Carol K. Hall

North Carolina State University, Raleigh, North Carolina, United States

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Publications (138)370.83 Total impact

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    [show abstract] [hide abstract]
    ABSTRACT: How nanoparticles interact with biomembranes is central for understanding their bioactivity. Biomembranes wrap around nanoparticles if the adhesive interaction between the nanoparticles and membranes is sufficiently strong to compensate for the cost of membrane bending. In this article, we review recent results from theory and simulations that provide new insights on the interplay of bending and adhesion energies during the wrapping of nanoparticles by membranes. These results indicate that the interplay of bending and adhesion during wrapping is strongly affected by the interaction range of the particle-membrane adhesion potential, by the shape of the nanoparticles, and by shape changes of membrane vesicles during wrapping. The interaction range of the particle-membrane adhesion potential is crucial both for the wrapping process of single nanoparticles and the cooperative wrapping of nanoparticles by membrane tubules.
    Advances in colloid and interface science 03/2014; · 5.68 Impact Factor
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    ABSTRACT: Human tRNA(Lys3)UUU is the primer for replication HIV. The HIV-1 nucleocapsid protein, NCp7, facilitates htRNA(Lys3)UUU recruitment from the host cell by binding to and remodeling the tRNA structure. Human tRNA(Lys3)UUU is post-transcriptionally modified, but until recently the importance of those modifications in tRNA recognition by NCp7 was unknown. Modifications such as the 5-methoxycarbonylmethyl-2-thiouridine at anticodon wobble position-34 and 2-methylthio-N6-threonylcarbamoyladenosine, adjacent to the anticodon at position-37, are important to the recognition of htRNA(Lys3)UUU by NCp7. Several short peptides selected from phage display libraries were found to also preferentially recognize these modifications. Evolutionary algorithms (Monte Carlo and self-consistent mean field) and Assisted Model Building with Energy Refinement were used to optimize the peptide sequence in silico while fluorescence assays were developed and conducted to verify the in silico results and elucidate a 15-amino acid signature sequence (R-W-Q/N-H-X2-F-Pho-X-G/A-W-R-X2-G, where X can be most amino acids and Pho is hydrophobic) that recognized the tRNA's fully modified anticodon stem and loop domain, hASL(Lys3)UUU. Peptides of this sequence specifically recognized and bound modified tRNALys3 with an affinity 10-fold higher than the starting sequence. Thus, this approach provides an effective means of predicting sequences of RNA binding peptides that have better binding properties. Such peptides can be used in cell and molecular biology, as well as biochemistry to explore RNA binding proteins, and to inhibit those protein functions.
    Biochemistry 01/2014; · 3.38 Impact Factor
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    ABSTRACT: The goal of this work is to understand how the sequence of a protein affects the likelihood that it will form an amyloid fibril and the kinetics along the fibrillization pathway. The focus is on very short fragments of amyloid proteins since these play a role in the fibrillization of the parent protein and can form fibrils themselves. Discontinuous molecular dynamics simulations using the PRIME20 force field were performed of the aggregation of 48-peptide systems containing SNQNNF (PrP (170-175), SSTSAA (RNaseA(15-20), MVGGVV (Aβ(35-40)), GGVVIA (Aβ(37-42) and MVGGVVIA (Aβ(35-42)). In our simulations SNQQNF, SSTTSAA and MVGGVV form large numbers of fibrillar structures spontaneously (as in experiment). GGVVIA forms β-sheets that do not stack into fibrils (unlike experiment). The combination sequence MVGGVVIA forms less fibrils than MVGGVV, hindered by the presence of the hydrophobic residues at the C- terminal. Analysis of the simulation kinetics and energetics reveals why MVGGVV forms fibrils and GGVVIA does not, and why adding I and A to MVGGVVIA reduces fibrillization and enhances amorphous aggregation into oligomeric structures. The latter helps explain why Aβ(1-42) assembles into more complex oligomers than Aβ(1-40), a consequence of which is that it is more strongly associated with Alzheimer's disease. © Proteins 2014;. © 2014 Wiley Periodicals, Inc.
