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Results for “Ring polymers”
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Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends
Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, in this work, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ d,R for rings of length N R blended with linear chains of length N l to scale as τ d,R ~ N$^2_R$N$^{3.4}_L$.
Composite entanglement topology and extensional rheology of symmetric ring-linear polymer blends
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction ϕR. Chains with degree of entanglement Z≈14 are mixed to produce 10 well-entangled systems with ϕR varying from neat linear to neat ring melts. Z is large enough that except for very large ϕR, the rings are threaded by multiple linear chains in equilibrium. Primitive path analysis is used to visualize and quantify the structure of the composite ring-linear entanglement network. We measure the quantity of ring-linear threading and linear-linear entanglement as a function of ϕR and identify with simple arguments a ring fraction ϕR≈0.4 where the topological constraints of the composite entanglement network are maximized. These topological analyses are used to rationalize the ϕR-dependence of ring and linear chain dynamics, conformations, and rheology. Simulations of startup uniaxial elongation flows demonstrate the extensional stress overshoot observed in recent filament stretching experiments and characterize how it depends on the blend composition and entanglement topology. The overshoot is driven by an overstretching and recoil of ring polymers due to the convective unthreading of rings from linear chains.
Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics
Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.
Accelerating Instanton Theory with the Line Integral Nudged Elastic Band Method and Gaussian Process Regression
Quantum tunneling plays a fundamental role in many chemical reactions, particularly proton transfer processes. Ring polymer instanton theory offers a practical framework for computing tunneling rates in complex molecular systems. However, applying the ring polymer instanton method with a potential energy surface generated on-the-fly using electronic structure calculations can be computationally demanding. Here, in this work, we present a new efficient implementation of the ring polymer instanton method by combining the Line Integral Nudged Elastic Band (LI-NEB) approach with Gaussian Process Regression (GPR). We benchmarked this method on prototypical ground-state proton transfer systems, including the benchmark gas-phase hydrogen abstraction reaction H + CH 4 → H 2 + CH 3 , malonaldehyde, and Z-3-amino-propenal (aminopropenal). Our results show that this approach is an order of magnitude faster than traditional instanton algorithms while maintaining excellent agreement with their tunneling rates. This development opens the door to studying proton transfer in larger systems with improved efficiency.
Nuclear–Electronic Orbital General Rate Theory: Predicting Hydrogen Kinetic Isotope Effects in the Deep Tunneling Regime
Hydrogen transfer is a critical component of many chemical and biological processes. The ratio of rate constants for hydrogen and deuterium transfer defines the H/D kinetic isotope effect (KIE), which is a powerful tool for elucidating hydrogen transfer mechanisms. Interpretation of experimental H/D KIEs relies on accurate and affordable computational methods. However, due to their light mass, hydrogen and deuterium can undergo tunneling, which is challenging to describe in multidimensional molecular systems. Herein, we introduce the nuclear–electronic orbital general rate theory (NEO-GRT), which enables the efficient prediction of H/D KIEs based on full-dimensional molecular quantum chemistry calculations. The NEO-GRT approach describes the hydrogen transfer rate constant with a general expression that spans the vibrationally adiabatic and nonadiabatic hydrogen tunneling regimes. The input quantities are computed using NEO density functional theory, which treats the transferring hydrogen or deuterium nucleus quantum mechanically on the same level as the electrons. We investigate two intramolecular proton transfer reactions in organic molecules at temperatures down to 50 K to evaluate the performance of NEO-GRT by comparison to transition state theory and ring-polymer instanton theory. The KIEs computed with NEO-GRT agree with those calculated using ring-polymer instanton theory for the full-dimensional molecular systems at the same level of electronic structure theory. This agreement indicates that NEO-GRT captures the deep hydrogen tunneling effects, in contrast to transition state theory, which neglects such effects. Given its relatively low computational cost, NEO-GRT is a promising approach for predicting H/D KIEs in large organic and organometallic systems.
