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  • 1
    Electronic Resource
    Electronic Resource
    Concentration fluctuation effects on disorder–order transitions in block copolymer melts (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 4670-4677 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study transitions to periodic structures in block copolymers melts, including concentration fluctuations self-consistently in the analysis. Phase diagrams are constructed for diblock and triblock copolymers of finite molecular weight. The concentration fluctuations increase the stability of the isotropic state, and induce a shift in k*, the wave vector of maximum scattered intensity, to lower values as the transition is approached. We calculate the shift in k* near the transition, and obtain the anisotropic scattering function in the ordered state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461736
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  • 2
    Electronic Resource
    Electronic Resource
    Concentration fluctuations in polymer blend thermodynamics (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 1704-1708 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Monomer concentration fluctuations in high molecular weight polymer blends are investigated. The fluctuations reduce the value of the χ interaction term in the Flory–Huggins free energy by a factor of (1-6/π2) and add a concentration and molecular weight contribution which decreases phase stability for off-critical compositions. Except at the critical point, the spinodal values are smaller than those predicted from a Flory–Huggins-type free energy. For an incompressible blend with components of equal size N, the corrections to the spinodal were found to vary as ||1−2φ0||4/3N−1/3, where φ0 is the mean concentration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455116
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  • 3
    Electronic Resource
    Electronic Resource
    Theory of microphase separation in block copolymer solutions (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 1995-2002 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Microphase separation in semidilute solutions of block copolymers in nonselective good solvent is analyzed. The swelling due to the presence of solvent is taken into account. The solvent effects on the thermodynamics in the disordered region and in the ordered region in the weak segregation limit are discussed. It is found that the concentration of block copolymer at the microphase separation transition scales as N−0.62 in good solvents and as N−1/2 in Φ solvents. In the asymptotic semidilute regime in good solvents, the coexistence curve at the microphase separation transition is negligible, and the transition scales as (χ'AB φ1.61N)t ∼constant, where the constant is determined by the relative composition of the blocks in the block copolymer and χAB is proportional to the usual Flory interaction parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456042
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  • 4
    Electronic Resource
    Electronic Resource
    Phase transitions in random copolymers (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 7385-7397 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Ideal random AB copolymers with degree of polymerization N are mixtures of N+1 types of chains with different compositions (fractions fi of A monomers). Conditions for single phase and multiphase equilibria are studied using Flory–Huggins free energy of mixing with χ representing the A–B interaction parameter. The spinodal for one phase instability is given by χs=[2f(1−f)]−1 for all N, where f is the average A fraction in the system. The transition from one to two phases is continuous at χ=χs when f=0.5 and discontinuous at χ≤χs when f≠0.5. Three, four, and more phases become stable at larger values of χ. Our numerical solution suggests that the stability range for multiple phases approaches Δχ≈0.15 at large (but finite) N. Macroscopically and microscopically phase separated states are investigated with the Landau approach of Fredrickson, Milner and Leibler. The Landau method gives reasonable but inexact results for two macroscopic phases when the random copolymer has compositional symmetry (f=0.5). A disordered mesophase is expected to be the most stable state at least over a range Δχ≈0.15 above the critical point when N(very-much-greater-than)1. The Landau approach with a single order parameter cannot be used for discontinuous transitions in random copolymers (f≠0.5).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.464729
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  • 5
    Electronic Resource
    Electronic Resource
    Transitions to periodic structures: Higher harmonic corrections with concentration fluctuations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 5272-5279 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Weakly first order transitions from a disordered state to periodic ordered phases, are observed in many physical systems, such as diblock copolymer melts, weak crystallization in liquids and micellar systems. In the weak segregation regime, successful theories have used a Landau–Ginzburg form of the free energy. It is well established that a complete description of the system necessitates the inclusion of thermally induced concentration fluctuations in the theory. In some cases it may also be important to construct the density in the periodic structure from higher harmonic vectors other than simply the first ones. Recently, exotic structures have been observed experimentally which cannot be distinguished from simple morphologies unless higher harmonics and their phases are included. In this paper we present a general theory where the order parameter is expanded up to the second harmonic vectors with phase factors, and where the concentration fluctuations are included self-consistently in the analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467191
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  • 6
    Electronic Resource
    Electronic Resource
