The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007     

About Thinning Invariant Partition Structures

Bernoulli-p thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences (X ₁,X ₂,??); (2) gaps of such sequences (X _n+1?X ₁) _n???; (3) partition structures. For the first case we characterize the distributions which are simultaneously invariant under Bernoulli-p thinning for all p??(0,1]. Based on this, we make conjectures for the latter two cases, and provide a potential approach for proof. We explain the relation to spin glasses, which is complementary to important previous work of Aizenman and Ruzmaikina, Arguin, and Shkolnikov.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

Higher Aliphatic Aldehyde Polymers. V. Cyclic Trimers of C9 to C12, Normal Aliphatic Aldehydes

Cyclic trimers of n-nonaldehyde (NA), n-decaldehyde (DA), n-undecaldehyde, (UA) and n-dodecaldehyde (DDA) were prepared by reacting the individual aldehydes with protic or Lewis acids. Higher aliphatic aldehydes whose long paraffinic chains dominate the general properties of these compounds do not trimerize readily the trimers, when formed, are purified with difficulty. The cyclic trimers, characterized by IR and NMR spectroscopy, are exclusively the cis isomers and commonly exist in all equatorial conformations. The melting behavior of the cyclic trimers was studied by DSC. The melting endotherms and the enthalpies of fusion increase with increasing chain length. Although the melting temperatures of the cyclic trimers are similar to the melting range of the side-chain crystallization of the corresponding crystalline isotactic polyaldehydes, the transition peaks of the trimers are single peaks and much sharper than the corresponding polymer peaks.     

A Comparison of Conventional Gel Stiffness Characterization Techniques with Cavitation Rheology

Experimental Mechanics - Interest in soft gels has arisen in recent years as they can be applied to many fields such as tissue engineering, food additives, and drug delivery. The importance of...     

Further properties of nonzero-sum differential games

The general nonzero-sum differential game hasN players, each controlling a different set of inputs to a single nonlinear dynamic system and each trying to minimize a different performance criterion. These general games have several interesting features which are absent in the two bestknown special cases (the optimal control problem and the two-person, zero-sum differential game). This paper considers some of the difficulties which arise in attempting to generalize ideas which are well known in optimal control theory, such as theprinciple of optimality and the relation betweenopen-loop andclosed-loop controls. Two types of solutions are discussed: theNash equilibrium and thenoninferior set. Some simple multistage discrete games are used to illustrate phenomena which also arise in the continuous formulation.This research was supported by Joint Services Electronics Contracts Nos. N00014-67-A-0298-0006, 0005, 0008 and by NASA Grant No. NGR 22-007-068.     

Intra-operative acoustic hemostasis of liver: production of a homogenate for effective treatment

Objective: We have shown that High-Intensity Focused Ultrasound (HIFU) can effectively control bleeding from injuries to solid organs such as liver, spleen, and lung. Achievement of hemostasis was augmented when a homogenate of tissue and blood was formed. The objective of this study was to investigate quantitatively the effect of homogenate production on HIFU application time for hemostasis. Possible mechanisms involved in homogenate production were also studied.Methods: Ten anesthetized rabbits had laparotomy and liver exposure. Liver incisions, 15-25 mm long and 3-4 mm deep, were made followed immediately by HIFU application. Two electrical powers of 80 and 100 W corresponding to focal acoustic intensities of 2264 and 2829 W/cm², respectively were used. Tissue and homogenate temperatures were measured. Smear and histological tissue sample analysis using light microscopy were performed.Results: In treatments with homogenate formation, hemostasis was achieved in 76 ± 1.3 s (Mean ± Standard Error Mean: SEM) at 80 W. In treatments without homogenate formation (at 80 W), hemostasis was achieved in 106 ± 0.87 s. At 100 W, hemostasis was achieved in 46 ± 0.3 s. The time required for homogenate formation, at 80 and 100 W were 60 ± 2.5 and 23 ± 0.3 s, respectively. The homogenate temperature was 83 °C (SEM 0.6 °C), and the non-homogenate tissue temperature at the treatment site was 60 °C (SEM 0.4 °C). The smear and histological analysis showed significant blood components and cellular debris in the homogenate, with some intact cells.Conclusion: The HIFU-induced homogenate of blood and tissue resulted in a statistically significant shorter HIFU application time for hemostasis. The incisions with homogenate had higher temperatures as compared to incisions without homogenate. Further studies of the correlation between homogenate formation and temperature must be done, as well as studies on the long-term effects of homogenate in achieving hemostasis.     

Enhanced diffraction from a grating on the surface of a negative-index metamaterial

We show by numerical simulation as well as by measurements on negative-index metamaterial wedge samples, that the unavoidable stepping of the refraction interface-due to the finite unit-cell size inherent to metamaterials-can give rise to a well-defined diffracted beam in addition to the negatively refracted beam. The direction of the diffracted beam is consistent with elementary diffraction theory; however, the coupling to this higher order beam is much larger than would be the case for a positive index material. The results confirm recent theoretical predictions of enhanced diffraction for negative-index grating surfaces.