    Proteins Structure Function and Bioinformatics 01/2014; · 3.34 Impact Factor
  • Xingqing Xiao, Paul F Agris, Carol K Hall
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    ABSTRACT: The mechanism by which proteins recognize and bind the post-transcriptional modifications of RNAs is unknown, yet these interactions play important functions in biology. Atomistic molecular dynamics simulations were performed to examine the folding of the model peptide chain -RVTHHAFLGAHRTVG- and the complex formed by the folded peptide with the native anticodon stem and loop of the human tRNA(Lys3) (hASL(Lys3)) in order to explore the binding mechanism. By analyzing and comparing two folded conformations of this peptide obtained from the folding simulation, we found that the van der Waals (VDW) energy is necessary for the thermal stability of the peptide, and the charge-charge (ELE + EGB) energy is crucial for determining the three-dimensional folded structure of the peptide backbone. Subsequently, two conformations of the peptide were employed to investigate their binding behaviors to hASL(Lys3). The metastable folded peptide was found to bind to hASL(Lys3) much easier than the stable folded peptide in the binding simulations. An energetic analysis reveals that the VDW energy favors the binding, whereas the ELE + EGB energies disfavor the binding. Arginines on the peptide preferentially attract the phosphate backbone via the inter-chain ELE + EGB interaction, significantly contributing to the binding affinity. The hydrophobic phenylalanine interacts with the anticodon loop of hASL(Lys3) via the inter-chain VDW interaction, significantly contributing to the binding specificity.
    Journal of biomolecular structure & dynamics 01/2014; · 4.99 Impact Factor
  • Xingqing Xiao, Carol K Hall, Paul F Agris
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    ABSTRACT: We developed a search algorithm combining Monte Carlo (MC) and self-consistent mean field techniques to evolve a peptide sequence that has good binding capability to the anticodon stem and loop (ASL) of human lysine tRNA species, tRNA(Lys3), with the ultimate purpose of breaking the replication cycle of human immunodeficiency virus-1. The starting point is the 15-amino-acid sequence, RVTHHAFLGAHRTVG, found experimentally by Agris and co-workers to bind selectively to hypermodified tRNA(Lys3). The peptide backbone conformation is determined via atomistic simulation of the peptide-ASL(Lys3) complex and then held fixed throughout the search. The proportion of amino acids of various types (hydrophobic, polar, charged, etc.) is varied to mimic different peptide hydration properties. Three different sets of hydration properties were examined in the search algorithm to see how this affects evolution to the best-binding peptide sequences. Certain amino acids are commonly found at fixed sites for all three hydration states, some necessary for binding affinity and some necessary for binding specificity. Analysis of the binding structure and the various contributions to the binding energy shows that: 1) two hydrophilic residues (asparagine at site 11 and the cysteine at site 12) "recognize" the ASL(Lys3) due to the VDW energy, and thereby contribute to its binding specificity and 2) the positively charged arginines at sites 4 and 13 preferentially attract the negatively charged sugar rings and the phosphate linkages, and thereby contribute to the binding affinity.
    Journal of biomolecular structure & dynamics 10/2013; · 4.99 Impact Factor
  • Ravish Malik, Carol K. Hall, Jan Genzer
    Macromolecules 05/2013; 46(10):4207-4214. · 5.52 Impact Factor
  • Emily Marie Curtis, Carol K Hall
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    ABSTRACT: A new intermediate resolution model for phospholipids, LIME, designed for use with discontinuous molecular dynamics (DMD) simulations is presented. The implicit-solvent model was developed using a multi-scale modeling approach in which the geometric and energetic parameters are obtained by collecting data from atomistic simulations of a system composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecules and explicit water. In the model, 14 coarse-grained sites that are classified as 1 of 6 types represent DPPC. DMD simulations performed on a random solution of DPPC resulted in the formation of a defect free bilayer in less than 4 hours. The bilayer formed quantitatively reproduces the main structural properties (e.g. area per lipid, bilayer thickness, bond order parameters) that are observed experimentally. In addition, the bilayer transitions from a liquid-crystalline phase to a tilted gel phase when the temperature is reduced. Transbilayer movement of a lipid from the bottom leaflet to the top leaflet is observed when the temperature is increased.
