Notes: The hydrodynamic radii of two types of aggregates, diffusion-limited aggregation clusters (DLA) and bond-percolation clusters (BPC), are calculated by numerically solving the hydrodynamic interaction between different particles in the cluster. Though they have almost the same fractal dimensionality, DLA and BPC clusters exhibit different effective hydrodynamic scaling behaviors. For BPC, the ratio between the hydrodynamic radius and the radius of gyration, Rh/Rg, remains almost constant (1.14) for clusters of up to 900 particles; while for DLA the hydrodynamic radius Rh increases faster than the radius of gyration Rg, with Rh∼N0.45 for the same range of N.

Notes: The diffusion limited aggregation of particles with anisotropic sticking probabilities has been investigated using computer models. All of our simulations have been carried out using 2d square lattices with square "particles'' having two more sticky and two less sticky sides with sides of different kinds adjacent to each other. In both the limits of fast and slow particle rotation the anisotropy of the particles enhances the anisotropy of the square lattice and cross-shaped clusters (with side branches) are formed which resemble those generated by very much larger scale simulations of the regular DLA process. In the slow rotation limit a bias in the number of particles launched with sticky sides facing in the X or Y directions on the lattice leads to the formation of needle-shaped clusters whose radius of gyration (Rg) increases with cluster mass (M) according to Rg ∼M2/3.

Notes: To date, both the intermolecular multiple-quantum coherence (MQC) and demagnetizing field models have led to fully quantitative predictions of NMR signals in a highly polarized system using the CRAZED and similar sequences. In this paper, measurements of apparent MQC diffusion rates, Dnapp, for a specific apparent coherence order, n, were used to investigate the equivalent between the intermolecular MQC and demagnetizing field treatments. A number of physical effects were analyzed both theoretically and experimentally. These effects include molecular diffusion, variation in dipolar correlation distance, radiation damping, inhomogeneous broadening, and spin relaxation, all of which may alter the NMR signal. Two variations of a two-pulse CRAZED sequence, where the signal attenuation is almost entirely caused by the diffusion weighting, were designed to accurately measure and characterize Dnapp during the evolution period. Apparent diffusion rates were extracted from a least-squares fitting of a series of 1H spectra, measured with varying diffusion weighting factors. Complete theoretical formations were explicitly derived from both the intermolecular MQC and demagnetizing field treatments. Numerical simulations based on the demagnetizing field treatment were performed and it was found that the model can be used to predict the apparent diffusion rates. A novel diffusion model for intermolecular MQC is proposed in which the phase shift of each individual spin on different molecules is considered to be uncorrelated. This model successfully predicts the unconventional diffusion behaviors of intermolecular MQCs, specifically for differences of apparent diffusion rates between inter- and intramolecular MQCs. Our theoretical predictions and experimental confirmation demonstrate, for the first time, that Dnapp for intermolecular MQCs of order n are characterized by Dnapp=nDT for n≥2 and D0app=2DT for n=0, where DT is the translational molecular diffusion rate of the single quantum coherences. These results do not coincide with Dn=n2DT for n≥0 which is a general relationship for an intramolecular n-quantum coherence. These works about the apparent diffusion rates during the evolution period of the CRAZED sequences provide additional evidence to support the argument of the equivalence between the intermolecular MQC and demagnetizing field models. The general results derived from both intermolecular MQC and demagnetizing field treatments in this report can reasonably explain new observations of diffusion phenomena in nonlinear spin echoes by Kimmich and co-workers. Even though the theoretical prediction about intermolecular MQC diffusion is verified only with specific experiments using tailor-made pulse sequences, it is demonstrated that the function dependence of diffusion rate on coherence order is general. These results provide independent evidence to support the intermolecular MQC theory proposed by Warren and co-workers. © 2001 American Institute of Physics.

Notes: The diffusion coefficient of clusters D formed by cluster–cluster aggregation is computed according to the Kirkwood–Riseman Theory. In three dimensions one finds D proportional to sγ where s is the number of particles in the cluster and γ=−0.544±0.014. This relationship is employed to simulate the time evolution of the cluster size distribution Ns(t) which is found to exhibit simple scaling behavior Ns(t) ∼s−2g(s/tz) with z∼1.1.

