scholarly journals Topological changes in telechelic micelles: flowers versus stars

2021 ◽  
Author(s):  
Vladimir Baulin
Keyword(s):  
Smart Materials ◽  
Linear Chain ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Chains ◽  
Linear Polymers ◽  
Stimuli Responsive ◽  
Single Chain ◽  
Low Concentrations ◽  
Effective Attraction

Micellization and morphology of spherical telechelic micelles formed by tri-block copolymers with short solvophobic end blocks at low concentrations is discussed within scaling arguments and Single Chain Mean Field Theory (SCMFT). In ultra-dilute regime, individual telechelic polymer chains can exist in solution in two distinct states: open linear chain conformation with two free ends and closed loop conformation, when two ends are connected by the effective attraction between two solvophobic ends. At concentrations below gelation point, closed loops tend to form micelles comprised mostly of loops in flower-like micelles, while linear polymers in open conformations tend to form star-shaped aggregates with one hydrophobic dangling end. Resulting two kinds of micelles have remarkably different topology and dimensions, while the transition between them can be driven by the entropy, namely conformation changes between domination of the looped and linear conformations. As a result, the transition between two types of micelles lies in a narrow interaction parameters range. Thus, these topological micelles are very sensitive to the changes in external environment and they can serve as a very sensitive stimuli-responsive smart materials.

scholarly journals Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 778
Author(s):  
Yingli Niu ◽  
Xiangyu Bu ◽  
Xinghua Zhang
Keyword(s):  
Field Theory ◽  
Message Passing Interface ◽  
Mean Field Theory ◽  
Mean Field ◽  
Algorithmic Complexity ◽  
Ensemble Average ◽  
Single Chain ◽  
Metropolis Monte Carlo ◽  
Rigid Rod ◽  
Chain Conformations

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

scholarly journals A non-local diffusion equation arising in terminally attached polymer chains

1990 ◽  
Vol 1 (4) ◽  
pp. 311-326 ◽  
Author(s):  
Xinfu Chen ◽  
Avner Friedman
Keyword(s):  
Field Theory ◽  
Diffusion Equation ◽  
Polymer Chain ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Melt ◽  
Polymer Chains ◽  
Number Density ◽  
Non Local ◽  
Local Diffusion

We consider a polymer melt in a domain Ω whereby each polymer chain is attached at one endpoint to a fixed surface S contained in ∂Ω. Denote by G(x, t;y) the normalized number density of all subchains from x to y of length t. Then, according to the selfconsistent mean field theory, G satisfies, for each y: Gt - Δ2G + σϕG = 0, where σ is a real parameter, and ϕ is a functional of G(·, ·; ·) both non-local and nonlinear. We establish the existence of G and C∞ regularity of ϕ, as a function of x.

Development of an Importance Sampling Single Chain Mean Field Theory for Polymer Adsorption onto a Flat Wall

2004 ◽  
Vol 37 (3) ◽  
pp. 1124-1133 ◽  
Author(s):  
Josep Bonet Avalos ◽  
Allan D. Mackie ◽  
Silvia Díez-Orrite
Keyword(s):  
Field Theory ◽  
Importance Sampling ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Adsorption ◽  
Single Chain ◽  
Flat Wall

Collapse of Isolated Chains in a Network

1994 ◽  
Vol 376 ◽  
Author(s):  
R. M. Briber ◽  
X. Liu ◽  
B.J. Bauer
Keyword(s):  
Crosslink Density ◽  
Virial Coefficient ◽  
Linear Chain ◽  
Second Virial Coefficient ◽  
Polymer Chains ◽  
Network Density ◽  
Radius Of Gyration ◽  
Single Chain ◽  
Polystyrene Matrix ◽  
Wide Range

