arXiv subjects

T. A. Vilgis

Publications and source records attributed to T. A. Vilgis.

52 records · Page 3Linked to original sources

arXiv1998

Compression of finite size polymer brushes

We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $ξ\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a disk), the lateral extension $u_S$ of the border chains follows the scaling law $u_S = ξϕ(S/ξ)$. The scaling function $ϕ(x)$ is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small $x$, $ϕ(x)$ decays as a power law in agreement with simple arguments. The effective line tension and the variation with compression height of the force applied on the brush are also calculated.

cond-mat.soft↗

arXiv1998

Dynamics of polymeric manifolds in melts: Hartree approximation

The Martin-Siggia-Rose functional technique and the self-consistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds.The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension discriminate between Gaussian and non-Gaussian regimes, whereas its dynamic counterpart discriminates between Rouse- and renormalized-Rouse behavior. The dynamic exponents are calculated explicitly. The special case of linear chains shows agreement with MD- and MC-simulations.

cond-mat.soft↗

arXiv1998

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, $d_{\rm uc}=2D/(2-D)$, discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, ${\tilde d}_{uc}=2d_{\rm uc}$, 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.

cond-mat.soft↗

arXiv1998

Behavior of a polymer chain in a critical binary solvent

We present a field-theoretic renormalization group analysis of a polymer chain immersed in a binary good solvent close to its critical demixing point. We first show that this problem can be mapped on a bicritical field theory, i.e. a $(Φ^{2})^{2}$-model with a mass anisotropy. This implies that the end-to-end distance of the polymer is now controlled by a new critical exponent $ν_{B}$ related to the quadratic mass anisotropy operator $B$. To show this we solve the RG equation and calculate explicitly the exponents and the mean end-to-end length of the chain.

cond-mat.stat-mech↗

arXiv1998

Elasticity in strongly interacting soft solids: polyelectrolyte network

This paper discusses the elastic behavior of a very long crosslinked polyelectrolyte chain (Debye-Hückel chain), which is weakly charged. Therefore the response of the crosslinked chain (network) on an external constant force $f$ acting on the ends of the chain is considered. A selfconsistent variational computation of an effective field theory is employed. It is shown, that the modulus of the polyelectrolyte network has two parts: the first term represents the usual entropy elasticity of connected flexible chains and the second term takes into account the electrostatic interaction of the monomers. It is proportional to the squared crosslink density and the Debye - screening parameter.

cond-mat.soft↗

arXiv1997

Polyelectrolyte Networks: Elasticity, Swelling, and the Violation of the Flory - Rehner Hypothesis

This paper discusses the elastic behavior of polyelectrolyte networks. The deformation behavior of single polyelectrolyte chains is discussed. It is shown that a strong coupling between interactions and chain elasticity exists. The theory of the complete crosslinked networks shows that the Flory - Rehner - Hypothesis (FRH) does not hold. The modulus contains contributions from the classical rubber elasticity and from the electrostatic interactions. The equilibrium degree of swelling is estimated by the assumption of a $c^{*}$-network.

cond-mat.soft↗

arXiv1997

Topological interactions in DNA catenanes

The elasticity of DNA catenanes, i.e. multiply linked DNA rings, is investigated using the Gauss invariant as a minimal model for topology conservation. An effective elastic free energy as a function of the distance $R$ between segments located on different rings is obtained. An anharmonic part at large distances, growing as $R^{4}$, if $R\gg R_{G}$ ($R_{G}$ being the radius of gyration of a random walk ring) is found, while for $R\ll R_{G}$ the interaction is strongly repulsive. Treating the attractive interaction as the dominant one, distribution functions for the distance between segments located on different rings for several linking numbers are derived which are in qualitative agreement with distributions functions obtained experimentally from electron micrographs of DNA catenanes (S. D. Levene et al., Biophys.J. 69, 277, 1995).

cond-mat.soft↗

arXiv1997

Crosslinked polymer chains with excluded volume: A new class of branched polymers?

