Determination of the Compositional Profile for Tapered Copolymers of Ethylene Oxide and 1,2-Butylene Oxide by In-situ-NMR

In this work, ¹H NMR was used to examine the anionic copolymerization kinetics of ethylene oxide and 1,2-butylene oxide. The in situ NMR technique allows monitoring the concentration profiles of both monomers simultaneously. A series of polymerization experiments at different monomer and initiator concentrations were done in order to determine the copolymerization rate constants. The data were evaluated by fitting the result of a numerical solution of the kinetic differential equations to the NMR data. This procedure allowed calculating all four rate constants, <i>k</i>_EE, <i>k</i>_EB, <i>k</i>_BE, and <i>k</i>_BB, individually instead of the commonly determined reactivity ratios <i>r</i>_E = <i>k</i>_EE/<i>k</i>_EB and <i>r</i>_B = <i>k</i>_BB/<i>k</i>_BE. The monomer incorporation into the copolymer chains is dominated by the different reactivities of the monomers, whereas the nature of the chain ends is of minor importance. In the system investigated ethylene oxide is about 6.5 times more reactive than 1,2-butylene oxide. The compositional profiles of the final copolymers can be calculated from the time-resolved concentration profiles. If both monomers are present at the start of the polymerization the compositional profiles have a sigmoidal shape with one chain end containing mainly ethylene oxide and the other chain end being formed almost exclusively of butylene oxide units. However, with the knowledge of the copolymerization rate constants it is possible to realize other compositional profiles. If the reactor is first charged with ethylene oxide the addition rates of butylene oxide can be calculated in order to obtain any other arbitrarily chosen compositional profile

Cooperative Dynamics of Highly Entangled Linear Polymers within the Entanglement Tube

We present a quantitative comparison of the dynamic structure factors from unentangled and strongly entangled poly(butylene oxide) (PBO) melts. As expected, the low molecular weight PBO displays Rouse dynamics, however, with very significant subdiffusive center-of-mass diffusion. The spectra from high molecular weight entangled PBO can be very well described by the dynamic structure factor based on the concept of local reptation, including the Rouse dynamics within the tube and allowing for non-Gaussian corrections. Comparing quantitatively the spectra from both polymers leads to the surprising result that their spectra differ only by the contribution of classical Rouse diffusion for the low molecular weight melt. The subdiffusive component is common for both the low and high molecular weight PBO melts, indicating that in both melts the same interchain potential is active, thereby supporting the validity of the Generalized Langevin Equation approach

Spin Relaxation and Dynamics of Ring Poly(ethylene oxide) in Melts

The spin relaxation of protons and deuterons was investigated in melts of ring poly(ethylene oxide) (PEO) macromolecules with a molecular mass varying from 5280 to 96,000 Da. Comparison of the frequency dispersion of NMR spin–lattice relaxation rates with corresponding rates in the melts of linear PEO of similar molecular masses shows that there is a significant mutual interpenetration of neighboring ring macromolecules, although less pronounced than in their linear counterparts. The mean-squared displacement of ring segments in the investigated frequency interval corresponding to the time interval 8 × 10–9 to 2 × 10–5 s depends on time as ⟨rn2(t)⟩ ∝ t0.39, in agreement with neutron spin echo (NSE) results. Decays of the normalized Hahn echo signal in ring macromolecules are exponential within experimental errors, unlike for their linear counterparts where strongly nonexponential behavior is found. This indicates the absence of dynamic heterogeneity of ring segments seen by NMR and associated with the presence of end segments in their linear analogues

Influence of PEGylation on Domain Dynamics of Phosphoglycerate Kinase: PEG Acts Like Entropic Spring for the Protein

Protein–polymer conjugation is a widely used technique to develop protein therapeutics with improved pharmacokinetic properties as prolonged half-life, higher stability, water solubility, lower immunogenicity, and antigenicity. Combining biochemical methods, small angle scattering (SAXS/SANS), and neutron spin–echo spectroscopy, here we examine the impact of PEGylation (i.e., the covalent conjugation with poly­(ethylene glycol) or PEG) on structure and internal domain dynamics of phosphoglycerate kinase (PGK) to elucidate the reason for reduced activity that is connected to PEGylation. PGK is a protein with a hinge motion between the two main domains that is directly related to function. We find that secondary structure and ligand access to the binding sites are not affected. The ligand induced cleft closing is unchanged. We observe an additional internal motion between covalent bonded PEG and the protein compatible with Brownian motion of PGK in a harmonic potential. Entropic interaction with the full PEG chain leads to a force constant of about 8 pN/nm independent of PEG chain length. This additional force preserves protein structure and has negligible effects on the functional domain dynamics of the protein. PEGylation seems to reduce activity just by acting as a local crowder for the ligands. The newly identified interaction mechanism might open possibilities to improve rational design of protein–polymer conjugates

Chain Confinement and Anomalous Diffusion in the Cross over Regime between Rouse and Reptation

By neutron spin echo (NSE) and pulsed field gradient (PFG) NMR, we study the dynamics of a polyethylene-oxide melt (PEO) with a molecular weight in the transition regime between Rouse and reptation dynamics. We analyze the data with a Rouse mode analysis allowing for reduced long wavelength Rouse modes amplitudes. For short times, subdiffusive center-of-mass mean square displacement ⟨rcom2(t)⟩ was allowed. This approach captures the NSE data well and provides accurate information on the topological constraints in a chain length regime, where the tube model is inapplicable. As predicted by reptation for the polymer ⟨rcom2(t)⟩, we experimentally found the subdiffusive regime with an exponent close to μ=12, which, however, crosses over to Fickian diffusion not at the Rouse time, but at a later time, when the ⟨rcom2(t)⟩ has covered a distance related to the tube diameter