    The Journal of Physical Chemistry B 03/2013; · 3.61 Impact Factor
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    ABSTRACT: Based on Monte Carlo and Molecular Dynamics computer simulations we investigate the aggregation patterns and dynamics of model colloidal mixtures consisting of particles with either one or two, oppositely oriented, induced dipole moments. The mixtures are confined to two spatial dimensions. Our model is inspired by recent optical-microscopy experiments involving polystyrene particles with (and without) gold patches. For a broad range of parameters, we find the model systems to self-assemble via a two-step scenario involving first percolation along the field, followed by a percolation transition in the transverse direction. The resulting two-dimensional networks are characterized by strongly hindered translational dynamics.
    Soft Matter 01/2013; 9(8):2518-2524. · 3.91 Impact Factor
  • Mookyung Cheon, Iksoo Chang, Carol K Hall
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    ABSTRACT: We investigate the fibrillization process for amyloid tau fragment peptides (VQIVYK) by applying the discontinuous molecular dynamics method to a system of 48 VQIVYK peptides modeled using a new protein model/force field, PRIME20. The aim of the article is to ascertain which factors are most important in determining whether or not a peptide system forms perfect coherent fibrillar structures. Two different directional criteria are used to determine when a hydrogen bond occurs: the original H-bond constraints and a parallel preference H-bond constraint that imparts a slight bias towards the formation of parallel versus antiparallel strands in a β-sheet. Under the original H-bond constraints, the resulting fibrillar structures contain a mixture of parallel and antiparallel pairs of strands within each β-sheet over the whole fibrillization temperature range. Under the parallel preference H-bond constraints, the β-sheets within the fibrillar structures are more likely to be parallel and indeed become perfectly parallel, consistent with X-ray crystallography, at a high temperature slightly below the fibrillization temperature. The high temperature environment encourages the formation of perfect fibril structures by providing enough time and space for peptides to rearrange during the aggregation process. There are two different kinetic mechanisms, template assembly with monomer addition at high temperature and merging/rearrangement without monomer addition at low temperature, which lead to significant differences in the final fibrillar structure. This suggests that the diverse fibril morphologies generally observed in vitro depend more on environmental conditions than has heretofore been appreciated.
    Protein Science 08/2012; 21(10):1514-27. · 2.74 Impact Factor
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    ABSTRACT: Assembly of normally soluble proteins into ordered aggregates, known as amyloid fibrils, is a cause or associated symptom of numerous human disorders, including Alzheimer's and the prion diseases. Here, we test the ability of discontinuous molecular dynamics (DMD) simulations based on PRIME20, a new intermediate-resolution protein force field, to predict which designed hexapeptide sequences will form fibrils, which will not, and how this depends on temperature and concentration. Simulations were performed on 48-peptide systems containing STVIIE, STVIFE, STVIVE, STAIIE, STVIAE, STVIGE, and STVIEE starting from random-coil configurations. By the end of the simulations, STVIIE and STVIFE (which form fibrils in vitro) form fibrils over a range of temperatures, STVIEE (which does not form fibrils in vitro) does not form fibrils, and STVIVE, STAIIE, STVIAE, and STVIGE (which do not form fibrils in vitro) form fibrils at lower temperatures but stop forming fibrils at higher temperatures. At the highest temperatures simulated, the results on the fibrillization propensity of the seven short de novo designed peptides all agree with the experiments of López de la Paz and Serrano. Our results suggest that the fibrillization temperature (temperature above which fibrils cease to form) is a measure of fibril stability and that by rank ordering the fibrillization temperatures of various sequences, PRIME20/DMD simulations could be used to ascertain their relative fibrillization propensities. A phase diagram showing regions in the temperature-concentration plane where fibrils are formed in our simulations is presented.
    Journal of Molecular Biology 03/2012; 416(4):598-609. · 3.91 Impact Factor
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    Erin M Phelps, Carol K Hall
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    ABSTRACT: The results of a computer simulation study of the aggregation kinetics of a large system of model peptides with particular focus on the formation of intermediates are presented. Discontinuous molecular dynamic simulations were used in combination with our intermediate-resolution protein model, PRIME, to simulate the aggregation of a system of 192 polyalanine (KA(14) K) peptides at a concentration of 5 mM and a reduced temperature of T* = 0.13 starting from a random configuration and ending in the assembly of a fibrillar structure. The population of various structures, including free monomers, beta sheets, amorphous aggregates, hybrid aggregates, and fibrils, and the transitions between the structures were tracked over the course of 30 independent simulations and averaged together. The aggregation pathway for this system starts with the association of free monomers into small amorphous aggregates that then grow to moderate size by incorporating other free monomers or merging with other small amorphous aggregates. These then rearrange into either small beta sheets or hybrid aggregates formed by association between unstructured chains and beta sheets, both of which grow in size by adding free monomer chains or other small aggregates, one at a time. Fibrillar structures are formed initially either by the stacking of beta sheets, rearrangement of hybrid aggregates or association between beta sheets and hybrid aggregates. They grow by the addition of beta sheets, hybrid aggregates, and other small fibrillar structures. The rearrangement of amorphous aggregates into beta sheets is a critical and necessary step in the fibril formation pathway.
