83 research outputs found
Mesophase formation in two-component cylindrical bottle-brush polymers
When two types of side chains (A,B) are densely grafted to a (stiff) backbone
and the resulting bottle-brush polymer is in a solution under poor solvent
conditions, an incompatibility between A and B leads to microphase separation
in the resulting cylindrical brush. The possible types of ordering are
reminiscent of the ordering of block copolymers in cylindrical confinement.
Starting from this analogy, Leibler's theory of microphase separation in block
copolymer melts is generalized to derive a description of the system in the
weak segregation limit. Also molecular dynamics simulation results of a
corresponding coarse-grained bead-spring model are presented. Using side chain
lengths up to N = 50 effective monomers, the ratio of the Lennard-Jones energy
parameter between unlike monomers and monomers of the same
kind is varied. Various correlation
functions are analyzed to study the conditions when (local) Janus cylinder-type
ordering and when (local) microphase separation in the direction along the
cylinder axis occurs. Both the analytical theory and the simulations give
evidence for short range order due to a tendency towards microphase separation
in the axial direction, with a wavelength proportional to the side chain
gyration radius, irrespective of temperature and grafting density, for a wide
range of these parameters.Comment: 26 pages, 19 figure
Statistics of randomly branched polymers in a semi-space
We investigate the statistical properties of a randomly branched
3--functional --link polymer chain without excluded volume, whose one point
is fixed at the distance from the impenetrable surface in a 3--dimensional
space. Exactly solving the Dyson-type equation for the partition function
in 3D, we find the "surface" critical
exponent , as well as the density profiles of 3--functional units
and of dead ends. Our approach enables to compute also the pairwise correlation
function of a randomly branched polymer in a 3D semi-space.Comment: 15 pages 7 figsures; section VII is slightly reorganized, discussion
is revise
Ordering Lamellar-Forming Copolymer Thin Films in 3D Bicontinuous Morphologies via Lamellar Patterned Substrate
The formation of ordered morphologies in thin films of symmetric diblock copolymer melts is considered theoretically. Somewhat surprisingly, under proper boundary conditions the presence of a lamellar chemical pattern on the substrate, being sufficiently pronounced and with the right period, is found to induce the formation of diamond-like morphologies. The phase diagram of the most stable phases on the plane (the substrate period Lx the film width H) is built within the self-consistent field theory numerical procedure. We also discuss the behavior of the order parameter Fourier spectrum at the transitions between the various morphologies
Frequency Dispersion of Sound Propagation in Rouse Polymer Melts via Generalized Dynamic Random Phase Approximation
An extended generalization of the dynamic random phase approximation (DRPA)
for L-component polymer systems is presented. Unlike the original version of
the DRPA, which relates the (LxL) matrices of the collective density-density
time correlation fumctions and the corresponding susceptibilities of polymer
concentrated systems to those of the tracer macromolecules and so-called broken
links system (BLS), our generalized DRPA solves this problem for (5xL)x(5xL)
matrices of the coupled susceptibilities and time correlation functions of the
component number, kinetic energy and flux densities. The presented technique is
used to study propagation of sound and dynamic form-factor in disentangled
(Rouse) monodisperse homopolymer melt. The calculated sound velocity and
absorption coefficient reveal substantial frequency dispersion. The relaxation
time is found to be N times less than the Rouse time (N is the degree of
polymerization), which evidences strong dynamic screening because of interchain
interaction. We discuss also some peculiarities of the Brillouin scattering in
polymer melts. Besides, a new convenient expression for the dynamic structural
function of the Rouse chain in (q,p)-representation is found.Comment: 37 pages, 2 appendices, 48 references, 1 figur
Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers
We consider a diblock copolymer, whose links are capable
of forming local reversible bonds with each other. We assume that the resulting
structure of the bonds is RNA--like, i.e. topologically isomorphic to a tree.
