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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor

Reduced models describing the Lagrangian dynamics of the velocity gradient tensor (VGT) in homogeneous isotropic turbulence (HIT) are developed under the physics-informed machine learning (PIML) framework. We consider the VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and subfilter contributions, which is accomplished by constructing them using the integrity bases and invariants of the VGT. The developed models can be expressed using the extended tensor basis neural network (TBNN) introduced by Ling et al. [J. Fluid Mech. 807, 155 (2016)]. Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number direct numerical simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the “ground-truth” DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into the TBNN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Performance analysis and tank test validation of a hybrid ocean wave-current energy converter with a single power takeoff

This paper introduces a hybrid ocean wave-current energy converter (HWCEC) that harvests energy from ocean waves and current simultaneously with a single power takeoff (PTO). Specifically, the wave energy is extracted through relative heaving motion between a floating buoy and a submerged second body, while the current energy is extracted using a marine current turbine (MCT). Energy from both sources are integrated by a hybrid PTO whose concept is based on a mechanical motion rectifier (MMR). The hybrid PTO with two one-way clutches converts bidirectional, up-and-down motion from the waves into unidirectional rotation of the generator. Meanwhile a third one-way clutch couples the MCT with the same generator. The wave and current can simultaneously or separately drive the same generator through different engagement and disengagement statuses of the one-way clutches. Time-domain simulation is conducted with hydrodynamic coefficients obtained from computational fluid dynamics analysis and boundary element method. Tank tests were conducted for a HWCEC under co-existing wave and current inputs. For comparison, separate baseline tests of a turbine and a two-body point absorber, each acting in isolation, are conducted. Experimental results validate the dynamic modeling and show that a HWCEC can increase the output power with a range between 29-87% over either current turbine and wave energy converter acting individually, and it can reduce by up to 70% the peak-to-average power ratio compared with the wave energy converter on the tested conditions.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Genetic algorithm-based geometry calibration for dynamic compression x-ray diffraction experiments

An important component of dynamic compression x-ray diffraction (XRD) experiment analysis is geometry calibration: proper data interpretation requires knowledge of the precise detector position and orientation and, if the experiment involves a single-crystal sample, knowledge of the lattice orientation. The determination of these parameters in the arbitrary three-dimensional (3D) scattering geometries often present in dynamic compression facilities is challenging, as the associated optimization problem can be highly nonlinear, nonsmooth, and discontinuous. We present a genetic algorithm-based approach for performing dynamic compression XRD calibrations that overcomes these obstacles. We provide details regarding the image processing, algorithm implementation, and open-source software deployment and demonstrate the capability of the approach to calibrate the detector and crystal parameters in 3D geometries. Notably, we demonstrate the solver’s capacity to find the crystal orientation without a priori rotation constraints.

Brown, Nathan P. [Sandia National Laboratories (SN↗
DOE OSTI2025

Triaxiality and shape dynamics in 70 Ge

The electromagnetic properties of low-lying states in 70 Ge were investigated via multi-step Coulomb excitation of a 70 Ge beam impinging on a 208 Pb target at the ATLAS facility of the Argonne National Laboratory. A total of 27 transitional elements and six diagonal matrix elements coupling 11 low-lying states, were extracted from the measured cross sections. These were used to calculate reduced transition probabilities, spectroscopic quadrupole moments, and rotational invariant shape parameters, providing enhanced precision and expanding on previous studies. The experimental data were compared within several theoretical frameworks, including the generalized triaxial rotor model, configuration interaction shell-model calculations, and computations within the combined frameworks of relativistic density functional theory and the five-dimensional collective Hamiltonian. The results demonstrate a good agreement with the experimental data and, in conjunction with calculations using a two-state mixing model, support significant triaxiality and strong mixing between the 0$^{+}_{1}$ and 0$^{+}_{2}$ states. This results in the magnitudes of their respective quadrupole deformations [β rms (0$^{+}_{1}$) = 0.228 (3), β rms (0$^{+}_{2}$) = 0.273 (1)] being more similar than previously observed. Furthermore, the implications of these results for understanding the complex shape coexistence phenomena, the role of triaxiality, and shape evolution along the Ge isotopic chain are discussed.