    Proteins Structure Function and Bioinformatics 02/2012; 80(6):1582-97. · 3.34 Impact Factor
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    ABSTRACT: Based on Discontinuous Molecular Dynamics (DMD) simulations we present a phase diagram of two-dimensional nano-particles with dipole-like short-ranged interactions. Similar to systems with true, long-ranged dipolar interactions the present system undergoes a transition from an isotropic fluid phase into a polymer-like fluid, characterized by an association of most particles into clusters. Further decrease of the temperature leads to a percolated system which, moreover, displays dynamical properties reminiscent of a gel. Specifically, we find a plateau in the mean-squared displacement and a non-gaussian behavior of the self-part of the van Hove correlation function. In the high density region we observe crystallization from the isotropic fluid into a solid phase with hexagonal order. Surprisingly, the crystallization is accompanied by a global parallel ordering of the dipole moments, i.e., a ferroelectric phase. This behavior is in marked contrast to what is found in 2D systems with long-ranged dipolar interactions. Our results allow insights into the design of gel-like or highly ordered structures at interfaces, shells around droplets and bubbles and new-sheet like materials.
    Soft Matter 01/2012; 8(5):1521-1531. · 3.91 Impact Factor
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    Mookyung Cheon, Iksoo Chang, Carol K Hall
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    ABSTRACT: Protein aggregation is associated with fatal neurodegenerative diseases, including Alzheimer's and Parkinson's. Mapping out kinetics along the aggregation pathway could provide valuable insights into the mechanisms that drive oligomerization and fibrillization, but that is beyond the current scope of computational research. Here we trace out the full kinetics of the spontaneous formation of fibrils by 48 Aβ(16-22) peptides, following the trajectories in molecular detail from an initial random configuration to a final configuration of twisted protofilaments with cross-β-structure. We accomplish this by performing large-scale molecular-dynamics simulations based on an implicit-solvent, intermediate-resolution protein model, PRIME20. Structural details such as the intersheet distance, perfectly antiparallel β-strands, and interdigitating side chains analogous to a steric zipper interface are explained by and in agreement with experiment. Two characteristic fibrillization mechanisms - nucleation/templated growth and oligomeric merging/structural rearrangement - emerge depending on the temperature.
    Biophysical Journal 11/2011; 101(10):2493-501. · 3.67 Impact Factor
  • Ravish Malik, Carol K. Hall, Jan Genzer
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    ABSTRACT: We present the results of kinetic Monte Carlo simulations aimed at exploring the effect of copolymer sequence distribution on the dynamics of phase separation of an immiscible A/B binary homopolymer blend. Diblock, protein-like copolymers (PLCs), simple linear gradient, random, and alternating copolymers having equal number of A and B segments, identical chemical composition, and chain length are considered as compatibilizers. All copolymers, irrespective of their sequence, retard the phase separation process by migrating to the biphasic interface between the A/B interface, thereby minimizing the interfacial energy and promoting adhesion between the homopolymer-rich phases. As expected, diblock copolymers perform the best and each block of the diblock copolymer penetrates the energetically favorable homopolymer-rich phase. Alternating copolymers lie at the interface and PLCs, simple linear gradient, and random copolymers weave back and forth across the interface. The weaving and penetration is more pronounced for PLCs than for simple linear gradient and random copolymers. Judging by the contact analysis, extension and conformation of the copolymers at the interface, and structure factor calculations, it is evident that for the chain lengths considered in our simulations, PLCs are better compatibilizers than alternating and random copolymers, while being on a par with simple linear gradient copolymers, but not as good as diblocks.