ABSTRACTIn this study we use small angle neutron scattering to investigate the conformation of linear deuterated polystyrene chains trapped in a crosslinked protonated polystyrene matrix. The second virial coefficient was obtained as a function of crosslink density for a wide range of crosslink density. It is shown that the second virial coefficient decreases with increasing crosslink density. By extrapolating the scattering to zero concentration of the linear chain at all values of q, the single chain scattering was obtained and radius of gyration was measured the function of network density. It was found that when the network density is low (NI < Nc where NI and Nc are the number of monomer units in the linear chain and the monomer units between crosslinks, respectively) the radius of gyration does not change. As the network density increases (NI > Nc ) radius of gyration decreases. In this region the inverse of the radius of gyration varies linearly with the inverse of Nc. When the crosslink density is very high (NI » Nc ), segregation of linear polymer chains occurs. These results are in agreement with prediction and computer simulation results of polymer chain conformation in a field of random obstacles where the crosslink junctions act as the effective obstacles.

SELF-CONSISTENT MEAN FIELD MODEL OF HYDROGEL AND ITS NUMERICAL SIMULATION

2013 ◽  
Vol 12 (06) ◽  
pp. 1350048 ◽  
Author(s):  
CHAOHUI YUAN ◽  
HUI ZHANG
Keyword(s):  
Numerical Simulation ◽  
Volume Fraction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Chains ◽  
Model Parameters ◽  
Micro Structure ◽  
Mean Field Model ◽  
Self Consistent ◽  
Micro Structures

A model to describe the micro-structure of macromolecular microsphere composite (MMC) hydrogel is proposed in the framework of self-consistent mean field theory (SCMFT),1 which is usually used to investigate copolymer. Based on the SCMFT approximation, a system of equations associated with the complex topology of MMC hydrogel is derived and solved by a new kind of relaxation algorithm successfully. From the numerical simulation of the model, we find that the two model parameters play important roles in describing the micro-structure of MMC hydrogel, the interactions between two species (polymer chains and MMS spheres) and the volume fraction of MMS spheres. The role of other model parameters on the structure of the MMC hydrogel is also discussed. The numerical results are consistent with the observation from the chemical experiments. Moreover, we also show some new micro-structures obtained by using the SCMFT model, but discovered in chemical experiments.

Ultimate Properties of Polymer Chains

1993 ◽  
Vol 305 ◽  
Author(s):  
W. Wade Adams ◽  
Ruth Pachter ◽  
Peter D. Haaland ◽  
Thomas R. Horn ◽  
Scott G. Wierschke ◽  
...  
Keyword(s):  
Smart Materials ◽  
High Performance ◽  
Mechanical Response ◽  
Alpha Helix ◽  
Polymer Chains ◽  
Single Chain ◽  
Tension And Compression ◽  
Rigid Rod ◽  
Different Response ◽  
Semi Empirical

AbstractNew polymers with exceptional properties are needed for applications in high-performance structures, novel electrical, optical and electro-optical devices, and for multi-functional smart materials. Concurrently, new computational capabilities and methods for properties prediction and analysis have enabled the study of a variety of polymer chain architectures to examine the principles that govern their high-performance properties. By semi-empirical and ab initio computational methods, flexible, stiff-chain, rigid-rod, and biological structures could be analyzed. Single chain molecular stress-strain curves for axial tension and compression were calculated, and the strain dependence of the molecular modulus and vibrational frequencies were compared to measurements of molecular deformation, such as IR and Raman spectroscopy. However, of special interest is the distinctly different response of alpha-helical biopolymer chains to strain. Indeed, in this study we compare on a theoretical basis the ‘spring-like’ microscopic mechanical response of alpha-helical biopolymers having a reinforcing intra-molecular hydrogen bonding network to analogous synthetic extended chain polymers, especially poly(para-phenylene terephthalamide) (PPTA) [KEVLARTM]. The theoretical verification of the absence of compressive buckling in alpha-helical biopolymer chains rationalizes the molecular elasticity and resistance to ‘kinking’ of those strands, manifested by the prevalence in Nature for coiled coils. The understanding of the structure-tofunction relationship in biopolymers explaining the role of the alpha-helix in these systems as a requirement for superior compressive mechanical properties, may enable new guidance for the synthesis of motifs consistent with molecular frameworks optimized by Nature.

Sign in / Sign up

Export Citation Format

Share Document