In this note microgels with and without excluded volume interactions are considered. Based on earlier exact computations on Gaussian mircogels, which are formed by self-crosslinking (with $M$ crosslinks) of polymer chains with chain length $N$ Flory type approximations are used to get first insight to their behavior in solution. It is shown that two different types of microgels exist: A special type of branched polymer whose size scales as $R \propto N^{2/5} M^{-1/5}$, instead of $R \propto N^{1/2}$. The second type are $c^*$ - microgels whose average mesh sizes $r$ are swollen and form self avoiding walks with a scaling law of the form $r = a (N/M)^{3/5}$.

cond-mat.soft↗

arXiv1997

Langevin dynamics of the glass forming polymer melt: fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all water-melon diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation.

cond-mat.soft↗

arXiv1997

On the elasticity of a single polyelectrolyte chain

This paper discusses the elastic behavior of a single polyelectrolyte chain. A simple scaling analysis as in self avoiding walk chains are not possible, because three interplaying relevant length scales are involved, i.e., the Debye screening length and the Pincus blob size. Therefore a selfconsistent computation of an effective variational propagator is employed. It is shown that the elastic force f is proportional to the end to end distance R for small f. For larger forces we find a new regime, characterized by deformations larger than a computed electrostatic "blob size". These results are supported by simulations and intuitive physical arguments.

cond-mat.stat-mech↗

arXiv1997

Dynamics of a polymer test chain in a glass forming matrix: The Hartree Approximation

In this paper the Martin-Siggia-Rose formalism is used to derive a generalized Rouse equation for a test chain in a matrix which can undergo the glass transition. It is shown that the surrounding matrix renormalizes the static properties of the test chain. Furthermore the freezing of the different Rouse modes is investigated. This yields freezing temperatures which depend from the Rouse mode index.

physics.chem-ph↗

arXiv1997

Elasticity of entangled polymer loops: Olympic gels

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto λ^{5/2}$ where $λ$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.

cond-mat.soft↗

arXiv1996

Langevin Dynamics of a Polymer with Internal Distance Constraints

We present a novel and rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modelled by harmonic potentials in the limit when the strength of the potential approaches infinity (hard crosslinks). The crosslinks are assumed to exist between arbitrary pairs of monomers. Formally exact expressions for the resolvent and spectral density matrix of the system are derived. To illustrate the method we study the diffusional behavior of monomers in the vicinity of a single crosslink within the framework of the Rouse model. The same problem has been studied previously by Warner (J. Phys. C: Solid State Phys. {\bf 14}, 4985, (1981)) on the basis of Lagrangian multipliers. Here we derive the full, hence exact, solution to the problem.

cond-mat.soft↗

arXiv1996

Size and scaling in ideal polymer networks

The scattering function and radius of gyration of an ideal polymer network are calculated depending on the strength of the bonds that form the crosslinks. Our calculations are based on an {\it exact} theorem for the characteristic function of a polydisperse phantom network that allows for treating the crosslinks between pairs of randomly selected monomers as quenched variables without resorting to replica methods. From this new approach it is found that the scattering function of an ideal network obeys a master curve which depends on one single parameter $x= (ak)^2 N/M$, where $ak$ is the product of the persistence length times the scattering wavevector, $N$ the total number of monomers and $M$ the crosslinks in the system. By varying the crosslinking potential from infinity (hard $δ$-constraints) to zero (free chain), we have also studied the crossover of the radius of gyration from the collapsed regime where $R_{\mbox{\tiny g}}\simeq {\cal O}(1)$ to the extended regime $R_{\mbox{\tiny g}}\simeq {\cal O}(\sqrt{N})$. In the crossover regime the network size $R_{\mbox{\tiny g}}$ is found to be proportional to $(N/M)^{1/4}$.

cond-mat↗

arXiv1996

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: the Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chain close to critical points, fluctuations induced shift of phase boundaries. We concentrate on static, equilibrium properties of the polymer systems.

cond-mat↗

arXiv1994

The conformation of conducting polymer chains: Hubbard polymers

The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are presented. One important result is that the electronic degrees of freedom greatly affect the conformational statistics of the walks and vice versa. The electronic degrees of freedom extend the size of the chain. The end-to-end distance behaves as $R\propto L^ν$ with $ν=(d+1)/(d+2)$, where $d$ is the spatial dimension.

cond-mat↗