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Register a new userNon-extensivity of the chemical potential of polymer melts
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Following Florys ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $delta mu_c(n) sim +1/rhosqrt{n}$ arises ($rho$ being the monomer density) for all $P(N)$ if $n ll <N>$ which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory distributed melts we obtain $delta mu_c(n) approx (1- 2 n/<N>) / rho sqrt{n}$ for $n ll <N>^2$, hence, $delta mu_c(n) approx - 1/rho sqrt{n}$ if $n$ is similar to the typical length of the bath $<N>$. Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond-fluctuation model. As predicted we find, e.g., the non-exponentiality parameter $K_p equiv 1 - <N^>/p!<N>^p$ to decay as $K_p approx 1 / sqrt{<N>}$ for all moments $p$ of the distribution.
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It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain should exponentially decay with $s$. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, $P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise method for obtaining the statistical segment length bstar in a computer experiment.
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling. The probability distributions of block length $k$, which are analogous to the first-passage probabilities, are calculated analytically and determined from the computer simulations. In any domain, the probability distribution can be described by the asymptote $~k^{-3/2}$ at moderate values of $k$ if the spatial size of the block is less than the smallest characteristic size of the domain. For large blocks, the exponential asymptote $exp(-const , k a^2/d_{as}^2)$ is valid, $d_{as}$ being the asymptotic domain length (a is the monomer unit size). The number average block lengths and their dispersities change linearly with the block length for lamellae, cylinders, and balls, when the domain is characterized by a single characteristic size. If the domain is described by more than one size, the number average block length can grow nonlinearly with the domain sizes and the length das can depend on all of them.
We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, $G(t)$, into the plateau regime for chains with $Z=40$ entanglements and into the terminal relaxation regime for $Z=10$. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter -free tests of several different tube models. We find excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.
The temperature dependence of the hydrodynamic boundary condition between a PDMS melt and two different non-attractive surfaces made of either an OTS (octadecyltrichlorosilane) self-assembled monolayer (SAM) or a grafted layer of short PDMS chains has been characterized. A slip length proportional to the fluid viscosity is observed on both surfaces. The slip temperature dependence is deeply influenced by the surfaces. The viscous stress exerted by the polymer liquid on the surface is observed to follow exactly the same temperature dependences as the friction stress of a cross-linked elastomer sliding on the same surfaces. Far above the glass transition temperature, these observations are rationalized in the framework of a molecular model based on activation energies: increase or decrease of the slip length with increasing temperatures can be observed depending on how the activation energy of the bulk viscosity compares to that of the interfacial Naviers friction coefficient.
In addition to the terminal flow (the region I) and the shear thinning (the region II), we discover two new flow regions in capillary flow at the wall stress higher than the plateau modulus of the polymer. The region III violates the empirical Cox-Merz rule with a significantly weaker shear thinning than the region II, and the region IV exhibits unexpected shear thickening. Moreover, the crossover shear rates between the regions II and III and between the regions III and IV scale with the number of entanglement per chain, Z=M_w/M_e, as Z^(-2.0) and Z^(-1.2) respectively. We attribute the weakening in shear thinning and the emergence of shear thickening to the deformation-induced non-Gaussian stretching of polymers. These observations offer the first experimental quantification of the deformation behaviors of polymer melts at high-stress shear.
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