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  • 1
    Electronic Resource
    Electronic Resource
    Interplay between gelation and phase separation in tree polymers, and the calculation of macroscopic loop density in the postgel regime (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 8151-8164 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider a very general model of equilibrium polycondensation of tree polymers and elucidate (i) the conditions that must be met for gelation to compete with phase separation under a variety of conditions; (ii) how gelation is different from a thermal transition; and (iii) how gelation can be induced not only by lowering but also by raising the temperature, thereby giving rise to the [lower critical solution temperature for gelation] phenomenon observed recently. We also preset a new and direct scheme to calculate the contributions to various functional densities from finite (sol) and infinite (gel) clusters. The scheme presents us with an elegant method to calculate the loop density explicitly and helps settle a long-standing controversy about the presence and the nature of loops in the postgel regime. The loops are macroscopic in size. Other important features are also discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480167
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  • 2
    Electronic Resource
    Electronic Resource
    Polydisperse solution of randomly branched homopolymers, inversion symmetry and critical and theta states (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 5089-5103 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We discuss the phase behavior of a model of a binary mixture of randomly branched homopolymers in a solution. The monomer–solvent interaction is determined by a Boltzmann weight w. The theory has been presented recently and is obtained by approximating the underlying lattice by a Bethe lattice of the same coordination number q. Of special interest is the class of randomly branched polymers with inversion symmetry (see the text). This class includes linear polymers. The phase diagram for the special class of polymers is very simple. There is a line C of critical points in the dilute limit on which branched polymers become a critical object in a good solvent. This is an extension of the result due to de Gennes for linear chains in an athermal solution to the above class of branched polymers in any good solvent. The line C meets with another critical line C′ for phase separation in a poor solvent. We identify the theta point as a tricritical point as first suggested by de Gennes for linear chains only. The theta point appears only in the limit of infinite polymers such that the second virial coefficient A2 vanishes. We calculate various exponents and identify the order parameter. We point out a subtle difference between the theta state and the random walk state. However, the radius of gyration exponent does have its mean-field value of 1/2 in the theta state but only in d≥3. There does not exist a tricritical point for randomly branched polymers without inversion symmetry. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475915
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  • 3
    Electronic Resource
    Electronic Resource
    Composition dependence of chi from neutron scattering, compressibility, and a purely interaction chi (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 4806-4821 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We demonstrate that the concept of a bare chi parameter as exchange energy is meaningful only within the context of a lattice theory. We introduce a simple ensemble to describe a compressible system. The ensemble shares many features present in the ensemble describing an incompressible system. This allows us to express the intensity in terms of fluctuations in only one species, a feature also present in the incompressible model. We demonstrate that the perplexing features seen experimentally and theoretically in the wings of small-angle-neutron-scattering (SANS) measured χSANS are spurious and unrelated to the energetics, and result from a definition that leaves behind some nonenergetic contribution, which dominates the behavior in the wings and controls the sign of the curvature. It is easy to identify an appropriate χscatt that properly characterizes the interactions without any superfluous composition dependence. We use our recently developed lattice theory, which gives rise to genuine composition dependence in χscatt due to nonrandomness. For a symmetric blend, χscatt depends only weakly on compressibility. This is not true of an asymmetric blend, where compressibility effects can be strong. In particular, we demonstrate that a linear χscatt results from the asymmetry in the model and not from the compressibility. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481084
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  • 4
    Electronic Resource
    Electronic Resource
    A binary mixture of monodisperse polymers of fixed architectures, and the critical and the theta states (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 5104-5121 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study the complete phase diagram for a model of a binary mixture of two interacting polymer species A and A′, each of fixed architecture (dendrimer, star, linear, or regularly branched polymer, brush, etc.) and size given by the number M (or M′) of monomers in it, on a lattice of coordination number q. For M′=1, the model describes a solution. Branchings, if any, are regular in these architectures. This feature alone makes these polymers different from polymers with random branchings studied in the preceding paper [J. Chem. Phys. 108, 5089 (1998)]. There exists a theta point regardless of the fixed architecture, which is not the case for random branchings. We identify this point as a tricritical point T at which one of the two sizes M and M′ diverges. Two critical lines C and C′ meet at T. The criticality along C corresponds to the criticality of an infinitely large polymer of any fixed architecture, not necessarily linear. This polymer is a fractal object. We identify the relevant order parameter and calculate all the exponents along C. The criticality along C′ is that of the Ising model. Connected to T is a line t of triple points. The above results are well-known for a solution of linear polymers which we have now extended to a binary mixture of polymers of any arbitrary but fixed architecture. Our results show that regular branchings have no effects on the topology of the phase diagram and, in particular, on the existence of a theta state. The critical properties are also unaffected which is a surprising result. We point out the same subtle difference between polymers at the theta point and random walks as was found for a very special class of randomly branched polymers in the preceding paper (see the text). The behavior of a blend of a fixed aspect ratio a=M/M′, M→∞, is singular, as discussed in the text. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475916
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  • 5
    Electronic Resource
    Electronic Resource
    Universal equation of state for an interacting multicomponent mixture of polymers (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 6952-6962 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a closed form universal equation of state for an interacting multicomponent mixture of polymers of any architecture and dispersity. The equation is obtained by solving the model on a Bethe lattice and goes beyond the random mixing approximation. The latter property endows our theory with features that are consistent with real systems. The equation of state, though an approximate one, is thermodynamically consistent and is valid even in the incompressible limit. The predictions of the equation are consistent with simulations and experiments, as discussed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476111