Confinement Effects in Block Copolymer Modified Bicontinuous Microemulsions

It has been established that the addition of amphiphilic diblock copolymers has a boosting effect in bicontinuous microemulsions by decreasing the minimum amount of surfactant needed to solubilize equal volumes of oil and water. The strength of the polymer effect was found to be about twice larger than the theoretical prediction. This discrepancy is explained by confinement. Previous experimental studies always considered large oil and water domains of size <i>d</i> compared to the typical polymer end-to-end radius, <i>R</i>_ee. The ratio of these two parameters <i>R</i>_ee/<i>d</i> defines the confinement parameter. We investigated the sensitivity of the polymer influence extending the range of confinement. We combined macroscopic observations of the phase behavior with microscopic measurements of the structure by small-angle neutron scattering (SANS). Both results were compared with computer simulations on the basis of the theoretical concept of Helfrich. The simulations predict an enhanced sensitivity of the polymer at medium confinement and a reversed behavior at larger confinement. The higher sensitivity at medium confinement is only slightly visible experimentally, whereas the reversed behavior (antiboosting) is clearly present. Finally, a comparison with homopolymer addition showed a common high confinement behavior for diblock copolymers and for homopolymers

Monitoring the Internal Structure of Poly(<i>N</i>‑vinylcaprolactam) Microgels with Variable Cross-Link Concentration

The combination of a set of complementary techniques allows us to construct an unprecedented and comprehensive picture of the internal structure, temperature dependent swelling behavior, and the dependence of these properties on the cross-linker concentration of microgel particles based on <i>N</i>-vinylcaprolactam (VCL). The microgels were synthesized by precipitation polymerization using different amounts of cross-linking agent. Characterization was performed by small-angle neutron scattering (SANS) using two complementary neutron instruments to cover a uniquely broad Q-range with one probe. Additionally we used dynamic light scattering (DLS), atomic force microscopy (AFM), and differential scanning calorimetry (DSC). Previously obtained nuclear magnetic resonance spectroscopy (NMR) results on the same PVCL particles are utilized to round the picture off. Our study shows that both the particle radius and the cross-link density and therefore also the stiffness of the microgels rises with increasing cross-linker content. Hence, more cross-linker reduces the swelling capability distinctly. These findings are supported by SANS and AFM measurements. Independent DLS experiments also found the increase in particle size but suggest an unchanged cross-link density. The reason for the apparent contradiction is the indirect extraction of the parameters via a model in the evaluation of DLS measurements. The more direct approach in AFM by evaluating the cross section profiles of observed microgel particles gives evidence of significantly softer and more deformable particles at lower cross-linker concentrations and therefore verifies the change in cross-link density. DSC data indicate a minor but unexpected shift of the volume phase transition temperature (VPTT) to higher temperatures and exposes a more heterogeneous internal structure of the microgels with increasing cross-link density. Moreover, a change in the total energy transfer during the VPT gives evidence that the strength of hydrogen bonds is significantly affected by the cross-link density. A strong and reproducible deviation of the material density of the cross-linked microgel polymer chains toward a higher value compared to the respective linear chains has yet to be explained

The Initiation Mechanism of Butadiene Polymerization in Aliphatic Hydrocarbons: A Full Mechanistic Approach

An <i>in situ</i> ¹H NMR study has been carried out to examine the anionic initiation mechanism of 1,3-butadiene and <i>tert</i>-butyllithium (<i>t</i>-BuLi) using <i>n</i>-heptane as solvent. Additionally, mixtures of model compounds have been investigated <i>ex situ</i> to simulate very early stages of polymerization. The analysis of the NMR spectra in combination with density functional theory (DFT) calculations proves the coexistence of cross-aggregates of <i>t</i>-BuLi and initiated chains and their crucial role for the initiation mechanism. From the low concentrations of these species showing a characteristic maximum at <i>t</i> ≈ 50 min and the increase of the overall initiation rate constant with ongoing initiation, we propose a double-stage autocatalytic mechanism for this process. We first assume a fairly small reactivity of butadiene and <i>t</i>-BuLi, which exists under these reaction conditions as a tetrameric aggregate. However, after the reaction of the first <i>t</i>-BuLi unit with a monomer molecule, the reactivity of the remaining three <i>t</i>-BuLi units in the aggregate is increased considerably. The crucial second step of the autocatalytic mechanism is based on the unimer exchange between partially or fully initiated <i>t</i>-BuLi aggregates and the residual unreacted <i>t</i>-BuLi tetramers. As a result, the initiation rate constantly increases and leads to a sigmoidal consumption of initiator molecules during the polymerization. In addition, the time-dependent cross-aggregate concentrations are used as a benchmark for a full mechanistic approach compiling all literature assumptions. Numerical modeling allows a semiquantitative description of the data

Viscosity of Ring Polymer Melts

We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes, and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts η_0,linear to their ring counterparts η_0,ring at isofrictional conditions is discussed as a function of the number of entanglements <i>Z</i>. In the unentangled regime η_0,linear/η_0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation η_0,linear/η_0,ring = 2. In the entanglement regime, the <i>Z</i>-dependence of ring viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1 < <i>Z</i> < 20, η_0,linear/η_0,ring ∼ <i>Z</i>^1.2±0.3, is weaker than the scaling prediction (η_0,linear/η_0,ring ∼<i> Z</i>^1.6±0.3) and the simulations (η_0,linear/η_0,ring ∼ <i>Z</i>^2.0±0.3). Nevertheless, the present collection of state-of-the-art experimental data unambiguously demonstrates that rings exhibit a universal trend clearly departing from that of their linear counterparts, and hence it represents a major step toward resolving a 30-year-old problem