59 ≤ A ≤ 89↗
DOE OSTI2023

A comparison of the baryonic Tully–Fisher relation in MaNGA and IllustrisTNG

We compare an observed baryonic Tully–Fisher relation (BTFR) from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) and HI-MaNGA surveys to a simulated BTFR from the cosmological magnetohydrodynamical simulation, IllustrisTNG. To do so, we calibrate the BTFR of the local universe using 377 galaxies from the MaNGA and HI-MaNGA surveys, and perform mock 21 cm observations of matching galaxies from IllustrisTNG. The mock observations are used to ensure that the comparison with the observed galaxies is fair since it has identical measurement algorithms, observational limitations, biases, and uncertainties. For comparison, we also calculate the BTFR for the simulation without mock observations and demonstrate how mock observations are necessary to fairly and consistently compare between observational and theoretical data. We report a MaNGA BTFR of log$_{10} (M_{ \rm Bary}/M_\odot)= (2.97 \pm 0.18)$ log$_{10} V_{ \rm Rot} + (4.04 \pm 0.41)\, \log _{10}{M_{\odot }}$ and an IllustrisTNG BTFR of log$_{10} (M_{ \rm Bary}/M_\odot) = (2.94 \pm 0.23$) log$_{10} V_{ \rm Rot} + (4.15 \pm 0.44)\, \log _{10}{M_{\odot }}$. Thus, MaNGA and IllustrisTNG produce BTFRs that agree within uncertainties, demonstrating that IllustrisTNG has created a galaxy population that obeys the observed relationship between mass and rotation velocity in the observed universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Probing Conformational Evolution and Associated Dynamics of Mg(N(SO 2 CF 3 ) 2 ) 2 ·Dimethoxyethane Adduct Using Solid-State 19 F and 1 H NMR

Bis(trifluoromethanesulfonimide) or TFSI is widely used as a counter anion in electrolyte design due to its structural flexibility and chemical stability. Here we studied the conformational variations and associated dynamics of TFSI in adduct of Mg(TFSI) 2 with dimethoxyethane (DME), a solvate crystalline material using solid-state 1 H and 19 F NMR. TFSI molecular motion in this solvate structure falls within the timescale of the 19 F NMR experiment, yielding spectroscopic signatures for unique TFSI conformers under the coordination environment of Mg 2+ cation. Within the temperature range of -5 to 82 °C, we observe nine distinct TFSI sites in both crystalline and disordered regions using 19 F NMR, reflecting complexity of structural and dynamics of TFS1 anions within solvate structure. The four distinguishable sites in the disordered region for the two CF 3 groups of the same TFSI molecule are identified using chemical shift analysis. The exchange rate constants from site to site are calculated through variable temperature 19 F NMR and two-dimensional (2D) exchange spectroscopy (EXSY) experiments, along with respective activation enthalpies using Eyring's formulation. The flip rate of CF 3 around the S-C bond is estimated as ~ 15 s -1 at 8 °C with ΔH ≠ ~ 22 kJ/mol, but the rotation of the entire TFSI is 4.8 s -1 at 8 °C with a significantly greater ΔH ≠ = 98 ± 10 kJ/mol. Furthermore, the slow conversion of trans to cis conformers at a lower temperature (T ≤ 1 °C) in the crystalline region is monitored, with a conversion rate of ~ 2 x 10 -5 s -1 at -5 °C. Density functional theory (DFT)-based calculations were performed to support further the assignment of experimental chemical shifts, and the activation energy E a = 21.1 kJ/mol obtained for the cis to trans transition is consistent with experimental values. The combined set of 19 F and 1 H under both one-dimensional (1D) and 2D NMR methods demonstrated here can be further used for examining electrode-electrolyte interfaces to probe the motions of various constituents that can enable detailed studies of interfacial processes and dynamics. Ultimately, such studies will aid in the design and discovery of interfacial constructs in which directed defect chemistry, chemical moiety distribution, and nanostructure are employed to drive efficient charge transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Gravity Probe Spin: Prospects for measuring general-relativistic precession of intrinsic spin using a ferromagnetic gyroscope

