arXiv subjects

Ting Ge

Publications and source records attributed to Ting Ge.

13 recordsLinked to original sources

arXiv2025

From Structural Equation Modeling to Targeted Learning: A Tutorial Introduction to Targeted Maximum Likelihood Estimation for SEM Researchers

Structural equation modeling (SEM) and path analysis have long been central tools for studying complex causal relationships in the social and behavioral sciences, yet their reliance on parametric assumptions can lead to biased inference under model misspecification. To bridge traditional SEM with modern causal machine learning, this paper introduces targeted maximum likelihood estimation (TMLE), a doubly robust framework built on nonparametric structural equation modeling. We formally connect TMLE to classical path analysis, showing that standard SEM estimators arise as special cases of TMLE under restrictive parametric specifications and that both approaches can estimate common causal quantities such as direct, indirect, and total effects. Through simulation studies under both correctly specified and misspecified models, we demonstrate that while the two methods perform similarly when models are correctly specified, TMLE consistently achieves lower bias, reduced mean squared error, and improved confidence interval coverage when parametric assumptions are violated. We further illustrate these differences using an applied mediation analysis examining the role of poverty in access to high school education, where path analysis suggests a significant direct effect, whereas TMLE does not, highlighting the practical consequences of robustness in causal inference. Overall, this tutorial offers SEM researchers a conceptual and practical introduction to targeted learning, providing guidance on leveraging TMLE to enhance causal analysis beyond traditional parametric frameworks.

stat.OT↗

arXiv2024

Molecular simulations of crazes in glassy polymers under cyclic loading

We study with molecular dynamics simulations of a generic bead-spring model the cyclic crazing behaviour of glassy polymers. The aim is to elucidate the mechanical response of sole fibrillated craze matter as well as its interaction with bulk material. The macroscopic stress response exhibits a hysteresis, which is quasi stationary after the first cycle and largely independent of deformation rate and temperature. It results from a complex interplay between constraints imposed by the entanglement network, pore space and pore space closure. Once the craze fibrils are oriented, stretching of the covalent backbone bonds leads to a rapid stress increase. In the initial stages of unloading, a loss in entanglement contact yields a quick stress relaxation in the backbone. During unloading, the craze fibrils undergo a rigid body (i.e.\ stress-free) folding motion due to the surrounding pore space, so that the structural behaviour of craze fibrils during unloading is most accurately described as string-like. The reloading response depends significantly on the degree of pore space closure and the enforced intermolecular interaction during unloading. It ranges from a linear stress increase to a re-cavitation with a re-drawing response. Compared to the bulk stiffness, the craze stiffness is two orders of magnitude lower and as a result, the macro response of coexisting craze and bulk matter is governed by the sole fibrillated craze matter.

cond-mat.soft↗

arXiv2024

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, 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 $\tau_{d,R}$ for rings of length $N_R$ blended with linear chains of length $N_l$ to scale as $\tau_{d,R}\sim N_R^2N_L^{3.4}$.

cond-mat.soft↗

arXiv2022

Dynamics of Associative Polymers with High Density of Reversible Bonds

We design and synthesize unentangled associative polymers carrying unprecedented high fractions of stickers, up to eight per Kuhn segment, that can form strong pairwise hydrogen bonding of $\sim20k_BT$ without microphase separation. The reversible bonds significantly slow down the polymer dynamics but nearly do not change the shape of linear viscoelastic spectra. Moreover, the structural relaxation time of associative polymers increases exponentially with the fraction of stickers and exhibits a universal yet non-Arrhenius dependence on the distance from polymer glass transition temperature. These results cannot be understood within the framework of the classic sticky-Rouse model but are rationalized by a renormalized Rouse model, which highlights an unexpected influence of reversible bonds on the structural relaxation rather than the shape of viscoelastic spectra for associative polymers with high concentrations of stickers.

cond-mat.soft↗

arXiv2022

Super-stretchable Elastomer from Cross-linked Ring Polymers

The stretchability of polymeric materials is critical to many applications such as stretchable electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extension of polymer strands between cross-links, rather than between entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.

cond-mat.soft↗

arXiv2021

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 $\phi_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10 well-entangled systems with $\phi_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a function of $\phi_R$, and identify with simple arguments a ring fraction $\phi_R\approx0.4$ where the topological constraints of the entanglement network are maximized. These topological analyses are used to rationalize the $\phi_R$-dependence of ring and linear chain dynamics, conformations, and blend viscosity. Complimentary 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 polymer conformations that is caused by the convective unthreading of rings from linear chains. This produces significant changes in the entanglement structure of blends that we directly visualize and quantify with primitive path analyses during flow.

cond-mat.soft↗

arXiv2019

Topological Linking Drives Anomalous Thickening of Ring Polymers In Weak Extensional Flows

Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme elongation of a minority population of rings that grows with $Wi$. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower $Wi$ and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings generated by flow depends non-monotonically on $Wi$, increasing to a maximum when $Wi\sim1$ before rapidly decreasing when the strain rate approaches the relaxation rate of the smallest ring loops $\sim 1/\tau_e$.

