Degree of electron–nuclear entanglement in molecular states

The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground‐state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double‐well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000     

Viscoelastic properties of entangled polymers. II. The interchain–intrachain entanglement model

Our earlier model of entangled chain dynamics represented the elastic effects at entanglement points as a coupling with the surrounding medium, which was propagated weakly to every other entanglement site on the parent chain. In this way, a great variety of linear viscoelastic phenomena could be successfully predicted, with the only significant deficiency being a quantitative failure in curve fitting the local minimum in dynamic loss modulus G″(ω). Here we introduce the “intrachain entanglement,” or the “internal entanglement,” in which the parent chain entangles directly with itself. Elastic forces between pairs of internal entanglements are assumed to be stronger than those with the medium (“external entanglement”). Predictions of the new model are compared with rheological data on monodisperse polystyrene. Good agreement is obtained between theory and experiment, including G″(ω).     

Quantum entanglement phenomena in photosynthetic light harvesting complexes

We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.     

Pre-Averaged Sampling On the Entanglement Kinetics for Polymer Dynamics

A new model for entangled polymer dynamics based on pre-averaged sampling of the entanglement structure is proposed. Although it has been reported that sliplink simulations are powerful and promising to predict entangled polymer dynamics, it is still unpractical to calculate polymers with many entanglements. In the present study, a possible approach to achieve fast calculation is proposed by pre-averaged sampling of entanglement structure with skipping detail kinetics of entanglements dominated by chain ends in conventional sliplink models. To achieve time development of the chain conformation and entanglement structure, i) number of entanglement per chain and number of monomers for each segment are randomly obtained from the equilibrium distribution proposed by Schieber [J. Chem. Phys. 2003 , 118, 5162] and ii) the renewed entanglement structure is mechanically equilibrated. The established power-laws on molecular weight dependence of chain dimension, the longest relaxation time and self-diffusion coefficient were reasonably reproduced. Comparison on linear viscoelastic response is also discussed.     

The Effect of Synthesis Method on Three-component IPNs Morphology and Property

Three-component IPNs were synthesized from polyurethane/poly (methyl acrylate aminoethyl methacrylate)/epoxy resin [PU/P(MADMA)/EP] by simultaneous synthesis interpenetrating polymer networks method(SINs) and sequential synthesis interpenetrating polymer networks method (STPNs). Comparing the effect of the two synthesis methods on the morphology and mechanical properties of three-component IPNs, it was found that the compatibility of three-component IPNs depends on the component ratios and interpenetrating formation , the different synthesis methods make the entanglement and interpenetrating between networks changed. The tensile strength of SIPNs is bigger than that of SINs, while the elongation at break of SINs is bigger than that of SIPNs. It is feasible to use stepwise staining method to observe the morphology change.     

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.     

Brittle fracture of entangled polymers

A stochastic model is presented to calculate the number of chain segments entangled about a unit plane when the segment length is a stochastic variable. This crossing density to which the brittle fracture energy and the critical strength of entangled polymers scale is a function of the number of moles of entanglement network strands per unit volume and the mesh size of the entanglement network. Experimental results of the molecular weight dependence of the fracture energy and strength validate the theoretical predictions.     

Strain hardening of polymer glasses: Effect of entanglement density,temperature, and rate

The strain hardening behavior of model polymer glasses is studied with simulations over a wide range of entanglement densities, temperatures, strain rates, and chain lengths. Entangled polymers deform affinely at scales larger than the entanglement length as assumed in entropic network models of strain hardening. The dependence of strain hardening on strain and entanglement density is also consistent with these models, but the temperature dependence has the opposite trend. The dependence on temperature, rate, and interaction strength can instead be understood as reflecting changes in the flow stress. Microscopic analysis of local rearrangements and the primitive paths between entanglements is used to test models of strain hardening. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3487–3500, 2006     

Mesoscopic simulation of the crossing dynamics at an entanglement point of surfactant threadlike micelles

The crossing dynamics at an entanglement point of surfactant threadlike micelles in an aqueous solution was studied using a mesoscopic simulation method, dissipative particle dynamics, with a coarse-grained surfactant model. The possibility of a phantom crossing, which is the relaxation mechanism for the pronounced viscoelastic behavior of surfactant threadlike micellar solution, was investigated. When two threadlike micelles were encountered at an entanglement point under the condition close to thermal equilibrium, they fused to form a four-armed branch point. Then, a phantom crossing reaction occurred occasionally, or one micelle was cut down at the branch point. Increasing the repulsive forces between hydrophilic parts of the surfactants, fusion occurred less and the threadlike micelle was frequently broken down at an entanglement point. In these three schemes (a phantom crossing cut down at the branch point, and break down at the entanglement point), the breakage occurs at somewhere along the threadlike micelle. The breakage is considered as an essential process in the relaxation mechanism, and a phantom crossing can be seen as a special case of these processes. To explain the experimental evidence that a terminal of threadlike micelles is scarcely observed, a mechanism was also proposed where the generated terminal merges into the connected micelle part between two entanglement points due to the thermal motion.     

A highly coarse-grained model to simulate entangled polymer melts

We introduce a highly coarse-grained model to simulate the entangled polymer melts. In this model, a polymer chain is taken as a single coarse-grained particle, and the creation and annihilation of entanglements are regarded as stochastic events in proper time intervals according to certain rules and possibilities. We build the relationship between the probability of appearance of an entanglement between any pair of neighboring chains at a given time interval and the rate of variation of entanglements which describes the concurrence of birth and death of entanglements. The probability of disappearance of entanglements is tuned to keep the total entanglement number around the target value. This useful model can reflect many characteristics of entanglements and macroscopic properties of polymer melts. As an illustration, we apply this model to simulate the polyethylene melt of C(1000)H(2002) at 450 K and further validate this model by comparing to experimental data and other simulation results.     