Notes: Liquid nuclear magnetic resonance behaviors related to intermolecular dipolar interactions were investigated theoretically and experimentally in highly polarized two-component spin systems. A modified CRAZED pulse sequence was designed to investigate relative signal intensities with considerations of spin transverse relaxation, longitudinal relaxation, molecular diffusion, and optimal radio-frequency flip angles. The dissipation of the demagnetizing field due to relaxation and diffusion processes during the detection period was taken into account as well. For the first time, vigorous analytical expressions of the spin dynamics, including all the effects mentioned above, were derived from the combination of the demagnetizing field model and product operator formalism. In the regime where the linear approximation (γμ0M0t(very-much-less-than)1) is valid, these explicit analytical expressions can quantitatively describe the signal behaviors related to intermolecular dipolar interactions. All the theoretical predictions based on the analytical expressions for the directly excited component are in excellent agreement with experimental observations reported previously. Several valuable insights for the indirectly excited component were gained from the analytical expressions and verified by experimental measurements, including optimal radio-frequency flip angles, unusual relative signal intensities for n=−2 and n=2, and unconventional diffusion and multi-exponential longitudinal relaxation processes, where n is the ratio of the coherence-selection gradient areas in the CRAZED pulse sequence. In addition, n-order diffusion coefficients of the directly and indirectly excited spins during the evolution period predicted by the demagnetizing field picture are found to be the same as those obtained with the combination of the intermolecular multiple-quantum picture and Gaussian phase distribution approximation which is valid in the case of unrestricted isotropic diffusion. These results suggest that a combination of the demagnetizing field model and product operator formalism provides excellent predictive power and computational convenience for diffusion and relaxation behaviors in two-component systems. These quantitative studies may also provide an opportunity to probe specific sources of new contrast for medical MR imaging. © 2001 American Institute of Physics.

Notes: A novel Monte Carlo technique, the rebridging configurational-bias (RCB) method, has been developed to rearrange inner sections of chain molecules having strong intramolecular interactions along the backbone. The ability of sampling inner chain segments is important for the simulation of systems with low concentration of chain ends, such as polymers and molecules with cyclic structures. In the RCB method, inner segments are removed and then regrown site-by-site in a configurational-bias fashion. However, a short preliminary simulation is carried out to calculate weighting functions based on histograms of the separation distance between pairs of sites along the chain; these functions are used to bias the trial positions of growing inner sites so as to promote efficient chain closure. A look-ahead search scheme is employed for the sampling of the last two sites to increase the overall acceptance rate of the reconstruction process. The validity and performance of the new algorithm were tested by studying linear alkane systems of various chain lengths. Fast conformational equilibration was observed, from the level of local bond orientations to the level of the chain end-to-end vector orientations. Cyclic alkanes containing from 8 to 100 carbon atoms were also studied by using the RCB method. Our results for the conformational properties of cyclooctane are generally consistent with previous molecular dynamics (MD) results and with experimental data. The vapor–liquid coexistence curve of cyclooctane was also mapped out by using the RCB method in conjunction with a histogram reweighting technique for the analysis of isothermal–isobaric simulations. © 2000 American Institute of Physics.

Notes: In this paper we present a rigid-rod model (involving a restricted set of orientations) which is solved first with mean-field theory and then by Monte Carlo simulation. It is shown that both interparticle attractions and anisotropic adsorption energies are necessary in order for two successive fluid–fluid transitions to occur. The first is basically a gas–liquid condensation of "lying down'' rods in the plane of the surface, and the second involves a "standing up'' of the particles. A close qualitative correspondence is established between the results obtained in the mean-field and Monte Carlo descriptions. The role of biaxial states, i.e., in-plane orientational ordering, is also discussed in both contexts. To this end, we develop an analogy between our one-component rod monolayer and a bidisperse system of interconverting isotropic particles.