cond-mat.soft↗

arXiv2018

Chain Length Dispersity Effects on Mobility of Entangled Polymers

While nearly all theoretical and computational studies of entangled polymer melts have focused on uniform samples, polymer synthesis routes always result in some dispersity, albeit narrow, of distribution of molecular weights (D_M=M_w/M_n ~ 1.02-1.04). Here the effects of dispersity on chain mobility are studied for entangled, disperse melts using a coarse-grained model for polyethylene. Polymer melts with chain lengths set to follow a Schulz-Zimm distribution for the same average M_w = 36 kg/mol with D_M = 1.0 to 1.16, were studied for times of $600-800$ $\mu$s using molecular dynamics simulations. This time frame is longer than the time required to reach the diffusive regime. We find that dispersity in this range does not affect the entanglement time or tube diameter. However, while there is negligible difference in the average mobility of chains for the uniform distribution D_M=1.0 and D_M = 1.02, the shortest chains move significantly faster than the longest ones offering a constraint release pathway for the melts for larger D_M.

cond-mat.soft↗

arXiv2016

Crazing of Nanocomposites with Polymer-Tethered Nanoparticles

The crazing behavior of polymer nanocomposites formed by blending polymer grafted nanoparticles with an entangled polymer melt is studied by molecular dynamics simulations. We focus on the three key differences in the crazing behavior of a composite relative to the pure homopolymer matrix, namely, a lower yield stress, a smaller extension ratio and a grafted chain length dependent failure stress. The yield behavior is found to be mostly controlled by the local nanoparticle-grafted polymer interfacial energy, with the grafted polymer-polymer matrix interfacial structure being of little to no relevance. Increasing the attraction between nanoparticle core and the grafted polymer inhibits void nucleation and leads to a higher yield stress. In the craze growth regime, the presence of grafted chain sections of 100 monomers alters the mechanical response of composite samples, giving rise to smaller extension ratios and higher drawing stresses than for the homopolymer matrix. The dominant failure mechanism of composite samples depends strongly on the length of the grafted chains, with disentanglement being the dominant mechanism for short chains, while bond breaking is the failure mode for chain lengths greater than 10Ne, where Ne is the entanglement length.

cond-mat.soft↗

arXiv2014

Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements and Crazing

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time $t$. Changes in the tensile stress, mode of failure and interfacial fracture energy $G_I$ are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small $t$ welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy $G_I$ is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, $G_I$ increases as $t^{1/2}$ before saturating at the average bulk fracture energy $G_b$. As in previous simulations of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, $G_I$ is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and $G_I \ll G_b$.

cond-mat.soft↗

arXiv2014

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Self-healing of polymer films often takes place as the molecules diffuse across a damaged region, above their melting temperature. Using molecular dynamics simulations we probe the healing of polymer films and compare the results with those for thermal welding of homopolymer slabs. The two processes differ in their interfacial structure since damage leads to increased polydispersity and more short chains. A polymer sample was cut into two separate films that were then held together in the melt state. The recovery of the damaged film was followed as time elapsed and polymer molecules diffused across the interface. The mass uptake and formation of entanglements, as obtained from primitive path analysis, are extracted and correlated with the interfacial strength obtained from shear simulations. We find that the interdiffusion is significantly faster in the damaged film compared to welding because of the presence of short chains. Though interfacial entanglements increase more rapidly for the damaged films, a large fraction of them are near chain ends. As a result, the interfacial strength of the healing film increases more slowly than for welding. For both healing and welding, the interfacial strength saturates as the bulk entanglement density is recovered across the interface. However, the saturation strength of the damaged film is below the bulk strength for the polymer sample. At saturation, cut chains remain near the healing interface. They are less entangled and thus mechanically weaken the interface. When the interfacial strength saturates, the number of interfacial entanglements scales with the corresponding bulk entanglement density. Chain stiffness increases the density of entanglements, which increases the interfacial strength. Our results show that a few entanglements across the interface are sufficient to resist interfacial chain pullout and enhance the mechanical strength.

cond-mat.soft↗

arXiv2013

Structure and Strength at Immiscible Polymer Interfaces

Thermal welding of polymer-polymer interfaces is important for integrating polymeric elements into devices. When two different polymers are joined, the strength of the weld depends critically on the degree of immiscibility. We perform large-scale molecular dynamics simulations of the structure-strength relation at immiscible polymer interfaces. Our simulations show that immiscibility arrests interdiffusion and limits the equilibrium interfacial width. Even for weakly immiscible films, the narrow interface is unable to transfer stress upon deformation as effectively as the bulk material, and chain pullout at the interface becomes the dominant failure mechanism. This greatly reduces the interfacial strength. The weak response of immiscible interfaces is shown to arise from an insufficient density of entanglements across the interface. We demonstrate that there is a threshold interfacial width below which no significant entanglements can form between opposite sides to strengthen the interface.

cond-mat.soft↗

arXiv2012

Polymer Welding: Strength Through Entanglements

Large-scale simulations of thermal welding of polymers are performed to investigate the rise of mechanical strength at the polymer-polymer interface with the welding time. The welding process is in the core of integrating polymeric elements into devices as well as in thermal induced healing of polymers; processes that require development of interfacial strength equal to that of the bulk. Our simulations show that the interfacial strength saturates at the bulk shear strength much before polymers diffuse by their radius of gyration. Along with the strength increase, the dominant failure mode changes from chain pullout at the interface to chain scission as in the bulk. Formation of sufficient entanglements across the interface, which we track using a Primitive Path Analysis is required to arrest catastrophic chain pullout at the interface. The bulk response is not fully recovered until the density of entanglements at the interface reaches the bulk value. Moreover, the increase of interfacial strength before saturation is proportional to the number of interfacial entanglements between chains from opposite sides.

cond-mat.soft↗