Path integral molecular dynamics: A high-fidelity approach to quantum dynamics of electrons
We investigate electron transport in the uniform electron gas using ring-polymer molecular dynamics (RPMD). Working in the weakly coupled, non-degenerate regime, we use RPMD to probe how the onset of quantum diffraction effects at high temperature reshapes electron–electron collisions and leads to a classical-to-quantum crossover in macroscopic transport properties. Static thermodynamics obtained with RPMD are consistent with the weak-coupling equation of state, confirming correct quantum Boltzmann sampling. Real-time transport extracted from mean square displacements exhibits the expected ballistic-to-diffusive transition and a systematic reduction of the electronic self-diffusivity as quantum effects strengthen, due to quantum diffraction modifying electron–electron collisions. Direct ring-polymer scattering simulations reveal diffractive “softening” of binary deflections, providing a micro-to-macro link between collision physics and diffusion. The present study establishes RPMD as a quantitative, trajectory-based tool for electron transport across the classical–quantum crossover and furnishes benchmarks for improving Coulomb-log interpolation models. We outline extensions to multi-component plasmas and a path to incorporate Fermi–Dirac statistics within path-integral dynamics.
Polymer Macrocycles: A novel topology to control dynamics of rubbery materials (Final Report)
We have successfully made synthetic polymer rings that are larger than previously reported having entanglement numbers as high as Z w ≈300 if the rings entangled as do linear chains. The synthesis was carried out using reversible radical recombination polymerization (R3P) of dithiols which produces a polymer with a very small persistence length. The reported results show surprising dilute solution behaviors due to the fact that polymeric rings expand more than their linear counterparts for polymer chains having a large number of persistence lengths, as developed in this study. The results strongly argue for a systematic investigation of the dilute solution properties of rings having different persistence lengths in different quality solvents, where the theta-condition should lead to results that are independent of the persistence length. For the rheological investigations related to chain entanglements, the polyDODT rings could be diluted so that the rheological data covered from less than one entanglement spacing relative to the linear counterpart to a value of Z w =300. Importantly, because we were able to dilute extremely high entanglement number polyDODT rings to a similar entanglement number as those reported for polystyrene rings that were highly purified using LCCC, we demonstrated that the dynamics of the polyDODT rings virtually overlaps with the dynamics of the polystyrene rings which is very strong evidence that these high molecular weight polyDODT rings are of high purity. Our results demonstrate that the onset of entanglement in rings, as evidenced by the appearance of a rubbery plateau G N 0 and by the onset of a strong power-law dependence of the viscosity on molecular weight (η~M w 5.8 ) or entanglement number (η~Z w 5.8 ), occurs at much higher molecular weights or polymer concentrations than is the case for linear chains. These results should serve as a benchmark for future investigations of the behavior of entangled, circular macromolecules.
Polymer Macrocycles: A novel topology to control dynamics of rubbery materials
We have successfully made synthetic polymer rings that are larger than previously reported having entanglement numbers as high as $Z_w$≈300 if the rings entangled as do linear chains. The synthesis was carried out using reversible radical recombination polymerization (R3P) of dithiols which produces a polymer with a very small persistence length. The reported results show surprising dilute solution behaviors due to the fact that polymeric rings expand more than their linear counterparts for polymer chains having a large number of persistence lengths, as developed in this study. The results strongly argue for a systematic investigation of the dilute solution properties of rings having different persistence lengths in different quality solvents, where the theta-condition should lead to results that are independent of the persistence length. For the rheological investigations related to chain entanglements, the polyDODT rings could be diluted so that the rheological data covered from less than one entanglement spacing relative to the linear counterpart to a value of $Z_w$=300. Importantly, because we were able to dilute extremely high entanglement number polyDODT rings to a similar entanglement number as those reported for polystyrene rings that were highly purified using LCCC, we demonstrated that the dynamics of the polyDODT rings virtually overlaps with the dynamics of the polystyrene rings which is very strong evidence that these high molecular weight polyDODT rings are of high purity. Our results demonstrate that the onset of entanglement in rings, as evidenced by the appearance of a rubbery plateau $G_N^0$ and by the onset of a strong power-law dependence of the viscosity on molecular weight (η~$M_w^{5.8}$) or entanglement number (η~$Z_w^{5.8}$), occurs at much higher molecular weights or polymer concentrations than is the case for linear chains. These results should serve as a benchmark for future investigations of the behavior of entangled, circular macromolecules.
