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In the melt polymer conformations are nearly ideal according to Flory's ideality hypothesis. Silberberg generalized this statement for chains in the interfacial region. We check the Silberberg argument by analyzing the conformations of a probe chain end-grafted at a solid surface in a sea of floating free chains of concentration φ by the self-consistent field (SCF) method. Apart from the grafting, probe chain and floating chains are identical. Most of the results were obtained for a standard SCF model with freely jointed chains on a six-choice lattice, where immediate step reversals are allowed. A few data were generated for a five-choice lattice, where such step reversals are forbidden. These coarse-grained models describe the equilibrium properties of flexible atactic polymer chains at the scale of the segment length. The concentration was varied over the whole range from φ = 0 (single grafted chain) to φ = 1 (probe chain in the melt). The number of contacts with the surface, average height of the free end and its dispersion, average loop and train length, tail size distribution, end-point and overall segment distributions were calculated for a grafted probe chain as a function of φ, for several chain lengths and substrate∕polymer interactions, which were varied from strong repulsion to strong adsorption. The computations show that the conformations of the probe chain in the melt do not depend on substrate∕polymer interactions and are very similar to the conformations of a single end-grafted chain under critical conditions, and can thus be described analytically. When the substrate∕polymer interaction is fixed at the value corresponding to critical conditions, all equilibrium properties of a probe chain are independent of φ, over the whole range from a dilute solution to the melt. We believe that the conformations of all flexible chains in the surface region of the melt are close to those of an appropriate single chain in critical conditions, provided that one end of the single chain is fixed at the same point as a chain in the melt.

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It is well known that lattice and continuum descriptions for polymers at interfaces are, in principle, equivalent. In order to compare the two models quantitatively, one needs a relation between the inverse extrapolation length c as used in continuum theories and the lattice adsorption parameter Δχ(s) (defined with respect to the critical point). So far, this has been done only for ideal chains with zero segment volume in extremely dilute solutions. The relation Δχ(s)(c) is obtained by matching the boundary conditions in the two models. For depletion (positive c and Δχ(s)) the result is very simple: Δχ(s) = ln(1 + c/5). For adsorption (negative c and Δχ(s)) the ideal-chain treatment leads to an unrealistic divergence for strong adsorption: c decreases without bounds and the train volume fraction exceeds unity. This due to the fact that for ideal chains the volume filling cannot be accounted for. We extend the treatment to real chains with finite segment volume at finite concentrations, for both good and theta solvents. For depletion the volume filling is not important and the ideal-chain result Δχ(s) = ln(1 + c/5) is generally valid also for non-ideal chains, at any concentration, chain length, or solvency. Depletion profiles can be accurately described in terms of two length scales: ρ = tanh(2)[(z + p)/δ], where the depletion thickness (distal length) δ is a known function of chain length and polymer concentration, and the proximal length p is a known function of c (or Δχ(s)) and δ. For strong repulsion p = 1/c (then the proximal length equals the extrapolation length), for weaker repulsion p depends also on chain length and polymer concentration (then p is smaller than 1/c). In very dilute solutions we find quantitative agreement with previous analytical results for ideal chains, for any chain length, down to oligomers. In more concentrated solutions there is excellent agreement with numerical self-consistent depletion profiles, for both weak and strong repulsion, for any chain length, and for any solvency. For adsorption the volume filling dominates. As a result c now reaches a lower limit c ≈ -0.5 (depending slightly on solvency). This limit follows immediately from the condition of a fully occupied train layer. Comparison with numerical SCF calculations corroborates that our analytical result is a good approximation. We suggest some simple methods to determine the interaction parameter (either c or Δχ(s)) from experiments. The relation Δχ(s)(c) provides a quantitative connection between continuum and lattice theories, and enables the use of analytical continuum results to describe the adsorption (and stretching) of lattice chains of any chain length. For example, a fully analytical treatment of mechanical desorption of a polymer chain (including the temperature dependence and the phase transitions) is now feasible.

