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Register a new userAbsorption/Expulsion of Oligomers and Linear Macromolecules in a Polymer Brush
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The absorption of free linear chains in a polymer brush was studied with respect to chain size $L$ and compatibility $chi$ with the brush by means of Monte Carlo (MC) simulations and Density Functional Theory (DFT) / Self-Consistent Field Theory (SCFT) at both moderate, $sigma_g = 0.25$, and high, $sigma_g = 1.00$, grafting densities using a bead-spring model. Different concentrations of the free chains $0.0625 le phi_o le 0.375$ are examined. Contrary to the case of $chi = 0$ when all species are almost completely ejected by the polymer brush irrespective of their length $L$, for $chi < 0$ we find that the degree of absorption (absorbed amount) $Gamma(L)$ undergoes a sharp crossover from weak to strong ($approx 100%$) absorption, discriminating between oligomers, $1le Lle 8$, and longer chains. For a moderately dense brush, $sigma_g = 0.25$, the longer species, $L > 8$, populate predominantly the deep inner part of the brush whereas in a dense brush $sigma_g = 1.00$ they penetrate into the fluffy tail of the dense brush only. Gyration radius $R_g$ and end-to-end distance $R_e$ of absorbed chains thereby scale with length $L$ as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length $32 le N le 256$, we demonstrate the existence of unique {em critical} value of compatibility $chi = chi^{c}<0$. For $chi^{c}(phi_o)$ the energy of free chains attains the {em same} value, irrespective of length $L$ whereas the entropy of free chain displays a pronounced minimum. At $chi^{c}$ all density profiles of absorbing chains with different $L$ intersect at the same distance from the grafting plane. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility $chi$ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length $L$: I ($1le Lle 8$), II ($8 le L le N$), and III ($L > N$), in which the time of absorption $tau$ grows with $L$ at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of $Gamma propto t^alpha$ with power $alpha propto -ln phi_o$ whereby penetration of the free chains into the brush gets {em slower} as their concentration rises.
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The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time $<tau>$ decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time $<tau>$ declines with growing contour length $L$ as $<tau>propto L^{-0.17}$, and with side chain length as $<tau>propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.
Shear responsive surfaces offer potential advances in a number of applications. Surface functionalisation using polymer brushes is one route to such properties, particularly in the case of entangled polymers. We report on neutron reflectometry measurements of polymer brushes in entangled polymer solutions performed under controlled shear, as well as coarse-grained computer simulations corresponding to these interfaces. Here we show a reversible and reproducible collapse of the brushes, increasing with the shear rate. Using two brushes of greatly different chain lengths and grafting densities, we demonstrate that the dynamics responsible for the structural change of the brush are governed by the free chains in solution rather than the brush itself, within the range of parameters examined. The phenomenon of the brush collapse could find applications in the tailoring of nanosensors, and as a way to dynamically control surface friction and adhesion.
A comparative dynamic Monte Carlo simulation study of polydisperse living polymer brushes, created by surface initiated living polymerization, and conventional polymer monodisperse brush, comprising linear polymer chains, grafted to a planar substrate under good solvent conditions, is presented. The living brush is created by end-monomer (de)polymerization reaction after placing an array of initiators on a grafting plane in contact with a solution of initially non-bonded segments (monomers). At equilibrium, the monomer density profile phi(z) of the LPB is found to decline as phi(z) ~ z^{-alpha} with the distance from the grafting plane z, while the distribution of chain lengths in the brush scales as c(N) ~ N^{-tau}. The measured values alpha = 0.64 and tau = 1.70 are very close to those, predicted within the framework of the Diffusion-Limited Aggregation theory, alpha = 2/3 and tau = 7/4. At varying mean degree of polymerization (from L = 28 to L = 170) and effective grafting density (from sigma_g = 0.0625 to sigma_g = 1.0), we observe a nearly perfect agreement in the force-distance behavior of the simulated LPB with own experimental data obtained from colloidal probe AFM analysis on PNIPAAm brush and with data obtained by Plunkett et. al., [Langmuir 2006, 22, 4259] from SFA measurements on same polymer.
A necessary condition for the validity of the linear viscoelastic model for a (passive) polymeric cylinder with an ultrasonic hysteresis-type absorption submerged in a non-viscous fluid requires that the absorption efficiency is positive (Qabs > 0) satisfying the law of the conservation of energy. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce negative axial radiation force, absorption and extinction efficiencies, as well as an enhancement of the scattering efficiency, not in agreement with the conservation of energy law. Numerical results for the radiation force, extinction, absorption and scattering efficiencies are performed for three viscoelastic (VE) polymer cylinders immersed in a non-viscous host liquid (i.e. water) with particular emphasis on the shear-wave absorption coefficient of the cylinder, the dimensionless size parameter and the partial-wave mode number n. Mathematical constraints are established for the non-dimensional absorption coefficients of the longitudinal and shear waves for a cylinder (i.e. 2D case) and a sphere (i.e. 3D case) in terms of the sound velocities in the VE material. The analysis suggests that the domain of validity for any viscoelastic model describing acoustic attenuation inside a lossy cylinder (or sphere) in a non-viscous fluid must be verified based upon the optical theorem.
The structural properties of a linear polymer and its evolution in time have a strong bearing on its anisotropic stress response. The mean-square bond length and mean bond angle are the critical parameters that influence the time-varying stress developed in the polymer. The bond length distribution along the chain is uniform without any abrupt changes at the ends. Among the externally set parameters such as density, temperature, strain rate, and chain length, the density as well as the chain length of the polymer have a significant effect on the stress. At high density values, changes in mean-square bond length dominates over changes in radius of gyration and end-to-end length. In other words, bond deformations dominate as opposed to changes in size and shape. Also, there is a large change in the mean-square bond length that is reflected as a jump in the stress. Beyond a particular value of the chain length, $n = 50$, called the entanglement length, stress-response is found to have distinctly different behavior which we attribute to the entanglement effects. Short chain polymers more or less behave like rigid molecules. There is no significant change in their internal structure when loaded. Further, temperature and rate of loading have a very mild effect on the stress. Besides these new results, we can now explain well known polymeric mechanical behavior under dynamic loading from the point of view of the evolution of the molecular dynamics and the derived structural properties. This could possibly lead to polymer synthesis with desired mechanical behavior.
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