An experimental test at the intersection of quantum physics and general relativity is proposed: measurement of relativistic frame dragging and geodetic precession using intrinsic spin of electrons. Furthermore, the behavior of intrinsic spin in spacetime dragged and warped by a massive rotating body is an experimentally open question, hence the results of such a measurement could have important theoretical consequences. Such a measurement is possible by using mm-scale ferromagnetic gyroscopes in orbit around the Earth. Under conditions where the rotational angular momentum of a ferromagnet is sufficiently small, a ferromagnet’s angular momentum is dominated by atomic electron spins and is predicted to exhibit macroscopic gyroscopic behavior. If such a ferromagnetic gyroscope is sufficiently isolated from the environment, rapid averaging of quantum uncertainty via the spin-lattice interaction enables readout of the ferromagnetic gyroscope dynamics with sufficient sensitivity to measure both the Lense-Thirring (frame dragging) and de Sitter (geodetic precession) effects due to the Earth.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Identifying Characteristics of Wildfire Towers and Troughs

Wildfire behavior is dictated by the complex interaction of numerous physical phenomena including dynamic ambient and fire-induced winds, heat transfer, aerodynamic drag on the wind by the fuel and combustion. These phenomena create complex feedback effects between the fire and its surroundings. In this study, we aim to study the mechanisms by which buoyant flame dynamics along with vortical motions and instabilities control wildfire propagation. Specifically, this study employs a suite of simulations conducted with the physics-based coupled fire-atmosphere behavior model (FIRETEC). The simulations are initialized with a fire line and the fires are allowed to propagate on a grass bed, where the fuel heights and wind conditions are varied systematically. Flow variables are extracted to identify the characteristics of the alternating counter-rotational vortices, called towers and troughs, that drive convective heat transfer and fire spread. These vortices have previously been observed in wildfires and laboratory fires, and have also been observed to arise spontaneously in FIRETEC due to the fundamental physics incorporated in the model. However, these past observations have been qualitative in nature and no quantitative studies can be found in the literature which connected these coherent structures fundamental to fire behavior with the constitutive flow variables. To that end, a variety of state variables are examined in the context of these coherent structures under various wind profile and grass height conditions. Identification of various correlated signatures and fire-atmosphere feedbacks in simulations provides a hypothesis that can be tested in future observational or experimental efforts, potentially assisting experimental design, and can aid in the interpretation of data from in situ detectors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Simulating Neutron Stars with Solid Quark Cores: Rotations, Oscillations, and Binary Mergers [Slides]

Neutron stars feature complexity from GR, QM, particle physics and nuclear physics effects which cannot be investigated in the lab up to the densities in their core. GWs from binary neutron star mergers are on the rise to provide more insight into the physics inside NSs. There is a possibility that involves crystalline, color-superconducting quark matter, with implications towards altering the GW signal if NSs harbor this exotic matter. There are no 3D dynamical simulations of solid quark matter inside Neutron stars. We perform the first 3D dynamical simulations of solid quark matter inside NSs. These are performed in the Newtonian Approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Insights into oxygen diffusion in rare earth disilicate environmental barrier coatings

Environmental barrier coatings (EBC) are crucial for the use of SiC-based ceramic matrix composites in high-temperature combustion environments, yet knowledge of oxygen diffusion in these coatings is limited. This study investigates oxygen diffusion dynamics in the β-RE 2 Si 2 O 7 system to minimize oxygen penetration in rare earth disilicates. We analyze defect formation energy under varying oxygen conditions, identifying key diffusion mechanisms. In oxygen-rich environments, the most favorable neutral interstitial oxygen diffuses along the [110] direction. In oxygen-poor conditions, neutral oxygen vacancies rotate around Y and Si atoms, exhibiting a diffusivity of 6.59×10 −22 m 2 /s at 1500 K for β-Yb 2 Si 2 O 7 . Under intermediate oxygen levels, charged interstitial oxygen diffuses via concerted interstitialcy along the [001] direction with a diffusivity of 6.21×10 −17 m 2 /s. Additionally, alloying rare earth Y with Er and Yb increases diffusion barriers, contributing to improved EBC performance in extreme environments. The insights gained provides valuable guidance for designing robust coatings tailored to withstand extreme operational environments.

