Threads of time

This thesis advances the fundamental understanding of dilute polymer solution rheology through systematic investigation of extensional flow behavior, with particular focus on polyethylene oxide (PEO) and polystyrene (PS) solutions. By addressing critical methodological challenges and revealing underlying physical mechanisms, this work establishes new frameworks for characterizing polymer dynamics in extension and controlling degradation processes that compromise long-term stability. Chapter 1 provides comprehensive background on dilute polymer solutions in extensional flow, establishing the theoretical foundation for single-chain dynamics, molecular models (Rouse, Zimm, FENE), and experimental techniques. The review identifies key challenges in the field: apparent concentration dependence of relaxation times even below the overlap concentration, discrepancies between measurement techniques, poor reproducibility across laboratories, and the fundamental question of whether measured relaxation times reflect intrinsic single-chain properties or measurement artifacts. Chapter 2 resolves a fundamental challenge in capillary breakup rheometry: achieving rate-independent relaxation time measurements in dilute polymer solutions. Through systematic velocity-controlled stretching experiments on PEO solutions (10-960 mg/L), this work demonstrates that the initial extension rate during visco-capillary stretching critically determines whether subsequent elasto-capillary thinning yields the true longest relaxation time. A minimum stretching criterion is established--the initial strain rate must exceed approximately 2/3 the inverse relaxation time--to ensure sufficient chain extension before the Rayleigh-Plateau instability. Below this threshold, polymer chains remain insufficiently stretched, resulting in rate-dependent, artificially low relaxation times. The work introduces "stretchability" as a new dimensionless parameter characterizing material deformation behavior beyond simple relaxation time, with the asymptotic stretchability index providing concentration-dependent information about extensional response. These findings explain systematic discrepancies in the literature where different experimental protocols yielded vastly different relaxation times for identical polymer-solvent systems, and establish a reproducible methodology for measuring intrinsic polymer properties. Chapter 3 investigates whether extensional relaxation time can serve as a predictive tool for molecular weight and concentration through universal scaling relationships. Parallel studies of polydisperse PEO in water and nearly monodisperse PS in dioctyl phthalate (DOP) reveal that while power law concentration scaling (lambda proportional to c^m) is robust and reproducible within individual samples (m approximately 0.31 for PS, m approximately 0.37 for PEO), attempts to construct universal master curves fail. Critical to this investigation is the finding that measured molecular weights deviate substantially from nominal values--GPC analysis revealed that the "4 MDa" sample had higher actual Mw (6.148 MDa) than the "8 MDa" sample (5.492 MDa), with all samples exhibiting high polydispersity (PDI = 2.3-2.6). This molecular weight uncertainty, combined with fundamental ambiguities in determining overlap concentration (c*--which varies up to 20-fold depending on calculation method), prevents universal master curve construction. The measured relaxation time proves strain-dependent, increasing by 2.5-3x across the elastocapillary regime--a phenomenon potentially attributable to preferential solvent drainage from the thinning filament, where quantitative analysis shows only 0.05-0.08% of initial solvent volume need be lost to produce the observed concentration enrichment effects. Sample preparation artifacts compound these challenges: mechanical degradation from shaker bath agitation reduces relaxation times by approximately 60% compared to gentle manual preparation. Crucially, extension-determined overlap differs from equilibrium overlap: shear-measured c* does not mark any transition in extensional behavior, suggesting that chain stretching creates effective overlap at concentrations nominally below c*. For polydisperse samples, the concept of a unique "longest relaxation time" becomes ambiguous--measured values represent weighted averages over molecular weight distributions. Nevertheless, the intercept of concentration scaling relationships (phi) correlates systematically with measured molecular weight, confirming proper separation of concentration effects (slope m) and molecular weight effects (intercept phi) and suggesting a pragmatic path forward through empirical calibration curves that would bypass theoretical ambiguities. While universal prediction from first principles fails, sample-specific calibration provides robust empirical frameworks for quality control, degradation tracking, and batch comparison. Chapter 4 leverages the reproducible measurement methodology from Chapter 2 and the concentration scaling insights from Chapter 3 to characterize and control PEO degradation in aqueous solution. Extensional relaxation time is validated as a direct proxy for molecular weight loss, confirmed through independent GPC analysis showing 90% molecular weight reduction (from 5.492 MDa to 0.519 MDa) over 234 days for an aged 8 MDa sample. A critical finding emerges: PEO degradation kinetics are concentration-dependent but molecular-weight-independent (across 4-8 MDa), revealing that local radical chemistry rather than chain dynamics governs scission. A sharp concentration threshold at 90-120 wppm separates two distinct mechanistic regimes. Below this threshold, the ultra-dilute regime exhibits faster degradation (X = 0.007C + 1.30) characterized by maximum oxygen availability, reduced radical termination, enhanced interfacial catalysis, and a "radically lean" environment favoring chain scission. Above this threshold, degradation slows significantly (X = 0.0129C - 0.0261) due to increased viscosity reducing oxygen transport, enhanced radical termination in polymer-rich domains, physical shielding of reactive sites through chain entanglement, and reduced interfacial fraction. This concentration-dependent degradation is accurately modeled using a stretched exponential framework: lambda(t_d) = lambda₀ exp(-t_d^X), where the exponent X is determined solely by concentration and is independent of molecular weight. Systematic testing of 22 treatments across five categories (antimicrobials, antioxidants, pH modulators, combination treatments, and preservation methods) reveals that only organic acid conjugate base salts (calcium lactate, chlorhexidine digluconate), benzyl alcohol, and refrigeration successfully stabilize PEO, while conventional antioxidants (BHT, EDTA, hydroquinone) fail or accelerate degradation. A striking finding: antimicrobial activity proves neither necessary nor sufficient for stabilization--calcium lactate protected solutions despite visible bacterial growth, indicating that microbial degradation is not the primary mechanism. These results point toward mass-transfer-limited autoxidation as the dominant degradation pathway under ambient laboratory conditions, with successful stabilizers functioning through mechanisms that reduce oxygen accessibility or scavenge reactive oxygen species rather than preventing biological contamination. This thesis makes four principal contributions to the field: (1) establishment of minimum stretching criteria for measuring true polymer relaxation times in capillary breakup experiments, explaining widespread literature discrepancies; (2) validation of robust power law concentration scaling (lambda proportional to c^m) with reproducible, universal exponents within individual polymer-solvent systems (m approximately 0.31 for PS, m approximately 0.37 for PEO), demonstrating that concentration effects are separable from molecular weight effects; (3) revelation that universal master curves fail not because the physics is unknowable but because polydispersity, flow history, and strain-dependent dynamics are not captured by equilibrium scaling theories; and (4) identification of mass-transfer-limited autoxidation as the dominant PEO degradation mechanism with practical stabilization strategies. Together, these advances provide both fundamental insights into polymer physics in extensional flow and practical tools for formulation scientists working with dilute polymer solutions in industrial applications ranging from pharmaceuticals to agriculture to turbulent drag reduction.