    Soft Matter 11/2011; 7(22):10620-10630. · 3.91 Impact Factor
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    Ravish Malik, Carol K. Hall, Jan Genzer
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    ABSTRACT: We use Monte Carlo simulation based on the bond fluctuation model to investigate how adding ≈4.92% protein-like copolymer (PLC) to an immiscible binary polymer blend affects the dynamics of phase separation. PLCs slow down effectively the process of phase separation in binary blends by migrating to the biphasic interface between the immiscible homopolymers, thereby reducing the interfacial tension. The ability of PLCs to retard effectively the process of phase separation depends sensitively on the interaction energy between the PLCs and homopolymers and the PLC chain length. PLCs compatibilize the binary blend more effectively with increasing attractive interaction between the PLC blocks and homopolymers. Nominal improvement in compatibilization of the binary blend is achieved with increasing PLC chain length. The growth of phase-separated domains follows a dynamical scaling law for both the binary blend and PLC compatibilized ternary blend in the late stages of phase separation. The universal scaling functions are nearly independent of the interaction energy and PLC chain length. Thus, the phase-separated domains grow with dynamical self-similarity irrespective of the type of PLC added to the binary blend, although the type of PLC significantly alters the growth rate of the phase-separated domains.
    Macromolecules. 09/2011; 44(20).
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    ABSTRACT: We simulate the aggregation of large systems containing palindromic peptides from the Syrian hamster prion protein SHaPrP 113-120 (AGAAAAGA) and the mouse prion protein MoPrP 111-120 (VAGAAAAGAV) and eight sequence variations: GAAAAAAG, (AG)(4) , A8, GAAAGAAA, A10, V10, GAVAAAAVAG, and VAVAAAAVAV The first two peptides are thought to act as the Velcro that holds the parent prion proteins together in amyloid structures and can form fibrils themselves. Kinetic events along the fibrillization pathway influence the types of structures that occur and variations in the sequence affect aggregation kinetics and fibrillar structure. Discontinuous molecular dynamics simulations using the PRIME20 force field are performed on systems containing 48 peptides starting from a random coil configuration. Depending on the sequence, fibrillar structures form spontaneously over a range of temperatures, below which amorphous aggregates form and above which no aggregation occurs. AGAAAAGA forms well organized fibrillar structures whereas VAGAAAAGAV forms less well organized structures that are partially fibrillar and partially amorphous. The degree of order in the fibrillar structure stems in part from the types of kinetic events leading up to its formation, with AGAAAAGA forming less amorphous structures early in the simulation than VAGAAAAGAV. The ability to form fibrils increases as the chain length and the length of the stretch of hydrophobic residues increase. However as the hydrophobicity of the sequence increases, the ability to form well-ordered structures decreases. Thus, longer hydrophobic sequences form slightly disordered aggregates that are partially fibrillar and partially amorphous. Subtle changes in sequence result in slightly different fibril structures.
    Proteins Structure Function and Bioinformatics 07/2011; 79(7):2132-45. · 3.34 Impact Factor
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    Jeffrey L Woodhead, Carol K Hall
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    ABSTRACT: We use discontinuous molecular dynamics (DMD) computer simulation to investigate the encapsulation efficiency and micellar structure of solute-carrying block copolymer nanoparticles as a function of packing fraction, polymer volume fraction, solute mole fraction, and the interaction parameters between the hydrophobic head blocks and between the head and the solute. The encapsulation efficiency increases with increasing polymer volume fraction and packing fraction but decreases with increasing head-head interaction strength. The latter is due to an increased tendency for the solute to remain on the micelle surface. We compared two different nanoparticle assembly methods, one in which the solute and copolymer co-associate and the other in which the copolymer micelle is formed before the introduction of solute. The assembly method does not affect the encapsulation efficiency but does affect the solute uptake kinetics. Both head-solute interaction strength and head-head interaction strength affect the density profile of the micelles; increases in the former cause the solute to distribute more evenly throughout the micelle, while increases in the latter cause the solute to concentrate further from the center of the micelle. We explain our results in the context of a model of drug insertion into micelles formulated by Kumar and Prud'homme; as conditions become more conducive to micelle formation, a stronger energy barrier to solute insertion forms which in turn decreases the encapsulation efficiency of the system.
