers with embedded proteins. (c) 2014 American Institute of Physics.
- 24Rosenbluth, M. N.; Rosenbluth, A. W. Monte Carlo Calculation of the Average Extension of Molecular Chains. J. Chem. Phys. 1955, 23, 356– 359, DOI: 10.1063/1.1741967Google Scholar24Monte Carlo calculation of the average extension of molecular chainsRosenbluth, Marshall N.; Rosenbluth, Arianna W.Journal of Chemical Physics (1955), 23 (), 356-9CODEN: JCPSA6; ISSN:0021-9606.The behavior of chains of many mols. was investigated by solving a restricted random-walk problem on a cubic lattice in 3 dimensions and a square lattice in 2 dimensions. For chains of length up to 64 links, the av. squared extension of the chain R2 was related to the no. of links N by the relation, 〈R2〉 = N1.22 in the 3-dimensional case, and by the relation 〈R2〉 = 0.917(N)1.45 in the 2-dimensional case. Along with the results of Wall, et al. (C.A. 48, 12505b)the same exponent, 1.22, applies to 3 different types of lattice
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Abstract
Figure 1
Figure 1. Two distinct conformations of telechelic unimers: (a) hydrophobic blocks (red) are separated and (b) hydrophobic blocks are reversibly connected, and the hydrophilic block (blue) forms a loop.
Figure 2
Figure 2. Possible structures of individual triblock copolymer micelles: all loops are closed (flower-like or “camomile” micelle), a mixture of loops and free ends (mixed micelle), and all loops are opened (a star-like or “aster” micelle).
Figure 3
Figure 3. Aggregation of triblock copolymers into micelles. (A) Variation of Ω with the aggregation number p and (B) the corresponding size distributions for γ = 0.57. The length of a hydrophilic block N = 500, and the length of the hydrophobic block Lc = 50.
Figure 4
Figure 4. SCMF theory of telechelic micelles. (A) Chemical potential difference Δμ between monomers in the micelles and in the solution as a function of the aggregation number p for strong attraction, εTT = −3.8, flower-like micelle, green curve, open squares, and weak attraction, εTT = −1.9, star-like micelle, orange curve, closed squares. Minimum volume fractions of hydrophobic blocks (red), hydrophilic blocks (blue), and the sum (gray) as a function of the distance from the center in the (B) flower-like micelle, p = 14 and (C) star-like micelle, p = 19.
References
This article references 24 other publications.
- 1Gil, E. S.; Hudson, S. M. Stimuli-reponsive polymers and their bioconjugates. Prog. Polym. Sci. 2004, 29, 1173– 1222, DOI: 10.1016/j.progpolymsci.2004.08.0031Stimuli-responsive polymers and their bioconjugatesGil, Eun Seok; Hudson, Samuel M.Progress in Polymer Science (2004), 29 (12), 1173-1222CODEN: PRPSB8; ISSN:0079-6700. (Elsevier B.V.)A review. Stimuli responsive polymers can provide a variety of applications for the biomedical fields. The interest in these polymers has exponentially increased due to their promising potential. Among them, temp. and pH responsive mechanisms were considerably investigated because they are relatively convenient and effective stimuli in many applications. In this review, the authors' main purposes are focused on temp. and pH responsive polymer systems and addnl. the other stimuli-based responsive polymers will be assessed. Dozens of reviews were recently reported to introduce the field of stimuli responsive polymers. However, most of these reviews were focused on one specific application such as drug delivery or one specific phys. form such as hydrogels. In the authors' point of view, the whole range of applications and phys. forms of stimuli responsive polymers will be elucidated, which is more helpful to design new approaches because the basic concepts and mechanisms are systematically connected. This means that any new advanced concepts and mechanisms can be utilized in a variety of other applications as well as other phys. forms. Also, the authors will describe the classification of stimuli responsive polymers by their mechanism of response to stimuli. Moreover, this review focuses on recent approaches of mol. designs which are extremely necessary to develop more desirable and functional stimuli responsive polymers.