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We discuss a unique system that allows exact analytical investigation of first- and second-order transitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain grafted with one end to a solid substrate with a pulling force applied to the other end. We exploit the analogy with a continuum model and use accurate mapping between the parameters in continuum and lattice descriptions, which leads to a fully analytical partition function as a function of chain length, temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram, which gives the critical force as a function of temperature, is nonmonotonic and gives rise to re-entrance. We analyze the chain length dependence of several chain properties (bound fraction, chain extension, and heat capacity) for different cross sections of the phase diagram. Close to the transition a single parameter (the product of the chain length N and the deviation from the transition point) describes all thermodynamic properties. We discuss finite-size effects at the second-order transition (adsorption without force) and at the first-order transition (mechanical desorption). The first-order transition has some unusual features: The heat capacity in the transition region increases anomalously with temperature as a power law, metastable states are completely absent, and instead of a bimodal distribution there is a flat region that becomes more pronounced with increasing chain length. The reason for this anomaly is the absence of an excess surface energy for the boundary between adsorbed and stretched coexisting phases (this boundary is one segment only): The two states strongly fluctuate in the transition point. The relation between mechanical desorption and mechanical unzipping of DNA is discussed.

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We consider the mechanical desorption of an infinitely long lattice polymer chain tethered at one end to an adsorbing surface. The external force is applied to the free end of the chain and is normal to the surface. There is a critical value of the desorption force f(tr) at which the chain desorbs in a first-order phase transition. We present the phase diagram for mechanical desorption with exact analytical solutions for the detachment curve: the dependence of f(tr) on the adsorption energy epsilon (at fixed temperature T) and on T (at fixed epsilon). For most lattice models f(tr)(T) displays a maximum. This implies that at some given force the chain is adsorbed in a certain temperature window and desorbed outside it: the stretched state is re-entered at low temperature. We also discuss the energy and heat capacity as a function of T; these quantities display a jump at the transition(s). We analyze short-range and long-range excluded-volume effects on the detachment curve f(tr)(T). For short-range effects (local stiffness), the maximum value of f(tr) decreases with stiffness, and the force interval where re-entrance occurs become narrower for stiffer chains. For long-range excluded-volume effects we propose a scaling f(tr) approximately T(1-nu)(T(c)-T)(nu/phi) around the critical temperature T(c), where nu=0.588 is the Flory exponent and phi approximately 0.5 the crossover exponent, and we estimated the amplitude. We compare our results for a model where immediate step reversals are forbidden with recent self-avoiding walk simulations. We conclude that re-entrance is the general situation for lattice models. Only for a zigzag lattice model (where both forward and back steps are forbidden) is the coexistence curve f(tr)(T) monotonic, so that there is no re-entrance.

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We consider a mutually incompatible polymer mixture composed of two major components AN and BN and a third minority component C(N). The interactions, parameterized by short-range Flory-Huggins interaction parameters, are chosen such that C wets the A/B interface completely at three-phase coexistence. At sub-saturated conditions the adsorption of C remains necessarily microscopic. We study such a system in a stationary off-equilibrium state: due to imposed chemical potential gradients, polymer AN diffuses from the A-rich bulk phase through the interface to the A-poor bulk phase. Polymer BN travels in the opposite direction. Symmetric conditions are selected for which the polymer CN that accumulates at the A/B-interface has no net flux in the stationary state. This system is described by the Mean Field Stationary Diffusion (MFSD) model, an approach that solves the Scheutjens Fleer self-consistent-field (SF-SCF) equations with the boundary condition that the chemical potentials in the two bulk phases are different (but constant) so that a stationary state can be described. When the chemical potentials in the two bulk phases are the same, MFSD reduces to the equilibrium SF-SCF results. From the MFSD method we obtain the stationary volume fraction profiles and segmental fluxes. By forcing the system further from three-phase coexistence, i.e. by imposing larger concentration gradients, the adsorption of C goes unexpectedly from a thin adsorption layer to a thick adsorption film. The susceptibility partial differential J(A)/partial differential Delta(phi)A of the flux of A (equal to minus the flux of B) with respect to the imposed concentration gradient changes abruptly at the transition in adsorption behaviour. Interestingly, upon variation of the concentration gradients, the fluxes of A and B are enhanced by the accumulation of C at the interface. This means that the adsorbed C-film does not behave as an inert barrier.

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Phase separation in polymer blends is an important process. However, the compositions of the coexisting phases can only be predicted by numerical methods. We provide simple analytical expressions which serve as good approximations for the compositions after phase separation of binary homopolymer blends. These approximations are obtained by a stationary dynamics approach: we calculate the compositions of two polymer mixtures such that the stationary diffusion between these distinguishable mixtures vanishes. For the diffusion equations we employ composition-dependent diffusion coefficients, as derived according to the slow- and fast-mode theory from the Flory-Huggins free energy. The analytical results are in good agreement with exact (numerically calculated) binodal compositions. Our coexistence curves are more accurate than some conventional approximations. Another advantage of the stationary dynamics approach is that it is not only applicable to binary polymer blends or polymer solutions, but also to symmetrical multicomponent blends. The same diffusion coefficients may be used to obtain the exact spinodal compositions in multicomponent systems.