Decoding polymer self-dynamics using a two-step approach
The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. Here, we show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a “two-step” approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.
Facile polymerization in a bicellar template to produce polymer nano-rings
We report a well-defined discoidal bicelle composed of three lipids, specifically zwitterionic long-chain 1,2-dipalmitoyl phosphocholine (DPPC) and short-chain 1,2-dihexanoyl phosphocholine (DHPC) doped with anionic 1,2-dipalmitoyl phosphoglycerol (DPPG) provides a generalized template for the synthesis of hydrophobic polymer nano-rings. The lipid molar ratio of DPPC/DHPC/DPPG is 0.71/0.25/0.04. The detailed investigation and discussion were based on styrene but tested on three other vinyl monomers. The structure of nano-rings is identified through the detailed analysis of small angle X-ray/neutron scattering (SAXS and SANS) data and transmission electron micrographs (TEM), supported by the differential scanning calorimetric (DSC) data before and after polymerization. The investigation covers samples with a styrene-to-lipid ratio ranged varied from 1:50 to 1:10.The styrene monomers are initially located at both the discoidal planar (long-chain lipid rich) and rim (short-chain lipid rich) regions. During polymerization, they migrate to the more fluid rim region-section. The formation mechanism involves the interplay of hydrophobic interaction, mismatched miscibility of polystyrene between the ordered and disordered phases, and crystallinity of the long lipid acyl chains. This facile synthesis is proven applicable for several hydrophobic monomers. The well-defined nano-rings greatly enhance the interfacial area and have the potential to be the building blocks for functional materials, if monomers are incorporated with desirable functions, for future applications. Crosslinked polymer nano-rings are produced in well-defined discoidal bicelles. The enhanced immiscibility in the planar region drives the hydrophobic polymers to the fluidic rim. The platform can be generalized for synthesis of other hydrophobic polymer nano-rings.
Full‐dimensional coupled‐channel statistical approach to atom‐triatom systems and applications to H/D + O 3 reaction
Abstract The statistical quantum model (SQM), which assumes that the reactivity is controlled by entrance/exit channel quantum capture probabilities, is well suited for chemical reactions with a long‐lived intermediate complex. In this work, a time‐independent coupled‐channel implementation of the SQM approach is developed for atom‐triatom systems in full dimensionality. As SQM treats the capture dynamics quantum mechanically, it is capable of handling quantum effects such as tunneling. A detailed study of the H/D + O 3 capture dynamics was performed by applying the newly developed SQM method on an accurate global potential energy surface. Agreement with previous ring polymer molecular dynamics (RPMD) results on the same potential energy surface is excellent except for very low temperatures. The SQM results are also in reasonably good agreement with available experimental rate coefficients. The strong H/D kinetic isotope effect underscores the dominant role of quantum tunneling under an entrance channel barrier at low temperatures.
Importance of Nuclear Quantum Effects on Aqueous Electrolyte Transport under Confinement in Ti 3 C 2 MXenes
Protons display a high chemical activity and strongly affect the charge storage capability in confined interlayer spaces of two-dimensional (2D) materials. As such, an accurate representation of proton dynamics under confinement is important for understanding and predicting charge storage dynamics in these materials. While often ignored in atomistic-scale simulations, nuclear quantum effects (NQEs), e.g., tunneling, can be significant under confinement even at room temperature. Here, using the thermostatted ring polymer molecular dynamics implementation of path integral molecular dynamics (PIMD) in conjunction with the ReaxFF force field, density functional tight binding (DFTB), and NequIP neural network potential simulations, we investigate the role of NQEs on proton and water transport in bulk water and aqueous electrolytes under confinement in Ti 3 C 2 MXenes. Although overall NQEs are relatively small, especially in bulk, we find that they can alter both quantitative values and qualitative trends on both proton transport and water self-diffusion under confinement relative to classical MD predictions. Therefore, our results suggest the need for NQEs to be considered to simulate aqueous systems under confinement for both qualitative and quantitative accuracy.