氯磺化聚乙烯/聚甲基丙烯酸丁酯/环氧树脂三组分IPNs的合成与表征

采用同步-分步结合的方法合成了氯磺化聚乙烯/聚甲基丙烯酸丁酯/环氧树脂(CSM/PB-MA/EP)三组分IPNs.先用同步法合成CSM/EP二组分IPNs作为骨架网络,再将PBMA溶胀进入骨架网络中.得到三组分IPNs.网络间经两次相互缠结贯穿后,比单独用同步法或分步法合成的IPNs对网络间束缚作用大,且骨架网络与PBMA组成比较接近时,相容性较好.TEM结果表明:用分步染色方法可以观察三相间的形态变化和相区尺寸的相对大小.     

Latent fluorophore based on the trimethyl lock

Fluorescent molecules are essential for basic research in the biological sciences and have numerous practical applications. Herein is described the synthesis and use of a new class of latent fluorophores based on a novel design element, the trimethyl lock, that confers distinct advantages over extant fluorophores and pro-fluorophores. A diacetyl version of the latent fluorophore is stable in a biological environment, but rapidly yields rhodamine 110 upon acetyl-group hydrolysis by pig liver esterase or endogenous esterases in the cytosol and lysosomes of human cells. This design element is general and, hence, provides access to an ensemble of useful latent fluorophores.     

Constrained-pairing mean-field theory. V. Triplet pairing formalism

Describing strong (also known as static) correlation caused by degenerate or nearly degenerate orbitals near the Fermi level remains a theoretical challenge, particularly in molecular systems. Constrained-pairing mean-field theory has been quite successful, capturing the effects of static correlation in bond formation and breaking in closed-shell molecular systems by using singlet electron entanglement to model static correlation at mean-field computational cost. This work extends the previous formalism to include triplet pairing. Additionally, a spin orbital extension of the "odd-electron" formalism is presented as a method for understanding electron entanglement in molecules.     

Multipartite quantum entanglement evolution in photosynthetic complexes

We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.     

Effect of chemical structure of polycarbonates on entanglement spacing

The master curves of a series of aliphatic polycarbonates(APCs) with different lengths of methylene segments in the repeat unit were obtained by dynamic rheological measurements.The plateau modulus and entanglement molecular weight were determined and cross-checked by different methods.Though having distinct difference in chemical structure of repeat units,both APCs and bisphenol-A polycarbonates have the similar entanglement weight and entanglement spacing.On the other side,the plateau modulus decreases with increasing the length of the side group of aliphatic polycarbonates with different side-chain lengths in the literature.The packing length model can explain the relationship between chain structure and entanglements.     

Synthesis of Amphiphilic Silica Nanoparticles for Latent Fingerprint Detection

4-(Chloromethyl) phenyltrichlorosilane was used to modify silica spheres to obtain a sensitive and selective nanoparticle powder for detecting latent fingerprints. Various analytical techniques were used to characterize the nanoparticles and to show that the structure and properties are well-suited for forensic science. The synthesis of the particles was optimized based on the performance in terms of detection and the development of a test set of latent prints. The new material offers simple synthesis, convenient use for routine casework, and low price. These advantages suggest potential application for crime scene investigations.     

Effect of strong electron correlation on the efficiency of photosynthetic light harvesting

Research into the efficiency of photosynthetic light harvesting has focused on two factors: (1) entanglement of chromophores, and (2) environmental noise. While chromophores are conjugated π-bonding molecules with strongly correlated electrons, previous models have treated this correlation implicitly without a mathematical variable to gauge correlation-enhanced efficiency. Here we generalize the single-electron/exciton models to a multi-electron/exciton model that explicitly shows the effects of enhanced electron correlation within chromophores on the efficiency of energy transfer. The model provides more detailed insight into the interplay of electron correlation within chromophores and electron entanglement between chromophores. Exploiting this interplay is assisting in the design of new energy-efficient materials, which are just beginning to emerge.     

辐射交联顺-1,4-聚丁二烯的网络结构特性和力学性能

本文根据Flory的溶胀理论和橡胶弹性理论,考察了顺-1 4-聚丁二烯辐射交联产物的化学网络和物理缠结网络结构特性及其对固体力学性能的影响。结果表明,交联产物的物理缠结网络密度远远大于化学交联网络密度。随着辐照剂量的增大,化学交联密度增高,物理缠结数下降。探讨了交联、缠结密度与Mooney-Rivlin方程的常数项C_1和C_2的关系。C_1来自化学交联网络的贡献;C_2来自物理缠结的贡献。物理缠结网络主要贡献于交联物体在小形变下的起始弹性模量G_0;化学交联网络则主要贡献于交联物体在大形变下的非线性弹性,即断裂强度(?)_B。     

Special entangled fermionic systems and exceptional symmetries

Special fermionic systems entered the realm of quantum chemistry in the seventies in the work of Borland and Dennis in the form of a toy model. This work was leading to a detailed study of the N-representability problem by Klyachko. The topic then has been reconsidered in the light of entanglement theory boiling down to the notion of entanglement polytopes. Recently building on certain properties of such special fermionic systems, a connection between the coupled cluster method and entanglement has been established. In this paper we show that precisely such a special class of systems also provides an interesting physical realization for structures related to the Lie algebras of exceptional groups. This result draws such exotic symmetry structures under the umbrella of entangled systems of physical relevance.