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- 3Meng, X.-X.; Russel, W. B. Structure and Size of Spherical Micelles of Telechelic Polymers. Macromolecules 2005, 38, 593– 600, DOI: 10.1021/ma048968t3Structure and Size of Spherical Micelles of Telechelic PolymersMeng, Xiao-Xia; Russel, William B.Macromolecules (2005), 38 (2), 593-600CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)This paper addresses the prediction and measurement of the aggregation no. and radius of spherical micelles composed of telechelic polymers. The free energy of micellization balances the interfacial energy against the energy of stretching the end blocks to form the core, the configurational entropy, and excluded-vol. interactions of the sol. chains that form the corona. In a good solvent, the latter are strongly stretched and form spherical brushes as treated by the Li-Witten model. The min. in the free energy sets the most probable size, while the curvature at the min. indicates the breadth of the distribution. From these we predict the various avs. of the aggregation no. and micellar radius detected by fluorescence measurements, dynamic and static light scattering, and viscometry. The effects of polydispersity explain in part the discrepancies among values reported by different groups for polymers of the same nominal structure.
- 4Lo Verso, F.; Likos, C. N. End-functionalized polymers: Versatile building blocks for soft materials. Polymer 2008, 49, 1425– 1434, DOI: 10.1016/j.polymer.2007.11.0514End-functionalized polymers: versatile building blocks for soft materialsLo Verso, Federica; Likos, Christos N.Polymer (2008), 49 (6), 1425-1434CODEN: POLMAG; ISSN:0032-3861. (Elsevier Ltd.)A review. We present a concise review of telechelic polymers of various architectures, focusing on the structure, solute solvent interactions, aggregation processes, equil. and dynamical properties and applications. Telechelics are macromols. with functionalized, mutually attractive end-groups, which assume a variety of conformations that depend on solvent quality, salinity and pH of the solvent, and on the particular macromol. architecture. In concd. solns., telechelic polymers offer unique possibilities to create novel materials with distinct rheol. properties. Depending on chem. and architecture, they can create percolating clusters and transient gels or they can show macroscopic phase sepn. into a dil. and a structured dense phase. The possibility to externally steer the morphol. of these structures and the concomitant phys. properties of the materials renders telechelic polymers into important and versatile building blocks for modern materials science.
- 5Lombardo, D.; Kiselev, M. A.; Magazù, S.; Calandra, P. Amphiphiles Self-Assembly: Basic Concepts and Future Perspectives of Supramolecular Approaches. Adv. Condens. Matter Phys. 2015, 2015, e151683 DOI: 10.1155/2015/151683There is no corresponding record for this reference.
- 6Zinn, T.; Willner, L.; Knudsen, K. D.; Lund, R. Self-Assembly of Mixtures of Telechelic and Monofunctional Amphiphilic Polymers in Water: From Clusters to Flowerlike Micelles. Macromolecules 2017, 50, 7321– 7332, DOI: 10.1021/acs.macromol.7b015016Self-Assembly of Mixtures of Telechelic and Monofunctional Amphiphilic Polymers in Water: From Clusters to Flowerlike MicellesZinn, Thomas; Willner, Lutz; Knudsen, Kenneth D.; Lund, ReidarMacromolecules (Washington, DC, United States) (2017), 50 (18), 7321-7332CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)In this work we study the self-assembly of mixts. of n-alkyl mono- and difunctionalized poly(ethylene oxide) (PEO) chains in the dil. concn. regime. The monofunctional PEOs were prepd. by living anionic polymn. with varying n-alkyl length (n = 14, 16, 22, 28) and const. PEO mol. wt. of 5 kg/mol. The difunctional materials were obtained through end-to-end coupling of two of the monofunctionalized PEOs via their terminal hydroxyl groups. The chosen synthetic pathway yields well-defined model compds. with narrow mol. wt. distribution and complete end-group functionalization. By using both small-angle neutron scattering (SANS) and dynamic light scattering (DLS) combined with theor. data modeling, we have systematically investigated both the global and inner structure of the self-assembled micellar structures. For short n-alkyl chain-ends, we find a formation of clustered micelles with a finite size whereas, intriguingly, at longer n-alkyls, we observe a crossover to flower-like micelles. This was confirmed both by DLS, which is very sensitive to formation of larger clusters, as well as with SANS which also showed a clear transition from attractive to repulsive intermicellar interactions upon increasing n-alkyl length. We attribute this to the balance between the hydrophobic enthalpic terms that favor anchoring of both chain-ends to the core, and the entropic cost assocd. with the bending of the polymer chains. For short n-alkyls, exposure of the chain-ends in the corona structure leads to net dominance of the attractive interactions, while for longer hydrophobic chains leads to a stabilization of loops and consequently flower-like micellar morphol. Using contrast-variation SANS, the contribution of mono- and difunctional chains could be sepd., confirming the flower-like micellar structure.