Quantum Simulations of Vibrational Strong Coupling via Path Integrals
A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. Furthermore, this result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.
Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional
We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.
Two-temperature warm dense hydrogen as a test of quantum protons driven by orbital-free density functional theory electronic forces
We consider a steady-state (but transient) situation in which a warm dense aggregate is a two-temperature system with equilibrium electrons at temperature Te, ions at Ti, and Te ≠ Ti. Such states are achievable by pump–probe experiments. For warm dense hydrogen in such a two-temperature situation, we investigate nuclear quantum effects (NQEs) on structure and thermodynamic properties, thereby delineating the limitations of ordinary ab initio molecular dynamics. We use path integral molecular dynamics (PIMD) simulations driven by orbital-free density functional theory (OFDFT) calculations with state-of-the-art noninteracting free-energy and exchange-correlation functionals for the explicit temperature dependence. We calibrate the OFDFT calculations against conventional (explicit orbitals) Kohn–Sham DFT. We find that when the ratio of the ionic thermal de Broglie wavelength to the mean interionic distance is larger than about 0.30, the ionic radial distribution function is meaningfully affected by the inclusion of NQEs. Moreover, NQEs induce a substantial increase in both the ionic and electronic pressures. This confirms the importance of NQEs for highly accurate equation-of-state data on highly driven hydrogen. For Te > 20 kK, increasing Te in the warm dense hydrogen has slight effects on the ionic radial distribution function and equation of state in the range of densities considered. In addition, we confirm that compared with thermostatted ring-polymer molecular dynamics, the primitive PIMD algorithm overestimates electronic pressures, a consequence of the overly localized ionic description from the primitive scheme.
A generalized class of strongly stable and dimension-free T-RPMD integrators
Here, recent work shows that strong stability and dimensionality freedom are essential for robust numerical integration of thermostatted ringpolymer molecular dynamics (T-RPMD) and path-integral molecular dynamics, without which standard integrators exhibit non-ergodicity and other pathologies [R. Korol et al., J. Chem. Phys. 151, 124103 (2019) and R. Korol et al., J. Chem. Phys. 152, 104102 (2020)]. In particular, the BCOCB scheme, obtained via Cayley modification of the standard BAOAB scheme, features a simple reparametrization of the free ring-polymer sub-step that confers strong stability and dimensionality freedom and has been shown to yield excellent numerical accuracy in condensed-phase systems with large time steps. Here, we introduce a broader class of T-RPMD numerical integrators that exhibit strong stability and dimensionality freedom, irrespective of the Ornstein–Uhlenbeck friction schedule. In addition to considering equilibrium accuracy and time step stability as in previous work, we evaluate the integrators on the basis of their rates of convergence to equilibrium and their efficiency at evaluating equilibrium expectation values. Within the generalized class, we find BCOCB to be superior with respect to accuracy and efficiency for various configuration-dependent observables, although other integrators within the generalized class perform better for velocity-dependent quantities. Extensive numerical evidence indicates that the stated performance guarantees hold for the strongly anharmonic case of liquid water. Both analytical and numerical results indicate that BCOCB excels over other known integrators in terms of accuracy, efficiency, and stability with respect to time step for practical applications.
Zero-cost corrections to influence functional coefficients from bath response functions
Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly generate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the accuracy of this procedure depends on the validity of the high temperature approximation. In this work, an alternative derivation based on the Kubo formalism is provided. This enables the calculation of additional correction terms that increases the range of applicability of the procedure to lower temperatures. Because it is based on the Kubo-transformed correlation function, this approach allows the direct use of correlation functions obtained from methods such as ring-polymer molecular dynamics and centroid molecular dynamics in determining the influence functional coefficients for subsequent system-solvent simulations. The accuracy of the original procedure and the corrected procedure is investigated across a range of parameters. It is interesting that the correction term comes at zero additional cost. Furthermore, it is possible to improve upon the correction using zero-cost physical intuition and heuristics making the method even more accurate.