We show that, depending on the relative strengths of A--A, A--B and B--B
contacts, such a polymer can be in one of two different states. Namely, if a
self--association is preferable (i.e., A--A and B--B bonds are comparatively
stronger than A--B contacts) then the polymer forms a typical randomly branched
cloverleaf structure. On the contrary, if alternating association is preferable
(i.e. A--B bonds are stronger than A--A and B--B contacts) then the polymer
tends to form a generally linear necklace structure (with, probably, some rear
side branches and loops, which do not influence the overall characteristics of
the chain). The transition between cloverleaf and necklace states is studied in
details and it is shown that it is a 2nd order phase transition.Comment: 17 pages, 9 figure
The Hartree approximation in dynamics of polymeric manifolds in the melt
The Martin-Siggia-Rose (MSR) functional integral technique is applied to the
dynamics of a D - dimensional manifold in a melt of similar manifolds. The
integration over the collective variables of the melt can be simply implemented
in the framework of the dynamical random phase approximation (RPA). The
resulting effective action functional of the test manifold is treated by making
use of the selfconsistent Hartree approximation. As an outcome the generalized
Rouse equation (GRE) of the test manifold is derived and its static and dynamic
properties are studied. It was found that the static upper critical dimension,
, discriminates between Gaussian (or screened) and
non-Gaussian regimes, whereas its dynamical counterpart, , distinguishes between the simple Rouse and the
renormalized Rouse behavior. We have argued that the Rouse mode correlation
function has a stretched exponential form. The subdiffusional exponents for
this regime are calculated explicitly. The special case of linear chains, D=1,
shows good agreement with MD- and MC-simulations.Comment: 35 pages,3 figures, accepted by J.Chem.Phy
Helical, Angular and Radial Ordering in Narrow Capillaries
To enlighten the nature of the order-disorder and order-order transitions in
block copolymer melts confined in narrow capillaries we analyze peculiarities
of the conventional Landau weak crystallization theory of systems confined to
cylindrical geometry. This phenomenological approach provides a quantitative
classification of the cylindrical ordered morphologies by expansion of the
order parameter spatial distribution into the eigenfunctions of the Laplace
operator. The symmetry of the resulting ordered morphologies is shown to
strongly depend both on the boundary conditions (wall preference) and the ratio
of the cylinder radius and the wave length of the critical order parameter
fluctuations, which determine the bulk ordering of the system under
consideration. In particular, occurrence of the helical morphologies is a
rather general consequence of the imposed cylindrical symmetry for narrow
enough capillaries. We discuss also the ODT and OOT involving some other
simplest morphologies. The presented results are relevant also to other
ordering systems as charge-density waves appearing under addition of an ionic
solute to a solvent in its critical region, weakly charged polyelectrolyte
solutions in poor solvent, microemulsions etc.Comment: 6 pages, 3 figure
Weak Segregation Theory and Non-Conventional Morphologies in the Ternary ABC Triblock Copolymers
The Leibler weak segregation theory in molten diblock copolymers is
generalized with due regard for the 2nd shell harmonics contributions defined
in the paper and the phase diagrams are built for the linear and miktoarm
ternary ABC triblock copolymers. The symmetric linear copolymers with the
middle block non-selective with respect to the side ones are shown to undergo
the continuous ODT not only into the lamellar phase but also into various
non-conventional cubic phases (depending on the middle block composition it
could be the simple cubic, face-centered cubic or non-centrosymmetric phase
revealing the symmetry of space group No.214 first predicted to appear in
molten block copolymers). For asymmetric linear ABC copolymers a region of
compositions is found where the weakly segregated gyroid (double gyroid) phase
exists between the planar hexagonal and lamellar or one of the non-conventional
cubic phases up to the very critical point. In contrast, the miktoarm ABC block
copolymers with one of its arm non-selective with respect to the two others are
shown to reveal a pronounced tendency towards strong segregation, which is
preceded by increase of stability of the conventional BCC phase and a peculiar
weakly segregated BCC phase (BCC3), where the dominant harmonics belong to the
3rd co-ordination sphere of the reciprocal lattice. The validity region of the
developed theory is discussed and outlined in the composition triangles both
for linear and miktoarm copolymers.Comment: 61 pages, 12 figure
Localization transition of random copolymers at interfaces
We consider adsorption of random copolymer chains onto an interface within
the model of Garel et al. Europhysics Letters 8, 9 (1989). By using the replica
method the adsorption of the copolymer at the interface is mapped onto the
problem of finding the ground state of a quantum mechanical Hamiltonian. To
study this ground state we introduce a novel variational principle for the
Green's function, which generalizes the well-known Rayleigh-Ritz method of
Quantum Mechanics to nonstationary states. Minimization with an appropriate
trial Green's function enables us to find the phase diagram for the
localization-delocalization transition for an ideal random copolymer at the
interface.Comment: 5 page
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