36 MATERIALS SCIENCE↗
DOE OSTI2022

On the Origin of Pulsar and Magnetar Magnetic Fields

Abstract In order to address the generation of neutron star magnetic fields, with particular focus on the dichotomy between magnetars and radio pulsars, we consider the properties of dynamos as inferred from other astrophysical systems. With sufficiently low (modified) Rossby number, convective dynamos are known to produce dipole-dominated fields whose strength scales with convective flux, and we argue that these expectations should apply to the convective protoneutron stars (PNSs) at the centers of core-collapse supernovae. We analyze a suite of three-dimensional simulations of core collapse, featuring a realistic equation of state and full neutrino transport, in this context. All our progenitor models, ranging from 9 M ⊙ to 25 M ⊙ , including one with initial rotation, have sufficiently vigorous PNS convection to generate dipole fields of order ∼10 15 Gauss, if the modified Rossby number resides in the critical range. Thus, the magnetar/radio pulsar dichotomy may arise naturally in part from the distribution of core rotation rates in massive stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Wave packet dynamics and control in excited states of molecular nitrogen

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N 2 . Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ~ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Temperature-dependent dynamic fouling on superhydrophobic and slippery nonwetting copper surfaces

Bioinspired, superhydrophobic and slippery liquid infused surfaces that offer nonwetting characteristics have been explored in recent years for fouling mitigation. However, most of the studies are in the context of biofouling or under static immersion at ambient temperature conditions that are not reflective of the dynamic flow environment in practice. This article presents, for the first time, a systematic study of dynamic fouling of superhydrophobic (SHS) and slippery lubricant-infused surfaces (LIS) over a range of flow and temperature conditions. In this work, copper metallic surfaces were textured via electrodeposition or etching and further functionalized to achieve SHS and, additionally, infiltrated with a lubricant to fabricate LIS. The nonwetting surfaces were studied for their fouling behavior in a rotating Couette flow of a supersaturated calcium sulfate solution at different rotational speed and temperature. Fouling mineral mass accumulation on the different surfaces was measured as a function of time over a period of days using inductively coupled plasma mass spectroscopy and the fouled surfaces were investigated using scanning electron microscopy. Both SHS and LIS showed superior anti-scaling performance at all ranges of variables. An analytical Hill-Langmuir model is presented, for the first time, to describe the time evolution of scaling within 20% accuracy over the range of parameters studied. The study is the first to juxtapose two surface texturing methods, electrodeposition and etching, and two nonwetting surface types, SHS and LIS, subject to a common suite of experiments to elucidate fundamental understanding of mineral fouling on nonwetting surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗
DOE OSTI2024

Autonomous Inverter Controls for Resilient and Secure Grid Operation: Vector Control Design for Grid Forming

The project addresses both fundamental and practical challenges of GFM/GFL inverter control for the power grids with high inverter based resources (IBRs) penetration. A data- driven modeling technique is applied to accurately model dynamics of PWM inverters, including electromagnetic-transient (EMT). Systematic and integrative designs of grid- forming (GFM) and grid-following (GFL) primary controls are developed to guarantee system performance under either normal or abnormal operating conditions without violating constraints. This modeling and control framework provides black-start capability in case of an outage without relying on rotating generators, and its secondary control is also shown to enhance resilience against cyber-physical attacks.