    Precipitation of highly charged polyelectrolyte solutions in the presence of multivalent salts (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 5781-5791 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Solutions of highly charged polyelectrolyte chains are described by a model that introduces ion condensation as a random charge along the polymer. The degree of condensation is obtained by solving the Poisson–Boltzmann equation with cylindrical geometry. Short range electrostatic attractions between the monomers via the condensed counterions of high enough valency lead to reversible chain precipitation. The range of polymer concentration over which salt-free solutions are unstable is determined, as well as the miscibility of the chains when salt is added. Redissolution at high salt concentration is due to a screening of the short range electrostatic attractions. Precipitation of chains in mixtures of movalent and multivalent salts is also studied. We find the range of salt concentration where chains precipitate. The model explains the experimental results on the precipitation of sodium and lanthanum polystyrene sulfonate solutions in presence of multivalent salts [LaCl3 and Th(NO3)4]. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470459
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  • 7
    Electronic Resource
    Electronic Resource
    Study of random copolymers in dilute solution (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 7744-7748 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Single chain AB random copolymers in a solvent which is good for B and bad for A are studied by Monte Carlo simulation. The chain statistics of the polymer coil are analyzed as a function of the number of chain beads, N, and A monomer fraction, fe, in the regime where the chain obeys self-avoiding walk (SAW) statistics. The results are compared to a modified Flory argument [S. P. Obukhov, J. Phys. A 19, 3655 (1986)]. The argument predicts a correction to the mean radius of gyration of the coil, Rg, which scales as N−0.5 in the SAW regime. We fit the model equation to the simulations data and find good agreement. We also calculate the dispersion of Rg as a function of fe. We find that as fe is increased from fe=0 to fe=0.3, the dispersion of Rg increases. Finally, we generate contours of A and B monomer density as a function of the distance from the center of mass of the chain. The contours show the emergence of an A rich region approximately the size of Rg at the center of the coil suggesting the structure of collapsed heterogeneous macromolecules [H. S. Chan and K. A. Dill, Physics Today 2, 24 (1993)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466817
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  • 8
    Electronic Resource
    Electronic Resource
    Random phase approximation for complex charged systems: Application to copolyelectrolytes (polyampholytes) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 507-517 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study binary polyelectrolytes in the melt state and in concentrated solutions using the random phase approximation (RPA). We compute the thermodynamics and electrostatics of chemically linked polyelectrolytes chains into block copolymer molecules (copolyelectrolytes). Polyelectrolytes blends and copolyelectrolytes in the presence of free ions have Debye–Hückel-type effective monomer–monomer interactions, even when the polymer chains are not charged. Copolyelectrolyte of chemically linked chains of opposite charge in the absence of counterions, have ion–ion effective interactions characteristic of a dielectric medium, contrary to the case of polyelectrolyte blends where these effective interactions are Debye–Hückel type, even on the absence of free ions. The dielectric constant in such a diblock copolymer melt is proportional to the square of the degree of polymerization Np. In the reference state (without interactions) RPA assumes random walk statistics, which are nearly unperturbed in the dielectric; we find the scaling of the end-to-end vector square of a chain in the dielectric. We also discuss the physics of other copolyelectrolytes (polyampholytes).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466965
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  • 9
    Electronic Resource
    Electronic Resource
    Ion condensation in salt-free dilute polyelectrolyte solutions (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 3145-3157 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study ion condensation in salt-free dilute solutions of polyelectrolyte chains of different fractal geometries, from random walks to rigid rods. In finite size chains with a discrete charge distribution, ion condensation is only observed in multiple chain systems. A thermodynamic analysis of ion condensation with linearized interactions among the condensed counterions and the monomers leads to rigid rod lowest free energy conformations, regardless of the values of the valency of the monomers (zm), the negative value of the ratio of the valency of the counterions to the valency of the monomers (Pz), and the ratio of the Bjerrum length (lB) to the distance between charges along the polyion (b). As z2mPzlB/b increases, however, the fraction of condensed counterions increases and the polyion concentration at which ion condensation appears decreases. Above this critical polyion concentration, ion condensation is observed even when lB/b〈1/z2mPz. When correlations are included, representing the tendency of the condensed counterions to be surrounded by opposite sign charges, the chain conformation is strongly dependent on the valency of the counterions and lB/b. For large valency counterions and/or lB/b values, collapsed finite chains have lower free energies than rigid rods. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470248
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  • 10
    Electronic Resource
    Electronic Resource
    The Early Stages of the Phase Separation Dynamics in Polydisperse Polymer Blends (1994)
    s.l. : American Chemical Society
    Macromolecules 27 (1994), S. 4231-4241 
    Details
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ma00093a026
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