- 7Sun, H.; Kabb, C. P.; Sims, M. B.; Sumerlin, B. S. Architecture-transformable polymers: Reshaping the future of stimuli-responsive polymers. Prog. Polym. Sci. 2019, 89, 61– 75, DOI: 10.1016/j.progpolymsci.2018.09.0067Architecture-transformable polymers: Reshaping the future of stimuli-responsive polymersSun, Hao; Kabb, Christopher P.; Sims, Michael B.; Sumerlin, Brent S.Progress in Polymer Science (2019), 89 (), 61-75CODEN: PRPSB8; ISSN:0079-6700. (Elsevier Ltd.)The field of stimuli-responsive, or smart polymers, has commanded significant interest over the past decade. However, most examples of stimuli-responsive polymers have relied on macroscopic changes that arise via simple alterations in chain conformation or changes in polymer-polymer or polymer-solvent interactions. In recent years, there has been an effort to expand the scope of modifiable variables to include the covalent architecture of a polymer through the use of reversible covalent bonds. Polymers capable of architectural transformation are those that can undergo changes in their chain topol. (e.g., linear to branched, star to comb, etc.) via rearrangement in the chain structure. This approach has proven particularly interesting because it allows access to materials capable of dramatic macromol. property changes that cannot be replicated by the more traditional approaches to responsive polymer systems, which often rely on soly. or swelling transitions in soln. This review aims to highlight the main synthetic strategies to architecture-transformable polymers, including dynamic-covalent and supramol. chem. approaches. In addn., the properties and applications of those smart polymers are highlighted. It is clear from recent research in this area that macromols. capable of undergoing transformations in topol. represent a paradigm shift in the field of stimuli-responsive materials.
- 8König, N.; Willner, L.; Pipich, V.; Mahmoudi, N.; Lund, R. Tale of Two Tails: Molecular Exchange Kinetics of Telechelic Polymer Micelles. Phys. Rev. Lett. 2020, 124, 197801, DOI: 10.1103/PhysRevLett.124.1978018Molecular exchange kinetics of telechelic polymer micellesKonig, Nico; Willner, Lutz; Pipich, Vitaliy; Mahmoudi, Najet; Lund, ReidarPhysical Review Letters (2020), 124 (19), 197801CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)Telechelic polymers contain two chain ends that are able to promote self-assembly into "flowerlike" or interconnected micellar structures. Here, we investigate the mol. exchange kinetics of such micelles using time-resolved small-angle neutron scattering. We show that the activation energies of monofunctional and telechelic chain exchange are identical. This demonstrates that the two chain ends are not simultaneously released in a single event. Instead, the results show that, contrary to regular micelles, the kinetics occurs in a multistep process involving a collision-induced single-mol. exchange mechanism where the exchange rate is directly proportional to the polymer concn. We show that this novel mechanism can be quant. explained by a simple kinetic model.
- 9Wu, C.; Zhou, S. Thermodynamically Stable Globule State of a Single Poly(N-isopropylacrylamide) Chain in Water. Macromolecules 1995, 28, 5388– 5390, DOI: 10.1021/ma00119a0369Thermodynamically Stable Globule State of a Single Poly(N-isopropylacrylamide) Chain in WaterWu, Chi; Zhou, ShuiqingMacromolecules (1995), 28 (15), 5388-90CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)A thermodynamically stable globule state of a single polymer chain was exptl. realized with an extremely dil. soln. (∼5 μg/mL) of a narrowly distributed high-mol.-wt. poly(N-isopropylacrylamide) (I) sample in water. The results supported a four-stage coil-to-globule transition process for a single I chain in water.
- 10Séréro, Y.; Aznar, R.; Porte, G.; Calvet, D.; Collet, A.; Viguier, M.; Berret, J.-F. Associating Polymers: From “Flowers” to Transient Networks. Phys. Rev. Lett. 1998, 81, 5584, DOI: 10.1103/PhysRevLett.81.558410Associating Polymers: From "Flowers" to Transient NetworksSerero, Y.; Aznar, R.; Porte, G.; Berret, J.-F.; Calvet, D.; Collet, A.; Viguier, M.Physical Review Letters (1998), 81 (25), 5584-5587CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We report on a novel telechelic assocg. polymers that self-assemble in soln. into starlike flowers in the dil. regime and develop a fully connected network of flowers above some threshold concn. .vphi.*. Small-angle neutron scattering has been used to investigate the form and structure factors of the starlike aggregates, whereas linear rheol. was performed to identify the viscoelastic features of the temporary network. These findings are compared to those obtained on an assocg. polymer which is half of the telechelic in mol. wt. and monofunctionalized (no bridging). Although the neutron scattering signatures are the same, the latter solns. remain Newtonian and fluid even for .vphi.».vphi.*.