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  • 6
    Electronic Resource
    Electronic Resource
    Multicomponent system with polydisperse species (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 9101-9104 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider a multicomponent system containing polydisperse species of polymers produced in equilibrium polymerization. We present a general theory of such a system by solving the model on a Bethe lattice. We show that the resulting free energy has certain universal features regardless of the number of components, their architecture, and dispersity. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475201
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  • 7
    Electronic Resource
    Electronic Resource
    Cluster size distribution of voids in a polymer melt (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 3947-3956 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: By extending a recently developed Bethe lattice theory, we calculate the cluster size distribution and average cluster size of voids in the presence of polymers. Because of the presence of interactions and because polymers have a size different from that of voids, the model we investigate is a correlated percolation model. The effects of interactions, the pressure P, the degree of polymerization (DP) M, the coordination number q, and the possibility of void percolation on the above properties are evaluated. It is found that small-sized clusters are in overwhelming majority and constitute a large fraction of the total free volume in cases of interest. Attractive monomer–monomer interactions favor the formation of larger clusters. As a function of the DP, the average cluster size shows very different behavior in two regions: with void percolation and without void percolation. The following results are valid at constant temperature and pressure. In the presence of percolation, the average cluster size increases with M, whereas in the absence of percolation it decreases with M. In the absence of void percolation, the average cluster size decreases with increasing q due to the decrease in the total free volume. We present and discuss the results and compare them with those from experiments, simulations and random percolation. We conclude that we are able to qualitatively explain experimental results if we assume that there is no void percolation. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1446432
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  • 8
    Electronic Resource
    Electronic Resource
    New statistical mechanical treatment of systems near surfaces. V. Incompressible blend of interacting polydisperse linear polymers (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 4890-4903 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider a lattice model of an incompressible blend of interacting (repulsive, attractive, or neutral) polydisperse polymers of two species, A and B. The blend is next to an infinite plane surface whose interaction with A can be attractive, repulsive, or neutral. This is the only parameter required to completely specify the effect of the surface on both components of the blend. We numerically study various density profiles and surface functions, as we move away from the surface, by using the method of Chhajer and Gujrati that has already been successfully applied to study a polymer solution next to a surface. The resulting density profiles show the oscillations that are seen in Monte Carlo simulations (but with magnitude enhanced and range diminished due to the presence of free volume in simulations), and the enrichment of the smaller species at a neutral surface. The method is computationally ultrafast and can be carried out on a PC, even in the incompressible case, when Monte Carlo simulations are not feasible. The calculations usually take a few seconds to a minute. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1395560
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  • 9
    Electronic Resource
    Electronic Resource
    Thermal and percolative transitions and the need for independent symmetry breakings in branched polymers on a Bethe lattice (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 1613-1634 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider a very general model of equilibrium polymerization of branched polymers. Our model contains, as a special case, the "a priori equal probability'' model considered by Flory and Stockmayer. In this limit, the model exhibits only percolation transition. We solve our general model in the interior of a Bethe lattice. There are thermal as well as percolation transitions in the model. Each of the two transitions requires an independent spontaneous symmetry breaking; neither implies the other. Without spontaneous symmetry breaking, the transitions do not manifest themselves. Thermal transitions correspond to singularities in the equation of state. Percolation transitions, on the other hand, do not correspond to any singularity in the equation of state. We also discuss the failure of a topological identity, valid for any finite Cayley tree, in the interior of the Bethe lattice. We consider various different cases to show the usefulness of our model. In particular, we argue that one must distinguish between the "tree approximation'' of Flory on a general lattice and our exact solution on the Bethe lattice. The former, in general, allows for loop formation, whereas there are no loops allowed in the latter solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.464279
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  • 10
    Electronic Resource
    Electronic Resource
    New statistical mechanical treatment of systems near surfaces. I. Theory and principles (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 5599-5614 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a new theoretical framework for a statistical mechanical and thermodynamic description of any general inhomogeneous system (not necessarily polymeric) in the presence of surfaces. The framework is an extension of a lattice theory recently developed for a homogeneous system and requires approximating the original lattice by a recursive lattice which, for simplicity, we take to be a modified tree structure (see Fig. 4), TM as described in the text. The tree is formed recursively by two basic elements, the main tree T and the surface tree T¯. The model is solved exactly using a recursion technique. The technique allows us to account for connectivity, architecture, excluded-volume effects, interactions, etc. exactly. The resulting description goes beyond the random-mixing approximation used in most mean-field theories. We consider a general model of a multicomponent system and its exact solution on the modified tree TM provides us with an approximate theory of the inhomogeneous system on the original lattice. We provide a general discussion of the theory and principles involved. Our method produces results similar to those of Monte Carlo simulations but can even be applied to cases where Monte Carlo simulations are not possible. We also obtain surface free energy and the surface entropy that is not easily obtained in a Monte Carlo simulation. Our method is more reliable than the mean-field method of Scheutjens and Fleer, whose predictions are, in many cases, in direct contradiction with the Monte Carlo simulations. Our method is fast by at least three orders of magnitude compared to rival methods. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473600
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