6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

Quantum mechanical continuum solvation models.

We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters and χ-parameters in Flory-Huggins-type models. This is possible because the equation of state of the DPD fluid is essentially quadratic in density. This link opens the way to do large scale simulations, effectively describing millions of atoms, by firstly performing simulations of molecular fragments retaining all atomistic details to derive χ-parameters, then secondly using these results as input to a DPD simulation to study the formation of micelles, networks, mesophases and so forth. As an example application, we have calculated the interfacial tension σ between homopolymer melts as a function of χ and N and have found a universal scaling collapse when σ/ρkBTχ0.4 is plotted against χN for N>1. We also discuss the use of DPD to simulate the dynamics of mesoscopic systems, and indicate a possible problem with...

https://www.physics.iitm.ac.in/~iol/lecture_notes/groot-warren.pdf

Dissipative particle dynamics : bridging the gap between atomistic and mesoscopic simulation

We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N<Ne, while the dynamics of the long chains can be described by the reptation model. By mapping the model chains onto chemical species we give estimates of the times and distances of onset of the slowing down in motion due to reptation. Comparison to neutron spin‐echo data confirm our mapping procedure, resolving a discrepancy between various experiments. By considering the primitive chain we are able to directly visualize the confinement to a tube. Analyzing the Rouse mode relaxation allows us to exclude the generalized Rouse models, while the original reptation prediction gives a good description of the data.

Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation

https://www.tcd.ie/Physics/people/Graham.Cross/SF%20Poster%202011/Schuh-ActaMater07-Mechanical%20behaviour%20of%20amorphous%20alloys.pdf

Mechanical behavior of amorphous alloys

Block copolymers are all around us, found in such products as upholstery foam, adhesive tape and asphalt additives. This class of macromolecules is produced by joining two or more chemically distinct polymer blocks, each a linear series of identical monomers, that may be thermodynamically incompatible (like oil and vinegar). Segregation of these blocks on the molecular scale (5–100 nm) can produce astonishingly complex nanostructures, such as the “knitting pattern” shown on the cover of this issue of PHYSICS TODAY. This striking pattern, discovered by Reimund Stadler and his coworkers, reflects a delicate free‐energy minimization that is common to all block copolymer materials.

Block Copolymers—Designer Soft Materials

A previously obtained solution of the linearized Gor'kov equations for the upper critical magnetic field ${H}_{c2}$ of a bulk type-II superconductor is extended to include the effects of Pauli spin paramagnetism and spin-orbit impurity scattering. To carry out the calculation, it is necessary to introduce an approximation which assumes that spin-orbit scattering is infrequent in comparison with spin-independent scattering. It is found that spin-orbit scattering counteracts the effects of the spin paramagnetism in limiting the critical field and improves agreement between theory and experiment.

Temperature and Purity Dependence of the Superconducting Critical Field, H c 2 . III. Electron Spin and Spin-Orbit Effects

The effect of composition fluctuations on the microphase separation transition in diblock copolymers is investigated. Such fluctuation corrections, which were neglected in the mean field treatment of Leibler, are found to be significant for the molecular weights usually encountered. The analysis is facilitated by reducing the block copolymer Hamiltonian to a form previously studied by Brazovskii. Our principal results are the following: (i) A symmetric diblock copolymer is predicted to undergo a first order phase transition at a larger value of χN than the second order transition found by Leibler. The Flory interaction parameter is denoted χ and N is the number of statistical segments per chain. The location of the transition is predicted to be at (χN)t=10.495+41.022 N−1/3, where the peak in the scattering function attains its maximum value of 0.12328 N1/3. (ii) We find windows in composition, with finite width, through which it is possible to pass from the disordered phase to each of the ordered micropha...

Fluctuation effects in the theory of microphase separation in block copolymers

A theory is developed to predict the interfacial properties between two immiscible polymers. A self‐consistent‐field approach is employed to describe the configurational statistics of polymer molecules in the interfacial region. The density profiles and surface tension are calculated, and compare well with experiments. The interfaces are found to be much broader than for ordinary liquids. Also discussed are the distribution of chain ends and block‐copolymer joints in the interface, and the effects of adding moderate amounts of solvent.

Theory of the Interface between Immiscible Polymers. II

A rigorous gauge-invariant solution of the linearized Gor'kov equations is presented, yielding the complete temperature and electron-mean-free-path dependences of the upper critical magnetic field ${H}_{c2}$ of a bulk type-II superconductor. Comparison is made with previously known results in special cases, and it is pointed out that localized approximations such as the "dirty," or the Ginzburg-Landau, limits represent the leading term in an asymptotic rather than convergent, expansion.

Temperature and Purity Dependence of the Superconducting Critical Field, H c 2 . II

An extension of a previous one‐component theory of hard‐sphere systems (in three, two, and one dimensions) and the surface tension of real systems is made to mixtures. The theory is based on consideration of an approximate expression for the work of adding an additional hard sphere to a mixture. Comparison between theory and molecular‐dynamics calculations of the various contributions to the virial pressure (related to contact distribution functions) of such hard‐sphere mixtures is excellent. Comparison of the theory with experimental surface tensions of mixtures of simple liquids is satisfactory.

Eugene Helfand

Papers

Temperature and Purity Dependence of the Superconducting Critical Field, H c 2 . III. Electron Spin and Spin-Orbit Effects

Fluctuation effects in the theory of microphase separation in block copolymers

Theory of the Interface between Immiscible Polymers. II

Temperature and Purity Dependence of the Superconducting Critical Field, H c 2 . II

Scaled Particle Theory of Fluid Mixtures