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We present a method to study mean-field stationary diffusion (MFSD) in polymer systems. When gradients in chemical potentials vanish, our method reduces to the Scheutjens-Fleer self-consistent field (SF-SCF) method for inhomogeneous polymer systems in equilibrium. To illustrate the concept of our MFSD method, we studied stationary diffusion between two different bulk mixtures, containing, for simplicity, noninteracting homopolymers. Four alternatives for the diffusion equation are implemented. These alternatives are based on two different theories for polymer diffusion (the slow- and fast-mode theories) and on two different ways to evaluate the driving forces for diffusion, one of which is in the spirit of the SF-SCF method. The diffusion profiles are primarily determined by the diffusion theory and they are less sensitive to the evaluation of the driving forces. The numerical stationary state results are in excellent agreement with analytical results, in spite of a minor inconsistency at the system boundaries in the numerical method. Our extension of the equilibrium SF method might be useful for the study of fluxes, steady state profiles and chain conformations in membranes (e.g., during drug delivery), and for many other systems for which simulation techniques are too time consuming.

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The coil-globule transition has been studied for A-B copolymer chains both by means of lattice Monte Carlo (MC) simulations using bond fluctuation algorithm and by a numerical self-consistent-field (SCF) method. Copolymer chains of fixed length with A and B monomeric units with regular, random, and specially designed (proteinlike) primary sequences have been investigated. The dependence of the transition temperature on the AB sequence has been analyzed. A proteinlike copolymer is more stable than a copolymer with statistically random sequence. The transition is more sharp for random copolymers. It is found that there exists a temperature below which the chain appears to be in the lowest energy state (ground state). Both for random and proteinlike sequences and for regular copolymers with a relatively long repeating block, a molten globule regime is found between the ground state temperature and the transition temperature. For regular block copolymers the transition temperature increases with block size. Qualitatively, the results from both methods are in agreement. Differences between the methods result from approximations in the SCF theory and equilibration problems in MC simulations. The two methods are thus complementary.

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The physical properties of a polysaccharide produced by the lactic acid bacterium Lactococcus lactis subsp. cremoris strain NIZO B40 were investigated. Separation of the polysaccharide from most low molar mass compounds in the culture broth was performed by filtration processes. Residual proteins and peptides were removed by washing with a mixture of formic acid, ethanol, and water. Gel permeation chromatography (GPC) was used to size fractionate the polysaccharide. Fractions were analyzed by multiangle static light scattering in aqueous 0.10 M NaNO3 solutions from which a number- (Mn) and weight-averaged (Mw) molar mass of (1.47 +/- 0.06).10(3) and (1.62 +/- 0.07).10(3) kg/mol, respectively, were calculated so that Mw/Mn approximately 1.13. The number-averaged radius of gyration was found to be 86 +/- 2 nm. From dynamic light scattering an apparent z-averaged diffusion coefficient was obtained. Upon correcting for the contributions from intramolecular modes by extrapolating to zero wave vector a hydrodynamic radius of 86 +/- 4 nm was calculated. Theoretical models for random coil polymers show that this z-averaged hydrodynamic radius is consistent with the z-averaged radius of gyration, 97 +/- 3 nm, as found with GPC.

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The ordering process and kinetics in thin films (200-800-nm thick) of a thermotropic side-chain liquid-crystalline polymer have been investigated vertically and laterally, respectively, by x-ray reflectivity and atomic-force microscopy. The original smooth and amorphous spin-coated films initially become corrugated upon annealing in the smectic mesophase. The roughening of the surface results from the formation of randomly oriented microcrystalline domains in the film. At the same time, however, a laterally macroscopic crystal starts to grow from the substrate surface in the direction of the polymer-air interface at the expense of these domain structures. Finally, a nicely ordered single crystal with parallel-ordered bilayers is formed in the film as well as at the polymer-air interface. This one-dimensional crystallization, actually recrystallization, depends strongly on the temperature due to viscosity effects. At low temperatures, just above the glass-transition temperature, the ordering is very slow, but with increasing temperature the crystal growth is faster. An Arrhenius-type plot gives an activation energy of 122 kJ/mol, which we ascribe to the expected reorientations of the mesogenic groups during the recrystallization process.

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