- 11Meng, W.; He, Q.; Yu, M.; Zhou, Y.; Wang, C.; Yu, B.; Zhang, B.; Bu, W. Telechelic amphiphilic metallopolymers end-functionalized with platinum(II) complexes: synthesis, luminescence enhancement, and their self-assembly into flowerlike vesicles and giant flowerlike vesicles. Polym. Chem. 2019, 10, 4477– 4484, DOI: 10.1039/C9PY00652D11Telechelic amphiphilic metallopolymers end-functionalized with platinum(II) complexes: synthesis, luminescence enhancement, and their self-assembly into flowerlike vesicles and giant flowerlike vesiclesMeng, Weisheng; He, Qun; Yu, Manman; Zhou, Yufeng; Wang, Chen; Yu, Bingran; Zhang, Bin; Bu, WeifengPolymer Chemistry (2019), 10 (32), 4477-4484CODEN: PCOHC2; ISSN:1759-9962. (Royal Society of Chemistry)Here we have designed and synthesized a series of platinum(II) complex end-difunctionalized poly(ethylene glycol)s (PEGs). For the first time, these telechelic amphiphilic metallopolymers can self-assemble in soln. to create nanosized flowerlike vesicles, where the two platinum(II) complex ends are connected to the same vesicular core and the central PEG chains form loops as a corona. Such a self-assembly process correlates well with spectroscopic changes and luminescence enhancements that originate from Pt···Pt and π-π stacking interactions. Moreover, thermal annealing of the nanosized flowers leads to a morphol. transformation to micrometer size, giant flowerlike vesicles. The present work, combining telechelic polymers with metal complexes, will open up a new approach for the design of functional metallopolymers with controllable self-assembly.
- 12Ogawa, T.; Usuki, N.; Nakazono, K.; Koyama, Y.; Takata, T. Linear–cyclic polymer structural transformation and its reversible control using a rational rotaxane strategy. Chem. Commun. 2015, 51, 5606– 5609, DOI: 10.1039/C4CC08982K12Linear-cyclic polymer structural transformation and its reversible control using a rational rotaxane strategyOgawa, Takahiro; Usuki, Naoya; Nakazono, Kazuko; Koyama, Yasuhito; Takata, ToshikazuChemical Communications (Cambridge, United Kingdom) (2015), 51 (26), 5606-5609CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)Linear-cyclic polymer structural transformation and its reversibility are demonstrated by a simple but rational strategy using the structural characteristics of crown ether-based rotaxanes. The structure of a polymer contg. a [1]rotaxane unit at one end was controlled by conventional protection-deprotection reactions, giving rise to a reversible linear-cyclic polymer structural transformation.
- 13Schäfer, L. In Excluded Volume Effects in Polymer Solutions: As Explained by the Renormalization Group; Schäfer, L., Ed.; Springer: Berlin, Heidelberg, 1999; pp 143– 154, DOI: 10.1007/978-3-642-60093-7_9 .There is no corresponding record for this reference.
- 14Duplantier, B. Exact contact critical exponents of a self-avoiding polymer chain in two dimensions. Phys. Rev. B 1987, 35, 5290– 5293, DOI: 10.1103/PhysRevB.35.529014Exact contact critical exponents of a self-avoiding polymer chain in two dimensionsDuplantierPhysical review. B, Condensed matter (1987), 35 (10), 5290-5293 ISSN:0163-1829.There is no expanded citation for this reference.
- 15Duplantier, B. Statistical mechanics of polymer networks of any topology. J. Stat. Phys. 1989, 54, 581– 680, DOI: 10.1007/BF01019770There is no corresponding record for this reference.