    Macromolecules 06/2011; 44(13):5443-5451. · 5.52 Impact Factor
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    Mookyung Cheon, Iksoo Chang, Carol K Hall
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    ABSTRACT: We extend PRIME, an intermediate-resolution protein model previously used in simulations of the aggregation of polyalanine and polyglutamine, to the description of the geometry and energetics of peptides containing all 20 amino acid residues. The 20 amino acid side chains are classified into 14 groups according to their hydrophobicity, polarity, size, charge, and potential for side chain hydrogen bonding. The parameters for extended PRIME, called PRIME 20, include hydrogen-bonding energies, side chain interaction range and energy, and excluded volume. The parameters are obtained by applying a perceptron-learning algorithm and a modified stochastic learning algorithm that optimizes the energy gap between 711 known native states from the PDB and decoy structures generated by gapless threading. The number of independent pair interaction parameters is chosen to be small enough to be physically meaningful yet large enough to give reasonably accurate results in discriminating decoys from native structures. The most physically meaningful results are obtained with 19 energy parameters.
    Proteins Structure Function and Bioinformatics 11/2010; 78(14):2950-60. · 3.34 Impact Factor
  • Jeffrey L Woodhead, Carol K Hall
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    ABSTRACT: We investigate solute encapsulation by copolymer micelles by performing discontinuous molecular dynamics simulations on a model solute-copolymer-solvent system. In this paper, we detail the effect of system density, copolymer mole fraction, and hydrophobic interaction between copolymer head and solute on the encapsulation efficiency and phase behavior of the system. The relative hydrophobicity of solute and copolymer head units acts as a coupling parameter that determines whether the system encapsulates or the copolymer and solute aggregate separately. The presence of solute particles makes micelles form more easily than they would otherwise. Five different mesophases or morphologies are possible. The micelle-unimer transition that occurs in a solute-free copolymer-solvent system is, for moderately hydrophobic solute particles, replaced by a transition between a micelle phase and a morphology in which copolymers surround a large aggregate of solute particles. The best encapsulation occurs for highly hydrophobic solute particles where solutes are dispersed throughout the micelle's core. The manner in which our results might be used by experimentalists to improve the encapsulation behavior of drug-copolymer systems is discussed.
    Langmuir 10/2010; 26(19):15135-41. · 4.19 Impact Factor
  • Amit Goyal, Carol K Hall, Orlin D Velev
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    ABSTRACT: Dipolar colloid particles tend to align end-to-end and self-assemble into micro- and nanostructures, including gels and cocrystals depending on external conditions. We use molecular dynamics computer simulation to explore the phase behavior including formation, structure, crystallization, and/or gelation of binary systems of colloid particles with permanent dipole moments. Particle-particle interactions are modeled with a discontinuous potential. The phase diagrams of an equimolar binary mixture of dipolar colloid particles with different diameter ratios and different dipole moment ratios are calculated in the temperature-volume fraction plane. Several types of phases are found in our simulations: ordered phases including face centered cubic (fcc), hexagonal-close packed (hcp), and body-centered tetragonal (bct) at high volume fractions, and fluid, string-fluid, and gel phases at low volume fractions. We also find several coexistence regions containing ordered phases including fcc(a)+fcc(b), fcc(a)+hcp(b), hcp(a)+hcp(b), bct(a)+bct(b), and bct(a)+bct(b)+large voids where a and b are the two species. Two novel aspects of our results are the appearance of a bicontinuous gel consisting of two interpenetrating networks--one formed by chains of particles with high dipole moment and the other formed by chains of particles with low dipole moment, and cocrystals of large and small dipolar colloid particles.
    The Journal of Chemical Physics 08/2010; 133(6):064511. · 3.16 Impact Factor

Publication Stats

1k Citations
133 Downloads
370.83 Total Impact Points

Institutions

  • 1157–2014
    • North Carolina State University
      • • Department of Chemistry
      • • Department of Chemical and Biomolecular Engineering
      • • Department of Materials Science and Engineering
      Raleigh, North Carolina, United States
  • 2011–2012
    • Pusan National University
      • Department of Physics
      Pusan, Busan, South Korea
  • 2003
    • Johns Hopkins University
      • Department of Physiology
      Baltimore, MD, United States
  • 1989–2002
    • Princeton University
      • Department of Chemical and Biological Engineering
      Princeton, NJ, United States
  • 1990
    • Sandia National Laboratories
      Albuquerque, New Mexico, United States