14 SOLAR ENERGY↗
DOE OSTI2022

Stability Evaluation for a Damped, Constrained-Motion Cutting Force Dynamometer

This paper describes the dynamic stability evaluation of a constrained-motion dynamometer (CMD) with passive damping. The CMD’s flexure-based design offers an alternative to traditional piezoelectric cutting force dynamometers, which can exhibit adverse effects of the complex structural dynamics on the measurement accuracy. In contrast, the CMD system’s structural dynamics are nominally single degree of freedom and are conveniently altered by material selection, flexure element geometry, and element arrangement. In this research, a passive damping approach is applied to increase the viscous damping ratio and, subsequently, the stability limit. Cutting tests were completed and the in situ CMD displacement and velocity signals were sampled at the spindle rotating frequency. The periodic sampling approach was used to determine if the milling response was synchronous with the spindle rotation (stable) or not (chatter) by constructing Poincaré maps for both experiment and prediction (time-domain simulation). It was found that the viscous damping coefficient was increased by 130% and the critical stability limit was increased from 4.3 mm (no damping) to 15.4 mm (with damping).

36 MATERIALS SCIENCE↗
DOE OSTI2022

Nonidealities in Rotating Detonation Engines

A rotating detonation engine (RDE) is a realization of pressure-gain combustion, wherein a traveling detonation wave confined in a chamber provides shock-based compression along with chemical heat release. Due to the high wave speeds, such devices can process high mass flow rates in small volumes, leading to compact and unconventional designs. RDEs involve unsteady and multiscale physics, and their operational characteristics are determined by an equilibrium between large- and small-scale processes. While RDEs can provide a significant theoretical gain in efficiency, achieving this improvement requires an understanding of the multiscale coupling. Specifically, unavoidable nonidealities, such as unsteady mixing, secondary combustion, and multiple competing waves associated with practical designs, need to be understood and managed. The secondary combustion processes arise from fuel/air injection and unsteady and incomplete mixing, and can create spurious losses. In addition, a combination of multiple detonation and secondary waves compete and define the dynamical behavior of mixing, heat release distribution, and the overall mode of operation of the device. This review discusses the current understanding of such nonidealities and describes the tools and techniques used to gain insight into the extreme unsteady environment in such combustors.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Chain flexibility and glass transition temperatures of poly(n-alkyl (meth)acrylate)s: Implications of tacticity and chain dynamics

The relationship between chain microstructure and glass transition temperature (T g ) is complicated for poly(alkyl methacrylate)s and poly(alkyl acrylate)s. Despite intensive studies, relationships between the structures of these polymers and their properties, including solution characteristics and T g , are still controversial. Solution properties, chain conformations, including Flory's characteristic ratio (C ∞ ), persistence length (l p ), and chain diameters, and T g are reported for series of poly(n-alkyl acrylate)s and poly(n-alkyl methacrylate)s having alkyl side chain lengths (n) ranging from 1 to 10 carbons in length, with uniform and well-characterized tacticities. Chain flexibilities of both series of polymers decrease as n increases, reflecting increased hindrances to rotation about backbone bonds as side chains become longer. Conversely, the T g s for both series of polymers decrease substantially as n increases, reflecting the greater side chain mobilities of long alkyl substituents. For shorter alkyl chain lengths, T g s for the poly(n-alkyl acrylate)s are much lower than for the corresponding poly(n-alkyl methacrylate)s, a difference which has been attributed in the past to the presumed reduced chain flexibility of polymethacrylates due to the presence of the α-methyl substituent. However, contrary to such expectations, C ∞ and l p values for these two series of polymers are nearly identical at a given n value, except for the longest n-alkyl substituents. Instead, the differences in T g may be attributed to the differences in tacticity of the two series – almost ideally atactic for the poly(n-alkyl acrylate)s but high in syndiotacticity for the poly(n-alkyl methacrylate)s. The T g s for the two series of polymers approach that of polyethylene at longer alkyl chain lengths. In addition, the effects of tacticity and chain dynamics on C ∞ , l p , and T g of poly(methyl methacrylate) is discussed.

36 MATERIALS SCIENCE↗