- 16Hsu, H.-P.; Nadler, W.; Grassberger, P. Scaling of Star Polymers with 1–80 Arms. Macromolecules 2004, 37, 4658– 4663, DOI: 10.1021/ma035595816Scaling of Star Polymers with 1-80 ArmsHsu, Hsiao-Ping; Nadler, Walter; Grassberger, PeterMacromolecules (2004), 37 (12), 4658-4663CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)We present large statistics simulations of 3-dimensional star polymers with up to f = 80 arms and with up to 4000 monomers per arm for small values of f. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor v < 1. We use this to allow all arms to be attached at the central site, and we use the "magic" value v = 0.6 to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as obsd. from the center-to-end distances) but also the partition sum. The latter gives very precise ests. of the crit. exponents γf. For completeness we made also extensive simulations of linear (unbranched) polymers which give the best ests. for the exponent γ.
- 17Baulin, V. A.; Lee, N.-K.; Johner, A.; Marques, C. M. Micellization of Sliding Polymer Surfactants. Macromolecules 2006, 39, 871– 876, DOI: 10.1021/ma051955a17Micellization of Sliding Polymer SurfactantsBaulin, Vladimir A.; Lee, Nam-Kyung; Johner, Albert; Marques, Carlos M.Macromolecules (2006), 39 (2), 871-876CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)Following up a recent paper on grafted sliding polymer layers [Macromols. 2005, 38, 1434-1441], we investigated the influence of the sliding degree of freedom on the self-assembly of sliding polymeric surfactants that can be obtained by complexation of polymers with cyclodextrins. In contrast to the micelles of quenched block copolymer surfactants, the free energy of micelles of sliding surfactants can exhibit two min.: the first corresponding to small micelles with sym. arm lengths and the second corresponding to large micelles with asym. arm lengths. The relative sizes and concns. of small and large micelles in the soln. depend on the mol. parameters of the system. The appearance of small micelles drastically reduces the kinetic barrier, allowing for the fast formation of equil. micelles.
- 18Ben-Shaul, A.; Szleifer, I.; Gelbart, W. M. Chain Organization and Thermodynamics in Micelles and Bilayers. I. Theory. J. Chem. Phys. 1985, 83, 3597– 3611, DOI: 10.1063/1.44916618Chain organization and thermodynamics in micelles and bilayers. I. TheoryBen-Shaul, A.; Szleifer, I.; Gelbart, W. M.Journal of Chemical Physics (1985), 83 (7), 3597-611CODEN: JCPSA6; ISSN:0021-9606.Starting from the partition function of a micellar aggregate, the various assumptions involved in decompg. the aggregate's std. chem. potential into surface and core terms are explicitly stated and discussed. The conformational statistics of the amphiphile hydrocarbon chains (tails) composing the hydrophobic core is governed by the hard core repulsive interactions between chain segments. The d. within the core is uniform and liq.-like. By appropriate expansion of the aggregate's configurational integral, explicit expressions are derived for the (singlet) distribution function of chain conformations and the chain's conformational partition function (free energy). These quantities depend on the thickness and curvature (geometry) of the hydrophobic core via the lateral pressures representing the geometric packing constraints. The variations in the conformational contribution of the aggregate's chem. potential may be comparable to those due to the surface term. Geometric packing constraints rather than internal energy (gauche-trans) effects are the dominant factors detg. chain statistics.
- 19Szleifer, I.; Ben-Shaul, A.; Gelbart, W. M. Chain organization and thermodynamics in micelles and bilayers. II. Model calculations. J. Chem. Phys. 1985, 83, 3612, DOI: 10.1063/1.44916719Chain organization and thermodynamics in micelles and bilayers. II. Model calculationsSzleifer, I.; Ben-Shaul, A.; Gelbart, W. M.Journal of Chemical Physics (1985), 83 (7), 3612-20CODEN: JCPSA6; ISSN:0021-9606.Based on the theory presented in preceding paper (B-S et al., 1985) mol. and thermodn. properties were calcd. for model chains packed in micellar aggregates of 3 typical geometries: spheres, cylinders, and planar bilayers. Each possible conformation of a model chain is equiv. to a sequence of walks on a regular cubic lattice. The internal energy of a given conformation is proportional to the no. of "kinks" (π/2 bond angles). The kink (gauche) energy measures the inherent flexibility of the chain. Bond order parameter profiles were calcd. for chains packed in aggregates of various curvature and radius. In all cases the degree of conformational freedom increases from the chain head towards its end. The same qual. behavior is obsd. for entirely flexible (zero kink energy) chains. This implies that the internal energy of the chain plays only a secondary role, compared to that of the packing constraints in detg. chain conformational statistics in micellar aggregates. The geometry dependence of the conformational free energy is dominated by the entropic contribution. The differences between the minimal free energies of chains in different geometries are generally small. Yet, they may be comparable in magnitude to the changes assocd. with the surface ("opposing forces") contributions to the geometry dependence of the micelle's free energy.
- 20Gezae Daful, A.; Baulin, V. A.; Bonet Avalos, J.; Mackie, A. D. Accurate Critical Micelle Concentrations from a Microscopic Surfactant Model. J. Phys. Chem. B 2011, 115, 3434– 3443, DOI: 10.1021/jp110230220Accurate critical micelle concentrations from a microscopic surfactant modelGezae Daful Asfaw; Baulin Vladimir A; Bonet Avalos Josep; Mackie Allan DThe journal of physical chemistry. B (2011), 115 (13), 3434-43 ISSN:.A single chain mean field theory is used to quantitatively describe the micellization process of the nonionic polyethylene oxide alkyl ether, C(n)E(m) class of surfactants at 25 °C. An explicit but simple microscopic model with only three interaction parameters is shown to be able to reproduce with high accuracy the critical micelle concentrations of a wide range of head and tail surfactant lengths. In addition, the aggregation number of the micelles is studied, the effect of the number of the hydrophobic and hydrophilic segments on CMC and aggregation number of the micelles are discussed and volume fraction profiles are given.
- 21Israelachvili, J. N. Intermolecular and surface forces, 2nd ed.; Academic Press: Orlando, FL, 1991.There is no corresponding record for this reference.
- 22Pogodin, S.; Baulin, V. A. Coarse-Grained Models of Phospholipid Membranes within the Single Chain Mean Field Theory. Soft Matter 2010, 6, 2216– 2226, DOI: 10.1039/b927437e22Coarse-grained models of phospholipid membranes within the single chain mean field theoryPogodin, Sergey; Baulin, Vladimir A.Soft Matter (2010), 6 (10), 2216-2226CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)The single chain mean field theory is used to simulate the equil. structure of phospholipid membranes at the mol. level. Three levels of coarse-graining of DMPC phospholipid surfactants are present: The detailed 44-beads double tails model, the 10-beads double tails model and the minimal 3-beads model. The authors show that all 3 models are able to reproduce the essential equil. properties of the phospholipid bilayer, while the simplest 3-beads model is the fastest model which can describe adequately the thickness of the layer, the area per lipid and the rigidity of the membrane. The accuracy of the method in description of equil. structures of membranes compete with Monte Carlo simulations while the speed of computation and the mean field nature of the approach allows for straightforward applications to systems with great complexity.
- 23Guo, Y.; Pogodin, S.; Baulin, V. A. General model of phospholipid bilayers in fluid phase within the single chain mean field theory. J. Chem. Phys. 2014, 140, 174903, DOI: 10.1063/1.487358623General model of phospholipid bilayers in fluid phase within the single chain mean field theoryGuo, Yachong; Pogodin, Sergey; Baulin, Vladimir A.Journal of Chemical Physics (2014), 140 (17), 174903/1-174903/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Coarse-grained model for satd. phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsatd. phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equil. and mech. properties of a range of satd. lipid mols. that differ only in length of their hydrophobic tails and unsatd. (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as satd. lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equil. area per lipid correspond to exptl. measured values for each lipid, changing linearly with the length of the tail. The model for unsatd. phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estn. of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable ests. for free energies. The proposed model may further be used for studies of mixts. of lipids, small mol. inclusions, interactions of bilayers with embedded proteins. (c) 2014 American Institute of Physics.
- 24Rosenbluth, M. N.; Rosenbluth, A. W. Monte Carlo Calculation of the Average Extension of Molecular Chains. J. Chem. Phys. 1955, 23, 356– 359, DOI: 10.1063/1.174196724Monte Carlo calculation of the average extension of molecular chainsRosenbluth, Marshall N.; Rosenbluth, Arianna W.Journal of Chemical Physics (1955), 23 (), 356-9CODEN: JCPSA6; ISSN:0021-9606.The behavior of chains of many mols. was investigated by solving a restricted random-walk problem on a cubic lattice in 3 dimensions and a square lattice in 2 dimensions. For chains of length up to 64 links, the av. squared extension of the chain R2 was related to the no. of links N by the relation, 〈R2〉 = N1.22 in the 3-dimensional case, and by the relation 〈R2〉 = 0.917(N)1.45 in the 2-dimensional case. Along with the results of Wall, et al. (C.A. 48, 12505b)the same exponent, 1.22, applies to 3 different types of lattice